Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.19806 | −0.535790 | −0.267895 | − | 0.963448i | \(-0.586328\pi\) | ||||
−0.267895 | + | 0.963448i | \(0.586328\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.19806 | −0.378861 | ||||||||
\(11\) | −1.55496 | −0.468838 | −0.234419 | − | 0.972136i | \(-0.575319\pi\) | ||||
−0.234419 | + | 0.972136i | \(0.575319\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.19806 | −0.309338 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.74094 | −1.39238 | −0.696191 | − | 0.717857i | \(-0.745123\pi\) | ||||
−0.696191 | + | 0.717857i | \(0.745123\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −4.93900 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(20\) | −1.19806 | −0.267895 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −1.55496 | −0.331518 | ||||||||
\(23\) | −0.417895 | −0.0871371 | −0.0435685 | − | 0.999050i | \(-0.513873\pi\) | ||||
−0.0435685 | + | 0.999050i | \(0.513873\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.56465 | −0.712929 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −2.46681 | −0.458076 | −0.229038 | − | 0.973418i | \(-0.573558\pi\) | ||||
−0.229038 | + | 0.973418i | \(0.573558\pi\) | |||||||
\(30\) | −1.19806 | −0.218735 | ||||||||
\(31\) | 10.2567 | 1.84215 | 0.921076 | − | 0.389383i | \(-0.127312\pi\) | ||||
0.921076 | + | 0.389383i | \(0.127312\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.55496 | −0.270683 | ||||||||
\(34\) | −5.74094 | −0.984563 | ||||||||
\(35\) | −1.19806 | −0.202509 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.58211 | 0.424495 | 0.212248 | − | 0.977216i | \(-0.431922\pi\) | ||||
0.212248 | + | 0.977216i | \(0.431922\pi\) | |||||||
\(38\) | −4.93900 | −0.801212 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.19806 | −0.189430 | ||||||||
\(41\) | −11.0761 | −1.72979 | −0.864895 | − | 0.501952i | \(-0.832615\pi\) | ||||
−0.864895 | + | 0.501952i | \(0.832615\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | 2.91185 | 0.444054 | 0.222027 | − | 0.975041i | \(-0.428733\pi\) | ||||
0.222027 | + | 0.975041i | \(0.428733\pi\) | |||||||
\(44\) | −1.55496 | −0.234419 | ||||||||
\(45\) | −1.19806 | −0.178597 | ||||||||
\(46\) | −0.417895 | −0.0616152 | ||||||||
\(47\) | −7.89008 | −1.15089 | −0.575443 | − | 0.817842i | \(-0.695171\pi\) | ||||
−0.575443 | + | 0.817842i | \(0.695171\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.56465 | −0.504117 | ||||||||
\(51\) | −5.74094 | −0.803892 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.62133 | −0.222707 | −0.111354 | − | 0.993781i | \(-0.535519\pi\) | ||||
−0.111354 | + | 0.993781i | \(0.535519\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.86294 | 0.251198 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −4.93900 | −0.654187 | ||||||||
\(58\) | −2.46681 | −0.323908 | ||||||||
\(59\) | −6.13169 | −0.798278 | −0.399139 | − | 0.916891i | \(-0.630691\pi\) | ||||
−0.399139 | + | 0.916891i | \(0.630691\pi\) | |||||||
\(60\) | −1.19806 | −0.154669 | ||||||||
\(61\) | 14.7017 | 1.88236 | 0.941181 | − | 0.337904i | \(-0.109718\pi\) | ||||
0.941181 | + | 0.337904i | \(0.109718\pi\) | |||||||
\(62\) | 10.2567 | 1.30260 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.55496 | −0.191402 | ||||||||
\(67\) | −10.5646 | −1.29068 | −0.645339 | − | 0.763897i | \(-0.723284\pi\) | ||||
−0.645339 | + | 0.763897i | \(0.723284\pi\) | |||||||
\(68\) | −5.74094 | −0.696191 | ||||||||
\(69\) | −0.417895 | −0.0503086 | ||||||||
\(70\) | −1.19806 | −0.143196 | ||||||||
\(71\) | −1.20775 | −0.143334 | −0.0716668 | − | 0.997429i | \(-0.522832\pi\) | ||||
−0.0716668 | + | 0.997429i | \(0.522832\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −5.86294 | −0.686205 | −0.343102 | − | 0.939298i | \(-0.611478\pi\) | ||||
−0.343102 | + | 0.939298i | \(0.611478\pi\) | |||||||
\(74\) | 2.58211 | 0.300164 | ||||||||
\(75\) | −3.56465 | −0.411610 | ||||||||
\(76\) | −4.93900 | −0.566542 | ||||||||
\(77\) | −1.55496 | −0.177204 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.67994 | −0.751552 | −0.375776 | − | 0.926711i | \(-0.622624\pi\) | ||||
−0.375776 | + | 0.926711i | \(0.622624\pi\) | |||||||
\(80\) | −1.19806 | −0.133947 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −11.0761 | −1.22315 | ||||||||
\(83\) | −9.06100 | −0.994574 | −0.497287 | − | 0.867586i | \(-0.665670\pi\) | ||||
−0.497287 | + | 0.867586i | \(0.665670\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 6.87800 | 0.746024 | ||||||||
\(86\) | 2.91185 | 0.313993 | ||||||||
\(87\) | −2.46681 | −0.264470 | ||||||||
\(88\) | −1.55496 | −0.165759 | ||||||||
\(89\) | −3.67456 | −0.389503 | −0.194751 | − | 0.980853i | \(-0.562390\pi\) | ||||
−0.194751 | + | 0.980853i | \(0.562390\pi\) | |||||||
\(90\) | −1.19806 | −0.126287 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.417895 | −0.0435685 | ||||||||
\(93\) | 10.2567 | 1.06357 | ||||||||
\(94\) | −7.89008 | −0.813800 | ||||||||
\(95\) | 5.91723 | 0.607095 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −17.3937 | −1.76607 | −0.883033 | − | 0.469311i | \(-0.844502\pi\) | ||||
−0.883033 | + | 0.469311i | \(0.844502\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −1.55496 | −0.156279 | ||||||||
\(100\) | −3.56465 | −0.356465 | ||||||||
\(101\) | 0.674563 | 0.0671215 | 0.0335608 | − | 0.999437i | \(-0.489315\pi\) | ||||
0.0335608 | + | 0.999437i | \(0.489315\pi\) | |||||||
\(102\) | −5.74094 | −0.568438 | ||||||||
\(103\) | −7.75063 | −0.763692 | −0.381846 | − | 0.924226i | \(-0.624712\pi\) | ||||
−0.381846 | + | 0.924226i | \(0.624712\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.19806 | −0.116919 | ||||||||
\(106\) | −1.62133 | −0.157478 | ||||||||
\(107\) | −6.20775 | −0.600126 | −0.300063 | − | 0.953919i | \(-0.597008\pi\) | ||||
−0.300063 | + | 0.953919i | \(0.597008\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −4.91185 | −0.470470 | −0.235235 | − | 0.971938i | \(-0.575586\pi\) | ||||
−0.235235 | + | 0.971938i | \(0.575586\pi\) | |||||||
\(110\) | 1.86294 | 0.177624 | ||||||||
\(111\) | 2.58211 | 0.245083 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 19.2054 | 1.80669 | 0.903344 | − | 0.428917i | \(-0.141105\pi\) | ||||
0.903344 | + | 0.428917i | \(0.141105\pi\) | |||||||
\(114\) | −4.93900 | −0.462580 | ||||||||
\(115\) | 0.500664 | 0.0466872 | ||||||||
\(116\) | −2.46681 | −0.229038 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.13169 | −0.564467 | ||||||||
\(119\) | −5.74094 | −0.526271 | ||||||||
\(120\) | −1.19806 | −0.109368 | ||||||||
\(121\) | −8.58211 | −0.780191 | ||||||||
\(122\) | 14.7017 | 1.33103 | ||||||||
\(123\) | −11.0761 | −0.998695 | ||||||||
\(124\) | 10.2567 | 0.921076 | ||||||||
\(125\) | 10.2610 | 0.917770 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 6.72886 | 0.597090 | 0.298545 | − | 0.954396i | \(-0.403499\pi\) | ||||
0.298545 | + | 0.954396i | \(0.403499\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.91185 | 0.256374 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.19269 | 0.278946 | 0.139473 | − | 0.990226i | \(-0.455459\pi\) | ||||
0.139473 | + | 0.990226i | \(0.455459\pi\) | |||||||
\(132\) | −1.55496 | −0.135342 | ||||||||
\(133\) | −4.93900 | −0.428266 | ||||||||
\(134\) | −10.5646 | −0.912646 | ||||||||
\(135\) | −1.19806 | −0.103113 | ||||||||
\(136\) | −5.74094 | −0.492281 | ||||||||
\(137\) | −3.21014 | −0.274261 | −0.137131 | − | 0.990553i | \(-0.543788\pi\) | ||||
−0.137131 | + | 0.990553i | \(0.543788\pi\) | |||||||
\(138\) | −0.417895 | −0.0355736 | ||||||||
\(139\) | −10.5308 | −0.893210 | −0.446605 | − | 0.894731i | \(-0.647367\pi\) | ||||
−0.446605 | + | 0.894731i | \(0.647367\pi\) | |||||||
\(140\) | −1.19806 | −0.101255 | ||||||||
\(141\) | −7.89008 | −0.664465 | ||||||||
\(142\) | −1.20775 | −0.101352 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.95539 | 0.245432 | ||||||||
\(146\) | −5.86294 | −0.485220 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 2.58211 | 0.212248 | ||||||||
\(149\) | −2.44504 | −0.200306 | −0.100153 | − | 0.994972i | \(-0.531933\pi\) | ||||
−0.100153 | + | 0.994972i | \(0.531933\pi\) | |||||||
\(150\) | −3.56465 | −0.291052 | ||||||||
\(151\) | 21.8364 | 1.77702 | 0.888510 | − | 0.458858i | \(-0.151741\pi\) | ||||
0.888510 | + | 0.458858i | \(0.151741\pi\) | |||||||
\(152\) | −4.93900 | −0.400606 | ||||||||
\(153\) | −5.74094 | −0.464127 | ||||||||
\(154\) | −1.55496 | −0.125302 | ||||||||
\(155\) | −12.2881 | −0.987006 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3599 | 1.22585 | 0.612926 | − | 0.790140i | \(-0.289992\pi\) | ||||
0.612926 | + | 0.790140i | \(0.289992\pi\) | |||||||
\(158\) | −6.67994 | −0.531427 | ||||||||
\(159\) | −1.62133 | −0.128580 | ||||||||
\(160\) | −1.19806 | −0.0947151 | ||||||||
\(161\) | −0.417895 | −0.0329347 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −16.0911 | −1.26035 | −0.630177 | − | 0.776451i | \(-0.717018\pi\) | ||||
−0.630177 | + | 0.776451i | \(0.717018\pi\) | |||||||
\(164\) | −11.0761 | −0.864895 | ||||||||
\(165\) | 1.86294 | 0.145029 | ||||||||
\(166\) | −9.06100 | −0.703270 | ||||||||
\(167\) | −6.65519 | −0.514994 | −0.257497 | − | 0.966279i | \(-0.582898\pi\) | ||||
−0.257497 | + | 0.966279i | \(0.582898\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 6.87800 | 0.527519 | ||||||||
\(171\) | −4.93900 | −0.377695 | ||||||||
\(172\) | 2.91185 | 0.222027 | ||||||||
\(173\) | 3.83446 | 0.291529 | 0.145764 | − | 0.989319i | \(-0.453436\pi\) | ||||
0.145764 | + | 0.989319i | \(0.453436\pi\) | |||||||
\(174\) | −2.46681 | −0.187009 | ||||||||
\(175\) | −3.56465 | −0.269462 | ||||||||
\(176\) | −1.55496 | −0.117209 | ||||||||
\(177\) | −6.13169 | −0.460886 | ||||||||
\(178\) | −3.67456 | −0.275420 | ||||||||
\(179\) | −6.48188 | −0.484478 | −0.242239 | − | 0.970217i | \(-0.577882\pi\) | ||||
−0.242239 | + | 0.970217i | \(0.577882\pi\) | |||||||
\(180\) | −1.19806 | −0.0892983 | ||||||||
\(181\) | 10.1075 | 0.751286 | 0.375643 | − | 0.926764i | \(-0.377422\pi\) | ||||
0.375643 | + | 0.926764i | \(0.377422\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.7017 | 1.08678 | ||||||||
\(184\) | −0.417895 | −0.0308076 | ||||||||
\(185\) | −3.09352 | −0.227440 | ||||||||
\(186\) | 10.2567 | 0.752055 | ||||||||
\(187\) | 8.92692 | 0.652801 | ||||||||
\(188\) | −7.89008 | −0.575443 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 5.91723 | 0.429281 | ||||||||
\(191\) | 22.9681 | 1.66191 | 0.830956 | − | 0.556339i | \(-0.187794\pi\) | ||||
0.830956 | + | 0.556339i | \(0.187794\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −4.37435 | −0.314873 | −0.157436 | − | 0.987529i | \(-0.550323\pi\) | ||||
−0.157436 | + | 0.987529i | \(0.550323\pi\) | |||||||
\(194\) | −17.3937 | −1.24880 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −4.90515 | −0.349477 | −0.174739 | − | 0.984615i | \(-0.555908\pi\) | ||||
−0.174739 | + | 0.984615i | \(0.555908\pi\) | |||||||
\(198\) | −1.55496 | −0.110506 | ||||||||
\(199\) | −7.73125 | −0.548054 | −0.274027 | − | 0.961722i | \(-0.588356\pi\) | ||||
−0.274027 | + | 0.961722i | \(0.588356\pi\) | |||||||
\(200\) | −3.56465 | −0.252059 | ||||||||
\(201\) | −10.5646 | −0.745173 | ||||||||
\(202\) | 0.674563 | 0.0474621 | ||||||||
\(203\) | −2.46681 | −0.173136 | ||||||||
\(204\) | −5.74094 | −0.401946 | ||||||||
\(205\) | 13.2698 | 0.926804 | ||||||||
\(206\) | −7.75063 | −0.540012 | ||||||||
\(207\) | −0.417895 | −0.0290457 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.67994 | 0.531233 | ||||||||
\(210\) | −1.19806 | −0.0826742 | ||||||||
\(211\) | 6.35690 | 0.437627 | 0.218813 | − | 0.975767i | \(-0.429781\pi\) | ||||
0.218813 | + | 0.975767i | \(0.429781\pi\) | |||||||
\(212\) | −1.62133 | −0.111354 | ||||||||
\(213\) | −1.20775 | −0.0827537 | ||||||||
\(214\) | −6.20775 | −0.424353 | ||||||||
\(215\) | −3.48858 | −0.237919 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 10.2567 | 0.696268 | ||||||||
\(218\) | −4.91185 | −0.332673 | ||||||||
\(219\) | −5.86294 | −0.396181 | ||||||||
\(220\) | 1.86294 | 0.125599 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.58211 | 0.173300 | ||||||||
\(223\) | 6.49157 | 0.434707 | 0.217354 | − | 0.976093i | \(-0.430257\pi\) | ||||
0.217354 | + | 0.976093i | \(0.430257\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −3.56465 | −0.237643 | ||||||||
\(226\) | 19.2054 | 1.27752 | ||||||||
\(227\) | −7.92931 | −0.526287 | −0.263143 | − | 0.964757i | \(-0.584759\pi\) | ||||
−0.263143 | + | 0.964757i | \(0.584759\pi\) | |||||||
\(228\) | −4.93900 | −0.327093 | ||||||||
\(229\) | 21.3502 | 1.41086 | 0.705430 | − | 0.708779i | \(-0.250754\pi\) | ||||
0.705430 | + | 0.708779i | \(0.250754\pi\) | |||||||
\(230\) | 0.500664 | 0.0330128 | ||||||||
\(231\) | −1.55496 | −0.102309 | ||||||||
\(232\) | −2.46681 | −0.161954 | ||||||||
\(233\) | 10.3002 | 0.674789 | 0.337395 | − | 0.941363i | \(-0.390454\pi\) | ||||
0.337395 | + | 0.941363i | \(0.390454\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.45281 | 0.616633 | ||||||||
\(236\) | −6.13169 | −0.399139 | ||||||||
\(237\) | −6.67994 | −0.433909 | ||||||||
\(238\) | −5.74094 | −0.372130 | ||||||||
\(239\) | 19.2814 | 1.24721 | 0.623606 | − | 0.781739i | \(-0.285667\pi\) | ||||
0.623606 | + | 0.781739i | \(0.285667\pi\) | |||||||
\(240\) | −1.19806 | −0.0773346 | ||||||||
\(241\) | 10.6920 | 0.688734 | 0.344367 | − | 0.938835i | \(-0.388094\pi\) | ||||
0.344367 | + | 0.938835i | \(0.388094\pi\) | |||||||
\(242\) | −8.58211 | −0.551679 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 14.7017 | 0.941181 | ||||||||
\(245\) | −1.19806 | −0.0765414 | ||||||||
\(246\) | −11.0761 | −0.706184 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 10.2567 | 0.651299 | ||||||||
\(249\) | −9.06100 | −0.574217 | ||||||||
\(250\) | 10.2610 | 0.648961 | ||||||||
\(251\) | −6.49827 | −0.410167 | −0.205084 | − | 0.978744i | \(-0.565747\pi\) | ||||
−0.205084 | + | 0.978744i | \(0.565747\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 0.649809 | 0.0408531 | ||||||||
\(254\) | 6.72886 | 0.422206 | ||||||||
\(255\) | 6.87800 | 0.430717 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.907542 | 0.0566109 | 0.0283055 | − | 0.999599i | \(-0.490989\pi\) | ||||
0.0283055 | + | 0.999599i | \(0.490989\pi\) | |||||||
\(258\) | 2.91185 | 0.181284 | ||||||||
\(259\) | 2.58211 | 0.160444 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.46681 | −0.152692 | ||||||||
\(262\) | 3.19269 | 0.197245 | ||||||||
\(263\) | 17.1564 | 1.05791 | 0.528956 | − | 0.848649i | \(-0.322584\pi\) | ||||
0.528956 | + | 0.848649i | \(0.322584\pi\) | |||||||
\(264\) | −1.55496 | −0.0957011 | ||||||||
\(265\) | 1.94246 | 0.119324 | ||||||||
\(266\) | −4.93900 | −0.302830 | ||||||||
\(267\) | −3.67456 | −0.224880 | ||||||||
\(268\) | −10.5646 | −0.645339 | ||||||||
\(269\) | −19.7047 | −1.20142 | −0.600708 | − | 0.799468i | \(-0.705115\pi\) | ||||
−0.600708 | + | 0.799468i | \(0.705115\pi\) | |||||||
\(270\) | −1.19806 | −0.0729117 | ||||||||
\(271\) | −16.0194 | −0.973108 | −0.486554 | − | 0.873651i | \(-0.661746\pi\) | ||||
−0.486554 | + | 0.873651i | \(0.661746\pi\) | |||||||
\(272\) | −5.74094 | −0.348096 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.21014 | −0.193932 | ||||||||
\(275\) | 5.54288 | 0.334248 | ||||||||
\(276\) | −0.417895 | −0.0251543 | ||||||||
\(277\) | −10.6571 | −0.640323 | −0.320162 | − | 0.947363i | \(-0.603737\pi\) | ||||
−0.320162 | + | 0.947363i | \(0.603737\pi\) | |||||||
\(278\) | −10.5308 | −0.631595 | ||||||||
\(279\) | 10.2567 | 0.614051 | ||||||||
\(280\) | −1.19806 | −0.0715979 | ||||||||
\(281\) | 28.6286 | 1.70784 | 0.853920 | − | 0.520404i | \(-0.174218\pi\) | ||||
0.853920 | + | 0.520404i | \(0.174218\pi\) | |||||||
\(282\) | −7.89008 | −0.469848 | ||||||||
\(283\) | −7.11960 | −0.423217 | −0.211608 | − | 0.977355i | \(-0.567870\pi\) | ||||
−0.211608 | + | 0.977355i | \(0.567870\pi\) | |||||||
\(284\) | −1.20775 | −0.0716668 | ||||||||
\(285\) | 5.91723 | 0.350507 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.0761 | −0.653799 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 15.9584 | 0.938728 | ||||||||
\(290\) | 2.95539 | 0.173547 | ||||||||
\(291\) | −17.3937 | −1.01964 | ||||||||
\(292\) | −5.86294 | −0.343102 | ||||||||
\(293\) | −25.0978 | −1.46623 | −0.733116 | − | 0.680104i | \(-0.761935\pi\) | ||||
−0.733116 | + | 0.680104i | \(0.761935\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 7.34614 | 0.427709 | ||||||||
\(296\) | 2.58211 | 0.150082 | ||||||||
\(297\) | −1.55496 | −0.0902278 | ||||||||
\(298\) | −2.44504 | −0.141637 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.56465 | −0.205805 | ||||||||
\(301\) | 2.91185 | 0.167836 | ||||||||
\(302\) | 21.8364 | 1.25654 | ||||||||
\(303\) | 0.674563 | 0.0387526 | ||||||||
\(304\) | −4.93900 | −0.283271 | ||||||||
\(305\) | −17.6136 | −1.00855 | ||||||||
\(306\) | −5.74094 | −0.328188 | ||||||||
\(307\) | 8.36658 | 0.477506 | 0.238753 | − | 0.971080i | \(-0.423261\pi\) | ||||
0.238753 | + | 0.971080i | \(0.423261\pi\) | |||||||
\(308\) | −1.55496 | −0.0886020 | ||||||||
\(309\) | −7.75063 | −0.440918 | ||||||||
\(310\) | −12.2881 | −0.697919 | ||||||||
\(311\) | −21.6668 | −1.22861 | −0.614306 | − | 0.789068i | \(-0.710564\pi\) | ||||
−0.614306 | + | 0.789068i | \(0.710564\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.6950 | 0.830611 | 0.415305 | − | 0.909682i | \(-0.363675\pi\) | ||||
0.415305 | + | 0.909682i | \(0.363675\pi\) | |||||||
\(314\) | 15.3599 | 0.866808 | ||||||||
\(315\) | −1.19806 | −0.0675032 | ||||||||
\(316\) | −6.67994 | −0.375776 | ||||||||
\(317\) | −27.1672 | −1.52586 | −0.762931 | − | 0.646480i | \(-0.776240\pi\) | ||||
−0.762931 | + | 0.646480i | \(0.776240\pi\) | |||||||
\(318\) | −1.62133 | −0.0909199 | ||||||||
\(319\) | 3.83579 | 0.214763 | ||||||||
\(320\) | −1.19806 | −0.0669737 | ||||||||
\(321\) | −6.20775 | −0.346483 | ||||||||
\(322\) | −0.417895 | −0.0232884 | ||||||||
\(323\) | 28.3545 | 1.57769 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −16.0911 | −0.891205 | ||||||||
\(327\) | −4.91185 | −0.271626 | ||||||||
\(328\) | −11.0761 | −0.611573 | ||||||||
\(329\) | −7.89008 | −0.434994 | ||||||||
\(330\) | 1.86294 | 0.102551 | ||||||||
\(331\) | −30.9885 | −1.70328 | −0.851641 | − | 0.524125i | \(-0.824392\pi\) | ||||
−0.851641 | + | 0.524125i | \(0.824392\pi\) | |||||||
\(332\) | −9.06100 | −0.497287 | ||||||||
\(333\) | 2.58211 | 0.141498 | ||||||||
\(334\) | −6.65519 | −0.364156 | ||||||||
\(335\) | 12.6571 | 0.691532 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | −1.95539 | −0.106517 | −0.0532586 | − | 0.998581i | \(-0.516961\pi\) | ||||
−0.0532586 | + | 0.998581i | \(0.516961\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.2054 | 1.04309 | ||||||||
\(340\) | 6.87800 | 0.373012 | ||||||||
\(341\) | −15.9487 | −0.863670 | ||||||||
\(342\) | −4.93900 | −0.267071 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 2.91185 | 0.156997 | ||||||||
\(345\) | 0.500664 | 0.0269548 | ||||||||
\(346\) | 3.83446 | 0.206142 | ||||||||
\(347\) | 22.9259 | 1.23072 | 0.615362 | − | 0.788244i | \(-0.289010\pi\) | ||||
0.615362 | + | 0.788244i | \(0.289010\pi\) | |||||||
\(348\) | −2.46681 | −0.132235 | ||||||||
\(349\) | −3.67994 | −0.196983 | −0.0984913 | − | 0.995138i | \(-0.531402\pi\) | ||||
−0.0984913 | + | 0.995138i | \(0.531402\pi\) | |||||||
\(350\) | −3.56465 | −0.190538 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.55496 | −0.0828795 | ||||||||
\(353\) | −26.6353 | −1.41766 | −0.708828 | − | 0.705381i | \(-0.750776\pi\) | ||||
−0.708828 | + | 0.705381i | \(0.750776\pi\) | |||||||
\(354\) | −6.13169 | −0.325895 | ||||||||
\(355\) | 1.44696 | 0.0767967 | ||||||||
\(356\) | −3.67456 | −0.194751 | ||||||||
\(357\) | −5.74094 | −0.303843 | ||||||||
\(358\) | −6.48188 | −0.342578 | ||||||||
\(359\) | 3.05967 | 0.161483 | 0.0807416 | − | 0.996735i | \(-0.474271\pi\) | ||||
0.0807416 | + | 0.996735i | \(0.474271\pi\) | |||||||
\(360\) | −1.19806 | −0.0631434 | ||||||||
\(361\) | 5.39373 | 0.283881 | ||||||||
\(362\) | 10.1075 | 0.531240 | ||||||||
\(363\) | −8.58211 | −0.450444 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.02416 | 0.367662 | ||||||||
\(366\) | 14.7017 | 0.768471 | ||||||||
\(367\) | −25.6582 | −1.33935 | −0.669673 | − | 0.742656i | \(-0.733566\pi\) | ||||
−0.669673 | + | 0.742656i | \(0.733566\pi\) | |||||||
\(368\) | −0.417895 | −0.0217843 | ||||||||
\(369\) | −11.0761 | −0.576597 | ||||||||
\(370\) | −3.09352 | −0.160825 | ||||||||
\(371\) | −1.62133 | −0.0841755 | ||||||||
\(372\) | 10.2567 | 0.531783 | ||||||||
\(373\) | −21.6612 | −1.12157 | −0.560786 | − | 0.827961i | \(-0.689501\pi\) | ||||
−0.560786 | + | 0.827961i | \(0.689501\pi\) | |||||||
\(374\) | 8.92692 | 0.461600 | ||||||||
\(375\) | 10.2610 | 0.529875 | ||||||||
\(376\) | −7.89008 | −0.406900 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 6.93602 | 0.356279 | 0.178140 | − | 0.984005i | \(-0.442992\pi\) | ||||
0.178140 | + | 0.984005i | \(0.442992\pi\) | |||||||
\(380\) | 5.91723 | 0.303548 | ||||||||
\(381\) | 6.72886 | 0.344730 | ||||||||
\(382\) | 22.9681 | 1.17515 | ||||||||
\(383\) | −19.9734 | −1.02060 | −0.510298 | − | 0.859998i | \(-0.670465\pi\) | ||||
−0.510298 | + | 0.859998i | \(0.670465\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 1.86294 | 0.0949440 | ||||||||
\(386\) | −4.37435 | −0.222649 | ||||||||
\(387\) | 2.91185 | 0.148018 | ||||||||
\(388\) | −17.3937 | −0.883033 | ||||||||
\(389\) | −30.7289 | −1.55801 | −0.779007 | − | 0.627015i | \(-0.784277\pi\) | ||||
−0.779007 | + | 0.627015i | \(0.784277\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.39911 | 0.121328 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 3.19269 | 0.161050 | ||||||||
\(394\) | −4.90515 | −0.247118 | ||||||||
\(395\) | 8.00298 | 0.402674 | ||||||||
\(396\) | −1.55496 | −0.0781396 | ||||||||
\(397\) | 12.3405 | 0.619352 | 0.309676 | − | 0.950842i | \(-0.399779\pi\) | ||||
0.309676 | + | 0.950842i | \(0.399779\pi\) | |||||||
\(398\) | −7.73125 | −0.387533 | ||||||||
\(399\) | −4.93900 | −0.247259 | ||||||||
\(400\) | −3.56465 | −0.178232 | ||||||||
\(401\) | −10.2241 | −0.510569 | −0.255285 | − | 0.966866i | \(-0.582169\pi\) | ||||
−0.255285 | + | 0.966866i | \(0.582169\pi\) | |||||||
\(402\) | −10.5646 | −0.526917 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.674563 | 0.0335608 | ||||||||
\(405\) | −1.19806 | −0.0595322 | ||||||||
\(406\) | −2.46681 | −0.122426 | ||||||||
\(407\) | −4.01507 | −0.199019 | ||||||||
\(408\) | −5.74094 | −0.284219 | ||||||||
\(409\) | −14.0127 | −0.692882 | −0.346441 | − | 0.938072i | \(-0.612610\pi\) | ||||
−0.346441 | + | 0.938072i | \(0.612610\pi\) | |||||||
\(410\) | 13.2698 | 0.655349 | ||||||||
\(411\) | −3.21014 | −0.158345 | ||||||||
\(412\) | −7.75063 | −0.381846 | ||||||||
\(413\) | −6.13169 | −0.301721 | ||||||||
\(414\) | −0.417895 | −0.0205384 | ||||||||
\(415\) | 10.8556 | 0.532882 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.5308 | −0.515695 | ||||||||
\(418\) | 7.67994 | 0.375638 | ||||||||
\(419\) | 1.10859 | 0.0541581 | 0.0270790 | − | 0.999633i | \(-0.491379\pi\) | ||||
0.0270790 | + | 0.999633i | \(0.491379\pi\) | |||||||
\(420\) | −1.19806 | −0.0584595 | ||||||||
\(421\) | 5.63342 | 0.274556 | 0.137278 | − | 0.990533i | \(-0.456165\pi\) | ||||
0.137278 | + | 0.990533i | \(0.456165\pi\) | |||||||
\(422\) | 6.35690 | 0.309449 | ||||||||
\(423\) | −7.89008 | −0.383629 | ||||||||
\(424\) | −1.62133 | −0.0787389 | ||||||||
\(425\) | 20.4644 | 0.992670 | ||||||||
\(426\) | −1.20775 | −0.0585157 | ||||||||
\(427\) | 14.7017 | 0.711466 | ||||||||
\(428\) | −6.20775 | −0.300063 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.48858 | −0.168234 | ||||||||
\(431\) | −18.6907 | −0.900299 | −0.450150 | − | 0.892953i | \(-0.648629\pi\) | ||||
−0.450150 | + | 0.892953i | \(0.648629\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −26.2640 | −1.26217 | −0.631083 | − | 0.775715i | \(-0.717389\pi\) | ||||
−0.631083 | + | 0.775715i | \(0.717389\pi\) | |||||||
\(434\) | 10.2567 | 0.492336 | ||||||||
\(435\) | 2.95539 | 0.141700 | ||||||||
\(436\) | −4.91185 | −0.235235 | ||||||||
\(437\) | 2.06398 | 0.0987337 | ||||||||
\(438\) | −5.86294 | −0.280142 | ||||||||
\(439\) | 11.8092 | 0.563624 | 0.281812 | − | 0.959470i | \(-0.409065\pi\) | ||||
0.281812 | + | 0.959470i | \(0.409065\pi\) | |||||||
\(440\) | 1.86294 | 0.0888120 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.16660 | 0.340496 | 0.170248 | − | 0.985401i | \(-0.445543\pi\) | ||||
0.170248 | + | 0.985401i | \(0.445543\pi\) | |||||||
\(444\) | 2.58211 | 0.122541 | ||||||||
\(445\) | 4.40236 | 0.208692 | ||||||||
\(446\) | 6.49157 | 0.307385 | ||||||||
\(447\) | −2.44504 | −0.115647 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −31.3357 | −1.47882 | −0.739412 | − | 0.673253i | \(-0.764896\pi\) | ||||
−0.739412 | + | 0.673253i | \(0.764896\pi\) | |||||||
\(450\) | −3.56465 | −0.168039 | ||||||||
\(451\) | 17.2228 | 0.810991 | ||||||||
\(452\) | 19.2054 | 0.903344 | ||||||||
\(453\) | 21.8364 | 1.02596 | ||||||||
\(454\) | −7.92931 | −0.372141 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.93900 | −0.231290 | ||||||||
\(457\) | 25.4058 | 1.18843 | 0.594217 | − | 0.804305i | \(-0.297462\pi\) | ||||
0.594217 | + | 0.804305i | \(0.297462\pi\) | |||||||
\(458\) | 21.3502 | 0.997629 | ||||||||
\(459\) | −5.74094 | −0.267964 | ||||||||
\(460\) | 0.500664 | 0.0233436 | ||||||||
\(461\) | 37.0417 | 1.72521 | 0.862603 | − | 0.505882i | \(-0.168833\pi\) | ||||
0.862603 | + | 0.505882i | \(0.168833\pi\) | |||||||
\(462\) | −1.55496 | −0.0723432 | ||||||||
\(463\) | 10.2929 | 0.478352 | 0.239176 | − | 0.970976i | \(-0.423123\pi\) | ||||
0.239176 | + | 0.970976i | \(0.423123\pi\) | |||||||
\(464\) | −2.46681 | −0.114519 | ||||||||
\(465\) | −12.2881 | −0.569848 | ||||||||
\(466\) | 10.3002 | 0.477148 | ||||||||
\(467\) | −12.1890 | −0.564038 | −0.282019 | − | 0.959409i | \(-0.591004\pi\) | ||||
−0.282019 | + | 0.959409i | \(0.591004\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.5646 | −0.487830 | ||||||||
\(470\) | 9.45281 | 0.436026 | ||||||||
\(471\) | 15.3599 | 0.707746 | ||||||||
\(472\) | −6.13169 | −0.282234 | ||||||||
\(473\) | −4.52781 | −0.208189 | ||||||||
\(474\) | −6.67994 | −0.306820 | ||||||||
\(475\) | 17.6058 | 0.807809 | ||||||||
\(476\) | −5.74094 | −0.263135 | ||||||||
\(477\) | −1.62133 | −0.0742358 | ||||||||
\(478\) | 19.2814 | 0.881912 | ||||||||
\(479\) | −42.4413 | −1.93919 | −0.969597 | − | 0.244708i | \(-0.921308\pi\) | ||||
−0.969597 | + | 0.244708i | \(0.921308\pi\) | |||||||
\(480\) | −1.19806 | −0.0546838 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 10.6920 | 0.487008 | ||||||||
\(483\) | −0.417895 | −0.0190149 | ||||||||
\(484\) | −8.58211 | −0.390096 | ||||||||
\(485\) | 20.8388 | 0.946240 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 7.26742 | 0.329318 | 0.164659 | − | 0.986351i | \(-0.447348\pi\) | ||||
0.164659 | + | 0.986351i | \(0.447348\pi\) | |||||||
\(488\) | 14.7017 | 0.665515 | ||||||||
\(489\) | −16.0911 | −0.727666 | ||||||||
\(490\) | −1.19806 | −0.0541229 | ||||||||
\(491\) | 14.3763 | 0.648792 | 0.324396 | − | 0.945921i | \(-0.394839\pi\) | ||||
0.324396 | + | 0.945921i | \(0.394839\pi\) | |||||||
\(492\) | −11.0761 | −0.499348 | ||||||||
\(493\) | 14.1618 | 0.637816 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.86294 | 0.0837328 | ||||||||
\(496\) | 10.2567 | 0.460538 | ||||||||
\(497\) | −1.20775 | −0.0541750 | ||||||||
\(498\) | −9.06100 | −0.406033 | ||||||||
\(499\) | 5.55602 | 0.248722 | 0.124361 | − | 0.992237i | \(-0.460312\pi\) | ||||
0.124361 | + | 0.992237i | \(0.460312\pi\) | |||||||
\(500\) | 10.2610 | 0.458885 | ||||||||
\(501\) | −6.65519 | −0.297332 | ||||||||
\(502\) | −6.49827 | −0.290032 | ||||||||
\(503\) | 38.2747 | 1.70659 | 0.853293 | − | 0.521432i | \(-0.174602\pi\) | ||||
0.853293 | + | 0.521432i | \(0.174602\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −0.808169 | −0.0359630 | ||||||||
\(506\) | 0.649809 | 0.0288875 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.72886 | 0.298545 | ||||||||
\(509\) | 33.3685 | 1.47903 | 0.739516 | − | 0.673138i | \(-0.235054\pi\) | ||||
0.739516 | + | 0.673138i | \(0.235054\pi\) | |||||||
\(510\) | 6.87800 | 0.304563 | ||||||||
\(511\) | −5.86294 | −0.259361 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.93900 | −0.218062 | ||||||||
\(514\) | 0.907542 | 0.0400300 | ||||||||
\(515\) | 9.28573 | 0.409178 | ||||||||
\(516\) | 2.91185 | 0.128187 | ||||||||
\(517\) | 12.2687 | 0.539579 | ||||||||
\(518\) | 2.58211 | 0.113451 | ||||||||
\(519\) | 3.83446 | 0.168314 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.8291 | 0.649674 | 0.324837 | − | 0.945770i | \(-0.394691\pi\) | ||||
0.324837 | + | 0.945770i | \(0.394691\pi\) | |||||||
\(522\) | −2.46681 | −0.107969 | ||||||||
\(523\) | −27.8625 | −1.21834 | −0.609170 | − | 0.793040i | \(-0.708497\pi\) | ||||
−0.609170 | + | 0.793040i | \(0.708497\pi\) | |||||||
\(524\) | 3.19269 | 0.139473 | ||||||||
\(525\) | −3.56465 | −0.155574 | ||||||||
\(526\) | 17.1564 | 0.748056 | ||||||||
\(527\) | −58.8829 | −2.56498 | ||||||||
\(528\) | −1.55496 | −0.0676709 | ||||||||
\(529\) | −22.8254 | −0.992407 | ||||||||
\(530\) | 1.94246 | 0.0843750 | ||||||||
\(531\) | −6.13169 | −0.266093 | ||||||||
\(532\) | −4.93900 | −0.214133 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.67456 | −0.159014 | ||||||||
\(535\) | 7.43727 | 0.321541 | ||||||||
\(536\) | −10.5646 | −0.456323 | ||||||||
\(537\) | −6.48188 | −0.279714 | ||||||||
\(538\) | −19.7047 | −0.849530 | ||||||||
\(539\) | −1.55496 | −0.0669768 | ||||||||
\(540\) | −1.19806 | −0.0515564 | ||||||||
\(541\) | 27.8019 | 1.19530 | 0.597649 | − | 0.801758i | \(-0.296102\pi\) | ||||
0.597649 | + | 0.801758i | \(0.296102\pi\) | |||||||
\(542\) | −16.0194 | −0.688091 | ||||||||
\(543\) | 10.1075 | 0.433755 | ||||||||
\(544\) | −5.74094 | −0.246141 | ||||||||
\(545\) | 5.88471 | 0.252073 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.2500 | −0.481014 | −0.240507 | − | 0.970647i | \(-0.577314\pi\) | ||||
−0.240507 | + | 0.970647i | \(0.577314\pi\) | |||||||
\(548\) | −3.21014 | −0.137131 | ||||||||
\(549\) | 14.7017 | 0.627454 | ||||||||
\(550\) | 5.54288 | 0.236349 | ||||||||
\(551\) | 12.1836 | 0.519038 | ||||||||
\(552\) | −0.417895 | −0.0177868 | ||||||||
\(553\) | −6.67994 | −0.284060 | ||||||||
\(554\) | −10.6571 | −0.452777 | ||||||||
\(555\) | −3.09352 | −0.131313 | ||||||||
\(556\) | −10.5308 | −0.446605 | ||||||||
\(557\) | −30.0062 | −1.27140 | −0.635702 | − | 0.771934i | \(-0.719289\pi\) | ||||
−0.635702 | + | 0.771934i | \(0.719289\pi\) | |||||||
\(558\) | 10.2567 | 0.434199 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.19806 | −0.0506274 | ||||||||
\(561\) | 8.92692 | 0.376895 | ||||||||
\(562\) | 28.6286 | 1.20763 | ||||||||
\(563\) | 39.3491 | 1.65837 | 0.829184 | − | 0.558976i | \(-0.188806\pi\) | ||||
0.829184 | + | 0.558976i | \(0.188806\pi\) | |||||||
\(564\) | −7.89008 | −0.332232 | ||||||||
\(565\) | −23.0092 | −0.968005 | ||||||||
\(566\) | −7.11960 | −0.299259 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −1.20775 | −0.0506761 | ||||||||
\(569\) | 9.36360 | 0.392543 | 0.196271 | − | 0.980550i | \(-0.437117\pi\) | ||||
0.196271 | + | 0.980550i | \(0.437117\pi\) | |||||||
\(570\) | 5.91723 | 0.247846 | ||||||||
\(571\) | 24.1540 | 1.01082 | 0.505408 | − | 0.862881i | \(-0.331342\pi\) | ||||
0.505408 | + | 0.862881i | \(0.331342\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.9681 | 0.959505 | ||||||||
\(574\) | −11.0761 | −0.462306 | ||||||||
\(575\) | 1.48965 | 0.0621226 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 28.7885 | 1.19848 | 0.599241 | − | 0.800569i | \(-0.295469\pi\) | ||||
0.599241 | + | 0.800569i | \(0.295469\pi\) | |||||||
\(578\) | 15.9584 | 0.663781 | ||||||||
\(579\) | −4.37435 | −0.181792 | ||||||||
\(580\) | 2.95539 | 0.122716 | ||||||||
\(581\) | −9.06100 | −0.375914 | ||||||||
\(582\) | −17.3937 | −0.720993 | ||||||||
\(583\) | 2.52111 | 0.104414 | ||||||||
\(584\) | −5.86294 | −0.242610 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.0978 | −1.03678 | ||||||||
\(587\) | −6.58211 | −0.271673 | −0.135836 | − | 0.990731i | \(-0.543372\pi\) | ||||
−0.135836 | + | 0.990731i | \(0.543372\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | −50.6577 | −2.08731 | ||||||||
\(590\) | 7.34614 | 0.302436 | ||||||||
\(591\) | −4.90515 | −0.201771 | ||||||||
\(592\) | 2.58211 | 0.106124 | ||||||||
\(593\) | −1.66355 | −0.0683137 | −0.0341568 | − | 0.999416i | \(-0.510875\pi\) | ||||
−0.0341568 | + | 0.999416i | \(0.510875\pi\) | |||||||
\(594\) | −1.55496 | −0.0638007 | ||||||||
\(595\) | 6.87800 | 0.281971 | ||||||||
\(596\) | −2.44504 | −0.100153 | ||||||||
\(597\) | −7.73125 | −0.316419 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.9788 | 1.34748 | 0.673739 | − | 0.738969i | \(-0.264687\pi\) | ||||
0.673739 | + | 0.738969i | \(0.264687\pi\) | |||||||
\(600\) | −3.56465 | −0.145526 | ||||||||
\(601\) | −30.2107 | −1.23232 | −0.616161 | − | 0.787620i | \(-0.711313\pi\) | ||||
−0.616161 | + | 0.787620i | \(0.711313\pi\) | |||||||
\(602\) | 2.91185 | 0.118678 | ||||||||
\(603\) | −10.5646 | −0.430226 | ||||||||
\(604\) | 21.8364 | 0.888510 | ||||||||
\(605\) | 10.2819 | 0.418019 | ||||||||
\(606\) | 0.674563 | 0.0274023 | ||||||||
\(607\) | 7.50471 | 0.304607 | 0.152303 | − | 0.988334i | \(-0.451331\pi\) | ||||
0.152303 | + | 0.988334i | \(0.451331\pi\) | |||||||
\(608\) | −4.93900 | −0.200303 | ||||||||
\(609\) | −2.46681 | −0.0999603 | ||||||||
\(610\) | −17.6136 | −0.713152 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −5.74094 | −0.232064 | ||||||||
\(613\) | −18.5187 | −0.747964 | −0.373982 | − | 0.927436i | \(-0.622008\pi\) | ||||
−0.373982 | + | 0.927436i | \(0.622008\pi\) | |||||||
\(614\) | 8.36658 | 0.337648 | ||||||||
\(615\) | 13.2698 | 0.535091 | ||||||||
\(616\) | −1.55496 | −0.0626510 | ||||||||
\(617\) | 31.8998 | 1.28424 | 0.642118 | − | 0.766606i | \(-0.278056\pi\) | ||||
0.642118 | + | 0.766606i | \(0.278056\pi\) | |||||||
\(618\) | −7.75063 | −0.311776 | ||||||||
\(619\) | 48.4566 | 1.94764 | 0.973819 | − | 0.227327i | \(-0.0729985\pi\) | ||||
0.973819 | + | 0.227327i | \(0.0729985\pi\) | |||||||
\(620\) | −12.2881 | −0.493503 | ||||||||
\(621\) | −0.417895 | −0.0167695 | ||||||||
\(622\) | −21.6668 | −0.868759 | ||||||||
\(623\) | −3.67456 | −0.147218 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.52994 | 0.221198 | ||||||||
\(626\) | 14.6950 | 0.587331 | ||||||||
\(627\) | 7.67994 | 0.306707 | ||||||||
\(628\) | 15.3599 | 0.612926 | ||||||||
\(629\) | −14.8237 | −0.591060 | ||||||||
\(630\) | −1.19806 | −0.0477319 | ||||||||
\(631\) | −3.20477 | −0.127580 | −0.0637899 | − | 0.997963i | \(-0.520319\pi\) | ||||
−0.0637899 | + | 0.997963i | \(0.520319\pi\) | |||||||
\(632\) | −6.67994 | −0.265714 | ||||||||
\(633\) | 6.35690 | 0.252664 | ||||||||
\(634\) | −27.1672 | −1.07895 | ||||||||
\(635\) | −8.06159 | −0.319914 | ||||||||
\(636\) | −1.62133 | −0.0642901 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.83579 | 0.151860 | ||||||||
\(639\) | −1.20775 | −0.0477779 | ||||||||
\(640\) | −1.19806 | −0.0473576 | ||||||||
\(641\) | −32.5515 | −1.28571 | −0.642853 | − | 0.765989i | \(-0.722250\pi\) | ||||
−0.642853 | + | 0.765989i | \(0.722250\pi\) | |||||||
\(642\) | −6.20775 | −0.245000 | ||||||||
\(643\) | 9.77107 | 0.385333 | 0.192667 | − | 0.981264i | \(-0.438286\pi\) | ||||
0.192667 | + | 0.981264i | \(0.438286\pi\) | |||||||
\(644\) | −0.417895 | −0.0164674 | ||||||||
\(645\) | −3.48858 | −0.137363 | ||||||||
\(646\) | 28.3545 | 1.11559 | ||||||||
\(647\) | −12.4829 | −0.490755 | −0.245378 | − | 0.969428i | \(-0.578912\pi\) | ||||
−0.245378 | + | 0.969428i | \(0.578912\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 9.53452 | 0.374262 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.2567 | 0.401991 | ||||||||
\(652\) | −16.0911 | −0.630177 | ||||||||
\(653\) | 42.5488 | 1.66506 | 0.832532 | − | 0.553976i | \(-0.186890\pi\) | ||||
0.832532 | + | 0.553976i | \(0.186890\pi\) | |||||||
\(654\) | −4.91185 | −0.192069 | ||||||||
\(655\) | −3.82504 | −0.149457 | ||||||||
\(656\) | −11.0761 | −0.432448 | ||||||||
\(657\) | −5.86294 | −0.228735 | ||||||||
\(658\) | −7.89008 | −0.307587 | ||||||||
\(659\) | −40.8068 | −1.58961 | −0.794804 | − | 0.606866i | \(-0.792427\pi\) | ||||
−0.794804 | + | 0.606866i | \(0.792427\pi\) | |||||||
\(660\) | 1.86294 | 0.0725147 | ||||||||
\(661\) | 39.2597 | 1.52702 | 0.763512 | − | 0.645794i | \(-0.223473\pi\) | ||||
0.763512 | + | 0.645794i | \(0.223473\pi\) | |||||||
\(662\) | −30.9885 | −1.20440 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.06100 | −0.351635 | ||||||||
\(665\) | 5.91723 | 0.229460 | ||||||||
\(666\) | 2.58211 | 0.100055 | ||||||||
\(667\) | 1.03087 | 0.0399154 | ||||||||
\(668\) | −6.65519 | −0.257497 | ||||||||
\(669\) | 6.49157 | 0.250978 | ||||||||
\(670\) | 12.6571 | 0.488987 | ||||||||
\(671\) | −22.8605 | −0.882522 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | 40.8353 | 1.57409 | 0.787043 | − | 0.616898i | \(-0.211611\pi\) | ||||
0.787043 | + | 0.616898i | \(0.211611\pi\) | |||||||
\(674\) | −1.95539 | −0.0753190 | ||||||||
\(675\) | −3.56465 | −0.137203 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.3817 | −0.860197 | −0.430098 | − | 0.902782i | \(-0.641521\pi\) | ||||
−0.430098 | + | 0.902782i | \(0.641521\pi\) | |||||||
\(678\) | 19.2054 | 0.737577 | ||||||||
\(679\) | −17.3937 | −0.667510 | ||||||||
\(680\) | 6.87800 | 0.263759 | ||||||||
\(681\) | −7.92931 | −0.303852 | ||||||||
\(682\) | −15.9487 | −0.610707 | ||||||||
\(683\) | 9.96482 | 0.381293 | 0.190647 | − | 0.981659i | \(-0.438942\pi\) | ||||
0.190647 | + | 0.981659i | \(0.438942\pi\) | |||||||
\(684\) | −4.93900 | −0.188847 | ||||||||
\(685\) | 3.84595 | 0.146946 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 21.3502 | 0.814561 | ||||||||
\(688\) | 2.91185 | 0.111013 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.500664 | 0.0190600 | ||||||||
\(691\) | −24.9366 | −0.948633 | −0.474317 | − | 0.880354i | \(-0.657305\pi\) | ||||
−0.474317 | + | 0.880354i | \(0.657305\pi\) | |||||||
\(692\) | 3.83446 | 0.145764 | ||||||||
\(693\) | −1.55496 | −0.0590680 | ||||||||
\(694\) | 22.9259 | 0.870254 | ||||||||
\(695\) | 12.6165 | 0.478573 | ||||||||
\(696\) | −2.46681 | −0.0935043 | ||||||||
\(697\) | 63.5870 | 2.40853 | ||||||||
\(698\) | −3.67994 | −0.139288 | ||||||||
\(699\) | 10.3002 | 0.389590 | ||||||||
\(700\) | −3.56465 | −0.134731 | ||||||||
\(701\) | 12.2567 | 0.462928 | 0.231464 | − | 0.972843i | \(-0.425648\pi\) | ||||
0.231464 | + | 0.972843i | \(0.425648\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.7530 | −0.480989 | ||||||||
\(704\) | −1.55496 | −0.0586047 | ||||||||
\(705\) | 9.45281 | 0.356013 | ||||||||
\(706\) | −26.6353 | −1.00243 | ||||||||
\(707\) | 0.674563 | 0.0253696 | ||||||||
\(708\) | −6.13169 | −0.230443 | ||||||||
\(709\) | 27.1825 | 1.02086 | 0.510431 | − | 0.859919i | \(-0.329486\pi\) | ||||
0.510431 | + | 0.859919i | \(0.329486\pi\) | |||||||
\(710\) | 1.44696 | 0.0543035 | ||||||||
\(711\) | −6.67994 | −0.250517 | ||||||||
\(712\) | −3.67456 | −0.137710 | ||||||||
\(713\) | −4.28621 | −0.160520 | ||||||||
\(714\) | −5.74094 | −0.214849 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.48188 | −0.242239 | ||||||||
\(717\) | 19.2814 | 0.720078 | ||||||||
\(718\) | 3.05967 | 0.114186 | ||||||||
\(719\) | 24.6625 | 0.919755 | 0.459878 | − | 0.887982i | \(-0.347893\pi\) | ||||
0.459878 | + | 0.887982i | \(0.347893\pi\) | |||||||
\(720\) | −1.19806 | −0.0446491 | ||||||||
\(721\) | −7.75063 | −0.288648 | ||||||||
\(722\) | 5.39373 | 0.200734 | ||||||||
\(723\) | 10.6920 | 0.397641 | ||||||||
\(724\) | 10.1075 | 0.375643 | ||||||||
\(725\) | 8.79331 | 0.326575 | ||||||||
\(726\) | −8.58211 | −0.318512 | ||||||||
\(727\) | 38.9657 | 1.44516 | 0.722578 | − | 0.691289i | \(-0.242957\pi\) | ||||
0.722578 | + | 0.691289i | \(0.242957\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.02416 | 0.259976 | ||||||||
\(731\) | −16.7168 | −0.618292 | ||||||||
\(732\) | 14.7017 | 0.543391 | ||||||||
\(733\) | 8.73855 | 0.322766 | 0.161383 | − | 0.986892i | \(-0.448405\pi\) | ||||
0.161383 | + | 0.986892i | \(0.448405\pi\) | |||||||
\(734\) | −25.6582 | −0.947060 | ||||||||
\(735\) | −1.19806 | −0.0441912 | ||||||||
\(736\) | −0.417895 | −0.0154038 | ||||||||
\(737\) | 16.4276 | 0.605118 | ||||||||
\(738\) | −11.0761 | −0.407716 | ||||||||
\(739\) | −21.8200 | −0.802661 | −0.401331 | − | 0.915933i | \(-0.631452\pi\) | ||||
−0.401331 | + | 0.915933i | \(0.631452\pi\) | |||||||
\(740\) | −3.09352 | −0.113720 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.62133 | −0.0595210 | ||||||||
\(743\) | −25.6437 | −0.940776 | −0.470388 | − | 0.882460i | \(-0.655886\pi\) | ||||
−0.470388 | + | 0.882460i | \(0.655886\pi\) | |||||||
\(744\) | 10.2567 | 0.376028 | ||||||||
\(745\) | 2.92931 | 0.107322 | ||||||||
\(746\) | −21.6612 | −0.793071 | ||||||||
\(747\) | −9.06100 | −0.331525 | ||||||||
\(748\) | 8.92692 | 0.326401 | ||||||||
\(749\) | −6.20775 | −0.226826 | ||||||||
\(750\) | 10.2610 | 0.374678 | ||||||||
\(751\) | 43.4034 | 1.58381 | 0.791907 | − | 0.610642i | \(-0.209089\pi\) | ||||
0.791907 | + | 0.610642i | \(0.209089\pi\) | |||||||
\(752\) | −7.89008 | −0.287722 | ||||||||
\(753\) | −6.49827 | −0.236810 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26.1613 | −0.952109 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | 39.9111 | 1.45059 | 0.725297 | − | 0.688436i | \(-0.241702\pi\) | ||||
0.725297 | + | 0.688436i | \(0.241702\pi\) | |||||||
\(758\) | 6.93602 | 0.251927 | ||||||||
\(759\) | 0.649809 | 0.0235866 | ||||||||
\(760\) | 5.91723 | 0.214641 | ||||||||
\(761\) | −3.46011 | −0.125429 | −0.0627144 | − | 0.998032i | \(-0.519976\pi\) | ||||
−0.0627144 | + | 0.998032i | \(0.519976\pi\) | |||||||
\(762\) | 6.72886 | 0.243761 | ||||||||
\(763\) | −4.91185 | −0.177821 | ||||||||
\(764\) | 22.9681 | 0.830956 | ||||||||
\(765\) | 6.87800 | 0.248675 | ||||||||
\(766\) | −19.9734 | −0.721670 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 31.8146 | 1.14726 | 0.573632 | − | 0.819113i | \(-0.305534\pi\) | ||||
0.573632 | + | 0.819113i | \(0.305534\pi\) | |||||||
\(770\) | 1.86294 | 0.0671356 | ||||||||
\(771\) | 0.907542 | 0.0326843 | ||||||||
\(772\) | −4.37435 | −0.157436 | ||||||||
\(773\) | 1.18300 | 0.0425494 | 0.0212747 | − | 0.999774i | \(-0.493228\pi\) | ||||
0.0212747 | + | 0.999774i | \(0.493228\pi\) | |||||||
\(774\) | 2.91185 | 0.104664 | ||||||||
\(775\) | −36.5614 | −1.31332 | ||||||||
\(776\) | −17.3937 | −0.624399 | ||||||||
\(777\) | 2.58211 | 0.0926325 | ||||||||
\(778\) | −30.7289 | −1.10168 | ||||||||
\(779\) | 54.7047 | 1.96000 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.87800 | 0.0672002 | ||||||||
\(782\) | 2.39911 | 0.0857919 | ||||||||
\(783\) | −2.46681 | −0.0881567 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −18.4021 | −0.656799 | ||||||||
\(786\) | 3.19269 | 0.113879 | ||||||||
\(787\) | −15.2553 | −0.543794 | −0.271897 | − | 0.962326i | \(-0.587651\pi\) | ||||
−0.271897 | + | 0.962326i | \(0.587651\pi\) | |||||||
\(788\) | −4.90515 | −0.174739 | ||||||||
\(789\) | 17.1564 | 0.610785 | ||||||||
\(790\) | 8.00298 | 0.284733 | ||||||||
\(791\) | 19.2054 | 0.682864 | ||||||||
\(792\) | −1.55496 | −0.0552530 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 12.3405 | 0.437948 | ||||||||
\(795\) | 1.94246 | 0.0688919 | ||||||||
\(796\) | −7.73125 | −0.274027 | ||||||||
\(797\) | −20.1575 | −0.714015 | −0.357008 | − | 0.934101i | \(-0.616203\pi\) | ||||
−0.357008 | + | 0.934101i | \(0.616203\pi\) | |||||||
\(798\) | −4.93900 | −0.174839 | ||||||||
\(799\) | 45.2965 | 1.60247 | ||||||||
\(800\) | −3.56465 | −0.126029 | ||||||||
\(801\) | −3.67456 | −0.129834 | ||||||||
\(802\) | −10.2241 | −0.361027 | ||||||||
\(803\) | 9.11662 | 0.321719 | ||||||||
\(804\) | −10.5646 | −0.372586 | ||||||||
\(805\) | 0.500664 | 0.0176461 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.7047 | −0.693638 | ||||||||
\(808\) | 0.674563 | 0.0237310 | ||||||||
\(809\) | −27.9842 | −0.983872 | −0.491936 | − | 0.870631i | \(-0.663711\pi\) | ||||
−0.491936 | + | 0.870631i | \(0.663711\pi\) | |||||||
\(810\) | −1.19806 | −0.0420956 | ||||||||
\(811\) | −43.1196 | −1.51413 | −0.757067 | − | 0.653337i | \(-0.773368\pi\) | ||||
−0.757067 | + | 0.653337i | \(0.773368\pi\) | |||||||
\(812\) | −2.46681 | −0.0865681 | ||||||||
\(813\) | −16.0194 | −0.561824 | ||||||||
\(814\) | −4.01507 | −0.140728 | ||||||||
\(815\) | 19.2782 | 0.675285 | ||||||||
\(816\) | −5.74094 | −0.200973 | ||||||||
\(817\) | −14.3817 | −0.503150 | ||||||||
\(818\) | −14.0127 | −0.489942 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.2698 | 0.463402 | ||||||||
\(821\) | 46.3075 | 1.61614 | 0.808072 | − | 0.589084i | \(-0.200511\pi\) | ||||
0.808072 | + | 0.589084i | \(0.200511\pi\) | |||||||
\(822\) | −3.21014 | −0.111967 | ||||||||
\(823\) | 0.214456 | 0.00747546 | 0.00373773 | − | 0.999993i | \(-0.498810\pi\) | ||||
0.00373773 | + | 0.999993i | \(0.498810\pi\) | |||||||
\(824\) | −7.75063 | −0.270006 | ||||||||
\(825\) | 5.54288 | 0.192978 | ||||||||
\(826\) | −6.13169 | −0.213349 | ||||||||
\(827\) | −5.83100 | −0.202764 | −0.101382 | − | 0.994848i | \(-0.532326\pi\) | ||||
−0.101382 | + | 0.994848i | \(0.532326\pi\) | |||||||
\(828\) | −0.417895 | −0.0145228 | ||||||||
\(829\) | −11.0718 | −0.384538 | −0.192269 | − | 0.981342i | \(-0.561585\pi\) | ||||
−0.192269 | + | 0.981342i | \(0.561585\pi\) | |||||||
\(830\) | 10.8556 | 0.376805 | ||||||||
\(831\) | −10.6571 | −0.369691 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.74094 | −0.198912 | ||||||||
\(834\) | −10.5308 | −0.364652 | ||||||||
\(835\) | 7.97333 | 0.275928 | ||||||||
\(836\) | 7.67994 | 0.265616 | ||||||||
\(837\) | 10.2567 | 0.354522 | ||||||||
\(838\) | 1.10859 | 0.0382955 | ||||||||
\(839\) | −49.6601 | −1.71446 | −0.857228 | − | 0.514936i | \(-0.827815\pi\) | ||||
−0.857228 | + | 0.514936i | \(0.827815\pi\) | |||||||
\(840\) | −1.19806 | −0.0413371 | ||||||||
\(841\) | −22.9148 | −0.790167 | ||||||||
\(842\) | 5.63342 | 0.194140 | ||||||||
\(843\) | 28.6286 | 0.986022 | ||||||||
\(844\) | 6.35690 | 0.218813 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.89008 | −0.271267 | ||||||||
\(847\) | −8.58211 | −0.294885 | ||||||||
\(848\) | −1.62133 | −0.0556768 | ||||||||
\(849\) | −7.11960 | −0.244344 | ||||||||
\(850\) | 20.4644 | 0.701924 | ||||||||
\(851\) | −1.07905 | −0.0369893 | ||||||||
\(852\) | −1.20775 | −0.0413769 | ||||||||
\(853\) | −45.7120 | −1.56515 | −0.782574 | − | 0.622557i | \(-0.786094\pi\) | ||||
−0.782574 | + | 0.622557i | \(0.786094\pi\) | |||||||
\(854\) | 14.7017 | 0.503082 | ||||||||
\(855\) | 5.91723 | 0.202365 | ||||||||
\(856\) | −6.20775 | −0.212177 | ||||||||
\(857\) | 27.3913 | 0.935670 | 0.467835 | − | 0.883816i | \(-0.345034\pi\) | ||||
0.467835 | + | 0.883816i | \(0.345034\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.4325 | −1.20894 | −0.604470 | − | 0.796628i | \(-0.706615\pi\) | ||||
−0.604470 | + | 0.796628i | \(0.706615\pi\) | |||||||
\(860\) | −3.48858 | −0.118960 | ||||||||
\(861\) | −11.0761 | −0.377471 | ||||||||
\(862\) | −18.6907 | −0.636608 | ||||||||
\(863\) | −10.0489 | −0.342069 | −0.171035 | − | 0.985265i | \(-0.554711\pi\) | ||||
−0.171035 | + | 0.985265i | \(0.554711\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −4.59392 | −0.156198 | ||||||||
\(866\) | −26.2640 | −0.892486 | ||||||||
\(867\) | 15.9584 | 0.541975 | ||||||||
\(868\) | 10.2567 | 0.348134 | ||||||||
\(869\) | 10.3870 | 0.352356 | ||||||||
\(870\) | 2.95539 | 0.100197 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −4.91185 | −0.166336 | ||||||||
\(873\) | −17.3937 | −0.588689 | ||||||||
\(874\) | 2.06398 | 0.0698153 | ||||||||
\(875\) | 10.2610 | 0.346884 | ||||||||
\(876\) | −5.86294 | −0.198090 | ||||||||
\(877\) | 43.7676 | 1.47793 | 0.738964 | − | 0.673745i | \(-0.235316\pi\) | ||||
0.738964 | + | 0.673745i | \(0.235316\pi\) | |||||||
\(878\) | 11.8092 | 0.398542 | ||||||||
\(879\) | −25.0978 | −0.846529 | ||||||||
\(880\) | 1.86294 | 0.0627996 | ||||||||
\(881\) | 15.3612 | 0.517532 | 0.258766 | − | 0.965940i | \(-0.416684\pi\) | ||||
0.258766 | + | 0.965940i | \(0.416684\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | −6.10752 | −0.205535 | −0.102767 | − | 0.994705i | \(-0.532770\pi\) | ||||
−0.102767 | + | 0.994705i | \(0.532770\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.34614 | 0.246938 | ||||||||
\(886\) | 7.16660 | 0.240767 | ||||||||
\(887\) | −7.64801 | −0.256795 | −0.128397 | − | 0.991723i | \(-0.540983\pi\) | ||||
−0.128397 | + | 0.991723i | \(0.540983\pi\) | |||||||
\(888\) | 2.58211 | 0.0866498 | ||||||||
\(889\) | 6.72886 | 0.225679 | ||||||||
\(890\) | 4.40236 | 0.147567 | ||||||||
\(891\) | −1.55496 | −0.0520931 | ||||||||
\(892\) | 6.49157 | 0.217354 | ||||||||
\(893\) | 38.9691 | 1.30405 | ||||||||
\(894\) | −2.44504 | −0.0817744 | ||||||||
\(895\) | 7.76569 | 0.259578 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −31.3357 | −1.04569 | ||||||||
\(899\) | −25.3013 | −0.843845 | ||||||||
\(900\) | −3.56465 | −0.118822 | ||||||||
\(901\) | 9.30798 | 0.310094 | ||||||||
\(902\) | 17.2228 | 0.573457 | ||||||||
\(903\) | 2.91185 | 0.0969004 | ||||||||
\(904\) | 19.2054 | 0.638761 | ||||||||
\(905\) | −12.1094 | −0.402531 | ||||||||
\(906\) | 21.8364 | 0.725465 | ||||||||
\(907\) | 33.3038 | 1.10583 | 0.552917 | − | 0.833236i | \(-0.313515\pi\) | ||||
0.552917 | + | 0.833236i | \(0.313515\pi\) | |||||||
\(908\) | −7.92931 | −0.263143 | ||||||||
\(909\) | 0.674563 | 0.0223738 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.0780 | 0.665213 | 0.332607 | − | 0.943066i | \(-0.392072\pi\) | ||||
0.332607 | + | 0.943066i | \(0.392072\pi\) | |||||||
\(912\) | −4.93900 | −0.163547 | ||||||||
\(913\) | 14.0895 | 0.466294 | ||||||||
\(914\) | 25.4058 | 0.840350 | ||||||||
\(915\) | −17.6136 | −0.582286 | ||||||||
\(916\) | 21.3502 | 0.705430 | ||||||||
\(917\) | 3.19269 | 0.105432 | ||||||||
\(918\) | −5.74094 | −0.189479 | ||||||||
\(919\) | 46.9541 | 1.54887 | 0.774436 | − | 0.632652i | \(-0.218034\pi\) | ||||
0.774436 | + | 0.632652i | \(0.218034\pi\) | |||||||
\(920\) | 0.500664 | 0.0165064 | ||||||||
\(921\) | 8.36658 | 0.275688 | ||||||||
\(922\) | 37.0417 | 1.21990 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.55496 | −0.0511544 | ||||||||
\(925\) | −9.20429 | −0.302635 | ||||||||
\(926\) | 10.2929 | 0.338246 | ||||||||
\(927\) | −7.75063 | −0.254564 | ||||||||
\(928\) | −2.46681 | −0.0809771 | ||||||||
\(929\) | 3.66727 | 0.120319 | 0.0601596 | − | 0.998189i | \(-0.480839\pi\) | ||||
0.0601596 | + | 0.998189i | \(0.480839\pi\) | |||||||
\(930\) | −12.2881 | −0.402944 | ||||||||
\(931\) | −4.93900 | −0.161869 | ||||||||
\(932\) | 10.3002 | 0.337395 | ||||||||
\(933\) | −21.6668 | −0.709339 | ||||||||
\(934\) | −12.1890 | −0.398835 | ||||||||
\(935\) | −10.6950 | −0.349764 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.10992 | −0.101597 | −0.0507983 | − | 0.998709i | \(-0.516177\pi\) | ||||
−0.0507983 | + | 0.998709i | \(0.516177\pi\) | |||||||
\(938\) | −10.5646 | −0.344948 | ||||||||
\(939\) | 14.6950 | 0.479553 | ||||||||
\(940\) | 9.45281 | 0.308317 | ||||||||
\(941\) | 7.25475 | 0.236498 | 0.118249 | − | 0.992984i | \(-0.462272\pi\) | ||||
0.118249 | + | 0.992984i | \(0.462272\pi\) | |||||||
\(942\) | 15.3599 | 0.500452 | ||||||||
\(943\) | 4.62863 | 0.150729 | ||||||||
\(944\) | −6.13169 | −0.199569 | ||||||||
\(945\) | −1.19806 | −0.0389730 | ||||||||
\(946\) | −4.52781 | −0.147212 | ||||||||
\(947\) | 9.91782 | 0.322286 | 0.161143 | − | 0.986931i | \(-0.448482\pi\) | ||||
0.161143 | + | 0.986931i | \(0.448482\pi\) | |||||||
\(948\) | −6.67994 | −0.216954 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 17.6058 | 0.571207 | ||||||||
\(951\) | −27.1672 | −0.880957 | ||||||||
\(952\) | −5.74094 | −0.186065 | ||||||||
\(953\) | −0.0204423 | −0.000662191 0 | −0.000331096 | − | 1.00000i | \(-0.500105\pi\) | ||||
−0.000331096 | 1.00000i | \(0.500105\pi\) | ||||||||
\(954\) | −1.62133 | −0.0524926 | ||||||||
\(955\) | −27.5172 | −0.890435 | ||||||||
\(956\) | 19.2814 | 0.623606 | ||||||||
\(957\) | 3.83579 | 0.123993 | ||||||||
\(958\) | −42.4413 | −1.37122 | ||||||||
\(959\) | −3.21014 | −0.103661 | ||||||||
\(960\) | −1.19806 | −0.0386673 | ||||||||
\(961\) | 74.1992 | 2.39352 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.20775 | −0.200042 | ||||||||
\(964\) | 10.6920 | 0.344367 | ||||||||
\(965\) | 5.24075 | 0.168706 | ||||||||
\(966\) | −0.417895 | −0.0134455 | ||||||||
\(967\) | 13.2731 | 0.426833 | 0.213416 | − | 0.976961i | \(-0.431541\pi\) | ||||
0.213416 | + | 0.976961i | \(0.431541\pi\) | |||||||
\(968\) | −8.58211 | −0.275839 | ||||||||
\(969\) | 28.3545 | 0.910878 | ||||||||
\(970\) | 20.8388 | 0.669093 | ||||||||
\(971\) | 55.2409 | 1.77276 | 0.886382 | − | 0.462955i | \(-0.153211\pi\) | ||||
0.886382 | + | 0.462955i | \(0.153211\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −10.5308 | −0.337602 | ||||||||
\(974\) | 7.26742 | 0.232863 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.7017 | 0.470590 | ||||||||
\(977\) | 35.9235 | 1.14929 | 0.574647 | − | 0.818402i | \(-0.305139\pi\) | ||||
0.574647 | + | 0.818402i | \(0.305139\pi\) | |||||||
\(978\) | −16.0911 | −0.514538 | ||||||||
\(979\) | 5.71379 | 0.182614 | ||||||||
\(980\) | −1.19806 | −0.0382707 | ||||||||
\(981\) | −4.91185 | −0.156823 | ||||||||
\(982\) | 14.3763 | 0.458765 | ||||||||
\(983\) | −31.1360 | −0.993084 | −0.496542 | − | 0.868013i | \(-0.665397\pi\) | ||||
−0.496542 | + | 0.868013i | \(0.665397\pi\) | |||||||
\(984\) | −11.0761 | −0.353092 | ||||||||
\(985\) | 5.87667 | 0.187246 | ||||||||
\(986\) | 14.1618 | 0.451004 | ||||||||
\(987\) | −7.89008 | −0.251144 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.21685 | −0.0386935 | ||||||||
\(990\) | 1.86294 | 0.0592080 | ||||||||
\(991\) | −51.4161 | −1.63329 | −0.816643 | − | 0.577143i | \(-0.804167\pi\) | ||||
−0.816643 | + | 0.577143i | \(0.804167\pi\) | |||||||
\(992\) | 10.2567 | 0.325650 | ||||||||
\(993\) | −30.9885 | −0.983391 | ||||||||
\(994\) | −1.20775 | −0.0383075 | ||||||||
\(995\) | 9.26252 | 0.293642 | ||||||||
\(996\) | −9.06100 | −0.287109 | ||||||||
\(997\) | −32.4993 | −1.02926 | −0.514632 | − | 0.857411i | \(-0.672072\pi\) | ||||
−0.514632 | + | 0.857411i | \(0.672072\pi\) | |||||||
\(998\) | 5.55602 | 0.175873 | ||||||||
\(999\) | 2.58211 | 0.0816942 |
(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 | 7098.2.a.cl.1.3 | yes | 3 | |
13.12 | even | 2 | 7098.2.a.cg.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.cg.1.1 | ✓ | 3 | 13.12 | even | 2 | ||
7098.2.a.cl.1.3 | yes | 3 | 1.1 | even | 1 | trivial |