Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [539,2,Mod(1,539)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(539, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("539.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 539.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: | \(4.30393666895\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 26x^{8} + 245x^{6} - 1038x^{4} + 1884x^{2} - 968 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.32267\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 539.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.566092 | 0.400288 | 0.200144 | − | 0.979767i | \(-0.435859\pi\) | ||||
0.200144 | + | 0.979767i | \(0.435859\pi\) | |||||||
\(3\) | −2.32267 | −1.34099 | −0.670497 | − | 0.741913i | \(-0.733919\pi\) | ||||
−0.670497 | + | 0.741913i | \(0.733919\pi\) | |||||||
\(4\) | −1.67954 | −0.839770 | ||||||||
\(5\) | −3.58219 | −1.60201 | −0.801003 | − | 0.598661i | \(-0.795700\pi\) | ||||
−0.801003 | + | 0.598661i | \(0.795700\pi\) | |||||||
\(6\) | −1.31484 | −0.536783 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.08296 | −0.736437 | ||||||||
\(9\) | 2.39479 | 0.798263 | ||||||||
\(10\) | −2.02785 | −0.641263 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 3.90101 | 1.12613 | ||||||||
\(13\) | 2.11542 | 0.586712 | 0.293356 | − | 0.956003i | \(-0.405228\pi\) | ||||
0.293356 | + | 0.956003i | \(0.405228\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.32025 | 2.14828 | ||||||||
\(16\) | 2.17993 | 0.544983 | ||||||||
\(17\) | −7.87739 | −1.91055 | −0.955274 | − | 0.295722i | \(-0.904440\pi\) | ||||
−0.955274 | + | 0.295722i | \(0.904440\pi\) | |||||||
\(18\) | 1.35567 | 0.319535 | ||||||||
\(19\) | 5.56323 | 1.27629 | 0.638147 | − | 0.769915i | \(-0.279701\pi\) | ||||
0.638147 | + | 0.769915i | \(0.279701\pi\) | |||||||
\(20\) | 6.01643 | 1.34532 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.566092 | 0.120691 | ||||||||
\(23\) | −1.25426 | −0.261532 | −0.130766 | − | 0.991413i | \(-0.541744\pi\) | ||||
−0.130766 | + | 0.991413i | \(0.541744\pi\) | |||||||
\(24\) | 4.83802 | 0.987557 | ||||||||
\(25\) | 7.83210 | 1.56642 | ||||||||
\(26\) | 1.19752 | 0.234854 | ||||||||
\(27\) | 1.40570 | 0.270528 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.991656 | −0.184146 | −0.0920730 | − | 0.995752i | \(-0.529349\pi\) | ||||
−0.0920730 | + | 0.995752i | \(0.529349\pi\) | |||||||
\(30\) | 4.71003 | 0.859929 | ||||||||
\(31\) | 6.06899 | 1.09002 | 0.545012 | − | 0.838428i | \(-0.316525\pi\) | ||||
0.545012 | + | 0.838428i | \(0.316525\pi\) | |||||||
\(32\) | 5.39996 | 0.954587 | ||||||||
\(33\) | −2.32267 | −0.404325 | ||||||||
\(34\) | −4.45933 | −0.764769 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.02214 | −0.670357 | ||||||||
\(37\) | −1.67120 | −0.274743 | −0.137371 | − | 0.990520i | \(-0.543865\pi\) | ||||
−0.137371 | + | 0.990520i | \(0.543865\pi\) | |||||||
\(38\) | 3.14930 | 0.510885 | ||||||||
\(39\) | −4.91342 | −0.786777 | ||||||||
\(40\) | 7.46156 | 1.17978 | ||||||||
\(41\) | 5.35834 | 0.836833 | 0.418416 | − | 0.908255i | \(-0.362585\pi\) | ||||
0.418416 | + | 0.908255i | \(0.362585\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.21855 | −1.40582 | −0.702908 | − | 0.711281i | \(-0.748115\pi\) | ||||
−0.702908 | + | 0.711281i | \(0.748115\pi\) | |||||||
\(44\) | −1.67954 | −0.253200 | ||||||||
\(45\) | −8.57860 | −1.27882 | ||||||||
\(46\) | −0.710028 | −0.104688 | ||||||||
\(47\) | −9.40225 | −1.37146 | −0.685729 | − | 0.727857i | \(-0.740517\pi\) | ||||
−0.685729 | + | 0.727857i | \(0.740517\pi\) | |||||||
\(48\) | −5.06326 | −0.730819 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.43369 | 0.627019 | ||||||||
\(51\) | 18.2966 | 2.56203 | ||||||||
\(52\) | −3.55293 | −0.492703 | ||||||||
\(53\) | 12.2102 | 1.67720 | 0.838600 | − | 0.544747i | \(-0.183374\pi\) | ||||
0.838600 | + | 0.544747i | \(0.183374\pi\) | |||||||
\(54\) | 0.795757 | 0.108289 | ||||||||
\(55\) | −3.58219 | −0.483023 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.9216 | −1.71150 | ||||||||
\(58\) | −0.561369 | −0.0737113 | ||||||||
\(59\) | −3.88070 | −0.505224 | −0.252612 | − | 0.967568i | \(-0.581290\pi\) | ||||
−0.252612 | + | 0.967568i | \(0.581290\pi\) | |||||||
\(60\) | −13.9742 | −1.80406 | ||||||||
\(61\) | 2.52992 | 0.323923 | 0.161961 | − | 0.986797i | \(-0.448218\pi\) | ||||
0.161961 | + | 0.986797i | \(0.448218\pi\) | |||||||
\(62\) | 3.43561 | 0.436323 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.30299 | −0.162873 | ||||||||
\(65\) | −7.57784 | −0.939916 | ||||||||
\(66\) | −1.31484 | −0.161846 | ||||||||
\(67\) | −3.51863 | −0.429869 | −0.214935 | − | 0.976628i | \(-0.568954\pi\) | ||||
−0.214935 | + | 0.976628i | \(0.568954\pi\) | |||||||
\(68\) | 13.2304 | 1.60442 | ||||||||
\(69\) | 2.91323 | 0.350712 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.481369 | 0.0571280 | 0.0285640 | − | 0.999592i | \(-0.490907\pi\) | ||||
0.0285640 | + | 0.999592i | \(0.490907\pi\) | |||||||
\(72\) | −4.98825 | −0.587871 | ||||||||
\(73\) | 14.9367 | 1.74820 | 0.874102 | − | 0.485743i | \(-0.161451\pi\) | ||||
0.874102 | + | 0.485743i | \(0.161451\pi\) | |||||||
\(74\) | −0.946051 | −0.109976 | ||||||||
\(75\) | −18.1914 | −2.10056 | ||||||||
\(76\) | −9.34367 | −1.07179 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.78145 | −0.314937 | ||||||||
\(79\) | −8.00813 | −0.900985 | −0.450493 | − | 0.892780i | \(-0.648752\pi\) | ||||
−0.450493 | + | 0.892780i | \(0.648752\pi\) | |||||||
\(80\) | −7.80894 | −0.873066 | ||||||||
\(81\) | −10.4494 | −1.16104 | ||||||||
\(82\) | 3.03332 | 0.334974 | ||||||||
\(83\) | 4.23084 | 0.464395 | 0.232198 | − | 0.972669i | \(-0.425408\pi\) | ||||
0.232198 | + | 0.972669i | \(0.425408\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28.2183 | 3.06071 | ||||||||
\(86\) | −5.21855 | −0.562731 | ||||||||
\(87\) | 2.30329 | 0.246938 | ||||||||
\(88\) | −2.08296 | −0.222044 | ||||||||
\(89\) | −3.58219 | −0.379712 | −0.189856 | − | 0.981812i | \(-0.560802\pi\) | ||||
−0.189856 | + | 0.981812i | \(0.560802\pi\) | |||||||
\(90\) | −4.85628 | −0.511897 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.10658 | 0.219626 | ||||||||
\(93\) | −14.0963 | −1.46171 | ||||||||
\(94\) | −5.32254 | −0.548978 | ||||||||
\(95\) | −19.9286 | −2.04463 | ||||||||
\(96\) | −12.5423 | −1.28010 | ||||||||
\(97\) | −0.164132 | −0.0166650 | −0.00833252 | − | 0.999965i | \(-0.502652\pi\) | ||||
−0.00833252 | + | 0.999965i | \(0.502652\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.39479 | 0.240685 | ||||||||
\(100\) | −13.1543 | −1.31543 | ||||||||
\(101\) | 12.1489 | 1.20886 | 0.604428 | − | 0.796660i | \(-0.293402\pi\) | ||||
0.604428 | + | 0.796660i | \(0.293402\pi\) | |||||||
\(102\) | 10.3575 | 1.02555 | ||||||||
\(103\) | 6.46318 | 0.636836 | 0.318418 | − | 0.947950i | \(-0.396848\pi\) | ||||
0.318418 | + | 0.947950i | \(0.396848\pi\) | |||||||
\(104\) | −4.40633 | −0.432077 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.91210 | 0.671363 | ||||||||
\(107\) | 15.4910 | 1.49758 | 0.748788 | − | 0.662809i | \(-0.230636\pi\) | ||||
0.748788 | + | 0.662809i | \(0.230636\pi\) | |||||||
\(108\) | −2.36093 | −0.227181 | ||||||||
\(109\) | 18.3507 | 1.75768 | 0.878841 | − | 0.477115i | \(-0.158318\pi\) | ||||
0.878841 | + | 0.477115i | \(0.158318\pi\) | |||||||
\(110\) | −2.02785 | −0.193348 | ||||||||
\(111\) | 3.88163 | 0.368428 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.17993 | 0.110999 | 0.0554993 | − | 0.998459i | \(-0.482325\pi\) | ||||
0.0554993 | + | 0.998459i | \(0.482325\pi\) | |||||||
\(114\) | −7.31479 | −0.685093 | ||||||||
\(115\) | 4.49301 | 0.418975 | ||||||||
\(116\) | 1.66553 | 0.154640 | ||||||||
\(117\) | 5.06599 | 0.468351 | ||||||||
\(118\) | −2.19684 | −0.202235 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −17.3307 | −1.58207 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.43217 | 0.129662 | ||||||||
\(123\) | −12.4457 | −1.12219 | ||||||||
\(124\) | −10.1931 | −0.915369 | ||||||||
\(125\) | −10.1451 | −0.907409 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.50852 | −0.577538 | −0.288769 | − | 0.957399i | \(-0.593246\pi\) | ||||
−0.288769 | + | 0.957399i | \(0.593246\pi\) | |||||||
\(128\) | −11.5375 | −1.01978 | ||||||||
\(129\) | 21.4116 | 1.88519 | ||||||||
\(130\) | −4.28976 | −0.376237 | ||||||||
\(131\) | 7.36312 | 0.643319 | 0.321660 | − | 0.946855i | \(-0.395759\pi\) | ||||
0.321660 | + | 0.946855i | \(0.395759\pi\) | |||||||
\(132\) | 3.90101 | 0.339540 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.99187 | −0.172071 | ||||||||
\(135\) | −5.03550 | −0.433387 | ||||||||
\(136\) | 16.4083 | 1.40700 | ||||||||
\(137\) | 8.76591 | 0.748922 | 0.374461 | − | 0.927243i | \(-0.377828\pi\) | ||||
0.374461 | + | 0.927243i | \(0.377828\pi\) | |||||||
\(138\) | 1.64916 | 0.140386 | ||||||||
\(139\) | 3.64121 | 0.308843 | 0.154422 | − | 0.988005i | \(-0.450649\pi\) | ||||
0.154422 | + | 0.988005i | \(0.450649\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.8383 | 1.83912 | ||||||||
\(142\) | 0.272500 | 0.0228677 | ||||||||
\(143\) | 2.11542 | 0.176900 | ||||||||
\(144\) | 5.22048 | 0.435040 | ||||||||
\(145\) | 3.55230 | 0.295003 | ||||||||
\(146\) | 8.45553 | 0.699784 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.80684 | 0.230721 | ||||||||
\(149\) | 0.728603 | 0.0596895 | 0.0298448 | − | 0.999555i | \(-0.490499\pi\) | ||||
0.0298448 | + | 0.999555i | \(0.490499\pi\) | |||||||
\(150\) | −10.2980 | −0.840828 | ||||||||
\(151\) | −6.42897 | −0.523182 | −0.261591 | − | 0.965179i | \(-0.584247\pi\) | ||||
−0.261591 | + | 0.965179i | \(0.584247\pi\) | |||||||
\(152\) | −11.5880 | −0.939910 | ||||||||
\(153\) | −18.8647 | −1.52512 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.7403 | −1.74622 | ||||||||
\(156\) | 8.25228 | 0.660711 | ||||||||
\(157\) | −3.55610 | −0.283808 | −0.141904 | − | 0.989880i | \(-0.545322\pi\) | ||||
−0.141904 | + | 0.989880i | \(0.545322\pi\) | |||||||
\(158\) | −4.53334 | −0.360653 | ||||||||
\(159\) | −28.3603 | −2.24912 | ||||||||
\(160\) | −19.3437 | −1.52925 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.91530 | −0.464750 | ||||||||
\(163\) | 13.8255 | 1.08290 | 0.541449 | − | 0.840733i | \(-0.317876\pi\) | ||||
0.541449 | + | 0.840733i | \(0.317876\pi\) | |||||||
\(164\) | −8.99955 | −0.702747 | ||||||||
\(165\) | 8.32025 | 0.647730 | ||||||||
\(166\) | 2.39505 | 0.185892 | ||||||||
\(167\) | −0.589634 | −0.0456272 | −0.0228136 | − | 0.999740i | \(-0.507262\pi\) | ||||
−0.0228136 | + | 0.999740i | \(0.507262\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.52500 | −0.655769 | ||||||||
\(170\) | 15.9742 | 1.22516 | ||||||||
\(171\) | 13.3228 | 1.01882 | ||||||||
\(172\) | 15.4829 | 1.18056 | ||||||||
\(173\) | −4.28419 | −0.325721 | −0.162861 | − | 0.986649i | \(-0.552072\pi\) | ||||
−0.162861 | + | 0.986649i | \(0.552072\pi\) | |||||||
\(174\) | 1.30387 | 0.0988464 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.17993 | 0.164319 | ||||||||
\(177\) | 9.01359 | 0.677503 | ||||||||
\(178\) | −2.02785 | −0.151994 | ||||||||
\(179\) | −13.4606 | −1.00609 | −0.503045 | − | 0.864260i | \(-0.667787\pi\) | ||||
−0.503045 | + | 0.864260i | \(0.667787\pi\) | |||||||
\(180\) | 14.4081 | 1.07392 | ||||||||
\(181\) | 20.2099 | 1.50219 | 0.751095 | − | 0.660194i | \(-0.229526\pi\) | ||||
0.751095 | + | 0.660194i | \(0.229526\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.87616 | −0.434378 | ||||||||
\(184\) | 2.61258 | 0.192602 | ||||||||
\(185\) | 5.98654 | 0.440140 | ||||||||
\(186\) | −7.97978 | −0.585106 | ||||||||
\(187\) | −7.87739 | −0.576052 | ||||||||
\(188\) | 15.7914 | 1.15171 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.2814 | −0.818440 | ||||||||
\(191\) | 20.1625 | 1.45890 | 0.729452 | − | 0.684032i | \(-0.239775\pi\) | ||||
0.729452 | + | 0.684032i | \(0.239775\pi\) | |||||||
\(192\) | 3.02641 | 0.218412 | ||||||||
\(193\) | 1.85134 | 0.133262 | 0.0666312 | − | 0.997778i | \(-0.478775\pi\) | ||||
0.0666312 | + | 0.997778i | \(0.478775\pi\) | |||||||
\(194\) | −0.0929136 | −0.00667081 | ||||||||
\(195\) | 17.6008 | 1.26042 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.28141 | 0.661273 | 0.330637 | − | 0.943758i | \(-0.392737\pi\) | ||||
0.330637 | + | 0.943758i | \(0.392737\pi\) | |||||||
\(198\) | 1.35567 | 0.0963434 | ||||||||
\(199\) | −0.993564 | −0.0704319 | −0.0352159 | − | 0.999380i | \(-0.511212\pi\) | ||||
−0.0352159 | + | 0.999380i | \(0.511212\pi\) | |||||||
\(200\) | −16.3140 | −1.15357 | ||||||||
\(201\) | 8.17261 | 0.576452 | ||||||||
\(202\) | 6.87737 | 0.483890 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −30.7298 | −2.15152 | ||||||||
\(205\) | −19.1946 | −1.34061 | ||||||||
\(206\) | 3.65876 | 0.254918 | ||||||||
\(207\) | −3.00369 | −0.208771 | ||||||||
\(208\) | 4.61147 | 0.319748 | ||||||||
\(209\) | 5.56323 | 0.384817 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.4840 | 1.13481 | 0.567403 | − | 0.823440i | \(-0.307948\pi\) | ||||
0.567403 | + | 0.823440i | \(0.307948\pi\) | |||||||
\(212\) | −20.5075 | −1.40846 | ||||||||
\(213\) | −1.11806 | −0.0766083 | ||||||||
\(214\) | 8.76936 | 0.599461 | ||||||||
\(215\) | 33.0226 | 2.25212 | ||||||||
\(216\) | −2.92802 | −0.199227 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.3882 | 0.703578 | ||||||||
\(219\) | −34.6929 | −2.34433 | ||||||||
\(220\) | 6.01643 | 0.405628 | ||||||||
\(221\) | −16.6640 | −1.12094 | ||||||||
\(222\) | 2.19736 | 0.147477 | ||||||||
\(223\) | −26.2084 | −1.75504 | −0.877521 | − | 0.479538i | \(-0.840804\pi\) | ||||
−0.877521 | + | 0.479538i | \(0.840804\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 18.7562 | 1.25042 | ||||||||
\(226\) | 0.667950 | 0.0444314 | ||||||||
\(227\) | −18.3200 | −1.21594 | −0.607970 | − | 0.793960i | \(-0.708016\pi\) | ||||
−0.607970 | + | 0.793960i | \(0.708016\pi\) | |||||||
\(228\) | 21.7023 | 1.43727 | ||||||||
\(229\) | −13.4169 | −0.886613 | −0.443307 | − | 0.896370i | \(-0.646195\pi\) | ||||
−0.443307 | + | 0.896370i | \(0.646195\pi\) | |||||||
\(230\) | 2.54346 | 0.167711 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.06558 | 0.135612 | ||||||||
\(233\) | −4.43884 | −0.290798 | −0.145399 | − | 0.989373i | \(-0.546447\pi\) | ||||
−0.145399 | + | 0.989373i | \(0.546447\pi\) | |||||||
\(234\) | 2.86782 | 0.187475 | ||||||||
\(235\) | 33.6807 | 2.19708 | ||||||||
\(236\) | 6.51779 | 0.424272 | ||||||||
\(237\) | 18.6002 | 1.20822 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.13900 | 0.591153 | 0.295576 | − | 0.955319i | \(-0.404488\pi\) | ||||
0.295576 | + | 0.955319i | \(0.404488\pi\) | |||||||
\(240\) | 18.1376 | 1.17078 | ||||||||
\(241\) | −17.1870 | −1.10711 | −0.553554 | − | 0.832813i | \(-0.686729\pi\) | ||||
−0.553554 | + | 0.832813i | \(0.686729\pi\) | |||||||
\(242\) | 0.566092 | 0.0363898 | ||||||||
\(243\) | 20.0533 | 1.28642 | ||||||||
\(244\) | −4.24910 | −0.272020 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.04539 | −0.449198 | ||||||||
\(247\) | 11.7686 | 0.748817 | ||||||||
\(248\) | −12.6415 | −0.802734 | ||||||||
\(249\) | −9.82684 | −0.622751 | ||||||||
\(250\) | −5.74309 | −0.363225 | ||||||||
\(251\) | 17.7972 | 1.12335 | 0.561675 | − | 0.827358i | \(-0.310157\pi\) | ||||
0.561675 | + | 0.827358i | \(0.310157\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.25426 | −0.0788547 | ||||||||
\(254\) | −3.68442 | −0.231181 | ||||||||
\(255\) | −65.5418 | −4.10439 | ||||||||
\(256\) | −3.92533 | −0.245333 | ||||||||
\(257\) | −6.99447 | −0.436303 | −0.218152 | − | 0.975915i | \(-0.570003\pi\) | ||||
−0.218152 | + | 0.975915i | \(0.570003\pi\) | |||||||
\(258\) | 12.1210 | 0.754618 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 12.7273 | 0.789313 | ||||||||
\(261\) | −2.37481 | −0.146997 | ||||||||
\(262\) | 4.16821 | 0.257513 | ||||||||
\(263\) | −3.22711 | −0.198992 | −0.0994960 | − | 0.995038i | \(-0.531723\pi\) | ||||
−0.0994960 | + | 0.995038i | \(0.531723\pi\) | |||||||
\(264\) | 4.83802 | 0.297760 | ||||||||
\(265\) | −43.7393 | −2.68688 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.32025 | 0.509191 | ||||||||
\(268\) | 5.90968 | 0.360991 | ||||||||
\(269\) | −11.1383 | −0.679112 | −0.339556 | − | 0.940586i | \(-0.610277\pi\) | ||||
−0.339556 | + | 0.940586i | \(0.610277\pi\) | |||||||
\(270\) | −2.85056 | −0.173479 | ||||||||
\(271\) | −3.94320 | −0.239532 | −0.119766 | − | 0.992802i | \(-0.538214\pi\) | ||||
−0.119766 | + | 0.992802i | \(0.538214\pi\) | |||||||
\(272\) | −17.1722 | −1.04122 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.96231 | 0.299784 | ||||||||
\(275\) | 7.83210 | 0.472294 | ||||||||
\(276\) | −4.89289 | −0.294517 | ||||||||
\(277\) | 26.7624 | 1.60800 | 0.804000 | − | 0.594630i | \(-0.202701\pi\) | ||||
0.804000 | + | 0.594630i | \(0.202701\pi\) | |||||||
\(278\) | 2.06126 | 0.123626 | ||||||||
\(279\) | 14.5340 | 0.870126 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.19505 | −0.190601 | −0.0953003 | − | 0.995449i | \(-0.530381\pi\) | ||||
−0.0953003 | + | 0.995449i | \(0.530381\pi\) | |||||||
\(282\) | 12.3625 | 0.736176 | ||||||||
\(283\) | −4.65272 | −0.276576 | −0.138288 | − | 0.990392i | \(-0.544160\pi\) | ||||
−0.138288 | + | 0.990392i | \(0.544160\pi\) | |||||||
\(284\) | −0.808479 | −0.0479744 | ||||||||
\(285\) | 46.2875 | 2.74183 | ||||||||
\(286\) | 1.19752 | 0.0708110 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 12.9318 | 0.762012 | ||||||||
\(289\) | 45.0533 | 2.65019 | ||||||||
\(290\) | 2.01093 | 0.118086 | ||||||||
\(291\) | 0.381223 | 0.0223477 | ||||||||
\(292\) | −25.0867 | −1.46809 | ||||||||
\(293\) | −15.6199 | −0.912525 | −0.456263 | − | 0.889845i | \(-0.650812\pi\) | ||||
−0.456263 | + | 0.889845i | \(0.650812\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.9014 | 0.809372 | ||||||||
\(296\) | 3.48103 | 0.202331 | ||||||||
\(297\) | 1.40570 | 0.0815671 | ||||||||
\(298\) | 0.412457 | 0.0238930 | ||||||||
\(299\) | −2.65329 | −0.153444 | ||||||||
\(300\) | 30.5531 | 1.76399 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.63939 | −0.209423 | ||||||||
\(303\) | −28.2178 | −1.62107 | ||||||||
\(304\) | 12.1275 | 0.695558 | ||||||||
\(305\) | −9.06265 | −0.518926 | ||||||||
\(306\) | −10.6792 | −0.610487 | ||||||||
\(307\) | −18.9815 | −1.08333 | −0.541666 | − | 0.840594i | \(-0.682206\pi\) | ||||
−0.541666 | + | 0.840594i | \(0.682206\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.0118 | −0.853993 | ||||||||
\(310\) | −12.3070 | −0.698992 | ||||||||
\(311\) | 17.5896 | 0.997417 | 0.498709 | − | 0.866770i | \(-0.333808\pi\) | ||||
0.498709 | + | 0.866770i | \(0.333808\pi\) | |||||||
\(312\) | 10.2345 | 0.579412 | ||||||||
\(313\) | 18.0021 | 1.01754 | 0.508769 | − | 0.860903i | \(-0.330101\pi\) | ||||
0.508769 | + | 0.860903i | \(0.330101\pi\) | |||||||
\(314\) | −2.01308 | −0.113605 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.4500 | 0.756620 | ||||||||
\(317\) | 6.97654 | 0.391841 | 0.195921 | − | 0.980620i | \(-0.437230\pi\) | ||||
0.195921 | + | 0.980620i | \(0.437230\pi\) | |||||||
\(318\) | −16.0545 | −0.900293 | ||||||||
\(319\) | −0.991656 | −0.0555221 | ||||||||
\(320\) | 4.66755 | 0.260924 | ||||||||
\(321\) | −35.9806 | −2.00824 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −43.8238 | −2.43842 | ||||||||
\(324\) | 17.5501 | 0.975005 | ||||||||
\(325\) | 16.5682 | 0.919038 | ||||||||
\(326\) | 7.82652 | 0.433471 | ||||||||
\(327\) | −42.6227 | −2.35704 | ||||||||
\(328\) | −11.1612 | −0.616275 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.71003 | 0.259278 | ||||||||
\(331\) | 15.0208 | 0.825619 | 0.412810 | − | 0.910817i | \(-0.364547\pi\) | ||||
0.412810 | + | 0.910817i | \(0.364547\pi\) | |||||||
\(332\) | −7.10586 | −0.389985 | ||||||||
\(333\) | −4.00216 | −0.219317 | ||||||||
\(334\) | −0.333787 | −0.0182640 | ||||||||
\(335\) | 12.6044 | 0.688653 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.4314 | 0.622708 | 0.311354 | − | 0.950294i | \(-0.399218\pi\) | ||||
0.311354 | + | 0.950294i | \(0.399218\pi\) | |||||||
\(338\) | −4.82594 | −0.262496 | ||||||||
\(339\) | −2.74059 | −0.148848 | ||||||||
\(340\) | −47.3938 | −2.57029 | ||||||||
\(341\) | 6.06899 | 0.328654 | ||||||||
\(342\) | 7.54192 | 0.407820 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 19.2019 | 1.03530 | ||||||||
\(345\) | −10.4358 | −0.561843 | ||||||||
\(346\) | −2.42525 | −0.130382 | ||||||||
\(347\) | 9.14713 | 0.491044 | 0.245522 | − | 0.969391i | \(-0.421041\pi\) | ||||
0.245522 | + | 0.969391i | \(0.421041\pi\) | |||||||
\(348\) | −3.86846 | −0.207371 | ||||||||
\(349\) | 28.2369 | 1.51149 | 0.755743 | − | 0.654868i | \(-0.227276\pi\) | ||||
0.755743 | + | 0.654868i | \(0.227276\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.97365 | 0.158722 | ||||||||
\(352\) | 5.39996 | 0.287819 | ||||||||
\(353\) | −5.54734 | −0.295255 | −0.147627 | − | 0.989043i | \(-0.547164\pi\) | ||||
−0.147627 | + | 0.989043i | \(0.547164\pi\) | |||||||
\(354\) | 5.10252 | 0.271196 | ||||||||
\(355\) | −1.72436 | −0.0915194 | ||||||||
\(356\) | 6.01643 | 0.318870 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.61992 | −0.402725 | ||||||||
\(359\) | −0.333903 | −0.0176227 | −0.00881137 | − | 0.999961i | \(-0.502805\pi\) | ||||
−0.00881137 | + | 0.999961i | \(0.502805\pi\) | |||||||
\(360\) | 17.8689 | 0.941772 | ||||||||
\(361\) | 11.9496 | 0.628925 | ||||||||
\(362\) | 11.4407 | 0.601308 | ||||||||
\(363\) | −2.32267 | −0.121908 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −53.5060 | −2.80063 | ||||||||
\(366\) | −3.32645 | −0.173876 | ||||||||
\(367\) | −8.11154 | −0.423419 | −0.211710 | − | 0.977333i | \(-0.567903\pi\) | ||||
−0.211710 | + | 0.977333i | \(0.567903\pi\) | |||||||
\(368\) | −2.73420 | −0.142530 | ||||||||
\(369\) | 12.8321 | 0.668013 | ||||||||
\(370\) | 3.38894 | 0.176182 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 23.6752 | 1.22750 | ||||||||
\(373\) | 34.2270 | 1.77221 | 0.886104 | − | 0.463486i | \(-0.153401\pi\) | ||||
0.886104 | + | 0.463486i | \(0.153401\pi\) | |||||||
\(374\) | −4.45933 | −0.230587 | ||||||||
\(375\) | 23.5638 | 1.21683 | ||||||||
\(376\) | 19.5845 | 1.00999 | ||||||||
\(377\) | −2.09777 | −0.108041 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.9557 | −1.12779 | −0.563895 | − | 0.825846i | \(-0.690698\pi\) | ||||
−0.563895 | + | 0.825846i | \(0.690698\pi\) | |||||||
\(380\) | 33.4708 | 1.71702 | ||||||||
\(381\) | 15.1171 | 0.774475 | ||||||||
\(382\) | 11.4138 | 0.583981 | ||||||||
\(383\) | −7.77526 | −0.397297 | −0.198649 | − | 0.980071i | \(-0.563655\pi\) | ||||
−0.198649 | + | 0.980071i | \(0.563655\pi\) | |||||||
\(384\) | 26.7979 | 1.36752 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.04803 | 0.0533433 | ||||||||
\(387\) | −22.0765 | −1.12221 | ||||||||
\(388\) | 0.275665 | 0.0139948 | ||||||||
\(389\) | 5.77816 | 0.292964 | 0.146482 | − | 0.989213i | \(-0.453205\pi\) | ||||
0.146482 | + | 0.989213i | \(0.453205\pi\) | |||||||
\(390\) | 9.96369 | 0.504531 | ||||||||
\(391\) | 9.88031 | 0.499669 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.1021 | −0.862687 | ||||||||
\(394\) | 5.25414 | 0.264700 | ||||||||
\(395\) | 28.6867 | 1.44338 | ||||||||
\(396\) | −4.02214 | −0.202120 | ||||||||
\(397\) | 20.0863 | 1.00810 | 0.504052 | − | 0.863673i | \(-0.331842\pi\) | ||||
0.504052 | + | 0.863673i | \(0.331842\pi\) | |||||||
\(398\) | −0.562449 | −0.0281930 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.0735 | 0.853673 | ||||||||
\(401\) | −13.8268 | −0.690479 | −0.345240 | − | 0.938515i | \(-0.612202\pi\) | ||||
−0.345240 | + | 0.938515i | \(0.612202\pi\) | |||||||
\(402\) | 4.62645 | 0.230747 | ||||||||
\(403\) | 12.8385 | 0.639530 | ||||||||
\(404\) | −20.4045 | −1.01516 | ||||||||
\(405\) | 37.4316 | 1.85999 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.67120 | −0.0828381 | ||||||||
\(408\) | −38.1110 | −1.88678 | ||||||||
\(409\) | 5.33474 | 0.263786 | 0.131893 | − | 0.991264i | \(-0.457894\pi\) | ||||
0.131893 | + | 0.991264i | \(0.457894\pi\) | |||||||
\(410\) | −10.8659 | −0.536630 | ||||||||
\(411\) | −20.3603 | −1.00430 | ||||||||
\(412\) | −10.8552 | −0.534796 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.70037 | −0.0835685 | ||||||||
\(415\) | −15.1557 | −0.743963 | ||||||||
\(416\) | 11.4232 | 0.560068 | ||||||||
\(417\) | −8.45732 | −0.414157 | ||||||||
\(418\) | 3.14930 | 0.154038 | ||||||||
\(419\) | 8.67099 | 0.423605 | 0.211803 | − | 0.977312i | \(-0.432067\pi\) | ||||
0.211803 | + | 0.977312i | \(0.432067\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.7894 | 1.45184 | 0.725922 | − | 0.687777i | \(-0.241413\pi\) | ||||
0.725922 | + | 0.687777i | \(0.241413\pi\) | |||||||
\(422\) | 9.33148 | 0.454249 | ||||||||
\(423\) | −22.5164 | −1.09479 | ||||||||
\(424\) | −25.4334 | −1.23515 | ||||||||
\(425\) | −61.6966 | −2.99272 | ||||||||
\(426\) | −0.632926 | −0.0306654 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −26.0178 | −1.25762 | ||||||||
\(429\) | −4.91342 | −0.237222 | ||||||||
\(430\) | 18.6939 | 0.901498 | ||||||||
\(431\) | 12.6486 | 0.609263 | 0.304631 | − | 0.952470i | \(-0.401467\pi\) | ||||
0.304631 | + | 0.952470i | \(0.401467\pi\) | |||||||
\(432\) | 3.06434 | 0.147433 | ||||||||
\(433\) | −6.32172 | −0.303802 | −0.151901 | − | 0.988396i | \(-0.548540\pi\) | ||||
−0.151901 | + | 0.988396i | \(0.548540\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.25082 | −0.395597 | ||||||||
\(436\) | −30.8208 | −1.47605 | ||||||||
\(437\) | −6.97775 | −0.333791 | ||||||||
\(438\) | −19.6394 | −0.938406 | ||||||||
\(439\) | 22.2462 | 1.06175 | 0.530876 | − | 0.847450i | \(-0.321863\pi\) | ||||
0.530876 | + | 0.847450i | \(0.321863\pi\) | |||||||
\(440\) | 7.46156 | 0.355716 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.43336 | −0.448699 | ||||||||
\(443\) | −14.3049 | −0.679645 | −0.339823 | − | 0.940490i | \(-0.610367\pi\) | ||||
−0.339823 | + | 0.940490i | \(0.610367\pi\) | |||||||
\(444\) | −6.51936 | −0.309395 | ||||||||
\(445\) | 12.8321 | 0.608300 | ||||||||
\(446\) | −14.8364 | −0.702522 | ||||||||
\(447\) | −1.69230 | −0.0800432 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.9196 | 1.03445 | 0.517224 | − | 0.855850i | \(-0.326965\pi\) | ||||
0.517224 | + | 0.855850i | \(0.326965\pi\) | |||||||
\(450\) | 10.6178 | 0.500526 | ||||||||
\(451\) | 5.35834 | 0.252315 | ||||||||
\(452\) | −1.98174 | −0.0932133 | ||||||||
\(453\) | 14.9324 | 0.701584 | ||||||||
\(454\) | −10.3708 | −0.486726 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 26.9151 | 1.26041 | ||||||||
\(457\) | −25.9527 | −1.21401 | −0.607007 | − | 0.794697i | \(-0.707630\pi\) | ||||
−0.607007 | + | 0.794697i | \(0.707630\pi\) | |||||||
\(458\) | −7.59520 | −0.354900 | ||||||||
\(459\) | −11.0733 | −0.516856 | ||||||||
\(460\) | −7.54618 | −0.351843 | ||||||||
\(461\) | −18.5060 | −0.861910 | −0.430955 | − | 0.902374i | \(-0.641823\pi\) | ||||
−0.430955 | + | 0.902374i | \(0.641823\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.76243 | −0.407224 | −0.203612 | − | 0.979052i | \(-0.565268\pi\) | ||||
−0.203612 | + | 0.979052i | \(0.565268\pi\) | |||||||
\(464\) | −2.16174 | −0.100356 | ||||||||
\(465\) | 50.4955 | 2.34167 | ||||||||
\(466\) | −2.51280 | −0.116403 | ||||||||
\(467\) | −24.3313 | −1.12592 | −0.562960 | − | 0.826484i | \(-0.690337\pi\) | ||||
−0.562960 | + | 0.826484i | \(0.690337\pi\) | |||||||
\(468\) | −8.50853 | −0.393307 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 19.0664 | 0.879466 | ||||||||
\(471\) | 8.25964 | 0.380584 | ||||||||
\(472\) | 8.08334 | 0.372066 | ||||||||
\(473\) | −9.21855 | −0.423869 | ||||||||
\(474\) | 10.5294 | 0.483634 | ||||||||
\(475\) | 43.5718 | 1.99921 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.2409 | 1.33885 | ||||||||
\(478\) | 5.17352 | 0.236631 | ||||||||
\(479\) | −3.43695 | −0.157038 | −0.0785190 | − | 0.996913i | \(-0.525019\pi\) | ||||
−0.0785190 | + | 0.996913i | \(0.525019\pi\) | |||||||
\(480\) | 44.9290 | 2.05072 | ||||||||
\(481\) | −3.53528 | −0.161195 | ||||||||
\(482\) | −9.72940 | −0.443162 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.67954 | −0.0763427 | ||||||||
\(485\) | 0.587951 | 0.0266975 | ||||||||
\(486\) | 11.3520 | 0.514937 | ||||||||
\(487\) | −29.6366 | −1.34296 | −0.671482 | − | 0.741021i | \(-0.734342\pi\) | ||||
−0.671482 | + | 0.741021i | \(0.734342\pi\) | |||||||
\(488\) | −5.26971 | −0.238549 | ||||||||
\(489\) | −32.1121 | −1.45216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.5364 | −1.73913 | −0.869563 | − | 0.493823i | \(-0.835599\pi\) | ||||
−0.869563 | + | 0.493823i | \(0.835599\pi\) | |||||||
\(492\) | 20.9030 | 0.942379 | ||||||||
\(493\) | 7.81166 | 0.351820 | ||||||||
\(494\) | 6.66210 | 0.299742 | ||||||||
\(495\) | −8.57860 | −0.385579 | ||||||||
\(496\) | 13.2300 | 0.594044 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −5.56290 | −0.249279 | ||||||||
\(499\) | −40.8755 | −1.82984 | −0.914920 | − | 0.403636i | \(-0.867746\pi\) | ||||
−0.914920 | + | 0.403636i | \(0.867746\pi\) | |||||||
\(500\) | 17.0392 | 0.762015 | ||||||||
\(501\) | 1.36952 | 0.0611858 | ||||||||
\(502\) | 10.0749 | 0.449663 | ||||||||
\(503\) | −26.9049 | −1.19963 | −0.599814 | − | 0.800139i | \(-0.704759\pi\) | ||||
−0.599814 | + | 0.800139i | \(0.704759\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −43.5195 | −1.93659 | ||||||||
\(506\) | −0.710028 | −0.0315646 | ||||||||
\(507\) | 19.8007 | 0.879382 | ||||||||
\(508\) | 10.9313 | 0.484999 | ||||||||
\(509\) | 39.9683 | 1.77156 | 0.885781 | − | 0.464103i | \(-0.153623\pi\) | ||||
0.885781 | + | 0.464103i | \(0.153623\pi\) | |||||||
\(510\) | −37.1027 | −1.64294 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.8530 | 0.921580 | ||||||||
\(513\) | 7.82025 | 0.345273 | ||||||||
\(514\) | −3.95952 | −0.174647 | ||||||||
\(515\) | −23.1524 | −1.02021 | ||||||||
\(516\) | −35.9617 | −1.58313 | ||||||||
\(517\) | −9.40225 | −0.413510 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.95076 | 0.436790 | ||||||||
\(520\) | 15.7843 | 0.692189 | ||||||||
\(521\) | −35.9052 | −1.57303 | −0.786517 | − | 0.617568i | \(-0.788118\pi\) | ||||
−0.786517 | + | 0.617568i | \(0.788118\pi\) | |||||||
\(522\) | −1.34436 | −0.0588411 | ||||||||
\(523\) | 12.1191 | 0.529931 | 0.264966 | − | 0.964258i | \(-0.414639\pi\) | ||||
0.264966 | + | 0.964258i | \(0.414639\pi\) | |||||||
\(524\) | −12.3667 | −0.540240 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.82684 | −0.0796541 | ||||||||
\(527\) | −47.8078 | −2.08254 | ||||||||
\(528\) | −5.06326 | −0.220350 | ||||||||
\(529\) | −21.4268 | −0.931601 | ||||||||
\(530\) | −24.7605 | −1.07553 | ||||||||
\(531\) | −9.29347 | −0.403302 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.3352 | 0.490980 | ||||||||
\(534\) | 4.71003 | 0.203823 | ||||||||
\(535\) | −55.4919 | −2.39913 | ||||||||
\(536\) | 7.32916 | 0.316572 | ||||||||
\(537\) | 31.2644 | 1.34916 | ||||||||
\(538\) | −6.30529 | −0.271840 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.45732 | 0.363945 | ||||||||
\(541\) | 38.0198 | 1.63460 | 0.817299 | − | 0.576214i | \(-0.195470\pi\) | ||||
0.817299 | + | 0.576214i | \(0.195470\pi\) | |||||||
\(542\) | −2.23222 | −0.0958818 | ||||||||
\(543\) | −46.9409 | −2.01443 | ||||||||
\(544\) | −42.5376 | −1.82378 | ||||||||
\(545\) | −65.7359 | −2.81582 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.8268 | −0.933248 | −0.466624 | − | 0.884456i | \(-0.654530\pi\) | ||||
−0.466624 | + | 0.884456i | \(0.654530\pi\) | |||||||
\(548\) | −14.7227 | −0.628922 | ||||||||
\(549\) | 6.05862 | 0.258576 | ||||||||
\(550\) | 4.43369 | 0.189053 | ||||||||
\(551\) | −5.51682 | −0.235024 | ||||||||
\(552\) | −6.06815 | −0.258277 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 15.1500 | 0.643662 | ||||||||
\(555\) | −13.9048 | −0.590224 | ||||||||
\(556\) | −6.11555 | −0.259357 | ||||||||
\(557\) | −21.0982 | −0.893961 | −0.446981 | − | 0.894544i | \(-0.647501\pi\) | ||||
−0.446981 | + | 0.894544i | \(0.647501\pi\) | |||||||
\(558\) | 8.22756 | 0.348301 | ||||||||
\(559\) | −19.5011 | −0.824809 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.2966 | 0.772482 | ||||||||
\(562\) | −1.80869 | −0.0762951 | ||||||||
\(563\) | 36.7160 | 1.54739 | 0.773696 | − | 0.633557i | \(-0.218406\pi\) | ||||
0.773696 | + | 0.633557i | \(0.218406\pi\) | |||||||
\(564\) | −36.6783 | −1.54443 | ||||||||
\(565\) | −4.22674 | −0.177820 | ||||||||
\(566\) | −2.63387 | −0.110710 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.00267 | −0.0420712 | ||||||||
\(569\) | −21.9167 | −0.918797 | −0.459399 | − | 0.888230i | \(-0.651935\pi\) | ||||
−0.459399 | + | 0.888230i | \(0.651935\pi\) | |||||||
\(570\) | 26.2030 | 1.09752 | ||||||||
\(571\) | −11.8342 | −0.495247 | −0.247623 | − | 0.968856i | \(-0.579650\pi\) | ||||
−0.247623 | + | 0.968856i | \(0.579650\pi\) | |||||||
\(572\) | −3.55293 | −0.148556 | ||||||||
\(573\) | −46.8307 | −1.95638 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.82351 | −0.409669 | ||||||||
\(576\) | −3.12038 | −0.130016 | ||||||||
\(577\) | 30.6197 | 1.27471 | 0.637357 | − | 0.770568i | \(-0.280028\pi\) | ||||
0.637357 | + | 0.770568i | \(0.280028\pi\) | |||||||
\(578\) | 25.5043 | 1.06084 | ||||||||
\(579\) | −4.30005 | −0.178704 | ||||||||
\(580\) | −5.96623 | −0.247734 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.215808 | 0.00894551 | ||||||||
\(583\) | 12.2102 | 0.505695 | ||||||||
\(584\) | −31.1125 | −1.28744 | ||||||||
\(585\) | −18.1473 | −0.750300 | ||||||||
\(586\) | −8.84231 | −0.365273 | ||||||||
\(587\) | 40.9866 | 1.69170 | 0.845848 | − | 0.533424i | \(-0.179095\pi\) | ||||
0.845848 | + | 0.533424i | \(0.179095\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.7632 | 1.39119 | ||||||||
\(590\) | 7.86949 | 0.323982 | ||||||||
\(591\) | −21.5577 | −0.886763 | ||||||||
\(592\) | −3.64309 | −0.149730 | ||||||||
\(593\) | 6.69626 | 0.274983 | 0.137491 | − | 0.990503i | \(-0.456096\pi\) | ||||
0.137491 | + | 0.990503i | \(0.456096\pi\) | |||||||
\(594\) | 0.795757 | 0.0326503 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.22372 | −0.0501255 | ||||||||
\(597\) | 2.30772 | 0.0944487 | ||||||||
\(598\) | −1.50201 | −0.0614216 | ||||||||
\(599\) | 17.9097 | 0.731770 | 0.365885 | − | 0.930660i | \(-0.380766\pi\) | ||||
0.365885 | + | 0.930660i | \(0.380766\pi\) | |||||||
\(600\) | 37.8919 | 1.54693 | ||||||||
\(601\) | 21.3193 | 0.869630 | 0.434815 | − | 0.900520i | \(-0.356814\pi\) | ||||
0.434815 | + | 0.900520i | \(0.356814\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.42638 | −0.343149 | ||||||||
\(604\) | 10.7977 | 0.439353 | ||||||||
\(605\) | −3.58219 | −0.145637 | ||||||||
\(606\) | −15.9739 | −0.648894 | ||||||||
\(607\) | 6.67801 | 0.271052 | 0.135526 | − | 0.990774i | \(-0.456728\pi\) | ||||
0.135526 | + | 0.990774i | \(0.456728\pi\) | |||||||
\(608\) | 30.0412 | 1.21833 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.13030 | −0.207720 | ||||||||
\(611\) | −19.8897 | −0.804651 | ||||||||
\(612\) | 31.6840 | 1.28075 | ||||||||
\(613\) | 24.7905 | 1.00128 | 0.500639 | − | 0.865656i | \(-0.333098\pi\) | ||||
0.500639 | + | 0.865656i | \(0.333098\pi\) | |||||||
\(614\) | −10.7453 | −0.433644 | ||||||||
\(615\) | 44.5827 | 1.79775 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.0708 | 0.928795 | 0.464397 | − | 0.885627i | \(-0.346271\pi\) | ||||
0.464397 | + | 0.885627i | \(0.346271\pi\) | |||||||
\(618\) | −8.49808 | −0.341843 | ||||||||
\(619\) | −27.1443 | −1.09102 | −0.545512 | − | 0.838103i | \(-0.683665\pi\) | ||||
−0.545512 | + | 0.838103i | \(0.683665\pi\) | |||||||
\(620\) | 36.5137 | 1.46643 | ||||||||
\(621\) | −1.76312 | −0.0707515 | ||||||||
\(622\) | 9.95736 | 0.399254 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −10.7109 | −0.428780 | ||||||||
\(625\) | −2.81866 | −0.112746 | ||||||||
\(626\) | 10.1908 | 0.407308 | ||||||||
\(627\) | −12.9216 | −0.516037 | ||||||||
\(628\) | 5.97261 | 0.238333 | ||||||||
\(629\) | 13.1647 | 0.524909 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.850302 | 0.0338500 | 0.0169250 | − | 0.999857i | \(-0.494612\pi\) | ||||
0.0169250 | + | 0.999857i | \(0.494612\pi\) | |||||||
\(632\) | 16.6806 | 0.663519 | ||||||||
\(633\) | −38.2869 | −1.52177 | ||||||||
\(634\) | 3.94937 | 0.156849 | ||||||||
\(635\) | 23.3148 | 0.925219 | ||||||||
\(636\) | 47.6322 | 1.88874 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.561369 | −0.0222248 | ||||||||
\(639\) | 1.15278 | 0.0456032 | ||||||||
\(640\) | 41.3297 | 1.63370 | ||||||||
\(641\) | 40.6878 | 1.60707 | 0.803536 | − | 0.595256i | \(-0.202949\pi\) | ||||
0.803536 | + | 0.595256i | \(0.202949\pi\) | |||||||
\(642\) | −20.3683 | −0.803874 | ||||||||
\(643\) | 3.89995 | 0.153799 | 0.0768994 | − | 0.997039i | \(-0.475498\pi\) | ||||
0.0768994 | + | 0.997039i | \(0.475498\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −76.7006 | −3.02008 | ||||||||
\(646\) | −24.8083 | −0.976070 | ||||||||
\(647\) | 21.3898 | 0.840918 | 0.420459 | − | 0.907311i | \(-0.361869\pi\) | ||||
0.420459 | + | 0.907311i | \(0.361869\pi\) | |||||||
\(648\) | 21.7656 | 0.855032 | ||||||||
\(649\) | −3.88070 | −0.152331 | ||||||||
\(650\) | 9.37913 | 0.367880 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.2205 | −0.909386 | ||||||||
\(653\) | −9.70937 | −0.379957 | −0.189978 | − | 0.981788i | \(-0.560842\pi\) | ||||
−0.189978 | + | 0.981788i | \(0.560842\pi\) | |||||||
\(654\) | −24.1284 | −0.943494 | ||||||||
\(655\) | −26.3761 | −1.03060 | ||||||||
\(656\) | 11.6808 | 0.456060 | ||||||||
\(657\) | 35.7702 | 1.39553 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.3120 | 1.76511 | 0.882553 | − | 0.470212i | \(-0.155823\pi\) | ||||
0.882553 | + | 0.470212i | \(0.155823\pi\) | |||||||
\(660\) | −13.9742 | −0.543944 | ||||||||
\(661\) | −25.1885 | −0.979719 | −0.489859 | − | 0.871802i | \(-0.662952\pi\) | ||||
−0.489859 | + | 0.871802i | \(0.662952\pi\) | |||||||
\(662\) | 8.50317 | 0.330485 | ||||||||
\(663\) | 38.7049 | 1.50318 | ||||||||
\(664\) | −8.81267 | −0.341998 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.26559 | −0.0877900 | ||||||||
\(667\) | 1.24380 | 0.0481600 | ||||||||
\(668\) | 0.990314 | 0.0383164 | ||||||||
\(669\) | 60.8734 | 2.35350 | ||||||||
\(670\) | 7.13526 | 0.275659 | ||||||||
\(671\) | 2.52992 | 0.0976664 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.5134 | −0.944924 | −0.472462 | − | 0.881351i | \(-0.656635\pi\) | ||||
−0.472462 | + | 0.881351i | \(0.656635\pi\) | |||||||
\(674\) | 6.47122 | 0.249262 | ||||||||
\(675\) | 11.0096 | 0.423760 | ||||||||
\(676\) | 14.3181 | 0.550695 | ||||||||
\(677\) | −9.46644 | −0.363825 | −0.181912 | − | 0.983315i | \(-0.558229\pi\) | ||||
−0.181912 | + | 0.983315i | \(0.558229\pi\) | |||||||
\(678\) | −1.55143 | −0.0595822 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −58.7776 | −2.25402 | ||||||||
\(681\) | 42.5512 | 1.63057 | ||||||||
\(682\) | 3.43561 | 0.131556 | ||||||||
\(683\) | −1.90836 | −0.0730215 | −0.0365107 | − | 0.999333i | \(-0.511624\pi\) | ||||
−0.0365107 | + | 0.999333i | \(0.511624\pi\) | |||||||
\(684\) | −22.3761 | −0.855573 | ||||||||
\(685\) | −31.4012 | −1.19978 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 31.1630 | 1.18894 | ||||||||
\(688\) | −20.0958 | −0.766146 | ||||||||
\(689\) | 25.8297 | 0.984034 | ||||||||
\(690\) | −5.90761 | −0.224899 | ||||||||
\(691\) | 5.38145 | 0.204720 | 0.102360 | − | 0.994747i | \(-0.467361\pi\) | ||||
0.102360 | + | 0.994747i | \(0.467361\pi\) | |||||||
\(692\) | 7.19547 | 0.273531 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.17812 | 0.196559 | ||||||||
\(695\) | −13.0435 | −0.494768 | ||||||||
\(696\) | −4.79766 | −0.181855 | ||||||||
\(697\) | −42.2098 | −1.59881 | ||||||||
\(698\) | 15.9847 | 0.605029 | ||||||||
\(699\) | 10.3100 | 0.389959 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.3569 | 1.56203 | 0.781014 | − | 0.624513i | \(-0.214703\pi\) | ||||
0.781014 | + | 0.624513i | \(0.214703\pi\) | |||||||
\(702\) | 1.68336 | 0.0635344 | ||||||||
\(703\) | −9.29725 | −0.350653 | ||||||||
\(704\) | −1.30299 | −0.0491082 | ||||||||
\(705\) | −78.2290 | −2.94628 | ||||||||
\(706\) | −3.14031 | −0.118187 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −15.1387 | −0.568946 | ||||||||
\(709\) | −11.3771 | −0.427276 | −0.213638 | − | 0.976913i | \(-0.568531\pi\) | ||||
−0.213638 | + | 0.976913i | \(0.568531\pi\) | |||||||
\(710\) | −0.976146 | −0.0366341 | ||||||||
\(711\) | −19.1778 | −0.719223 | ||||||||
\(712\) | 7.46156 | 0.279634 | ||||||||
\(713\) | −7.61210 | −0.285076 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.57784 | −0.283395 | ||||||||
\(716\) | 22.6075 | 0.844884 | ||||||||
\(717\) | −21.2269 | −0.792732 | ||||||||
\(718\) | −0.189020 | −0.00705416 | ||||||||
\(719\) | 26.5668 | 0.990776 | 0.495388 | − | 0.868672i | \(-0.335026\pi\) | ||||
0.495388 | + | 0.868672i | \(0.335026\pi\) | |||||||
\(720\) | −18.7008 | −0.696936 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.76456 | 0.251751 | ||||||||
\(723\) | 39.9196 | 1.48463 | ||||||||
\(724\) | −33.9433 | −1.26149 | ||||||||
\(725\) | −7.76675 | −0.288450 | ||||||||
\(726\) | −1.31484 | −0.0487985 | ||||||||
\(727\) | 20.1922 | 0.748889 | 0.374444 | − | 0.927249i | \(-0.377833\pi\) | ||||
0.374444 | + | 0.927249i | \(0.377833\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.2291 | −0.564039 | ||||||||
\(730\) | −30.2893 | −1.12106 | ||||||||
\(731\) | 72.6181 | 2.68588 | ||||||||
\(732\) | 9.86924 | 0.364778 | ||||||||
\(733\) | 33.9684 | 1.25465 | 0.627326 | − | 0.778757i | \(-0.284149\pi\) | ||||
0.627326 | + | 0.778757i | \(0.284149\pi\) | |||||||
\(734\) | −4.59188 | −0.169489 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.77296 | −0.249655 | ||||||||
\(737\) | −3.51863 | −0.129610 | ||||||||
\(738\) | 7.26416 | 0.267397 | ||||||||
\(739\) | −3.64752 | −0.134176 | −0.0670881 | − | 0.997747i | \(-0.521371\pi\) | ||||
−0.0670881 | + | 0.997747i | \(0.521371\pi\) | |||||||
\(740\) | −10.0546 | −0.369616 | ||||||||
\(741\) | −27.3345 | −1.00416 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.0411 | 0.478432 | 0.239216 | − | 0.970966i | \(-0.423110\pi\) | ||||
0.239216 | + | 0.970966i | \(0.423110\pi\) | |||||||
\(744\) | 29.3619 | 1.07646 | ||||||||
\(745\) | −2.61000 | −0.0956229 | ||||||||
\(746\) | 19.3757 | 0.709393 | ||||||||
\(747\) | 10.1320 | 0.370710 | ||||||||
\(748\) | 13.2304 | 0.483751 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 13.3393 | 0.487082 | ||||||||
\(751\) | 28.6269 | 1.04461 | 0.522305 | − | 0.852759i | \(-0.325072\pi\) | ||||
0.522305 | + | 0.852759i | \(0.325072\pi\) | |||||||
\(752\) | −20.4963 | −0.747422 | ||||||||
\(753\) | −41.3370 | −1.50640 | ||||||||
\(754\) | −1.18753 | −0.0432473 | ||||||||
\(755\) | 23.0298 | 0.838141 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.8901 | −1.52252 | −0.761261 | − | 0.648446i | \(-0.775419\pi\) | ||||
−0.761261 | + | 0.648446i | \(0.775419\pi\) | |||||||
\(758\) | −12.4290 | −0.451441 | ||||||||
\(759\) | 2.91323 | 0.105744 | ||||||||
\(760\) | 41.5104 | 1.50574 | ||||||||
\(761\) | −22.7774 | −0.825682 | −0.412841 | − | 0.910803i | \(-0.635463\pi\) | ||||
−0.412841 | + | 0.910803i | \(0.635463\pi\) | |||||||
\(762\) | 8.55770 | 0.310013 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −33.8636 | −1.22514 | ||||||||
\(765\) | 67.5770 | 2.44325 | ||||||||
\(766\) | −4.40152 | −0.159033 | ||||||||
\(767\) | −8.20932 | −0.296421 | ||||||||
\(768\) | 9.11725 | 0.328990 | ||||||||
\(769\) | 13.3517 | 0.481475 | 0.240738 | − | 0.970590i | \(-0.422611\pi\) | ||||
0.240738 | + | 0.970590i | \(0.422611\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.2458 | 0.585080 | ||||||||
\(772\) | −3.10940 | −0.111910 | ||||||||
\(773\) | −17.9214 | −0.644588 | −0.322294 | − | 0.946640i | \(-0.604454\pi\) | ||||
−0.322294 | + | 0.946640i | \(0.604454\pi\) | |||||||
\(774\) | −12.4973 | −0.449207 | ||||||||
\(775\) | 47.5330 | 1.70744 | ||||||||
\(776\) | 0.341879 | 0.0122728 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.27097 | 0.117270 | ||||||||
\(779\) | 29.8097 | 1.06804 | ||||||||
\(780\) | −29.5613 | −1.05846 | ||||||||
\(781\) | 0.481369 | 0.0172248 | ||||||||
\(782\) | 5.59317 | 0.200011 | ||||||||
\(783\) | −1.39397 | −0.0498165 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.7386 | 0.454661 | ||||||||
\(786\) | −9.68136 | −0.345323 | ||||||||
\(787\) | 8.61899 | 0.307234 | 0.153617 | − | 0.988130i | \(-0.450908\pi\) | ||||
0.153617 | + | 0.988130i | \(0.450908\pi\) | |||||||
\(788\) | −15.5885 | −0.555317 | ||||||||
\(789\) | 7.49550 | 0.266847 | ||||||||
\(790\) | 16.2393 | 0.577768 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.98825 | −0.177250 | ||||||||
\(793\) | 5.35184 | 0.190049 | ||||||||
\(794\) | 11.3707 | 0.403532 | ||||||||
\(795\) | 101.592 | 3.60309 | ||||||||
\(796\) | 1.66873 | 0.0591466 | ||||||||
\(797\) | −8.15199 | −0.288758 | −0.144379 | − | 0.989522i | \(-0.546118\pi\) | ||||
−0.144379 | + | 0.989522i | \(0.546118\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 74.0652 | 2.62024 | ||||||||
\(800\) | 42.2931 | 1.49529 | ||||||||
\(801\) | −8.57860 | −0.303110 | ||||||||
\(802\) | −7.82727 | −0.276390 | ||||||||
\(803\) | 14.9367 | 0.527103 | ||||||||
\(804\) | −13.7262 | −0.484087 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.26776 | 0.255996 | ||||||||
\(807\) | 25.8705 | 0.910685 | ||||||||
\(808\) | −25.3056 | −0.890247 | ||||||||
\(809\) | 17.8331 | 0.626978 | 0.313489 | − | 0.949592i | \(-0.398502\pi\) | ||||
0.313489 | + | 0.949592i | \(0.398502\pi\) | |||||||
\(810\) | 21.1897 | 0.744531 | ||||||||
\(811\) | 33.8231 | 1.18769 | 0.593845 | − | 0.804580i | \(-0.297609\pi\) | ||||
0.593845 | + | 0.804580i | \(0.297609\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.15875 | 0.321211 | ||||||||
\(814\) | −0.946051 | −0.0331591 | ||||||||
\(815\) | −49.5257 | −1.73481 | ||||||||
\(816\) | 39.8853 | 1.39626 | ||||||||
\(817\) | −51.2850 | −1.79423 | ||||||||
\(818\) | 3.01996 | 0.105590 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 32.2381 | 1.12580 | ||||||||
\(821\) | 18.0163 | 0.628772 | 0.314386 | − | 0.949295i | \(-0.398201\pi\) | ||||
0.314386 | + | 0.949295i | \(0.398201\pi\) | |||||||
\(822\) | −11.5258 | −0.402009 | ||||||||
\(823\) | −6.20675 | −0.216354 | −0.108177 | − | 0.994132i | \(-0.534501\pi\) | ||||
−0.108177 | + | 0.994132i | \(0.534501\pi\) | |||||||
\(824\) | −13.4625 | −0.468990 | ||||||||
\(825\) | −18.1914 | −0.633343 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.4737 | 0.503299 | 0.251650 | − | 0.967818i | \(-0.419027\pi\) | ||||
0.251650 | + | 0.967818i | \(0.419027\pi\) | |||||||
\(828\) | 5.04482 | 0.175320 | ||||||||
\(829\) | −17.3725 | −0.603371 | −0.301685 | − | 0.953408i | \(-0.597549\pi\) | ||||
−0.301685 | + | 0.953408i | \(0.597549\pi\) | |||||||
\(830\) | −8.57952 | −0.297799 | ||||||||
\(831\) | −62.1603 | −2.15632 | ||||||||
\(832\) | −2.75637 | −0.0955598 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.78762 | −0.165782 | ||||||||
\(835\) | 2.11218 | 0.0730951 | ||||||||
\(836\) | −9.34367 | −0.323158 | ||||||||
\(837\) | 8.53120 | 0.294881 | ||||||||
\(838\) | 4.90858 | 0.169564 | ||||||||
\(839\) | 1.93117 | 0.0666713 | 0.0333357 | − | 0.999444i | \(-0.489387\pi\) | ||||
0.0333357 | + | 0.999444i | \(0.489387\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0166 | −0.966090 | ||||||||
\(842\) | 16.8635 | 0.581156 | ||||||||
\(843\) | 7.42104 | 0.255594 | ||||||||
\(844\) | −27.6856 | −0.952977 | ||||||||
\(845\) | 30.5382 | 1.05055 | ||||||||
\(846\) | −12.7464 | −0.438229 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 26.6174 | 0.914046 | ||||||||
\(849\) | 10.8067 | 0.370886 | ||||||||
\(850\) | −34.9259 | −1.19795 | ||||||||
\(851\) | 2.09612 | 0.0718539 | ||||||||
\(852\) | 1.87783 | 0.0643334 | ||||||||
\(853\) | −1.10204 | −0.0377332 | −0.0188666 | − | 0.999822i | \(-0.506006\pi\) | ||||
−0.0188666 | + | 0.999822i | \(0.506006\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −47.7248 | −1.63215 | ||||||||
\(856\) | −32.2672 | −1.10287 | ||||||||
\(857\) | 21.7149 | 0.741766 | 0.370883 | − | 0.928680i | \(-0.379055\pi\) | ||||
0.370883 | + | 0.928680i | \(0.379055\pi\) | |||||||
\(858\) | −2.78145 | −0.0949571 | ||||||||
\(859\) | 39.6186 | 1.35177 | 0.675885 | − | 0.737007i | \(-0.263762\pi\) | ||||
0.675885 | + | 0.737007i | \(0.263762\pi\) | |||||||
\(860\) | −55.4628 | −1.89127 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.16029 | 0.243880 | ||||||||
\(863\) | 2.29774 | 0.0782161 | 0.0391081 | − | 0.999235i | \(-0.487548\pi\) | ||||
0.0391081 | + | 0.999235i | \(0.487548\pi\) | |||||||
\(864\) | 7.59074 | 0.258242 | ||||||||
\(865\) | 15.3468 | 0.521807 | ||||||||
\(866\) | −3.57867 | −0.121608 | ||||||||
\(867\) | −104.644 | −3.55389 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.00813 | −0.271657 | ||||||||
\(870\) | −4.67073 | −0.158352 | ||||||||
\(871\) | −7.44338 | −0.252209 | ||||||||
\(872\) | −38.2238 | −1.29442 | ||||||||
\(873\) | −0.393061 | −0.0133031 | ||||||||
\(874\) | −3.95005 | −0.133612 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 58.2681 | 1.96870 | ||||||||
\(877\) | 16.2876 | 0.549992 | 0.274996 | − | 0.961445i | \(-0.411324\pi\) | ||||
0.274996 | + | 0.961445i | \(0.411324\pi\) | |||||||
\(878\) | 12.5934 | 0.425006 | ||||||||
\(879\) | 36.2799 | 1.22369 | ||||||||
\(880\) | −7.80894 | −0.263239 | ||||||||
\(881\) | 23.8815 | 0.804588 | 0.402294 | − | 0.915511i | \(-0.368213\pi\) | ||||
0.402294 | + | 0.915511i | \(0.368213\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.7760 | 1.17031 | 0.585153 | − | 0.810923i | \(-0.301035\pi\) | ||||
0.585153 | + | 0.810923i | \(0.301035\pi\) | |||||||
\(884\) | 27.9878 | 0.941333 | ||||||||
\(885\) | −32.2884 | −1.08536 | ||||||||
\(886\) | −8.09788 | −0.272054 | ||||||||
\(887\) | 20.9659 | 0.703965 | 0.351983 | − | 0.936006i | \(-0.385508\pi\) | ||||
0.351983 | + | 0.936006i | \(0.385508\pi\) | |||||||
\(888\) | −8.08528 | −0.271324 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.26416 | 0.243495 | ||||||||
\(891\) | −10.4494 | −0.350066 | ||||||||
\(892\) | 44.0180 | 1.47383 | ||||||||
\(893\) | −52.3069 | −1.75038 | ||||||||
\(894\) | −0.958000 | −0.0320403 | ||||||||
\(895\) | 48.2183 | 1.61176 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.16271 | 0.205767 | ||||||||
\(898\) | 12.4085 | 0.414077 | ||||||||
\(899\) | −6.01835 | −0.200723 | ||||||||
\(900\) | −31.5019 | −1.05006 | ||||||||
\(901\) | −96.1846 | −3.20437 | ||||||||
\(902\) | 3.03332 | 0.100998 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.45775 | −0.0817435 | ||||||||
\(905\) | −72.3957 | −2.40652 | ||||||||
\(906\) | 8.45310 | 0.280835 | ||||||||
\(907\) | −32.4206 | −1.07651 | −0.538254 | − | 0.842783i | \(-0.680916\pi\) | ||||
−0.538254 | + | 0.842783i | \(0.680916\pi\) | |||||||
\(908\) | 30.7691 | 1.02111 | ||||||||
\(909\) | 29.0940 | 0.964986 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.2801 | 1.03636 | 0.518178 | − | 0.855273i | \(-0.326610\pi\) | ||||
0.518178 | + | 0.855273i | \(0.326610\pi\) | |||||||
\(912\) | −28.1681 | −0.932739 | ||||||||
\(913\) | 4.23084 | 0.140020 | ||||||||
\(914\) | −14.6916 | −0.485955 | ||||||||
\(915\) | 21.0495 | 0.695876 | ||||||||
\(916\) | 22.5342 | 0.744551 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.26849 | −0.206891 | ||||||||
\(919\) | −12.0241 | −0.396638 | −0.198319 | − | 0.980138i | \(-0.563548\pi\) | ||||
−0.198319 | + | 0.980138i | \(0.563548\pi\) | |||||||
\(920\) | −9.35875 | −0.308549 | ||||||||
\(921\) | 44.0877 | 1.45274 | ||||||||
\(922\) | −10.4761 | −0.345012 | ||||||||
\(923\) | 1.01830 | 0.0335177 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.0890 | −0.430363 | ||||||||
\(926\) | −4.96034 | −0.163007 | ||||||||
\(927\) | 15.4780 | 0.508363 | ||||||||
\(928\) | −5.35490 | −0.175783 | ||||||||
\(929\) | 46.3451 | 1.52053 | 0.760267 | − | 0.649611i | \(-0.225068\pi\) | ||||
0.760267 | + | 0.649611i | \(0.225068\pi\) | |||||||
\(930\) | 28.5851 | 0.937343 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.45522 | 0.244204 | ||||||||
\(933\) | −40.8549 | −1.33753 | ||||||||
\(934\) | −13.7738 | −0.450692 | ||||||||
\(935\) | 28.2183 | 0.922838 | ||||||||
\(936\) | −10.5522 | −0.344911 | ||||||||
\(937\) | 47.5786 | 1.55433 | 0.777163 | − | 0.629299i | \(-0.216658\pi\) | ||||
0.777163 | + | 0.629299i | \(0.216658\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −41.8129 | −1.36451 | ||||||||
\(940\) | −56.5680 | −1.84504 | ||||||||
\(941\) | −51.5693 | −1.68111 | −0.840556 | − | 0.541725i | \(-0.817771\pi\) | ||||
−0.840556 | + | 0.541725i | \(0.817771\pi\) | |||||||
\(942\) | 4.67572 | 0.152343 | ||||||||
\(943\) | −6.72076 | −0.218858 | ||||||||
\(944\) | −8.45967 | −0.275339 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.21855 | −0.169670 | ||||||||
\(947\) | 17.2878 | 0.561779 | 0.280889 | − | 0.959740i | \(-0.409371\pi\) | ||||
0.280889 | + | 0.959740i | \(0.409371\pi\) | |||||||
\(948\) | −31.2398 | −1.01462 | ||||||||
\(949\) | 31.5973 | 1.02569 | ||||||||
\(950\) | 24.6657 | 0.800260 | ||||||||
\(951\) | −16.2042 | −0.525457 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.25417 | 0.137806 | 0.0689031 | − | 0.997623i | \(-0.478050\pi\) | ||||
0.0689031 | + | 0.997623i | \(0.478050\pi\) | |||||||
\(954\) | 16.5530 | 0.535924 | ||||||||
\(955\) | −72.2258 | −2.33717 | ||||||||
\(956\) | −15.3493 | −0.496432 | ||||||||
\(957\) | 2.30329 | 0.0744547 | ||||||||
\(958\) | −1.94563 | −0.0628604 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −10.8412 | −0.349898 | ||||||||
\(961\) | 5.83268 | 0.188151 | ||||||||
\(962\) | −2.00130 | −0.0645244 | ||||||||
\(963\) | 37.0978 | 1.19546 | ||||||||
\(964\) | 28.8662 | 0.929717 | ||||||||
\(965\) | −6.63186 | −0.213487 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.87353 | 0.188880 | 0.0944399 | − | 0.995531i | \(-0.469894\pi\) | ||||
0.0944399 | + | 0.995531i | \(0.469894\pi\) | |||||||
\(968\) | −2.08296 | −0.0669488 | ||||||||
\(969\) | 101.788 | 3.26991 | ||||||||
\(970\) | 0.332835 | 0.0106867 | ||||||||
\(971\) | −25.2611 | −0.810667 | −0.405333 | − | 0.914169i | \(-0.632845\pi\) | ||||
−0.405333 | + | 0.914169i | \(0.632845\pi\) | |||||||
\(972\) | −33.6803 | −1.08029 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −16.7771 | −0.537572 | ||||||||
\(975\) | −38.4824 | −1.23242 | ||||||||
\(976\) | 5.51505 | 0.176532 | ||||||||
\(977\) | −25.4971 | −0.815724 | −0.407862 | − | 0.913043i | \(-0.633726\pi\) | ||||
−0.407862 | + | 0.913043i | \(0.633726\pi\) | |||||||
\(978\) | −18.1784 | −0.581282 | ||||||||
\(979\) | −3.58219 | −0.114487 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.9462 | 1.40309 | ||||||||
\(982\) | −21.8152 | −0.696150 | ||||||||
\(983\) | 37.0719 | 1.18241 | 0.591205 | − | 0.806521i | \(-0.298653\pi\) | ||||
0.591205 | + | 0.806521i | \(0.298653\pi\) | |||||||
\(984\) | 25.9238 | 0.826420 | ||||||||
\(985\) | −33.2478 | −1.05936 | ||||||||
\(986\) | 4.42212 | 0.140829 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −19.7658 | −0.628834 | ||||||||
\(989\) | 11.5625 | 0.367665 | ||||||||
\(990\) | −4.85628 | −0.154343 | ||||||||
\(991\) | 18.7006 | 0.594044 | 0.297022 | − | 0.954871i | \(-0.404007\pi\) | ||||
0.297022 | + | 0.954871i | \(0.404007\pi\) | |||||||
\(992\) | 32.7723 | 1.04052 | ||||||||
\(993\) | −34.8884 | −1.10715 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.55914 | 0.112832 | ||||||||
\(996\) | 16.5046 | 0.522967 | ||||||||
\(997\) | −32.8555 | −1.04054 | −0.520272 | − | 0.854001i | \(-0.674169\pi\) | ||||
−0.520272 | + | 0.854001i | \(0.674169\pi\) | |||||||
\(998\) | −23.1393 | −0.732462 | ||||||||
\(999\) | −2.34920 | −0.0743255 |
(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 | 539.2.a.l.1.5 | ✓ | 10 | |
3.2 | odd | 2 | 4851.2.a.cg.1.6 | 10 | |||
4.3 | odd | 2 | 8624.2.a.df.1.9 | 10 | |||
7.2 | even | 3 | 539.2.e.o.67.6 | 20 | |||
7.3 | odd | 6 | 539.2.e.o.177.5 | 20 | |||
7.4 | even | 3 | 539.2.e.o.177.6 | 20 | |||
7.5 | odd | 6 | 539.2.e.o.67.5 | 20 | |||
7.6 | odd | 2 | inner | 539.2.a.l.1.6 | yes | 10 | |
11.10 | odd | 2 | 5929.2.a.bv.1.5 | 10 | |||
21.20 | even | 2 | 4851.2.a.cg.1.5 | 10 | |||
28.27 | even | 2 | 8624.2.a.df.1.2 | 10 | |||
77.76 | even | 2 | 5929.2.a.bv.1.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
539.2.a.l.1.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
539.2.a.l.1.6 | yes | 10 | 7.6 | odd | 2 | inner | |
539.2.e.o.67.5 | 20 | 7.5 | odd | 6 | |||
539.2.e.o.67.6 | 20 | 7.2 | even | 3 | |||
539.2.e.o.177.5 | 20 | 7.3 | odd | 6 | |||
539.2.e.o.177.6 | 20 | 7.4 | even | 3 | |||
4851.2.a.cg.1.5 | 10 | 21.20 | even | 2 | |||
4851.2.a.cg.1.6 | 10 | 3.2 | odd | 2 | |||
5929.2.a.bv.1.5 | 10 | 11.10 | odd | 2 | |||
5929.2.a.bv.1.6 | 10 | 77.76 | even | 2 | |||
8624.2.a.df.1.2 | 10 | 28.27 | even | 2 | |||
8624.2.a.df.1.9 | 10 | 4.3 | odd | 2 |