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 | 7.1 | ||
Root | \(-1.28897 - 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.7 |
Dual form | 300.2.j.b.43.1 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.28897 | − | 0.581861i | −0.911438 | − | 0.411438i | ||||
\(3\) | −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 | \(0.373376\pi\) | |||||||
\(8\) | −0.832353 | − | 2.70318i | −0.294281 | − | 0.955719i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.29150i | − | 1.59545i | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||
0.603023 | − | 0.797724i | \(-0.293963\pi\) | |||||||
\(12\) | 0.125246 | − | 1.99607i | 0.0361554 | − | 0.576217i | ||||
\(13\) | 3.74166 | − | 3.74166i | 1.03775 | − | 1.03775i | 0.0384901 | − | 0.999259i | \(-0.487745\pi\) |
0.999259 | − | 0.0384901i | \(-0.0122548\pi\) | |||||||
\(14\) | 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 | \(0.750000\pi\) | |||||||
\(18\) | 0.581861 | − | 1.28897i | 0.137146 | − | 0.303813i | ||||
\(19\) | −5.29150 | −1.21395 | −0.606977 | − | 0.794719i | \(-0.707618\pi\) | ||||
−0.606977 | + | 0.794719i | \(0.707618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | −3.07892 | + | 6.82058i | −0.656428 | + | 1.45415i | ||||
\(23\) | −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 | ||||
\(28\) | −3.99215 | − | 0.250492i | −0.754445 | − | 0.0473385i | ||||
\(29\) | − | 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 | \(-0.842379\pi\) | ||
0.879883 | − | 0.475191i | \(-0.157621\pi\) | |||||||
\(32\) | 2.95367 | − | 4.82450i | 0.522141 | − | 0.852859i | ||||
\(33\) | −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 | 0.329152 | − | 0.944277i | \(-0.393237\pi\) |
−0.944277 | + | 0.329152i | \(0.893237\pi\) | |||||||
\(38\) | 6.82058 | + | 3.07892i | 1.10644 | + | 0.499467i | ||||
\(39\) | −5.29150 | −0.847319 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | −2.57794 | − | 1.16372i | −0.397784 | − | 0.179566i | ||||
\(43\) | 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 | \(0.250000\pi\) | |||||||
\(48\) | 3.15980 | − | 2.45269i | 0.456077 | − | 0.354015i | ||||
\(49\) | 3.00000i | 0.428571i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.5622 | + | 0.662739i | 1.46472 | + | 0.0919053i | ||||
\(53\) | −7.48331 | + | 7.48331i | −1.02791 | + | 1.02791i | −0.0283132 | + | 0.999599i | \(0.509014\pi\) |
−0.999599 | + | 0.0283132i | \(0.990986\pi\) | |||||||
\(54\) | −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 | ||||
\(58\) | −4.65489 | + | 10.3117i | −0.611217 | + | 1.35400i | ||||
\(59\) | 5.29150 | 0.688895 | 0.344447 | − | 0.938806i | \(-0.388066\pi\) | ||||
0.344447 | + | 0.938806i | \(0.388066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | −3.07892 | + | 6.82058i | −0.391023 | + | 0.866214i | ||||
\(63\) | −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 | \(\pi\) | |||||||||
\(72\) | 2.70318 | − | 0.832353i | 0.318573 | − | 0.0980937i | ||||
\(73\) | 7.48331 | − | 7.48331i | 0.875856 | − | 0.875856i | −0.117247 | − | 0.993103i | \(-0.537407\pi\) |
0.993103 | + | 0.117247i | \(0.0374069\pi\) | |||||||
\(74\) | 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 | ||||
\(78\) | 6.82058 | + | 3.07892i | 0.772278 | + | 0.348619i | ||||
\(79\) | 5.29150 | 0.595341 | 0.297670 | − | 0.954669i | \(-0.403790\pi\) | ||||
0.297670 | + | 0.954669i | \(0.403790\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 2.57794 | + | 1.16372i | 0.284685 | + | 0.128512i | ||||
\(83\) | 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 | ||||
\(88\) | −14.3039 | + | 4.40440i | −1.52480 | + | 0.469510i | ||||
\(89\) | 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 | ||||||||
\(92\) | 0.500983 | − | 7.98430i | 0.0522311 | − | 0.832421i | ||||
\(93\) | −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 | 0.216473 | − | 0.976289i | \(-0.430545\pi\) |
−0.976289 | + | 0.216473i | \(0.930545\pi\) | |||||||
\(98\) | 1.74558 | − | 3.86690i | 0.176330 | − | 0.390616i | ||||
\(99\) | 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 | \(0.311934\pi\) | |||||||
\(108\) | 1.99607 | + | 0.125246i | 0.192072 | + | 0.0120518i | ||||
\(109\) | 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 | ||||||||
\(112\) | −4.90538 | − | 6.31959i | −0.463515 | − | 0.597145i | ||||
\(113\) | 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 | ||||
\(118\) | −6.82058 | − | 3.07892i | −0.627885 | − | 0.283437i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.0000 | −1.54545 | ||||||||
\(122\) | −7.73381 | − | 3.49117i | −0.700186 | − | 0.316075i | ||||
\(123\) | 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 | \(0.278283\pi\) | |||||||
\(128\) | 11.1441 | − | 1.95171i | 0.985008 | − | 0.172508i | ||||
\(129\) | − | 8.00000i | − | 0.704361i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.8745i | 1.38696i | 0.720475 | + | 0.693481i | \(0.243924\pi\) | ||||
−0.720475 | + | 0.693481i | \(0.756076\pi\) | |||||||
\(132\) | −10.5622 | − | 0.662739i | −0.919324 | − | 0.0576840i | ||||
\(133\) | 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 | \(0.750000\pi\) | |||||||
\(138\) | 2.32744 | − | 5.15587i | 0.198125 | − | 0.438897i | ||||
\(139\) | 5.29150 | 0.448819 | 0.224410 | − | 0.974495i | \(-0.427955\pi\) | ||||
0.224410 | + | 0.974495i | \(0.427955\pi\) | |||||||
\(140\) | 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 | ||||
\(148\) | 0.662739 | − | 10.5622i | 0.0544768 | − | 0.868210i | ||||
\(149\) | 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 | \(0.223528\pi\) | ||||
−0.763401 | + | 0.645925i | \(0.776472\pi\) | |||||||
\(152\) | 4.40440 | + | 14.3039i | 0.357244 | + | 1.16020i | ||||
\(153\) | 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 | 0.541855 | − | 0.840472i | \(-0.317722\pi\) |
−0.840472 | + | 0.541855i | \(0.817722\pi\) | |||||||
\(158\) | −6.82058 | − | 3.07892i | −0.542616 | − | 0.244946i | ||||
\(159\) | 10.5830 | 0.839287 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.00000 | 0.630488 | ||||||||
\(162\) | 1.28897 | + | 0.581861i | 0.101271 | + | 0.0457153i | ||||
\(163\) | 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 | \(0.403692\pi\) | |||||||
\(168\) | −1.66471 | − | 5.40636i | −0.128435 | − | 0.417110i | ||||
\(169\) | − | 15.0000i | − | 1.15385i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 5.29150i | − | 0.404651i | ||||||
\(172\) | −1.00197 | + | 15.9686i | −0.0763992 | + | 1.21759i | ||||
\(173\) | 7.48331 | − | 7.48331i | 0.568946 | − | 0.568946i | −0.362887 | − | 0.931833i | \(-0.618209\pi\) |
0.931833 | + | 0.362887i | \(0.118209\pi\) | |||||||
\(174\) | 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 | ||||
\(178\) | 3.49117 | − | 7.73381i | 0.261674 | − | 0.579673i | ||||
\(179\) | −5.29150 | −0.395505 | −0.197753 | − | 0.980252i | \(-0.563364\pi\) | ||||
−0.197753 | + | 0.980252i | \(0.563364\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 6.15784 | − | 13.6412i | 0.456449 | − | 1.01115i | ||||
\(183\) | −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 | \(0.125068\pi\) | ||||
−0.923798 | + | 0.382880i | \(0.874932\pi\) | |||||||
\(192\) | 7.85905 | + | 1.49509i | 0.567178 | + | 0.107899i | ||||
\(193\) | 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 | \(-0.978118\pi\) |
−0.0686902 | − | 0.997638i | \(-0.521882\pi\) | |||||||
\(198\) | −6.82058 | − | 3.07892i | −0.484717 | − | 0.218809i | ||||
\(199\) | 5.29150 | 0.375105 | 0.187552 | − | 0.982255i | \(-0.439945\pi\) | ||||
0.187552 | + | 0.982255i | \(0.439945\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.0000 | −0.846415 | ||||||||
\(202\) | 5.15587 | + | 2.32744i | 0.362766 | + | 0.163758i | ||||
\(203\) | 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 | ||||
\(208\) | 12.9784 | + | 16.7201i | 0.899891 | + | 1.15933i | ||||
\(209\) | 28.0000i | 1.93680i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 26.4575i | − | 1.82141i | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||
0.413057 | − | 0.910705i | \(-0.364461\pi\) | |||||||
\(212\) | −21.1245 | − | 1.32548i | −1.45083 | − | 0.0910341i | ||||
\(213\) | 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 | ||||
\(218\) | 1.16372 | − | 2.57794i | 0.0788172 | − | 0.174600i | ||||
\(219\) | −10.5830 | −0.715133 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.07892 | − | 6.82058i | 0.206643 | − | 0.457767i | ||||
\(223\) | −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 | \(-0.129513\pi\) | |||||||
\(228\) | −0.662739 | + | 10.5622i | −0.0438909 | + | 0.699501i | ||||
\(229\) | 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 | ||||||
\(232\) | −21.6255 | + | 6.65882i | −1.41978 | + | 0.437173i | ||||
\(233\) | −14.9666 | + | 14.9666i | −0.980497 | + | 0.980497i | −0.999813 | − | 0.0193169i | \(-0.993851\pi\) |
0.0193169 | + | 0.999813i | \(0.493851\pi\) | |||||||
\(234\) | −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 | \(-0.611199\pi\) | ||||
−0.342279 | + | 0.939598i | \(0.611199\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 21.9125 | + | 9.89164i | 1.40859 | + | 0.635858i | ||||
\(243\) | 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 | ||||
\(248\) | −14.3039 | + | 4.40440i | −0.908298 | + | 0.279679i | ||||
\(249\) | − | 12.0000i | − | 0.760469i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 5.29150i | − | 0.333997i | −0.985957 | − | 0.166998i | \(-0.946593\pi\) | ||
0.985957 | − | 0.166998i | \(-0.0534075\pi\) | |||||||
\(252\) | 0.250492 | − | 3.99215i | 0.0157795 | − | 0.251482i | ||||
\(253\) | −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 | 0.997928 | − | 0.0643356i | \(-0.0204928\pi\) |
−0.0643356 | + | 0.997928i | \(0.520493\pi\) | |||||||
\(258\) | −4.65489 | + | 10.3117i | −0.289801 | + | 0.641981i | ||||
\(259\) | 10.5830 | 0.657596 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | 0.495188 | ||||||||
\(262\) | 9.23676 | − | 20.4617i | 0.570649 | − | 1.26413i | ||||
\(263\) | 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 | ||||
\(268\) | 23.9529 | + | 1.50295i | 1.46316 | + | 0.0918073i | ||||
\(269\) | − | 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 | \(-0.839855\pi\) | ||
0.876087 | − | 0.482154i | \(-0.160145\pi\) | |||||||
\(272\) | 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 | \(0.0424447\pi\) |
0.132949 | + | 0.991123i | \(0.457555\pi\) | |||||||
\(278\) | −6.82058 | − | 3.07892i | −0.409071 | − | 0.184661i | ||||
\(279\) | 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 | ||||
\(288\) | 4.82450 | + | 2.95367i | 0.284286 | + | 0.174047i | ||||
\(289\) | − | 17.0000i | − | 1.00000i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.5830i | 0.620387i | ||||||||
\(292\) | 21.1245 | + | 1.32548i | 1.23622 | + | 0.0775677i | ||||
\(293\) | 14.9666 | − | 14.9666i | 0.874360 | − | 0.874360i | −0.118584 | − | 0.992944i | \(-0.537836\pi\) |
0.992944 | + | 0.118584i | \(0.0378355\pi\) | |||||||
\(294\) | −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 | ||||
\(298\) | 2.32744 | − | 5.15587i | 0.134825 | − | 0.298672i | ||||
\(299\) | −21.1660 | −1.22406 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0000 | −0.922225 | ||||||||
\(302\) | 9.23676 | − | 20.4617i | 0.531516 | − | 1.17744i | ||||
\(303\) | 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 | \(0.138747\pi\) | |||||||
\(308\) | −1.32548 | + | 21.1245i | −0.0755261 | + | 1.20368i | ||||
\(309\) | 6.00000i | 0.341328i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 31.7490i | − | 1.80032i | −0.435558 | − | 0.900161i | \(-0.643449\pi\) | ||
0.435558 | − | 0.900161i | \(-0.356551\pi\) | |||||||
\(312\) | 4.40440 | + | 14.3039i | 0.249350 | + | 0.809798i | ||||
\(313\) | −14.9666 | + | 14.9666i | −0.845964 | + | 0.845964i | −0.989627 | − | 0.143663i | \(-0.954112\pi\) |
0.143663 | + | 0.989627i | \(0.454112\pi\) | |||||||
\(314\) | 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 | \(0.750000\pi\) | |||||||
\(318\) | −13.6412 | − | 6.15784i | −0.764958 | − | 0.345314i | ||||
\(319\) | −42.3320 | −2.37014 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.00000 | 0.223258 | ||||||||
\(322\) | −10.3117 | − | 4.65489i | −0.574651 | − | 0.259407i | ||||
\(323\) | 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 | ||||
\(328\) | 1.66471 | + | 5.40636i | 0.0919180 | + | 0.298516i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.29150i | 0.290847i | 0.989369 | + | 0.145424i | \(0.0464545\pi\) | ||||
−0.989369 | + | 0.145424i | \(0.953545\pi\) | |||||||
\(332\) | −1.50295 | + | 23.9529i | −0.0824851 | + | 1.31459i | ||||
\(333\) | 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 | 0.880916 | − | 0.473273i | \(-0.156928\pi\) |
−0.473273 | + | 0.880916i | \(0.656928\pi\) | |||||||
\(338\) | −8.72791 | + | 19.3345i | −0.474736 | + | 1.05166i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.0000 | −1.51629 | ||||||||
\(342\) | −3.07892 | + | 6.82058i | −0.166489 | + | 0.368815i | ||||
\(343\) | −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 | \(0.354388\pi\) | |||||||
\(348\) | −15.9686 | − | 1.00197i | −0.856007 | − | 0.0537110i | ||||
\(349\) | − | 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 | ||||||
\(352\) | −25.5289 | − | 15.6294i | −1.36069 | − | 0.833048i | ||||
\(353\) | 14.9666 | − | 14.9666i | 0.796593 | − | 0.796593i | −0.185963 | − | 0.982557i | \(-0.559541\pi\) |
0.982557 | + | 0.185963i | \(0.0595406\pi\) | |||||||
\(354\) | 2.64575 | + | 7.00000i | 0.140620 | + | 0.372046i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.00000 | + | 7.93725i | −0.476999 | + | 0.420674i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.82058 | + | 3.07892i | 0.360479 | + | 0.162726i | ||||
\(359\) | 10.5830 | 0.558550 | 0.279275 | − | 0.960211i | \(-0.409906\pi\) | ||||
0.279275 | + | 0.960211i | \(0.409906\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | 0.473684 | ||||||||
\(362\) | −2.57794 | − | 1.16372i | −0.135493 | − | 0.0611639i | ||||
\(363\) | 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 | \(0.0943274\pi\) | |||||||
\(368\) | 12.6392 | − | 9.81076i | 0.658863 | − | 0.511421i | ||||
\(369\) | − | 2.00000i | − | 0.104116i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 21.1660i | − | 1.09888i | ||||||
\(372\) | −10.5622 | − | 0.662739i | −0.547626 | − | 0.0343614i | ||||
\(373\) | −18.7083 | + | 18.7083i | −0.968678 | + | 0.968678i | −0.999524 | − | 0.0308458i | \(-0.990180\pi\) |
0.0308458 | + | 0.999524i | \(0.490180\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −29.9333 | − | 29.9333i | −1.54164 | − | 1.54164i | ||||
\(378\) | 1.16372 | − | 2.57794i | 0.0598554 | − | 0.132595i | ||||
\(379\) | 5.29150 | 0.271806 | 0.135903 | − | 0.990722i | \(-0.456606\pi\) | ||||
0.135903 | + | 0.990722i | \(0.456606\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.00000 | 0.102463 | ||||||||
\(382\) | 6.15784 | − | 13.6412i | 0.315062 | − | 0.697942i | ||||
\(383\) | −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 | ||||
\(388\) | 1.32548 | − | 21.1245i | 0.0672909 | − | 1.07243i | ||||
\(389\) | − | 24.0000i | − | 1.21685i | −0.793612 | − | 0.608424i | \(-0.791802\pi\) | ||
0.793612 | − | 0.608424i | \(-0.208198\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 8.10954 | − | 2.49706i | 0.409594 | − | 0.126120i | ||||
\(393\) | 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 | 0.606951 | − | 0.794739i | \(-0.292392\pi\) |
−0.794739 | + | 0.606951i | \(0.792392\pi\) | |||||||
\(398\) | −6.82058 | − | 3.07892i | −0.341885 | − | 0.154332i | ||||
\(399\) | −10.5830 | −0.529813 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.0000 | 0.499376 | 0.249688 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249688 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(402\) | 15.4676 | + | 6.98233i | 0.771454 | + | 0.348247i | ||||
\(403\) | −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 | ||||||||
\(412\) | 0.751475 | − | 11.9764i | 0.0370225 | − | 0.590037i | ||||
\(413\) | −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 | ||||
\(418\) | 16.2921 | − | 36.0911i | 0.796873 | − | 1.76527i | ||||
\(419\) | 15.8745 | 0.775520 | 0.387760 | − | 0.921760i | \(-0.373249\pi\) | ||||
0.387760 | + | 0.921760i | \(0.373249\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0000 | 1.65706 | 0.828529 | − | 0.559946i | \(-0.189178\pi\) | ||||
0.828529 | + | 0.559946i | \(0.189178\pi\) | |||||||
\(422\) | −15.3946 | + | 34.1029i | −0.749397 | + | 1.66010i | ||||
\(423\) | 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 | ||||
\(428\) | −7.98430 | − | 0.500983i | −0.385936 | − | 0.0242159i | ||||
\(429\) | 28.0000i | 1.35185i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.5830i | 0.509765i | 0.966972 | + | 0.254883i | \(0.0820369\pi\) | ||||
−0.966972 | + | 0.254883i | \(0.917963\pi\) | |||||||
\(432\) | 2.45269 | + | 3.15980i | 0.118005 | + | 0.152026i | ||||
\(433\) | −7.48331 | + | 7.48331i | −0.359625 | + | 0.359625i | −0.863675 | − | 0.504050i | \(-0.831843\pi\) |
0.504050 | + | 0.863675i | \(0.331843\pi\) | |||||||
\(434\) | −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 | ||||
\(438\) | 13.6412 | + | 6.15784i | 0.651799 | + | 0.294233i | ||||
\(439\) | 5.29150 | 0.252550 | 0.126275 | − | 0.991995i | \(-0.459698\pi\) | ||||
0.126275 | + | 0.991995i | \(0.459698\pi\) | |||||||
\(440\) | 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 | ||||
\(448\) | 2.99018 | − | 15.7181i | 0.141273 | − | 0.742611i | ||||
\(449\) | 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 | 0.510075 | − | 0.860130i | \(-0.329618\pi\) |
−0.860130 | + | 0.510075i | \(0.829618\pi\) | |||||||
\(458\) | 8.14605 | − | 18.0455i | 0.380640 | − | 0.843213i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.0000 | −1.30409 | −0.652045 | − | 0.758180i | \(-0.726089\pi\) | ||||
−0.652045 | + | 0.758180i | \(0.726089\pi\) | |||||||
\(462\) | −6.15784 | + | 13.6412i | −0.286489 | + | 0.634644i | ||||
\(463\) | −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 | \(-0.0633445\pi\) | |||||||
\(468\) | −0.662739 | + | 10.5622i | −0.0306351 | + | 0.488239i | ||||
\(469\) | 24.0000i | 1.10822i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.29150i | 0.243820i | ||||||||
\(472\) | −4.40440 | − | 14.3039i | −0.202729 | − | 0.658390i | ||||
\(473\) | 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 | ||||
\(478\) | 13.6412 | + | 6.15784i | 0.623932 | + | 0.281653i | ||||
\(479\) | 42.3320 | 1.93420 | 0.967100 | − | 0.254398i | \(-0.0818772\pi\) | ||||
0.967100 | + | 0.254398i | \(0.0818772\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.0000 | −1.27669 | ||||||||
\(482\) | −18.0455 | − | 8.14605i | −0.821952 | − | 0.371043i | ||||
\(483\) | −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 | \(0.322752\pi\) | |||||||
\(488\) | −4.99412 | − | 16.2191i | −0.226073 | − | 0.734204i | ||||
\(489\) | − | 8.00000i | − | 0.361773i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.8745i | 0.716407i | 0.933644 | + | 0.358203i | \(0.116611\pi\) | ||||
−0.933644 | + | 0.358203i | \(0.883389\pi\) | |||||||
\(492\) | −0.250492 | + | 3.99215i | −0.0112930 | + | 0.179980i | ||||
\(493\) | 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 | ||||||||
\(498\) | −6.98233 | + | 15.4676i | −0.312886 | + | 0.693120i | ||||
\(499\) | −15.8745 | −0.710641 | −0.355320 | − | 0.934745i | \(-0.615628\pi\) | ||||
−0.355320 | + | 0.934745i | \(0.615628\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.0000 | 0.536120 | ||||||||
\(502\) | −3.07892 | + | 6.82058i | −0.137419 | + | 0.304417i | ||||
\(503\) | 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 | ||||
\(508\) | −3.99215 | − | 0.250492i | −0.177123 | − | 0.0111138i | ||||
\(509\) | − | 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 | ||||||||
\(512\) | 17.6698 | + | 14.1343i | 0.780903 | + | 0.624653i | ||||
\(513\) | −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 | ||||||||
\(518\) | −13.6412 | − | 6.15784i | −0.599358 | − | 0.270560i | ||||
\(519\) | −10.5830 | −0.464542 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.0000 | 0.613351 | 0.306676 | − | 0.951814i | \(-0.400783\pi\) | ||||
0.306676 | + | 0.951814i | \(0.400783\pi\) | |||||||
\(522\) | −10.3117 | − | 4.65489i | −0.451333 | − | 0.203739i | ||||
\(523\) | 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 | ||||||||
\(528\) | −12.9784 | − | 16.7201i | −0.564813 | − | 0.727648i | ||||
\(529\) | − | 7.00000i | − | 0.304348i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.29150i | 0.229632i | ||||||||
\(532\) | 21.1245 | + | 1.32548i | 0.915862 | + | 0.0574667i | ||||
\(533\) | −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 | ||||
\(538\) | −13.9647 | + | 30.9352i | −0.602059 | + | 1.33371i | ||||
\(539\) | 15.8745 | 0.683763 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | −9.23676 | + | 20.4617i | −0.396753 | + | 0.878906i | ||||
\(543\) | −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 | ||||||||
\(552\) | 10.8127 | − | 3.32941i | 0.460220 | − | 0.141709i | ||||
\(553\) | −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 | 0.0476304 | − | 0.998865i | \(-0.484833\pi\) |
−0.998865 | + | 0.0476304i | \(0.984833\pi\) | |||||||
\(558\) | −6.82058 | − | 3.07892i | −0.288738 | − | 0.130341i | ||||
\(559\) | 42.3320 | 1.79045 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −33.5132 | − | 15.1284i | −1.41367 | − | 0.638152i | ||||
\(563\) | −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 | \(0.0353161\pi\) | ||||
−0.993852 | + | 0.110721i | \(0.964684\pi\) | |||||||
\(572\) | 3.50688 | − | 55.8901i | 0.146630 | − | 2.33688i | ||||
\(573\) | 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 | 0.997989 | − | 0.0633857i | \(-0.0201898\pi\) |
−0.0633857 | + | 0.997989i | \(0.520190\pi\) | |||||||
\(578\) | −9.89164 | + | 21.9125i | −0.411438 | + | 0.911438i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0000 | −0.995688 | ||||||||
\(582\) | 6.15784 | − | 13.6412i | 0.255251 | − | 0.565444i | ||||
\(583\) | 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 | \(0.446105\pi\) | |||||||
\(588\) | 5.98822 | + | 0.375737i | 0.246950 | + | 0.0154952i | ||||
\(589\) | 28.0000i | 1.15372i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.1660i | 0.870653i | ||||||||
\(592\) | 16.7201 | − | 12.9784i | 0.687191 | − | 0.533410i | ||||
\(593\) | −14.9666 | + | 14.9666i | −0.614606 | + | 0.614606i | −0.944143 | − | 0.329537i | \(-0.893107\pi\) |
0.329537 | + | 0.944143i | \(0.393107\pi\) | |||||||
\(594\) | 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 | ||||
\(598\) | 27.2823 | + | 12.3157i | 1.11566 | + | 0.503625i | ||||
\(599\) | −31.7490 | −1.29723 | −0.648615 | − | 0.761117i | \(-0.724651\pi\) | ||||
−0.648615 | + | 0.761117i | \(0.724651\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0000 | −0.571072 | −0.285536 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285536 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(602\) | 20.6235 | + | 9.30978i | 0.840550 | + | 0.379438i | ||||
\(603\) | 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 | \(0.00760667\pi\) | |||||||
\(608\) | −15.6294 | + | 25.5289i | −0.633855 | + | 1.03533i | ||||
\(609\) | − | 16.0000i | − | 0.648353i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.2250 | − | 11.2250i | 0.453372 | − | 0.453372i | −0.443100 | − | 0.896472i | \(-0.646121\pi\) |
0.896472 | + | 0.443100i | \(0.146121\pi\) | |||||||
\(614\) | −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 | \(0.0746782\pi\) |
0.232462 | + | 0.972605i | \(0.425322\pi\) | |||||||
\(618\) | 3.49117 | − | 7.73381i | 0.140435 | − | 0.311099i | ||||
\(619\) | −5.29150 | −0.212683 | −0.106342 | − | 0.994330i | \(-0.533914\pi\) | ||||
−0.106342 | + | 0.994330i | \(0.533914\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | −18.4735 | + | 40.9235i | −0.740720 | + | 1.64088i | ||||
\(623\) | −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 | ||||
\(628\) | 0.662739 | − | 10.5622i | 0.0264461 | − | 0.421479i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.29150i | 0.210651i | 0.994438 | + | 0.105326i | \(0.0335885\pi\) | ||||
−0.994438 | + | 0.105326i | \(0.966411\pi\) | |||||||
\(632\) | −4.40440 | − | 14.3039i | −0.175197 | − | 0.568978i | ||||
\(633\) | −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 | ||||
\(638\) | 54.5646 | + | 24.6314i | 2.16023 | + | 0.975164i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.0000 | −1.18493 | −0.592464 | − | 0.805597i | \(-0.701845\pi\) | ||||
−0.592464 | + | 0.805597i | \(0.701845\pi\) | |||||||
\(642\) | −5.15587 | − | 2.32744i | −0.203486 | − | 0.0918569i | ||||
\(643\) | 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 | \(0.0936157\pi\) | |||||||
\(648\) | 0.832353 | + | 2.70318i | 0.0326979 | + | 0.106191i | ||||
\(649\) | − | 28.0000i | − | 1.09910i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 10.5830i | − | 0.414781i | ||||||
\(652\) | −1.00197 | + | 15.9686i | −0.0392400 | + | 0.625378i | ||||
\(653\) | 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 | \(-0.399942\pi\) | ||||
0.309192 | + | 0.951000i | \(0.399942\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.0000 | 0.700119 | 0.350059 | − | 0.936727i | \(-0.386161\pi\) | ||||
0.350059 | + | 0.936727i | \(0.386161\pi\) | |||||||
\(662\) | 3.07892 | − | 6.82058i | 0.119666 | − | 0.265089i | ||||
\(663\) | 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 | ||||
\(668\) | −23.9529 | − | 1.50295i | −0.926765 | − | 0.0581509i | ||||
\(669\) | 14.0000i | 0.541271i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 31.7490i | − | 1.22566i | ||||||
\(672\) | 5.90735 | − | 9.64900i | 0.227881 | − | 0.372218i | ||||
\(673\) | −7.48331 | + | 7.48331i | −0.288461 | + | 0.288461i | −0.836471 | − | 0.548011i | \(-0.815385\pi\) |
0.548011 | + | 0.836471i | \(0.315385\pi\) | |||||||
\(674\) | −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 | 0.933581 | − | 0.358367i | \(-0.116666\pi\) |
−0.358367 | + | 0.933581i | \(0.616666\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.1660 | 0.812277 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.0000 | −1.07296 | ||||||||
\(682\) | 36.0911 | + | 16.2921i | 1.38200 | + | 0.623857i | ||||
\(683\) | −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 | ||||
\(688\) | −25.2784 | + | 19.6215i | −0.963729 | + | 0.748063i | ||||
\(689\) | 56.0000i | 2.13343i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.0405i | 1.40909i | 0.709660 | + | 0.704544i | \(0.248848\pi\) | ||||
−0.709660 | + | 0.704544i | \(0.751152\pi\) | |||||||
\(692\) | 21.1245 | + | 1.32548i | 0.803032 | + | 0.0503871i | ||||
\(693\) | −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 | ||||||||
\(698\) | −1.16372 | + | 2.57794i | −0.0440475 | + | 0.0975763i | ||||
\(699\) | 21.1660 | 0.800572 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.0000 | 1.35970 | 0.679851 | − | 0.733351i | \(-0.262045\pi\) | ||||
0.679851 | + | 0.733351i | \(0.262045\pi\) | |||||||
\(702\) | −3.07892 | + | 6.82058i | −0.116206 | + | 0.257426i | ||||
\(703\) | 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 | ||||
\(708\) | 0.662739 | − | 10.5622i | 0.0249072 | − | 0.396953i | ||||
\(709\) | − | 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 | ||||||||
\(712\) | 16.2191 | − | 4.99412i | 0.607836 | − | 0.187162i | ||||
\(713\) | −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 | ||||
\(718\) | −13.6412 | − | 6.15784i | −0.509083 | − | 0.229808i | ||||
\(719\) | −31.7490 | −1.18404 | −0.592019 | − | 0.805924i | \(-0.701669\pi\) | ||||
−0.592019 | + | 0.805924i | \(0.701669\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | −11.6007 | − | 5.23675i | −0.431734 | − | 0.194892i | ||||
\(723\) | −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 | \(0.437787\pi\) | |||||||
\(728\) | 28.6078 | − | 8.80879i | 1.06027 | − | 0.326476i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.751475 | − | 11.9764i | 0.0277753 | − | 0.442662i | ||||
\(733\) | 26.1916 | − | 26.1916i | 0.967409 | − | 0.967409i | −0.0320765 | − | 0.999485i | \(-0.510212\pi\) |
0.999485 | + | 0.0320765i | \(0.0102120\pi\) | |||||||
\(734\) | −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 | ||||
\(738\) | −1.16372 | + | 2.57794i | −0.0428372 | + | 0.0948951i | ||||
\(739\) | −26.4575 | −0.973255 | −0.486628 | − | 0.873609i | \(-0.661773\pi\) | ||||
−0.486628 | + | 0.873609i | \(0.661773\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.0000 | 1.02861 | ||||||||
\(742\) | −12.3157 | + | 27.2823i | −0.452123 | + | 1.00156i | ||||
\(743\) | 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 | \(-0.839647\pi\) | ||
0.875772 | − | 0.482724i | \(-0.160353\pi\) | |||||||
\(752\) | 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 | \(-0.917031\pi\) |
−0.257715 | − | 0.966221i | \(-0.582969\pi\) | |||||||
\(758\) | −6.82058 | − | 3.07892i | −0.247734 | − | 0.111831i | ||||
\(759\) | 21.1660 | 0.768278 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.0000 | 1.52250 | 0.761249 | − | 0.648459i | \(-0.224586\pi\) | ||||
0.761249 | + | 0.648459i | \(0.224586\pi\) | |||||||
\(762\) | −2.57794 | − | 1.16372i | −0.0933887 | − | 0.0421572i | ||||
\(763\) | −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 | ||||
\(768\) | 8.15391 | + | 13.7664i | 0.294229 | + | 0.496752i | ||||
\(769\) | − | 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 | −0.923033 | − | 0.384721i | \(-0.874298\pi\) |
0.384721 | + | 0.923033i | \(0.374298\pi\) | |||||||
\(774\) | 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 | ||||
\(778\) | −13.9647 | + | 30.9352i | −0.500657 | + | 1.10908i | ||||
\(779\) | 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 | \(0.0568121\pi\) | |||||||
\(788\) | 2.65095 | − | 42.2489i | 0.0944363 | − | 1.50506i | ||||
\(789\) | − | 12.0000i | − | 0.427211i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.40440 | − | 14.3039i | −0.156503 | − | 0.508267i | ||||
\(793\) | 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 | 0.982337 | − | 0.187119i | \(-0.0599151\pi\) |
−0.187119 | + | 0.982337i | \(0.559915\pi\) | |||||||
\(798\) | 13.6412 | + | 6.15784i | 0.482892 | + | 0.217985i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | −12.8897 | − | 5.81861i | −0.455150 | − | 0.205462i | ||||
\(803\) | −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 | ||||
\(808\) | 3.32941 | + | 10.8127i | 0.117128 | + | 0.380390i | ||||
\(809\) | 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 | \(-0.774629\pi\) | ||
0.759648 | − | 0.650334i | \(-0.225371\pi\) | |||||||
\(812\) | −2.00393 | + | 31.9372i | −0.0703243 | + | 1.12078i | ||||
\(813\) | −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 | ||||
\(818\) | 5.81861 | − | 12.8897i | 0.203443 | − | 0.450677i | ||||
\(819\) | −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 | \(0.363049\pi\) | |||||||
\(828\) | 7.98430 | + | 0.500983i | 0.277474 | + | 0.0174104i | ||||
\(829\) | 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 | ||||||
\(832\) | −7.91128 | + | 41.5862i | −0.274274 | + | 1.44174i | ||||
\(833\) | 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 | ||||
\(838\) | −20.4617 | − | 9.23676i | −0.706839 | − | 0.319078i | ||||
\(839\) | −31.7490 | −1.09610 | −0.548049 | − | 0.836446i | \(-0.684629\pi\) | ||||
−0.548049 | + | 0.836446i | \(0.684629\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −35.0000 | −1.20690 | ||||||||
\(842\) | −43.8249 | − | 19.7833i | −1.51031 | − | 0.681777i | ||||
\(843\) | −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 | ||||
\(848\) | −25.9568 | − | 33.4401i | −0.891361 | − | 1.14834i | ||||
\(849\) | − | 28.0000i | − | 0.960958i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.1660i | 0.725561i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.2250 | − | 11.2250i | 0.384336 | − | 0.384336i | −0.488326 | − | 0.872661i | \(-0.662392\pi\) |
0.872661 | + | 0.488326i | \(0.162392\pi\) | |||||||
\(854\) | 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 | \(0.00724526\pi\) |
0.0227597 | + | 0.999741i | \(0.492755\pi\) | |||||||
\(858\) | 16.2921 | − | 36.0911i | 0.556203 | − | 1.23213i | ||||
\(859\) | −5.29150 | −0.180544 | −0.0902719 | − | 0.995917i | \(-0.528774\pi\) | ||||
−0.0902719 | + | 0.995917i | \(0.528774\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00000 | −0.136320 | ||||||||
\(862\) | 6.15784 | − | 13.6412i | 0.209737 | − | 0.464619i | ||||
\(863\) | 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 | ||||
\(868\) | −1.32548 | + | 21.1245i | −0.0449896 | + | 0.717011i | ||||
\(869\) | − | 28.0000i | − | 0.949835i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 63.4980i | − | 2.15155i | ||||||
\(872\) | 5.40636 | − | 1.66471i | 0.183083 | − | 0.0563740i | ||||
\(873\) | 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 | 0.767453 | − | 0.641106i | \(-0.221524\pi\) |
−0.641106 | + | 0.767453i | \(0.721524\pi\) | |||||||
\(878\) | −6.82058 | − | 3.07892i | −0.230183 | − | 0.103908i | ||||
\(879\) | −21.1660 | −0.713912 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.00000 | −0.0673817 | −0.0336909 | − | 0.999432i | \(-0.510726\pi\) | ||||
−0.0336909 | + | 0.999432i | \(0.510726\pi\) | |||||||
\(882\) | 3.86690 | + | 1.74558i | 0.130205 | + | 0.0587768i | ||||
\(883\) | −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 | \(0.456579\pi\) | |||||||
\(888\) | 14.3039 | − | 4.40440i | 0.480007 | − | 0.147802i | ||||
\(889\) | − | 4.00000i | − | 0.134156i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.29150i | 0.177272i | ||||||||
\(892\) | 1.75344 | − | 27.9450i | 0.0587096 | − | 0.935669i | ||||
\(893\) | 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 | ||||
\(898\) | 12.8009 | − | 28.3573i | 0.427173 | − | 0.946295i | ||||
\(899\) | −42.3320 | −1.41185 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 6.15784 | − | 13.6412i | 0.205034 | − | 0.454201i | ||||
\(903\) | 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 | \(0.335582\pi\) | |||||||
\(908\) | 55.8901 | + | 3.50688i | 1.85478 | + | 0.116380i | ||||
\(909\) | − | 4.00000i | − | 0.132672i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 21.1660i | − | 0.701261i | −0.936514 | − | 0.350631i | \(-0.885967\pi\) | ||
0.936514 | − | 0.350631i | \(-0.114033\pi\) | |||||||
\(912\) | −16.7201 | + | 12.9784i | −0.553657 | + | 0.429758i | ||||
\(913\) | 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 | \(-0.787583\pi\) | ||||
−0.785478 | + | 0.618890i | \(0.787583\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.0000 | −0.395413 | ||||||||
\(922\) | 36.0911 | + | 16.2921i | 1.18860 | + | 0.536552i | ||||
\(923\) | 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 | ||||
\(928\) | −38.5960 | − | 23.6294i | −1.26698 | − | 0.775673i | ||||
\(929\) | 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 | ||||||
\(932\) | −42.2489 | − | 2.65095i | −1.38391 | − | 0.0868349i | ||||
\(933\) | −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 | 0.419033 | − | 0.907971i | \(-0.362369\pi\) |
−0.907971 | + | 0.419033i | \(0.862369\pi\) | |||||||
\(938\) | 13.9647 | − | 30.9352i | 0.455962 | − | 1.01007i | ||||
\(939\) | 21.1660 | 0.690727 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 3.07892 | − | 6.82058i | 0.100317 | − | 0.222226i | ||||
\(943\) | 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 | \(0.929668\pi\) | |||||||
\(948\) | 0.662739 | − | 10.5622i | 0.0215247 | − | 0.343045i | ||||
\(949\) | − | 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 | ||||
\(958\) | −54.5646 | − | 24.6314i | −1.76290 | − | 0.795803i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | 0.0967742 | ||||||||
\(962\) | 36.0911 | + | 16.2921i | 1.16362 | + | 0.525279i | ||||
\(963\) | −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 | \(0.219244\pi\) | |||||||
\(968\) | 14.1500 | + | 45.9541i | 0.454798 | + | 1.47702i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 15.8745i | − | 0.509437i | −0.967015 | − | 0.254719i | \(-0.918017\pi\) | ||
0.967015 | − | 0.254719i | \(-0.0819828\pi\) | |||||||
\(972\) | −0.125246 | + | 1.99607i | −0.00401726 | + | 0.0640241i | ||||
\(973\) | −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 | 0.904756 | − | 0.425931i | \(-0.140053\pi\) |
−0.425931 | + | 0.904756i | \(0.640053\pi\) | |||||||
\(978\) | −4.65489 | + | 10.3117i | −0.148847 | + | 0.329733i | ||||
\(979\) | 31.7490 | 1.01470 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | 9.23676 | − | 20.4617i | 0.294757 | − | 0.652960i | ||||
\(983\) | −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 | ||||||||
\(988\) | −55.8901 | − | 3.50688i | −1.77810 | − | 0.111569i | ||||
\(989\) | − | 32.0000i | − | 1.01754i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.6235i | 1.51281i | 0.654103 | + | 0.756406i | \(0.273046\pi\) | ||||
−0.654103 | + | 0.756406i | \(0.726954\pi\) | |||||||
\(992\) | −25.5289 | − | 15.6294i | −0.810542 | − | 0.496233i | ||||
\(993\) | 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 | 0.506652 | − | 0.862151i | \(-0.330883\pi\) |
−0.862151 | + | 0.506652i | \(0.830883\pi\) | |||||||
\(998\) | 20.4617 | + | 9.23676i | 0.647705 | + | 0.292384i | ||||
\(999\) | −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.7.1 | ✓ | 8 | |
3.2 | odd | 2 | 900.2.k.h.307.4 | 8 | |||
4.3 | odd | 2 | inner | 300.2.j.b.7.2 | yes | 8 | |
5.2 | odd | 4 | inner | 300.2.j.b.43.3 | yes | 8 | |
5.3 | odd | 4 | inner | 300.2.j.b.43.2 | yes | 8 | |
5.4 | even | 2 | inner | 300.2.j.b.7.4 | yes | 8 | |
12.11 | even | 2 | 900.2.k.h.307.3 | 8 | |||
15.2 | even | 4 | 900.2.k.h.343.2 | 8 | |||
15.8 | even | 4 | 900.2.k.h.343.3 | 8 | |||
15.14 | odd | 2 | 900.2.k.h.307.1 | 8 | |||
20.3 | even | 4 | inner | 300.2.j.b.43.1 | yes | 8 | |
20.7 | even | 4 | inner | 300.2.j.b.43.4 | yes | 8 | |
20.19 | odd | 2 | inner | 300.2.j.b.7.3 | yes | 8 | |
60.23 | odd | 4 | 900.2.k.h.343.4 | 8 | |||
60.47 | odd | 4 | 900.2.k.h.343.1 | 8 | |||
60.59 | even | 2 | 900.2.k.h.307.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.j.b.7.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
300.2.j.b.7.2 | yes | 8 | 4.3 | odd | 2 | inner | |
300.2.j.b.7.3 | yes | 8 | 20.19 | odd | 2 | inner | |
300.2.j.b.7.4 | yes | 8 | 5.4 | even | 2 | inner | |
300.2.j.b.43.1 | yes | 8 | 20.3 | even | 4 | inner | |
300.2.j.b.43.2 | yes | 8 | 5.3 | odd | 4 | inner | |
300.2.j.b.43.3 | yes | 8 | 5.2 | odd | 4 | inner | |
300.2.j.b.43.4 | yes | 8 | 20.7 | even | 4 | inner | |
900.2.k.h.307.1 | 8 | 15.14 | odd | 2 | |||
900.2.k.h.307.2 | 8 | 60.59 | even | 2 | |||
900.2.k.h.307.3 | 8 | 12.11 | even | 2 | |||
900.2.k.h.307.4 | 8 | 3.2 | odd | 2 | |||
900.2.k.h.343.1 | 8 | 60.47 | odd | 4 | |||
900.2.k.h.343.2 | 8 | 15.2 | even | 4 | |||
900.2.k.h.343.3 | 8 | 15.8 | even | 4 | |||
900.2.k.h.343.4 | 8 | 60.23 | odd | 4 |