Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | 7.7.31056073.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 241) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.27758\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.277577 | −0.196277 | −0.0981383 | − | 0.995173i | \(-0.531289\pi\) | ||||
−0.0981383 | + | 0.995173i | \(0.531289\pi\) | |||||||
\(3\) | 0.494846 | 0.285699 | 0.142850 | − | 0.989744i | \(-0.454373\pi\) | ||||
0.142850 | + | 0.989744i | \(0.454373\pi\) | |||||||
\(4\) | −1.92295 | −0.961475 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.137358 | −0.0560761 | ||||||||
\(7\) | −1.36627 | −0.516400 | −0.258200 | − | 0.966092i | \(-0.583129\pi\) | ||||
−0.258200 | + | 0.966092i | \(0.583129\pi\) | |||||||
\(8\) | 1.08892 | 0.384992 | ||||||||
\(9\) | −2.75513 | −0.918376 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.69806 | −1.41652 | −0.708259 | − | 0.705952i | \(-0.750519\pi\) | ||||
−0.708259 | + | 0.705952i | \(0.750519\pi\) | |||||||
\(12\) | −0.951564 | −0.274693 | ||||||||
\(13\) | 0.0431968 | 0.0119806 | 0.00599032 | − | 0.999982i | \(-0.498093\pi\) | ||||
0.00599032 | + | 0.999982i | \(0.498093\pi\) | |||||||
\(14\) | 0.379244 | 0.101357 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.54364 | 0.885911 | ||||||||
\(17\) | 7.31430 | 1.77398 | 0.886989 | − | 0.461790i | \(-0.152793\pi\) | ||||
0.886989 | + | 0.461790i | \(0.152793\pi\) | |||||||
\(18\) | 0.764761 | 0.180256 | ||||||||
\(19\) | −0.697489 | −0.160015 | −0.0800075 | − | 0.996794i | \(-0.525494\pi\) | ||||
−0.0800075 | + | 0.996794i | \(0.525494\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.676090 | −0.147535 | ||||||||
\(22\) | 1.30407 | 0.278030 | ||||||||
\(23\) | −1.41195 | −0.294412 | −0.147206 | − | 0.989106i | \(-0.547028\pi\) | ||||
−0.147206 | + | 0.989106i | \(0.547028\pi\) | |||||||
\(24\) | 0.538848 | 0.109992 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.0119904 | −0.00235152 | ||||||||
\(27\) | −2.84790 | −0.548078 | ||||||||
\(28\) | 2.62726 | 0.496506 | ||||||||
\(29\) | 8.30334 | 1.54189 | 0.770946 | − | 0.636901i | \(-0.219784\pi\) | ||||
0.770946 | + | 0.636901i | \(0.219784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.39655 | 0.610038 | 0.305019 | − | 0.952346i | \(-0.401337\pi\) | ||||
0.305019 | + | 0.952346i | \(0.401337\pi\) | |||||||
\(32\) | −3.16148 | −0.558875 | ||||||||
\(33\) | −2.32481 | −0.404698 | ||||||||
\(34\) | −2.03028 | −0.348191 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.29798 | 0.882996 | ||||||||
\(37\) | −7.15948 | −1.17701 | −0.588506 | − | 0.808493i | \(-0.700284\pi\) | ||||
−0.588506 | + | 0.808493i | \(0.700284\pi\) | |||||||
\(38\) | 0.193607 | 0.0314072 | ||||||||
\(39\) | 0.0213757 | 0.00342286 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.45541 | 0.851992 | 0.425996 | − | 0.904725i | \(-0.359924\pi\) | ||||
0.425996 | + | 0.904725i | \(0.359924\pi\) | |||||||
\(42\) | 0.187667 | 0.0289577 | ||||||||
\(43\) | 11.7568 | 1.79290 | 0.896448 | − | 0.443149i | \(-0.146139\pi\) | ||||
0.896448 | + | 0.443149i | \(0.146139\pi\) | |||||||
\(44\) | 9.03414 | 1.36195 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.391925 | 0.0577862 | ||||||||
\(47\) | 5.24836 | 0.765551 | 0.382776 | − | 0.923841i | \(-0.374968\pi\) | ||||
0.382776 | + | 0.923841i | \(0.374968\pi\) | |||||||
\(48\) | 1.75356 | 0.253104 | ||||||||
\(49\) | −5.13332 | −0.733331 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.61945 | 0.506824 | ||||||||
\(52\) | −0.0830653 | −0.0115191 | ||||||||
\(53\) | 8.57769 | 1.17824 | 0.589118 | − | 0.808047i | \(-0.299475\pi\) | ||||
0.589118 | + | 0.808047i | \(0.299475\pi\) | |||||||
\(54\) | 0.790512 | 0.107575 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.48776 | −0.198810 | ||||||||
\(57\) | −0.345149 | −0.0457162 | ||||||||
\(58\) | −2.30482 | −0.302637 | ||||||||
\(59\) | −12.9925 | −1.69148 | −0.845738 | − | 0.533598i | \(-0.820840\pi\) | ||||
−0.845738 | + | 0.533598i | \(0.820840\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1636 | 1.30132 | 0.650658 | − | 0.759371i | \(-0.274493\pi\) | ||||
0.650658 | + | 0.759371i | \(0.274493\pi\) | |||||||
\(62\) | −0.942804 | −0.119736 | ||||||||
\(63\) | 3.76423 | 0.474249 | ||||||||
\(64\) | −6.20973 | −0.776216 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.645315 | 0.0794328 | ||||||||
\(67\) | −10.1259 | −1.23707 | −0.618536 | − | 0.785757i | \(-0.712274\pi\) | ||||
−0.618536 | + | 0.785757i | \(0.712274\pi\) | |||||||
\(68\) | −14.0650 | −1.70564 | ||||||||
\(69\) | −0.698697 | −0.0841132 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.86703 | 0.221576 | 0.110788 | − | 0.993844i | \(-0.464663\pi\) | ||||
0.110788 | + | 0.993844i | \(0.464663\pi\) | |||||||
\(72\) | −3.00012 | −0.353567 | ||||||||
\(73\) | −6.47826 | −0.758223 | −0.379111 | − | 0.925351i | \(-0.623770\pi\) | ||||
−0.379111 | + | 0.925351i | \(0.623770\pi\) | |||||||
\(74\) | 1.98731 | 0.231020 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.34124 | 0.153850 | ||||||||
\(77\) | 6.41880 | 0.731490 | ||||||||
\(78\) | −0.00593342 | −0.000671827 0 | ||||||||
\(79\) | −12.9436 | −1.45627 | −0.728136 | − | 0.685432i | \(-0.759613\pi\) | ||||
−0.728136 | + | 0.685432i | \(0.759613\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.85611 | 0.761790 | ||||||||
\(82\) | −1.51430 | −0.167226 | ||||||||
\(83\) | 2.32915 | 0.255657 | 0.127829 | − | 0.991796i | \(-0.459199\pi\) | ||||
0.127829 | + | 0.991796i | \(0.459199\pi\) | |||||||
\(84\) | 1.30009 | 0.141851 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.26342 | −0.351904 | ||||||||
\(87\) | 4.10887 | 0.440517 | ||||||||
\(88\) | −5.11582 | −0.545348 | ||||||||
\(89\) | −14.5180 | −1.53890 | −0.769450 | − | 0.638707i | \(-0.779470\pi\) | ||||
−0.769450 | + | 0.638707i | \(0.779470\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0590183 | −0.00618680 | ||||||||
\(92\) | 2.71511 | 0.283070 | ||||||||
\(93\) | 1.68077 | 0.174287 | ||||||||
\(94\) | −1.45682 | −0.150260 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.56444 | −0.159670 | ||||||||
\(97\) | 2.23725 | 0.227158 | 0.113579 | − | 0.993529i | \(-0.463769\pi\) | ||||
0.113579 | + | 0.993529i | \(0.463769\pi\) | |||||||
\(98\) | 1.42489 | 0.143936 | ||||||||
\(99\) | 12.9438 | 1.30090 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.01607 | −0.399614 | −0.199807 | − | 0.979835i | \(-0.564031\pi\) | ||||
−0.199807 | + | 0.979835i | \(0.564031\pi\) | |||||||
\(102\) | −1.00468 | −0.0994778 | ||||||||
\(103\) | 5.25187 | 0.517482 | 0.258741 | − | 0.965947i | \(-0.416692\pi\) | ||||
0.258741 | + | 0.965947i | \(0.416692\pi\) | |||||||
\(104\) | 0.0470379 | 0.00461245 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.38097 | −0.231260 | ||||||||
\(107\) | −5.60385 | −0.541745 | −0.270873 | − | 0.962615i | \(-0.587312\pi\) | ||||
−0.270873 | + | 0.962615i | \(0.587312\pi\) | |||||||
\(108\) | 5.47637 | 0.526964 | ||||||||
\(109\) | −4.77557 | −0.457416 | −0.228708 | − | 0.973495i | \(-0.573450\pi\) | ||||
−0.228708 | + | 0.973495i | \(0.573450\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.54284 | −0.336271 | ||||||||
\(112\) | −4.84155 | −0.457484 | ||||||||
\(113\) | 12.6186 | 1.18706 | 0.593531 | − | 0.804811i | \(-0.297733\pi\) | ||||
0.593531 | + | 0.804811i | \(0.297733\pi\) | |||||||
\(114\) | 0.0958056 | 0.00897301 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −15.9669 | −1.48249 | ||||||||
\(117\) | −0.119013 | −0.0110027 | ||||||||
\(118\) | 3.60642 | 0.331997 | ||||||||
\(119\) | −9.99327 | −0.916082 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0718 | 1.00653 | ||||||||
\(122\) | −2.82118 | −0.255418 | ||||||||
\(123\) | 2.69959 | 0.243413 | ||||||||
\(124\) | −6.53139 | −0.586536 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.04487 | −0.0930840 | ||||||||
\(127\) | −0.427651 | −0.0379479 | −0.0189740 | − | 0.999820i | \(-0.506040\pi\) | ||||
−0.0189740 | + | 0.999820i | \(0.506040\pi\) | |||||||
\(128\) | 8.04663 | 0.711229 | ||||||||
\(129\) | 5.81780 | 0.512229 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.3633 | −1.16756 | −0.583780 | − | 0.811912i | \(-0.698427\pi\) | ||||
−0.583780 | + | 0.811912i | \(0.698427\pi\) | |||||||
\(132\) | 4.47050 | 0.389107 | ||||||||
\(133\) | 0.952955 | 0.0826317 | ||||||||
\(134\) | 2.81071 | 0.242808 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.96470 | 0.682967 | ||||||||
\(137\) | −11.2702 | −0.962874 | −0.481437 | − | 0.876481i | \(-0.659885\pi\) | ||||
−0.481437 | + | 0.876481i | \(0.659885\pi\) | |||||||
\(138\) | 0.193942 | 0.0165095 | ||||||||
\(139\) | −0.927184 | −0.0786427 | −0.0393214 | − | 0.999227i | \(-0.512520\pi\) | ||||
−0.0393214 | + | 0.999227i | \(0.512520\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.59713 | 0.218717 | ||||||||
\(142\) | −0.518245 | −0.0434902 | ||||||||
\(143\) | −0.202941 | −0.0169708 | ||||||||
\(144\) | −9.76319 | −0.813599 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.79822 | 0.148821 | ||||||||
\(147\) | −2.54020 | −0.209512 | ||||||||
\(148\) | 13.7673 | 1.13167 | ||||||||
\(149\) | 12.8757 | 1.05481 | 0.527407 | − | 0.849612i | \(-0.323164\pi\) | ||||
0.527407 | + | 0.849612i | \(0.323164\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.2436 | −1.72878 | −0.864390 | − | 0.502823i | \(-0.832295\pi\) | ||||
−0.864390 | + | 0.502823i | \(0.832295\pi\) | |||||||
\(152\) | −0.759511 | −0.0616045 | ||||||||
\(153\) | −20.1518 | −1.62918 | ||||||||
\(154\) | −1.78171 | −0.143574 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0411045 | −0.00329099 | ||||||||
\(157\) | −17.1798 | −1.37110 | −0.685550 | − | 0.728026i | \(-0.740438\pi\) | ||||
−0.685550 | + | 0.728026i | \(0.740438\pi\) | |||||||
\(158\) | 3.59286 | 0.285832 | ||||||||
\(159\) | 4.24463 | 0.336621 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.92910 | 0.152034 | ||||||||
\(162\) | −1.90310 | −0.149522 | ||||||||
\(163\) | −11.1081 | −0.870055 | −0.435028 | − | 0.900417i | \(-0.643261\pi\) | ||||
−0.435028 | + | 0.900417i | \(0.643261\pi\) | |||||||
\(164\) | −10.4905 | −0.819170 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.646519 | −0.0501796 | ||||||||
\(167\) | 22.3791 | 1.73174 | 0.865872 | − | 0.500266i | \(-0.166764\pi\) | ||||
0.865872 | + | 0.500266i | \(0.166764\pi\) | |||||||
\(168\) | −0.736209 | −0.0567998 | ||||||||
\(169\) | −12.9981 | −0.999856 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.92167 | 0.146954 | ||||||||
\(172\) | −22.6078 | −1.72383 | ||||||||
\(173\) | −4.16100 | −0.316355 | −0.158178 | − | 0.987411i | \(-0.550562\pi\) | ||||
−0.158178 | + | 0.987411i | \(0.550562\pi\) | |||||||
\(174\) | −1.14053 | −0.0864633 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.6482 | −1.25491 | ||||||||
\(177\) | −6.42927 | −0.483254 | ||||||||
\(178\) | 4.02985 | 0.302050 | ||||||||
\(179\) | −5.79009 | −0.432772 | −0.216386 | − | 0.976308i | \(-0.569427\pi\) | ||||
−0.216386 | + | 0.976308i | \(0.569427\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4917 | 1.30015 | 0.650076 | − | 0.759869i | \(-0.274737\pi\) | ||||
0.650076 | + | 0.759869i | \(0.274737\pi\) | |||||||
\(182\) | 0.0163821 | 0.00121432 | ||||||||
\(183\) | 5.02941 | 0.371785 | ||||||||
\(184\) | −1.53750 | −0.113346 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.466542 | −0.0342085 | ||||||||
\(187\) | −34.3630 | −2.51287 | ||||||||
\(188\) | −10.0923 | −0.736059 | ||||||||
\(189\) | 3.89099 | 0.283028 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.6074 | −1.56346 | −0.781728 | − | 0.623620i | \(-0.785661\pi\) | ||||
−0.781728 | + | 0.623620i | \(0.785661\pi\) | |||||||
\(192\) | −3.07286 | −0.221764 | ||||||||
\(193\) | −2.30886 | −0.166195 | −0.0830977 | − | 0.996541i | \(-0.526481\pi\) | ||||
−0.0830977 | + | 0.996541i | \(0.526481\pi\) | |||||||
\(194\) | −0.621008 | −0.0445858 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.87112 | 0.705080 | ||||||||
\(197\) | −1.91876 | −0.136706 | −0.0683531 | − | 0.997661i | \(-0.521774\pi\) | ||||
−0.0683531 | + | 0.997661i | \(0.521774\pi\) | |||||||
\(198\) | −3.59289 | −0.255336 | ||||||||
\(199\) | 21.2430 | 1.50588 | 0.752938 | − | 0.658091i | \(-0.228636\pi\) | ||||
0.752938 | + | 0.658091i | \(0.228636\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.01074 | −0.353430 | ||||||||
\(202\) | 1.11477 | 0.0784349 | ||||||||
\(203\) | −11.3446 | −0.796232 | ||||||||
\(204\) | −6.96002 | −0.487299 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.45780 | −0.101570 | ||||||||
\(207\) | 3.89010 | 0.270381 | ||||||||
\(208\) | 0.153074 | 0.0106138 | ||||||||
\(209\) | 3.27685 | 0.226664 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.0961 | −1.31463 | −0.657314 | − | 0.753616i | \(-0.728308\pi\) | ||||
−0.657314 | + | 0.753616i | \(0.728308\pi\) | |||||||
\(212\) | −16.4945 | −1.13285 | ||||||||
\(213\) | 0.923892 | 0.0633040 | ||||||||
\(214\) | 1.55550 | 0.106332 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.10114 | −0.211006 | ||||||||
\(217\) | −4.64058 | −0.315023 | ||||||||
\(218\) | 1.32559 | 0.0897802 | ||||||||
\(219\) | −3.20574 | −0.216624 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.315954 | 0.0212534 | ||||||||
\(222\) | 0.983410 | 0.0660022 | ||||||||
\(223\) | −8.41781 | −0.563698 | −0.281849 | − | 0.959459i | \(-0.590948\pi\) | ||||
−0.281849 | + | 0.959459i | \(0.590948\pi\) | |||||||
\(224\) | 4.31942 | 0.288603 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.50265 | −0.232993 | ||||||||
\(227\) | −1.82854 | −0.121364 | −0.0606821 | − | 0.998157i | \(-0.519328\pi\) | ||||
−0.0606821 | + | 0.998157i | \(0.519328\pi\) | |||||||
\(228\) | 0.663705 | 0.0439550 | ||||||||
\(229\) | 2.52038 | 0.166551 | 0.0832756 | − | 0.996527i | \(-0.473462\pi\) | ||||
0.0832756 | + | 0.996527i | \(0.473462\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.17631 | 0.208986 | ||||||||
\(232\) | 9.04169 | 0.593616 | ||||||||
\(233\) | −16.3812 | −1.07317 | −0.536585 | − | 0.843847i | \(-0.680286\pi\) | ||||
−0.536585 | + | 0.843847i | \(0.680286\pi\) | |||||||
\(234\) | 0.0330352 | 0.00215958 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 24.9839 | 1.62631 | ||||||||
\(237\) | −6.40510 | −0.416056 | ||||||||
\(238\) | 2.77390 | 0.179805 | ||||||||
\(239\) | −10.7430 | −0.694909 | −0.347455 | − | 0.937697i | \(-0.612954\pi\) | ||||
−0.347455 | + | 0.937697i | \(0.612954\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | −3.07327 | −0.197557 | ||||||||
\(243\) | 11.9364 | 0.765721 | ||||||||
\(244\) | −19.5441 | −1.25118 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.749343 | −0.0477764 | ||||||||
\(247\) | −0.0301293 | −0.00191708 | ||||||||
\(248\) | 3.69857 | 0.234860 | ||||||||
\(249\) | 1.15257 | 0.0730411 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.8819 | 1.50741 | 0.753706 | − | 0.657212i | \(-0.228264\pi\) | ||||
0.753706 | + | 0.657212i | \(0.228264\pi\) | |||||||
\(252\) | −7.23844 | −0.455979 | ||||||||
\(253\) | 6.63342 | 0.417040 | ||||||||
\(254\) | 0.118706 | 0.00744829 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.1859 | 0.636619 | ||||||||
\(257\) | −5.25407 | −0.327740 | −0.163870 | − | 0.986482i | \(-0.552398\pi\) | ||||
−0.163870 | + | 0.986482i | \(0.552398\pi\) | |||||||
\(258\) | −1.61489 | −0.100539 | ||||||||
\(259\) | 9.78175 | 0.607808 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.8768 | −1.41604 | ||||||||
\(262\) | 3.70936 | 0.229165 | ||||||||
\(263\) | 1.10964 | 0.0684235 | 0.0342118 | − | 0.999415i | \(-0.489108\pi\) | ||||
0.0342118 | + | 0.999415i | \(0.489108\pi\) | |||||||
\(264\) | −2.53154 | −0.155806 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.264519 | −0.0162187 | ||||||||
\(267\) | −7.18414 | −0.439662 | ||||||||
\(268\) | 19.4715 | 1.18941 | ||||||||
\(269\) | −2.84634 | −0.173544 | −0.0867722 | − | 0.996228i | \(-0.527655\pi\) | ||||
−0.0867722 | + | 0.996228i | \(0.527655\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.1029 | 0.795946 | 0.397973 | − | 0.917397i | \(-0.369714\pi\) | ||||
0.397973 | + | 0.917397i | \(0.369714\pi\) | |||||||
\(272\) | 25.9193 | 1.57159 | ||||||||
\(273\) | −0.0292049 | −0.00176756 | ||||||||
\(274\) | 3.12834 | 0.188990 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.34356 | 0.0808728 | ||||||||
\(277\) | 23.4634 | 1.40978 | 0.704888 | − | 0.709318i | \(-0.250997\pi\) | ||||
0.704888 | + | 0.709318i | \(0.250997\pi\) | |||||||
\(278\) | 0.257365 | 0.0154357 | ||||||||
\(279\) | −9.35792 | −0.560244 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.91165 | 0.531625 | 0.265812 | − | 0.964025i | \(-0.414360\pi\) | ||||
0.265812 | + | 0.964025i | \(0.414360\pi\) | |||||||
\(282\) | −0.720903 | −0.0429291 | ||||||||
\(283\) | 15.8040 | 0.939453 | 0.469726 | − | 0.882812i | \(-0.344353\pi\) | ||||
0.469726 | + | 0.882812i | \(0.344353\pi\) | |||||||
\(284\) | −3.59021 | −0.213040 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.0563318 | 0.00333097 | ||||||||
\(287\) | −7.45354 | −0.439968 | ||||||||
\(288\) | 8.71027 | 0.513258 | ||||||||
\(289\) | 36.4990 | 2.14700 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.10709 | 0.0648988 | ||||||||
\(292\) | 12.4574 | 0.729013 | ||||||||
\(293\) | −32.9425 | −1.92452 | −0.962261 | − | 0.272127i | \(-0.912273\pi\) | ||||
−0.962261 | + | 0.272127i | \(0.912273\pi\) | |||||||
\(294\) | 0.705102 | 0.0411224 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.79611 | −0.453140 | ||||||||
\(297\) | 13.3796 | 0.776363 | ||||||||
\(298\) | −3.57399 | −0.207036 | ||||||||
\(299\) | −0.0609917 | −0.00352724 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0629 | −0.925851 | ||||||||
\(302\) | 5.89674 | 0.339319 | ||||||||
\(303\) | −1.98733 | −0.114169 | ||||||||
\(304\) | −2.47165 | −0.141759 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.59369 | 0.319770 | ||||||||
\(307\) | −20.2343 | −1.15483 | −0.577416 | − | 0.816450i | \(-0.695939\pi\) | ||||
−0.577416 | + | 0.816450i | \(0.695939\pi\) | |||||||
\(308\) | −12.3430 | −0.703309 | ||||||||
\(309\) | 2.59886 | 0.147844 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.27289 | 0.128884 | 0.0644420 | − | 0.997921i | \(-0.479473\pi\) | ||||
0.0644420 | + | 0.997921i | \(0.479473\pi\) | |||||||
\(312\) | 0.0232765 | 0.00131777 | ||||||||
\(313\) | −13.1142 | −0.741257 | −0.370629 | − | 0.928781i | \(-0.620858\pi\) | ||||
−0.370629 | + | 0.928781i | \(0.620858\pi\) | |||||||
\(314\) | 4.76873 | 0.269115 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.8900 | 1.40017 | ||||||||
\(317\) | 7.86525 | 0.441757 | 0.220878 | − | 0.975301i | \(-0.429108\pi\) | ||||
0.220878 | + | 0.975301i | \(0.429108\pi\) | |||||||
\(318\) | −1.17821 | −0.0660709 | ||||||||
\(319\) | −39.0096 | −2.18412 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.77304 | −0.154776 | ||||||||
\(322\) | −0.535473 | −0.0298407 | ||||||||
\(323\) | −5.10164 | −0.283863 | ||||||||
\(324\) | −13.1840 | −0.732443 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.08336 | 0.170772 | ||||||||
\(327\) | −2.36317 | −0.130683 | ||||||||
\(328\) | 5.94051 | 0.328010 | ||||||||
\(329\) | −7.17065 | −0.395331 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.3752 | −1.06496 | −0.532480 | − | 0.846443i | \(-0.678740\pi\) | ||||
−0.532480 | + | 0.846443i | \(0.678740\pi\) | |||||||
\(332\) | −4.47884 | −0.245808 | ||||||||
\(333\) | 19.7253 | 1.08094 | ||||||||
\(334\) | −6.21192 | −0.339901 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.39582 | −0.130703 | ||||||||
\(337\) | 26.2459 | 1.42970 | 0.714852 | − | 0.699276i | \(-0.246494\pi\) | ||||
0.714852 | + | 0.699276i | \(0.246494\pi\) | |||||||
\(338\) | 3.60798 | 0.196249 | ||||||||
\(339\) | 6.24428 | 0.339143 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.9572 | −0.864130 | ||||||||
\(342\) | −0.533412 | −0.0288436 | ||||||||
\(343\) | 16.5773 | 0.895092 | ||||||||
\(344\) | 12.8022 | 0.690250 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.15500 | 0.0620931 | ||||||||
\(347\) | 3.65189 | 0.196044 | 0.0980219 | − | 0.995184i | \(-0.468748\pi\) | ||||
0.0980219 | + | 0.995184i | \(0.468748\pi\) | |||||||
\(348\) | −7.90116 | −0.423547 | ||||||||
\(349\) | −0.818652 | −0.0438214 | −0.0219107 | − | 0.999760i | \(-0.506975\pi\) | ||||
−0.0219107 | + | 0.999760i | \(0.506975\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.123020 | −0.00656633 | ||||||||
\(352\) | 14.8528 | 0.791658 | ||||||||
\(353\) | 28.5367 | 1.51886 | 0.759428 | − | 0.650591i | \(-0.225479\pi\) | ||||
0.759428 | + | 0.650591i | \(0.225479\pi\) | |||||||
\(354\) | 1.78462 | 0.0948514 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 27.9173 | 1.47961 | ||||||||
\(357\) | −4.94513 | −0.261724 | ||||||||
\(358\) | 1.60720 | 0.0849430 | ||||||||
\(359\) | −15.8623 | −0.837180 | −0.418590 | − | 0.908175i | \(-0.637476\pi\) | ||||
−0.418590 | + | 0.908175i | \(0.637476\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5135 | −0.974395 | ||||||||
\(362\) | −4.85531 | −0.255189 | ||||||||
\(363\) | 5.47882 | 0.287563 | ||||||||
\(364\) | 0.113489 | 0.00594845 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.39605 | −0.0729727 | ||||||||
\(367\) | −13.9937 | −0.730463 | −0.365232 | − | 0.930917i | \(-0.619010\pi\) | ||||
−0.365232 | + | 0.930917i | \(0.619010\pi\) | |||||||
\(368\) | −5.00344 | −0.260822 | ||||||||
\(369\) | −15.0304 | −0.782449 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.7194 | −0.608441 | ||||||||
\(372\) | −3.23203 | −0.167573 | ||||||||
\(373\) | −12.2336 | −0.633434 | −0.316717 | − | 0.948520i | \(-0.602581\pi\) | ||||
−0.316717 | + | 0.948520i | \(0.602581\pi\) | |||||||
\(374\) | 9.53839 | 0.493218 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.71505 | 0.294731 | ||||||||
\(377\) | 0.358678 | 0.0184728 | ||||||||
\(378\) | −1.08005 | −0.0555517 | ||||||||
\(379\) | 0.284829 | 0.0146307 | 0.00731535 | − | 0.999973i | \(-0.497671\pi\) | ||||
0.00731535 | + | 0.999973i | \(0.497671\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.211621 | −0.0108417 | ||||||||
\(382\) | 5.99772 | 0.306870 | ||||||||
\(383\) | −29.8268 | −1.52408 | −0.762038 | − | 0.647532i | \(-0.775801\pi\) | ||||
−0.762038 | + | 0.647532i | \(0.775801\pi\) | |||||||
\(384\) | 3.98184 | 0.203197 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.640887 | 0.0326203 | ||||||||
\(387\) | −32.3915 | −1.64655 | ||||||||
\(388\) | −4.30211 | −0.218407 | ||||||||
\(389\) | −8.88544 | −0.450510 | −0.225255 | − | 0.974300i | \(-0.572321\pi\) | ||||
−0.225255 | + | 0.974300i | \(0.572321\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.3274 | −0.522280 | ||||||||
\(392\) | −5.58978 | −0.282327 | ||||||||
\(393\) | −6.61279 | −0.333571 | ||||||||
\(394\) | 0.532605 | 0.0268322 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −24.8902 | −1.25078 | ||||||||
\(397\) | 29.5831 | 1.48473 | 0.742367 | − | 0.669993i | \(-0.233703\pi\) | ||||
0.742367 | + | 0.669993i | \(0.233703\pi\) | |||||||
\(398\) | −5.89657 | −0.295569 | ||||||||
\(399\) | 0.471566 | 0.0236078 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.30306 | 0.314760 | 0.157380 | − | 0.987538i | \(-0.449695\pi\) | ||||
0.157380 | + | 0.987538i | \(0.449695\pi\) | |||||||
\(402\) | 1.39087 | 0.0693701 | ||||||||
\(403\) | 0.146720 | 0.00730864 | ||||||||
\(404\) | 7.72270 | 0.384219 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.14899 | 0.156282 | ||||||||
\(407\) | 33.6357 | 1.66726 | ||||||||
\(408\) | 3.94130 | 0.195123 | ||||||||
\(409\) | −7.63163 | −0.377360 | −0.188680 | − | 0.982039i | \(-0.560421\pi\) | ||||
−0.188680 | + | 0.982039i | \(0.560421\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.57699 | −0.275092 | ||||||||
\(412\) | −10.0991 | −0.497546 | ||||||||
\(413\) | 17.7512 | 0.873478 | ||||||||
\(414\) | −1.07980 | −0.0530694 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.136566 | −0.00669568 | ||||||||
\(417\) | −0.458813 | −0.0224682 | ||||||||
\(418\) | −0.909578 | −0.0444889 | ||||||||
\(419\) | 2.34760 | 0.114688 | 0.0573439 | − | 0.998354i | \(-0.481737\pi\) | ||||
0.0573439 | + | 0.998354i | \(0.481737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.61693 | 0.419963 | 0.209982 | − | 0.977705i | \(-0.432660\pi\) | ||||
0.209982 | + | 0.977705i | \(0.432660\pi\) | |||||||
\(422\) | 5.30064 | 0.258031 | ||||||||
\(423\) | −14.4599 | −0.703064 | ||||||||
\(424\) | 9.34043 | 0.453611 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.256451 | −0.0124251 | ||||||||
\(427\) | −13.8862 | −0.671999 | ||||||||
\(428\) | 10.7759 | 0.520875 | ||||||||
\(429\) | −0.100425 | −0.00484854 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.73295 | −0.131641 | −0.0658207 | − | 0.997831i | \(-0.520967\pi\) | ||||
−0.0658207 | + | 0.997831i | \(0.520967\pi\) | |||||||
\(432\) | −10.0919 | −0.485549 | ||||||||
\(433\) | −14.8768 | −0.714934 | −0.357467 | − | 0.933926i | \(-0.616360\pi\) | ||||
−0.357467 | + | 0.933926i | \(0.616360\pi\) | |||||||
\(434\) | 1.28812 | 0.0618317 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.18318 | 0.439795 | ||||||||
\(437\) | 0.984819 | 0.0471103 | ||||||||
\(438\) | 0.889839 | 0.0425182 | ||||||||
\(439\) | −19.8115 | −0.945552 | −0.472776 | − | 0.881183i | \(-0.656748\pi\) | ||||
−0.472776 | + | 0.881183i | \(0.656748\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.1430 | 0.673474 | ||||||||
\(442\) | −0.0877017 | −0.00417154 | ||||||||
\(443\) | 39.5818 | 1.88059 | 0.940293 | − | 0.340366i | \(-0.110551\pi\) | ||||
0.940293 | + | 0.340366i | \(0.110551\pi\) | |||||||
\(444\) | 6.81270 | 0.323316 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.33659 | 0.110641 | ||||||||
\(447\) | 6.37146 | 0.301360 | ||||||||
\(448\) | 8.48414 | 0.400838 | ||||||||
\(449\) | −22.9205 | −1.08169 | −0.540843 | − | 0.841124i | \(-0.681895\pi\) | ||||
−0.540843 | + | 0.841124i | \(0.681895\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.6299 | −1.20686 | ||||||||
\(452\) | −24.2650 | −1.14133 | ||||||||
\(453\) | −10.5123 | −0.493911 | ||||||||
\(454\) | 0.507560 | 0.0238210 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.375841 | −0.0176003 | ||||||||
\(457\) | 9.66494 | 0.452107 | 0.226053 | − | 0.974115i | \(-0.427418\pi\) | ||||
0.226053 | + | 0.974115i | \(0.427418\pi\) | |||||||
\(458\) | −0.699599 | −0.0326901 | ||||||||
\(459\) | −20.8304 | −0.972279 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.28046 | 0.292510 | 0.146255 | − | 0.989247i | \(-0.453278\pi\) | ||||
0.146255 | + | 0.989247i | \(0.453278\pi\) | |||||||
\(462\) | −0.881672 | −0.0410191 | ||||||||
\(463\) | 7.64337 | 0.355218 | 0.177609 | − | 0.984101i | \(-0.443164\pi\) | ||||
0.177609 | + | 0.984101i | \(0.443164\pi\) | |||||||
\(464\) | 29.4241 | 1.36598 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.54705 | 0.210638 | ||||||||
\(467\) | −25.8943 | −1.19824 | −0.599122 | − | 0.800658i | \(-0.704484\pi\) | ||||
−0.599122 | + | 0.800658i | \(0.704484\pi\) | |||||||
\(468\) | 0.228856 | 0.0105789 | ||||||||
\(469\) | 13.8346 | 0.638823 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.50136 | −0.391722 | ||||||||
\(472\) | −14.1478 | −0.651205 | ||||||||
\(473\) | −55.2342 | −2.53967 | ||||||||
\(474\) | 1.77791 | 0.0816621 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 19.2166 | 0.880790 | ||||||||
\(477\) | −23.6326 | −1.08206 | ||||||||
\(478\) | 2.98202 | 0.136394 | ||||||||
\(479\) | 12.6131 | 0.576309 | 0.288155 | − | 0.957584i | \(-0.406958\pi\) | ||||
0.288155 | + | 0.957584i | \(0.406958\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.309267 | −0.0141013 | ||||||||
\(482\) | 0.277577 | 0.0126433 | ||||||||
\(483\) | 0.954605 | 0.0434360 | ||||||||
\(484\) | −21.2905 | −0.967749 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.31328 | −0.150293 | ||||||||
\(487\) | −31.7807 | −1.44012 | −0.720061 | − | 0.693910i | \(-0.755886\pi\) | ||||
−0.720061 | + | 0.693910i | \(0.755886\pi\) | |||||||
\(488\) | 11.0674 | 0.500996 | ||||||||
\(489\) | −5.49680 | −0.248574 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.2151 | −0.461001 | −0.230500 | − | 0.973072i | \(-0.574036\pi\) | ||||
−0.230500 | + | 0.973072i | \(0.574036\pi\) | |||||||
\(492\) | −5.19117 | −0.234036 | ||||||||
\(493\) | 60.7331 | 2.73528 | ||||||||
\(494\) | 0.00836321 | 0.000376278 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.0361 | 0.540439 | ||||||||
\(497\) | −2.55086 | −0.114422 | ||||||||
\(498\) | −0.319927 | −0.0143363 | ||||||||
\(499\) | −9.35390 | −0.418738 | −0.209369 | − | 0.977837i | \(-0.567141\pi\) | ||||
−0.209369 | + | 0.977837i | \(0.567141\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.0742 | 0.494758 | ||||||||
\(502\) | −6.62907 | −0.295870 | ||||||||
\(503\) | 13.7659 | 0.613792 | 0.306896 | − | 0.951743i | \(-0.400710\pi\) | ||||
0.306896 | + | 0.951743i | \(0.400710\pi\) | |||||||
\(504\) | 4.09896 | 0.182582 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.84129 | −0.0818552 | ||||||||
\(507\) | −6.43207 | −0.285658 | ||||||||
\(508\) | 0.822353 | 0.0364860 | ||||||||
\(509\) | 22.6367 | 1.00335 | 0.501677 | − | 0.865055i | \(-0.332717\pi\) | ||||
0.501677 | + | 0.865055i | \(0.332717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.85102 | 0.391546 | ||||||||
\(512\) | −18.9206 | −0.836182 | ||||||||
\(513\) | 1.98638 | 0.0877008 | ||||||||
\(514\) | 1.45841 | 0.0643277 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11.1873 | −0.492496 | ||||||||
\(517\) | −24.6571 | −1.08442 | ||||||||
\(518\) | −2.71519 | −0.119299 | ||||||||
\(519\) | −2.05905 | −0.0903824 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.8738 | −0.476389 | −0.238194 | − | 0.971218i | \(-0.576555\pi\) | ||||
−0.238194 | + | 0.971218i | \(0.576555\pi\) | |||||||
\(522\) | 6.35007 | 0.277935 | ||||||||
\(523\) | 3.43232 | 0.150085 | 0.0750424 | − | 0.997180i | \(-0.476091\pi\) | ||||
0.0750424 | + | 0.997180i | \(0.476091\pi\) | |||||||
\(524\) | 25.6970 | 1.12258 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.308011 | −0.0134299 | ||||||||
\(527\) | 24.8434 | 1.08219 | ||||||||
\(528\) | −8.23831 | −0.358526 | ||||||||
\(529\) | −21.0064 | −0.913322 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 35.7959 | 1.55341 | ||||||||
\(532\) | −1.83249 | −0.0794483 | ||||||||
\(533\) | 0.235656 | 0.0102074 | ||||||||
\(534\) | 1.99415 | 0.0862955 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −11.0263 | −0.476263 | ||||||||
\(537\) | −2.86520 | −0.123643 | ||||||||
\(538\) | 0.790079 | 0.0340627 | ||||||||
\(539\) | 24.1167 | 1.03878 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00758 | −0.0433193 | −0.0216597 | − | 0.999765i | \(-0.506895\pi\) | ||||
−0.0216597 | + | 0.999765i | \(0.506895\pi\) | |||||||
\(542\) | −3.63707 | −0.156226 | ||||||||
\(543\) | 8.65571 | 0.371452 | ||||||||
\(544\) | −23.1240 | −0.991433 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.00810662 | 0.000346931 0 | ||||||||
\(547\) | −10.6391 | −0.454894 | −0.227447 | − | 0.973791i | \(-0.573038\pi\) | ||||
−0.227447 | + | 0.973791i | \(0.573038\pi\) | |||||||
\(548\) | 21.6720 | 0.925780 | ||||||||
\(549\) | −28.0020 | −1.19510 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.79149 | −0.246726 | ||||||||
\(552\) | −0.760826 | −0.0323829 | ||||||||
\(553\) | 17.6844 | 0.752019 | ||||||||
\(554\) | −6.51289 | −0.276706 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.78293 | 0.0756130 | ||||||||
\(557\) | −18.9092 | −0.801207 | −0.400603 | − | 0.916252i | \(-0.631199\pi\) | ||||
−0.400603 | + | 0.916252i | \(0.631199\pi\) | |||||||
\(558\) | 2.59755 | 0.109963 | ||||||||
\(559\) | 0.507856 | 0.0214800 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.0044 | −0.717926 | ||||||||
\(562\) | −2.47367 | −0.104346 | ||||||||
\(563\) | −28.1768 | −1.18751 | −0.593756 | − | 0.804645i | \(-0.702356\pi\) | ||||
−0.593756 | + | 0.804645i | \(0.702356\pi\) | |||||||
\(564\) | −4.99415 | −0.210291 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.38684 | −0.184393 | ||||||||
\(567\) | −9.36727 | −0.393388 | ||||||||
\(568\) | 2.03305 | 0.0853049 | ||||||||
\(569\) | −0.499818 | −0.0209534 | −0.0104767 | − | 0.999945i | \(-0.503335\pi\) | ||||
−0.0104767 | + | 0.999945i | \(0.503335\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.2303 | −1.18140 | −0.590702 | − | 0.806890i | \(-0.701149\pi\) | ||||
−0.590702 | + | 0.806890i | \(0.701149\pi\) | |||||||
\(572\) | 0.390246 | 0.0163170 | ||||||||
\(573\) | −10.6923 | −0.446678 | ||||||||
\(574\) | 2.06893 | 0.0863555 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 17.1086 | 0.712858 | ||||||||
\(577\) | 36.3728 | 1.51422 | 0.757111 | − | 0.653287i | \(-0.226610\pi\) | ||||
0.757111 | + | 0.653287i | \(0.226610\pi\) | |||||||
\(578\) | −10.1313 | −0.421406 | ||||||||
\(579\) | −1.14253 | −0.0474819 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.18224 | −0.132021 | ||||||||
\(582\) | −0.307303 | −0.0127381 | ||||||||
\(583\) | −40.2985 | −1.66899 | ||||||||
\(584\) | −7.05432 | −0.291910 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.14409 | 0.377739 | ||||||||
\(587\) | −16.1223 | −0.665437 | −0.332718 | − | 0.943026i | \(-0.607966\pi\) | ||||
−0.332718 | + | 0.943026i | \(0.607966\pi\) | |||||||
\(588\) | 4.88468 | 0.201441 | ||||||||
\(589\) | −2.36905 | −0.0976152 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.949491 | −0.0390569 | ||||||||
\(592\) | −25.3706 | −1.04273 | ||||||||
\(593\) | −24.8487 | −1.02041 | −0.510207 | − | 0.860052i | \(-0.670431\pi\) | ||||
−0.510207 | + | 0.860052i | \(0.670431\pi\) | |||||||
\(594\) | −3.71387 | −0.152382 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −24.7593 | −1.01418 | ||||||||
\(597\) | 10.5120 | 0.430228 | ||||||||
\(598\) | 0.0169299 | 0.000692315 0 | ||||||||
\(599\) | −1.50155 | −0.0613517 | −0.0306759 | − | 0.999529i | \(-0.509766\pi\) | ||||
−0.0306759 | + | 0.999529i | \(0.509766\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.0828 | −0.982356 | −0.491178 | − | 0.871059i | \(-0.663434\pi\) | ||||
−0.491178 | + | 0.871059i | \(0.663434\pi\) | |||||||
\(602\) | 4.45870 | 0.181723 | ||||||||
\(603\) | 27.8981 | 1.13610 | ||||||||
\(604\) | 40.8504 | 1.66218 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.551638 | 0.0224088 | ||||||||
\(607\) | −16.0760 | −0.652506 | −0.326253 | − | 0.945283i | \(-0.605786\pi\) | ||||
−0.326253 | + | 0.945283i | \(0.605786\pi\) | |||||||
\(608\) | 2.20510 | 0.0894284 | ||||||||
\(609\) | −5.61381 | −0.227483 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.226712 | 0.00917179 | ||||||||
\(612\) | 38.7510 | 1.56642 | ||||||||
\(613\) | −43.5233 | −1.75789 | −0.878945 | − | 0.476923i | \(-0.841752\pi\) | ||||
−0.878945 | + | 0.476923i | \(0.841752\pi\) | |||||||
\(614\) | 5.61658 | 0.226667 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.98957 | 0.281618 | ||||||||
\(617\) | 3.82544 | 0.154006 | 0.0770032 | − | 0.997031i | \(-0.475465\pi\) | ||||
0.0770032 | + | 0.997031i | \(0.475465\pi\) | |||||||
\(618\) | −0.721385 | −0.0290183 | ||||||||
\(619\) | 8.69881 | 0.349635 | 0.174817 | − | 0.984601i | \(-0.444066\pi\) | ||||
0.174817 | + | 0.984601i | \(0.444066\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.02109 | 0.161361 | ||||||||
\(622\) | −0.630903 | −0.0252969 | ||||||||
\(623\) | 19.8354 | 0.794687 | ||||||||
\(624\) | 0.0757480 | 0.00303235 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.64020 | 0.145492 | ||||||||
\(627\) | 1.62153 | 0.0647578 | ||||||||
\(628\) | 33.0360 | 1.31828 | ||||||||
\(629\) | −52.3666 | −2.08799 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.0264 | −1.11571 | −0.557856 | − | 0.829938i | \(-0.688376\pi\) | ||||
−0.557856 | + | 0.829938i | \(0.688376\pi\) | |||||||
\(632\) | −14.0946 | −0.560653 | ||||||||
\(633\) | −9.44961 | −0.375588 | ||||||||
\(634\) | −2.18321 | −0.0867065 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.16222 | −0.323653 | ||||||||
\(637\) | −0.221743 | −0.00878578 | ||||||||
\(638\) | 10.8282 | 0.428692 | ||||||||
\(639\) | −5.14391 | −0.203490 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.7621 | 0.899048 | 0.449524 | − | 0.893268i | \(-0.351594\pi\) | ||||
0.449524 | + | 0.893268i | \(0.351594\pi\) | |||||||
\(642\) | 0.769733 | 0.0303789 | ||||||||
\(643\) | −35.9559 | −1.41796 | −0.708981 | − | 0.705228i | \(-0.750845\pi\) | ||||
−0.708981 | + | 0.705228i | \(0.750845\pi\) | |||||||
\(644\) | −3.70956 | −0.146177 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.41610 | 0.0557157 | ||||||||
\(647\) | 1.94619 | 0.0765127 | 0.0382564 | − | 0.999268i | \(-0.487820\pi\) | ||||
0.0382564 | + | 0.999268i | \(0.487820\pi\) | |||||||
\(648\) | 7.46577 | 0.293283 | ||||||||
\(649\) | 61.0395 | 2.39601 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.29637 | −0.0900019 | ||||||||
\(652\) | 21.3604 | 0.836537 | ||||||||
\(653\) | −24.3392 | −0.952467 | −0.476233 | − | 0.879319i | \(-0.657998\pi\) | ||||
−0.476233 | + | 0.879319i | \(0.657998\pi\) | |||||||
\(654\) | 0.655961 | 0.0256501 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 19.3320 | 0.754789 | ||||||||
\(657\) | 17.8484 | 0.696334 | ||||||||
\(658\) | 1.99041 | 0.0775942 | ||||||||
\(659\) | −6.16907 | −0.240313 | −0.120156 | − | 0.992755i | \(-0.538340\pi\) | ||||
−0.120156 | + | 0.992755i | \(0.538340\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −48.1704 | −1.87361 | −0.936807 | − | 0.349848i | \(-0.886233\pi\) | ||||
−0.936807 | + | 0.349848i | \(0.886233\pi\) | |||||||
\(662\) | 5.37812 | 0.209027 | ||||||||
\(663\) | 0.156349 | 0.00607208 | ||||||||
\(664\) | 2.53626 | 0.0984260 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.47529 | −0.212163 | ||||||||
\(667\) | −11.7239 | −0.453951 | ||||||||
\(668\) | −43.0338 | −1.66503 | ||||||||
\(669\) | −4.16551 | −0.161048 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −47.7492 | −1.84334 | ||||||||
\(672\) | 2.13744 | 0.0824537 | ||||||||
\(673\) | 19.2071 | 0.740381 | 0.370190 | − | 0.928956i | \(-0.379292\pi\) | ||||
0.370190 | + | 0.928956i | \(0.379292\pi\) | |||||||
\(674\) | −7.28525 | −0.280617 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 24.9948 | 0.961337 | ||||||||
\(677\) | 14.9094 | 0.573014 | 0.286507 | − | 0.958078i | \(-0.407506\pi\) | ||||
0.286507 | + | 0.958078i | \(0.407506\pi\) | |||||||
\(678\) | −1.73327 | −0.0665658 | ||||||||
\(679\) | −3.05667 | −0.117304 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.904843 | −0.0346737 | ||||||||
\(682\) | 4.42935 | 0.169609 | ||||||||
\(683\) | 22.8682 | 0.875029 | 0.437515 | − | 0.899211i | \(-0.355859\pi\) | ||||
0.437515 | + | 0.899211i | \(0.355859\pi\) | |||||||
\(684\) | −3.69528 | −0.141293 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.60149 | −0.175686 | ||||||||
\(687\) | 1.24720 | 0.0475835 | ||||||||
\(688\) | 41.6619 | 1.58835 | ||||||||
\(689\) | 0.370529 | 0.0141160 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.5210 | −1.35128 | −0.675641 | − | 0.737231i | \(-0.736133\pi\) | ||||
−0.675641 | + | 0.737231i | \(0.736133\pi\) | |||||||
\(692\) | 8.00140 | 0.304168 | ||||||||
\(693\) | −17.6846 | −0.671783 | ||||||||
\(694\) | −1.01368 | −0.0384788 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.47424 | 0.169596 | ||||||||
\(697\) | 39.9025 | 1.51142 | ||||||||
\(698\) | 0.227239 | 0.00860112 | ||||||||
\(699\) | −8.10617 | −0.306604 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.22303 | 0.348349 | 0.174175 | − | 0.984715i | \(-0.444274\pi\) | ||||
0.174175 | + | 0.984715i | \(0.444274\pi\) | |||||||
\(702\) | 0.0341476 | 0.00128882 | ||||||||
\(703\) | 4.99366 | 0.188339 | ||||||||
\(704\) | 29.1737 | 1.09952 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.92114 | −0.298116 | ||||||||
\(707\) | 5.48701 | 0.206360 | ||||||||
\(708\) | 12.3632 | 0.464636 | ||||||||
\(709\) | 28.7763 | 1.08072 | 0.540358 | − | 0.841435i | \(-0.318289\pi\) | ||||
0.540358 | + | 0.841435i | \(0.318289\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 35.6614 | 1.33741 | ||||||||
\(712\) | −15.8089 | −0.592464 | ||||||||
\(713\) | −4.79575 | −0.179602 | ||||||||
\(714\) | 1.37265 | 0.0513703 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.1341 | 0.416100 | ||||||||
\(717\) | −5.31614 | −0.198535 | ||||||||
\(718\) | 4.40301 | 0.164319 | ||||||||
\(719\) | −24.1878 | −0.902055 | −0.451027 | − | 0.892510i | \(-0.648942\pi\) | ||||
−0.451027 | + | 0.892510i | \(0.648942\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.17544 | −0.267227 | ||||||||
\(722\) | 5.13893 | 0.191251 | ||||||||
\(723\) | −0.494846 | −0.0184035 | ||||||||
\(724\) | −33.6358 | −1.25006 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.52080 | −0.0564420 | ||||||||
\(727\) | −9.73994 | −0.361235 | −0.180617 | − | 0.983553i | \(-0.557810\pi\) | ||||
−0.180617 | + | 0.983553i | \(0.557810\pi\) | |||||||
\(728\) | −0.0642663 | −0.00238187 | ||||||||
\(729\) | −14.6617 | −0.543024 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 85.9928 | 3.18056 | ||||||||
\(732\) | −9.67131 | −0.357462 | ||||||||
\(733\) | 4.38060 | 0.161801 | 0.0809006 | − | 0.996722i | \(-0.474220\pi\) | ||||
0.0809006 | + | 0.996722i | \(0.474220\pi\) | |||||||
\(734\) | 3.88432 | 0.143373 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.46384 | 0.164539 | ||||||||
\(737\) | 47.5719 | 1.75234 | ||||||||
\(738\) | 4.17208 | 0.153577 | ||||||||
\(739\) | −6.21520 | −0.228630 | −0.114315 | − | 0.993445i | \(-0.536467\pi\) | ||||
−0.114315 | + | 0.993445i | \(0.536467\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0149094 | −0.000547709 0 | ||||||||
\(742\) | 3.25304 | 0.119423 | ||||||||
\(743\) | −26.7097 | −0.979885 | −0.489942 | − | 0.871755i | \(-0.662982\pi\) | ||||
−0.489942 | + | 0.871755i | \(0.662982\pi\) | |||||||
\(744\) | 1.83022 | 0.0670992 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.39578 | 0.124328 | ||||||||
\(747\) | −6.41710 | −0.234790 | ||||||||
\(748\) | 66.0784 | 2.41607 | ||||||||
\(749\) | 7.65635 | 0.279757 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.9924 | 1.71478 | 0.857388 | − | 0.514670i | \(-0.172085\pi\) | ||||
0.857388 | + | 0.514670i | \(0.172085\pi\) | |||||||
\(752\) | 18.5983 | 0.678210 | ||||||||
\(753\) | 11.8178 | 0.430666 | ||||||||
\(754\) | −0.0995608 | −0.00362579 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −7.48217 | −0.272124 | ||||||||
\(757\) | 35.2425 | 1.28091 | 0.640456 | − | 0.767995i | \(-0.278745\pi\) | ||||
0.640456 | + | 0.767995i | \(0.278745\pi\) | |||||||
\(758\) | −0.0790621 | −0.00287166 | ||||||||
\(759\) | 3.28252 | 0.119148 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −47.1109 | −1.70777 | −0.853885 | − | 0.520461i | \(-0.825760\pi\) | ||||
−0.853885 | + | 0.520461i | \(0.825760\pi\) | |||||||
\(762\) | 0.0587413 | 0.00212797 | ||||||||
\(763\) | 6.52469 | 0.236210 | ||||||||
\(764\) | 41.5499 | 1.50322 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.27923 | 0.299141 | ||||||||
\(767\) | −0.561234 | −0.0202650 | ||||||||
\(768\) | 5.04045 | 0.181881 | ||||||||
\(769\) | −53.8827 | −1.94306 | −0.971530 | − | 0.236915i | \(-0.923864\pi\) | ||||
−0.971530 | + | 0.236915i | \(0.923864\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.59995 | −0.0936350 | ||||||||
\(772\) | 4.43983 | 0.159793 | ||||||||
\(773\) | 7.33241 | 0.263728 | 0.131864 | − | 0.991268i | \(-0.457904\pi\) | ||||
0.131864 | + | 0.991268i | \(0.457904\pi\) | |||||||
\(774\) | 8.99114 | 0.323180 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.43618 | 0.0874539 | ||||||||
\(777\) | 4.84045 | 0.173650 | ||||||||
\(778\) | 2.46639 | 0.0884245 | ||||||||
\(779\) | −3.80509 | −0.136332 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.77143 | −0.313866 | ||||||||
\(782\) | 2.86666 | 0.102511 | ||||||||
\(783\) | −23.6471 | −0.845078 | ||||||||
\(784\) | −18.1906 | −0.649666 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.83556 | 0.0654722 | ||||||||
\(787\) | 0.274880 | 0.00979841 | 0.00489921 | − | 0.999988i | \(-0.498441\pi\) | ||||
0.00489921 | + | 0.999988i | \(0.498441\pi\) | |||||||
\(788\) | 3.68969 | 0.131440 | ||||||||
\(789\) | 0.549102 | 0.0195485 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.2404 | −0.612998 | ||||||||
\(792\) | 14.0947 | 0.500835 | ||||||||
\(793\) | 0.439035 | 0.0155906 | ||||||||
\(794\) | −8.21160 | −0.291419 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −40.8493 | −1.44786 | ||||||||
\(797\) | 7.42858 | 0.263134 | 0.131567 | − | 0.991307i | \(-0.457999\pi\) | ||||
0.131567 | + | 0.991307i | \(0.457999\pi\) | |||||||
\(798\) | −0.130896 | −0.00463366 | ||||||||
\(799\) | 38.3881 | 1.35807 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 39.9988 | 1.41329 | ||||||||
\(802\) | −1.74958 | −0.0617800 | ||||||||
\(803\) | 30.4353 | 1.07404 | ||||||||
\(804\) | 9.63541 | 0.339815 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.0407261 | −0.00143452 | ||||||||
\(807\) | −1.40850 | −0.0495815 | ||||||||
\(808\) | −4.37318 | −0.153848 | ||||||||
\(809\) | 42.6491 | 1.49946 | 0.749730 | − | 0.661743i | \(-0.230183\pi\) | ||||
0.749730 | + | 0.661743i | \(0.230183\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.6139 | 0.899425 | 0.449713 | − | 0.893173i | \(-0.351526\pi\) | ||||
0.449713 | + | 0.893173i | \(0.351526\pi\) | |||||||
\(812\) | 21.8150 | 0.765558 | ||||||||
\(813\) | 6.48392 | 0.227401 | ||||||||
\(814\) | −9.33649 | −0.327244 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.8260 | 0.449001 | ||||||||
\(817\) | −8.20024 | −0.286890 | ||||||||
\(818\) | 2.11837 | 0.0740669 | ||||||||
\(819\) | 0.162603 | 0.00568181 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.8573 | 0.762826 | 0.381413 | − | 0.924405i | \(-0.375438\pi\) | ||||
0.381413 | + | 0.924405i | \(0.375438\pi\) | |||||||
\(822\) | 1.54804 | 0.0539942 | ||||||||
\(823\) | −1.58270 | −0.0551693 | −0.0275847 | − | 0.999619i | \(-0.508782\pi\) | ||||
−0.0275847 | + | 0.999619i | \(0.508782\pi\) | |||||||
\(824\) | 5.71887 | 0.199226 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.92732 | −0.171443 | ||||||||
\(827\) | −36.2198 | −1.25949 | −0.629743 | − | 0.776803i | \(-0.716840\pi\) | ||||
−0.629743 | + | 0.776803i | \(0.716840\pi\) | |||||||
\(828\) | −7.48047 | −0.259964 | ||||||||
\(829\) | 30.5957 | 1.06263 | 0.531316 | − | 0.847174i | \(-0.321698\pi\) | ||||
0.531316 | + | 0.847174i | \(0.321698\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.6107 | 0.402772 | ||||||||
\(832\) | −0.268241 | −0.00929957 | ||||||||
\(833\) | −37.5466 | −1.30091 | ||||||||
\(834\) | 0.127356 | 0.00440998 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.30122 | −0.217932 | ||||||||
\(837\) | −9.67303 | −0.334349 | ||||||||
\(838\) | −0.651640 | −0.0225105 | ||||||||
\(839\) | −9.85906 | −0.340373 | −0.170186 | − | 0.985412i | \(-0.554437\pi\) | ||||
−0.170186 | + | 0.985412i | \(0.554437\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.9455 | 1.37743 | ||||||||
\(842\) | −2.39186 | −0.0824290 | ||||||||
\(843\) | 4.40989 | 0.151885 | ||||||||
\(844\) | 36.7208 | 1.26398 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.01374 | 0.137995 | ||||||||
\(847\) | −15.1270 | −0.519769 | ||||||||
\(848\) | 30.3963 | 1.04381 | ||||||||
\(849\) | 7.82056 | 0.268401 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.1088 | 0.346526 | ||||||||
\(852\) | −1.77660 | −0.0608653 | ||||||||
\(853\) | −20.6701 | −0.707730 | −0.353865 | − | 0.935296i | \(-0.615133\pi\) | ||||
−0.353865 | + | 0.935296i | \(0.615133\pi\) | |||||||
\(854\) | 3.85448 | 0.131898 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.10216 | −0.208567 | ||||||||
\(857\) | −36.0858 | −1.23267 | −0.616334 | − | 0.787485i | \(-0.711383\pi\) | ||||
−0.616334 | + | 0.787485i | \(0.711383\pi\) | |||||||
\(858\) | 0.0278756 | 0.000951656 0 | ||||||||
\(859\) | 40.7566 | 1.39060 | 0.695299 | − | 0.718720i | \(-0.255272\pi\) | ||||
0.695299 | + | 0.718720i | \(0.255272\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.68835 | −0.125699 | ||||||||
\(862\) | 0.758604 | 0.0258381 | ||||||||
\(863\) | −21.5125 | −0.732295 | −0.366148 | − | 0.930557i | \(-0.619323\pi\) | ||||
−0.366148 | + | 0.930557i | \(0.619323\pi\) | |||||||
\(864\) | 9.00357 | 0.306308 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.12947 | 0.140325 | ||||||||
\(867\) | 18.0614 | 0.613396 | ||||||||
\(868\) | 8.92362 | 0.302887 | ||||||||
\(869\) | 60.8100 | 2.06284 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.437405 | −0.0148209 | ||||||||
\(872\) | −5.20022 | −0.176102 | ||||||||
\(873\) | −6.16390 | −0.208616 | ||||||||
\(874\) | −0.273363 | −0.00924665 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.16448 | 0.208278 | ||||||||
\(877\) | 47.8912 | 1.61717 | 0.808586 | − | 0.588378i | \(-0.200233\pi\) | ||||
0.808586 | + | 0.588378i | \(0.200233\pi\) | |||||||
\(878\) | 5.49922 | 0.185590 | ||||||||
\(879\) | −16.3015 | −0.549835 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.2689 | −0.615496 | −0.307748 | − | 0.951468i | \(-0.599575\pi\) | ||||
−0.307748 | + | 0.951468i | \(0.599575\pi\) | |||||||
\(882\) | −3.92576 | −0.132187 | ||||||||
\(883\) | 37.0354 | 1.24634 | 0.623170 | − | 0.782087i | \(-0.285845\pi\) | ||||
0.623170 | + | 0.782087i | \(0.285845\pi\) | |||||||
\(884\) | −0.607565 | −0.0204346 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.9870 | −0.369115 | ||||||||
\(887\) | 13.7619 | 0.462080 | 0.231040 | − | 0.972944i | \(-0.425787\pi\) | ||||
0.231040 | + | 0.972944i | \(0.425787\pi\) | |||||||
\(888\) | −3.85787 | −0.129462 | ||||||||
\(889\) | 0.584285 | 0.0195963 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −32.2104 | −1.07909 | ||||||||
\(892\) | 16.1870 | 0.541982 | ||||||||
\(893\) | −3.66067 | −0.122500 | ||||||||
\(894\) | −1.76857 | −0.0591499 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −10.9938 | −0.367278 | ||||||||
\(897\) | −0.0301815 | −0.00100773 | ||||||||
\(898\) | 6.36221 | 0.212310 | ||||||||
\(899\) | 28.2027 | 0.940613 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 62.7398 | 2.09017 | ||||||||
\(902\) | 7.11426 | 0.236879 | ||||||||
\(903\) | −7.94866 | −0.264515 | ||||||||
\(904\) | 13.7407 | 0.457009 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.91797 | 0.0969432 | ||||||||
\(907\) | 27.1842 | 0.902637 | 0.451319 | − | 0.892363i | \(-0.350954\pi\) | ||||
0.451319 | + | 0.892363i | \(0.350954\pi\) | |||||||
\(908\) | 3.51619 | 0.116689 | ||||||||
\(909\) | 11.0648 | 0.366996 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.4894 | 0.977027 | 0.488513 | − | 0.872556i | \(-0.337539\pi\) | ||||
0.488513 | + | 0.872556i | \(0.337539\pi\) | |||||||
\(912\) | −1.22309 | −0.0405004 | ||||||||
\(913\) | −10.9425 | −0.362143 | ||||||||
\(914\) | −2.68277 | −0.0887380 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.84656 | −0.160135 | ||||||||
\(917\) | 18.2579 | 0.602928 | ||||||||
\(918\) | 5.78204 | 0.190836 | ||||||||
\(919\) | −44.2354 | −1.45919 | −0.729596 | − | 0.683878i | \(-0.760292\pi\) | ||||
−0.729596 | + | 0.683878i | \(0.760292\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0128 | −0.329935 | ||||||||
\(922\) | −1.74331 | −0.0574130 | ||||||||
\(923\) | 0.0806498 | 0.00265462 | ||||||||
\(924\) | −6.10789 | −0.200935 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.12163 | −0.0697210 | ||||||||
\(927\) | −14.4696 | −0.475243 | ||||||||
\(928\) | −26.2508 | −0.861726 | ||||||||
\(929\) | 17.7425 | 0.582112 | 0.291056 | − | 0.956706i | \(-0.405993\pi\) | ||||
0.291056 | + | 0.956706i | \(0.405993\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.58043 | 0.117344 | ||||||||
\(932\) | 31.5003 | 1.03183 | ||||||||
\(933\) | 1.12473 | 0.0368220 | ||||||||
\(934\) | 7.18766 | 0.235187 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.129596 | −0.00423596 | ||||||||
\(937\) | −46.1680 | −1.50824 | −0.754121 | − | 0.656735i | \(-0.771937\pi\) | ||||
−0.754121 | + | 0.656735i | \(0.771937\pi\) | |||||||
\(938\) | −3.84017 | −0.125386 | ||||||||
\(939\) | −6.48949 | −0.211777 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.0383 | −0.718428 | −0.359214 | − | 0.933255i | \(-0.616955\pi\) | ||||
−0.359214 | + | 0.933255i | \(0.616955\pi\) | |||||||
\(942\) | 2.35978 | 0.0768859 | ||||||||
\(943\) | −7.70276 | −0.250836 | ||||||||
\(944\) | −46.0407 | −1.49850 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.3317 | 0.498478 | ||||||||
\(947\) | 34.5940 | 1.12416 | 0.562078 | − | 0.827085i | \(-0.310002\pi\) | ||||
0.562078 | + | 0.827085i | \(0.310002\pi\) | |||||||
\(948\) | 12.3167 | 0.400028 | ||||||||
\(949\) | −0.279840 | −0.00908399 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.89209 | 0.126210 | ||||||||
\(952\) | −10.8819 | −0.352684 | ||||||||
\(953\) | 20.9799 | 0.679607 | 0.339803 | − | 0.940496i | \(-0.389639\pi\) | ||||
0.339803 | + | 0.940496i | \(0.389639\pi\) | |||||||
\(954\) | 6.55988 | 0.212384 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.6583 | 0.668138 | ||||||||
\(957\) | −19.3037 | −0.624001 | ||||||||
\(958\) | −3.50112 | −0.113116 | ||||||||
\(959\) | 15.3980 | 0.497228 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.4635 | −0.627854 | ||||||||
\(962\) | 0.0858453 | 0.00276777 | ||||||||
\(963\) | 15.4393 | 0.497526 | ||||||||
\(964\) | 1.92295 | 0.0619341 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.264976 | −0.00852548 | ||||||||
\(967\) | 0.0716187 | 0.00230310 | 0.00115155 | − | 0.999999i | \(-0.499633\pi\) | ||||
0.00115155 | + | 0.999999i | \(0.499633\pi\) | |||||||
\(968\) | 12.0563 | 0.387504 | ||||||||
\(969\) | −2.52453 | −0.0810995 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.18205 | −0.262575 | −0.131287 | − | 0.991344i | \(-0.541911\pi\) | ||||
−0.131287 | + | 0.991344i | \(0.541911\pi\) | |||||||
\(972\) | −22.9531 | −0.736222 | ||||||||
\(973\) | 1.26678 | 0.0406111 | ||||||||
\(974\) | 8.82161 | 0.282663 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 36.0162 | 1.15285 | ||||||||
\(977\) | −22.6886 | −0.725872 | −0.362936 | − | 0.931814i | \(-0.618226\pi\) | ||||
−0.362936 | + | 0.931814i | \(0.618226\pi\) | |||||||
\(978\) | 1.52579 | 0.0487893 | ||||||||
\(979\) | 68.2062 | 2.17988 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.1573 | 0.420080 | ||||||||
\(982\) | 2.83548 | 0.0904837 | ||||||||
\(983\) | 18.8463 | 0.601103 | 0.300551 | − | 0.953766i | \(-0.402829\pi\) | ||||
0.300551 | + | 0.953766i | \(0.402829\pi\) | |||||||
\(984\) | 2.93964 | 0.0937122 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −16.8581 | −0.536872 | ||||||||
\(987\) | −3.54836 | −0.112946 | ||||||||
\(988\) | 0.0579372 | 0.00184323 | ||||||||
\(989\) | −16.6000 | −0.527850 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.8310 | −0.534655 | −0.267328 | − | 0.963606i | \(-0.586141\pi\) | ||||
−0.267328 | + | 0.963606i | \(0.586141\pi\) | |||||||
\(992\) | −10.7381 | −0.340935 | ||||||||
\(993\) | −9.58775 | −0.304258 | ||||||||
\(994\) | 0.708060 | 0.0224583 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.21633 | −0.0702272 | ||||||||
\(997\) | −60.1343 | −1.90447 | −0.952236 | − | 0.305363i | \(-0.901222\pi\) | ||||
−0.952236 | + | 0.305363i | \(0.901222\pi\) | |||||||
\(998\) | 2.59643 | 0.0821885 | ||||||||
\(999\) | 20.3895 | 0.645095 |
(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 | 6025.2.a.f.1.3 | 7 | ||
5.4 | even | 2 | 241.2.a.a.1.5 | ✓ | 7 | ||
15.14 | odd | 2 | 2169.2.a.e.1.3 | 7 | |||
20.19 | odd | 2 | 3856.2.a.j.1.4 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
241.2.a.a.1.5 | ✓ | 7 | 5.4 | even | 2 | ||
2169.2.a.e.1.3 | 7 | 15.14 | odd | 2 | |||
3856.2.a.j.1.4 | 7 | 20.19 | odd | 2 | |||
6025.2.a.f.1.3 | 7 | 1.1 | even | 1 | trivial |