Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,2,Mod(307,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, 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("900.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.k (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: | \(7.18653618192\) |
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: | \(\Z[a_1, \ldots, a_{49}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.4 | ||
Root | \(1.28897 + 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.307 |
Dual form | 900.2.k.h.343.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | 0 | ||||||||
\(4\) | 1.32288 | + | 1.50000i | 0.661438 | + | 0.750000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −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 | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.29150i | 1.59545i | 0.603023 | + | 0.797724i | \(0.293963\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 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 | 0 | ||||||||
\(19\) | −5.29150 | −1.21395 | −0.606977 | − | 0.794719i | \(-0.707618\pi\) | ||||
−0.606977 | + | 0.794719i | \(0.707618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.07892 | + | 6.82058i | −0.656428 | + | 1.45415i | ||||
\(23\) | 2.82843 | + | 2.82843i | 0.589768 | + | 0.589768i | 0.937568 | − | 0.347801i | \(-0.113071\pi\) |
−0.347801 | + | 0.937568i | \(0.613071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.00000 | − | 2.64575i | 1.37281 | − | 0.518875i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.99215 | − | 0.250492i | −0.754445 | − | 0.0473385i | ||||
\(29\) | 8.00000i | 1.48556i | 0.669534 | + | 0.742781i | \(0.266494\pi\) | ||||
−0.669534 | + | 0.742781i | \(0.733506\pi\) | |||||||
\(30\) | 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 | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −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 | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 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 | \(0.250000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 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 | \(-0.490986\pi\) |
0.999599 | − | 0.0283132i | \(-0.00901359\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.00000 | − | 2.64575i | −0.668153 | − | 0.353553i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.65489 | + | 10.3117i | −0.611217 | + | 1.35400i | ||||
\(59\) | −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 | \(0.374508\pi\) | |||||||
\(62\) | 3.07892 | − | 6.82058i | 0.391023 | − | 0.866214i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.61438 | + | 4.50000i | −0.826797 | + | 0.562500i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 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 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 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 | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.29150 | 0.595341 | 0.297670 | − | 0.954669i | \(-0.403790\pi\) | ||||
0.297670 | + | 0.954669i | \(0.403790\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.57794 | + | 1.16372i | 0.284685 | + | 0.128512i | ||||
\(83\) | −8.48528 | − | 8.48528i | −0.931381 | − | 0.931381i | 0.0664117 | − | 0.997792i | \(-0.478845\pi\) |
−0.997792 | + | 0.0664117i | \(0.978845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | + | 10.5830i | 0.431331 | + | 1.14119i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −14.3039 | + | 4.40440i | −1.52480 | + | 0.469510i | ||||
\(89\) | − | 6.00000i | − | 0.635999i | −0.948091 | − | 0.317999i | \(-0.896989\pi\) | ||
0.948091 | − | 0.317999i | \(-0.103011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.5830i | 1.10940i | ||||||||
\(92\) | −0.500983 | + | 7.98430i | −0.0522311 | + | 0.832421i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −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 | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.00000 | 0.398015 | 0.199007 | − | 0.979998i | \(-0.436228\pi\) | ||||
0.199007 | + | 0.979998i | \(0.436228\pi\) | |||||||
\(102\) | 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 | −0.557047 | − | 0.830481i | \(-0.688066\pi\) |
0.830481 | + | 0.557047i | \(0.188066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000i | 0.191565i | 0.995402 | + | 0.0957826i | \(0.0305354\pi\) | ||||
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.90538 | − | 6.31959i | −0.463515 | − | 0.597145i | ||||
\(113\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.0000 | + | 10.5830i | −1.11417 | + | 0.982607i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −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 | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.93725 | − | 7.00000i | 0.712786 | − | 0.628619i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −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 | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 15.8745i | − | 1.38696i | −0.720475 | − | 0.693481i | \(-0.756076\pi\) | ||
0.720475 | − | 0.693481i | \(-0.243924\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 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 | \(0.750000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 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 | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 14.0000 | − | 5.29150i | 1.15865 | − | 0.437928i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.662739 | − | 10.5622i | 0.0544768 | − | 0.868210i | ||||
\(149\) | − | 4.00000i | − | 0.327693i | −0.986486 | − | 0.163846i | \(-0.947610\pi\) | ||
0.986486 | − | 0.163846i | \(-0.0523901\pi\) | |||||||
\(150\) | 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 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −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 | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00000 | −0.630488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 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 | −0.297966 | − | 0.954577i | \(-0.596308\pi\) |
0.954577 | + | 0.297966i | \(0.0963081\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 15.0000i | − | 1.15385i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.00197 | + | 15.9686i | −0.0763992 | + | 1.21759i | ||||
\(173\) | −7.48331 | + | 7.48331i | −0.568946 | + | 0.568946i | −0.931833 | − | 0.362887i | \(-0.881791\pi\) |
0.362887 | + | 0.931833i | \(0.381791\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −21.0000 | − | 2.64575i | −1.58293 | − | 0.199431i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.49117 | − | 7.73381i | 0.261674 | − | 0.579673i | ||||
\(179\) | 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 | \(0.476318\pi\) | |||||||
\(182\) | −6.15784 | + | 13.6412i | −0.456449 | + | 1.01115i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.29150 | + | 10.0000i | −0.390095 | + | 0.737210i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.5830i | − | 0.765759i | −0.923798 | − | 0.382880i | \(-0.874932\pi\) | ||
0.923798 | − | 0.382880i | \(-0.125068\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 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 | \(0.478118\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.29150 | 0.375105 | 0.187552 | − | 0.982255i | \(-0.439945\pi\) | ||||
0.187552 | + | 0.982255i | \(0.439945\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 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 | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.48331 | + | 7.48331i | 0.508001 | + | 0.508001i | ||||
\(218\) | −1.16372 | + | 2.57794i | −0.0788172 | + | 0.174600i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −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 | \(0.629513\pi\) |
−0.918361 | + | 0.395744i | \(0.870487\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000i | 0.925146i | 0.886581 | + | 0.462573i | \(0.153074\pi\) | ||||
−0.886581 | + | 0.462573i | \(0.846926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −21.6255 | + | 6.65882i | −1.41978 | + | 0.437173i | ||||
\(233\) | 14.9666 | − | 14.9666i | 0.980497 | − | 0.980497i | −0.0193169 | − | 0.999813i | \(-0.506149\pi\) |
0.999813 | + | 0.0193169i | \(0.00614915\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.00000 | − | 7.93725i | −0.455661 | − | 0.516671i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 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 | \(0.351100\pi\) | |||||||
\(242\) | −21.9125 | − | 9.89164i | −1.40859 | − | 0.635858i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.93725 | + | 9.00000i | 0.508131 | + | 0.576166i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.7990 | + | 19.7990i | −1.25978 | + | 1.25978i | ||||
\(248\) | 14.3039 | − | 4.40440i | 0.908298 | − | 0.279679i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.29150i | 0.333997i | 0.985957 | + | 0.166998i | \(0.0534075\pi\) | ||||
−0.985957 | + | 0.166998i | \(0.946593\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −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 | \(0.979507\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.5830 | 0.657596 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.23676 | − | 20.4617i | 0.570649 | − | 1.26413i | ||||
\(263\) | −8.48528 | − | 8.48528i | −0.523225 | − | 0.523225i | 0.395319 | − | 0.918544i | \(-0.370634\pi\) |
−0.918544 | + | 0.395319i | \(0.870634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 14.0000 | − | 5.29150i | 0.858395 | − | 0.324443i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 23.9529 | + | 1.50295i | 1.46316 | + | 0.0918073i | ||||
\(269\) | 24.0000i | 1.46331i | 0.681677 | + | 0.731653i | \(0.261251\pi\) | ||||
−0.681677 | + | 0.731653i | \(0.738749\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 15.8745i | − | 0.964308i | −0.876087 | − | 0.482154i | \(-0.839855\pi\) | ||
0.876087 | − | 0.482154i | \(-0.160145\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 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 | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.0000 | −1.55103 | −0.775515 | − | 0.631329i | \(-0.782510\pi\) | ||||
−0.775515 | + | 0.631329i | \(0.782510\pi\) | |||||||
\(282\) | 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 | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 17.0000i | − | 1.00000i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 21.1245 | + | 1.32548i | 1.23622 | + | 0.0775677i | ||||
\(293\) | −14.9666 | + | 14.9666i | −0.874360 | + | 0.874360i | −0.992944 | − | 0.118584i | \(-0.962164\pi\) |
0.118584 | + | 0.992944i | \(0.462164\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.00000 | − | 13.2288i | 0.406867 | − | 0.768906i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 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 | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 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 | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.7490i | 1.80032i | 0.435558 | + | 0.900161i | \(0.356551\pi\) | ||||
−0.435558 | + | 0.900161i | \(0.643449\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −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 | \(0.750000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −42.3320 | −2.37014 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.3117 | − | 4.65489i | −0.574651 | − | 0.259407i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.00000 | + | 10.5830i | 0.221540 | + | 0.586138i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.8745 | − | 6.00000i | 0.868614 | − | 0.328305i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 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 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −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 | −0.441666 | − | 0.897180i | \(-0.645612\pi\) |
0.897180 | + | 0.441666i | \(0.145612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.00000i | − | 0.107058i | −0.998566 | − | 0.0535288i | \(-0.982953\pi\) | ||
0.998566 | − | 0.0535288i | \(-0.0170469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −25.5289 | − | 15.6294i | −1.36069 | − | 0.833048i | ||||
\(353\) | −14.9666 | + | 14.9666i | −0.796593 | + | 0.796593i | −0.982557 | − | 0.185963i | \(-0.940459\pi\) |
0.185963 | + | 0.982557i | \(0.440459\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 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 | \(-0.590094\pi\) | ||||
−0.279275 | + | 0.960211i | \(0.590094\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | 0.473684 | ||||||||
\(362\) | 2.57794 | + | 1.16372i | 0.135493 | + | 0.0611639i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −15.8745 | + | 14.0000i | −0.832050 | + | 0.733799i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 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 | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.1660i | 1.09888i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −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 | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.29150 | 0.271806 | 0.135903 | − | 0.990722i | \(-0.456606\pi\) | ||||
0.135903 | + | 0.990722i | \(0.456606\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.15784 | − | 13.6412i | 0.315062 | − | 0.697942i | ||||
\(383\) | 5.65685 | + | 5.65685i | 0.289052 | + | 0.289052i | 0.836705 | − | 0.547653i | \(-0.184479\pi\) |
−0.547653 | + | 0.836705i | \(0.684479\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.32548 | − | 21.1245i | 0.0672909 | − | 1.07243i | ||||
\(389\) | 24.0000i | 1.21685i | 0.793612 | + | 0.608424i | \(0.208198\pi\) | ||||
−0.793612 | + | 0.608424i | \(0.791802\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −8.10954 | + | 2.49706i | −0.409594 | + | 0.126120i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.5830 | + | 28.0000i | 0.533164 | + | 1.41062i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −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 | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.0000 | −0.499376 | −0.249688 | − | 0.968326i | \(-0.580328\pi\) | ||||
−0.249688 | + | 0.968326i | \(0.580328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −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 | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.00000 | + | 29.1033i | 0.343203 | + | 1.42690i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16.2921 | − | 36.0911i | 0.796873 | − | 1.76527i | ||||
\(419\) | −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 | \(0.189178\pi\) | |||||||
\(422\) | 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 | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10.5830i | − | 0.509765i | −0.966972 | − | 0.254883i | \(-0.917963\pi\) | ||
0.966972 | − | 0.254883i | \(-0.0820369\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −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 | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.29150 | 0.252550 | 0.126275 | − | 0.991995i | \(-0.459698\pi\) | ||||
0.126275 | + | 0.991995i | \(0.459698\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.82843 | − | 2.82843i | −0.134383 | − | 0.134383i | 0.636716 | − | 0.771099i | \(-0.280292\pi\) |
−0.771099 | + | 0.636716i | \(0.780292\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.00000 | − | 18.5203i | −0.331460 | − | 0.876960i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.99018 | − | 15.7181i | 0.141273 | − | 0.742611i | ||||
\(449\) | − | 22.0000i | − | 1.03824i | −0.854700 | − | 0.519122i | \(-0.826259\pi\) | ||
0.854700 | − | 0.519122i | \(-0.173741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.5830i | 0.498334i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −37.0405 | + | 14.0000i | −1.73840 | + | 0.657053i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −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 | \(-0.273911\pi\) | ||||
0.652045 | + | 0.758180i | \(0.273911\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −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 | \(0.563345\pi\) |
−0.980264 | + | 0.197692i | \(0.936655\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.0000i | 1.10822i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.40440 | − | 14.3039i | −0.202729 | − | 0.658390i | ||||
\(473\) | −29.9333 | + | 29.9333i | −1.37633 | + | 1.37633i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.6412 | + | 6.15784i | 0.623932 | + | 0.281653i | ||||
\(479\) | −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 | ||||||||
\(482\) | 18.0455 | + | 8.14605i | 0.821952 | + | 0.371043i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22.4889 | − | 25.5000i | −1.02222 | − | 1.15909i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −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 | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15.8745i | − | 0.716407i | −0.933644 | − | 0.358203i | \(-0.883389\pi\) | ||
0.933644 | − | 0.358203i | \(-0.116611\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 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 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.8745 | −0.710641 | −0.355320 | − | 0.934745i | \(-0.615628\pi\) | ||||
−0.355320 | + | 0.934745i | \(0.615628\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.07892 | + | 6.82058i | −0.137419 | + | 0.304417i | ||||
\(503\) | −11.3137 | − | 11.3137i | −0.504453 | − | 0.504453i | 0.408365 | − | 0.912819i | \(-0.366099\pi\) |
−0.912819 | + | 0.408365i | \(0.866099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −28.0000 | + | 10.5830i | −1.24475 | + | 0.470472i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.99215 | − | 0.250492i | −0.177123 | − | 0.0111138i | ||||
\(509\) | 36.0000i | 1.59567i | 0.602875 | + | 0.797836i | \(0.294022\pi\) | ||||
−0.602875 | + | 0.797836i | \(0.705978\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.1660i | 0.936329i | ||||||||
\(512\) | −17.6698 | − | 14.1343i | −0.780903 | − | 0.624653i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.5830 | − | 28.0000i | −0.466796 | − | 1.23503i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 13.6412 | + | 6.15784i | 0.599358 | + | 0.270560i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.0000 | −0.613351 | −0.306676 | − | 0.951814i | \(-0.599217\pi\) | ||||
−0.306676 | + | 0.951814i | \(0.599217\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 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 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 7.00000i | − | 0.304348i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 21.1245 | + | 1.32548i | 0.915862 | + | 0.0574667i | ||||
\(533\) | 7.48331 | − | 7.48331i | 0.324138 | − | 0.324138i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 30.0000 | + | 15.8745i | 1.29580 | + | 0.685674i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −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 | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −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 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 42.3320i | − | 1.80340i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −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 | \(0.515167\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 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 | 0.764192 | − | 0.644988i | \(-0.223138\pi\) |
−0.644988 | + | 0.764192i | \(0.723138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.0000 | + | 37.0405i | 0.588464 | + | 1.55693i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00000i | 0.251533i | 0.992060 | + | 0.125767i | \(0.0401390\pi\) | ||||
−0.992060 | + | 0.125767i | \(0.959861\pi\) | |||||||
\(570\) | 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 | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.29150 | + | 2.00000i | −0.220863 | + | 0.0834784i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 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 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 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 | −0.168508 | − | 0.985700i | \(-0.553895\pi\) |
0.985700 | + | 0.168508i | \(0.0538950\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.0000i | 1.15372i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 16.7201 | − | 12.9784i | 0.687191 | − | 0.533410i | ||||
\(593\) | 14.9666 | − | 14.9666i | 0.614606 | − | 0.614606i | −0.329537 | − | 0.944143i | \(-0.606893\pi\) |
0.944143 | + | 0.329537i | \(0.106893\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.00000 | − | 5.29150i | 0.245770 | − | 0.216748i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 27.2823 | + | 12.3157i | 1.11566 | + | 0.503625i | ||||
\(599\) | 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 | \(0.592172\pi\) | |||||||
\(602\) | −20.6235 | − | 9.30978i | −0.840550 | − | 0.379438i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −23.8118 | + | 21.0000i | −0.968887 | + | 0.854478i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 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 | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | \(-0.925322\pi\) |
−0.232462 | − | 0.972605i | \(-0.574678\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.29150 | −0.212683 | −0.106342 | − | 0.994330i | \(-0.533914\pi\) | ||||
−0.106342 | + | 0.994330i | \(0.533914\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.4735 | + | 40.9235i | −0.740720 | + | 1.64088i | ||||
\(623\) | 8.48528 | + | 8.48528i | 0.339956 | + | 0.339956i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −28.0000 | + | 10.5830i | −1.11911 | + | 0.422982i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 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 | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 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 | −0.957063 | − | 0.289881i | \(-0.906384\pi\) |
0.289881 | + | 0.957063i | \(0.406384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 28.0000i | − | 1.09910i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.00197 | + | 15.9686i | −0.0392400 | + | 0.625378i | ||||
\(653\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.00000 | + | 7.93725i | −0.0390434 | + | 0.309898i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 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 | \(0.386161\pi\) | |||||||
\(662\) | −3.07892 | + | 6.82058i | −0.119666 | + | 0.265089i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.8745 | − | 30.0000i | 0.616050 | − | 1.16423i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.6274 | + | 22.6274i | −0.876137 | + | 0.876137i | ||||
\(668\) | 23.9529 | + | 1.50295i | 0.926765 | + | 0.0581509i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.7490i | 1.22566i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −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 | 0.358367 | − | 0.933581i | \(-0.383334\pi\) |
−0.933581 | + | 0.358367i | \(0.883334\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.1660 | 0.812277 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 36.0911 | + | 16.2921i | 1.38200 | + | 0.623857i | ||||
\(683\) | 8.48528 | + | 8.48528i | 0.324680 | + | 0.324680i | 0.850559 | − | 0.525879i | \(-0.176264\pi\) |
−0.525879 | + | 0.850559i | \(0.676264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.0000 | − | 26.4575i | −0.381802 | − | 1.01015i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −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 | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.8745 | − | 6.00000i | 0.602588 | − | 0.227757i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.16372 | − | 2.57794i | 0.0440475 | − | 0.0975763i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.0000 | −1.35970 | −0.679851 | − | 0.733351i | \(-0.737955\pi\) | ||||
−0.679851 | + | 0.733351i | \(0.737955\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 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 | 0 | ||||||||
\(709\) | − | 10.0000i | − | 0.375558i | −0.982211 | − | 0.187779i | \(-0.939871\pi\) | ||
0.982211 | − | 0.187779i | \(-0.0601289\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 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 | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13.6412 | − | 6.15784i | −0.509083 | − | 0.229808i | ||||
\(719\) | 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 | ||||||||
\(722\) | 11.6007 | + | 5.23675i | 0.431734 | + | 0.194892i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.64575 | + | 3.00000i | 0.0983286 | + | 0.111494i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −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 | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 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 | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.4575 | −0.973255 | −0.486628 | − | 0.873609i | \(-0.661773\pi\) | ||||
−0.486628 | + | 0.873609i | \(0.661773\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.3157 | + | 27.2823i | −0.452123 | + | 1.00156i | ||||
\(743\) | −33.9411 | − | 33.9411i | −1.24518 | − | 1.24518i | −0.957824 | − | 0.287355i | \(-0.907224\pi\) |
−0.287355 | − | 0.957824i | \(-0.592776\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −35.0000 | + | 13.2288i | −1.28144 | + | 0.484339i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 21.1660 | + | 56.0000i | 0.770821 | + | 2.03940i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −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 | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.0000 | −1.52250 | −0.761249 | − | 0.648459i | \(-0.775414\pi\) | ||||
−0.761249 | + | 0.648459i | \(0.775414\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −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 | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 14.0000i | − | 0.504853i | −0.967616 | − | 0.252426i | \(-0.918771\pi\) | ||
0.967616 | − | 0.252426i | \(-0.0812286\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.9666 | − | 14.9666i | 0.538312 | − | 0.538312i | −0.384721 | − | 0.923033i | \(-0.625702\pi\) |
0.923033 | + | 0.384721i | \(0.125702\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.0000 | − | 26.4575i | 0.502571 | − | 0.949769i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13.9647 | + | 30.9352i | −0.500657 | + | 1.10908i | ||||
\(779\) | −10.5830 | −0.379176 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −11.9059 | − | 1.50000i | −0.425210 | − | 0.0535714i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 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 | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 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 | \(0.940085\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.8897 | − | 5.81861i | −0.455150 | − | 0.205462i | ||||
\(803\) | 39.5980 | + | 39.5980i | 1.39738 | + | 1.39738i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.0000 | − | 37.0405i | −0.493129 | − | 1.30470i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.32941 | + | 10.8127i | 0.117128 | + | 0.380390i | ||||
\(809\) | − | 30.0000i | − | 1.05474i | −0.849635 | − | 0.527372i | \(-0.823177\pi\) | ||
0.849635 | − | 0.527372i | \(-0.176823\pi\) | |||||||
\(810\) | 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 | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 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 | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.00000 | −0.279202 | −0.139601 | − | 0.990208i | \(-0.544582\pi\) | ||||
−0.139601 | + | 0.990208i | \(0.544582\pi\) | |||||||
\(822\) | 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 | −0.417093 | − | 0.908864i | \(-0.636951\pi\) |
0.908864 | + | 0.417093i | \(0.136951\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0000i | 0.486240i | 0.969996 | + | 0.243120i | \(0.0781709\pi\) | ||||
−0.969996 | + | 0.243120i | \(0.921829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.91128 | + | 41.5862i | −0.274274 | + | 1.44174i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 42.0000 | − | 37.0405i | 1.45260 | − | 1.28107i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.4617 | − | 9.23676i | −0.706839 | − | 0.319078i | ||||
\(839\) | 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 | ||||||||
\(842\) | 43.8249 | + | 19.7833i | 1.51031 | + | 0.681777i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 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 | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 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 | \(-0.992755\pi\) |
−0.0227597 | − | 0.999741i | \(-0.507245\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.29150 | −0.180544 | −0.0902719 | − | 0.995917i | \(-0.528774\pi\) | ||||
−0.0902719 | + | 0.995917i | \(0.528774\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.15784 | − | 13.6412i | 0.209737 | − | 0.464619i | ||||
\(863\) | −2.82843 | − | 2.82843i | −0.0962808 | − | 0.0962808i | 0.657326 | − | 0.753607i | \(-0.271688\pi\) |
−0.753607 | + | 0.657326i | \(0.771688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.0000 | + | 5.29150i | −0.475739 | + | 0.179813i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −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 | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.5830 | − | 28.0000i | −0.357975 | − | 0.947114i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 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 | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −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 | −0.135987 | − | 0.990711i | \(-0.543421\pi\) |
0.990711 | + | 0.135987i | \(0.0434205\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 4.00000i | − | 0.134156i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.75344 | − | 27.9450i | 0.0587096 | − | 0.935669i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13.0000 | − | 18.5203i | 0.434300 | − | 0.618718i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −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 | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.1660i | 0.701261i | 0.936514 | + | 0.350631i | \(0.114033\pi\) | ||||
−0.936514 | + | 0.350631i | \(0.885967\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 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 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 36.0911 | + | 16.2921i | 1.18860 | + | 0.536552i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −17.0000 | − | 44.9778i | −0.558655 | − | 1.47806i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −38.5960 | − | 23.6294i | −1.26698 | − | 0.775673i | ||||
\(929\) | − | 22.0000i | − | 0.721797i | −0.932605 | − | 0.360898i | \(-0.882470\pi\) | ||
0.932605 | − | 0.360898i | \(-0.117530\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 15.8745i | − | 0.520266i | ||||||
\(932\) | 42.2489 | + | 2.65095i | 1.38391 | + | 0.0868349i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −47.6235 | + | 18.0000i | −1.55829 | + | 0.588978i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −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 | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 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 | \(-0.429668\pi\) |
0.975689 | − | 0.219161i | \(-0.0703321\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 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 | \(0.250000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.0000 | + | 15.8745i | 0.452792 | + | 0.513418i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −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 | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 18.5203 | + | 21.0000i | 0.596497 | + | 0.676364i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 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 | \(0.0819828\pi\) | ||||
−0.967015 | + | 0.254719i | \(0.918017\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −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 | \(0.859947\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.7490 | 1.01470 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.23676 | − | 20.4617i | 0.294757 | − | 0.652960i | ||||
\(983\) | 16.9706 | + | 16.9706i | 0.541277 | + | 0.541277i | 0.923903 | − | 0.382626i | \(-0.124980\pi\) |
−0.382626 | + | 0.923903i | \(0.624980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −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 | ||||
\(999\) | 0 | 0 |
(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 | 900.2.k.h.307.4 | 8 | ||
3.2 | odd | 2 | 300.2.j.b.7.1 | ✓ | 8 | ||
4.3 | odd | 2 | inner | 900.2.k.h.307.3 | 8 | ||
5.2 | odd | 4 | inner | 900.2.k.h.343.2 | 8 | ||
5.3 | odd | 4 | inner | 900.2.k.h.343.3 | 8 | ||
5.4 | even | 2 | inner | 900.2.k.h.307.1 | 8 | ||
12.11 | even | 2 | 300.2.j.b.7.2 | yes | 8 | ||
15.2 | even | 4 | 300.2.j.b.43.3 | yes | 8 | ||
15.8 | even | 4 | 300.2.j.b.43.2 | yes | 8 | ||
15.14 | odd | 2 | 300.2.j.b.7.4 | yes | 8 | ||
20.3 | even | 4 | inner | 900.2.k.h.343.4 | 8 | ||
20.7 | even | 4 | inner | 900.2.k.h.343.1 | 8 | ||
20.19 | odd | 2 | inner | 900.2.k.h.307.2 | 8 | ||
60.23 | odd | 4 | 300.2.j.b.43.1 | yes | 8 | ||
60.47 | odd | 4 | 300.2.j.b.43.4 | yes | 8 | ||
60.59 | even | 2 | 300.2.j.b.7.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.j.b.7.1 | ✓ | 8 | 3.2 | odd | 2 | ||
300.2.j.b.7.2 | yes | 8 | 12.11 | even | 2 | ||
300.2.j.b.7.3 | yes | 8 | 60.59 | even | 2 | ||
300.2.j.b.7.4 | yes | 8 | 15.14 | odd | 2 | ||
300.2.j.b.43.1 | yes | 8 | 60.23 | odd | 4 | ||
300.2.j.b.43.2 | yes | 8 | 15.8 | even | 4 | ||
300.2.j.b.43.3 | yes | 8 | 15.2 | even | 4 | ||
300.2.j.b.43.4 | yes | 8 | 60.47 | odd | 4 | ||
900.2.k.h.307.1 | 8 | 5.4 | even | 2 | inner | ||
900.2.k.h.307.2 | 8 | 20.19 | odd | 2 | inner | ||
900.2.k.h.307.3 | 8 | 4.3 | odd | 2 | inner | ||
900.2.k.h.307.4 | 8 | 1.1 | even | 1 | trivial | ||
900.2.k.h.343.1 | 8 | 20.7 | even | 4 | inner | ||
900.2.k.h.343.2 | 8 | 5.2 | odd | 4 | inner | ||
900.2.k.h.343.3 | 8 | 5.3 | odd | 4 | inner | ||
900.2.k.h.343.4 | 8 | 20.3 | even | 4 | inner |