Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2738,2,Mod(1,2738)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2738, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2738.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2738 = 2 \cdot 37^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2738.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: | \(21.8630400734\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{36})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 6x^{4} + 9x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.96962\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2738.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.53209 | 0.884552 | 0.442276 | − | 0.896879i | \(-0.354171\pi\) | ||||
0.442276 | + | 0.896879i | \(0.354171\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.07935 | −1.37713 | −0.688563 | − | 0.725177i | \(-0.741758\pi\) | ||||
−0.688563 | + | 0.725177i | \(0.741758\pi\) | |||||||
\(6\) | 1.53209 | 0.625473 | ||||||||
\(7\) | 0.199962 | 0.0755785 | 0.0377893 | − | 0.999286i | \(-0.487968\pi\) | ||||
0.0377893 | + | 0.999286i | \(0.487968\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.652704 | −0.217568 | ||||||||
\(10\) | −3.07935 | −0.973775 | ||||||||
\(11\) | 4.34349 | 1.30961 | 0.654805 | − | 0.755798i | \(-0.272751\pi\) | ||||
0.654805 | + | 0.755798i | \(0.272751\pi\) | |||||||
\(12\) | 1.53209 | 0.442276 | ||||||||
\(13\) | −4.67033 | −1.29532 | −0.647658 | − | 0.761931i | \(-0.724252\pi\) | ||||
−0.647658 | + | 0.761931i | \(0.724252\pi\) | |||||||
\(14\) | 0.199962 | 0.0534421 | ||||||||
\(15\) | −4.71783 | −1.21814 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.79623 | −1.64833 | −0.824164 | − | 0.566352i | \(-0.808354\pi\) | ||||
−0.824164 | + | 0.566352i | \(0.808354\pi\) | |||||||
\(18\) | −0.652704 | −0.153844 | ||||||||
\(19\) | −4.14257 | −0.950371 | −0.475186 | − | 0.879886i | \(-0.657619\pi\) | ||||
−0.475186 | + | 0.879886i | \(0.657619\pi\) | |||||||
\(20\) | −3.07935 | −0.688563 | ||||||||
\(21\) | 0.306359 | 0.0668531 | ||||||||
\(22\) | 4.34349 | 0.926035 | ||||||||
\(23\) | −1.03567 | −0.215952 | −0.107976 | − | 0.994154i | \(-0.534437\pi\) | ||||
−0.107976 | + | 0.994154i | \(0.534437\pi\) | |||||||
\(24\) | 1.53209 | 0.312736 | ||||||||
\(25\) | 4.48238 | 0.896476 | ||||||||
\(26\) | −4.67033 | −0.915927 | ||||||||
\(27\) | −5.59627 | −1.07700 | ||||||||
\(28\) | 0.199962 | 0.0377893 | ||||||||
\(29\) | 1.45420 | 0.270038 | 0.135019 | − | 0.990843i | \(-0.456890\pi\) | ||||
0.135019 | + | 0.990843i | \(0.456890\pi\) | |||||||
\(30\) | −4.71783 | −0.861355 | ||||||||
\(31\) | 5.10852 | 0.917518 | 0.458759 | − | 0.888561i | \(-0.348294\pi\) | ||||
0.458759 | + | 0.888561i | \(0.348294\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.65461 | 1.15842 | ||||||||
\(34\) | −6.79623 | −1.16554 | ||||||||
\(35\) | −0.615752 | −0.104081 | ||||||||
\(36\) | −0.652704 | −0.108784 | ||||||||
\(37\) | 0 | 0 | ||||||||
\(38\) | −4.14257 | −0.672014 | ||||||||
\(39\) | −7.15536 | −1.14577 | ||||||||
\(40\) | −3.07935 | −0.486888 | ||||||||
\(41\) | −4.75161 | −0.742077 | −0.371038 | − | 0.928617i | \(-0.620998\pi\) | ||||
−0.371038 | + | 0.928617i | \(0.620998\pi\) | |||||||
\(42\) | 0.306359 | 0.0472723 | ||||||||
\(43\) | 0.399970 | 0.0609948 | 0.0304974 | − | 0.999535i | \(-0.490291\pi\) | ||||
0.0304974 | + | 0.999535i | \(0.490291\pi\) | |||||||
\(44\) | 4.34349 | 0.654805 | ||||||||
\(45\) | 2.00990 | 0.299618 | ||||||||
\(46\) | −1.03567 | −0.152701 | ||||||||
\(47\) | −8.20949 | −1.19748 | −0.598739 | − | 0.800944i | \(-0.704331\pi\) | ||||
−0.598739 | + | 0.800944i | \(0.704331\pi\) | |||||||
\(48\) | 1.53209 | 0.221138 | ||||||||
\(49\) | −6.96002 | −0.994288 | ||||||||
\(50\) | 4.48238 | 0.633904 | ||||||||
\(51\) | −10.4124 | −1.45803 | ||||||||
\(52\) | −4.67033 | −0.647658 | ||||||||
\(53\) | −11.2997 | −1.55213 | −0.776065 | − | 0.630653i | \(-0.782787\pi\) | ||||
−0.776065 | + | 0.630653i | \(0.782787\pi\) | |||||||
\(54\) | −5.59627 | −0.761555 | ||||||||
\(55\) | −13.3751 | −1.80350 | ||||||||
\(56\) | 0.199962 | 0.0267210 | ||||||||
\(57\) | −6.34679 | −0.840653 | ||||||||
\(58\) | 1.45420 | 0.190946 | ||||||||
\(59\) | 4.19601 | 0.546274 | 0.273137 | − | 0.961975i | \(-0.411939\pi\) | ||||
0.273137 | + | 0.961975i | \(0.411939\pi\) | |||||||
\(60\) | −4.71783 | −0.609070 | ||||||||
\(61\) | 10.5302 | 1.34825 | 0.674126 | − | 0.738616i | \(-0.264520\pi\) | ||||
0.674126 | + | 0.738616i | \(0.264520\pi\) | |||||||
\(62\) | 5.10852 | 0.648783 | ||||||||
\(63\) | −0.130516 | −0.0164435 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 14.3816 | 1.78381 | ||||||||
\(66\) | 6.65461 | 0.819126 | ||||||||
\(67\) | −8.71096 | −1.06421 | −0.532107 | − | 0.846677i | \(-0.678600\pi\) | ||||
−0.532107 | + | 0.846677i | \(0.678600\pi\) | |||||||
\(68\) | −6.79623 | −0.824164 | ||||||||
\(69\) | −1.58674 | −0.191021 | ||||||||
\(70\) | −0.615752 | −0.0735965 | ||||||||
\(71\) | 14.1639 | 1.68095 | 0.840473 | − | 0.541854i | \(-0.182277\pi\) | ||||
0.840473 | + | 0.541854i | \(0.182277\pi\) | |||||||
\(72\) | −0.652704 | −0.0769219 | ||||||||
\(73\) | −7.27588 | −0.851577 | −0.425789 | − | 0.904823i | \(-0.640003\pi\) | ||||
−0.425789 | + | 0.904823i | \(0.640003\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.86740 | 0.792979 | ||||||||
\(76\) | −4.14257 | −0.475186 | ||||||||
\(77\) | 0.868532 | 0.0989784 | ||||||||
\(78\) | −7.15536 | −0.810185 | ||||||||
\(79\) | −6.29548 | −0.708296 | −0.354148 | − | 0.935189i | \(-0.615229\pi\) | ||||
−0.354148 | + | 0.935189i | \(0.615229\pi\) | |||||||
\(80\) | −3.07935 | −0.344281 | ||||||||
\(81\) | −6.61587 | −0.735096 | ||||||||
\(82\) | −4.75161 | −0.524728 | ||||||||
\(83\) | 15.4158 | 1.69210 | 0.846051 | − | 0.533102i | \(-0.178974\pi\) | ||||
0.846051 | + | 0.533102i | \(0.178974\pi\) | |||||||
\(84\) | 0.306359 | 0.0334266 | ||||||||
\(85\) | 20.9279 | 2.26995 | ||||||||
\(86\) | 0.399970 | 0.0431298 | ||||||||
\(87\) | 2.22796 | 0.238863 | ||||||||
\(88\) | 4.34349 | 0.463017 | ||||||||
\(89\) | 3.21429 | 0.340714 | 0.170357 | − | 0.985382i | \(-0.445508\pi\) | ||||
0.170357 | + | 0.985382i | \(0.445508\pi\) | |||||||
\(90\) | 2.00990 | 0.211862 | ||||||||
\(91\) | −0.933888 | −0.0978981 | ||||||||
\(92\) | −1.03567 | −0.107976 | ||||||||
\(93\) | 7.82671 | 0.811592 | ||||||||
\(94\) | −8.20949 | −0.846744 | ||||||||
\(95\) | 12.7564 | 1.30878 | ||||||||
\(96\) | 1.53209 | 0.156368 | ||||||||
\(97\) | 2.39427 | 0.243101 | 0.121551 | − | 0.992585i | \(-0.461213\pi\) | ||||
0.121551 | + | 0.992585i | \(0.461213\pi\) | |||||||
\(98\) | −6.96002 | −0.703068 | ||||||||
\(99\) | −2.83501 | −0.284929 | ||||||||
\(100\) | 4.48238 | 0.448238 | ||||||||
\(101\) | 10.9630 | 1.09086 | 0.545429 | − | 0.838157i | \(-0.316367\pi\) | ||||
0.545429 | + | 0.838157i | \(0.316367\pi\) | |||||||
\(102\) | −10.4124 | −1.03098 | ||||||||
\(103\) | −15.7356 | −1.55048 | −0.775238 | − | 0.631670i | \(-0.782370\pi\) | ||||
−0.775238 | + | 0.631670i | \(0.782370\pi\) | |||||||
\(104\) | −4.67033 | −0.457964 | ||||||||
\(105\) | −0.943387 | −0.0920652 | ||||||||
\(106\) | −11.2997 | −1.09752 | ||||||||
\(107\) | −18.6160 | −1.79968 | −0.899838 | − | 0.436225i | \(-0.856315\pi\) | ||||
−0.899838 | + | 0.436225i | \(0.856315\pi\) | |||||||
\(108\) | −5.59627 | −0.538501 | ||||||||
\(109\) | 0.00702336 | 0.000672715 0 | 0.000336358 | − | 1.00000i | \(-0.499893\pi\) | ||||
0.000336358 | 1.00000i | \(0.499893\pi\) | ||||||||
\(110\) | −13.3751 | −1.27527 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.199962 | 0.0188946 | ||||||||
\(113\) | −2.56262 | −0.241071 | −0.120535 | − | 0.992709i | \(-0.538461\pi\) | ||||
−0.120535 | + | 0.992709i | \(0.538461\pi\) | |||||||
\(114\) | −6.34679 | −0.594431 | ||||||||
\(115\) | 3.18918 | 0.297393 | ||||||||
\(116\) | 1.45420 | 0.135019 | ||||||||
\(117\) | 3.04834 | 0.281819 | ||||||||
\(118\) | 4.19601 | 0.386274 | ||||||||
\(119\) | −1.35899 | −0.124578 | ||||||||
\(120\) | −4.71783 | −0.430677 | ||||||||
\(121\) | 7.86588 | 0.715080 | ||||||||
\(122\) | 10.5302 | 0.953358 | ||||||||
\(123\) | −7.27989 | −0.656406 | ||||||||
\(124\) | 5.10852 | 0.458759 | ||||||||
\(125\) | 1.59393 | 0.142566 | ||||||||
\(126\) | −0.130516 | −0.0116273 | ||||||||
\(127\) | −5.80702 | −0.515289 | −0.257645 | − | 0.966240i | \(-0.582946\pi\) | ||||
−0.257645 | + | 0.966240i | \(0.582946\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.612789 | 0.0539531 | ||||||||
\(130\) | 14.3816 | 1.26135 | ||||||||
\(131\) | −8.36959 | −0.731254 | −0.365627 | − | 0.930761i | \(-0.619145\pi\) | ||||
−0.365627 | + | 0.930761i | \(0.619145\pi\) | |||||||
\(132\) | 6.65461 | 0.579209 | ||||||||
\(133\) | −0.828357 | −0.0718276 | ||||||||
\(134\) | −8.71096 | −0.752513 | ||||||||
\(135\) | 17.2328 | 1.48317 | ||||||||
\(136\) | −6.79623 | −0.582772 | ||||||||
\(137\) | −1.57799 | −0.134817 | −0.0674084 | − | 0.997725i | \(-0.521473\pi\) | ||||
−0.0674084 | + | 0.997725i | \(0.521473\pi\) | |||||||
\(138\) | −1.58674 | −0.135072 | ||||||||
\(139\) | −9.92368 | −0.841716 | −0.420858 | − | 0.907127i | \(-0.638271\pi\) | ||||
−0.420858 | + | 0.907127i | \(0.638271\pi\) | |||||||
\(140\) | −0.615752 | −0.0520406 | ||||||||
\(141\) | −12.5777 | −1.05923 | ||||||||
\(142\) | 14.1639 | 1.18861 | ||||||||
\(143\) | −20.2855 | −1.69636 | ||||||||
\(144\) | −0.652704 | −0.0543920 | ||||||||
\(145\) | −4.47799 | −0.371877 | ||||||||
\(146\) | −7.27588 | −0.602156 | ||||||||
\(147\) | −10.6634 | −0.879499 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.8504 | 1.05274 | 0.526372 | − | 0.850254i | \(-0.323552\pi\) | ||||
0.526372 | + | 0.850254i | \(0.323552\pi\) | |||||||
\(150\) | 6.86740 | 0.560721 | ||||||||
\(151\) | −5.18633 | −0.422058 | −0.211029 | − | 0.977480i | \(-0.567681\pi\) | ||||
−0.211029 | + | 0.977480i | \(0.567681\pi\) | |||||||
\(152\) | −4.14257 | −0.336007 | ||||||||
\(153\) | 4.43592 | 0.358623 | ||||||||
\(154\) | 0.868532 | 0.0699883 | ||||||||
\(155\) | −15.7309 | −1.26354 | ||||||||
\(156\) | −7.15536 | −0.572887 | ||||||||
\(157\) | 11.9635 | 0.954795 | 0.477398 | − | 0.878687i | \(-0.341580\pi\) | ||||
0.477398 | + | 0.878687i | \(0.341580\pi\) | |||||||
\(158\) | −6.29548 | −0.500841 | ||||||||
\(159\) | −17.3121 | −1.37294 | ||||||||
\(160\) | −3.07935 | −0.243444 | ||||||||
\(161\) | −0.207094 | −0.0163213 | ||||||||
\(162\) | −6.61587 | −0.519792 | ||||||||
\(163\) | −0.706906 | −0.0553691 | −0.0276846 | − | 0.999617i | \(-0.508813\pi\) | ||||
−0.0276846 | + | 0.999617i | \(0.508813\pi\) | |||||||
\(164\) | −4.75161 | −0.371038 | ||||||||
\(165\) | −20.4918 | −1.59529 | ||||||||
\(166\) | 15.4158 | 1.19650 | ||||||||
\(167\) | 6.60985 | 0.511486 | 0.255743 | − | 0.966745i | \(-0.417680\pi\) | ||||
0.255743 | + | 0.966745i | \(0.417680\pi\) | |||||||
\(168\) | 0.306359 | 0.0236361 | ||||||||
\(169\) | 8.81198 | 0.677845 | ||||||||
\(170\) | 20.9279 | 1.60510 | ||||||||
\(171\) | 2.70387 | 0.206770 | ||||||||
\(172\) | 0.399970 | 0.0304974 | ||||||||
\(173\) | −15.4016 | −1.17096 | −0.585482 | − | 0.810685i | \(-0.699095\pi\) | ||||
−0.585482 | + | 0.810685i | \(0.699095\pi\) | |||||||
\(174\) | 2.22796 | 0.168902 | ||||||||
\(175\) | 0.896305 | 0.0677543 | ||||||||
\(176\) | 4.34349 | 0.327403 | ||||||||
\(177\) | 6.42866 | 0.483208 | ||||||||
\(178\) | 3.21429 | 0.240922 | ||||||||
\(179\) | 2.55438 | 0.190923 | 0.0954617 | − | 0.995433i | \(-0.469567\pi\) | ||||
0.0954617 | + | 0.995433i | \(0.469567\pi\) | |||||||
\(180\) | 2.00990 | 0.149809 | ||||||||
\(181\) | 8.38797 | 0.623473 | 0.311736 | − | 0.950169i | \(-0.399089\pi\) | ||||
0.311736 | + | 0.950169i | \(0.399089\pi\) | |||||||
\(182\) | −0.933888 | −0.0692244 | ||||||||
\(183\) | 16.1332 | 1.19260 | ||||||||
\(184\) | −1.03567 | −0.0763505 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.82671 | 0.573882 | ||||||||
\(187\) | −29.5193 | −2.15867 | ||||||||
\(188\) | −8.20949 | −0.598739 | ||||||||
\(189\) | −1.11904 | −0.0813982 | ||||||||
\(190\) | 12.7564 | 0.925448 | ||||||||
\(191\) | 6.48182 | 0.469008 | 0.234504 | − | 0.972115i | \(-0.424653\pi\) | ||||
0.234504 | + | 0.972115i | \(0.424653\pi\) | |||||||
\(192\) | 1.53209 | 0.110569 | ||||||||
\(193\) | 20.9828 | 1.51037 | 0.755186 | − | 0.655511i | \(-0.227547\pi\) | ||||
0.755186 | + | 0.655511i | \(0.227547\pi\) | |||||||
\(194\) | 2.39427 | 0.171898 | ||||||||
\(195\) | 22.0338 | 1.57788 | ||||||||
\(196\) | −6.96002 | −0.497144 | ||||||||
\(197\) | −1.65809 | −0.118134 | −0.0590672 | − | 0.998254i | \(-0.518813\pi\) | ||||
−0.0590672 | + | 0.998254i | \(0.518813\pi\) | |||||||
\(198\) | −2.83501 | −0.201475 | ||||||||
\(199\) | −7.21981 | −0.511799 | −0.255900 | − | 0.966703i | \(-0.582372\pi\) | ||||
−0.255900 | + | 0.966703i | \(0.582372\pi\) | |||||||
\(200\) | 4.48238 | 0.316952 | ||||||||
\(201\) | −13.3460 | −0.941352 | ||||||||
\(202\) | 10.9630 | 0.771354 | ||||||||
\(203\) | 0.290785 | 0.0204091 | ||||||||
\(204\) | −10.4124 | −0.729016 | ||||||||
\(205\) | 14.6319 | 1.02193 | ||||||||
\(206\) | −15.7356 | −1.09635 | ||||||||
\(207\) | 0.675985 | 0.0469842 | ||||||||
\(208\) | −4.67033 | −0.323829 | ||||||||
\(209\) | −17.9932 | −1.24462 | ||||||||
\(210\) | −0.943387 | −0.0650999 | ||||||||
\(211\) | 4.50868 | 0.310390 | 0.155195 | − | 0.987884i | \(-0.450399\pi\) | ||||
0.155195 | + | 0.987884i | \(0.450399\pi\) | |||||||
\(212\) | −11.2997 | −0.776065 | ||||||||
\(213\) | 21.7003 | 1.48688 | ||||||||
\(214\) | −18.6160 | −1.27256 | ||||||||
\(215\) | −1.23165 | −0.0839975 | ||||||||
\(216\) | −5.59627 | −0.380778 | ||||||||
\(217\) | 1.02151 | 0.0693446 | ||||||||
\(218\) | 0.00702336 | 0.000475682 0 | ||||||||
\(219\) | −11.1473 | −0.753264 | ||||||||
\(220\) | −13.3751 | −0.901749 | ||||||||
\(221\) | 31.7406 | 2.13511 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.6418 | 0.913526 | 0.456763 | − | 0.889588i | \(-0.349009\pi\) | ||||
0.456763 | + | 0.889588i | \(0.349009\pi\) | |||||||
\(224\) | 0.199962 | 0.0133605 | ||||||||
\(225\) | −2.92567 | −0.195044 | ||||||||
\(226\) | −2.56262 | −0.170463 | ||||||||
\(227\) | −27.2382 | −1.80786 | −0.903931 | − | 0.427679i | \(-0.859331\pi\) | ||||
−0.903931 | + | 0.427679i | \(0.859331\pi\) | |||||||
\(228\) | −6.34679 | −0.420326 | ||||||||
\(229\) | 2.03796 | 0.134672 | 0.0673362 | − | 0.997730i | \(-0.478550\pi\) | ||||
0.0673362 | + | 0.997730i | \(0.478550\pi\) | |||||||
\(230\) | 3.18918 | 0.210289 | ||||||||
\(231\) | 1.33067 | 0.0875515 | ||||||||
\(232\) | 1.45420 | 0.0954729 | ||||||||
\(233\) | 3.88495 | 0.254511 | 0.127256 | − | 0.991870i | \(-0.459383\pi\) | ||||
0.127256 | + | 0.991870i | \(0.459383\pi\) | |||||||
\(234\) | 3.04834 | 0.199276 | ||||||||
\(235\) | 25.2799 | 1.64908 | ||||||||
\(236\) | 4.19601 | 0.273137 | ||||||||
\(237\) | −9.64523 | −0.626525 | ||||||||
\(238\) | −1.35899 | −0.0880900 | ||||||||
\(239\) | 18.5705 | 1.20123 | 0.600613 | − | 0.799540i | \(-0.294923\pi\) | ||||
0.600613 | + | 0.799540i | \(0.294923\pi\) | |||||||
\(240\) | −4.71783 | −0.304535 | ||||||||
\(241\) | −25.3378 | −1.63215 | −0.816074 | − | 0.577947i | \(-0.803854\pi\) | ||||
−0.816074 | + | 0.577947i | \(0.803854\pi\) | |||||||
\(242\) | 7.86588 | 0.505638 | ||||||||
\(243\) | 6.65270 | 0.426771 | ||||||||
\(244\) | 10.5302 | 0.674126 | ||||||||
\(245\) | 21.4323 | 1.36926 | ||||||||
\(246\) | −7.27989 | −0.464149 | ||||||||
\(247\) | 19.3472 | 1.23103 | ||||||||
\(248\) | 5.10852 | 0.324392 | ||||||||
\(249\) | 23.6184 | 1.49675 | ||||||||
\(250\) | 1.59393 | 0.100809 | ||||||||
\(251\) | 12.7123 | 0.802394 | 0.401197 | − | 0.915992i | \(-0.368594\pi\) | ||||
0.401197 | + | 0.915992i | \(0.368594\pi\) | |||||||
\(252\) | −0.130516 | −0.00822173 | ||||||||
\(253\) | −4.49841 | −0.282813 | ||||||||
\(254\) | −5.80702 | −0.364365 | ||||||||
\(255\) | 32.0635 | 2.00789 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.34710 | 0.271165 | 0.135582 | − | 0.990766i | \(-0.456709\pi\) | ||||
0.135582 | + | 0.990766i | \(0.456709\pi\) | |||||||
\(258\) | 0.612789 | 0.0381506 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 14.3816 | 0.891907 | ||||||||
\(261\) | −0.949162 | −0.0587517 | ||||||||
\(262\) | −8.36959 | −0.517075 | ||||||||
\(263\) | 6.51139 | 0.401509 | 0.200755 | − | 0.979642i | \(-0.435661\pi\) | ||||
0.200755 | + | 0.979642i | \(0.435661\pi\) | |||||||
\(264\) | 6.65461 | 0.409563 | ||||||||
\(265\) | 34.7956 | 2.13748 | ||||||||
\(266\) | −0.828357 | −0.0507898 | ||||||||
\(267\) | 4.92458 | 0.301380 | ||||||||
\(268\) | −8.71096 | −0.532107 | ||||||||
\(269\) | −9.90213 | −0.603743 | −0.301872 | − | 0.953349i | \(-0.597611\pi\) | ||||
−0.301872 | + | 0.953349i | \(0.597611\pi\) | |||||||
\(270\) | 17.2328 | 1.04876 | ||||||||
\(271\) | 9.02508 | 0.548235 | 0.274117 | − | 0.961696i | \(-0.411614\pi\) | ||||
0.274117 | + | 0.961696i | \(0.411614\pi\) | |||||||
\(272\) | −6.79623 | −0.412082 | ||||||||
\(273\) | −1.43080 | −0.0865959 | ||||||||
\(274\) | −1.57799 | −0.0953298 | ||||||||
\(275\) | 19.4692 | 1.17403 | ||||||||
\(276\) | −1.58674 | −0.0955103 | ||||||||
\(277\) | −0.208088 | −0.0125028 | −0.00625138 | − | 0.999980i | \(-0.501990\pi\) | ||||
−0.00625138 | + | 0.999980i | \(0.501990\pi\) | |||||||
\(278\) | −9.92368 | −0.595183 | ||||||||
\(279\) | −3.33435 | −0.199622 | ||||||||
\(280\) | −0.615752 | −0.0367982 | ||||||||
\(281\) | 27.0593 | 1.61422 | 0.807111 | − | 0.590400i | \(-0.201030\pi\) | ||||
0.807111 | + | 0.590400i | \(0.201030\pi\) | |||||||
\(282\) | −12.5777 | −0.748989 | ||||||||
\(283\) | −0.812894 | −0.0483215 | −0.0241608 | − | 0.999708i | \(-0.507691\pi\) | ||||
−0.0241608 | + | 0.999708i | \(0.507691\pi\) | |||||||
\(284\) | 14.1639 | 0.840473 | ||||||||
\(285\) | 19.5440 | 1.15768 | ||||||||
\(286\) | −20.2855 | −1.19951 | ||||||||
\(287\) | −0.950141 | −0.0560851 | ||||||||
\(288\) | −0.652704 | −0.0384609 | ||||||||
\(289\) | 29.1887 | 1.71698 | ||||||||
\(290\) | −4.47799 | −0.262957 | ||||||||
\(291\) | 3.66823 | 0.215036 | ||||||||
\(292\) | −7.27588 | −0.425789 | ||||||||
\(293\) | −8.79957 | −0.514076 | −0.257038 | − | 0.966401i | \(-0.582747\pi\) | ||||
−0.257038 | + | 0.966401i | \(0.582747\pi\) | |||||||
\(294\) | −10.6634 | −0.621900 | ||||||||
\(295\) | −12.9210 | −0.752288 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −24.3073 | −1.41045 | ||||||||
\(298\) | 12.8504 | 0.744403 | ||||||||
\(299\) | 4.83691 | 0.279726 | ||||||||
\(300\) | 6.86740 | 0.396490 | ||||||||
\(301\) | 0.0799787 | 0.00460989 | ||||||||
\(302\) | −5.18633 | −0.298440 | ||||||||
\(303\) | 16.7963 | 0.964921 | ||||||||
\(304\) | −4.14257 | −0.237593 | ||||||||
\(305\) | −32.4261 | −1.85671 | ||||||||
\(306\) | 4.43592 | 0.253585 | ||||||||
\(307\) | −24.4541 | −1.39567 | −0.697836 | − | 0.716258i | \(-0.745854\pi\) | ||||
−0.697836 | + | 0.716258i | \(0.745854\pi\) | |||||||
\(308\) | 0.868532 | 0.0494892 | ||||||||
\(309\) | −24.1083 | −1.37148 | ||||||||
\(310\) | −15.7309 | −0.893456 | ||||||||
\(311\) | 0.0126953 | 0.000719885 0 | 0.000359942 | − | 1.00000i | \(-0.499885\pi\) | ||||
0.000359942 | 1.00000i | \(0.499885\pi\) | ||||||||
\(312\) | −7.15536 | −0.405093 | ||||||||
\(313\) | −17.4684 | −0.987375 | −0.493687 | − | 0.869639i | \(-0.664351\pi\) | ||||
−0.493687 | + | 0.869639i | \(0.664351\pi\) | |||||||
\(314\) | 11.9635 | 0.675142 | ||||||||
\(315\) | 0.401904 | 0.0226447 | ||||||||
\(316\) | −6.29548 | −0.354148 | ||||||||
\(317\) | −2.72890 | −0.153270 | −0.0766352 | − | 0.997059i | \(-0.524418\pi\) | ||||
−0.0766352 | + | 0.997059i | \(0.524418\pi\) | |||||||
\(318\) | −17.3121 | −0.970815 | ||||||||
\(319\) | 6.31630 | 0.353645 | ||||||||
\(320\) | −3.07935 | −0.172141 | ||||||||
\(321\) | −28.5213 | −1.59191 | ||||||||
\(322\) | −0.207094 | −0.0115409 | ||||||||
\(323\) | 28.1539 | 1.56652 | ||||||||
\(324\) | −6.61587 | −0.367548 | ||||||||
\(325\) | −20.9342 | −1.16122 | ||||||||
\(326\) | −0.706906 | −0.0391519 | ||||||||
\(327\) | 0.0107604 | 0.000595052 0 | ||||||||
\(328\) | −4.75161 | −0.262364 | ||||||||
\(329\) | −1.64159 | −0.0905036 | ||||||||
\(330\) | −20.4918 | −1.12804 | ||||||||
\(331\) | −23.6161 | −1.29806 | −0.649028 | − | 0.760765i | \(-0.724824\pi\) | ||||
−0.649028 | + | 0.760765i | \(0.724824\pi\) | |||||||
\(332\) | 15.4158 | 0.846051 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.60985 | 0.361675 | ||||||||
\(335\) | 26.8241 | 1.46556 | ||||||||
\(336\) | 0.306359 | 0.0167133 | ||||||||
\(337\) | 22.4456 | 1.22269 | 0.611345 | − | 0.791364i | \(-0.290629\pi\) | ||||
0.611345 | + | 0.791364i | \(0.290629\pi\) | |||||||
\(338\) | 8.81198 | 0.479308 | ||||||||
\(339\) | −3.92616 | −0.213240 | ||||||||
\(340\) | 20.9279 | 1.13498 | ||||||||
\(341\) | 22.1888 | 1.20159 | ||||||||
\(342\) | 2.70387 | 0.146209 | ||||||||
\(343\) | −2.79147 | −0.150725 | ||||||||
\(344\) | 0.399970 | 0.0215649 | ||||||||
\(345\) | 4.88611 | 0.263059 | ||||||||
\(346\) | −15.4016 | −0.827997 | ||||||||
\(347\) | 1.21511 | 0.0652306 | 0.0326153 | − | 0.999468i | \(-0.489616\pi\) | ||||
0.0326153 | + | 0.999468i | \(0.489616\pi\) | |||||||
\(348\) | 2.22796 | 0.119431 | ||||||||
\(349\) | 17.7395 | 0.949573 | 0.474786 | − | 0.880101i | \(-0.342525\pi\) | ||||
0.474786 | + | 0.880101i | \(0.342525\pi\) | |||||||
\(350\) | 0.896305 | 0.0479095 | ||||||||
\(351\) | 26.1364 | 1.39506 | ||||||||
\(352\) | 4.34349 | 0.231509 | ||||||||
\(353\) | 1.60606 | 0.0854818 | 0.0427409 | − | 0.999086i | \(-0.486391\pi\) | ||||
0.0427409 | + | 0.999086i | \(0.486391\pi\) | |||||||
\(354\) | 6.42866 | 0.341680 | ||||||||
\(355\) | −43.6156 | −2.31487 | ||||||||
\(356\) | 3.21429 | 0.170357 | ||||||||
\(357\) | −2.08209 | −0.110196 | ||||||||
\(358\) | 2.55438 | 0.135003 | ||||||||
\(359\) | −32.0124 | −1.68955 | −0.844775 | − | 0.535121i | \(-0.820266\pi\) | ||||
−0.844775 | + | 0.535121i | \(0.820266\pi\) | |||||||
\(360\) | 2.00990 | 0.105931 | ||||||||
\(361\) | −1.83909 | −0.0967942 | ||||||||
\(362\) | 8.38797 | 0.440862 | ||||||||
\(363\) | 12.0512 | 0.632525 | ||||||||
\(364\) | −0.933888 | −0.0489490 | ||||||||
\(365\) | 22.4050 | 1.17273 | ||||||||
\(366\) | 16.1332 | 0.843295 | ||||||||
\(367\) | 16.0363 | 0.837088 | 0.418544 | − | 0.908197i | \(-0.362541\pi\) | ||||
0.418544 | + | 0.908197i | \(0.362541\pi\) | |||||||
\(368\) | −1.03567 | −0.0539880 | ||||||||
\(369\) | 3.10139 | 0.161452 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.25951 | −0.117308 | ||||||||
\(372\) | 7.82671 | 0.405796 | ||||||||
\(373\) | 1.11639 | 0.0578043 | 0.0289022 | − | 0.999582i | \(-0.490799\pi\) | ||||
0.0289022 | + | 0.999582i | \(0.490799\pi\) | |||||||
\(374\) | −29.5193 | −1.52641 | ||||||||
\(375\) | 2.44205 | 0.126107 | ||||||||
\(376\) | −8.20949 | −0.423372 | ||||||||
\(377\) | −6.79160 | −0.349785 | ||||||||
\(378\) | −1.11904 | −0.0575572 | ||||||||
\(379\) | 36.4410 | 1.87185 | 0.935924 | − | 0.352201i | \(-0.114567\pi\) | ||||
0.935924 | + | 0.352201i | \(0.114567\pi\) | |||||||
\(380\) | 12.7564 | 0.654391 | ||||||||
\(381\) | −8.89686 | −0.455800 | ||||||||
\(382\) | 6.48182 | 0.331639 | ||||||||
\(383\) | 6.03086 | 0.308162 | 0.154081 | − | 0.988058i | \(-0.450758\pi\) | ||||
0.154081 | + | 0.988058i | \(0.450758\pi\) | |||||||
\(384\) | 1.53209 | 0.0781841 | ||||||||
\(385\) | −2.67451 | −0.136306 | ||||||||
\(386\) | 20.9828 | 1.06799 | ||||||||
\(387\) | −0.261062 | −0.0132705 | ||||||||
\(388\) | 2.39427 | 0.121551 | ||||||||
\(389\) | −18.8329 | −0.954867 | −0.477434 | − | 0.878668i | \(-0.658433\pi\) | ||||
−0.477434 | + | 0.878668i | \(0.658433\pi\) | |||||||
\(390\) | 22.0338 | 1.11573 | ||||||||
\(391\) | 7.03864 | 0.355959 | ||||||||
\(392\) | −6.96002 | −0.351534 | ||||||||
\(393\) | −12.8229 | −0.646832 | ||||||||
\(394\) | −1.65809 | −0.0835336 | ||||||||
\(395\) | 19.3860 | 0.975413 | ||||||||
\(396\) | −2.83501 | −0.142465 | ||||||||
\(397\) | −27.5114 | −1.38076 | −0.690378 | − | 0.723449i | \(-0.742556\pi\) | ||||
−0.690378 | + | 0.723449i | \(0.742556\pi\) | |||||||
\(398\) | −7.21981 | −0.361897 | ||||||||
\(399\) | −1.26912 | −0.0635353 | ||||||||
\(400\) | 4.48238 | 0.224119 | ||||||||
\(401\) | 22.0721 | 1.10223 | 0.551114 | − | 0.834430i | \(-0.314203\pi\) | ||||
0.551114 | + | 0.834430i | \(0.314203\pi\) | |||||||
\(402\) | −13.3460 | −0.665637 | ||||||||
\(403\) | −23.8585 | −1.18848 | ||||||||
\(404\) | 10.9630 | 0.545429 | ||||||||
\(405\) | 20.3726 | 1.01232 | ||||||||
\(406\) | 0.290785 | 0.0144314 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −10.4124 | −0.515492 | ||||||||
\(409\) | 1.42090 | 0.0702591 | 0.0351296 | − | 0.999383i | \(-0.488816\pi\) | ||||
0.0351296 | + | 0.999383i | \(0.488816\pi\) | |||||||
\(410\) | 14.6319 | 0.722616 | ||||||||
\(411\) | −2.41762 | −0.119252 | ||||||||
\(412\) | −15.7356 | −0.775238 | ||||||||
\(413\) | 0.839043 | 0.0412866 | ||||||||
\(414\) | 0.675985 | 0.0332228 | ||||||||
\(415\) | −47.4706 | −2.33024 | ||||||||
\(416\) | −4.67033 | −0.228982 | ||||||||
\(417\) | −15.2040 | −0.744541 | ||||||||
\(418\) | −17.9932 | −0.880077 | ||||||||
\(419\) | −13.6400 | −0.666358 | −0.333179 | − | 0.942864i | \(-0.608121\pi\) | ||||
−0.333179 | + | 0.942864i | \(0.608121\pi\) | |||||||
\(420\) | −0.943387 | −0.0460326 | ||||||||
\(421\) | 27.9978 | 1.36453 | 0.682264 | − | 0.731106i | \(-0.260995\pi\) | ||||
0.682264 | + | 0.731106i | \(0.260995\pi\) | |||||||
\(422\) | 4.50868 | 0.219479 | ||||||||
\(423\) | 5.35837 | 0.260533 | ||||||||
\(424\) | −11.2997 | −0.548761 | ||||||||
\(425\) | −30.4633 | −1.47769 | ||||||||
\(426\) | 21.7003 | 1.05139 | ||||||||
\(427\) | 2.10564 | 0.101899 | ||||||||
\(428\) | −18.6160 | −0.899838 | ||||||||
\(429\) | −31.0792 | −1.50052 | ||||||||
\(430\) | −1.23165 | −0.0593952 | ||||||||
\(431\) | 2.84949 | 0.137255 | 0.0686275 | − | 0.997642i | \(-0.478138\pi\) | ||||
0.0686275 | + | 0.997642i | \(0.478138\pi\) | |||||||
\(432\) | −5.59627 | −0.269251 | ||||||||
\(433\) | −31.1352 | −1.49626 | −0.748130 | − | 0.663552i | \(-0.769048\pi\) | ||||
−0.748130 | + | 0.663552i | \(0.769048\pi\) | |||||||
\(434\) | 1.02151 | 0.0490341 | ||||||||
\(435\) | −6.86068 | −0.328944 | ||||||||
\(436\) | 0.00702336 | 0.000336358 0 | ||||||||
\(437\) | 4.29033 | 0.205234 | ||||||||
\(438\) | −11.1473 | −0.532638 | ||||||||
\(439\) | 28.7800 | 1.37359 | 0.686796 | − | 0.726850i | \(-0.259016\pi\) | ||||
0.686796 | + | 0.726850i | \(0.259016\pi\) | |||||||
\(440\) | −13.3751 | −0.637633 | ||||||||
\(441\) | 4.54283 | 0.216325 | ||||||||
\(442\) | 31.7406 | 1.50975 | ||||||||
\(443\) | 19.3903 | 0.921259 | 0.460630 | − | 0.887592i | \(-0.347624\pi\) | ||||
0.460630 | + | 0.887592i | \(0.347624\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.89793 | −0.469207 | ||||||||
\(446\) | 13.6418 | 0.645960 | ||||||||
\(447\) | 19.6879 | 0.931208 | ||||||||
\(448\) | 0.199962 | 0.00944731 | ||||||||
\(449\) | 17.0799 | 0.806052 | 0.403026 | − | 0.915188i | \(-0.367958\pi\) | ||||
0.403026 | + | 0.915188i | \(0.367958\pi\) | |||||||
\(450\) | −2.92567 | −0.137917 | ||||||||
\(451\) | −20.6386 | −0.971832 | ||||||||
\(452\) | −2.56262 | −0.120535 | ||||||||
\(453\) | −7.94592 | −0.373332 | ||||||||
\(454\) | −27.2382 | −1.27835 | ||||||||
\(455\) | 2.87577 | 0.134818 | ||||||||
\(456\) | −6.34679 | −0.297216 | ||||||||
\(457\) | −2.41654 | −0.113041 | −0.0565206 | − | 0.998401i | \(-0.518001\pi\) | ||||
−0.0565206 | + | 0.998401i | \(0.518001\pi\) | |||||||
\(458\) | 2.03796 | 0.0952278 | ||||||||
\(459\) | 38.0335 | 1.77525 | ||||||||
\(460\) | 3.18918 | 0.148696 | ||||||||
\(461\) | 18.7400 | 0.872808 | 0.436404 | − | 0.899751i | \(-0.356252\pi\) | ||||
0.436404 | + | 0.899751i | \(0.356252\pi\) | |||||||
\(462\) | 1.33067 | 0.0619083 | ||||||||
\(463\) | −5.15947 | −0.239781 | −0.119890 | − | 0.992787i | \(-0.538254\pi\) | ||||
−0.119890 | + | 0.992787i | \(0.538254\pi\) | |||||||
\(464\) | 1.45420 | 0.0675096 | ||||||||
\(465\) | −24.1012 | −1.11766 | ||||||||
\(466\) | 3.88495 | 0.179967 | ||||||||
\(467\) | −30.9314 | −1.43134 | −0.715668 | − | 0.698441i | \(-0.753878\pi\) | ||||
−0.715668 | + | 0.698441i | \(0.753878\pi\) | |||||||
\(468\) | 3.04834 | 0.140910 | ||||||||
\(469\) | −1.74186 | −0.0804317 | ||||||||
\(470\) | 25.2799 | 1.16607 | ||||||||
\(471\) | 18.3292 | 0.844566 | ||||||||
\(472\) | 4.19601 | 0.193137 | ||||||||
\(473\) | 1.73726 | 0.0798794 | ||||||||
\(474\) | −9.64523 | −0.443020 | ||||||||
\(475\) | −18.5686 | −0.851985 | ||||||||
\(476\) | −1.35899 | −0.0622891 | ||||||||
\(477\) | 7.37534 | 0.337694 | ||||||||
\(478\) | 18.5705 | 0.849395 | ||||||||
\(479\) | 12.8783 | 0.588425 | 0.294212 | − | 0.955740i | \(-0.404943\pi\) | ||||
0.294212 | + | 0.955740i | \(0.404943\pi\) | |||||||
\(480\) | −4.71783 | −0.215339 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −25.3378 | −1.15410 | ||||||||
\(483\) | −0.317287 | −0.0144371 | ||||||||
\(484\) | 7.86588 | 0.357540 | ||||||||
\(485\) | −7.37278 | −0.334781 | ||||||||
\(486\) | 6.65270 | 0.301773 | ||||||||
\(487\) | −17.2601 | −0.782130 | −0.391065 | − | 0.920363i | \(-0.627893\pi\) | ||||
−0.391065 | + | 0.920363i | \(0.627893\pi\) | |||||||
\(488\) | 10.5302 | 0.476679 | ||||||||
\(489\) | −1.08304 | −0.0489769 | ||||||||
\(490\) | 21.4323 | 0.968213 | ||||||||
\(491\) | 17.1066 | 0.772011 | 0.386005 | − | 0.922496i | \(-0.373855\pi\) | ||||
0.386005 | + | 0.922496i | \(0.373855\pi\) | |||||||
\(492\) | −7.27989 | −0.328203 | ||||||||
\(493\) | −9.88308 | −0.445111 | ||||||||
\(494\) | 19.3472 | 0.870471 | ||||||||
\(495\) | 8.72998 | 0.392383 | ||||||||
\(496\) | 5.10852 | 0.229379 | ||||||||
\(497\) | 2.83224 | 0.127043 | ||||||||
\(498\) | 23.6184 | 1.05836 | ||||||||
\(499\) | −18.5412 | −0.830020 | −0.415010 | − | 0.909817i | \(-0.636222\pi\) | ||||
−0.415010 | + | 0.909817i | \(0.636222\pi\) | |||||||
\(500\) | 1.59393 | 0.0712829 | ||||||||
\(501\) | 10.1269 | 0.452436 | ||||||||
\(502\) | 12.7123 | 0.567378 | ||||||||
\(503\) | −3.35590 | −0.149632 | −0.0748162 | − | 0.997197i | \(-0.523837\pi\) | ||||
−0.0748162 | + | 0.997197i | \(0.523837\pi\) | |||||||
\(504\) | −0.130516 | −0.00581364 | ||||||||
\(505\) | −33.7589 | −1.50225 | ||||||||
\(506\) | −4.49841 | −0.199979 | ||||||||
\(507\) | 13.5007 | 0.599589 | ||||||||
\(508\) | −5.80702 | −0.257645 | ||||||||
\(509\) | 11.0197 | 0.488441 | 0.244221 | − | 0.969720i | \(-0.421468\pi\) | ||||
0.244221 | + | 0.969720i | \(0.421468\pi\) | |||||||
\(510\) | 32.0635 | 1.41979 | ||||||||
\(511\) | −1.45490 | −0.0643609 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 23.1829 | 1.02355 | ||||||||
\(514\) | 4.34710 | 0.191742 | ||||||||
\(515\) | 48.4554 | 2.13520 | ||||||||
\(516\) | 0.612789 | 0.0269765 | ||||||||
\(517\) | −35.6578 | −1.56823 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.5967 | −1.03578 | ||||||||
\(520\) | 14.3816 | 0.630673 | ||||||||
\(521\) | 7.83217 | 0.343134 | 0.171567 | − | 0.985172i | \(-0.445117\pi\) | ||||
0.171567 | + | 0.985172i | \(0.445117\pi\) | |||||||
\(522\) | −0.949162 | −0.0415437 | ||||||||
\(523\) | 1.81284 | 0.0792700 | 0.0396350 | − | 0.999214i | \(-0.487380\pi\) | ||||
0.0396350 | + | 0.999214i | \(0.487380\pi\) | |||||||
\(524\) | −8.36959 | −0.365627 | ||||||||
\(525\) | 1.37322 | 0.0599322 | ||||||||
\(526\) | 6.51139 | 0.283910 | ||||||||
\(527\) | −34.7187 | −1.51237 | ||||||||
\(528\) | 6.65461 | 0.289605 | ||||||||
\(529\) | −21.9274 | −0.953365 | ||||||||
\(530\) | 34.7956 | 1.51143 | ||||||||
\(531\) | −2.73875 | −0.118852 | ||||||||
\(532\) | −0.828357 | −0.0359138 | ||||||||
\(533\) | 22.1916 | 0.961224 | ||||||||
\(534\) | 4.92458 | 0.213108 | ||||||||
\(535\) | 57.3251 | 2.47838 | ||||||||
\(536\) | −8.71096 | −0.376256 | ||||||||
\(537\) | 3.91354 | 0.168882 | ||||||||
\(538\) | −9.90213 | −0.426911 | ||||||||
\(539\) | −30.2307 | −1.30213 | ||||||||
\(540\) | 17.2328 | 0.741584 | ||||||||
\(541\) | −6.95357 | −0.298958 | −0.149479 | − | 0.988765i | \(-0.547760\pi\) | ||||
−0.149479 | + | 0.988765i | \(0.547760\pi\) | |||||||
\(542\) | 9.02508 | 0.387660 | ||||||||
\(543\) | 12.8511 | 0.551494 | ||||||||
\(544\) | −6.79623 | −0.291386 | ||||||||
\(545\) | −0.0216274 | −0.000926414 0 | ||||||||
\(546\) | −1.43080 | −0.0612326 | ||||||||
\(547\) | 4.86631 | 0.208068 | 0.104034 | − | 0.994574i | \(-0.466825\pi\) | ||||
0.104034 | + | 0.994574i | \(0.466825\pi\) | |||||||
\(548\) | −1.57799 | −0.0674084 | ||||||||
\(549\) | −6.87309 | −0.293336 | ||||||||
\(550\) | 19.4692 | 0.830168 | ||||||||
\(551\) | −6.02413 | −0.256637 | ||||||||
\(552\) | −1.58674 | −0.0675360 | ||||||||
\(553\) | −1.25886 | −0.0535320 | ||||||||
\(554\) | −0.208088 | −0.00884079 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.92368 | −0.420858 | ||||||||
\(557\) | 7.28236 | 0.308563 | 0.154282 | − | 0.988027i | \(-0.450694\pi\) | ||||
0.154282 | + | 0.988027i | \(0.450694\pi\) | |||||||
\(558\) | −3.33435 | −0.141154 | ||||||||
\(559\) | −1.86799 | −0.0790075 | ||||||||
\(560\) | −0.615752 | −0.0260203 | ||||||||
\(561\) | −45.2262 | −1.90945 | ||||||||
\(562\) | 27.0593 | 1.14143 | ||||||||
\(563\) | −27.6116 | −1.16369 | −0.581845 | − | 0.813300i | \(-0.697669\pi\) | ||||
−0.581845 | + | 0.813300i | \(0.697669\pi\) | |||||||
\(564\) | −12.5777 | −0.529616 | ||||||||
\(565\) | 7.89119 | 0.331985 | ||||||||
\(566\) | −0.812894 | −0.0341685 | ||||||||
\(567\) | −1.32292 | −0.0555575 | ||||||||
\(568\) | 14.1639 | 0.594304 | ||||||||
\(569\) | 5.64776 | 0.236766 | 0.118383 | − | 0.992968i | \(-0.462229\pi\) | ||||
0.118383 | + | 0.992968i | \(0.462229\pi\) | |||||||
\(570\) | 19.5440 | 0.818607 | ||||||||
\(571\) | 13.4951 | 0.564753 | 0.282377 | − | 0.959304i | \(-0.408877\pi\) | ||||
0.282377 | + | 0.959304i | \(0.408877\pi\) | |||||||
\(572\) | −20.2855 | −0.848180 | ||||||||
\(573\) | 9.93073 | 0.414862 | ||||||||
\(574\) | −0.950141 | −0.0396581 | ||||||||
\(575\) | −4.64226 | −0.193596 | ||||||||
\(576\) | −0.652704 | −0.0271960 | ||||||||
\(577\) | −42.1146 | −1.75326 | −0.876628 | − | 0.481169i | \(-0.840212\pi\) | ||||
−0.876628 | + | 0.481169i | \(0.840212\pi\) | |||||||
\(578\) | 29.1887 | 1.21409 | ||||||||
\(579\) | 32.1475 | 1.33600 | ||||||||
\(580\) | −4.47799 | −0.185938 | ||||||||
\(581\) | 3.08257 | 0.127887 | ||||||||
\(582\) | 3.66823 | 0.152053 | ||||||||
\(583\) | −49.0800 | −2.03269 | ||||||||
\(584\) | −7.27588 | −0.301078 | ||||||||
\(585\) | −9.38690 | −0.388101 | ||||||||
\(586\) | −8.79957 | −0.363507 | ||||||||
\(587\) | 41.4835 | 1.71221 | 0.856104 | − | 0.516804i | \(-0.172879\pi\) | ||||
0.856104 | + | 0.516804i | \(0.172879\pi\) | |||||||
\(588\) | −10.6634 | −0.439750 | ||||||||
\(589\) | −21.1624 | −0.871983 | ||||||||
\(590\) | −12.9210 | −0.531948 | ||||||||
\(591\) | −2.54035 | −0.104496 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.6746 | −1.21859 | −0.609295 | − | 0.792944i | \(-0.708548\pi\) | ||||
−0.609295 | + | 0.792944i | \(0.708548\pi\) | |||||||
\(594\) | −24.3073 | −0.997341 | ||||||||
\(595\) | 4.18479 | 0.171560 | ||||||||
\(596\) | 12.8504 | 0.526372 | ||||||||
\(597\) | −11.0614 | −0.452713 | ||||||||
\(598\) | 4.83691 | 0.197796 | ||||||||
\(599\) | −4.48941 | −0.183432 | −0.0917162 | − | 0.995785i | \(-0.529235\pi\) | ||||
−0.0917162 | + | 0.995785i | \(0.529235\pi\) | |||||||
\(600\) | 6.86740 | 0.280361 | ||||||||
\(601\) | −14.2046 | −0.579419 | −0.289710 | − | 0.957115i | \(-0.593559\pi\) | ||||
−0.289710 | + | 0.957115i | \(0.593559\pi\) | |||||||
\(602\) | 0.0799787 | 0.00325969 | ||||||||
\(603\) | 5.68568 | 0.231539 | ||||||||
\(604\) | −5.18633 | −0.211029 | ||||||||
\(605\) | −24.2218 | −0.984755 | ||||||||
\(606\) | 16.7963 | 0.682302 | ||||||||
\(607\) | −25.2743 | −1.02585 | −0.512926 | − | 0.858433i | \(-0.671438\pi\) | ||||
−0.512926 | + | 0.858433i | \(0.671438\pi\) | |||||||
\(608\) | −4.14257 | −0.168004 | ||||||||
\(609\) | 0.445508 | 0.0180529 | ||||||||
\(610\) | −32.4261 | −1.31289 | ||||||||
\(611\) | 38.3410 | 1.55111 | ||||||||
\(612\) | 4.43592 | 0.179312 | ||||||||
\(613\) | −1.47148 | −0.0594326 | −0.0297163 | − | 0.999558i | \(-0.509460\pi\) | ||||
−0.0297163 | + | 0.999558i | \(0.509460\pi\) | |||||||
\(614\) | −24.4541 | −0.986889 | ||||||||
\(615\) | 22.4173 | 0.903953 | ||||||||
\(616\) | 0.868532 | 0.0349942 | ||||||||
\(617\) | 15.6742 | 0.631020 | 0.315510 | − | 0.948922i | \(-0.397824\pi\) | ||||
0.315510 | + | 0.948922i | \(0.397824\pi\) | |||||||
\(618\) | −24.1083 | −0.969780 | ||||||||
\(619\) | −40.3039 | −1.61995 | −0.809974 | − | 0.586465i | \(-0.800519\pi\) | ||||
−0.809974 | + | 0.586465i | \(0.800519\pi\) | |||||||
\(620\) | −15.7309 | −0.631769 | ||||||||
\(621\) | 5.79588 | 0.232581 | ||||||||
\(622\) | 0.0126953 | 0.000509035 0 | ||||||||
\(623\) | 0.642736 | 0.0257507 | ||||||||
\(624\) | −7.15536 | −0.286444 | ||||||||
\(625\) | −27.3202 | −1.09281 | ||||||||
\(626\) | −17.4684 | −0.698179 | ||||||||
\(627\) | −27.5672 | −1.10093 | ||||||||
\(628\) | 11.9635 | 0.477398 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0.401904 | 0.0160122 | ||||||||
\(631\) | −29.5332 | −1.17570 | −0.587848 | − | 0.808971i | \(-0.700025\pi\) | ||||
−0.587848 | + | 0.808971i | \(0.700025\pi\) | |||||||
\(632\) | −6.29548 | −0.250421 | ||||||||
\(633\) | 6.90770 | 0.274556 | ||||||||
\(634\) | −2.72890 | −0.108379 | ||||||||
\(635\) | 17.8818 | 0.709618 | ||||||||
\(636\) | −17.3121 | −0.686470 | ||||||||
\(637\) | 32.5056 | 1.28792 | ||||||||
\(638\) | 6.31630 | 0.250065 | ||||||||
\(639\) | −9.24483 | −0.365720 | ||||||||
\(640\) | −3.07935 | −0.121722 | ||||||||
\(641\) | −23.8544 | −0.942191 | −0.471096 | − | 0.882082i | \(-0.656141\pi\) | ||||
−0.471096 | + | 0.882082i | \(0.656141\pi\) | |||||||
\(642\) | −28.5213 | −1.12565 | ||||||||
\(643\) | −20.1057 | −0.792891 | −0.396445 | − | 0.918058i | \(-0.629756\pi\) | ||||
−0.396445 | + | 0.918058i | \(0.629756\pi\) | |||||||
\(644\) | −0.207094 | −0.00816066 | ||||||||
\(645\) | −1.88699 | −0.0743002 | ||||||||
\(646\) | 28.1539 | 1.10770 | ||||||||
\(647\) | 15.5440 | 0.611099 | 0.305549 | − | 0.952176i | \(-0.401160\pi\) | ||||
0.305549 | + | 0.952176i | \(0.401160\pi\) | |||||||
\(648\) | −6.61587 | −0.259896 | ||||||||
\(649\) | 18.2253 | 0.715407 | ||||||||
\(650\) | −20.9342 | −0.821106 | ||||||||
\(651\) | 1.56504 | 0.0613389 | ||||||||
\(652\) | −0.706906 | −0.0276846 | ||||||||
\(653\) | −3.24230 | −0.126881 | −0.0634404 | − | 0.997986i | \(-0.520207\pi\) | ||||
−0.0634404 | + | 0.997986i | \(0.520207\pi\) | |||||||
\(654\) | 0.0107604 | 0.000420765 0 | ||||||||
\(655\) | 25.7729 | 1.00703 | ||||||||
\(656\) | −4.75161 | −0.185519 | ||||||||
\(657\) | 4.74899 | 0.185276 | ||||||||
\(658\) | −1.64159 | −0.0639957 | ||||||||
\(659\) | 14.1540 | 0.551360 | 0.275680 | − | 0.961250i | \(-0.411097\pi\) | ||||
0.275680 | + | 0.961250i | \(0.411097\pi\) | |||||||
\(660\) | −20.4918 | −0.797644 | ||||||||
\(661\) | −47.1036 | −1.83212 | −0.916059 | − | 0.401044i | \(-0.868647\pi\) | ||||
−0.916059 | + | 0.401044i | \(0.868647\pi\) | |||||||
\(662\) | −23.6161 | −0.917864 | ||||||||
\(663\) | 48.6295 | 1.88861 | ||||||||
\(664\) | 15.4158 | 0.598248 | ||||||||
\(665\) | 2.55080 | 0.0989157 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.50607 | −0.0583153 | ||||||||
\(668\) | 6.60985 | 0.255743 | ||||||||
\(669\) | 20.9005 | 0.808061 | ||||||||
\(670\) | 26.8241 | 1.03630 | ||||||||
\(671\) | 45.7377 | 1.76568 | ||||||||
\(672\) | 0.306359 | 0.0118181 | ||||||||
\(673\) | −4.88924 | −0.188466 | −0.0942332 | − | 0.995550i | \(-0.530040\pi\) | ||||
−0.0942332 | + | 0.995550i | \(0.530040\pi\) | |||||||
\(674\) | 22.4456 | 0.864573 | ||||||||
\(675\) | −25.0846 | −0.965506 | ||||||||
\(676\) | 8.81198 | 0.338922 | ||||||||
\(677\) | −5.90249 | −0.226851 | −0.113426 | − | 0.993546i | \(-0.536182\pi\) | ||||
−0.113426 | + | 0.993546i | \(0.536182\pi\) | |||||||
\(678\) | −3.92616 | −0.150783 | ||||||||
\(679\) | 0.478763 | 0.0183732 | ||||||||
\(680\) | 20.9279 | 0.802550 | ||||||||
\(681\) | −41.7313 | −1.59915 | ||||||||
\(682\) | 22.1888 | 0.849653 | ||||||||
\(683\) | −22.6465 | −0.866544 | −0.433272 | − | 0.901263i | \(-0.642641\pi\) | ||||
−0.433272 | + | 0.901263i | \(0.642641\pi\) | |||||||
\(684\) | 2.70387 | 0.103385 | ||||||||
\(685\) | 4.85918 | 0.185660 | ||||||||
\(686\) | −2.79147 | −0.106579 | ||||||||
\(687\) | 3.12234 | 0.119125 | ||||||||
\(688\) | 0.399970 | 0.0152487 | ||||||||
\(689\) | 52.7732 | 2.01050 | ||||||||
\(690\) | 4.88611 | 0.186011 | ||||||||
\(691\) | −41.8846 | −1.59336 | −0.796682 | − | 0.604398i | \(-0.793414\pi\) | ||||
−0.796682 | + | 0.604398i | \(0.793414\pi\) | |||||||
\(692\) | −15.4016 | −0.585482 | ||||||||
\(693\) | −0.566894 | −0.0215345 | ||||||||
\(694\) | 1.21511 | 0.0461250 | ||||||||
\(695\) | 30.5585 | 1.15915 | ||||||||
\(696\) | 2.22796 | 0.0844508 | ||||||||
\(697\) | 32.2930 | 1.22319 | ||||||||
\(698\) | 17.7395 | 0.671449 | ||||||||
\(699\) | 5.95209 | 0.225129 | ||||||||
\(700\) | 0.896305 | 0.0338771 | ||||||||
\(701\) | 8.86456 | 0.334810 | 0.167405 | − | 0.985888i | \(-0.446461\pi\) | ||||
0.167405 | + | 0.985888i | \(0.446461\pi\) | |||||||
\(702\) | 26.1364 | 0.986455 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 4.34349 | 0.163701 | ||||||||
\(705\) | 38.7310 | 1.45869 | ||||||||
\(706\) | 1.60606 | 0.0604448 | ||||||||
\(707\) | 2.19218 | 0.0824455 | ||||||||
\(708\) | 6.42866 | 0.241604 | ||||||||
\(709\) | −45.8415 | −1.72161 | −0.860807 | − | 0.508931i | \(-0.830041\pi\) | ||||
−0.860807 | + | 0.508931i | \(0.830041\pi\) | |||||||
\(710\) | −43.6156 | −1.63686 | ||||||||
\(711\) | 4.10908 | 0.154103 | ||||||||
\(712\) | 3.21429 | 0.120461 | ||||||||
\(713\) | −5.29074 | −0.198140 | ||||||||
\(714\) | −2.08209 | −0.0779202 | ||||||||
\(715\) | 62.4661 | 2.33610 | ||||||||
\(716\) | 2.55438 | 0.0954617 | ||||||||
\(717\) | 28.4517 | 1.06255 | ||||||||
\(718\) | −32.0124 | −1.19469 | ||||||||
\(719\) | −6.49120 | −0.242081 | −0.121040 | − | 0.992648i | \(-0.538623\pi\) | ||||
−0.121040 | + | 0.992648i | \(0.538623\pi\) | |||||||
\(720\) | 2.00990 | 0.0749046 | ||||||||
\(721\) | −3.14652 | −0.117183 | ||||||||
\(722\) | −1.83909 | −0.0684439 | ||||||||
\(723\) | −38.8197 | −1.44372 | ||||||||
\(724\) | 8.38797 | 0.311736 | ||||||||
\(725\) | 6.51828 | 0.242083 | ||||||||
\(726\) | 12.0512 | 0.447263 | ||||||||
\(727\) | −26.6650 | −0.988951 | −0.494476 | − | 0.869192i | \(-0.664640\pi\) | ||||
−0.494476 | + | 0.869192i | \(0.664640\pi\) | |||||||
\(728\) | −0.933888 | −0.0346122 | ||||||||
\(729\) | 30.0401 | 1.11260 | ||||||||
\(730\) | 22.4050 | 0.829245 | ||||||||
\(731\) | −2.71828 | −0.100539 | ||||||||
\(732\) | 16.1332 | 0.596299 | ||||||||
\(733\) | 48.8996 | 1.80615 | 0.903075 | − | 0.429484i | \(-0.141304\pi\) | ||||
0.903075 | + | 0.429484i | \(0.141304\pi\) | |||||||
\(734\) | 16.0363 | 0.591910 | ||||||||
\(735\) | 32.8362 | 1.21118 | ||||||||
\(736\) | −1.03567 | −0.0381753 | ||||||||
\(737\) | −37.8360 | −1.39371 | ||||||||
\(738\) | 3.10139 | 0.114164 | ||||||||
\(739\) | 53.7875 | 1.97861 | 0.989303 | − | 0.145878i | \(-0.0466006\pi\) | ||||
0.989303 | + | 0.145878i | \(0.0466006\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 29.6416 | 1.08891 | ||||||||
\(742\) | −2.25951 | −0.0829491 | ||||||||
\(743\) | 22.4907 | 0.825104 | 0.412552 | − | 0.910934i | \(-0.364637\pi\) | ||||
0.412552 | + | 0.910934i | \(0.364637\pi\) | |||||||
\(744\) | 7.82671 | 0.286941 | ||||||||
\(745\) | −39.5708 | −1.44976 | ||||||||
\(746\) | 1.11639 | 0.0408738 | ||||||||
\(747\) | −10.0619 | −0.368147 | ||||||||
\(748\) | −29.5193 | −1.07933 | ||||||||
\(749\) | −3.72249 | −0.136017 | ||||||||
\(750\) | 2.44205 | 0.0891711 | ||||||||
\(751\) | −7.12554 | −0.260015 | −0.130007 | − | 0.991513i | \(-0.541500\pi\) | ||||
−0.130007 | + | 0.991513i | \(0.541500\pi\) | |||||||
\(752\) | −8.20949 | −0.299369 | ||||||||
\(753\) | 19.4764 | 0.709759 | ||||||||
\(754\) | −6.79160 | −0.247335 | ||||||||
\(755\) | 15.9705 | 0.581226 | ||||||||
\(756\) | −1.11904 | −0.0406991 | ||||||||
\(757\) | 5.41741 | 0.196899 | 0.0984495 | − | 0.995142i | \(-0.468612\pi\) | ||||
0.0984495 | + | 0.995142i | \(0.468612\pi\) | |||||||
\(758\) | 36.4410 | 1.32360 | ||||||||
\(759\) | −6.89197 | −0.250163 | ||||||||
\(760\) | 12.7564 | 0.462724 | ||||||||
\(761\) | −25.7999 | −0.935246 | −0.467623 | − | 0.883928i | \(-0.654890\pi\) | ||||
−0.467623 | + | 0.883928i | \(0.654890\pi\) | |||||||
\(762\) | −8.89686 | −0.322299 | ||||||||
\(763\) | 0.00140440 | 5.08428e−5 0 | ||||||||
\(764\) | 6.48182 | 0.234504 | ||||||||
\(765\) | −13.6597 | −0.493869 | ||||||||
\(766\) | 6.03086 | 0.217904 | ||||||||
\(767\) | −19.5968 | −0.707598 | ||||||||
\(768\) | 1.53209 | 0.0552845 | ||||||||
\(769\) | −1.92534 | −0.0694296 | −0.0347148 | − | 0.999397i | \(-0.511052\pi\) | ||||
−0.0347148 | + | 0.999397i | \(0.511052\pi\) | |||||||
\(770\) | −2.67451 | −0.0963827 | ||||||||
\(771\) | 6.66015 | 0.239859 | ||||||||
\(772\) | 20.9828 | 0.755186 | ||||||||
\(773\) | 27.3985 | 0.985455 | 0.492727 | − | 0.870184i | \(-0.336000\pi\) | ||||
0.492727 | + | 0.870184i | \(0.336000\pi\) | |||||||
\(774\) | −0.261062 | −0.00938366 | ||||||||
\(775\) | 22.8983 | 0.822533 | ||||||||
\(776\) | 2.39427 | 0.0859492 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18.8329 | −0.675193 | ||||||||
\(779\) | 19.6839 | 0.705249 | ||||||||
\(780\) | 22.0338 | 0.788938 | ||||||||
\(781\) | 61.5207 | 2.20138 | ||||||||
\(782\) | 7.03864 | 0.251701 | ||||||||
\(783\) | −8.13809 | −0.290832 | ||||||||
\(784\) | −6.96002 | −0.248572 | ||||||||
\(785\) | −36.8399 | −1.31487 | ||||||||
\(786\) | −12.8229 | −0.457379 | ||||||||
\(787\) | −35.5331 | −1.26662 | −0.633309 | − | 0.773899i | \(-0.718304\pi\) | ||||
−0.633309 | + | 0.773899i | \(0.718304\pi\) | |||||||
\(788\) | −1.65809 | −0.0590672 | ||||||||
\(789\) | 9.97602 | 0.355156 | ||||||||
\(790\) | 19.3860 | 0.689721 | ||||||||
\(791\) | −0.512426 | −0.0182198 | ||||||||
\(792\) | −2.83501 | −0.100738 | ||||||||
\(793\) | −49.1794 | −1.74641 | ||||||||
\(794\) | −27.5114 | −0.976342 | ||||||||
\(795\) | 53.3100 | 1.89071 | ||||||||
\(796\) | −7.21981 | −0.255900 | ||||||||
\(797\) | 51.3638 | 1.81940 | 0.909699 | − | 0.415269i | \(-0.136312\pi\) | ||||
0.909699 | + | 0.415269i | \(0.136312\pi\) | |||||||
\(798\) | −1.26912 | −0.0449262 | ||||||||
\(799\) | 55.7936 | 1.97384 | ||||||||
\(800\) | 4.48238 | 0.158476 | ||||||||
\(801\) | −2.09798 | −0.0741285 | ||||||||
\(802\) | 22.0721 | 0.779392 | ||||||||
\(803\) | −31.6027 | −1.11523 | ||||||||
\(804\) | −13.3460 | −0.470676 | ||||||||
\(805\) | 0.637715 | 0.0224765 | ||||||||
\(806\) | −23.8585 | −0.840379 | ||||||||
\(807\) | −15.1709 | −0.534042 | ||||||||
\(808\) | 10.9630 | 0.385677 | ||||||||
\(809\) | −16.6586 | −0.585684 | −0.292842 | − | 0.956161i | \(-0.594601\pi\) | ||||
−0.292842 | + | 0.956161i | \(0.594601\pi\) | |||||||
\(810\) | 20.3726 | 0.715818 | ||||||||
\(811\) | −34.1029 | −1.19751 | −0.598757 | − | 0.800931i | \(-0.704339\pi\) | ||||
−0.598757 | + | 0.800931i | \(0.704339\pi\) | |||||||
\(812\) | 0.290785 | 0.0102045 | ||||||||
\(813\) | 13.8272 | 0.484942 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.17681 | 0.0762503 | ||||||||
\(816\) | −10.4124 | −0.364508 | ||||||||
\(817\) | −1.65690 | −0.0579677 | ||||||||
\(818\) | 1.42090 | 0.0496807 | ||||||||
\(819\) | 0.609552 | 0.0212995 | ||||||||
\(820\) | 14.6319 | 0.510967 | ||||||||
\(821\) | 21.6278 | 0.754816 | 0.377408 | − | 0.926047i | \(-0.376815\pi\) | ||||
0.377408 | + | 0.926047i | \(0.376815\pi\) | |||||||
\(822\) | −2.41762 | −0.0843242 | ||||||||
\(823\) | 22.4604 | 0.782920 | 0.391460 | − | 0.920195i | \(-0.371970\pi\) | ||||
0.391460 | + | 0.920195i | \(0.371970\pi\) | |||||||
\(824\) | −15.7356 | −0.548176 | ||||||||
\(825\) | 29.8285 | 1.03849 | ||||||||
\(826\) | 0.839043 | 0.0291940 | ||||||||
\(827\) | −32.9258 | −1.14494 | −0.572472 | − | 0.819924i | \(-0.694015\pi\) | ||||
−0.572472 | + | 0.819924i | \(0.694015\pi\) | |||||||
\(828\) | 0.675985 | 0.0234921 | ||||||||
\(829\) | −18.3840 | −0.638501 | −0.319251 | − | 0.947670i | \(-0.603431\pi\) | ||||
−0.319251 | + | 0.947670i | \(0.603431\pi\) | |||||||
\(830\) | −47.4706 | −1.64773 | ||||||||
\(831\) | −0.318809 | −0.0110593 | ||||||||
\(832\) | −4.67033 | −0.161915 | ||||||||
\(833\) | 47.3019 | 1.63891 | ||||||||
\(834\) | −15.2040 | −0.526470 | ||||||||
\(835\) | −20.3540 | −0.704380 | ||||||||
\(836\) | −17.9932 | −0.622308 | ||||||||
\(837\) | −28.5887 | −0.988169 | ||||||||
\(838\) | −13.6400 | −0.471186 | ||||||||
\(839\) | −11.2213 | −0.387401 | −0.193701 | − | 0.981061i | \(-0.562049\pi\) | ||||
−0.193701 | + | 0.981061i | \(0.562049\pi\) | |||||||
\(840\) | −0.943387 | −0.0325499 | ||||||||
\(841\) | −26.8853 | −0.927079 | ||||||||
\(842\) | 27.9978 | 0.964868 | ||||||||
\(843\) | 41.4572 | 1.42786 | ||||||||
\(844\) | 4.50868 | 0.155195 | ||||||||
\(845\) | −27.1351 | −0.933477 | ||||||||
\(846\) | 5.35837 | 0.184224 | ||||||||
\(847\) | 1.57288 | 0.0540447 | ||||||||
\(848\) | −11.2997 | −0.388033 | ||||||||
\(849\) | −1.24543 | −0.0427429 | ||||||||
\(850\) | −30.4633 | −1.04488 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 21.7003 | 0.743442 | ||||||||
\(853\) | 0.0974550 | 0.00333680 | 0.00166840 | − | 0.999999i | \(-0.499469\pi\) | ||||
0.00166840 | + | 0.999999i | \(0.499469\pi\) | |||||||
\(854\) | 2.10564 | 0.0720534 | ||||||||
\(855\) | −8.32616 | −0.284749 | ||||||||
\(856\) | −18.6160 | −0.636281 | ||||||||
\(857\) | 27.1799 | 0.928447 | 0.464223 | − | 0.885718i | \(-0.346333\pi\) | ||||
0.464223 | + | 0.885718i | \(0.346333\pi\) | |||||||
\(858\) | −31.0792 | −1.06103 | ||||||||
\(859\) | −16.1327 | −0.550442 | −0.275221 | − | 0.961381i | \(-0.588751\pi\) | ||||
−0.275221 | + | 0.961381i | \(0.588751\pi\) | |||||||
\(860\) | −1.23165 | −0.0419987 | ||||||||
\(861\) | −1.45570 | −0.0496102 | ||||||||
\(862\) | 2.84949 | 0.0970539 | ||||||||
\(863\) | 41.7582 | 1.42146 | 0.710732 | − | 0.703463i | \(-0.248364\pi\) | ||||
0.710732 | + | 0.703463i | \(0.248364\pi\) | |||||||
\(864\) | −5.59627 | −0.190389 | ||||||||
\(865\) | 47.4270 | 1.61257 | ||||||||
\(866\) | −31.1352 | −1.05802 | ||||||||
\(867\) | 44.7197 | 1.51876 | ||||||||
\(868\) | 1.02151 | 0.0346723 | ||||||||
\(869\) | −27.3443 | −0.927592 | ||||||||
\(870\) | −6.86068 | −0.232599 | ||||||||
\(871\) | 40.6831 | 1.37849 | ||||||||
\(872\) | 0.00702336 | 0.000237841 0 | ||||||||
\(873\) | −1.56275 | −0.0528910 | ||||||||
\(874\) | 4.29033 | 0.145123 | ||||||||
\(875\) | 0.318726 | 0.0107749 | ||||||||
\(876\) | −11.1473 | −0.376632 | ||||||||
\(877\) | 13.0499 | 0.440665 | 0.220332 | − | 0.975425i | \(-0.429286\pi\) | ||||
0.220332 | + | 0.975425i | \(0.429286\pi\) | |||||||
\(878\) | 28.7800 | 0.971277 | ||||||||
\(879\) | −13.4817 | −0.454727 | ||||||||
\(880\) | −13.3751 | −0.450875 | ||||||||
\(881\) | 10.4442 | 0.351875 | 0.175938 | − | 0.984401i | \(-0.443704\pi\) | ||||
0.175938 | + | 0.984401i | \(0.443704\pi\) | |||||||
\(882\) | 4.54283 | 0.152965 | ||||||||
\(883\) | −32.3018 | −1.08704 | −0.543520 | − | 0.839396i | \(-0.682909\pi\) | ||||
−0.543520 | + | 0.839396i | \(0.682909\pi\) | |||||||
\(884\) | 31.7406 | 1.06755 | ||||||||
\(885\) | −19.7961 | −0.665438 | ||||||||
\(886\) | 19.3903 | 0.651429 | ||||||||
\(887\) | 9.33190 | 0.313334 | 0.156667 | − | 0.987651i | \(-0.449925\pi\) | ||||
0.156667 | + | 0.987651i | \(0.449925\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.16118 | −0.0389448 | ||||||||
\(890\) | −9.89793 | −0.331779 | ||||||||
\(891\) | −28.7359 | −0.962690 | ||||||||
\(892\) | 13.6418 | 0.456763 | ||||||||
\(893\) | 34.0084 | 1.13805 | ||||||||
\(894\) | 19.6879 | 0.658463 | ||||||||
\(895\) | −7.86583 | −0.262926 | ||||||||
\(896\) | 0.199962 | 0.00668026 | ||||||||
\(897\) | 7.41058 | 0.247432 | ||||||||
\(898\) | 17.0799 | 0.569965 | ||||||||
\(899\) | 7.42882 | 0.247765 | ||||||||
\(900\) | −2.92567 | −0.0975222 | ||||||||
\(901\) | 76.7952 | 2.55842 | ||||||||
\(902\) | −20.6386 | −0.687189 | ||||||||
\(903\) | 0.122534 | 0.00407769 | ||||||||
\(904\) | −2.56262 | −0.0852314 | ||||||||
\(905\) | −25.8295 | −0.858601 | ||||||||
\(906\) | −7.94592 | −0.263985 | ||||||||
\(907\) | −31.7333 | −1.05369 | −0.526843 | − | 0.849963i | \(-0.676624\pi\) | ||||
−0.526843 | + | 0.849963i | \(0.676624\pi\) | |||||||
\(908\) | −27.2382 | −0.903931 | ||||||||
\(909\) | −7.15559 | −0.237336 | ||||||||
\(910\) | 2.87577 | 0.0953307 | ||||||||
\(911\) | 47.0729 | 1.55959 | 0.779797 | − | 0.626033i | \(-0.215322\pi\) | ||||
0.779797 | + | 0.626033i | \(0.215322\pi\) | |||||||
\(912\) | −6.34679 | −0.210163 | ||||||||
\(913\) | 66.9583 | 2.21599 | ||||||||
\(914\) | −2.41654 | −0.0799322 | ||||||||
\(915\) | −49.6797 | −1.64236 | ||||||||
\(916\) | 2.03796 | 0.0673362 | ||||||||
\(917\) | −1.67360 | −0.0552671 | ||||||||
\(918\) | 38.0335 | 1.25529 | ||||||||
\(919\) | −36.4389 | −1.20201 | −0.601004 | − | 0.799246i | \(-0.705233\pi\) | ||||
−0.601004 | + | 0.799246i | \(0.705233\pi\) | |||||||
\(920\) | 3.18918 | 0.105144 | ||||||||
\(921\) | −37.4659 | −1.23454 | ||||||||
\(922\) | 18.7400 | 0.617169 | ||||||||
\(923\) | −66.1501 | −2.17736 | ||||||||
\(924\) | 1.33067 | 0.0437758 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.15947 | −0.169551 | ||||||||
\(927\) | 10.2707 | 0.337334 | ||||||||
\(928\) | 1.45420 | 0.0477365 | ||||||||
\(929\) | −34.2969 | −1.12524 | −0.562622 | − | 0.826715i | \(-0.690207\pi\) | ||||
−0.562622 | + | 0.826715i | \(0.690207\pi\) | |||||||
\(930\) | −24.1012 | −0.790308 | ||||||||
\(931\) | 28.8324 | 0.944943 | ||||||||
\(932\) | 3.88495 | 0.127256 | ||||||||
\(933\) | 0.0194503 | 0.000636775 0 | ||||||||
\(934\) | −30.9314 | −1.01211 | ||||||||
\(935\) | 90.9003 | 2.97276 | ||||||||
\(936\) | 3.04834 | 0.0996381 | ||||||||
\(937\) | −5.44402 | −0.177848 | −0.0889242 | − | 0.996038i | \(-0.528343\pi\) | ||||
−0.0889242 | + | 0.996038i | \(0.528343\pi\) | |||||||
\(938\) | −1.74186 | −0.0568738 | ||||||||
\(939\) | −26.7632 | −0.873384 | ||||||||
\(940\) | 25.2799 | 0.824539 | ||||||||
\(941\) | −40.0282 | −1.30488 | −0.652441 | − | 0.757839i | \(-0.726255\pi\) | ||||
−0.652441 | + | 0.757839i | \(0.726255\pi\) | |||||||
\(942\) | 18.3292 | 0.597198 | ||||||||
\(943\) | 4.92109 | 0.160253 | ||||||||
\(944\) | 4.19601 | 0.136569 | ||||||||
\(945\) | 3.44591 | 0.112096 | ||||||||
\(946\) | 1.73726 | 0.0564833 | ||||||||
\(947\) | 35.1144 | 1.14106 | 0.570532 | − | 0.821275i | \(-0.306737\pi\) | ||||
0.570532 | + | 0.821275i | \(0.306737\pi\) | |||||||
\(948\) | −9.64523 | −0.313262 | ||||||||
\(949\) | 33.9808 | 1.10306 | ||||||||
\(950\) | −18.5686 | −0.602444 | ||||||||
\(951\) | −4.18092 | −0.135576 | ||||||||
\(952\) | −1.35899 | −0.0440450 | ||||||||
\(953\) | 9.02673 | 0.292405 | 0.146202 | − | 0.989255i | \(-0.453295\pi\) | ||||
0.146202 | + | 0.989255i | \(0.453295\pi\) | |||||||
\(954\) | 7.37534 | 0.238786 | ||||||||
\(955\) | −19.9598 | −0.645883 | ||||||||
\(956\) | 18.5705 | 0.600613 | ||||||||
\(957\) | 9.67713 | 0.312817 | ||||||||
\(958\) | 12.8783 | 0.416079 | ||||||||
\(959\) | −0.315538 | −0.0101892 | ||||||||
\(960\) | −4.71783 | −0.152267 | ||||||||
\(961\) | −4.90299 | −0.158161 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.1507 | 0.391552 | ||||||||
\(964\) | −25.3378 | −0.816074 | ||||||||
\(965\) | −64.6132 | −2.07997 | ||||||||
\(966\) | −0.317287 | −0.0102085 | ||||||||
\(967\) | 38.8473 | 1.24925 | 0.624623 | − | 0.780927i | \(-0.285253\pi\) | ||||
0.624623 | + | 0.780927i | \(0.285253\pi\) | |||||||
\(968\) | 7.86588 | 0.252819 | ||||||||
\(969\) | 43.1342 | 1.38567 | ||||||||
\(970\) | −7.37278 | −0.236726 | ||||||||
\(971\) | −26.4600 | −0.849142 | −0.424571 | − | 0.905395i | \(-0.639575\pi\) | ||||
−0.424571 | + | 0.905395i | \(0.639575\pi\) | |||||||
\(972\) | 6.65270 | 0.213386 | ||||||||
\(973\) | −1.98436 | −0.0636156 | ||||||||
\(974\) | −17.2601 | −0.553050 | ||||||||
\(975\) | −32.0730 | −1.02716 | ||||||||
\(976\) | 10.5302 | 0.337063 | ||||||||
\(977\) | 55.2016 | 1.76606 | 0.883028 | − | 0.469320i | \(-0.155501\pi\) | ||||
0.883028 | + | 0.469320i | \(0.155501\pi\) | |||||||
\(978\) | −1.08304 | −0.0346319 | ||||||||
\(979\) | 13.9612 | 0.446203 | ||||||||
\(980\) | 21.4323 | 0.684630 | ||||||||
\(981\) | −0.00458417 | −0.000146361 0 | ||||||||
\(982\) | 17.1066 | 0.545894 | ||||||||
\(983\) | 29.7000 | 0.947283 | 0.473641 | − | 0.880718i | \(-0.342939\pi\) | ||||
0.473641 | + | 0.880718i | \(0.342939\pi\) | |||||||
\(984\) | −7.27989 | −0.232074 | ||||||||
\(985\) | 5.10585 | 0.162686 | ||||||||
\(986\) | −9.88308 | −0.314741 | ||||||||
\(987\) | −2.51506 | −0.0800551 | ||||||||
\(988\) | 19.3472 | 0.615516 | ||||||||
\(989\) | −0.414236 | −0.0131719 | ||||||||
\(990\) | 8.72998 | 0.277457 | ||||||||
\(991\) | −20.1762 | −0.640917 | −0.320458 | − | 0.947263i | \(-0.603837\pi\) | ||||
−0.320458 | + | 0.947263i | \(0.603837\pi\) | |||||||
\(992\) | 5.10852 | 0.162196 | ||||||||
\(993\) | −36.1819 | −1.14820 | ||||||||
\(994\) | 2.83224 | 0.0898332 | ||||||||
\(995\) | 22.2323 | 0.704812 | ||||||||
\(996\) | 23.6184 | 0.748376 | ||||||||
\(997\) | 36.9911 | 1.17152 | 0.585759 | − | 0.810485i | \(-0.300796\pi\) | ||||
0.585759 | + | 0.810485i | \(0.300796\pi\) | |||||||
\(998\) | −18.5412 | −0.586913 | ||||||||
\(999\) | 0 | 0 |
(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 | 2738.2.a.s.1.5 | 6 | ||
37.18 | odd | 36 | 74.2.h.a.65.1 | yes | 12 | ||
37.35 | odd | 36 | 74.2.h.a.41.1 | ✓ | 12 | ||
37.36 | even | 2 | 2738.2.a.r.1.6 | 6 | |||
111.35 | even | 36 | 666.2.bj.c.559.2 | 12 | |||
111.92 | even | 36 | 666.2.bj.c.361.2 | 12 | |||
148.35 | even | 36 | 592.2.bq.b.337.1 | 12 | |||
148.55 | even | 36 | 592.2.bq.b.65.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.h.a.41.1 | ✓ | 12 | 37.35 | odd | 36 | ||
74.2.h.a.65.1 | yes | 12 | 37.18 | odd | 36 | ||
592.2.bq.b.65.1 | 12 | 148.55 | even | 36 | |||
592.2.bq.b.337.1 | 12 | 148.35 | even | 36 | |||
666.2.bj.c.361.2 | 12 | 111.92 | even | 36 | |||
666.2.bj.c.559.2 | 12 | 111.35 | even | 36 | |||
2738.2.a.r.1.6 | 6 | 37.36 | even | 2 | |||
2738.2.a.s.1.5 | 6 | 1.1 | even | 1 | trivial |