Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(65,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.i (of order \(3\), degree \(2\), not 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: | \(3.57729801055\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 65.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.65 |
Dual form | 448.2.i.i.193.2 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0.866025 | + | 1.50000i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | −0.732294 | − | 0.680989i | \(-0.761550\pi\) |
0.955901 | + | 0.293691i | \(0.0948835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | − | 2.00000i | 0.654654 | − | 0.755929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.59808 | + | 4.50000i | 0.783349 | + | 1.35680i | 0.929980 | + | 0.367610i | \(0.119824\pi\) |
−0.146631 | + | 0.989191i | \(0.546843\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.73205 | 0.447214 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.50000 | − | 4.33013i | −0.606339 | − | 1.05021i | −0.991838 | − | 0.127502i | \(-0.959304\pi\) |
0.385499 | − | 0.922708i | \(-0.374029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.866025 | − | 1.50000i | 0.198680 | − | 0.344124i | −0.749421 | − | 0.662094i | \(-0.769668\pi\) |
0.948101 | + | 0.317970i | \(0.103001\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.50000 | + | 0.866025i | 0.981981 | + | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.866025 | − | 1.50000i | 0.180579 | − | 0.312772i | −0.761499 | − | 0.648166i | \(-0.775536\pi\) |
0.942078 | + | 0.335394i | \(0.108870\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.00000 | −1.48556 | −0.742781 | − | 0.669534i | \(-0.766494\pi\) | ||||
−0.742781 | + | 0.669534i | \(0.766494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.33013 | + | 7.50000i | 0.777714 | + | 1.34704i | 0.933257 | + | 0.359211i | \(0.116954\pi\) |
−0.155543 | + | 0.987829i | \(0.549713\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.50000 | + | 7.79423i | −0.783349 | + | 1.35680i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.866025 | − | 2.50000i | −0.146385 | − | 0.422577i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.50000 | + | 4.33013i | −0.410997 | + | 0.711868i | −0.994999 | − | 0.0998840i | \(-0.968153\pi\) |
0.584002 | + | 0.811752i | \(0.301486\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000 | 0.624695 | 0.312348 | − | 0.949968i | \(-0.398885\pi\) | ||||
0.312348 | + | 0.949968i | \(0.398885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.92820 | −1.05654 | −0.528271 | − | 0.849076i | \(-0.677159\pi\) | ||||
−0.528271 | + | 0.849076i | \(0.677159\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.33013 | + | 7.50000i | −0.631614 | + | 1.09399i | 0.355608 | + | 0.934635i | \(0.384274\pi\) |
−0.987222 | + | 0.159352i | \(0.949059\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.33013 | − | 7.50000i | 0.606339 | − | 1.05021i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.500000 | − | 0.866025i | −0.0686803 | − | 0.118958i | 0.829640 | − | 0.558298i | \(-0.188546\pi\) |
−0.898321 | + | 0.439340i | \(0.855212\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.19615 | 0.700649 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | 0.397360 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.866025 | + | 1.50000i | 0.112747 | + | 0.195283i | 0.916877 | − | 0.399170i | \(-0.130702\pi\) |
−0.804130 | + | 0.594454i | \(0.797368\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.50000 | − | 9.52628i | 0.704203 | − | 1.21972i | −0.262776 | − | 0.964857i | \(-0.584638\pi\) |
0.966978 | − | 0.254858i | \(-0.0820288\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.06218 | − | 10.5000i | −0.740613 | − | 1.28278i | −0.952217 | − | 0.305424i | \(-0.901202\pi\) |
0.211604 | − | 0.977356i | \(-0.432131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.00000 | 0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.8564 | −1.64445 | −0.822226 | − | 0.569160i | \(-0.807268\pi\) | ||||
−0.822226 | + | 0.569160i | \(0.807268\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.50000 | − | 12.9904i | −0.877809 | − | 1.52041i | −0.853740 | − | 0.520699i | \(-0.825671\pi\) |
−0.0240681 | − | 0.999710i | \(-0.507662\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.46410 | + | 6.00000i | −0.400000 | + | 0.692820i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.5000 | + | 2.59808i | 1.53847 | + | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.866025 | − | 1.50000i | 0.0974355 | − | 0.168763i | −0.813187 | − | 0.582003i | \(-0.802269\pi\) |
0.910622 | + | 0.413239i | \(0.135603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.50000 | + | 7.79423i | 0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.92820 | −0.760469 | −0.380235 | − | 0.924890i | \(-0.624157\pi\) | ||||
−0.380235 | + | 0.924890i | \(0.624157\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.00000 | −0.542326 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.92820 | − | 12.0000i | −0.742781 | − | 1.28654i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.50000 | + | 6.06218i | −0.370999 | + | 0.642590i | −0.989720 | − | 0.143022i | \(-0.954318\pi\) |
0.618720 | + | 0.785611i | \(0.287651\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.50000 | + | 12.9904i | −0.777714 | + | 1.34704i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.866025 | − | 1.50000i | −0.0888523 | − | 0.153897i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0000 | 1.21842 | 0.609208 | − | 0.793011i | \(-0.291488\pi\) | ||||
0.609208 | + | 0.793011i | \(0.291488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.50000 | − | 9.52628i | −0.547270 | − | 0.947900i | −0.998460 | − | 0.0554722i | \(-0.982334\pi\) |
0.451190 | − | 0.892428i | \(-0.351000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.79423 | − | 13.5000i | 0.767988 | − | 1.33019i | −0.170664 | − | 0.985329i | \(-0.554591\pi\) |
0.938652 | − | 0.344865i | \(-0.112075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.00000 | − | 3.46410i | 0.292770 | − | 0.338062i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.06218 | + | 10.5000i | −0.586053 | + | 1.01507i | 0.408690 | + | 0.912673i | \(0.365986\pi\) |
−0.994743 | + | 0.102400i | \(0.967348\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.50000 | − | 2.59808i | −0.143674 | − | 0.248851i | 0.785203 | − | 0.619238i | \(-0.212558\pi\) |
−0.928877 | + | 0.370387i | \(0.879225\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.66025 | −0.821995 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.866025 | − | 1.50000i | −0.0807573 | − | 0.139876i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.9904 | − | 2.50000i | −1.19083 | − | 0.229175i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.00000 | + | 13.8564i | −0.727273 | + | 1.25967i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.46410 | + | 6.00000i | 0.312348 | + | 0.541002i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.00000 | − | 10.3923i | −0.528271 | − | 0.914991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.33013 | + | 7.50000i | −0.378325 | + | 0.655278i | −0.990819 | − | 0.135197i | \(-0.956833\pi\) |
0.612494 | + | 0.790475i | \(0.290166\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.50000 | − | 4.33013i | −0.130066 | − | 0.375470i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.59808 | − | 4.50000i | 0.223607 | − | 0.387298i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.50000 | − | 4.33013i | −0.213589 | − | 0.369948i | 0.739246 | − | 0.673436i | \(-0.235182\pi\) |
−0.952835 | + | 0.303488i | \(0.901849\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.92820 | −0.587643 | −0.293821 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.0000 | −1.26323 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00000 | + | 6.92820i | −0.332182 | + | 0.575356i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.52628 | − | 7.50000i | 0.785714 | − | 0.618590i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.50000 | + | 6.06218i | −0.286731 | + | 0.496633i | −0.973028 | − | 0.230689i | \(-0.925902\pi\) |
0.686296 | + | 0.727322i | \(0.259235\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.33013 | + | 7.50000i | 0.352381 | + | 0.610341i | 0.986666 | − | 0.162758i | \(-0.0520389\pi\) |
−0.634285 | + | 0.773099i | \(0.718706\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.66025 | 0.695608 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.50000 | + | 6.06218i | 0.279330 | + | 0.483814i | 0.971219 | − | 0.238190i | \(-0.0765542\pi\) |
−0.691888 | + | 0.722005i | \(0.743221\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.866025 | − | 1.50000i | 0.0686803 | − | 0.118958i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.50000 | − | 4.33013i | −0.118217 | − | 0.341262i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.33013 | + | 7.50000i | −0.339162 | + | 0.587445i | −0.984275 | − | 0.176641i | \(-0.943477\pi\) |
0.645114 | + | 0.764087i | \(0.276810\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.50000 | + | 7.79423i | 0.350325 | + | 0.606780i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.46410 | −0.268060 | −0.134030 | − | 0.990977i | \(-0.542792\pi\) | ||||
−0.134030 | + | 0.990977i | \(0.542792\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.50000 | + | 4.33013i | −0.190071 | + | 0.329213i | −0.945274 | − | 0.326278i | \(-0.894205\pi\) |
0.755202 | + | 0.655492i | \(0.227539\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.3923 | + | 2.00000i | 0.785584 | + | 0.151186i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.50000 | + | 2.59808i | −0.112747 | + | 0.195283i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.33013 | − | 7.50000i | −0.323649 | − | 0.560576i | 0.657589 | − | 0.753377i | \(-0.271576\pi\) |
−0.981238 | + | 0.192800i | \(0.938243\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.0526 | 1.40841 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.50000 | + | 4.33013i | 0.183804 | + | 0.318357i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.9904 | − | 22.5000i | 0.949951 | − | 1.64536i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.00000 | − | 10.3923i | 0.654654 | − | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.2583 | + | 19.5000i | −0.814624 | + | 1.41097i | 0.0949733 | + | 0.995480i | \(0.469723\pi\) |
−0.909597 | + | 0.415491i | \(0.863610\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.50000 | + | 9.52628i | 0.395899 | + | 0.685717i | 0.993215 | − | 0.116289i | \(-0.0370998\pi\) |
−0.597317 | + | 0.802005i | \(0.703766\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.00000 | 0.569976 | 0.284988 | − | 0.958531i | \(-0.408010\pi\) | ||||
0.284988 | + | 0.958531i | \(0.408010\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.33013 | + | 7.50000i | 0.306955 | + | 0.531661i | 0.977695 | − | 0.210032i | \(-0.0673567\pi\) |
−0.670740 | + | 0.741693i | \(0.734023\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.5000 | − | 18.1865i | 0.740613 | − | 1.28278i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.8564 | + | 16.0000i | −0.972529 | + | 1.12298i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | − | 3.46410i | 0.139686 | − | 0.241943i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.00000 | 0.622543 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.7846 | 1.43087 | 0.715436 | − | 0.698679i | \(-0.246228\pi\) | ||||
0.715436 | + | 0.698679i | \(0.246228\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.0000 | − | 20.7846i | −0.822226 | − | 1.42414i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.46410 | + | 6.00000i | −0.236250 | + | 0.409197i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.5000 | + | 4.33013i | 1.52740 | + | 0.293948i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.9904 | − | 22.5000i | 0.877809 | − | 1.52041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.8564 | 0.927894 | 0.463947 | − | 0.885863i | \(-0.346433\pi\) | ||||
0.463947 | + | 0.885863i | \(0.346433\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.33013 | − | 7.50000i | −0.287401 | − | 0.497792i | 0.685788 | − | 0.727801i | \(-0.259458\pi\) |
−0.973189 | + | 0.230009i | \(0.926124\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.50000 | + | 12.9904i | −0.495614 | + | 0.858429i | −0.999987 | − | 0.00505719i | \(-0.998390\pi\) |
0.504373 | + | 0.863486i | \(0.331724\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.79423 | + | 22.5000i | 0.512823 | + | 1.48039i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.50000 | + | 4.33013i | −0.163780 | + | 0.283676i | −0.936222 | − | 0.351410i | \(-0.885702\pi\) |
0.772441 | + | 0.635086i | \(0.219036\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.33013 | + | 7.50000i | 0.282466 | + | 0.489246i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.00000 | 0.194871 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.3205 | 1.12037 | 0.560185 | − | 0.828367i | \(-0.310730\pi\) | ||||
0.560185 | + | 0.828367i | \(0.310730\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.50000 | − | 12.9904i | −0.483117 | − | 0.836784i | 0.516695 | − | 0.856170i | \(-0.327162\pi\) |
−0.999812 | + | 0.0193858i | \(0.993829\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.50000 | − | 2.59808i | −0.415270 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | − | 10.3923i | −0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.3205 | 1.09326 | 0.546630 | − | 0.837374i | \(-0.315910\pi\) | ||||
0.546630 | + | 0.837374i | \(0.315910\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00000 | 0.565825 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.33013 | − | 7.50000i | −0.271163 | − | 0.469668i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.50000 | + | 4.33013i | −0.155946 | + | 0.270106i | −0.933403 | − | 0.358830i | \(-0.883176\pi\) |
0.777457 | + | 0.628936i | \(0.216509\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.33013 | + | 12.5000i | 0.269061 | + | 0.776712i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.866025 | − | 1.50000i | −0.0534014 | − | 0.0924940i | 0.838089 | − | 0.545534i | \(-0.183673\pi\) |
−0.891490 | + | 0.453040i | \(0.850340\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.00000 | −0.0614295 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.1244 | −0.741999 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.50000 | − | 14.7224i | −0.518254 | − | 0.897643i | −0.999775 | − | 0.0212079i | \(-0.993249\pi\) |
0.481521 | − | 0.876435i | \(-0.340085\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.06218 | + | 10.5000i | −0.368251 | + | 0.637830i | −0.989292 | − | 0.145948i | \(-0.953377\pi\) |
0.621041 | + | 0.783778i | \(0.286710\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.3923 | + | 18.0000i | −0.626680 | + | 1.08544i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.50000 | + | 12.9904i | 0.450631 | + | 0.780516i | 0.998425 | − | 0.0560969i | \(-0.0178656\pi\) |
−0.547794 | + | 0.836613i | \(0.684532\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0000 | −1.19310 | −0.596550 | − | 0.802576i | \(-0.703462\pi\) | ||||
−0.596550 | + | 0.802576i | \(0.703462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.33013 | − | 7.50000i | −0.257399 | − | 0.445829i | 0.708145 | − | 0.706067i | \(-0.249532\pi\) |
−0.965544 | + | 0.260238i | \(0.916199\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.50000 | − | 2.59808i | 0.0888523 | − | 0.153897i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.92820 | − | 8.00000i | 0.408959 | − | 0.472225i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.3923 | + | 18.0000i | 0.609208 | + | 1.05518i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.0000 | 0.584206 | 0.292103 | − | 0.956387i | \(-0.405645\pi\) | ||||
0.292103 | + | 0.956387i | \(0.405645\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.73205 | 0.100844 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.5000 | + | 23.3827i | 0.783349 | + | 1.35680i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0000 | + | 13.8564i | −0.691669 | + | 0.798670i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.52628 | − | 16.5000i | 0.547270 | − | 0.947900i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.50000 | − | 9.52628i | −0.314929 | − | 0.545473i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.7846 | 1.18624 | 0.593120 | − | 0.805114i | \(-0.297896\pi\) | ||||
0.593120 | + | 0.805114i | \(0.297896\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.0000 | 1.53598 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.06218 | + | 10.5000i | 0.343755 | + | 0.595400i | 0.985127 | − | 0.171830i | \(-0.0549678\pi\) |
−0.641372 | + | 0.767230i | \(0.721635\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.5000 | − | 21.6506i | 0.706542 | − | 1.22377i | −0.259590 | − | 0.965719i | \(-0.583588\pi\) |
0.966132 | − | 0.258047i | \(-0.0830791\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.50000 | + | 4.33013i | −0.140414 | + | 0.243204i | −0.927653 | − | 0.373444i | \(-0.878177\pi\) |
0.787239 | + | 0.616649i | \(0.211510\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.7846 | − | 36.0000i | −1.16371 | − | 2.01561i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.0000 | −1.17211 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.66025 | −0.481869 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.59808 | − | 4.50000i | 0.143674 | − | 0.248851i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.50000 | + | 21.6506i | 0.413488 | + | 1.19364i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.33013 | + | 7.50000i | −0.238005 | + | 0.412237i | −0.960142 | − | 0.279513i | \(-0.909827\pi\) |
0.722137 | + | 0.691751i | \(0.243160\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.1244 | −0.662424 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.0000 | −0.653682 | −0.326841 | − | 0.945079i | \(-0.605984\pi\) | ||||
−0.326841 | + | 0.945079i | \(0.605984\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.46410 | + | 6.00000i | 0.188144 | + | 0.325875i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.5000 | + | 38.9711i | −1.21844 | + | 2.11041i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.50000 | − | 2.59808i | 0.0807573 | − | 0.139876i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.06218 | − | 10.5000i | −0.325435 | − | 0.563670i | 0.656165 | − | 0.754617i | \(-0.272177\pi\) |
−0.981600 | + | 0.190947i | \(0.938844\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.0000 | −1.71292 | −0.856460 | − | 0.516213i | \(-0.827341\pi\) | ||||
−0.856460 | + | 0.516213i | \(0.827341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.50000 | + | 9.52628i | 0.292735 | + | 0.507033i | 0.974456 | − | 0.224580i | \(-0.0721011\pi\) |
−0.681720 | + | 0.731613i | \(0.738768\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.92820 | + | 12.0000i | −0.367711 | + | 0.636894i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.50000 | − | 21.6506i | −0.396942 | − | 1.14587i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.33013 | + | 7.50000i | −0.228535 | + | 0.395835i | −0.957374 | − | 0.288850i | \(-0.906727\pi\) |
0.728839 | + | 0.684685i | \(0.240060\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.00000 | + | 13.8564i | 0.421053 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −27.7128 | −1.45455 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.0000 | −0.785136 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.7224 | − | 25.5000i | −0.768505 | − | 1.33109i | −0.938374 | − | 0.345623i | \(-0.887668\pi\) |
0.169869 | − | 0.985467i | \(-0.445666\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.59808 | − | 0.500000i | −0.134885 | − | 0.0259587i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.5000 | − | 30.3109i | 0.906116 | − | 1.56944i | 0.0867031 | − | 0.996234i | \(-0.472367\pi\) |
0.819413 | − | 0.573204i | \(-0.194300\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.79423 | + | 13.5000i | 0.402492 | + | 0.697137i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3923 | 0.533817 | 0.266908 | − | 0.963722i | \(-0.413998\pi\) | ||||
0.266908 | + | 0.963722i | \(0.413998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.52628 | − | 16.5000i | 0.486770 | − | 0.843111i | −0.513114 | − | 0.858320i | \(-0.671508\pi\) |
0.999884 | + | 0.0152097i | \(0.00484160\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.00000 | − | 10.3923i | 0.458682 | − | 0.529641i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.50000 | + | 4.33013i | 0.126755 | + | 0.219546i | 0.922418 | − | 0.386194i | \(-0.126210\pi\) |
−0.795663 | + | 0.605740i | \(0.792877\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.66025 | −0.437968 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.0000 | −0.756650 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.866025 | − | 1.50000i | −0.0435745 | − | 0.0754732i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.50000 | − | 14.7224i | 0.426603 | − | 0.738898i | −0.569966 | − | 0.821668i | \(-0.693044\pi\) |
0.996569 | + | 0.0827707i | \(0.0263769\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.19615 | − | 6.00000i | 0.260133 | − | 0.300376i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.50000 | − | 16.4545i | 0.474407 | − | 0.821698i | −0.525163 | − | 0.851002i | \(-0.675996\pi\) |
0.999571 | + | 0.0293039i | \(0.00932905\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.00000 | 0.447214 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.9808 | −1.28782 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.50000 | + | 2.59808i | 0.0741702 | + | 0.128467i | 0.900725 | − | 0.434389i | \(-0.143036\pi\) |
−0.826555 | + | 0.562856i | \(0.809703\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.33013 | − | 7.50000i | 0.213589 | − | 0.369948i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.50000 | + | 0.866025i | 0.221431 | + | 0.0426143i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.46410 | + | 6.00000i | −0.170046 | + | 0.294528i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.00000 | − | 10.3923i | −0.293821 | − | 0.508913i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.6410 | −1.69232 | −0.846162 | − | 0.532925i | \(-0.821093\pi\) | ||||
−0.846162 | + | 0.532925i | \(0.821093\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.0000 | 1.16969 | 0.584844 | − | 0.811146i | \(-0.301156\pi\) | ||||
0.584844 | + | 0.811146i | \(0.301156\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.0000 | − | 17.3205i | 0.485071 | − | 0.840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.52628 | − | 27.5000i | −0.461009 | − | 1.33082i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.2583 | + | 19.5000i | 0.542295 | + | 0.939282i | 0.998772 | + | 0.0495468i | \(0.0157777\pi\) |
−0.456477 | + | 0.889735i | \(0.650889\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.00000 | 0.192228 | 0.0961139 | − | 0.995370i | \(-0.469359\pi\) | ||||
0.0961139 | + | 0.995370i | \(0.469359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.8564 | −0.664364 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.50000 | − | 2.59808i | −0.0717547 | − | 0.124283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.33013 | + | 7.50000i | −0.206666 | + | 0.357955i | −0.950662 | − | 0.310228i | \(-0.899595\pi\) |
0.743996 | + | 0.668184i | \(0.232928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.79423 | − | 13.5000i | 0.370315 | − | 0.641404i | −0.619299 | − | 0.785155i | \(-0.712583\pi\) |
0.989614 | + | 0.143751i | \(0.0459164\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.50000 | + | 6.06218i | 0.165916 | + | 0.287375i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.1244 | −0.573462 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.0000 | 1.32140 | 0.660701 | − | 0.750649i | \(-0.270259\pi\) | ||||
0.660701 | + | 0.750649i | \(0.270259\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.3923 | + | 18.0000i | 0.489355 | + | 0.847587i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.50000 | + | 12.9904i | −0.352381 | + | 0.610341i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.50000 | + | 12.9904i | −0.350835 | + | 0.607664i | −0.986396 | − | 0.164386i | \(-0.947436\pi\) |
0.635561 | + | 0.772051i | \(0.280769\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.9904 | − | 22.5000i | −0.606339 | − | 1.05021i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.0000 | 1.86299 | 0.931493 | − | 0.363760i | \(-0.118507\pi\) | ||||
0.931493 | + | 0.363760i | \(0.118507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.7128 | −1.28792 | −0.643962 | − | 0.765058i | \(-0.722710\pi\) | ||||
−0.643962 | + | 0.765058i | \(0.722710\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.50000 | + | 12.9904i | 0.347804 | + | 0.602414i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.59808 | − | 4.50000i | 0.120225 | − | 0.208235i | −0.799632 | − | 0.600491i | \(-0.794972\pi\) |
0.919856 | + | 0.392256i | \(0.128305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −31.5000 | − | 6.06218i | −1.45453 | − | 0.279925i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.06218 | + | 10.5000i | −0.279330 | + | 0.483814i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.0000 | − | 31.1769i | −0.827641 | − | 1.43352i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.92820 | 0.317888 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.9904 | + | 22.5000i | 0.593546 | + | 1.02805i | 0.993750 | + | 0.111625i | \(0.0356057\pi\) |
−0.400205 | + | 0.916426i | \(0.631061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.19615 | − | 6.00000i | 0.236433 | − | 0.273009i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.00000 | − | 10.3923i | 0.272446 | − | 0.471890i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.9904 | + | 22.5000i | 0.588650 | + | 1.01957i | 0.994410 | + | 0.105592i | \(0.0336738\pi\) |
−0.405759 | + | 0.913980i | \(0.632993\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.0000 | −0.678323 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.3205 | −0.781664 | −0.390832 | − | 0.920462i | \(-0.627813\pi\) | ||||
−0.390832 | + | 0.920462i | \(0.627813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0000 | + | 34.6410i | 0.900755 | + | 1.56015i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.0000 | + | 27.7128i | −1.07655 | + | 1.24309i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.52628 | − | 16.5000i | 0.426455 | − | 0.738641i | −0.570100 | − | 0.821575i | \(-0.693096\pi\) |
0.996555 | + | 0.0829337i | \(0.0264290\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.00000 | − | 5.19615i | −0.134030 | − | 0.232147i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.7128 | 1.23565 | 0.617827 | − | 0.786314i | \(-0.288013\pi\) | ||||
0.617827 | + | 0.786314i | \(0.288013\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.0000 | −0.489494 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.2583 | − | 19.5000i | −0.500000 | − | 0.866025i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.50000 | − | 14.7224i | 0.376756 | − | 0.652560i | −0.613832 | − | 0.789436i | \(-0.710373\pi\) |
0.990588 | + | 0.136876i | \(0.0437062\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −38.9711 | − | 7.50000i | −1.72398 | − | 0.331780i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.50000 | − | 7.79423i | 0.198680 | − | 0.344124i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.79423 | − | 13.5000i | −0.343455 | − | 0.594881i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −45.0000 | −1.97910 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.66025 | −0.380143 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5000 | + | 21.6506i | 0.547635 | + | 0.948532i | 0.998436 | + | 0.0559071i | \(0.0178051\pi\) |
−0.450801 | + | 0.892624i | \(0.648862\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.9904 | + | 22.5000i | −0.568030 | + | 0.983856i | 0.428731 | + | 0.903432i | \(0.358961\pi\) |
−0.996761 | + | 0.0804241i | \(0.974373\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.00000 | + | 17.3205i | 0.261861 | + | 0.755929i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.6506 | − | 37.5000i | 0.943116 | − | 1.63353i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.0000 | + | 17.3205i | 0.434783 | + | 0.753066i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.06218 | + | 10.5000i | 0.262091 | + | 0.453955i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.50000 | − | 12.9904i | 0.323649 | − | 0.560576i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.5788 | − | 22.5000i | 1.23098 | − | 0.969144i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.50000 | − | 7.79423i | 0.193470 | − | 0.335100i | −0.752928 | − | 0.658103i | \(-0.771359\pi\) |
0.946398 | + | 0.323003i | \(0.104692\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.19615 | + | 9.00000i | 0.222988 | + | 0.386227i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.00000 | −0.128506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.46410 | 0.148114 | 0.0740571 | − | 0.997254i | \(-0.476405\pi\) | ||||
0.0740571 | + | 0.997254i | \(0.476405\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.92820 | + | 12.0000i | −0.295151 | + | 0.511217i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.50000 | − | 4.33013i | −0.0637865 | − | 0.184136i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.33013 | + | 7.50000i | −0.183804 | + | 0.318357i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.5000 | − | 37.2391i | −0.910984 | − | 1.57787i | −0.812677 | − | 0.582715i | \(-0.801990\pi\) |
−0.0983076 | − | 0.995156i | \(-0.531343\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 45.0000 | 1.89990 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.79423 | + | 13.5000i | 0.328488 | + | 0.568957i | 0.982212 | − | 0.187776i | \(-0.0601278\pi\) |
−0.653724 | + | 0.756733i | \(0.726794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00000 | − | 3.46410i | 0.0841406 | − | 0.145736i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.3827 | + | 4.50000i | 0.981981 | + | 0.188982i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.5000 | − | 21.6506i | 0.524027 | − | 0.907642i | −0.475581 | − | 0.879672i | \(-0.657762\pi\) |
0.999609 | − | 0.0279702i | \(-0.00890434\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.59808 | + | 4.50000i | 0.108726 | + | 0.188319i | 0.915254 | − | 0.402876i | \(-0.131990\pi\) |
−0.806528 | + | 0.591195i | \(0.798656\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −39.0000 | −1.62925 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.92820 | 0.288926 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.5000 | − | 19.9186i | −0.478751 | − | 0.829222i | 0.520952 | − | 0.853586i | \(-0.325577\pi\) |
−0.999703 | + | 0.0243645i | \(0.992244\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.52628 | + | 16.5000i | −0.395899 | + | 0.685717i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | + | 13.8564i | −0.497844 | + | 0.574861i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.59808 | − | 4.50000i | 0.107601 | − | 0.186371i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.6410 | 1.42979 | 0.714894 | − | 0.699233i | \(-0.246475\pi\) | ||||
0.714894 | + | 0.699233i | \(0.246475\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.0000 | 0.618064 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.92820 | + | 12.0000i | 0.284988 | + | 0.493614i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.5000 | + | 25.1147i | −0.595444 | + | 1.03134i | 0.398040 | + | 0.917368i | \(0.369690\pi\) |
−0.993484 | + | 0.113971i | \(0.963643\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.66025 | + | 10.0000i | −0.355036 | + | 0.409960i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.50000 | + | 12.9904i | −0.306955 | + | 0.531661i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.6506 | − | 37.5000i | −0.884621 | − | 1.53221i | −0.846147 | − | 0.532949i | \(-0.821084\pi\) |
−0.0384735 | − | 0.999260i | \(-0.512250\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.0000 | −0.815817 | −0.407909 | − | 0.913023i | \(-0.633742\pi\) | ||||
−0.407909 | + | 0.913023i | \(0.633742\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.00000 | + | 13.8564i | 0.325246 | + | 0.563343i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.59808 | − | 4.50000i | 0.105453 | − | 0.182649i | −0.808470 | − | 0.588537i | \(-0.799704\pi\) |
0.913923 | + | 0.405887i | \(0.133038\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −36.0000 | − | 6.92820i | −1.45879 | − | 0.280745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.50000 | + | 4.33013i | 0.100974 | + | 0.174892i | 0.912086 | − | 0.409998i | \(-0.134471\pi\) |
−0.811112 | + | 0.584891i | \(0.801137\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.92820 | 0.279372 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.0000 | −0.805170 | −0.402585 | − | 0.915383i | \(-0.631888\pi\) | ||||
−0.402585 | + | 0.915383i | \(0.631888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.79423 | + | 13.5000i | 0.313276 | + | 0.542611i | 0.979070 | − | 0.203526i | \(-0.0652400\pi\) |
−0.665793 | + | 0.746136i | \(0.731907\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.50000 | − | 7.79423i | 0.180579 | − | 0.312772i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.06218 | + | 17.5000i | 0.242876 | + | 0.701123i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.79423 | + | 13.5000i | 0.311272 | + | 0.539138i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.0000 | 0.996815 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.8564 | 0.551615 | 0.275807 | − | 0.961213i | \(-0.411055\pi\) | ||||
0.275807 | + | 0.961213i | \(0.411055\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.0000 | + | 31.1769i | 0.715436 | + | 1.23917i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.500000 | + | 0.866025i | 0.0197488 | + | 0.0342059i | 0.875731 | − | 0.482800i | \(-0.160380\pi\) |
−0.855982 | + | 0.517005i | \(0.827047\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.6410 | 1.36611 | 0.683054 | − | 0.730368i | \(-0.260651\pi\) | ||||
0.683054 | + | 0.730368i | \(0.260651\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.0000 | −0.472500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.7224 | − | 25.5000i | −0.578799 | − | 1.00251i | −0.995618 | − | 0.0935189i | \(-0.970188\pi\) |
0.416819 | − | 0.908990i | \(-0.363145\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.50000 | + | 7.79423i | −0.176640 | + | 0.305950i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.9904 | + | 37.5000i | 0.509133 | + | 1.46974i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.50000 | + | 4.33013i | −0.0978326 | + | 0.169451i | −0.910787 | − | 0.412876i | \(-0.864524\pi\) |
0.812955 | + | 0.582327i | \(0.197858\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.33013 | + | 7.50000i | 0.169192 | + | 0.293049i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.92820 | 0.269884 | 0.134942 | − | 0.990853i | \(-0.456915\pi\) | ||||
0.134942 | + | 0.990853i | \(0.456915\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.5000 | + | 26.8468i | 0.602880 | + | 1.04422i | 0.992383 | + | 0.123194i | \(0.0393136\pi\) |
−0.389503 | + | 0.921025i | \(0.627353\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.50000 | − | 0.866025i | −0.174503 | − | 0.0335830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.92820 | + | 12.0000i | −0.268261 | + | 0.464642i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.0000 | + | 20.7846i | 0.463947 | + | 0.803579i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 57.1577 | 2.20655 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0000 | 0.770943 | 0.385472 | − | 0.922720i | \(-0.374039\pi\) | ||||
0.385472 | + | 0.922720i | \(0.374039\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.3923 | + | 18.0000i | 0.400000 | + | 0.692820i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.5000 | − | 21.6506i | 0.480414 | − | 0.832102i | −0.519333 | − | 0.854572i | \(-0.673820\pi\) |
0.999748 | + | 0.0224702i | \(0.00715308\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.7846 | − | 24.0000i | 0.797640 | − | 0.921035i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.50000 | − | 12.9904i | 0.287401 | − | 0.497792i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.4545 | + | 28.5000i | 0.629613 | + | 1.09052i | 0.987629 | + | 0.156807i | \(0.0501200\pi\) |
−0.358016 | + | 0.933715i | \(0.616547\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.00000 | −0.191040 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.9808 | −0.991228 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.59808 | − | 4.50000i | 0.0988355 | − | 0.171188i | −0.812367 | − | 0.583146i | \(-0.801822\pi\) |
0.911203 | + | 0.411958i | \(0.135155\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.46410 | + | 6.00000i | −0.131401 | + | 0.227593i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.0000 | − | 17.3205i | −0.378777 | − | 0.656061i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.66025 | −0.327561 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.0000 | −0.528773 | −0.264386 | − | 0.964417i | \(-0.585169\pi\) | ||||
−0.264386 | + | 0.964417i | \(0.585169\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.33013 | + | 7.50000i | 0.163314 | + | 0.282868i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.50000 | + | 12.9904i | −0.282466 | + | 0.489246i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.5788 | − | 5.50000i | −1.07482 | − | 0.206849i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5000 | − | 23.3827i | 0.507003 | − | 0.878155i | −0.492964 | − | 0.870050i | \(-0.664087\pi\) |
0.999967 | − | 0.00810550i | \(-0.00258009\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.0000 | 0.561754 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.0000 | + | 25.9808i | 0.560185 | + | 0.970269i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.79423 | − | 13.5000i | 0.290676 | − | 0.503465i | −0.683294 | − | 0.730143i | \(-0.739453\pi\) |
0.973970 | + | 0.226678i | \(0.0727866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.5000 | − | 38.9711i | −0.502766 | − | 1.45136i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.9904 | − | 22.5000i | 0.483117 | − | 0.836784i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.0000 | − | 27.7128i | −0.594225 | − | 1.02923i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.8564 | −0.513906 | −0.256953 | − | 0.966424i | \(-0.582719\pi\) | ||||
−0.256953 | + | 0.966424i | \(0.582719\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.3205 | + | 30.0000i | 0.640622 | + | 1.10959i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.5000 | − | 44.1673i | 0.941864 | − | 1.63136i | 0.179952 | − | 0.983675i | \(-0.442406\pi\) |
0.761912 | − | 0.647681i | \(-0.224261\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.73205 | − | 12.0000i | −0.0638877 | − | 0.442627i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.5000 | − | 54.5596i | 1.16032 | − | 2.00973i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.52628 | + | 16.5000i | 0.350430 | + | 0.606962i | 0.986325 | − | 0.164813i | \(-0.0527022\pi\) |
−0.635895 | + | 0.771776i | \(0.719369\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.7128 | 1.01668 | 0.508342 | − | 0.861155i | \(-0.330258\pi\) | ||||
0.508342 | + | 0.861155i | \(0.330258\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.50000 | + | 6.06218i | 0.128230 | + | 0.222101i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.5000 | + | 30.3109i | 0.383662 | + | 1.10754i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.33013 | + | 7.50000i | −0.158009 | + | 0.273679i | −0.934150 | − | 0.356879i | \(-0.883841\pi\) |
0.776142 | + | 0.630558i | \(0.217174\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.0000 | + | 25.9808i | 0.546630 | + | 0.946792i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.66025 | 0.315179 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.79423 | + | 13.5000i | 0.282913 | + | 0.490019i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.50000 | + | 11.2583i | −0.235625 | + | 0.408114i | −0.959454 | − | 0.281865i | \(-0.909047\pi\) |
0.723829 | + | 0.689979i | \(0.242380\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.79423 | − | 1.50000i | −0.282170 | − | 0.0543036i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.0000 | 0.721218 | 0.360609 | − | 0.932717i | \(-0.382569\pi\) | ||||
0.360609 | + | 0.932717i | \(0.382569\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.66025 | −0.311891 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.50000 | + | 4.33013i | 0.0899188 | + | 0.155744i | 0.907477 | − | 0.420103i | \(-0.138006\pi\) |
−0.817558 | + | 0.575846i | \(0.804673\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.3205 | + | 30.0000i | −0.622171 | + | 1.07763i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.0000 | + | 17.3205i | −0.538122 | + | 0.621370i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.46410 | − | 6.00000i | 0.124114 | − | 0.214972i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.0000 | − | 62.3538i | −1.28818 | − | 2.23120i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −41.5692 | −1.48556 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.00000 | 0.249841 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.9186 | − | 34.5000i | −0.710021 | − | 1.22979i | −0.964849 | − | 0.262806i | \(-0.915352\pi\) |
0.254828 | − | 0.966986i | \(-0.417981\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.50000 | − | 2.59808i | 0.0534014 | − | 0.0924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.92820 | − | 8.00000i | 0.246339 | − | 0.284447i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.866025 | − | 1.50000i | −0.0307148 | − | 0.0531995i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.0000 | −1.41687 | −0.708436 | − | 0.705775i | \(-0.750599\pi\) | ||||
−0.708436 | + | 0.705775i | \(0.750599\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.3013 | 1.53189 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.9711 | − | 67.5000i | 1.37526 | − | 2.38202i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.50000 | − | 0.866025i | −0.158604 | − | 0.0305234i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.7224 | − | 25.5000i | 0.518254 | − | 0.897643i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.50000 | − | 6.06218i | −0.123053 | − | 0.213135i | 0.797917 | − | 0.602767i | \(-0.205935\pi\) |
−0.920970 | + | 0.389633i | \(0.872602\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.6410 | −1.21641 | −0.608205 | − | 0.793780i | \(-0.708110\pi\) | ||||
−0.608205 | + | 0.793780i | \(0.708110\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.0000 | −0.736502 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.33013 | + | 7.50000i | 0.151678 | + | 0.262714i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.00000 | + | 10.3923i | −0.209913 | + | 0.363581i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.5000 | − | 21.6506i | 0.436253 | − | 0.755612i | −0.561144 | − | 0.827718i | \(-0.689639\pi\) |
0.997397 | + | 0.0721058i | \(0.0229719\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.79423 | − | 13.5000i | −0.271690 | − | 0.470580i | 0.697605 | − | 0.716483i | \(-0.254249\pi\) |
−0.969295 | + | 0.245902i | \(0.920916\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −36.0000 | −1.25336 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.7846 | 0.722752 | 0.361376 | − | 0.932420i | \(-0.382307\pi\) | ||||
0.361376 | + | 0.932420i | \(0.382307\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.5000 | + | 38.9711i | 0.781457 | + | 1.35352i | 0.931093 | + | 0.364783i | \(0.118857\pi\) |
−0.149635 | + | 0.988741i | \(0.547810\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.9904 | + | 22.5000i | −0.450631 | + | 0.780516i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.5000 | + | 21.6506i | −0.952819 | + | 0.750150i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.73205 | + | 3.00000i | −0.0599401 | + | 0.103819i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.5000 | + | 38.9711i | 0.777714 | + | 1.34704i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.5692 | −1.43513 | −0.717564 | − | 0.696492i | \(-0.754743\pi\) | ||||
−0.717564 | + | 0.696492i | \(0.754743\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.3205 | − | 30.0000i | −0.596550 | − | 1.03325i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.50000 | + | 11.2583i | −0.223607 | + | 0.387298i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.8564 | + | 40.0000i | 0.476112 | + | 1.37442i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.50000 | − | 12.9904i | 0.257399 | − | 0.445829i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.33013 | + | 7.50000i | 0.148435 | + | 0.257097i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.0000 | −0.547830 | −0.273915 | − | 0.961754i | \(-0.588319\pi\) | ||||
−0.273915 | + | 0.961754i | \(0.588319\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.50000 | − | 6.06218i | −0.119558 | − | 0.207080i | 0.800035 | − | 0.599954i | \(-0.204814\pi\) |
−0.919592 | + | 0.392874i | \(0.871481\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.9904 | + | 22.5000i | −0.443226 | + | 0.767690i | −0.997927 | − | 0.0643599i | \(-0.979499\pi\) |
0.554701 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.0000 | + | 3.46410i | 0.613438 | + | 0.118056i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.8468 | + | 46.5000i | −0.913875 | + | 1.58288i | −0.105336 | + | 0.994437i | \(0.533592\pi\) |
−0.808540 | + | 0.588442i | \(0.799742\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.50000 | + | 4.33013i | 0.0850026 | + | 0.147229i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.8564 | −0.470588 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.00000 | 0.305304 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.5885 | − | 18.0000i | 0.526986 | − | 0.608511i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.50000 | + | 6.06218i | −0.118187 | + | 0.204705i | −0.919049 | − | 0.394143i | \(-0.871041\pi\) |
0.800862 | + | 0.598848i | \(0.204375\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.66025 | + | 15.0000i | 0.292103 | + | 0.505937i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.0000 | −1.14549 | −0.572745 | − | 0.819734i | \(-0.694121\pi\) | ||||
−0.572745 | + | 0.819734i | \(0.694121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.6410 | −1.16576 | −0.582882 | − | 0.812557i | \(-0.698075\pi\) | ||||
−0.582882 | + | 0.812557i | \(0.698075\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.50000 | + | 2.59808i | 0.0504219 | + | 0.0873334i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.3827 | − | 40.5000i | 0.785114 | − | 1.35986i | −0.143817 | − | 0.989604i | \(-0.545938\pi\) |
0.928931 | − | 0.370253i | \(-0.120729\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.3827 | + | 40.5000i | −0.783349 | + | 1.35680i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.50000 | + | 12.9904i | 0.250978 | + | 0.434707i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.66025 | −0.289480 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.6410 | − | 60.0000i | −1.15534 | − | 2.00111i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.50000 | + | 4.33013i | −0.0832871 | + | 0.144257i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −31.1769 | − | 6.00000i | −1.03750 | − | 0.199667i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.00000 | − | 5.19615i | 0.0997234 | − | 0.172726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.9186 | − | 34.5000i | −0.661386 | − | 1.14555i | −0.980252 | − | 0.197754i | \(-0.936635\pi\) |
0.318866 | − | 0.947800i | \(-0.396698\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.8564 | 0.459083 | 0.229542 | − | 0.973299i | \(-0.426277\pi\) | ||||
0.229542 | + | 0.973299i | \(0.426277\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | − | 31.1769i | −0.595713 | − | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.52628 | − | 16.5000i | 0.314929 | − | 0.545473i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.50000 | + | 21.6506i | 0.247672 | + | 0.714967i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.1865 | + | 31.5000i | −0.599918 | + | 1.03909i | 0.392914 | + | 0.919575i | \(0.371467\pi\) |
−0.992833 | + | 0.119514i | \(0.961866\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.0000 | + | 31.1769i | 0.593120 | + | 1.02731i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.0000 | −0.657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.5000 | + | 40.7032i | −0.771010 | + | 1.33543i | 0.166000 | + | 0.986126i | \(0.446915\pi\) |
−0.937010 | + | 0.349303i | \(0.886418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.2583 | − | 4.50000i | −0.368977 | − | 0.147482i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.5000 | + | 18.1865i | −0.343755 | + | 0.595400i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.9904 | − | 22.5000i | −0.424831 | − | 0.735829i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.0000 | 0.326686 | 0.163343 | − | 0.986569i | \(-0.447772\pi\) | ||||
0.163343 | + | 0.986569i | \(0.447772\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 43.3013 | 1.41308 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.5000 | − | 21.6506i | −0.407488 | − | 0.705791i | 0.587119 | − | 0.809500i | \(-0.300262\pi\) |
−0.994608 | + | 0.103710i | \(0.966929\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.46410 | − | 6.00000i | 0.112807 | − | 0.195387i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.50000 | − | 12.9904i | −0.146385 | − | 0.422577i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.59808 | − | 4.50000i | 0.0844261 | − | 0.146230i | −0.820720 | − | 0.571330i | \(-0.806428\pi\) |
0.905147 | + | 0.425100i | \(0.139761\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.66025 | −0.280828 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.0000 | 0.647864 | 0.323932 | − | 0.946080i | \(-0.394995\pi\) | ||||
0.323932 | + | 0.946080i | \(0.394995\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.2583 | + | 19.5000i | 0.364311 | + | 0.631005i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 36.0000 | − | 62.3538i | 1.16371 | − | 2.01561i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.9904 | − | 2.50000i | −0.419481 | − | 0.0807292i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | + | 38.1051i | −0.709677 | + | 1.22920i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.0000 | 0.354103 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.8564 | 0.445592 | 0.222796 | − | 0.974865i | \(-0.428482\pi\) | ||||
0.222796 | + | 0.974865i | \(0.428482\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.50000 | − | 12.9904i | −0.240935 | − | 0.417311i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.33013 | + | 7.50000i | −0.138960 | + | 0.240686i | −0.927103 | − | 0.374806i | \(-0.877709\pi\) |
0.788143 | + | 0.615492i | \(0.211043\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0000 | + | 13.8564i | −0.384702 | + | 0.444216i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.5000 | − | 32.0429i | −0.591867 | − | 1.02514i | −0.993981 | − | 0.109555i | \(-0.965058\pi\) |
0.402113 | − | 0.915590i | \(-0.368276\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.3731 | −1.16249 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.4545 | − | 28.5000i | −0.524816 | − | 0.909009i | −0.999582 | − | 0.0288967i | \(-0.990801\pi\) |
0.474766 | − | 0.880112i | \(-0.342533\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.00000 | − | 6.92820i | 0.127451 | − | 0.220751i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −25.9808 | + | 30.0000i | −0.826977 | + | 0.954911i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.00000 | + | 10.3923i | −0.190789 | + | 0.330456i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.9904 | + | 22.5000i | 0.412653 | + | 0.714736i | 0.995179 | − | 0.0980761i | \(-0.0312689\pi\) |
−0.582526 | + | 0.812812i | \(0.697936\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.0000 | −0.476011 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.66025 | 0.274549 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.5000 | + | 19.9186i | 0.364209 | + | 0.630828i | 0.988649 | − | 0.150245i | \(-0.0480062\pi\) |
−0.624440 | + | 0.781073i | \(0.714673\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.9904 | + | 22.5000i | −0.410997 | + | 0.711868i |
(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 | 448.2.i.i.65.2 | 4 | ||
4.3 | odd | 2 | inner | 448.2.i.i.65.1 | 4 | ||
7.2 | even | 3 | 3136.2.a.bh.1.1 | 2 | |||
7.4 | even | 3 | inner | 448.2.i.i.193.2 | 4 | ||
7.5 | odd | 6 | 3136.2.a.bu.1.2 | 2 | |||
8.3 | odd | 2 | 224.2.i.b.65.2 | yes | 4 | ||
8.5 | even | 2 | 224.2.i.b.65.1 | ✓ | 4 | ||
24.5 | odd | 2 | 2016.2.s.r.289.2 | 4 | |||
24.11 | even | 2 | 2016.2.s.r.289.1 | 4 | |||
28.11 | odd | 6 | inner | 448.2.i.i.193.1 | 4 | ||
28.19 | even | 6 | 3136.2.a.bu.1.1 | 2 | |||
28.23 | odd | 6 | 3136.2.a.bh.1.2 | 2 | |||
56.3 | even | 6 | 1568.2.i.u.1537.1 | 4 | |||
56.5 | odd | 6 | 1568.2.a.n.1.1 | 2 | |||
56.11 | odd | 6 | 224.2.i.b.193.2 | yes | 4 | ||
56.13 | odd | 2 | 1568.2.i.u.961.2 | 4 | |||
56.19 | even | 6 | 1568.2.a.n.1.2 | 2 | |||
56.27 | even | 2 | 1568.2.i.u.961.1 | 4 | |||
56.37 | even | 6 | 1568.2.a.s.1.2 | 2 | |||
56.45 | odd | 6 | 1568.2.i.u.1537.2 | 4 | |||
56.51 | odd | 6 | 1568.2.a.s.1.1 | 2 | |||
56.53 | even | 6 | 224.2.i.b.193.1 | yes | 4 | ||
168.11 | even | 6 | 2016.2.s.r.865.1 | 4 | |||
168.53 | odd | 6 | 2016.2.s.r.865.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.i.b.65.1 | ✓ | 4 | 8.5 | even | 2 | ||
224.2.i.b.65.2 | yes | 4 | 8.3 | odd | 2 | ||
224.2.i.b.193.1 | yes | 4 | 56.53 | even | 6 | ||
224.2.i.b.193.2 | yes | 4 | 56.11 | odd | 6 | ||
448.2.i.i.65.1 | 4 | 4.3 | odd | 2 | inner | ||
448.2.i.i.65.2 | 4 | 1.1 | even | 1 | trivial | ||
448.2.i.i.193.1 | 4 | 28.11 | odd | 6 | inner | ||
448.2.i.i.193.2 | 4 | 7.4 | even | 3 | inner | ||
1568.2.a.n.1.1 | 2 | 56.5 | odd | 6 | |||
1568.2.a.n.1.2 | 2 | 56.19 | even | 6 | |||
1568.2.a.s.1.1 | 2 | 56.51 | odd | 6 | |||
1568.2.a.s.1.2 | 2 | 56.37 | even | 6 | |||
1568.2.i.u.961.1 | 4 | 56.27 | even | 2 | |||
1568.2.i.u.961.2 | 4 | 56.13 | odd | 2 | |||
1568.2.i.u.1537.1 | 4 | 56.3 | even | 6 | |||
1568.2.i.u.1537.2 | 4 | 56.45 | odd | 6 | |||
2016.2.s.r.289.1 | 4 | 24.11 | even | 2 | |||
2016.2.s.r.289.2 | 4 | 24.5 | odd | 2 | |||
2016.2.s.r.865.1 | 4 | 168.11 | even | 6 | |||
2016.2.s.r.865.2 | 4 | 168.53 | odd | 6 | |||
3136.2.a.bh.1.1 | 2 | 7.2 | even | 3 | |||
3136.2.a.bh.1.2 | 2 | 28.23 | odd | 6 | |||
3136.2.a.bu.1.1 | 2 | 28.19 | even | 6 | |||
3136.2.a.bu.1.2 | 2 | 7.5 | odd | 6 |