Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 | ||||||||
\(3\) | 2.73205 | 1.57735 | 0.788675 | − | 0.614810i | \(-0.210767\pi\) | ||||
0.788675 | + | 0.614810i | \(0.210767\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.73205 | 0.774597 | 0.387298 | − | 0.921954i | \(-0.373408\pi\) | ||||
0.387298 | + | 0.921954i | \(0.373408\pi\) | |||||||
\(6\) | 2.73205 | 1.11536 | ||||||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.46410 | 1.48803 | ||||||||
\(10\) | 1.73205 | 0.547723 | ||||||||
\(11\) | 1.73205 | 0.522233 | 0.261116 | − | 0.965307i | \(-0.415909\pi\) | ||||
0.261116 | + | 0.965307i | \(0.415909\pi\) | |||||||
\(12\) | 2.73205 | 0.788675 | ||||||||
\(13\) | −2.73205 | −0.757735 | −0.378867 | − | 0.925451i | \(-0.623686\pi\) | ||||
−0.378867 | + | 0.925451i | \(0.623686\pi\) | |||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | 4.73205 | 1.22181 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.73205 | −0.420084 | −0.210042 | − | 0.977692i | \(-0.567360\pi\) | ||||
−0.210042 | + | 0.977692i | \(0.567360\pi\) | |||||||
\(18\) | 4.46410 | 1.05220 | ||||||||
\(19\) | 3.26795 | 0.749719 | 0.374859 | − | 0.927082i | \(-0.377691\pi\) | ||||
0.374859 | + | 0.927082i | \(0.377691\pi\) | |||||||
\(20\) | 1.73205 | 0.387298 | ||||||||
\(21\) | 5.46410 | 1.19236 | ||||||||
\(22\) | 1.73205 | 0.369274 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 2.73205 | 0.557678 | ||||||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | −2.73205 | −0.535799 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 2.00000 | 0.377964 | ||||||||
\(29\) | −2.53590 | −0.470905 | −0.235452 | − | 0.971886i | \(-0.575657\pi\) | ||||
−0.235452 | + | 0.971886i | \(0.575657\pi\) | |||||||
\(30\) | 4.73205 | 0.863950 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.73205 | 0.823744 | ||||||||
\(34\) | −1.73205 | −0.297044 | ||||||||
\(35\) | 3.46410 | 0.585540 | ||||||||
\(36\) | 4.46410 | 0.744017 | ||||||||
\(37\) | −7.46410 | −1.22709 | −0.613545 | − | 0.789659i | \(-0.710257\pi\) | ||||
−0.613545 | + | 0.789659i | \(0.710257\pi\) | |||||||
\(38\) | 3.26795 | 0.530131 | ||||||||
\(39\) | −7.46410 | −1.19521 | ||||||||
\(40\) | 1.73205 | 0.273861 | ||||||||
\(41\) | 6.46410 | 1.00952 | 0.504762 | − | 0.863259i | \(-0.331580\pi\) | ||||
0.504762 | + | 0.863259i | \(0.331580\pi\) | |||||||
\(42\) | 5.46410 | 0.843129 | ||||||||
\(43\) | 1.19615 | 0.182412 | 0.0912058 | − | 0.995832i | \(-0.470928\pi\) | ||||
0.0912058 | + | 0.995832i | \(0.470928\pi\) | |||||||
\(44\) | 1.73205 | 0.261116 | ||||||||
\(45\) | 7.73205 | 1.15263 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −5.66025 | −0.825633 | −0.412816 | − | 0.910814i | \(-0.635455\pi\) | ||||
−0.412816 | + | 0.910814i | \(0.635455\pi\) | |||||||
\(48\) | 2.73205 | 0.394338 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | −2.00000 | −0.282843 | ||||||||
\(51\) | −4.73205 | −0.662620 | ||||||||
\(52\) | −2.73205 | −0.378867 | ||||||||
\(53\) | 3.46410 | 0.475831 | 0.237915 | − | 0.971286i | \(-0.423536\pi\) | ||||
0.237915 | + | 0.971286i | \(0.423536\pi\) | |||||||
\(54\) | 4.00000 | 0.544331 | ||||||||
\(55\) | 3.00000 | 0.404520 | ||||||||
\(56\) | 2.00000 | 0.267261 | ||||||||
\(57\) | 8.92820 | 1.18257 | ||||||||
\(58\) | −2.53590 | −0.332980 | ||||||||
\(59\) | 10.7321 | 1.39719 | 0.698597 | − | 0.715515i | \(-0.253808\pi\) | ||||
0.698597 | + | 0.715515i | \(0.253808\pi\) | |||||||
\(60\) | 4.73205 | 0.610905 | ||||||||
\(61\) | 7.19615 | 0.921373 | 0.460686 | − | 0.887563i | \(-0.347603\pi\) | ||||
0.460686 | + | 0.887563i | \(0.347603\pi\) | |||||||
\(62\) | 8.00000 | 1.01600 | ||||||||
\(63\) | 8.92820 | 1.12485 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.73205 | −0.586939 | ||||||||
\(66\) | 4.73205 | 0.582475 | ||||||||
\(67\) | −13.1244 | −1.60340 | −0.801698 | − | 0.597730i | \(-0.796070\pi\) | ||||
−0.801698 | + | 0.597730i | \(0.796070\pi\) | |||||||
\(68\) | −1.73205 | −0.210042 | ||||||||
\(69\) | −2.73205 | −0.328900 | ||||||||
\(70\) | 3.46410 | 0.414039 | ||||||||
\(71\) | 10.7321 | 1.27366 | 0.636830 | − | 0.771004i | \(-0.280245\pi\) | ||||
0.636830 | + | 0.771004i | \(0.280245\pi\) | |||||||
\(72\) | 4.46410 | 0.526099 | ||||||||
\(73\) | −6.19615 | −0.725205 | −0.362602 | − | 0.931944i | \(-0.618112\pi\) | ||||
−0.362602 | + | 0.931944i | \(0.618112\pi\) | |||||||
\(74\) | −7.46410 | −0.867684 | ||||||||
\(75\) | −5.46410 | −0.630940 | ||||||||
\(76\) | 3.26795 | 0.374859 | ||||||||
\(77\) | 3.46410 | 0.394771 | ||||||||
\(78\) | −7.46410 | −0.845143 | ||||||||
\(79\) | −13.4641 | −1.51483 | −0.757415 | − | 0.652934i | \(-0.773538\pi\) | ||||
−0.757415 | + | 0.652934i | \(0.773538\pi\) | |||||||
\(80\) | 1.73205 | 0.193649 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | 6.46410 | 0.713841 | ||||||||
\(83\) | 8.19615 | 0.899645 | 0.449822 | − | 0.893118i | \(-0.351487\pi\) | ||||
0.449822 | + | 0.893118i | \(0.351487\pi\) | |||||||
\(84\) | 5.46410 | 0.596182 | ||||||||
\(85\) | −3.00000 | −0.325396 | ||||||||
\(86\) | 1.19615 | 0.128984 | ||||||||
\(87\) | −6.92820 | −0.742781 | ||||||||
\(88\) | 1.73205 | 0.184637 | ||||||||
\(89\) | 2.53590 | 0.268805 | 0.134402 | − | 0.990927i | \(-0.457089\pi\) | ||||
0.134402 | + | 0.990927i | \(0.457089\pi\) | |||||||
\(90\) | 7.73205 | 0.815030 | ||||||||
\(91\) | −5.46410 | −0.572793 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 21.8564 | 2.26640 | ||||||||
\(94\) | −5.66025 | −0.583811 | ||||||||
\(95\) | 5.66025 | 0.580730 | ||||||||
\(96\) | 2.73205 | 0.278839 | ||||||||
\(97\) | −7.46410 | −0.757865 | −0.378932 | − | 0.925424i | \(-0.623709\pi\) | ||||
−0.378932 | + | 0.925424i | \(0.623709\pi\) | |||||||
\(98\) | −3.00000 | −0.303046 | ||||||||
\(99\) | 7.73205 | 0.777100 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | −2.53590 | −0.252331 | −0.126166 | − | 0.992009i | \(-0.540267\pi\) | ||||
−0.126166 | + | 0.992009i | \(0.540267\pi\) | |||||||
\(102\) | −4.73205 | −0.468543 | ||||||||
\(103\) | 9.73205 | 0.958927 | 0.479464 | − | 0.877562i | \(-0.340831\pi\) | ||||
0.479464 | + | 0.877562i | \(0.340831\pi\) | |||||||
\(104\) | −2.73205 | −0.267900 | ||||||||
\(105\) | 9.46410 | 0.923602 | ||||||||
\(106\) | 3.46410 | 0.336463 | ||||||||
\(107\) | 4.26795 | 0.412598 | 0.206299 | − | 0.978489i | \(-0.433858\pi\) | ||||
0.206299 | + | 0.978489i | \(0.433858\pi\) | |||||||
\(108\) | 4.00000 | 0.384900 | ||||||||
\(109\) | −9.19615 | −0.880832 | −0.440416 | − | 0.897794i | \(-0.645169\pi\) | ||||
−0.440416 | + | 0.897794i | \(0.645169\pi\) | |||||||
\(110\) | 3.00000 | 0.286039 | ||||||||
\(111\) | −20.3923 | −1.93555 | ||||||||
\(112\) | 2.00000 | 0.188982 | ||||||||
\(113\) | −8.19615 | −0.771029 | −0.385515 | − | 0.922702i | \(-0.625976\pi\) | ||||
−0.385515 | + | 0.922702i | \(0.625976\pi\) | |||||||
\(114\) | 8.92820 | 0.836203 | ||||||||
\(115\) | −1.73205 | −0.161515 | ||||||||
\(116\) | −2.53590 | −0.235452 | ||||||||
\(117\) | −12.1962 | −1.12753 | ||||||||
\(118\) | 10.7321 | 0.987965 | ||||||||
\(119\) | −3.46410 | −0.317554 | ||||||||
\(120\) | 4.73205 | 0.431975 | ||||||||
\(121\) | −8.00000 | −0.727273 | ||||||||
\(122\) | 7.19615 | 0.651509 | ||||||||
\(123\) | 17.6603 | 1.59237 | ||||||||
\(124\) | 8.00000 | 0.718421 | ||||||||
\(125\) | −12.1244 | −1.08444 | ||||||||
\(126\) | 8.92820 | 0.795388 | ||||||||
\(127\) | 5.80385 | 0.515008 | 0.257504 | − | 0.966277i | \(-0.417100\pi\) | ||||
0.257504 | + | 0.966277i | \(0.417100\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.26795 | 0.287727 | ||||||||
\(130\) | −4.73205 | −0.415028 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | 4.73205 | 0.411872 | ||||||||
\(133\) | 6.53590 | 0.566734 | ||||||||
\(134\) | −13.1244 | −1.13377 | ||||||||
\(135\) | 6.92820 | 0.596285 | ||||||||
\(136\) | −1.73205 | −0.148522 | ||||||||
\(137\) | −18.1244 | −1.54847 | −0.774234 | − | 0.632899i | \(-0.781865\pi\) | ||||
−0.774234 | + | 0.632899i | \(0.781865\pi\) | |||||||
\(138\) | −2.73205 | −0.232568 | ||||||||
\(139\) | 17.0000 | 1.44192 | 0.720961 | − | 0.692976i | \(-0.243701\pi\) | ||||
0.720961 | + | 0.692976i | \(0.243701\pi\) | |||||||
\(140\) | 3.46410 | 0.292770 | ||||||||
\(141\) | −15.4641 | −1.30231 | ||||||||
\(142\) | 10.7321 | 0.900614 | ||||||||
\(143\) | −4.73205 | −0.395714 | ||||||||
\(144\) | 4.46410 | 0.372008 | ||||||||
\(145\) | −4.39230 | −0.364761 | ||||||||
\(146\) | −6.19615 | −0.512797 | ||||||||
\(147\) | −8.19615 | −0.676007 | ||||||||
\(148\) | −7.46410 | −0.613545 | ||||||||
\(149\) | 14.1962 | 1.16299 | 0.581497 | − | 0.813549i | \(-0.302467\pi\) | ||||
0.581497 | + | 0.813549i | \(0.302467\pi\) | |||||||
\(150\) | −5.46410 | −0.446142 | ||||||||
\(151\) | 2.46410 | 0.200526 | 0.100263 | − | 0.994961i | \(-0.468032\pi\) | ||||
0.100263 | + | 0.994961i | \(0.468032\pi\) | |||||||
\(152\) | 3.26795 | 0.265066 | ||||||||
\(153\) | −7.73205 | −0.625099 | ||||||||
\(154\) | 3.46410 | 0.279145 | ||||||||
\(155\) | 13.8564 | 1.11297 | ||||||||
\(156\) | −7.46410 | −0.597606 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | −13.4641 | −1.07115 | ||||||||
\(159\) | 9.46410 | 0.750552 | ||||||||
\(160\) | 1.73205 | 0.136931 | ||||||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | −2.46410 | −0.193598 | ||||||||
\(163\) | 14.4641 | 1.13292 | 0.566458 | − | 0.824091i | \(-0.308313\pi\) | ||||
0.566458 | + | 0.824091i | \(0.308313\pi\) | |||||||
\(164\) | 6.46410 | 0.504762 | ||||||||
\(165\) | 8.19615 | 0.638070 | ||||||||
\(166\) | 8.19615 | 0.636145 | ||||||||
\(167\) | −16.8564 | −1.30439 | −0.652194 | − | 0.758052i | \(-0.726151\pi\) | ||||
−0.652194 | + | 0.758052i | \(0.726151\pi\) | |||||||
\(168\) | 5.46410 | 0.421565 | ||||||||
\(169\) | −5.53590 | −0.425838 | ||||||||
\(170\) | −3.00000 | −0.230089 | ||||||||
\(171\) | 14.5885 | 1.11561 | ||||||||
\(172\) | 1.19615 | 0.0912058 | ||||||||
\(173\) | −19.3923 | −1.47437 | −0.737185 | − | 0.675691i | \(-0.763845\pi\) | ||||
−0.737185 | + | 0.675691i | \(0.763845\pi\) | |||||||
\(174\) | −6.92820 | −0.525226 | ||||||||
\(175\) | −4.00000 | −0.302372 | ||||||||
\(176\) | 1.73205 | 0.130558 | ||||||||
\(177\) | 29.3205 | 2.20386 | ||||||||
\(178\) | 2.53590 | 0.190074 | ||||||||
\(179\) | −6.92820 | −0.517838 | −0.258919 | − | 0.965899i | \(-0.583366\pi\) | ||||
−0.258919 | + | 0.965899i | \(0.583366\pi\) | |||||||
\(180\) | 7.73205 | 0.576313 | ||||||||
\(181\) | 17.4641 | 1.29810 | 0.649048 | − | 0.760747i | \(-0.275167\pi\) | ||||
0.649048 | + | 0.760747i | \(0.275167\pi\) | |||||||
\(182\) | −5.46410 | −0.405026 | ||||||||
\(183\) | 19.6603 | 1.45333 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −12.9282 | −0.950500 | ||||||||
\(186\) | 21.8564 | 1.60259 | ||||||||
\(187\) | −3.00000 | −0.219382 | ||||||||
\(188\) | −5.66025 | −0.412816 | ||||||||
\(189\) | 8.00000 | 0.581914 | ||||||||
\(190\) | 5.66025 | 0.410638 | ||||||||
\(191\) | −25.5167 | −1.84632 | −0.923160 | − | 0.384415i | \(-0.874403\pi\) | ||||
−0.923160 | + | 0.384415i | \(0.874403\pi\) | |||||||
\(192\) | 2.73205 | 0.197169 | ||||||||
\(193\) | −24.3205 | −1.75063 | −0.875314 | − | 0.483555i | \(-0.839345\pi\) | ||||
−0.875314 | + | 0.483555i | \(0.839345\pi\) | |||||||
\(194\) | −7.46410 | −0.535891 | ||||||||
\(195\) | −12.9282 | −0.925808 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | −21.0000 | −1.49619 | −0.748094 | − | 0.663593i | \(-0.769031\pi\) | ||||
−0.748094 | + | 0.663593i | \(0.769031\pi\) | |||||||
\(198\) | 7.73205 | 0.549493 | ||||||||
\(199\) | 21.7321 | 1.54054 | 0.770272 | − | 0.637715i | \(-0.220120\pi\) | ||||
0.770272 | + | 0.637715i | \(0.220120\pi\) | |||||||
\(200\) | −2.00000 | −0.141421 | ||||||||
\(201\) | −35.8564 | −2.52912 | ||||||||
\(202\) | −2.53590 | −0.178425 | ||||||||
\(203\) | −5.07180 | −0.355970 | ||||||||
\(204\) | −4.73205 | −0.331310 | ||||||||
\(205\) | 11.1962 | 0.781973 | ||||||||
\(206\) | 9.73205 | 0.678064 | ||||||||
\(207\) | −4.46410 | −0.310277 | ||||||||
\(208\) | −2.73205 | −0.189434 | ||||||||
\(209\) | 5.66025 | 0.391528 | ||||||||
\(210\) | 9.46410 | 0.653085 | ||||||||
\(211\) | −26.0526 | −1.79353 | −0.896766 | − | 0.442505i | \(-0.854090\pi\) | ||||
−0.896766 | + | 0.442505i | \(0.854090\pi\) | |||||||
\(212\) | 3.46410 | 0.237915 | ||||||||
\(213\) | 29.3205 | 2.00901 | ||||||||
\(214\) | 4.26795 | 0.291751 | ||||||||
\(215\) | 2.07180 | 0.141295 | ||||||||
\(216\) | 4.00000 | 0.272166 | ||||||||
\(217\) | 16.0000 | 1.08615 | ||||||||
\(218\) | −9.19615 | −0.622842 | ||||||||
\(219\) | −16.9282 | −1.14390 | ||||||||
\(220\) | 3.00000 | 0.202260 | ||||||||
\(221\) | 4.73205 | 0.318312 | ||||||||
\(222\) | −20.3923 | −1.36864 | ||||||||
\(223\) | 26.0000 | 1.74109 | 0.870544 | − | 0.492090i | \(-0.163767\pi\) | ||||
0.870544 | + | 0.492090i | \(0.163767\pi\) | |||||||
\(224\) | 2.00000 | 0.133631 | ||||||||
\(225\) | −8.92820 | −0.595214 | ||||||||
\(226\) | −8.19615 | −0.545200 | ||||||||
\(227\) | −6.00000 | −0.398234 | −0.199117 | − | 0.979976i | \(-0.563807\pi\) | ||||
−0.199117 | + | 0.979976i | \(0.563807\pi\) | |||||||
\(228\) | 8.92820 | 0.591285 | ||||||||
\(229\) | −12.7846 | −0.844831 | −0.422415 | − | 0.906402i | \(-0.638818\pi\) | ||||
−0.422415 | + | 0.906402i | \(0.638818\pi\) | |||||||
\(230\) | −1.73205 | −0.114208 | ||||||||
\(231\) | 9.46410 | 0.622692 | ||||||||
\(232\) | −2.53590 | −0.166490 | ||||||||
\(233\) | −7.39230 | −0.484286 | −0.242143 | − | 0.970241i | \(-0.577850\pi\) | ||||
−0.242143 | + | 0.970241i | \(0.577850\pi\) | |||||||
\(234\) | −12.1962 | −0.797287 | ||||||||
\(235\) | −9.80385 | −0.639532 | ||||||||
\(236\) | 10.7321 | 0.698597 | ||||||||
\(237\) | −36.7846 | −2.38942 | ||||||||
\(238\) | −3.46410 | −0.224544 | ||||||||
\(239\) | 10.3923 | 0.672222 | 0.336111 | − | 0.941822i | \(-0.390888\pi\) | ||||
0.336111 | + | 0.941822i | \(0.390888\pi\) | |||||||
\(240\) | 4.73205 | 0.305453 | ||||||||
\(241\) | −5.73205 | −0.369234 | −0.184617 | − | 0.982811i | \(-0.559104\pi\) | ||||
−0.184617 | + | 0.982811i | \(0.559104\pi\) | |||||||
\(242\) | −8.00000 | −0.514259 | ||||||||
\(243\) | −18.7321 | −1.20166 | ||||||||
\(244\) | 7.19615 | 0.460686 | ||||||||
\(245\) | −5.19615 | −0.331970 | ||||||||
\(246\) | 17.6603 | 1.12598 | ||||||||
\(247\) | −8.92820 | −0.568088 | ||||||||
\(248\) | 8.00000 | 0.508001 | ||||||||
\(249\) | 22.3923 | 1.41905 | ||||||||
\(250\) | −12.1244 | −0.766812 | ||||||||
\(251\) | 31.5167 | 1.98931 | 0.994657 | − | 0.103235i | \(-0.0329194\pi\) | ||||
0.994657 | + | 0.103235i | \(0.0329194\pi\) | |||||||
\(252\) | 8.92820 | 0.562424 | ||||||||
\(253\) | −1.73205 | −0.108893 | ||||||||
\(254\) | 5.80385 | 0.364166 | ||||||||
\(255\) | −8.19615 | −0.513263 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.3205 | 0.706154 | 0.353077 | − | 0.935594i | \(-0.385135\pi\) | ||||
0.353077 | + | 0.935594i | \(0.385135\pi\) | |||||||
\(258\) | 3.26795 | 0.203454 | ||||||||
\(259\) | −14.9282 | −0.927593 | ||||||||
\(260\) | −4.73205 | −0.293469 | ||||||||
\(261\) | −11.3205 | −0.700722 | ||||||||
\(262\) | −1.00000 | −0.0617802 | ||||||||
\(263\) | −2.87564 | −0.177320 | −0.0886599 | − | 0.996062i | \(-0.528258\pi\) | ||||
−0.0886599 | + | 0.996062i | \(0.528258\pi\) | |||||||
\(264\) | 4.73205 | 0.291238 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | 6.53590 | 0.400742 | ||||||||
\(267\) | 6.92820 | 0.423999 | ||||||||
\(268\) | −13.1244 | −0.801698 | ||||||||
\(269\) | −20.1962 | −1.23138 | −0.615691 | − | 0.787988i | \(-0.711123\pi\) | ||||
−0.615691 | + | 0.787988i | \(0.711123\pi\) | |||||||
\(270\) | 6.92820 | 0.421637 | ||||||||
\(271\) | 26.4641 | 1.60758 | 0.803790 | − | 0.594913i | \(-0.202814\pi\) | ||||
0.803790 | + | 0.594913i | \(0.202814\pi\) | |||||||
\(272\) | −1.73205 | −0.105021 | ||||||||
\(273\) | −14.9282 | −0.903496 | ||||||||
\(274\) | −18.1244 | −1.09493 | ||||||||
\(275\) | −3.46410 | −0.208893 | ||||||||
\(276\) | −2.73205 | −0.164450 | ||||||||
\(277\) | −14.3923 | −0.864750 | −0.432375 | − | 0.901694i | \(-0.642324\pi\) | ||||
−0.432375 | + | 0.901694i | \(0.642324\pi\) | |||||||
\(278\) | 17.0000 | 1.01959 | ||||||||
\(279\) | 35.7128 | 2.13807 | ||||||||
\(280\) | 3.46410 | 0.207020 | ||||||||
\(281\) | 21.5885 | 1.28786 | 0.643930 | − | 0.765085i | \(-0.277303\pi\) | ||||
0.643930 | + | 0.765085i | \(0.277303\pi\) | |||||||
\(282\) | −15.4641 | −0.920874 | ||||||||
\(283\) | −2.39230 | −0.142208 | −0.0711039 | − | 0.997469i | \(-0.522652\pi\) | ||||
−0.0711039 | + | 0.997469i | \(0.522652\pi\) | |||||||
\(284\) | 10.7321 | 0.636830 | ||||||||
\(285\) | 15.4641 | 0.916014 | ||||||||
\(286\) | −4.73205 | −0.279812 | ||||||||
\(287\) | 12.9282 | 0.763128 | ||||||||
\(288\) | 4.46410 | 0.263050 | ||||||||
\(289\) | −14.0000 | −0.823529 | ||||||||
\(290\) | −4.39230 | −0.257925 | ||||||||
\(291\) | −20.3923 | −1.19542 | ||||||||
\(292\) | −6.19615 | −0.362602 | ||||||||
\(293\) | −0.339746 | −0.0198482 | −0.00992409 | − | 0.999951i | \(-0.503159\pi\) | ||||
−0.00992409 | + | 0.999951i | \(0.503159\pi\) | |||||||
\(294\) | −8.19615 | −0.478009 | ||||||||
\(295\) | 18.5885 | 1.08226 | ||||||||
\(296\) | −7.46410 | −0.433842 | ||||||||
\(297\) | 6.92820 | 0.402015 | ||||||||
\(298\) | 14.1962 | 0.822361 | ||||||||
\(299\) | 2.73205 | 0.157999 | ||||||||
\(300\) | −5.46410 | −0.315470 | ||||||||
\(301\) | 2.39230 | 0.137890 | ||||||||
\(302\) | 2.46410 | 0.141793 | ||||||||
\(303\) | −6.92820 | −0.398015 | ||||||||
\(304\) | 3.26795 | 0.187430 | ||||||||
\(305\) | 12.4641 | 0.713692 | ||||||||
\(306\) | −7.73205 | −0.442012 | ||||||||
\(307\) | −12.1962 | −0.696071 | −0.348036 | − | 0.937481i | \(-0.613151\pi\) | ||||
−0.348036 | + | 0.937481i | \(0.613151\pi\) | |||||||
\(308\) | 3.46410 | 0.197386 | ||||||||
\(309\) | 26.5885 | 1.51256 | ||||||||
\(310\) | 13.8564 | 0.786991 | ||||||||
\(311\) | 9.00000 | 0.510343 | 0.255172 | − | 0.966896i | \(-0.417868\pi\) | ||||
0.255172 | + | 0.966896i | \(0.417868\pi\) | |||||||
\(312\) | −7.46410 | −0.422572 | ||||||||
\(313\) | −4.92820 | −0.278559 | −0.139279 | − | 0.990253i | \(-0.544479\pi\) | ||||
−0.139279 | + | 0.990253i | \(0.544479\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 15.4641 | 0.871303 | ||||||||
\(316\) | −13.4641 | −0.757415 | ||||||||
\(317\) | −14.1962 | −0.797335 | −0.398668 | − | 0.917095i | \(-0.630527\pi\) | ||||
−0.398668 | + | 0.917095i | \(0.630527\pi\) | |||||||
\(318\) | 9.46410 | 0.530720 | ||||||||
\(319\) | −4.39230 | −0.245922 | ||||||||
\(320\) | 1.73205 | 0.0968246 | ||||||||
\(321\) | 11.6603 | 0.650812 | ||||||||
\(322\) | −2.00000 | −0.111456 | ||||||||
\(323\) | −5.66025 | −0.314945 | ||||||||
\(324\) | −2.46410 | −0.136895 | ||||||||
\(325\) | 5.46410 | 0.303094 | ||||||||
\(326\) | 14.4641 | 0.801092 | ||||||||
\(327\) | −25.1244 | −1.38938 | ||||||||
\(328\) | 6.46410 | 0.356920 | ||||||||
\(329\) | −11.3205 | −0.624120 | ||||||||
\(330\) | 8.19615 | 0.451183 | ||||||||
\(331\) | 6.39230 | 0.351353 | 0.175676 | − | 0.984448i | \(-0.443789\pi\) | ||||
0.175676 | + | 0.984448i | \(0.443789\pi\) | |||||||
\(332\) | 8.19615 | 0.449822 | ||||||||
\(333\) | −33.3205 | −1.82595 | ||||||||
\(334\) | −16.8564 | −0.922342 | ||||||||
\(335\) | −22.7321 | −1.24198 | ||||||||
\(336\) | 5.46410 | 0.298091 | ||||||||
\(337\) | −0.196152 | −0.0106851 | −0.00534255 | − | 0.999986i | \(-0.501701\pi\) | ||||
−0.00534255 | + | 0.999986i | \(0.501701\pi\) | |||||||
\(338\) | −5.53590 | −0.301113 | ||||||||
\(339\) | −22.3923 | −1.21618 | ||||||||
\(340\) | −3.00000 | −0.162698 | ||||||||
\(341\) | 13.8564 | 0.750366 | ||||||||
\(342\) | 14.5885 | 0.788853 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 1.19615 | 0.0644922 | ||||||||
\(345\) | −4.73205 | −0.254765 | ||||||||
\(346\) | −19.3923 | −1.04254 | ||||||||
\(347\) | −10.8564 | −0.582802 | −0.291401 | − | 0.956601i | \(-0.594121\pi\) | ||||
−0.291401 | + | 0.956601i | \(0.594121\pi\) | |||||||
\(348\) | −6.92820 | −0.371391 | ||||||||
\(349\) | 33.8564 | 1.81229 | 0.906146 | − | 0.422965i | \(-0.139011\pi\) | ||||
0.906146 | + | 0.422965i | \(0.139011\pi\) | |||||||
\(350\) | −4.00000 | −0.213809 | ||||||||
\(351\) | −10.9282 | −0.583304 | ||||||||
\(352\) | 1.73205 | 0.0923186 | ||||||||
\(353\) | 26.3205 | 1.40090 | 0.700450 | − | 0.713702i | \(-0.252983\pi\) | ||||
0.700450 | + | 0.713702i | \(0.252983\pi\) | |||||||
\(354\) | 29.3205 | 1.55837 | ||||||||
\(355\) | 18.5885 | 0.986573 | ||||||||
\(356\) | 2.53590 | 0.134402 | ||||||||
\(357\) | −9.46410 | −0.500893 | ||||||||
\(358\) | −6.92820 | −0.366167 | ||||||||
\(359\) | 27.5885 | 1.45606 | 0.728032 | − | 0.685544i | \(-0.240435\pi\) | ||||
0.728032 | + | 0.685544i | \(0.240435\pi\) | |||||||
\(360\) | 7.73205 | 0.407515 | ||||||||
\(361\) | −8.32051 | −0.437921 | ||||||||
\(362\) | 17.4641 | 0.917893 | ||||||||
\(363\) | −21.8564 | −1.14716 | ||||||||
\(364\) | −5.46410 | −0.286397 | ||||||||
\(365\) | −10.7321 | −0.561741 | ||||||||
\(366\) | 19.6603 | 1.02766 | ||||||||
\(367\) | −34.5885 | −1.80550 | −0.902751 | − | 0.430163i | \(-0.858456\pi\) | ||||
−0.902751 | + | 0.430163i | \(0.858456\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 28.8564 | 1.50220 | ||||||||
\(370\) | −12.9282 | −0.672105 | ||||||||
\(371\) | 6.92820 | 0.359694 | ||||||||
\(372\) | 21.8564 | 1.13320 | ||||||||
\(373\) | 18.0526 | 0.934726 | 0.467363 | − | 0.884065i | \(-0.345204\pi\) | ||||
0.467363 | + | 0.884065i | \(0.345204\pi\) | |||||||
\(374\) | −3.00000 | −0.155126 | ||||||||
\(375\) | −33.1244 | −1.71053 | ||||||||
\(376\) | −5.66025 | −0.291905 | ||||||||
\(377\) | 6.92820 | 0.356821 | ||||||||
\(378\) | 8.00000 | 0.411476 | ||||||||
\(379\) | 8.12436 | 0.417320 | 0.208660 | − | 0.977988i | \(-0.433090\pi\) | ||||
0.208660 | + | 0.977988i | \(0.433090\pi\) | |||||||
\(380\) | 5.66025 | 0.290365 | ||||||||
\(381\) | 15.8564 | 0.812348 | ||||||||
\(382\) | −25.5167 | −1.30555 | ||||||||
\(383\) | −1.60770 | −0.0821494 | −0.0410747 | − | 0.999156i | \(-0.513078\pi\) | ||||
−0.0410747 | + | 0.999156i | \(0.513078\pi\) | |||||||
\(384\) | 2.73205 | 0.139419 | ||||||||
\(385\) | 6.00000 | 0.305788 | ||||||||
\(386\) | −24.3205 | −1.23788 | ||||||||
\(387\) | 5.33975 | 0.271435 | ||||||||
\(388\) | −7.46410 | −0.378932 | ||||||||
\(389\) | −13.2679 | −0.672712 | −0.336356 | − | 0.941735i | \(-0.609194\pi\) | ||||
−0.336356 | + | 0.941735i | \(0.609194\pi\) | |||||||
\(390\) | −12.9282 | −0.654645 | ||||||||
\(391\) | 1.73205 | 0.0875936 | ||||||||
\(392\) | −3.00000 | −0.151523 | ||||||||
\(393\) | −2.73205 | −0.137814 | ||||||||
\(394\) | −21.0000 | −1.05796 | ||||||||
\(395\) | −23.3205 | −1.17338 | ||||||||
\(396\) | 7.73205 | 0.388550 | ||||||||
\(397\) | 10.1962 | 0.511730 | 0.255865 | − | 0.966712i | \(-0.417640\pi\) | ||||
0.255865 | + | 0.966712i | \(0.417640\pi\) | |||||||
\(398\) | 21.7321 | 1.08933 | ||||||||
\(399\) | 17.8564 | 0.893938 | ||||||||
\(400\) | −2.00000 | −0.100000 | ||||||||
\(401\) | −39.7128 | −1.98316 | −0.991582 | − | 0.129483i | \(-0.958668\pi\) | ||||
−0.991582 | + | 0.129483i | \(0.958668\pi\) | |||||||
\(402\) | −35.8564 | −1.78836 | ||||||||
\(403\) | −21.8564 | −1.08875 | ||||||||
\(404\) | −2.53590 | −0.126166 | ||||||||
\(405\) | −4.26795 | −0.212076 | ||||||||
\(406\) | −5.07180 | −0.251709 | ||||||||
\(407\) | −12.9282 | −0.640827 | ||||||||
\(408\) | −4.73205 | −0.234271 | ||||||||
\(409\) | −13.2487 | −0.655107 | −0.327553 | − | 0.944833i | \(-0.606224\pi\) | ||||
−0.327553 | + | 0.944833i | \(0.606224\pi\) | |||||||
\(410\) | 11.1962 | 0.552939 | ||||||||
\(411\) | −49.5167 | −2.44248 | ||||||||
\(412\) | 9.73205 | 0.479464 | ||||||||
\(413\) | 21.4641 | 1.05618 | ||||||||
\(414\) | −4.46410 | −0.219399 | ||||||||
\(415\) | 14.1962 | 0.696862 | ||||||||
\(416\) | −2.73205 | −0.133950 | ||||||||
\(417\) | 46.4449 | 2.27441 | ||||||||
\(418\) | 5.66025 | 0.276852 | ||||||||
\(419\) | 5.66025 | 0.276522 | 0.138261 | − | 0.990396i | \(-0.455849\pi\) | ||||
0.138261 | + | 0.990396i | \(0.455849\pi\) | |||||||
\(420\) | 9.46410 | 0.461801 | ||||||||
\(421\) | −2.14359 | −0.104472 | −0.0522362 | − | 0.998635i | \(-0.516635\pi\) | ||||
−0.0522362 | + | 0.998635i | \(0.516635\pi\) | |||||||
\(422\) | −26.0526 | −1.26822 | ||||||||
\(423\) | −25.2679 | −1.22857 | ||||||||
\(424\) | 3.46410 | 0.168232 | ||||||||
\(425\) | 3.46410 | 0.168034 | ||||||||
\(426\) | 29.3205 | 1.42058 | ||||||||
\(427\) | 14.3923 | 0.696492 | ||||||||
\(428\) | 4.26795 | 0.206299 | ||||||||
\(429\) | −12.9282 | −0.624180 | ||||||||
\(430\) | 2.07180 | 0.0999109 | ||||||||
\(431\) | −28.9808 | −1.39595 | −0.697977 | − | 0.716120i | \(-0.745916\pi\) | ||||
−0.697977 | + | 0.716120i | \(0.745916\pi\) | |||||||
\(432\) | 4.00000 | 0.192450 | ||||||||
\(433\) | −25.5885 | −1.22970 | −0.614851 | − | 0.788643i | \(-0.710784\pi\) | ||||
−0.614851 | + | 0.788643i | \(0.710784\pi\) | |||||||
\(434\) | 16.0000 | 0.768025 | ||||||||
\(435\) | −12.0000 | −0.575356 | ||||||||
\(436\) | −9.19615 | −0.440416 | ||||||||
\(437\) | −3.26795 | −0.156327 | ||||||||
\(438\) | −16.9282 | −0.808861 | ||||||||
\(439\) | 31.7846 | 1.51700 | 0.758498 | − | 0.651675i | \(-0.225933\pi\) | ||||
0.758498 | + | 0.651675i | \(0.225933\pi\) | |||||||
\(440\) | 3.00000 | 0.143019 | ||||||||
\(441\) | −13.3923 | −0.637729 | ||||||||
\(442\) | 4.73205 | 0.225081 | ||||||||
\(443\) | 20.5359 | 0.975690 | 0.487845 | − | 0.872930i | \(-0.337783\pi\) | ||||
0.487845 | + | 0.872930i | \(0.337783\pi\) | |||||||
\(444\) | −20.3923 | −0.967776 | ||||||||
\(445\) | 4.39230 | 0.208215 | ||||||||
\(446\) | 26.0000 | 1.23114 | ||||||||
\(447\) | 38.7846 | 1.83445 | ||||||||
\(448\) | 2.00000 | 0.0944911 | ||||||||
\(449\) | −8.53590 | −0.402834 | −0.201417 | − | 0.979506i | \(-0.564555\pi\) | ||||
−0.201417 | + | 0.979506i | \(0.564555\pi\) | |||||||
\(450\) | −8.92820 | −0.420880 | ||||||||
\(451\) | 11.1962 | 0.527206 | ||||||||
\(452\) | −8.19615 | −0.385515 | ||||||||
\(453\) | 6.73205 | 0.316299 | ||||||||
\(454\) | −6.00000 | −0.281594 | ||||||||
\(455\) | −9.46410 | −0.443684 | ||||||||
\(456\) | 8.92820 | 0.418101 | ||||||||
\(457\) | 28.7846 | 1.34649 | 0.673244 | − | 0.739421i | \(-0.264901\pi\) | ||||
0.673244 | + | 0.739421i | \(0.264901\pi\) | |||||||
\(458\) | −12.7846 | −0.597386 | ||||||||
\(459\) | −6.92820 | −0.323381 | ||||||||
\(460\) | −1.73205 | −0.0807573 | ||||||||
\(461\) | 12.4641 | 0.580511 | 0.290256 | − | 0.956949i | \(-0.406260\pi\) | ||||
0.290256 | + | 0.956949i | \(0.406260\pi\) | |||||||
\(462\) | 9.46410 | 0.440310 | ||||||||
\(463\) | −27.3205 | −1.26969 | −0.634846 | − | 0.772639i | \(-0.718936\pi\) | ||||
−0.634846 | + | 0.772639i | \(0.718936\pi\) | |||||||
\(464\) | −2.53590 | −0.117726 | ||||||||
\(465\) | 37.8564 | 1.75555 | ||||||||
\(466\) | −7.39230 | −0.342442 | ||||||||
\(467\) | 36.1244 | 1.67164 | 0.835818 | − | 0.549007i | \(-0.184994\pi\) | ||||
0.835818 | + | 0.549007i | \(0.184994\pi\) | |||||||
\(468\) | −12.1962 | −0.563767 | ||||||||
\(469\) | −26.2487 | −1.21205 | ||||||||
\(470\) | −9.80385 | −0.452218 | ||||||||
\(471\) | 38.2487 | 1.76241 | ||||||||
\(472\) | 10.7321 | 0.493983 | ||||||||
\(473\) | 2.07180 | 0.0952613 | ||||||||
\(474\) | −36.7846 | −1.68957 | ||||||||
\(475\) | −6.53590 | −0.299888 | ||||||||
\(476\) | −3.46410 | −0.158777 | ||||||||
\(477\) | 15.4641 | 0.708053 | ||||||||
\(478\) | 10.3923 | 0.475333 | ||||||||
\(479\) | 22.5167 | 1.02881 | 0.514406 | − | 0.857547i | \(-0.328012\pi\) | ||||
0.514406 | + | 0.857547i | \(0.328012\pi\) | |||||||
\(480\) | 4.73205 | 0.215988 | ||||||||
\(481\) | 20.3923 | 0.929809 | ||||||||
\(482\) | −5.73205 | −0.261088 | ||||||||
\(483\) | −5.46410 | −0.248625 | ||||||||
\(484\) | −8.00000 | −0.363636 | ||||||||
\(485\) | −12.9282 | −0.587039 | ||||||||
\(486\) | −18.7321 | −0.849703 | ||||||||
\(487\) | −3.78461 | −0.171497 | −0.0857485 | − | 0.996317i | \(-0.527328\pi\) | ||||
−0.0857485 | + | 0.996317i | \(0.527328\pi\) | |||||||
\(488\) | 7.19615 | 0.325755 | ||||||||
\(489\) | 39.5167 | 1.78701 | ||||||||
\(490\) | −5.19615 | −0.234738 | ||||||||
\(491\) | 21.0000 | 0.947717 | 0.473858 | − | 0.880601i | \(-0.342861\pi\) | ||||
0.473858 | + | 0.880601i | \(0.342861\pi\) | |||||||
\(492\) | 17.6603 | 0.796186 | ||||||||
\(493\) | 4.39230 | 0.197819 | ||||||||
\(494\) | −8.92820 | −0.401699 | ||||||||
\(495\) | 13.3923 | 0.601939 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 21.4641 | 0.962797 | ||||||||
\(498\) | 22.3923 | 1.00342 | ||||||||
\(499\) | 36.1769 | 1.61950 | 0.809751 | − | 0.586774i | \(-0.199602\pi\) | ||||
0.809751 | + | 0.586774i | \(0.199602\pi\) | |||||||
\(500\) | −12.1244 | −0.542218 | ||||||||
\(501\) | −46.0526 | −2.05748 | ||||||||
\(502\) | 31.5167 | 1.40666 | ||||||||
\(503\) | 24.1244 | 1.07565 | 0.537826 | − | 0.843056i | \(-0.319246\pi\) | ||||
0.537826 | + | 0.843056i | \(0.319246\pi\) | |||||||
\(504\) | 8.92820 | 0.397694 | ||||||||
\(505\) | −4.39230 | −0.195455 | ||||||||
\(506\) | −1.73205 | −0.0769991 | ||||||||
\(507\) | −15.1244 | −0.671696 | ||||||||
\(508\) | 5.80385 | 0.257504 | ||||||||
\(509\) | −15.9282 | −0.706005 | −0.353003 | − | 0.935622i | \(-0.614839\pi\) | ||||
−0.353003 | + | 0.935622i | \(0.614839\pi\) | |||||||
\(510\) | −8.19615 | −0.362932 | ||||||||
\(511\) | −12.3923 | −0.548203 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 13.0718 | 0.577134 | ||||||||
\(514\) | 11.3205 | 0.499326 | ||||||||
\(515\) | 16.8564 | 0.742782 | ||||||||
\(516\) | 3.26795 | 0.143863 | ||||||||
\(517\) | −9.80385 | −0.431173 | ||||||||
\(518\) | −14.9282 | −0.655908 | ||||||||
\(519\) | −52.9808 | −2.32560 | ||||||||
\(520\) | −4.73205 | −0.207514 | ||||||||
\(521\) | 27.5885 | 1.20867 | 0.604336 | − | 0.796729i | \(-0.293438\pi\) | ||||
0.604336 | + | 0.796729i | \(0.293438\pi\) | |||||||
\(522\) | −11.3205 | −0.495485 | ||||||||
\(523\) | 15.2679 | 0.667621 | 0.333810 | − | 0.942640i | \(-0.391665\pi\) | ||||
0.333810 | + | 0.942640i | \(0.391665\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | −10.9282 | −0.476946 | ||||||||
\(526\) | −2.87564 | −0.125384 | ||||||||
\(527\) | −13.8564 | −0.603595 | ||||||||
\(528\) | 4.73205 | 0.205936 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 6.00000 | 0.260623 | ||||||||
\(531\) | 47.9090 | 2.07907 | ||||||||
\(532\) | 6.53590 | 0.283367 | ||||||||
\(533\) | −17.6603 | −0.764951 | ||||||||
\(534\) | 6.92820 | 0.299813 | ||||||||
\(535\) | 7.39230 | 0.319597 | ||||||||
\(536\) | −13.1244 | −0.566886 | ||||||||
\(537\) | −18.9282 | −0.816812 | ||||||||
\(538\) | −20.1962 | −0.870718 | ||||||||
\(539\) | −5.19615 | −0.223814 | ||||||||
\(540\) | 6.92820 | 0.298142 | ||||||||
\(541\) | 12.8564 | 0.552740 | 0.276370 | − | 0.961051i | \(-0.410868\pi\) | ||||
0.276370 | + | 0.961051i | \(0.410868\pi\) | |||||||
\(542\) | 26.4641 | 1.13673 | ||||||||
\(543\) | 47.7128 | 2.04755 | ||||||||
\(544\) | −1.73205 | −0.0742611 | ||||||||
\(545\) | −15.9282 | −0.682289 | ||||||||
\(546\) | −14.9282 | −0.638868 | ||||||||
\(547\) | 5.92820 | 0.253472 | 0.126736 | − | 0.991937i | \(-0.459550\pi\) | ||||
0.126736 | + | 0.991937i | \(0.459550\pi\) | |||||||
\(548\) | −18.1244 | −0.774234 | ||||||||
\(549\) | 32.1244 | 1.37103 | ||||||||
\(550\) | −3.46410 | −0.147710 | ||||||||
\(551\) | −8.28719 | −0.353046 | ||||||||
\(552\) | −2.73205 | −0.116284 | ||||||||
\(553\) | −26.9282 | −1.14510 | ||||||||
\(554\) | −14.3923 | −0.611470 | ||||||||
\(555\) | −35.3205 | −1.49927 | ||||||||
\(556\) | 17.0000 | 0.720961 | ||||||||
\(557\) | −13.9808 | −0.592384 | −0.296192 | − | 0.955128i | \(-0.595717\pi\) | ||||
−0.296192 | + | 0.955128i | \(0.595717\pi\) | |||||||
\(558\) | 35.7128 | 1.51184 | ||||||||
\(559\) | −3.26795 | −0.138220 | ||||||||
\(560\) | 3.46410 | 0.146385 | ||||||||
\(561\) | −8.19615 | −0.346042 | ||||||||
\(562\) | 21.5885 | 0.910654 | ||||||||
\(563\) | −3.46410 | −0.145994 | −0.0729972 | − | 0.997332i | \(-0.523256\pi\) | ||||
−0.0729972 | + | 0.997332i | \(0.523256\pi\) | |||||||
\(564\) | −15.4641 | −0.651156 | ||||||||
\(565\) | −14.1962 | −0.597237 | ||||||||
\(566\) | −2.39230 | −0.100556 | ||||||||
\(567\) | −4.92820 | −0.206965 | ||||||||
\(568\) | 10.7321 | 0.450307 | ||||||||
\(569\) | −11.3205 | −0.474580 | −0.237290 | − | 0.971439i | \(-0.576259\pi\) | ||||
−0.237290 | + | 0.971439i | \(0.576259\pi\) | |||||||
\(570\) | 15.4641 | 0.647720 | ||||||||
\(571\) | −11.6077 | −0.485767 | −0.242883 | − | 0.970055i | \(-0.578093\pi\) | ||||
−0.242883 | + | 0.970055i | \(0.578093\pi\) | |||||||
\(572\) | −4.73205 | −0.197857 | ||||||||
\(573\) | −69.7128 | −2.91229 | ||||||||
\(574\) | 12.9282 | 0.539613 | ||||||||
\(575\) | 2.00000 | 0.0834058 | ||||||||
\(576\) | 4.46410 | 0.186004 | ||||||||
\(577\) | −15.7846 | −0.657122 | −0.328561 | − | 0.944483i | \(-0.606564\pi\) | ||||
−0.328561 | + | 0.944483i | \(0.606564\pi\) | |||||||
\(578\) | −14.0000 | −0.582323 | ||||||||
\(579\) | −66.4449 | −2.76135 | ||||||||
\(580\) | −4.39230 | −0.182381 | ||||||||
\(581\) | 16.3923 | 0.680067 | ||||||||
\(582\) | −20.3923 | −0.845288 | ||||||||
\(583\) | 6.00000 | 0.248495 | ||||||||
\(584\) | −6.19615 | −0.256399 | ||||||||
\(585\) | −21.1244 | −0.873385 | ||||||||
\(586\) | −0.339746 | −0.0140348 | ||||||||
\(587\) | −28.6410 | −1.18214 | −0.591071 | − | 0.806620i | \(-0.701295\pi\) | ||||
−0.591071 | + | 0.806620i | \(0.701295\pi\) | |||||||
\(588\) | −8.19615 | −0.338004 | ||||||||
\(589\) | 26.1436 | 1.07723 | ||||||||
\(590\) | 18.5885 | 0.765275 | ||||||||
\(591\) | −57.3731 | −2.36001 | ||||||||
\(592\) | −7.46410 | −0.306773 | ||||||||
\(593\) | −22.9808 | −0.943707 | −0.471853 | − | 0.881677i | \(-0.656415\pi\) | ||||
−0.471853 | + | 0.881677i | \(0.656415\pi\) | |||||||
\(594\) | 6.92820 | 0.284268 | ||||||||
\(595\) | −6.00000 | −0.245976 | ||||||||
\(596\) | 14.1962 | 0.581497 | ||||||||
\(597\) | 59.3731 | 2.42998 | ||||||||
\(598\) | 2.73205 | 0.111722 | ||||||||
\(599\) | 25.3923 | 1.03750 | 0.518751 | − | 0.854926i | \(-0.326397\pi\) | ||||
0.518751 | + | 0.854926i | \(0.326397\pi\) | |||||||
\(600\) | −5.46410 | −0.223071 | ||||||||
\(601\) | −32.1769 | −1.31252 | −0.656262 | − | 0.754533i | \(-0.727863\pi\) | ||||
−0.656262 | + | 0.754533i | \(0.727863\pi\) | |||||||
\(602\) | 2.39230 | 0.0975031 | ||||||||
\(603\) | −58.5885 | −2.38591 | ||||||||
\(604\) | 2.46410 | 0.100263 | ||||||||
\(605\) | −13.8564 | −0.563343 | ||||||||
\(606\) | −6.92820 | −0.281439 | ||||||||
\(607\) | −28.5885 | −1.16037 | −0.580185 | − | 0.814485i | \(-0.697020\pi\) | ||||
−0.580185 | + | 0.814485i | \(0.697020\pi\) | |||||||
\(608\) | 3.26795 | 0.132533 | ||||||||
\(609\) | −13.8564 | −0.561490 | ||||||||
\(610\) | 12.4641 | 0.504657 | ||||||||
\(611\) | 15.4641 | 0.625611 | ||||||||
\(612\) | −7.73205 | −0.312550 | ||||||||
\(613\) | 27.9808 | 1.13013 | 0.565066 | − | 0.825046i | \(-0.308851\pi\) | ||||
0.565066 | + | 0.825046i | \(0.308851\pi\) | |||||||
\(614\) | −12.1962 | −0.492197 | ||||||||
\(615\) | 30.5885 | 1.23345 | ||||||||
\(616\) | 3.46410 | 0.139573 | ||||||||
\(617\) | 32.6603 | 1.31485 | 0.657426 | − | 0.753519i | \(-0.271645\pi\) | ||||
0.657426 | + | 0.753519i | \(0.271645\pi\) | |||||||
\(618\) | 26.5885 | 1.06954 | ||||||||
\(619\) | −31.3731 | −1.26099 | −0.630495 | − | 0.776193i | \(-0.717148\pi\) | ||||
−0.630495 | + | 0.776193i | \(0.717148\pi\) | |||||||
\(620\) | 13.8564 | 0.556487 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 9.00000 | 0.360867 | ||||||||
\(623\) | 5.07180 | 0.203197 | ||||||||
\(624\) | −7.46410 | −0.298803 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −4.92820 | −0.196971 | ||||||||
\(627\) | 15.4641 | 0.617577 | ||||||||
\(628\) | 14.0000 | 0.558661 | ||||||||
\(629\) | 12.9282 | 0.515481 | ||||||||
\(630\) | 15.4641 | 0.616105 | ||||||||
\(631\) | −32.6410 | −1.29942 | −0.649709 | − | 0.760183i | \(-0.725109\pi\) | ||||
−0.649709 | + | 0.760183i | \(0.725109\pi\) | |||||||
\(632\) | −13.4641 | −0.535573 | ||||||||
\(633\) | −71.1769 | −2.82903 | ||||||||
\(634\) | −14.1962 | −0.563801 | ||||||||
\(635\) | 10.0526 | 0.398924 | ||||||||
\(636\) | 9.46410 | 0.375276 | ||||||||
\(637\) | 8.19615 | 0.324743 | ||||||||
\(638\) | −4.39230 | −0.173893 | ||||||||
\(639\) | 47.9090 | 1.89525 | ||||||||
\(640\) | 1.73205 | 0.0684653 | ||||||||
\(641\) | 26.4449 | 1.04451 | 0.522255 | − | 0.852790i | \(-0.325091\pi\) | ||||
0.522255 | + | 0.852790i | \(0.325091\pi\) | |||||||
\(642\) | 11.6603 | 0.460194 | ||||||||
\(643\) | −44.3923 | −1.75066 | −0.875331 | − | 0.483525i | \(-0.839356\pi\) | ||||
−0.875331 | + | 0.483525i | \(0.839356\pi\) | |||||||
\(644\) | −2.00000 | −0.0788110 | ||||||||
\(645\) | 5.66025 | 0.222872 | ||||||||
\(646\) | −5.66025 | −0.222700 | ||||||||
\(647\) | 22.8564 | 0.898578 | 0.449289 | − | 0.893386i | \(-0.351677\pi\) | ||||
0.449289 | + | 0.893386i | \(0.351677\pi\) | |||||||
\(648\) | −2.46410 | −0.0967991 | ||||||||
\(649\) | 18.5885 | 0.729661 | ||||||||
\(650\) | 5.46410 | 0.214320 | ||||||||
\(651\) | 43.7128 | 1.71324 | ||||||||
\(652\) | 14.4641 | 0.566458 | ||||||||
\(653\) | −17.0718 | −0.668071 | −0.334036 | − | 0.942560i | \(-0.608411\pi\) | ||||
−0.334036 | + | 0.942560i | \(0.608411\pi\) | |||||||
\(654\) | −25.1244 | −0.982440 | ||||||||
\(655\) | −1.73205 | −0.0676768 | ||||||||
\(656\) | 6.46410 | 0.252381 | ||||||||
\(657\) | −27.6603 | −1.07913 | ||||||||
\(658\) | −11.3205 | −0.441319 | ||||||||
\(659\) | −14.6603 | −0.571082 | −0.285541 | − | 0.958366i | \(-0.592173\pi\) | ||||
−0.285541 | + | 0.958366i | \(0.592173\pi\) | |||||||
\(660\) | 8.19615 | 0.319035 | ||||||||
\(661\) | 40.1962 | 1.56345 | 0.781725 | − | 0.623624i | \(-0.214340\pi\) | ||||
0.781725 | + | 0.623624i | \(0.214340\pi\) | |||||||
\(662\) | 6.39230 | 0.248444 | ||||||||
\(663\) | 12.9282 | 0.502090 | ||||||||
\(664\) | 8.19615 | 0.318072 | ||||||||
\(665\) | 11.3205 | 0.438990 | ||||||||
\(666\) | −33.3205 | −1.29114 | ||||||||
\(667\) | 2.53590 | 0.0981904 | ||||||||
\(668\) | −16.8564 | −0.652194 | ||||||||
\(669\) | 71.0333 | 2.74631 | ||||||||
\(670\) | −22.7321 | −0.878216 | ||||||||
\(671\) | 12.4641 | 0.481171 | ||||||||
\(672\) | 5.46410 | 0.210782 | ||||||||
\(673\) | −33.6603 | −1.29751 | −0.648754 | − | 0.760998i | \(-0.724709\pi\) | ||||
−0.648754 | + | 0.760998i | \(0.724709\pi\) | |||||||
\(674\) | −0.196152 | −0.00755551 | ||||||||
\(675\) | −8.00000 | −0.307920 | ||||||||
\(676\) | −5.53590 | −0.212919 | ||||||||
\(677\) | 5.41154 | 0.207982 | 0.103991 | − | 0.994578i | \(-0.466839\pi\) | ||||
0.103991 | + | 0.994578i | \(0.466839\pi\) | |||||||
\(678\) | −22.3923 | −0.859971 | ||||||||
\(679\) | −14.9282 | −0.572892 | ||||||||
\(680\) | −3.00000 | −0.115045 | ||||||||
\(681\) | −16.3923 | −0.628154 | ||||||||
\(682\) | 13.8564 | 0.530589 | ||||||||
\(683\) | −39.8038 | −1.52305 | −0.761526 | − | 0.648134i | \(-0.775549\pi\) | ||||
−0.761526 | + | 0.648134i | \(0.775549\pi\) | |||||||
\(684\) | 14.5885 | 0.557804 | ||||||||
\(685\) | −31.3923 | −1.19944 | ||||||||
\(686\) | −20.0000 | −0.763604 | ||||||||
\(687\) | −34.9282 | −1.33259 | ||||||||
\(688\) | 1.19615 | 0.0456029 | ||||||||
\(689\) | −9.46410 | −0.360554 | ||||||||
\(690\) | −4.73205 | −0.180146 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | −19.3923 | −0.737185 | ||||||||
\(693\) | 15.4641 | 0.587433 | ||||||||
\(694\) | −10.8564 | −0.412104 | ||||||||
\(695\) | 29.4449 | 1.11691 | ||||||||
\(696\) | −6.92820 | −0.262613 | ||||||||
\(697\) | −11.1962 | −0.424085 | ||||||||
\(698\) | 33.8564 | 1.28148 | ||||||||
\(699\) | −20.1962 | −0.763889 | ||||||||
\(700\) | −4.00000 | −0.151186 | ||||||||
\(701\) | 34.3923 | 1.29898 | 0.649490 | − | 0.760370i | \(-0.274983\pi\) | ||||
0.649490 | + | 0.760370i | \(0.274983\pi\) | |||||||
\(702\) | −10.9282 | −0.412458 | ||||||||
\(703\) | −24.3923 | −0.919973 | ||||||||
\(704\) | 1.73205 | 0.0652791 | ||||||||
\(705\) | −26.7846 | −1.00877 | ||||||||
\(706\) | 26.3205 | 0.990585 | ||||||||
\(707\) | −5.07180 | −0.190745 | ||||||||
\(708\) | 29.3205 | 1.10193 | ||||||||
\(709\) | −28.9282 | −1.08642 | −0.543211 | − | 0.839596i | \(-0.682792\pi\) | ||||
−0.543211 | + | 0.839596i | \(0.682792\pi\) | |||||||
\(710\) | 18.5885 | 0.697612 | ||||||||
\(711\) | −60.1051 | −2.25412 | ||||||||
\(712\) | 2.53590 | 0.0950368 | ||||||||
\(713\) | −8.00000 | −0.299602 | ||||||||
\(714\) | −9.46410 | −0.354185 | ||||||||
\(715\) | −8.19615 | −0.306519 | ||||||||
\(716\) | −6.92820 | −0.258919 | ||||||||
\(717\) | 28.3923 | 1.06033 | ||||||||
\(718\) | 27.5885 | 1.02959 | ||||||||
\(719\) | 9.24871 | 0.344919 | 0.172459 | − | 0.985017i | \(-0.444829\pi\) | ||||
0.172459 | + | 0.985017i | \(0.444829\pi\) | |||||||
\(720\) | 7.73205 | 0.288157 | ||||||||
\(721\) | 19.4641 | 0.724881 | ||||||||
\(722\) | −8.32051 | −0.309657 | ||||||||
\(723\) | −15.6603 | −0.582411 | ||||||||
\(724\) | 17.4641 | 0.649048 | ||||||||
\(725\) | 5.07180 | 0.188362 | ||||||||
\(726\) | −21.8564 | −0.811167 | ||||||||
\(727\) | 10.4115 | 0.386143 | 0.193071 | − | 0.981185i | \(-0.438155\pi\) | ||||
0.193071 | + | 0.981185i | \(0.438155\pi\) | |||||||
\(728\) | −5.46410 | −0.202513 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | −10.7321 | −0.397211 | ||||||||
\(731\) | −2.07180 | −0.0766282 | ||||||||
\(732\) | 19.6603 | 0.726664 | ||||||||
\(733\) | 28.7846 | 1.06318 | 0.531592 | − | 0.847001i | \(-0.321594\pi\) | ||||
0.531592 | + | 0.847001i | \(0.321594\pi\) | |||||||
\(734\) | −34.5885 | −1.27668 | ||||||||
\(735\) | −14.1962 | −0.523633 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −22.7321 | −0.837346 | ||||||||
\(738\) | 28.8564 | 1.06222 | ||||||||
\(739\) | 12.9808 | 0.477505 | 0.238753 | − | 0.971080i | \(-0.423262\pi\) | ||||
0.238753 | + | 0.971080i | \(0.423262\pi\) | |||||||
\(740\) | −12.9282 | −0.475250 | ||||||||
\(741\) | −24.3923 | −0.896074 | ||||||||
\(742\) | 6.92820 | 0.254342 | ||||||||
\(743\) | −11.1962 | −0.410747 | −0.205373 | − | 0.978684i | \(-0.565841\pi\) | ||||
−0.205373 | + | 0.978684i | \(0.565841\pi\) | |||||||
\(744\) | 21.8564 | 0.801295 | ||||||||
\(745\) | 24.5885 | 0.900851 | ||||||||
\(746\) | 18.0526 | 0.660951 | ||||||||
\(747\) | 36.5885 | 1.33870 | ||||||||
\(748\) | −3.00000 | −0.109691 | ||||||||
\(749\) | 8.53590 | 0.311895 | ||||||||
\(750\) | −33.1244 | −1.20953 | ||||||||
\(751\) | 35.5885 | 1.29864 | 0.649321 | − | 0.760515i | \(-0.275053\pi\) | ||||
0.649321 | + | 0.760515i | \(0.275053\pi\) | |||||||
\(752\) | −5.66025 | −0.206408 | ||||||||
\(753\) | 86.1051 | 3.13784 | ||||||||
\(754\) | 6.92820 | 0.252310 | ||||||||
\(755\) | 4.26795 | 0.155327 | ||||||||
\(756\) | 8.00000 | 0.290957 | ||||||||
\(757\) | 50.3731 | 1.83084 | 0.915420 | − | 0.402500i | \(-0.131859\pi\) | ||||
0.915420 | + | 0.402500i | \(0.131859\pi\) | |||||||
\(758\) | 8.12436 | 0.295090 | ||||||||
\(759\) | −4.73205 | −0.171763 | ||||||||
\(760\) | 5.66025 | 0.205319 | ||||||||
\(761\) | −18.6795 | −0.677131 | −0.338566 | − | 0.940943i | \(-0.609942\pi\) | ||||
−0.338566 | + | 0.940943i | \(0.609942\pi\) | |||||||
\(762\) | 15.8564 | 0.574417 | ||||||||
\(763\) | −18.3923 | −0.665846 | ||||||||
\(764\) | −25.5167 | −0.923160 | ||||||||
\(765\) | −13.3923 | −0.484200 | ||||||||
\(766\) | −1.60770 | −0.0580884 | ||||||||
\(767\) | −29.3205 | −1.05870 | ||||||||
\(768\) | 2.73205 | 0.0985844 | ||||||||
\(769\) | 21.1769 | 0.763659 | 0.381830 | − | 0.924233i | \(-0.375294\pi\) | ||||
0.381830 | + | 0.924233i | \(0.375294\pi\) | |||||||
\(770\) | 6.00000 | 0.216225 | ||||||||
\(771\) | 30.9282 | 1.11385 | ||||||||
\(772\) | −24.3205 | −0.875314 | ||||||||
\(773\) | −36.9282 | −1.32822 | −0.664108 | − | 0.747637i | \(-0.731188\pi\) | ||||
−0.664108 | + | 0.747637i | \(0.731188\pi\) | |||||||
\(774\) | 5.33975 | 0.191933 | ||||||||
\(775\) | −16.0000 | −0.574737 | ||||||||
\(776\) | −7.46410 | −0.267946 | ||||||||
\(777\) | −40.7846 | −1.46314 | ||||||||
\(778\) | −13.2679 | −0.475679 | ||||||||
\(779\) | 21.1244 | 0.756859 | ||||||||
\(780\) | −12.9282 | −0.462904 | ||||||||
\(781\) | 18.5885 | 0.665147 | ||||||||
\(782\) | 1.73205 | 0.0619380 | ||||||||
\(783\) | −10.1436 | −0.362502 | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | 24.2487 | 0.865474 | ||||||||
\(786\) | −2.73205 | −0.0974490 | ||||||||
\(787\) | 55.1962 | 1.96753 | 0.983765 | − | 0.179461i | \(-0.0574352\pi\) | ||||
0.983765 | + | 0.179461i | \(0.0574352\pi\) | |||||||
\(788\) | −21.0000 | −0.748094 | ||||||||
\(789\) | −7.85641 | −0.279695 | ||||||||
\(790\) | −23.3205 | −0.829706 | ||||||||
\(791\) | −16.3923 | −0.582843 | ||||||||
\(792\) | 7.73205 | 0.274746 | ||||||||
\(793\) | −19.6603 | −0.698156 | ||||||||
\(794\) | 10.1962 | 0.361848 | ||||||||
\(795\) | 16.3923 | 0.581375 | ||||||||
\(796\) | 21.7321 | 0.770272 | ||||||||
\(797\) | −47.1962 | −1.67177 | −0.835887 | − | 0.548902i | \(-0.815046\pi\) | ||||
−0.835887 | + | 0.548902i | \(0.815046\pi\) | |||||||
\(798\) | 17.8564 | 0.632110 | ||||||||
\(799\) | 9.80385 | 0.346835 | ||||||||
\(800\) | −2.00000 | −0.0707107 | ||||||||
\(801\) | 11.3205 | 0.399990 | ||||||||
\(802\) | −39.7128 | −1.40231 | ||||||||
\(803\) | −10.7321 | −0.378726 | ||||||||
\(804\) | −35.8564 | −1.26456 | ||||||||
\(805\) | −3.46410 | −0.122094 | ||||||||
\(806\) | −21.8564 | −0.769859 | ||||||||
\(807\) | −55.1769 | −1.94232 | ||||||||
\(808\) | −2.53590 | −0.0892126 | ||||||||
\(809\) | −21.8038 | −0.766582 | −0.383291 | − | 0.923628i | \(-0.625209\pi\) | ||||
−0.383291 | + | 0.923628i | \(0.625209\pi\) | |||||||
\(810\) | −4.26795 | −0.149960 | ||||||||
\(811\) | 22.7846 | 0.800076 | 0.400038 | − | 0.916499i | \(-0.368997\pi\) | ||||
0.400038 | + | 0.916499i | \(0.368997\pi\) | |||||||
\(812\) | −5.07180 | −0.177985 | ||||||||
\(813\) | 72.3013 | 2.53572 | ||||||||
\(814\) | −12.9282 | −0.453133 | ||||||||
\(815\) | 25.0526 | 0.877553 | ||||||||
\(816\) | −4.73205 | −0.165655 | ||||||||
\(817\) | 3.90897 | 0.136757 | ||||||||
\(818\) | −13.2487 | −0.463230 | ||||||||
\(819\) | −24.3923 | −0.852336 | ||||||||
\(820\) | 11.1962 | 0.390987 | ||||||||
\(821\) | 0.588457 | 0.0205373 | 0.0102687 | − | 0.999947i | \(-0.496731\pi\) | ||||
0.0102687 | + | 0.999947i | \(0.496731\pi\) | |||||||
\(822\) | −49.5167 | −1.72709 | ||||||||
\(823\) | −25.8038 | −0.899466 | −0.449733 | − | 0.893163i | \(-0.648481\pi\) | ||||
−0.449733 | + | 0.893163i | \(0.648481\pi\) | |||||||
\(824\) | 9.73205 | 0.339032 | ||||||||
\(825\) | −9.46410 | −0.329498 | ||||||||
\(826\) | 21.4641 | 0.746832 | ||||||||
\(827\) | 20.7846 | 0.722752 | 0.361376 | − | 0.932420i | \(-0.382307\pi\) | ||||
0.361376 | + | 0.932420i | \(0.382307\pi\) | |||||||
\(828\) | −4.46410 | −0.155138 | ||||||||
\(829\) | −26.0526 | −0.904843 | −0.452421 | − | 0.891804i | \(-0.649440\pi\) | ||||
−0.452421 | + | 0.891804i | \(0.649440\pi\) | |||||||
\(830\) | 14.1962 | 0.492756 | ||||||||
\(831\) | −39.3205 | −1.36401 | ||||||||
\(832\) | −2.73205 | −0.0947168 | ||||||||
\(833\) | 5.19615 | 0.180036 | ||||||||
\(834\) | 46.4449 | 1.60825 | ||||||||
\(835\) | −29.1962 | −1.01037 | ||||||||
\(836\) | 5.66025 | 0.195764 | ||||||||
\(837\) | 32.0000 | 1.10608 | ||||||||
\(838\) | 5.66025 | 0.195530 | ||||||||
\(839\) | 31.8564 | 1.09981 | 0.549903 | − | 0.835229i | \(-0.314665\pi\) | ||||
0.549903 | + | 0.835229i | \(0.314665\pi\) | |||||||
\(840\) | 9.46410 | 0.326543 | ||||||||
\(841\) | −22.5692 | −0.778249 | ||||||||
\(842\) | −2.14359 | −0.0738731 | ||||||||
\(843\) | 58.9808 | 2.03141 | ||||||||
\(844\) | −26.0526 | −0.896766 | ||||||||
\(845\) | −9.58846 | −0.329853 | ||||||||
\(846\) | −25.2679 | −0.868730 | ||||||||
\(847\) | −16.0000 | −0.549767 | ||||||||
\(848\) | 3.46410 | 0.118958 | ||||||||
\(849\) | −6.53590 | −0.224311 | ||||||||
\(850\) | 3.46410 | 0.118818 | ||||||||
\(851\) | 7.46410 | 0.255866 | ||||||||
\(852\) | 29.3205 | 1.00450 | ||||||||
\(853\) | −6.53590 | −0.223785 | −0.111892 | − | 0.993720i | \(-0.535691\pi\) | ||||
−0.111892 | + | 0.993720i | \(0.535691\pi\) | |||||||
\(854\) | 14.3923 | 0.492495 | ||||||||
\(855\) | 25.2679 | 0.864146 | ||||||||
\(856\) | 4.26795 | 0.145876 | ||||||||
\(857\) | 44.1051 | 1.50660 | 0.753301 | − | 0.657676i | \(-0.228460\pi\) | ||||
0.753301 | + | 0.657676i | \(0.228460\pi\) | |||||||
\(858\) | −12.9282 | −0.441362 | ||||||||
\(859\) | −40.0000 | −1.36478 | −0.682391 | − | 0.730987i | \(-0.739060\pi\) | ||||
−0.682391 | + | 0.730987i | \(0.739060\pi\) | |||||||
\(860\) | 2.07180 | 0.0706477 | ||||||||
\(861\) | 35.3205 | 1.20372 | ||||||||
\(862\) | −28.9808 | −0.987089 | ||||||||
\(863\) | 36.9282 | 1.25705 | 0.628525 | − | 0.777789i | \(-0.283659\pi\) | ||||
0.628525 | + | 0.777789i | \(0.283659\pi\) | |||||||
\(864\) | 4.00000 | 0.136083 | ||||||||
\(865\) | −33.5885 | −1.14204 | ||||||||
\(866\) | −25.5885 | −0.869531 | ||||||||
\(867\) | −38.2487 | −1.29899 | ||||||||
\(868\) | 16.0000 | 0.543075 | ||||||||
\(869\) | −23.3205 | −0.791094 | ||||||||
\(870\) | −12.0000 | −0.406838 | ||||||||
\(871\) | 35.8564 | 1.21495 | ||||||||
\(872\) | −9.19615 | −0.311421 | ||||||||
\(873\) | −33.3205 | −1.12773 | ||||||||
\(874\) | −3.26795 | −0.110540 | ||||||||
\(875\) | −24.2487 | −0.819756 | ||||||||
\(876\) | −16.9282 | −0.571951 | ||||||||
\(877\) | −34.2487 | −1.15650 | −0.578248 | − | 0.815861i | \(-0.696264\pi\) | ||||
−0.578248 | + | 0.815861i | \(0.696264\pi\) | |||||||
\(878\) | 31.7846 | 1.07268 | ||||||||
\(879\) | −0.928203 | −0.0313075 | ||||||||
\(880\) | 3.00000 | 0.101130 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | −13.3923 | −0.450942 | ||||||||
\(883\) | 30.8564 | 1.03840 | 0.519200 | − | 0.854653i | \(-0.326230\pi\) | ||||
0.519200 | + | 0.854653i | \(0.326230\pi\) | |||||||
\(884\) | 4.73205 | 0.159156 | ||||||||
\(885\) | 50.7846 | 1.70711 | ||||||||
\(886\) | 20.5359 | 0.689917 | ||||||||
\(887\) | −46.1769 | −1.55047 | −0.775235 | − | 0.631674i | \(-0.782368\pi\) | ||||
−0.775235 | + | 0.631674i | \(0.782368\pi\) | |||||||
\(888\) | −20.3923 | −0.684321 | ||||||||
\(889\) | 11.6077 | 0.389310 | ||||||||
\(890\) | 4.39230 | 0.147230 | ||||||||
\(891\) | −4.26795 | −0.142982 | ||||||||
\(892\) | 26.0000 | 0.870544 | ||||||||
\(893\) | −18.4974 | −0.618993 | ||||||||
\(894\) | 38.7846 | 1.29715 | ||||||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | 2.00000 | 0.0668153 | ||||||||
\(897\) | 7.46410 | 0.249219 | ||||||||
\(898\) | −8.53590 | −0.284847 | ||||||||
\(899\) | −20.2872 | −0.676616 | ||||||||
\(900\) | −8.92820 | −0.297607 | ||||||||
\(901\) | −6.00000 | −0.199889 | ||||||||
\(902\) | 11.1962 | 0.372791 | ||||||||
\(903\) | 6.53590 | 0.217501 | ||||||||
\(904\) | −8.19615 | −0.272600 | ||||||||
\(905\) | 30.2487 | 1.00550 | ||||||||
\(906\) | 6.73205 | 0.223657 | ||||||||
\(907\) | 16.9090 | 0.561453 | 0.280726 | − | 0.959788i | \(-0.409425\pi\) | ||||
0.280726 | + | 0.959788i | \(0.409425\pi\) | |||||||
\(908\) | −6.00000 | −0.199117 | ||||||||
\(909\) | −11.3205 | −0.375478 | ||||||||
\(910\) | −9.46410 | −0.313732 | ||||||||
\(911\) | 57.9615 | 1.92035 | 0.960175 | − | 0.279398i | \(-0.0901348\pi\) | ||||
0.960175 | + | 0.279398i | \(0.0901348\pi\) | |||||||
\(912\) | 8.92820 | 0.295642 | ||||||||
\(913\) | 14.1962 | 0.469824 | ||||||||
\(914\) | 28.7846 | 0.952110 | ||||||||
\(915\) | 34.0526 | 1.12574 | ||||||||
\(916\) | −12.7846 | −0.422415 | ||||||||
\(917\) | −2.00000 | −0.0660458 | ||||||||
\(918\) | −6.92820 | −0.228665 | ||||||||
\(919\) | 39.9808 | 1.31884 | 0.659422 | − | 0.751773i | \(-0.270801\pi\) | ||||
0.659422 | + | 0.751773i | \(0.270801\pi\) | |||||||
\(920\) | −1.73205 | −0.0571040 | ||||||||
\(921\) | −33.3205 | −1.09795 | ||||||||
\(922\) | 12.4641 | 0.410483 | ||||||||
\(923\) | −29.3205 | −0.965096 | ||||||||
\(924\) | 9.46410 | 0.311346 | ||||||||
\(925\) | 14.9282 | 0.490836 | ||||||||
\(926\) | −27.3205 | −0.897808 | ||||||||
\(927\) | 43.4449 | 1.42692 | ||||||||
\(928\) | −2.53590 | −0.0832449 | ||||||||
\(929\) | −40.8564 | −1.34046 | −0.670228 | − | 0.742156i | \(-0.733804\pi\) | ||||
−0.670228 | + | 0.742156i | \(0.733804\pi\) | |||||||
\(930\) | 37.8564 | 1.24136 | ||||||||
\(931\) | −9.80385 | −0.321308 | ||||||||
\(932\) | −7.39230 | −0.242143 | ||||||||
\(933\) | 24.5885 | 0.804990 | ||||||||
\(934\) | 36.1244 | 1.18203 | ||||||||
\(935\) | −5.19615 | −0.169932 | ||||||||
\(936\) | −12.1962 | −0.398644 | ||||||||
\(937\) | −23.8564 | −0.779355 | −0.389677 | − | 0.920951i | \(-0.627413\pi\) | ||||
−0.389677 | + | 0.920951i | \(0.627413\pi\) | |||||||
\(938\) | −26.2487 | −0.857051 | ||||||||
\(939\) | −13.4641 | −0.439384 | ||||||||
\(940\) | −9.80385 | −0.319766 | ||||||||
\(941\) | −28.7321 | −0.936638 | −0.468319 | − | 0.883559i | \(-0.655140\pi\) | ||||
−0.468319 | + | 0.883559i | \(0.655140\pi\) | |||||||
\(942\) | 38.2487 | 1.24621 | ||||||||
\(943\) | −6.46410 | −0.210500 | ||||||||
\(944\) | 10.7321 | 0.349299 | ||||||||
\(945\) | 13.8564 | 0.450749 | ||||||||
\(946\) | 2.07180 | 0.0673599 | ||||||||
\(947\) | 20.7846 | 0.675409 | 0.337705 | − | 0.941252i | \(-0.390350\pi\) | ||||
0.337705 | + | 0.941252i | \(0.390350\pi\) | |||||||
\(948\) | −36.7846 | −1.19471 | ||||||||
\(949\) | 16.9282 | 0.549513 | ||||||||
\(950\) | −6.53590 | −0.212053 | ||||||||
\(951\) | −38.7846 | −1.25768 | ||||||||
\(952\) | −3.46410 | −0.112272 | ||||||||
\(953\) | 59.3205 | 1.92158 | 0.960790 | − | 0.277278i | \(-0.0894321\pi\) | ||||
0.960790 | + | 0.277278i | \(0.0894321\pi\) | |||||||
\(954\) | 15.4641 | 0.500669 | ||||||||
\(955\) | −44.1962 | −1.43015 | ||||||||
\(956\) | 10.3923 | 0.336111 | ||||||||
\(957\) | −12.0000 | −0.387905 | ||||||||
\(958\) | 22.5167 | 0.727480 | ||||||||
\(959\) | −36.2487 | −1.17053 | ||||||||
\(960\) | 4.73205 | 0.152726 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 20.3923 | 0.657474 | ||||||||
\(963\) | 19.0526 | 0.613960 | ||||||||
\(964\) | −5.73205 | −0.184617 | ||||||||
\(965\) | −42.1244 | −1.35603 | ||||||||
\(966\) | −5.46410 | −0.175805 | ||||||||
\(967\) | −20.3923 | −0.655772 | −0.327886 | − | 0.944717i | \(-0.606336\pi\) | ||||
−0.327886 | + | 0.944717i | \(0.606336\pi\) | |||||||
\(968\) | −8.00000 | −0.257130 | ||||||||
\(969\) | −15.4641 | −0.496779 | ||||||||
\(970\) | −12.9282 | −0.415100 | ||||||||
\(971\) | 7.60770 | 0.244143 | 0.122071 | − | 0.992521i | \(-0.461046\pi\) | ||||
0.122071 | + | 0.992521i | \(0.461046\pi\) | |||||||
\(972\) | −18.7321 | −0.600831 | ||||||||
\(973\) | 34.0000 | 1.08999 | ||||||||
\(974\) | −3.78461 | −0.121267 | ||||||||
\(975\) | 14.9282 | 0.478085 | ||||||||
\(976\) | 7.19615 | 0.230343 | ||||||||
\(977\) | −16.0526 | −0.513567 | −0.256783 | − | 0.966469i | \(-0.582663\pi\) | ||||
−0.256783 | + | 0.966469i | \(0.582663\pi\) | |||||||
\(978\) | 39.5167 | 1.26360 | ||||||||
\(979\) | 4.39230 | 0.140379 | ||||||||
\(980\) | −5.19615 | −0.165985 | ||||||||
\(981\) | −41.0526 | −1.31071 | ||||||||
\(982\) | 21.0000 | 0.670137 | ||||||||
\(983\) | 12.2487 | 0.390673 | 0.195337 | − | 0.980736i | \(-0.437420\pi\) | ||||
0.195337 | + | 0.980736i | \(0.437420\pi\) | |||||||
\(984\) | 17.6603 | 0.562988 | ||||||||
\(985\) | −36.3731 | −1.15894 | ||||||||
\(986\) | 4.39230 | 0.139879 | ||||||||
\(987\) | −30.9282 | −0.984456 | ||||||||
\(988\) | −8.92820 | −0.284044 | ||||||||
\(989\) | −1.19615 | −0.0380354 | ||||||||
\(990\) | 13.3923 | 0.425635 | ||||||||
\(991\) | 51.1769 | 1.62569 | 0.812844 | − | 0.582481i | \(-0.197918\pi\) | ||||
0.812844 | + | 0.582481i | \(0.197918\pi\) | |||||||
\(992\) | 8.00000 | 0.254000 | ||||||||
\(993\) | 17.4641 | 0.554207 | ||||||||
\(994\) | 21.4641 | 0.680800 | ||||||||
\(995\) | 37.6410 | 1.19330 | ||||||||
\(996\) | 22.3923 | 0.709527 | ||||||||
\(997\) | 8.58846 | 0.271999 | 0.136000 | − | 0.990709i | \(-0.456575\pi\) | ||||
0.136000 | + | 0.990709i | \(0.456575\pi\) | |||||||
\(998\) | 36.1769 | 1.14516 | ||||||||
\(999\) | −29.8564 | −0.944615 |
(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 | 6026.2.a.e.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.e.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |