Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,2,Mod(177,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1232.177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.83756952902\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.529 |
Dual form | 1232.2.q.a.177.1 |
$q$-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 \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).
\(n\) | \(309\) | \(353\) | \(463\) | \(673\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | + | 2.59808i | −0.866025 | + | 1.50000i | 1.00000i | \(0.5\pi\) | ||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | + | 3.46410i | 0.894427 | + | 1.54919i | 0.834512 | + | 0.550990i | \(0.185750\pi\) |
0.0599153 | + | 0.998203i | \(0.480917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | + | 0.866025i | 0.944911 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | − | 5.19615i | −1.00000 | − | 1.73205i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −12.0000 | −3.09839 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | + | 1.73205i | −0.242536 | + | 0.420084i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.718900 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | + | 5.19615i | 0.688247 | + | 1.19208i | 0.972404 | + | 0.233301i | \(0.0749529\pi\) |
−0.284157 | + | 0.958778i | \(0.591714\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.00000 | + | 5.19615i | −1.30931 | + | 1.13389i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | − | 1.73205i | −0.208514 | − | 0.361158i | 0.742732 | − | 0.669588i | \(-0.233529\pi\) |
−0.951247 | + | 0.308431i | \(0.900196\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.50000 | + | 9.52628i | −1.10000 | + | 1.90526i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.00000 | 1.73205 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | − | 3.46410i | 0.359211 | − | 0.622171i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.987829 | + | 0.155543i | \(0.0497126\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.50000 | − | 2.59808i | −0.261116 | − | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | + | 10.3923i | 0.338062 | + | 1.75662i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | + | 1.73205i | 0.164399 | + | 0.284747i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.50000 | − | 2.59808i | 0.240192 | − | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.0000 | − | 20.7846i | 1.78885 | − | 3.09839i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.00000 | + | 1.73205i | 0.145865 | + | 0.252646i | 0.929695 | − | 0.368329i | \(-0.120070\pi\) |
−0.783830 | + | 0.620975i | \(0.786737\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | − | 5.19615i | −0.420084 | − | 0.727607i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | − | 10.3923i | 0.824163 | − | 1.42749i | −0.0783936 | − | 0.996922i | \(-0.524979\pi\) |
0.902557 | − | 0.430570i | \(-0.141688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.0000 | −2.38416 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.50000 | − | 7.79423i | 0.585850 | − | 1.01472i | −0.408919 | − | 0.912571i | \(-0.634094\pi\) |
0.994769 | − | 0.102151i | \(-0.0325726\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.50000 | + | 4.33013i | 0.320092 | + | 0.554416i | 0.980507 | − | 0.196485i | \(-0.0629528\pi\) |
−0.660415 | + | 0.750901i | \(0.729619\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.00000 | − | 15.5885i | −0.377964 | − | 1.96396i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.00000 | − | 3.46410i | −0.248069 | − | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.50000 | + | 7.79423i | −0.549762 | + | 0.952217i | 0.448528 | + | 0.893769i | \(0.351948\pi\) |
−0.998290 | + | 0.0584478i | \(0.981385\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000 | − | 1.73205i | 0.117041 | − | 0.202721i | −0.801553 | − | 0.597924i | \(-0.795992\pi\) |
0.918594 | + | 0.395203i | \(0.129326\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −16.5000 | − | 28.5788i | −1.90526 | − | 3.30000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.00000 | + | 1.73205i | −0.227921 | + | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.50000 | − | 12.9904i | −0.843816 | − | 1.46153i | −0.886646 | − | 0.462450i | \(-0.846971\pi\) |
0.0428296 | − | 0.999082i | \(-0.486363\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | −0.867722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.50000 | + | 2.59808i | −0.160817 | + | 0.278543i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | − | 5.19615i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.50000 | − | 0.866025i | −0.262071 | − | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.00000 | + | 10.3923i | 0.622171 | + | 1.07763i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.0000 | + | 20.7846i | −1.23117 | + | 2.13246i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.00000 | −0.507673 | −0.253837 | − | 0.967247i | \(-0.581693\pi\) | ||||
−0.253837 | + | 0.967247i | \(0.581693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.50000 | − | 12.9904i | 0.746278 | − | 1.29259i | −0.203317 | − | 0.979113i | \(-0.565172\pi\) |
0.949595 | − | 0.313478i | \(-0.101494\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000 | + | 10.3923i | 0.591198 | + | 1.02398i | 0.994071 | + | 0.108729i | \(0.0346780\pi\) |
−0.402874 | + | 0.915255i | \(0.631989\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −30.0000 | − | 10.3923i | −2.92770 | − | 1.01419i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | + | 6.92820i | 0.386695 | + | 0.669775i | 0.992003 | − | 0.126217i | \(-0.0402834\pi\) |
−0.605308 | + | 0.795991i | \(0.706950\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.00000 | + | 8.66025i | −0.478913 | + | 0.829502i | −0.999708 | − | 0.0241802i | \(-0.992302\pi\) |
0.520794 | + | 0.853682i | \(0.325636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | −0.569495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.0000 | 1.59923 | 0.799613 | − | 0.600516i | \(-0.205038\pi\) | ||||
0.799613 | + | 0.600516i | \(0.205038\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | − | 6.92820i | 0.373002 | − | 0.646058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.00000 | + | 5.19615i | 0.277350 | + | 0.480384i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.00000 | + | 3.46410i | −0.366679 | + | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.00000 | − | 5.19615i | 0.270501 | − | 0.468521i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −24.0000 | −2.14663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.00000 | −0.443678 | −0.221839 | − | 0.975083i | \(-0.571206\pi\) | ||||
−0.221839 | + | 0.975083i | \(0.571206\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000 | − | 10.3923i | 0.528271 | − | 0.914991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.00000 | − | 15.5885i | −0.786334 | − | 1.36197i | −0.928199 | − | 0.372084i | \(-0.878643\pi\) |
0.141865 | − | 0.989886i | \(-0.454690\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | + | 15.5885i | 0.260133 | + | 1.35169i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.0000 | + | 31.1769i | 1.54919 | + | 2.68328i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.50000 | − | 7.79423i | 0.384461 | − | 0.665906i | −0.607233 | − | 0.794524i | \(-0.707721\pi\) |
0.991694 | + | 0.128618i | \(0.0410540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00000 | −0.678551 | −0.339276 | − | 0.940687i | \(-0.610182\pi\) | ||||
−0.339276 | + | 0.940687i | \(0.610182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.500000 | − | 0.866025i | 0.0418121 | − | 0.0724207i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | + | 3.46410i | 0.166091 | + | 0.287678i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −19.5000 | + | 7.79423i | −1.60833 | + | 0.642857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.00000 | + | 8.66025i | 0.409616 | + | 0.709476i | 0.994847 | − | 0.101391i | \(-0.0323294\pi\) |
−0.585231 | + | 0.810867i | \(0.698996\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.50000 | − | 7.79423i | 0.366205 | − | 0.634285i | −0.622764 | − | 0.782410i | \(-0.713990\pi\) |
0.988969 | + | 0.148124i | \(0.0473236\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.0000 | 0.970143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.0000 | 1.28515 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | + | 3.46410i | −0.159617 | + | 0.276465i | −0.934731 | − | 0.355357i | \(-0.884359\pi\) |
0.775113 | + | 0.631822i | \(0.217693\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 18.0000 | + | 31.1769i | 1.42749 | + | 2.47249i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | − | 5.19615i | −0.0788110 | − | 0.409514i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.50000 | + | 11.2583i | 0.509119 | + | 0.881820i | 0.999944 | + | 0.0105623i | \(0.00336213\pi\) |
−0.490825 | + | 0.871258i | \(0.663305\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.00000 | − | 10.3923i | 0.467099 | − | 0.809040i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.0000 | 1.31550 | 0.657750 | − | 0.753237i | \(-0.271508\pi\) | ||||
0.657750 | + | 0.753237i | \(0.271508\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.0000 | − | 31.1769i | 1.37649 | − | 2.38416i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.50000 | + | 4.33013i | 0.190071 | + | 0.329213i | 0.945274 | − | 0.326278i | \(-0.105795\pi\) |
−0.755202 | + | 0.655492i | \(0.772461\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −22.0000 | + | 19.0526i | −1.66304 | + | 1.44024i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.5000 | + | 23.3827i | 1.01472 | + | 1.75755i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.50000 | − | 11.2583i | 0.485833 | − | 0.841487i | −0.514035 | − | 0.857769i | \(-0.671850\pi\) |
0.999867 | + | 0.0162823i | \(0.00518305\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.0000 | −1.10883 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | + | 6.92820i | −0.294086 | + | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.00000 | − | 1.73205i | −0.0731272 | − | 0.126660i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 22.5000 | + | 7.79423i | 1.63663 | + | 0.566947i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.00000 | + | 12.1244i | 0.506502 | + | 0.877288i | 0.999972 | + | 0.00752447i | \(0.00239513\pi\) |
−0.493469 | + | 0.869763i | \(0.664272\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0000 | − | 19.0526i | 0.791797 | − | 1.37143i | −0.133056 | − | 0.991109i | \(-0.542479\pi\) |
0.924853 | − | 0.380325i | \(-0.124188\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.0000 | 0.859338 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.00000 | −0.213741 | −0.106871 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106871 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.00000 | − | 8.66025i | 0.354441 | − | 0.613909i | −0.632581 | − | 0.774494i | \(-0.718005\pi\) |
0.987022 | + | 0.160585i | \(0.0513380\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.5000 | − | 23.3827i | −0.952217 | − | 1.64929i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.50000 | + | 0.866025i | 0.175466 | + | 0.0607831i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | − | 6.92820i | −0.279372 | − | 0.483887i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.00000 | + | 10.3923i | −0.417029 | + | 0.722315i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0000 | 0.963800 | 0.481900 | − | 0.876226i | \(-0.339947\pi\) | ||||
0.481900 | + | 0.876226i | \(0.339947\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.00000 | − | 10.3923i | 0.411113 | − | 0.712069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.00000 | − | 13.8564i | −0.545595 | − | 0.944999i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | − | 6.92820i | 0.543075 | − | 0.470317i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.00000 | + | 5.19615i | 0.202721 | + | 0.351123i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.00000 | − | 1.73205i | 0.0672673 | − | 0.116510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.0000 | 1.74109 | 0.870544 | − | 0.492090i | \(-0.163767\pi\) | ||||
0.870544 | + | 0.492090i | \(0.163767\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 66.0000 | 4.40000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.00000 | − | 8.66025i | 0.331862 | − | 0.574801i | −0.651015 | − | 0.759065i | \(-0.725657\pi\) |
0.982877 | + | 0.184263i | \(0.0589899\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.00000 | + | 13.8564i | 0.528655 | + | 0.915657i | 0.999442 | + | 0.0334101i | \(0.0106368\pi\) |
−0.470787 | + | 0.882247i | \(0.656030\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.50000 | − | 7.79423i | −0.0986928 | − | 0.512823i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.00000 | − | 5.19615i | −0.196537 | − | 0.340411i | 0.750867 | − | 0.660454i | \(-0.229636\pi\) |
−0.947403 | + | 0.320043i | \(0.896303\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | + | 6.92820i | −0.260931 | + | 0.451946i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 45.0000 | 2.92306 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.0000 | −1.22901 | −0.614504 | − | 0.788914i | \(-0.710644\pi\) | ||||
−0.614504 | + | 0.788914i | \(0.710644\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.0000 | + | 25.9808i | −0.966235 | + | 1.67357i | −0.259975 | + | 0.965615i | \(0.583714\pi\) |
−0.706260 | + | 0.707953i | \(0.749619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.00000 | + | 27.7128i | −0.255551 | + | 1.77051i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.00000 | − | 5.19615i | −0.190885 | − | 0.330623i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.00000 | + | 15.5885i | −0.570352 | + | 0.987878i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000 | 0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.0000 | − | 20.7846i | 0.751469 | − | 1.30158i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.5000 | + | 18.1865i | 0.654972 | + | 1.13444i | 0.981901 | + | 0.189396i | \(0.0606529\pi\) |
−0.326929 | + | 0.945049i | \(0.606014\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.00000 | + | 5.19615i | 0.0621370 | + | 0.322873i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.50000 | − | 2.59808i | 0.0924940 | − | 0.160204i | −0.816066 | − | 0.577959i | \(-0.803849\pi\) |
0.908560 | + | 0.417755i | \(0.137183\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 48.0000 | 2.94862 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.0000 | 1.10158 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.00000 | + | 10.3923i | −0.365826 | + | 0.633630i | −0.988908 | − | 0.148527i | \(-0.952547\pi\) |
0.623082 | + | 0.782157i | \(0.285880\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5000 | + | 21.6506i | 0.759321 | + | 1.31518i | 0.943197 | + | 0.332233i | \(0.107802\pi\) |
−0.183876 | + | 0.982949i | \(0.558865\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.00000 | − | 5.19615i | 0.363137 | − | 0.314485i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.50000 | − | 9.52628i | −0.331662 | − | 0.574456i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.50000 | − | 2.59808i | 0.0901263 | − | 0.156103i | −0.817438 | − | 0.576017i | \(-0.804606\pi\) |
0.907564 | + | 0.419914i | \(0.137940\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −24.0000 | −1.43684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.00000 | + | 5.19615i | −0.178331 | + | 0.308879i | −0.941309 | − | 0.337546i | \(-0.890403\pi\) |
0.762978 | + | 0.646425i | \(0.223737\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −36.0000 | − | 62.3538i | −2.13246 | − | 3.69352i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.00000 | − | 1.73205i | −0.295141 | − | 0.102240i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.50000 | − | 12.9904i | 0.439658 | − | 0.761510i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 36.0000 | 2.09600 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.50000 | + | 7.79423i | −0.261116 | + | 0.452267i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.00000 | + | 1.73205i | 0.0578315 | + | 0.100167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0000 | − | 3.46410i | −0.576390 | − | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.5000 | + | 38.9711i | 1.29259 | + | 2.23883i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.0000 | + | 17.3205i | −0.572598 | + | 0.991769i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.0000 | −1.82634 | −0.913168 | − | 0.407583i | \(-0.866372\pi\) | ||||
−0.913168 | + | 0.407583i | \(0.866372\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −36.0000 | −2.04797 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.0000 | + | 24.2487i | −0.793867 | + | 1.37502i | 0.129689 | + | 0.991555i | \(0.458602\pi\) |
−0.923556 | + | 0.383464i | \(0.874731\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.500000 | − | 0.866025i | −0.0282617 | − | 0.0489506i | 0.851549 | − | 0.524276i | \(-0.175664\pi\) |
−0.879810 | + | 0.475325i | \(0.842331\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 48.0000 | − | 41.5692i | 2.70449 | − | 2.34216i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | + | 10.3923i | 0.336994 | + | 0.583690i | 0.983866 | − | 0.178908i | \(-0.0572566\pi\) |
−0.646872 | + | 0.762598i | \(0.723923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.500000 | + | 0.866025i | −0.0279946 | + | 0.0484881i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.0000 | −1.33955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.50000 | − | 9.52628i | 0.305085 | − | 0.528423i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.0000 | − | 25.9808i | −0.829502 | − | 1.43674i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.00000 | + | 5.19615i | 0.0551318 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.50000 | + | 6.06218i | 0.192377 | + | 0.333207i | 0.946038 | − | 0.324057i | \(-0.105047\pi\) |
−0.753660 | + | 0.657264i | \(0.771714\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.00000 | − | 10.3923i | 0.328798 | − | 0.569495i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −36.0000 | −1.96689 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.0000 | −1.63420 | −0.817102 | − | 0.576493i | \(-0.804421\pi\) | ||||
−0.817102 | + | 0.576493i | \(0.804421\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −25.5000 | + | 44.1673i | −1.38497 | + | 2.39884i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | + | 3.46410i | 0.108306 | + | 0.187592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.0000 | + | 20.7846i | 0.646058 | + | 1.11901i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.0000 | + | 24.2487i | −0.751559 | + | 1.30174i | 0.195507 | + | 0.980702i | \(0.437365\pi\) |
−0.947067 | + | 0.321037i | \(0.895969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.00000 | −0.480384 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.00000 | − | 15.5885i | 0.479022 | − | 0.829690i | −0.520689 | − | 0.853746i | \(-0.674325\pi\) |
0.999711 | + | 0.0240566i | \(0.00765819\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.00000 | − | 13.8564i | −0.424596 | − | 0.735422i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.00000 | − | 15.5885i | −0.158777 | − | 0.825029i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.5000 | − | 26.8468i | −0.818059 | − | 1.41692i | −0.907111 | − | 0.420892i | \(-0.861717\pi\) |
0.0890519 | − | 0.996027i | \(-0.471616\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.00000 | 0.157459 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.00000 | 0.418739 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.00000 | + | 12.1244i | −0.365397 | + | 0.632886i | −0.988840 | − | 0.148983i | \(-0.952400\pi\) |
0.623443 | + | 0.781869i | \(0.285733\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000 | + | 10.3923i | 0.312348 | + | 0.541002i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.0000 | − | 20.7846i | 1.24602 | − | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.50000 | + | 6.06218i | 0.181223 | + | 0.313888i | 0.942297 | − | 0.334777i | \(-0.108661\pi\) |
−0.761074 | + | 0.648665i | \(0.775328\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 36.0000 | − | 62.3538i | 1.85903 | − | 3.21994i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.00000 | −0.0515026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.0000 | 1.48963 | 0.744815 | − | 0.667271i | \(-0.232538\pi\) | ||||
0.744815 | + | 0.667271i | \(0.232538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.50000 | − | 12.9904i | 0.384237 | − | 0.665517i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.00000 | + | 6.92820i | 0.204390 | + | 0.354015i | 0.949938 | − | 0.312437i | \(-0.101145\pi\) |
−0.745548 | + | 0.666452i | \(0.767812\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.0000 | − | 3.46410i | −0.509647 | − | 0.176547i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.0000 | + | 20.7846i | 0.609994 | + | 1.05654i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.00000 | 0.202289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 54.0000 | 2.72394 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.0000 | − | 51.9615i | 1.50946 | − | 2.61447i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.0000 | + | 25.9808i | 0.752828 | + | 1.30394i | 0.946447 | + | 0.322860i | \(0.104644\pi\) |
−0.193618 | + | 0.981077i | \(0.562022\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −45.0000 | − | 15.5885i | −2.25282 | − | 0.780399i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.50000 | − | 12.9904i | −0.374532 | − | 0.648709i | 0.615725 | − | 0.787961i | \(-0.288863\pi\) |
−0.990257 | + | 0.139253i | \(0.955530\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | + | 3.46410i | −0.0996271 | + | 0.172559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −36.0000 | −1.78885 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.00000 | −0.0991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.0000 | − | 27.7128i | 0.791149 | − | 1.37031i | −0.134107 | − | 0.990967i | \(-0.542817\pi\) |
0.925256 | − | 0.379344i | \(-0.123850\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.5000 | + | 23.3827i | 0.665906 | + | 1.15338i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.0000 | − | 15.5885i | 0.885722 | − | 0.767058i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000 | + | 20.7846i | 0.589057 | + | 1.02028i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.0000 | − | 20.7846i | 0.587643 | − | 1.01783i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.0000 | 0.977064 | 0.488532 | − | 0.872546i | \(-0.337533\pi\) | ||||
0.488532 | + | 0.872546i | \(0.337533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.00000 | − | 10.3923i | 0.291730 | − | 0.505291i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.0000 | − | 19.0526i | −0.533578 | − | 0.924185i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.50000 | + | 12.9904i | 0.120983 | + | 0.628649i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.50000 | + | 2.59808i | 0.0724207 | + | 0.125436i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.500000 | − | 0.866025i | 0.0240842 | − | 0.0417150i | −0.853732 | − | 0.520712i | \(-0.825666\pi\) |
0.877816 | + | 0.478997i | \(0.159000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0000 | −0.480569 | −0.240285 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240285 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.0000 | −0.575356 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.00000 | − | 10.3923i | 0.287019 | − | 0.497131i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.50000 | − | 4.33013i | −0.119318 | − | 0.206666i | 0.800179 | − | 0.599761i | \(-0.204738\pi\) |
−0.919498 | + | 0.393095i | \(0.871404\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.00000 | − | 41.5692i | 0.285714 | − | 1.97949i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.00000 | − | 10.3923i | −0.285069 | − | 0.493753i | 0.687557 | − | 0.726130i | \(-0.258683\pi\) |
−0.972626 | + | 0.232377i | \(0.925350\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0000 | − | 20.7846i | 0.568855 | − | 0.985285i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −30.0000 | −1.41895 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.00000 | − | 1.73205i | 0.0470882 | − | 0.0815591i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.5000 | + | 23.3827i | 0.634285 | + | 1.09861i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00000 | − | 10.3923i | −0.0937614 | − | 0.487199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | − | 1.73205i | −0.0467780 | − | 0.0810219i | 0.841688 | − | 0.539964i | \(-0.181562\pi\) |
−0.888466 | + | 0.458942i | \(0.848229\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.00000 | + | 15.5885i | −0.420084 | + | 0.727607i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.00000 | −0.139724 | −0.0698620 | − | 0.997557i | \(-0.522256\pi\) | ||||
−0.0698620 | + | 0.997557i | \(0.522256\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0000 | 0.650635 | 0.325318 | − | 0.945605i | \(-0.394529\pi\) | ||||
0.325318 | + | 0.945605i | \(0.394529\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −24.0000 | + | 41.5692i | −1.11297 | + | 1.92773i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.00000 | − | 10.3923i | −0.277647 | − | 0.480899i | 0.693153 | − | 0.720791i | \(-0.256221\pi\) |
−0.970799 | + | 0.239892i | \(0.922888\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.0000 | + | 15.5885i | −0.831163 | + | 0.719808i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.00000 | − | 10.3923i | −0.276465 | − | 0.478852i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.00000 | − | 3.46410i | 0.0919601 | − | 0.159280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −66.0000 | −3.02829 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −72.0000 | −3.29665 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.5000 | + | 32.0429i | −0.845287 | + | 1.46408i | 0.0400855 | + | 0.999196i | \(0.487237\pi\) |
−0.885372 | + | 0.464883i | \(0.846096\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.00000 | − | 1.73205i | −0.0455961 | − | 0.0789747i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.0000 | + | 5.19615i | 0.682524 | + | 0.236433i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.0000 | − | 17.3205i | −0.454077 | − | 0.786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.00000 | + | 3.46410i | −0.0906287 | + | 0.156973i | −0.907776 | − | 0.419456i | \(-0.862221\pi\) |
0.817147 | + | 0.576429i | \(0.195554\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −39.0000 | −1.76364 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.0000 | −0.812329 | −0.406164 | − | 0.913800i | \(-0.633134\pi\) | ||||
−0.406164 | + | 0.913800i | \(0.633134\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.00000 | + | 1.73205i | −0.0450377 | + | 0.0780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.0000 | + | 20.7846i | 0.539360 | + | 0.934199i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.0000 | − | 3.46410i | −0.448561 | − | 0.155386i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.00000 | − | 13.8564i | −0.358129 | − | 0.620298i | 0.629519 | − | 0.776985i | \(-0.283252\pi\) |
−0.987648 | + | 0.156687i | \(0.949919\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.5000 | + | 44.1673i | −1.13926 | + | 1.97325i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.0000 | 0.936344 | 0.468172 | − | 0.883637i | \(-0.344913\pi\) | ||||
0.468172 | + | 0.883637i | \(0.344913\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 60.0000 | 2.66996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.0000 | − | 31.1769i | 0.799408 | − | 1.38462i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.00000 | − | 1.73205i | −0.0443242 | − | 0.0767718i | 0.843012 | − | 0.537895i | \(-0.180780\pi\) |
−0.887336 | + | 0.461123i | \(0.847447\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.00000 | − | 3.46410i | 0.176950 | − | 0.153243i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 27.0000 | + | 46.7654i | 1.19208 | + | 2.06474i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.0000 | + | 41.5692i | −1.05757 | + | 1.83176i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.00000 | −0.0879599 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.0000 | −0.658427 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0000 | − | 22.5167i | 0.569540 | − | 0.986473i | −0.427071 | − | 0.904218i | \(-0.640455\pi\) |
0.996611 | − | 0.0822547i | \(-0.0262121\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.0000 | + | 17.3205i | 0.437269 | + | 0.757373i | 0.997478 | − | 0.0709788i | \(-0.0226123\pi\) |
−0.560208 | + | 0.828352i | \(0.689279\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −16.5000 | − | 85.7365i | −0.720119 | − | 3.74185i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.00000 | + | 6.92820i | 0.174243 | + | 0.301797i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.50000 | − | 16.4545i | 0.413043 | − | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −54.0000 | −2.34340 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.00000 | 0.0866296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.0000 | + | 27.7128i | −0.691740 | + | 1.19813i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.5000 | + | 33.7750i | 0.841487 | + | 1.45750i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.50000 | + | 2.59808i | −0.279975 | + | 0.111907i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5000 | + | 21.6506i | 0.537417 | + | 0.930834i | 0.999042 | + | 0.0437584i | \(0.0139332\pi\) |
−0.461625 | + | 0.887075i | \(0.652733\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 33.0000 | − | 57.1577i | 1.41617 | − | 2.45287i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −40.0000 | −1.71341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.0000 | − | 25.9808i | 0.640184 | − | 1.10883i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.00000 | + | 5.19615i | 0.127804 | + | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.50000 | − | 38.9711i | −0.318932 | − | 1.65722i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.0000 | − | 20.7846i | −0.509372 | − | 0.882258i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.0000 | + | 32.9090i | −0.805056 | + | 1.39440i | 0.111198 | + | 0.993798i | \(0.464531\pi\) |
−0.916253 | + | 0.400599i | \(0.868802\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.00000 | 0.253320 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.0000 | − | 22.5167i | 0.547885 | − | 0.948964i | −0.450535 | − | 0.892759i | \(-0.648767\pi\) |
0.998419 | − | 0.0562051i | \(-0.0179001\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 34.0000 | + | 58.8897i | 1.43039 | + | 2.47751i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.0000 | + | 15.5885i | −0.755929 | + | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.0000 | − | 31.1769i | −0.754599 | − | 1.30700i | −0.945573 | − | 0.325409i | \(-0.894498\pi\) |
0.190974 | − | 0.981595i | \(-0.438835\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −42.0000 | −1.75458 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.0000 | 0.917463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.50000 | − | 6.06218i | 0.145707 | − | 0.252372i | −0.783930 | − | 0.620850i | \(-0.786788\pi\) |
0.929636 | + | 0.368478i | \(0.120121\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 33.0000 | + | 57.1577i | 1.37143 | + | 2.37539i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.0000 | + | 5.19615i | 0.622305 | + | 0.215573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.00000 | + | 10.3923i | 0.248495 | + | 0.430405i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.0000 | + | 20.7846i | −0.496139 | + | 0.859338i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.00000 | 0.123823 | 0.0619116 | − | 0.998082i | \(-0.480280\pi\) | ||||
0.0619116 | + | 0.998082i | \(0.480280\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.0000 | 0.988903 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.50000 | − | 7.79423i | 0.185105 | − | 0.320612i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.0000 | − | 6.92820i | −0.819920 | − | 0.284029i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.0000 | + | 25.9808i | 0.613909 | + | 1.06332i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.0000 | + | 20.7846i | −0.490307 | + | 0.849236i | −0.999938 | − | 0.0111569i | \(-0.996449\pi\) |
0.509631 | + | 0.860393i | \(0.329782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 54.0000 | 2.19905 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.00000 | − | 3.46410i | 0.0813116 | − | 0.140836i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.00000 | − | 13.8564i | −0.324710 | − | 0.562414i | 0.656744 | − | 0.754114i | \(-0.271933\pi\) |
−0.981454 | + | 0.191700i | \(0.938600\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.00000 | + | 5.19615i | −0.243132 | + | 0.210559i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.00000 | − | 1.73205i | −0.0404557 | − | 0.0700713i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.0000 | + | 19.0526i | −0.444286 | + | 0.769526i | −0.998002 | − | 0.0631797i | \(-0.979876\pi\) |
0.553716 | + | 0.832705i | \(0.313209\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.0000 | 0.967773 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.0000 | −1.08698 | −0.543490 | − | 0.839416i | \(-0.682897\pi\) | ||||
−0.543490 | + | 0.839416i | \(0.682897\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0000 | − | 17.3205i | 0.401934 | − | 0.696170i | −0.592025 | − | 0.805919i | \(-0.701671\pi\) |
0.993959 | + | 0.109749i | \(0.0350048\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.00000 | − | 15.5885i | −0.361158 | − | 0.625543i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.00000 | − | 15.5885i | −0.120192 | − | 0.624538i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.5000 | − | 35.5070i | −0.820000 | − | 1.42028i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.00000 | − | 15.5885i | 0.359425 | − | 0.622543i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.00000 | −0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.0000 | + | 36.3731i | −0.834675 | + | 1.44570i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.0000 | − | 17.3205i | −0.396838 | − | 0.687343i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.50000 | − | 4.33013i | −0.217918 | − | 0.171566i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | + | 20.7846i | 0.474713 | + | 0.822226i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.50000 | + | 7.79423i | −0.177739 | + | 0.307854i | −0.941106 | − | 0.338112i | \(-0.890212\pi\) |
0.763367 | + | 0.645966i | \(0.223545\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.00000 | −0.0394362 | −0.0197181 | − | 0.999806i | \(-0.506277\pi\) | ||||
−0.0197181 | + | 0.999806i | \(0.506277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 48.0000 | 1.89000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000 | − | 20.7846i | 0.471769 | − | 0.817127i | −0.527710 | − | 0.849425i | \(-0.676949\pi\) |
0.999478 | + | 0.0322975i | \(0.0102824\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.50000 | + | 7.79423i | 0.176640 | + | 0.305950i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.00000 | + | 31.1769i | 0.235159 | + | 1.22192i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.0000 | − | 19.0526i | −0.430463 | − | 0.745584i | 0.566450 | − | 0.824096i | \(-0.308316\pi\) |
−0.996913 | + | 0.0785119i | \(0.974983\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 36.0000 | − | 62.3538i | 1.40664 | − | 2.43637i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.0000 | −0.468165 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.0000 | 1.24654 | 0.623272 | − | 0.782006i | \(-0.285803\pi\) | ||||
0.623272 | + | 0.782006i | \(0.285803\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00000 | − | 8.66025i | 0.194477 | − | 0.336845i | −0.752252 | − | 0.658876i | \(-0.771032\pi\) |
0.946729 | + | 0.322031i | \(0.104366\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.00000 | + | 5.19615i | 0.116510 | + | 0.201802i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −48.0000 | + | 41.5692i | −1.86136 | + | 1.61199i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | − | 1.73205i | −0.0387202 | − | 0.0670653i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −39.0000 | + | 67.5500i | −1.50783 | + | 2.61163i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.00000 | −0.193023 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.0000 | 0.616755 | 0.308377 | − | 0.951264i | \(-0.400214\pi\) | ||||
0.308377 | + | 0.951264i | \(0.400214\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −49.5000 | + | 85.7365i | −1.90526 | + | 3.30000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.0000 | − | 32.9090i | −0.730229 | − | 1.26479i | −0.956785 | − | 0.290796i | \(-0.906080\pi\) |
0.226556 | − | 0.973998i | \(-0.427253\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.5000 | − | 4.33013i | −0.479706 | − | 0.166175i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.0000 | + | 25.9808i | 0.574801 | + | 0.995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.5000 | + | 28.5788i | −0.631355 | + | 1.09354i | 0.355920 | + | 0.934516i | \(0.384168\pi\) |
−0.987275 | + | 0.159022i | \(0.949166\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.0000 | 1.37549 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −48.0000 | −1.83131 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.00000 | + | 10.3923i | −0.228582 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.50000 | + | 12.9904i | 0.285313 | + | 0.494177i | 0.972685 | − | 0.232128i | \(-0.0745690\pi\) |
−0.687372 | + | 0.726306i | \(0.741236\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.0000 | + | 5.19615i | 0.569803 | + | 0.197386i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.0000 | − | 27.7128i | −0.606915 | − | 1.05121i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.00000 | − | 3.46410i | 0.0757554 | − | 0.131212i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.0000 | 0.680823 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.0000 | 1.47301 | 0.736505 | − | 0.676432i | \(-0.236475\pi\) | ||||
0.736505 | + | 0.676432i | \(0.236475\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.00000 | + | 10.3923i | −0.226294 | + | 0.391953i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.0000 | − | 20.7846i | −0.451946 | − | 0.782794i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 30.0000 | − | 25.9808i | 1.12827 | − | 0.977107i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.00000 | − | 5.19615i | −0.112667 | − | 0.195146i | 0.804178 | − | 0.594389i | \(-0.202606\pi\) |
−0.916845 | + | 0.399244i | \(0.869273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −45.0000 | + | 77.9423i | −1.68763 | + | 2.92306i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.00000 | −0.299602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28.5000 | − | 49.3634i | 1.06435 | − | 1.84351i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.0000 | − | 22.5167i | −0.484818 | − | 0.839730i | 0.515030 | − | 0.857172i | \(-0.327781\pi\) |
−0.999848 | + | 0.0174426i | \(0.994448\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | + | 31.1769i | 0.223452 | + | 1.16109i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −45.0000 | − | 77.9423i | −1.67357 | − | 2.89870i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.50000 | + | 9.52628i | −0.204265 | + | 0.353797i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.0000 | 1.26099 | 0.630495 | − | 0.776193i | \(-0.282852\pi\) | ||||
0.630495 | + | 0.776193i | \(0.282852\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.00000 | − | 6.92820i | 0.147945 | − | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.500000 | + | 0.866025i | 0.0184679 | + | 0.0319874i | 0.875112 | − | 0.483921i | \(-0.160788\pi\) |
−0.856644 | + | 0.515908i | \(0.827454\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −66.0000 | − | 51.9615i | −2.43445 | − | 1.91663i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.50000 | − | 7.79423i | −0.165760 | − | 0.287104i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.00000 | − | 15.5885i | 0.331070 | − | 0.573431i | −0.651652 | − | 0.758518i | \(-0.725924\pi\) |
0.982722 | + | 0.185088i | \(0.0592569\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.0000 | 0.661247 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.0000 | −1.32071 | −0.660356 | − | 0.750953i | \(-0.729595\pi\) | ||||
−0.660356 | + | 0.750953i | \(0.729595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.0000 | + | 34.6410i | −0.732743 | + | 1.26915i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.0000 | − | 31.1769i | −0.658586 | − | 1.14070i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.00000 | + | 20.7846i | 0.146157 | + | 0.759453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.0000 | − | 38.1051i | −0.802791 | − | 1.39048i | −0.917772 | − | 0.397108i | \(-0.870014\pi\) |
0.114981 | − | 0.993368i | \(-0.463319\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.0000 | − | 31.1769i | 0.655956 | − | 1.13615i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 36.0000 | 1.31017 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.00000 | + | 5.19615i | −0.108893 | + | 0.188608i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.0000 | − | 46.7654i | −0.978749 | − | 1.69524i | −0.666962 | − | 0.745091i | \(-0.732406\pi\) |
−0.311787 | − | 0.950152i | \(-0.600927\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.0000 | + | 17.3205i | −0.724049 | + | 0.627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 24.0000 | + | 41.5692i | 0.867722 | + | 1.50294i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.50000 | + | 7.79423i | −0.162486 | + | 0.281433i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.0000 | −1.37032 | −0.685158 | − | 0.728395i | \(-0.740267\pi\) | ||||
−0.685158 | + | 0.728395i | \(0.740267\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −63.0000 | −2.26889 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.0000 | − | 20.7846i | 0.431610 | − | 0.747570i | −0.565402 | − | 0.824815i | \(-0.691279\pi\) |
0.997012 | + | 0.0772449i | \(0.0246123\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.0000 | + | 38.1051i | 0.790263 | + | 1.36878i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.0000 | − | 5.19615i | −0.538122 | − | 0.186411i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.00000 | − | 10.3923i | −0.214972 | − | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | − | 3.46410i | 0.0715656 | − | 0.123955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.00000 | 0.321634 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.0000 | −0.571064 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.0000 | + | 19.0526i | −0.392108 | + | 0.679150i | −0.992727 | − | 0.120384i | \(-0.961587\pi\) |
0.600620 | + | 0.799535i | \(0.294921\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.50000 | + | 7.79423i | 0.160204 | + | 0.277482i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42.5000 | + | 14.7224i | 1.51113 | + | 0.523469i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.50000 | − | 4.33013i | −0.0887776 | − | 0.153767i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −72.0000 | + | 124.708i | −2.55358 | + | 4.42292i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.0000 | 1.34603 | 0.673015 | − | 0.739629i | \(-0.264999\pi\) | ||||
0.673015 | + | 0.739629i | \(0.264999\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.00000 | −0.141510 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.0000 | + | 31.1769i | −0.635999 | + | 1.10158i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.00000 | + | 1.73205i | 0.0352892 | + | 0.0611227i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0000 | − | 13.8564i | 0.563926 | − | 0.488374i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.0000 | − | 31.1769i | −0.633630 | − | 1.09748i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.0000 | − | 41.5692i | 0.843795 | − | 1.46150i | −0.0428684 | − | 0.999081i | \(-0.513650\pi\) |
0.886664 | − | 0.462415i | \(-0.153017\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.0000 | 0.983213 | 0.491606 | − | 0.870817i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870817i | \(0.336410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −75.0000 | −2.63036 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26.0000 | + | 45.0333i | −0.910740 | + | 1.57745i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0000 | − | 20.7846i | −0.419827 | − | 0.727161i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.00000 | + | 15.5885i | 0.104828 | + | 0.544705i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.50000 | + | 12.9904i | 0.261752 | + | 0.453367i | 0.966708 | − | 0.255884i | \(-0.0823665\pi\) |
−0.704956 | + | 0.709251i | \(0.749033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.0000 | − | 32.9090i | 0.662298 | − | 1.14713i | −0.317712 | − | 0.948187i | \(-0.602914\pi\) |
0.980010 | − | 0.198947i | \(-0.0637522\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 33.0000 | 1.14891 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.0000 | 0.765015 | 0.382507 | − | 0.923952i | \(-0.375061\pi\) | ||||
0.382507 | + | 0.923952i | \(0.375061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.00000 | + | 13.8564i | −0.277851 | + | 0.481253i | −0.970851 | − | 0.239686i | \(-0.922956\pi\) |
0.692999 | + | 0.720938i | \(0.256289\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.50000 | + | 7.79423i | 0.156103 | + | 0.270379i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.0000 | + | 5.19615i | −0.450423 | + | 0.180036i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.0000 | + | 58.8897i | 1.17662 | + | 2.03796i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.0000 | − | 31.1769i | 0.622171 | − | 1.07763i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −54.0000 | −1.86429 | −0.932144 | − | 0.362089i | \(-0.882064\pi\) | ||||
−0.932144 | + | 0.362089i | \(0.882064\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.0000 | − | 25.9808i | 0.516627 | − | 0.894825i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.0000 | − | 41.5692i | −0.825625 | − | 1.43002i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.500000 | − | 2.59808i | −0.0171802 | − | 0.0892710i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.00000 | − | 15.5885i | −0.308879 | − | 0.534994i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.00000 | − | 3.46410i | 0.0685591 | − | 0.118748i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.0000 | 1.71197 | 0.855984 | − | 0.517003i | \(-0.172952\pi\) | ||||
0.855984 | + | 0.517003i | \(0.172952\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 144.000 | 4.92470 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.00000 | − | 3.46410i | 0.0683187 | − | 0.118331i | −0.829843 | − | 0.557998i | \(-0.811570\pi\) |
0.898161 | + | 0.439666i | \(0.144903\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.50000 | − | 14.7224i | −0.290016 | − | 0.502323i | 0.683797 | − | 0.729672i | \(-0.260327\pi\) |
−0.973813 | + | 0.227349i | \(0.926994\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.0000 | − | 10.3923i | 0.408959 | − | 0.354169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.00000 | + | 8.66025i | 0.170202 | + | 0.294798i | 0.938490 | − | 0.345305i | \(-0.112225\pi\) |
−0.768288 | + | 0.640104i | \(0.778891\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0000 | + | 17.3205i | −0.340010 | + | 0.588915i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −39.0000 | −1.32451 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.0000 | 0.508840 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.50000 | − | 7.79423i | 0.152477 | − | 0.264097i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.0000 | + | 25.9808i | 0.507673 | + | 0.879316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −60.0000 | − | 20.7846i | −2.02837 | − | 0.702648i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.5000 | − | 21.6506i | −0.422095 | − | 0.731090i | 0.574049 | − | 0.818821i | \(-0.305372\pi\) |
−0.996144 | + | 0.0877308i | \(0.972038\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.00000 | − | 15.5885i | 0.303562 | − | 0.525786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.00000 | 0.303218 | 0.151609 | − | 0.988441i | \(-0.451555\pi\) | ||||
0.151609 | + | 0.988441i | \(0.451555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.00000 | −0.0336527 | −0.0168263 | − | 0.999858i | \(-0.505356\pi\) | ||||
−0.0168263 | + | 0.999858i | \(0.505356\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −54.0000 | + | 93.5307i | −1.81519 | + | 3.14400i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.50000 | − | 14.7224i | −0.285402 | − | 0.494331i | 0.687305 | − | 0.726369i | \(-0.258794\pi\) |
−0.972707 | + | 0.232038i | \(0.925460\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.5000 | − | 4.33013i | −0.419237 | − | 0.145228i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.50000 | − | 7.79423i | −0.150756 | − | 0.261116i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.00000 | + | 10.3923i | −0.200782 | + | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 52.0000 | 1.73817 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.00000 | −0.200334 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.00000 | − | 3.46410i | 0.0667037 | − | 0.115534i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | + | 20.7846i | 0.399778 | + | 0.692436i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.0000 | − | 20.7846i | 0.798670 | − | 0.691669i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44.0000 | − | 76.2102i | −1.46261 | − | 2.53331i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.0000 | − | 38.1051i | 0.730498 | − | 1.26526i | −0.226173 | − | 0.974087i | \(-0.572621\pi\) |
0.956671 | − | 0.291172i | \(-0.0940453\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −90.0000 | −2.98511 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.0000 | 1.78910 | 0.894550 | − | 0.446968i | \(-0.147496\pi\) | ||||
0.894550 | + | 0.446968i | \(0.147496\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.00000 | + | 5.19615i | −0.0992855 | + | 0.171968i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −30.0000 | − | 51.9615i | −0.991769 | − | 1.71780i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.00000 | − | 46.7654i | −0.297206 | − | 1.54433i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.0000 | − | 20.7846i | −0.395843 | − | 0.685621i | 0.597365 | − | 0.801970i | \(-0.296214\pi\) |
−0.993208 | + | 0.116348i | \(0.962881\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 48.0000 | − | 83.1384i | 1.58165 | − | 2.73950i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.00000 | 0.131662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.0000 | −0.723356 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 36.0000 | − | 62.3538i | 1.18240 | − | 2.04797i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.5000 | + | 28.5788i | 0.541347 | + | 0.937641i | 0.998827 | + | 0.0484211i | \(0.0154190\pi\) |
−0.457480 | + | 0.889220i | \(0.651248\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.00000 | + | 41.5692i | −0.196642 | + | 1.36238i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −42.0000 | − | 72.7461i | −1.37502 | − | 2.38160i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.00000 | − | 6.92820i | 0.130814 | − | 0.226576i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.0000 | −0.392023 | −0.196011 | − | 0.980602i | \(-0.562799\pi\) | ||||
−0.196011 | + | 0.980602i | \(0.562799\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.00000 | 0.0979013 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.5000 | + | 47.6314i | −0.896474 | + | 1.55274i | −0.0645052 | + | 0.997917i | \(0.520547\pi\) |
−0.831969 | + | 0.554822i | \(0.812786\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.00000 | + | 3.46410i | 0.0651290 | + | 0.112807i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.0000 | + | 93.5307i | 0.585540 | + | 3.04256i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.00000 | − | 13.8564i | −0.259965 | − | 0.450273i | 0.706267 | − | 0.707945i | \(-0.250378\pi\) |
−0.966232 | + | 0.257673i | \(0.917044\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.00000 | + | 1.73205i | −0.0324614 | + | 0.0562247i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −36.0000 | −1.16738 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.0000 | 1.81402 | 0.907009 | − | 0.421111i | \(-0.138360\pi\) | ||||
0.907009 | + | 0.421111i | \(0.138360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.0000 | + | 48.4974i | −0.906059 | + | 1.56934i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.50000 | − | 2.59808i | −0.0484881 | − | 0.0839839i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.0000 | − | 15.5885i | 0.581250 | − | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 24.0000 | − | 41.5692i | 0.773389 | − | 1.33955i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 88.0000 | 2.83282 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56.0000 | −1.80084 | −0.900419 | − | 0.435023i | \(-0.856740\pi\) | ||||
−0.900419 | + | 0.435023i | \(0.856740\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.0000 | − | 31.1769i | 0.578243 | − | 1.00155i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.50000 | − | 11.2583i | −0.208595 | − | 0.361297i | 0.742677 | − | 0.669650i | \(-0.233556\pi\) |
−0.951272 | + | 0.308353i | \(0.900222\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.0000 | − | 6.92820i | −0.641171 | − | 0.222108i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.5000 | + | 28.5788i | 0.528423 | + | 0.915255i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.00000 | + | 12.1244i | −0.223950 | + | 0.387893i | −0.956004 | − | 0.293354i | \(-0.905229\pi\) |
0.732054 | + | 0.681247i | \(0.238562\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 60.0000 | 1.91565 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.00000 | − | 15.5885i | 0.287055 | − | 0.497195i | −0.686050 | − | 0.727554i | \(-0.740657\pi\) |
0.973106 | + | 0.230360i | \(0.0739903\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | − | 10.3923i | −0.191176 | − | 0.331126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.0000 | − | 5.19615i | −0.477455 | − | 0.165395i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.00000 | + | 6.92820i | 0.127193 | + | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.0000 | + | 17.3205i | −0.317660 | + | 0.550204i | −0.979999 | − | 0.199000i | \(-0.936231\pi\) |
0.662339 | + | 0.749204i | \(0.269564\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.0000 | −0.666415 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 40.0000 | 1.26809 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.0000 | − | 36.3731i | 0.665077 | − | 1.15195i | −0.314188 | − | 0.949361i | \(-0.601732\pi\) |
0.979265 | − | 0.202586i | \(-0.0649345\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.00000 | + | 15.5885i | 0.284747 | + | 0.493197i |
(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 | 1232.2.q.a.529.1 | 2 | ||
4.3 | odd | 2 | 154.2.e.d.67.1 | yes | 2 | ||
7.2 | even | 3 | inner | 1232.2.q.a.177.1 | 2 | ||
7.3 | odd | 6 | 8624.2.a.d.1.1 | 1 | |||
7.4 | even | 3 | 8624.2.a.bd.1.1 | 1 | |||
12.11 | even | 2 | 1386.2.k.a.991.1 | 2 | |||
28.3 | even | 6 | 1078.2.a.f.1.1 | 1 | |||
28.11 | odd | 6 | 1078.2.a.a.1.1 | 1 | |||
28.19 | even | 6 | 1078.2.e.g.177.1 | 2 | |||
28.23 | odd | 6 | 154.2.e.d.23.1 | ✓ | 2 | ||
28.27 | even | 2 | 1078.2.e.g.67.1 | 2 | |||
84.11 | even | 6 | 9702.2.a.cg.1.1 | 1 | |||
84.23 | even | 6 | 1386.2.k.a.793.1 | 2 | |||
84.59 | odd | 6 | 9702.2.a.bb.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.d.23.1 | ✓ | 2 | 28.23 | odd | 6 | ||
154.2.e.d.67.1 | yes | 2 | 4.3 | odd | 2 | ||
1078.2.a.a.1.1 | 1 | 28.11 | odd | 6 | |||
1078.2.a.f.1.1 | 1 | 28.3 | even | 6 | |||
1078.2.e.g.67.1 | 2 | 28.27 | even | 2 | |||
1078.2.e.g.177.1 | 2 | 28.19 | even | 6 | |||
1232.2.q.a.177.1 | 2 | 7.2 | even | 3 | inner | ||
1232.2.q.a.529.1 | 2 | 1.1 | even | 1 | trivial | ||
1386.2.k.a.793.1 | 2 | 84.23 | even | 6 | |||
1386.2.k.a.991.1 | 2 | 12.11 | even | 2 | |||
8624.2.a.d.1.1 | 1 | 7.3 | odd | 6 | |||
8624.2.a.bd.1.1 | 1 | 7.4 | even | 3 | |||
9702.2.a.bb.1.1 | 1 | 84.59 | odd | 6 | |||
9702.2.a.cg.1.1 | 1 | 84.11 | even | 6 |