Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(524,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.524");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.g (of order \(2\), degree \(1\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 524.3 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.524 |
Dual form | 525.2.g.b.524.4 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | 1.22474 | 0.612372 | − | 0.790569i | \(-0.290215\pi\) | ||||
0.612372 | + | 0.790569i | \(0.290215\pi\) | |||||||
\(3\) | −1.73205 | −1.00000 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.00000 | −1.22474 | ||||||||
\(7\) | −1.73205 | − | 2.00000i | −0.654654 | − | 0.755929i | ||||
\(8\) | −1.73205 | −0.612372 | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.46410i | − | 1.04447i | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||
0.852803 | − | 0.522233i | \(-0.174901\pi\) | |||||||
\(12\) | −1.73205 | −0.500000 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | −3.00000 | − | 3.46410i | −0.801784 | − | 0.925820i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | − | 6.00000i | − | 1.45521i | −0.685994 | − | 0.727607i | \(-0.740633\pi\) | ||
0.685994 | − | 0.727607i | \(-0.259367\pi\) | |||||||
\(18\) | 5.19615 | 1.22474 | ||||||||
\(19\) | − | 3.46410i | − | 0.794719i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) | ||
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000 | + | 3.46410i | 0.654654 | + | 0.755929i | ||||
\(22\) | − | 6.00000i | − | 1.27920i | ||||||
\(23\) | −3.46410 | −0.722315 | −0.361158 | − | 0.932505i | \(-0.617618\pi\) | ||||
−0.361158 | + | 0.932505i | \(0.617618\pi\) | |||||||
\(24\) | 3.00000 | 0.612372 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | −1.73205 | − | 2.00000i | −0.327327 | − | 0.377964i | ||||
\(29\) | 6.92820i | 1.28654i | 0.765641 | + | 0.643268i | \(0.222422\pi\) | ||||
−0.765641 | + | 0.643268i | \(0.777578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.46410i | − | 0.622171i | −0.950382 | − | 0.311086i | \(-0.899307\pi\) | ||
0.950382 | − | 0.311086i | \(-0.100693\pi\) | |||||||
\(32\) | −5.19615 | −0.918559 | ||||||||
\(33\) | 6.00000i | 1.04447i | ||||||||
\(34\) | − | 10.3923i | − | 1.78227i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | − | 6.00000i | − | 0.973329i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 5.19615 | + | 6.00000i | 0.801784 | + | 0.925820i | ||||
\(43\) | − | 8.00000i | − | 1.21999i | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||
0.792406 | − | 0.609994i | \(-0.208828\pi\) | |||||||
\(44\) | − | 3.46410i | − | 0.522233i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | 12.0000i | 1.75038i | 0.483779 | + | 0.875190i | \(0.339264\pi\) | ||||
−0.483779 | + | 0.875190i | \(0.660736\pi\) | |||||||
\(48\) | 8.66025 | 1.25000 | ||||||||
\(49\) | −1.00000 | + | 6.92820i | −0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.3923i | 1.45521i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −9.00000 | −1.22474 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.00000 | + | 3.46410i | 0.400892 | + | 0.462910i | ||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | 12.0000i | 1.57568i | ||||||||
\(59\) | 12.0000 | 1.56227 | 0.781133 | − | 0.624364i | \(-0.214642\pi\) | ||||
0.781133 | + | 0.624364i | \(0.214642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.92820i | − | 0.887066i | −0.896258 | − | 0.443533i | \(-0.853725\pi\) | ||
0.896258 | − | 0.443533i | \(-0.146275\pi\) | |||||||
\(62\) | − | 6.00000i | − | 0.762001i | ||||||
\(63\) | −5.19615 | − | 6.00000i | −0.654654 | − | 0.755929i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10.3923i | 1.27920i | ||||||||
\(67\) | − | 8.00000i | − | 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | − | 6.00000i | − | 0.727607i | ||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.46410i | 0.411113i | 0.978645 | + | 0.205557i | \(0.0659005\pi\) | ||||
−0.978645 | + | 0.205557i | \(0.934100\pi\) | |||||||
\(72\) | −5.19615 | −0.612372 | ||||||||
\(73\) | −6.92820 | −0.810885 | −0.405442 | − | 0.914121i | \(-0.632883\pi\) | ||||
−0.405442 | + | 0.914121i | \(0.632883\pi\) | |||||||
\(74\) | 3.46410i | 0.402694i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.46410i | − | 0.397360i | ||||||
\(77\) | −6.92820 | + | 6.00000i | −0.789542 | + | 0.683763i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 10.3923 | 1.14764 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 3.00000 | + | 3.46410i | 0.327327 | + | 0.377964i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 13.8564i | − | 1.49417i | ||||||
\(87\) | − | 12.0000i | − | 1.28654i | ||||||
\(88\) | 6.00000i | 0.639602i | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.46410 | −0.361158 | ||||||||
\(93\) | 6.00000i | 0.622171i | ||||||||
\(94\) | 20.7846i | 2.14377i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.00000 | 0.918559 | ||||||||
\(97\) | 6.92820 | 0.703452 | 0.351726 | − | 0.936103i | \(-0.385595\pi\) | ||||
0.351726 | + | 0.936103i | \(0.385595\pi\) | |||||||
\(98\) | −1.73205 | + | 12.0000i | −0.174964 | + | 1.21218i | ||||
\(99\) | − | 10.3923i | − | 1.04447i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 18.0000i | 1.78227i | ||||||||
\(103\) | 3.46410 | 0.341328 | 0.170664 | − | 0.985329i | \(-0.445409\pi\) | ||||
0.170664 | + | 0.985329i | \(0.445409\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.3923 | 1.00466 | 0.502331 | − | 0.864675i | \(-0.332476\pi\) | ||||
0.502331 | + | 0.864675i | \(0.332476\pi\) | |||||||
\(108\) | −5.19615 | −0.500000 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.46410i | − | 0.328798i | ||||||
\(112\) | 8.66025 | + | 10.0000i | 0.818317 | + | 0.944911i | ||||
\(113\) | 6.92820 | 0.651751 | 0.325875 | − | 0.945413i | \(-0.394341\pi\) | ||||
0.325875 | + | 0.945413i | \(0.394341\pi\) | |||||||
\(114\) | 10.3923i | 0.973329i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.92820i | 0.643268i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 20.7846 | 1.91338 | ||||||||
\(119\) | −12.0000 | + | 10.3923i | −1.10004 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | − | 12.0000i | − | 1.08643i | ||||||
\(123\) | −10.3923 | −0.937043 | ||||||||
\(124\) | − | 3.46410i | − | 0.311086i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9.00000 | − | 10.3923i | −0.801784 | − | 0.925820i | ||||
\(127\) | 4.00000i | 0.354943i | 0.984126 | + | 0.177471i | \(0.0567917\pi\) | ||||
−0.984126 | + | 0.177471i | \(0.943208\pi\) | |||||||
\(128\) | 12.1244 | 1.07165 | ||||||||
\(129\) | 13.8564i | 1.21999i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 6.00000i | 0.522233i | ||||||||
\(133\) | −6.92820 | + | 6.00000i | −0.600751 | + | 0.520266i | ||||
\(134\) | − | 13.8564i | − | 1.19701i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.3923i | 0.891133i | ||||||||
\(137\) | 20.7846 | 1.77575 | 0.887875 | − | 0.460086i | \(-0.152181\pi\) | ||||
0.887875 | + | 0.460086i | \(0.152181\pi\) | |||||||
\(138\) | 10.3923 | 0.884652 | ||||||||
\(139\) | − | 17.3205i | − | 1.46911i | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||
0.678551 | − | 0.734553i | \(-0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 20.7846i | − | 1.75038i | ||||||
\(142\) | 6.00000i | 0.503509i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −15.0000 | −1.25000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.0000 | −0.993127 | ||||||||
\(147\) | 1.73205 | − | 12.0000i | 0.142857 | − | 0.989743i | ||||
\(148\) | 2.00000i | 0.164399i | ||||||||
\(149\) | − | 6.92820i | − | 0.567581i | −0.958886 | − | 0.283790i | \(-0.908408\pi\) | ||
0.958886 | − | 0.283790i | \(-0.0915919\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 6.00000i | 0.486664i | ||||||||
\(153\) | − | 18.0000i | − | 1.45521i | ||||||
\(154\) | −12.0000 | + | 10.3923i | −0.966988 | + | 0.837436i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.8564 | 1.10586 | 0.552931 | − | 0.833227i | \(-0.313509\pi\) | ||||
0.552931 | + | 0.833227i | \(0.313509\pi\) | |||||||
\(158\) | −13.8564 | −1.10236 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | + | 6.92820i | 0.472866 | + | 0.546019i | ||||
\(162\) | 15.5885 | 1.22474 | ||||||||
\(163\) | − | 16.0000i | − | 1.25322i | −0.779334 | − | 0.626608i | \(-0.784443\pi\) | ||
0.779334 | − | 0.626608i | \(-0.215557\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12.0000i | − | 0.928588i | −0.885681 | − | 0.464294i | \(-0.846308\pi\) | ||
0.885681 | − | 0.464294i | \(-0.153692\pi\) | |||||||
\(168\) | −5.19615 | − | 6.00000i | −0.400892 | − | 0.462910i | ||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 10.3923i | − | 0.794719i | ||||||
\(172\) | − | 8.00000i | − | 0.609994i | ||||||
\(173\) | 18.0000i | 1.36851i | 0.729241 | + | 0.684257i | \(0.239873\pi\) | ||||
−0.729241 | + | 0.684257i | \(0.760127\pi\) | |||||||
\(174\) | − | 20.7846i | − | 1.57568i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 17.3205i | 1.30558i | ||||||||
\(177\) | −20.7846 | −1.56227 | ||||||||
\(178\) | −10.3923 | −0.778936 | ||||||||
\(179\) | − | 10.3923i | − | 0.776757i | −0.921500 | − | 0.388379i | \(-0.873035\pi\) | ||
0.921500 | − | 0.388379i | \(-0.126965\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 20.7846i | − | 1.54491i | −0.635071 | − | 0.772454i | \(-0.719029\pi\) | ||
0.635071 | − | 0.772454i | \(-0.280971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.0000i | 0.887066i | ||||||||
\(184\) | 6.00000 | 0.442326 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.3923i | 0.762001i | ||||||||
\(187\) | −20.7846 | −1.51992 | ||||||||
\(188\) | 12.0000i | 0.875190i | ||||||||
\(189\) | 9.00000 | + | 10.3923i | 0.654654 | + | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.3923i | − | 0.751961i | −0.926628 | − | 0.375980i | \(-0.877306\pi\) | ||
0.926628 | − | 0.375980i | \(-0.122694\pi\) | |||||||
\(192\) | −1.73205 | −0.125000 | ||||||||
\(193\) | − | 14.0000i | − | 1.00774i | −0.863779 | − | 0.503871i | \(-0.831909\pi\) | ||
0.863779 | − | 0.503871i | \(-0.168091\pi\) | |||||||
\(194\) | 12.0000 | 0.861550 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | + | 6.92820i | −0.0714286 | + | 0.494872i | ||||
\(197\) | −13.8564 | −0.987228 | −0.493614 | − | 0.869681i | \(-0.664324\pi\) | ||||
−0.493614 | + | 0.869681i | \(0.664324\pi\) | |||||||
\(198\) | − | 18.0000i | − | 1.27920i | ||||||
\(199\) | − | 10.3923i | − | 0.736691i | −0.929689 | − | 0.368345i | \(-0.879924\pi\) | ||
0.929689 | − | 0.368345i | \(-0.120076\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.8564i | 0.977356i | ||||||||
\(202\) | −10.3923 | −0.731200 | ||||||||
\(203\) | 13.8564 | − | 12.0000i | 0.972529 | − | 0.842235i | ||||
\(204\) | 10.3923i | 0.727607i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.00000 | 0.418040 | ||||||||
\(207\) | −10.3923 | −0.722315 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 6.00000i | − | 0.411113i | ||||||
\(214\) | 18.0000 | 1.23045 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.00000 | 0.612372 | ||||||||
\(217\) | −6.92820 | + | 6.00000i | −0.470317 | + | 0.407307i | ||||
\(218\) | 3.46410 | 0.234619 | ||||||||
\(219\) | 12.0000 | 0.810885 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | − | 6.00000i | − | 0.402694i | ||||||
\(223\) | 17.3205 | 1.15987 | 0.579934 | − | 0.814664i | \(-0.303079\pi\) | ||||
0.579934 | + | 0.814664i | \(0.303079\pi\) | |||||||
\(224\) | 9.00000 | + | 10.3923i | 0.601338 | + | 0.694365i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.0000 | 0.798228 | ||||||||
\(227\) | 24.0000i | 1.59294i | 0.604681 | + | 0.796468i | \(0.293301\pi\) | ||||
−0.604681 | + | 0.796468i | \(0.706699\pi\) | |||||||
\(228\) | 6.00000i | 0.397360i | ||||||||
\(229\) | 6.92820i | 0.457829i | 0.973447 | + | 0.228914i | \(0.0735176\pi\) | ||||
−0.973447 | + | 0.228914i | \(0.926482\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | − | 10.3923i | 0.789542 | − | 0.683763i | ||||
\(232\) | − | 12.0000i | − | 0.787839i | ||||||
\(233\) | −6.92820 | −0.453882 | −0.226941 | − | 0.973909i | \(-0.572872\pi\) | ||||
−0.226941 | + | 0.973909i | \(0.572872\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.0000 | 0.781133 | ||||||||
\(237\) | 13.8564 | 0.900070 | ||||||||
\(238\) | −20.7846 | + | 18.0000i | −1.34727 | + | 1.16677i | ||||
\(239\) | 10.3923i | 0.672222i | 0.941822 | + | 0.336111i | \(0.109112\pi\) | ||||
−0.941822 | + | 0.336111i | \(0.890888\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −1.73205 | −0.111340 | ||||||||
\(243\) | −15.5885 | −1.00000 | ||||||||
\(244\) | − | 6.92820i | − | 0.443533i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −18.0000 | −1.14764 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.00000i | 0.381000i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | −5.19615 | − | 6.00000i | −0.327327 | − | 0.377964i | ||||
\(253\) | 12.0000i | 0.754434i | ||||||||
\(254\) | 6.92820i | 0.434714i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | − | 6.00000i | − | 0.374270i | −0.982334 | − | 0.187135i | \(-0.940080\pi\) | ||
0.982334 | − | 0.187135i | \(-0.0599201\pi\) | |||||||
\(258\) | 24.0000i | 1.49417i | ||||||||
\(259\) | 4.00000 | − | 3.46410i | 0.248548 | − | 0.215249i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.7846i | 1.28654i | ||||||||
\(262\) | −20.7846 | −1.28408 | ||||||||
\(263\) | 24.2487 | 1.49524 | 0.747620 | − | 0.664127i | \(-0.231197\pi\) | ||||
0.747620 | + | 0.664127i | \(0.231197\pi\) | |||||||
\(264\) | − | 10.3923i | − | 0.639602i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −12.0000 | + | 10.3923i | −0.735767 | + | 0.637193i | ||||
\(267\) | 10.3923 | 0.635999 | ||||||||
\(268\) | − | 8.00000i | − | 0.488678i | ||||||
\(269\) | −18.0000 | −1.09748 | −0.548740 | − | 0.835993i | \(-0.684892\pi\) | ||||
−0.548740 | + | 0.835993i | \(0.684892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.2487i | 1.47300i | 0.676435 | + | 0.736502i | \(0.263524\pi\) | ||||
−0.676435 | + | 0.736502i | \(0.736476\pi\) | |||||||
\(272\) | 30.0000i | 1.81902i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 36.0000 | 2.17484 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.00000 | 0.361158 | ||||||||
\(277\) | − | 14.0000i | − | 0.841178i | −0.907251 | − | 0.420589i | \(-0.861823\pi\) | ||
0.907251 | − | 0.420589i | \(-0.138177\pi\) | |||||||
\(278\) | − | 30.0000i | − | 1.79928i | ||||||
\(279\) | − | 10.3923i | − | 0.622171i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.8564i | 0.826604i | 0.910594 | + | 0.413302i | \(0.135625\pi\) | ||||
−0.910594 | + | 0.413302i | \(0.864375\pi\) | |||||||
\(282\) | − | 36.0000i | − | 2.14377i | ||||||
\(283\) | −17.3205 | −1.02960 | −0.514799 | − | 0.857311i | \(-0.672133\pi\) | ||||
−0.514799 | + | 0.857311i | \(0.672133\pi\) | |||||||
\(284\) | 3.46410i | 0.205557i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.3923 | − | 12.0000i | −0.613438 | − | 0.708338i | ||||
\(288\) | −15.5885 | −0.918559 | ||||||||
\(289\) | −19.0000 | −1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0000 | −0.703452 | ||||||||
\(292\) | −6.92820 | −0.405442 | ||||||||
\(293\) | − | 6.00000i | − | 0.350524i | −0.984522 | − | 0.175262i | \(-0.943923\pi\) | ||
0.984522 | − | 0.175262i | \(-0.0560772\pi\) | |||||||
\(294\) | 3.00000 | − | 20.7846i | 0.174964 | − | 1.21218i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 3.46410i | − | 0.201347i | ||||||
\(297\) | 18.0000i | 1.04447i | ||||||||
\(298\) | − | 12.0000i | − | 0.695141i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0000 | + | 13.8564i | −0.922225 | + | 0.798670i | ||||
\(302\) | −13.8564 | −0.797347 | ||||||||
\(303\) | 10.3923 | 0.597022 | ||||||||
\(304\) | 17.3205i | 0.993399i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 31.1769i | − | 1.78227i | ||||||
\(307\) | −24.2487 | −1.38395 | −0.691974 | − | 0.721923i | \(-0.743259\pi\) | ||||
−0.691974 | + | 0.721923i | \(0.743259\pi\) | |||||||
\(308\) | −6.92820 | + | 6.00000i | −0.394771 | + | 0.341882i | ||||
\(309\) | −6.00000 | −0.341328 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.7846 | 1.17482 | 0.587408 | − | 0.809291i | \(-0.300148\pi\) | ||||
0.587408 | + | 0.809291i | \(0.300148\pi\) | |||||||
\(314\) | 24.0000 | 1.35440 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 27.7128 | 1.55651 | 0.778253 | − | 0.627950i | \(-0.216106\pi\) | ||||
0.778253 | + | 0.627950i | \(0.216106\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.0000 | 1.34374 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.0000 | −1.00466 | ||||||||
\(322\) | 10.3923 | + | 12.0000i | 0.579141 | + | 0.668734i | ||||
\(323\) | −20.7846 | −1.15649 | ||||||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 27.7128i | − | 1.53487i | ||||||
\(327\) | −3.46410 | −0.191565 | ||||||||
\(328\) | −10.3923 | −0.573819 | ||||||||
\(329\) | 24.0000 | − | 20.7846i | 1.32316 | − | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.0000 | 1.53902 | 0.769510 | − | 0.638635i | \(-0.220501\pi\) | ||||
0.769510 | + | 0.638635i | \(0.220501\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.00000i | 0.328798i | ||||||||
\(334\) | − | 20.7846i | − | 1.13728i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −15.0000 | − | 17.3205i | −0.818317 | − | 0.944911i | ||||
\(337\) | 14.0000i | 0.762629i | 0.924445 | + | 0.381314i | \(0.124528\pi\) | ||||
−0.924445 | + | 0.381314i | \(0.875472\pi\) | |||||||
\(338\) | −22.5167 | −1.22474 | ||||||||
\(339\) | −12.0000 | −0.651751 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | − | 18.0000i | − | 0.973329i | ||||||
\(343\) | 15.5885 | − | 10.0000i | 0.841698 | − | 0.539949i | ||||
\(344\) | 13.8564i | 0.747087i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 31.1769i | 1.67608i | ||||||||
\(347\) | −17.3205 | −0.929814 | −0.464907 | − | 0.885360i | \(-0.653912\pi\) | ||||
−0.464907 | + | 0.885360i | \(0.653912\pi\) | |||||||
\(348\) | − | 12.0000i | − | 0.643268i | ||||||
\(349\) | − | 6.92820i | − | 0.370858i | −0.982658 | − | 0.185429i | \(-0.940632\pi\) | ||
0.982658 | − | 0.185429i | \(-0.0593675\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 18.0000i | 0.959403i | ||||||||
\(353\) | 6.00000i | 0.319348i | 0.987170 | + | 0.159674i | \(0.0510443\pi\) | ||||
−0.987170 | + | 0.159674i | \(0.948956\pi\) | |||||||
\(354\) | −36.0000 | −1.91338 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 20.7846 | − | 18.0000i | 1.10004 | − | 0.952661i | ||||
\(358\) | − | 18.0000i | − | 0.951330i | ||||||
\(359\) | − | 3.46410i | − | 0.182828i | −0.995813 | − | 0.0914141i | \(-0.970861\pi\) | ||
0.995813 | − | 0.0914141i | \(-0.0291387\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | − | 36.0000i | − | 1.89212i | ||||||
\(363\) | 1.73205 | 0.0909091 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 20.7846i | 1.08643i | ||||||||
\(367\) | 10.3923 | 0.542474 | 0.271237 | − | 0.962513i | \(-0.412567\pi\) | ||||
0.271237 | + | 0.962513i | \(0.412567\pi\) | |||||||
\(368\) | 17.3205 | 0.902894 | ||||||||
\(369\) | 18.0000 | 0.937043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.00000i | 0.311086i | ||||||||
\(373\) | 14.0000i | 0.724893i | 0.932005 | + | 0.362446i | \(0.118058\pi\) | ||||
−0.932005 | + | 0.362446i | \(0.881942\pi\) | |||||||
\(374\) | −36.0000 | −1.86152 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 20.7846i | − | 1.07188i | ||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 15.5885 | + | 18.0000i | 0.801784 | + | 0.925820i | ||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 6.92820i | − | 0.354943i | ||||||
\(382\) | − | 18.0000i | − | 0.920960i | ||||||
\(383\) | 12.0000i | 0.613171i | 0.951843 | + | 0.306586i | \(0.0991866\pi\) | ||||
−0.951843 | + | 0.306586i | \(0.900813\pi\) | |||||||
\(384\) | −21.0000 | −1.07165 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 24.2487i | − | 1.23423i | ||||||
\(387\) | − | 24.0000i | − | 1.21999i | ||||||
\(388\) | 6.92820 | 0.351726 | ||||||||
\(389\) | − | 6.92820i | − | 0.351274i | −0.984455 | − | 0.175637i | \(-0.943802\pi\) | ||
0.984455 | − | 0.175637i | \(-0.0561985\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.7846i | 1.05112i | ||||||||
\(392\) | 1.73205 | − | 12.0000i | 0.0874818 | − | 0.606092i | ||||
\(393\) | 20.7846 | 1.04844 | ||||||||
\(394\) | −24.0000 | −1.20910 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | − | 10.3923i | − | 0.522233i | ||||||
\(397\) | 13.8564 | 0.695433 | 0.347717 | − | 0.937600i | \(-0.386957\pi\) | ||||
0.347717 | + | 0.937600i | \(0.386957\pi\) | |||||||
\(398\) | − | 18.0000i | − | 0.902258i | ||||||
\(399\) | 12.0000 | − | 10.3923i | 0.600751 | − | 0.520266i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 27.7128i | − | 1.38391i | −0.721940 | − | 0.691956i | \(-0.756749\pi\) | ||
0.721940 | − | 0.691956i | \(-0.243251\pi\) | |||||||
\(402\) | 24.0000i | 1.19701i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 24.0000 | − | 20.7846i | 1.19110 | − | 1.03152i | ||||
\(407\) | 6.92820 | 0.343418 | ||||||||
\(408\) | − | 18.0000i | − | 0.891133i | ||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −36.0000 | −1.77575 | ||||||||
\(412\) | 3.46410 | 0.170664 | ||||||||
\(413\) | −20.7846 | − | 24.0000i | −1.02274 | − | 1.18096i | ||||
\(414\) | −18.0000 | −0.884652 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.0000i | 1.46911i | ||||||||
\(418\) | −20.7846 | −1.01661 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 6.92820 | 0.337260 | ||||||||
\(423\) | 36.0000i | 1.75038i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 10.3923i | − | 0.503509i | ||||||
\(427\) | −13.8564 | + | 12.0000i | −0.670559 | + | 0.580721i | ||||
\(428\) | 10.3923 | 0.502331 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10.3923i | − | 0.500580i | −0.968171 | − | 0.250290i | \(-0.919474\pi\) | ||
0.968171 | − | 0.250290i | \(-0.0805259\pi\) | |||||||
\(432\) | 25.9808 | 1.25000 | ||||||||
\(433\) | 6.92820 | 0.332948 | 0.166474 | − | 0.986046i | \(-0.446762\pi\) | ||||
0.166474 | + | 0.986046i | \(0.446762\pi\) | |||||||
\(434\) | −12.0000 | + | 10.3923i | −0.576018 | + | 0.498847i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | 12.0000i | 0.574038i | ||||||||
\(438\) | 20.7846 | 0.993127 | ||||||||
\(439\) | 17.3205i | 0.826663i | 0.910581 | + | 0.413331i | \(0.135635\pi\) | ||||
−0.910581 | + | 0.413331i | \(0.864365\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | + | 20.7846i | −0.142857 | + | 0.989743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.3923 | −0.493753 | −0.246877 | − | 0.969047i | \(-0.579404\pi\) | ||||
−0.246877 | + | 0.969047i | \(0.579404\pi\) | |||||||
\(444\) | − | 3.46410i | − | 0.164399i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 30.0000 | 1.42054 | ||||||||
\(447\) | 12.0000i | 0.567581i | ||||||||
\(448\) | −1.73205 | − | 2.00000i | −0.0818317 | − | 0.0944911i | ||||
\(449\) | 13.8564i | 0.653924i | 0.945037 | + | 0.326962i | \(0.106025\pi\) | ||||
−0.945037 | + | 0.326962i | \(0.893975\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 20.7846i | − | 0.978709i | ||||||
\(452\) | 6.92820 | 0.325875 | ||||||||
\(453\) | 13.8564 | 0.651031 | ||||||||
\(454\) | 41.5692i | 1.95094i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | − | 10.3923i | − | 0.486664i | ||||||
\(457\) | 38.0000i | 1.77757i | 0.458329 | + | 0.888783i | \(0.348448\pi\) | ||||
−0.458329 | + | 0.888783i | \(0.651552\pi\) | |||||||
\(458\) | 12.0000i | 0.560723i | ||||||||
\(459\) | 31.1769i | 1.45521i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0000 | 0.838344 | 0.419172 | − | 0.907907i | \(-0.362320\pi\) | ||||
0.419172 | + | 0.907907i | \(0.362320\pi\) | |||||||
\(462\) | 20.7846 | − | 18.0000i | 0.966988 | − | 0.837436i | ||||
\(463\) | 20.0000i | 0.929479i | 0.885448 | + | 0.464739i | \(0.153852\pi\) | ||||
−0.885448 | + | 0.464739i | \(0.846148\pi\) | |||||||
\(464\) | − | 34.6410i | − | 1.60817i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.0000 | −0.555889 | ||||||||
\(467\) | − | 24.0000i | − | 1.11059i | −0.831654 | − | 0.555294i | \(-0.812606\pi\) | ||
0.831654 | − | 0.555294i | \(-0.187394\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.0000 | + | 13.8564i | −0.738811 | + | 0.639829i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.0000 | −1.10586 | ||||||||
\(472\) | −20.7846 | −0.956689 | ||||||||
\(473\) | −27.7128 | −1.27424 | ||||||||
\(474\) | 24.0000 | 1.10236 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.0000 | + | 10.3923i | −0.550019 | + | 0.476331i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.0000i | 0.823301i | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.3923 | − | 12.0000i | −0.472866 | − | 0.546019i | ||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −27.0000 | −1.22474 | ||||||||
\(487\) | − | 4.00000i | − | 0.181257i | −0.995885 | − | 0.0906287i | \(-0.971112\pi\) | ||
0.995885 | − | 0.0906287i | \(-0.0288876\pi\) | |||||||
\(488\) | 12.0000i | 0.543214i | ||||||||
\(489\) | 27.7128i | 1.25322i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.2487i | 1.09433i | 0.837025 | + | 0.547165i | \(0.184293\pi\) | ||||
−0.837025 | + | 0.547165i | \(0.815707\pi\) | |||||||
\(492\) | −10.3923 | −0.468521 | ||||||||
\(493\) | 41.5692 | 1.87218 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.3205i | 0.777714i | ||||||||
\(497\) | 6.92820 | − | 6.00000i | 0.310772 | − | 0.269137i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000 | 0.895323 | 0.447661 | − | 0.894203i | \(-0.352257\pi\) | ||||
0.447661 | + | 0.894203i | \(0.352257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.7846i | 0.928588i | ||||||||
\(502\) | 20.7846 | 0.927663 | ||||||||
\(503\) | − | 12.0000i | − | 0.535054i | −0.963550 | − | 0.267527i | \(-0.913794\pi\) | ||
0.963550 | − | 0.267527i | \(-0.0862064\pi\) | |||||||
\(504\) | 9.00000 | + | 10.3923i | 0.400892 | + | 0.462910i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 20.7846i | 0.923989i | ||||||||
\(507\) | 22.5167 | 1.00000 | ||||||||
\(508\) | 4.00000i | 0.177471i | ||||||||
\(509\) | 30.0000 | 1.32973 | 0.664863 | − | 0.746965i | \(-0.268490\pi\) | ||||
0.664863 | + | 0.746965i | \(0.268490\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | + | 13.8564i | 0.530849 | + | 0.612971i | ||||
\(512\) | 8.66025 | 0.382733 | ||||||||
\(513\) | 18.0000i | 0.794719i | ||||||||
\(514\) | − | 10.3923i | − | 0.458385i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 13.8564i | 0.609994i | ||||||||
\(517\) | 41.5692 | 1.82821 | ||||||||
\(518\) | 6.92820 | − | 6.00000i | 0.304408 | − | 0.263625i | ||||
\(519\) | − | 31.1769i | − | 1.36851i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 36.0000i | 1.57568i | ||||||||
\(523\) | −17.3205 | −0.757373 | −0.378686 | − | 0.925525i | \(-0.623624\pi\) | ||||
−0.378686 | + | 0.925525i | \(0.623624\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 42.0000 | 1.83129 | ||||||||
\(527\) | −20.7846 | −0.905392 | ||||||||
\(528\) | − | 30.0000i | − | 1.30558i | ||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 36.0000 | 1.56227 | ||||||||
\(532\) | −6.92820 | + | 6.00000i | −0.300376 | + | 0.260133i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 18.0000 | 0.778936 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 13.8564i | 0.598506i | ||||||||
\(537\) | 18.0000i | 0.776757i | ||||||||
\(538\) | −31.1769 | −1.34413 | ||||||||
\(539\) | 24.0000 | + | 3.46410i | 1.03375 | + | 0.149209i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.0000 | −1.46177 | −0.730887 | − | 0.682498i | \(-0.760893\pi\) | ||||
−0.730887 | + | 0.682498i | \(0.760893\pi\) | |||||||
\(542\) | 42.0000i | 1.80405i | ||||||||
\(543\) | 36.0000i | 1.54491i | ||||||||
\(544\) | 31.1769i | 1.33670i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 8.00000i | − | 0.342055i | −0.985266 | − | 0.171028i | \(-0.945291\pi\) | ||
0.985266 | − | 0.171028i | \(-0.0547087\pi\) | |||||||
\(548\) | 20.7846 | 0.887875 | ||||||||
\(549\) | − | 20.7846i | − | 0.887066i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.0000 | 1.02243 | ||||||||
\(552\) | −10.3923 | −0.442326 | ||||||||
\(553\) | 13.8564 | + | 16.0000i | 0.589234 | + | 0.680389i | ||||
\(554\) | − | 24.2487i | − | 1.03023i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 17.3205i | − | 0.734553i | ||||||
\(557\) | −27.7128 | −1.17423 | −0.587115 | − | 0.809504i | \(-0.699736\pi\) | ||||
−0.587115 | + | 0.809504i | \(0.699736\pi\) | |||||||
\(558\) | − | 18.0000i | − | 0.762001i | ||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.0000 | 1.51992 | ||||||||
\(562\) | 24.0000i | 1.01238i | ||||||||
\(563\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(564\) | − | 20.7846i | − | 0.875190i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −30.0000 | −1.26099 | ||||||||
\(567\) | −15.5885 | − | 18.0000i | −0.654654 | − | 0.755929i | ||||
\(568\) | − | 6.00000i | − | 0.251754i | ||||||
\(569\) | 27.7128i | 1.16178i | 0.813982 | + | 0.580891i | \(0.197296\pi\) | ||||
−0.813982 | + | 0.580891i | \(0.802704\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.0000i | 0.751961i | ||||||||
\(574\) | −18.0000 | − | 20.7846i | −0.751305 | − | 0.867533i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.00000 | 0.125000 | ||||||||
\(577\) | 34.6410 | 1.44212 | 0.721062 | − | 0.692870i | \(-0.243654\pi\) | ||||
0.721062 | + | 0.692870i | \(0.243654\pi\) | |||||||
\(578\) | −32.9090 | −1.36883 | ||||||||
\(579\) | 24.2487i | 1.00774i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −20.7846 | −0.861550 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 12.0000 | 0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 10.3923i | − | 0.429302i | ||||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | 1.73205 | − | 12.0000i | 0.0714286 | − | 0.494872i | ||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.0000 | 0.987228 | ||||||||
\(592\) | − | 10.0000i | − | 0.410997i | ||||||
\(593\) | 6.00000i | 0.246390i | 0.992382 | + | 0.123195i | \(0.0393141\pi\) | ||||
−0.992382 | + | 0.123195i | \(0.960686\pi\) | |||||||
\(594\) | 31.1769i | 1.27920i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 6.92820i | − | 0.283790i | ||||||
\(597\) | 18.0000i | 0.736691i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.2487i | 0.990775i | 0.868672 | + | 0.495388i | \(0.164974\pi\) | ||||
−0.868672 | + | 0.495388i | \(0.835026\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.8564i | 0.565215i | 0.959236 | + | 0.282607i | \(0.0911993\pi\) | ||||
−0.959236 | + | 0.282607i | \(0.908801\pi\) | |||||||
\(602\) | −27.7128 | + | 24.0000i | −1.12949 | + | 0.978167i | ||||
\(603\) | − | 24.0000i | − | 0.977356i | ||||||
\(604\) | −8.00000 | −0.325515 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.0000 | 0.731200 | ||||||||
\(607\) | −17.3205 | −0.703018 | −0.351509 | − | 0.936185i | \(-0.614331\pi\) | ||||
−0.351509 | + | 0.936185i | \(0.614331\pi\) | |||||||
\(608\) | 18.0000i | 0.729996i | ||||||||
\(609\) | −24.0000 | + | 20.7846i | −0.972529 | + | 0.842235i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | − | 18.0000i | − | 0.727607i | ||||||
\(613\) | − | 34.0000i | − | 1.37325i | −0.727013 | − | 0.686624i | \(-0.759092\pi\) | ||
0.727013 | − | 0.686624i | \(-0.240908\pi\) | |||||||
\(614\) | −42.0000 | −1.69498 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.0000 | − | 10.3923i | 0.483494 | − | 0.418718i | ||||
\(617\) | −6.92820 | −0.278919 | −0.139459 | − | 0.990228i | \(-0.544536\pi\) | ||||
−0.139459 | + | 0.990228i | \(0.544536\pi\) | |||||||
\(618\) | −10.3923 | −0.418040 | ||||||||
\(619\) | − | 17.3205i | − | 0.696170i | −0.937463 | − | 0.348085i | \(-0.886832\pi\) | ||
0.937463 | − | 0.348085i | \(-0.113168\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.0000 | 0.722315 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.3923 | + | 12.0000i | 0.416359 | + | 0.480770i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 36.0000 | 1.43885 | ||||||||
\(627\) | 20.7846 | 0.830057 | ||||||||
\(628\) | 13.8564 | 0.552931 | ||||||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.0000 | −1.59237 | −0.796187 | − | 0.605050i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605050i | \(0.793153\pi\) | |||||||
\(632\) | 13.8564 | 0.551178 | ||||||||
\(633\) | −6.92820 | −0.275371 | ||||||||
\(634\) | 48.0000 | 1.90632 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 41.5692 | 1.64574 | ||||||||
\(639\) | 10.3923i | 0.411113i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.7128i | 1.09459i | 0.836940 | + | 0.547295i | \(0.184342\pi\) | ||||
−0.836940 | + | 0.547295i | \(0.815658\pi\) | |||||||
\(642\) | −31.1769 | −1.23045 | ||||||||
\(643\) | −31.1769 | −1.22950 | −0.614749 | − | 0.788723i | \(-0.710743\pi\) | ||||
−0.614749 | + | 0.788723i | \(0.710743\pi\) | |||||||
\(644\) | 6.00000 | + | 6.92820i | 0.236433 | + | 0.273009i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −36.0000 | −1.41640 | ||||||||
\(647\) | − | 12.0000i | − | 0.471769i | −0.971781 | − | 0.235884i | \(-0.924201\pi\) | ||
0.971781 | − | 0.235884i | \(-0.0757987\pi\) | |||||||
\(648\) | −15.5885 | −0.612372 | ||||||||
\(649\) | − | 41.5692i | − | 1.63173i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.0000 | − | 10.3923i | 0.470317 | − | 0.407307i | ||||
\(652\) | − | 16.0000i | − | 0.626608i | ||||||
\(653\) | 41.5692 | 1.62673 | 0.813365 | − | 0.581754i | \(-0.197633\pi\) | ||||
0.813365 | + | 0.581754i | \(0.197633\pi\) | |||||||
\(654\) | −6.00000 | −0.234619 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −30.0000 | −1.17130 | ||||||||
\(657\) | −20.7846 | −0.810885 | ||||||||
\(658\) | 41.5692 | − | 36.0000i | 1.62054 | − | 1.40343i | ||||
\(659\) | − | 10.3923i | − | 0.404827i | −0.979300 | − | 0.202413i | \(-0.935122\pi\) | ||
0.979300 | − | 0.202413i | \(-0.0648785\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 48.4974i | − | 1.88633i | −0.332323 | − | 0.943166i | \(-0.607832\pi\) | ||
0.332323 | − | 0.943166i | \(-0.392168\pi\) | |||||||
\(662\) | 48.4974 | 1.88491 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.3923i | 0.402694i | ||||||||
\(667\) | − | 24.0000i | − | 0.929284i | ||||||
\(668\) | − | 12.0000i | − | 0.464294i | ||||||
\(669\) | −30.0000 | −1.15987 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.0000 | −0.926510 | ||||||||
\(672\) | −15.5885 | − | 18.0000i | −0.601338 | − | 0.694365i | ||||
\(673\) | − | 14.0000i | − | 0.539660i | −0.962908 | − | 0.269830i | \(-0.913032\pi\) | ||
0.962908 | − | 0.269830i | \(-0.0869676\pi\) | |||||||
\(674\) | 24.2487i | 0.934025i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | 6.00000i | 0.230599i | 0.993331 | + | 0.115299i | \(0.0367827\pi\) | ||||
−0.993331 | + | 0.115299i | \(0.963217\pi\) | |||||||
\(678\) | −20.7846 | −0.798228 | ||||||||
\(679\) | −12.0000 | − | 13.8564i | −0.460518 | − | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 41.5692i | − | 1.59294i | ||||||
\(682\) | −20.7846 | −0.795884 | ||||||||
\(683\) | 17.3205 | 0.662751 | 0.331375 | − | 0.943499i | \(-0.392487\pi\) | ||||
0.331375 | + | 0.943499i | \(0.392487\pi\) | |||||||
\(684\) | − | 10.3923i | − | 0.397360i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 27.0000 | − | 17.3205i | 1.03086 | − | 0.661300i | ||||
\(687\) | − | 12.0000i | − | 0.457829i | ||||||
\(688\) | 40.0000i | 1.52499i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.1769i | 1.18603i | 0.805193 | + | 0.593013i | \(0.202062\pi\) | ||||
−0.805193 | + | 0.593013i | \(0.797938\pi\) | |||||||
\(692\) | 18.0000i | 0.684257i | ||||||||
\(693\) | −20.7846 | + | 18.0000i | −0.789542 | + | 0.683763i | ||||
\(694\) | −30.0000 | −1.13878 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 20.7846i | 0.787839i | ||||||||
\(697\) | − | 36.0000i | − | 1.36360i | ||||||
\(698\) | − | 12.0000i | − | 0.454207i | ||||||
\(699\) | 12.0000 | 0.453882 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 20.7846i | − | 0.785024i | −0.919747 | − | 0.392512i | \(-0.871606\pi\) | ||
0.919747 | − | 0.392512i | \(-0.128394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.92820 | 0.261302 | ||||||||
\(704\) | − | 3.46410i | − | 0.130558i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.3923i | 0.391120i | ||||||||
\(707\) | 10.3923 | + | 12.0000i | 0.390843 | + | 0.451306i | ||||
\(708\) | −20.7846 | −0.781133 | ||||||||
\(709\) | −22.0000 | −0.826227 | −0.413114 | − | 0.910679i | \(-0.635559\pi\) | ||||
−0.413114 | + | 0.910679i | \(0.635559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.0000 | −0.900070 | ||||||||
\(712\) | 10.3923 | 0.389468 | ||||||||
\(713\) | 12.0000i | 0.449404i | ||||||||
\(714\) | 36.0000 | − | 31.1769i | 1.34727 | − | 1.16677i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 10.3923i | − | 0.388379i | ||||||
\(717\) | − | 18.0000i | − | 0.672222i | ||||||
\(718\) | − | 6.00000i | − | 0.223918i | ||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.00000 | − | 6.92820i | −0.223452 | − | 0.258020i | ||||
\(722\) | 12.1244 | 0.451222 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 20.7846i | − | 0.772454i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.00000 | 0.111340 | ||||||||
\(727\) | −3.46410 | −0.128476 | −0.0642382 | − | 0.997935i | \(-0.520462\pi\) | ||||
−0.0642382 | + | 0.997935i | \(0.520462\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.0000 | −1.77534 | ||||||||
\(732\) | 12.0000i | 0.443533i | ||||||||
\(733\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(734\) | 18.0000 | 0.664392 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.0000 | 0.663489 | ||||||||
\(737\) | −27.7128 | −1.02081 | ||||||||
\(738\) | 31.1769 | 1.14764 | ||||||||
\(739\) | 4.00000 | 0.147142 | 0.0735712 | − | 0.997290i | \(-0.476560\pi\) | ||||
0.0735712 | + | 0.997290i | \(0.476560\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.1769 | −1.14377 | −0.571885 | − | 0.820334i | \(-0.693788\pi\) | ||||
−0.571885 | + | 0.820334i | \(0.693788\pi\) | |||||||
\(744\) | − | 10.3923i | − | 0.381000i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 24.2487i | 0.887808i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20.7846 | −0.759961 | ||||||||
\(749\) | −18.0000 | − | 20.7846i | −0.657706 | − | 0.759453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0000 | 0.583848 | 0.291924 | − | 0.956441i | \(-0.405705\pi\) | ||||
0.291924 | + | 0.956441i | \(0.405705\pi\) | |||||||
\(752\) | − | 60.0000i | − | 2.18797i | ||||||
\(753\) | −20.7846 | −0.757433 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 9.00000 | + | 10.3923i | 0.327327 | + | 0.377964i | ||||
\(757\) | 2.00000i | 0.0726912i | 0.999339 | + | 0.0363456i | \(0.0115717\pi\) | ||||
−0.999339 | + | 0.0363456i | \(0.988428\pi\) | |||||||
\(758\) | −6.92820 | −0.251644 | ||||||||
\(759\) | − | 20.7846i | − | 0.754434i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.0000 | −1.52250 | −0.761249 | − | 0.648459i | \(-0.775414\pi\) | ||||
−0.761249 | + | 0.648459i | \(0.775414\pi\) | |||||||
\(762\) | − | 12.0000i | − | 0.434714i | ||||||
\(763\) | −3.46410 | − | 4.00000i | −0.125409 | − | 0.144810i | ||||
\(764\) | − | 10.3923i | − | 0.375980i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.7846i | 0.750978i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −32.9090 | −1.18750 | ||||||||
\(769\) | 41.5692i | 1.49902i | 0.661991 | + | 0.749512i | \(0.269712\pi\) | ||||
−0.661991 | + | 0.749512i | \(0.730288\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3923i | 0.374270i | ||||||||
\(772\) | − | 14.0000i | − | 0.503871i | ||||||
\(773\) | − | 6.00000i | − | 0.215805i | −0.994161 | − | 0.107903i | \(-0.965587\pi\) | ||
0.994161 | − | 0.107903i | \(-0.0344134\pi\) | |||||||
\(774\) | − | 41.5692i | − | 1.49417i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.0000 | −0.430775 | ||||||||
\(777\) | −6.92820 | + | 6.00000i | −0.248548 | + | 0.215249i | ||||
\(778\) | − | 12.0000i | − | 0.430221i | ||||||
\(779\) | − | 20.7846i | − | 0.744686i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.0000 | 0.429394 | ||||||||
\(782\) | 36.0000i | 1.28736i | ||||||||
\(783\) | − | 36.0000i | − | 1.28654i | ||||||
\(784\) | 5.00000 | − | 34.6410i | 0.178571 | − | 1.23718i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 36.0000 | 1.28408 | ||||||||
\(787\) | −24.2487 | −0.864373 | −0.432187 | − | 0.901784i | \(-0.642258\pi\) | ||||
−0.432187 | + | 0.901784i | \(0.642258\pi\) | |||||||
\(788\) | −13.8564 | −0.493614 | ||||||||
\(789\) | −42.0000 | −1.49524 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | − | 13.8564i | −0.426671 | − | 0.492677i | ||||
\(792\) | 18.0000i | 0.639602i | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 24.0000 | 0.851728 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 10.3923i | − | 0.368345i | ||||||
\(797\) | − | 18.0000i | − | 0.637593i | −0.947823 | − | 0.318796i | \(-0.896721\pi\) | ||
0.947823 | − | 0.318796i | \(-0.103279\pi\) | |||||||
\(798\) | 20.7846 | − | 18.0000i | 0.735767 | − | 0.637193i | ||||
\(799\) | 72.0000 | 2.54718 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.0000 | −0.635999 | ||||||||
\(802\) | − | 48.0000i | − | 1.69494i | ||||||
\(803\) | 24.0000i | 0.846942i | ||||||||
\(804\) | 13.8564i | 0.488678i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.1769 | 1.09748 | ||||||||
\(808\) | 10.3923 | 0.365600 | ||||||||
\(809\) | − | 55.4256i | − | 1.94866i | −0.225122 | − | 0.974331i | \(-0.572278\pi\) | ||
0.225122 | − | 0.974331i | \(-0.427722\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 38.1051i | − | 1.33805i | −0.743239 | − | 0.669026i | \(-0.766712\pi\) | ||
0.743239 | − | 0.669026i | \(-0.233288\pi\) | |||||||
\(812\) | 13.8564 | − | 12.0000i | 0.486265 | − | 0.421117i | ||||
\(813\) | − | 42.0000i | − | 1.47300i | ||||||
\(814\) | 12.0000 | 0.420600 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 51.9615i | − | 1.81902i | ||||||
\(817\) | −27.7128 | −0.969549 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.7846i | 0.725388i | 0.931908 | + | 0.362694i | \(0.118143\pi\) | ||||
−0.931908 | + | 0.362694i | \(0.881857\pi\) | |||||||
\(822\) | −62.3538 | −2.17484 | ||||||||
\(823\) | 44.0000i | 1.53374i | 0.641800 | + | 0.766872i | \(0.278188\pi\) | ||||
−0.641800 | + | 0.766872i | \(0.721812\pi\) | |||||||
\(824\) | −6.00000 | −0.209020 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −36.0000 | − | 41.5692i | −1.25260 | − | 1.44638i | ||||
\(827\) | 38.1051 | 1.32504 | 0.662522 | − | 0.749042i | \(-0.269486\pi\) | ||||
0.662522 | + | 0.749042i | \(0.269486\pi\) | |||||||
\(828\) | −10.3923 | −0.361158 | ||||||||
\(829\) | − | 34.6410i | − | 1.20313i | −0.798823 | − | 0.601566i | \(-0.794544\pi\) | ||
0.798823 | − | 0.601566i | \(-0.205456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.2487i | 0.841178i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 41.5692 | + | 6.00000i | 1.44029 | + | 0.207888i | ||||
\(834\) | 51.9615i | 1.79928i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.0000 | −0.415029 | ||||||||
\(837\) | 18.0000i | 0.622171i | ||||||||
\(838\) | −20.7846 | −0.717992 | ||||||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0000 | −0.655172 | ||||||||
\(842\) | −17.3205 | −0.596904 | ||||||||
\(843\) | − | 24.0000i | − | 0.826604i | ||||||
\(844\) | 4.00000 | 0.137686 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 62.3538i | 2.14377i | ||||||||
\(847\) | 1.73205 | + | 2.00000i | 0.0595140 | + | 0.0687208i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.0000 | 1.02960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 6.92820i | − | 0.237496i | ||||||
\(852\) | − | 6.00000i | − | 0.205557i | ||||||
\(853\) | −41.5692 | −1.42330 | −0.711651 | − | 0.702533i | \(-0.752052\pi\) | ||||
−0.711651 | + | 0.702533i | \(0.752052\pi\) | |||||||
\(854\) | −24.0000 | + | 20.7846i | −0.821263 | + | 0.711235i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.0000 | −0.615227 | ||||||||
\(857\) | − | 30.0000i | − | 1.02478i | −0.858753 | − | 0.512390i | \(-0.828760\pi\) | ||
0.858753 | − | 0.512390i | \(-0.171240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.1051i | 1.30013i | 0.759879 | + | 0.650065i | \(0.225258\pi\) | ||||
−0.759879 | + | 0.650065i | \(0.774742\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.0000 | + | 20.7846i | 0.613438 | + | 0.708338i | ||||
\(862\) | − | 18.0000i | − | 0.613082i | ||||||
\(863\) | −17.3205 | −0.589597 | −0.294798 | − | 0.955559i | \(-0.595253\pi\) | ||||
−0.294798 | + | 0.955559i | \(0.595253\pi\) | |||||||
\(864\) | 27.0000 | 0.918559 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.0000 | 0.407777 | ||||||||
\(867\) | 32.9090 | 1.11765 | ||||||||
\(868\) | −6.92820 | + | 6.00000i | −0.235159 | + | 0.203653i | ||||
\(869\) | 27.7128i | 0.940093i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −3.46410 | −0.117309 | ||||||||
\(873\) | 20.7846 | 0.703452 | ||||||||
\(874\) | 20.7846i | 0.703050i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.0000 | 0.405442 | ||||||||
\(877\) | − | 38.0000i | − | 1.28317i | −0.767052 | − | 0.641584i | \(-0.778277\pi\) | ||
0.767052 | − | 0.641584i | \(-0.221723\pi\) | |||||||
\(878\) | 30.0000i | 1.01245i | ||||||||
\(879\) | 10.3923i | 0.350524i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | −5.19615 | + | 36.0000i | −0.174964 | + | 1.21218i | ||||
\(883\) | 16.0000i | 0.538443i | 0.963078 | + | 0.269221i | \(0.0867663\pi\) | ||||
−0.963078 | + | 0.269221i | \(0.913234\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.0000 | −0.604722 | ||||||||
\(887\) | 36.0000i | 1.20876i | 0.796696 | + | 0.604381i | \(0.206579\pi\) | ||||
−0.796696 | + | 0.604381i | \(0.793421\pi\) | |||||||
\(888\) | 6.00000i | 0.201347i | ||||||||
\(889\) | 8.00000 | − | 6.92820i | 0.268311 | − | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 31.1769i | − | 1.04447i | ||||||
\(892\) | 17.3205 | 0.579934 | ||||||||
\(893\) | 41.5692 | 1.39106 | ||||||||
\(894\) | 20.7846i | 0.695141i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −21.0000 | − | 24.2487i | −0.701561 | − | 0.810093i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.0000i | 0.800890i | ||||||||
\(899\) | 24.0000 | 0.800445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | − | 36.0000i | − | 1.19867i | ||||||
\(903\) | 27.7128 | − | 24.0000i | 0.922225 | − | 0.798670i | ||||
\(904\) | −12.0000 | −0.399114 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 24.0000 | 0.797347 | ||||||||
\(907\) | 32.0000i | 1.06254i | 0.847202 | + | 0.531271i | \(0.178286\pi\) | ||||
−0.847202 | + | 0.531271i | \(0.821714\pi\) | |||||||
\(908\) | 24.0000i | 0.796468i | ||||||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.3205i | 0.573854i | 0.957952 | + | 0.286927i | \(0.0926337\pi\) | ||||
−0.957952 | + | 0.286927i | \(0.907366\pi\) | |||||||
\(912\) | − | 30.0000i | − | 0.993399i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 65.8179i | 2.17706i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.92820i | 0.228914i | ||||||||
\(917\) | 20.7846 | + | 24.0000i | 0.686368 | + | 0.792550i | ||||
\(918\) | 54.0000i | 1.78227i | ||||||||
\(919\) | −16.0000 | −0.527791 | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.0000 | 1.38395 | ||||||||
\(922\) | 31.1769 | 1.02676 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 12.0000 | − | 10.3923i | 0.394771 | − | 0.341882i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 34.6410i | 1.13837i | ||||||||
\(927\) | 10.3923 | 0.341328 | ||||||||
\(928\) | − | 36.0000i | − | 1.18176i | ||||||
\(929\) | −30.0000 | −0.984268 | −0.492134 | − | 0.870519i | \(-0.663783\pi\) | ||||
−0.492134 | + | 0.870519i | \(0.663783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.0000 | + | 3.46410i | 0.786568 | + | 0.113531i | ||||
\(932\) | −6.92820 | −0.226941 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 41.5692i | − | 1.36019i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.92820 | −0.226335 | −0.113167 | − | 0.993576i | \(-0.536100\pi\) | ||||
−0.113167 | + | 0.993576i | \(0.536100\pi\) | |||||||
\(938\) | −27.7128 | + | 24.0000i | −0.904855 | + | 0.783628i | ||||
\(939\) | −36.0000 | −1.17482 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.0000 | 0.586783 | 0.293392 | − | 0.955992i | \(-0.405216\pi\) | ||||
0.293392 | + | 0.955992i | \(0.405216\pi\) | |||||||
\(942\) | −41.5692 | −1.35440 | ||||||||
\(943\) | −20.7846 | −0.676840 | ||||||||
\(944\) | −60.0000 | −1.95283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −48.0000 | −1.56061 | ||||||||
\(947\) | −31.1769 | −1.01311 | −0.506557 | − | 0.862207i | \(-0.669082\pi\) | ||||
−0.506557 | + | 0.862207i | \(0.669082\pi\) | |||||||
\(948\) | 13.8564 | 0.450035 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −48.0000 | −1.55651 | ||||||||
\(952\) | 20.7846 | − | 18.0000i | 0.673633 | − | 0.583383i | ||||
\(953\) | −34.6410 | −1.12213 | −0.561066 | − | 0.827771i | \(-0.689609\pi\) | ||||
−0.561066 | + | 0.827771i | \(0.689609\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.3923i | 0.336111i | ||||||||
\(957\) | −41.5692 | −1.34374 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36.0000 | − | 41.5692i | −1.16250 | − | 1.34234i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.1769 | 1.00466 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −18.0000 | − | 20.7846i | −0.579141 | − | 0.668734i | ||||
\(967\) | − | 20.0000i | − | 0.643157i | −0.946883 | − | 0.321578i | \(-0.895787\pi\) | ||
0.946883 | − | 0.321578i | \(-0.104213\pi\) | |||||||
\(968\) | 1.73205 | 0.0556702 | ||||||||
\(969\) | 36.0000 | 1.15649 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 60.0000 | 1.92549 | 0.962746 | − | 0.270408i | \(-0.0871586\pi\) | ||||
0.962746 | + | 0.270408i | \(0.0871586\pi\) | |||||||
\(972\) | −15.5885 | −0.500000 | ||||||||
\(973\) | −34.6410 | + | 30.0000i | −1.11054 | + | 0.961756i | ||||
\(974\) | − | 6.92820i | − | 0.221994i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 34.6410i | 1.10883i | ||||||||
\(977\) | 6.92820 | 0.221653 | 0.110826 | − | 0.993840i | \(-0.464650\pi\) | ||||
0.110826 | + | 0.993840i | \(0.464650\pi\) | |||||||
\(978\) | 48.0000i | 1.53487i | ||||||||
\(979\) | 20.7846i | 0.664279i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.00000 | 0.191565 | ||||||||
\(982\) | 42.0000i | 1.34027i | ||||||||
\(983\) | − | 60.0000i | − | 1.91370i | −0.290578 | − | 0.956851i | \(-0.593847\pi\) | ||
0.290578 | − | 0.956851i | \(-0.406153\pi\) | |||||||
\(984\) | 18.0000 | 0.573819 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 72.0000 | 2.29295 | ||||||||
\(987\) | −41.5692 | + | 36.0000i | −1.32316 | + | 1.14589i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.7128i | 0.881216i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 18.0000i | 0.571501i | ||||||||
\(993\) | −48.4974 | −1.53902 | ||||||||
\(994\) | 12.0000 | − | 10.3923i | 0.380617 | − | 0.329624i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(998\) | 34.6410 | 1.09654 | ||||||||
\(999\) | − | 10.3923i | − | 0.328798i |
(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 | 525.2.g.b.524.3 | 4 | ||
3.2 | odd | 2 | 525.2.g.c.524.1 | 4 | |||
5.2 | odd | 4 | 105.2.b.a.41.2 | yes | 2 | ||
5.3 | odd | 4 | 525.2.b.a.251.1 | 2 | |||
5.4 | even | 2 | inner | 525.2.g.b.524.2 | 4 | ||
7.6 | odd | 2 | 525.2.g.c.524.3 | 4 | |||
15.2 | even | 4 | 105.2.b.b.41.1 | yes | 2 | ||
15.8 | even | 4 | 525.2.b.b.251.2 | 2 | |||
15.14 | odd | 2 | 525.2.g.c.524.4 | 4 | |||
20.7 | even | 4 | 1680.2.f.b.881.1 | 2 | |||
21.20 | even | 2 | inner | 525.2.g.b.524.1 | 4 | ||
35.2 | odd | 12 | 735.2.s.d.521.1 | 2 | |||
35.12 | even | 12 | 735.2.s.f.521.1 | 2 | |||
35.13 | even | 4 | 525.2.b.b.251.1 | 2 | |||
35.17 | even | 12 | 735.2.s.a.656.1 | 2 | |||
35.27 | even | 4 | 105.2.b.b.41.2 | yes | 2 | ||
35.32 | odd | 12 | 735.2.s.b.656.1 | 2 | |||
35.34 | odd | 2 | 525.2.g.c.524.2 | 4 | |||
60.47 | odd | 4 | 1680.2.f.c.881.1 | 2 | |||
105.2 | even | 12 | 735.2.s.a.521.1 | 2 | |||
105.17 | odd | 12 | 735.2.s.d.656.1 | 2 | |||
105.32 | even | 12 | 735.2.s.f.656.1 | 2 | |||
105.47 | odd | 12 | 735.2.s.b.521.1 | 2 | |||
105.62 | odd | 4 | 105.2.b.a.41.1 | ✓ | 2 | ||
105.83 | odd | 4 | 525.2.b.a.251.2 | 2 | |||
105.104 | even | 2 | inner | 525.2.g.b.524.4 | 4 | ||
140.27 | odd | 4 | 1680.2.f.c.881.2 | 2 | |||
420.167 | even | 4 | 1680.2.f.b.881.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.b.a.41.1 | ✓ | 2 | 105.62 | odd | 4 | ||
105.2.b.a.41.2 | yes | 2 | 5.2 | odd | 4 | ||
105.2.b.b.41.1 | yes | 2 | 15.2 | even | 4 | ||
105.2.b.b.41.2 | yes | 2 | 35.27 | even | 4 | ||
525.2.b.a.251.1 | 2 | 5.3 | odd | 4 | |||
525.2.b.a.251.2 | 2 | 105.83 | odd | 4 | |||
525.2.b.b.251.1 | 2 | 35.13 | even | 4 | |||
525.2.b.b.251.2 | 2 | 15.8 | even | 4 | |||
525.2.g.b.524.1 | 4 | 21.20 | even | 2 | inner | ||
525.2.g.b.524.2 | 4 | 5.4 | even | 2 | inner | ||
525.2.g.b.524.3 | 4 | 1.1 | even | 1 | trivial | ||
525.2.g.b.524.4 | 4 | 105.104 | even | 2 | inner | ||
525.2.g.c.524.1 | 4 | 3.2 | odd | 2 | |||
525.2.g.c.524.2 | 4 | 35.34 | odd | 2 | |||
525.2.g.c.524.3 | 4 | 7.6 | odd | 2 | |||
525.2.g.c.524.4 | 4 | 15.14 | odd | 2 | |||
735.2.s.a.521.1 | 2 | 105.2 | even | 12 | |||
735.2.s.a.656.1 | 2 | 35.17 | even | 12 | |||
735.2.s.b.521.1 | 2 | 105.47 | odd | 12 | |||
735.2.s.b.656.1 | 2 | 35.32 | odd | 12 | |||
735.2.s.d.521.1 | 2 | 35.2 | odd | 12 | |||
735.2.s.d.656.1 | 2 | 105.17 | odd | 12 | |||
735.2.s.f.521.1 | 2 | 35.12 | even | 12 | |||
735.2.s.f.656.1 | 2 | 105.32 | even | 12 | |||
1680.2.f.b.881.1 | 2 | 20.7 | even | 4 | |||
1680.2.f.b.881.2 | 2 | 420.167 | even | 4 | |||
1680.2.f.c.881.1 | 2 | 60.47 | odd | 4 | |||
1680.2.f.c.881.2 | 2 | 140.27 | odd | 4 |