Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3630,2,Mod(1,3630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3630, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3630.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3630.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: | \(28.9856959337\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3630.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −3.73205 | −1.41058 | −0.705291 | − | 0.708918i | \(-0.749184\pi\) | ||||
−0.705291 | + | 0.708918i | \(0.749184\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 2.46410 | 0.683419 | 0.341709 | − | 0.939806i | \(-0.388994\pi\) | ||||
0.341709 | + | 0.939806i | \(0.388994\pi\) | |||||||
\(14\) | −3.73205 | −0.997433 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.73205 | 0.420084 | 0.210042 | − | 0.977692i | \(-0.432640\pi\) | ||||
0.210042 | + | 0.977692i | \(0.432640\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −7.00000 | −1.60591 | −0.802955 | − | 0.596040i | \(-0.796740\pi\) | ||||
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −3.73205 | −0.814400 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.26795 | −0.681415 | −0.340707 | − | 0.940169i | \(-0.610666\pi\) | ||||
−0.340707 | + | 0.940169i | \(0.610666\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.46410 | 0.483250 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.73205 | −0.705291 | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −4.19615 | −0.753651 | −0.376826 | − | 0.926284i | \(-0.622984\pi\) | ||||
−0.376826 | + | 0.926284i | \(0.622984\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.73205 | 0.297044 | ||||||||
\(35\) | 3.73205 | 0.630832 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.19615 | 0.525444 | 0.262722 | − | 0.964872i | \(-0.415380\pi\) | ||||
0.262722 | + | 0.964872i | \(0.415380\pi\) | |||||||
\(38\) | −7.00000 | −1.13555 | ||||||||
\(39\) | 2.46410 | 0.394572 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −6.19615 | −0.967676 | −0.483838 | − | 0.875157i | \(-0.660758\pi\) | ||||
−0.483838 | + | 0.875157i | \(0.660758\pi\) | |||||||
\(42\) | −3.73205 | −0.575868 | ||||||||
\(43\) | −8.19615 | −1.24990 | −0.624951 | − | 0.780664i | \(-0.714881\pi\) | ||||
−0.624951 | + | 0.780664i | \(0.714881\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −3.26795 | −0.481833 | ||||||||
\(47\) | −8.92820 | −1.30231 | −0.651156 | − | 0.758944i | \(-0.725716\pi\) | ||||
−0.651156 | + | 0.758944i | \(0.725716\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 6.92820 | 0.989743 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 1.73205 | 0.242536 | ||||||||
\(52\) | 2.46410 | 0.341709 | ||||||||
\(53\) | −2.73205 | −0.375276 | −0.187638 | − | 0.982238i | \(-0.560083\pi\) | ||||
−0.187638 | + | 0.982238i | \(0.560083\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.73205 | −0.498716 | ||||||||
\(57\) | −7.00000 | −0.927173 | ||||||||
\(58\) | −5.00000 | −0.656532 | ||||||||
\(59\) | 5.66025 | 0.736902 | 0.368451 | − | 0.929647i | \(-0.379888\pi\) | ||||
0.368451 | + | 0.929647i | \(0.379888\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 9.12436 | 1.16825 | 0.584127 | − | 0.811662i | \(-0.301437\pi\) | ||||
0.584127 | + | 0.811662i | \(0.301437\pi\) | |||||||
\(62\) | −4.19615 | −0.532912 | ||||||||
\(63\) | −3.73205 | −0.470194 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.46410 | −0.305634 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.4641 | 1.40056 | 0.700281 | − | 0.713867i | \(-0.253058\pi\) | ||||
0.700281 | + | 0.713867i | \(0.253058\pi\) | |||||||
\(68\) | 1.73205 | 0.210042 | ||||||||
\(69\) | −3.26795 | −0.393415 | ||||||||
\(70\) | 3.73205 | 0.446065 | ||||||||
\(71\) | 4.46410 | 0.529791 | 0.264896 | − | 0.964277i | \(-0.414662\pi\) | ||||
0.264896 | + | 0.964277i | \(0.414662\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −7.66025 | −0.896565 | −0.448282 | − | 0.893892i | \(-0.647964\pi\) | ||||
−0.448282 | + | 0.893892i | \(0.647964\pi\) | |||||||
\(74\) | 3.19615 | 0.371545 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −7.00000 | −0.802955 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.46410 | 0.279005 | ||||||||
\(79\) | −10.3923 | −1.16923 | −0.584613 | − | 0.811312i | \(-0.698754\pi\) | ||||
−0.584613 | + | 0.811312i | \(0.698754\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.19615 | −0.684251 | ||||||||
\(83\) | −16.4641 | −1.80717 | −0.903585 | − | 0.428409i | \(-0.859074\pi\) | ||||
−0.903585 | + | 0.428409i | \(0.859074\pi\) | |||||||
\(84\) | −3.73205 | −0.407200 | ||||||||
\(85\) | −1.73205 | −0.187867 | ||||||||
\(86\) | −8.19615 | −0.883814 | ||||||||
\(87\) | −5.00000 | −0.536056 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.53590 | 0.268805 | 0.134402 | − | 0.990927i | \(-0.457089\pi\) | ||||
0.134402 | + | 0.990927i | \(0.457089\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | −9.19615 | −0.964019 | ||||||||
\(92\) | −3.26795 | −0.340707 | ||||||||
\(93\) | −4.19615 | −0.435121 | ||||||||
\(94\) | −8.92820 | −0.920874 | ||||||||
\(95\) | 7.00000 | 0.718185 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 5.26795 | 0.534879 | 0.267440 | − | 0.963575i | \(-0.413822\pi\) | ||||
0.267440 | + | 0.963575i | \(0.413822\pi\) | |||||||
\(98\) | 6.92820 | 0.699854 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 8.46410 | 0.842210 | 0.421105 | − | 0.907012i | \(-0.361642\pi\) | ||||
0.421105 | + | 0.907012i | \(0.361642\pi\) | |||||||
\(102\) | 1.73205 | 0.171499 | ||||||||
\(103\) | −17.3923 | −1.71371 | −0.856857 | − | 0.515554i | \(-0.827586\pi\) | ||||
−0.856857 | + | 0.515554i | \(0.827586\pi\) | |||||||
\(104\) | 2.46410 | 0.241625 | ||||||||
\(105\) | 3.73205 | 0.364211 | ||||||||
\(106\) | −2.73205 | −0.265360 | ||||||||
\(107\) | 14.3923 | 1.39136 | 0.695678 | − | 0.718353i | \(-0.255104\pi\) | ||||
0.695678 | + | 0.718353i | \(0.255104\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 12.3923 | 1.18697 | 0.593484 | − | 0.804846i | \(-0.297752\pi\) | ||||
0.593484 | + | 0.804846i | \(0.297752\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.19615 | 0.303365 | ||||||||
\(112\) | −3.73205 | −0.352646 | ||||||||
\(113\) | −13.8564 | −1.30350 | −0.651751 | − | 0.758433i | \(-0.725965\pi\) | ||||
−0.651751 | + | 0.758433i | \(0.725965\pi\) | |||||||
\(114\) | −7.00000 | −0.655610 | ||||||||
\(115\) | 3.26795 | 0.304738 | ||||||||
\(116\) | −5.00000 | −0.464238 | ||||||||
\(117\) | 2.46410 | 0.227806 | ||||||||
\(118\) | 5.66025 | 0.521069 | ||||||||
\(119\) | −6.46410 | −0.592563 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 9.12436 | 0.826080 | ||||||||
\(123\) | −6.19615 | −0.558688 | ||||||||
\(124\) | −4.19615 | −0.376826 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.73205 | −0.332478 | ||||||||
\(127\) | −13.4641 | −1.19475 | −0.597373 | − | 0.801964i | \(-0.703789\pi\) | ||||
−0.597373 | + | 0.801964i | \(0.703789\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −8.19615 | −0.721631 | ||||||||
\(130\) | −2.46410 | −0.216116 | ||||||||
\(131\) | −21.1244 | −1.84564 | −0.922822 | − | 0.385227i | \(-0.874123\pi\) | ||||
−0.922822 | + | 0.385227i | \(0.874123\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.1244 | 2.26527 | ||||||||
\(134\) | 11.4641 | 0.990348 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 1.73205 | 0.148522 | ||||||||
\(137\) | 10.4641 | 0.894009 | 0.447004 | − | 0.894532i | \(-0.352491\pi\) | ||||
0.447004 | + | 0.894532i | \(0.352491\pi\) | |||||||
\(138\) | −3.26795 | −0.278186 | ||||||||
\(139\) | −7.00000 | −0.593732 | −0.296866 | − | 0.954919i | \(-0.595942\pi\) | ||||
−0.296866 | + | 0.954919i | \(0.595942\pi\) | |||||||
\(140\) | 3.73205 | 0.315416 | ||||||||
\(141\) | −8.92820 | −0.751890 | ||||||||
\(142\) | 4.46410 | 0.374619 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.00000 | 0.415227 | ||||||||
\(146\) | −7.66025 | −0.633967 | ||||||||
\(147\) | 6.92820 | 0.571429 | ||||||||
\(148\) | 3.19615 | 0.262722 | ||||||||
\(149\) | 8.39230 | 0.687524 | 0.343762 | − | 0.939057i | \(-0.388299\pi\) | ||||
0.343762 | + | 0.939057i | \(0.388299\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −20.1962 | −1.64354 | −0.821770 | − | 0.569820i | \(-0.807013\pi\) | ||||
−0.821770 | + | 0.569820i | \(0.807013\pi\) | |||||||
\(152\) | −7.00000 | −0.567775 | ||||||||
\(153\) | 1.73205 | 0.140028 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.19615 | 0.337043 | ||||||||
\(156\) | 2.46410 | 0.197286 | ||||||||
\(157\) | −14.6603 | −1.17002 | −0.585008 | − | 0.811028i | \(-0.698909\pi\) | ||||
−0.585008 | + | 0.811028i | \(0.698909\pi\) | |||||||
\(158\) | −10.3923 | −0.826767 | ||||||||
\(159\) | −2.73205 | −0.216666 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 12.1962 | 0.961191 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 8.19615 | 0.641972 | 0.320986 | − | 0.947084i | \(-0.395986\pi\) | ||||
0.320986 | + | 0.947084i | \(0.395986\pi\) | |||||||
\(164\) | −6.19615 | −0.483838 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.4641 | −1.27786 | ||||||||
\(167\) | 6.53590 | 0.505763 | 0.252882 | − | 0.967497i | \(-0.418622\pi\) | ||||
0.252882 | + | 0.967497i | \(0.418622\pi\) | |||||||
\(168\) | −3.73205 | −0.287934 | ||||||||
\(169\) | −6.92820 | −0.532939 | ||||||||
\(170\) | −1.73205 | −0.132842 | ||||||||
\(171\) | −7.00000 | −0.535303 | ||||||||
\(172\) | −8.19615 | −0.624951 | ||||||||
\(173\) | −23.6603 | −1.79886 | −0.899428 | − | 0.437069i | \(-0.856016\pi\) | ||||
−0.899428 | + | 0.437069i | \(0.856016\pi\) | |||||||
\(174\) | −5.00000 | −0.379049 | ||||||||
\(175\) | −3.73205 | −0.282117 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.66025 | 0.425451 | ||||||||
\(178\) | 2.53590 | 0.190074 | ||||||||
\(179\) | −12.5885 | −0.940905 | −0.470453 | − | 0.882425i | \(-0.655909\pi\) | ||||
−0.470453 | + | 0.882425i | \(0.655909\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | −20.1962 | −1.50117 | −0.750584 | − | 0.660775i | \(-0.770228\pi\) | ||||
−0.750584 | + | 0.660775i | \(0.770228\pi\) | |||||||
\(182\) | −9.19615 | −0.681664 | ||||||||
\(183\) | 9.12436 | 0.674492 | ||||||||
\(184\) | −3.26795 | −0.240916 | ||||||||
\(185\) | −3.19615 | −0.234986 | ||||||||
\(186\) | −4.19615 | −0.307677 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −8.92820 | −0.651156 | ||||||||
\(189\) | −3.73205 | −0.271467 | ||||||||
\(190\) | 7.00000 | 0.507833 | ||||||||
\(191\) | 0.0717968 | 0.00519503 | 0.00259752 | − | 0.999997i | \(-0.499173\pi\) | ||||
0.00259752 | + | 0.999997i | \(0.499173\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 11.3205 | 0.814868 | 0.407434 | − | 0.913235i | \(-0.366424\pi\) | ||||
0.407434 | + | 0.913235i | \(0.366424\pi\) | |||||||
\(194\) | 5.26795 | 0.378217 | ||||||||
\(195\) | −2.46410 | −0.176458 | ||||||||
\(196\) | 6.92820 | 0.494872 | ||||||||
\(197\) | −9.46410 | −0.674289 | −0.337145 | − | 0.941453i | \(-0.609461\pi\) | ||||
−0.337145 | + | 0.941453i | \(0.609461\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.3205 | 1.36959 | 0.684797 | − | 0.728734i | \(-0.259891\pi\) | ||||
0.684797 | + | 0.728734i | \(0.259891\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 11.4641 | 0.808615 | ||||||||
\(202\) | 8.46410 | 0.595532 | ||||||||
\(203\) | 18.6603 | 1.30969 | ||||||||
\(204\) | 1.73205 | 0.121268 | ||||||||
\(205\) | 6.19615 | 0.432758 | ||||||||
\(206\) | −17.3923 | −1.21178 | ||||||||
\(207\) | −3.26795 | −0.227138 | ||||||||
\(208\) | 2.46410 | 0.170855 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.73205 | 0.257536 | ||||||||
\(211\) | −6.60770 | −0.454892 | −0.227446 | − | 0.973791i | \(-0.573038\pi\) | ||||
−0.227446 | + | 0.973791i | \(0.573038\pi\) | |||||||
\(212\) | −2.73205 | −0.187638 | ||||||||
\(213\) | 4.46410 | 0.305875 | ||||||||
\(214\) | 14.3923 | 0.983838 | ||||||||
\(215\) | 8.19615 | 0.558973 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 15.6603 | 1.06309 | ||||||||
\(218\) | 12.3923 | 0.839313 | ||||||||
\(219\) | −7.66025 | −0.517632 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.26795 | 0.287093 | ||||||||
\(222\) | 3.19615 | 0.214512 | ||||||||
\(223\) | 29.2487 | 1.95864 | 0.979319 | − | 0.202321i | \(-0.0648484\pi\) | ||||
0.979319 | + | 0.202321i | \(0.0648484\pi\) | |||||||
\(224\) | −3.73205 | −0.249358 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −13.8564 | −0.921714 | ||||||||
\(227\) | 27.4641 | 1.82286 | 0.911428 | − | 0.411459i | \(-0.134981\pi\) | ||||
0.911428 | + | 0.411459i | \(0.134981\pi\) | |||||||
\(228\) | −7.00000 | −0.463586 | ||||||||
\(229\) | −5.85641 | −0.387002 | −0.193501 | − | 0.981100i | \(-0.561984\pi\) | ||||
−0.193501 | + | 0.981100i | \(0.561984\pi\) | |||||||
\(230\) | 3.26795 | 0.215482 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.00000 | −0.328266 | ||||||||
\(233\) | 9.07180 | 0.594313 | 0.297157 | − | 0.954829i | \(-0.403962\pi\) | ||||
0.297157 | + | 0.954829i | \(0.403962\pi\) | |||||||
\(234\) | 2.46410 | 0.161083 | ||||||||
\(235\) | 8.92820 | 0.582412 | ||||||||
\(236\) | 5.66025 | 0.368451 | ||||||||
\(237\) | −10.3923 | −0.675053 | ||||||||
\(238\) | −6.46410 | −0.419005 | ||||||||
\(239\) | −3.19615 | −0.206742 | −0.103371 | − | 0.994643i | \(-0.532963\pi\) | ||||
−0.103371 | + | 0.994643i | \(0.532963\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −0.803848 | −0.0517804 | −0.0258902 | − | 0.999665i | \(-0.508242\pi\) | ||||
−0.0258902 | + | 0.999665i | \(0.508242\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 9.12436 | 0.584127 | ||||||||
\(245\) | −6.92820 | −0.442627 | ||||||||
\(246\) | −6.19615 | −0.395052 | ||||||||
\(247\) | −17.2487 | −1.09751 | ||||||||
\(248\) | −4.19615 | −0.266456 | ||||||||
\(249\) | −16.4641 | −1.04337 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 31.3205 | 1.97693 | 0.988466 | − | 0.151440i | \(-0.0483910\pi\) | ||||
0.988466 | + | 0.151440i | \(0.0483910\pi\) | |||||||
\(252\) | −3.73205 | −0.235097 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −13.4641 | −0.844813 | ||||||||
\(255\) | −1.73205 | −0.108465 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.7846 | 1.23413 | 0.617065 | − | 0.786912i | \(-0.288322\pi\) | ||||
0.617065 | + | 0.786912i | \(0.288322\pi\) | |||||||
\(258\) | −8.19615 | −0.510270 | ||||||||
\(259\) | −11.9282 | −0.741182 | ||||||||
\(260\) | −2.46410 | −0.152817 | ||||||||
\(261\) | −5.00000 | −0.309492 | ||||||||
\(262\) | −21.1244 | −1.30507 | ||||||||
\(263\) | 3.26795 | 0.201510 | 0.100755 | − | 0.994911i | \(-0.467874\pi\) | ||||
0.100755 | + | 0.994911i | \(0.467874\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.73205 | 0.167829 | ||||||||
\(266\) | 26.1244 | 1.60179 | ||||||||
\(267\) | 2.53590 | 0.155194 | ||||||||
\(268\) | 11.4641 | 0.700281 | ||||||||
\(269\) | 21.9808 | 1.34019 | 0.670095 | − | 0.742275i | \(-0.266253\pi\) | ||||
0.670095 | + | 0.742275i | \(0.266253\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −23.8564 | −1.44917 | −0.724587 | − | 0.689184i | \(-0.757969\pi\) | ||||
−0.724587 | + | 0.689184i | \(0.757969\pi\) | |||||||
\(272\) | 1.73205 | 0.105021 | ||||||||
\(273\) | −9.19615 | −0.556576 | ||||||||
\(274\) | 10.4641 | 0.632159 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.26795 | −0.196707 | ||||||||
\(277\) | 2.14359 | 0.128796 | 0.0643980 | − | 0.997924i | \(-0.479487\pi\) | ||||
0.0643980 | + | 0.997924i | \(0.479487\pi\) | |||||||
\(278\) | −7.00000 | −0.419832 | ||||||||
\(279\) | −4.19615 | −0.251217 | ||||||||
\(280\) | 3.73205 | 0.223033 | ||||||||
\(281\) | 3.12436 | 0.186383 | 0.0931917 | − | 0.995648i | \(-0.470293\pi\) | ||||
0.0931917 | + | 0.995648i | \(0.470293\pi\) | |||||||
\(282\) | −8.92820 | −0.531667 | ||||||||
\(283\) | 8.39230 | 0.498871 | 0.249435 | − | 0.968391i | \(-0.419755\pi\) | ||||
0.249435 | + | 0.968391i | \(0.419755\pi\) | |||||||
\(284\) | 4.46410 | 0.264896 | ||||||||
\(285\) | 7.00000 | 0.414644 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.1244 | 1.36499 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −14.0000 | −0.823529 | ||||||||
\(290\) | 5.00000 | 0.293610 | ||||||||
\(291\) | 5.26795 | 0.308813 | ||||||||
\(292\) | −7.66025 | −0.448282 | ||||||||
\(293\) | 14.9282 | 0.872115 | 0.436057 | − | 0.899919i | \(-0.356374\pi\) | ||||
0.436057 | + | 0.899919i | \(0.356374\pi\) | |||||||
\(294\) | 6.92820 | 0.404061 | ||||||||
\(295\) | −5.66025 | −0.329553 | ||||||||
\(296\) | 3.19615 | 0.185773 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.39230 | 0.486153 | ||||||||
\(299\) | −8.05256 | −0.465692 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 30.5885 | 1.76309 | ||||||||
\(302\) | −20.1962 | −1.16216 | ||||||||
\(303\) | 8.46410 | 0.486250 | ||||||||
\(304\) | −7.00000 | −0.401478 | ||||||||
\(305\) | −9.12436 | −0.522459 | ||||||||
\(306\) | 1.73205 | 0.0990148 | ||||||||
\(307\) | 16.5885 | 0.946753 | 0.473377 | − | 0.880860i | \(-0.343035\pi\) | ||||
0.473377 | + | 0.880860i | \(0.343035\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.3923 | −0.989414 | ||||||||
\(310\) | 4.19615 | 0.238325 | ||||||||
\(311\) | 13.0718 | 0.741234 | 0.370617 | − | 0.928786i | \(-0.379146\pi\) | ||||
0.370617 | + | 0.928786i | \(0.379146\pi\) | |||||||
\(312\) | 2.46410 | 0.139502 | ||||||||
\(313\) | 11.8038 | 0.667193 | 0.333596 | − | 0.942716i | \(-0.391738\pi\) | ||||
0.333596 | + | 0.942716i | \(0.391738\pi\) | |||||||
\(314\) | −14.6603 | −0.827326 | ||||||||
\(315\) | 3.73205 | 0.210277 | ||||||||
\(316\) | −10.3923 | −0.584613 | ||||||||
\(317\) | 8.19615 | 0.460342 | 0.230171 | − | 0.973150i | \(-0.426071\pi\) | ||||
0.230171 | + | 0.973150i | \(0.426071\pi\) | |||||||
\(318\) | −2.73205 | −0.153206 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 14.3923 | 0.803300 | ||||||||
\(322\) | 12.1962 | 0.679665 | ||||||||
\(323\) | −12.1244 | −0.674617 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 2.46410 | 0.136684 | ||||||||
\(326\) | 8.19615 | 0.453943 | ||||||||
\(327\) | 12.3923 | 0.685296 | ||||||||
\(328\) | −6.19615 | −0.342125 | ||||||||
\(329\) | 33.3205 | 1.83702 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.87564 | 0.322955 | 0.161477 | − | 0.986876i | \(-0.448374\pi\) | ||||
0.161477 | + | 0.986876i | \(0.448374\pi\) | |||||||
\(332\) | −16.4641 | −0.903585 | ||||||||
\(333\) | 3.19615 | 0.175148 | ||||||||
\(334\) | 6.53590 | 0.357628 | ||||||||
\(335\) | −11.4641 | −0.626351 | ||||||||
\(336\) | −3.73205 | −0.203600 | ||||||||
\(337\) | 30.1962 | 1.64489 | 0.822445 | − | 0.568845i | \(-0.192610\pi\) | ||||
0.822445 | + | 0.568845i | \(0.192610\pi\) | |||||||
\(338\) | −6.92820 | −0.376845 | ||||||||
\(339\) | −13.8564 | −0.752577 | ||||||||
\(340\) | −1.73205 | −0.0939336 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −7.00000 | −0.378517 | ||||||||
\(343\) | 0.267949 | 0.0144679 | ||||||||
\(344\) | −8.19615 | −0.441907 | ||||||||
\(345\) | 3.26795 | 0.175940 | ||||||||
\(346\) | −23.6603 | −1.27198 | ||||||||
\(347\) | 14.4641 | 0.776474 | 0.388237 | − | 0.921560i | \(-0.373084\pi\) | ||||
0.388237 | + | 0.921560i | \(0.373084\pi\) | |||||||
\(348\) | −5.00000 | −0.268028 | ||||||||
\(349\) | −34.0000 | −1.81998 | −0.909989 | − | 0.414632i | \(-0.863910\pi\) | ||||
−0.909989 | + | 0.414632i | \(0.863910\pi\) | |||||||
\(350\) | −3.73205 | −0.199487 | ||||||||
\(351\) | 2.46410 | 0.131524 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.85641 | 0.0988065 | 0.0494033 | − | 0.998779i | \(-0.484268\pi\) | ||||
0.0494033 | + | 0.998779i | \(0.484268\pi\) | |||||||
\(354\) | 5.66025 | 0.300839 | ||||||||
\(355\) | −4.46410 | −0.236930 | ||||||||
\(356\) | 2.53590 | 0.134402 | ||||||||
\(357\) | −6.46410 | −0.342117 | ||||||||
\(358\) | −12.5885 | −0.665321 | ||||||||
\(359\) | 31.1769 | 1.64545 | 0.822727 | − | 0.568436i | \(-0.192451\pi\) | ||||
0.822727 | + | 0.568436i | \(0.192451\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | −20.1962 | −1.06149 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.19615 | −0.482009 | ||||||||
\(365\) | 7.66025 | 0.400956 | ||||||||
\(366\) | 9.12436 | 0.476938 | ||||||||
\(367\) | −17.0000 | −0.887393 | −0.443696 | − | 0.896177i | \(-0.646333\pi\) | ||||
−0.443696 | + | 0.896177i | \(0.646333\pi\) | |||||||
\(368\) | −3.26795 | −0.170354 | ||||||||
\(369\) | −6.19615 | −0.322559 | ||||||||
\(370\) | −3.19615 | −0.166160 | ||||||||
\(371\) | 10.1962 | 0.529358 | ||||||||
\(372\) | −4.19615 | −0.217560 | ||||||||
\(373\) | −17.3923 | −0.900539 | −0.450270 | − | 0.892893i | \(-0.648672\pi\) | ||||
−0.450270 | + | 0.892893i | \(0.648672\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −8.92820 | −0.460437 | ||||||||
\(377\) | −12.3205 | −0.634538 | ||||||||
\(378\) | −3.73205 | −0.191956 | ||||||||
\(379\) | 6.12436 | 0.314587 | 0.157294 | − | 0.987552i | \(-0.449723\pi\) | ||||
0.157294 | + | 0.987552i | \(0.449723\pi\) | |||||||
\(380\) | 7.00000 | 0.359092 | ||||||||
\(381\) | −13.4641 | −0.689787 | ||||||||
\(382\) | 0.0717968 | 0.00367344 | ||||||||
\(383\) | −4.14359 | −0.211728 | −0.105864 | − | 0.994381i | \(-0.533761\pi\) | ||||
−0.105864 | + | 0.994381i | \(0.533761\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.3205 | 0.576199 | ||||||||
\(387\) | −8.19615 | −0.416634 | ||||||||
\(388\) | 5.26795 | 0.267440 | ||||||||
\(389\) | −19.7128 | −0.999479 | −0.499740 | − | 0.866176i | \(-0.666571\pi\) | ||||
−0.499740 | + | 0.866176i | \(0.666571\pi\) | |||||||
\(390\) | −2.46410 | −0.124775 | ||||||||
\(391\) | −5.66025 | −0.286251 | ||||||||
\(392\) | 6.92820 | 0.349927 | ||||||||
\(393\) | −21.1244 | −1.06558 | ||||||||
\(394\) | −9.46410 | −0.476795 | ||||||||
\(395\) | 10.3923 | 0.522894 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.9808 | 1.40431 | 0.702157 | − | 0.712022i | \(-0.252220\pi\) | ||||
0.702157 | + | 0.712022i | \(0.252220\pi\) | |||||||
\(398\) | 19.3205 | 0.968450 | ||||||||
\(399\) | 26.1244 | 1.30785 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 34.7321 | 1.73444 | 0.867218 | − | 0.497929i | \(-0.165906\pi\) | ||||
0.867218 | + | 0.497929i | \(0.165906\pi\) | |||||||
\(402\) | 11.4641 | 0.571777 | ||||||||
\(403\) | −10.3397 | −0.515059 | ||||||||
\(404\) | 8.46410 | 0.421105 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 18.6603 | 0.926093 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.73205 | 0.0857493 | ||||||||
\(409\) | −12.9282 | −0.639259 | −0.319629 | − | 0.947543i | \(-0.603558\pi\) | ||||
−0.319629 | + | 0.947543i | \(0.603558\pi\) | |||||||
\(410\) | 6.19615 | 0.306006 | ||||||||
\(411\) | 10.4641 | 0.516156 | ||||||||
\(412\) | −17.3923 | −0.856857 | ||||||||
\(413\) | −21.1244 | −1.03946 | ||||||||
\(414\) | −3.26795 | −0.160611 | ||||||||
\(415\) | 16.4641 | 0.808191 | ||||||||
\(416\) | 2.46410 | 0.120813 | ||||||||
\(417\) | −7.00000 | −0.342791 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.2487 | −0.989214 | −0.494607 | − | 0.869117i | \(-0.664688\pi\) | ||||
−0.494607 | + | 0.869117i | \(0.664688\pi\) | |||||||
\(420\) | 3.73205 | 0.182105 | ||||||||
\(421\) | −15.6603 | −0.763234 | −0.381617 | − | 0.924321i | \(-0.624633\pi\) | ||||
−0.381617 | + | 0.924321i | \(0.624633\pi\) | |||||||
\(422\) | −6.60770 | −0.321658 | ||||||||
\(423\) | −8.92820 | −0.434104 | ||||||||
\(424\) | −2.73205 | −0.132680 | ||||||||
\(425\) | 1.73205 | 0.0840168 | ||||||||
\(426\) | 4.46410 | 0.216286 | ||||||||
\(427\) | −34.0526 | −1.64792 | ||||||||
\(428\) | 14.3923 | 0.695678 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.19615 | 0.395254 | ||||||||
\(431\) | −21.4449 | −1.03296 | −0.516481 | − | 0.856298i | \(-0.672758\pi\) | ||||
−0.516481 | + | 0.856298i | \(0.672758\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 4.00000 | 0.192228 | 0.0961139 | − | 0.995370i | \(-0.469359\pi\) | ||||
0.0961139 | + | 0.995370i | \(0.469359\pi\) | |||||||
\(434\) | 15.6603 | 0.751716 | ||||||||
\(435\) | 5.00000 | 0.239732 | ||||||||
\(436\) | 12.3923 | 0.593484 | ||||||||
\(437\) | 22.8756 | 1.09429 | ||||||||
\(438\) | −7.66025 | −0.366021 | ||||||||
\(439\) | 14.0000 | 0.668184 | 0.334092 | − | 0.942541i | \(-0.391570\pi\) | ||||
0.334092 | + | 0.942541i | \(0.391570\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.92820 | 0.329914 | ||||||||
\(442\) | 4.26795 | 0.203006 | ||||||||
\(443\) | 10.8038 | 0.513306 | 0.256653 | − | 0.966504i | \(-0.417380\pi\) | ||||
0.256653 | + | 0.966504i | \(0.417380\pi\) | |||||||
\(444\) | 3.19615 | 0.151683 | ||||||||
\(445\) | −2.53590 | −0.120213 | ||||||||
\(446\) | 29.2487 | 1.38497 | ||||||||
\(447\) | 8.39230 | 0.396942 | ||||||||
\(448\) | −3.73205 | −0.176323 | ||||||||
\(449\) | 5.32051 | 0.251090 | 0.125545 | − | 0.992088i | \(-0.459932\pi\) | ||||
0.125545 | + | 0.992088i | \(0.459932\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −13.8564 | −0.651751 | ||||||||
\(453\) | −20.1962 | −0.948898 | ||||||||
\(454\) | 27.4641 | 1.28895 | ||||||||
\(455\) | 9.19615 | 0.431122 | ||||||||
\(456\) | −7.00000 | −0.327805 | ||||||||
\(457\) | 21.2679 | 0.994873 | 0.497436 | − | 0.867500i | \(-0.334275\pi\) | ||||
0.497436 | + | 0.867500i | \(0.334275\pi\) | |||||||
\(458\) | −5.85641 | −0.273652 | ||||||||
\(459\) | 1.73205 | 0.0808452 | ||||||||
\(460\) | 3.26795 | 0.152369 | ||||||||
\(461\) | −5.39230 | −0.251145 | −0.125572 | − | 0.992084i | \(-0.540077\pi\) | ||||
−0.125572 | + | 0.992084i | \(0.540077\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.2487 | −1.12693 | −0.563467 | − | 0.826139i | \(-0.690533\pi\) | ||||
−0.563467 | + | 0.826139i | \(0.690533\pi\) | |||||||
\(464\) | −5.00000 | −0.232119 | ||||||||
\(465\) | 4.19615 | 0.194592 | ||||||||
\(466\) | 9.07180 | 0.420243 | ||||||||
\(467\) | 28.8038 | 1.33288 | 0.666442 | − | 0.745557i | \(-0.267817\pi\) | ||||
0.666442 | + | 0.745557i | \(0.267817\pi\) | |||||||
\(468\) | 2.46410 | 0.113903 | ||||||||
\(469\) | −42.7846 | −1.97561 | ||||||||
\(470\) | 8.92820 | 0.411827 | ||||||||
\(471\) | −14.6603 | −0.675509 | ||||||||
\(472\) | 5.66025 | 0.260534 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −10.3923 | −0.477334 | ||||||||
\(475\) | −7.00000 | −0.321182 | ||||||||
\(476\) | −6.46410 | −0.296282 | ||||||||
\(477\) | −2.73205 | −0.125092 | ||||||||
\(478\) | −3.19615 | −0.146189 | ||||||||
\(479\) | −25.9808 | −1.18709 | −0.593546 | − | 0.804800i | \(-0.702272\pi\) | ||||
−0.593546 | + | 0.804800i | \(0.702272\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 7.87564 | 0.359098 | ||||||||
\(482\) | −0.803848 | −0.0366143 | ||||||||
\(483\) | 12.1962 | 0.554944 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.26795 | −0.239205 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −5.67949 | −0.257362 | −0.128681 | − | 0.991686i | \(-0.541074\pi\) | ||||
−0.128681 | + | 0.991686i | \(0.541074\pi\) | |||||||
\(488\) | 9.12436 | 0.413040 | ||||||||
\(489\) | 8.19615 | 0.370643 | ||||||||
\(490\) | −6.92820 | −0.312984 | ||||||||
\(491\) | 1.26795 | 0.0572217 | 0.0286109 | − | 0.999591i | \(-0.490892\pi\) | ||||
0.0286109 | + | 0.999591i | \(0.490892\pi\) | |||||||
\(492\) | −6.19615 | −0.279344 | ||||||||
\(493\) | −8.66025 | −0.390038 | ||||||||
\(494\) | −17.2487 | −0.776056 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.19615 | −0.188413 | ||||||||
\(497\) | −16.6603 | −0.747315 | ||||||||
\(498\) | −16.4641 | −0.737774 | ||||||||
\(499\) | −27.1962 | −1.21747 | −0.608733 | − | 0.793375i | \(-0.708322\pi\) | ||||
−0.608733 | + | 0.793375i | \(0.708322\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 6.53590 | 0.292002 | ||||||||
\(502\) | 31.3205 | 1.39790 | ||||||||
\(503\) | 23.9090 | 1.06605 | 0.533024 | − | 0.846100i | \(-0.321056\pi\) | ||||
0.533024 | + | 0.846100i | \(0.321056\pi\) | |||||||
\(504\) | −3.73205 | −0.166239 | ||||||||
\(505\) | −8.46410 | −0.376648 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.92820 | −0.307692 | ||||||||
\(508\) | −13.4641 | −0.597373 | ||||||||
\(509\) | 11.8564 | 0.525526 | 0.262763 | − | 0.964860i | \(-0.415366\pi\) | ||||
0.262763 | + | 0.964860i | \(0.415366\pi\) | |||||||
\(510\) | −1.73205 | −0.0766965 | ||||||||
\(511\) | 28.5885 | 1.26468 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −7.00000 | −0.309058 | ||||||||
\(514\) | 19.7846 | 0.872662 | ||||||||
\(515\) | 17.3923 | 0.766397 | ||||||||
\(516\) | −8.19615 | −0.360815 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −11.9282 | −0.524095 | ||||||||
\(519\) | −23.6603 | −1.03857 | ||||||||
\(520\) | −2.46410 | −0.108058 | ||||||||
\(521\) | −18.5885 | −0.814375 | −0.407188 | − | 0.913345i | \(-0.633490\pi\) | ||||
−0.407188 | + | 0.913345i | \(0.633490\pi\) | |||||||
\(522\) | −5.00000 | −0.218844 | ||||||||
\(523\) | 2.87564 | 0.125743 | 0.0628716 | − | 0.998022i | \(-0.479974\pi\) | ||||
0.0628716 | + | 0.998022i | \(0.479974\pi\) | |||||||
\(524\) | −21.1244 | −0.922822 | ||||||||
\(525\) | −3.73205 | −0.162880 | ||||||||
\(526\) | 3.26795 | 0.142489 | ||||||||
\(527\) | −7.26795 | −0.316597 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.3205 | −0.535674 | ||||||||
\(530\) | 2.73205 | 0.118673 | ||||||||
\(531\) | 5.66025 | 0.245634 | ||||||||
\(532\) | 26.1244 | 1.13263 | ||||||||
\(533\) | −15.2679 | −0.661328 | ||||||||
\(534\) | 2.53590 | 0.109739 | ||||||||
\(535\) | −14.3923 | −0.622234 | ||||||||
\(536\) | 11.4641 | 0.495174 | ||||||||
\(537\) | −12.5885 | −0.543232 | ||||||||
\(538\) | 21.9808 | 0.947658 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −30.7321 | −1.32127 | −0.660637 | − | 0.750705i | \(-0.729714\pi\) | ||||
−0.660637 | + | 0.750705i | \(0.729714\pi\) | |||||||
\(542\) | −23.8564 | −1.02472 | ||||||||
\(543\) | −20.1962 | −0.866700 | ||||||||
\(544\) | 1.73205 | 0.0742611 | ||||||||
\(545\) | −12.3923 | −0.530828 | ||||||||
\(546\) | −9.19615 | −0.393559 | ||||||||
\(547\) | 23.8564 | 1.02003 | 0.510013 | − | 0.860167i | \(-0.329641\pi\) | ||||
0.510013 | + | 0.860167i | \(0.329641\pi\) | |||||||
\(548\) | 10.4641 | 0.447004 | ||||||||
\(549\) | 9.12436 | 0.389418 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.0000 | 1.49105 | ||||||||
\(552\) | −3.26795 | −0.139093 | ||||||||
\(553\) | 38.7846 | 1.64929 | ||||||||
\(554\) | 2.14359 | 0.0910726 | ||||||||
\(555\) | −3.19615 | −0.135669 | ||||||||
\(556\) | −7.00000 | −0.296866 | ||||||||
\(557\) | 37.3205 | 1.58132 | 0.790660 | − | 0.612255i | \(-0.209737\pi\) | ||||
0.790660 | + | 0.612255i | \(0.209737\pi\) | |||||||
\(558\) | −4.19615 | −0.177637 | ||||||||
\(559\) | −20.1962 | −0.854206 | ||||||||
\(560\) | 3.73205 | 0.157708 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.12436 | 0.131793 | ||||||||
\(563\) | −5.53590 | −0.233310 | −0.116655 | − | 0.993172i | \(-0.537217\pi\) | ||||
−0.116655 | + | 0.993172i | \(0.537217\pi\) | |||||||
\(564\) | −8.92820 | −0.375945 | ||||||||
\(565\) | 13.8564 | 0.582943 | ||||||||
\(566\) | 8.39230 | 0.352755 | ||||||||
\(567\) | −3.73205 | −0.156731 | ||||||||
\(568\) | 4.46410 | 0.187310 | ||||||||
\(569\) | −23.6603 | −0.991889 | −0.495945 | − | 0.868354i | \(-0.665178\pi\) | ||||
−0.495945 | + | 0.868354i | \(0.665178\pi\) | |||||||
\(570\) | 7.00000 | 0.293198 | ||||||||
\(571\) | −4.53590 | −0.189821 | −0.0949107 | − | 0.995486i | \(-0.530257\pi\) | ||||
−0.0949107 | + | 0.995486i | \(0.530257\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.0717968 | 0.00299935 | ||||||||
\(574\) | 23.1244 | 0.965192 | ||||||||
\(575\) | −3.26795 | −0.136283 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −45.0333 | −1.87476 | −0.937381 | − | 0.348306i | \(-0.886757\pi\) | ||||
−0.937381 | + | 0.348306i | \(0.886757\pi\) | |||||||
\(578\) | −14.0000 | −0.582323 | ||||||||
\(579\) | 11.3205 | 0.470464 | ||||||||
\(580\) | 5.00000 | 0.207614 | ||||||||
\(581\) | 61.4449 | 2.54916 | ||||||||
\(582\) | 5.26795 | 0.218364 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −7.66025 | −0.316984 | ||||||||
\(585\) | −2.46410 | −0.101878 | ||||||||
\(586\) | 14.9282 | 0.616678 | ||||||||
\(587\) | −1.87564 | −0.0774161 | −0.0387081 | − | 0.999251i | \(-0.512324\pi\) | ||||
−0.0387081 | + | 0.999251i | \(0.512324\pi\) | |||||||
\(588\) | 6.92820 | 0.285714 | ||||||||
\(589\) | 29.3731 | 1.21030 | ||||||||
\(590\) | −5.66025 | −0.233029 | ||||||||
\(591\) | −9.46410 | −0.389301 | ||||||||
\(592\) | 3.19615 | 0.131361 | ||||||||
\(593\) | −34.7846 | −1.42843 | −0.714216 | − | 0.699925i | \(-0.753217\pi\) | ||||
−0.714216 | + | 0.699925i | \(0.753217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.46410 | 0.265002 | ||||||||
\(596\) | 8.39230 | 0.343762 | ||||||||
\(597\) | 19.3205 | 0.790736 | ||||||||
\(598\) | −8.05256 | −0.329294 | ||||||||
\(599\) | 40.2487 | 1.64452 | 0.822259 | − | 0.569114i | \(-0.192714\pi\) | ||||
0.822259 | + | 0.569114i | \(0.192714\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 30.5885 | 1.24669 | ||||||||
\(603\) | 11.4641 | 0.466854 | ||||||||
\(604\) | −20.1962 | −0.821770 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 8.46410 | 0.343831 | ||||||||
\(607\) | −28.1244 | −1.14153 | −0.570766 | − | 0.821113i | \(-0.693354\pi\) | ||||
−0.570766 | + | 0.821113i | \(0.693354\pi\) | |||||||
\(608\) | −7.00000 | −0.283887 | ||||||||
\(609\) | 18.6603 | 0.756152 | ||||||||
\(610\) | −9.12436 | −0.369434 | ||||||||
\(611\) | −22.0000 | −0.890025 | ||||||||
\(612\) | 1.73205 | 0.0700140 | ||||||||
\(613\) | 15.5359 | 0.627489 | 0.313745 | − | 0.949507i | \(-0.398416\pi\) | ||||
0.313745 | + | 0.949507i | \(0.398416\pi\) | |||||||
\(614\) | 16.5885 | 0.669456 | ||||||||
\(615\) | 6.19615 | 0.249853 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.1051 | −1.65483 | −0.827415 | − | 0.561591i | \(-0.810189\pi\) | ||||
−0.827415 | + | 0.561591i | \(0.810189\pi\) | |||||||
\(618\) | −17.3923 | −0.699621 | ||||||||
\(619\) | −11.8756 | −0.477322 | −0.238661 | − | 0.971103i | \(-0.576709\pi\) | ||||
−0.238661 | + | 0.971103i | \(0.576709\pi\) | |||||||
\(620\) | 4.19615 | 0.168522 | ||||||||
\(621\) | −3.26795 | −0.131138 | ||||||||
\(622\) | 13.0718 | 0.524131 | ||||||||
\(623\) | −9.46410 | −0.379171 | ||||||||
\(624\) | 2.46410 | 0.0986430 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 11.8038 | 0.471777 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.6603 | −0.585008 | ||||||||
\(629\) | 5.53590 | 0.220731 | ||||||||
\(630\) | 3.73205 | 0.148688 | ||||||||
\(631\) | 26.9808 | 1.07409 | 0.537044 | − | 0.843554i | \(-0.319541\pi\) | ||||
0.537044 | + | 0.843554i | \(0.319541\pi\) | |||||||
\(632\) | −10.3923 | −0.413384 | ||||||||
\(633\) | −6.60770 | −0.262632 | ||||||||
\(634\) | 8.19615 | 0.325511 | ||||||||
\(635\) | 13.4641 | 0.534307 | ||||||||
\(636\) | −2.73205 | −0.108333 | ||||||||
\(637\) | 17.0718 | 0.676409 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.46410 | 0.176597 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 31.8564 | 1.25825 | 0.629126 | − | 0.777303i | \(-0.283413\pi\) | ||||
0.629126 | + | 0.777303i | \(0.283413\pi\) | |||||||
\(642\) | 14.3923 | 0.568019 | ||||||||
\(643\) | 44.7846 | 1.76613 | 0.883066 | − | 0.469248i | \(-0.155475\pi\) | ||||
0.883066 | + | 0.469248i | \(0.155475\pi\) | |||||||
\(644\) | 12.1962 | 0.480596 | ||||||||
\(645\) | 8.19615 | 0.322723 | ||||||||
\(646\) | −12.1244 | −0.477026 | ||||||||
\(647\) | −26.5359 | −1.04323 | −0.521617 | − | 0.853180i | \(-0.674671\pi\) | ||||
−0.521617 | + | 0.853180i | \(0.674671\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.46410 | 0.0966500 | ||||||||
\(651\) | 15.6603 | 0.613774 | ||||||||
\(652\) | 8.19615 | 0.320986 | ||||||||
\(653\) | −5.51666 | −0.215884 | −0.107942 | − | 0.994157i | \(-0.534426\pi\) | ||||
−0.107942 | + | 0.994157i | \(0.534426\pi\) | |||||||
\(654\) | 12.3923 | 0.484577 | ||||||||
\(655\) | 21.1244 | 0.825397 | ||||||||
\(656\) | −6.19615 | −0.241919 | ||||||||
\(657\) | −7.66025 | −0.298855 | ||||||||
\(658\) | 33.3205 | 1.29897 | ||||||||
\(659\) | 16.2487 | 0.632960 | 0.316480 | − | 0.948599i | \(-0.397499\pi\) | ||||
0.316480 | + | 0.948599i | \(0.397499\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.4449 | −1.57312 | −0.786561 | − | 0.617512i | \(-0.788141\pi\) | ||||
−0.786561 | + | 0.617512i | \(0.788141\pi\) | |||||||
\(662\) | 5.87564 | 0.228363 | ||||||||
\(663\) | 4.26795 | 0.165753 | ||||||||
\(664\) | −16.4641 | −0.638931 | ||||||||
\(665\) | −26.1244 | −1.01306 | ||||||||
\(666\) | 3.19615 | 0.123848 | ||||||||
\(667\) | 16.3397 | 0.632677 | ||||||||
\(668\) | 6.53590 | 0.252882 | ||||||||
\(669\) | 29.2487 | 1.13082 | ||||||||
\(670\) | −11.4641 | −0.442897 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −3.73205 | −0.143967 | ||||||||
\(673\) | −17.0718 | −0.658069 | −0.329035 | − | 0.944318i | \(-0.606723\pi\) | ||||
−0.329035 | + | 0.944318i | \(0.606723\pi\) | |||||||
\(674\) | 30.1962 | 1.16311 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −6.92820 | −0.266469 | ||||||||
\(677\) | 27.1244 | 1.04247 | 0.521237 | − | 0.853412i | \(-0.325471\pi\) | ||||
0.521237 | + | 0.853412i | \(0.325471\pi\) | |||||||
\(678\) | −13.8564 | −0.532152 | ||||||||
\(679\) | −19.6603 | −0.754491 | ||||||||
\(680\) | −1.73205 | −0.0664211 | ||||||||
\(681\) | 27.4641 | 1.05243 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.3731 | −1.62136 | −0.810680 | − | 0.585489i | \(-0.800902\pi\) | ||||
−0.810680 | + | 0.585489i | \(0.800902\pi\) | |||||||
\(684\) | −7.00000 | −0.267652 | ||||||||
\(685\) | −10.4641 | −0.399813 | ||||||||
\(686\) | 0.267949 | 0.0102303 | ||||||||
\(687\) | −5.85641 | −0.223436 | ||||||||
\(688\) | −8.19615 | −0.312475 | ||||||||
\(689\) | −6.73205 | −0.256471 | ||||||||
\(690\) | 3.26795 | 0.124409 | ||||||||
\(691\) | 12.5167 | 0.476156 | 0.238078 | − | 0.971246i | \(-0.423483\pi\) | ||||
0.238078 | + | 0.971246i | \(0.423483\pi\) | |||||||
\(692\) | −23.6603 | −0.899428 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.4641 | 0.549050 | ||||||||
\(695\) | 7.00000 | 0.265525 | ||||||||
\(696\) | −5.00000 | −0.189525 | ||||||||
\(697\) | −10.7321 | −0.406505 | ||||||||
\(698\) | −34.0000 | −1.28692 | ||||||||
\(699\) | 9.07180 | 0.343127 | ||||||||
\(700\) | −3.73205 | −0.141058 | ||||||||
\(701\) | −3.24871 | −0.122702 | −0.0613511 | − | 0.998116i | \(-0.519541\pi\) | ||||
−0.0613511 | + | 0.998116i | \(0.519541\pi\) | |||||||
\(702\) | 2.46410 | 0.0930015 | ||||||||
\(703\) | −22.3731 | −0.843816 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.92820 | 0.336256 | ||||||||
\(706\) | 1.85641 | 0.0698668 | ||||||||
\(707\) | −31.5885 | −1.18801 | ||||||||
\(708\) | 5.66025 | 0.212725 | ||||||||
\(709\) | −24.7321 | −0.928832 | −0.464416 | − | 0.885617i | \(-0.653736\pi\) | ||||
−0.464416 | + | 0.885617i | \(0.653736\pi\) | |||||||
\(710\) | −4.46410 | −0.167535 | ||||||||
\(711\) | −10.3923 | −0.389742 | ||||||||
\(712\) | 2.53590 | 0.0950368 | ||||||||
\(713\) | 13.7128 | 0.513549 | ||||||||
\(714\) | −6.46410 | −0.241913 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.5885 | −0.470453 | ||||||||
\(717\) | −3.19615 | −0.119362 | ||||||||
\(718\) | 31.1769 | 1.16351 | ||||||||
\(719\) | −46.3923 | −1.73014 | −0.865071 | − | 0.501650i | \(-0.832726\pi\) | ||||
−0.865071 | + | 0.501650i | \(0.832726\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 64.9090 | 2.41734 | ||||||||
\(722\) | 30.0000 | 1.11648 | ||||||||
\(723\) | −0.803848 | −0.0298954 | ||||||||
\(724\) | −20.1962 | −0.750584 | ||||||||
\(725\) | −5.00000 | −0.185695 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.1436 | −0.784172 | −0.392086 | − | 0.919928i | \(-0.628247\pi\) | ||||
−0.392086 | + | 0.919928i | \(0.628247\pi\) | |||||||
\(728\) | −9.19615 | −0.340832 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.66025 | 0.283519 | ||||||||
\(731\) | −14.1962 | −0.525064 | ||||||||
\(732\) | 9.12436 | 0.337246 | ||||||||
\(733\) | 4.78461 | 0.176724 | 0.0883618 | − | 0.996088i | \(-0.471837\pi\) | ||||
0.0883618 | + | 0.996088i | \(0.471837\pi\) | |||||||
\(734\) | −17.0000 | −0.627481 | ||||||||
\(735\) | −6.92820 | −0.255551 | ||||||||
\(736\) | −3.26795 | −0.120458 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −6.19615 | −0.228084 | ||||||||
\(739\) | 19.0000 | 0.698926 | 0.349463 | − | 0.936950i | \(-0.386364\pi\) | ||||
0.349463 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(740\) | −3.19615 | −0.117493 | ||||||||
\(741\) | −17.2487 | −0.633647 | ||||||||
\(742\) | 10.1962 | 0.374313 | ||||||||
\(743\) | 5.26795 | 0.193262 | 0.0966312 | − | 0.995320i | \(-0.469193\pi\) | ||||
0.0966312 | + | 0.995320i | \(0.469193\pi\) | |||||||
\(744\) | −4.19615 | −0.153838 | ||||||||
\(745\) | −8.39230 | −0.307470 | ||||||||
\(746\) | −17.3923 | −0.636778 | ||||||||
\(747\) | −16.4641 | −0.602390 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −53.7128 | −1.96262 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −1.66025 | −0.0605835 | −0.0302918 | − | 0.999541i | \(-0.509644\pi\) | ||||
−0.0302918 | + | 0.999541i | \(0.509644\pi\) | |||||||
\(752\) | −8.92820 | −0.325578 | ||||||||
\(753\) | 31.3205 | 1.14138 | ||||||||
\(754\) | −12.3205 | −0.448686 | ||||||||
\(755\) | 20.1962 | 0.735013 | ||||||||
\(756\) | −3.73205 | −0.135733 | ||||||||
\(757\) | 8.53590 | 0.310243 | 0.155121 | − | 0.987895i | \(-0.450423\pi\) | ||||
0.155121 | + | 0.987895i | \(0.450423\pi\) | |||||||
\(758\) | 6.12436 | 0.222447 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.00000 | 0.253917 | ||||||||
\(761\) | 46.2487 | 1.67651 | 0.838257 | − | 0.545275i | \(-0.183575\pi\) | ||||
0.838257 | + | 0.545275i | \(0.183575\pi\) | |||||||
\(762\) | −13.4641 | −0.487753 | ||||||||
\(763\) | −46.2487 | −1.67432 | ||||||||
\(764\) | 0.0717968 | 0.00259752 | ||||||||
\(765\) | −1.73205 | −0.0626224 | ||||||||
\(766\) | −4.14359 | −0.149714 | ||||||||
\(767\) | 13.9474 | 0.503613 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −47.8372 | −1.72505 | −0.862526 | − | 0.506012i | \(-0.831119\pi\) | ||||
−0.862526 | + | 0.506012i | \(0.831119\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.7846 | 0.712525 | ||||||||
\(772\) | 11.3205 | 0.407434 | ||||||||
\(773\) | −29.6603 | −1.06681 | −0.533403 | − | 0.845861i | \(-0.679087\pi\) | ||||
−0.533403 | + | 0.845861i | \(0.679087\pi\) | |||||||
\(774\) | −8.19615 | −0.294605 | ||||||||
\(775\) | −4.19615 | −0.150730 | ||||||||
\(776\) | 5.26795 | 0.189108 | ||||||||
\(777\) | −11.9282 | −0.427922 | ||||||||
\(778\) | −19.7128 | −0.706739 | ||||||||
\(779\) | 43.3731 | 1.55400 | ||||||||
\(780\) | −2.46410 | −0.0882290 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.66025 | −0.202410 | ||||||||
\(783\) | −5.00000 | −0.178685 | ||||||||
\(784\) | 6.92820 | 0.247436 | ||||||||
\(785\) | 14.6603 | 0.523247 | ||||||||
\(786\) | −21.1244 | −0.753481 | ||||||||
\(787\) | 38.1962 | 1.36155 | 0.680773 | − | 0.732495i | \(-0.261644\pi\) | ||||
0.680773 | + | 0.732495i | \(0.261644\pi\) | |||||||
\(788\) | −9.46410 | −0.337145 | ||||||||
\(789\) | 3.26795 | 0.116342 | ||||||||
\(790\) | 10.3923 | 0.369742 | ||||||||
\(791\) | 51.7128 | 1.83870 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.4833 | 0.798407 | ||||||||
\(794\) | 27.9808 | 0.993000 | ||||||||
\(795\) | 2.73205 | 0.0968959 | ||||||||
\(796\) | 19.3205 | 0.684797 | ||||||||
\(797\) | −51.1244 | −1.81092 | −0.905459 | − | 0.424434i | \(-0.860473\pi\) | ||||
−0.905459 | + | 0.424434i | \(0.860473\pi\) | |||||||
\(798\) | 26.1244 | 0.924792 | ||||||||
\(799\) | −15.4641 | −0.547081 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 2.53590 | 0.0896016 | ||||||||
\(802\) | 34.7321 | 1.22643 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 11.4641 | 0.404308 | ||||||||
\(805\) | −12.1962 | −0.429858 | ||||||||
\(806\) | −10.3397 | −0.364202 | ||||||||
\(807\) | 21.9808 | 0.773759 | ||||||||
\(808\) | 8.46410 | 0.297766 | ||||||||
\(809\) | −2.19615 | −0.0772126 | −0.0386063 | − | 0.999254i | \(-0.512292\pi\) | ||||
−0.0386063 | + | 0.999254i | \(0.512292\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 44.1769 | 1.55126 | 0.775631 | − | 0.631187i | \(-0.217432\pi\) | ||||
0.775631 | + | 0.631187i | \(0.217432\pi\) | |||||||
\(812\) | 18.6603 | 0.654847 | ||||||||
\(813\) | −23.8564 | −0.836681 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.19615 | −0.287099 | ||||||||
\(816\) | 1.73205 | 0.0606339 | ||||||||
\(817\) | 57.3731 | 2.00723 | ||||||||
\(818\) | −12.9282 | −0.452024 | ||||||||
\(819\) | −9.19615 | −0.321340 | ||||||||
\(820\) | 6.19615 | 0.216379 | ||||||||
\(821\) | 23.6077 | 0.823914 | 0.411957 | − | 0.911203i | \(-0.364845\pi\) | ||||
0.411957 | + | 0.911203i | \(0.364845\pi\) | |||||||
\(822\) | 10.4641 | 0.364977 | ||||||||
\(823\) | −1.67949 | −0.0585434 | −0.0292717 | − | 0.999571i | \(-0.509319\pi\) | ||||
−0.0292717 | + | 0.999571i | \(0.509319\pi\) | |||||||
\(824\) | −17.3923 | −0.605890 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.1244 | −0.735010 | ||||||||
\(827\) | 21.0000 | 0.730242 | 0.365121 | − | 0.930960i | \(-0.381028\pi\) | ||||
0.365121 | + | 0.930960i | \(0.381028\pi\) | |||||||
\(828\) | −3.26795 | −0.113569 | ||||||||
\(829\) | −20.5885 | −0.715067 | −0.357533 | − | 0.933900i | \(-0.616382\pi\) | ||||
−0.357533 | + | 0.933900i | \(0.616382\pi\) | |||||||
\(830\) | 16.4641 | 0.571477 | ||||||||
\(831\) | 2.14359 | 0.0743604 | ||||||||
\(832\) | 2.46410 | 0.0854274 | ||||||||
\(833\) | 12.0000 | 0.415775 | ||||||||
\(834\) | −7.00000 | −0.242390 | ||||||||
\(835\) | −6.53590 | −0.226184 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.19615 | −0.145040 | ||||||||
\(838\) | −20.2487 | −0.699480 | ||||||||
\(839\) | −15.5359 | −0.536359 | −0.268179 | − | 0.963369i | \(-0.586422\pi\) | ||||
−0.268179 | + | 0.963369i | \(0.586422\pi\) | |||||||
\(840\) | 3.73205 | 0.128768 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | −15.6603 | −0.539688 | ||||||||
\(843\) | 3.12436 | 0.107609 | ||||||||
\(844\) | −6.60770 | −0.227446 | ||||||||
\(845\) | 6.92820 | 0.238337 | ||||||||
\(846\) | −8.92820 | −0.306958 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.73205 | −0.0938190 | ||||||||
\(849\) | 8.39230 | 0.288023 | ||||||||
\(850\) | 1.73205 | 0.0594089 | ||||||||
\(851\) | −10.4449 | −0.358045 | ||||||||
\(852\) | 4.46410 | 0.152938 | ||||||||
\(853\) | 26.7128 | 0.914629 | 0.457315 | − | 0.889305i | \(-0.348811\pi\) | ||||
0.457315 | + | 0.889305i | \(0.348811\pi\) | |||||||
\(854\) | −34.0526 | −1.16525 | ||||||||
\(855\) | 7.00000 | 0.239395 | ||||||||
\(856\) | 14.3923 | 0.491919 | ||||||||
\(857\) | 8.51666 | 0.290924 | 0.145462 | − | 0.989364i | \(-0.453533\pi\) | ||||
0.145462 | + | 0.989364i | \(0.453533\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.3205 | −1.27336 | −0.636680 | − | 0.771128i | \(-0.719693\pi\) | ||||
−0.636680 | + | 0.771128i | \(0.719693\pi\) | |||||||
\(860\) | 8.19615 | 0.279486 | ||||||||
\(861\) | 23.1244 | 0.788076 | ||||||||
\(862\) | −21.4449 | −0.730415 | ||||||||
\(863\) | −4.53590 | −0.154404 | −0.0772019 | − | 0.997015i | \(-0.524599\pi\) | ||||
−0.0772019 | + | 0.997015i | \(0.524599\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 23.6603 | 0.804473 | ||||||||
\(866\) | 4.00000 | 0.135926 | ||||||||
\(867\) | −14.0000 | −0.475465 | ||||||||
\(868\) | 15.6603 | 0.531544 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 5.00000 | 0.169516 | ||||||||
\(871\) | 28.2487 | 0.957171 | ||||||||
\(872\) | 12.3923 | 0.419656 | ||||||||
\(873\) | 5.26795 | 0.178293 | ||||||||
\(874\) | 22.8756 | 0.773780 | ||||||||
\(875\) | 3.73205 | 0.126166 | ||||||||
\(876\) | −7.66025 | −0.258816 | ||||||||
\(877\) | 15.5359 | 0.524610 | 0.262305 | − | 0.964985i | \(-0.415517\pi\) | ||||
0.262305 | + | 0.964985i | \(0.415517\pi\) | |||||||
\(878\) | 14.0000 | 0.472477 | ||||||||
\(879\) | 14.9282 | 0.503516 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.58846 | 0.154589 | 0.0772945 | − | 0.997008i | \(-0.475372\pi\) | ||||
0.0772945 | + | 0.997008i | \(0.475372\pi\) | |||||||
\(882\) | 6.92820 | 0.233285 | ||||||||
\(883\) | −12.0526 | −0.405601 | −0.202800 | − | 0.979220i | \(-0.565004\pi\) | ||||
−0.202800 | + | 0.979220i | \(0.565004\pi\) | |||||||
\(884\) | 4.26795 | 0.143547 | ||||||||
\(885\) | −5.66025 | −0.190267 | ||||||||
\(886\) | 10.8038 | 0.362962 | ||||||||
\(887\) | −4.78461 | −0.160651 | −0.0803257 | − | 0.996769i | \(-0.525596\pi\) | ||||
−0.0803257 | + | 0.996769i | \(0.525596\pi\) | |||||||
\(888\) | 3.19615 | 0.107256 | ||||||||
\(889\) | 50.2487 | 1.68529 | ||||||||
\(890\) | −2.53590 | −0.0850035 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 29.2487 | 0.979319 | ||||||||
\(893\) | 62.4974 | 2.09140 | ||||||||
\(894\) | 8.39230 | 0.280681 | ||||||||
\(895\) | 12.5885 | 0.420786 | ||||||||
\(896\) | −3.73205 | −0.124679 | ||||||||
\(897\) | −8.05256 | −0.268867 | ||||||||
\(898\) | 5.32051 | 0.177548 | ||||||||
\(899\) | 20.9808 | 0.699748 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −4.73205 | −0.157647 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 30.5885 | 1.01792 | ||||||||
\(904\) | −13.8564 | −0.460857 | ||||||||
\(905\) | 20.1962 | 0.671343 | ||||||||
\(906\) | −20.1962 | −0.670972 | ||||||||
\(907\) | −35.0718 | −1.16454 | −0.582270 | − | 0.812996i | \(-0.697835\pi\) | ||||
−0.582270 | + | 0.812996i | \(0.697835\pi\) | |||||||
\(908\) | 27.4641 | 0.911428 | ||||||||
\(909\) | 8.46410 | 0.280737 | ||||||||
\(910\) | 9.19615 | 0.304849 | ||||||||
\(911\) | −31.1051 | −1.03056 | −0.515279 | − | 0.857022i | \(-0.672312\pi\) | ||||
−0.515279 | + | 0.857022i | \(0.672312\pi\) | |||||||
\(912\) | −7.00000 | −0.231793 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 21.2679 | 0.703481 | ||||||||
\(915\) | −9.12436 | −0.301642 | ||||||||
\(916\) | −5.85641 | −0.193501 | ||||||||
\(917\) | 78.8372 | 2.60343 | ||||||||
\(918\) | 1.73205 | 0.0571662 | ||||||||
\(919\) | 2.05256 | 0.0677077 | 0.0338538 | − | 0.999427i | \(-0.489222\pi\) | ||||
0.0338538 | + | 0.999427i | \(0.489222\pi\) | |||||||
\(920\) | 3.26795 | 0.107741 | ||||||||
\(921\) | 16.5885 | 0.546608 | ||||||||
\(922\) | −5.39230 | −0.177586 | ||||||||
\(923\) | 11.0000 | 0.362069 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.19615 | 0.105089 | ||||||||
\(926\) | −24.2487 | −0.796862 | ||||||||
\(927\) | −17.3923 | −0.571238 | ||||||||
\(928\) | −5.00000 | −0.164133 | ||||||||
\(929\) | −6.87564 | −0.225583 | −0.112791 | − | 0.993619i | \(-0.535979\pi\) | ||||
−0.112791 | + | 0.993619i | \(0.535979\pi\) | |||||||
\(930\) | 4.19615 | 0.137597 | ||||||||
\(931\) | −48.4974 | −1.58944 | ||||||||
\(932\) | 9.07180 | 0.297157 | ||||||||
\(933\) | 13.0718 | 0.427951 | ||||||||
\(934\) | 28.8038 | 0.942491 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.46410 | 0.0805417 | ||||||||
\(937\) | 4.92820 | 0.160997 | 0.0804987 | − | 0.996755i | \(-0.474349\pi\) | ||||
0.0804987 | + | 0.996755i | \(0.474349\pi\) | |||||||
\(938\) | −42.7846 | −1.39697 | ||||||||
\(939\) | 11.8038 | 0.385204 | ||||||||
\(940\) | 8.92820 | 0.291206 | ||||||||
\(941\) | 6.07180 | 0.197935 | 0.0989675 | − | 0.995091i | \(-0.468446\pi\) | ||||
0.0989675 | + | 0.995091i | \(0.468446\pi\) | |||||||
\(942\) | −14.6603 | −0.477657 | ||||||||
\(943\) | 20.2487 | 0.659389 | ||||||||
\(944\) | 5.66025 | 0.184226 | ||||||||
\(945\) | 3.73205 | 0.121404 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.3731 | 1.44193 | 0.720965 | − | 0.692971i | \(-0.243699\pi\) | ||||
0.720965 | + | 0.692971i | \(0.243699\pi\) | |||||||
\(948\) | −10.3923 | −0.337526 | ||||||||
\(949\) | −18.8756 | −0.612729 | ||||||||
\(950\) | −7.00000 | −0.227110 | ||||||||
\(951\) | 8.19615 | 0.265778 | ||||||||
\(952\) | −6.46410 | −0.209503 | ||||||||
\(953\) | −10.7846 | −0.349348 | −0.174674 | − | 0.984626i | \(-0.555887\pi\) | ||||
−0.174674 | + | 0.984626i | \(0.555887\pi\) | |||||||
\(954\) | −2.73205 | −0.0884534 | ||||||||
\(955\) | −0.0717968 | −0.00232329 | ||||||||
\(956\) | −3.19615 | −0.103371 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −25.9808 | −0.839400 | ||||||||
\(959\) | −39.0526 | −1.26107 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −13.3923 | −0.432010 | ||||||||
\(962\) | 7.87564 | 0.253921 | ||||||||
\(963\) | 14.3923 | 0.463786 | ||||||||
\(964\) | −0.803848 | −0.0258902 | ||||||||
\(965\) | −11.3205 | −0.364420 | ||||||||
\(966\) | 12.1962 | 0.392405 | ||||||||
\(967\) | −47.1769 | −1.51711 | −0.758554 | − | 0.651611i | \(-0.774094\pi\) | ||||
−0.758554 | + | 0.651611i | \(0.774094\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.1244 | −0.389490 | ||||||||
\(970\) | −5.26795 | −0.169144 | ||||||||
\(971\) | −39.6077 | −1.27107 | −0.635536 | − | 0.772071i | \(-0.719221\pi\) | ||||
−0.635536 | + | 0.772071i | \(0.719221\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 26.1244 | 0.837508 | ||||||||
\(974\) | −5.67949 | −0.181983 | ||||||||
\(975\) | 2.46410 | 0.0789144 | ||||||||
\(976\) | 9.12436 | 0.292064 | ||||||||
\(977\) | 28.1436 | 0.900393 | 0.450197 | − | 0.892929i | \(-0.351354\pi\) | ||||
0.450197 | + | 0.892929i | \(0.351354\pi\) | |||||||
\(978\) | 8.19615 | 0.262084 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.92820 | −0.221313 | ||||||||
\(981\) | 12.3923 | 0.395656 | ||||||||
\(982\) | 1.26795 | 0.0404619 | ||||||||
\(983\) | 23.9090 | 0.762578 | 0.381289 | − | 0.924456i | \(-0.375480\pi\) | ||||
0.381289 | + | 0.924456i | \(0.375480\pi\) | |||||||
\(984\) | −6.19615 | −0.197526 | ||||||||
\(985\) | 9.46410 | 0.301551 | ||||||||
\(986\) | −8.66025 | −0.275799 | ||||||||
\(987\) | 33.3205 | 1.06060 | ||||||||
\(988\) | −17.2487 | −0.548755 | ||||||||
\(989\) | 26.7846 | 0.851701 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.7846 | −1.35910 | −0.679549 | − | 0.733630i | \(-0.737824\pi\) | ||||
−0.679549 | + | 0.733630i | \(0.737824\pi\) | |||||||
\(992\) | −4.19615 | −0.133228 | ||||||||
\(993\) | 5.87564 | 0.186458 | ||||||||
\(994\) | −16.6603 | −0.528431 | ||||||||
\(995\) | −19.3205 | −0.612501 | ||||||||
\(996\) | −16.4641 | −0.521685 | ||||||||
\(997\) | −6.71281 | −0.212597 | −0.106298 | − | 0.994334i | \(-0.533900\pi\) | ||||
−0.106298 | + | 0.994334i | \(0.533900\pi\) | |||||||
\(998\) | −27.1962 | −0.860879 | ||||||||
\(999\) | 3.19615 | 0.101122 |
(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 | 3630.2.a.bo.1.1 | yes | 2 | |
11.10 | odd | 2 | 3630.2.a.bg.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3630.2.a.bg.1.2 | ✓ | 2 | 11.10 | odd | 2 | ||
3630.2.a.bo.1.1 | yes | 2 | 1.1 | even | 1 | trivial |