Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(7,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("300.7");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.j (of order \(4\), degree \(2\), 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: | \(2.39551206064\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.157351936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.3 | ||
Root | \(0.581861 + 1.28897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.7 |
Dual form | 300.2.j.b.43.3 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.581861 | + | 1.28897i | 0.411438 | + | 0.911438i | ||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | −1.32288 | + | 1.50000i | −0.661438 | + | 0.750000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.500000 | − | 1.32288i | 0.204124 | − | 0.540062i | ||||
\(7\) | −1.41421 | + | 1.41421i | −0.534522 | + | 0.534522i | −0.921915 | − | 0.387392i | \(-0.873376\pi\) |
0.387392 | + | 0.921915i | \(0.373376\pi\) | |||||||
\(8\) | −2.70318 | − | 0.832353i | −0.955719 | − | 0.294281i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.29150i | 1.59545i | 0.603023 | + | 0.797724i | \(0.293963\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 1.99607 | − | 0.125246i | 0.576217 | − | 0.0361554i | ||||
\(13\) | −3.74166 | + | 3.74166i | −1.03775 | + | 1.03775i | −0.0384901 | + | 0.999259i | \(0.512255\pi\) |
−0.999259 | + | 0.0384901i | \(0.987745\pi\) | |||||||
\(14\) | −2.64575 | − | 1.00000i | −0.707107 | − | 0.267261i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 3.96863i | −0.125000 | − | 0.992157i | ||||
\(17\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(18\) | −1.28897 | + | 0.581861i | −0.303813 | + | 0.137146i | ||||
\(19\) | 5.29150 | 1.21395 | 0.606977 | − | 0.794719i | \(-0.292382\pi\) | ||||
0.606977 | + | 0.794719i | \(0.292382\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | −6.82058 | + | 3.07892i | −1.45415 | + | 0.656428i | ||||
\(23\) | −2.82843 | − | 2.82843i | −0.589768 | − | 0.589768i | 0.347801 | − | 0.937568i | \(-0.386929\pi\) |
−0.937568 | + | 0.347801i | \(0.886929\pi\) | |||||||
\(24\) | 1.32288 | + | 2.50000i | 0.270031 | + | 0.510310i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.00000 | − | 2.64575i | −1.37281 | − | 0.518875i | ||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | −0.250492 | − | 3.99215i | −0.0473385 | − | 0.754445i | ||||
\(29\) | − | 8.00000i | − | 1.48556i | −0.669534 | − | 0.742781i | \(-0.733506\pi\) | ||
0.669534 | − | 0.742781i | \(-0.266494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.29150i | 0.950382i | 0.879883 | + | 0.475191i | \(0.157621\pi\) | ||||
−0.879883 | + | 0.475191i | \(0.842379\pi\) | |||||||
\(32\) | 4.82450 | − | 2.95367i | 0.852859 | − | 0.522141i | ||||
\(33\) | 3.74166 | − | 3.74166i | 0.651339 | − | 0.651339i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.50000 | − | 1.32288i | −0.250000 | − | 0.220479i | ||||
\(37\) | 3.74166 | + | 3.74166i | 0.615125 | + | 0.615125i | 0.944277 | − | 0.329152i | \(-0.106763\pi\) |
−0.329152 | + | 0.944277i | \(0.606763\pi\) | |||||||
\(38\) | 3.07892 | + | 6.82058i | 0.499467 | + | 1.10644i | ||||
\(39\) | 5.29150 | 0.847319 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 1.16372 | + | 2.57794i | 0.179566 | + | 0.397784i | ||||
\(43\) | 5.65685 | + | 5.65685i | 0.862662 | + | 0.862662i | 0.991647 | − | 0.128984i | \(-0.0411717\pi\) |
−0.128984 | + | 0.991647i | \(0.541172\pi\) | |||||||
\(44\) | −7.93725 | − | 7.00000i | −1.19659 | − | 1.05529i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | − | 5.29150i | 0.294884 | − | 0.780189i | ||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | −2.45269 | + | 3.15980i | −0.354015 | + | 0.456077i | ||||
\(49\) | 3.00000i | 0.428571i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.662739 | − | 10.5622i | −0.0919053 | − | 1.46472i | ||||
\(53\) | 7.48331 | − | 7.48331i | 1.02791 | − | 1.02791i | 0.0283132 | − | 0.999599i | \(-0.490986\pi\) |
0.999599 | − | 0.0283132i | \(-0.00901359\pi\) | |||||||
\(54\) | 1.32288 | + | 0.500000i | 0.180021 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.00000 | − | 2.64575i | 0.668153 | − | 0.353553i | ||||
\(57\) | −3.74166 | − | 3.74166i | −0.495595 | − | 0.495595i | ||||
\(58\) | 10.3117 | − | 4.65489i | 1.35400 | − | 0.611217i | ||||
\(59\) | −5.29150 | −0.688895 | −0.344447 | − | 0.938806i | \(-0.611934\pi\) | ||||
−0.344447 | + | 0.938806i | \(0.611934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | −6.82058 | + | 3.07892i | −0.866214 | + | 0.391023i | ||||
\(63\) | −1.41421 | − | 1.41421i | −0.178174 | − | 0.178174i | ||||
\(64\) | 6.61438 | + | 4.50000i | 0.826797 | + | 0.562500i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.00000 | + | 2.64575i | 0.861640 | + | 0.325669i | ||||
\(67\) | 8.48528 | − | 8.48528i | 1.03664 | − | 1.03664i | 0.0373395 | − | 0.999303i | \(-0.488112\pi\) |
0.999303 | − | 0.0373395i | \(-0.0118883\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000i | 0.481543i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0.832353 | − | 2.70318i | 0.0980937 | − | 0.318573i | ||||
\(73\) | −7.48331 | + | 7.48331i | −0.875856 | + | 0.875856i | −0.993103 | − | 0.117247i | \(-0.962593\pi\) |
0.117247 | + | 0.993103i | \(0.462593\pi\) | |||||||
\(74\) | −2.64575 | + | 7.00000i | −0.307562 | + | 0.813733i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.00000 | + | 7.93725i | −0.802955 | + | 0.910465i | ||||
\(77\) | −7.48331 | − | 7.48331i | −0.852803 | − | 0.852803i | ||||
\(78\) | 3.07892 | + | 6.82058i | 0.348619 | + | 0.772278i | ||||
\(79\) | −5.29150 | −0.595341 | −0.297670 | − | 0.954669i | \(-0.596210\pi\) | ||||
−0.297670 | + | 0.954669i | \(0.596210\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −1.16372 | − | 2.57794i | −0.128512 | − | 0.284685i | ||||
\(83\) | 8.48528 | + | 8.48528i | 0.931381 | + | 0.931381i | 0.997792 | − | 0.0664117i | \(-0.0211551\pi\) |
−0.0664117 | + | 0.997792i | \(0.521155\pi\) | |||||||
\(84\) | −2.64575 | + | 3.00000i | −0.288675 | + | 0.327327i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | + | 10.5830i | −0.431331 | + | 1.14119i | ||||
\(87\) | −5.65685 | + | 5.65685i | −0.606478 | + | 0.606478i | ||||
\(88\) | 4.40440 | − | 14.3039i | 0.469510 | − | 1.52480i | ||||
\(89\) | 6.00000i | 0.635999i | 0.948091 | + | 0.317999i | \(0.103011\pi\) | ||||
−0.948091 | + | 0.317999i | \(0.896989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 10.5830i | − | 1.10940i | ||||||
\(92\) | 7.98430 | − | 0.500983i | 0.832421 | − | 0.0522311i | ||||
\(93\) | 3.74166 | − | 3.74166i | 0.387992 | − | 0.387992i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.50000 | − | 1.32288i | −0.561341 | − | 0.135015i | ||||
\(97\) | 7.48331 | + | 7.48331i | 0.759815 | + | 0.759815i | 0.976289 | − | 0.216473i | \(-0.0694554\pi\) |
−0.216473 | + | 0.976289i | \(0.569455\pi\) | |||||||
\(98\) | −3.86690 | + | 1.74558i | −0.390616 | + | 0.176330i | ||||
\(99\) | −5.29150 | −0.531816 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.00000 | −0.398015 | −0.199007 | − | 0.979998i | \(-0.563772\pi\) | ||||
−0.199007 | + | 0.979998i | \(0.563772\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.24264 | − | 4.24264i | −0.418040 | − | 0.418040i | 0.466488 | − | 0.884528i | \(-0.345519\pi\) |
−0.884528 | + | 0.466488i | \(0.845519\pi\) | |||||||
\(104\) | 13.2288 | − | 7.00000i | 1.29719 | − | 0.686406i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.0000 | + | 5.29150i | 1.35980 | + | 0.513956i | ||||
\(107\) | −2.82843 | + | 2.82843i | −0.273434 | + | 0.273434i | −0.830481 | − | 0.557047i | \(-0.811934\pi\) |
0.557047 | + | 0.830481i | \(0.311934\pi\) | |||||||
\(108\) | 0.125246 | + | 1.99607i | 0.0120518 | + | 0.192072i | ||||
\(109\) | 2.00000i | 0.191565i | 0.995402 | + | 0.0957826i | \(0.0305354\pi\) | ||||
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 5.29150i | − | 0.502247i | ||||||
\(112\) | 6.31959 | + | 4.90538i | 0.597145 | + | 0.463515i | ||||
\(113\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(114\) | 2.64575 | − | 7.00000i | 0.247797 | − | 0.655610i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 12.0000 | + | 10.5830i | 1.11417 | + | 0.982607i | ||||
\(117\) | −3.74166 | − | 3.74166i | −0.345916 | − | 0.345916i | ||||
\(118\) | −3.07892 | − | 6.82058i | −0.283437 | − | 0.627885i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.0000 | −1.54545 | ||||||||
\(122\) | 3.49117 | + | 7.73381i | 0.316075 | + | 0.700186i | ||||
\(123\) | 1.41421 | + | 1.41421i | 0.127515 | + | 0.127515i | ||||
\(124\) | −7.93725 | − | 7.00000i | −0.712786 | − | 0.628619i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.00000 | − | 2.64575i | 0.0890871 | − | 0.235702i | ||||
\(127\) | −1.41421 | + | 1.41421i | −0.125491 | + | 0.125491i | −0.767063 | − | 0.641572i | \(-0.778283\pi\) |
0.641572 | + | 0.767063i | \(0.278283\pi\) | |||||||
\(128\) | −1.95171 | + | 11.1441i | −0.172508 | + | 0.985008i | ||||
\(129\) | − | 8.00000i | − | 0.704361i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 15.8745i | − | 1.38696i | −0.720475 | − | 0.693481i | \(-0.756076\pi\) | ||
0.720475 | − | 0.693481i | \(-0.243924\pi\) | |||||||
\(132\) | 0.662739 | + | 10.5622i | 0.0576840 | + | 0.919324i | ||||
\(133\) | −7.48331 | + | 7.48331i | −0.648886 | + | 0.648886i | ||||
\(134\) | 15.8745 | + | 6.00000i | 1.37135 | + | 0.518321i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(138\) | −5.15587 | + | 2.32744i | −0.438897 | + | 0.198125i | ||||
\(139\) | −5.29150 | −0.448819 | −0.224410 | − | 0.974495i | \(-0.572045\pi\) | ||||
−0.224410 | + | 0.974495i | \(0.572045\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.7990 | − | 19.7990i | −1.65567 | − | 1.65567i | ||||
\(144\) | 3.96863 | − | 0.500000i | 0.330719 | − | 0.0416667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.0000 | − | 5.29150i | −1.15865 | − | 0.437928i | ||||
\(147\) | 2.12132 | − | 2.12132i | 0.174964 | − | 0.174964i | ||||
\(148\) | −10.5622 | + | 0.662739i | −0.868210 | + | 0.0544768i | ||||
\(149\) | 4.00000i | 0.327693i | 0.986486 | + | 0.163846i | \(0.0523901\pi\) | ||||
−0.986486 | + | 0.163846i | \(0.947610\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15.8745i | − | 1.29185i | −0.763401 | − | 0.645925i | \(-0.776472\pi\) | ||
0.763401 | − | 0.645925i | \(-0.223528\pi\) | |||||||
\(152\) | −14.3039 | − | 4.40440i | −1.16020 | − | 0.357244i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.29150 | − | 14.0000i | 0.426401 | − | 1.12815i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.00000 | + | 7.93725i | −0.560449 | + | 0.635489i | ||||
\(157\) | 3.74166 | + | 3.74166i | 0.298617 | + | 0.298617i | 0.840472 | − | 0.541855i | \(-0.182278\pi\) |
−0.541855 | + | 0.840472i | \(0.682278\pi\) | |||||||
\(158\) | −3.07892 | − | 6.82058i | −0.244946 | − | 0.542616i | ||||
\(159\) | −10.5830 | −0.839287 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.00000 | 0.630488 | ||||||||
\(162\) | −0.581861 | − | 1.28897i | −0.0457153 | − | 0.101271i | ||||
\(163\) | 5.65685 | + | 5.65685i | 0.443079 | + | 0.443079i | 0.893045 | − | 0.449966i | \(-0.148564\pi\) |
−0.449966 | + | 0.893045i | \(0.648564\pi\) | |||||||
\(164\) | 2.64575 | − | 3.00000i | 0.206598 | − | 0.234261i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | + | 15.8745i | −0.465690 | + | 1.23210i | ||||
\(167\) | −8.48528 | + | 8.48528i | −0.656611 | + | 0.656611i | −0.954577 | − | 0.297966i | \(-0.903692\pi\) |
0.297966 | + | 0.954577i | \(0.403692\pi\) | |||||||
\(168\) | −5.40636 | − | 1.66471i | −0.417110 | − | 0.128435i | ||||
\(169\) | − | 15.0000i | − | 1.15385i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.29150i | 0.404651i | ||||||||
\(172\) | −15.9686 | + | 1.00197i | −1.21759 | + | 0.0763992i | ||||
\(173\) | −7.48331 | + | 7.48331i | −0.568946 | + | 0.568946i | −0.931833 | − | 0.362887i | \(-0.881791\pi\) |
0.362887 | + | 0.931833i | \(0.381791\pi\) | |||||||
\(174\) | −10.5830 | − | 4.00000i | −0.802296 | − | 0.303239i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 21.0000 | − | 2.64575i | 1.58293 | − | 0.199431i | ||||
\(177\) | 3.74166 | + | 3.74166i | 0.281240 | + | 0.281240i | ||||
\(178\) | −7.73381 | + | 3.49117i | −0.579673 | + | 0.261674i | ||||
\(179\) | 5.29150 | 0.395505 | 0.197753 | − | 0.980252i | \(-0.436636\pi\) | ||||
0.197753 | + | 0.980252i | \(0.436636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 13.6412 | − | 6.15784i | 1.01115 | − | 0.456449i | ||||
\(183\) | −4.24264 | − | 4.24264i | −0.313625 | − | 0.313625i | ||||
\(184\) | 5.29150 | + | 10.0000i | 0.390095 | + | 0.737210i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.00000 | + | 2.64575i | 0.513265 | + | 0.193996i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.00000i | 0.145479i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.5830i | − | 0.765759i | −0.923798 | − | 0.382880i | \(-0.874932\pi\) | ||
0.923798 | − | 0.382880i | \(-0.125068\pi\) | |||||||
\(192\) | −1.49509 | − | 7.85905i | −0.107899 | − | 0.567178i | ||||
\(193\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(194\) | −5.29150 | + | 14.0000i | −0.379908 | + | 1.00514i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.50000 | − | 3.96863i | −0.321429 | − | 0.283473i | ||||
\(197\) | 14.9666 | + | 14.9666i | 1.06633 | + | 1.06633i | 0.997638 | + | 0.0686902i | \(0.0218820\pi\) |
0.0686902 | + | 0.997638i | \(0.478118\pi\) | |||||||
\(198\) | −3.07892 | − | 6.82058i | −0.218809 | − | 0.484717i | ||||
\(199\) | −5.29150 | −0.375105 | −0.187552 | − | 0.982255i | \(-0.560055\pi\) | ||||
−0.187552 | + | 0.982255i | \(0.560055\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.0000 | −0.846415 | ||||||||
\(202\) | −2.32744 | − | 5.15587i | −0.163758 | − | 0.362766i | ||||
\(203\) | 11.3137 | + | 11.3137i | 0.794067 | + | 0.794067i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.00000 | − | 7.93725i | 0.209020 | − | 0.553015i | ||||
\(207\) | 2.82843 | − | 2.82843i | 0.196589 | − | 0.196589i | ||||
\(208\) | 16.7201 | + | 12.9784i | 1.15933 | + | 0.899891i | ||||
\(209\) | 28.0000i | 1.93680i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.4575i | 1.82141i | 0.413057 | + | 0.910705i | \(0.364461\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 1.32548 | + | 21.1245i | 0.0910341 | + | 1.45083i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.29150 | − | 2.00000i | −0.361720 | − | 0.136717i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.50000 | + | 1.32288i | −0.170103 | + | 0.0900103i | ||||
\(217\) | −7.48331 | − | 7.48331i | −0.508001 | − | 0.508001i | ||||
\(218\) | −2.57794 | + | 1.16372i | −0.174600 | + | 0.0788172i | ||||
\(219\) | 10.5830 | 0.715133 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 6.82058 | − | 3.07892i | 0.457767 | − | 0.206643i | ||||
\(223\) | −9.89949 | − | 9.89949i | −0.662919 | − | 0.662919i | 0.293148 | − | 0.956067i | \(-0.405297\pi\) |
−0.956067 | + | 0.293148i | \(0.905297\pi\) | |||||||
\(224\) | −2.64575 | + | 11.0000i | −0.176777 | + | 0.734968i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.7990 | − | 19.7990i | 1.31411 | − | 1.31411i | 0.395744 | − | 0.918361i | \(-0.370487\pi\) |
0.918361 | − | 0.395744i | \(-0.129513\pi\) | |||||||
\(228\) | 10.5622 | − | 0.662739i | 0.699501 | − | 0.0438909i | ||||
\(229\) | 14.0000i | 0.925146i | 0.886581 | + | 0.462573i | \(0.153074\pi\) | ||||
−0.886581 | + | 0.462573i | \(0.846926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.5830i | 0.696311i | ||||||||
\(232\) | −6.65882 | + | 21.6255i | −0.437173 | + | 1.41978i | ||||
\(233\) | 14.9666 | − | 14.9666i | 0.980497 | − | 0.980497i | −0.0193169 | − | 0.999813i | \(-0.506149\pi\) |
0.999813 | + | 0.0193169i | \(0.00614915\pi\) | |||||||
\(234\) | 2.64575 | − | 7.00000i | 0.172958 | − | 0.457604i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.00000 | − | 7.93725i | 0.455661 | − | 0.516671i | ||||
\(237\) | 3.74166 | + | 3.74166i | 0.243047 | + | 0.243047i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.5830 | 0.684558 | 0.342279 | − | 0.939598i | \(-0.388801\pi\) | ||||
0.342279 | + | 0.939598i | \(0.388801\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | −9.89164 | − | 21.9125i | −0.635858 | − | 1.40859i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | −7.93725 | + | 9.00000i | −0.508131 | + | 0.576166i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.00000 | + | 2.64575i | −0.0637577 | + | 0.168687i | ||||
\(247\) | −19.7990 | + | 19.7990i | −1.25978 | + | 1.25978i | ||||
\(248\) | 4.40440 | − | 14.3039i | 0.279679 | − | 0.908298i | ||||
\(249\) | − | 12.0000i | − | 0.760469i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.29150i | 0.333997i | 0.985957 | + | 0.166998i | \(0.0534075\pi\) | ||||
−0.985957 | + | 0.166998i | \(0.946593\pi\) | |||||||
\(252\) | 3.99215 | − | 0.250492i | 0.251482 | − | 0.0157795i | ||||
\(253\) | 14.9666 | − | 14.9666i | 0.940944 | − | 0.940944i | ||||
\(254\) | −2.64575 | − | 1.00000i | −0.166009 | − | 0.0627456i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.5000 | + | 3.96863i | −0.968750 | + | 0.248039i | ||||
\(257\) | −14.9666 | − | 14.9666i | −0.933593 | − | 0.933593i | 0.0643356 | − | 0.997928i | \(-0.479507\pi\) |
−0.997928 | + | 0.0643356i | \(0.979507\pi\) | |||||||
\(258\) | 10.3117 | − | 4.65489i | 0.641981 | − | 0.289801i | ||||
\(259\) | −10.5830 | −0.657596 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | 0.495188 | ||||||||
\(262\) | 20.4617 | − | 9.23676i | 1.26413 | − | 0.570649i | ||||
\(263\) | 8.48528 | + | 8.48528i | 0.523225 | + | 0.523225i | 0.918544 | − | 0.395319i | \(-0.129366\pi\) |
−0.395319 | + | 0.918544i | \(0.629366\pi\) | |||||||
\(264\) | −13.2288 | + | 7.00000i | −0.814174 | + | 0.430820i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −14.0000 | − | 5.29150i | −0.858395 | − | 0.324443i | ||||
\(267\) | 4.24264 | − | 4.24264i | 0.259645 | − | 0.259645i | ||||
\(268\) | 1.50295 | + | 23.9529i | 0.0918073 | + | 1.46316i | ||||
\(269\) | − | 24.0000i | − | 1.46331i | −0.681677 | − | 0.731653i | \(-0.738749\pi\) | ||
0.681677 | − | 0.731653i | \(-0.261251\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.8745i | 0.964308i | 0.876087 | + | 0.482154i | \(0.160145\pi\) | ||||
−0.876087 | + | 0.482154i | \(0.839855\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.48331 | + | 7.48331i | −0.452911 | + | 0.452911i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.00000 | − | 5.29150i | −0.361158 | − | 0.318511i | ||||
\(277\) | −18.7083 | − | 18.7083i | −1.12407 | − | 1.12407i | −0.991123 | − | 0.132949i | \(-0.957555\pi\) |
−0.132949 | − | 0.991123i | \(-0.542445\pi\) | |||||||
\(278\) | −3.07892 | − | 6.82058i | −0.184661 | − | 0.409071i | ||||
\(279\) | −5.29150 | −0.316794 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.0000 | 1.55103 | 0.775515 | − | 0.631329i | \(-0.217490\pi\) | ||||
0.775515 | + | 0.631329i | \(0.217490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.7990 | + | 19.7990i | 1.17693 | + | 1.17693i | 0.980523 | + | 0.196405i | \(0.0629267\pi\) |
0.196405 | + | 0.980523i | \(0.437073\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.0000 | − | 37.0405i | 0.827837 | − | 2.19025i | ||||
\(287\) | 2.82843 | − | 2.82843i | 0.166957 | − | 0.166957i | ||||
\(288\) | 2.95367 | + | 4.82450i | 0.174047 | + | 0.284286i | ||||
\(289\) | − | 17.0000i | − | 1.00000i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 10.5830i | − | 0.620387i | ||||||
\(292\) | −1.32548 | − | 21.1245i | −0.0775677 | − | 1.23622i | ||||
\(293\) | −14.9666 | + | 14.9666i | −0.874360 | + | 0.874360i | −0.992944 | − | 0.118584i | \(-0.962164\pi\) |
0.118584 | + | 0.992944i | \(0.462164\pi\) | |||||||
\(294\) | 3.96863 | + | 1.50000i | 0.231455 | + | 0.0874818i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.00000 | − | 13.2288i | −0.406867 | − | 0.768906i | ||||
\(297\) | 3.74166 | + | 3.74166i | 0.217113 | + | 0.217113i | ||||
\(298\) | −5.15587 | + | 2.32744i | −0.298672 | + | 0.134825i | ||||
\(299\) | 21.1660 | 1.22406 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0000 | −0.922225 | ||||||||
\(302\) | 20.4617 | − | 9.23676i | 1.17744 | − | 0.531516i | ||||
\(303\) | 2.82843 | + | 2.82843i | 0.162489 | + | 0.162489i | ||||
\(304\) | −2.64575 | − | 21.0000i | −0.151744 | − | 1.20443i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.48528 | − | 8.48528i | 0.484281 | − | 0.484281i | −0.422215 | − | 0.906496i | \(-0.638747\pi\) |
0.906496 | + | 0.422215i | \(0.138747\pi\) | |||||||
\(308\) | 21.1245 | − | 1.32548i | 1.20368 | − | 0.0755261i | ||||
\(309\) | 6.00000i | 0.341328i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.7490i | 1.80032i | 0.435558 | + | 0.900161i | \(0.356551\pi\) | ||||
−0.435558 | + | 0.900161i | \(0.643449\pi\) | |||||||
\(312\) | −14.3039 | − | 4.40440i | −0.809798 | − | 0.249350i | ||||
\(313\) | 14.9666 | − | 14.9666i | 0.845964 | − | 0.845964i | −0.143663 | − | 0.989627i | \(-0.545888\pi\) |
0.989627 | + | 0.143663i | \(0.0458881\pi\) | |||||||
\(314\) | −2.64575 | + | 7.00000i | −0.149308 | + | 0.395033i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.00000 | − | 7.93725i | 0.393781 | − | 0.446505i | ||||
\(317\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(318\) | −6.15784 | − | 13.6412i | −0.345314 | − | 0.764958i | ||||
\(319\) | 42.3320 | 2.37014 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.00000 | 0.223258 | ||||||||
\(322\) | 4.65489 | + | 10.3117i | 0.259407 | + | 0.574651i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.32288 | − | 1.50000i | 0.0734931 | − | 0.0833333i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.00000 | + | 10.5830i | −0.221540 | + | 0.586138i | ||||
\(327\) | 1.41421 | − | 1.41421i | 0.0782062 | − | 0.0782062i | ||||
\(328\) | 5.40636 | + | 1.66471i | 0.298516 | + | 0.0919180i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 5.29150i | − | 0.290847i | −0.989369 | − | 0.145424i | \(-0.953545\pi\) | ||
0.989369 | − | 0.145424i | \(-0.0464545\pi\) | |||||||
\(332\) | −23.9529 | + | 1.50295i | −1.31459 | + | 0.0824851i | ||||
\(333\) | −3.74166 | + | 3.74166i | −0.205042 | + | 0.205042i | ||||
\(334\) | −15.8745 | − | 6.00000i | −0.868614 | − | 0.328305i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.00000 | − | 7.93725i | −0.0545545 | − | 0.433013i | ||||
\(337\) | −7.48331 | − | 7.48331i | −0.407642 | − | 0.407642i | 0.473273 | − | 0.880916i | \(-0.343072\pi\) |
−0.880916 | + | 0.473273i | \(0.843072\pi\) | |||||||
\(338\) | 19.3345 | − | 8.72791i | 1.05166 | − | 0.474736i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.0000 | −1.51629 | ||||||||
\(342\) | −6.82058 | + | 3.07892i | −0.368815 | + | 0.166489i | ||||
\(343\) | −14.1421 | − | 14.1421i | −0.763604 | − | 0.763604i | ||||
\(344\) | −10.5830 | − | 20.0000i | −0.570597 | − | 1.07833i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.0000 | − | 5.29150i | −0.752645 | − | 0.284473i | ||||
\(347\) | −8.48528 | + | 8.48528i | −0.455514 | + | 0.455514i | −0.897180 | − | 0.441666i | \(-0.854388\pi\) |
0.441666 | + | 0.897180i | \(0.354388\pi\) | |||||||
\(348\) | −1.00197 | − | 15.9686i | −0.0537110 | − | 0.856007i | ||||
\(349\) | − | 2.00000i | − | 0.107058i | −0.998566 | − | 0.0535288i | \(-0.982953\pi\) | ||
0.998566 | − | 0.0535288i | \(-0.0170469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.29150i | 0.282440i | ||||||||
\(352\) | 15.6294 | + | 25.5289i | 0.833048 | + | 1.36069i | ||||
\(353\) | −14.9666 | + | 14.9666i | −0.796593 | + | 0.796593i | −0.982557 | − | 0.185963i | \(-0.940459\pi\) |
0.185963 | + | 0.982557i | \(0.440459\pi\) | |||||||
\(354\) | −2.64575 | + | 7.00000i | −0.140620 | + | 0.372046i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.00000 | − | 7.93725i | −0.476999 | − | 0.420674i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.07892 | + | 6.82058i | 0.162726 | + | 0.360479i | ||||
\(359\) | −10.5830 | −0.558550 | −0.279275 | − | 0.960211i | \(-0.590094\pi\) | ||||
−0.279275 | + | 0.960211i | \(0.590094\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | 0.473684 | ||||||||
\(362\) | 1.16372 | + | 2.57794i | 0.0611639 | + | 0.135493i | ||||
\(363\) | 12.0208 | + | 12.0208i | 0.630929 | + | 0.630929i | ||||
\(364\) | 15.8745 | + | 14.0000i | 0.832050 | + | 0.733799i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.00000 | − | 7.93725i | 0.156813 | − | 0.414887i | ||||
\(367\) | 12.7279 | − | 12.7279i | 0.664392 | − | 0.664392i | −0.292020 | − | 0.956412i | \(-0.594327\pi\) |
0.956412 | + | 0.292020i | \(0.0943274\pi\) | |||||||
\(368\) | −9.81076 | + | 12.6392i | −0.511421 | + | 0.658863i | ||||
\(369\) | − | 2.00000i | − | 0.104116i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.1660i | 1.09888i | ||||||||
\(372\) | 0.662739 | + | 10.5622i | 0.0343614 | + | 0.547626i | ||||
\(373\) | 18.7083 | − | 18.7083i | 0.968678 | − | 0.968678i | −0.0308458 | − | 0.999524i | \(-0.509820\pi\) |
0.999524 | + | 0.0308458i | \(0.00982007\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.9333 | + | 29.9333i | 1.54164 | + | 1.54164i | ||||
\(378\) | −2.57794 | + | 1.16372i | −0.132595 | + | 0.0598554i | ||||
\(379\) | −5.29150 | −0.271806 | −0.135903 | − | 0.990722i | \(-0.543394\pi\) | ||||
−0.135903 | + | 0.990722i | \(0.543394\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.00000 | 0.102463 | ||||||||
\(382\) | 13.6412 | − | 6.15784i | 0.697942 | − | 0.315062i | ||||
\(383\) | −5.65685 | − | 5.65685i | −0.289052 | − | 0.289052i | 0.547653 | − | 0.836705i | \(-0.315521\pi\) |
−0.836705 | + | 0.547653i | \(0.815521\pi\) | |||||||
\(384\) | 9.26013 | − | 6.50000i | 0.472554 | − | 0.331702i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.65685 | + | 5.65685i | −0.287554 | + | 0.287554i | ||||
\(388\) | −21.1245 | + | 1.32548i | −1.07243 | + | 0.0672909i | ||||
\(389\) | − | 24.0000i | − | 1.21685i | −0.793612 | − | 0.608424i | \(-0.791802\pi\) | ||
0.793612 | − | 0.608424i | \(-0.208198\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2.49706 | − | 8.10954i | 0.126120 | − | 0.409594i | ||||
\(393\) | −11.2250 | + | 11.2250i | −0.566225 | + | 0.566225i | ||||
\(394\) | −10.5830 | + | 28.0000i | −0.533164 | + | 1.41062i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.00000 | − | 7.93725i | 0.351763 | − | 0.398862i | ||||
\(397\) | 3.74166 | + | 3.74166i | 0.187788 | + | 0.187788i | 0.794739 | − | 0.606951i | \(-0.207608\pi\) |
−0.606951 | + | 0.794739i | \(0.707608\pi\) | |||||||
\(398\) | −3.07892 | − | 6.82058i | −0.154332 | − | 0.341885i | ||||
\(399\) | 10.5830 | 0.529813 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.0000 | 0.499376 | 0.249688 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249688 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(402\) | −6.98233 | − | 15.4676i | −0.348247 | − | 0.771454i | ||||
\(403\) | −19.7990 | − | 19.7990i | −0.986258 | − | 0.986258i | ||||
\(404\) | 5.29150 | − | 6.00000i | 0.263262 | − | 0.298511i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.00000 | + | 21.1660i | −0.397033 | + | 1.05045i | ||||
\(407\) | −19.7990 | + | 19.7990i | −0.981399 | + | 0.981399i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0000i | 0.494468i | 0.968956 | + | 0.247234i | \(0.0795217\pi\) | ||||
−0.968956 | + | 0.247234i | \(0.920478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.9764 | − | 0.751475i | 0.590037 | − | 0.0370225i | ||||
\(413\) | 7.48331 | − | 7.48331i | 0.368230 | − | 0.368230i | ||||
\(414\) | 5.29150 | + | 2.00000i | 0.260063 | + | 0.0982946i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.00000 | + | 29.1033i | −0.343203 | + | 1.42690i | ||||
\(417\) | 3.74166 | + | 3.74166i | 0.183230 | + | 0.183230i | ||||
\(418\) | −36.0911 | + | 16.2921i | −1.76527 | + | 0.796873i | ||||
\(419\) | −15.8745 | −0.775520 | −0.387760 | − | 0.921760i | \(-0.626751\pi\) | ||||
−0.387760 | + | 0.921760i | \(0.626751\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0000 | 1.65706 | 0.828529 | − | 0.559946i | \(-0.189178\pi\) | ||||
0.828529 | + | 0.559946i | \(0.189178\pi\) | |||||||
\(422\) | −34.1029 | + | 15.3946i | −1.66010 | + | 0.749397i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −26.4575 | + | 14.0000i | −1.28489 | + | 0.679900i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.48528 | + | 8.48528i | −0.410632 | + | 0.410632i | ||||
\(428\) | −0.500983 | − | 7.98430i | −0.0242159 | − | 0.385936i | ||||
\(429\) | 28.0000i | 1.35185i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10.5830i | − | 0.509765i | −0.966972 | − | 0.254883i | \(-0.917963\pi\) | ||
0.966972 | − | 0.254883i | \(-0.0820369\pi\) | |||||||
\(432\) | −3.15980 | − | 2.45269i | −0.152026 | − | 0.118005i | ||||
\(433\) | 7.48331 | − | 7.48331i | 0.359625 | − | 0.359625i | −0.504050 | − | 0.863675i | \(-0.668157\pi\) |
0.863675 | + | 0.504050i | \(0.168157\pi\) | |||||||
\(434\) | 5.29150 | − | 14.0000i | 0.254000 | − | 0.672022i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.00000 | − | 2.64575i | −0.143674 | − | 0.126709i | ||||
\(437\) | −14.9666 | − | 14.9666i | −0.715951 | − | 0.715951i | ||||
\(438\) | 6.15784 | + | 13.6412i | 0.294233 | + | 0.651799i | ||||
\(439\) | −5.29150 | −0.252550 | −0.126275 | − | 0.991995i | \(-0.540302\pi\) | ||||
−0.126275 | + | 0.991995i | \(0.540302\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.82843 | + | 2.82843i | 0.134383 | + | 0.134383i | 0.771099 | − | 0.636716i | \(-0.219708\pi\) |
−0.636716 | + | 0.771099i | \(0.719708\pi\) | |||||||
\(444\) | 7.93725 | + | 7.00000i | 0.376685 | + | 0.332205i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.00000 | − | 18.5203i | 0.331460 | − | 0.876960i | ||||
\(447\) | 2.82843 | − | 2.82843i | 0.133780 | − | 0.133780i | ||||
\(448\) | −15.7181 | + | 2.99018i | −0.742611 | + | 0.141273i | ||||
\(449\) | 22.0000i | 1.03824i | 0.854700 | + | 0.519122i | \(0.173741\pi\) | ||||
−0.854700 | + | 0.519122i | \(0.826259\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 10.5830i | − | 0.498334i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.2250 | + | 11.2250i | −0.527395 | + | 0.527395i | ||||
\(454\) | 37.0405 | + | 14.0000i | 1.73840 | + | 0.657053i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.00000 | + | 13.2288i | 0.327805 | + | 0.619493i | ||||
\(457\) | 7.48331 | + | 7.48331i | 0.350055 | + | 0.350055i | 0.860130 | − | 0.510075i | \(-0.170382\pi\) |
−0.510075 | + | 0.860130i | \(0.670382\pi\) | |||||||
\(458\) | −18.0455 | + | 8.14605i | −0.843213 | + | 0.380640i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.0000 | −1.30409 | −0.652045 | − | 0.758180i | \(-0.726089\pi\) | ||||
−0.652045 | + | 0.758180i | \(0.726089\pi\) | |||||||
\(462\) | −13.6412 | + | 6.15784i | −0.634644 | + | 0.286489i | ||||
\(463\) | −24.0416 | − | 24.0416i | −1.11731 | − | 1.11731i | −0.992135 | − | 0.125175i | \(-0.960051\pi\) |
−0.125175 | − | 0.992135i | \(-0.539949\pi\) | |||||||
\(464\) | −31.7490 | + | 4.00000i | −1.47391 | + | 0.185695i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.0000 | + | 10.5830i | 1.29707 | + | 0.490248i | ||||
\(467\) | 25.4558 | − | 25.4558i | 1.17796 | − | 1.17796i | 0.197692 | − | 0.980264i | \(-0.436655\pi\) |
0.980264 | − | 0.197692i | \(-0.0633445\pi\) | |||||||
\(468\) | 10.5622 | − | 0.662739i | 0.488239 | − | 0.0306351i | ||||
\(469\) | 24.0000i | 1.10822i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 5.29150i | − | 0.243820i | ||||||
\(472\) | 14.3039 | + | 4.40440i | 0.658390 | + | 0.202729i | ||||
\(473\) | −29.9333 | + | 29.9333i | −1.37633 | + | 1.37633i | ||||
\(474\) | −2.64575 | + | 7.00000i | −0.121523 | + | 0.321521i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.48331 | + | 7.48331i | 0.342637 | + | 0.342637i | ||||
\(478\) | 6.15784 | + | 13.6412i | 0.281653 | + | 0.623932i | ||||
\(479\) | −42.3320 | −1.93420 | −0.967100 | − | 0.254398i | \(-0.918123\pi\) | ||||
−0.967100 | + | 0.254398i | \(0.918123\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.0000 | −1.27669 | ||||||||
\(482\) | 8.14605 | + | 18.0455i | 0.371043 | + | 0.821952i | ||||
\(483\) | −5.65685 | − | 5.65685i | −0.257396 | − | 0.257396i | ||||
\(484\) | 22.4889 | − | 25.5000i | 1.02222 | − | 1.15909i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.500000 | + | 1.32288i | −0.0226805 | + | 0.0600069i | ||||
\(487\) | −7.07107 | + | 7.07107i | −0.320421 | + | 0.320421i | −0.848928 | − | 0.528508i | \(-0.822752\pi\) |
0.528508 | + | 0.848928i | \(0.322752\pi\) | |||||||
\(488\) | −16.2191 | − | 4.99412i | −0.734204 | − | 0.226073i | ||||
\(489\) | − | 8.00000i | − | 0.361773i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15.8745i | − | 0.716407i | −0.933644 | − | 0.358203i | \(-0.883389\pi\) | ||
0.933644 | − | 0.358203i | \(-0.116611\pi\) | |||||||
\(492\) | −3.99215 | + | 0.250492i | −0.179980 | + | 0.0112930i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −37.0405 | − | 14.0000i | −1.66653 | − | 0.629890i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21.0000 | − | 2.64575i | 0.942928 | − | 0.118798i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 15.4676 | − | 6.98233i | 0.693120 | − | 0.312886i | ||||
\(499\) | 15.8745 | 0.710641 | 0.355320 | − | 0.934745i | \(-0.384372\pi\) | ||||
0.355320 | + | 0.934745i | \(0.384372\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.0000 | 0.536120 | ||||||||
\(502\) | −6.82058 | + | 3.07892i | −0.304417 | + | 0.137419i | ||||
\(503\) | 11.3137 | + | 11.3137i | 0.504453 | + | 0.504453i | 0.912819 | − | 0.408365i | \(-0.133901\pi\) |
−0.408365 | + | 0.912819i | \(0.633901\pi\) | |||||||
\(504\) | 2.64575 | + | 5.00000i | 0.117851 | + | 0.222718i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 28.0000 | + | 10.5830i | 1.24475 | + | 0.470472i | ||||
\(507\) | −10.6066 | + | 10.6066i | −0.471056 | + | 0.471056i | ||||
\(508\) | −0.250492 | − | 3.99215i | −0.0111138 | − | 0.177123i | ||||
\(509\) | − | 36.0000i | − | 1.59567i | −0.602875 | − | 0.797836i | \(-0.705978\pi\) | ||
0.602875 | − | 0.797836i | \(-0.294022\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 21.1660i | − | 0.936329i | ||||||
\(512\) | −14.1343 | − | 17.6698i | −0.624653 | − | 0.780903i | ||||
\(513\) | 3.74166 | − | 3.74166i | 0.165198 | − | 0.165198i | ||||
\(514\) | 10.5830 | − | 28.0000i | 0.466796 | − | 1.23503i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 12.0000 | + | 10.5830i | 0.528271 | + | 0.465891i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −6.15784 | − | 13.6412i | −0.270560 | − | 0.599358i | ||||
\(519\) | 10.5830 | 0.464542 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.0000 | 0.613351 | 0.306676 | − | 0.951814i | \(-0.400783\pi\) | ||||
0.306676 | + | 0.951814i | \(0.400783\pi\) | |||||||
\(522\) | 4.65489 | + | 10.3117i | 0.203739 | + | 0.451333i | ||||
\(523\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(524\) | 23.8118 | + | 21.0000i | 1.04022 | + | 0.917389i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.00000 | + | 15.8745i | −0.261612 | + | 0.692161i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −16.7201 | − | 12.9784i | −0.727648 | − | 0.564813i | ||||
\(529\) | − | 7.00000i | − | 0.304348i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 5.29150i | − | 0.229632i | ||||||
\(532\) | −1.32548 | − | 21.1245i | −0.0574667 | − | 0.915862i | ||||
\(533\) | 7.48331 | − | 7.48331i | 0.324138 | − | 0.324138i | ||||
\(534\) | 7.93725 | + | 3.00000i | 0.343479 | + | 0.129823i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −30.0000 | + | 15.8745i | −1.29580 | + | 0.685674i | ||||
\(537\) | −3.74166 | − | 3.74166i | −0.161464 | − | 0.161464i | ||||
\(538\) | 30.9352 | − | 13.9647i | 1.33371 | − | 0.602059i | ||||
\(539\) | −15.8745 | −0.683763 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | −20.4617 | + | 9.23676i | −0.878906 | + | 0.396753i | ||||
\(543\) | −1.41421 | − | 1.41421i | −0.0606897 | − | 0.0606897i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −14.0000 | − | 5.29150i | −0.599145 | − | 0.226455i | ||||
\(547\) | −5.65685 | + | 5.65685i | −0.241870 | + | 0.241870i | −0.817623 | − | 0.575754i | \(-0.804709\pi\) |
0.575754 | + | 0.817623i | \(0.304709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.00000i | 0.256074i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 42.3320i | − | 1.80340i | ||||||
\(552\) | 3.32941 | − | 10.8127i | 0.141709 | − | 0.460220i | ||||
\(553\) | 7.48331 | − | 7.48331i | 0.318223 | − | 0.318223i | ||||
\(554\) | 13.2288 | − | 35.0000i | 0.562036 | − | 1.48701i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.00000 | − | 7.93725i | 0.296866 | − | 0.336615i | ||||
\(557\) | 22.4499 | + | 22.4499i | 0.951235 | + | 0.951235i | 0.998865 | − | 0.0476304i | \(-0.0151670\pi\) |
−0.0476304 | + | 0.998865i | \(0.515167\pi\) | |||||||
\(558\) | −3.07892 | − | 6.82058i | −0.130341 | − | 0.288738i | ||||
\(559\) | −42.3320 | −1.79045 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.1284 | + | 33.5132i | 0.638152 | + | 1.41367i | ||||
\(563\) | −2.82843 | − | 2.82843i | −0.119204 | − | 0.119204i | 0.644988 | − | 0.764192i | \(-0.276862\pi\) |
−0.764192 | + | 0.644988i | \(0.776862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.0000 | + | 37.0405i | −0.588464 | + | 1.55693i | ||||
\(567\) | 1.41421 | − | 1.41421i | 0.0593914 | − | 0.0593914i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 6.00000i | − | 0.251533i | −0.992060 | − | 0.125767i | \(-0.959861\pi\) | ||
0.992060 | − | 0.125767i | \(-0.0401390\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 5.29150i | − | 0.221442i | −0.993852 | − | 0.110721i | \(-0.964684\pi\) | ||
0.993852 | − | 0.110721i | \(-0.0353161\pi\) | |||||||
\(572\) | 55.8901 | − | 3.50688i | 2.33688 | − | 0.146630i | ||||
\(573\) | −7.48331 | + | 7.48331i | −0.312620 | + | 0.312620i | ||||
\(574\) | 5.29150 | + | 2.00000i | 0.220863 | + | 0.0834784i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.50000 | + | 6.61438i | −0.187500 | + | 0.275599i | ||||
\(577\) | −22.4499 | − | 22.4499i | −0.934603 | − | 0.934603i | 0.0633857 | − | 0.997989i | \(-0.479810\pi\) |
−0.997989 | + | 0.0633857i | \(0.979810\pi\) | |||||||
\(578\) | 21.9125 | − | 9.89164i | 0.911438 | − | 0.411438i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0000 | −0.995688 | ||||||||
\(582\) | 13.6412 | − | 6.15784i | 0.565444 | − | 0.255251i | ||||
\(583\) | 39.5980 | + | 39.5980i | 1.63998 | + | 1.63998i | ||||
\(584\) | 26.4575 | − | 14.0000i | 1.09482 | − | 0.579324i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.0000 | − | 10.5830i | −1.15667 | − | 0.437180i | ||||
\(587\) | −19.7990 | + | 19.7990i | −0.817192 | + | 0.817192i | −0.985700 | − | 0.168508i | \(-0.946105\pi\) |
0.168508 | + | 0.985700i | \(0.446105\pi\) | |||||||
\(588\) | 0.375737 | + | 5.98822i | 0.0154952 | + | 0.246950i | ||||
\(589\) | 28.0000i | 1.15372i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 21.1660i | − | 0.870653i | ||||||
\(592\) | 12.9784 | − | 16.7201i | 0.533410 | − | 0.687191i | ||||
\(593\) | 14.9666 | − | 14.9666i | 0.614606 | − | 0.614606i | −0.329537 | − | 0.944143i | \(-0.606893\pi\) |
0.944143 | + | 0.329537i | \(0.106893\pi\) | |||||||
\(594\) | −2.64575 | + | 7.00000i | −0.108556 | + | 0.287213i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | − | 5.29150i | −0.245770 | − | 0.216748i | ||||
\(597\) | 3.74166 | + | 3.74166i | 0.153136 | + | 0.153136i | ||||
\(598\) | 12.3157 | + | 27.2823i | 0.503625 | + | 1.11566i | ||||
\(599\) | 31.7490 | 1.29723 | 0.648615 | − | 0.761117i | \(-0.275349\pi\) | ||||
0.648615 | + | 0.761117i | \(0.275349\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0000 | −0.571072 | −0.285536 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285536 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(602\) | −9.30978 | − | 20.6235i | −0.379438 | − | 0.840550i | ||||
\(603\) | 8.48528 | + | 8.48528i | 0.345547 | + | 0.345547i | ||||
\(604\) | 23.8118 | + | 21.0000i | 0.968887 | + | 0.854478i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.00000 | + | 5.29150i | −0.0812444 | + | 0.214953i | ||||
\(607\) | 24.0416 | − | 24.0416i | 0.975820 | − | 0.975820i | −0.0238948 | − | 0.999714i | \(-0.507607\pi\) |
0.999714 | + | 0.0238948i | \(0.00760667\pi\) | |||||||
\(608\) | 25.5289 | − | 15.6294i | 1.03533 | − | 0.633855i | ||||
\(609\) | − | 16.0000i | − | 0.648353i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.2250 | + | 11.2250i | −0.453372 | + | 0.453372i | −0.896472 | − | 0.443100i | \(-0.853879\pi\) |
0.443100 | + | 0.896472i | \(0.353879\pi\) | |||||||
\(614\) | 15.8745 | + | 6.00000i | 0.640643 | + | 0.242140i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.0000 | + | 26.4575i | 0.564076 | + | 1.06600i | ||||
\(617\) | −29.9333 | − | 29.9333i | −1.20507 | − | 1.20507i | −0.972605 | − | 0.232462i | \(-0.925322\pi\) |
−0.232462 | − | 0.972605i | \(-0.574678\pi\) | |||||||
\(618\) | −7.73381 | + | 3.49117i | −0.311099 | + | 0.140435i | ||||
\(619\) | 5.29150 | 0.212683 | 0.106342 | − | 0.994330i | \(-0.466086\pi\) | ||||
0.106342 | + | 0.994330i | \(0.466086\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | −40.9235 | + | 18.4735i | −1.64088 | + | 0.740720i | ||||
\(623\) | −8.48528 | − | 8.48528i | −0.339956 | − | 0.339956i | ||||
\(624\) | −2.64575 | − | 21.0000i | −0.105915 | − | 0.840673i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 28.0000 | + | 10.5830i | 1.11911 | + | 0.422982i | ||||
\(627\) | 19.7990 | − | 19.7990i | 0.790695 | − | 0.790695i | ||||
\(628\) | −10.5622 | + | 0.662739i | −0.421479 | + | 0.0264461i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 5.29150i | − | 0.210651i | −0.994438 | − | 0.105326i | \(-0.966411\pi\) | ||
0.994438 | − | 0.105326i | \(-0.0335885\pi\) | |||||||
\(632\) | 14.3039 | + | 4.40440i | 0.568978 | + | 0.175197i | ||||
\(633\) | 18.7083 | − | 18.7083i | 0.743588 | − | 0.743588i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14.0000 | − | 15.8745i | 0.555136 | − | 0.629465i | ||||
\(637\) | −11.2250 | − | 11.2250i | −0.444750 | − | 0.444750i | ||||
\(638\) | 24.6314 | + | 54.5646i | 0.975164 | + | 2.16023i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.0000 | −1.18493 | −0.592464 | − | 0.805597i | \(-0.701845\pi\) | ||||
−0.592464 | + | 0.805597i | \(0.701845\pi\) | |||||||
\(642\) | 2.32744 | + | 5.15587i | 0.0918569 | + | 0.203486i | ||||
\(643\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(644\) | −10.5830 | + | 12.0000i | −0.417029 | + | 0.472866i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.9706 | − | 16.9706i | 0.667182 | − | 0.667182i | −0.289881 | − | 0.957063i | \(-0.593616\pi\) |
0.957063 | + | 0.289881i | \(0.0936157\pi\) | |||||||
\(648\) | 2.70318 | + | 0.832353i | 0.106191 | + | 0.0326979i | ||||
\(649\) | − | 28.0000i | − | 1.09910i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.5830i | 0.414781i | ||||||||
\(652\) | −15.9686 | + | 1.00197i | −0.625378 | + | 0.0392400i | ||||
\(653\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(654\) | 2.64575 | + | 1.00000i | 0.103457 | + | 0.0391031i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.00000 | + | 7.93725i | 0.0390434 | + | 0.309898i | ||||
\(657\) | −7.48331 | − | 7.48331i | −0.291952 | − | 0.291952i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.8745 | −0.618383 | −0.309192 | − | 0.951000i | \(-0.600058\pi\) | ||||
−0.309192 | + | 0.951000i | \(0.600058\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.0000 | 0.700119 | 0.350059 | − | 0.936727i | \(-0.386161\pi\) | ||||
0.350059 | + | 0.936727i | \(0.386161\pi\) | |||||||
\(662\) | 6.82058 | − | 3.07892i | 0.265089 | − | 0.119666i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.8745 | − | 30.0000i | −0.616050 | − | 1.16423i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.00000 | − | 2.64575i | −0.271244 | − | 0.102521i | ||||
\(667\) | −22.6274 | + | 22.6274i | −0.876137 | + | 0.876137i | ||||
\(668\) | −1.50295 | − | 23.9529i | −0.0581509 | − | 0.926765i | ||||
\(669\) | 14.0000i | 0.541271i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.7490i | 1.22566i | ||||||||
\(672\) | 9.64900 | − | 5.90735i | 0.372218 | − | 0.227881i | ||||
\(673\) | 7.48331 | − | 7.48331i | 0.288461 | − | 0.288461i | −0.548011 | − | 0.836471i | \(-0.684615\pi\) |
0.836471 | + | 0.548011i | \(0.184615\pi\) | |||||||
\(674\) | 5.29150 | − | 14.0000i | 0.203821 | − | 0.539260i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 22.5000 | + | 19.8431i | 0.865385 | + | 0.763197i | ||||
\(677\) | −14.9666 | − | 14.9666i | −0.575214 | − | 0.575214i | 0.358367 | − | 0.933581i | \(-0.383334\pi\) |
−0.933581 | + | 0.358367i | \(0.883334\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.1660 | −0.812277 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.0000 | −1.07296 | ||||||||
\(682\) | −16.2921 | − | 36.0911i | −0.623857 | − | 1.38200i | ||||
\(683\) | −8.48528 | − | 8.48528i | −0.324680 | − | 0.324680i | 0.525879 | − | 0.850559i | \(-0.323736\pi\) |
−0.850559 | + | 0.525879i | \(0.823736\pi\) | |||||||
\(684\) | −7.93725 | − | 7.00000i | −0.303488 | − | 0.267652i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.0000 | − | 26.4575i | 0.381802 | − | 1.01015i | ||||
\(687\) | 9.89949 | − | 9.89949i | 0.377689 | − | 0.377689i | ||||
\(688\) | 19.6215 | − | 25.2784i | 0.748063 | − | 0.963729i | ||||
\(689\) | 56.0000i | 2.13343i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 37.0405i | − | 1.40909i | −0.709660 | − | 0.704544i | \(-0.751152\pi\) | ||
0.709660 | − | 0.704544i | \(-0.248848\pi\) | |||||||
\(692\) | −1.32548 | − | 21.1245i | −0.0503871 | − | 0.803032i | ||||
\(693\) | 7.48331 | − | 7.48331i | 0.284268 | − | 0.284268i | ||||
\(694\) | −15.8745 | − | 6.00000i | −0.602588 | − | 0.227757i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 20.0000 | − | 10.5830i | 0.758098 | − | 0.401148i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 2.57794 | − | 1.16372i | 0.0975763 | − | 0.0440475i | ||||
\(699\) | −21.1660 | −0.800572 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.0000 | 1.35970 | 0.679851 | − | 0.733351i | \(-0.262045\pi\) | ||||
0.679851 | + | 0.733351i | \(0.262045\pi\) | |||||||
\(702\) | −6.82058 | + | 3.07892i | −0.257426 | + | 0.116206i | ||||
\(703\) | 19.7990 | + | 19.7990i | 0.746733 | + | 0.746733i | ||||
\(704\) | −23.8118 | + | 35.0000i | −0.897440 | + | 1.31911i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −28.0000 | − | 10.5830i | −1.05379 | − | 0.398297i | ||||
\(707\) | 5.65685 | − | 5.65685i | 0.212748 | − | 0.212748i | ||||
\(708\) | −10.5622 | + | 0.662739i | −0.396953 | + | 0.0249072i | ||||
\(709\) | − | 10.0000i | − | 0.375558i | −0.982211 | − | 0.187779i | \(-0.939871\pi\) | ||
0.982211 | − | 0.187779i | \(-0.0601289\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 5.29150i | − | 0.198447i | ||||||
\(712\) | 4.99412 | − | 16.2191i | 0.187162 | − | 0.607836i | ||||
\(713\) | 14.9666 | − | 14.9666i | 0.560505 | − | 0.560505i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.00000 | + | 7.93725i | −0.261602 | + | 0.296629i | ||||
\(717\) | −7.48331 | − | 7.48331i | −0.279470 | − | 0.279470i | ||||
\(718\) | −6.15784 | − | 13.6412i | −0.229808 | − | 0.509083i | ||||
\(719\) | 31.7490 | 1.18404 | 0.592019 | − | 0.805924i | \(-0.298331\pi\) | ||||
0.592019 | + | 0.805924i | \(0.298331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | 5.23675 | + | 11.6007i | 0.194892 | + | 0.431734i | ||||
\(723\) | −9.89949 | − | 9.89949i | −0.368166 | − | 0.368166i | ||||
\(724\) | −2.64575 | + | 3.00000i | −0.0983286 | + | 0.111494i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −8.50000 | + | 22.4889i | −0.315465 | + | 0.834641i | ||||
\(727\) | −21.2132 | + | 21.2132i | −0.786754 | + | 0.786754i | −0.980961 | − | 0.194207i | \(-0.937787\pi\) |
0.194207 | + | 0.980961i | \(0.437787\pi\) | |||||||
\(728\) | −8.80879 | + | 28.6078i | −0.326476 | + | 1.06027i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 11.9764 | − | 0.751475i | 0.442662 | − | 0.0277753i | ||||
\(733\) | −26.1916 | + | 26.1916i | −0.967409 | + | 0.967409i | −0.999485 | − | 0.0320765i | \(-0.989788\pi\) |
0.0320765 | + | 0.999485i | \(0.489788\pi\) | |||||||
\(734\) | 23.8118 | + | 9.00000i | 0.878908 | + | 0.332196i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −22.0000 | − | 5.29150i | −0.810931 | − | 0.195047i | ||||
\(737\) | 44.8999 | + | 44.8999i | 1.65391 | + | 1.65391i | ||||
\(738\) | 2.57794 | − | 1.16372i | 0.0948951 | − | 0.0428372i | ||||
\(739\) | 26.4575 | 0.973255 | 0.486628 | − | 0.873609i | \(-0.338227\pi\) | ||||
0.486628 | + | 0.873609i | \(0.338227\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.0000 | 1.02861 | ||||||||
\(742\) | −27.2823 | + | 12.3157i | −1.00156 | + | 0.452123i | ||||
\(743\) | 33.9411 | + | 33.9411i | 1.24518 | + | 1.24518i | 0.957824 | + | 0.287355i | \(0.0927759\pi\) |
0.287355 | + | 0.957824i | \(0.407224\pi\) | |||||||
\(744\) | −13.2288 | + | 7.00000i | −0.484990 | + | 0.256632i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 35.0000 | + | 13.2288i | 1.28144 | + | 0.484339i | ||||
\(747\) | −8.48528 | + | 8.48528i | −0.310460 | + | 0.310460i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 8.00000i | − | 0.292314i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.4575i | 0.965448i | 0.875772 | + | 0.482724i | \(0.160353\pi\) | ||||
−0.875772 | + | 0.482724i | \(0.839647\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.74166 | − | 3.74166i | 0.136354 | − | 0.136354i | ||||
\(754\) | −21.1660 | + | 56.0000i | −0.770821 | + | 2.03940i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.00000 | − | 2.64575i | −0.109109 | − | 0.0962250i | ||||
\(757\) | 33.6749 | + | 33.6749i | 1.22394 | + | 1.22394i | 0.966221 | + | 0.257715i | \(0.0829694\pi\) |
0.257715 | + | 0.966221i | \(0.417031\pi\) | |||||||
\(758\) | −3.07892 | − | 6.82058i | −0.111831 | − | 0.247734i | ||||
\(759\) | −21.1660 | −0.768278 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.0000 | 1.52250 | 0.761249 | − | 0.648459i | \(-0.224586\pi\) | ||||
0.761249 | + | 0.648459i | \(0.224586\pi\) | |||||||
\(762\) | 1.16372 | + | 2.57794i | 0.0421572 | + | 0.0933887i | ||||
\(763\) | −2.82843 | − | 2.82843i | −0.102396 | − | 0.102396i | ||||
\(764\) | 15.8745 | + | 14.0000i | 0.574320 | + | 0.506502i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.00000 | − | 10.5830i | 0.144526 | − | 0.382380i | ||||
\(767\) | 19.7990 | − | 19.7990i | 0.714900 | − | 0.714900i | ||||
\(768\) | 13.7664 | + | 8.15391i | 0.496752 | + | 0.294229i | ||||
\(769\) | − | 14.0000i | − | 0.504853i | −0.967616 | − | 0.252426i | \(-0.918771\pi\) | ||
0.967616 | − | 0.252426i | \(-0.0812286\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.1660i | 0.762275i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.9666 | − | 14.9666i | 0.538312 | − | 0.538312i | −0.384721 | − | 0.923033i | \(-0.625702\pi\) |
0.923033 | + | 0.384721i | \(0.125702\pi\) | |||||||
\(774\) | −10.5830 | − | 4.00000i | −0.380398 | − | 0.143777i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.0000 | − | 26.4575i | −0.502571 | − | 0.949769i | ||||
\(777\) | 7.48331 | + | 7.48331i | 0.268462 | + | 0.268462i | ||||
\(778\) | 30.9352 | − | 13.9647i | 1.10908 | − | 0.500657i | ||||
\(779\) | −10.5830 | −0.379176 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.65685 | − | 5.65685i | −0.202159 | − | 0.202159i | ||||
\(784\) | 11.9059 | − | 1.50000i | 0.425210 | − | 0.0535714i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21.0000 | − | 7.93725i | −0.749045 | − | 0.283112i | ||||
\(787\) | 22.6274 | − | 22.6274i | 0.806580 | − | 0.806580i | −0.177534 | − | 0.984115i | \(-0.556812\pi\) |
0.984115 | + | 0.177534i | \(0.0568121\pi\) | |||||||
\(788\) | −42.2489 | + | 2.65095i | −1.50506 | + | 0.0944363i | ||||
\(789\) | − | 12.0000i | − | 0.427211i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 14.3039 | + | 4.40440i | 0.508267 | + | 0.156503i | ||||
\(793\) | −22.4499 | + | 22.4499i | −0.797221 | + | 0.797221i | ||||
\(794\) | −2.64575 | + | 7.00000i | −0.0938942 | + | 0.248421i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.00000 | − | 7.93725i | 0.248108 | − | 0.281329i | ||||
\(797\) | −22.4499 | − | 22.4499i | −0.795218 | − | 0.795218i | 0.187119 | − | 0.982337i | \(-0.440085\pi\) |
−0.982337 | + | 0.187119i | \(0.940085\pi\) | |||||||
\(798\) | 6.15784 | + | 13.6412i | 0.217985 | + | 0.482892i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | 5.81861 | + | 12.8897i | 0.205462 | + | 0.455150i | ||||
\(803\) | −39.5980 | − | 39.5980i | −1.39738 | − | 1.39738i | ||||
\(804\) | 15.8745 | − | 18.0000i | 0.559851 | − | 0.634811i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.0000 | − | 37.0405i | 0.493129 | − | 1.30470i | ||||
\(807\) | −16.9706 | + | 16.9706i | −0.597392 | + | 0.597392i | ||||
\(808\) | 10.8127 | + | 3.32941i | 0.380390 | + | 0.117128i | ||||
\(809\) | 30.0000i | 1.05474i | 0.849635 | + | 0.527372i | \(0.176823\pi\) | ||||
−0.849635 | + | 0.527372i | \(0.823177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.0405i | 1.30067i | 0.759648 | + | 0.650334i | \(0.225371\pi\) | ||||
−0.759648 | + | 0.650334i | \(0.774629\pi\) | |||||||
\(812\) | −31.9372 | + | 2.00393i | −1.12078 | + | 0.0703243i | ||||
\(813\) | 11.2250 | − | 11.2250i | 0.393677 | − | 0.393677i | ||||
\(814\) | −37.0405 | − | 14.0000i | −1.29827 | − | 0.490700i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.9333 | + | 29.9333i | 1.04723 | + | 1.04723i | ||||
\(818\) | −12.8897 | + | 5.81861i | −0.450677 | + | 0.203443i | ||||
\(819\) | 10.5830 | 0.369800 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.00000 | 0.279202 | 0.139601 | − | 0.990208i | \(-0.455418\pi\) | ||||
0.139601 | + | 0.990208i | \(0.455418\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.41421 | + | 1.41421i | 0.0492964 | + | 0.0492964i | 0.731325 | − | 0.682029i | \(-0.238902\pi\) |
−0.682029 | + | 0.731325i | \(0.738902\pi\) | |||||||
\(824\) | 7.93725 | + | 15.0000i | 0.276507 | + | 0.522550i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.0000 | + | 5.29150i | 0.487122 | + | 0.184115i | ||||
\(827\) | −14.1421 | + | 14.1421i | −0.491770 | + | 0.491770i | −0.908864 | − | 0.417093i | \(-0.863049\pi\) |
0.417093 | + | 0.908864i | \(0.363049\pi\) | |||||||
\(828\) | 0.500983 | + | 7.98430i | 0.0174104 | + | 0.277474i | ||||
\(829\) | 14.0000i | 0.486240i | 0.969996 | + | 0.243120i | \(0.0781709\pi\) | ||||
−0.969996 | + | 0.243120i | \(0.921829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.4575i | 0.917801i | ||||||||
\(832\) | −41.5862 | + | 7.91128i | −1.44174 | + | 0.274274i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.64575 | + | 7.00000i | −0.0916149 | + | 0.242390i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −42.0000 | − | 37.0405i | −1.45260 | − | 1.28107i | ||||
\(837\) | 3.74166 | + | 3.74166i | 0.129331 | + | 0.129331i | ||||
\(838\) | −9.23676 | − | 20.4617i | −0.319078 | − | 0.706839i | ||||
\(839\) | 31.7490 | 1.09610 | 0.548049 | − | 0.836446i | \(-0.315371\pi\) | ||||
0.548049 | + | 0.836446i | \(0.315371\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −35.0000 | −1.20690 | ||||||||
\(842\) | 19.7833 | + | 43.8249i | 0.681777 | + | 1.51031i | ||||
\(843\) | −18.3848 | − | 18.3848i | −0.633205 | − | 0.633205i | ||||
\(844\) | −39.6863 | − | 35.0000i | −1.36606 | − | 1.20475i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.0416 | − | 24.0416i | 0.826080 | − | 0.826080i | ||||
\(848\) | −33.4401 | − | 25.9568i | −1.14834 | − | 0.891361i | ||||
\(849\) | − | 28.0000i | − | 0.960958i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 21.1660i | − | 0.725561i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.2250 | + | 11.2250i | −0.384336 | + | 0.384336i | −0.872661 | − | 0.488326i | \(-0.837608\pi\) |
0.488326 | + | 0.872661i | \(0.337608\pi\) | |||||||
\(854\) | −15.8745 | − | 6.00000i | −0.543214 | − | 0.205316i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.0000 | − | 5.29150i | 0.341793 | − | 0.180860i | ||||
\(857\) | −29.9333 | − | 29.9333i | −1.02250 | − | 1.02250i | −0.999741 | − | 0.0227597i | \(-0.992755\pi\) |
−0.0227597 | − | 0.999741i | \(-0.507245\pi\) | |||||||
\(858\) | −36.0911 | + | 16.2921i | −1.23213 | + | 0.556203i | ||||
\(859\) | 5.29150 | 0.180544 | 0.0902719 | − | 0.995917i | \(-0.471226\pi\) | ||||
0.0902719 | + | 0.995917i | \(0.471226\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00000 | −0.136320 | ||||||||
\(862\) | 13.6412 | − | 6.15784i | 0.464619 | − | 0.209737i | ||||
\(863\) | 2.82843 | + | 2.82843i | 0.0962808 | + | 0.0962808i | 0.753607 | − | 0.657326i | \(-0.228312\pi\) |
−0.657326 | + | 0.753607i | \(0.728312\pi\) | |||||||
\(864\) | 1.32288 | − | 5.50000i | 0.0450051 | − | 0.187114i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.0000 | + | 5.29150i | 0.475739 | + | 0.179813i | ||||
\(867\) | −12.0208 | + | 12.0208i | −0.408248 | + | 0.408248i | ||||
\(868\) | 21.1245 | − | 1.32548i | 0.717011 | − | 0.0449896i | ||||
\(869\) | − | 28.0000i | − | 0.949835i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 63.4980i | 2.15155i | ||||||||
\(872\) | 1.66471 | − | 5.40636i | 0.0563740 | − | 0.183083i | ||||
\(873\) | −7.48331 | + | 7.48331i | −0.253272 | + | 0.253272i | ||||
\(874\) | 10.5830 | − | 28.0000i | 0.357975 | − | 0.947114i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14.0000 | + | 15.8745i | −0.473016 | + | 0.536350i | ||||
\(877\) | −3.74166 | − | 3.74166i | −0.126347 | − | 0.126347i | 0.641106 | − | 0.767453i | \(-0.278476\pi\) |
−0.767453 | + | 0.641106i | \(0.778476\pi\) | |||||||
\(878\) | −3.07892 | − | 6.82058i | −0.103908 | − | 0.230183i | ||||
\(879\) | 21.1660 | 0.713912 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.00000 | −0.0673817 | −0.0336909 | − | 0.999432i | \(-0.510726\pi\) | ||||
−0.0336909 | + | 0.999432i | \(0.510726\pi\) | |||||||
\(882\) | −1.74558 | − | 3.86690i | −0.0587768 | − | 0.130205i | ||||
\(883\) | −28.2843 | − | 28.2843i | −0.951842 | − | 0.951842i | 0.0470510 | − | 0.998892i | \(-0.485018\pi\) |
−0.998892 | + | 0.0470510i | \(0.985018\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.00000 | + | 5.29150i | −0.0671913 | + | 0.177772i | ||||
\(887\) | −25.4558 | + | 25.4558i | −0.854724 | + | 0.854724i | −0.990711 | − | 0.135987i | \(-0.956579\pi\) |
0.135987 | + | 0.990711i | \(0.456579\pi\) | |||||||
\(888\) | −4.40440 | + | 14.3039i | −0.147802 | + | 0.480007i | ||||
\(889\) | − | 4.00000i | − | 0.134156i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 5.29150i | − | 0.177272i | ||||||
\(892\) | 27.9450 | − | 1.75344i | 0.935669 | − | 0.0587096i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 5.29150 | + | 2.00000i | 0.176974 | + | 0.0668900i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.0000 | − | 18.5203i | −0.434300 | − | 0.618718i | ||||
\(897\) | −14.9666 | − | 14.9666i | −0.499721 | − | 0.499721i | ||||
\(898\) | −28.3573 | + | 12.8009i | −0.946295 | + | 0.427173i | ||||
\(899\) | 42.3320 | 1.41185 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 13.6412 | − | 6.15784i | 0.454201 | − | 0.205034i | ||||
\(903\) | 11.3137 | + | 11.3137i | 0.376497 | + | 0.376497i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −21.0000 | − | 7.93725i | −0.697678 | − | 0.263698i | ||||
\(907\) | −11.3137 | + | 11.3137i | −0.375666 | + | 0.375666i | −0.869536 | − | 0.493870i | \(-0.835582\pi\) |
0.493870 | + | 0.869536i | \(0.335582\pi\) | |||||||
\(908\) | 3.50688 | + | 55.8901i | 0.116380 | + | 1.85478i | ||||
\(909\) | − | 4.00000i | − | 0.132672i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.1660i | 0.701261i | 0.936514 | + | 0.350631i | \(0.114033\pi\) | ||||
−0.936514 | + | 0.350631i | \(0.885967\pi\) | |||||||
\(912\) | −12.9784 | + | 16.7201i | −0.429758 | + | 0.553657i | ||||
\(913\) | −44.8999 | + | 44.8999i | −1.48597 | + | 1.48597i | ||||
\(914\) | −5.29150 | + | 14.0000i | −0.175027 | + | 0.463079i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21.0000 | − | 18.5203i | −0.693860 | − | 0.611927i | ||||
\(917\) | 22.4499 | + | 22.4499i | 0.741362 | + | 0.741362i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.6235 | 1.57096 | 0.785478 | − | 0.618890i | \(-0.212417\pi\) | ||||
0.785478 | + | 0.618890i | \(0.212417\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.0000 | −0.395413 | ||||||||
\(922\) | −16.2921 | − | 36.0911i | −0.536552 | − | 1.18860i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −15.8745 | − | 14.0000i | −0.522233 | − | 0.460566i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.0000 | − | 44.9778i | 0.558655 | − | 1.47806i | ||||
\(927\) | 4.24264 | − | 4.24264i | 0.139347 | − | 0.139347i | ||||
\(928\) | −23.6294 | − | 38.5960i | −0.775673 | − | 1.26698i | ||||
\(929\) | 22.0000i | 0.721797i | 0.932605 | + | 0.360898i | \(0.117530\pi\) | ||||
−0.932605 | + | 0.360898i | \(0.882470\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.8745i | 0.520266i | ||||||||
\(932\) | 2.65095 | + | 42.2489i | 0.0868349 | + | 1.38391i | ||||
\(933\) | 22.4499 | − | 22.4499i | 0.734978 | − | 0.734978i | ||||
\(934\) | 47.6235 | + | 18.0000i | 1.55829 | + | 0.588978i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.00000 | + | 13.2288i | 0.228802 | + | 0.432395i | ||||
\(937\) | 14.9666 | + | 14.9666i | 0.488938 | + | 0.488938i | 0.907971 | − | 0.419033i | \(-0.137631\pi\) |
−0.419033 | + | 0.907971i | \(0.637631\pi\) | |||||||
\(938\) | −30.9352 | + | 13.9647i | −1.01007 | + | 0.455962i | ||||
\(939\) | −21.1660 | −0.690727 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 6.82058 | − | 3.07892i | 0.222226 | − | 0.100317i | ||||
\(943\) | 5.65685 | + | 5.65685i | 0.184213 | + | 0.184213i | ||||
\(944\) | 2.64575 | + | 21.0000i | 0.0861119 | + | 0.683492i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −56.0000 | − | 21.1660i | −1.82072 | − | 0.688166i | ||||
\(947\) | −36.7696 | + | 36.7696i | −1.19485 | + | 1.19485i | −0.219161 | + | 0.975689i | \(0.570332\pi\) |
−0.975689 | + | 0.219161i | \(0.929668\pi\) | |||||||
\(948\) | −10.5622 | + | 0.662739i | −0.343045 | + | 0.0215247i | ||||
\(949\) | − | 56.0000i | − | 1.81784i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(954\) | −5.29150 | + | 14.0000i | −0.171319 | + | 0.453267i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.0000 | + | 15.8745i | −0.452792 | + | 0.513418i | ||||
\(957\) | −29.9333 | − | 29.9333i | −0.967605 | − | 0.967605i | ||||
\(958\) | −24.6314 | − | 54.5646i | −0.795803 | − | 1.76290i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | 0.0967742 | ||||||||
\(962\) | −16.2921 | − | 36.0911i | −0.525279 | − | 1.16362i | ||||
\(963\) | −2.82843 | − | 2.82843i | −0.0911448 | − | 0.0911448i | ||||
\(964\) | −18.5203 | + | 21.0000i | −0.596497 | + | 0.676364i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.00000 | − | 10.5830i | 0.128698 | − | 0.340503i | ||||
\(967\) | 4.24264 | − | 4.24264i | 0.136434 | − | 0.136434i | −0.635591 | − | 0.772026i | \(-0.719244\pi\) |
0.772026 | + | 0.635591i | \(0.219244\pi\) | |||||||
\(968\) | 45.9541 | + | 14.1500i | 1.47702 | + | 0.454798i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.8745i | 0.509437i | 0.967015 | + | 0.254719i | \(0.0819828\pi\) | ||||
−0.967015 | + | 0.254719i | \(0.918017\pi\) | |||||||
\(972\) | −1.99607 | + | 0.125246i | −0.0640241 | + | 0.00401726i | ||||
\(973\) | 7.48331 | − | 7.48331i | 0.239904 | − | 0.239904i | ||||
\(974\) | −13.2288 | − | 5.00000i | −0.423877 | − | 0.160210i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.00000 | − | 23.8118i | −0.0960277 | − | 0.762196i | ||||
\(977\) | −14.9666 | − | 14.9666i | −0.478825 | − | 0.478825i | 0.425931 | − | 0.904756i | \(-0.359947\pi\) |
−0.904756 | + | 0.425931i | \(0.859947\pi\) | |||||||
\(978\) | 10.3117 | − | 4.65489i | 0.329733 | − | 0.148847i | ||||
\(979\) | −31.7490 | −1.01470 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | 20.4617 | − | 9.23676i | 0.652960 | − | 0.294757i | ||||
\(983\) | −16.9706 | − | 16.9706i | −0.541277 | − | 0.541277i | 0.382626 | − | 0.923903i | \(-0.375020\pi\) |
−0.923903 | + | 0.382626i | \(0.875020\pi\) | |||||||
\(984\) | −2.64575 | − | 5.00000i | −0.0843435 | − | 0.159394i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.50688 | − | 55.8901i | −0.111569 | − | 1.77810i | ||||
\(989\) | − | 32.0000i | − | 1.01754i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 47.6235i | − | 1.51281i | −0.654103 | − | 0.756406i | \(-0.726954\pi\) | ||
0.654103 | − | 0.756406i | \(-0.273046\pi\) | |||||||
\(992\) | 15.6294 | + | 25.5289i | 0.496233 | + | 0.810542i | ||||
\(993\) | −3.74166 | + | 3.74166i | −0.118738 | + | 0.118738i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 18.0000 | + | 15.8745i | 0.570352 | + | 0.503003i | ||||
\(997\) | 11.2250 | + | 11.2250i | 0.355498 | + | 0.355498i | 0.862151 | − | 0.506652i | \(-0.169117\pi\) |
−0.506652 | + | 0.862151i | \(0.669117\pi\) | |||||||
\(998\) | 9.23676 | + | 20.4617i | 0.292384 | + | 0.647705i | ||||
\(999\) | 5.29150 | 0.167416 |
(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 | 300.2.j.b.7.3 | yes | 8 | |
3.2 | odd | 2 | 900.2.k.h.307.2 | 8 | |||
4.3 | odd | 2 | inner | 300.2.j.b.7.4 | yes | 8 | |
5.2 | odd | 4 | inner | 300.2.j.b.43.1 | yes | 8 | |
5.3 | odd | 4 | inner | 300.2.j.b.43.4 | yes | 8 | |
5.4 | even | 2 | inner | 300.2.j.b.7.2 | yes | 8 | |
12.11 | even | 2 | 900.2.k.h.307.1 | 8 | |||
15.2 | even | 4 | 900.2.k.h.343.4 | 8 | |||
15.8 | even | 4 | 900.2.k.h.343.1 | 8 | |||
15.14 | odd | 2 | 900.2.k.h.307.3 | 8 | |||
20.3 | even | 4 | inner | 300.2.j.b.43.3 | yes | 8 | |
20.7 | even | 4 | inner | 300.2.j.b.43.2 | yes | 8 | |
20.19 | odd | 2 | inner | 300.2.j.b.7.1 | ✓ | 8 | |
60.23 | odd | 4 | 900.2.k.h.343.2 | 8 | |||
60.47 | odd | 4 | 900.2.k.h.343.3 | 8 | |||
60.59 | even | 2 | 900.2.k.h.307.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.j.b.7.1 | ✓ | 8 | 20.19 | odd | 2 | inner | |
300.2.j.b.7.2 | yes | 8 | 5.4 | even | 2 | inner | |
300.2.j.b.7.3 | yes | 8 | 1.1 | even | 1 | trivial | |
300.2.j.b.7.4 | yes | 8 | 4.3 | odd | 2 | inner | |
300.2.j.b.43.1 | yes | 8 | 5.2 | odd | 4 | inner | |
300.2.j.b.43.2 | yes | 8 | 20.7 | even | 4 | inner | |
300.2.j.b.43.3 | yes | 8 | 20.3 | even | 4 | inner | |
300.2.j.b.43.4 | yes | 8 | 5.3 | odd | 4 | inner | |
900.2.k.h.307.1 | 8 | 12.11 | even | 2 | |||
900.2.k.h.307.2 | 8 | 3.2 | odd | 2 | |||
900.2.k.h.307.3 | 8 | 15.14 | odd | 2 | |||
900.2.k.h.307.4 | 8 | 60.59 | even | 2 | |||
900.2.k.h.343.1 | 8 | 15.8 | even | 4 | |||
900.2.k.h.343.2 | 8 | 60.23 | odd | 4 | |||
900.2.k.h.343.3 | 8 | 60.47 | odd | 4 | |||
900.2.k.h.343.4 | 8 | 15.2 | even | 4 |