Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 33 x^{9} + 22 x^{8} + 417 x^{7} - 151 x^{6} - 2470 x^{5} + 272 x^{4} + 6584 x^{3} + \cdots + 242 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-3.01685\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.01685 | 1.79639 | 0.898195 | − | 0.439597i | \(-0.144879\pi\) | ||||
0.898195 | + | 0.439597i | \(0.144879\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.41557 | −1.66893 | −0.834465 | − | 0.551062i | \(-0.814223\pi\) | ||||
−0.834465 | + | 0.551062i | \(0.814223\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.91880 | 1.18156 | 0.590781 | − | 0.806832i | \(-0.298820\pi\) | ||||
0.590781 | + | 0.806832i | \(0.298820\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.33293 | 0.369690 | 0.184845 | − | 0.982768i | \(-0.440822\pi\) | ||||
0.184845 | + | 0.982768i | \(0.440822\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.01685 | −1.03715 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.36767 | 1.30185 | 0.650926 | − | 0.759141i | \(-0.274381\pi\) | ||||
0.650926 | + | 0.759141i | \(0.274381\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.32150 | 0.991420 | 0.495710 | − | 0.868488i | \(-0.334908\pi\) | ||||
0.495710 | + | 0.868488i | \(0.334908\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.41557 | 0.963557 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.96332 | 0.617894 | 0.308947 | − | 0.951079i | \(-0.400023\pi\) | ||||
0.308947 | + | 0.951079i | \(0.400023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.1351 | 2.22702 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.641815 | 0.119182 | 0.0595910 | − | 0.998223i | \(-0.481020\pi\) | ||||
0.0595910 | + | 0.998223i | \(0.481020\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.50410 | −0.808960 | −0.404480 | − | 0.914547i | \(-0.632547\pi\) | ||||
−0.404480 | + | 0.914547i | \(0.632547\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.91880 | −0.682175 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −17.7367 | −2.99805 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.58361 | −0.589141 | −0.294571 | − | 0.955630i | \(-0.595177\pi\) | ||||
−0.294571 | + | 0.955630i | \(0.595177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.33293 | −0.213440 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.78387 | −1.37181 | −0.685905 | − | 0.727691i | \(-0.740594\pi\) | ||||
−0.685905 | + | 0.727691i | \(0.740594\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.83087 | 1.04170 | 0.520849 | − | 0.853649i | \(-0.325615\pi\) | ||||
0.520849 | + | 0.853649i | \(0.325615\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.01685 | 0.598797 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.1340 | −1.62406 | −0.812031 | − | 0.583615i | \(-0.801638\pi\) | ||||
−0.812031 | + | 0.583615i | \(0.801638\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.4973 | 1.78532 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.36767 | −0.751625 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.90890 | −0.262208 | −0.131104 | − | 0.991369i | \(-0.541852\pi\) | ||||
−0.131104 | + | 0.991369i | \(0.541852\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.7412 | 2.12255 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.32150 | −0.572397 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.60930 | −0.860458 | −0.430229 | − | 0.902720i | \(-0.641567\pi\) | ||||
−0.430229 | + | 0.902720i | \(0.641567\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.00823330 | 0.00105417 | 0.000527083 | − | 1.00000i | \(-0.499832\pi\) | ||||
0.000527083 | 1.00000i | \(0.499832\pi\) | ||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.41557 | −0.556310 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.35420 | 0.664107 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.03013 | 0.492359 | 0.246179 | − | 0.969224i | \(-0.420825\pi\) | ||||
0.246179 | + | 0.969224i | \(0.420825\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.96332 | −0.356741 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.34031 | −0.277744 | −0.138872 | − | 0.990310i | \(-0.544348\pi\) | ||||
−0.138872 | + | 0.990310i | \(0.544348\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.99602 | 0.584740 | 0.292370 | − | 0.956305i | \(-0.405556\pi\) | ||||
0.292370 | + | 0.956305i | \(0.405556\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.1351 | −1.28577 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −17.3037 | −1.97194 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.33451 | 0.150144 | 0.0750718 | − | 0.997178i | \(-0.476081\pi\) | ||||
0.0750718 | + | 0.997178i | \(0.476081\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.1756 | 1.55597 | 0.777986 | − | 0.628281i | \(-0.216241\pi\) | ||||
0.777986 | + | 0.628281i | \(0.216241\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.5611 | 2.33863 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.641815 | −0.0688098 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.3702 | 1.31124 | 0.655621 | − | 0.755090i | \(-0.272407\pi\) | ||||
0.655621 | + | 0.755090i | \(0.272407\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.88567 | −0.616986 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.50410 | 0.467053 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 17.3588 | 1.78098 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.3417 | 1.35464 | 0.677321 | − | 0.735688i | \(-0.263141\pi\) | ||||
0.677321 | + | 0.735688i | \(0.263141\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.91880 | 0.393854 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.0616138 | 0.00613081 | 0.00306540 | − | 0.999995i | \(-0.499024\pi\) | ||||
0.00306540 | + | 0.999995i | \(0.499024\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.58232 | −0.155910 | −0.0779552 | − | 0.996957i | \(-0.524839\pi\) | ||||
−0.0779552 | + | 0.996957i | \(0.524839\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 17.7367 | 1.73092 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.1136 | −1.46109 | −0.730544 | − | 0.682865i | \(-0.760734\pi\) | ||||
−0.730544 | + | 0.682865i | \(0.760734\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.1743 | −1.26187 | −0.630934 | − | 0.775836i | \(-0.717328\pi\) | ||||
−0.630934 | + | 0.775836i | \(0.717328\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.58361 | 0.340141 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.1380 | 1.89443 | 0.947213 | − | 0.320604i | \(-0.103886\pi\) | ||||
0.947213 | + | 0.320604i | \(0.103886\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.9032 | 1.10998 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.33293 | 0.123230 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −23.7013 | −2.17270 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.35696 | 0.396088 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.78387 | 0.792015 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 24.6438 | 2.20421 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.1668 | 1.61204 | 0.806019 | − | 0.591889i | \(-0.201618\pi\) | ||||
0.806019 | + | 0.591889i | \(0.201618\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.83087 | −0.601425 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.0441 | 0.964932 | 0.482466 | − | 0.875915i | \(-0.339741\pi\) | ||||
0.482466 | + | 0.875915i | \(0.339741\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.0819 | −1.65461 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.01685 | −0.345716 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.8528 | 1.26896 | 0.634480 | − | 0.772939i | \(-0.281214\pi\) | ||||
0.634480 | + | 0.772939i | \(0.281214\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.3986 | −1.05164 | −0.525818 | − | 0.850597i | \(-0.676241\pi\) | ||||
−0.525818 | + | 0.850597i | \(0.676241\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.1340 | 0.937652 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.22350 | 0.436811 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.57808 | 0.214098 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.4973 | −1.03076 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.3220 | −1.41908 | −0.709538 | − | 0.704667i | \(-0.751096\pi\) | ||||
−0.709538 | + | 0.704667i | \(0.751096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.7672 | −1.03898 | −0.519490 | − | 0.854477i | \(-0.673878\pi\) | ||||
−0.519490 | + | 0.854477i | \(0.673878\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.36767 | 0.433951 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.0923 | −1.45321 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.00398 | 0.0801265 | 0.0400632 | − | 0.999197i | \(-0.487244\pi\) | ||||
0.0400632 | + | 0.999197i | \(0.487244\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.90890 | 0.151386 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.0847 | −1.03122 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.70804 | 0.760392 | 0.380196 | − | 0.924906i | \(-0.375857\pi\) | ||||
0.380196 | + | 0.924906i | \(0.375857\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.7412 | −1.22545 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2233 | −0.863330 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.32150 | 0.330473 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.0933 | 1.75575 | 0.877876 | − | 0.478888i | \(-0.158960\pi\) | ||||
0.877876 | + | 0.478888i | \(0.158960\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −49.1678 | −3.71674 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.60930 | 0.496786 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.0863 | −1.35183 | −0.675917 | − | 0.736978i | \(-0.736252\pi\) | ||||
−0.675917 | + | 0.736978i | \(0.736252\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.8159 | −1.39858 | −0.699289 | − | 0.714839i | \(-0.746500\pi\) | ||||
−0.699289 | + | 0.714839i | \(0.746500\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.00823330 | −0.000608623 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.3948 | −1.05833 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.0348 | 1.53822 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.41557 | 0.321186 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.24773 | 0.379712 | 0.189856 | − | 0.981812i | \(-0.439198\pi\) | ||||
0.189856 | + | 0.981812i | \(0.439198\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.4295 | 1.11064 | 0.555321 | − | 0.831636i | \(-0.312595\pi\) | ||||
0.555321 | + | 0.831636i | \(0.312595\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.35420 | −0.383422 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.27605 | −0.304656 | −0.152328 | − | 0.988330i | \(-0.548677\pi\) | ||||
−0.152328 | + | 0.988330i | \(0.548677\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.93953 | 0.633707 | 0.316853 | − | 0.948475i | \(-0.397374\pi\) | ||||
0.316853 | + | 0.948475i | \(0.397374\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.03013 | −0.284263 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.83398 | −0.198906 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −35.2835 | −2.46431 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.96332 | 0.205965 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.9351 | 1.17142 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.7250 | 1.42677 | 0.713383 | − | 0.700774i | \(-0.247162\pi\) | ||||
0.713383 | + | 0.700774i | \(0.247162\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.34031 | 0.160356 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 27.4386 | 1.87130 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.8882 | 1.35010 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.99602 | −0.337600 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.15476 | 0.481281 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.2434 | 0.685948 | 0.342974 | − | 0.939345i | \(-0.388566\pi\) | ||||
0.342974 | + | 0.939345i | \(0.388566\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.1351 | 0.742340 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.0924 | 1.13446 | 0.567230 | − | 0.823559i | \(-0.308015\pi\) | ||||
0.567230 | + | 0.823559i | \(0.308015\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.4530 | 1.61590 | 0.807949 | − | 0.589252i | \(-0.200578\pi\) | ||||
0.807949 | + | 0.589252i | \(0.200578\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.3037 | 1.13850 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.7612 | −1.29460 | −0.647300 | − | 0.762236i | \(-0.724102\pi\) | ||||
−0.647300 | + | 0.762236i | \(0.724102\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −44.7236 | −2.91745 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.33451 | −0.0866854 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.5708 | 0.877819 | 0.438910 | − | 0.898531i | \(-0.355365\pi\) | ||||
0.438910 | + | 0.898531i | \(0.355365\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.3143 | 1.24414 | 0.622072 | − | 0.782960i | \(-0.286291\pi\) | ||||
0.622072 | + | 0.782960i | \(0.286291\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 50.1997 | 3.20714 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.76028 | 0.366518 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.1756 | −0.898341 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.8135 | −0.682540 | −0.341270 | − | 0.939965i | \(-0.610857\pi\) | ||||
−0.341270 | + | 0.939965i | \(0.610857\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.6126 | 0.730080 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −21.5611 | −1.35021 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.473302 | −0.0295238 | −0.0147619 | − | 0.999891i | \(-0.504699\pi\) | ||||
−0.0147619 | + | 0.999891i | \(0.504699\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.8237 | 0.983235 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.641815 | 0.0397274 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.76686 | 0.355600 | 0.177800 | − | 0.984067i | \(-0.443102\pi\) | ||||
0.177800 | + | 0.984067i | \(0.443102\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.66777 | −0.471028 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.3702 | −0.757046 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.62828 | −0.160249 | −0.0801247 | − | 0.996785i | \(-0.525532\pi\) | ||||
−0.0801247 | + | 0.996785i | \(0.525532\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.50936 | 0.0916873 | 0.0458437 | − | 0.998949i | \(-0.485402\pi\) | ||||
0.0458437 | + | 0.998949i | \(0.485402\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.88567 | 0.356217 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 43.6362 | 2.63136 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.3632 | −0.682751 | −0.341375 | − | 0.939927i | \(-0.610893\pi\) | ||||
−0.341375 | + | 0.939927i | \(0.610893\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.50410 | −0.269653 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.3821 | −1.57382 | −0.786911 | − | 0.617066i | \(-0.788321\pi\) | ||||
−0.786911 | + | 0.617066i | \(0.788321\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.9376 | 1.18517 | 0.592584 | − | 0.805509i | \(-0.298108\pi\) | ||||
0.592584 | + | 0.805509i | \(0.298108\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.3588 | −1.02825 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 38.7858 | 2.28945 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.8119 | 0.694819 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.3417 | −0.782103 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.6368 | −1.78982 | −0.894911 | − | 0.446244i | \(-0.852761\pi\) | ||||
−0.894911 | + | 0.446244i | \(0.852761\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26.5486 | −1.54572 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.91880 | −0.227392 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.94991 | 0.228429 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.1622 | −1.73852 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.0616138 | −0.00353962 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.0330719 | 0.00189369 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.699590 | −0.0399277 | −0.0199638 | − | 0.999801i | \(-0.506355\pi\) | ||||
−0.0199638 | + | 0.999801i | \(0.506355\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.58232 | 0.0900149 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.0625 | 0.854118 | 0.427059 | − | 0.904224i | \(-0.359550\pi\) | ||||
0.427059 | + | 0.904224i | \(0.359550\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.76381 | −0.438836 | −0.219418 | − | 0.975631i | \(-0.570416\pi\) | ||||
−0.219418 | + | 0.975631i | \(0.570416\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.7367 | −0.999350 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0203 | 0.675129 | 0.337565 | − | 0.941302i | \(-0.390397\pi\) | ||||
0.337565 | + | 0.941302i | \(0.390397\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.51514 | 0.140821 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.1136 | 0.843560 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.1964 | 1.29068 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.8424 | 0.823306 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.1743 | 0.728540 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 49.1630 | 2.71044 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.62791 | −0.254373 | −0.127186 | − | 0.991879i | \(-0.540595\pi\) | ||||
−0.127186 | + | 0.991879i | \(0.540595\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.58361 | −0.196380 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.1884 | 0.884469 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.04164 | −0.220162 | −0.110081 | − | 0.993923i | \(-0.535111\pi\) | ||||
−0.110081 | + | 0.993923i | \(0.535111\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.1380 | −1.09375 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.6506 | −0.955836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −24.2736 | −1.31065 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.9032 | −0.640847 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −37.0090 | −1.98675 | −0.993373 | − | 0.114933i | \(-0.963335\pi\) | ||||
−0.993373 | + | 0.114933i | \(0.963335\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.18184 | −0.277378 | −0.138689 | − | 0.990336i | \(-0.544289\pi\) | ||||
−0.138689 | + | 0.990336i | \(0.544289\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.33293 | −0.0711468 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.9215 | −1.53934 | −0.769668 | − | 0.638444i | \(-0.779578\pi\) | ||||
−0.769668 | + | 0.638444i | \(0.779578\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.40068 | −0.498937 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 23.7013 | 1.25441 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.0737 | 1.69279 | 0.846393 | − | 0.532559i | \(-0.178770\pi\) | ||||
0.846393 | + | 0.532559i | \(0.178770\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.324636 | −0.0170861 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.35696 | −0.228681 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.0683 | 1.05042 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.98571 | −0.155853 | −0.0779264 | − | 0.996959i | \(-0.524830\pi\) | ||||
−0.0779264 | + | 0.996959i | \(0.524830\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.78387 | −0.457270 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.42889 | 0.437606 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.5306 | −1.37370 | −0.686852 | − | 0.726797i | \(-0.741008\pi\) | ||||
−0.686852 | + | 0.726797i | \(0.741008\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −24.6438 | −1.27260 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.855498 | 0.0440604 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.6976 | 0.600864 | 0.300432 | − | 0.953803i | \(-0.402869\pi\) | ||||
0.300432 | + | 0.953803i | \(0.402869\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.1668 | −0.930711 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.4782 | −0.739800 | −0.369900 | − | 0.929072i | \(-0.620608\pi\) | ||||
−0.369900 | + | 0.929072i | \(0.620608\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −69.5065 | −3.54238 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.83087 | 0.347233 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.9739 | 1.72255 | 0.861273 | − | 0.508143i | \(-0.169668\pi\) | ||||
0.861273 | + | 0.508143i | \(0.169668\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.9061 | 0.804406 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.0441 | −0.557104 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.36051 | 0.269716 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.9115 | 1.09971 | 0.549853 | − | 0.835262i | \(-0.314684\pi\) | ||||
0.549853 | + | 0.835262i | \(0.314684\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.0819 | 0.955290 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.2013 | −0.759115 | −0.379557 | − | 0.925168i | \(-0.623924\pi\) | ||||
−0.379557 | + | 0.925168i | \(0.623924\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.00367 | −0.299064 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.01685 | 0.199599 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.0434 | −0.696106 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.8815 | −1.13141 | −0.565707 | − | 0.824606i | \(-0.691397\pi\) | ||||
−0.565707 | + | 0.824606i | \(0.691397\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.8528 | −0.732635 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.1838 | 1.43604 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 56.9412 | 2.79513 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.3986 | 0.607162 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.44289 | −0.363609 | −0.181804 | − | 0.983335i | \(-0.558194\pi\) | ||||
−0.181804 | + | 0.983335i | \(0.558194\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.2244 | −0.595780 | −0.297890 | − | 0.954600i | \(-0.596283\pi\) | ||||
−0.297890 | + | 0.954600i | \(0.596283\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.1340 | −0.541354 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 59.7696 | 2.89925 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0363547 | −0.00175933 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.22350 | −0.252193 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.14112 | 0.343976 | 0.171988 | − | 0.985099i | \(-0.444981\pi\) | ||||
0.171988 | + | 0.985099i | \(0.444981\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.96710 | −0.334818 | −0.167409 | − | 0.985888i | \(-0.553540\pi\) | ||||
−0.167409 | + | 0.985888i | \(0.553540\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.57808 | −0.123609 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.8060 | 0.612593 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.01824 | −0.430417 | −0.215209 | − | 0.976568i | \(-0.569043\pi\) | ||||
−0.215209 | + | 0.976568i | \(0.569043\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.4973 | 0.595108 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.8441 | 1.18038 | 0.590189 | − | 0.807265i | \(-0.299053\pi\) | ||||
0.590189 | + | 0.807265i | \(0.299053\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 49.6894 | 2.35550 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.3220 | 0.819304 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.68633 | −0.315548 | −0.157774 | − | 0.987475i | \(-0.550432\pi\) | ||||
−0.157774 | + | 0.987475i | \(0.550432\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −34.4222 | −1.62088 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.7672 | 0.599855 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −23.6419 | −1.10835 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.5537 | −0.493683 | −0.246842 | − | 0.969056i | \(-0.579393\pi\) | ||||
−0.246842 | + | 0.969056i | \(0.579393\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.36767 | −0.250542 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.5758 | −0.818587 | −0.409293 | − | 0.912403i | \(-0.634225\pi\) | ||||
−0.409293 | + | 0.912403i | \(0.634225\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.242028 | −0.0112480 | −0.00562400 | − | 0.999984i | \(-0.501790\pi\) | ||||
−0.00562400 | + | 0.999984i | \(0.501790\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.0923 | 0.839010 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 32.1216 | 1.48641 | 0.743205 | − | 0.669064i | \(-0.233305\pi\) | ||||
0.743205 | + | 0.669064i | \(0.233305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.7953 | −0.821712 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.00398 | −0.0462611 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26.7688 | 1.23083 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 48.1203 | 2.20791 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.90890 | −0.0874026 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.7450 | 0.719405 | 0.359703 | − | 0.933067i | \(-0.382878\pi\) | ||||
0.359703 | + | 0.933067i | \(0.382878\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.77671 | −0.217799 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.0847 | 0.595376 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 53.5915 | 2.43347 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.7962 | 1.03299 | 0.516496 | − | 0.856289i | \(-0.327236\pi\) | ||||
0.516496 | + | 0.856289i | \(0.327236\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.70804 | −0.439013 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.40062 | −0.108338 | −0.0541692 | − | 0.998532i | \(-0.517251\pi\) | ||||
−0.0541692 | + | 0.998532i | \(0.517251\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.44505 | 0.155157 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.7412 | 0.707515 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.3338 | 0.463535 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.1018 | −0.676049 | −0.338024 | − | 0.941137i | \(-0.609759\pi\) | ||||
−0.338024 | + | 0.941137i | \(0.609759\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.3038 | −1.57412 | −0.787059 | − | 0.616878i | \(-0.788397\pi\) | ||||
−0.787059 | + | 0.616878i | \(0.788397\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.247494 | 0.0110133 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.2233 | 0.498444 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.51112 | −0.288601 | −0.144300 | − | 0.989534i | \(-0.546093\pi\) | ||||
−0.144300 | + | 0.989534i | \(0.546093\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.0603 | −0.975890 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.32150 | −0.190799 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.35594 | −0.280076 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −43.6319 | −1.91893 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.0933 | −1.01368 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.3745 | −0.717380 | −0.358690 | − | 0.933457i | \(-0.616776\pi\) | ||||
−0.358690 | + | 0.933457i | \(0.616776\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.9619 | 1.48505 | 0.742526 | − | 0.669817i | \(-0.233628\pi\) | ||||
0.742526 | + | 0.669817i | \(0.233628\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 49.1678 | 2.14586 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.1765 | −1.05315 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.2188 | −0.618207 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.60930 | −0.286819 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.7083 | −0.507144 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −60.7092 | −2.62469 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.0863 | 0.780482 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 48.9743 | 2.10947 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.99706 | 0.386814 | 0.193407 | − | 0.981119i | \(-0.438046\pi\) | ||||
0.193407 | + | 0.981119i | \(0.438046\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.8159 | 0.807470 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −52.9192 | −2.26681 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.4728 | −0.875355 | −0.437677 | − | 0.899132i | \(-0.644199\pi\) | ||||
−0.437677 | + | 0.899132i | \(0.644199\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.00823330 | 0.000351389 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.77360 | 0.118160 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.89260 | −0.250579 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.3948 | 0.611026 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.5319 | 0.869965 | 0.434983 | − | 0.900439i | \(-0.356754\pi\) | ||||
0.434983 | + | 0.900439i | \(0.356754\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.10511 | 0.385105 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.0348 | −0.888091 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.3977 | −0.817514 | −0.408757 | − | 0.912643i | \(-0.634038\pi\) | ||||
−0.408757 | + | 0.912643i | \(0.634038\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 80.8915 | 3.40313 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.41557 | −0.185437 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.4646 | 1.36098 | 0.680492 | − | 0.732755i | \(-0.261766\pi\) | ||||
0.680492 | + | 0.732755i | \(0.261766\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.5493 | 1.11105 | 0.555527 | − | 0.831499i | \(-0.312517\pi\) | ||||
0.555527 | + | 0.831499i | \(0.312517\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.24773 | −0.219227 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.9968 | 1.37606 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.82004 | −0.117400 | −0.0586999 | − | 0.998276i | \(-0.518696\pi\) | ||||
−0.0586999 | + | 0.998276i | \(0.518696\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.4295 | −0.641230 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −62.5933 | −2.59681 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.48059 | −0.309815 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.35420 | 0.221369 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.9907 | −1.11403 | −0.557013 | − | 0.830504i | \(-0.688052\pi\) | ||||
−0.557013 | + | 0.830504i | \(0.688052\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.4645 | −0.802019 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.27605 | 0.175893 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.1868 | 1.52708 | 0.763538 | − | 0.645762i | \(-0.223460\pi\) | ||||
0.763538 | + | 0.645762i | \(0.223460\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −95.2048 | −3.90302 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.93953 | −0.365871 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.6209 | 1.16942 | 0.584709 | − | 0.811243i | \(-0.301209\pi\) | ||||
0.584709 | + | 0.811243i | \(0.301209\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.6774 | −0.680285 | −0.340142 | − | 0.940374i | \(-0.610475\pi\) | ||||
−0.340142 | + | 0.940374i | \(0.610475\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.03013 | 0.164120 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.5013 | 0.711528 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.8248 | −0.967020 | −0.483510 | − | 0.875339i | \(-0.660638\pi\) | ||||
−0.483510 | + | 0.875339i | \(0.660638\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.83398 | 0.114839 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.8409 | −0.600399 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.8091 | 1.36554 | 0.682769 | − | 0.730635i | \(-0.260776\pi\) | ||||
0.682769 | + | 0.730635i | \(0.260776\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 35.2835 | 1.42277 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.75349 | 0.0705928 | 0.0352964 | − | 0.999377i | \(-0.488762\pi\) | ||||
0.0352964 | + | 0.999377i | \(0.488762\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.9500 | −1.76650 | −0.883251 | − | 0.468901i | \(-0.844650\pi\) | ||||
−0.883251 | + | 0.468901i | \(0.844650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.96332 | −0.118914 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −54.6217 | −2.18837 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 43.3149 | 1.73260 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.9351 | −0.676322 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.2356 | −0.766975 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.5677 | 0.938215 | 0.469108 | − | 0.883141i | \(-0.344576\pi\) | ||||
0.469108 | + | 0.883141i | \(0.344576\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.7250 | −0.823744 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 72.9731 | 2.89585 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.6581 | 0.660016 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.34031 | −0.0925813 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −45.5487 | −1.79907 | −0.899533 | − | 0.436854i | \(-0.856093\pi\) | ||||
−0.899533 | + | 0.436854i | \(0.856093\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.60193 | 0.102610 | 0.0513050 | − | 0.998683i | \(-0.483662\pi\) | ||||
0.0513050 | + | 0.998683i | \(0.483662\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27.4386 | −1.08039 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.0801218 | −0.00314991 | −0.00157496 | − | 0.999999i | \(-0.500501\pi\) | ||||
−0.00157496 | + | 0.999999i | \(0.500501\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.9005 | −1.01668 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.8882 | −0.779479 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.6905 | 1.59234 | 0.796171 | − | 0.605072i | \(-0.206856\pi\) | ||||
0.796171 | + | 0.605072i | \(0.206856\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 44.3627 | 1.73339 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.99602 | 0.194913 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.4684 | 1.57642 | 0.788212 | − | 0.615404i | \(-0.211007\pi\) | ||||
0.788212 | + | 0.615404i | \(0.211007\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0618 | −0.702523 | −0.351262 | − | 0.936277i | \(-0.614247\pi\) | ||||
−0.351262 | + | 0.936277i | \(0.614247\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.15476 | −0.277868 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −76.6491 | −2.97233 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.90190 | 0.0736419 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.2434 | −0.396032 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0322646 | 0.00124556 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.2906 | 1.28326 | 0.641630 | − | 0.767015i | \(-0.278259\pi\) | ||||
0.641630 | + | 0.767015i | \(0.278259\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.1351 | −0.428590 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.0968 | 1.57948 | 0.789738 | − | 0.613444i | \(-0.210216\pi\) | ||||
0.789738 | + | 0.613444i | \(0.210216\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −58.9111 | −2.26080 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.0924 | −0.654981 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.2871 | −1.15890 | −0.579451 | − | 0.815007i | \(-0.696733\pi\) | ||||
−0.579451 | + | 0.815007i | \(0.696733\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 59.6615 | 2.27955 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.4530 | −0.932939 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.54444 | −0.0969355 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.2114 | −1.33951 | −0.669753 | − | 0.742584i | \(-0.733600\pi\) | ||||
−0.669753 | + | 0.742584i | \(0.733600\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −17.3037 | −0.657314 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −49.8033 | −1.88915 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −47.1490 | −1.78589 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.7612 | 0.747437 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.6585 | 0.515876 | 0.257938 | − | 0.966162i | \(-0.416957\pi\) | ||||
0.257938 | + | 0.966162i | \(0.416957\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.4866 | −0.584086 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 44.7236 | 1.68439 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.272060 | −0.0102319 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.6575 | −1.07626 | −0.538128 | − | 0.842863i | \(-0.680868\pi\) | ||||
−0.538128 | + | 0.842863i | \(0.680868\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.33451 | 0.0500479 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.3471 | −0.499851 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.9820 | 0.784683 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.5708 | −0.506809 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −49.4611 | −1.84459 | −0.922295 | − | 0.386487i | \(-0.873688\pi\) | ||||
−0.922295 | + | 0.386487i | \(0.873688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.98684 | 0.260204 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.3143 | −0.718307 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.14667 | 0.265421 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.4539 | 0.536067 | 0.268034 | − | 0.963410i | \(-0.413626\pi\) | ||||
0.268034 | + | 0.963410i | \(0.413626\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.6659 | 1.35614 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.5450 | −0.869653 | −0.434827 | − | 0.900514i | \(-0.643190\pi\) | ||||
−0.434827 | + | 0.900514i | \(0.643190\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −50.1997 | −1.85164 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.7933 | 0.581752 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.1706 | −0.447704 | −0.223852 | − | 0.974623i | \(-0.571863\pi\) | ||||
−0.223852 | + | 0.974623i | \(0.571863\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.76028 | −0.211609 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.7882 | −0.836017 | −0.418008 | − | 0.908443i | \(-0.637272\pi\) | ||||
−0.418008 | + | 0.908443i | \(0.637272\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −69.5800 | −2.54921 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.1756 | 0.518658 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 66.7353 | 2.43845 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.0391 | −1.27859 | −0.639297 | − | 0.768960i | \(-0.720775\pi\) | ||||
−0.639297 | + | 0.768960i | \(0.720775\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.8135 | 0.394065 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −51.2839 | −1.86641 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.874303 | 0.0317771 | 0.0158885 | − | 0.999874i | \(-0.494942\pi\) | ||||
0.0158885 | + | 0.999874i | \(0.494942\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.6126 | −0.421512 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.2232 | −0.769340 | −0.384670 | − | 0.923054i | \(-0.625685\pi\) | ||||
−0.384670 | + | 0.923054i | \(0.625685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 58.1720 | 2.10597 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21.5611 | 0.779545 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.80977 | −0.318102 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −53.3473 | −1.92375 | −0.961876 | − | 0.273487i | \(-0.911823\pi\) | ||||
−0.961876 | + | 0.273487i | \(0.911823\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.473302 | 0.0170456 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.4161 | 0.410609 | 0.205305 | − | 0.978698i | \(-0.434181\pi\) | ||||
0.205305 | + | 0.978698i | \(0.434181\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −50.1535 | −1.80157 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.8237 | −0.567671 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −37.9595 | −1.36004 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.17120 | −0.328172 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.641815 | −0.0229366 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.03285 | 0.143938 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.1510 | −1.32429 | −0.662145 | − | 0.749375i | \(-0.730354\pi\) | ||||
−0.662145 | + | 0.749375i | \(0.730354\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.76686 | −0.205306 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −88.9209 | −3.16166 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0109745 | 0.000389714 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.66777 | 0.271948 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.4526 | 0.441093 | 0.220547 | − | 0.975376i | \(-0.429216\pi\) | ||||
0.220547 | + | 0.975376i | \(0.429216\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −59.7637 | −2.11429 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.3702 | 0.437081 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.5784 | 0.690906 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −52.5594 | −1.85248 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.62828 | 0.0925200 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.0293 | 1.75894 | 0.879469 | − | 0.475957i | \(-0.157898\pi\) | ||||
0.879469 | + | 0.475957i | \(0.157898\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.8278 | 1.43366 | 0.716829 | − | 0.697249i | \(-0.245593\pi\) | ||||
0.716829 | + | 0.697249i | \(0.245593\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.50936 | −0.0529357 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38.9957 | 1.36596 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.5196 | 1.03276 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.88567 | −0.205662 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.7502 | −0.968490 | −0.484245 | − | 0.874932i | \(-0.660906\pi\) | ||||
−0.484245 | + | 0.874932i | \(0.660906\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.3295 | −1.54523 | −0.772614 | − | 0.634876i | \(-0.781051\pi\) | ||||
−0.772614 | + | 0.634876i | \(0.781051\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −43.6362 | −1.51922 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.50957 | −0.295907 | −0.147953 | − | 0.988994i | \(-0.547269\pi\) | ||||
−0.147953 | + | 0.988994i | \(0.547269\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.03665 | −0.0360045 | −0.0180022 | − | 0.999838i | \(-0.505731\pi\) | ||||
−0.0180022 | + | 0.999838i | \(0.505731\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.3632 | 0.394186 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 67.0813 | 2.32423 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.01685 | 0.139009 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.50410 | 0.155684 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.5492 | −0.916580 | −0.458290 | − | 0.888803i | \(-0.651538\pi\) | ||||
−0.458290 | + | 0.888803i | \(0.651538\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5881 | −0.985796 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26.3821 | 0.908647 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −45.0823 | −1.55088 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.2385 | −0.661042 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.9376 | −0.684257 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.6194 | −0.364027 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.6529 | −1.28921 | −0.644606 | − | 0.764515i | \(-0.722978\pi\) | ||||
−0.644606 | + | 0.764515i | \(0.722978\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17.3588 | 0.593659 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.32877 | 0.284505 | 0.142253 | − | 0.989830i | \(-0.454565\pi\) | ||||
0.142253 | + | 0.989830i | \(0.454565\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.27936 | 0.214249 | 0.107125 | − | 0.994246i | \(-0.465836\pi\) | ||||
0.107125 | + | 0.994246i | \(0.465836\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −38.7858 | −1.32182 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.750794 | 0.0255573 | 0.0127787 | − | 0.999918i | \(-0.495932\pi\) | ||||
0.0127787 | + | 0.999918i | \(0.495932\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 92.7624 | 3.15402 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.8119 | −0.401154 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.22965 | 0.177404 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.37190 | 0.182020 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.3417 | 0.451547 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −108.816 | −3.67866 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.08436 | −0.0703839 | −0.0351920 | − | 0.999381i | \(-0.511204\pi\) | ||||
−0.0351920 | + | 0.999381i | \(0.511204\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.6368 | 1.03335 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.7826 | −0.936018 | −0.468009 | − | 0.883724i | \(-0.655029\pi\) | ||||
−0.468009 | + | 0.883724i | \(0.655029\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.29815 | −0.178297 | −0.0891484 | − | 0.996018i | \(-0.528415\pi\) | ||||
−0.0891484 | + | 0.996018i | \(0.528415\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 26.5486 | 0.892421 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −48.2315 | −1.61946 | −0.809728 | − | 0.586805i | \(-0.800385\pi\) | ||||
−0.809728 | + | 0.586805i | \(0.800385\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −80.2166 | −2.69038 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.91880 | 0.131285 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −48.1156 | −1.61013 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −72.6500 | −2.42842 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.94991 | −0.131884 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.89080 | −0.0964135 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.2464 | −0.341356 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 30.1622 | 1.00374 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −75.5809 | −2.51239 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.6247 | −0.784445 | −0.392222 | − | 0.919870i | \(-0.628294\pi\) | ||||
−0.392222 | + | 0.919870i | \(0.628294\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.0616138 | 0.00204360 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.1298 | −1.03138 | −0.515688 | − | 0.856777i | \(-0.672464\pi\) | ||||
−0.515688 | + | 0.856777i | \(0.672464\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 55.5512 | 1.83848 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0330719 | −0.00109332 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −48.7662 | −1.61040 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.7448 | 1.11314 | 0.556569 | − | 0.830801i | \(-0.312117\pi\) | ||||
0.556569 | + | 0.830801i | \(0.312117\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.699590 | 0.0230523 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.11948 | −0.102679 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −39.9038 | −1.31203 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.58232 | −0.0519702 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.5423 | −0.706779 | −0.353390 | − | 0.935476i | \(-0.614971\pi\) | ||||
−0.353390 | + | 0.935476i | \(0.614971\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 54.0070 | 1.77001 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.0625 | −0.493125 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 84.4937 | 2.76324 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.7027 | 1.72172 | 0.860861 | − | 0.508841i | \(-0.169926\pi\) | ||||
0.860861 | + | 0.508841i | \(0.169926\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.76381 | 0.253362 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 55.8970 | 1.82219 | 0.911094 | − | 0.412198i | \(-0.135239\pi\) | ||||
0.911094 | + | 0.412198i | \(0.135239\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.0294 | −0.847633 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.7367 | 0.576975 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.46512 | −0.307575 | −0.153788 | − | 0.988104i | \(-0.549147\pi\) | ||||
−0.153788 | + | 0.988104i | \(0.549147\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.65937 | 0.216172 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.0203 | −0.389786 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.4719 | −0.663151 | −0.331575 | − | 0.943429i | \(-0.607580\pi\) | ||||
−0.331575 | + | 0.943429i | \(0.607580\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.0794 | 0.682112 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.51514 | −0.0813030 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −65.5836 | −2.11781 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.7131 | −0.345584 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.1136 | −0.487030 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 61.9782 | 1.99515 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 60.8243 | 1.95598 | 0.977988 | − | 0.208660i | \(-0.0669103\pi\) | ||||
0.977988 | + | 0.208660i | \(0.0669103\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23.1964 | −0.745176 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.6775 | 1.46586 | 0.732930 | − | 0.680304i | \(-0.238152\pi\) | ||||
0.732930 | + | 0.680304i | \(0.238152\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 54.7469 | 1.75511 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.8424 | −0.475336 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −56.6492 | −1.81237 | −0.906183 | − | 0.422885i | \(-0.861018\pi\) | ||||
−0.906183 | + | 0.422885i | \(0.861018\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.4765 | 1.54931 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.1743 | −0.420623 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.9879 | −1.27542 | −0.637708 | − | 0.770278i | \(-0.720117\pi\) | ||||
−0.637708 | + | 0.770278i | \(0.720117\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.1762 | −0.547281 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −49.1630 | −1.56488 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.2420 | 0.643659 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.6527 | 0.433692 | 0.216846 | − | 0.976206i | \(-0.430423\pi\) | ||||
0.216846 | + | 0.976206i | \(0.430423\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.62791 | 0.146862 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 35.9088 | 1.13838 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.9689 | 0.537410 | 0.268705 | − | 0.963223i | \(-0.413404\pi\) | ||||
0.268705 | + | 0.963223i | \(0.413404\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.58361 | 0.113380 |
(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 | 4008.2.a.k.1.11 | ✓ | 11 | |
4.3 | odd | 2 | 8016.2.a.be.1.11 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.k.1.11 | ✓ | 11 | 1.1 | even | 1 | trivial | |
8016.2.a.be.1.11 | 11 | 4.3 | odd | 2 |