Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.84393 | −1.30385 | −0.651927 | − | 0.758282i | \(-0.726039\pi\) | ||||
−0.651927 | + | 0.758282i | \(0.726039\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.40007 | 0.700034 | ||||||||
\(5\) | 2.87244 | 1.28459 | 0.642296 | − | 0.766456i | \(-0.277982\pi\) | ||||
0.642296 | + | 0.766456i | \(0.277982\pi\) | |||||||
\(6\) | 1.84393 | 0.752780 | ||||||||
\(7\) | −1.74244 | −0.658581 | −0.329290 | − | 0.944229i | \(-0.606809\pi\) | ||||
−0.329290 | + | 0.944229i | \(0.606809\pi\) | |||||||
\(8\) | 1.10623 | 0.391111 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.29656 | −1.67492 | ||||||||
\(11\) | −6.38626 | −1.92553 | −0.962765 | − | 0.270339i | \(-0.912864\pi\) | ||||
−0.962765 | + | 0.270339i | \(0.912864\pi\) | |||||||
\(12\) | −1.40007 | −0.404165 | ||||||||
\(13\) | 4.06957 | 1.12870 | 0.564348 | − | 0.825537i | \(-0.309127\pi\) | ||||
0.564348 | + | 0.825537i | \(0.309127\pi\) | |||||||
\(14\) | 3.21293 | 0.858693 | ||||||||
\(15\) | −2.87244 | −0.741660 | ||||||||
\(16\) | −4.83995 | −1.20999 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.84393 | −0.434618 | ||||||||
\(19\) | −6.09433 | −1.39813 | −0.699067 | − | 0.715056i | \(-0.746401\pi\) | ||||
−0.699067 | + | 0.715056i | \(0.746401\pi\) | |||||||
\(20\) | 4.02161 | 0.899259 | ||||||||
\(21\) | 1.74244 | 0.380232 | ||||||||
\(22\) | 11.7758 | 2.51061 | ||||||||
\(23\) | −8.30391 | −1.73148 | −0.865742 | − | 0.500490i | \(-0.833153\pi\) | ||||
−0.865742 | + | 0.500490i | \(0.833153\pi\) | |||||||
\(24\) | −1.10623 | −0.225808 | ||||||||
\(25\) | 3.25089 | 0.650178 | ||||||||
\(26\) | −7.50400 | −1.47166 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.43954 | −0.461029 | ||||||||
\(29\) | −3.49057 | −0.648182 | −0.324091 | − | 0.946026i | \(-0.605058\pi\) | ||||
−0.324091 | + | 0.946026i | \(0.605058\pi\) | |||||||
\(30\) | 5.29656 | 0.967016 | ||||||||
\(31\) | −4.29002 | −0.770511 | −0.385256 | − | 0.922810i | \(-0.625887\pi\) | ||||
−0.385256 | + | 0.922810i | \(0.625887\pi\) | |||||||
\(32\) | 6.71205 | 1.18653 | ||||||||
\(33\) | 6.38626 | 1.11171 | ||||||||
\(34\) | 1.84393 | 0.316231 | ||||||||
\(35\) | −5.00505 | −0.846008 | ||||||||
\(36\) | 1.40007 | 0.233345 | ||||||||
\(37\) | −7.30902 | −1.20159 | −0.600797 | − | 0.799401i | \(-0.705150\pi\) | ||||
−0.600797 | + | 0.799401i | \(0.705150\pi\) | |||||||
\(38\) | 11.2375 | 1.82296 | ||||||||
\(39\) | −4.06957 | −0.651653 | ||||||||
\(40\) | 3.17758 | 0.502419 | ||||||||
\(41\) | 6.07531 | 0.948804 | 0.474402 | − | 0.880308i | \(-0.342664\pi\) | ||||
0.474402 | + | 0.880308i | \(0.342664\pi\) | |||||||
\(42\) | −3.21293 | −0.495767 | ||||||||
\(43\) | −0.766371 | −0.116870 | −0.0584352 | − | 0.998291i | \(-0.518611\pi\) | ||||
−0.0584352 | + | 0.998291i | \(0.518611\pi\) | |||||||
\(44\) | −8.94120 | −1.34794 | ||||||||
\(45\) | 2.87244 | 0.428198 | ||||||||
\(46\) | 15.3118 | 2.25760 | ||||||||
\(47\) | −5.74712 | −0.838304 | −0.419152 | − | 0.907916i | \(-0.637672\pi\) | ||||
−0.419152 | + | 0.907916i | \(0.637672\pi\) | |||||||
\(48\) | 4.83995 | 0.698586 | ||||||||
\(49\) | −3.96390 | −0.566271 | ||||||||
\(50\) | −5.99441 | −0.847737 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 5.69768 | 0.790126 | ||||||||
\(53\) | −12.5814 | −1.72819 | −0.864096 | − | 0.503326i | \(-0.832109\pi\) | ||||
−0.864096 | + | 0.503326i | \(0.832109\pi\) | |||||||
\(54\) | 1.84393 | 0.250927 | ||||||||
\(55\) | −18.3441 | −2.47352 | ||||||||
\(56\) | −1.92754 | −0.257578 | ||||||||
\(57\) | 6.09433 | 0.807213 | ||||||||
\(58\) | 6.43635 | 0.845134 | ||||||||
\(59\) | −12.0709 | −1.57150 | −0.785748 | − | 0.618546i | \(-0.787722\pi\) | ||||
−0.785748 | + | 0.618546i | \(0.787722\pi\) | |||||||
\(60\) | −4.02161 | −0.519187 | ||||||||
\(61\) | 10.8757 | 1.39249 | 0.696245 | − | 0.717804i | \(-0.254853\pi\) | ||||
0.696245 | + | 0.717804i | \(0.254853\pi\) | |||||||
\(62\) | 7.91049 | 1.00463 | ||||||||
\(63\) | −1.74244 | −0.219527 | ||||||||
\(64\) | −2.69664 | −0.337080 | ||||||||
\(65\) | 11.6896 | 1.44992 | ||||||||
\(66\) | −11.7758 | −1.44950 | ||||||||
\(67\) | −11.7712 | −1.43808 | −0.719042 | − | 0.694967i | \(-0.755419\pi\) | ||||
−0.719042 | + | 0.694967i | \(0.755419\pi\) | |||||||
\(68\) | −1.40007 | −0.169783 | ||||||||
\(69\) | 8.30391 | 0.999673 | ||||||||
\(70\) | 9.22895 | 1.10307 | ||||||||
\(71\) | 8.95117 | 1.06231 | 0.531154 | − | 0.847275i | \(-0.321759\pi\) | ||||
0.531154 | + | 0.847275i | \(0.321759\pi\) | |||||||
\(72\) | 1.10623 | 0.130370 | ||||||||
\(73\) | −2.35685 | −0.275848 | −0.137924 | − | 0.990443i | \(-0.544043\pi\) | ||||
−0.137924 | + | 0.990443i | \(0.544043\pi\) | |||||||
\(74\) | 13.4773 | 1.56670 | ||||||||
\(75\) | −3.25089 | −0.375380 | ||||||||
\(76\) | −8.53248 | −0.978742 | ||||||||
\(77\) | 11.1277 | 1.26812 | ||||||||
\(78\) | 7.50400 | 0.849661 | ||||||||
\(79\) | 9.35621 | 1.05266 | 0.526328 | − | 0.850282i | \(-0.323568\pi\) | ||||
0.526328 | + | 0.850282i | \(0.323568\pi\) | |||||||
\(80\) | −13.9024 | −1.55434 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −11.2024 | −1.23710 | ||||||||
\(83\) | 13.8585 | 1.52117 | 0.760585 | − | 0.649238i | \(-0.224912\pi\) | ||||
0.760585 | + | 0.649238i | \(0.224912\pi\) | |||||||
\(84\) | 2.43954 | 0.266175 | ||||||||
\(85\) | −2.87244 | −0.311559 | ||||||||
\(86\) | 1.41313 | 0.152382 | ||||||||
\(87\) | 3.49057 | 0.374228 | ||||||||
\(88\) | −7.06468 | −0.753097 | ||||||||
\(89\) | −4.68455 | −0.496562 | −0.248281 | − | 0.968688i | \(-0.579866\pi\) | ||||
−0.248281 | + | 0.968688i | \(0.579866\pi\) | |||||||
\(90\) | −5.29656 | −0.558307 | ||||||||
\(91\) | −7.09099 | −0.743338 | ||||||||
\(92\) | −11.6260 | −1.21210 | ||||||||
\(93\) | 4.29002 | 0.444855 | ||||||||
\(94\) | 10.5973 | 1.09303 | ||||||||
\(95\) | −17.5056 | −1.79603 | ||||||||
\(96\) | −6.71205 | −0.685045 | ||||||||
\(97\) | −1.63896 | −0.166411 | −0.0832056 | − | 0.996532i | \(-0.526516\pi\) | ||||
−0.0832056 | + | 0.996532i | \(0.526516\pi\) | |||||||
\(98\) | 7.30914 | 0.738335 | ||||||||
\(99\) | −6.38626 | −0.641843 | ||||||||
\(100\) | 4.55147 | 0.455147 | ||||||||
\(101\) | −6.70134 | −0.666808 | −0.333404 | − | 0.942784i | \(-0.608197\pi\) | ||||
−0.333404 | + | 0.942784i | \(0.608197\pi\) | |||||||
\(102\) | −1.84393 | −0.182576 | ||||||||
\(103\) | 7.08223 | 0.697833 | 0.348917 | − | 0.937154i | \(-0.386550\pi\) | ||||
0.348917 | + | 0.937154i | \(0.386550\pi\) | |||||||
\(104\) | 4.50189 | 0.441446 | ||||||||
\(105\) | 5.00505 | 0.488443 | ||||||||
\(106\) | 23.1993 | 2.25331 | ||||||||
\(107\) | 13.0973 | 1.26616 | 0.633080 | − | 0.774086i | \(-0.281790\pi\) | ||||
0.633080 | + | 0.774086i | \(0.281790\pi\) | |||||||
\(108\) | −1.40007 | −0.134722 | ||||||||
\(109\) | −3.34572 | −0.320462 | −0.160231 | − | 0.987080i | \(-0.551224\pi\) | ||||
−0.160231 | + | 0.987080i | \(0.551224\pi\) | |||||||
\(110\) | 33.8252 | 3.22511 | ||||||||
\(111\) | 7.30902 | 0.693741 | ||||||||
\(112\) | 8.43332 | 0.796874 | ||||||||
\(113\) | 11.0536 | 1.03983 | 0.519916 | − | 0.854217i | \(-0.325963\pi\) | ||||
0.519916 | + | 0.854217i | \(0.325963\pi\) | |||||||
\(114\) | −11.2375 | −1.05249 | ||||||||
\(115\) | −23.8524 | −2.22425 | ||||||||
\(116\) | −4.88703 | −0.453750 | ||||||||
\(117\) | 4.06957 | 0.376232 | ||||||||
\(118\) | 22.2579 | 2.04900 | ||||||||
\(119\) | 1.74244 | 0.159729 | ||||||||
\(120\) | −3.17758 | −0.290072 | ||||||||
\(121\) | 29.7843 | 2.70767 | ||||||||
\(122\) | −20.0540 | −1.81560 | ||||||||
\(123\) | −6.07531 | −0.547792 | ||||||||
\(124\) | −6.00633 | −0.539384 | ||||||||
\(125\) | −5.02421 | −0.449379 | ||||||||
\(126\) | 3.21293 | 0.286231 | ||||||||
\(127\) | 16.6414 | 1.47668 | 0.738342 | − | 0.674427i | \(-0.235609\pi\) | ||||
0.738342 | + | 0.674427i | \(0.235609\pi\) | |||||||
\(128\) | −8.45169 | −0.747031 | ||||||||
\(129\) | 0.766371 | 0.0674752 | ||||||||
\(130\) | −21.5548 | −1.89048 | ||||||||
\(131\) | 14.6603 | 1.28087 | 0.640436 | − | 0.768011i | \(-0.278754\pi\) | ||||
0.640436 | + | 0.768011i | \(0.278754\pi\) | |||||||
\(132\) | 8.94120 | 0.778232 | ||||||||
\(133\) | 10.6190 | 0.920785 | ||||||||
\(134\) | 21.7053 | 1.87505 | ||||||||
\(135\) | −2.87244 | −0.247220 | ||||||||
\(136\) | −1.10623 | −0.0948585 | ||||||||
\(137\) | 18.7892 | 1.60527 | 0.802634 | − | 0.596472i | \(-0.203431\pi\) | ||||
0.802634 | + | 0.596472i | \(0.203431\pi\) | |||||||
\(138\) | −15.3118 | −1.30343 | ||||||||
\(139\) | 14.7231 | 1.24880 | 0.624399 | − | 0.781106i | \(-0.285344\pi\) | ||||
0.624399 | + | 0.781106i | \(0.285344\pi\) | |||||||
\(140\) | −7.00741 | −0.592234 | ||||||||
\(141\) | 5.74712 | 0.483995 | ||||||||
\(142\) | −16.5053 | −1.38509 | ||||||||
\(143\) | −25.9894 | −2.17334 | ||||||||
\(144\) | −4.83995 | −0.403329 | ||||||||
\(145\) | −10.0264 | −0.832650 | ||||||||
\(146\) | 4.34585 | 0.359665 | ||||||||
\(147\) | 3.96390 | 0.326937 | ||||||||
\(148\) | −10.2331 | −0.841158 | ||||||||
\(149\) | 6.73151 | 0.551467 | 0.275733 | − | 0.961234i | \(-0.411079\pi\) | ||||
0.275733 | + | 0.961234i | \(0.411079\pi\) | |||||||
\(150\) | 5.99441 | 0.489441 | ||||||||
\(151\) | 7.59344 | 0.617946 | 0.308973 | − | 0.951071i | \(-0.400015\pi\) | ||||
0.308973 | + | 0.951071i | \(0.400015\pi\) | |||||||
\(152\) | −6.74173 | −0.546827 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −20.5186 | −1.65344 | ||||||||
\(155\) | −12.3228 | −0.989793 | ||||||||
\(156\) | −5.69768 | −0.456180 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | −17.2522 | −1.37251 | ||||||||
\(159\) | 12.5814 | 0.997773 | ||||||||
\(160\) | 19.2799 | 1.52421 | ||||||||
\(161\) | 14.4691 | 1.14032 | ||||||||
\(162\) | −1.84393 | −0.144873 | ||||||||
\(163\) | −22.5844 | −1.76895 | −0.884475 | − | 0.466587i | \(-0.845483\pi\) | ||||
−0.884475 | + | 0.466587i | \(0.845483\pi\) | |||||||
\(164\) | 8.50585 | 0.664195 | ||||||||
\(165\) | 18.3441 | 1.42809 | ||||||||
\(166\) | −25.5541 | −1.98338 | ||||||||
\(167\) | −12.0242 | −0.930461 | −0.465231 | − | 0.885190i | \(-0.654029\pi\) | ||||
−0.465231 | + | 0.885190i | \(0.654029\pi\) | |||||||
\(168\) | 1.92754 | 0.148713 | ||||||||
\(169\) | 3.56143 | 0.273956 | ||||||||
\(170\) | 5.29656 | 0.406228 | ||||||||
\(171\) | −6.09433 | −0.466045 | ||||||||
\(172\) | −1.07297 | −0.0818133 | ||||||||
\(173\) | −2.15505 | −0.163846 | −0.0819228 | − | 0.996639i | \(-0.526106\pi\) | ||||
−0.0819228 | + | 0.996639i | \(0.526106\pi\) | |||||||
\(174\) | −6.43635 | −0.487939 | ||||||||
\(175\) | −5.66448 | −0.428195 | ||||||||
\(176\) | 30.9092 | 2.32987 | ||||||||
\(177\) | 12.0709 | 0.907304 | ||||||||
\(178\) | 8.63797 | 0.647444 | ||||||||
\(179\) | 12.8703 | 0.961974 | 0.480987 | − | 0.876728i | \(-0.340278\pi\) | ||||
0.480987 | + | 0.876728i | \(0.340278\pi\) | |||||||
\(180\) | 4.02161 | 0.299753 | ||||||||
\(181\) | −15.4372 | −1.14744 | −0.573719 | − | 0.819052i | \(-0.694500\pi\) | ||||
−0.573719 | + | 0.819052i | \(0.694500\pi\) | |||||||
\(182\) | 13.0753 | 0.969204 | ||||||||
\(183\) | −10.8757 | −0.803955 | ||||||||
\(184\) | −9.18603 | −0.677203 | ||||||||
\(185\) | −20.9947 | −1.54356 | ||||||||
\(186\) | −7.91049 | −0.580025 | ||||||||
\(187\) | 6.38626 | 0.467010 | ||||||||
\(188\) | −8.04636 | −0.586841 | ||||||||
\(189\) | 1.74244 | 0.126744 | ||||||||
\(190\) | 32.2790 | 2.34176 | ||||||||
\(191\) | 8.39748 | 0.607620 | 0.303810 | − | 0.952733i | \(-0.401741\pi\) | ||||
0.303810 | + | 0.952733i | \(0.401741\pi\) | |||||||
\(192\) | 2.69664 | 0.194613 | ||||||||
\(193\) | 6.68955 | 0.481524 | 0.240762 | − | 0.970584i | \(-0.422603\pi\) | ||||
0.240762 | + | 0.970584i | \(0.422603\pi\) | |||||||
\(194\) | 3.02212 | 0.216976 | ||||||||
\(195\) | −11.6896 | −0.837109 | ||||||||
\(196\) | −5.54973 | −0.396409 | ||||||||
\(197\) | −10.0098 | −0.713169 | −0.356584 | − | 0.934263i | \(-0.616059\pi\) | ||||
−0.356584 | + | 0.934263i | \(0.616059\pi\) | |||||||
\(198\) | 11.7758 | 0.836870 | ||||||||
\(199\) | 18.0143 | 1.27700 | 0.638499 | − | 0.769623i | \(-0.279556\pi\) | ||||
0.638499 | + | 0.769623i | \(0.279556\pi\) | |||||||
\(200\) | 3.59623 | 0.254292 | ||||||||
\(201\) | 11.7712 | 0.830278 | ||||||||
\(202\) | 12.3568 | 0.869420 | ||||||||
\(203\) | 6.08211 | 0.426880 | ||||||||
\(204\) | 1.40007 | 0.0980244 | ||||||||
\(205\) | 17.4509 | 1.21883 | ||||||||
\(206\) | −13.0591 | −0.909872 | ||||||||
\(207\) | −8.30391 | −0.577161 | ||||||||
\(208\) | −19.6965 | −1.36571 | ||||||||
\(209\) | 38.9200 | 2.69215 | ||||||||
\(210\) | −9.22895 | −0.636858 | ||||||||
\(211\) | 11.3747 | 0.783070 | 0.391535 | − | 0.920163i | \(-0.371944\pi\) | ||||
0.391535 | + | 0.920163i | \(0.371944\pi\) | |||||||
\(212\) | −17.6149 | −1.20979 | ||||||||
\(213\) | −8.95117 | −0.613324 | ||||||||
\(214\) | −24.1504 | −1.65089 | ||||||||
\(215\) | −2.20135 | −0.150131 | ||||||||
\(216\) | −1.10623 | −0.0752694 | ||||||||
\(217\) | 7.47511 | 0.507444 | ||||||||
\(218\) | 6.16927 | 0.417836 | ||||||||
\(219\) | 2.35685 | 0.159261 | ||||||||
\(220\) | −25.6830 | −1.73155 | ||||||||
\(221\) | −4.06957 | −0.273749 | ||||||||
\(222\) | −13.4773 | −0.904537 | ||||||||
\(223\) | −6.20725 | −0.415668 | −0.207834 | − | 0.978164i | \(-0.566641\pi\) | ||||
−0.207834 | + | 0.978164i | \(0.566641\pi\) | |||||||
\(224\) | −11.6953 | −0.781428 | ||||||||
\(225\) | 3.25089 | 0.216726 | ||||||||
\(226\) | −20.3820 | −1.35579 | ||||||||
\(227\) | 1.84375 | 0.122374 | 0.0611870 | − | 0.998126i | \(-0.480511\pi\) | ||||
0.0611870 | + | 0.998126i | \(0.480511\pi\) | |||||||
\(228\) | 8.53248 | 0.565077 | ||||||||
\(229\) | 23.4872 | 1.55208 | 0.776039 | − | 0.630684i | \(-0.217226\pi\) | ||||
0.776039 | + | 0.630684i | \(0.217226\pi\) | |||||||
\(230\) | 43.9822 | 2.90010 | ||||||||
\(231\) | −11.1277 | −0.732148 | ||||||||
\(232\) | −3.86137 | −0.253511 | ||||||||
\(233\) | 2.97745 | 0.195059 | 0.0975296 | − | 0.995233i | \(-0.468906\pi\) | ||||
0.0975296 | + | 0.995233i | \(0.468906\pi\) | |||||||
\(234\) | −7.50400 | −0.490552 | ||||||||
\(235\) | −16.5082 | −1.07688 | ||||||||
\(236\) | −16.9001 | −1.10010 | ||||||||
\(237\) | −9.35621 | −0.607751 | ||||||||
\(238\) | −3.21293 | −0.208264 | ||||||||
\(239\) | −12.8232 | −0.829466 | −0.414733 | − | 0.909943i | \(-0.636125\pi\) | ||||
−0.414733 | + | 0.909943i | \(0.636125\pi\) | |||||||
\(240\) | 13.9024 | 0.897398 | ||||||||
\(241\) | 1.75410 | 0.112991 | 0.0564957 | − | 0.998403i | \(-0.482007\pi\) | ||||
0.0564957 | + | 0.998403i | \(0.482007\pi\) | |||||||
\(242\) | −54.9202 | −3.53040 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 15.2267 | 0.974791 | ||||||||
\(245\) | −11.3861 | −0.727428 | ||||||||
\(246\) | 11.2024 | 0.714241 | ||||||||
\(247\) | −24.8013 | −1.57807 | ||||||||
\(248\) | −4.74575 | −0.301356 | ||||||||
\(249\) | −13.8585 | −0.878248 | ||||||||
\(250\) | 9.26427 | 0.585924 | ||||||||
\(251\) | −27.3628 | −1.72712 | −0.863562 | − | 0.504243i | \(-0.831772\pi\) | ||||
−0.863562 | + | 0.504243i | \(0.831772\pi\) | |||||||
\(252\) | −2.43954 | −0.153676 | ||||||||
\(253\) | 53.0309 | 3.33403 | ||||||||
\(254\) | −30.6855 | −1.92538 | ||||||||
\(255\) | 2.87244 | 0.179879 | ||||||||
\(256\) | 20.9776 | 1.31110 | ||||||||
\(257\) | 30.5389 | 1.90496 | 0.952482 | − | 0.304596i | \(-0.0985215\pi\) | ||||
0.952482 | + | 0.304596i | \(0.0985215\pi\) | |||||||
\(258\) | −1.41313 | −0.0879778 | ||||||||
\(259\) | 12.7355 | 0.791347 | ||||||||
\(260\) | 16.3662 | 1.01499 | ||||||||
\(261\) | −3.49057 | −0.216061 | ||||||||
\(262\) | −27.0325 | −1.67007 | ||||||||
\(263\) | 6.00881 | 0.370519 | 0.185260 | − | 0.982690i | \(-0.440687\pi\) | ||||
0.185260 | + | 0.982690i | \(0.440687\pi\) | |||||||
\(264\) | 7.06468 | 0.434801 | ||||||||
\(265\) | −36.1394 | −2.22002 | ||||||||
\(266\) | −19.5807 | −1.20057 | ||||||||
\(267\) | 4.68455 | 0.286690 | ||||||||
\(268\) | −16.4805 | −1.00671 | ||||||||
\(269\) | −6.01468 | −0.366722 | −0.183361 | − | 0.983046i | \(-0.558698\pi\) | ||||
−0.183361 | + | 0.983046i | \(0.558698\pi\) | |||||||
\(270\) | 5.29656 | 0.322339 | ||||||||
\(271\) | −24.3492 | −1.47911 | −0.739553 | − | 0.673098i | \(-0.764963\pi\) | ||||
−0.739553 | + | 0.673098i | \(0.764963\pi\) | |||||||
\(272\) | 4.83995 | 0.293465 | ||||||||
\(273\) | 7.09099 | 0.429166 | ||||||||
\(274\) | −34.6459 | −2.09303 | ||||||||
\(275\) | −20.7610 | −1.25194 | ||||||||
\(276\) | 11.6260 | 0.699805 | ||||||||
\(277\) | −0.321627 | −0.0193247 | −0.00966235 | − | 0.999953i | \(-0.503076\pi\) | ||||
−0.00966235 | + | 0.999953i | \(0.503076\pi\) | |||||||
\(278\) | −27.1483 | −1.62825 | ||||||||
\(279\) | −4.29002 | −0.256837 | ||||||||
\(280\) | −5.53674 | −0.330883 | ||||||||
\(281\) | 3.42570 | 0.204360 | 0.102180 | − | 0.994766i | \(-0.467418\pi\) | ||||
0.102180 | + | 0.994766i | \(0.467418\pi\) | |||||||
\(282\) | −10.5973 | −0.631058 | ||||||||
\(283\) | 22.1038 | 1.31394 | 0.656968 | − | 0.753919i | \(-0.271839\pi\) | ||||
0.656968 | + | 0.753919i | \(0.271839\pi\) | |||||||
\(284\) | 12.5322 | 0.743652 | ||||||||
\(285\) | 17.5056 | 1.03694 | ||||||||
\(286\) | 47.9225 | 2.83372 | ||||||||
\(287\) | −10.5859 | −0.624864 | ||||||||
\(288\) | 6.71205 | 0.395511 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 18.4880 | 1.08565 | ||||||||
\(291\) | 1.63896 | 0.0960775 | ||||||||
\(292\) | −3.29975 | −0.193103 | ||||||||
\(293\) | −32.9636 | −1.92575 | −0.962877 | − | 0.269940i | \(-0.912996\pi\) | ||||
−0.962877 | + | 0.269940i | \(0.912996\pi\) | |||||||
\(294\) | −7.30914 | −0.426278 | ||||||||
\(295\) | −34.6729 | −2.01873 | ||||||||
\(296\) | −8.08546 | −0.469958 | ||||||||
\(297\) | 6.38626 | 0.370568 | ||||||||
\(298\) | −12.4124 | −0.719032 | ||||||||
\(299\) | −33.7934 | −1.95432 | ||||||||
\(300\) | −4.55147 | −0.262779 | ||||||||
\(301\) | 1.33536 | 0.0769686 | ||||||||
\(302\) | −14.0018 | −0.805711 | ||||||||
\(303\) | 6.70134 | 0.384982 | ||||||||
\(304\) | 29.4962 | 1.69172 | ||||||||
\(305\) | 31.2398 | 1.78878 | ||||||||
\(306\) | 1.84393 | 0.105410 | ||||||||
\(307\) | 31.1103 | 1.77556 | 0.887778 | − | 0.460272i | \(-0.152248\pi\) | ||||
0.887778 | + | 0.460272i | \(0.152248\pi\) | |||||||
\(308\) | 15.5795 | 0.887725 | ||||||||
\(309\) | −7.08223 | −0.402894 | ||||||||
\(310\) | 22.7224 | 1.29054 | ||||||||
\(311\) | −2.37507 | −0.134678 | −0.0673388 | − | 0.997730i | \(-0.521451\pi\) | ||||
−0.0673388 | + | 0.997730i | \(0.521451\pi\) | |||||||
\(312\) | −4.50189 | −0.254869 | ||||||||
\(313\) | 15.5403 | 0.878389 | 0.439195 | − | 0.898392i | \(-0.355264\pi\) | ||||
0.439195 | + | 0.898392i | \(0.355264\pi\) | |||||||
\(314\) | −1.84393 | −0.104059 | ||||||||
\(315\) | −5.00505 | −0.282003 | ||||||||
\(316\) | 13.0993 | 0.736895 | ||||||||
\(317\) | 11.6488 | 0.654261 | 0.327130 | − | 0.944979i | \(-0.393918\pi\) | ||||
0.327130 | + | 0.944979i | \(0.393918\pi\) | |||||||
\(318\) | −23.1993 | −1.30095 | ||||||||
\(319\) | 22.2917 | 1.24809 | ||||||||
\(320\) | −7.74592 | −0.433010 | ||||||||
\(321\) | −13.0973 | −0.731018 | ||||||||
\(322\) | −26.6799 | −1.48681 | ||||||||
\(323\) | 6.09433 | 0.339097 | ||||||||
\(324\) | 1.40007 | 0.0777816 | ||||||||
\(325\) | 13.2297 | 0.733854 | ||||||||
\(326\) | 41.6441 | 2.30645 | ||||||||
\(327\) | 3.34572 | 0.185019 | ||||||||
\(328\) | 6.72069 | 0.371088 | ||||||||
\(329\) | 10.0140 | 0.552091 | ||||||||
\(330\) | −33.8252 | −1.86202 | ||||||||
\(331\) | 25.0357 | 1.37609 | 0.688044 | − | 0.725669i | \(-0.258470\pi\) | ||||
0.688044 | + | 0.725669i | \(0.258470\pi\) | |||||||
\(332\) | 19.4029 | 1.06487 | ||||||||
\(333\) | −7.30902 | −0.400532 | ||||||||
\(334\) | 22.1718 | 1.21319 | ||||||||
\(335\) | −33.8121 | −1.84735 | ||||||||
\(336\) | −8.43332 | −0.460075 | ||||||||
\(337\) | 23.8472 | 1.29904 | 0.649519 | − | 0.760346i | \(-0.274970\pi\) | ||||
0.649519 | + | 0.760346i | \(0.274970\pi\) | |||||||
\(338\) | −6.56702 | −0.357199 | ||||||||
\(339\) | −11.0536 | −0.600348 | ||||||||
\(340\) | −4.02161 | −0.218102 | ||||||||
\(341\) | 27.3972 | 1.48364 | ||||||||
\(342\) | 11.2375 | 0.607654 | ||||||||
\(343\) | 19.1039 | 1.03152 | ||||||||
\(344\) | −0.847783 | −0.0457094 | ||||||||
\(345\) | 23.8524 | 1.28417 | ||||||||
\(346\) | 3.97376 | 0.213631 | ||||||||
\(347\) | −30.6975 | −1.64793 | −0.823964 | − | 0.566641i | \(-0.808242\pi\) | ||||
−0.823964 | + | 0.566641i | \(0.808242\pi\) | |||||||
\(348\) | 4.88703 | 0.261972 | ||||||||
\(349\) | −11.7481 | −0.628859 | −0.314430 | − | 0.949281i | \(-0.601813\pi\) | ||||
−0.314430 | + | 0.949281i | \(0.601813\pi\) | |||||||
\(350\) | 10.4449 | 0.558303 | ||||||||
\(351\) | −4.06957 | −0.217218 | ||||||||
\(352\) | −42.8649 | −2.28471 | ||||||||
\(353\) | −28.6255 | −1.52358 | −0.761790 | − | 0.647824i | \(-0.775679\pi\) | ||||
−0.761790 | + | 0.647824i | \(0.775679\pi\) | |||||||
\(354\) | −22.2579 | −1.18299 | ||||||||
\(355\) | 25.7117 | 1.36463 | ||||||||
\(356\) | −6.55869 | −0.347610 | ||||||||
\(357\) | −1.74244 | −0.0922197 | ||||||||
\(358\) | −23.7320 | −1.25427 | ||||||||
\(359\) | 3.06994 | 0.162025 | 0.0810126 | − | 0.996713i | \(-0.474185\pi\) | ||||
0.0810126 | + | 0.996713i | \(0.474185\pi\) | |||||||
\(360\) | 3.17758 | 0.167473 | ||||||||
\(361\) | 18.1408 | 0.954781 | ||||||||
\(362\) | 28.4651 | 1.49609 | ||||||||
\(363\) | −29.7843 | −1.56327 | ||||||||
\(364\) | −9.92787 | −0.520362 | ||||||||
\(365\) | −6.76989 | −0.354352 | ||||||||
\(366\) | 20.0540 | 1.04824 | ||||||||
\(367\) | −10.2859 | −0.536921 | −0.268461 | − | 0.963291i | \(-0.586515\pi\) | ||||
−0.268461 | + | 0.963291i | \(0.586515\pi\) | |||||||
\(368\) | 40.1905 | 2.09507 | ||||||||
\(369\) | 6.07531 | 0.316268 | ||||||||
\(370\) | 38.7127 | 2.01258 | ||||||||
\(371\) | 21.9224 | 1.13815 | ||||||||
\(372\) | 6.00633 | 0.311414 | ||||||||
\(373\) | −19.8035 | −1.02539 | −0.512694 | − | 0.858571i | \(-0.671353\pi\) | ||||
−0.512694 | + | 0.858571i | \(0.671353\pi\) | |||||||
\(374\) | −11.7758 | −0.608912 | ||||||||
\(375\) | 5.02421 | 0.259449 | ||||||||
\(376\) | −6.35764 | −0.327870 | ||||||||
\(377\) | −14.2051 | −0.731601 | ||||||||
\(378\) | −3.21293 | −0.165256 | ||||||||
\(379\) | −14.7351 | −0.756892 | −0.378446 | − | 0.925623i | \(-0.623541\pi\) | ||||
−0.378446 | + | 0.925623i | \(0.623541\pi\) | |||||||
\(380\) | −24.5090 | −1.25728 | ||||||||
\(381\) | −16.6414 | −0.852564 | ||||||||
\(382\) | −15.4843 | −0.792248 | ||||||||
\(383\) | −33.1654 | −1.69467 | −0.847337 | − | 0.531055i | \(-0.821796\pi\) | ||||
−0.847337 | + | 0.531055i | \(0.821796\pi\) | |||||||
\(384\) | 8.45169 | 0.431299 | ||||||||
\(385\) | 31.9636 | 1.62901 | ||||||||
\(386\) | −12.3350 | −0.627837 | ||||||||
\(387\) | −0.766371 | −0.0389568 | ||||||||
\(388\) | −2.29466 | −0.116493 | ||||||||
\(389\) | −17.0589 | −0.864922 | −0.432461 | − | 0.901653i | \(-0.642355\pi\) | ||||
−0.432461 | + | 0.901653i | \(0.642355\pi\) | |||||||
\(390\) | 21.5548 | 1.09147 | ||||||||
\(391\) | 8.30391 | 0.419947 | ||||||||
\(392\) | −4.38499 | −0.221475 | ||||||||
\(393\) | −14.6603 | −0.739512 | ||||||||
\(394\) | 18.4573 | 0.929868 | ||||||||
\(395\) | 26.8751 | 1.35223 | ||||||||
\(396\) | −8.94120 | −0.449312 | ||||||||
\(397\) | 10.7867 | 0.541370 | 0.270685 | − | 0.962668i | \(-0.412750\pi\) | ||||
0.270685 | + | 0.962668i | \(0.412750\pi\) | |||||||
\(398\) | −33.2170 | −1.66502 | ||||||||
\(399\) | −10.6190 | −0.531615 | ||||||||
\(400\) | −15.7341 | −0.786707 | ||||||||
\(401\) | −37.9872 | −1.89699 | −0.948495 | − | 0.316793i | \(-0.897394\pi\) | ||||
−0.948495 | + | 0.316793i | \(0.897394\pi\) | |||||||
\(402\) | −21.7053 | −1.08256 | ||||||||
\(403\) | −17.4586 | −0.869673 | ||||||||
\(404\) | −9.38233 | −0.466788 | ||||||||
\(405\) | 2.87244 | 0.142733 | ||||||||
\(406\) | −11.2150 | −0.556589 | ||||||||
\(407\) | 46.6773 | 2.31371 | ||||||||
\(408\) | 1.10623 | 0.0547666 | ||||||||
\(409\) | −19.9989 | −0.988880 | −0.494440 | − | 0.869212i | \(-0.664627\pi\) | ||||
−0.494440 | + | 0.869212i | \(0.664627\pi\) | |||||||
\(410\) | −32.1783 | −1.58917 | ||||||||
\(411\) | −18.7892 | −0.926802 | ||||||||
\(412\) | 9.91561 | 0.488507 | ||||||||
\(413\) | 21.0328 | 1.03496 | ||||||||
\(414\) | 15.3118 | 0.752534 | ||||||||
\(415\) | 39.8077 | 1.95408 | ||||||||
\(416\) | 27.3152 | 1.33924 | ||||||||
\(417\) | −14.7231 | −0.720993 | ||||||||
\(418\) | −71.7656 | −3.51017 | ||||||||
\(419\) | −32.3690 | −1.58133 | −0.790665 | − | 0.612249i | \(-0.790265\pi\) | ||||
−0.790665 | + | 0.612249i | \(0.790265\pi\) | |||||||
\(420\) | 7.00741 | 0.341927 | ||||||||
\(421\) | −23.9798 | −1.16870 | −0.584351 | − | 0.811501i | \(-0.698651\pi\) | ||||
−0.584351 | + | 0.811501i | \(0.698651\pi\) | |||||||
\(422\) | −20.9742 | −1.02101 | ||||||||
\(423\) | −5.74712 | −0.279435 | ||||||||
\(424\) | −13.9180 | −0.675916 | ||||||||
\(425\) | −3.25089 | −0.157691 | ||||||||
\(426\) | 16.5053 | 0.799685 | ||||||||
\(427\) | −18.9503 | −0.917068 | ||||||||
\(428\) | 18.3371 | 0.886356 | ||||||||
\(429\) | 25.9894 | 1.25478 | ||||||||
\(430\) | 4.05913 | 0.195749 | ||||||||
\(431\) | 7.52381 | 0.362409 | 0.181205 | − | 0.983445i | \(-0.442000\pi\) | ||||
0.181205 | + | 0.983445i | \(0.442000\pi\) | |||||||
\(432\) | 4.83995 | 0.232862 | ||||||||
\(433\) | 37.5045 | 1.80235 | 0.901177 | − | 0.433452i | \(-0.142705\pi\) | ||||
0.901177 | + | 0.433452i | \(0.142705\pi\) | |||||||
\(434\) | −13.7836 | −0.661632 | ||||||||
\(435\) | 10.0264 | 0.480731 | ||||||||
\(436\) | −4.68424 | −0.224334 | ||||||||
\(437\) | 50.6067 | 2.42085 | ||||||||
\(438\) | −4.34585 | −0.207653 | ||||||||
\(439\) | 8.11706 | 0.387406 | 0.193703 | − | 0.981060i | \(-0.437950\pi\) | ||||
0.193703 | + | 0.981060i | \(0.437950\pi\) | |||||||
\(440\) | −20.2928 | −0.967423 | ||||||||
\(441\) | −3.96390 | −0.188757 | ||||||||
\(442\) | 7.50400 | 0.356929 | ||||||||
\(443\) | −5.87092 | −0.278936 | −0.139468 | − | 0.990227i | \(-0.544539\pi\) | ||||
−0.139468 | + | 0.990227i | \(0.544539\pi\) | |||||||
\(444\) | 10.2331 | 0.485643 | ||||||||
\(445\) | −13.4561 | −0.637879 | ||||||||
\(446\) | 11.4457 | 0.541971 | ||||||||
\(447\) | −6.73151 | −0.318390 | ||||||||
\(448\) | 4.69873 | 0.221994 | ||||||||
\(449\) | −38.4946 | −1.81667 | −0.908337 | − | 0.418239i | \(-0.862647\pi\) | ||||
−0.908337 | + | 0.418239i | \(0.862647\pi\) | |||||||
\(450\) | −5.99441 | −0.282579 | ||||||||
\(451\) | −38.7985 | −1.82695 | ||||||||
\(452\) | 15.4758 | 0.727918 | ||||||||
\(453\) | −7.59344 | −0.356771 | ||||||||
\(454\) | −3.39974 | −0.159558 | ||||||||
\(455\) | −20.3684 | −0.954886 | ||||||||
\(456\) | 6.74173 | 0.315710 | ||||||||
\(457\) | 15.8746 | 0.742585 | 0.371292 | − | 0.928516i | \(-0.378915\pi\) | ||||
0.371292 | + | 0.928516i | \(0.378915\pi\) | |||||||
\(458\) | −43.3087 | −2.02368 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −33.3950 | −1.55705 | ||||||||
\(461\) | −7.16872 | −0.333880 | −0.166940 | − | 0.985967i | \(-0.553389\pi\) | ||||
−0.166940 | + | 0.985967i | \(0.553389\pi\) | |||||||
\(462\) | 20.5186 | 0.954613 | ||||||||
\(463\) | −19.7678 | −0.918686 | −0.459343 | − | 0.888259i | \(-0.651915\pi\) | ||||
−0.459343 | + | 0.888259i | \(0.651915\pi\) | |||||||
\(464\) | 16.8942 | 0.784291 | ||||||||
\(465\) | 12.3228 | 0.571457 | ||||||||
\(466\) | −5.49020 | −0.254329 | ||||||||
\(467\) | −3.37582 | −0.156214 | −0.0781071 | − | 0.996945i | \(-0.524888\pi\) | ||||
−0.0781071 | + | 0.996945i | \(0.524888\pi\) | |||||||
\(468\) | 5.69768 | 0.263375 | ||||||||
\(469\) | 20.5107 | 0.947094 | ||||||||
\(470\) | 30.4400 | 1.40409 | ||||||||
\(471\) | −1.00000 | −0.0460776 | ||||||||
\(472\) | −13.3532 | −0.614630 | ||||||||
\(473\) | 4.89425 | 0.225038 | ||||||||
\(474\) | 17.2522 | 0.792418 | ||||||||
\(475\) | −19.8120 | −0.909036 | ||||||||
\(476\) | 2.43954 | 0.111816 | ||||||||
\(477\) | −12.5814 | −0.576064 | ||||||||
\(478\) | 23.6451 | 1.08150 | ||||||||
\(479\) | −16.2842 | −0.744044 | −0.372022 | − | 0.928224i | \(-0.621335\pi\) | ||||
−0.372022 | + | 0.928224i | \(0.621335\pi\) | |||||||
\(480\) | −19.2799 | −0.880004 | ||||||||
\(481\) | −29.7446 | −1.35624 | ||||||||
\(482\) | −3.23443 | −0.147324 | ||||||||
\(483\) | −14.4691 | −0.658365 | ||||||||
\(484\) | 41.7001 | 1.89546 | ||||||||
\(485\) | −4.70781 | −0.213771 | ||||||||
\(486\) | 1.84393 | 0.0836422 | ||||||||
\(487\) | 16.4040 | 0.743337 | 0.371668 | − | 0.928366i | \(-0.378786\pi\) | ||||
0.371668 | + | 0.928366i | \(0.378786\pi\) | |||||||
\(488\) | 12.0310 | 0.544619 | ||||||||
\(489\) | 22.5844 | 1.02130 | ||||||||
\(490\) | 20.9951 | 0.948460 | ||||||||
\(491\) | −10.0739 | −0.454629 | −0.227315 | − | 0.973821i | \(-0.572995\pi\) | ||||
−0.227315 | + | 0.973821i | \(0.572995\pi\) | |||||||
\(492\) | −8.50585 | −0.383473 | ||||||||
\(493\) | 3.49057 | 0.157207 | ||||||||
\(494\) | 45.7318 | 2.05757 | ||||||||
\(495\) | −18.3441 | −0.824507 | ||||||||
\(496\) | 20.7635 | 0.932308 | ||||||||
\(497\) | −15.5969 | −0.699616 | ||||||||
\(498\) | 25.5541 | 1.14511 | ||||||||
\(499\) | −7.05969 | −0.316035 | −0.158018 | − | 0.987436i | \(-0.550510\pi\) | ||||
−0.158018 | + | 0.987436i | \(0.550510\pi\) | |||||||
\(500\) | −7.03423 | −0.314580 | ||||||||
\(501\) | 12.0242 | 0.537202 | ||||||||
\(502\) | 50.4550 | 2.25192 | ||||||||
\(503\) | −1.95177 | −0.0870251 | −0.0435126 | − | 0.999053i | \(-0.513855\pi\) | ||||
−0.0435126 | + | 0.999053i | \(0.513855\pi\) | |||||||
\(504\) | −1.92754 | −0.0858595 | ||||||||
\(505\) | −19.2492 | −0.856576 | ||||||||
\(506\) | −97.7852 | −4.34708 | ||||||||
\(507\) | −3.56143 | −0.158169 | ||||||||
\(508\) | 23.2991 | 1.03373 | ||||||||
\(509\) | 11.5547 | 0.512154 | 0.256077 | − | 0.966656i | \(-0.417570\pi\) | ||||
0.256077 | + | 0.966656i | \(0.417570\pi\) | |||||||
\(510\) | −5.29656 | −0.234536 | ||||||||
\(511\) | 4.10666 | 0.181668 | ||||||||
\(512\) | −21.7778 | −0.962450 | ||||||||
\(513\) | 6.09433 | 0.269071 | ||||||||
\(514\) | −56.3115 | −2.48379 | ||||||||
\(515\) | 20.3433 | 0.896431 | ||||||||
\(516\) | 1.07297 | 0.0472349 | ||||||||
\(517\) | 36.7026 | 1.61418 | ||||||||
\(518\) | −23.4834 | −1.03180 | ||||||||
\(519\) | 2.15505 | 0.0945963 | ||||||||
\(520\) | 12.9314 | 0.567079 | ||||||||
\(521\) | 17.5320 | 0.768089 | 0.384044 | − | 0.923315i | \(-0.374531\pi\) | ||||
0.384044 | + | 0.923315i | \(0.374531\pi\) | |||||||
\(522\) | 6.43635 | 0.281711 | ||||||||
\(523\) | −8.81713 | −0.385546 | −0.192773 | − | 0.981243i | \(-0.561748\pi\) | ||||
−0.192773 | + | 0.981243i | \(0.561748\pi\) | |||||||
\(524\) | 20.5254 | 0.896655 | ||||||||
\(525\) | 5.66448 | 0.247218 | ||||||||
\(526\) | −11.0798 | −0.483103 | ||||||||
\(527\) | 4.29002 | 0.186876 | ||||||||
\(528\) | −30.9092 | −1.34515 | ||||||||
\(529\) | 45.9549 | 1.99804 | ||||||||
\(530\) | 66.6384 | 2.89459 | ||||||||
\(531\) | −12.0709 | −0.523832 | ||||||||
\(532\) | 14.8673 | 0.644581 | ||||||||
\(533\) | 24.7239 | 1.07091 | ||||||||
\(534\) | −8.63797 | −0.373802 | ||||||||
\(535\) | 37.6211 | 1.62650 | ||||||||
\(536\) | −13.0217 | −0.562451 | ||||||||
\(537\) | −12.8703 | −0.555396 | ||||||||
\(538\) | 11.0906 | 0.478151 | ||||||||
\(539\) | 25.3145 | 1.09037 | ||||||||
\(540\) | −4.02161 | −0.173062 | ||||||||
\(541\) | −11.8970 | −0.511493 | −0.255747 | − | 0.966744i | \(-0.582321\pi\) | ||||
−0.255747 | + | 0.966744i | \(0.582321\pi\) | |||||||
\(542\) | 44.8981 | 1.92854 | ||||||||
\(543\) | 15.4372 | 0.662474 | ||||||||
\(544\) | −6.71205 | −0.287777 | ||||||||
\(545\) | −9.61037 | −0.411663 | ||||||||
\(546\) | −13.0753 | −0.559570 | ||||||||
\(547\) | −0.931758 | −0.0398391 | −0.0199195 | − | 0.999802i | \(-0.506341\pi\) | ||||
−0.0199195 | + | 0.999802i | \(0.506341\pi\) | |||||||
\(548\) | 26.3061 | 1.12374 | ||||||||
\(549\) | 10.8757 | 0.464164 | ||||||||
\(550\) | 38.2818 | 1.63234 | ||||||||
\(551\) | 21.2727 | 0.906246 | ||||||||
\(552\) | 9.18603 | 0.390984 | ||||||||
\(553\) | −16.3026 | −0.693259 | ||||||||
\(554\) | 0.593057 | 0.0251966 | ||||||||
\(555\) | 20.9947 | 0.891175 | ||||||||
\(556\) | 20.6134 | 0.874201 | ||||||||
\(557\) | −43.0936 | −1.82593 | −0.912967 | − | 0.408033i | \(-0.866215\pi\) | ||||
−0.912967 | + | 0.408033i | \(0.866215\pi\) | |||||||
\(558\) | 7.91049 | 0.334878 | ||||||||
\(559\) | −3.11880 | −0.131911 | ||||||||
\(560\) | 24.2242 | 1.02366 | ||||||||
\(561\) | −6.38626 | −0.269628 | ||||||||
\(562\) | −6.31674 | −0.266455 | ||||||||
\(563\) | 0.250716 | 0.0105664 | 0.00528321 | − | 0.999986i | \(-0.498318\pi\) | ||||
0.00528321 | + | 0.999986i | \(0.498318\pi\) | |||||||
\(564\) | 8.04636 | 0.338813 | ||||||||
\(565\) | 31.7507 | 1.33576 | ||||||||
\(566\) | −40.7578 | −1.71318 | ||||||||
\(567\) | −1.74244 | −0.0731756 | ||||||||
\(568\) | 9.90205 | 0.415481 | ||||||||
\(569\) | 36.2795 | 1.52091 | 0.760457 | − | 0.649388i | \(-0.224975\pi\) | ||||
0.760457 | + | 0.649388i | \(0.224975\pi\) | |||||||
\(570\) | −32.2790 | −1.35202 | ||||||||
\(571\) | −17.0886 | −0.715136 | −0.357568 | − | 0.933887i | \(-0.616394\pi\) | ||||
−0.357568 | + | 0.933887i | \(0.616394\pi\) | |||||||
\(572\) | −36.3869 | −1.52141 | ||||||||
\(573\) | −8.39748 | −0.350810 | ||||||||
\(574\) | 19.5196 | 0.814731 | ||||||||
\(575\) | −26.9951 | −1.12577 | ||||||||
\(576\) | −2.69664 | −0.112360 | ||||||||
\(577\) | −7.90358 | −0.329030 | −0.164515 | − | 0.986375i | \(-0.552606\pi\) | ||||
−0.164515 | + | 0.986375i | \(0.552606\pi\) | |||||||
\(578\) | −1.84393 | −0.0766973 | ||||||||
\(579\) | −6.68955 | −0.278008 | ||||||||
\(580\) | −14.0377 | −0.582883 | ||||||||
\(581\) | −24.1477 | −1.00181 | ||||||||
\(582\) | −3.02212 | −0.125271 | ||||||||
\(583\) | 80.3483 | 3.32769 | ||||||||
\(584\) | −2.60721 | −0.107887 | ||||||||
\(585\) | 11.6896 | 0.483305 | ||||||||
\(586\) | 60.7825 | 2.51090 | ||||||||
\(587\) | 2.67259 | 0.110310 | 0.0551548 | − | 0.998478i | \(-0.482435\pi\) | ||||
0.0551548 | + | 0.998478i | \(0.482435\pi\) | |||||||
\(588\) | 5.54973 | 0.228867 | ||||||||
\(589\) | 26.1448 | 1.07728 | ||||||||
\(590\) | 63.9343 | 2.63213 | ||||||||
\(591\) | 10.0098 | 0.411748 | ||||||||
\(592\) | 35.3752 | 1.45391 | ||||||||
\(593\) | −14.6989 | −0.603610 | −0.301805 | − | 0.953370i | \(-0.597589\pi\) | ||||
−0.301805 | + | 0.953370i | \(0.597589\pi\) | |||||||
\(594\) | −11.7758 | −0.483167 | ||||||||
\(595\) | 5.00505 | 0.205187 | ||||||||
\(596\) | 9.42458 | 0.386046 | ||||||||
\(597\) | −18.0143 | −0.737275 | ||||||||
\(598\) | 62.3125 | 2.54815 | ||||||||
\(599\) | 17.1705 | 0.701567 | 0.350784 | − | 0.936457i | \(-0.385915\pi\) | ||||
0.350784 | + | 0.936457i | \(0.385915\pi\) | |||||||
\(600\) | −3.59623 | −0.146816 | ||||||||
\(601\) | 41.5047 | 1.69301 | 0.846505 | − | 0.532380i | \(-0.178702\pi\) | ||||
0.846505 | + | 0.532380i | \(0.178702\pi\) | |||||||
\(602\) | −2.46230 | −0.100356 | ||||||||
\(603\) | −11.7712 | −0.479361 | ||||||||
\(604\) | 10.6313 | 0.432583 | ||||||||
\(605\) | 85.5536 | 3.47825 | ||||||||
\(606\) | −12.3568 | −0.501960 | ||||||||
\(607\) | 44.2334 | 1.79538 | 0.897689 | − | 0.440630i | \(-0.145245\pi\) | ||||
0.897689 | + | 0.440630i | \(0.145245\pi\) | |||||||
\(608\) | −40.9054 | −1.65893 | ||||||||
\(609\) | −6.08211 | −0.246459 | ||||||||
\(610\) | −57.6039 | −2.33231 | ||||||||
\(611\) | −23.3883 | −0.946190 | ||||||||
\(612\) | −1.40007 | −0.0565944 | ||||||||
\(613\) | −32.0608 | −1.29492 | −0.647462 | − | 0.762098i | \(-0.724170\pi\) | ||||
−0.647462 | + | 0.762098i | \(0.724170\pi\) | |||||||
\(614\) | −57.3651 | −2.31507 | ||||||||
\(615\) | −17.4509 | −0.703690 | ||||||||
\(616\) | 12.3098 | 0.495975 | ||||||||
\(617\) | 6.55433 | 0.263867 | 0.131934 | − | 0.991259i | \(-0.457881\pi\) | ||||
0.131934 | + | 0.991259i | \(0.457881\pi\) | |||||||
\(618\) | 13.0591 | 0.525315 | ||||||||
\(619\) | 14.9034 | 0.599018 | 0.299509 | − | 0.954093i | \(-0.403177\pi\) | ||||
0.299509 | + | 0.954093i | \(0.403177\pi\) | |||||||
\(620\) | −17.2528 | −0.692889 | ||||||||
\(621\) | 8.30391 | 0.333224 | ||||||||
\(622\) | 4.37945 | 0.175600 | ||||||||
\(623\) | 8.16255 | 0.327026 | ||||||||
\(624\) | 19.6965 | 0.788492 | ||||||||
\(625\) | −30.6862 | −1.22745 | ||||||||
\(626\) | −28.6552 | −1.14529 | ||||||||
\(627\) | −38.9200 | −1.55431 | ||||||||
\(628\) | 1.40007 | 0.0558688 | ||||||||
\(629\) | 7.30902 | 0.291430 | ||||||||
\(630\) | 9.22895 | 0.367690 | ||||||||
\(631\) | −30.5432 | −1.21590 | −0.607952 | − | 0.793974i | \(-0.708009\pi\) | ||||
−0.607952 | + | 0.793974i | \(0.708009\pi\) | |||||||
\(632\) | 10.3501 | 0.411706 | ||||||||
\(633\) | −11.3747 | −0.452106 | ||||||||
\(634\) | −21.4795 | −0.853060 | ||||||||
\(635\) | 47.8013 | 1.89694 | ||||||||
\(636\) | 17.6149 | 0.698475 | ||||||||
\(637\) | −16.1314 | −0.639149 | ||||||||
\(638\) | −41.1042 | −1.62733 | ||||||||
\(639\) | 8.95117 | 0.354103 | ||||||||
\(640\) | −24.2769 | −0.959630 | ||||||||
\(641\) | −8.03845 | −0.317500 | −0.158750 | − | 0.987319i | \(-0.550746\pi\) | ||||
−0.158750 | + | 0.987319i | \(0.550746\pi\) | |||||||
\(642\) | 24.1504 | 0.953141 | ||||||||
\(643\) | 5.66131 | 0.223260 | 0.111630 | − | 0.993750i | \(-0.464393\pi\) | ||||
0.111630 | + | 0.993750i | \(0.464393\pi\) | |||||||
\(644\) | 20.2577 | 0.798264 | ||||||||
\(645\) | 2.20135 | 0.0866781 | ||||||||
\(646\) | −11.2375 | −0.442133 | ||||||||
\(647\) | 35.3551 | 1.38995 | 0.694977 | − | 0.719032i | \(-0.255415\pi\) | ||||
0.694977 | + | 0.719032i | \(0.255415\pi\) | |||||||
\(648\) | 1.10623 | 0.0434568 | ||||||||
\(649\) | 77.0879 | 3.02596 | ||||||||
\(650\) | −24.3947 | −0.956838 | ||||||||
\(651\) | −7.47511 | −0.292973 | ||||||||
\(652\) | −31.6198 | −1.23833 | ||||||||
\(653\) | −31.5659 | −1.23527 | −0.617635 | − | 0.786465i | \(-0.711909\pi\) | ||||
−0.617635 | + | 0.786465i | \(0.711909\pi\) | |||||||
\(654\) | −6.16927 | −0.241237 | ||||||||
\(655\) | 42.1107 | 1.64540 | ||||||||
\(656\) | −29.4042 | −1.14804 | ||||||||
\(657\) | −2.35685 | −0.0919493 | ||||||||
\(658\) | −18.4651 | −0.719845 | ||||||||
\(659\) | 20.5937 | 0.802215 | 0.401108 | − | 0.916031i | \(-0.368625\pi\) | ||||
0.401108 | + | 0.916031i | \(0.368625\pi\) | |||||||
\(660\) | 25.6830 | 0.999711 | ||||||||
\(661\) | 17.4598 | 0.679106 | 0.339553 | − | 0.940587i | \(-0.389724\pi\) | ||||
0.339553 | + | 0.940587i | \(0.389724\pi\) | |||||||
\(662\) | −46.1640 | −1.79422 | ||||||||
\(663\) | 4.06957 | 0.158049 | ||||||||
\(664\) | 15.3307 | 0.594947 | ||||||||
\(665\) | 30.5024 | 1.18283 | ||||||||
\(666\) | 13.4773 | 0.522235 | ||||||||
\(667\) | 28.9853 | 1.12232 | ||||||||
\(668\) | −16.8347 | −0.651355 | ||||||||
\(669\) | 6.20725 | 0.239986 | ||||||||
\(670\) | 62.3470 | 2.40868 | ||||||||
\(671\) | −69.4551 | −2.68128 | ||||||||
\(672\) | 11.6953 | 0.451158 | ||||||||
\(673\) | 0.851723 | 0.0328315 | 0.0164158 | − | 0.999865i | \(-0.494774\pi\) | ||||
0.0164158 | + | 0.999865i | \(0.494774\pi\) | |||||||
\(674\) | −43.9724 | −1.69375 | ||||||||
\(675\) | −3.25089 | −0.125127 | ||||||||
\(676\) | 4.98625 | 0.191779 | ||||||||
\(677\) | 4.49723 | 0.172842 | 0.0864212 | − | 0.996259i | \(-0.472457\pi\) | ||||
0.0864212 | + | 0.996259i | \(0.472457\pi\) | |||||||
\(678\) | 20.3820 | 0.782766 | ||||||||
\(679\) | 2.85579 | 0.109595 | ||||||||
\(680\) | −3.17758 | −0.121854 | ||||||||
\(681\) | −1.84375 | −0.0706527 | ||||||||
\(682\) | −50.5185 | −1.93445 | ||||||||
\(683\) | 25.7454 | 0.985122 | 0.492561 | − | 0.870278i | \(-0.336061\pi\) | ||||
0.492561 | + | 0.870278i | \(0.336061\pi\) | |||||||
\(684\) | −8.53248 | −0.326247 | ||||||||
\(685\) | 53.9707 | 2.06212 | ||||||||
\(686\) | −35.2263 | −1.34495 | ||||||||
\(687\) | −23.4872 | −0.896093 | ||||||||
\(688\) | 3.70919 | 0.141412 | ||||||||
\(689\) | −51.2011 | −1.95061 | ||||||||
\(690\) | −43.9822 | −1.67437 | ||||||||
\(691\) | 13.0508 | 0.496475 | 0.248237 | − | 0.968699i | \(-0.420149\pi\) | ||||
0.248237 | + | 0.968699i | \(0.420149\pi\) | |||||||
\(692\) | −3.01722 | −0.114697 | ||||||||
\(693\) | 11.1277 | 0.422706 | ||||||||
\(694\) | 56.6040 | 2.14866 | ||||||||
\(695\) | 42.2912 | 1.60420 | ||||||||
\(696\) | 3.86137 | 0.146365 | ||||||||
\(697\) | −6.07531 | −0.230119 | ||||||||
\(698\) | 21.6626 | 0.819940 | ||||||||
\(699\) | −2.97745 | −0.112617 | ||||||||
\(700\) | −7.93066 | −0.299751 | ||||||||
\(701\) | −17.5580 | −0.663158 | −0.331579 | − | 0.943427i | \(-0.607581\pi\) | ||||
−0.331579 | + | 0.943427i | \(0.607581\pi\) | |||||||
\(702\) | 7.50400 | 0.283220 | ||||||||
\(703\) | 44.5435 | 1.67999 | ||||||||
\(704\) | 17.2214 | 0.649057 | ||||||||
\(705\) | 16.5082 | 0.621736 | ||||||||
\(706\) | 52.7833 | 1.98653 | ||||||||
\(707\) | 11.6767 | 0.439147 | ||||||||
\(708\) | 16.9001 | 0.635144 | ||||||||
\(709\) | 34.6324 | 1.30065 | 0.650324 | − | 0.759657i | \(-0.274633\pi\) | ||||
0.650324 | + | 0.759657i | \(0.274633\pi\) | |||||||
\(710\) | −47.4104 | −1.77928 | ||||||||
\(711\) | 9.35621 | 0.350885 | ||||||||
\(712\) | −5.18219 | −0.194211 | ||||||||
\(713\) | 35.6240 | 1.33413 | ||||||||
\(714\) | 3.21293 | 0.120241 | ||||||||
\(715\) | −74.6528 | −2.79186 | ||||||||
\(716\) | 18.0193 | 0.673415 | ||||||||
\(717\) | 12.8232 | 0.478893 | ||||||||
\(718\) | −5.66074 | −0.211257 | ||||||||
\(719\) | 7.03284 | 0.262281 | 0.131140 | − | 0.991364i | \(-0.458136\pi\) | ||||
0.131140 | + | 0.991364i | \(0.458136\pi\) | |||||||
\(720\) | −13.9024 | −0.518113 | ||||||||
\(721\) | −12.3404 | −0.459579 | ||||||||
\(722\) | −33.4504 | −1.24489 | ||||||||
\(723\) | −1.75410 | −0.0652357 | ||||||||
\(724\) | −21.6132 | −0.803246 | ||||||||
\(725\) | −11.3474 | −0.421434 | ||||||||
\(726\) | 54.9202 | 2.03828 | ||||||||
\(727\) | 18.8703 | 0.699859 | 0.349930 | − | 0.936776i | \(-0.386205\pi\) | ||||
0.349930 | + | 0.936776i | \(0.386205\pi\) | |||||||
\(728\) | −7.84427 | −0.290728 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.4832 | 0.462023 | ||||||||
\(731\) | 0.766371 | 0.0283453 | ||||||||
\(732\) | −15.2267 | −0.562796 | ||||||||
\(733\) | −7.90924 | −0.292134 | −0.146067 | − | 0.989275i | \(-0.546662\pi\) | ||||
−0.146067 | + | 0.989275i | \(0.546662\pi\) | |||||||
\(734\) | 18.9665 | 0.700067 | ||||||||
\(735\) | 11.3861 | 0.419981 | ||||||||
\(736\) | −55.7362 | −2.05446 | ||||||||
\(737\) | 75.1741 | 2.76907 | ||||||||
\(738\) | −11.2024 | −0.412367 | ||||||||
\(739\) | 27.1490 | 0.998694 | 0.499347 | − | 0.866402i | \(-0.333573\pi\) | ||||
0.499347 | + | 0.866402i | \(0.333573\pi\) | |||||||
\(740\) | −29.3940 | −1.08054 | ||||||||
\(741\) | 24.8013 | 0.911099 | ||||||||
\(742\) | −40.4233 | −1.48399 | ||||||||
\(743\) | 22.2019 | 0.814510 | 0.407255 | − | 0.913314i | \(-0.366486\pi\) | ||||
0.407255 | + | 0.913314i | \(0.366486\pi\) | |||||||
\(744\) | 4.74575 | 0.173988 | ||||||||
\(745\) | 19.3358 | 0.708410 | ||||||||
\(746\) | 36.5163 | 1.33696 | ||||||||
\(747\) | 13.8585 | 0.507057 | ||||||||
\(748\) | 8.94120 | 0.326923 | ||||||||
\(749\) | −22.8212 | −0.833869 | ||||||||
\(750\) | −9.26427 | −0.338283 | ||||||||
\(751\) | −19.0570 | −0.695398 | −0.347699 | − | 0.937606i | \(-0.613037\pi\) | ||||
−0.347699 | + | 0.937606i | \(0.613037\pi\) | |||||||
\(752\) | 27.8157 | 1.01434 | ||||||||
\(753\) | 27.3628 | 0.997155 | ||||||||
\(754\) | 26.1932 | 0.953900 | ||||||||
\(755\) | 21.8117 | 0.793808 | ||||||||
\(756\) | 2.43954 | 0.0887251 | ||||||||
\(757\) | 33.1730 | 1.20569 | 0.602847 | − | 0.797857i | \(-0.294033\pi\) | ||||
0.602847 | + | 0.797857i | \(0.294033\pi\) | |||||||
\(758\) | 27.1705 | 0.986876 | ||||||||
\(759\) | −53.0309 | −1.92490 | ||||||||
\(760\) | −19.3652 | −0.702449 | ||||||||
\(761\) | 4.57317 | 0.165777 | 0.0828886 | − | 0.996559i | \(-0.473585\pi\) | ||||
0.0828886 | + | 0.996559i | \(0.473585\pi\) | |||||||
\(762\) | 30.6855 | 1.11162 | ||||||||
\(763\) | 5.82972 | 0.211050 | ||||||||
\(764\) | 11.7570 | 0.425355 | ||||||||
\(765\) | −2.87244 | −0.103853 | ||||||||
\(766\) | 61.1547 | 2.20961 | ||||||||
\(767\) | −49.1234 | −1.77374 | ||||||||
\(768\) | −20.9776 | −0.756963 | ||||||||
\(769\) | 28.7835 | 1.03796 | 0.518979 | − | 0.854787i | \(-0.326312\pi\) | ||||
0.518979 | + | 0.854787i | \(0.326312\pi\) | |||||||
\(770\) | −58.9385 | −2.12400 | ||||||||
\(771\) | −30.5389 | −1.09983 | ||||||||
\(772\) | 9.36583 | 0.337083 | ||||||||
\(773\) | 40.1050 | 1.44248 | 0.721238 | − | 0.692687i | \(-0.243573\pi\) | ||||
0.721238 | + | 0.692687i | \(0.243573\pi\) | |||||||
\(774\) | 1.41313 | 0.0507940 | ||||||||
\(775\) | −13.9464 | −0.500969 | ||||||||
\(776\) | −1.81307 | −0.0650853 | ||||||||
\(777\) | −12.7355 | −0.456885 | ||||||||
\(778\) | 31.4554 | 1.12773 | ||||||||
\(779\) | −37.0249 | −1.32656 | ||||||||
\(780\) | −16.3662 | −0.586005 | ||||||||
\(781\) | −57.1645 | −2.04551 | ||||||||
\(782\) | −15.3118 | −0.547549 | ||||||||
\(783\) | 3.49057 | 0.124743 | ||||||||
\(784\) | 19.1851 | 0.685181 | ||||||||
\(785\) | 2.87244 | 0.102522 | ||||||||
\(786\) | 27.0325 | 0.964216 | ||||||||
\(787\) | 15.9291 | 0.567812 | 0.283906 | − | 0.958852i | \(-0.408370\pi\) | ||||
0.283906 | + | 0.958852i | \(0.408370\pi\) | |||||||
\(788\) | −14.0144 | −0.499243 | ||||||||
\(789\) | −6.00881 | −0.213919 | ||||||||
\(790\) | −49.5558 | −1.76311 | ||||||||
\(791\) | −19.2602 | −0.684814 | ||||||||
\(792\) | −7.06468 | −0.251032 | ||||||||
\(793\) | 44.2595 | 1.57170 | ||||||||
\(794\) | −19.8899 | −0.705868 | ||||||||
\(795\) | 36.1394 | 1.28173 | ||||||||
\(796\) | 25.2212 | 0.893942 | ||||||||
\(797\) | −45.8689 | −1.62476 | −0.812381 | − | 0.583128i | \(-0.801829\pi\) | ||||
−0.812381 | + | 0.583128i | \(0.801829\pi\) | |||||||
\(798\) | 19.5807 | 0.693148 | ||||||||
\(799\) | 5.74712 | 0.203318 | ||||||||
\(800\) | 21.8201 | 0.771458 | ||||||||
\(801\) | −4.68455 | −0.165521 | ||||||||
\(802\) | 70.0456 | 2.47340 | ||||||||
\(803\) | 15.0514 | 0.531154 | ||||||||
\(804\) | 16.4805 | 0.581223 | ||||||||
\(805\) | 41.5615 | 1.46485 | ||||||||
\(806\) | 32.1923 | 1.13393 | ||||||||
\(807\) | 6.01468 | 0.211727 | ||||||||
\(808\) | −7.41322 | −0.260796 | ||||||||
\(809\) | 27.3337 | 0.961003 | 0.480502 | − | 0.876994i | \(-0.340455\pi\) | ||||
0.480502 | + | 0.876994i | \(0.340455\pi\) | |||||||
\(810\) | −5.29656 | −0.186102 | ||||||||
\(811\) | 33.6663 | 1.18218 | 0.591092 | − | 0.806604i | \(-0.298697\pi\) | ||||
0.591092 | + | 0.806604i | \(0.298697\pi\) | |||||||
\(812\) | 8.51536 | 0.298831 | ||||||||
\(813\) | 24.3492 | 0.853962 | ||||||||
\(814\) | −86.0695 | −3.01674 | ||||||||
\(815\) | −64.8724 | −2.27238 | ||||||||
\(816\) | −4.83995 | −0.169432 | ||||||||
\(817\) | 4.67052 | 0.163401 | ||||||||
\(818\) | 36.8765 | 1.28935 | ||||||||
\(819\) | −7.09099 | −0.247779 | ||||||||
\(820\) | 24.4325 | 0.853221 | ||||||||
\(821\) | 16.0006 | 0.558425 | 0.279213 | − | 0.960229i | \(-0.409927\pi\) | ||||
0.279213 | + | 0.960229i | \(0.409927\pi\) | |||||||
\(822\) | 34.6459 | 1.20841 | ||||||||
\(823\) | 13.6616 | 0.476214 | 0.238107 | − | 0.971239i | \(-0.423473\pi\) | ||||
0.238107 | + | 0.971239i | \(0.423473\pi\) | |||||||
\(824\) | 7.83458 | 0.272931 | ||||||||
\(825\) | 20.7610 | 0.722806 | ||||||||
\(826\) | −38.7830 | −1.34943 | ||||||||
\(827\) | 41.8606 | 1.45563 | 0.727817 | − | 0.685771i | \(-0.240535\pi\) | ||||
0.727817 | + | 0.685771i | \(0.240535\pi\) | |||||||
\(828\) | −11.6260 | −0.404033 | ||||||||
\(829\) | 32.7708 | 1.13818 | 0.569088 | − | 0.822277i | \(-0.307296\pi\) | ||||
0.569088 | + | 0.822277i | \(0.307296\pi\) | |||||||
\(830\) | −73.4026 | −2.54784 | ||||||||
\(831\) | 0.321627 | 0.0111571 | ||||||||
\(832\) | −10.9742 | −0.380461 | ||||||||
\(833\) | 3.96390 | 0.137341 | ||||||||
\(834\) | 27.1483 | 0.940070 | ||||||||
\(835\) | −34.5388 | −1.19526 | ||||||||
\(836\) | 54.4906 | 1.88460 | ||||||||
\(837\) | 4.29002 | 0.148285 | ||||||||
\(838\) | 59.6861 | 2.06182 | ||||||||
\(839\) | −3.14118 | −0.108446 | −0.0542228 | − | 0.998529i | \(-0.517268\pi\) | ||||
−0.0542228 | + | 0.998529i | \(0.517268\pi\) | |||||||
\(840\) | 5.53674 | 0.191036 | ||||||||
\(841\) | −16.8159 | −0.579860 | ||||||||
\(842\) | 44.2169 | 1.52382 | ||||||||
\(843\) | −3.42570 | −0.117987 | ||||||||
\(844\) | 15.9254 | 0.548176 | ||||||||
\(845\) | 10.2300 | 0.351922 | ||||||||
\(846\) | 10.5973 | 0.364342 | ||||||||
\(847\) | −51.8974 | −1.78322 | ||||||||
\(848\) | 60.8935 | 2.09109 | ||||||||
\(849\) | −22.1038 | −0.758601 | ||||||||
\(850\) | 5.99441 | 0.205606 | ||||||||
\(851\) | 60.6934 | 2.08054 | ||||||||
\(852\) | −12.5322 | −0.429348 | ||||||||
\(853\) | −30.4555 | −1.04278 | −0.521389 | − | 0.853319i | \(-0.674586\pi\) | ||||
−0.521389 | + | 0.853319i | \(0.674586\pi\) | |||||||
\(854\) | 34.9429 | 1.19572 | ||||||||
\(855\) | −17.5056 | −0.598678 | ||||||||
\(856\) | 14.4886 | 0.495210 | ||||||||
\(857\) | 32.1949 | 1.09976 | 0.549878 | − | 0.835245i | \(-0.314674\pi\) | ||||
0.549878 | + | 0.835245i | \(0.314674\pi\) | |||||||
\(858\) | −47.9225 | −1.63605 | ||||||||
\(859\) | 6.01925 | 0.205374 | 0.102687 | − | 0.994714i | \(-0.467256\pi\) | ||||
0.102687 | + | 0.994714i | \(0.467256\pi\) | |||||||
\(860\) | −3.08204 | −0.105097 | ||||||||
\(861\) | 10.5859 | 0.360765 | ||||||||
\(862\) | −13.8734 | −0.472528 | ||||||||
\(863\) | −46.7530 | −1.59149 | −0.795745 | − | 0.605632i | \(-0.792920\pi\) | ||||
−0.795745 | + | 0.605632i | \(0.792920\pi\) | |||||||
\(864\) | −6.71205 | −0.228348 | ||||||||
\(865\) | −6.19025 | −0.210475 | ||||||||
\(866\) | −69.1557 | −2.35000 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 10.4657 | 0.355228 | ||||||||
\(869\) | −59.7512 | −2.02692 | ||||||||
\(870\) | −18.4880 | −0.626802 | ||||||||
\(871\) | −47.9039 | −1.62316 | ||||||||
\(872\) | −3.70114 | −0.125336 | ||||||||
\(873\) | −1.63896 | −0.0554704 | ||||||||
\(874\) | −93.3151 | −3.15643 | ||||||||
\(875\) | 8.75438 | 0.295952 | ||||||||
\(876\) | 3.29975 | 0.111488 | ||||||||
\(877\) | 30.1199 | 1.01708 | 0.508539 | − | 0.861039i | \(-0.330186\pi\) | ||||
0.508539 | + | 0.861039i | \(0.330186\pi\) | |||||||
\(878\) | −14.9673 | −0.505121 | ||||||||
\(879\) | 32.9636 | 1.11183 | ||||||||
\(880\) | 88.7846 | 2.99293 | ||||||||
\(881\) | −34.6280 | −1.16665 | −0.583323 | − | 0.812240i | \(-0.698248\pi\) | ||||
−0.583323 | + | 0.812240i | \(0.698248\pi\) | |||||||
\(882\) | 7.30914 | 0.246112 | ||||||||
\(883\) | 2.50462 | 0.0842870 | 0.0421435 | − | 0.999112i | \(-0.486581\pi\) | ||||
0.0421435 | + | 0.999112i | \(0.486581\pi\) | |||||||
\(884\) | −5.69768 | −0.191634 | ||||||||
\(885\) | 34.6729 | 1.16552 | ||||||||
\(886\) | 10.8256 | 0.363692 | ||||||||
\(887\) | −36.8409 | −1.23700 | −0.618498 | − | 0.785787i | \(-0.712258\pi\) | ||||
−0.618498 | + | 0.785787i | \(0.712258\pi\) | |||||||
\(888\) | 8.08546 | 0.271330 | ||||||||
\(889\) | −28.9966 | −0.972515 | ||||||||
\(890\) | 24.8120 | 0.831701 | ||||||||
\(891\) | −6.38626 | −0.213948 | ||||||||
\(892\) | −8.69058 | −0.290982 | ||||||||
\(893\) | 35.0248 | 1.17206 | ||||||||
\(894\) | 12.4124 | 0.415133 | ||||||||
\(895\) | 36.9692 | 1.23574 | ||||||||
\(896\) | 14.7266 | 0.491980 | ||||||||
\(897\) | 33.7934 | 1.12833 | ||||||||
\(898\) | 70.9813 | 2.36868 | ||||||||
\(899\) | 14.9746 | 0.499431 | ||||||||
\(900\) | 4.55147 | 0.151716 | ||||||||
\(901\) | 12.5814 | 0.419148 | ||||||||
\(902\) | 71.5417 | 2.38208 | ||||||||
\(903\) | −1.33536 | −0.0444379 | ||||||||
\(904\) | 12.2278 | 0.406691 | ||||||||
\(905\) | −44.3424 | −1.47399 | ||||||||
\(906\) | 14.0018 | 0.465177 | ||||||||
\(907\) | −39.8726 | −1.32395 | −0.661973 | − | 0.749528i | \(-0.730281\pi\) | ||||
−0.661973 | + | 0.749528i | \(0.730281\pi\) | |||||||
\(908\) | 2.58138 | 0.0856660 | ||||||||
\(909\) | −6.70134 | −0.222269 | ||||||||
\(910\) | 37.5579 | 1.24503 | ||||||||
\(911\) | −52.5470 | −1.74096 | −0.870479 | − | 0.492205i | \(-0.836191\pi\) | ||||
−0.870479 | + | 0.492205i | \(0.836191\pi\) | |||||||
\(912\) | −29.4962 | −0.976717 | ||||||||
\(913\) | −88.5042 | −2.92906 | ||||||||
\(914\) | −29.2717 | −0.968222 | ||||||||
\(915\) | −31.2398 | −1.03275 | ||||||||
\(916\) | 32.8837 | 1.08651 | ||||||||
\(917\) | −25.5446 | −0.843558 | ||||||||
\(918\) | −1.84393 | −0.0608587 | ||||||||
\(919\) | −54.9549 | −1.81280 | −0.906398 | − | 0.422425i | \(-0.861179\pi\) | ||||
−0.906398 | + | 0.422425i | \(0.861179\pi\) | |||||||
\(920\) | −26.3863 | −0.869930 | ||||||||
\(921\) | −31.1103 | −1.02512 | ||||||||
\(922\) | 13.2186 | 0.435331 | ||||||||
\(923\) | 36.4274 | 1.19902 | ||||||||
\(924\) | −15.5795 | −0.512528 | ||||||||
\(925\) | −23.7608 | −0.781251 | ||||||||
\(926\) | 36.4503 | 1.19783 | ||||||||
\(927\) | 7.08223 | 0.232611 | ||||||||
\(928\) | −23.4289 | −0.769090 | ||||||||
\(929\) | 43.1027 | 1.41415 | 0.707077 | − | 0.707137i | \(-0.250013\pi\) | ||||
0.707077 | + | 0.707137i | \(0.250013\pi\) | |||||||
\(930\) | −22.7224 | −0.745096 | ||||||||
\(931\) | 24.1573 | 0.791724 | ||||||||
\(932\) | 4.16863 | 0.136548 | ||||||||
\(933\) | 2.37507 | 0.0777562 | ||||||||
\(934\) | 6.22476 | 0.203680 | ||||||||
\(935\) | 18.3441 | 0.599917 | ||||||||
\(936\) | 4.50189 | 0.147149 | ||||||||
\(937\) | 12.4661 | 0.407251 | 0.203625 | − | 0.979049i | \(-0.434728\pi\) | ||||
0.203625 | + | 0.979049i | \(0.434728\pi\) | |||||||
\(938\) | −37.8202 | −1.23487 | ||||||||
\(939\) | −15.5403 | −0.507138 | ||||||||
\(940\) | −23.1127 | −0.753852 | ||||||||
\(941\) | −50.2431 | −1.63788 | −0.818939 | − | 0.573881i | \(-0.805437\pi\) | ||||
−0.818939 | + | 0.573881i | \(0.805437\pi\) | |||||||
\(942\) | 1.84393 | 0.0600784 | ||||||||
\(943\) | −50.4488 | −1.64284 | ||||||||
\(944\) | 58.4225 | 1.90149 | ||||||||
\(945\) | 5.00505 | 0.162814 | ||||||||
\(946\) | −9.02463 | −0.293416 | ||||||||
\(947\) | 40.2429 | 1.30772 | 0.653859 | − | 0.756616i | \(-0.273149\pi\) | ||||
0.653859 | + | 0.756616i | \(0.273149\pi\) | |||||||
\(948\) | −13.0993 | −0.425446 | ||||||||
\(949\) | −9.59136 | −0.311349 | ||||||||
\(950\) | 36.5319 | 1.18525 | ||||||||
\(951\) | −11.6488 | −0.377738 | ||||||||
\(952\) | 1.92754 | 0.0624720 | ||||||||
\(953\) | −28.8519 | −0.934606 | −0.467303 | − | 0.884097i | \(-0.654774\pi\) | ||||
−0.467303 | + | 0.884097i | \(0.654774\pi\) | |||||||
\(954\) | 23.1993 | 0.751103 | ||||||||
\(955\) | 24.1212 | 0.780544 | ||||||||
\(956\) | −17.9534 | −0.580655 | ||||||||
\(957\) | −22.2917 | −0.720587 | ||||||||
\(958\) | 30.0269 | 0.970124 | ||||||||
\(959\) | −32.7390 | −1.05720 | ||||||||
\(960\) | 7.74592 | 0.249998 | ||||||||
\(961\) | −12.5957 | −0.406313 | ||||||||
\(962\) | 54.8469 | 1.76833 | ||||||||
\(963\) | 13.0973 | 0.422054 | ||||||||
\(964\) | 2.45586 | 0.0790979 | ||||||||
\(965\) | 19.2153 | 0.618563 | ||||||||
\(966\) | 26.6799 | 0.858412 | ||||||||
\(967\) | 18.9260 | 0.608621 | 0.304310 | − | 0.952573i | \(-0.401574\pi\) | ||||
0.304310 | + | 0.952573i | \(0.401574\pi\) | |||||||
\(968\) | 32.9483 | 1.05900 | ||||||||
\(969\) | −6.09433 | −0.195778 | ||||||||
\(970\) | 8.68086 | 0.278725 | ||||||||
\(971\) | 5.12362 | 0.164425 | 0.0822124 | − | 0.996615i | \(-0.473801\pi\) | ||||
0.0822124 | + | 0.996615i | \(0.473801\pi\) | |||||||
\(972\) | −1.40007 | −0.0449072 | ||||||||
\(973\) | −25.6541 | −0.822434 | ||||||||
\(974\) | −30.2478 | −0.969202 | ||||||||
\(975\) | −13.2297 | −0.423691 | ||||||||
\(976\) | −52.6378 | −1.68490 | ||||||||
\(977\) | −23.3811 | −0.748029 | −0.374014 | − | 0.927423i | \(-0.622019\pi\) | ||||
−0.374014 | + | 0.927423i | \(0.622019\pi\) | |||||||
\(978\) | −41.6441 | −1.33163 | ||||||||
\(979\) | 29.9168 | 0.956144 | ||||||||
\(980\) | −15.9413 | −0.509225 | ||||||||
\(981\) | −3.34572 | −0.106821 | ||||||||
\(982\) | 18.5756 | 0.592770 | ||||||||
\(983\) | 25.5210 | 0.813994 | 0.406997 | − | 0.913430i | \(-0.366576\pi\) | ||||
0.406997 | + | 0.913430i | \(0.366576\pi\) | |||||||
\(984\) | −6.72069 | −0.214248 | ||||||||
\(985\) | −28.7525 | −0.916131 | ||||||||
\(986\) | −6.43635 | −0.204975 | ||||||||
\(987\) | −10.0140 | −0.318750 | ||||||||
\(988\) | −34.7235 | −1.10470 | ||||||||
\(989\) | 6.36387 | 0.202359 | ||||||||
\(990\) | 33.8252 | 1.07504 | ||||||||
\(991\) | −49.6811 | −1.57817 | −0.789086 | − | 0.614282i | \(-0.789446\pi\) | ||||
−0.789086 | + | 0.614282i | \(0.789446\pi\) | |||||||
\(992\) | −28.7948 | −0.914237 | ||||||||
\(993\) | −25.0357 | −0.794484 | ||||||||
\(994\) | 28.7595 | 0.912196 | ||||||||
\(995\) | 51.7448 | 1.64042 | ||||||||
\(996\) | −19.4029 | −0.614804 | ||||||||
\(997\) | −19.8543 | −0.628791 | −0.314395 | − | 0.949292i | \(-0.601802\pi\) | ||||
−0.314395 | + | 0.949292i | \(0.601802\pi\) | |||||||
\(998\) | 13.0176 | 0.412064 | ||||||||
\(999\) | 7.30902 | 0.231247 |
(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 | 8007.2.a.g.1.13 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.g.1.13 | ✓ | 56 | 1.1 | even | 1 | trivial |