Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [931,2,Mod(1,931)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(931, 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("931.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 931 = 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 931.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: | \(7.43407242818\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 133) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 931.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | −1.70711 | −0.853553 | − | 0.521005i | \(-0.825557\pi\) | ||||
−0.853553 | + | 0.521005i | \(0.825557\pi\) | |||||||
\(3\) | 1.41421 | 0.816497 | 0.408248 | − | 0.912871i | \(-0.366140\pi\) | ||||
0.408248 | + | 0.912871i | \(0.366140\pi\) | |||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | 1.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | −3.41421 | −1.39385 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −2.41421 | −0.763441 | ||||||||
\(11\) | −0.414214 | −0.124890 | −0.0624450 | − | 0.998048i | \(-0.519890\pi\) | ||||
−0.0624450 | + | 0.998048i | \(0.519890\pi\) | |||||||
\(12\) | 5.41421 | 1.56295 | ||||||||
\(13\) | −2.24264 | −0.621997 | −0.310998 | − | 0.950410i | \(-0.600663\pi\) | ||||
−0.310998 | + | 0.950410i | \(0.600663\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.41421 | 0.365148 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 2.41421 | 0.569036 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 3.82843 | 0.856062 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −5.58579 | −1.16472 | −0.582358 | − | 0.812932i | \(-0.697870\pi\) | ||||
−0.582358 | + | 0.812932i | \(0.697870\pi\) | |||||||
\(24\) | −6.24264 | −1.27427 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 5.41421 | 1.06181 | ||||||||
\(27\) | −5.65685 | −1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.58579 | −1.22295 | −0.611475 | − | 0.791264i | \(-0.709423\pi\) | ||||
−0.611475 | + | 0.791264i | \(0.709423\pi\) | |||||||
\(30\) | −3.41421 | −0.623347 | ||||||||
\(31\) | −6.24264 | −1.12121 | −0.560606 | − | 0.828083i | \(-0.689432\pi\) | ||||
−0.560606 | + | 0.828083i | \(0.689432\pi\) | |||||||
\(32\) | 1.58579 | 0.280330 | ||||||||
\(33\) | −0.585786 | −0.101972 | ||||||||
\(34\) | 9.65685 | 1.65614 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.82843 | −0.638071 | ||||||||
\(37\) | 9.07107 | 1.49127 | 0.745637 | − | 0.666352i | \(-0.232145\pi\) | ||||
0.745637 | + | 0.666352i | \(0.232145\pi\) | |||||||
\(38\) | 2.41421 | 0.391637 | ||||||||
\(39\) | −3.17157 | −0.507858 | ||||||||
\(40\) | −4.41421 | −0.697948 | ||||||||
\(41\) | −3.17157 | −0.495316 | −0.247658 | − | 0.968847i | \(-0.579661\pi\) | ||||
−0.247658 | + | 0.968847i | \(0.579661\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.07107 | 1.23083 | 0.615413 | − | 0.788205i | \(-0.288989\pi\) | ||||
0.615413 | + | 0.788205i | \(0.288989\pi\) | |||||||
\(44\) | −1.58579 | −0.239066 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 13.4853 | 1.98830 | ||||||||
\(47\) | −4.41421 | −0.643879 | −0.321940 | − | 0.946760i | \(-0.604335\pi\) | ||||
−0.321940 | + | 0.946760i | \(0.604335\pi\) | |||||||
\(48\) | 4.24264 | 0.612372 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9.65685 | 1.36569 | ||||||||
\(51\) | −5.65685 | −0.792118 | ||||||||
\(52\) | −8.58579 | −1.19063 | ||||||||
\(53\) | −4.24264 | −0.582772 | −0.291386 | − | 0.956606i | \(-0.594116\pi\) | ||||
−0.291386 | + | 0.956606i | \(0.594116\pi\) | |||||||
\(54\) | 13.6569 | 1.85846 | ||||||||
\(55\) | −0.414214 | −0.0558525 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.41421 | −0.187317 | ||||||||
\(58\) | 15.8995 | 2.08771 | ||||||||
\(59\) | 6.82843 | 0.888985 | 0.444493 | − | 0.895782i | \(-0.353384\pi\) | ||||
0.444493 | + | 0.895782i | \(0.353384\pi\) | |||||||
\(60\) | 5.41421 | 0.698972 | ||||||||
\(61\) | 11.8284 | 1.51447 | 0.757237 | − | 0.653140i | \(-0.226549\pi\) | ||||
0.757237 | + | 0.653140i | \(0.226549\pi\) | |||||||
\(62\) | 15.0711 | 1.91403 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | −2.24264 | −0.278165 | ||||||||
\(66\) | 1.41421 | 0.174078 | ||||||||
\(67\) | 1.17157 | 0.143130 | 0.0715652 | − | 0.997436i | \(-0.477201\pi\) | ||||
0.0715652 | + | 0.997436i | \(0.477201\pi\) | |||||||
\(68\) | −15.3137 | −1.85706 | ||||||||
\(69\) | −7.89949 | −0.950987 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.2426 | −1.69029 | −0.845145 | − | 0.534537i | \(-0.820486\pi\) | ||||
−0.845145 | + | 0.534537i | \(0.820486\pi\) | |||||||
\(72\) | 4.41421 | 0.520220 | ||||||||
\(73\) | 15.1421 | 1.77225 | 0.886126 | − | 0.463444i | \(-0.153386\pi\) | ||||
0.886126 | + | 0.463444i | \(0.153386\pi\) | |||||||
\(74\) | −21.8995 | −2.54576 | ||||||||
\(75\) | −5.65685 | −0.653197 | ||||||||
\(76\) | −3.82843 | −0.439151 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.65685 | 0.866968 | ||||||||
\(79\) | 1.41421 | 0.159111 | 0.0795557 | − | 0.996830i | \(-0.474650\pi\) | ||||
0.0795557 | + | 0.996830i | \(0.474650\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 7.65685 | 0.845558 | ||||||||
\(83\) | 9.24264 | 1.01451 | 0.507256 | − | 0.861796i | \(-0.330660\pi\) | ||||
0.507256 | + | 0.861796i | \(0.330660\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | −19.4853 | −2.10115 | ||||||||
\(87\) | −9.31371 | −0.998534 | ||||||||
\(88\) | 1.82843 | 0.194911 | ||||||||
\(89\) | −11.4142 | −1.20990 | −0.604952 | − | 0.796262i | \(-0.706808\pi\) | ||||
−0.604952 | + | 0.796262i | \(0.706808\pi\) | |||||||
\(90\) | 2.41421 | 0.254480 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −21.3848 | −2.22952 | ||||||||
\(93\) | −8.82843 | −0.915465 | ||||||||
\(94\) | 10.6569 | 1.09917 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 2.24264 | 0.228889 | ||||||||
\(97\) | −3.17157 | −0.322024 | −0.161012 | − | 0.986952i | \(-0.551476\pi\) | ||||
−0.161012 | + | 0.986952i | \(0.551476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.414214 | 0.0416300 | ||||||||
\(100\) | −15.3137 | −1.53137 | ||||||||
\(101\) | 18.3137 | 1.82228 | 0.911141 | − | 0.412095i | \(-0.135203\pi\) | ||||
0.911141 | + | 0.412095i | \(0.135203\pi\) | |||||||
\(102\) | 13.6569 | 1.35223 | ||||||||
\(103\) | −6.00000 | −0.591198 | −0.295599 | − | 0.955312i | \(-0.595519\pi\) | ||||
−0.295599 | + | 0.955312i | \(0.595519\pi\) | |||||||
\(104\) | 9.89949 | 0.970725 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.2426 | 0.994853 | ||||||||
\(107\) | −13.8995 | −1.34371 | −0.671857 | − | 0.740680i | \(-0.734503\pi\) | ||||
−0.671857 | + | 0.740680i | \(0.734503\pi\) | |||||||
\(108\) | −21.6569 | −2.08393 | ||||||||
\(109\) | −9.65685 | −0.924959 | −0.462479 | − | 0.886630i | \(-0.653040\pi\) | ||||
−0.462479 | + | 0.886630i | \(0.653040\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | 12.8284 | 1.21762 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.242641 | −0.0228257 | −0.0114129 | − | 0.999935i | \(-0.503633\pi\) | ||||
−0.0114129 | + | 0.999935i | \(0.503633\pi\) | |||||||
\(114\) | 3.41421 | 0.319770 | ||||||||
\(115\) | −5.58579 | −0.520877 | ||||||||
\(116\) | −25.2132 | −2.34099 | ||||||||
\(117\) | 2.24264 | 0.207332 | ||||||||
\(118\) | −16.4853 | −1.51759 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −6.24264 | −0.569873 | ||||||||
\(121\) | −10.8284 | −0.984402 | ||||||||
\(122\) | −28.5563 | −2.58537 | ||||||||
\(123\) | −4.48528 | −0.404424 | ||||||||
\(124\) | −23.8995 | −2.14624 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.24264 | 0.376473 | 0.188237 | − | 0.982124i | \(-0.439723\pi\) | ||||
0.188237 | + | 0.982124i | \(0.439723\pi\) | |||||||
\(128\) | 20.5563 | 1.81694 | ||||||||
\(129\) | 11.4142 | 1.00497 | ||||||||
\(130\) | 5.41421 | 0.474858 | ||||||||
\(131\) | 3.51472 | 0.307082 | 0.153541 | − | 0.988142i | \(-0.450932\pi\) | ||||
0.153541 | + | 0.988142i | \(0.450932\pi\) | |||||||
\(132\) | −2.24264 | −0.195197 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.82843 | −0.244339 | ||||||||
\(135\) | −5.65685 | −0.486864 | ||||||||
\(136\) | 17.6569 | 1.51406 | ||||||||
\(137\) | −19.8284 | −1.69406 | −0.847028 | − | 0.531548i | \(-0.821611\pi\) | ||||
−0.847028 | + | 0.531548i | \(0.821611\pi\) | |||||||
\(138\) | 19.0711 | 1.62344 | ||||||||
\(139\) | −6.07107 | −0.514941 | −0.257471 | − | 0.966286i | \(-0.582889\pi\) | ||||
−0.257471 | + | 0.966286i | \(0.582889\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.24264 | −0.525725 | ||||||||
\(142\) | 34.3848 | 2.88551 | ||||||||
\(143\) | 0.928932 | 0.0776812 | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | −6.58579 | −0.546920 | ||||||||
\(146\) | −36.5563 | −3.02542 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 34.7279 | 2.85462 | ||||||||
\(149\) | −0.171573 | −0.0140558 | −0.00702790 | − | 0.999975i | \(-0.502237\pi\) | ||||
−0.00702790 | + | 0.999975i | \(0.502237\pi\) | |||||||
\(150\) | 13.6569 | 1.11508 | ||||||||
\(151\) | −17.3137 | −1.40897 | −0.704485 | − | 0.709719i | \(-0.748822\pi\) | ||||
−0.704485 | + | 0.709719i | \(0.748822\pi\) | |||||||
\(152\) | 4.41421 | 0.358040 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.24264 | −0.501421 | ||||||||
\(156\) | −12.1421 | −0.972149 | ||||||||
\(157\) | 6.17157 | 0.492545 | 0.246273 | − | 0.969201i | \(-0.420794\pi\) | ||||
0.246273 | + | 0.969201i | \(0.420794\pi\) | |||||||
\(158\) | −3.41421 | −0.271620 | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 1.58579 | 0.125367 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 12.0711 | 0.948393 | ||||||||
\(163\) | 3.92893 | 0.307738 | 0.153869 | − | 0.988091i | \(-0.450827\pi\) | ||||
0.153869 | + | 0.988091i | \(0.450827\pi\) | |||||||
\(164\) | −12.1421 | −0.948141 | ||||||||
\(165\) | −0.585786 | −0.0456034 | ||||||||
\(166\) | −22.3137 | −1.73188 | ||||||||
\(167\) | 13.0711 | 1.01147 | 0.505735 | − | 0.862689i | \(-0.331221\pi\) | ||||
0.505735 | + | 0.862689i | \(0.331221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.97056 | −0.613120 | ||||||||
\(170\) | 9.65685 | 0.740647 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 30.8995 | 2.35606 | ||||||||
\(173\) | −7.31371 | −0.556051 | −0.278025 | − | 0.960574i | \(-0.589680\pi\) | ||||
−0.278025 | + | 0.960574i | \(0.589680\pi\) | |||||||
\(174\) | 22.4853 | 1.70460 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.24264 | −0.0936676 | ||||||||
\(177\) | 9.65685 | 0.725854 | ||||||||
\(178\) | 27.5563 | 2.06544 | ||||||||
\(179\) | 17.7990 | 1.33036 | 0.665179 | − | 0.746684i | \(-0.268355\pi\) | ||||
0.665179 | + | 0.746684i | \(0.268355\pi\) | |||||||
\(180\) | −3.82843 | −0.285354 | ||||||||
\(181\) | 9.89949 | 0.735824 | 0.367912 | − | 0.929861i | \(-0.380073\pi\) | ||||
0.367912 | + | 0.929861i | \(0.380073\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.7279 | 1.23656 | ||||||||
\(184\) | 24.6569 | 1.81773 | ||||||||
\(185\) | 9.07107 | 0.666918 | ||||||||
\(186\) | 21.3137 | 1.56280 | ||||||||
\(187\) | 1.65685 | 0.121161 | ||||||||
\(188\) | −16.8995 | −1.23252 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.41421 | 0.175145 | ||||||||
\(191\) | 8.41421 | 0.608831 | 0.304416 | − | 0.952539i | \(-0.401539\pi\) | ||||
0.304416 | + | 0.952539i | \(0.401539\pi\) | |||||||
\(192\) | −13.8995 | −1.00311 | ||||||||
\(193\) | 7.89949 | 0.568618 | 0.284309 | − | 0.958733i | \(-0.408236\pi\) | ||||
0.284309 | + | 0.958733i | \(0.408236\pi\) | |||||||
\(194\) | 7.65685 | 0.549730 | ||||||||
\(195\) | −3.17157 | −0.227121 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.51472 | 0.321660 | 0.160830 | − | 0.986982i | \(-0.448583\pi\) | ||||
0.160830 | + | 0.986982i | \(0.448583\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | 16.0711 | 1.13925 | 0.569624 | − | 0.821905i | \(-0.307089\pi\) | ||||
0.569624 | + | 0.821905i | \(0.307089\pi\) | |||||||
\(200\) | 17.6569 | 1.24853 | ||||||||
\(201\) | 1.65685 | 0.116865 | ||||||||
\(202\) | −44.2132 | −3.11083 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −21.6569 | −1.51628 | ||||||||
\(205\) | −3.17157 | −0.221512 | ||||||||
\(206\) | 14.4853 | 1.00924 | ||||||||
\(207\) | 5.58579 | 0.388239 | ||||||||
\(208\) | −6.72792 | −0.466497 | ||||||||
\(209\) | 0.414214 | 0.0286518 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.17157 | −0.0806544 | −0.0403272 | − | 0.999187i | \(-0.512840\pi\) | ||||
−0.0403272 | + | 0.999187i | \(0.512840\pi\) | |||||||
\(212\) | −16.2426 | −1.11555 | ||||||||
\(213\) | −20.1421 | −1.38012 | ||||||||
\(214\) | 33.5563 | 2.29386 | ||||||||
\(215\) | 8.07107 | 0.550442 | ||||||||
\(216\) | 24.9706 | 1.69903 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 23.3137 | 1.57900 | ||||||||
\(219\) | 21.4142 | 1.44704 | ||||||||
\(220\) | −1.58579 | −0.106914 | ||||||||
\(221\) | 8.97056 | 0.603425 | ||||||||
\(222\) | −30.9706 | −2.07861 | ||||||||
\(223\) | 2.24264 | 0.150178 | 0.0750892 | − | 0.997177i | \(-0.476076\pi\) | ||||
0.0750892 | + | 0.997177i | \(0.476076\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.00000 | 0.266667 | ||||||||
\(226\) | 0.585786 | 0.0389659 | ||||||||
\(227\) | −20.2426 | −1.34355 | −0.671776 | − | 0.740755i | \(-0.734468\pi\) | ||||
−0.671776 | + | 0.740755i | \(0.734468\pi\) | |||||||
\(228\) | −5.41421 | −0.358565 | ||||||||
\(229\) | 12.4853 | 0.825051 | 0.412525 | − | 0.910946i | \(-0.364647\pi\) | ||||
0.412525 | + | 0.910946i | \(0.364647\pi\) | |||||||
\(230\) | 13.4853 | 0.889193 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 29.0711 | 1.90861 | ||||||||
\(233\) | 0.485281 | 0.0317918 | 0.0158959 | − | 0.999874i | \(-0.494940\pi\) | ||||
0.0158959 | + | 0.999874i | \(0.494940\pi\) | |||||||
\(234\) | −5.41421 | −0.353938 | ||||||||
\(235\) | −4.41421 | −0.287952 | ||||||||
\(236\) | 26.1421 | 1.70171 | ||||||||
\(237\) | 2.00000 | 0.129914 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.00000 | 0.129369 | 0.0646846 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646846 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(240\) | 4.24264 | 0.273861 | ||||||||
\(241\) | −26.0416 | −1.67749 | −0.838744 | − | 0.544525i | \(-0.816710\pi\) | ||||
−0.838744 | + | 0.544525i | \(0.816710\pi\) | |||||||
\(242\) | 26.1421 | 1.68048 | ||||||||
\(243\) | 9.89949 | 0.635053 | ||||||||
\(244\) | 45.2843 | 2.89903 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.8284 | 0.690395 | ||||||||
\(247\) | 2.24264 | 0.142696 | ||||||||
\(248\) | 27.5563 | 1.74983 | ||||||||
\(249\) | 13.0711 | 0.828345 | ||||||||
\(250\) | 21.7279 | 1.37419 | ||||||||
\(251\) | −13.7279 | −0.866499 | −0.433249 | − | 0.901274i | \(-0.642633\pi\) | ||||
−0.433249 | + | 0.901274i | \(0.642633\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.31371 | 0.145462 | ||||||||
\(254\) | −10.2426 | −0.642680 | ||||||||
\(255\) | −5.65685 | −0.354246 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 9.31371 | 0.580973 | 0.290487 | − | 0.956879i | \(-0.406183\pi\) | ||||
0.290487 | + | 0.956879i | \(0.406183\pi\) | |||||||
\(258\) | −27.5563 | −1.71558 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8.58579 | −0.532468 | ||||||||
\(261\) | 6.58579 | 0.407650 | ||||||||
\(262\) | −8.48528 | −0.524222 | ||||||||
\(263\) | 16.4853 | 1.01653 | 0.508263 | − | 0.861202i | \(-0.330288\pi\) | ||||
0.508263 | + | 0.861202i | \(0.330288\pi\) | |||||||
\(264\) | 2.58579 | 0.159144 | ||||||||
\(265\) | −4.24264 | −0.260623 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.1421 | −0.987883 | ||||||||
\(268\) | 4.48528 | 0.273982 | ||||||||
\(269\) | −4.00000 | −0.243884 | −0.121942 | − | 0.992537i | \(-0.538912\pi\) | ||||
−0.121942 | + | 0.992537i | \(0.538912\pi\) | |||||||
\(270\) | 13.6569 | 0.831130 | ||||||||
\(271\) | −15.2426 | −0.925924 | −0.462962 | − | 0.886378i | \(-0.653213\pi\) | ||||
−0.462962 | + | 0.886378i | \(0.653213\pi\) | |||||||
\(272\) | −12.0000 | −0.727607 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 47.8701 | 2.89194 | ||||||||
\(275\) | 1.65685 | 0.0999121 | ||||||||
\(276\) | −30.2426 | −1.82039 | ||||||||
\(277\) | −22.4558 | −1.34924 | −0.674620 | − | 0.738165i | \(-0.735693\pi\) | ||||
−0.674620 | + | 0.738165i | \(0.735693\pi\) | |||||||
\(278\) | 14.6569 | 0.879060 | ||||||||
\(279\) | 6.24264 | 0.373737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.2426 | −1.68481 | −0.842407 | − | 0.538841i | \(-0.818862\pi\) | ||||
−0.842407 | + | 0.538841i | \(0.818862\pi\) | |||||||
\(282\) | 15.0711 | 0.897469 | ||||||||
\(283\) | 30.0711 | 1.78754 | 0.893770 | − | 0.448526i | \(-0.148051\pi\) | ||||
0.893770 | + | 0.448526i | \(0.148051\pi\) | |||||||
\(284\) | −54.5269 | −3.23558 | ||||||||
\(285\) | −1.41421 | −0.0837708 | ||||||||
\(286\) | −2.24264 | −0.132610 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.58579 | −0.0934434 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 15.8995 | 0.933650 | ||||||||
\(291\) | −4.48528 | −0.262932 | ||||||||
\(292\) | 57.9706 | 3.39247 | ||||||||
\(293\) | 3.17157 | 0.185285 | 0.0926426 | − | 0.995699i | \(-0.470469\pi\) | ||||
0.0926426 | + | 0.995699i | \(0.470469\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.82843 | 0.397566 | ||||||||
\(296\) | −40.0416 | −2.32737 | ||||||||
\(297\) | 2.34315 | 0.135963 | ||||||||
\(298\) | 0.414214 | 0.0239947 | ||||||||
\(299\) | 12.5269 | 0.724450 | ||||||||
\(300\) | −21.6569 | −1.25036 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 41.7990 | 2.40526 | ||||||||
\(303\) | 25.8995 | 1.48789 | ||||||||
\(304\) | −3.00000 | −0.172062 | ||||||||
\(305\) | 11.8284 | 0.677294 | ||||||||
\(306\) | −9.65685 | −0.552046 | ||||||||
\(307\) | 29.3137 | 1.67302 | 0.836511 | − | 0.547950i | \(-0.184592\pi\) | ||||
0.836511 | + | 0.547950i | \(0.184592\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.48528 | −0.482711 | ||||||||
\(310\) | 15.0711 | 0.855979 | ||||||||
\(311\) | −23.7990 | −1.34952 | −0.674758 | − | 0.738039i | \(-0.735752\pi\) | ||||
−0.674758 | + | 0.738039i | \(0.735752\pi\) | |||||||
\(312\) | 14.0000 | 0.792594 | ||||||||
\(313\) | −6.65685 | −0.376268 | −0.188134 | − | 0.982143i | \(-0.560244\pi\) | ||||
−0.188134 | + | 0.982143i | \(0.560244\pi\) | |||||||
\(314\) | −14.8995 | −0.840827 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.41421 | 0.304573 | ||||||||
\(317\) | −20.2426 | −1.13694 | −0.568470 | − | 0.822704i | \(-0.692464\pi\) | ||||
−0.568470 | + | 0.822704i | \(0.692464\pi\) | |||||||
\(318\) | 14.4853 | 0.812294 | ||||||||
\(319\) | 2.72792 | 0.152734 | ||||||||
\(320\) | −9.82843 | −0.549426 | ||||||||
\(321\) | −19.6569 | −1.09714 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.00000 | 0.222566 | ||||||||
\(324\) | −19.1421 | −1.06345 | ||||||||
\(325\) | 8.97056 | 0.497597 | ||||||||
\(326\) | −9.48528 | −0.525341 | ||||||||
\(327\) | −13.6569 | −0.755226 | ||||||||
\(328\) | 14.0000 | 0.773021 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.41421 | 0.0778499 | ||||||||
\(331\) | −31.4558 | −1.72897 | −0.864485 | − | 0.502659i | \(-0.832355\pi\) | ||||
−0.864485 | + | 0.502659i | \(0.832355\pi\) | |||||||
\(332\) | 35.3848 | 1.94199 | ||||||||
\(333\) | −9.07107 | −0.497091 | ||||||||
\(334\) | −31.5563 | −1.72669 | ||||||||
\(335\) | 1.17157 | 0.0640099 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.5563 | 1.06530 | 0.532651 | − | 0.846335i | \(-0.321196\pi\) | ||||
0.532651 | + | 0.846335i | \(0.321196\pi\) | |||||||
\(338\) | 19.2426 | 1.04666 | ||||||||
\(339\) | −0.343146 | −0.0186371 | ||||||||
\(340\) | −15.3137 | −0.830502 | ||||||||
\(341\) | 2.58579 | 0.140028 | ||||||||
\(342\) | −2.41421 | −0.130546 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −35.6274 | −1.92090 | ||||||||
\(345\) | −7.89949 | −0.425295 | ||||||||
\(346\) | 17.6569 | 0.949238 | ||||||||
\(347\) | 27.0416 | 1.45167 | 0.725835 | − | 0.687868i | \(-0.241453\pi\) | ||||
0.725835 | + | 0.687868i | \(0.241453\pi\) | |||||||
\(348\) | −35.6569 | −1.91141 | ||||||||
\(349\) | 4.48528 | 0.240092 | 0.120046 | − | 0.992768i | \(-0.461696\pi\) | ||||
0.120046 | + | 0.992768i | \(0.461696\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.6863 | 0.677144 | ||||||||
\(352\) | −0.656854 | −0.0350104 | ||||||||
\(353\) | 0.485281 | 0.0258289 | 0.0129145 | − | 0.999917i | \(-0.495889\pi\) | ||||
0.0129145 | + | 0.999917i | \(0.495889\pi\) | |||||||
\(354\) | −23.3137 | −1.23911 | ||||||||
\(355\) | −14.2426 | −0.755921 | ||||||||
\(356\) | −43.6985 | −2.31602 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −42.9706 | −2.27106 | ||||||||
\(359\) | 5.24264 | 0.276696 | 0.138348 | − | 0.990384i | \(-0.455821\pi\) | ||||
0.138348 | + | 0.990384i | \(0.455821\pi\) | |||||||
\(360\) | 4.41421 | 0.232649 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −23.8995 | −1.25613 | ||||||||
\(363\) | −15.3137 | −0.803761 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.1421 | 0.792576 | ||||||||
\(366\) | −40.3848 | −2.11095 | ||||||||
\(367\) | −24.3431 | −1.27070 | −0.635351 | − | 0.772224i | \(-0.719145\pi\) | ||||
−0.635351 | + | 0.772224i | \(0.719145\pi\) | |||||||
\(368\) | −16.7574 | −0.873538 | ||||||||
\(369\) | 3.17157 | 0.165105 | ||||||||
\(370\) | −21.8995 | −1.13850 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −33.7990 | −1.75240 | ||||||||
\(373\) | 11.3137 | 0.585802 | 0.292901 | − | 0.956143i | \(-0.405379\pi\) | ||||
0.292901 | + | 0.956143i | \(0.405379\pi\) | |||||||
\(374\) | −4.00000 | −0.206835 | ||||||||
\(375\) | −12.7279 | −0.657267 | ||||||||
\(376\) | 19.4853 | 1.00488 | ||||||||
\(377\) | 14.7696 | 0.760671 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.24264 | 0.217930 | 0.108965 | − | 0.994046i | \(-0.465246\pi\) | ||||
0.108965 | + | 0.994046i | \(0.465246\pi\) | |||||||
\(380\) | −3.82843 | −0.196394 | ||||||||
\(381\) | 6.00000 | 0.307389 | ||||||||
\(382\) | −20.3137 | −1.03934 | ||||||||
\(383\) | 19.7574 | 1.00955 | 0.504777 | − | 0.863250i | \(-0.331575\pi\) | ||||
0.504777 | + | 0.863250i | \(0.331575\pi\) | |||||||
\(384\) | 29.0711 | 1.48353 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −19.0711 | −0.970692 | ||||||||
\(387\) | −8.07107 | −0.410275 | ||||||||
\(388\) | −12.1421 | −0.616424 | ||||||||
\(389\) | −11.5147 | −0.583819 | −0.291910 | − | 0.956446i | \(-0.594291\pi\) | ||||
−0.291910 | + | 0.956446i | \(0.594291\pi\) | |||||||
\(390\) | 7.65685 | 0.387720 | ||||||||
\(391\) | 22.3431 | 1.12994 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.97056 | 0.250732 | ||||||||
\(394\) | −10.8995 | −0.549109 | ||||||||
\(395\) | 1.41421 | 0.0711568 | ||||||||
\(396\) | 1.58579 | 0.0796888 | ||||||||
\(397\) | −8.62742 | −0.432998 | −0.216499 | − | 0.976283i | \(-0.569464\pi\) | ||||
−0.216499 | + | 0.976283i | \(0.569464\pi\) | |||||||
\(398\) | −38.7990 | −1.94482 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.0000 | −0.600000 | ||||||||
\(401\) | 0.485281 | 0.0242338 | 0.0121169 | − | 0.999927i | \(-0.496143\pi\) | ||||
0.0121169 | + | 0.999927i | \(0.496143\pi\) | |||||||
\(402\) | −4.00000 | −0.199502 | ||||||||
\(403\) | 14.0000 | 0.697390 | ||||||||
\(404\) | 70.1127 | 3.48824 | ||||||||
\(405\) | −5.00000 | −0.248452 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.75736 | −0.186245 | ||||||||
\(408\) | 24.9706 | 1.23623 | ||||||||
\(409\) | −2.68629 | −0.132829 | −0.0664143 | − | 0.997792i | \(-0.521156\pi\) | ||||
−0.0664143 | + | 0.997792i | \(0.521156\pi\) | |||||||
\(410\) | 7.65685 | 0.378145 | ||||||||
\(411\) | −28.0416 | −1.38319 | ||||||||
\(412\) | −22.9706 | −1.13168 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −13.4853 | −0.662765 | ||||||||
\(415\) | 9.24264 | 0.453703 | ||||||||
\(416\) | −3.55635 | −0.174364 | ||||||||
\(417\) | −8.58579 | −0.420448 | ||||||||
\(418\) | −1.00000 | −0.0489116 | ||||||||
\(419\) | 6.07107 | 0.296591 | 0.148296 | − | 0.988943i | \(-0.452621\pi\) | ||||
0.148296 | + | 0.988943i | \(0.452621\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.2132 | −1.81366 | −0.906830 | − | 0.421496i | \(-0.861505\pi\) | ||||
−0.906830 | + | 0.421496i | \(0.861505\pi\) | |||||||
\(422\) | 2.82843 | 0.137686 | ||||||||
\(423\) | 4.41421 | 0.214626 | ||||||||
\(424\) | 18.7279 | 0.909508 | ||||||||
\(425\) | 16.0000 | 0.776114 | ||||||||
\(426\) | 48.6274 | 2.35601 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −53.2132 | −2.57216 | ||||||||
\(429\) | 1.31371 | 0.0634264 | ||||||||
\(430\) | −19.4853 | −0.939664 | ||||||||
\(431\) | −10.0416 | −0.483688 | −0.241844 | − | 0.970315i | \(-0.577752\pi\) | ||||
−0.241844 | + | 0.970315i | \(0.577752\pi\) | |||||||
\(432\) | −16.9706 | −0.816497 | ||||||||
\(433\) | 28.0000 | 1.34559 | 0.672797 | − | 0.739827i | \(-0.265093\pi\) | ||||
0.672797 | + | 0.739827i | \(0.265093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.31371 | −0.446558 | ||||||||
\(436\) | −36.9706 | −1.77057 | ||||||||
\(437\) | 5.58579 | 0.267204 | ||||||||
\(438\) | −51.6985 | −2.47025 | ||||||||
\(439\) | −24.4853 | −1.16862 | −0.584309 | − | 0.811531i | \(-0.698635\pi\) | ||||
−0.584309 | + | 0.811531i | \(0.698635\pi\) | |||||||
\(440\) | 1.82843 | 0.0871668 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21.6569 | −1.03011 | ||||||||
\(443\) | 17.6569 | 0.838902 | 0.419451 | − | 0.907778i | \(-0.362223\pi\) | ||||
0.419451 | + | 0.907778i | \(0.362223\pi\) | |||||||
\(444\) | 49.1127 | 2.33079 | ||||||||
\(445\) | −11.4142 | −0.541086 | ||||||||
\(446\) | −5.41421 | −0.256370 | ||||||||
\(447\) | −0.242641 | −0.0114765 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.65685 | 0.455735 | 0.227868 | − | 0.973692i | \(-0.426825\pi\) | ||||
0.227868 | + | 0.973692i | \(0.426825\pi\) | |||||||
\(450\) | −9.65685 | −0.455228 | ||||||||
\(451\) | 1.31371 | 0.0618601 | ||||||||
\(452\) | −0.928932 | −0.0436933 | ||||||||
\(453\) | −24.4853 | −1.15042 | ||||||||
\(454\) | 48.8701 | 2.29359 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.24264 | 0.292338 | ||||||||
\(457\) | −7.82843 | −0.366198 | −0.183099 | − | 0.983094i | \(-0.558613\pi\) | ||||
−0.183099 | + | 0.983094i | \(0.558613\pi\) | |||||||
\(458\) | −30.1421 | −1.40845 | ||||||||
\(459\) | 22.6274 | 1.05616 | ||||||||
\(460\) | −21.3848 | −0.997070 | ||||||||
\(461\) | 29.9706 | 1.39587 | 0.697934 | − | 0.716162i | \(-0.254103\pi\) | ||||
0.697934 | + | 0.716162i | \(0.254103\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.07107 | −0.189199 | −0.0945993 | − | 0.995515i | \(-0.530157\pi\) | ||||
−0.0945993 | + | 0.995515i | \(0.530157\pi\) | |||||||
\(464\) | −19.7574 | −0.917212 | ||||||||
\(465\) | −8.82843 | −0.409409 | ||||||||
\(466\) | −1.17157 | −0.0542721 | ||||||||
\(467\) | 19.1005 | 0.883866 | 0.441933 | − | 0.897048i | \(-0.354293\pi\) | ||||
0.441933 | + | 0.897048i | \(0.354293\pi\) | |||||||
\(468\) | 8.58579 | 0.396878 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10.6569 | 0.491564 | ||||||||
\(471\) | 8.72792 | 0.402161 | ||||||||
\(472\) | −30.1421 | −1.38740 | ||||||||
\(473\) | −3.34315 | −0.153718 | ||||||||
\(474\) | −4.82843 | −0.221777 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.24264 | 0.194257 | ||||||||
\(478\) | −4.82843 | −0.220847 | ||||||||
\(479\) | −25.3848 | −1.15986 | −0.579930 | − | 0.814666i | \(-0.696920\pi\) | ||||
−0.579930 | + | 0.814666i | \(0.696920\pi\) | |||||||
\(480\) | 2.24264 | 0.102362 | ||||||||
\(481\) | −20.3431 | −0.927568 | ||||||||
\(482\) | 62.8701 | 2.86365 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −41.4558 | −1.88436 | ||||||||
\(485\) | −3.17157 | −0.144014 | ||||||||
\(486\) | −23.8995 | −1.08410 | ||||||||
\(487\) | 15.1716 | 0.687490 | 0.343745 | − | 0.939063i | \(-0.388304\pi\) | ||||
0.343745 | + | 0.939063i | \(0.388304\pi\) | |||||||
\(488\) | −52.2132 | −2.36358 | ||||||||
\(489\) | 5.55635 | 0.251267 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.44365 | −0.0651510 | −0.0325755 | − | 0.999469i | \(-0.510371\pi\) | ||||
−0.0325755 | + | 0.999469i | \(0.510371\pi\) | |||||||
\(492\) | −17.1716 | −0.774154 | ||||||||
\(493\) | 26.3431 | 1.18644 | ||||||||
\(494\) | −5.41421 | −0.243597 | ||||||||
\(495\) | 0.414214 | 0.0186175 | ||||||||
\(496\) | −18.7279 | −0.840909 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −31.5563 | −1.41407 | ||||||||
\(499\) | 34.5563 | 1.54695 | 0.773477 | − | 0.633824i | \(-0.218516\pi\) | ||||
0.773477 | + | 0.633824i | \(0.218516\pi\) | |||||||
\(500\) | −34.4558 | −1.54091 | ||||||||
\(501\) | 18.4853 | 0.825861 | ||||||||
\(502\) | 33.1421 | 1.47921 | ||||||||
\(503\) | −29.0416 | −1.29490 | −0.647451 | − | 0.762107i | \(-0.724165\pi\) | ||||
−0.647451 | + | 0.762107i | \(0.724165\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.3137 | 0.814949 | ||||||||
\(506\) | −5.58579 | −0.248318 | ||||||||
\(507\) | −11.2721 | −0.500611 | ||||||||
\(508\) | 16.2426 | 0.720651 | ||||||||
\(509\) | −14.9706 | −0.663559 | −0.331779 | − | 0.943357i | \(-0.607649\pi\) | ||||
−0.331779 | + | 0.943357i | \(0.607649\pi\) | |||||||
\(510\) | 13.6569 | 0.604736 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | 5.65685 | 0.249756 | ||||||||
\(514\) | −22.4853 | −0.991783 | ||||||||
\(515\) | −6.00000 | −0.264392 | ||||||||
\(516\) | 43.6985 | 1.92372 | ||||||||
\(517\) | 1.82843 | 0.0804141 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.3431 | −0.454014 | ||||||||
\(520\) | 9.89949 | 0.434122 | ||||||||
\(521\) | 41.5563 | 1.82062 | 0.910308 | − | 0.413931i | \(-0.135844\pi\) | ||||
0.910308 | + | 0.413931i | \(0.135844\pi\) | |||||||
\(522\) | −15.8995 | −0.695902 | ||||||||
\(523\) | −12.3431 | −0.539728 | −0.269864 | − | 0.962898i | \(-0.586979\pi\) | ||||
−0.269864 | + | 0.962898i | \(0.586979\pi\) | |||||||
\(524\) | 13.4558 | 0.587821 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −39.7990 | −1.73532 | ||||||||
\(527\) | 24.9706 | 1.08773 | ||||||||
\(528\) | −1.75736 | −0.0764792 | ||||||||
\(529\) | 8.20101 | 0.356566 | ||||||||
\(530\) | 10.2426 | 0.444912 | ||||||||
\(531\) | −6.82843 | −0.296328 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.11270 | 0.308085 | ||||||||
\(534\) | 38.9706 | 1.68642 | ||||||||
\(535\) | −13.8995 | −0.600928 | ||||||||
\(536\) | −5.17157 | −0.223378 | ||||||||
\(537\) | 25.1716 | 1.08623 | ||||||||
\(538\) | 9.65685 | 0.416337 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −21.6569 | −0.931963 | ||||||||
\(541\) | −23.1421 | −0.994958 | −0.497479 | − | 0.867476i | \(-0.665741\pi\) | ||||
−0.497479 | + | 0.867476i | \(0.665741\pi\) | |||||||
\(542\) | 36.7990 | 1.58065 | ||||||||
\(543\) | 14.0000 | 0.600798 | ||||||||
\(544\) | −6.34315 | −0.271960 | ||||||||
\(545\) | −9.65685 | −0.413654 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.55635 | −0.0665447 | −0.0332723 | − | 0.999446i | \(-0.510593\pi\) | ||||
−0.0332723 | + | 0.999446i | \(0.510593\pi\) | |||||||
\(548\) | −75.9117 | −3.24279 | ||||||||
\(549\) | −11.8284 | −0.504825 | ||||||||
\(550\) | −4.00000 | −0.170561 | ||||||||
\(551\) | 6.58579 | 0.280564 | ||||||||
\(552\) | 34.8701 | 1.48417 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 54.2132 | 2.30330 | ||||||||
\(555\) | 12.8284 | 0.544536 | ||||||||
\(556\) | −23.2426 | −0.985708 | ||||||||
\(557\) | 15.8284 | 0.670672 | 0.335336 | − | 0.942099i | \(-0.391150\pi\) | ||||
0.335336 | + | 0.942099i | \(0.391150\pi\) | |||||||
\(558\) | −15.0711 | −0.638009 | ||||||||
\(559\) | −18.1005 | −0.765570 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.34315 | 0.0989277 | ||||||||
\(562\) | 68.1838 | 2.87616 | ||||||||
\(563\) | 5.89949 | 0.248634 | 0.124317 | − | 0.992243i | \(-0.460326\pi\) | ||||
0.124317 | + | 0.992243i | \(0.460326\pi\) | |||||||
\(564\) | −23.8995 | −1.00635 | ||||||||
\(565\) | −0.242641 | −0.0102080 | ||||||||
\(566\) | −72.5980 | −3.05152 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 62.8701 | 2.63797 | ||||||||
\(569\) | −9.02944 | −0.378534 | −0.189267 | − | 0.981926i | \(-0.560611\pi\) | ||||
−0.189267 | + | 0.981926i | \(0.560611\pi\) | |||||||
\(570\) | 3.41421 | 0.143006 | ||||||||
\(571\) | 0.899495 | 0.0376427 | 0.0188213 | − | 0.999823i | \(-0.494009\pi\) | ||||
0.0188213 | + | 0.999823i | \(0.494009\pi\) | |||||||
\(572\) | 3.55635 | 0.148698 | ||||||||
\(573\) | 11.8995 | 0.497109 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.3431 | 0.931774 | ||||||||
\(576\) | 9.82843 | 0.409518 | ||||||||
\(577\) | −5.97056 | −0.248558 | −0.124279 | − | 0.992247i | \(-0.539662\pi\) | ||||
−0.124279 | + | 0.992247i | \(0.539662\pi\) | |||||||
\(578\) | 2.41421 | 0.100418 | ||||||||
\(579\) | 11.1716 | 0.464275 | ||||||||
\(580\) | −25.2132 | −1.04692 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.8284 | 0.448853 | ||||||||
\(583\) | 1.75736 | 0.0727824 | ||||||||
\(584\) | −66.8406 | −2.76588 | ||||||||
\(585\) | 2.24264 | 0.0927218 | ||||||||
\(586\) | −7.65685 | −0.316302 | ||||||||
\(587\) | 14.0000 | 0.577842 | 0.288921 | − | 0.957353i | \(-0.406704\pi\) | ||||
0.288921 | + | 0.957353i | \(0.406704\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.24264 | 0.257224 | ||||||||
\(590\) | −16.4853 | −0.678688 | ||||||||
\(591\) | 6.38478 | 0.262635 | ||||||||
\(592\) | 27.2132 | 1.11846 | ||||||||
\(593\) | 11.8284 | 0.485735 | 0.242868 | − | 0.970059i | \(-0.421912\pi\) | ||||
0.242868 | + | 0.970059i | \(0.421912\pi\) | |||||||
\(594\) | −5.65685 | −0.232104 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.656854 | −0.0269058 | ||||||||
\(597\) | 22.7279 | 0.930192 | ||||||||
\(598\) | −30.2426 | −1.23671 | ||||||||
\(599\) | 27.6985 | 1.13173 | 0.565865 | − | 0.824498i | \(-0.308542\pi\) | ||||
0.565865 | + | 0.824498i | \(0.308542\pi\) | |||||||
\(600\) | 24.9706 | 1.01942 | ||||||||
\(601\) | −34.7279 | −1.41658 | −0.708291 | − | 0.705921i | \(-0.750533\pi\) | ||||
−0.708291 | + | 0.705921i | \(0.750533\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.17157 | −0.0477101 | ||||||||
\(604\) | −66.2843 | −2.69707 | ||||||||
\(605\) | −10.8284 | −0.440238 | ||||||||
\(606\) | −62.5269 | −2.53998 | ||||||||
\(607\) | −32.5269 | −1.32023 | −0.660113 | − | 0.751166i | \(-0.729492\pi\) | ||||
−0.660113 | + | 0.751166i | \(0.729492\pi\) | |||||||
\(608\) | −1.58579 | −0.0643121 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −28.5563 | −1.15621 | ||||||||
\(611\) | 9.89949 | 0.400491 | ||||||||
\(612\) | 15.3137 | 0.619020 | ||||||||
\(613\) | −31.3137 | −1.26475 | −0.632374 | − | 0.774663i | \(-0.717920\pi\) | ||||
−0.632374 | + | 0.774663i | \(0.717920\pi\) | |||||||
\(614\) | −70.7696 | −2.85603 | ||||||||
\(615\) | −4.48528 | −0.180864 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.45584 | 0.340419 | 0.170210 | − | 0.985408i | \(-0.445555\pi\) | ||||
0.170210 | + | 0.985408i | \(0.445555\pi\) | |||||||
\(618\) | 20.4853 | 0.824039 | ||||||||
\(619\) | 34.5563 | 1.38894 | 0.694468 | − | 0.719523i | \(-0.255640\pi\) | ||||
0.694468 | + | 0.719523i | \(0.255640\pi\) | |||||||
\(620\) | −23.8995 | −0.959827 | ||||||||
\(621\) | 31.5980 | 1.26798 | ||||||||
\(622\) | 57.4558 | 2.30377 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −9.51472 | −0.380894 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 16.0711 | 0.642329 | ||||||||
\(627\) | 0.585786 | 0.0233941 | ||||||||
\(628\) | 23.6274 | 0.942837 | ||||||||
\(629\) | −36.2843 | −1.44675 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.5563 | −1.45529 | −0.727643 | − | 0.685956i | \(-0.759384\pi\) | ||||
−0.727643 | + | 0.685956i | \(0.759384\pi\) | |||||||
\(632\) | −6.24264 | −0.248319 | ||||||||
\(633\) | −1.65685 | −0.0658540 | ||||||||
\(634\) | 48.8701 | 1.94088 | ||||||||
\(635\) | 4.24264 | 0.168364 | ||||||||
\(636\) | −22.9706 | −0.910842 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.58579 | −0.260734 | ||||||||
\(639\) | 14.2426 | 0.563430 | ||||||||
\(640\) | 20.5563 | 0.812561 | ||||||||
\(641\) | −35.7990 | −1.41398 | −0.706988 | − | 0.707226i | \(-0.749946\pi\) | ||||
−0.706988 | + | 0.707226i | \(0.749946\pi\) | |||||||
\(642\) | 47.4558 | 1.87293 | ||||||||
\(643\) | 1.85786 | 0.0732670 | 0.0366335 | − | 0.999329i | \(-0.488337\pi\) | ||||
0.0366335 | + | 0.999329i | \(0.488337\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.4142 | 0.449434 | ||||||||
\(646\) | −9.65685 | −0.379944 | ||||||||
\(647\) | −36.2132 | −1.42369 | −0.711844 | − | 0.702338i | \(-0.752140\pi\) | ||||
−0.711844 | + | 0.702338i | \(0.752140\pi\) | |||||||
\(648\) | 22.0711 | 0.867033 | ||||||||
\(649\) | −2.82843 | −0.111025 | ||||||||
\(650\) | −21.6569 | −0.849452 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.0416 | 0.589076 | ||||||||
\(653\) | −30.1421 | −1.17955 | −0.589776 | − | 0.807567i | \(-0.700784\pi\) | ||||
−0.589776 | + | 0.807567i | \(0.700784\pi\) | |||||||
\(654\) | 32.9706 | 1.28925 | ||||||||
\(655\) | 3.51472 | 0.137331 | ||||||||
\(656\) | −9.51472 | −0.371487 | ||||||||
\(657\) | −15.1421 | −0.590751 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.0416 | 0.391166 | 0.195583 | − | 0.980687i | \(-0.437340\pi\) | ||||
0.195583 | + | 0.980687i | \(0.437340\pi\) | |||||||
\(660\) | −2.24264 | −0.0872947 | ||||||||
\(661\) | 2.72792 | 0.106104 | 0.0530519 | − | 0.998592i | \(-0.483105\pi\) | ||||
0.0530519 | + | 0.998592i | \(0.483105\pi\) | |||||||
\(662\) | 75.9411 | 2.95154 | ||||||||
\(663\) | 12.6863 | 0.492695 | ||||||||
\(664\) | −40.7990 | −1.58331 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 21.8995 | 0.848588 | ||||||||
\(667\) | 36.7868 | 1.42439 | ||||||||
\(668\) | 50.0416 | 1.93617 | ||||||||
\(669\) | 3.17157 | 0.122620 | ||||||||
\(670\) | −2.82843 | −0.109272 | ||||||||
\(671\) | −4.89949 | −0.189143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.79899 | −0.146440 | −0.0732201 | − | 0.997316i | \(-0.523328\pi\) | ||||
−0.0732201 | + | 0.997316i | \(0.523328\pi\) | |||||||
\(674\) | −47.2132 | −1.81858 | ||||||||
\(675\) | 22.6274 | 0.870930 | ||||||||
\(676\) | −30.5147 | −1.17364 | ||||||||
\(677\) | 23.3137 | 0.896019 | 0.448009 | − | 0.894029i | \(-0.352133\pi\) | ||||
0.448009 | + | 0.894029i | \(0.352133\pi\) | |||||||
\(678\) | 0.828427 | 0.0318156 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 17.6569 | 0.677109 | ||||||||
\(681\) | −28.6274 | −1.09701 | ||||||||
\(682\) | −6.24264 | −0.239043 | ||||||||
\(683\) | −6.48528 | −0.248152 | −0.124076 | − | 0.992273i | \(-0.539597\pi\) | ||||
−0.124076 | + | 0.992273i | \(0.539597\pi\) | |||||||
\(684\) | 3.82843 | 0.146384 | ||||||||
\(685\) | −19.8284 | −0.757605 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.6569 | 0.673651 | ||||||||
\(688\) | 24.2132 | 0.923120 | ||||||||
\(689\) | 9.51472 | 0.362482 | ||||||||
\(690\) | 19.0711 | 0.726023 | ||||||||
\(691\) | 30.9706 | 1.17818 | 0.589088 | − | 0.808069i | \(-0.299487\pi\) | ||||
0.589088 | + | 0.808069i | \(0.299487\pi\) | |||||||
\(692\) | −28.0000 | −1.06440 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −65.2843 | −2.47816 | ||||||||
\(695\) | −6.07107 | −0.230289 | ||||||||
\(696\) | 41.1127 | 1.55837 | ||||||||
\(697\) | 12.6863 | 0.480528 | ||||||||
\(698\) | −10.8284 | −0.409862 | ||||||||
\(699\) | 0.686292 | 0.0259579 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.82843 | −0.0690587 | −0.0345294 | − | 0.999404i | \(-0.510993\pi\) | ||||
−0.0345294 | + | 0.999404i | \(0.510993\pi\) | |||||||
\(702\) | −30.6274 | −1.15596 | ||||||||
\(703\) | −9.07107 | −0.342122 | ||||||||
\(704\) | 4.07107 | 0.153434 | ||||||||
\(705\) | −6.24264 | −0.235111 | ||||||||
\(706\) | −1.17157 | −0.0440927 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 36.9706 | 1.38944 | ||||||||
\(709\) | −42.9411 | −1.61269 | −0.806344 | − | 0.591447i | \(-0.798557\pi\) | ||||
−0.806344 | + | 0.591447i | \(0.798557\pi\) | |||||||
\(710\) | 34.3848 | 1.29044 | ||||||||
\(711\) | −1.41421 | −0.0530372 | ||||||||
\(712\) | 50.3848 | 1.88825 | ||||||||
\(713\) | 34.8701 | 1.30589 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.928932 | 0.0347401 | ||||||||
\(716\) | 68.1421 | 2.54659 | ||||||||
\(717\) | 2.82843 | 0.105630 | ||||||||
\(718\) | −12.6569 | −0.472350 | ||||||||
\(719\) | 52.0833 | 1.94238 | 0.971189 | − | 0.238311i | \(-0.0765937\pi\) | ||||
0.971189 | + | 0.238311i | \(0.0765937\pi\) | |||||||
\(720\) | −3.00000 | −0.111803 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.41421 | −0.0898477 | ||||||||
\(723\) | −36.8284 | −1.36966 | ||||||||
\(724\) | 37.8995 | 1.40852 | ||||||||
\(725\) | 26.3431 | 0.978360 | ||||||||
\(726\) | 36.9706 | 1.37211 | ||||||||
\(727\) | 20.0711 | 0.744395 | 0.372197 | − | 0.928154i | \(-0.378604\pi\) | ||||
0.372197 | + | 0.928154i | \(0.378604\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | −36.5563 | −1.35301 | ||||||||
\(731\) | −32.2843 | −1.19408 | ||||||||
\(732\) | 64.0416 | 2.36705 | ||||||||
\(733\) | 21.4558 | 0.792490 | 0.396245 | − | 0.918145i | \(-0.370313\pi\) | ||||
0.396245 | + | 0.918145i | \(0.370313\pi\) | |||||||
\(734\) | 58.7696 | 2.16922 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.85786 | −0.326505 | ||||||||
\(737\) | −0.485281 | −0.0178756 | ||||||||
\(738\) | −7.65685 | −0.281853 | ||||||||
\(739\) | −8.34315 | −0.306908 | −0.153454 | − | 0.988156i | \(-0.549040\pi\) | ||||
−0.153454 | + | 0.988156i | \(0.549040\pi\) | |||||||
\(740\) | 34.7279 | 1.27662 | ||||||||
\(741\) | 3.17157 | 0.116511 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.87006 | −0.105292 | −0.0526461 | − | 0.998613i | \(-0.516766\pi\) | ||||
−0.0526461 | + | 0.998613i | \(0.516766\pi\) | |||||||
\(744\) | 38.9706 | 1.42873 | ||||||||
\(745\) | −0.171573 | −0.00628594 | ||||||||
\(746\) | −27.3137 | −1.00003 | ||||||||
\(747\) | −9.24264 | −0.338171 | ||||||||
\(748\) | 6.34315 | 0.231928 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 30.7279 | 1.12203 | ||||||||
\(751\) | 9.45584 | 0.345049 | 0.172524 | − | 0.985005i | \(-0.444808\pi\) | ||||
0.172524 | + | 0.985005i | \(0.444808\pi\) | |||||||
\(752\) | −13.2426 | −0.482909 | ||||||||
\(753\) | −19.4142 | −0.707493 | ||||||||
\(754\) | −35.6569 | −1.29855 | ||||||||
\(755\) | −17.3137 | −0.630110 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.00000 | −0.181728 | −0.0908640 | − | 0.995863i | \(-0.528963\pi\) | ||||
−0.0908640 | + | 0.995863i | \(0.528963\pi\) | |||||||
\(758\) | −10.2426 | −0.372029 | ||||||||
\(759\) | 3.27208 | 0.118769 | ||||||||
\(760\) | 4.41421 | 0.160120 | ||||||||
\(761\) | −34.1127 | −1.23658 | −0.618292 | − | 0.785948i | \(-0.712175\pi\) | ||||
−0.618292 | + | 0.785948i | \(0.712175\pi\) | |||||||
\(762\) | −14.4853 | −0.524746 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 32.2132 | 1.16543 | ||||||||
\(765\) | 4.00000 | 0.144620 | ||||||||
\(766\) | −47.6985 | −1.72342 | ||||||||
\(767\) | −15.3137 | −0.552946 | ||||||||
\(768\) | −42.3848 | −1.52943 | ||||||||
\(769\) | −43.4264 | −1.56600 | −0.782998 | − | 0.622024i | \(-0.786311\pi\) | ||||
−0.782998 | + | 0.622024i | \(0.786311\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.1716 | 0.474363 | ||||||||
\(772\) | 30.2426 | 1.08846 | ||||||||
\(773\) | −34.2426 | −1.23162 | −0.615811 | − | 0.787894i | \(-0.711172\pi\) | ||||
−0.615811 | + | 0.787894i | \(0.711172\pi\) | |||||||
\(774\) | 19.4853 | 0.700384 | ||||||||
\(775\) | 24.9706 | 0.896969 | ||||||||
\(776\) | 14.0000 | 0.502571 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.7990 | 0.996642 | ||||||||
\(779\) | 3.17157 | 0.113633 | ||||||||
\(780\) | −12.1421 | −0.434758 | ||||||||
\(781\) | 5.89949 | 0.211101 | ||||||||
\(782\) | −53.9411 | −1.92893 | ||||||||
\(783\) | 37.2548 | 1.33138 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.17157 | 0.220273 | ||||||||
\(786\) | −12.0000 | −0.428026 | ||||||||
\(787\) | 41.0122 | 1.46193 | 0.730963 | − | 0.682417i | \(-0.239071\pi\) | ||||
0.730963 | + | 0.682417i | \(0.239071\pi\) | |||||||
\(788\) | 17.2843 | 0.615727 | ||||||||
\(789\) | 23.3137 | 0.829990 | ||||||||
\(790\) | −3.41421 | −0.121472 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.82843 | −0.0649703 | ||||||||
\(793\) | −26.5269 | −0.941998 | ||||||||
\(794\) | 20.8284 | 0.739173 | ||||||||
\(795\) | −6.00000 | −0.212798 | ||||||||
\(796\) | 61.5269 | 2.18076 | ||||||||
\(797\) | −30.2426 | −1.07125 | −0.535625 | − | 0.844456i | \(-0.679924\pi\) | ||||
−0.535625 | + | 0.844456i | \(0.679924\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.6569 | 0.624655 | ||||||||
\(800\) | −6.34315 | −0.224264 | ||||||||
\(801\) | 11.4142 | 0.403301 | ||||||||
\(802\) | −1.17157 | −0.0413697 | ||||||||
\(803\) | −6.27208 | −0.221337 | ||||||||
\(804\) | 6.34315 | 0.223706 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −33.7990 | −1.19052 | ||||||||
\(807\) | −5.65685 | −0.199131 | ||||||||
\(808\) | −80.8406 | −2.84396 | ||||||||
\(809\) | 31.1421 | 1.09490 | 0.547450 | − | 0.836839i | \(-0.315599\pi\) | ||||
0.547450 | + | 0.836839i | \(0.315599\pi\) | |||||||
\(810\) | 12.0711 | 0.424134 | ||||||||
\(811\) | −0.544156 | −0.0191079 | −0.00955395 | − | 0.999954i | \(-0.503041\pi\) | ||||
−0.00955395 | + | 0.999954i | \(0.503041\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.5563 | −0.756014 | ||||||||
\(814\) | 9.07107 | 0.317941 | ||||||||
\(815\) | 3.92893 | 0.137624 | ||||||||
\(816\) | −16.9706 | −0.594089 | ||||||||
\(817\) | −8.07107 | −0.282371 | ||||||||
\(818\) | 6.48528 | 0.226753 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.1421 | −0.424022 | ||||||||
\(821\) | 10.1127 | 0.352936 | 0.176468 | − | 0.984306i | \(-0.443533\pi\) | ||||
0.176468 | + | 0.984306i | \(0.443533\pi\) | |||||||
\(822\) | 67.6985 | 2.36126 | ||||||||
\(823\) | −6.21320 | −0.216579 | −0.108289 | − | 0.994119i | \(-0.534537\pi\) | ||||
−0.108289 | + | 0.994119i | \(0.534537\pi\) | |||||||
\(824\) | 26.4853 | 0.922658 | ||||||||
\(825\) | 2.34315 | 0.0815779 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.2843 | 0.427166 | 0.213583 | − | 0.976925i | \(-0.431487\pi\) | ||||
0.213583 | + | 0.976925i | \(0.431487\pi\) | |||||||
\(828\) | 21.3848 | 0.743172 | ||||||||
\(829\) | −28.2843 | −0.982353 | −0.491177 | − | 0.871060i | \(-0.663433\pi\) | ||||
−0.491177 | + | 0.871060i | \(0.663433\pi\) | |||||||
\(830\) | −22.3137 | −0.774520 | ||||||||
\(831\) | −31.7574 | −1.10165 | ||||||||
\(832\) | 22.0416 | 0.764156 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 20.7279 | 0.717749 | ||||||||
\(835\) | 13.0711 | 0.452343 | ||||||||
\(836\) | 1.58579 | 0.0548456 | ||||||||
\(837\) | 35.3137 | 1.22062 | ||||||||
\(838\) | −14.6569 | −0.506313 | ||||||||
\(839\) | −19.7990 | −0.683537 | −0.341769 | − | 0.939784i | \(-0.611026\pi\) | ||||
−0.341769 | + | 0.939784i | \(0.611026\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.3726 | 0.495606 | ||||||||
\(842\) | 89.8406 | 3.09611 | ||||||||
\(843\) | −39.9411 | −1.37565 | ||||||||
\(844\) | −4.48528 | −0.154390 | ||||||||
\(845\) | −7.97056 | −0.274196 | ||||||||
\(846\) | −10.6569 | −0.366390 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −12.7279 | −0.437079 | ||||||||
\(849\) | 42.5269 | 1.45952 | ||||||||
\(850\) | −38.6274 | −1.32491 | ||||||||
\(851\) | −50.6690 | −1.73691 | ||||||||
\(852\) | −77.1127 | −2.64184 | ||||||||
\(853\) | 43.9706 | 1.50552 | 0.752762 | − | 0.658293i | \(-0.228721\pi\) | ||||
0.752762 | + | 0.658293i | \(0.228721\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | 61.3553 | 2.09708 | ||||||||
\(857\) | −12.9706 | −0.443066 | −0.221533 | − | 0.975153i | \(-0.571106\pi\) | ||||
−0.221533 | + | 0.975153i | \(0.571106\pi\) | |||||||
\(858\) | −3.17157 | −0.108276 | ||||||||
\(859\) | −12.0711 | −0.411860 | −0.205930 | − | 0.978567i | \(-0.566022\pi\) | ||||
−0.205930 | + | 0.978567i | \(0.566022\pi\) | |||||||
\(860\) | 30.8995 | 1.05366 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.2426 | 0.825708 | ||||||||
\(863\) | 4.58579 | 0.156102 | 0.0780510 | − | 0.996949i | \(-0.475130\pi\) | ||||
0.0780510 | + | 0.996949i | \(0.475130\pi\) | |||||||
\(864\) | −8.97056 | −0.305185 | ||||||||
\(865\) | −7.31371 | −0.248674 | ||||||||
\(866\) | −67.5980 | −2.29707 | ||||||||
\(867\) | −1.41421 | −0.0480292 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.585786 | −0.0198714 | ||||||||
\(870\) | 22.4853 | 0.762322 | ||||||||
\(871\) | −2.62742 | −0.0890266 | ||||||||
\(872\) | 42.6274 | 1.44355 | ||||||||
\(873\) | 3.17157 | 0.107341 | ||||||||
\(874\) | −13.4853 | −0.456146 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 81.9828 | 2.76994 | ||||||||
\(877\) | −27.8995 | −0.942099 | −0.471050 | − | 0.882107i | \(-0.656125\pi\) | ||||
−0.471050 | + | 0.882107i | \(0.656125\pi\) | |||||||
\(878\) | 59.1127 | 1.99496 | ||||||||
\(879\) | 4.48528 | 0.151285 | ||||||||
\(880\) | −1.24264 | −0.0418894 | ||||||||
\(881\) | −52.2843 | −1.76150 | −0.880751 | − | 0.473580i | \(-0.842962\pi\) | ||||
−0.880751 | + | 0.473580i | \(0.842962\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.65685 | −0.190368 | −0.0951842 | − | 0.995460i | \(-0.530344\pi\) | ||||
−0.0951842 | + | 0.995460i | \(0.530344\pi\) | |||||||
\(884\) | 34.3431 | 1.15508 | ||||||||
\(885\) | 9.65685 | 0.324612 | ||||||||
\(886\) | −42.6274 | −1.43210 | ||||||||
\(887\) | −21.3137 | −0.715644 | −0.357822 | − | 0.933790i | \(-0.616481\pi\) | ||||
−0.357822 | + | 0.933790i | \(0.616481\pi\) | |||||||
\(888\) | −56.6274 | −1.90029 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 27.5563 | 0.923691 | ||||||||
\(891\) | 2.07107 | 0.0693834 | ||||||||
\(892\) | 8.58579 | 0.287473 | ||||||||
\(893\) | 4.41421 | 0.147716 | ||||||||
\(894\) | 0.585786 | 0.0195916 | ||||||||
\(895\) | 17.7990 | 0.594955 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.7157 | 0.591511 | ||||||||
\(898\) | −23.3137 | −0.777989 | ||||||||
\(899\) | 41.1127 | 1.37119 | ||||||||
\(900\) | 15.3137 | 0.510457 | ||||||||
\(901\) | 16.9706 | 0.565371 | ||||||||
\(902\) | −3.17157 | −0.105602 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.07107 | 0.0356232 | ||||||||
\(905\) | 9.89949 | 0.329070 | ||||||||
\(906\) | 59.1127 | 1.96389 | ||||||||
\(907\) | 31.4142 | 1.04309 | 0.521546 | − | 0.853223i | \(-0.325356\pi\) | ||||
0.521546 | + | 0.853223i | \(0.325356\pi\) | |||||||
\(908\) | −77.4975 | −2.57184 | ||||||||
\(909\) | −18.3137 | −0.607427 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.27208 | 0.307198 | 0.153599 | − | 0.988133i | \(-0.450914\pi\) | ||||
0.153599 | + | 0.988133i | \(0.450914\pi\) | |||||||
\(912\) | −4.24264 | −0.140488 | ||||||||
\(913\) | −3.82843 | −0.126702 | ||||||||
\(914\) | 18.8995 | 0.625140 | ||||||||
\(915\) | 16.7279 | 0.553008 | ||||||||
\(916\) | 47.7990 | 1.57932 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −54.6274 | −1.80297 | ||||||||
\(919\) | −19.0416 | −0.628125 | −0.314063 | − | 0.949402i | \(-0.601690\pi\) | ||||
−0.314063 | + | 0.949402i | \(0.601690\pi\) | |||||||
\(920\) | 24.6569 | 0.812912 | ||||||||
\(921\) | 41.4558 | 1.36602 | ||||||||
\(922\) | −72.3553 | −2.38290 | ||||||||
\(923\) | 31.9411 | 1.05135 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.2843 | −1.19302 | ||||||||
\(926\) | 9.82843 | 0.322982 | ||||||||
\(927\) | 6.00000 | 0.197066 | ||||||||
\(928\) | −10.4437 | −0.342830 | ||||||||
\(929\) | 15.0000 | 0.492134 | 0.246067 | − | 0.969253i | \(-0.420862\pi\) | ||||
0.246067 | + | 0.969253i | \(0.420862\pi\) | |||||||
\(930\) | 21.3137 | 0.698904 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.85786 | 0.0608564 | ||||||||
\(933\) | −33.6569 | −1.10188 | ||||||||
\(934\) | −46.1127 | −1.50885 | ||||||||
\(935\) | 1.65685 | 0.0541849 | ||||||||
\(936\) | −9.89949 | −0.323575 | ||||||||
\(937\) | −33.6863 | −1.10048 | −0.550242 | − | 0.835006i | \(-0.685464\pi\) | ||||
−0.550242 | + | 0.835006i | \(0.685464\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.41421 | −0.307221 | ||||||||
\(940\) | −16.8995 | −0.551201 | ||||||||
\(941\) | 4.04163 | 0.131753 | 0.0658767 | − | 0.997828i | \(-0.479016\pi\) | ||||
0.0658767 | + | 0.997828i | \(0.479016\pi\) | |||||||
\(942\) | −21.0711 | −0.686532 | ||||||||
\(943\) | 17.7157 | 0.576904 | ||||||||
\(944\) | 20.4853 | 0.666739 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.07107 | 0.262413 | ||||||||
\(947\) | 3.65685 | 0.118832 | 0.0594159 | − | 0.998233i | \(-0.481076\pi\) | ||||
0.0594159 | + | 0.998233i | \(0.481076\pi\) | |||||||
\(948\) | 7.65685 | 0.248683 | ||||||||
\(949\) | −33.9584 | −1.10234 | ||||||||
\(950\) | −9.65685 | −0.313310 | ||||||||
\(951\) | −28.6274 | −0.928308 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.41421 | −0.110597 | −0.0552986 | − | 0.998470i | \(-0.517611\pi\) | ||||
−0.0552986 | + | 0.998470i | \(0.517611\pi\) | |||||||
\(954\) | −10.2426 | −0.331618 | ||||||||
\(955\) | 8.41421 | 0.272278 | ||||||||
\(956\) | 7.65685 | 0.247640 | ||||||||
\(957\) | 3.85786 | 0.124707 | ||||||||
\(958\) | 61.2843 | 1.98000 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −13.8995 | −0.448604 | ||||||||
\(961\) | 7.97056 | 0.257115 | ||||||||
\(962\) | 49.1127 | 1.58346 | ||||||||
\(963\) | 13.8995 | 0.447905 | ||||||||
\(964\) | −99.6985 | −3.21107 | ||||||||
\(965\) | 7.89949 | 0.254294 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.2843 | −1.16682 | −0.583412 | − | 0.812177i | \(-0.698283\pi\) | ||||
−0.583412 | + | 0.812177i | \(0.698283\pi\) | |||||||
\(968\) | 47.7990 | 1.53632 | ||||||||
\(969\) | 5.65685 | 0.181724 | ||||||||
\(970\) | 7.65685 | 0.245847 | ||||||||
\(971\) | 26.8701 | 0.862301 | 0.431151 | − | 0.902280i | \(-0.358108\pi\) | ||||
0.431151 | + | 0.902280i | \(0.358108\pi\) | |||||||
\(972\) | 37.8995 | 1.21563 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −36.6274 | −1.17362 | ||||||||
\(975\) | 12.6863 | 0.406286 | ||||||||
\(976\) | 35.4853 | 1.13586 | ||||||||
\(977\) | −44.7696 | −1.43230 | −0.716152 | − | 0.697944i | \(-0.754098\pi\) | ||||
−0.716152 | + | 0.697944i | \(0.754098\pi\) | |||||||
\(978\) | −13.4142 | −0.428939 | ||||||||
\(979\) | 4.72792 | 0.151105 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.65685 | 0.308320 | ||||||||
\(982\) | 3.48528 | 0.111220 | ||||||||
\(983\) | −46.0000 | −1.46717 | −0.733586 | − | 0.679597i | \(-0.762155\pi\) | ||||
−0.733586 | + | 0.679597i | \(0.762155\pi\) | |||||||
\(984\) | 19.7990 | 0.631169 | ||||||||
\(985\) | 4.51472 | 0.143851 | ||||||||
\(986\) | −63.5980 | −2.02537 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.58579 | 0.273150 | ||||||||
\(989\) | −45.0833 | −1.43356 | ||||||||
\(990\) | −1.00000 | −0.0317821 | ||||||||
\(991\) | 3.79899 | 0.120679 | 0.0603394 | − | 0.998178i | \(-0.480782\pi\) | ||||
0.0603394 | + | 0.998178i | \(0.480782\pi\) | |||||||
\(992\) | −9.89949 | −0.314309 | ||||||||
\(993\) | −44.4853 | −1.41170 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.0711 | 0.509487 | ||||||||
\(996\) | 50.0416 | 1.58563 | ||||||||
\(997\) | −28.2843 | −0.895772 | −0.447886 | − | 0.894091i | \(-0.647823\pi\) | ||||
−0.447886 | + | 0.894091i | \(0.647823\pi\) | |||||||
\(998\) | −83.4264 | −2.64082 | ||||||||
\(999\) | −51.3137 | −1.62349 |
(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 | 931.2.a.f.1.1 | 2 | ||
3.2 | odd | 2 | 8379.2.a.bi.1.2 | 2 | |||
7.2 | even | 3 | 133.2.f.c.39.2 | ✓ | 4 | ||
7.3 | odd | 6 | 931.2.f.i.324.2 | 4 | |||
7.4 | even | 3 | 133.2.f.c.58.2 | yes | 4 | ||
7.5 | odd | 6 | 931.2.f.i.704.2 | 4 | |||
7.6 | odd | 2 | 931.2.a.e.1.1 | 2 | |||
21.2 | odd | 6 | 1197.2.j.e.172.1 | 4 | |||
21.11 | odd | 6 | 1197.2.j.e.856.1 | 4 | |||
21.20 | even | 2 | 8379.2.a.bl.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
133.2.f.c.39.2 | ✓ | 4 | 7.2 | even | 3 | ||
133.2.f.c.58.2 | yes | 4 | 7.4 | even | 3 | ||
931.2.a.e.1.1 | 2 | 7.6 | odd | 2 | |||
931.2.a.f.1.1 | 2 | 1.1 | even | 1 | trivial | ||
931.2.f.i.324.2 | 4 | 7.3 | odd | 6 | |||
931.2.f.i.704.2 | 4 | 7.5 | odd | 6 | |||
1197.2.j.e.172.1 | 4 | 21.2 | odd | 6 | |||
1197.2.j.e.856.1 | 4 | 21.11 | odd | 6 | |||
8379.2.a.bi.1.2 | 2 | 3.2 | odd | 2 | |||
8379.2.a.bl.1.2 | 2 | 21.20 | even | 2 |