Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 13 x^{10} + 94 x^{9} + 15 x^{8} - 616 x^{7} + 368 x^{6} + 1643 x^{5} - 1463 x^{4} + \cdots - 208 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1006) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.264006\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | ||||||||
\(3\) | −0.264006 | −0.152424 | −0.0762121 | − | 0.997092i | \(-0.524283\pi\) | ||||
−0.0762121 | + | 0.997092i | \(0.524283\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.70058 | 0.760525 | 0.380262 | − | 0.924879i | \(-0.375834\pi\) | ||||
0.380262 | + | 0.924879i | \(0.375834\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.77338 | −1.04824 | −0.524119 | − | 0.851645i | \(-0.675605\pi\) | ||||
−0.524119 | + | 0.851645i | \(0.675605\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.93030 | −0.976767 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.489106 | 0.147471 | 0.0737355 | − | 0.997278i | \(-0.476508\pi\) | ||||
0.0737355 | + | 0.997278i | \(0.476508\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.503543 | 0.139658 | 0.0698289 | − | 0.997559i | \(-0.477755\pi\) | ||||
0.0698289 | + | 0.997559i | \(0.477755\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.448965 | −0.115922 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.96665 | 0.962055 | 0.481027 | − | 0.876706i | \(-0.340264\pi\) | ||||
0.481027 | + | 0.876706i | \(0.340264\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.91347 | −1.35664 | −0.678321 | − | 0.734765i | \(-0.737292\pi\) | ||||
−0.678321 | + | 0.734765i | \(0.737292\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.732189 | 0.159777 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.83634 | 1.00845 | 0.504223 | − | 0.863573i | \(-0.331779\pi\) | ||||
0.504223 | + | 0.863573i | \(0.331779\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.10801 | −0.421602 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.56564 | 0.301307 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.23806 | 0.601292 | 0.300646 | − | 0.953736i | \(-0.402798\pi\) | ||||
0.300646 | + | 0.953736i | \(0.402798\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.77062 | 0.318013 | 0.159007 | − | 0.987278i | \(-0.449171\pi\) | ||||
0.159007 | + | 0.987278i | \(0.449171\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.129127 | −0.0224781 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.71636 | −0.797211 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.45223 | 0.403145 | 0.201572 | − | 0.979474i | \(-0.435395\pi\) | ||||
0.201572 | + | 0.979474i | \(0.435395\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.132939 | −0.0212872 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.21510 | 0.189767 | 0.0948837 | − | 0.995488i | \(-0.469752\pi\) | ||||
0.0948837 | + | 0.995488i | \(0.469752\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.2109 | 1.55715 | 0.778577 | − | 0.627549i | \(-0.215942\pi\) | ||||
0.778577 | + | 0.627549i | \(0.215942\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.98322 | −0.742855 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.83131 | −1.43404 | −0.717022 | − | 0.697050i | \(-0.754495\pi\) | ||||
−0.717022 | + | 0.697050i | \(0.754495\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.691625 | 0.0988036 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.04722 | −0.146640 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.49671 | −0.205589 | −0.102794 | − | 0.994703i | \(-0.532778\pi\) | ||||
−0.102794 | + | 0.994703i | \(0.532778\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.831766 | 0.112155 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.56119 | 0.206785 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.72212 | 0.484578 | 0.242289 | − | 0.970204i | \(-0.422102\pi\) | ||||
0.242289 | + | 0.970204i | \(0.422102\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.69201 | −0.984860 | −0.492430 | − | 0.870352i | \(-0.663891\pi\) | ||||
−0.492430 | + | 0.870352i | \(0.663891\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.12683 | 1.02388 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.856318 | 0.106213 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.43313 | 0.297254 | 0.148627 | − | 0.988893i | \(-0.452515\pi\) | ||||
0.148627 | + | 0.988893i | \(0.452515\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.27682 | −0.153712 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.608248 | 0.0721857 | 0.0360929 | − | 0.999348i | \(-0.488509\pi\) | ||||
0.0360929 | + | 0.999348i | \(0.488509\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.67504 | −0.313090 | −0.156545 | − | 0.987671i | \(-0.550036\pi\) | ||||
−0.156545 | + | 0.987671i | \(0.550036\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.556528 | 0.0642624 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.35648 | −0.154585 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.84369 | −0.544958 | −0.272479 | − | 0.962162i | \(-0.587843\pi\) | ||||
−0.272479 | + | 0.962162i | \(0.587843\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.37756 | 0.930840 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.43632 | −0.926007 | −0.463003 | − | 0.886357i | \(-0.653228\pi\) | ||||
−0.463003 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.74563 | 0.731666 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.854867 | −0.0916514 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.160559 | −0.0170192 | −0.00850959 | − | 0.999964i | \(-0.502709\pi\) | ||||
−0.00850959 | + | 0.999964i | \(0.502709\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.39652 | −0.146395 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.467455 | −0.0484729 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.0564 | −1.03176 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.5610 | 1.68151 | 0.840757 | − | 0.541413i | \(-0.182111\pi\) | ||||
0.840757 | + | 0.541413i | \(0.182111\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.43323 | −0.144045 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.45694 | −0.244475 | −0.122237 | − | 0.992501i | \(-0.539007\pi\) | ||||
−0.122237 | + | 0.992501i | \(0.539007\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.10031 | −0.108416 | −0.0542081 | − | 0.998530i | \(-0.517263\pi\) | ||||
−0.0542081 | + | 0.998530i | \(0.517263\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.24515 | 0.121514 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.32925 | 0.805219 | 0.402609 | − | 0.915372i | \(-0.368103\pi\) | ||||
0.402609 | + | 0.915372i | \(0.368103\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.3568 | −1.85405 | −0.927024 | − | 0.375001i | \(-0.877642\pi\) | ||||
−0.927024 | + | 0.375001i | \(0.877642\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.647405 | −0.0614490 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.46055 | −0.325541 | −0.162771 | − | 0.986664i | \(-0.552043\pi\) | ||||
−0.162771 | + | 0.986664i | \(0.552043\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.22461 | 0.766948 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.47553 | −0.136413 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.0010 | −1.00846 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7608 | −0.978252 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.320795 | −0.0289251 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0878 | −1.08116 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.6546 | 0.945441 | 0.472721 | − | 0.881212i | \(-0.343272\pi\) | ||||
0.472721 | + | 0.881212i | \(0.343272\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.69575 | −0.237348 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.12465 | −0.709854 | −0.354927 | − | 0.934894i | \(-0.615494\pi\) | ||||
−0.354927 | + | 0.934894i | \(0.615494\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.4003 | 1.42208 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.66250 | 0.229151 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.5532 | −0.901623 | −0.450812 | − | 0.892619i | \(-0.648865\pi\) | ||||
−0.450812 | + | 0.892619i | \(0.648865\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.6019 | −0.899240 | −0.449620 | − | 0.893220i | \(-0.648441\pi\) | ||||
−0.449620 | + | 0.893220i | \(0.648441\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.59553 | 0.218583 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.246286 | 0.0205955 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.50659 | 0.457297 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.182593 | −0.0150601 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.0043 | −1.55690 | −0.778448 | − | 0.627709i | \(-0.783993\pi\) | ||||
−0.778448 | + | 0.627709i | \(0.783993\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.94327 | 0.402277 | 0.201139 | − | 0.979563i | \(-0.435536\pi\) | ||||
0.201139 | + | 0.979563i | \(0.435536\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.6235 | −0.939703 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.01109 | 0.241857 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.33027 | −0.425402 | −0.212701 | − | 0.977117i | \(-0.568226\pi\) | ||||
−0.212701 | + | 0.977117i | \(0.568226\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.395140 | 0.0313367 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.4130 | −1.05709 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.66004 | 0.365002 | 0.182501 | − | 0.983206i | \(-0.441581\pi\) | ||||
0.182501 | + | 0.983206i | \(0.441581\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.219592 | −0.0170952 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.01289 | −0.155762 | −0.0778810 | − | 0.996963i | \(-0.524815\pi\) | ||||
−0.0778810 | + | 0.996963i | \(0.524815\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7464 | −0.980496 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.3282 | 1.32512 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.62807 | 0.275837 | 0.137919 | − | 0.990444i | \(-0.455959\pi\) | ||||
0.137919 | + | 0.990444i | \(0.455959\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.84631 | 0.441940 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.982663 | −0.0738614 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −26.2469 | −1.96179 | −0.980893 | − | 0.194549i | \(-0.937676\pi\) | ||||
−0.980893 | + | 0.194549i | \(0.937676\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.3292 | −1.58539 | −0.792693 | − | 0.609621i | \(-0.791321\pi\) | ||||
−0.792693 | + | 0.609621i | \(0.791321\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.03074 | 0.150117 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.17023 | 0.306601 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.94011 | 0.141875 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.34210 | −0.315842 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.48768 | 0.107645 | 0.0538225 | − | 0.998551i | \(-0.482859\pi\) | ||||
0.0538225 | + | 0.998551i | \(0.482859\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.32190 | −0.311097 | −0.155549 | − | 0.987828i | \(-0.549715\pi\) | ||||
−0.155549 | + | 0.987828i | \(0.549715\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.226074 | −0.0161895 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.7020 | −0.904982 | −0.452491 | − | 0.891769i | \(-0.649464\pi\) | ||||
−0.452491 | + | 0.891769i | \(0.649464\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0140 | 0.851651 | 0.425825 | − | 0.904805i | \(-0.359984\pi\) | ||||
0.425825 | + | 0.904805i | \(0.359984\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.642362 | −0.0453087 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.98035 | −0.630297 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.06639 | 0.144323 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.1719 | −0.985017 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.89231 | −0.200065 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.08035 | 0.418588 | 0.209294 | − | 0.977853i | \(-0.432883\pi\) | ||||
0.209294 | + | 0.977853i | \(0.432883\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.160581 | −0.0110028 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.3646 | 1.18425 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.91060 | −0.333353 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.706229 | 0.0477225 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.99738 | 0.134358 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.47648 | −0.567627 | −0.283814 | − | 0.958879i | \(-0.591600\pi\) | ||||
−0.283814 | + | 0.958879i | \(0.591600\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.17711 | 0.411807 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.45625 | −0.428517 | −0.214258 | − | 0.976777i | \(-0.568733\pi\) | ||||
−0.214258 | + | 0.976777i | \(0.568733\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.7311 | 1.10562 | 0.552811 | − | 0.833307i | \(-0.313555\pi\) | ||||
0.552811 | + | 0.833307i | \(0.313555\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.358118 | 0.0235624 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.43703 | −0.618240 | −0.309120 | − | 0.951023i | \(-0.600035\pi\) | ||||
−0.309120 | + | 0.951023i | \(0.600035\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.7190 | −1.09063 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.27877 | 0.0830647 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.75425 | 0.436896 | 0.218448 | − | 0.975849i | \(-0.429901\pi\) | ||||
0.218448 | + | 0.975849i | \(0.429901\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.26912 | 0.146167 | 0.0730835 | − | 0.997326i | \(-0.476716\pi\) | ||||
0.0730835 | + | 0.997326i | \(0.476716\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.90864 | −0.443190 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.17617 | 0.0751426 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.97769 | −0.189466 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.22724 | 0.141146 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.04477 | 0.255304 | 0.127652 | − | 0.991819i | \(-0.459256\pi\) | ||||
0.127652 | + | 0.991819i | \(0.459256\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.36548 | 0.148717 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.78089 | −0.111524 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.06557 | −0.191225 | −0.0956123 | − | 0.995419i | \(-0.530481\pi\) | ||||
−0.0956123 | + | 0.995419i | \(0.530481\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.80097 | −0.422592 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.48848 | −0.587322 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.0913 | −1.79384 | −0.896922 | − | 0.442188i | \(-0.854202\pi\) | ||||
−0.896922 | + | 0.442188i | \(0.854202\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.54528 | −0.156355 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.0423885 | 0.00259413 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.49302 | −0.152002 | −0.0760010 | − | 0.997108i | \(-0.524215\pi\) | ||||
−0.0760010 | + | 0.997108i | \(0.524215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.3646 | 0.751099 | 0.375549 | − | 0.926802i | \(-0.377454\pi\) | ||||
0.375549 | + | 0.926802i | \(0.377454\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.368689 | 0.0223141 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.03104 | −0.0621741 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.8174 | 1.07054 | 0.535271 | − | 0.844680i | \(-0.320210\pi\) | ||||
0.535271 | + | 0.844680i | \(0.320210\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.18845 | −0.310625 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.87017 | −0.469495 | −0.234748 | − | 0.972056i | \(-0.575426\pi\) | ||||
−0.234748 | + | 0.972056i | \(0.575426\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.6378 | −1.04846 | −0.524228 | − | 0.851578i | \(-0.675646\pi\) | ||||
−0.524228 | + | 0.851578i | \(0.675646\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.65494 | 0.157265 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.36994 | −0.198921 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.26567 | −0.0744511 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.37221 | −0.256303 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.7670 | 1.09638 | 0.548189 | − | 0.836354i | \(-0.315317\pi\) | ||||
0.548189 | + | 0.836354i | \(0.315317\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.32978 | 0.368534 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.765762 | 0.0444340 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.43531 | 0.140837 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.3188 | −1.63227 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.648648 | 0.0372638 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.0809 | −0.749011 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.1411 | 1.37780 | 0.688901 | − | 0.724855i | \(-0.258093\pi\) | ||||
0.688901 | + | 0.724855i | \(0.258093\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.290488 | 0.0165253 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.6874 | 0.776141 | 0.388071 | − | 0.921630i | \(-0.373142\pi\) | ||||
0.388071 | + | 0.921630i | \(0.373142\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.33949 | −0.245282 | −0.122641 | − | 0.992451i | \(-0.539136\pi\) | ||||
−0.122641 | + | 0.992451i | \(0.539136\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.8204 | 0.778689 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.9221 | −0.669612 | −0.334806 | − | 0.942287i | \(-0.608671\pi\) | ||||
−0.334806 | + | 0.942287i | \(0.608671\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.58375 | 0.0886731 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.19897 | −0.122735 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.4567 | −1.30516 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.06148 | −0.0588801 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.11033 | 0.282602 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.2659 | 1.50322 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.6226 | −1.73813 | −0.869066 | − | 0.494695i | \(-0.835280\pi\) | ||||
−0.869066 | + | 0.494695i | \(0.835280\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.18578 | −0.393778 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.13775 | 0.226069 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.9225 | 1.19420 | 0.597098 | − | 0.802168i | \(-0.296320\pi\) | ||||
0.597098 | + | 0.802168i | \(0.296320\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.913608 | 0.0496204 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.866021 | 0.0468977 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.4955 | 0.944669 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.17135 | −0.116901 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.0383 | −1.39781 | −0.698903 | − | 0.715216i | \(-0.746328\pi\) | ||||
−0.698903 | + | 0.715216i | \(0.746328\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.387367 | 0.0207353 | 0.0103677 | − | 0.999946i | \(-0.496700\pi\) | ||||
0.0103677 | + | 0.999946i | \(0.496700\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.788366 | 0.0420799 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.6658 | −0.727359 | −0.363680 | − | 0.931524i | \(-0.618480\pi\) | ||||
−0.363680 | + | 0.931524i | \(0.618480\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.03438 | 0.0548990 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.90434 | 0.153714 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.9703 | −0.578992 | −0.289496 | − | 0.957179i | \(-0.593488\pi\) | ||||
−0.289496 | + | 0.957179i | \(0.593488\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.9691 | 0.840480 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.84091 | 0.149109 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.54914 | −0.238113 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.9231 | −0.935579 | −0.467789 | − | 0.883840i | \(-0.654949\pi\) | ||||
−0.467789 | + | 0.883840i | \(0.654949\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.56062 | −0.185358 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.15093 | 0.215506 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.01196 | −0.363066 | −0.181533 | − | 0.983385i | \(-0.558106\pi\) | ||||
−0.181533 | + | 0.983385i | \(0.558106\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.19125 | 0.164795 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.63050 | 0.0839751 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.0895 | −0.723729 | −0.361864 | − | 0.932231i | \(-0.617860\pi\) | ||||
−0.361864 | + | 0.932231i | \(0.617860\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.81288 | −0.144108 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.1366 | −0.773444 | −0.386722 | − | 0.922196i | \(-0.626393\pi\) | ||||
−0.386722 | + | 0.922196i | \(0.626393\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.30680 | −0.117565 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −29.9211 | −1.52098 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.1457 | 0.767915 | 0.383958 | − | 0.923351i | \(-0.374561\pi\) | ||||
0.383958 | + | 0.923351i | \(0.374561\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.1841 | 0.970181 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.14496 | 0.108199 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.23711 | −0.414454 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.0540 | 1.00648 | 0.503240 | − | 0.864147i | \(-0.332141\pi\) | ||||
0.503240 | + | 0.864147i | \(0.332141\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.32978 | −0.216760 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.2804 | 1.01276 | 0.506378 | − | 0.862312i | \(-0.330984\pi\) | ||||
0.506378 | + | 0.862312i | \(0.330984\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.891585 | 0.0444130 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.2468 | 0.707927 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.19940 | 0.0594521 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.7373 | −1.71765 | −0.858825 | − | 0.512270i | \(-0.828805\pi\) | ||||
−0.858825 | + | 0.512270i | \(0.828805\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.78612 | 0.137429 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.3228 | −0.507954 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.3467 | −0.704251 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.79896 | 0.137066 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.9600 | −0.584285 | −0.292143 | − | 0.956375i | \(-0.594368\pi\) | ||||
−0.292143 | + | 0.956375i | \(0.594368\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.12944 | 0.444942 | 0.222471 | − | 0.974939i | \(-0.428588\pi\) | ||||
0.222471 | + | 0.974939i | \(0.428588\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 28.8087 | 1.40073 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.36175 | −0.405604 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.3328 | 1.03237 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.0650211 | −0.00313925 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.3556 | −0.980493 | −0.490247 | − | 0.871584i | \(-0.663093\pi\) | ||||
−0.490247 | + | 0.871584i | \(0.663093\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.5212 | 0.505615 | 0.252808 | − | 0.967517i | \(-0.418646\pi\) | ||||
0.252808 | + | 0.967517i | \(0.418646\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.45377 | −0.0697031 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −28.5995 | −1.36810 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.6234 | 0.697939 | 0.348969 | − | 0.937134i | \(-0.386532\pi\) | ||||
0.348969 | + | 0.937134i | \(0.386532\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.02667 | −0.0965081 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.94640 | −0.330033 | −0.165017 | − | 0.986291i | \(-0.552768\pi\) | ||||
−0.165017 | + | 0.986291i | \(0.552768\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.273044 | −0.0129435 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.01726 | 0.237308 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.6844 | 0.645805 | 0.322903 | − | 0.946432i | \(-0.395341\pi\) | ||||
0.322903 | + | 0.946432i | \(0.395341\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.594315 | 0.0279852 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.30505 | −0.0613168 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.37489 | −0.111337 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.93983 | −0.418188 | −0.209094 | − | 0.977896i | \(-0.567051\pi\) | ||||
−0.209094 | + | 0.977896i | \(0.567051\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.21034 | 0.289874 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.8793 | 1.53134 | 0.765672 | − | 0.643231i | \(-0.222407\pi\) | ||||
0.765672 | + | 0.643231i | \(0.222407\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.0218 | −0.512226 | −0.256113 | − | 0.966647i | \(-0.582442\pi\) | ||||
−0.256113 | + | 0.966647i | \(0.582442\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.794948 | −0.0368648 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.7644 | −1.14596 | −0.572980 | − | 0.819570i | \(-0.694213\pi\) | ||||
−0.572980 | + | 0.819570i | \(0.694213\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.74799 | −0.311593 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.40722 | 0.0648415 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.99423 | 0.229635 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.4657 | 0.571964 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.38580 | 0.200812 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.1346 | −0.691516 | −0.345758 | − | 0.938324i | \(-0.612378\pi\) | ||||
−0.345758 | + | 0.938324i | \(0.612378\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.23481 | 0.0563023 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.54112 | 0.161126 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.1634 | 1.27883 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.94483 | 0.314700 | 0.157350 | − | 0.987543i | \(-0.449705\pi\) | ||||
0.157350 | + | 0.987543i | \(0.449705\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.23028 | −0.0556351 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.9100 | 1.07904 | 0.539522 | − | 0.841971i | \(-0.318605\pi\) | ||||
0.539522 | + | 0.841971i | \(0.318605\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.8442 | 0.578475 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.43732 | −0.109550 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.68690 | −0.0756678 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.0093 | −1.29864 | −0.649318 | − | 0.760517i | \(-0.724945\pi\) | ||||
−0.649318 | + | 0.760517i | \(0.724945\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.531415 | 0.0237419 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.17823 | −0.185929 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.36514 | 0.149451 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.76339 | 0.344106 | 0.172053 | − | 0.985088i | \(-0.444960\pi\) | ||||
0.172053 | + | 0.985088i | \(0.444960\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.41891 | 0.328193 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.25835 | −0.408766 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.87116 | −0.0824533 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.80855 | −0.211480 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.957834 | −0.0420443 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.71912 | −0.338181 | −0.169090 | − | 0.985601i | \(-0.554083\pi\) | ||||
−0.169090 | + | 0.985601i | \(0.554083\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.6173 | 0.857804 | 0.428902 | − | 0.903351i | \(-0.358901\pi\) | ||||
0.428902 | + | 0.903351i | \(0.358901\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.54346 | −0.0673623 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.02344 | 0.305946 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.390183 | 0.0169645 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.9069 | −0.473320 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.611858 | 0.0265025 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.1646 | 0.612389 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.92935 | 0.299024 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.338278 | 0.0145707 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.11159 | −0.0477908 | −0.0238954 | − | 0.999714i | \(-0.507607\pi\) | ||||
−0.0238954 | + | 0.999714i | \(0.507607\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.63104 | 0.241651 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −32.9179 | −1.41005 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.6931 | 1.48337 | 0.741685 | − | 0.670748i | \(-0.234027\pi\) | ||||
0.741685 | + | 0.670748i | \(0.234027\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 22.5399 | 0.961979 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.1481 | −0.815738 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.4334 | 0.571246 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.10097 | −0.0467335 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.52654 | −0.361281 | −0.180641 | − | 0.983549i | \(-0.557817\pi\) | ||||
−0.180641 | + | 0.983549i | \(0.557817\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.14165 | 0.217469 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.512202 | −0.0216252 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.84244 | −0.414809 | −0.207405 | − | 0.978255i | \(-0.566502\pi\) | ||||
−0.207405 | + | 0.978255i | \(0.566502\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.88496 | −0.247582 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.2342 | −0.975743 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.1793 | 1.43287 | 0.716435 | − | 0.697654i | \(-0.245773\pi\) | ||||
0.716435 | + | 0.697654i | \(0.245773\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.62723 | 0.277341 | 0.138670 | − | 0.990339i | \(-0.455717\pi\) | ||||
0.138670 | + | 0.990339i | \(0.455717\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.392758 | −0.0164077 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.1951 | −0.425163 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.9412 | −1.41299 | −0.706495 | − | 0.707718i | \(-0.749725\pi\) | ||||
−0.706495 | + | 0.707718i | \(0.749725\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.14101 | 0.0474187 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.3971 | 0.970676 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.732048 | −0.0303183 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.50927 | −0.103746 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.4015 | 1.83265 | 0.916323 | − | 0.400439i | \(-0.131142\pi\) | ||||
0.916323 | + | 0.400439i | \(0.131142\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.4705 | −0.431430 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.35341 | 0.137941 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.2137 | −0.460492 | −0.230246 | − | 0.973132i | \(-0.573953\pi\) | ||||
−0.230246 | + | 0.973132i | \(0.573953\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.7082 | −0.766961 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.17178 | −0.129812 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.0359 | −1.26809 | −0.634045 | − | 0.773296i | \(-0.718607\pi\) | ||||
−0.634045 | + | 0.773296i | \(0.718607\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.5547 | 1.40952 | 0.704758 | − | 0.709448i | \(-0.251056\pi\) | ||||
0.704758 | + | 0.709448i | \(0.251056\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.12981 | −0.290348 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.2996 | −0.743985 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.44624 | 0.0992896 | 0.0496448 | − | 0.998767i | \(-0.484191\pi\) | ||||
0.0496448 | + | 0.998767i | \(0.484191\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.37087 | 0.0960725 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.95049 | −0.200275 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.4211 | −1.10753 | −0.553764 | − | 0.832674i | \(-0.686809\pi\) | ||||
−0.553764 | + | 0.832674i | \(0.686809\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.545539 | −0.0219983 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 48.5663 | 1.95520 | 0.977602 | − | 0.210462i | \(-0.0674969\pi\) | ||||
0.977602 | + | 0.210462i | \(0.0674969\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.6758 | −0.911417 | −0.455709 | − | 0.890129i | \(-0.650614\pi\) | ||||
−0.455709 | + | 0.890129i | \(0.650614\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.57195 | 0.303852 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.445290 | 0.0178402 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.0162 | −0.400649 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.763589 | 0.0304948 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.72716 | 0.387847 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.8475 | −0.790116 | −0.395058 | − | 0.918656i | \(-0.629275\pi\) | ||||
−0.395058 | + | 0.918656i | \(0.629275\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.60525 | −0.0638030 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.1190 | 0.719031 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.348263 | 0.0137987 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.78235 | −0.0705086 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.1430 | −0.795602 | −0.397801 | − | 0.917472i | \(-0.630226\pi\) | ||||
−0.397801 | + | 0.917472i | \(0.630226\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.0146734 | 0.000578662 0 | 0.000289331 | − | 1.00000i | \(-0.499908\pi\) | ||||
0.000289331 | 1.00000i | \(0.499908\pi\) | ||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.58436 | −0.180509 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.9997 | −1.57255 | −0.786275 | − | 0.617876i | \(-0.787993\pi\) | ||||
−0.786275 | + | 0.617876i | \(0.787993\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.82051 | 0.0714612 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.29643 | 0.0508111 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.14083 | −0.0837771 | −0.0418886 | − | 0.999122i | \(-0.513337\pi\) | ||||
−0.0418886 | + | 0.999122i | \(0.513337\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.8167 | −0.539862 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.83868 | 0.305816 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.1414 | −1.09623 | −0.548117 | − | 0.836402i | \(-0.684655\pi\) | ||||
−0.548117 | + | 0.836402i | \(0.684655\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.41391 | 0.171681 | 0.0858406 | − | 0.996309i | \(-0.472642\pi\) | ||||
0.0858406 | + | 0.996309i | \(0.472642\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.527322 | −0.0204795 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 27.8901 | 1.08153 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.6603 | 0.606371 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.23785 | 0.0865201 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.76221 | −0.145238 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.4693 | −0.750485 | −0.375242 | − | 0.926927i | \(-0.622441\pi\) | ||||
−0.375242 | + | 0.926927i | \(0.622441\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.30038 | −0.127032 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.8642 | 1.37837 | 0.689187 | − | 0.724583i | \(-0.257968\pi\) | ||||
0.689187 | + | 0.724583i | \(0.257968\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −45.9299 | −1.76263 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.70449 | 0.0653163 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.47358 | 0.324233 | 0.162116 | − | 0.986772i | \(-0.448168\pi\) | ||||
0.162116 | + | 0.986772i | \(0.448168\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.9467 | −0.685707 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.41712 | −0.168524 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.753657 | −0.0287120 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.3402 | 1.45853 | 0.729264 | − | 0.684232i | \(-0.239863\pi\) | ||||
0.729264 | + | 0.684232i | \(0.239863\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.97488 | 0.150993 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.0294 | −0.683894 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.81989 | 0.182567 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.49144 | 0.0942347 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.8783 | 1.43064 | 0.715322 | − | 0.698795i | \(-0.246280\pi\) | ||||
0.715322 | + | 0.698795i | \(0.246280\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.5012 | −0.546923 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.41392 | 0.166238 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.81402 | 0.256268 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.2791 | 0.648930 | 0.324465 | − | 0.945898i | \(-0.394816\pi\) | ||||
0.324465 | + | 0.945898i | \(0.394816\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.1935 | 0.532297 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.56333 | 0.320699 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.418830 | 0.0156634 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.78317 | −0.0665935 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −44.6685 | −1.66585 | −0.832927 | − | 0.553383i | \(-0.813337\pi\) | ||||
−0.832927 | + | 0.553383i | \(0.813337\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.05156 | 0.113646 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.599063 | −0.0222794 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.82586 | −0.253506 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.3206 | −1.01327 | −0.506633 | − | 0.862162i | \(-0.669110\pi\) | ||||
−0.506633 | + | 0.862162i | \(0.669110\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.3088 | −0.863288 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40.5033 | 1.49807 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.7084 | 1.79908 | 0.899542 | − | 0.436834i | \(-0.143900\pi\) | ||||
0.899542 | + | 0.436834i | \(0.143900\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.310516 | −0.0114535 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.19006 | 0.0438364 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.1296 | −1.21869 | −0.609345 | − | 0.792905i | \(-0.708568\pi\) | ||||
−0.609345 | + | 0.792905i | \(0.708568\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.786129 | 0.0288792 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.0968 | 1.69113 | 0.845563 | − | 0.533875i | \(-0.179265\pi\) | ||||
0.845563 | + | 0.533875i | \(0.179265\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.3185 | −1.18406 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.7210 | 0.904493 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.1002 | −0.844061 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.237417 | 0.00866346 | 0.00433173 | − | 0.999991i | \(-0.498621\pi\) | ||||
0.00433173 | + | 0.999991i | \(0.498621\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.06785 | −0.0389145 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.40644 | 0.305942 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.6409 | −0.750206 | −0.375103 | − | 0.926983i | \(-0.622393\pi\) | ||||
−0.375103 | + | 0.926983i | \(0.622393\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.624502 | −0.0226680 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.2109 | −0.986396 | −0.493198 | − | 0.869917i | \(-0.664172\pi\) | ||||
−0.493198 | + | 0.869917i | \(0.664172\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 53.6838 | 1.94349 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19.7667 | −0.714667 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.87425 | 0.0676752 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.8623 | −1.11292 | −0.556462 | − | 0.830873i | \(-0.687842\pi\) | ||||
−0.556462 | + | 0.830873i | \(0.687842\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.809329 | 0.0291473 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.7390 | 1.24947 | 0.624737 | − | 0.780835i | \(-0.285206\pi\) | ||||
0.624737 | + | 0.780835i | \(0.285206\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.73249 | −0.134075 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.79550 | 0.0644132 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.18548 | −0.257446 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.297498 | 0.0106453 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.06962 | 0.181173 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.06457 | −0.323528 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.2937 | −0.509516 | −0.254758 | − | 0.967005i | \(-0.581996\pi\) | ||||
−0.254758 | + | 0.967005i | \(0.581996\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.68028 | 0.273425 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.59742 | 0.341245 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.87326 | −0.137543 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.671969 | 0.0238323 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.85845 | −0.0658296 | −0.0329148 | − | 0.999458i | \(-0.510479\pi\) | ||||
−0.0329148 | + | 0.999458i | \(0.510479\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.9974 | −1.37963 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.470485 | 0.0166238 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.30838 | −0.0461717 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.8099 | −0.803945 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.658173 | 0.0231688 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.11097 | −0.320325 | −0.160162 | − | 0.987091i | \(-0.551202\pi\) | ||||
−0.160162 | + | 0.987091i | \(0.551202\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.0817270 | −0.00286982 | −0.00143491 | − | 0.999999i | \(-0.500457\pi\) | ||||
−0.00143491 | + | 0.999999i | \(0.500457\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.26434 | −0.114486 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.92479 | 0.277593 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −60.3821 | −2.11250 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.09221 | 0.142993 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.0958 | 0.561747 | 0.280873 | − | 0.959745i | \(-0.409376\pi\) | ||||
0.280873 | + | 0.959745i | \(0.409376\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.0078 | 1.15058 | 0.575289 | − | 0.817950i | \(-0.304889\pi\) | ||||
0.575289 | + | 0.817950i | \(0.304889\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.272201 | 0.00947683 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.80801 | 0.132418 | 0.0662088 | − | 0.997806i | \(-0.478910\pi\) | ||||
0.0662088 | + | 0.997806i | \(0.478910\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.8116 | 0.514428 | 0.257214 | − | 0.966355i | \(-0.417196\pi\) | ||||
0.257214 | + | 0.966355i | \(0.417196\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.70390 | −0.163176 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.74344 | 0.0950544 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.42309 | −0.118461 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.77215 | 0.0958196 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.07929 | −0.278928 | −0.139464 | − | 0.990227i | \(-0.544538\pi\) | ||||
−0.139464 | + | 0.990227i | \(0.544538\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.5150 | −0.638448 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.07778 | 0.0715624 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.6764 | −0.745691 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.8437 | 1.02544 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.65648 | 0.159810 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.8598 | 0.406550 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.5131 | −0.907790 | −0.453895 | − | 0.891055i | \(-0.649966\pi\) | ||||
−0.453895 | + | 0.891055i | \(0.649966\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.4681 | 1.00779 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.21804 | −0.280723 | −0.140361 | − | 0.990100i | \(-0.544826\pi\) | ||||
−0.140361 | + | 0.990100i | \(0.544826\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.9731 | −1.60270 | −0.801351 | − | 0.598195i | \(-0.795885\pi\) | ||||
−0.801351 | + | 0.598195i | \(0.795885\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.889686 | 0.0303204 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.2051 | −0.415467 | −0.207734 | − | 0.978185i | \(-0.566609\pi\) | ||||
−0.207734 | + | 0.978185i | \(0.566609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.16985 | 0.209781 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.334145 | 0.0113481 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.36908 | −0.0803655 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.22519 | 0.0415139 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −48.5287 | −1.64245 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33.5240 | 1.13332 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.4995 | −0.624682 | −0.312341 | − | 0.949970i | \(-0.601113\pi\) | ||||
−0.312341 | + | 0.949970i | \(0.601113\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.95460 | −0.167115 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.6198 | −1.36851 | −0.684257 | − | 0.729241i | \(-0.739873\pi\) | ||||
−0.684257 | + | 0.729241i | \(0.739873\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.4724 | −0.453384 | −0.226692 | − | 0.973966i | \(-0.572791\pi\) | ||||
−0.226692 | + | 0.973966i | \(0.572791\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.67110 | −0.0561735 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.72980 | −0.326695 | −0.163347 | − | 0.986569i | \(-0.552229\pi\) | ||||
−0.163347 | + | 0.986569i | \(0.552229\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.5492 | −0.991048 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.09752 | 0.137272 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 58.1372 | 1.94549 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −44.6351 | −1.49199 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.642937 | −0.0214670 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.73337 | 0.191219 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.93692 | −0.197787 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.47634 | 0.248797 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −36.2721 | −1.20572 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.2977 | 0.607564 | 0.303782 | − | 0.952742i | \(-0.401751\pi\) | ||||
0.303782 | + | 0.952742i | \(0.401751\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.19957 | 0.238795 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.32911 | −0.275956 | −0.137978 | − | 0.990435i | \(-0.544060\pi\) | ||||
−0.137978 | + | 0.990435i | \(0.544060\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.12626 | −0.136559 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.45344 | 0.114167 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.5327 | 0.744096 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.3594 | 1.10042 | 0.550212 | − | 0.835025i | \(-0.314547\pi\) | ||||
0.550212 | + | 0.835025i | \(0.314547\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.37339 | −0.210010 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.306279 | 0.0100813 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.16934 | −0.169967 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.22423 | 0.105897 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.26346 | −0.205497 | −0.102749 | − | 0.994707i | \(-0.532764\pi\) | ||||
−0.102749 | + | 0.994707i | \(0.532764\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.08990 | −0.134041 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.61356 | −0.118303 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.29933 | 0.107900 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.8247 | −1.69304 | −0.846520 | − | 0.532356i | \(-0.821307\pi\) | ||||
−0.846520 | + | 0.532356i | \(0.821307\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.14565 | 0.0373870 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.8476 | −0.484018 | −0.242009 | − | 0.970274i | \(-0.577806\pi\) | ||||
−0.242009 | + | 0.970274i | \(0.577806\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.87666 | 0.191370 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.38412 | −0.240205 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.66651 | −0.216632 | −0.108316 | − | 0.994116i | \(-0.534546\pi\) | ||||
−0.108316 | + | 0.994116i | \(0.534546\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.34700 | −0.0437255 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.14751 | 0.102065 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.6563 | 1.05784 | 0.528921 | − | 0.848671i | \(-0.322597\pi\) | ||||
0.528921 | + | 0.848671i | \(0.322597\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.52993 | 0.0818666 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.418121 | −0.0135159 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.2681 | 0.945116 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.8649 | −0.898868 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24.4072 | −0.786511 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.34976 | −0.236597 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.87518 | 0.0603016 | 0.0301508 | − | 0.999545i | \(-0.490401\pi\) | ||||
0.0301508 | + | 0.999545i | \(0.490401\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.19271 | 0.198939 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.2018 | −1.22596 | −0.612978 | − | 0.790100i | \(-0.710029\pi\) | ||||
−0.612978 | + | 0.790100i | \(0.710029\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.4030 | 0.942618 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.280236 | 0.00897474 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −59.8224 | −1.91389 | −0.956944 | − | 0.290274i | \(-0.906254\pi\) | ||||
−0.956944 | + | 0.290274i | \(0.906254\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.0785302 | −0.00250984 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 56.7214 | 1.81097 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.3873 | 1.44763 | 0.723816 | − | 0.689993i | \(-0.242387\pi\) | ||||
0.723816 | + | 0.689993i | \(0.242387\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.6009 | −0.688261 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.19838 | −0.229127 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 49.3836 | 1.57031 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.1209 | −1.40155 | −0.700773 | − | 0.713384i | \(-0.747162\pi\) | ||||
−0.700773 | + | 0.713384i | \(0.747162\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.34856 | 0.264933 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.4308 | 0.647701 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.4025 | −0.487802 | −0.243901 | − | 0.969800i | \(-0.578427\pi\) | ||||
−0.243901 | + | 0.969800i | \(0.578427\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.83931 | 0.121470 |
(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 | 8048.2.a.q.1.7 | 12 | ||
4.3 | odd | 2 | 1006.2.a.j.1.6 | ✓ | 12 | ||
12.11 | even | 2 | 9054.2.a.bi.1.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1006.2.a.j.1.6 | ✓ | 12 | 4.3 | odd | 2 | ||
8048.2.a.q.1.7 | 12 | 1.1 | even | 1 | trivial | ||
9054.2.a.bi.1.5 | 12 | 12.11 | even | 2 |