Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.7457527933.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 6x^{6} + 23x^{5} - 4x^{4} - 27x^{3} + 8x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.35554\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.04183 | −1.44379 | −0.721897 | − | 0.692001i | \(-0.756729\pi\) | ||||
−0.721897 | + | 0.692001i | \(0.756729\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.16908 | 1.08454 | ||||||||
\(5\) | 3.68950 | 1.64999 | 0.824996 | − | 0.565138i | \(-0.191177\pi\) | ||||
0.824996 | + | 0.565138i | \(0.191177\pi\) | |||||||
\(6\) | −2.04183 | −0.833575 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.345232 | −0.122058 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −7.53333 | −2.38225 | ||||||||
\(11\) | 0.232219 | 0.0700165 | 0.0350083 | − | 0.999387i | \(-0.488854\pi\) | ||||
0.0350083 | + | 0.999387i | \(0.488854\pi\) | |||||||
\(12\) | 2.16908 | 0.626159 | ||||||||
\(13\) | −2.59232 | −0.718979 | −0.359490 | − | 0.933149i | \(-0.617049\pi\) | ||||
−0.359490 | + | 0.933149i | \(0.617049\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.68950 | 0.952624 | ||||||||
\(16\) | −3.63325 | −0.908313 | ||||||||
\(17\) | −4.71395 | −1.14330 | −0.571650 | − | 0.820497i | \(-0.693697\pi\) | ||||
−0.571650 | + | 0.820497i | \(0.693697\pi\) | |||||||
\(18\) | −2.04183 | −0.481265 | ||||||||
\(19\) | 7.74581 | 1.77701 | 0.888505 | − | 0.458866i | \(-0.151744\pi\) | ||||
0.888505 | + | 0.458866i | \(0.151744\pi\) | |||||||
\(20\) | 8.00281 | 1.78948 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.474151 | −0.101089 | ||||||||
\(23\) | 8.48752 | 1.76977 | 0.884885 | − | 0.465810i | \(-0.154237\pi\) | ||||
0.884885 | + | 0.465810i | \(0.154237\pi\) | |||||||
\(24\) | −0.345232 | −0.0704702 | ||||||||
\(25\) | 8.61238 | 1.72248 | ||||||||
\(26\) | 5.29308 | 1.03806 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.10946 | −0.763107 | −0.381554 | − | 0.924347i | \(-0.624611\pi\) | ||||
−0.381554 | + | 0.924347i | \(0.624611\pi\) | |||||||
\(30\) | −7.53333 | −1.37539 | ||||||||
\(31\) | 10.4125 | 1.87015 | 0.935074 | − | 0.354454i | \(-0.115333\pi\) | ||||
0.935074 | + | 0.354454i | \(0.115333\pi\) | |||||||
\(32\) | 8.10896 | 1.43347 | ||||||||
\(33\) | 0.232219 | 0.0404241 | ||||||||
\(34\) | 9.62509 | 1.65069 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.16908 | 0.361513 | ||||||||
\(37\) | −8.13831 | −1.33793 | −0.668965 | − | 0.743294i | \(-0.733262\pi\) | ||||
−0.668965 | + | 0.743294i | \(0.733262\pi\) | |||||||
\(38\) | −15.8156 | −2.56564 | ||||||||
\(39\) | −2.59232 | −0.415103 | ||||||||
\(40\) | −1.27373 | −0.201395 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.59910 | 0.396360 | 0.198180 | − | 0.980166i | \(-0.436497\pi\) | ||||
0.198180 | + | 0.980166i | \(0.436497\pi\) | |||||||
\(44\) | 0.503701 | 0.0759357 | ||||||||
\(45\) | 3.68950 | 0.549998 | ||||||||
\(46\) | −17.3301 | −2.55518 | ||||||||
\(47\) | −3.41324 | −0.497872 | −0.248936 | − | 0.968520i | \(-0.580081\pi\) | ||||
−0.248936 | + | 0.968520i | \(0.580081\pi\) | |||||||
\(48\) | −3.63325 | −0.524415 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −17.5850 | −2.48690 | ||||||||
\(51\) | −4.71395 | −0.660085 | ||||||||
\(52\) | −5.62294 | −0.779761 | ||||||||
\(53\) | −3.35153 | −0.460368 | −0.230184 | − | 0.973147i | \(-0.573933\pi\) | ||||
−0.230184 | + | 0.973147i | \(0.573933\pi\) | |||||||
\(54\) | −2.04183 | −0.277858 | ||||||||
\(55\) | 0.856770 | 0.115527 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.74581 | 1.02596 | ||||||||
\(58\) | 8.39082 | 1.10177 | ||||||||
\(59\) | 8.02496 | 1.04476 | 0.522380 | − | 0.852713i | \(-0.325044\pi\) | ||||
0.522380 | + | 0.852713i | \(0.325044\pi\) | |||||||
\(60\) | 8.00281 | 1.03316 | ||||||||
\(61\) | −13.1267 | −1.68070 | −0.840351 | − | 0.542042i | \(-0.817651\pi\) | ||||
−0.840351 | + | 0.542042i | \(0.817651\pi\) | |||||||
\(62\) | −21.2607 | −2.70011 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.29063 | −1.16133 | ||||||||
\(65\) | −9.56434 | −1.18631 | ||||||||
\(66\) | −0.474151 | −0.0583640 | ||||||||
\(67\) | 6.60562 | 0.807005 | 0.403503 | − | 0.914978i | \(-0.367793\pi\) | ||||
0.403503 | + | 0.914978i | \(0.367793\pi\) | |||||||
\(68\) | −10.2249 | −1.23996 | ||||||||
\(69\) | 8.48752 | 1.02178 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.23226 | 0.383599 | 0.191800 | − | 0.981434i | \(-0.438568\pi\) | ||||
0.191800 | + | 0.981434i | \(0.438568\pi\) | |||||||
\(72\) | −0.345232 | −0.0406860 | ||||||||
\(73\) | 6.63277 | 0.776307 | 0.388153 | − | 0.921595i | \(-0.373113\pi\) | ||||
0.388153 | + | 0.921595i | \(0.373113\pi\) | |||||||
\(74\) | 16.6171 | 1.93169 | ||||||||
\(75\) | 8.61238 | 0.994472 | ||||||||
\(76\) | 16.8013 | 1.92724 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.29308 | 0.599323 | ||||||||
\(79\) | −5.24998 | −0.590669 | −0.295334 | − | 0.955394i | \(-0.595431\pi\) | ||||
−0.295334 | + | 0.955394i | \(0.595431\pi\) | |||||||
\(80\) | −13.4049 | −1.49871 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.04183 | −0.225483 | ||||||||
\(83\) | −2.50998 | −0.275506 | −0.137753 | − | 0.990467i | \(-0.543988\pi\) | ||||
−0.137753 | + | 0.990467i | \(0.543988\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.3921 | −1.88644 | ||||||||
\(86\) | −5.30693 | −0.572261 | ||||||||
\(87\) | −4.10946 | −0.440580 | ||||||||
\(88\) | −0.0801693 | −0.00854607 | ||||||||
\(89\) | −13.2734 | −1.40698 | −0.703490 | − | 0.710705i | \(-0.748376\pi\) | ||||
−0.703490 | + | 0.710705i | \(0.748376\pi\) | |||||||
\(90\) | −7.53333 | −0.794083 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 18.4101 | 1.91939 | ||||||||
\(93\) | 10.4125 | 1.07973 | ||||||||
\(94\) | 6.96926 | 0.718825 | ||||||||
\(95\) | 28.5781 | 2.93206 | ||||||||
\(96\) | 8.10896 | 0.827617 | ||||||||
\(97\) | 7.90714 | 0.802848 | 0.401424 | − | 0.915892i | \(-0.368515\pi\) | ||||
0.401424 | + | 0.915892i | \(0.368515\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.232219 | 0.0233388 | ||||||||
\(100\) | 18.6809 | 1.86809 | ||||||||
\(101\) | 10.8529 | 1.07990 | 0.539950 | − | 0.841697i | \(-0.318443\pi\) | ||||
0.539950 | + | 0.841697i | \(0.318443\pi\) | |||||||
\(102\) | 9.62509 | 0.953026 | ||||||||
\(103\) | 5.28687 | 0.520931 | 0.260465 | − | 0.965483i | \(-0.416124\pi\) | ||||
0.260465 | + | 0.965483i | \(0.416124\pi\) | |||||||
\(104\) | 0.894950 | 0.0877571 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.84326 | 0.664676 | ||||||||
\(107\) | 6.23899 | 0.603146 | 0.301573 | − | 0.953443i | \(-0.402488\pi\) | ||||
0.301573 | + | 0.953443i | \(0.402488\pi\) | |||||||
\(108\) | 2.16908 | 0.208720 | ||||||||
\(109\) | 4.43703 | 0.424990 | 0.212495 | − | 0.977162i | \(-0.431841\pi\) | ||||
0.212495 | + | 0.977162i | \(0.431841\pi\) | |||||||
\(110\) | −1.74938 | −0.166797 | ||||||||
\(111\) | −8.13831 | −0.772454 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.5852 | 1.84243 | 0.921213 | − | 0.389060i | \(-0.127200\pi\) | ||||
0.921213 | + | 0.389060i | \(0.127200\pi\) | |||||||
\(114\) | −15.8156 | −1.48127 | ||||||||
\(115\) | 31.3147 | 2.92011 | ||||||||
\(116\) | −8.91374 | −0.827620 | ||||||||
\(117\) | −2.59232 | −0.239660 | ||||||||
\(118\) | −16.3856 | −1.50842 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.27373 | −0.116275 | ||||||||
\(121\) | −10.9461 | −0.995098 | ||||||||
\(122\) | 26.8025 | 2.42659 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 22.5856 | 2.02825 | ||||||||
\(125\) | 13.3279 | 1.19208 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.3392 | 1.36114 | 0.680568 | − | 0.732685i | \(-0.261733\pi\) | ||||
0.680568 | + | 0.732685i | \(0.261733\pi\) | |||||||
\(128\) | 2.75199 | 0.243244 | ||||||||
\(129\) | 2.59910 | 0.228838 | ||||||||
\(130\) | 19.5288 | 1.71279 | ||||||||
\(131\) | −17.1723 | −1.50035 | −0.750176 | − | 0.661239i | \(-0.770031\pi\) | ||||
−0.750176 | + | 0.661239i | \(0.770031\pi\) | |||||||
\(132\) | 0.503701 | 0.0438415 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.4876 | −1.16515 | ||||||||
\(135\) | 3.68950 | 0.317541 | ||||||||
\(136\) | 1.62741 | 0.139549 | ||||||||
\(137\) | 9.02525 | 0.771079 | 0.385540 | − | 0.922691i | \(-0.374015\pi\) | ||||
0.385540 | + | 0.922691i | \(0.374015\pi\) | |||||||
\(138\) | −17.3301 | −1.47524 | ||||||||
\(139\) | −11.0833 | −0.940071 | −0.470036 | − | 0.882647i | \(-0.655759\pi\) | ||||
−0.470036 | + | 0.882647i | \(0.655759\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.41324 | −0.287447 | ||||||||
\(142\) | −6.59974 | −0.553838 | ||||||||
\(143\) | −0.601984 | −0.0503404 | ||||||||
\(144\) | −3.63325 | −0.302771 | ||||||||
\(145\) | −15.1618 | −1.25912 | ||||||||
\(146\) | −13.5430 | −1.12083 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −17.6526 | −1.45104 | ||||||||
\(149\) | 10.2152 | 0.836862 | 0.418431 | − | 0.908249i | \(-0.362580\pi\) | ||||
0.418431 | + | 0.908249i | \(0.362580\pi\) | |||||||
\(150\) | −17.5850 | −1.43581 | ||||||||
\(151\) | −5.71699 | −0.465242 | −0.232621 | − | 0.972567i | \(-0.574730\pi\) | ||||
−0.232621 | + | 0.972567i | \(0.574730\pi\) | |||||||
\(152\) | −2.67410 | −0.216898 | ||||||||
\(153\) | −4.71395 | −0.381100 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 38.4170 | 3.08573 | ||||||||
\(156\) | −5.62294 | −0.450195 | ||||||||
\(157\) | 5.45503 | 0.435359 | 0.217679 | − | 0.976020i | \(-0.430151\pi\) | ||||
0.217679 | + | 0.976020i | \(0.430151\pi\) | |||||||
\(158\) | 10.7196 | 0.852804 | ||||||||
\(159\) | −3.35153 | −0.265794 | ||||||||
\(160\) | 29.9180 | 2.36522 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.04183 | −0.160422 | ||||||||
\(163\) | 12.6634 | 0.991874 | 0.495937 | − | 0.868358i | \(-0.334825\pi\) | ||||
0.495937 | + | 0.868358i | \(0.334825\pi\) | |||||||
\(164\) | 2.16908 | 0.169377 | ||||||||
\(165\) | 0.856770 | 0.0666994 | ||||||||
\(166\) | 5.12496 | 0.397774 | ||||||||
\(167\) | 11.4402 | 0.885268 | 0.442634 | − | 0.896702i | \(-0.354044\pi\) | ||||
0.442634 | + | 0.896702i | \(0.354044\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.27990 | −0.483069 | ||||||||
\(170\) | 35.5118 | 2.72363 | ||||||||
\(171\) | 7.74581 | 0.592337 | ||||||||
\(172\) | 5.63766 | 0.429868 | ||||||||
\(173\) | 12.2561 | 0.931818 | 0.465909 | − | 0.884833i | \(-0.345727\pi\) | ||||
0.465909 | + | 0.884833i | \(0.345727\pi\) | |||||||
\(174\) | 8.39082 | 0.636107 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.843709 | −0.0635970 | ||||||||
\(177\) | 8.02496 | 0.603193 | ||||||||
\(178\) | 27.1021 | 2.03139 | ||||||||
\(179\) | −6.29779 | −0.470719 | −0.235359 | − | 0.971908i | \(-0.575627\pi\) | ||||
−0.235359 | + | 0.971908i | \(0.575627\pi\) | |||||||
\(180\) | 8.00281 | 0.596494 | ||||||||
\(181\) | −18.8748 | −1.40296 | −0.701478 | − | 0.712691i | \(-0.747476\pi\) | ||||
−0.701478 | + | 0.712691i | \(0.747476\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.1267 | −0.970354 | ||||||||
\(184\) | −2.93016 | −0.216014 | ||||||||
\(185\) | −30.0263 | −2.20757 | ||||||||
\(186\) | −21.2607 | −1.55891 | ||||||||
\(187\) | −1.09467 | −0.0800500 | ||||||||
\(188\) | −7.40359 | −0.539962 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −58.3518 | −4.23328 | ||||||||
\(191\) | 7.98832 | 0.578014 | 0.289007 | − | 0.957327i | \(-0.406675\pi\) | ||||
0.289007 | + | 0.957327i | \(0.406675\pi\) | |||||||
\(192\) | −9.29063 | −0.670493 | ||||||||
\(193\) | −8.36539 | −0.602154 | −0.301077 | − | 0.953600i | \(-0.597346\pi\) | ||||
−0.301077 | + | 0.953600i | \(0.597346\pi\) | |||||||
\(194\) | −16.1451 | −1.15915 | ||||||||
\(195\) | −9.56434 | −0.684917 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.1945 | −1.43880 | −0.719401 | − | 0.694595i | \(-0.755583\pi\) | ||||
−0.719401 | + | 0.694595i | \(0.755583\pi\) | |||||||
\(198\) | −0.474151 | −0.0336965 | ||||||||
\(199\) | −2.42833 | −0.172140 | −0.0860700 | − | 0.996289i | \(-0.527431\pi\) | ||||
−0.0860700 | + | 0.996289i | \(0.527431\pi\) | |||||||
\(200\) | −2.97327 | −0.210242 | ||||||||
\(201\) | 6.60562 | 0.465925 | ||||||||
\(202\) | −22.1597 | −1.55915 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −10.2249 | −0.715888 | ||||||||
\(205\) | 3.68950 | 0.257686 | ||||||||
\(206\) | −10.7949 | −0.752116 | ||||||||
\(207\) | 8.48752 | 0.589923 | ||||||||
\(208\) | 9.41854 | 0.653058 | ||||||||
\(209\) | 1.79872 | 0.124420 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.1756 | −0.700514 | −0.350257 | − | 0.936654i | \(-0.613906\pi\) | ||||
−0.350257 | + | 0.936654i | \(0.613906\pi\) | |||||||
\(212\) | −7.26973 | −0.499287 | ||||||||
\(213\) | 3.23226 | 0.221471 | ||||||||
\(214\) | −12.7390 | −0.870819 | ||||||||
\(215\) | 9.58938 | 0.653991 | ||||||||
\(216\) | −0.345232 | −0.0234901 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.05967 | −0.613598 | ||||||||
\(219\) | 6.63277 | 0.448201 | ||||||||
\(220\) | 1.85840 | 0.125293 | ||||||||
\(221\) | 12.2200 | 0.822009 | ||||||||
\(222\) | 16.6171 | 1.11526 | ||||||||
\(223\) | −18.3685 | −1.23004 | −0.615022 | − | 0.788510i | \(-0.710853\pi\) | ||||
−0.615022 | + | 0.788510i | \(0.710853\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.61238 | 0.574159 | ||||||||
\(226\) | −39.9898 | −2.66008 | ||||||||
\(227\) | −16.6244 | −1.10340 | −0.551700 | − | 0.834042i | \(-0.686021\pi\) | ||||
−0.551700 | + | 0.834042i | \(0.686021\pi\) | |||||||
\(228\) | 16.8013 | 1.11269 | ||||||||
\(229\) | 15.2296 | 1.00640 | 0.503200 | − | 0.864170i | \(-0.332156\pi\) | ||||
0.503200 | + | 0.864170i | \(0.332156\pi\) | |||||||
\(230\) | −63.9393 | −4.21603 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.41872 | 0.0931433 | ||||||||
\(233\) | 14.7310 | 0.965057 | 0.482528 | − | 0.875880i | \(-0.339719\pi\) | ||||
0.482528 | + | 0.875880i | \(0.339719\pi\) | |||||||
\(234\) | 5.29308 | 0.346019 | ||||||||
\(235\) | −12.5931 | −0.821486 | ||||||||
\(236\) | 17.4068 | 1.13308 | ||||||||
\(237\) | −5.24998 | −0.341023 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.3660 | 0.799889 | 0.399945 | − | 0.916539i | \(-0.369029\pi\) | ||||
0.399945 | + | 0.916539i | \(0.369029\pi\) | |||||||
\(240\) | −13.4049 | −0.865281 | ||||||||
\(241\) | −10.7234 | −0.690754 | −0.345377 | − | 0.938464i | \(-0.612249\pi\) | ||||
−0.345377 | + | 0.938464i | \(0.612249\pi\) | |||||||
\(242\) | 22.3500 | 1.43672 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −28.4729 | −1.82279 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.04183 | −0.130182 | ||||||||
\(247\) | −20.0796 | −1.27763 | ||||||||
\(248\) | −3.59474 | −0.228266 | ||||||||
\(249\) | −2.50998 | −0.159064 | ||||||||
\(250\) | −27.2133 | −1.72112 | ||||||||
\(251\) | 10.5518 | 0.666026 | 0.333013 | − | 0.942922i | \(-0.391935\pi\) | ||||
0.333013 | + | 0.942922i | \(0.391935\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.97096 | 0.123913 | ||||||||
\(254\) | −31.3201 | −1.96520 | ||||||||
\(255\) | −17.3921 | −1.08914 | ||||||||
\(256\) | 12.9622 | 0.810135 | ||||||||
\(257\) | 26.8542 | 1.67512 | 0.837561 | − | 0.546344i | \(-0.183981\pi\) | ||||
0.837561 | + | 0.546344i | \(0.183981\pi\) | |||||||
\(258\) | −5.30693 | −0.330395 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −20.7458 | −1.28660 | ||||||||
\(261\) | −4.10946 | −0.254369 | ||||||||
\(262\) | 35.0630 | 2.16620 | ||||||||
\(263\) | 22.8337 | 1.40799 | 0.703993 | − | 0.710207i | \(-0.251399\pi\) | ||||
0.703993 | + | 0.710207i | \(0.251399\pi\) | |||||||
\(264\) | −0.0801693 | −0.00493408 | ||||||||
\(265\) | −12.3655 | −0.759604 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.2734 | −0.812320 | ||||||||
\(268\) | 14.3281 | 0.875229 | ||||||||
\(269\) | 26.4506 | 1.61272 | 0.806360 | − | 0.591424i | \(-0.201434\pi\) | ||||
0.806360 | + | 0.591424i | \(0.201434\pi\) | |||||||
\(270\) | −7.53333 | −0.458464 | ||||||||
\(271\) | −8.75300 | −0.531707 | −0.265854 | − | 0.964013i | \(-0.585654\pi\) | ||||
−0.265854 | + | 0.964013i | \(0.585654\pi\) | |||||||
\(272\) | 17.1270 | 1.03848 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.4280 | −1.11328 | ||||||||
\(275\) | 1.99996 | 0.120602 | ||||||||
\(276\) | 18.4101 | 1.10816 | ||||||||
\(277\) | 6.44745 | 0.387390 | 0.193695 | − | 0.981062i | \(-0.437953\pi\) | ||||
0.193695 | + | 0.981062i | \(0.437953\pi\) | |||||||
\(278\) | 22.6302 | 1.35727 | ||||||||
\(279\) | 10.4125 | 0.623382 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.5896 | −1.28793 | −0.643965 | − | 0.765055i | \(-0.722712\pi\) | ||||
−0.643965 | + | 0.765055i | \(0.722712\pi\) | |||||||
\(282\) | 6.96926 | 0.415014 | ||||||||
\(283\) | −0.145666 | −0.00865894 | −0.00432947 | − | 0.999991i | \(-0.501378\pi\) | ||||
−0.00432947 | + | 0.999991i | \(0.501378\pi\) | |||||||
\(284\) | 7.01104 | 0.416029 | ||||||||
\(285\) | 28.5781 | 1.69282 | ||||||||
\(286\) | 1.22915 | 0.0726812 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 8.10896 | 0.477825 | ||||||||
\(289\) | 5.22132 | 0.307137 | ||||||||
\(290\) | 30.9579 | 1.81791 | ||||||||
\(291\) | 7.90714 | 0.463525 | ||||||||
\(292\) | 14.3870 | 0.841935 | ||||||||
\(293\) | 7.84054 | 0.458049 | 0.229025 | − | 0.973421i | \(-0.426446\pi\) | ||||
0.229025 | + | 0.973421i | \(0.426446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.6081 | 1.72385 | ||||||||
\(296\) | 2.80960 | 0.163305 | ||||||||
\(297\) | 0.232219 | 0.0134747 | ||||||||
\(298\) | −20.8577 | −1.20826 | ||||||||
\(299\) | −22.0023 | −1.27243 | ||||||||
\(300\) | 18.6809 | 1.07854 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.6731 | 0.671713 | ||||||||
\(303\) | 10.8529 | 0.623481 | ||||||||
\(304\) | −28.1425 | −1.61408 | ||||||||
\(305\) | −48.4309 | −2.77315 | ||||||||
\(306\) | 9.62509 | 0.550230 | ||||||||
\(307\) | 20.8939 | 1.19248 | 0.596238 | − | 0.802808i | \(-0.296662\pi\) | ||||
0.596238 | + | 0.802808i | \(0.296662\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.28687 | 0.300759 | ||||||||
\(310\) | −78.4411 | −4.45516 | ||||||||
\(311\) | 28.5586 | 1.61941 | 0.809706 | − | 0.586836i | \(-0.199627\pi\) | ||||
0.809706 | + | 0.586836i | \(0.199627\pi\) | |||||||
\(312\) | 0.894950 | 0.0506666 | ||||||||
\(313\) | −29.9521 | −1.69299 | −0.846497 | − | 0.532394i | \(-0.821293\pi\) | ||||
−0.846497 | + | 0.532394i | \(0.821293\pi\) | |||||||
\(314\) | −11.1382 | −0.628568 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.3876 | −0.640604 | ||||||||
\(317\) | −13.5173 | −0.759204 | −0.379602 | − | 0.925150i | \(-0.623939\pi\) | ||||
−0.379602 | + | 0.925150i | \(0.623939\pi\) | |||||||
\(318\) | 6.84326 | 0.383751 | ||||||||
\(319\) | −0.954292 | −0.0534301 | ||||||||
\(320\) | −34.2777 | −1.91618 | ||||||||
\(321\) | 6.23899 | 0.348227 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −36.5134 | −2.03166 | ||||||||
\(324\) | 2.16908 | 0.120504 | ||||||||
\(325\) | −22.3260 | −1.23842 | ||||||||
\(326\) | −25.8565 | −1.43206 | ||||||||
\(327\) | 4.43703 | 0.245368 | ||||||||
\(328\) | −0.345232 | −0.0190622 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.74938 | −0.0963002 | ||||||||
\(331\) | −0.476790 | −0.0262068 | −0.0131034 | − | 0.999914i | \(-0.504171\pi\) | ||||
−0.0131034 | + | 0.999914i | \(0.504171\pi\) | |||||||
\(332\) | −5.44435 | −0.298797 | ||||||||
\(333\) | −8.13831 | −0.445976 | ||||||||
\(334\) | −23.3589 | −1.27814 | ||||||||
\(335\) | 24.3714 | 1.33155 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.8216 | −1.13422 | −0.567111 | − | 0.823641i | \(-0.691939\pi\) | ||||
−0.567111 | + | 0.823641i | \(0.691939\pi\) | |||||||
\(338\) | 12.8225 | 0.697452 | ||||||||
\(339\) | 19.5852 | 1.06372 | ||||||||
\(340\) | −37.7248 | −2.04592 | ||||||||
\(341\) | 2.41799 | 0.130941 | ||||||||
\(342\) | −15.8156 | −0.855212 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.897294 | −0.0483788 | ||||||||
\(345\) | 31.3147 | 1.68592 | ||||||||
\(346\) | −25.0250 | −1.34535 | ||||||||
\(347\) | 9.11769 | 0.489463 | 0.244732 | − | 0.969591i | \(-0.421300\pi\) | ||||
0.244732 | + | 0.969591i | \(0.421300\pi\) | |||||||
\(348\) | −8.91374 | −0.477827 | ||||||||
\(349\) | 10.4817 | 0.561071 | 0.280535 | − | 0.959844i | \(-0.409488\pi\) | ||||
0.280535 | + | 0.959844i | \(0.409488\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.59232 | −0.138368 | ||||||||
\(352\) | 1.88305 | 0.100367 | ||||||||
\(353\) | −4.33421 | −0.230687 | −0.115343 | − | 0.993326i | \(-0.536797\pi\) | ||||
−0.115343 | + | 0.993326i | \(0.536797\pi\) | |||||||
\(354\) | −16.3856 | −0.870886 | ||||||||
\(355\) | 11.9254 | 0.632936 | ||||||||
\(356\) | −28.7911 | −1.52593 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.8590 | 0.679620 | ||||||||
\(359\) | 1.63625 | 0.0863578 | 0.0431789 | − | 0.999067i | \(-0.486251\pi\) | ||||
0.0431789 | + | 0.999067i | \(0.486251\pi\) | |||||||
\(360\) | −1.27373 | −0.0671316 | ||||||||
\(361\) | 40.9976 | 2.15777 | ||||||||
\(362\) | 38.5393 | 2.02558 | ||||||||
\(363\) | −10.9461 | −0.574520 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.4716 | 1.28090 | ||||||||
\(366\) | 26.8025 | 1.40099 | ||||||||
\(367\) | −19.6883 | −1.02772 | −0.513861 | − | 0.857873i | \(-0.671785\pi\) | ||||
−0.513861 | + | 0.857873i | \(0.671785\pi\) | |||||||
\(368\) | −30.8373 | −1.60751 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 61.3086 | 3.18728 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 22.5856 | 1.17101 | ||||||||
\(373\) | −1.93972 | −0.100435 | −0.0502175 | − | 0.998738i | \(-0.515991\pi\) | ||||
−0.0502175 | + | 0.998738i | \(0.515991\pi\) | |||||||
\(374\) | 2.23513 | 0.115576 | ||||||||
\(375\) | 13.3279 | 0.688248 | ||||||||
\(376\) | 1.17836 | 0.0607693 | ||||||||
\(377\) | 10.6530 | 0.548658 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.47525 | −0.178512 | −0.0892559 | − | 0.996009i | \(-0.528449\pi\) | ||||
−0.0892559 | + | 0.996009i | \(0.528449\pi\) | |||||||
\(380\) | 61.9883 | 3.17993 | ||||||||
\(381\) | 15.3392 | 0.785852 | ||||||||
\(382\) | −16.3108 | −0.834533 | ||||||||
\(383\) | 10.0079 | 0.511382 | 0.255691 | − | 0.966759i | \(-0.417697\pi\) | ||||
0.255691 | + | 0.966759i | \(0.417697\pi\) | |||||||
\(384\) | 2.75199 | 0.140437 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.0807 | 0.869386 | ||||||||
\(387\) | 2.59910 | 0.132120 | ||||||||
\(388\) | 17.1512 | 0.870721 | ||||||||
\(389\) | 21.7567 | 1.10311 | 0.551553 | − | 0.834140i | \(-0.314035\pi\) | ||||
0.551553 | + | 0.834140i | \(0.314035\pi\) | |||||||
\(390\) | 19.5288 | 0.988878 | ||||||||
\(391\) | −40.0097 | −2.02338 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.1723 | −0.866228 | ||||||||
\(394\) | 41.2339 | 2.07733 | ||||||||
\(395\) | −19.3698 | −0.974599 | ||||||||
\(396\) | 0.503701 | 0.0253119 | ||||||||
\(397\) | −23.6233 | −1.18562 | −0.592811 | − | 0.805342i | \(-0.701982\pi\) | ||||
−0.592811 | + | 0.805342i | \(0.701982\pi\) | |||||||
\(398\) | 4.95825 | 0.248535 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −31.2910 | −1.56455 | ||||||||
\(401\) | −3.67183 | −0.183362 | −0.0916812 | − | 0.995788i | \(-0.529224\pi\) | ||||
−0.0916812 | + | 0.995788i | \(0.529224\pi\) | |||||||
\(402\) | −13.4876 | −0.672699 | ||||||||
\(403\) | −26.9926 | −1.34460 | ||||||||
\(404\) | 23.5407 | 1.17119 | ||||||||
\(405\) | 3.68950 | 0.183333 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.88987 | −0.0936772 | ||||||||
\(408\) | 1.62741 | 0.0805686 | ||||||||
\(409\) | −18.6205 | −0.920724 | −0.460362 | − | 0.887731i | \(-0.652280\pi\) | ||||
−0.460362 | + | 0.887731i | \(0.652280\pi\) | |||||||
\(410\) | −7.53333 | −0.372045 | ||||||||
\(411\) | 9.02525 | 0.445183 | ||||||||
\(412\) | 11.4676 | 0.564970 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −17.3301 | −0.851727 | ||||||||
\(415\) | −9.26056 | −0.454583 | ||||||||
\(416\) | −21.0210 | −1.03064 | ||||||||
\(417\) | −11.0833 | −0.542750 | ||||||||
\(418\) | −3.67269 | −0.179637 | ||||||||
\(419\) | 20.3870 | 0.995971 | 0.497985 | − | 0.867185i | \(-0.334073\pi\) | ||||
0.497985 | + | 0.867185i | \(0.334073\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.4425 | −1.19125 | −0.595627 | − | 0.803261i | \(-0.703096\pi\) | ||||
−0.595627 | + | 0.803261i | \(0.703096\pi\) | |||||||
\(422\) | 20.7768 | 1.01140 | ||||||||
\(423\) | −3.41324 | −0.165957 | ||||||||
\(424\) | 1.15706 | 0.0561916 | ||||||||
\(425\) | −40.5983 | −1.96931 | ||||||||
\(426\) | −6.59974 | −0.319759 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 13.5329 | 0.654136 | ||||||||
\(429\) | −0.601984 | −0.0290641 | ||||||||
\(430\) | −19.5799 | −0.944227 | ||||||||
\(431\) | 7.83717 | 0.377503 | 0.188752 | − | 0.982025i | \(-0.439556\pi\) | ||||
0.188752 | + | 0.982025i | \(0.439556\pi\) | |||||||
\(432\) | −3.63325 | −0.174805 | ||||||||
\(433\) | −10.6522 | −0.511914 | −0.255957 | − | 0.966688i | \(-0.582390\pi\) | ||||
−0.255957 | + | 0.966688i | \(0.582390\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.1618 | −0.726954 | ||||||||
\(436\) | 9.62427 | 0.460919 | ||||||||
\(437\) | 65.7427 | 3.14490 | ||||||||
\(438\) | −13.5430 | −0.647110 | ||||||||
\(439\) | 24.6501 | 1.17649 | 0.588243 | − | 0.808684i | \(-0.299820\pi\) | ||||
0.588243 | + | 0.808684i | \(0.299820\pi\) | |||||||
\(440\) | −0.295784 | −0.0141010 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.9513 | −1.18681 | ||||||||
\(443\) | −0.888234 | −0.0422013 | −0.0211006 | − | 0.999777i | \(-0.506717\pi\) | ||||
−0.0211006 | + | 0.999777i | \(0.506717\pi\) | |||||||
\(444\) | −17.6526 | −0.837757 | ||||||||
\(445\) | −48.9722 | −2.32151 | ||||||||
\(446\) | 37.5054 | 1.77593 | ||||||||
\(447\) | 10.2152 | 0.483162 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.6747 | −0.928505 | −0.464252 | − | 0.885703i | \(-0.653677\pi\) | ||||
−0.464252 | + | 0.885703i | \(0.653677\pi\) | |||||||
\(450\) | −17.5850 | −0.828967 | ||||||||
\(451\) | 0.232219 | 0.0109347 | ||||||||
\(452\) | 42.4820 | 1.99818 | ||||||||
\(453\) | −5.71699 | −0.268608 | ||||||||
\(454\) | 33.9443 | 1.59308 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.67410 | −0.125226 | ||||||||
\(457\) | −8.76520 | −0.410019 | −0.205009 | − | 0.978760i | \(-0.565722\pi\) | ||||
−0.205009 | + | 0.978760i | \(0.565722\pi\) | |||||||
\(458\) | −31.0963 | −1.45303 | ||||||||
\(459\) | −4.71395 | −0.220028 | ||||||||
\(460\) | 67.9240 | 3.16697 | ||||||||
\(461\) | −5.76370 | −0.268442 | −0.134221 | − | 0.990951i | \(-0.542853\pi\) | ||||
−0.134221 | + | 0.990951i | \(0.542853\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6187 | 0.493494 | 0.246747 | − | 0.969080i | \(-0.420638\pi\) | ||||
0.246747 | + | 0.969080i | \(0.420638\pi\) | |||||||
\(464\) | 14.9307 | 0.693140 | ||||||||
\(465\) | 38.4170 | 1.78155 | ||||||||
\(466\) | −30.0781 | −1.39334 | ||||||||
\(467\) | −31.6308 | −1.46370 | −0.731849 | − | 0.681467i | \(-0.761342\pi\) | ||||
−0.731849 | + | 0.681467i | \(0.761342\pi\) | |||||||
\(468\) | −5.62294 | −0.259920 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 25.7131 | 1.18606 | ||||||||
\(471\) | 5.45503 | 0.251354 | ||||||||
\(472\) | −2.77047 | −0.127521 | ||||||||
\(473\) | 0.603560 | 0.0277517 | ||||||||
\(474\) | 10.7196 | 0.492366 | ||||||||
\(475\) | 66.7099 | 3.06086 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.35153 | −0.153456 | ||||||||
\(478\) | −25.2493 | −1.15487 | ||||||||
\(479\) | −39.7627 | −1.81680 | −0.908401 | − | 0.418100i | \(-0.862696\pi\) | ||||
−0.908401 | + | 0.418100i | \(0.862696\pi\) | |||||||
\(480\) | 29.9180 | 1.36556 | ||||||||
\(481\) | 21.0971 | 0.961943 | ||||||||
\(482\) | 21.8954 | 0.997307 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −23.7429 | −1.07922 | ||||||||
\(485\) | 29.1734 | 1.32469 | ||||||||
\(486\) | −2.04183 | −0.0926194 | ||||||||
\(487\) | −13.8837 | −0.629132 | −0.314566 | − | 0.949236i | \(-0.601859\pi\) | ||||
−0.314566 | + | 0.949236i | \(0.601859\pi\) | |||||||
\(488\) | 4.53176 | 0.205143 | ||||||||
\(489\) | 12.6634 | 0.572659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.2751 | 0.915001 | 0.457501 | − | 0.889209i | \(-0.348745\pi\) | ||||
0.457501 | + | 0.889209i | \(0.348745\pi\) | |||||||
\(492\) | 2.16908 | 0.0977897 | ||||||||
\(493\) | 19.3718 | 0.872461 | ||||||||
\(494\) | 40.9992 | 1.84464 | ||||||||
\(495\) | 0.856770 | 0.0385089 | ||||||||
\(496\) | −37.8314 | −1.69868 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.12496 | 0.229655 | ||||||||
\(499\) | 9.76966 | 0.437350 | 0.218675 | − | 0.975798i | \(-0.429827\pi\) | ||||
0.218675 | + | 0.975798i | \(0.429827\pi\) | |||||||
\(500\) | 28.9092 | 1.29286 | ||||||||
\(501\) | 11.4402 | 0.511110 | ||||||||
\(502\) | −21.5451 | −0.961605 | ||||||||
\(503\) | 6.98768 | 0.311565 | 0.155783 | − | 0.987791i | \(-0.450210\pi\) | ||||
0.155783 | + | 0.987791i | \(0.450210\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 40.0416 | 1.78183 | ||||||||
\(506\) | −4.02437 | −0.178905 | ||||||||
\(507\) | −6.27990 | −0.278900 | ||||||||
\(508\) | 33.2720 | 1.47621 | ||||||||
\(509\) | −5.64474 | −0.250199 | −0.125099 | − | 0.992144i | \(-0.539925\pi\) | ||||
−0.125099 | + | 0.992144i | \(0.539925\pi\) | |||||||
\(510\) | 35.5118 | 1.57249 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −31.9705 | −1.41291 | ||||||||
\(513\) | 7.74581 | 0.341986 | ||||||||
\(514\) | −54.8319 | −2.41853 | ||||||||
\(515\) | 19.5059 | 0.859532 | ||||||||
\(516\) | 5.63766 | 0.248184 | ||||||||
\(517\) | −0.792618 | −0.0348593 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.2561 | 0.537985 | ||||||||
\(520\) | 3.30192 | 0.144799 | ||||||||
\(521\) | −18.6235 | −0.815910 | −0.407955 | − | 0.913002i | \(-0.633758\pi\) | ||||
−0.407955 | + | 0.913002i | \(0.633758\pi\) | |||||||
\(522\) | 8.39082 | 0.367256 | ||||||||
\(523\) | 27.5839 | 1.20616 | 0.603081 | − | 0.797680i | \(-0.293940\pi\) | ||||
0.603081 | + | 0.797680i | \(0.293940\pi\) | |||||||
\(524\) | −37.2481 | −1.62719 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −46.6226 | −2.03284 | ||||||||
\(527\) | −49.0842 | −2.13814 | ||||||||
\(528\) | −0.843709 | −0.0367177 | ||||||||
\(529\) | 49.0380 | 2.13208 | ||||||||
\(530\) | 25.2482 | 1.09671 | ||||||||
\(531\) | 8.02496 | 0.348254 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.59232 | −0.112286 | ||||||||
\(534\) | 27.1021 | 1.17282 | ||||||||
\(535\) | 23.0187 | 0.995187 | ||||||||
\(536\) | −2.28047 | −0.0985014 | ||||||||
\(537\) | −6.29779 | −0.271769 | ||||||||
\(538\) | −54.0077 | −2.32844 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.00281 | 0.344386 | ||||||||
\(541\) | −16.8601 | −0.724873 | −0.362437 | − | 0.932008i | \(-0.618055\pi\) | ||||
−0.362437 | + | 0.932008i | \(0.618055\pi\) | |||||||
\(542\) | 17.8722 | 0.767675 | ||||||||
\(543\) | −18.8748 | −0.809997 | ||||||||
\(544\) | −38.2252 | −1.63889 | ||||||||
\(545\) | 16.3704 | 0.701231 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.8296 | −0.762338 | −0.381169 | − | 0.924505i | \(-0.624478\pi\) | ||||
−0.381169 | + | 0.924505i | \(0.624478\pi\) | |||||||
\(548\) | 19.5765 | 0.836266 | ||||||||
\(549\) | −13.1267 | −0.560234 | ||||||||
\(550\) | −4.08357 | −0.174124 | ||||||||
\(551\) | −31.8311 | −1.35605 | ||||||||
\(552\) | −2.93016 | −0.124716 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −13.1646 | −0.559311 | ||||||||
\(555\) | −30.0263 | −1.27454 | ||||||||
\(556\) | −24.0405 | −1.01954 | ||||||||
\(557\) | −1.21738 | −0.0515820 | −0.0257910 | − | 0.999667i | \(-0.508210\pi\) | ||||
−0.0257910 | + | 0.999667i | \(0.508210\pi\) | |||||||
\(558\) | −21.2607 | −0.900036 | ||||||||
\(559\) | −6.73770 | −0.284974 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.09467 | −0.0462169 | ||||||||
\(562\) | 44.0824 | 1.85951 | ||||||||
\(563\) | 12.9116 | 0.544157 | 0.272079 | − | 0.962275i | \(-0.412289\pi\) | ||||
0.272079 | + | 0.962275i | \(0.412289\pi\) | |||||||
\(564\) | −7.40359 | −0.311747 | ||||||||
\(565\) | 72.2597 | 3.03999 | ||||||||
\(566\) | 0.297425 | 0.0125017 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.11588 | −0.0468213 | ||||||||
\(569\) | −6.13102 | −0.257026 | −0.128513 | − | 0.991708i | \(-0.541020\pi\) | ||||
−0.128513 | + | 0.991708i | \(0.541020\pi\) | |||||||
\(570\) | −58.3518 | −2.44409 | ||||||||
\(571\) | −30.1505 | −1.26176 | −0.630879 | − | 0.775881i | \(-0.717306\pi\) | ||||
−0.630879 | + | 0.775881i | \(0.717306\pi\) | |||||||
\(572\) | −1.30575 | −0.0545962 | ||||||||
\(573\) | 7.98832 | 0.333717 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 73.0977 | 3.04839 | ||||||||
\(576\) | −9.29063 | −0.387109 | ||||||||
\(577\) | 21.8970 | 0.911582 | 0.455791 | − | 0.890087i | \(-0.349356\pi\) | ||||
0.455791 | + | 0.890087i | \(0.349356\pi\) | |||||||
\(578\) | −10.6611 | −0.443442 | ||||||||
\(579\) | −8.36539 | −0.347654 | ||||||||
\(580\) | −32.8872 | −1.36557 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −16.1451 | −0.669234 | ||||||||
\(583\) | −0.778287 | −0.0322334 | ||||||||
\(584\) | −2.28984 | −0.0947544 | ||||||||
\(585\) | −9.56434 | −0.395437 | ||||||||
\(586\) | −16.0091 | −0.661329 | ||||||||
\(587\) | 18.7737 | 0.774873 | 0.387436 | − | 0.921896i | \(-0.373361\pi\) | ||||
0.387436 | + | 0.921896i | \(0.373361\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 80.6536 | 3.32327 | ||||||||
\(590\) | −60.4547 | −2.48888 | ||||||||
\(591\) | −20.1945 | −0.830692 | ||||||||
\(592\) | 29.5685 | 1.21526 | ||||||||
\(593\) | 1.40764 | 0.0578048 | 0.0289024 | − | 0.999582i | \(-0.490799\pi\) | ||||
0.0289024 | + | 0.999582i | \(0.490799\pi\) | |||||||
\(594\) | −0.474151 | −0.0194547 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.1576 | 0.907610 | ||||||||
\(597\) | −2.42833 | −0.0993850 | ||||||||
\(598\) | 44.9251 | 1.83712 | ||||||||
\(599\) | −31.7524 | −1.29737 | −0.648685 | − | 0.761057i | \(-0.724681\pi\) | ||||
−0.648685 | + | 0.761057i | \(0.724681\pi\) | |||||||
\(600\) | −2.97327 | −0.121383 | ||||||||
\(601\) | −16.8874 | −0.688853 | −0.344427 | − | 0.938813i | \(-0.611927\pi\) | ||||
−0.344427 | + | 0.938813i | \(0.611927\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.60562 | 0.269002 | ||||||||
\(604\) | −12.4006 | −0.504573 | ||||||||
\(605\) | −40.3855 | −1.64190 | ||||||||
\(606\) | −22.1597 | −0.900177 | ||||||||
\(607\) | 11.5151 | 0.467382 | 0.233691 | − | 0.972311i | \(-0.424920\pi\) | ||||
0.233691 | + | 0.972311i | \(0.424920\pi\) | |||||||
\(608\) | 62.8105 | 2.54730 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 98.8878 | 4.00385 | ||||||||
\(611\) | 8.84820 | 0.357960 | ||||||||
\(612\) | −10.2249 | −0.413318 | ||||||||
\(613\) | 20.5359 | 0.829438 | 0.414719 | − | 0.909949i | \(-0.363880\pi\) | ||||
0.414719 | + | 0.909949i | \(0.363880\pi\) | |||||||
\(614\) | −42.6618 | −1.72169 | ||||||||
\(615\) | 3.68950 | 0.148775 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.57898 | 0.0635675 | 0.0317837 | − | 0.999495i | \(-0.489881\pi\) | ||||
0.0317837 | + | 0.999495i | \(0.489881\pi\) | |||||||
\(618\) | −10.7949 | −0.434234 | ||||||||
\(619\) | 34.3577 | 1.38095 | 0.690476 | − | 0.723355i | \(-0.257401\pi\) | ||||
0.690476 | + | 0.723355i | \(0.257401\pi\) | |||||||
\(620\) | 83.3296 | 3.34660 | ||||||||
\(621\) | 8.48752 | 0.340592 | ||||||||
\(622\) | −58.3120 | −2.33810 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 9.41854 | 0.377043 | ||||||||
\(625\) | 6.11122 | 0.244449 | ||||||||
\(626\) | 61.1572 | 2.44433 | ||||||||
\(627\) | 1.79872 | 0.0718340 | ||||||||
\(628\) | 11.8324 | 0.472164 | ||||||||
\(629\) | 38.3636 | 1.52966 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.9149 | −0.792799 | −0.396399 | − | 0.918078i | \(-0.629740\pi\) | ||||
−0.396399 | + | 0.918078i | \(0.629740\pi\) | |||||||
\(632\) | 1.81246 | 0.0720958 | ||||||||
\(633\) | −10.1756 | −0.404442 | ||||||||
\(634\) | 27.6000 | 1.09613 | ||||||||
\(635\) | 56.5940 | 2.24586 | ||||||||
\(636\) | −7.26973 | −0.288264 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.94850 | 0.0771420 | ||||||||
\(639\) | 3.23226 | 0.127866 | ||||||||
\(640\) | 10.1534 | 0.401350 | ||||||||
\(641\) | 24.3992 | 0.963712 | 0.481856 | − | 0.876250i | \(-0.339963\pi\) | ||||
0.481856 | + | 0.876250i | \(0.339963\pi\) | |||||||
\(642\) | −12.7390 | −0.502767 | ||||||||
\(643\) | 42.8135 | 1.68840 | 0.844200 | − | 0.536028i | \(-0.180076\pi\) | ||||
0.844200 | + | 0.536028i | \(0.180076\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.58938 | 0.377582 | ||||||||
\(646\) | 74.5542 | 2.93329 | ||||||||
\(647\) | 9.68055 | 0.380582 | 0.190291 | − | 0.981728i | \(-0.439057\pi\) | ||||
0.190291 | + | 0.981728i | \(0.439057\pi\) | |||||||
\(648\) | −0.345232 | −0.0135620 | ||||||||
\(649\) | 1.86354 | 0.0731505 | ||||||||
\(650\) | 45.5860 | 1.78803 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 27.4679 | 1.07573 | ||||||||
\(653\) | −35.2294 | −1.37863 | −0.689317 | − | 0.724459i | \(-0.742089\pi\) | ||||
−0.689317 | + | 0.724459i | \(0.742089\pi\) | |||||||
\(654\) | −9.05967 | −0.354261 | ||||||||
\(655\) | −63.3572 | −2.47557 | ||||||||
\(656\) | −3.63325 | −0.141855 | ||||||||
\(657\) | 6.63277 | 0.258769 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.3702 | 0.481875 | 0.240937 | − | 0.970541i | \(-0.422545\pi\) | ||||
0.240937 | + | 0.970541i | \(0.422545\pi\) | |||||||
\(660\) | 1.85840 | 0.0723382 | ||||||||
\(661\) | 43.0998 | 1.67639 | 0.838193 | − | 0.545373i | \(-0.183612\pi\) | ||||
0.838193 | + | 0.545373i | \(0.183612\pi\) | |||||||
\(662\) | 0.973526 | 0.0378372 | ||||||||
\(663\) | 12.2200 | 0.474587 | ||||||||
\(664\) | 0.866525 | 0.0336277 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16.6171 | 0.643898 | ||||||||
\(667\) | −34.8791 | −1.35052 | ||||||||
\(668\) | 24.8147 | 0.960109 | ||||||||
\(669\) | −18.3685 | −0.710166 | ||||||||
\(670\) | −49.7624 | −1.92249 | ||||||||
\(671\) | −3.04827 | −0.117677 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.8091 | −1.61162 | −0.805811 | − | 0.592173i | \(-0.798270\pi\) | ||||
−0.805811 | + | 0.592173i | \(0.798270\pi\) | |||||||
\(674\) | 42.5141 | 1.63758 | ||||||||
\(675\) | 8.61238 | 0.331491 | ||||||||
\(676\) | −13.6216 | −0.523908 | ||||||||
\(677\) | 14.7030 | 0.565081 | 0.282541 | − | 0.959255i | \(-0.408823\pi\) | ||||
0.282541 | + | 0.959255i | \(0.408823\pi\) | |||||||
\(678\) | −39.9898 | −1.53580 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.00431 | 0.230255 | ||||||||
\(681\) | −16.6244 | −0.637049 | ||||||||
\(682\) | −4.93712 | −0.189052 | ||||||||
\(683\) | 25.6649 | 0.982040 | 0.491020 | − | 0.871148i | \(-0.336624\pi\) | ||||
0.491020 | + | 0.871148i | \(0.336624\pi\) | |||||||
\(684\) | 16.8013 | 0.642413 | ||||||||
\(685\) | 33.2986 | 1.27228 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.2296 | 0.581045 | ||||||||
\(688\) | −9.44320 | −0.360019 | ||||||||
\(689\) | 8.68822 | 0.330995 | ||||||||
\(690\) | −63.9393 | −2.43413 | ||||||||
\(691\) | −20.9970 | −0.798763 | −0.399381 | − | 0.916785i | \(-0.630775\pi\) | ||||
−0.399381 | + | 0.916785i | \(0.630775\pi\) | |||||||
\(692\) | 26.5846 | 1.01059 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.6168 | −0.706684 | ||||||||
\(695\) | −40.8917 | −1.55111 | ||||||||
\(696\) | 1.41872 | 0.0537763 | ||||||||
\(697\) | −4.71395 | −0.178554 | ||||||||
\(698\) | −21.4018 | −0.810070 | ||||||||
\(699\) | 14.7310 | 0.557176 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.6745 | 0.478709 | 0.239355 | − | 0.970932i | \(-0.423064\pi\) | ||||
0.239355 | + | 0.970932i | \(0.423064\pi\) | |||||||
\(702\) | 5.29308 | 0.199774 | ||||||||
\(703\) | −63.0378 | −2.37751 | ||||||||
\(704\) | −2.15746 | −0.0813122 | ||||||||
\(705\) | −12.5931 | −0.474285 | ||||||||
\(706\) | 8.84974 | 0.333064 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 17.4068 | 0.654187 | ||||||||
\(709\) | 2.37978 | 0.0893745 | 0.0446873 | − | 0.999001i | \(-0.485771\pi\) | ||||
0.0446873 | + | 0.999001i | \(0.485771\pi\) | |||||||
\(710\) | −24.3497 | −0.913829 | ||||||||
\(711\) | −5.24998 | −0.196890 | ||||||||
\(712\) | 4.58241 | 0.171733 | ||||||||
\(713\) | 88.3766 | 3.30973 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.22102 | −0.0830613 | ||||||||
\(716\) | −13.6604 | −0.510513 | ||||||||
\(717\) | 12.3660 | 0.461816 | ||||||||
\(718\) | −3.34094 | −0.124683 | ||||||||
\(719\) | 13.3645 | 0.498410 | 0.249205 | − | 0.968451i | \(-0.419831\pi\) | ||||
0.249205 | + | 0.968451i | \(0.419831\pi\) | |||||||
\(720\) | −13.4049 | −0.499570 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −83.7102 | −3.11537 | ||||||||
\(723\) | −10.7234 | −0.398807 | ||||||||
\(724\) | −40.9410 | −1.52156 | ||||||||
\(725\) | −35.3922 | −1.31443 | ||||||||
\(726\) | 22.3500 | 0.829488 | ||||||||
\(727\) | −3.33356 | −0.123635 | −0.0618175 | − | 0.998087i | \(-0.519690\pi\) | ||||
−0.0618175 | + | 0.998087i | \(0.519690\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −49.9668 | −1.84936 | ||||||||
\(731\) | −12.2520 | −0.453158 | ||||||||
\(732\) | −28.4729 | −1.05239 | ||||||||
\(733\) | 40.5226 | 1.49674 | 0.748368 | − | 0.663284i | \(-0.230838\pi\) | ||||
0.748368 | + | 0.663284i | \(0.230838\pi\) | |||||||
\(734\) | 40.2003 | 1.48382 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 68.8249 | 2.53692 | ||||||||
\(737\) | 1.53395 | 0.0565037 | ||||||||
\(738\) | −2.04183 | −0.0751609 | ||||||||
\(739\) | 0.959701 | 0.0353032 | 0.0176516 | − | 0.999844i | \(-0.494381\pi\) | ||||
0.0176516 | + | 0.999844i | \(0.494381\pi\) | |||||||
\(740\) | −65.1293 | −2.39420 | ||||||||
\(741\) | −20.0796 | −0.737642 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.4405 | −0.456399 | −0.228200 | − | 0.973614i | \(-0.573284\pi\) | ||||
−0.228200 | + | 0.973614i | \(0.573284\pi\) | |||||||
\(744\) | −3.59474 | −0.131790 | ||||||||
\(745\) | 37.6889 | 1.38082 | ||||||||
\(746\) | 3.96059 | 0.145007 | ||||||||
\(747\) | −2.50998 | −0.0918354 | ||||||||
\(748\) | −2.37442 | −0.0868174 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −27.2133 | −0.993689 | ||||||||
\(751\) | −46.6636 | −1.70278 | −0.851390 | − | 0.524534i | \(-0.824240\pi\) | ||||
−0.851390 | + | 0.524534i | \(0.824240\pi\) | |||||||
\(752\) | 12.4012 | 0.452224 | ||||||||
\(753\) | 10.5518 | 0.384531 | ||||||||
\(754\) | −21.7517 | −0.792149 | ||||||||
\(755\) | −21.0928 | −0.767646 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.4610 | −0.525593 | −0.262796 | − | 0.964851i | \(-0.584645\pi\) | ||||
−0.262796 | + | 0.964851i | \(0.584645\pi\) | |||||||
\(758\) | 7.09588 | 0.257734 | ||||||||
\(759\) | 1.97096 | 0.0715413 | ||||||||
\(760\) | −9.86609 | −0.357881 | ||||||||
\(761\) | 12.7440 | 0.461971 | 0.230985 | − | 0.972957i | \(-0.425805\pi\) | ||||
0.230985 | + | 0.972957i | \(0.425805\pi\) | |||||||
\(762\) | −31.3201 | −1.13461 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17.3273 | 0.626880 | ||||||||
\(765\) | −17.3921 | −0.628813 | ||||||||
\(766\) | −20.4345 | −0.738330 | ||||||||
\(767\) | −20.8032 | −0.751161 | ||||||||
\(768\) | 12.9622 | 0.467732 | ||||||||
\(769\) | −13.1820 | −0.475354 | −0.237677 | − | 0.971344i | \(-0.576386\pi\) | ||||
−0.237677 | + | 0.971344i | \(0.576386\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.8542 | 0.967132 | ||||||||
\(772\) | −18.1452 | −0.653060 | ||||||||
\(773\) | −7.05456 | −0.253735 | −0.126867 | − | 0.991920i | \(-0.540492\pi\) | ||||
−0.126867 | + | 0.991920i | \(0.540492\pi\) | |||||||
\(774\) | −5.30693 | −0.190754 | ||||||||
\(775\) | 89.6768 | 3.22128 | ||||||||
\(776\) | −2.72980 | −0.0979940 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −44.4235 | −1.59266 | ||||||||
\(779\) | 7.74581 | 0.277522 | ||||||||
\(780\) | −20.7458 | −0.742819 | ||||||||
\(781\) | 0.750592 | 0.0268583 | ||||||||
\(782\) | 81.6932 | 2.92134 | ||||||||
\(783\) | −4.10946 | −0.146860 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.1263 | 0.718338 | ||||||||
\(786\) | 35.0630 | 1.25065 | ||||||||
\(787\) | 27.9275 | 0.995507 | 0.497754 | − | 0.867318i | \(-0.334158\pi\) | ||||
0.497754 | + | 0.867318i | \(0.334158\pi\) | |||||||
\(788\) | −43.8036 | −1.56044 | ||||||||
\(789\) | 22.8337 | 0.812901 | ||||||||
\(790\) | 39.5498 | 1.40712 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.0801693 | −0.00284869 | ||||||||
\(793\) | 34.0286 | 1.20839 | ||||||||
\(794\) | 48.2349 | 1.71179 | ||||||||
\(795\) | −12.3655 | −0.438558 | ||||||||
\(796\) | −5.26725 | −0.186693 | ||||||||
\(797\) | 35.5823 | 1.26039 | 0.630196 | − | 0.776436i | \(-0.282975\pi\) | ||||
0.630196 | + | 0.776436i | \(0.282975\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.0898 | 0.569218 | ||||||||
\(800\) | 69.8374 | 2.46913 | ||||||||
\(801\) | −13.2734 | −0.468993 | ||||||||
\(802\) | 7.49726 | 0.264738 | ||||||||
\(803\) | 1.54025 | 0.0543543 | ||||||||
\(804\) | 14.3281 | 0.505314 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 55.1144 | 1.94132 | ||||||||
\(807\) | 26.4506 | 0.931105 | ||||||||
\(808\) | −3.74675 | −0.131810 | ||||||||
\(809\) | −35.9909 | −1.26537 | −0.632686 | − | 0.774408i | \(-0.718048\pi\) | ||||
−0.632686 | + | 0.774408i | \(0.718048\pi\) | |||||||
\(810\) | −7.53333 | −0.264694 | ||||||||
\(811\) | 26.9511 | 0.946380 | 0.473190 | − | 0.880960i | \(-0.343102\pi\) | ||||
0.473190 | + | 0.880960i | \(0.343102\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.75300 | −0.306981 | ||||||||
\(814\) | 3.85879 | 0.135251 | ||||||||
\(815\) | 46.7216 | 1.63659 | ||||||||
\(816\) | 17.1270 | 0.599564 | ||||||||
\(817\) | 20.1322 | 0.704335 | ||||||||
\(818\) | 38.0199 | 1.32934 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.00281 | 0.279470 | ||||||||
\(821\) | 15.8769 | 0.554109 | 0.277054 | − | 0.960854i | \(-0.410642\pi\) | ||||
0.277054 | + | 0.960854i | \(0.410642\pi\) | |||||||
\(822\) | −18.4280 | −0.642752 | ||||||||
\(823\) | 27.5922 | 0.961803 | 0.480902 | − | 0.876775i | \(-0.340309\pi\) | ||||
0.480902 | + | 0.876775i | \(0.340309\pi\) | |||||||
\(824\) | −1.82520 | −0.0635837 | ||||||||
\(825\) | 1.99996 | 0.0696295 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.0669 | −0.871661 | −0.435831 | − | 0.900029i | \(-0.643545\pi\) | ||||
−0.435831 | + | 0.900029i | \(0.643545\pi\) | |||||||
\(828\) | 18.4101 | 0.639795 | ||||||||
\(829\) | 41.4853 | 1.44084 | 0.720422 | − | 0.693536i | \(-0.243948\pi\) | ||||
0.720422 | + | 0.693536i | \(0.243948\pi\) | |||||||
\(830\) | 18.9085 | 0.656324 | ||||||||
\(831\) | 6.44745 | 0.223659 | ||||||||
\(832\) | 24.0842 | 0.834971 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 22.6302 | 0.783619 | ||||||||
\(835\) | 42.2085 | 1.46069 | ||||||||
\(836\) | 3.90157 | 0.134939 | ||||||||
\(837\) | 10.4125 | 0.359910 | ||||||||
\(838\) | −41.6269 | −1.43798 | ||||||||
\(839\) | 3.49825 | 0.120773 | 0.0603865 | − | 0.998175i | \(-0.480767\pi\) | ||||
0.0603865 | + | 0.998175i | \(0.480767\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.1124 | −0.417668 | ||||||||
\(842\) | 49.9075 | 1.71993 | ||||||||
\(843\) | −21.5896 | −0.743587 | ||||||||
\(844\) | −22.0716 | −0.759735 | ||||||||
\(845\) | −23.1697 | −0.797060 | ||||||||
\(846\) | 6.96926 | 0.239608 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.1770 | 0.418158 | ||||||||
\(849\) | −0.145666 | −0.00499924 | ||||||||
\(850\) | 82.8950 | 2.84328 | ||||||||
\(851\) | −69.0740 | −2.36783 | ||||||||
\(852\) | 7.01104 | 0.240194 | ||||||||
\(853\) | −46.0844 | −1.57790 | −0.788950 | − | 0.614458i | \(-0.789375\pi\) | ||||
−0.788950 | + | 0.614458i | \(0.789375\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 28.5781 | 0.977352 | ||||||||
\(856\) | −2.15390 | −0.0736188 | ||||||||
\(857\) | 48.0142 | 1.64013 | 0.820067 | − | 0.572267i | \(-0.193936\pi\) | ||||
0.820067 | + | 0.572267i | \(0.193936\pi\) | |||||||
\(858\) | 1.22915 | 0.0419625 | ||||||||
\(859\) | 20.2044 | 0.689365 | 0.344682 | − | 0.938719i | \(-0.387987\pi\) | ||||
0.344682 | + | 0.938719i | \(0.387987\pi\) | |||||||
\(860\) | 20.8001 | 0.709279 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.0022 | −0.545037 | ||||||||
\(863\) | −15.4157 | −0.524755 | −0.262377 | − | 0.964965i | \(-0.584507\pi\) | ||||
−0.262377 | + | 0.964965i | \(0.584507\pi\) | |||||||
\(864\) | 8.10896 | 0.275872 | ||||||||
\(865\) | 45.2190 | 1.53749 | ||||||||
\(866\) | 21.7501 | 0.739097 | ||||||||
\(867\) | 5.22132 | 0.177325 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.21914 | −0.0413566 | ||||||||
\(870\) | 30.9579 | 1.04957 | ||||||||
\(871\) | −17.1239 | −0.580220 | ||||||||
\(872\) | −1.53180 | −0.0518734 | ||||||||
\(873\) | 7.90714 | 0.267616 | ||||||||
\(874\) | −134.236 | −4.54059 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.3870 | 0.486092 | ||||||||
\(877\) | 14.7504 | 0.498084 | 0.249042 | − | 0.968493i | \(-0.419884\pi\) | ||||
0.249042 | + | 0.968493i | \(0.419884\pi\) | |||||||
\(878\) | −50.3314 | −1.69860 | ||||||||
\(879\) | 7.84054 | 0.264455 | ||||||||
\(880\) | −3.11286 | −0.104935 | ||||||||
\(881\) | −33.7312 | −1.13643 | −0.568216 | − | 0.822879i | \(-0.692366\pi\) | ||||
−0.568216 | + | 0.822879i | \(0.692366\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.2628 | 0.547286 | 0.273643 | − | 0.961831i | \(-0.411771\pi\) | ||||
0.273643 | + | 0.961831i | \(0.411771\pi\) | |||||||
\(884\) | 26.5063 | 0.891502 | ||||||||
\(885\) | 29.6081 | 0.995264 | ||||||||
\(886\) | 1.81362 | 0.0609299 | ||||||||
\(887\) | −32.9783 | −1.10730 | −0.553651 | − | 0.832749i | \(-0.686766\pi\) | ||||
−0.553651 | + | 0.832749i | \(0.686766\pi\) | |||||||
\(888\) | 2.80960 | 0.0942841 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 99.9931 | 3.35178 | ||||||||
\(891\) | 0.232219 | 0.00777962 | ||||||||
\(892\) | −39.8427 | −1.33403 | ||||||||
\(893\) | −26.4383 | −0.884724 | ||||||||
\(894\) | −20.8577 | −0.697587 | ||||||||
\(895\) | −23.2357 | −0.776682 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.0023 | −0.734636 | ||||||||
\(898\) | 40.1724 | 1.34057 | ||||||||
\(899\) | −42.7899 | −1.42712 | ||||||||
\(900\) | 18.6809 | 0.622698 | ||||||||
\(901\) | 15.7989 | 0.526339 | ||||||||
\(902\) | −0.474151 | −0.0157875 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.76145 | −0.224883 | ||||||||
\(905\) | −69.6386 | −2.31487 | ||||||||
\(906\) | 11.6731 | 0.387814 | ||||||||
\(907\) | −14.9899 | −0.497732 | −0.248866 | − | 0.968538i | \(-0.580058\pi\) | ||||
−0.248866 | + | 0.968538i | \(0.580058\pi\) | |||||||
\(908\) | −36.0597 | −1.19668 | ||||||||
\(909\) | 10.8529 | 0.359967 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.8616 | 1.25441 | 0.627205 | − | 0.778854i | \(-0.284199\pi\) | ||||
0.627205 | + | 0.778854i | \(0.284199\pi\) | |||||||
\(912\) | −28.1425 | −0.931891 | ||||||||
\(913\) | −0.582864 | −0.0192900 | ||||||||
\(914\) | 17.8971 | 0.591982 | ||||||||
\(915\) | −48.4309 | −1.60108 | ||||||||
\(916\) | 33.0342 | 1.09148 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 9.62509 | 0.317675 | ||||||||
\(919\) | −27.0097 | −0.890967 | −0.445484 | − | 0.895290i | \(-0.646968\pi\) | ||||
−0.445484 | + | 0.895290i | \(0.646968\pi\) | |||||||
\(920\) | −10.8108 | −0.356422 | ||||||||
\(921\) | 20.8939 | 0.688476 | ||||||||
\(922\) | 11.7685 | 0.387575 | ||||||||
\(923\) | −8.37905 | −0.275800 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −70.0902 | −2.30455 | ||||||||
\(926\) | −21.6817 | −0.712503 | ||||||||
\(927\) | 5.28687 | 0.173644 | ||||||||
\(928\) | −33.3234 | −1.09389 | ||||||||
\(929\) | 2.99013 | 0.0981030 | 0.0490515 | − | 0.998796i | \(-0.484380\pi\) | ||||
0.0490515 | + | 0.998796i | \(0.484380\pi\) | |||||||
\(930\) | −78.4411 | −2.57219 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 31.9526 | 1.04664 | ||||||||
\(933\) | 28.5586 | 0.934968 | ||||||||
\(934\) | 64.5848 | 2.11328 | ||||||||
\(935\) | −4.03877 | −0.132082 | ||||||||
\(936\) | 0.894950 | 0.0292524 | ||||||||
\(937\) | −24.0009 | −0.784076 | −0.392038 | − | 0.919949i | \(-0.628230\pi\) | ||||
−0.392038 | + | 0.919949i | \(0.628230\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.9521 | −0.977450 | ||||||||
\(940\) | −27.3155 | −0.890934 | ||||||||
\(941\) | 3.18393 | 0.103793 | 0.0518966 | − | 0.998652i | \(-0.483473\pi\) | ||||
0.0518966 | + | 0.998652i | \(0.483473\pi\) | |||||||
\(942\) | −11.1382 | −0.362904 | ||||||||
\(943\) | 8.48752 | 0.276392 | ||||||||
\(944\) | −29.1567 | −0.948970 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.23237 | −0.0400678 | ||||||||
\(947\) | 15.3342 | 0.498295 | 0.249147 | − | 0.968466i | \(-0.419850\pi\) | ||||
0.249147 | + | 0.968466i | \(0.419850\pi\) | |||||||
\(948\) | −11.3876 | −0.369853 | ||||||||
\(949\) | −17.1942 | −0.558148 | ||||||||
\(950\) | −136.210 | −4.41925 | ||||||||
\(951\) | −13.5173 | −0.438327 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.9900 | 0.841900 | 0.420950 | − | 0.907084i | \(-0.361697\pi\) | ||||
0.420950 | + | 0.907084i | \(0.361697\pi\) | |||||||
\(954\) | 6.84326 | 0.221559 | ||||||||
\(955\) | 29.4729 | 0.953720 | ||||||||
\(956\) | 26.8228 | 0.867511 | ||||||||
\(957\) | −0.954292 | −0.0308479 | ||||||||
\(958\) | 81.1887 | 2.62309 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −34.2777 | −1.10631 | ||||||||
\(961\) | 77.4210 | 2.49745 | ||||||||
\(962\) | −43.0767 | −1.38885 | ||||||||
\(963\) | 6.23899 | 0.201049 | ||||||||
\(964\) | −23.2599 | −0.749151 | ||||||||
\(965\) | −30.8641 | −0.993549 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.70119 | 0.183338 | 0.0916689 | − | 0.995790i | \(-0.470780\pi\) | ||||
0.0916689 | + | 0.995790i | \(0.470780\pi\) | |||||||
\(968\) | 3.77893 | 0.121460 | ||||||||
\(969\) | −36.5134 | −1.17298 | ||||||||
\(970\) | −59.5671 | −1.91258 | ||||||||
\(971\) | −46.4697 | −1.49128 | −0.745642 | − | 0.666347i | \(-0.767857\pi\) | ||||
−0.745642 | + | 0.666347i | \(0.767857\pi\) | |||||||
\(972\) | 2.16908 | 0.0695733 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 28.3482 | 0.908336 | ||||||||
\(975\) | −22.3260 | −0.715005 | ||||||||
\(976\) | 47.6926 | 1.52660 | ||||||||
\(977\) | 12.1107 | 0.387455 | 0.193728 | − | 0.981055i | \(-0.437942\pi\) | ||||
0.193728 | + | 0.981055i | \(0.437942\pi\) | |||||||
\(978\) | −25.8565 | −0.826801 | ||||||||
\(979\) | −3.08233 | −0.0985118 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.43703 | 0.141663 | ||||||||
\(982\) | −41.3983 | −1.32107 | ||||||||
\(983\) | −37.1662 | −1.18542 | −0.592709 | − | 0.805417i | \(-0.701942\pi\) | ||||
−0.592709 | + | 0.805417i | \(0.701942\pi\) | |||||||
\(984\) | −0.345232 | −0.0110056 | ||||||||
\(985\) | −74.5077 | −2.37401 | ||||||||
\(986\) | −39.5539 | −1.25965 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −43.5542 | −1.38564 | ||||||||
\(989\) | 22.0599 | 0.701465 | ||||||||
\(990\) | −1.74938 | −0.0555989 | ||||||||
\(991\) | −25.6087 | −0.813486 | −0.406743 | − | 0.913543i | \(-0.633336\pi\) | ||||
−0.406743 | + | 0.913543i | \(0.633336\pi\) | |||||||
\(992\) | 84.4348 | 2.68081 | ||||||||
\(993\) | −0.476790 | −0.0151305 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.95932 | −0.284030 | ||||||||
\(996\) | −5.44435 | −0.172511 | ||||||||
\(997\) | −4.04117 | −0.127985 | −0.0639925 | − | 0.997950i | \(-0.520383\pi\) | ||||
−0.0639925 | + | 0.997950i | \(0.520383\pi\) | |||||||
\(998\) | −19.9480 | −0.631443 | ||||||||
\(999\) | −8.13831 | −0.257485 |
(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 | 6027.2.a.bc.1.2 | 8 | ||
7.3 | odd | 6 | 861.2.i.d.247.7 | ✓ | 16 | ||
7.5 | odd | 6 | 861.2.i.d.739.7 | yes | 16 | ||
7.6 | odd | 2 | 6027.2.a.bb.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.d.247.7 | ✓ | 16 | 7.3 | odd | 6 | ||
861.2.i.d.739.7 | yes | 16 | 7.5 | odd | 6 | ||
6027.2.a.bb.1.2 | 8 | 7.6 | odd | 2 | |||
6027.2.a.bc.1.2 | 8 | 1.1 | even | 1 | trivial |