Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(379,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.e (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(10.9235349965\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.207360000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.3 | ||
Root | \(-0.437016 - 0.756934i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1368.379 |
Dual form | 1368.2.e.d.379.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 1.22474i | −0.500000 | + | 0.866025i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46410i | 1.30931i | 0.755929 | + | 0.654654i | \(0.227186\pi\) | ||||
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.16228 | −0.953463 | −0.476731 | − | 0.879049i | \(-0.658179\pi\) | ||||
−0.476731 | + | 0.879049i | \(0.658179\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | −4.24264 | − | 2.44949i | −1.13389 | − | 0.654654i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | 6.32456 | 1.53393 | 0.766965 | − | 0.641689i | \(-0.221766\pi\) | ||||
0.766965 | + | 0.641689i | \(0.221766\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | + | 3.87298i | −0.458831 | + | 0.888523i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.23607 | − | 3.87298i | 0.476731 | − | 0.825723i | ||||
\(23\) | − | 5.47723i | − | 1.14208i | −0.820922 | − | 0.571040i | \(-0.806540\pi\) | ||
0.820922 | − | 0.571040i | \(-0.193460\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 3.16228 | − | 5.47723i | 0.620174 | − | 1.07417i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.00000 | − | 3.46410i | 1.13389 | − | 0.654654i | ||||
\(29\) | −1.41421 | −0.262613 | −0.131306 | − | 0.991342i | \(-0.541917\pi\) | ||||
−0.131306 | + | 0.991342i | \(0.541917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.94427 | −1.60644 | −0.803219 | − | 0.595683i | \(-0.796881\pi\) | ||||
−0.803219 | + | 0.595683i | \(0.796881\pi\) | |||||||
\(32\) | −2.82843 | − | 4.89898i | −0.500000 | − | 0.866025i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.47214 | + | 7.74597i | −0.766965 | + | 1.32842i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | −3.32920 | − | 5.18810i | −0.540068 | − | 0.841621i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.44949i | − | 0.382546i | −0.981537 | − | 0.191273i | \(-0.938738\pi\) | ||
0.981537 | − | 0.191273i | \(-0.0612616\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 3.16228 | + | 5.47723i | 0.476731 | + | 0.825723i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.70820 | + | 3.87298i | 0.989071 | + | 0.571040i | ||||
\(47\) | − | 5.47723i | − | 0.798935i | −0.916747 | − | 0.399468i | \(-0.869195\pi\) | ||
0.916747 | − | 0.399468i | \(-0.130805\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | −3.53553 | + | 6.12372i | −0.500000 | + | 0.866025i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.47214 | + | 7.74597i | 0.620174 | + | 1.07417i | ||||
\(53\) | −4.24264 | −0.582772 | −0.291386 | − | 0.956606i | \(-0.594116\pi\) | ||||
−0.291386 | + | 0.956606i | \(0.594116\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.79796i | 1.30931i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.00000 | − | 1.73205i | 0.131306 | − | 0.227429i | ||||
\(59\) | 4.89898i | 0.637793i | 0.947790 | + | 0.318896i | \(0.103312\pi\) | ||||
−0.947790 | + | 0.318896i | \(0.896688\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.3923i | 1.33060i | 0.746577 | + | 0.665299i | \(0.231696\pi\) | ||||
−0.746577 | + | 0.665299i | \(0.768304\pi\) | |||||||
\(62\) | 6.32456 | − | 10.9545i | 0.803219 | − | 1.39122i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.74597i | − | 0.946320i | −0.880976 | − | 0.473160i | \(-0.843113\pi\) | ||
0.880976 | − | 0.473160i | \(-0.156887\pi\) | |||||||
\(68\) | −6.32456 | − | 10.9545i | −0.766965 | − | 1.32842i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3137 | −1.34269 | −0.671345 | − | 0.741145i | \(-0.734283\pi\) | ||||
−0.671345 | + | 0.741145i | \(0.734283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0000 | −1.40449 | −0.702247 | − | 0.711934i | \(-0.747820\pi\) | ||||
−0.702247 | + | 0.711934i | \(0.747820\pi\) | |||||||
\(74\) | 3.16228 | − | 5.47723i | 0.367607 | − | 0.636715i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.70820 | − | 0.408882i | 0.998899 | − | 0.0469020i | ||||
\(77\) | − | 10.9545i | − | 1.24838i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.47214 | −0.503155 | −0.251577 | − | 0.967837i | \(-0.580949\pi\) | ||||
−0.251577 | + | 0.967837i | \(0.580949\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | + | 1.73205i | 0.331295 | + | 0.191273i | ||||
\(83\) | −15.8114 | −1.73553 | −0.867763 | − | 0.496979i | \(-0.834443\pi\) | ||||
−0.867763 | + | 0.496979i | \(0.834443\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.94427 | −0.953463 | ||||||||
\(89\) | − | 17.1464i | − | 1.81752i | −0.417322 | − | 0.908759i | \(-0.637031\pi\) | ||
0.417322 | − | 0.908759i | \(-0.362969\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 15.4919i | − | 1.62400i | ||||||
\(92\) | −9.48683 | + | 5.47723i | −0.989071 | + | 0.571040i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.70820 | + | 3.87298i | 0.691898 | + | 0.399468i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.4919i | − | 1.57297i | −0.617611 | − | 0.786484i | \(-0.711899\pi\) | ||
0.617611 | − | 0.786484i | \(-0.288101\pi\) | |||||||
\(98\) | 3.53553 | − | 6.12372i | 0.357143 | − | 0.618590i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000 | − | 8.66025i | −0.500000 | − | 0.866025i | ||||
\(101\) | − | 10.9545i | − | 1.09001i | −0.838433 | − | 0.545004i | \(-0.816528\pi\) | ||
0.838433 | − | 0.545004i | \(-0.183472\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.47214 | 0.440653 | 0.220326 | − | 0.975426i | \(-0.429288\pi\) | ||||
0.220326 | + | 0.975426i | \(0.429288\pi\) | |||||||
\(104\) | −12.6491 | −1.24035 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | − | 5.19615i | 0.291386 | − | 0.504695i | ||||
\(107\) | 14.6969i | 1.42081i | 0.703795 | + | 0.710403i | \(0.251487\pi\) | ||||
−0.703795 | + | 0.710403i | \(0.748513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.47214 | 0.428353 | 0.214176 | − | 0.976795i | \(-0.431293\pi\) | ||||
0.214176 | + | 0.976795i | \(0.431293\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.0000 | − | 6.92820i | −1.13389 | − | 0.654654i | ||||
\(113\) | 12.2474i | 1.15214i | 0.817399 | + | 0.576072i | \(0.195415\pi\) | ||||
−0.817399 | + | 0.576072i | \(0.804585\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.41421 | + | 2.44949i | 0.131306 | + | 0.227429i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.00000 | − | 3.46410i | −0.552345 | − | 0.318896i | ||||
\(119\) | 21.9089i | 2.00839i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | −12.7279 | − | 7.34847i | −1.15233 | − | 0.665299i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.94427 | + | 15.4919i | 0.803219 | + | 1.39122i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.94427 | −0.793676 | −0.396838 | − | 0.917889i | \(-0.629892\pi\) | ||||
−0.396838 | + | 0.917889i | \(0.629892\pi\) | |||||||
\(128\) | −5.65685 | + | 9.79796i | −0.500000 | + | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.16228 | −0.276289 | −0.138145 | − | 0.990412i | \(-0.544114\pi\) | ||||
−0.138145 | + | 0.990412i | \(0.544114\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.4164 | − | 6.92820i | −1.16335 | − | 0.600751i | ||||
\(134\) | 9.48683 | + | 5.47723i | 0.819538 | + | 0.473160i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.8885 | 1.53393 | ||||||||
\(137\) | 12.6491 | 1.08069 | 0.540343 | − | 0.841445i | \(-0.318294\pi\) | ||||
0.540343 | + | 0.841445i | \(0.318294\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000 | 1.01783 | 0.508913 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508913 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.00000 | − | 13.8564i | 0.671345 | − | 1.16280i | ||||
\(143\) | 14.1421 | 1.18262 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.48528 | − | 14.6969i | 0.702247 | − | 1.21633i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.47214 | + | 7.74597i | 0.367607 | + | 0.636715i | ||||
\(149\) | − | 21.9089i | − | 1.79485i | −0.441170 | − | 0.897424i | \(-0.645436\pi\) | ||
0.441170 | − | 0.897424i | \(-0.354564\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.47214 | 0.363937 | 0.181969 | − | 0.983304i | \(-0.441753\pi\) | ||||
0.181969 | + | 0.983304i | \(0.441753\pi\) | |||||||
\(152\) | −5.65685 | + | 10.9545i | −0.458831 | + | 0.888523i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13.4164 | + | 7.74597i | 1.08112 | + | 0.624188i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.46410i | 0.276465i | 0.990400 | + | 0.138233i | \(0.0441422\pi\) | ||||
−0.990400 | + | 0.138233i | \(0.955858\pi\) | |||||||
\(158\) | 3.16228 | − | 5.47723i | 0.251577 | − | 0.435745i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.9737 | 1.49533 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | −4.24264 | + | 2.44949i | −0.331295 | + | 0.191273i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.1803 | − | 19.3649i | 0.867763 | − | 1.50301i | ||||
\(167\) | 19.7990 | 1.53209 | 0.766046 | − | 0.642786i | \(-0.222221\pi\) | ||||
0.766046 | + | 0.642786i | \(0.222221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.24264 | −0.322562 | −0.161281 | − | 0.986909i | \(-0.551563\pi\) | ||||
−0.161281 | + | 0.986909i | \(0.551563\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.3205i | 1.30931i | ||||||||
\(176\) | 6.32456 | − | 10.9545i | 0.476731 | − | 0.825723i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 21.0000 | + | 12.1244i | 1.57402 | + | 0.908759i | ||||
\(179\) | − | 19.5959i | − | 1.46467i | −0.680946 | − | 0.732334i | \(-0.738431\pi\) | ||
0.680946 | − | 0.732334i | \(-0.261569\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.47214 | −0.332411 | −0.166206 | − | 0.986091i | \(-0.553152\pi\) | ||||
−0.166206 | + | 0.986091i | \(0.553152\pi\) | |||||||
\(182\) | 18.9737 | + | 10.9545i | 1.40642 | + | 0.811998i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 15.4919i | − | 1.14208i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.0000 | −1.46254 | ||||||||
\(188\) | −9.48683 | + | 5.47723i | −0.691898 | + | 0.399468i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.4317i | 1.18895i | 0.804112 | + | 0.594477i | \(0.202641\pi\) | ||||
−0.804112 | + | 0.594477i | \(0.797359\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.4919i | 1.11513i | 0.830132 | + | 0.557567i | \(0.188265\pi\) | ||||
−0.830132 | + | 0.557567i | \(0.811735\pi\) | |||||||
\(194\) | 18.9737 | + | 10.9545i | 1.36223 | + | 0.786484i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.00000 | + | 8.66025i | 0.357143 | + | 0.618590i | ||||
\(197\) | 21.9089i | 1.56094i | 0.625190 | + | 0.780472i | \(0.285021\pi\) | ||||
−0.625190 | + | 0.780472i | \(0.714979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.46410i | − | 0.245564i | −0.992434 | − | 0.122782i | \(-0.960818\pi\) | ||
0.992434 | − | 0.122782i | \(-0.0391815\pi\) | |||||||
\(200\) | 14.1421 | 1.00000 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.4164 | + | 7.74597i | 0.943975 | + | 0.545004i | ||||
\(203\) | − | 4.89898i | − | 0.343841i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.16228 | + | 5.47723i | −0.220326 | + | 0.381616i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.94427 | − | 15.4919i | 0.620174 | − | 1.07417i | ||||
\(209\) | 6.32456 | − | 12.2474i | 0.437479 | − | 0.847174i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.2379i | 1.59976i | 0.600158 | + | 0.799882i | \(0.295104\pi\) | ||||
−0.600158 | + | 0.799882i | \(0.704896\pi\) | |||||||
\(212\) | 4.24264 | + | 7.34847i | 0.291386 | + | 0.504695i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.0000 | − | 10.3923i | −1.23045 | − | 0.710403i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 30.9839i | − | 2.10332i | ||||||
\(218\) | −3.16228 | + | 5.47723i | −0.214176 | + | 0.370965i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.2843 | −1.90261 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.3607 | −1.49738 | −0.748691 | − | 0.662919i | \(-0.769317\pi\) | ||||
−0.748691 | + | 0.662919i | \(0.769317\pi\) | |||||||
\(224\) | 16.9706 | − | 9.79796i | 1.13389 | − | 0.654654i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.0000 | − | 8.66025i | −0.997785 | − | 0.576072i | ||||
\(227\) | 14.6969i | 0.975470i | 0.872992 | + | 0.487735i | \(0.162177\pi\) | ||||
−0.872992 | + | 0.487735i | \(0.837823\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.00000 | −0.262613 | ||||||||
\(233\) | −6.32456 | −0.414335 | −0.207168 | − | 0.978305i | \(-0.566425\pi\) | ||||
−0.207168 | + | 0.978305i | \(0.566425\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.48528 | − | 4.89898i | 0.552345 | − | 0.318896i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −26.8328 | − | 15.4919i | −1.73931 | − | 1.00419i | ||||
\(239\) | 16.4317i | 1.06288i | 0.847097 | + | 0.531438i | \(0.178348\pi\) | ||||
−0.847097 | + | 0.531438i | \(0.821652\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.4919i | 0.997923i | 0.866624 | + | 0.498962i | \(0.166285\pi\) | ||||
−0.866624 | + | 0.498962i | \(0.833715\pi\) | |||||||
\(242\) | 0.707107 | − | 1.22474i | 0.0454545 | − | 0.0787296i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 18.0000 | − | 10.3923i | 1.15233 | − | 0.665299i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.94427 | − | 17.3205i | 0.569110 | − | 1.10208i | ||||
\(248\) | −25.2982 | −1.60644 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.8114 | −0.998006 | −0.499003 | − | 0.866600i | \(-0.666300\pi\) | ||||
−0.499003 | + | 0.866600i | \(0.666300\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.3205i | 1.08893i | ||||||||
\(254\) | 6.32456 | − | 10.9545i | 0.396838 | − | 0.687343i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | − | 2.44949i | − | 0.152795i | −0.997077 | − | 0.0763975i | \(-0.975658\pi\) | ||
0.997077 | − | 0.0763975i | \(-0.0243418\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 15.4919i | − | 0.962622i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.23607 | − | 3.87298i | 0.138145 | − | 0.239274i | ||||
\(263\) | 16.4317i | 1.01322i | 0.862175 | + | 0.506610i | \(0.169102\pi\) | ||||
−0.862175 | + | 0.506610i | \(0.830898\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 17.9721 | − | 11.5327i | 1.10194 | − | 0.707115i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.4164 | + | 7.74597i | −0.819538 | + | 0.473160i | ||||
\(269\) | 21.2132 | 1.29339 | 0.646696 | − | 0.762748i | \(-0.276150\pi\) | ||||
0.646696 | + | 0.762748i | \(0.276150\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.3923i | 0.631288i | 0.948878 | + | 0.315644i | \(0.102220\pi\) | ||||
−0.948878 | + | 0.315644i | \(0.897780\pi\) | |||||||
\(272\) | −12.6491 | + | 21.9089i | −0.766965 | + | 1.32842i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.94427 | + | 15.4919i | −0.540343 | + | 0.935902i | ||||
\(275\) | −15.8114 | −0.953463 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 13.8564i | − | 0.832551i | −0.909239 | − | 0.416275i | \(-0.863335\pi\) | ||
0.909239 | − | 0.416275i | \(-0.136665\pi\) | |||||||
\(278\) | −8.48528 | + | 14.6969i | −0.508913 | + | 0.881464i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7.34847i | − | 0.438373i | −0.975683 | − | 0.219186i | \(-0.929660\pi\) | ||
0.975683 | − | 0.219186i | \(-0.0703403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.0000 | 1.18888 | 0.594438 | − | 0.804141i | \(-0.297374\pi\) | ||||
0.594438 | + | 0.804141i | \(0.297374\pi\) | |||||||
\(284\) | 11.3137 | + | 19.5959i | 0.671345 | + | 1.16280i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.0000 | + | 17.3205i | −0.591312 | + | 1.02418i | ||||
\(287\) | 8.48528 | 0.500870 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.0000 | 1.35294 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.0000 | + | 20.7846i | 0.702247 | + | 1.21633i | ||||
\(293\) | −29.6985 | −1.73500 | −0.867502 | − | 0.497434i | \(-0.834276\pi\) | ||||
−0.867502 | + | 0.497434i | \(0.834276\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −12.6491 | −0.735215 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 26.8328 | + | 15.4919i | 1.55438 | + | 0.897424i | ||||
\(299\) | 24.4949i | 1.41658i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.16228 | + | 5.47723i | −0.181969 | + | 0.315179i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.41641 | − | 14.6742i | −0.540068 | − | 0.841621i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.4919i | − | 0.884171i | −0.896973 | − | 0.442086i | \(-0.854239\pi\) | ||
0.896973 | − | 0.442086i | \(-0.145761\pi\) | |||||||
\(308\) | −18.9737 | + | 10.9545i | −1.08112 | + | 0.624188i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5.47723i | − | 0.310585i | −0.987869 | − | 0.155292i | \(-0.950368\pi\) | ||
0.987869 | − | 0.155292i | \(-0.0496320\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.0000 | −1.13047 | −0.565233 | − | 0.824931i | \(-0.691214\pi\) | ||||
−0.565233 | + | 0.824931i | \(0.691214\pi\) | |||||||
\(314\) | −4.24264 | − | 2.44949i | −0.239426 | − | 0.138233i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.47214 | + | 7.74597i | 0.251577 | + | 0.435745i | ||||
\(317\) | 29.6985 | 1.66803 | 0.834017 | − | 0.551739i | \(-0.186036\pi\) | ||||
0.834017 | + | 0.551739i | \(0.186036\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.47214 | 0.250392 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −13.4164 | + | 23.2379i | −0.747667 | + | 1.29500i | ||||
\(323\) | −12.6491 | + | 24.4949i | −0.703815 | + | 1.36293i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.3607 | −1.24035 | ||||||||
\(326\) | 8.48528 | − | 14.6969i | 0.469956 | − | 0.813988i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 6.92820i | − | 0.382546i | ||||||
\(329\) | 18.9737 | 1.04605 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.4919i | 0.851514i | 0.904838 | + | 0.425757i | \(0.139992\pi\) | ||||
−0.904838 | + | 0.425757i | \(0.860008\pi\) | |||||||
\(332\) | 15.8114 | + | 27.3861i | 0.867763 | + | 1.50301i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.0000 | + | 24.2487i | −0.766046 | + | 1.32683i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.4919i | 0.843899i | 0.906619 | + | 0.421950i | \(0.138654\pi\) | ||||
−0.906619 | + | 0.421950i | \(0.861346\pi\) | |||||||
\(338\) | −4.94975 | + | 8.57321i | −0.269231 | + | 0.466321i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.2843 | 1.53168 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.92820i | 0.374088i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | − | 5.19615i | 0.161281 | − | 0.279347i | ||||
\(347\) | −15.8114 | −0.848800 | −0.424400 | − | 0.905475i | \(-0.639515\pi\) | ||||
−0.424400 | + | 0.905475i | \(0.639515\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.8564i | 0.741716i | 0.928689 | + | 0.370858i | \(0.120936\pi\) | ||||
−0.928689 | + | 0.370858i | \(0.879064\pi\) | |||||||
\(350\) | −21.2132 | − | 12.2474i | −1.13389 | − | 0.654654i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.94427 | + | 15.4919i | 0.476731 | + | 0.825723i | ||||
\(353\) | 6.32456 | 0.336622 | 0.168311 | − | 0.985734i | \(-0.446169\pi\) | ||||
0.168311 | + | 0.985734i | \(0.446169\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −29.6985 | + | 17.1464i | −1.57402 | + | 0.908759i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.0000 | + | 13.8564i | 1.26844 | + | 0.732334i | ||||
\(359\) | − | 5.47723i | − | 0.289077i | −0.989499 | − | 0.144538i | \(-0.953830\pi\) | ||
0.989499 | − | 0.144538i | \(-0.0461697\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | − | 15.4919i | −0.578947 | − | 0.815365i | ||||
\(362\) | 3.16228 | − | 5.47723i | 0.166206 | − | 0.287877i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −26.8328 | + | 15.4919i | −1.40642 | + | 0.811998i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.2487i | 1.26577i | 0.774245 | + | 0.632886i | \(0.218130\pi\) | ||||
−0.774245 | + | 0.632886i | \(0.781870\pi\) | |||||||
\(368\) | 18.9737 | + | 10.9545i | 0.989071 | + | 0.571040i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 14.6969i | − | 0.763027i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.3050 | 1.62091 | 0.810454 | − | 0.585802i | \(-0.199220\pi\) | ||||
0.810454 | + | 0.585802i | \(0.199220\pi\) | |||||||
\(374\) | 14.1421 | − | 24.4949i | 0.731272 | − | 1.26660i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 15.4919i | − | 0.798935i | ||||||
\(377\) | 6.32456 | 0.325731 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20.1246 | − | 11.6190i | −1.02966 | − | 0.594477i | ||||
\(383\) | 2.82843 | 0.144526 | 0.0722629 | − | 0.997386i | \(-0.476978\pi\) | ||||
0.0722629 | + | 0.997386i | \(0.476978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.9737 | − | 10.9545i | −0.965734 | − | 0.557567i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −26.8328 | + | 15.4919i | −1.36223 | + | 0.786484i | ||||
\(389\) | 10.9545i | 0.555413i | 0.960666 | + | 0.277706i | \(0.0895742\pi\) | ||||
−0.960666 | + | 0.277706i | \(0.910426\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 34.6410i | − | 1.75187i | ||||||
\(392\) | −14.1421 | −0.714286 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −26.8328 | − | 15.4919i | −1.35182 | − | 0.780472i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 27.7128i | − | 1.39087i | −0.718591 | − | 0.695433i | \(-0.755213\pi\) | ||
0.718591 | − | 0.695433i | \(-0.244787\pi\) | |||||||
\(398\) | 4.24264 | + | 2.44949i | 0.212664 | + | 0.122782i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.0000 | + | 17.3205i | −0.500000 | + | 0.866025i | ||||
\(401\) | − | 17.1464i | − | 0.856252i | −0.903719 | − | 0.428126i | \(-0.859174\pi\) | ||
0.903719 | − | 0.428126i | \(-0.140826\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 40.0000 | 1.99254 | ||||||||
\(404\) | −18.9737 | + | 10.9545i | −0.943975 | + | 0.545004i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00000 | + | 3.46410i | 0.297775 | + | 0.171920i | ||||
\(407\) | 14.1421 | 0.701000 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.47214 | − | 7.74597i | −0.220326 | − | 0.381616i | ||||
\(413\) | −16.9706 | −0.835067 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.6491 | + | 21.9089i | 0.620174 | + | 1.07417i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.5279 | + | 16.4062i | 0.514935 | + | 0.802454i | ||||
\(419\) | −3.16228 | −0.154487 | −0.0772437 | − | 0.997012i | \(-0.524612\pi\) | ||||
−0.0772437 | + | 0.997012i | \(0.524612\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.47214 | 0.217959 | 0.108979 | − | 0.994044i | \(-0.465242\pi\) | ||||
0.108979 | + | 0.994044i | \(0.465242\pi\) | |||||||
\(422\) | −28.4605 | − | 16.4317i | −1.38544 | − | 0.799882i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.0000 | −0.582772 | ||||||||
\(425\) | 31.6228 | 1.53393 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −36.0000 | −1.74216 | ||||||||
\(428\) | 25.4558 | − | 14.6969i | 1.23045 | − | 0.710403i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.4558 | −1.22616 | −0.613082 | − | 0.790019i | \(-0.710071\pi\) | ||||
−0.613082 | + | 0.790019i | \(0.710071\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.9839i | 1.48899i | 0.667628 | + | 0.744495i | \(0.267310\pi\) | ||||
−0.667628 | + | 0.744495i | \(0.732690\pi\) | |||||||
\(434\) | 37.9473 | + | 21.9089i | 1.82153 | + | 1.05166i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.47214 | − | 7.74597i | −0.214176 | − | 0.370965i | ||||
\(437\) | 21.2132 | + | 10.9545i | 1.01477 | + | 0.524022i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.3607 | 1.06722 | 0.533609 | − | 0.845732i | \(-0.320836\pi\) | ||||
0.533609 | + | 0.845732i | \(0.320836\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.0000 | − | 34.6410i | 0.951303 | − | 1.64771i | ||||
\(443\) | −15.8114 | −0.751222 | −0.375611 | − | 0.926777i | \(-0.622567\pi\) | ||||
−0.375611 | + | 0.926777i | \(0.622567\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 15.8114 | − | 27.3861i | 0.748691 | − | 1.29677i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 27.7128i | 1.30931i | ||||||||
\(449\) | 7.34847i | 0.346796i | 0.984852 | + | 0.173398i | \(0.0554746\pi\) | ||||
−0.984852 | + | 0.173398i | \(0.944525\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.74597i | 0.364743i | ||||||||
\(452\) | 21.2132 | − | 12.2474i | 0.997785 | − | 0.576072i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18.0000 | − | 10.3923i | −0.844782 | − | 0.487735i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.00000 | 0.187112 | 0.0935561 | − | 0.995614i | \(-0.470177\pi\) | ||||
0.0935561 | + | 0.995614i | \(0.470177\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 10.9545i | − | 0.510200i | −0.966915 | − | 0.255100i | \(-0.917892\pi\) | ||
0.966915 | − | 0.255100i | \(-0.0821083\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.46410i | 0.160990i | 0.996755 | + | 0.0804952i | \(0.0256502\pi\) | ||||
−0.996755 | + | 0.0804952i | \(0.974350\pi\) | |||||||
\(464\) | 2.82843 | − | 4.89898i | 0.131306 | − | 0.227429i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.47214 | − | 7.74597i | 0.207168 | − | 0.358825i | ||||
\(467\) | 3.16228 | 0.146333 | 0.0731664 | − | 0.997320i | \(-0.476690\pi\) | ||||
0.0731664 | + | 0.997320i | \(0.476690\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.8328 | 1.23902 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.8564i | 0.637793i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.0000 | + | 19.3649i | −0.458831 | + | 0.888523i | ||||
\(476\) | 37.9473 | − | 21.9089i | 1.73931 | − | 1.00419i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.1246 | − | 11.6190i | −0.920478 | − | 0.531438i | ||||
\(479\) | 27.3861i | 1.25130i | 0.780102 | + | 0.625652i | \(0.215167\pi\) | ||||
−0.780102 | + | 0.625652i | \(0.784833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.0000 | 0.911922 | ||||||||
\(482\) | −18.9737 | − | 10.9545i | −0.864227 | − | 0.498962i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.94427 | 0.405304 | 0.202652 | − | 0.979251i | \(-0.435044\pi\) | ||||
0.202652 | + | 0.979251i | \(0.435044\pi\) | |||||||
\(488\) | 29.3939i | 1.33060i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.1359 | 0.998981 | 0.499491 | − | 0.866319i | \(-0.333521\pi\) | ||||
0.499491 | + | 0.866319i | \(0.333521\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.94427 | −0.402830 | ||||||||
\(494\) | 14.8886 | + | 23.2019i | 0.669872 | + | 1.04390i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.8885 | − | 30.9839i | 0.803219 | − | 1.39122i | ||||
\(497\) | − | 39.1918i | − | 1.75799i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.00000 | −0.358129 | −0.179065 | − | 0.983837i | \(-0.557307\pi\) | ||||
−0.179065 | + | 0.983837i | \(0.557307\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.1803 | − | 19.3649i | 0.499003 | − | 0.864299i | ||||
\(503\) | − | 16.4317i | − | 0.732652i | −0.930487 | − | 0.366326i | \(-0.880615\pi\) | ||
0.930487 | − | 0.366326i | \(-0.119385\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −21.2132 | − | 12.2474i | −0.943042 | − | 0.544466i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.94427 | + | 15.4919i | 0.396838 | + | 0.687343i | ||||
\(509\) | −15.5563 | −0.689523 | −0.344762 | − | 0.938690i | \(-0.612040\pi\) | ||||
−0.344762 | + | 0.938690i | \(0.612040\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 41.5692i | − | 1.83891i | ||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.00000 | + | 1.73205i | 0.132324 | + | 0.0763975i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.3205i | 0.761755i | ||||||||
\(518\) | 18.9737 | + | 10.9545i | 0.833655 | + | 0.481311i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.9444i | 1.18046i | 0.807237 | + | 0.590228i | \(0.200962\pi\) | ||||
−0.807237 | + | 0.590228i | \(0.799038\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.74597i | 0.338707i | 0.985555 | + | 0.169354i | \(0.0541680\pi\) | ||||
−0.985555 | + | 0.169354i | \(0.945832\pi\) | |||||||
\(524\) | 3.16228 | + | 5.47723i | 0.138145 | + | 0.239274i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.1246 | − | 11.6190i | −0.877475 | − | 0.506610i | ||||
\(527\) | −56.5685 | −2.46416 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.41641 | + | 30.1661i | 0.0614091 | + | 1.30787i | ||||
\(533\) | 10.9545i | 0.474490i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 21.9089i | − | 0.946320i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.0000 | + | 25.9808i | −0.646696 | + | 1.12011i | ||||
\(539\) | 15.8114 | 0.681045 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 17.3205i | − | 0.744667i | −0.928099 | − | 0.372333i | \(-0.878558\pi\) | ||
0.928099 | − | 0.372333i | \(-0.121442\pi\) | |||||||
\(542\) | −12.7279 | − | 7.34847i | −0.546711 | − | 0.315644i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17.8885 | − | 30.9839i | −0.766965 | − | 1.32842i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | −12.6491 | − | 21.9089i | −0.540343 | − | 0.935902i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.1803 | − | 19.3649i | 0.476731 | − | 0.825723i | ||||
\(551\) | 2.82843 | − | 5.47723i | 0.120495 | − | 0.233338i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 15.4919i | − | 0.658784i | ||||||
\(554\) | 16.9706 | + | 9.79796i | 0.721010 | + | 0.416275i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.0000 | − | 20.7846i | −0.508913 | − | 0.881464i | ||||
\(557\) | 32.8634i | 1.39246i | 0.717816 | + | 0.696232i | \(0.245142\pi\) | ||||
−0.717816 | + | 0.696232i | \(0.754858\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.00000 | + | 5.19615i | 0.379642 | + | 0.219186i | ||||
\(563\) | − | 19.5959i | − | 0.825869i | −0.910761 | − | 0.412935i | \(-0.864504\pi\) | ||
0.910761 | − | 0.412935i | \(-0.135496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.1421 | + | 24.4949i | −0.594438 | + | 1.02960i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −32.0000 | −1.34269 | ||||||||
\(569\) | 7.34847i | 0.308064i | 0.988066 | + | 0.154032i | \(0.0492259\pi\) | ||||
−0.988066 | + | 0.154032i | \(0.950774\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.0000 | 1.00437 | 0.502184 | − | 0.864761i | \(-0.332530\pi\) | ||||
0.502184 | + | 0.864761i | \(0.332530\pi\) | |||||||
\(572\) | −14.1421 | − | 24.4949i | −0.591312 | − | 1.02418i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.00000 | + | 10.3923i | −0.250435 | + | 0.433766i | ||||
\(575\) | − | 27.3861i | − | 1.14208i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(578\) | −16.2635 | + | 28.1691i | −0.676471 | + | 1.17168i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 54.7723i | − | 2.27234i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.4164 | 0.555651 | ||||||||
\(584\) | −33.9411 | −1.40449 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.0000 | − | 36.3731i | 0.867502 | − | 1.50256i | ||||
\(587\) | −22.1359 | −0.913648 | −0.456824 | − | 0.889557i | \(-0.651013\pi\) | ||||
−0.456824 | + | 0.889557i | \(0.651013\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.8885 | − | 34.6410i | 0.737085 | − | 1.42736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.94427 | − | 15.4919i | 0.367607 | − | 0.636715i | ||||
\(593\) | −31.6228 | −1.29859 | −0.649296 | − | 0.760536i | \(-0.724936\pi\) | ||||
−0.649296 | + | 0.760536i | \(0.724936\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −37.9473 | + | 21.9089i | −1.55438 | + | 0.897424i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −30.0000 | − | 17.3205i | −1.22679 | − | 0.708288i | ||||
\(599\) | 28.2843 | 1.15566 | 0.577832 | − | 0.816156i | \(-0.303899\pi\) | ||||
0.577832 | + | 0.816156i | \(0.303899\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.9839i | 1.26386i | 0.775026 | + | 0.631929i | \(0.217737\pi\) | ||||
−0.775026 | + | 0.631929i | \(0.782263\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.47214 | − | 7.74597i | −0.181969 | − | 0.315179i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.94427 | 0.363037 | 0.181518 | − | 0.983388i | \(-0.441899\pi\) | ||||
0.181518 | + | 0.983388i | \(0.441899\pi\) | |||||||
\(608\) | 24.6305 | − | 1.15649i | 0.998899 | − | 0.0469020i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.4949i | 0.990957i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.2487i | 0.979396i | 0.871892 | + | 0.489698i | \(0.162893\pi\) | ||||
−0.871892 | + | 0.489698i | \(0.837107\pi\) | |||||||
\(614\) | 18.9737 | + | 10.9545i | 0.765715 | + | 0.442086i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 30.9839i | − | 1.24838i | ||||||
\(617\) | −25.2982 | −1.01847 | −0.509234 | − | 0.860628i | \(-0.670071\pi\) | ||||
−0.509234 | + | 0.860628i | \(0.670071\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.0000 | 1.28619 | 0.643094 | − | 0.765787i | \(-0.277650\pi\) | ||||
0.643094 | + | 0.765787i | \(0.277650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.70820 | + | 3.87298i | 0.268974 | + | 0.155292i | ||||
\(623\) | 59.3970 | 2.37969 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 14.1421 | − | 24.4949i | 0.565233 | − | 0.979013i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.00000 | − | 3.46410i | 0.239426 | − | 0.138233i | ||||
\(629\) | −28.2843 | −1.12777 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.3205i | 0.689519i | 0.938691 | + | 0.344759i | \(0.112039\pi\) | ||||
−0.938691 | + | 0.344759i | \(0.887961\pi\) | |||||||
\(632\) | −12.6491 | −0.503155 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.0000 | + | 36.3731i | −0.834017 | + | 1.44456i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.3607 | 0.885962 | ||||||||
\(638\) | −3.16228 | + | 5.47723i | −0.125196 | + | 0.216845i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 7.34847i | − | 0.290247i | −0.989414 | − | 0.145124i | \(-0.953642\pi\) | ||
0.989414 | − | 0.145124i | \(-0.0463580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.00000 | 0.315489 | 0.157745 | − | 0.987480i | \(-0.449578\pi\) | ||||
0.157745 | + | 0.987480i | \(0.449578\pi\) | |||||||
\(644\) | −18.9737 | − | 32.8634i | −0.747667 | − | 1.29500i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.0557 | − | 32.8124i | −0.828427 | − | 1.29099i | ||||
\(647\) | 5.47723i | 0.215332i | 0.994187 | + | 0.107666i | \(0.0343377\pi\) | ||||
−0.994187 | + | 0.107666i | \(0.965662\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 15.4919i | − | 0.608112i | ||||||
\(650\) | 15.8114 | − | 27.3861i | 0.620174 | − | 1.07417i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.0000 | + | 20.7846i | 0.469956 | + | 0.813988i | ||||
\(653\) | − | 32.8634i | − | 1.28604i | −0.765848 | − | 0.643021i | \(-0.777681\pi\) | ||
0.765848 | − | 0.643021i | \(-0.222319\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.48528 | + | 4.89898i | 0.331295 | + | 0.191273i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.4164 | + | 23.2379i | −0.523026 | + | 0.905908i | ||||
\(659\) | 9.79796i | 0.381674i | 0.981622 | + | 0.190837i | \(0.0611202\pi\) | ||||
−0.981622 | + | 0.190837i | \(0.938880\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.3050 | 1.21762 | 0.608811 | − | 0.793315i | \(-0.291647\pi\) | ||||
0.608811 | + | 0.793315i | \(0.291647\pi\) | |||||||
\(662\) | −18.9737 | − | 10.9545i | −0.737432 | − | 0.425757i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −44.7214 | −1.73553 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.74597i | 0.299925i | ||||||||
\(668\) | −19.7990 | − | 34.2929i | −0.766046 | − | 1.32683i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 32.8634i | − | 1.26868i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.4758i | 1.79151i | 0.444548 | + | 0.895755i | \(0.353364\pi\) | ||||
−0.444548 | + | 0.895755i | \(0.646636\pi\) | |||||||
\(674\) | −18.9737 | − | 10.9545i | −0.730838 | − | 0.421950i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.00000 | − | 12.1244i | −0.269231 | − | 0.466321i | ||||
\(677\) | −29.6985 | −1.14141 | −0.570703 | − | 0.821157i | \(-0.693329\pi\) | ||||
−0.570703 | + | 0.821157i | \(0.693329\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 53.6656 | 2.05950 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −20.0000 | + | 34.6410i | −0.765840 | + | 1.32647i | ||||
\(683\) | − | 44.0908i | − | 1.68709i | −0.537060 | − | 0.843544i | \(-0.680465\pi\) | ||
0.537060 | − | 0.843544i | \(-0.319535\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.48528 | − | 4.89898i | −0.323970 | − | 0.187044i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.9737 | 0.722839 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0000 | −0.456502 | −0.228251 | − | 0.973602i | \(-0.573301\pi\) | ||||
−0.228251 | + | 0.973602i | \(0.573301\pi\) | |||||||
\(692\) | 4.24264 | + | 7.34847i | 0.161281 | + | 0.279347i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.1803 | − | 19.3649i | 0.424400 | − | 0.735082i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 15.4919i | − | 0.586799i | ||||||
\(698\) | −16.9706 | − | 9.79796i | −0.642345 | − | 0.370858i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 30.0000 | − | 17.3205i | 1.13389 | − | 0.654654i | ||||
\(701\) | − | 21.9089i | − | 0.827488i | −0.910393 | − | 0.413744i | \(-0.864221\pi\) | ||
0.910393 | − | 0.413744i | \(-0.135779\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.94427 | − | 17.3205i | 0.337340 | − | 0.653255i | ||||
\(704\) | −25.2982 | −0.953463 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.47214 | + | 7.74597i | −0.168311 | + | 0.291523i | ||||
\(707\) | 37.9473 | 1.42716 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 3.46410i | − | 0.130097i | −0.997882 | − | 0.0650485i | \(-0.979280\pi\) | ||
0.997882 | − | 0.0650485i | \(-0.0207202\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 48.4974i | − | 1.81752i | ||||||
\(713\) | 48.9898i | 1.83468i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −33.9411 | + | 19.5959i | −1.26844 | + | 0.732334i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.70820 | + | 3.87298i | 0.250348 | + | 0.144538i | ||||
\(719\) | 5.47723i | 0.204266i | 0.994771 | + | 0.102133i | \(0.0325667\pi\) | ||||
−0.994771 | + | 0.102133i | \(0.967433\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.4919i | 0.576950i | ||||||||
\(722\) | 26.7518 | − | 2.51774i | 0.995600 | − | 0.0937007i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.47214 | + | 7.74597i | 0.166206 | + | 0.287877i | ||||
\(725\) | −7.07107 | −0.262613 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.46410i | 0.128476i | 0.997935 | + | 0.0642382i | \(0.0204617\pi\) | ||||
−0.997935 | + | 0.0642382i | \(0.979538\pi\) | |||||||
\(728\) | − | 43.8178i | − | 1.62400i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 45.0333i | − | 1.66334i | −0.555267 | − | 0.831672i | \(-0.687384\pi\) | ||
0.555267 | − | 0.831672i | \(-0.312616\pi\) | |||||||
\(734\) | −29.6985 | − | 17.1464i | −1.09619 | − | 0.632886i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −26.8328 | + | 15.4919i | −0.989071 | + | 0.571040i | ||||
\(737\) | 24.4949i | 0.902281i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.0000 | −0.441427 | −0.220714 | − | 0.975339i | \(-0.570839\pi\) | ||||
−0.220714 | + | 0.975339i | \(0.570839\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.0000 | + | 10.3923i | 0.660801 | + | 0.381514i | ||||
\(743\) | −16.9706 | −0.622590 | −0.311295 | − | 0.950313i | \(-0.600763\pi\) | ||||
−0.311295 | + | 0.950313i | \(0.600763\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −22.1359 | + | 38.3406i | −0.810454 | + | 1.40375i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 20.0000 | + | 34.6410i | 0.731272 | + | 1.26660i | ||||
\(749\) | −50.9117 | −1.86027 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.3050 | 1.14233 | 0.571167 | − | 0.820834i | \(-0.306491\pi\) | ||||
0.571167 | + | 0.820834i | \(0.306491\pi\) | |||||||
\(752\) | 18.9737 | + | 10.9545i | 0.691898 | + | 0.399468i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.47214 | + | 7.74597i | −0.162866 | + | 0.282091i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.8564i | 0.503620i | 0.967777 | + | 0.251810i | \(0.0810257\pi\) | ||||
−0.967777 | + | 0.251810i | \(0.918974\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.6491 | −0.458530 | −0.229265 | − | 0.973364i | \(-0.573632\pi\) | ||||
−0.229265 | + | 0.973364i | \(0.573632\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.4919i | 0.560846i | ||||||||
\(764\) | 28.4605 | − | 16.4317i | 1.02966 | − | 0.594477i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.00000 | + | 3.46410i | −0.0722629 | + | 0.125163i | ||||
\(767\) | − | 21.9089i | − | 0.791085i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.0000 | −1.00971 | −0.504853 | − | 0.863205i | \(-0.668453\pi\) | ||||
−0.504853 | + | 0.863205i | \(0.668453\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 26.8328 | − | 15.4919i | 0.965734 | − | 0.557567i | ||||
\(773\) | 24.0416 | 0.864717 | 0.432359 | − | 0.901702i | \(-0.357681\pi\) | ||||
0.432359 | + | 0.901702i | \(0.357681\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −44.7214 | −1.60644 | ||||||||
\(776\) | − | 43.8178i | − | 1.57297i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13.4164 | − | 7.74597i | −0.481002 | − | 0.277706i | ||||
\(779\) | 9.48683 | + | 4.89898i | 0.339901 | + | 0.175524i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.7771 | 1.28020 | ||||||||
\(782\) | 42.4264 | + | 24.4949i | 1.51717 | + | 0.875936i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.0000 | − | 17.3205i | 0.357143 | − | 0.618590i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.74597i | 0.276114i | 0.990424 | + | 0.138057i | \(0.0440857\pi\) | ||||
−0.990424 | + | 0.138057i | \(0.955914\pi\) | |||||||
\(788\) | 37.9473 | − | 21.9089i | 1.35182 | − | 0.780472i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −42.4264 | −1.50851 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 46.4758i | − | 1.65040i | ||||||
\(794\) | 33.9411 | + | 19.5959i | 1.20453 | + | 0.695433i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.00000 | + | 3.46410i | −0.212664 | + | 0.122782i | ||||
\(797\) | 41.0122 | 1.45273 | 0.726363 | − | 0.687311i | \(-0.241209\pi\) | ||||
0.726363 | + | 0.687311i | \(0.241209\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 34.6410i | − | 1.22551i | ||||||
\(800\) | −14.1421 | − | 24.4949i | −0.500000 | − | 0.866025i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.0000 | + | 12.1244i | 0.741536 | + | 0.428126i | ||||
\(803\) | 37.9473 | 1.33913 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −28.2843 | + | 48.9898i | −0.996271 | + | 1.72559i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 30.9839i | − | 1.09001i | ||||||
\(809\) | −31.6228 | −1.11180 | −0.555899 | − | 0.831250i | \(-0.687626\pi\) | ||||
−0.555899 | + | 0.831250i | \(0.687626\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30.9839i | − | 1.08799i | −0.839088 | − | 0.543995i | \(-0.816911\pi\) | ||
0.839088 | − | 0.543995i | \(-0.183089\pi\) | |||||||
\(812\) | −8.48528 | + | 4.89898i | −0.297775 | + | 0.171920i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.0000 | + | 17.3205i | −0.350500 | + | 0.607083i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 21.9089i | − | 0.764626i | −0.924033 | − | 0.382313i | \(-0.875128\pi\) | ||
0.924033 | − | 0.382313i | \(-0.124872\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 10.3923i | − | 0.362253i | −0.983460 | − | 0.181126i | \(-0.942026\pi\) | ||
0.983460 | − | 0.181126i | \(-0.0579743\pi\) | |||||||
\(824\) | 12.6491 | 0.440653 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.0000 | − | 20.7846i | 0.417533 | − | 0.723189i | ||||
\(827\) | − | 48.9898i | − | 1.70354i | −0.523914 | − | 0.851771i | \(-0.675529\pi\) | ||
0.523914 | − | 0.851771i | \(-0.324471\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −49.1935 | −1.70856 | −0.854280 | − | 0.519813i | \(-0.826002\pi\) | ||||
−0.854280 | + | 0.519813i | \(0.826002\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −35.7771 | −1.24035 | ||||||||
\(833\) | −31.6228 | −1.09566 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −27.5378 | + | 1.29300i | −0.952413 | + | 0.0447193i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.23607 | − | 3.87298i | 0.0772437 | − | 0.133790i | ||||
\(839\) | 8.48528 | 0.292944 | 0.146472 | − | 0.989215i | \(-0.453208\pi\) | ||||
0.146472 | + | 0.989215i | \(0.453208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0000 | −0.931034 | ||||||||
\(842\) | −3.16228 | + | 5.47723i | −0.108979 | + | 0.188758i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 40.2492 | − | 23.2379i | 1.38544 | − | 0.799882i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3.46410i | − | 0.119028i | ||||||
\(848\) | 8.48528 | − | 14.6969i | 0.291386 | − | 0.504695i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −22.3607 | + | 38.7298i | −0.766965 | + | 1.32842i | ||||
\(851\) | 24.4949i | 0.839674i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 27.7128i | − | 0.948869i | −0.880291 | − | 0.474434i | \(-0.842653\pi\) | ||
0.880291 | − | 0.474434i | \(-0.157347\pi\) | |||||||
\(854\) | 25.4558 | − | 44.0908i | 0.871081 | − | 1.50876i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 41.5692i | 1.42081i | ||||||||
\(857\) | − | 26.9444i | − | 0.920403i | −0.887815 | − | 0.460201i | \(-0.847777\pi\) | ||
0.887815 | − | 0.460201i | \(-0.152223\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.0000 | −1.77422 | −0.887109 | − | 0.461561i | \(-0.847290\pi\) | ||||
−0.887109 | + | 0.461561i | \(0.847290\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.0000 | − | 31.1769i | 0.613082 | − | 1.06189i | ||||
\(863\) | −16.9706 | −0.577685 | −0.288842 | − | 0.957377i | \(-0.593270\pi\) | ||||
−0.288842 | + | 0.957377i | \(0.593270\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −37.9473 | − | 21.9089i | −1.28950 | − | 0.744495i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −53.6656 | + | 30.9839i | −1.82153 | + | 1.05166i | ||||
\(869\) | 14.1421 | 0.479739 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.6410i | 1.17377i | ||||||||
\(872\) | 12.6491 | 0.428353 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −28.4164 | + | 18.2348i | −0.961199 | + | 0.616801i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.47214 | 0.151013 | 0.0755067 | − | 0.997145i | \(-0.475943\pi\) | ||||
0.0755067 | + | 0.997145i | \(0.475943\pi\) | |||||||
\(878\) | −15.8114 | + | 27.3861i | −0.533609 | + | 0.924237i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.6228 | −1.06540 | −0.532699 | − | 0.846305i | \(-0.678822\pi\) | ||||
−0.532699 | + | 0.846305i | \(0.678822\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.00000 | −0.269221 | −0.134611 | − | 0.990899i | \(-0.542978\pi\) | ||||
−0.134611 | + | 0.990899i | \(0.542978\pi\) | |||||||
\(884\) | 28.2843 | + | 48.9898i | 0.951303 | + | 1.64771i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.1803 | − | 19.3649i | 0.375611 | − | 0.650577i | ||||
\(887\) | −53.7401 | −1.80442 | −0.902208 | − | 0.431301i | \(-0.858055\pi\) | ||||
−0.902208 | + | 0.431301i | \(0.858055\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 30.9839i | − | 1.03917i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22.3607 | + | 38.7298i | 0.748691 | + | 1.29677i | ||||
\(893\) | 21.2132 | + | 10.9545i | 0.709873 | + | 0.366577i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −33.9411 | − | 19.5959i | −1.13389 | − | 0.654654i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.00000 | − | 5.19615i | −0.300334 | − | 0.173398i | ||||
\(899\) | 12.6491 | 0.421871 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.8328 | −0.893931 | ||||||||
\(902\) | −9.48683 | − | 5.47723i | −0.315877 | − | 0.182372i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 34.6410i | 1.15214i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 23.2379i | − | 0.771602i | −0.922582 | − | 0.385801i | \(-0.873925\pi\) | ||
0.922582 | − | 0.385801i | \(-0.126075\pi\) | |||||||
\(908\) | 25.4558 | − | 14.6969i | 0.844782 | − | 0.487735i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.1127 | 1.03081 | 0.515405 | − | 0.856947i | \(-0.327642\pi\) | ||||
0.515405 | + | 0.856947i | \(0.327642\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50.0000 | 1.65476 | ||||||||
\(914\) | −2.82843 | + | 4.89898i | −0.0935561 | + | 0.162044i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 10.9545i | − | 0.361748i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.1051i | 1.25697i | 0.777821 | + | 0.628486i | \(0.216325\pi\) | ||||
−0.777821 | + | 0.628486i | \(0.783675\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.4164 | + | 7.74597i | 0.441846 | + | 0.255100i | ||||
\(923\) | 50.5964 | 1.66540 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.3607 | −0.735215 | ||||||||
\(926\) | −4.24264 | − | 2.44949i | −0.139422 | − | 0.0804952i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.00000 | + | 6.92820i | 0.131306 | + | 0.227429i | ||||
\(929\) | −12.6491 | −0.415004 | −0.207502 | − | 0.978235i | \(-0.566533\pi\) | ||||
−0.207502 | + | 0.978235i | \(0.566533\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.0000 | − | 19.3649i | 0.327737 | − | 0.634660i | ||||
\(932\) | 6.32456 | + | 10.9545i | 0.207168 | + | 0.358825i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.23607 | + | 3.87298i | −0.0731664 | + | 0.126728i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.00000 | −0.196011 | −0.0980057 | − | 0.995186i | \(-0.531246\pi\) | ||||
−0.0980057 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(938\) | −18.9737 | + | 32.8634i | −0.619512 | + | 1.07303i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.3553 | 1.15255 | 0.576276 | − | 0.817255i | \(-0.304506\pi\) | ||||
0.576276 | + | 0.817255i | \(0.304506\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.4164 | −0.436898 | ||||||||
\(944\) | −16.9706 | − | 9.79796i | −0.552345 | − | 0.318896i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.7587 | −1.74692 | −0.873462 | − | 0.486893i | \(-0.838130\pi\) | ||||
−0.873462 | + | 0.486893i | \(0.838130\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 53.6656 | 1.74206 | ||||||||
\(950\) | −16.6460 | − | 25.9405i | −0.540068 | − | 0.841621i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 61.9677i | 2.00839i | ||||||||
\(953\) | − | 31.8434i | − | 1.03151i | −0.856737 | − | 0.515754i | \(-0.827512\pi\) | ||
0.856737 | − | 0.515754i | \(-0.172488\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 28.4605 | − | 16.4317i | 0.920478 | − | 0.531438i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −33.5410 | − | 19.3649i | −1.08366 | − | 0.625652i | ||||
\(959\) | 43.8178i | 1.41495i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.0000 | 1.58065 | ||||||||
\(962\) | −14.1421 | + | 24.4949i | −0.455961 | + | 0.789747i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.8328 | − | 15.4919i | 0.864227 | − | 0.498962i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.1769i | − | 1.00258i | −0.865279 | − | 0.501291i | \(-0.832859\pi\) | ||
0.865279 | − | 0.501291i | \(-0.167141\pi\) | |||||||
\(968\) | −2.82843 | −0.0909091 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 14.6969i | − | 0.471647i | −0.971796 | − | 0.235824i | \(-0.924221\pi\) | ||
0.971796 | − | 0.235824i | \(-0.0757788\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41.5692i | 1.33265i | ||||||||
\(974\) | −6.32456 | + | 10.9545i | −0.202652 | + | 0.351003i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −36.0000 | − | 20.7846i | −1.15233 | − | 0.665299i | ||||
\(977\) | 36.7423i | 1.17549i | 0.809046 | + | 0.587746i | \(0.199985\pi\) | ||||
−0.809046 | + | 0.587746i | \(0.800015\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.2218i | 1.73294i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.6525 | + | 27.1109i | −0.499491 | + | 0.865143i | ||||
\(983\) | −50.9117 | −1.62383 | −0.811915 | − | 0.583775i | \(-0.801575\pi\) | ||||
−0.811915 | + | 0.583775i | \(0.801575\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.32456 | − | 10.9545i | 0.201415 | − | 0.348861i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −38.9443 | + | 1.82857i | −1.23898 | + | 0.0581747i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.94427 | 0.284124 | 0.142062 | − | 0.989858i | \(-0.454627\pi\) | ||||
0.142062 | + | 0.989858i | \(0.454627\pi\) | |||||||
\(992\) | 25.2982 | + | 43.8178i | 0.803219 | + | 1.39122i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 48.0000 | + | 27.7128i | 1.52247 | + | 0.878997i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 58.8897i | 1.86506i | 0.361097 | + | 0.932528i | \(0.382402\pi\) | ||||
−0.361097 | + | 0.932528i | \(0.617598\pi\) | |||||||
\(998\) | 5.65685 | − | 9.79796i | 0.179065 | − | 0.310149i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1368.2.e.d.379.3 | yes | 8 | |
3.2 | odd | 2 | inner | 1368.2.e.d.379.6 | yes | 8 | |
4.3 | odd | 2 | 5472.2.e.d.5167.3 | 8 | |||
8.3 | odd | 2 | inner | 1368.2.e.d.379.7 | yes | 8 | |
8.5 | even | 2 | 5472.2.e.d.5167.8 | 8 | |||
12.11 | even | 2 | 5472.2.e.d.5167.1 | 8 | |||
19.18 | odd | 2 | inner | 1368.2.e.d.379.5 | yes | 8 | |
24.5 | odd | 2 | 5472.2.e.d.5167.6 | 8 | |||
24.11 | even | 2 | inner | 1368.2.e.d.379.2 | yes | 8 | |
57.56 | even | 2 | inner | 1368.2.e.d.379.4 | yes | 8 | |
76.75 | even | 2 | 5472.2.e.d.5167.4 | 8 | |||
152.37 | odd | 2 | 5472.2.e.d.5167.7 | 8 | |||
152.75 | even | 2 | inner | 1368.2.e.d.379.1 | ✓ | 8 | |
228.227 | odd | 2 | 5472.2.e.d.5167.2 | 8 | |||
456.227 | odd | 2 | inner | 1368.2.e.d.379.8 | yes | 8 | |
456.341 | even | 2 | 5472.2.e.d.5167.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.e.d.379.1 | ✓ | 8 | 152.75 | even | 2 | inner | |
1368.2.e.d.379.2 | yes | 8 | 24.11 | even | 2 | inner | |
1368.2.e.d.379.3 | yes | 8 | 1.1 | even | 1 | trivial | |
1368.2.e.d.379.4 | yes | 8 | 57.56 | even | 2 | inner | |
1368.2.e.d.379.5 | yes | 8 | 19.18 | odd | 2 | inner | |
1368.2.e.d.379.6 | yes | 8 | 3.2 | odd | 2 | inner | |
1368.2.e.d.379.7 | yes | 8 | 8.3 | odd | 2 | inner | |
1368.2.e.d.379.8 | yes | 8 | 456.227 | odd | 2 | inner | |
5472.2.e.d.5167.1 | 8 | 12.11 | even | 2 | |||
5472.2.e.d.5167.2 | 8 | 228.227 | odd | 2 | |||
5472.2.e.d.5167.3 | 8 | 4.3 | odd | 2 | |||
5472.2.e.d.5167.4 | 8 | 76.75 | even | 2 | |||
5472.2.e.d.5167.5 | 8 | 456.341 | even | 2 | |||
5472.2.e.d.5167.6 | 8 | 24.5 | odd | 2 | |||
5472.2.e.d.5167.7 | 8 | 152.37 | odd | 2 | |||
5472.2.e.d.5167.8 | 8 | 8.5 | even | 2 |