Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,2,Mod(41,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.838429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 41.2 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.41 |
Dual form | 105.2.b.b.41.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205i | 1.22474i | 0.790569 | + | 0.612372i | \(0.209785\pi\) | ||||
−0.790569 | + | 0.612372i | \(0.790215\pi\) | |||||||
\(3\) | − | 1.73205i | − | 1.00000i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 3.00000 | 1.22474 | ||||||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 1.73205i | 0.547723i | ||||||||
\(11\) | − | 3.46410i | − | 1.04447i | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||
0.852803 | − | 0.522233i | \(-0.174901\pi\) | |||||||
\(12\) | 1.73205i | 0.500000i | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | −3.00000 | + | 3.46410i | −0.801784 | + | 0.925820i | ||||
\(15\) | − | 1.73205i | − | 0.447214i | ||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | − | 5.19615i | − | 1.22474i | ||||||
\(19\) | − | 3.46410i | − | 0.794719i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) | ||
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 3.00000 | − | 3.46410i | 0.654654 | − | 0.755929i | ||||
\(22\) | 6.00000 | 1.27920 | ||||||||
\(23\) | 3.46410i | 0.722315i | 0.932505 | + | 0.361158i | \(0.117618\pi\) | ||||
−0.932505 | + | 0.361158i | \(0.882382\pi\) | |||||||
\(24\) | 3.00000 | 0.612372 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | −2.00000 | − | 1.73205i | −0.377964 | − | 0.327327i | ||||
\(29\) | − | 6.92820i | − | 1.28654i | −0.765641 | − | 0.643268i | \(-0.777578\pi\) | ||
0.765641 | − | 0.643268i | \(-0.222422\pi\) | |||||||
\(30\) | 3.00000 | 0.547723 | ||||||||
\(31\) | 3.46410i | 0.622171i | 0.950382 | + | 0.311086i | \(0.100693\pi\) | ||||
−0.950382 | + | 0.311086i | \(0.899307\pi\) | |||||||
\(32\) | − | 5.19615i | − | 0.918559i | ||||||
\(33\) | −6.00000 | −1.04447 | ||||||||
\(34\) | − | 10.3923i | − | 1.78227i | ||||||
\(35\) | 2.00000 | + | 1.73205i | 0.338062 | + | 0.292770i | ||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 6.00000 | 0.973329 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.73205i | 0.273861i | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 6.00000 | + | 5.19615i | 0.925820 | + | 0.801784i | ||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 3.46410i | 0.522233i | ||||||||
\(45\) | −3.00000 | −0.447214 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | 12.0000 | 1.75038 | 0.875190 | − | 0.483779i | \(-0.160736\pi\) | ||||
0.875190 | + | 0.483779i | \(0.160736\pi\) | |||||||
\(48\) | 8.66025i | 1.25000i | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 1.73205i | 0.244949i | ||||||||
\(51\) | 10.3923i | 1.45521i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | −9.00000 | −1.22474 | ||||||||
\(55\) | − | 3.46410i | − | 0.467099i | ||||||
\(56\) | −3.00000 | + | 3.46410i | −0.400892 | + | 0.462910i | ||||
\(57\) | −6.00000 | −0.794719 | ||||||||
\(58\) | 12.0000 | 1.57568 | ||||||||
\(59\) | 12.0000 | 1.56227 | 0.781133 | − | 0.624364i | \(-0.214642\pi\) | ||||
0.781133 | + | 0.624364i | \(0.214642\pi\) | |||||||
\(60\) | 1.73205i | 0.223607i | ||||||||
\(61\) | 6.92820i | 0.887066i | 0.896258 | + | 0.443533i | \(0.146275\pi\) | ||||
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | −6.00000 | − | 5.19615i | −0.755929 | − | 0.654654i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 10.3923i | − | 1.27920i | ||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 6.00000 | 0.727607 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | −3.00000 | + | 3.46410i | −0.358569 | + | 0.414039i | ||||
\(71\) | 3.46410i | 0.411113i | 0.978645 | + | 0.205557i | \(0.0659005\pi\) | ||||
−0.978645 | + | 0.205557i | \(0.934100\pi\) | |||||||
\(72\) | − | 5.19615i | − | 0.612372i | ||||||
\(73\) | − | 6.92820i | − | 0.810885i | −0.914121 | − | 0.405442i | \(-0.867117\pi\) | ||
0.914121 | − | 0.405442i | \(-0.132883\pi\) | |||||||
\(74\) | − | 3.46410i | − | 0.402694i | ||||||
\(75\) | − | 1.73205i | − | 0.200000i | ||||||
\(76\) | 3.46410i | 0.397360i | ||||||||
\(77\) | 6.00000 | − | 6.92820i | 0.683763 | − | 0.789542i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | −5.00000 | −0.559017 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | − | 10.3923i | − | 1.14764i | ||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | −3.00000 | + | 3.46410i | −0.327327 | + | 0.377964i | ||||
\(85\) | −6.00000 | −0.650791 | ||||||||
\(86\) | − | 13.8564i | − | 1.49417i | ||||||
\(87\) | −12.0000 | −1.28654 | ||||||||
\(88\) | 6.00000 | 0.639602 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | − | 5.19615i | − | 0.547723i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 3.46410i | − | 0.361158i | ||||||
\(93\) | 6.00000 | 0.622171 | ||||||||
\(94\) | 20.7846i | 2.14377i | ||||||||
\(95\) | − | 3.46410i | − | 0.355409i | ||||||
\(96\) | −9.00000 | −0.918559 | ||||||||
\(97\) | − | 6.92820i | − | 0.703452i | −0.936103 | − | 0.351726i | \(-0.885595\pi\) | ||
0.936103 | − | 0.351726i | \(-0.114405\pi\) | |||||||
\(98\) | −12.0000 | + | 1.73205i | −1.21218 | + | 0.174964i | ||||
\(99\) | 10.3923i | 1.04447i | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | −18.0000 | −1.78227 | ||||||||
\(103\) | 3.46410i | 0.341328i | 0.985329 | + | 0.170664i | \(0.0545913\pi\) | ||||
−0.985329 | + | 0.170664i | \(0.945409\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.00000 | − | 3.46410i | 0.292770 | − | 0.338062i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.3923i | 1.00466i | 0.864675 | + | 0.502331i | \(0.167524\pi\) | ||||
−0.864675 | + | 0.502331i | \(0.832476\pi\) | |||||||
\(108\) | − | 5.19615i | − | 0.500000i | ||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 6.00000 | 0.572078 | ||||||||
\(111\) | 3.46410i | 0.328798i | ||||||||
\(112\) | −10.0000 | − | 8.66025i | −0.944911 | − | 0.818317i | ||||
\(113\) | − | 6.92820i | − | 0.651751i | −0.945413 | − | 0.325875i | \(-0.894341\pi\) | ||
0.945413 | − | 0.325875i | \(-0.105659\pi\) | |||||||
\(114\) | − | 10.3923i | − | 0.973329i | ||||||
\(115\) | 3.46410i | 0.323029i | ||||||||
\(116\) | 6.92820i | 0.643268i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 20.7846i | 1.91338i | ||||||||
\(119\) | −12.0000 | − | 10.3923i | −1.10004 | − | 0.952661i | ||||
\(120\) | 3.00000 | 0.273861 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | −12.0000 | −1.08643 | ||||||||
\(123\) | 10.3923i | 0.937043i | ||||||||
\(124\) | − | 3.46410i | − | 0.311086i | ||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 9.00000 | − | 10.3923i | 0.801784 | − | 0.925820i | ||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | − | 12.1244i | − | 1.07165i | ||||||
\(129\) | 13.8564i | 1.21999i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 6.00000 | 0.522233 | ||||||||
\(133\) | 6.00000 | − | 6.92820i | 0.520266 | − | 0.600751i | ||||
\(134\) | 13.8564i | 1.19701i | ||||||||
\(135\) | 5.19615i | 0.447214i | ||||||||
\(136\) | − | 10.3923i | − | 0.891133i | ||||||
\(137\) | 20.7846i | 1.77575i | 0.460086 | + | 0.887875i | \(0.347819\pi\) | ||||
−0.460086 | + | 0.887875i | \(0.652181\pi\) | |||||||
\(138\) | 10.3923i | 0.884652i | ||||||||
\(139\) | − | 17.3205i | − | 1.46911i | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||
0.678551 | − | 0.734553i | \(-0.262608\pi\) | |||||||
\(140\) | −2.00000 | − | 1.73205i | −0.169031 | − | 0.146385i | ||||
\(141\) | − | 20.7846i | − | 1.75038i | ||||||
\(142\) | −6.00000 | −0.503509 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 15.0000 | 1.25000 | ||||||||
\(145\) | − | 6.92820i | − | 0.575356i | ||||||
\(146\) | 12.0000 | 0.993127 | ||||||||
\(147\) | 12.0000 | − | 1.73205i | 0.989743 | − | 0.142857i | ||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | 6.92820i | 0.567581i | 0.958886 | + | 0.283790i | \(0.0915919\pi\) | ||||
−0.958886 | + | 0.283790i | \(0.908408\pi\) | |||||||
\(150\) | 3.00000 | 0.244949 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 6.00000 | 0.486664 | ||||||||
\(153\) | 18.0000 | 1.45521 | ||||||||
\(154\) | 12.0000 | + | 10.3923i | 0.966988 | + | 0.837436i | ||||
\(155\) | 3.46410i | 0.278243i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 13.8564i | − | 1.10586i | −0.833227 | − | 0.552931i | \(-0.813509\pi\) | ||
0.833227 | − | 0.552931i | \(-0.186491\pi\) | |||||||
\(158\) | 13.8564i | 1.10236i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 5.19615i | − | 0.410792i | ||||||
\(161\) | −6.00000 | + | 6.92820i | −0.472866 | + | 0.546019i | ||||
\(162\) | 15.5885i | 1.22474i | ||||||||
\(163\) | −16.0000 | −1.25322 | −0.626608 | − | 0.779334i | \(-0.715557\pi\) | ||||
−0.626608 | + | 0.779334i | \(0.715557\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | −6.00000 | −0.467099 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 6.00000 | + | 5.19615i | 0.462910 | + | 0.400892i | ||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | − | 10.3923i | − | 0.797053i | ||||||
\(171\) | 10.3923i | 0.794719i | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | −18.0000 | −1.36851 | −0.684257 | − | 0.729241i | \(-0.739873\pi\) | ||||
−0.684257 | + | 0.729241i | \(0.739873\pi\) | |||||||
\(174\) | − | 20.7846i | − | 1.57568i | ||||||
\(175\) | 2.00000 | + | 1.73205i | 0.151186 | + | 0.130931i | ||||
\(176\) | 17.3205i | 1.30558i | ||||||||
\(177\) | − | 20.7846i | − | 1.56227i | ||||||
\(178\) | − | 10.3923i | − | 0.778936i | ||||||
\(179\) | 10.3923i | 0.776757i | 0.921500 | + | 0.388379i | \(0.126965\pi\) | ||||
−0.921500 | + | 0.388379i | \(0.873035\pi\) | |||||||
\(180\) | 3.00000 | 0.223607 | ||||||||
\(181\) | 20.7846i | 1.54491i | 0.635071 | + | 0.772454i | \(0.280971\pi\) | ||||
−0.635071 | + | 0.772454i | \(0.719029\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.0000 | 0.887066 | ||||||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | −2.00000 | −0.147043 | ||||||||
\(186\) | 10.3923i | 0.762001i | ||||||||
\(187\) | 20.7846i | 1.51992i | ||||||||
\(188\) | −12.0000 | −0.875190 | ||||||||
\(189\) | −9.00000 | + | 10.3923i | −0.654654 | + | 0.755929i | ||||
\(190\) | 6.00000 | 0.435286 | ||||||||
\(191\) | − | 10.3923i | − | 0.751961i | −0.926628 | − | 0.375980i | \(-0.877306\pi\) | ||
0.926628 | − | 0.375980i | \(-0.122694\pi\) | |||||||
\(192\) | 1.73205i | 0.125000i | ||||||||
\(193\) | −14.0000 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(194\) | 12.0000 | 0.861550 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | − | 6.92820i | −0.0714286 | − | 0.494872i | ||||
\(197\) | − | 13.8564i | − | 0.987228i | −0.869681 | − | 0.493614i | \(-0.835676\pi\) | ||
0.869681 | − | 0.493614i | \(-0.164324\pi\) | |||||||
\(198\) | −18.0000 | −1.27920 | ||||||||
\(199\) | − | 10.3923i | − | 0.736691i | −0.929689 | − | 0.368345i | \(-0.879924\pi\) | ||
0.929689 | − | 0.368345i | \(-0.120076\pi\) | |||||||
\(200\) | 1.73205i | 0.122474i | ||||||||
\(201\) | − | 13.8564i | − | 0.977356i | ||||||
\(202\) | 10.3923i | 0.731200i | ||||||||
\(203\) | 12.0000 | − | 13.8564i | 0.842235 | − | 0.972529i | ||||
\(204\) | − | 10.3923i | − | 0.727607i | ||||||
\(205\) | −6.00000 | −0.419058 | ||||||||
\(206\) | −6.00000 | −0.418040 | ||||||||
\(207\) | − | 10.3923i | − | 0.722315i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 6.00000 | + | 5.19615i | 0.414039 | + | 0.358569i | ||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.00000 | 0.411113 | ||||||||
\(214\) | −18.0000 | −1.23045 | ||||||||
\(215\) | −8.00000 | −0.545595 | ||||||||
\(216\) | −9.00000 | −0.612372 | ||||||||
\(217\) | −6.00000 | + | 6.92820i | −0.407307 | + | 0.470317i | ||||
\(218\) | − | 3.46410i | − | 0.234619i | ||||||
\(219\) | −12.0000 | −0.810885 | ||||||||
\(220\) | 3.46410i | 0.233550i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.00000 | −0.402694 | ||||||||
\(223\) | 17.3205i | 1.15987i | 0.814664 | + | 0.579934i | \(0.196921\pi\) | ||||
−0.814664 | + | 0.579934i | \(0.803079\pi\) | |||||||
\(224\) | 9.00000 | − | 10.3923i | 0.601338 | − | 0.694365i | ||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 12.0000 | 0.798228 | ||||||||
\(227\) | 24.0000 | 1.59294 | 0.796468 | − | 0.604681i | \(-0.206699\pi\) | ||||
0.796468 | + | 0.604681i | \(0.206699\pi\) | |||||||
\(228\) | 6.00000 | 0.397360 | ||||||||
\(229\) | 6.92820i | 0.457829i | 0.973447 | + | 0.228914i | \(0.0735176\pi\) | ||||
−0.973447 | + | 0.228914i | \(0.926482\pi\) | |||||||
\(230\) | −6.00000 | −0.395628 | ||||||||
\(231\) | −12.0000 | − | 10.3923i | −0.789542 | − | 0.683763i | ||||
\(232\) | 12.0000 | 0.787839 | ||||||||
\(233\) | 6.92820i | 0.453882i | 0.973909 | + | 0.226941i | \(0.0728724\pi\) | ||||
−0.973909 | + | 0.226941i | \(0.927128\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0000 | 0.782794 | ||||||||
\(236\) | −12.0000 | −0.781133 | ||||||||
\(237\) | − | 13.8564i | − | 0.900070i | ||||||
\(238\) | 18.0000 | − | 20.7846i | 1.16677 | − | 1.34727i | ||||
\(239\) | − | 10.3923i | − | 0.672222i | −0.941822 | − | 0.336111i | \(-0.890888\pi\) | ||
0.941822 | − | 0.336111i | \(-0.109112\pi\) | |||||||
\(240\) | 8.66025i | 0.559017i | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | − | 1.73205i | − | 0.111340i | ||||||
\(243\) | − | 15.5885i | − | 1.00000i | ||||||
\(244\) | − | 6.92820i | − | 0.443533i | ||||||
\(245\) | 1.00000 | + | 6.92820i | 0.0638877 | + | 0.442627i | ||||
\(246\) | −18.0000 | −1.14764 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.73205i | 0.109545i | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 6.00000 | + | 5.19615i | 0.377964 | + | 0.327327i | ||||
\(253\) | 12.0000 | 0.754434 | ||||||||
\(254\) | − | 6.92820i | − | 0.434714i | ||||||
\(255\) | 10.3923i | 0.650791i | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | −6.00000 | −0.374270 | −0.187135 | − | 0.982334i | \(-0.559920\pi\) | ||||
−0.187135 | + | 0.982334i | \(0.559920\pi\) | |||||||
\(258\) | −24.0000 | −1.49417 | ||||||||
\(259\) | −4.00000 | − | 3.46410i | −0.248548 | − | 0.215249i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.7846i | 1.28654i | ||||||||
\(262\) | 20.7846i | 1.28408i | ||||||||
\(263\) | − | 24.2487i | − | 1.49524i | −0.664127 | − | 0.747620i | \(-0.731197\pi\) | ||
0.664127 | − | 0.747620i | \(-0.268803\pi\) | |||||||
\(264\) | − | 10.3923i | − | 0.639602i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.0000 | + | 10.3923i | 0.735767 | + | 0.637193i | ||||
\(267\) | 10.3923i | 0.635999i | ||||||||
\(268\) | −8.00000 | −0.488678 | ||||||||
\(269\) | −18.0000 | −1.09748 | −0.548740 | − | 0.835993i | \(-0.684892\pi\) | ||||
−0.548740 | + | 0.835993i | \(0.684892\pi\) | |||||||
\(270\) | −9.00000 | −0.547723 | ||||||||
\(271\) | − | 24.2487i | − | 1.47300i | −0.676435 | − | 0.736502i | \(-0.736476\pi\) | ||
0.676435 | − | 0.736502i | \(-0.263524\pi\) | |||||||
\(272\) | 30.0000 | 1.81902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −36.0000 | −2.17484 | ||||||||
\(275\) | − | 3.46410i | − | 0.208893i | ||||||
\(276\) | −6.00000 | −0.361158 | ||||||||
\(277\) | 14.0000 | 0.841178 | 0.420589 | − | 0.907251i | \(-0.361823\pi\) | ||||
0.420589 | + | 0.907251i | \(0.361823\pi\) | |||||||
\(278\) | 30.0000 | 1.79928 | ||||||||
\(279\) | − | 10.3923i | − | 0.622171i | ||||||
\(280\) | −3.00000 | + | 3.46410i | −0.179284 | + | 0.207020i | ||||
\(281\) | 13.8564i | 0.826604i | 0.910594 | + | 0.413302i | \(0.135625\pi\) | ||||
−0.910594 | + | 0.413302i | \(0.864375\pi\) | |||||||
\(282\) | 36.0000 | 2.14377 | ||||||||
\(283\) | − | 17.3205i | − | 1.02960i | −0.857311 | − | 0.514799i | \(-0.827867\pi\) | ||
0.857311 | − | 0.514799i | \(-0.172133\pi\) | |||||||
\(284\) | − | 3.46410i | − | 0.205557i | ||||||
\(285\) | −6.00000 | −0.355409 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | − | 10.3923i | −0.708338 | − | 0.613438i | ||||
\(288\) | 15.5885i | 0.918559i | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 12.0000 | 0.704664 | ||||||||
\(291\) | −12.0000 | −0.703452 | ||||||||
\(292\) | 6.92820i | 0.405442i | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 3.00000 | + | 20.7846i | 0.174964 | + | 1.21218i | ||||
\(295\) | 12.0000 | 0.698667 | ||||||||
\(296\) | − | 3.46410i | − | 0.201347i | ||||||
\(297\) | 18.0000 | 1.04447 | ||||||||
\(298\) | −12.0000 | −0.695141 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.73205i | 0.100000i | ||||||||
\(301\) | −16.0000 | − | 13.8564i | −0.922225 | − | 0.798670i | ||||
\(302\) | − | 13.8564i | − | 0.797347i | ||||||
\(303\) | − | 10.3923i | − | 0.597022i | ||||||
\(304\) | 17.3205i | 0.993399i | ||||||||
\(305\) | 6.92820i | 0.396708i | ||||||||
\(306\) | 31.1769i | 1.78227i | ||||||||
\(307\) | 24.2487i | 1.38395i | 0.721923 | + | 0.691974i | \(0.243259\pi\) | ||||
−0.721923 | + | 0.691974i | \(0.756741\pi\) | |||||||
\(308\) | −6.00000 | + | 6.92820i | −0.341882 | + | 0.394771i | ||||
\(309\) | 6.00000 | 0.341328 | ||||||||
\(310\) | −6.00000 | −0.340777 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.7846i | 1.17482i | 0.809291 | + | 0.587408i | \(0.199852\pi\) | ||||
−0.809291 | + | 0.587408i | \(0.800148\pi\) | |||||||
\(314\) | 24.0000 | 1.35440 | ||||||||
\(315\) | −6.00000 | − | 5.19615i | −0.338062 | − | 0.292770i | ||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 27.7128i | 1.55651i | 0.627950 | + | 0.778253i | \(0.283894\pi\) | ||||
−0.627950 | + | 0.778253i | \(0.716106\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.0000 | −1.34374 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 18.0000 | 1.00466 | ||||||||
\(322\) | −12.0000 | − | 10.3923i | −0.668734 | − | 0.579141i | ||||
\(323\) | 20.7846i | 1.15649i | ||||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 27.7128i | − | 1.53487i | ||||||
\(327\) | 3.46410i | 0.191565i | ||||||||
\(328\) | − | 10.3923i | − | 0.573819i | ||||||
\(329\) | 24.0000 | + | 20.7846i | 1.32316 | + | 1.14589i | ||||
\(330\) | − | 10.3923i | − | 0.572078i | ||||||
\(331\) | 28.0000 | 1.53902 | 0.769510 | − | 0.638635i | \(-0.220501\pi\) | ||||
0.769510 | + | 0.638635i | \(0.220501\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.00000 | 0.328798 | ||||||||
\(334\) | − | 20.7846i | − | 1.13728i | ||||||
\(335\) | 8.00000 | 0.437087 | ||||||||
\(336\) | −15.0000 | + | 17.3205i | −0.818317 | + | 0.944911i | ||||
\(337\) | −14.0000 | −0.762629 | −0.381314 | − | 0.924445i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | 22.5167i | 1.22474i | ||||||||
\(339\) | −12.0000 | −0.651751 | ||||||||
\(340\) | 6.00000 | 0.325396 | ||||||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | −18.0000 | −0.973329 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | − | 13.8564i | − | 0.747087i | ||||||
\(345\) | 6.00000 | 0.323029 | ||||||||
\(346\) | − | 31.1769i | − | 1.67608i | ||||||
\(347\) | − | 17.3205i | − | 0.929814i | −0.885360 | − | 0.464907i | \(-0.846088\pi\) | ||
0.885360 | − | 0.464907i | \(-0.153912\pi\) | |||||||
\(348\) | 12.0000 | 0.643268 | ||||||||
\(349\) | − | 6.92820i | − | 0.370858i | −0.982658 | − | 0.185429i | \(-0.940632\pi\) | ||
0.982658 | − | 0.185429i | \(-0.0593675\pi\) | |||||||
\(350\) | −3.00000 | + | 3.46410i | −0.160357 | + | 0.185164i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −18.0000 | −0.959403 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 36.0000 | 1.91338 | ||||||||
\(355\) | 3.46410i | 0.183855i | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | −18.0000 | + | 20.7846i | −0.952661 | + | 1.10004i | ||||
\(358\) | −18.0000 | −0.951330 | ||||||||
\(359\) | 3.46410i | 0.182828i | 0.995813 | + | 0.0914141i | \(0.0291387\pi\) | ||||
−0.995813 | + | 0.0914141i | \(0.970861\pi\) | |||||||
\(360\) | − | 5.19615i | − | 0.273861i | ||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | −36.0000 | −1.89212 | ||||||||
\(363\) | 1.73205i | 0.0909091i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 6.92820i | − | 0.362639i | ||||||
\(366\) | 20.7846i | 1.08643i | ||||||||
\(367\) | − | 10.3923i | − | 0.542474i | −0.962513 | − | 0.271237i | \(-0.912567\pi\) | ||
0.962513 | − | 0.271237i | \(-0.0874327\pi\) | |||||||
\(368\) | − | 17.3205i | − | 0.902894i | ||||||
\(369\) | 18.0000 | 0.937043 | ||||||||
\(370\) | − | 3.46410i | − | 0.180090i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.00000 | −0.311086 | ||||||||
\(373\) | 14.0000 | 0.724893 | 0.362446 | − | 0.932005i | \(-0.381942\pi\) | ||||
0.362446 | + | 0.932005i | \(0.381942\pi\) | |||||||
\(374\) | −36.0000 | −1.86152 | ||||||||
\(375\) | − | 1.73205i | − | 0.0894427i | ||||||
\(376\) | 20.7846i | 1.07188i | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −18.0000 | − | 15.5885i | −0.925820 | − | 0.801784i | ||||
\(379\) | 4.00000 | 0.205466 | 0.102733 | − | 0.994709i | \(-0.467241\pi\) | ||||
0.102733 | + | 0.994709i | \(0.467241\pi\) | |||||||
\(380\) | 3.46410i | 0.177705i | ||||||||
\(381\) | 6.92820i | 0.354943i | ||||||||
\(382\) | 18.0000 | 0.920960 | ||||||||
\(383\) | −12.0000 | −0.613171 | −0.306586 | − | 0.951843i | \(-0.599187\pi\) | ||||
−0.306586 | + | 0.951843i | \(0.599187\pi\) | |||||||
\(384\) | −21.0000 | −1.07165 | ||||||||
\(385\) | 6.00000 | − | 6.92820i | 0.305788 | − | 0.353094i | ||||
\(386\) | − | 24.2487i | − | 1.23423i | ||||||
\(387\) | 24.0000 | 1.21999 | ||||||||
\(388\) | 6.92820i | 0.351726i | ||||||||
\(389\) | 6.92820i | 0.351274i | 0.984455 | + | 0.175637i | \(0.0561985\pi\) | ||||
−0.984455 | + | 0.175637i | \(0.943802\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 20.7846i | − | 1.05112i | ||||||
\(392\) | −12.0000 | + | 1.73205i | −0.606092 | + | 0.0874818i | ||||
\(393\) | − | 20.7846i | − | 1.04844i | ||||||
\(394\) | 24.0000 | 1.20910 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | − | 10.3923i | − | 0.522233i | ||||||
\(397\) | − | 13.8564i | − | 0.695433i | −0.937600 | − | 0.347717i | \(-0.886957\pi\) | ||
0.937600 | − | 0.347717i | \(-0.113043\pi\) | |||||||
\(398\) | 18.0000 | 0.902258 | ||||||||
\(399\) | −12.0000 | − | 10.3923i | −0.600751 | − | 0.520266i | ||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | − | 27.7128i | − | 1.38391i | −0.721940 | − | 0.691956i | \(-0.756749\pi\) | ||
0.721940 | − | 0.691956i | \(-0.243251\pi\) | |||||||
\(402\) | 24.0000 | 1.19701 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | 9.00000 | 0.447214 | ||||||||
\(406\) | 24.0000 | + | 20.7846i | 1.19110 | + | 1.03152i | ||||
\(407\) | 6.92820i | 0.343418i | ||||||||
\(408\) | −18.0000 | −0.891133 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | − | 10.3923i | − | 0.513239i | ||||||
\(411\) | 36.0000 | 1.77575 | ||||||||
\(412\) | − | 3.46410i | − | 0.170664i | ||||||
\(413\) | 24.0000 | + | 20.7846i | 1.18096 | + | 1.02274i | ||||
\(414\) | 18.0000 | 0.884652 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.0000 | −1.46911 | ||||||||
\(418\) | − | 20.7846i | − | 1.01661i | ||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | −3.00000 | + | 3.46410i | −0.146385 | + | 0.169031i | ||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 6.92820i | 0.337260i | ||||||||
\(423\) | −36.0000 | −1.75038 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00000 | −0.291043 | ||||||||
\(426\) | 10.3923i | 0.503509i | ||||||||
\(427\) | −12.0000 | + | 13.8564i | −0.580721 | + | 0.670559i | ||||
\(428\) | − | 10.3923i | − | 0.502331i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 13.8564i | − | 0.668215i | ||||||
\(431\) | − | 10.3923i | − | 0.500580i | −0.968171 | − | 0.250290i | \(-0.919474\pi\) | ||
0.968171 | − | 0.250290i | \(-0.0805259\pi\) | |||||||
\(432\) | − | 25.9808i | − | 1.25000i | ||||||
\(433\) | 6.92820i | 0.332948i | 0.986046 | + | 0.166474i | \(0.0532382\pi\) | ||||
−0.986046 | + | 0.166474i | \(0.946762\pi\) | |||||||
\(434\) | −12.0000 | − | 10.3923i | −0.576018 | − | 0.498847i | ||||
\(435\) | −12.0000 | −0.575356 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | 12.0000 | 0.574038 | ||||||||
\(438\) | − | 20.7846i | − | 0.993127i | ||||||
\(439\) | 17.3205i | 0.826663i | 0.910581 | + | 0.413331i | \(0.135635\pi\) | ||||
−0.910581 | + | 0.413331i | \(0.864365\pi\) | |||||||
\(440\) | 6.00000 | 0.286039 | ||||||||
\(441\) | −3.00000 | − | 20.7846i | −0.142857 | − | 0.989743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.3923i | 0.493753i | 0.969047 | + | 0.246877i | \(0.0794043\pi\) | ||||
−0.969047 | + | 0.246877i | \(0.920596\pi\) | |||||||
\(444\) | − | 3.46410i | − | 0.164399i | ||||||
\(445\) | −6.00000 | −0.284427 | ||||||||
\(446\) | −30.0000 | −1.42054 | ||||||||
\(447\) | 12.0000 | 0.567581 | ||||||||
\(448\) | −2.00000 | − | 1.73205i | −0.0944911 | − | 0.0818317i | ||||
\(449\) | − | 13.8564i | − | 0.653924i | −0.945037 | − | 0.326962i | \(-0.893975\pi\) | ||
0.945037 | − | 0.326962i | \(-0.106025\pi\) | |||||||
\(450\) | − | 5.19615i | − | 0.244949i | ||||||
\(451\) | 20.7846i | 0.978709i | ||||||||
\(452\) | 6.92820i | 0.325875i | ||||||||
\(453\) | 13.8564i | 0.651031i | ||||||||
\(454\) | 41.5692i | 1.95094i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | − | 10.3923i | − | 0.486664i | ||||||
\(457\) | −38.0000 | −1.77757 | −0.888783 | − | 0.458329i | \(-0.848448\pi\) | ||||
−0.888783 | + | 0.458329i | \(0.848448\pi\) | |||||||
\(458\) | −12.0000 | −0.560723 | ||||||||
\(459\) | − | 31.1769i | − | 1.45521i | ||||||
\(460\) | − | 3.46410i | − | 0.161515i | ||||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 18.0000 | − | 20.7846i | 0.837436 | − | 0.966988i | ||||
\(463\) | 20.0000 | 0.929479 | 0.464739 | − | 0.885448i | \(-0.346148\pi\) | ||||
0.464739 | + | 0.885448i | \(0.346148\pi\) | |||||||
\(464\) | 34.6410i | 1.60817i | ||||||||
\(465\) | 6.00000 | 0.278243 | ||||||||
\(466\) | −12.0000 | −0.555889 | ||||||||
\(467\) | −24.0000 | −1.11059 | −0.555294 | − | 0.831654i | \(-0.687394\pi\) | ||||
−0.555294 | + | 0.831654i | \(0.687394\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0000 | + | 13.8564i | 0.738811 | + | 0.639829i | ||||
\(470\) | 20.7846i | 0.958723i | ||||||||
\(471\) | −24.0000 | −1.10586 | ||||||||
\(472\) | 20.7846i | 0.956689i | ||||||||
\(473\) | 27.7128i | 1.27424i | ||||||||
\(474\) | 24.0000 | 1.10236 | ||||||||
\(475\) | − | 3.46410i | − | 0.158944i | ||||||
\(476\) | 12.0000 | + | 10.3923i | 0.550019 | + | 0.476331i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.0000 | 0.823301 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | −9.00000 | −0.410792 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.0000 | + | 10.3923i | 0.546019 | + | 0.472866i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | − | 6.92820i | − | 0.314594i | ||||||
\(486\) | 27.0000 | 1.22474 | ||||||||
\(487\) | 4.00000 | 0.181257 | 0.0906287 | − | 0.995885i | \(-0.471112\pi\) | ||||
0.0906287 | + | 0.995885i | \(0.471112\pi\) | |||||||
\(488\) | −12.0000 | −0.543214 | ||||||||
\(489\) | 27.7128i | 1.25322i | ||||||||
\(490\) | −12.0000 | + | 1.73205i | −0.542105 | + | 0.0782461i | ||||
\(491\) | 24.2487i | 1.09433i | 0.837025 | + | 0.547165i | \(0.184293\pi\) | ||||
−0.837025 | + | 0.547165i | \(0.815707\pi\) | |||||||
\(492\) | − | 10.3923i | − | 0.468521i | ||||||
\(493\) | 41.5692i | 1.87218i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.3923i | 0.467099i | ||||||||
\(496\) | − | 17.3205i | − | 0.777714i | ||||||
\(497\) | −6.00000 | + | 6.92820i | −0.269137 | + | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 20.7846i | 0.928588i | ||||||||
\(502\) | − | 20.7846i | − | 0.927663i | ||||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | 9.00000 | − | 10.3923i | 0.400892 | − | 0.462910i | ||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 20.7846i | 0.923989i | ||||||||
\(507\) | − | 22.5167i | − | 1.00000i | ||||||
\(508\) | 4.00000 | 0.177471 | ||||||||
\(509\) | 30.0000 | 1.32973 | 0.664863 | − | 0.746965i | \(-0.268490\pi\) | ||||
0.664863 | + | 0.746965i | \(0.268490\pi\) | |||||||
\(510\) | −18.0000 | −0.797053 | ||||||||
\(511\) | 12.0000 | − | 13.8564i | 0.530849 | − | 0.612971i | ||||
\(512\) | 8.66025i | 0.382733i | ||||||||
\(513\) | 18.0000 | 0.794719 | ||||||||
\(514\) | − | 10.3923i | − | 0.458385i | ||||||
\(515\) | 3.46410i | 0.152647i | ||||||||
\(516\) | − | 13.8564i | − | 0.609994i | ||||||
\(517\) | − | 41.5692i | − | 1.82821i | ||||||
\(518\) | 6.00000 | − | 6.92820i | 0.263625 | − | 0.304408i | ||||
\(519\) | 31.1769i | 1.36851i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | −0.262865 | −0.131432 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | −36.0000 | −1.57568 | ||||||||
\(523\) | − | 17.3205i | − | 0.757373i | −0.925525 | − | 0.378686i | \(-0.876376\pi\) | ||
0.925525 | − | 0.378686i | \(-0.123624\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 3.00000 | − | 3.46410i | 0.130931 | − | 0.151186i | ||||
\(526\) | 42.0000 | 1.83129 | ||||||||
\(527\) | − | 20.7846i | − | 0.905392i | ||||||
\(528\) | 30.0000 | 1.30558 | ||||||||
\(529\) | 11.0000 | 0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −36.0000 | −1.56227 | ||||||||
\(532\) | −6.00000 | + | 6.92820i | −0.260133 | + | 0.300376i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −18.0000 | −0.778936 | ||||||||
\(535\) | 10.3923i | 0.449299i | ||||||||
\(536\) | 13.8564i | 0.598506i | ||||||||
\(537\) | 18.0000 | 0.776757 | ||||||||
\(538\) | − | 31.1769i | − | 1.34413i | ||||||
\(539\) | 24.0000 | − | 3.46410i | 1.03375 | − | 0.149209i | ||||
\(540\) | − | 5.19615i | − | 0.223607i | ||||||
\(541\) | −34.0000 | −1.46177 | −0.730887 | − | 0.682498i | \(-0.760893\pi\) | ||||
−0.730887 | + | 0.682498i | \(0.760893\pi\) | |||||||
\(542\) | 42.0000 | 1.80405 | ||||||||
\(543\) | 36.0000 | 1.54491 | ||||||||
\(544\) | 31.1769i | 1.33670i | ||||||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | − | 20.7846i | − | 0.887875i | ||||||
\(549\) | − | 20.7846i | − | 0.887066i | ||||||
\(550\) | 6.00000 | 0.255841 | ||||||||
\(551\) | −24.0000 | −1.02243 | ||||||||
\(552\) | 10.3923i | 0.442326i | ||||||||
\(553\) | 16.0000 | + | 13.8564i | 0.680389 | + | 0.589234i | ||||
\(554\) | 24.2487i | 1.03023i | ||||||||
\(555\) | 3.46410i | 0.147043i | ||||||||
\(556\) | 17.3205i | 0.734553i | ||||||||
\(557\) | − | 27.7128i | − | 1.17423i | −0.809504 | − | 0.587115i | \(-0.800264\pi\) | ||
0.809504 | − | 0.587115i | \(-0.199736\pi\) | |||||||
\(558\) | 18.0000 | 0.762001 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −10.0000 | − | 8.66025i | −0.422577 | − | 0.365963i | ||||
\(561\) | 36.0000 | 1.51992 | ||||||||
\(562\) | −24.0000 | −1.01238 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 20.7846i | 0.875190i | ||||||||
\(565\) | − | 6.92820i | − | 0.291472i | ||||||
\(566\) | 30.0000 | 1.26099 | ||||||||
\(567\) | 18.0000 | + | 15.5885i | 0.755929 | + | 0.654654i | ||||
\(568\) | −6.00000 | −0.251754 | ||||||||
\(569\) | − | 27.7128i | − | 1.16178i | −0.813982 | − | 0.580891i | \(-0.802704\pi\) | ||
0.813982 | − | 0.580891i | \(-0.197296\pi\) | |||||||
\(570\) | − | 10.3923i | − | 0.435286i | ||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.0000 | −0.751961 | ||||||||
\(574\) | 18.0000 | − | 20.7846i | 0.751305 | − | 0.867533i | ||||
\(575\) | 3.46410i | 0.144463i | ||||||||
\(576\) | 3.00000 | 0.125000 | ||||||||
\(577\) | − | 34.6410i | − | 1.44212i | −0.692870 | − | 0.721062i | \(-0.743654\pi\) | ||
0.692870 | − | 0.721062i | \(-0.256346\pi\) | |||||||
\(578\) | 32.9090i | 1.36883i | ||||||||
\(579\) | 24.2487i | 1.00774i | ||||||||
\(580\) | 6.92820i | 0.287678i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 20.7846i | − | 0.861550i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 12.0000 | 0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.3923i | 0.429302i | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | −12.0000 | + | 1.73205i | −0.494872 | + | 0.0714286i | ||||
\(589\) | 12.0000 | 0.494451 | ||||||||
\(590\) | 20.7846i | 0.855689i | ||||||||
\(591\) | −24.0000 | −0.987228 | ||||||||
\(592\) | 10.0000 | 0.410997 | ||||||||
\(593\) | −6.00000 | −0.246390 | −0.123195 | − | 0.992382i | \(-0.539314\pi\) | ||||
−0.123195 | + | 0.992382i | \(0.539314\pi\) | |||||||
\(594\) | 31.1769i | 1.27920i | ||||||||
\(595\) | −12.0000 | − | 10.3923i | −0.491952 | − | 0.426043i | ||||
\(596\) | − | 6.92820i | − | 0.283790i | ||||||
\(597\) | −18.0000 | −0.736691 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 24.2487i | − | 0.990775i | −0.868672 | − | 0.495388i | \(-0.835026\pi\) | ||
0.868672 | − | 0.495388i | \(-0.164974\pi\) | |||||||
\(600\) | 3.00000 | 0.122474 | ||||||||
\(601\) | − | 13.8564i | − | 0.565215i | −0.959236 | − | 0.282607i | \(-0.908801\pi\) | ||
0.959236 | − | 0.282607i | \(-0.0911993\pi\) | |||||||
\(602\) | 24.0000 | − | 27.7128i | 0.978167 | − | 1.12949i | ||||
\(603\) | −24.0000 | −0.977356 | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 18.0000 | 0.731200 | ||||||||
\(607\) | 17.3205i | 0.703018i | 0.936185 | + | 0.351509i | \(0.114331\pi\) | ||||
−0.936185 | + | 0.351509i | \(0.885669\pi\) | |||||||
\(608\) | −18.0000 | −0.729996 | ||||||||
\(609\) | −24.0000 | − | 20.7846i | −0.972529 | − | 0.842235i | ||||
\(610\) | −12.0000 | −0.485866 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −18.0000 | −0.727607 | ||||||||
\(613\) | −34.0000 | −1.37325 | −0.686624 | − | 0.727013i | \(-0.740908\pi\) | ||||
−0.686624 | + | 0.727013i | \(0.740908\pi\) | |||||||
\(614\) | −42.0000 | −1.69498 | ||||||||
\(615\) | 10.3923i | 0.419058i | ||||||||
\(616\) | 12.0000 | + | 10.3923i | 0.483494 | + | 0.418718i | ||||
\(617\) | − | 6.92820i | − | 0.278919i | −0.990228 | − | 0.139459i | \(-0.955464\pi\) | ||
0.990228 | − | 0.139459i | \(-0.0445365\pi\) | |||||||
\(618\) | 10.3923i | 0.418040i | ||||||||
\(619\) | − | 17.3205i | − | 0.696170i | −0.937463 | − | 0.348085i | \(-0.886832\pi\) | ||
0.937463 | − | 0.348085i | \(-0.113168\pi\) | |||||||
\(620\) | − | 3.46410i | − | 0.139122i | ||||||
\(621\) | −18.0000 | −0.722315 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.0000 | − | 10.3923i | −0.480770 | − | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −36.0000 | −1.43885 | ||||||||
\(627\) | 20.7846i | 0.830057i | ||||||||
\(628\) | 13.8564i | 0.552931i | ||||||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 9.00000 | − | 10.3923i | 0.358569 | − | 0.414039i | ||||
\(631\) | −40.0000 | −1.59237 | −0.796187 | − | 0.605050i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605050i | \(0.793153\pi\) | |||||||
\(632\) | 13.8564i | 0.551178i | ||||||||
\(633\) | − | 6.92820i | − | 0.275371i | ||||||
\(634\) | −48.0000 | −1.90632 | ||||||||
\(635\) | −4.00000 | −0.158735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 41.5692i | − | 1.64574i | ||||||
\(639\) | − | 10.3923i | − | 0.411113i | ||||||
\(640\) | − | 12.1244i | − | 0.479257i | ||||||
\(641\) | 27.7128i | 1.09459i | 0.836940 | + | 0.547295i | \(0.184342\pi\) | ||||
−0.836940 | + | 0.547295i | \(0.815658\pi\) | |||||||
\(642\) | 31.1769i | 1.23045i | ||||||||
\(643\) | − | 31.1769i | − | 1.22950i | −0.788723 | − | 0.614749i | \(-0.789257\pi\) | ||
0.788723 | − | 0.614749i | \(-0.210743\pi\) | |||||||
\(644\) | 6.00000 | − | 6.92820i | 0.236433 | − | 0.273009i | ||||
\(645\) | 13.8564i | 0.545595i | ||||||||
\(646\) | −36.0000 | −1.41640 | ||||||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | 15.5885i | 0.612372i | ||||||||
\(649\) | − | 41.5692i | − | 1.63173i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.0000 | + | 10.3923i | 0.470317 | + | 0.407307i | ||||
\(652\) | 16.0000 | 0.626608 | ||||||||
\(653\) | − | 41.5692i | − | 1.62673i | −0.581754 | − | 0.813365i | \(-0.697633\pi\) | ||
0.581754 | − | 0.813365i | \(-0.302367\pi\) | |||||||
\(654\) | −6.00000 | −0.234619 | ||||||||
\(655\) | 12.0000 | 0.468879 | ||||||||
\(656\) | 30.0000 | 1.17130 | ||||||||
\(657\) | 20.7846i | 0.810885i | ||||||||
\(658\) | −36.0000 | + | 41.5692i | −1.40343 | + | 1.62054i | ||||
\(659\) | 10.3923i | 0.404827i | 0.979300 | + | 0.202413i | \(0.0648785\pi\) | ||||
−0.979300 | + | 0.202413i | \(0.935122\pi\) | |||||||
\(660\) | 6.00000 | 0.233550 | ||||||||
\(661\) | 48.4974i | 1.88633i | 0.332323 | + | 0.943166i | \(0.392168\pi\) | ||||
−0.332323 | + | 0.943166i | \(0.607832\pi\) | |||||||
\(662\) | 48.4974i | 1.88491i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.00000 | − | 6.92820i | 0.232670 | − | 0.268664i | ||||
\(666\) | 10.3923i | 0.402694i | ||||||||
\(667\) | 24.0000 | 0.929284 | ||||||||
\(668\) | 12.0000 | 0.464294 | ||||||||
\(669\) | 30.0000 | 1.15987 | ||||||||
\(670\) | 13.8564i | 0.535320i | ||||||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | −18.0000 | − | 15.5885i | −0.694365 | − | 0.601338i | ||||
\(673\) | −14.0000 | −0.539660 | −0.269830 | − | 0.962908i | \(-0.586968\pi\) | ||||
−0.269830 | + | 0.962908i | \(0.586968\pi\) | |||||||
\(674\) | − | 24.2487i | − | 0.934025i | ||||||
\(675\) | 5.19615i | 0.200000i | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | 6.00000 | 0.230599 | 0.115299 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115299 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(678\) | − | 20.7846i | − | 0.798228i | ||||||
\(679\) | 12.0000 | − | 13.8564i | 0.460518 | − | 0.531760i | ||||
\(680\) | − | 10.3923i | − | 0.398527i | ||||||
\(681\) | − | 41.5692i | − | 1.59294i | ||||||
\(682\) | 20.7846i | 0.795884i | ||||||||
\(683\) | − | 17.3205i | − | 0.662751i | −0.943499 | − | 0.331375i | \(-0.892487\pi\) | ||
0.943499 | − | 0.331375i | \(-0.107513\pi\) | |||||||
\(684\) | − | 10.3923i | − | 0.397360i | ||||||
\(685\) | 20.7846i | 0.794139i | ||||||||
\(686\) | −27.0000 | − | 17.3205i | −1.03086 | − | 0.661300i | ||||
\(687\) | 12.0000 | 0.457829 | ||||||||
\(688\) | 40.0000 | 1.52499 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 10.3923i | 0.395628i | ||||||||
\(691\) | − | 31.1769i | − | 1.18603i | −0.805193 | − | 0.593013i | \(-0.797938\pi\) | ||
0.805193 | − | 0.593013i | \(-0.202062\pi\) | |||||||
\(692\) | 18.0000 | 0.684257 | ||||||||
\(693\) | −18.0000 | + | 20.7846i | −0.683763 | + | 0.789542i | ||||
\(694\) | 30.0000 | 1.13878 | ||||||||
\(695\) | − | 17.3205i | − | 0.657004i | ||||||
\(696\) | − | 20.7846i | − | 0.787839i | ||||||
\(697\) | 36.0000 | 1.36360 | ||||||||
\(698\) | 12.0000 | 0.454207 | ||||||||
\(699\) | 12.0000 | 0.453882 | ||||||||
\(700\) | −2.00000 | − | 1.73205i | −0.0755929 | − | 0.0654654i | ||||
\(701\) | − | 20.7846i | − | 0.785024i | −0.919747 | − | 0.392512i | \(-0.871606\pi\) | ||
0.919747 | − | 0.392512i | \(-0.128394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.92820i | 0.261302i | ||||||||
\(704\) | 3.46410i | 0.130558i | ||||||||
\(705\) | − | 20.7846i | − | 0.782794i | ||||||
\(706\) | − | 10.3923i | − | 0.391120i | ||||||
\(707\) | 12.0000 | + | 10.3923i | 0.451306 | + | 0.390843i | ||||
\(708\) | 20.7846i | 0.781133i | ||||||||
\(709\) | 22.0000 | 0.826227 | 0.413114 | − | 0.910679i | \(-0.364441\pi\) | ||||
0.413114 | + | 0.910679i | \(0.364441\pi\) | |||||||
\(710\) | −6.00000 | −0.225176 | ||||||||
\(711\) | −24.0000 | −0.900070 | ||||||||
\(712\) | − | 10.3923i | − | 0.389468i | ||||||
\(713\) | −12.0000 | −0.449404 | ||||||||
\(714\) | −36.0000 | − | 31.1769i | −1.34727 | − | 1.16677i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 10.3923i | − | 0.388379i | ||||||
\(717\) | −18.0000 | −0.672222 | ||||||||
\(718\) | −6.00000 | −0.223918 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 15.0000 | 0.559017 | ||||||||
\(721\) | −6.00000 | + | 6.92820i | −0.223452 | + | 0.258020i | ||||
\(722\) | 12.1244i | 0.451222i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 20.7846i | − | 0.772454i | ||||||
\(725\) | − | 6.92820i | − | 0.257307i | ||||||
\(726\) | −3.00000 | −0.111340 | ||||||||
\(727\) | 3.46410i | 0.128476i | 0.997935 | + | 0.0642382i | \(0.0204617\pi\) | ||||
−0.997935 | + | 0.0642382i | \(0.979538\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 12.0000 | 0.444140 | ||||||||
\(731\) | 48.0000 | 1.77534 | ||||||||
\(732\) | −12.0000 | −0.443533 | ||||||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | 18.0000 | 0.664392 | ||||||||
\(735\) | 12.0000 | − | 1.73205i | 0.442627 | − | 0.0638877i | ||||
\(736\) | 18.0000 | 0.663489 | ||||||||
\(737\) | − | 27.7128i | − | 1.02081i | ||||||
\(738\) | 31.1769i | 1.14764i | ||||||||
\(739\) | −4.00000 | −0.147142 | −0.0735712 | − | 0.997290i | \(-0.523440\pi\) | ||||
−0.0735712 | + | 0.997290i | \(0.523440\pi\) | |||||||
\(740\) | 2.00000 | 0.0735215 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.1769i | 1.14377i | 0.820334 | + | 0.571885i | \(0.193788\pi\) | ||||
−0.820334 | + | 0.571885i | \(0.806212\pi\) | |||||||
\(744\) | 10.3923i | 0.381000i | ||||||||
\(745\) | 6.92820i | 0.253830i | ||||||||
\(746\) | 24.2487i | 0.887808i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 20.7846i | − | 0.759961i | ||||||
\(749\) | −18.0000 | + | 20.7846i | −0.657706 | + | 0.759453i | ||||
\(750\) | 3.00000 | 0.109545 | ||||||||
\(751\) | 16.0000 | 0.583848 | 0.291924 | − | 0.956441i | \(-0.405705\pi\) | ||||
0.291924 | + | 0.956441i | \(0.405705\pi\) | |||||||
\(752\) | −60.0000 | −2.18797 | ||||||||
\(753\) | 20.7846i | 0.757433i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 9.00000 | − | 10.3923i | 0.327327 | − | 0.377964i | ||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | 6.92820i | 0.251644i | ||||||||
\(759\) | − | 20.7846i | − | 0.754434i | ||||||
\(760\) | 6.00000 | 0.217643 | ||||||||
\(761\) | 42.0000 | 1.52250 | 0.761249 | − | 0.648459i | \(-0.224586\pi\) | ||||
0.761249 | + | 0.648459i | \(0.224586\pi\) | |||||||
\(762\) | −12.0000 | −0.434714 | ||||||||
\(763\) | −4.00000 | − | 3.46410i | −0.144810 | − | 0.125409i | ||||
\(764\) | 10.3923i | 0.375980i | ||||||||
\(765\) | 18.0000 | 0.650791 | ||||||||
\(766\) | − | 20.7846i | − | 0.750978i | ||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | − | 32.9090i | − | 1.18750i | ||||||
\(769\) | 41.5692i | 1.49902i | 0.661991 | + | 0.749512i | \(0.269712\pi\) | ||||
−0.661991 | + | 0.749512i | \(0.730288\pi\) | |||||||
\(770\) | 12.0000 | + | 10.3923i | 0.432450 | + | 0.374513i | ||||
\(771\) | 10.3923i | 0.374270i | ||||||||
\(772\) | 14.0000 | 0.503871 | ||||||||
\(773\) | 6.00000 | 0.215805 | 0.107903 | − | 0.994161i | \(-0.465587\pi\) | ||||
0.107903 | + | 0.994161i | \(0.465587\pi\) | |||||||
\(774\) | 41.5692i | 1.49417i | ||||||||
\(775\) | 3.46410i | 0.124434i | ||||||||
\(776\) | 12.0000 | 0.430775 | ||||||||
\(777\) | −6.00000 | + | 6.92820i | −0.215249 | + | 0.248548i | ||||
\(778\) | −12.0000 | −0.430221 | ||||||||
\(779\) | 20.7846i | 0.744686i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.0000 | 0.429394 | ||||||||
\(782\) | 36.0000 | 1.28736 | ||||||||
\(783\) | 36.0000 | 1.28654 | ||||||||
\(784\) | −5.00000 | − | 34.6410i | −0.178571 | − | 1.23718i | ||||
\(785\) | − | 13.8564i | − | 0.494556i | ||||||
\(786\) | 36.0000 | 1.28408 | ||||||||
\(787\) | 24.2487i | 0.864373i | 0.901784 | + | 0.432187i | \(0.142258\pi\) | ||||
−0.901784 | + | 0.432187i | \(0.857742\pi\) | |||||||
\(788\) | 13.8564i | 0.493614i | ||||||||
\(789\) | −42.0000 | −1.49524 | ||||||||
\(790\) | 13.8564i | 0.492989i | ||||||||
\(791\) | 12.0000 | − | 13.8564i | 0.426671 | − | 0.492677i | ||||
\(792\) | −18.0000 | −0.639602 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 24.0000 | 0.851728 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.3923i | 0.368345i | ||||||||
\(797\) | −18.0000 | −0.637593 | −0.318796 | − | 0.947823i | \(-0.603279\pi\) | ||||
−0.318796 | + | 0.947823i | \(0.603279\pi\) | |||||||
\(798\) | 18.0000 | − | 20.7846i | 0.637193 | − | 0.735767i | ||||
\(799\) | −72.0000 | −2.54718 | ||||||||
\(800\) | − | 5.19615i | − | 0.183712i | ||||||
\(801\) | 18.0000 | 0.635999 | ||||||||
\(802\) | 48.0000 | 1.69494 | ||||||||
\(803\) | −24.0000 | −0.846942 | ||||||||
\(804\) | 13.8564i | 0.488678i | ||||||||
\(805\) | −6.00000 | + | 6.92820i | −0.211472 | + | 0.244187i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.1769i | 1.09748i | ||||||||
\(808\) | 10.3923i | 0.365600i | ||||||||
\(809\) | 55.4256i | 1.94866i | 0.225122 | + | 0.974331i | \(0.427722\pi\) | ||||
−0.225122 | + | 0.974331i | \(0.572278\pi\) | |||||||
\(810\) | 15.5885i | 0.547723i | ||||||||
\(811\) | 38.1051i | 1.33805i | 0.743239 | + | 0.669026i | \(0.233288\pi\) | ||||
−0.743239 | + | 0.669026i | \(0.766712\pi\) | |||||||
\(812\) | −12.0000 | + | 13.8564i | −0.421117 | + | 0.486265i | ||||
\(813\) | −42.0000 | −1.47300 | ||||||||
\(814\) | −12.0000 | −0.420600 | ||||||||
\(815\) | −16.0000 | −0.560456 | ||||||||
\(816\) | − | 51.9615i | − | 1.81902i | ||||||
\(817\) | 27.7128i | 0.969549i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | 20.7846i | 0.725388i | 0.931908 | + | 0.362694i | \(0.118143\pi\) | ||||
−0.931908 | + | 0.362694i | \(0.881857\pi\) | |||||||
\(822\) | 62.3538i | 2.17484i | ||||||||
\(823\) | 44.0000 | 1.53374 | 0.766872 | − | 0.641800i | \(-0.221812\pi\) | ||||
0.766872 | + | 0.641800i | \(0.221812\pi\) | |||||||
\(824\) | −6.00000 | −0.209020 | ||||||||
\(825\) | −6.00000 | −0.208893 | ||||||||
\(826\) | −36.0000 | + | 41.5692i | −1.25260 | + | 1.44638i | ||||
\(827\) | 38.1051i | 1.32504i | 0.749042 | + | 0.662522i | \(0.230514\pi\) | ||||
−0.749042 | + | 0.662522i | \(0.769486\pi\) | |||||||
\(828\) | 10.3923i | 0.361158i | ||||||||
\(829\) | − | 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 | ||||||||
\(833\) | −6.00000 | − | 41.5692i | −0.207888 | − | 1.44029i | ||||
\(834\) | − | 51.9615i | − | 1.79928i | ||||||
\(835\) | −12.0000 | −0.415277 | ||||||||
\(836\) | 12.0000 | 0.415029 | ||||||||
\(837\) | −18.0000 | −0.622171 | ||||||||
\(838\) | − | 20.7846i | − | 0.717992i | ||||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | 6.00000 | + | 5.19615i | 0.207020 | + | 0.179284i | ||||
\(841\) | −19.0000 | −0.655172 | ||||||||
\(842\) | − | 17.3205i | − | 0.596904i | ||||||
\(843\) | 24.0000 | 0.826604 | ||||||||
\(844\) | −4.00000 | −0.137686 | ||||||||
\(845\) | 13.0000 | 0.447214 | ||||||||
\(846\) | − | 62.3538i | − | 2.14377i | ||||||
\(847\) | −2.00000 | − | 1.73205i | −0.0687208 | − | 0.0595140i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30.0000 | −1.02960 | ||||||||
\(850\) | − | 10.3923i | − | 0.356453i | ||||||
\(851\) | − | 6.92820i | − | 0.237496i | ||||||
\(852\) | −6.00000 | −0.205557 | ||||||||
\(853\) | − | 41.5692i | − | 1.42330i | −0.702533 | − | 0.711651i | \(-0.747948\pi\) | ||
0.702533 | − | 0.711651i | \(-0.252052\pi\) | |||||||
\(854\) | −24.0000 | − | 20.7846i | −0.821263 | − | 0.711235i | ||||
\(855\) | 10.3923i | 0.355409i | ||||||||
\(856\) | −18.0000 | −0.615227 | ||||||||
\(857\) | −30.0000 | −1.02478 | −0.512390 | − | 0.858753i | \(-0.671240\pi\) | ||||
−0.512390 | + | 0.858753i | \(0.671240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.1051i | 1.30013i | 0.759879 | + | 0.650065i | \(0.225258\pi\) | ||||
−0.759879 | + | 0.650065i | \(0.774742\pi\) | |||||||
\(860\) | 8.00000 | 0.272798 | ||||||||
\(861\) | −18.0000 | + | 20.7846i | −0.613438 | + | 0.708338i | ||||
\(862\) | 18.0000 | 0.613082 | ||||||||
\(863\) | 17.3205i | 0.589597i | 0.955559 | + | 0.294798i | \(0.0952525\pi\) | ||||
−0.955559 | + | 0.294798i | \(0.904747\pi\) | |||||||
\(864\) | 27.0000 | 0.918559 | ||||||||
\(865\) | −18.0000 | −0.612018 | ||||||||
\(866\) | −12.0000 | −0.407777 | ||||||||
\(867\) | − | 32.9090i | − | 1.11765i | ||||||
\(868\) | 6.00000 | − | 6.92820i | 0.203653 | − | 0.235159i | ||||
\(869\) | − | 27.7128i | − | 0.940093i | ||||||
\(870\) | − | 20.7846i | − | 0.704664i | ||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 3.46410i | − | 0.117309i | ||||||
\(873\) | 20.7846i | 0.703452i | ||||||||
\(874\) | 20.7846i | 0.703050i | ||||||||
\(875\) | 2.00000 | + | 1.73205i | 0.0676123 | + | 0.0585540i | ||||
\(876\) | 12.0000 | 0.405442 | ||||||||
\(877\) | 38.0000 | 1.28317 | 0.641584 | − | 0.767052i | \(-0.278277\pi\) | ||||
0.641584 | + | 0.767052i | \(0.278277\pi\) | |||||||
\(878\) | −30.0000 | −1.01245 | ||||||||
\(879\) | − | 10.3923i | − | 0.350524i | ||||||
\(880\) | 17.3205i | 0.583874i | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 36.0000 | − | 5.19615i | 1.21218 | − | 0.174964i | ||||
\(883\) | 16.0000 | 0.538443 | 0.269221 | − | 0.963078i | \(-0.413234\pi\) | ||||
0.269221 | + | 0.963078i | \(0.413234\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 20.7846i | − | 0.698667i | ||||||
\(886\) | −18.0000 | −0.604722 | ||||||||
\(887\) | 36.0000 | 1.20876 | 0.604381 | − | 0.796696i | \(-0.293421\pi\) | ||||
0.604381 | + | 0.796696i | \(0.293421\pi\) | |||||||
\(888\) | −6.00000 | −0.201347 | ||||||||
\(889\) | −8.00000 | − | 6.92820i | −0.268311 | − | 0.232364i | ||||
\(890\) | − | 10.3923i | − | 0.348351i | ||||||
\(891\) | − | 31.1769i | − | 1.04447i | ||||||
\(892\) | − | 17.3205i | − | 0.579934i | ||||||
\(893\) | − | 41.5692i | − | 1.39106i | ||||||
\(894\) | 20.7846i | 0.695141i | ||||||||
\(895\) | 10.3923i | 0.347376i | ||||||||
\(896\) | 21.0000 | − | 24.2487i | 0.701561 | − | 0.810093i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.0000 | 0.800890 | ||||||||
\(899\) | 24.0000 | 0.800445 | ||||||||
\(900\) | 3.00000 | 0.100000 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −36.0000 | −1.19867 | ||||||||
\(903\) | −24.0000 | + | 27.7128i | −0.798670 | + | 0.922225i | ||||
\(904\) | 12.0000 | 0.399114 | ||||||||
\(905\) | 20.7846i | 0.690904i | ||||||||
\(906\) | −24.0000 | −0.797347 | ||||||||
\(907\) | −32.0000 | −1.06254 | −0.531271 | − | 0.847202i | \(-0.678286\pi\) | ||||
−0.531271 | + | 0.847202i | \(0.678286\pi\) | |||||||
\(908\) | −24.0000 | −0.796468 | ||||||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.3205i | 0.573854i | 0.957952 | + | 0.286927i | \(0.0926337\pi\) | ||||
−0.957952 | + | 0.286927i | \(0.907366\pi\) | |||||||
\(912\) | 30.0000 | 0.993399 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 65.8179i | − | 2.17706i | ||||||
\(915\) | 12.0000 | 0.396708 | ||||||||
\(916\) | − | 6.92820i | − | 0.228914i | ||||||
\(917\) | 24.0000 | + | 20.7846i | 0.792550 | + | 0.686368i | ||||
\(918\) | 54.0000 | 1.78227 | ||||||||
\(919\) | 16.0000 | 0.527791 | 0.263896 | − | 0.964551i | \(-0.414993\pi\) | ||||
0.263896 | + | 0.964551i | \(0.414993\pi\) | |||||||
\(920\) | −6.00000 | −0.197814 | ||||||||
\(921\) | 42.0000 | 1.38395 | ||||||||
\(922\) | − | 31.1769i | − | 1.02676i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 12.0000 | + | 10.3923i | 0.394771 | + | 0.341882i | ||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | 34.6410i | 1.13837i | ||||||||
\(927\) | − | 10.3923i | − | 0.341328i | ||||||
\(928\) | −36.0000 | −1.18176 | ||||||||
\(929\) | −30.0000 | −0.984268 | −0.492134 | − | 0.870519i | \(-0.663783\pi\) | ||||
−0.492134 | + | 0.870519i | \(0.663783\pi\) | |||||||
\(930\) | 10.3923i | 0.340777i | ||||||||
\(931\) | 24.0000 | − | 3.46410i | 0.786568 | − | 0.113531i | ||||
\(932\) | − | 6.92820i | − | 0.226941i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 41.5692i | − | 1.36019i | ||||||
\(935\) | 20.7846i | 0.679729i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.92820i | 0.226335i | 0.993576 | + | 0.113167i | \(0.0360996\pi\) | ||||
−0.993576 | + | 0.113167i | \(0.963900\pi\) | |||||||
\(938\) | −24.0000 | + | 27.7128i | −0.783628 | + | 0.904855i | ||||
\(939\) | 36.0000 | 1.17482 | ||||||||
\(940\) | −12.0000 | −0.391397 | ||||||||
\(941\) | −18.0000 | −0.586783 | −0.293392 | − | 0.955992i | \(-0.594784\pi\) | ||||
−0.293392 | + | 0.955992i | \(0.594784\pi\) | |||||||
\(942\) | − | 41.5692i | − | 1.35440i | ||||||
\(943\) | − | 20.7846i | − | 0.676840i | ||||||
\(944\) | −60.0000 | −1.95283 | ||||||||
\(945\) | −9.00000 | + | 10.3923i | −0.292770 | + | 0.338062i | ||||
\(946\) | −48.0000 | −1.56061 | ||||||||
\(947\) | − | 31.1769i | − | 1.01311i | −0.862207 | − | 0.506557i | \(-0.830918\pi\) | ||
0.862207 | − | 0.506557i | \(-0.169082\pi\) | |||||||
\(948\) | 13.8564i | 0.450035i | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 6.00000 | 0.194666 | ||||||||
\(951\) | 48.0000 | 1.55651 | ||||||||
\(952\) | 18.0000 | − | 20.7846i | 0.583383 | − | 0.673633i | ||||
\(953\) | 34.6410i | 1.12213i | 0.827771 | + | 0.561066i | \(0.189609\pi\) | ||||
−0.827771 | + | 0.561066i | \(0.810391\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 10.3923i | − | 0.336287i | ||||||
\(956\) | 10.3923i | 0.336111i | ||||||||
\(957\) | 41.5692i | 1.34374i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36.0000 | + | 41.5692i | −1.16250 | + | 1.34234i | ||||
\(960\) | 1.73205i | 0.0559017i | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 31.1769i | − | 1.00466i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.0000 | −0.450676 | ||||||||
\(966\) | −18.0000 | + | 20.7846i | −0.579141 | + | 0.668734i | ||||
\(967\) | 20.0000 | 0.643157 | 0.321578 | − | 0.946883i | \(-0.395787\pi\) | ||||
0.321578 | + | 0.946883i | \(0.395787\pi\) | |||||||
\(968\) | − | 1.73205i | − | 0.0556702i | ||||||
\(969\) | 36.0000 | 1.15649 | ||||||||
\(970\) | 12.0000 | 0.385297 | ||||||||
\(971\) | −60.0000 | −1.92549 | −0.962746 | − | 0.270408i | \(-0.912841\pi\) | ||||
−0.962746 | + | 0.270408i | \(0.912841\pi\) | |||||||
\(972\) | 15.5885i | 0.500000i | ||||||||
\(973\) | 30.0000 | − | 34.6410i | 0.961756 | − | 1.11054i | ||||
\(974\) | 6.92820i | 0.221994i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 34.6410i | − | 1.10883i | ||||||
\(977\) | 6.92820i | 0.221653i | 0.993840 | + | 0.110826i | \(0.0353498\pi\) | ||||
−0.993840 | + | 0.110826i | \(0.964650\pi\) | |||||||
\(978\) | −48.0000 | −1.53487 | ||||||||
\(979\) | 20.7846i | 0.664279i | ||||||||
\(980\) | −1.00000 | − | 6.92820i | −0.0319438 | − | 0.221313i | ||||
\(981\) | 6.00000 | 0.191565 | ||||||||
\(982\) | −42.0000 | −1.34027 | ||||||||
\(983\) | 60.0000 | 1.91370 | 0.956851 | − | 0.290578i | \(-0.0938475\pi\) | ||||
0.956851 | + | 0.290578i | \(0.0938475\pi\) | |||||||
\(984\) | −18.0000 | −0.573819 | ||||||||
\(985\) | − | 13.8564i | − | 0.441502i | ||||||
\(986\) | −72.0000 | −2.29295 | ||||||||
\(987\) | 36.0000 | − | 41.5692i | 1.14589 | − | 1.32316i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 27.7128i | − | 0.881216i | ||||||
\(990\) | −18.0000 | −0.572078 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 18.0000 | 0.571501 | ||||||||
\(993\) | − | 48.4974i | − | 1.53902i | ||||||
\(994\) | −12.0000 | − | 10.3923i | −0.380617 | − | 0.329624i | ||||
\(995\) | − | 10.3923i | − | 0.329458i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | − | 34.6410i | − | 1.09654i | ||||||
\(999\) | − | 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 | 105.2.b.b.41.2 | yes | 2 | |
3.2 | odd | 2 | 105.2.b.a.41.1 | ✓ | 2 | ||
4.3 | odd | 2 | 1680.2.f.c.881.2 | 2 | |||
5.2 | odd | 4 | 525.2.g.c.524.2 | 4 | |||
5.3 | odd | 4 | 525.2.g.c.524.3 | 4 | |||
5.4 | even | 2 | 525.2.b.b.251.1 | 2 | |||
7.2 | even | 3 | 735.2.s.f.521.1 | 2 | |||
7.3 | odd | 6 | 735.2.s.b.656.1 | 2 | |||
7.4 | even | 3 | 735.2.s.a.656.1 | 2 | |||
7.5 | odd | 6 | 735.2.s.d.521.1 | 2 | |||
7.6 | odd | 2 | 105.2.b.a.41.2 | yes | 2 | ||
12.11 | even | 2 | 1680.2.f.b.881.2 | 2 | |||
15.2 | even | 4 | 525.2.g.b.524.4 | 4 | |||
15.8 | even | 4 | 525.2.g.b.524.1 | 4 | |||
15.14 | odd | 2 | 525.2.b.a.251.2 | 2 | |||
21.2 | odd | 6 | 735.2.s.b.521.1 | 2 | |||
21.5 | even | 6 | 735.2.s.a.521.1 | 2 | |||
21.11 | odd | 6 | 735.2.s.d.656.1 | 2 | |||
21.17 | even | 6 | 735.2.s.f.656.1 | 2 | |||
21.20 | even | 2 | inner | 105.2.b.b.41.1 | yes | 2 | |
28.27 | even | 2 | 1680.2.f.b.881.1 | 2 | |||
35.13 | even | 4 | 525.2.g.b.524.3 | 4 | |||
35.27 | even | 4 | 525.2.g.b.524.2 | 4 | |||
35.34 | odd | 2 | 525.2.b.a.251.1 | 2 | |||
84.83 | odd | 2 | 1680.2.f.c.881.1 | 2 | |||
105.62 | odd | 4 | 525.2.g.c.524.4 | 4 | |||
105.83 | odd | 4 | 525.2.g.c.524.1 | 4 | |||
105.104 | even | 2 | 525.2.b.b.251.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.b.a.41.1 | ✓ | 2 | 3.2 | odd | 2 | ||
105.2.b.a.41.2 | yes | 2 | 7.6 | odd | 2 | ||
105.2.b.b.41.1 | yes | 2 | 21.20 | even | 2 | inner | |
105.2.b.b.41.2 | yes | 2 | 1.1 | even | 1 | trivial | |
525.2.b.a.251.1 | 2 | 35.34 | odd | 2 | |||
525.2.b.a.251.2 | 2 | 15.14 | odd | 2 | |||
525.2.b.b.251.1 | 2 | 5.4 | even | 2 | |||
525.2.b.b.251.2 | 2 | 105.104 | even | 2 | |||
525.2.g.b.524.1 | 4 | 15.8 | even | 4 | |||
525.2.g.b.524.2 | 4 | 35.27 | even | 4 | |||
525.2.g.b.524.3 | 4 | 35.13 | even | 4 | |||
525.2.g.b.524.4 | 4 | 15.2 | even | 4 | |||
525.2.g.c.524.1 | 4 | 105.83 | odd | 4 | |||
525.2.g.c.524.2 | 4 | 5.2 | odd | 4 | |||
525.2.g.c.524.3 | 4 | 5.3 | odd | 4 | |||
525.2.g.c.524.4 | 4 | 105.62 | odd | 4 | |||
735.2.s.a.521.1 | 2 | 21.5 | even | 6 | |||
735.2.s.a.656.1 | 2 | 7.4 | even | 3 | |||
735.2.s.b.521.1 | 2 | 21.2 | odd | 6 | |||
735.2.s.b.656.1 | 2 | 7.3 | odd | 6 | |||
735.2.s.d.521.1 | 2 | 7.5 | odd | 6 | |||
735.2.s.d.656.1 | 2 | 21.11 | odd | 6 | |||
735.2.s.f.521.1 | 2 | 7.2 | even | 3 | |||
735.2.s.f.656.1 | 2 | 21.17 | even | 6 | |||
1680.2.f.b.881.1 | 2 | 28.27 | even | 2 | |||
1680.2.f.b.881.2 | 2 | 12.11 | even | 2 | |||
1680.2.f.c.881.1 | 2 | 84.83 | odd | 2 | |||
1680.2.f.c.881.2 | 2 | 4.3 | odd | 2 |