Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(793,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("1386.793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.k (of order \(3\), 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: | \(11.0672657201\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 793.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.793 |
Dual form | 1386.2.k.a.991.1 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −2.00000 | + | 3.46410i | −0.894427 | + | 1.54919i | −0.0599153 | + | 0.998203i | \(0.519083\pi\) |
−0.834512 | + | 0.550990i | \(0.814250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.00000 | − | 3.46410i | −0.632456 | − | 1.09545i | ||||
\(11\) | −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 | \(0.544284\pi\) | |||||||
\(14\) | 0.500000 | − | 2.59808i | 0.133631 | − | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.00000 | + | 1.73205i | 0.242536 | + | 0.420084i | 0.961436 | − | 0.275029i | \(-0.0886875\pi\) |
−0.718900 | + | 0.695113i | \(0.755354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | + | 5.19615i | −0.688247 | + | 1.19208i | 0.284157 | + | 0.958778i | \(0.408286\pi\) |
−0.972404 | + | 0.233301i | \(0.925047\pi\) | |||||||
\(20\) | 4.00000 | 0.894427 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −1.00000 | + | 1.73205i | −0.208514 | + | 0.361158i | −0.951247 | − | 0.308431i | \(-0.900196\pi\) |
0.742732 | + | 0.669588i | \(0.233529\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.50000 | − | 9.52628i | −1.10000 | − | 1.90526i | ||||
\(26\) | 0.500000 | − | 0.866025i | 0.0980581 | − | 0.169842i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.00000 | + | 1.73205i | 0.377964 | + | 0.327327i | ||||
\(29\) | −1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928477 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | − | 3.46410i | −0.359211 | − | 0.622171i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 2.00000 | − | 10.3923i | 0.338062 | − | 1.75662i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | − | 1.73205i | 0.164399 | − | 0.284747i | −0.772043 | − | 0.635571i | \(-0.780765\pi\) |
0.936442 | + | 0.350823i | \(0.114098\pi\) | |||||||
\(38\) | −3.00000 | − | 5.19615i | −0.486664 | − | 0.842927i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.00000 | + | 3.46410i | −0.316228 | + | 0.547723i | ||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | − | 1.73205i | −0.147442 | − | 0.255377i | ||||
\(47\) | 1.00000 | − | 1.73205i | 0.145865 | − | 0.252646i | −0.783830 | − | 0.620975i | \(-0.786737\pi\) |
0.929695 | + | 0.368329i | \(0.120070\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 11.0000 | 1.55563 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.500000 | + | 0.866025i | 0.0693375 | + | 0.120096i | ||||
\(53\) | −6.00000 | − | 10.3923i | −0.824163 | − | 1.42749i | −0.902557 | − | 0.430570i | \(-0.858312\pi\) |
0.0783936 | − | 0.996922i | \(-0.475021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | −2.50000 | + | 0.866025i | −0.334077 | + | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.500000 | − | 0.866025i | 0.0656532 | − | 0.113715i | ||||
\(59\) | 4.50000 | + | 7.79423i | 0.585850 | + | 1.01472i | 0.994769 | + | 0.102151i | \(0.0325726\pi\) |
−0.408919 | + | 0.912571i | \(0.634094\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.50000 | − | 4.33013i | 0.320092 | − | 0.554416i | −0.660415 | − | 0.750901i | \(-0.729619\pi\) |
0.980507 | + | 0.196485i | \(0.0629528\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.00000 | − | 3.46410i | 0.248069 | − | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.50000 | + | 7.79423i | 0.549762 | + | 0.952217i | 0.998290 | + | 0.0584478i | \(0.0186151\pi\) |
−0.448528 | + | 0.893769i | \(0.648052\pi\) | |||||||
\(68\) | 1.00000 | − | 1.73205i | 0.121268 | − | 0.210042i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.00000 | + | 6.92820i | 0.956183 | + | 0.828079i | ||||
\(71\) | −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 | 0.918594 | − | 0.395203i | \(-0.129326\pi\) |
−0.801553 | + | 0.597924i | \(0.795992\pi\) | |||||||
\(74\) | 1.00000 | + | 1.73205i | 0.116248 | + | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | 2.00000 | + | 1.73205i | 0.227921 | + | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.50000 | − | 12.9904i | 0.843816 | − | 1.46153i | −0.0428296 | − | 0.999082i | \(-0.513637\pi\) |
0.886646 | − | 0.462450i | \(-0.153029\pi\) | |||||||
\(80\) | −2.00000 | − | 3.46410i | −0.223607 | − | 0.387298i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.00000 | + | 1.73205i | −0.110432 | + | 0.191273i | ||||
\(83\) | 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 | ||||||||
\(86\) | −2.00000 | + | 3.46410i | −0.215666 | + | 0.373544i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.50000 | − | 0.866025i | 0.262071 | − | 0.0907841i | ||||
\(92\) | 2.00000 | 0.208514 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.00000 | + | 1.73205i | 0.103142 | + | 0.178647i | ||||
\(95\) | −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 | \(0.581693\pi\) | |||||||
\(98\) | 1.00000 | + | 6.92820i | 0.101015 | + | 0.699854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.50000 | + | 9.52628i | −0.550000 | + | 0.952628i | ||||
\(101\) | −7.50000 | − | 12.9904i | −0.746278 | − | 1.29259i | −0.949595 | − | 0.313478i | \(-0.898506\pi\) |
0.203317 | − | 0.979113i | \(-0.434828\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.00000 | + | 10.3923i | −0.591198 | + | 1.02398i | 0.402874 | + | 0.915255i | \(0.368011\pi\) |
−0.994071 | + | 0.108729i | \(0.965322\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.0000 | 1.16554 | ||||||||
\(107\) | 4.00000 | − | 6.92820i | 0.386695 | − | 0.669775i | −0.605308 | − | 0.795991i | \(-0.706950\pi\) |
0.992003 | + | 0.126217i | \(0.0402834\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.00000 | − | 8.66025i | −0.478913 | − | 0.829502i | 0.520794 | − | 0.853682i | \(-0.325636\pi\) |
−0.999708 | + | 0.0241802i | \(0.992302\pi\) | |||||||
\(110\) | −2.00000 | + | 3.46410i | −0.190693 | + | 0.330289i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | − | 2.59808i | 0.0472456 | − | 0.245495i | ||||
\(113\) | −17.0000 | −1.59923 | −0.799613 | − | 0.600516i | \(-0.794962\pi\) | ||||
−0.799613 | + | 0.600516i | \(0.794962\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | − | 6.92820i | −0.373002 | − | 0.646058i | ||||
\(116\) | 0.500000 | + | 0.866025i | 0.0464238 | + | 0.0804084i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.00000 | −0.828517 | ||||||||
\(119\) | −4.00000 | − | 3.46410i | −0.366679 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 2.50000 | + | 4.33013i | 0.226339 | + | 0.392031i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.00000 | + | 3.46410i | −0.179605 | + | 0.311086i | ||||
\(125\) | 24.0000 | 2.14663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.00000 | 0.443678 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | + | 3.46410i | 0.175412 | + | 0.303822i | ||||
\(131\) | −9.00000 | + | 15.5885i | −0.786334 | + | 1.36197i | 0.141865 | + | 0.989886i | \(0.454690\pi\) |
−0.928199 | + | 0.372084i | \(0.878643\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | − | 15.5885i | 0.260133 | − | 1.35169i | ||||
\(134\) | −9.00000 | −0.777482 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.00000 | + | 1.73205i | 0.0857493 | + | 0.148522i | ||||
\(137\) | −4.50000 | − | 7.79423i | −0.384461 | − | 0.665906i | 0.607233 | − | 0.794524i | \(-0.292279\pi\) |
−0.991694 | + | 0.128618i | \(0.958946\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | −10.0000 | + | 3.46410i | −0.845154 | + | 0.292770i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.00000 | − | 3.46410i | 0.167836 | − | 0.290701i | ||||
\(143\) | 0.500000 | + | 0.866025i | 0.0418121 | + | 0.0724207i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | − | 3.46410i | 0.166091 | − | 0.287678i | ||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | −5.00000 | + | 8.66025i | −0.409616 | + | 0.709476i | −0.994847 | − | 0.101391i | \(-0.967671\pi\) |
0.585231 | + | 0.810867i | \(0.301004\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.50000 | − | 7.79423i | −0.366205 | − | 0.634285i | 0.622764 | − | 0.782410i | \(-0.286010\pi\) |
−0.988969 | + | 0.148124i | \(0.952676\pi\) | |||||||
\(152\) | −3.00000 | + | 5.19615i | −0.243332 | + | 0.421464i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.50000 | + | 0.866025i | −0.201456 | + | 0.0697863i | ||||
\(155\) | 16.0000 | 1.28515 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | − | 3.46410i | −0.159617 | − | 0.276465i | 0.775113 | − | 0.631822i | \(-0.217693\pi\) |
−0.934731 | + | 0.355357i | \(0.884359\pi\) | |||||||
\(158\) | 7.50000 | + | 12.9904i | 0.596668 | + | 1.03346i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.00000 | 0.316228 | ||||||||
\(161\) | 1.00000 | − | 5.19615i | 0.0788110 | − | 0.409514i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.50000 | + | 11.2583i | −0.509119 | + | 0.881820i | 0.490825 | + | 0.871258i | \(0.336695\pi\) |
−0.999944 | + | 0.0105623i | \(0.996638\pi\) | |||||||
\(164\) | −1.00000 | − | 1.73205i | −0.0780869 | − | 0.135250i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.00000 | + | 5.19615i | −0.232845 | + | 0.403300i | ||||
\(167\) | 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 | ||||||||
\(170\) | 4.00000 | − | 6.92820i | 0.306786 | − | 0.531369i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.00000 | − | 3.46410i | −0.152499 | − | 0.264135i | ||||
\(173\) | −2.50000 | + | 4.33013i | −0.190071 | + | 0.329213i | −0.945274 | − | 0.326278i | \(-0.894205\pi\) |
0.755202 | + | 0.655492i | \(0.227539\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.0000 | + | 19.0526i | 1.66304 | + | 1.44024i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.00000 | + | 5.19615i | 0.224860 | + | 0.389468i | ||||
\(179\) | 6.50000 | + | 11.2583i | 0.485833 | + | 0.841487i | 0.999867 | − | 0.0162823i | \(-0.00518305\pi\) |
−0.514035 | + | 0.857769i | \(0.671850\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | −0.500000 | + | 2.59808i | −0.0370625 | + | 0.192582i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.00000 | + | 1.73205i | −0.0737210 | + | 0.127688i | ||||
\(185\) | 4.00000 | + | 6.92820i | 0.294086 | + | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.00000 | − | 1.73205i | 0.0731272 | − | 0.126660i | ||||
\(188\) | −2.00000 | −0.145865 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 24.0000 | 1.74114 | ||||||||
\(191\) | 7.00000 | − | 12.1244i | 0.506502 | − | 0.877288i | −0.493469 | − | 0.869763i | \(-0.664272\pi\) |
0.999972 | − | 0.00752447i | \(-0.00239513\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0000 | + | 19.0526i | 0.791797 | + | 1.37143i | 0.924853 | + | 0.380325i | \(0.124188\pi\) |
−0.133056 | + | 0.991109i | \(0.542479\pi\) | |||||||
\(194\) | 2.50000 | − | 4.33013i | 0.179490 | − | 0.310885i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | 3.00000 | 0.213741 | 0.106871 | − | 0.994273i | \(-0.465917\pi\) | ||||
0.106871 | + | 0.994273i | \(0.465917\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.00000 | − | 8.66025i | −0.354441 | − | 0.613909i | 0.632581 | − | 0.774494i | \(-0.281995\pi\) |
−0.987022 | + | 0.160585i | \(0.948662\pi\) | |||||||
\(200\) | −5.50000 | − | 9.52628i | −0.388909 | − | 0.673610i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.0000 | 1.05540 | ||||||||
\(203\) | 2.50000 | − | 0.866025i | 0.175466 | − | 0.0607831i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | + | 6.92820i | −0.279372 | + | 0.483887i | ||||
\(206\) | −6.00000 | − | 10.3923i | −0.418040 | − | 0.724066i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.500000 | − | 0.866025i | 0.0346688 | − | 0.0600481i | ||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.0000 | −0.963800 | −0.481900 | − | 0.876226i | \(-0.660053\pi\) | ||||
−0.481900 | + | 0.876226i | \(0.660053\pi\) | |||||||
\(212\) | −6.00000 | + | 10.3923i | −0.412082 | + | 0.713746i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.00000 | + | 6.92820i | 0.273434 | + | 0.473602i | ||||
\(215\) | −8.00000 | + | 13.8564i | −0.545595 | + | 0.944999i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | + | 6.92820i | 0.543075 | + | 0.470317i | ||||
\(218\) | 10.0000 | 0.677285 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.00000 | − | 3.46410i | −0.134840 | − | 0.233550i | ||||
\(221\) | −1.00000 | − | 1.73205i | −0.0672673 | − | 0.116510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.0000 | −1.74109 | −0.870544 | − | 0.492090i | \(-0.836233\pi\) | ||||
−0.870544 | + | 0.492090i | \(0.836233\pi\) | |||||||
\(224\) | 2.00000 | + | 1.73205i | 0.133631 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.50000 | − | 14.7224i | 0.565412 | − | 0.979322i | ||||
\(227\) | 5.00000 | + | 8.66025i | 0.331862 | + | 0.574801i | 0.982877 | − | 0.184263i | \(-0.0589899\pi\) |
−0.651015 | + | 0.759065i | \(0.725657\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.00000 | − | 13.8564i | 0.528655 | − | 0.915657i | −0.470787 | − | 0.882247i | \(-0.656030\pi\) |
0.999442 | − | 0.0334101i | \(-0.0106368\pi\) | |||||||
\(230\) | 8.00000 | 0.527504 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | 3.00000 | − | 5.19615i | 0.196537 | − | 0.340411i | −0.750867 | − | 0.660454i | \(-0.770364\pi\) |
0.947403 | + | 0.320043i | \(0.103697\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | + | 6.92820i | 0.260931 | + | 0.451946i | ||||
\(236\) | 4.50000 | − | 7.79423i | 0.292925 | − | 0.507361i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.00000 | − | 1.73205i | 0.324102 | − | 0.112272i | ||||
\(239\) | −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 | −0.706260 | − | 0.707953i | \(-0.749619\pi\) |
−0.259975 | − | 0.965615i | \(-0.583714\pi\) | |||||||
\(242\) | −0.500000 | − | 0.866025i | −0.0321412 | − | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.00000 | −0.320092 | ||||||||
\(245\) | 4.00000 | + | 27.7128i | 0.255551 | + | 1.77051i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.00000 | − | 5.19615i | 0.190885 | − | 0.330623i | ||||
\(248\) | −2.00000 | − | 3.46410i | −0.127000 | − | 0.219971i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.0000 | + | 20.7846i | −0.758947 | + | 1.31453i | ||||
\(251\) | −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 | ||||||||
\(254\) | −2.50000 | + | 4.33013i | −0.156864 | + | 0.271696i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −10.5000 | + | 18.1865i | −0.654972 | + | 1.13444i | 0.326929 | + | 0.945049i | \(0.393986\pi\) |
−0.981901 | + | 0.189396i | \(0.939347\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00000 | + | 5.19615i | −0.0621370 | + | 0.322873i | ||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.00000 | − | 15.5885i | −0.556022 | − | 0.963058i | ||||
\(263\) | 1.50000 | + | 2.59808i | 0.0924940 | + | 0.160204i | 0.908560 | − | 0.417755i | \(-0.137183\pi\) |
−0.816066 | + | 0.577959i | \(0.803849\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 48.0000 | 2.94862 | ||||||||
\(266\) | 12.0000 | + | 10.3923i | 0.735767 | + | 0.637193i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.50000 | − | 7.79423i | 0.274881 | − | 0.476108i | ||||
\(269\) | 6.00000 | + | 10.3923i | 0.365826 | + | 0.633630i | 0.988908 | − | 0.148527i | \(-0.0474530\pi\) |
−0.623082 | + | 0.782157i | \(0.714120\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5000 | + | 21.6506i | −0.759321 | + | 1.31518i | 0.183876 | + | 0.982949i | \(0.441135\pi\) |
−0.943197 | + | 0.332233i | \(0.892198\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.00000 | 0.543710 | ||||||||
\(275\) | −5.50000 | + | 9.52628i | −0.331662 | + | 0.574456i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.50000 | + | 2.59808i | 0.0901263 | + | 0.156103i | 0.907564 | − | 0.419914i | \(-0.137940\pi\) |
−0.817438 | + | 0.576017i | \(0.804606\pi\) | |||||||
\(278\) | −4.00000 | + | 6.92820i | −0.239904 | + | 0.415526i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.00000 | − | 10.3923i | 0.119523 | − | 0.621059i | ||||
\(281\) | 10.0000 | 0.596550 | 0.298275 | − | 0.954480i | \(-0.403589\pi\) | ||||
0.298275 | + | 0.954480i | \(0.403589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.00000 | + | 5.19615i | 0.178331 | + | 0.308879i | 0.941309 | − | 0.337546i | \(-0.109597\pi\) |
−0.762978 | + | 0.646425i | \(0.776263\pi\) | |||||||
\(284\) | 2.00000 | + | 3.46410i | 0.118678 | + | 0.205557i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.00000 | −0.0591312 | ||||||||
\(287\) | −5.00000 | + | 1.73205i | −0.295141 | + | 0.102240i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 2.00000 | + | 3.46410i | 0.117444 | + | 0.203419i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.00000 | − | 1.73205i | 0.0585206 | − | 0.101361i | ||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −36.0000 | −2.09600 | ||||||||
\(296\) | 1.00000 | − | 1.73205i | 0.0581238 | − | 0.100673i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.00000 | − | 8.66025i | −0.289642 | − | 0.501675i | ||||
\(299\) | 1.00000 | − | 1.73205i | 0.0578315 | − | 0.100167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0000 | + | 3.46410i | −0.576390 | + | 0.199667i | ||||
\(302\) | 9.00000 | 0.517892 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.00000 | − | 5.19615i | −0.172062 | − | 0.298020i | ||||
\(305\) | 10.0000 | + | 17.3205i | 0.572598 | + | 0.991769i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.0000 | 1.82634 | 0.913168 | − | 0.407583i | \(-0.133628\pi\) | ||||
0.913168 | + | 0.407583i | \(0.133628\pi\) | |||||||
\(308\) | 0.500000 | − | 2.59808i | 0.0284901 | − | 0.148039i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.00000 | + | 13.8564i | −0.454369 | + | 0.786991i | ||||
\(311\) | −14.0000 | − | 24.2487i | −0.793867 | − | 1.37502i | −0.923556 | − | 0.383464i | \(-0.874731\pi\) |
0.129689 | − | 0.991555i | \(-0.458602\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.500000 | + | 0.866025i | −0.0282617 | + | 0.0489506i | −0.879810 | − | 0.475325i | \(-0.842331\pi\) |
0.851549 | + | 0.524276i | \(0.175664\pi\) | |||||||
\(314\) | 4.00000 | 0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.0000 | −0.843816 | ||||||||
\(317\) | −6.00000 | + | 10.3923i | −0.336994 | + | 0.583690i | −0.983866 | − | 0.178908i | \(-0.942743\pi\) |
0.646872 | + | 0.762598i | \(0.276077\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.500000 | + | 0.866025i | 0.0279946 | + | 0.0484881i | ||||
\(320\) | −2.00000 | + | 3.46410i | −0.111803 | + | 0.193649i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.00000 | + | 3.46410i | 0.222911 | + | 0.193047i | ||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.50000 | + | 9.52628i | 0.305085 | + | 0.528423i | ||||
\(326\) | −6.50000 | − | 11.2583i | −0.360002 | − | 0.623541i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.00000 | 0.110432 | ||||||||
\(329\) | −1.00000 | + | 5.19615i | −0.0551318 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.50000 | + | 6.06218i | −0.192377 | + | 0.333207i | −0.946038 | − | 0.324057i | \(-0.894953\pi\) |
0.753660 | + | 0.657264i | \(0.228286\pi\) | |||||||
\(332\) | −3.00000 | − | 5.19615i | −0.164646 | − | 0.285176i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.50000 | + | 14.7224i | −0.465099 | + | 0.805576i | ||||
\(335\) | −36.0000 | −1.96689 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.0000 | −1.63420 | −0.817102 | − | 0.576493i | \(-0.804421\pi\) | ||||
−0.817102 | + | 0.576493i | \(0.804421\pi\) | |||||||
\(338\) | 6.00000 | − | 10.3923i | 0.326357 | − | 0.565267i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.00000 | + | 6.92820i | 0.216930 | + | 0.375735i | ||||
\(341\) | −2.00000 | + | 3.46410i | −0.108306 | + | 0.187592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.50000 | − | 4.33013i | −0.134401 | − | 0.232789i | ||||
\(347\) | −14.0000 | − | 24.2487i | −0.751559 | − | 1.30174i | −0.947067 | − | 0.321037i | \(-0.895969\pi\) |
0.195507 | − | 0.980702i | \(-0.437365\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | −27.5000 | + | 9.52628i | −1.46994 | + | 0.509201i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | −9.00000 | − | 15.5885i | −0.479022 | − | 0.829690i | 0.520689 | − | 0.853746i | \(-0.325675\pi\) |
−0.999711 | + | 0.0240566i | \(0.992342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | − | 13.8564i | 0.424596 | − | 0.735422i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.0000 | −0.687071 | ||||||||
\(359\) | −15.5000 | + | 26.8468i | −0.818059 | + | 1.41692i | 0.0890519 | + | 0.996027i | \(0.471616\pi\) |
−0.907111 | + | 0.420892i | \(0.861717\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | 11.0000 | − | 19.0526i | 0.578147 | − | 1.00138i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | − | 1.73205i | −0.104828 | − | 0.0907841i | ||||
\(365\) | −8.00000 | −0.418739 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.00000 | + | 12.1244i | 0.365397 | + | 0.632886i | 0.988840 | − | 0.148983i | \(-0.0475999\pi\) |
−0.623443 | + | 0.781869i | \(0.714267\pi\) | |||||||
\(368\) | −1.00000 | − | 1.73205i | −0.0521286 | − | 0.0902894i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.00000 | −0.415900 | ||||||||
\(371\) | 24.0000 | + | 20.7846i | 1.24602 | + | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.50000 | − | 6.06218i | 0.181223 | − | 0.313888i | −0.761074 | − | 0.648665i | \(-0.775328\pi\) |
0.942297 | + | 0.334777i | \(0.108661\pi\) | |||||||
\(374\) | 1.00000 | + | 1.73205i | 0.0517088 | + | 0.0895622i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.00000 | − | 1.73205i | 0.0515711 | − | 0.0893237i | ||||
\(377\) | 1.00000 | 0.0515026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.0000 | −1.48963 | −0.744815 | − | 0.667271i | \(-0.767462\pi\) | ||||
−0.744815 | + | 0.667271i | \(0.767462\pi\) | |||||||
\(380\) | −12.0000 | + | 20.7846i | −0.615587 | + | 1.06623i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.00000 | + | 12.1244i | 0.358151 | + | 0.620336i | ||||
\(383\) | 4.00000 | − | 6.92820i | 0.204390 | − | 0.354015i | −0.745548 | − | 0.666452i | \(-0.767812\pi\) |
0.949938 | + | 0.312437i | \(0.101145\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.0000 | + | 3.46410i | −0.509647 | + | 0.176547i | ||||
\(386\) | −22.0000 | −1.11977 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.50000 | + | 4.33013i | 0.126918 | + | 0.219829i | ||||
\(389\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 5.50000 | − | 4.33013i | 0.277792 | − | 0.218704i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.50000 | + | 2.59808i | −0.0755689 | + | 0.130889i | ||||
\(395\) | 30.0000 | + | 51.9615i | 1.50946 | + | 2.61447i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.0000 | − | 25.9808i | 0.752828 | − | 1.30394i | −0.193618 | − | 0.981077i | \(-0.562022\pi\) |
0.946447 | − | 0.322860i | \(-0.104644\pi\) | |||||||
\(398\) | 10.0000 | 0.501255 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.0000 | 0.550000 | ||||||||
\(401\) | 7.50000 | − | 12.9904i | 0.374532 | − | 0.648709i | −0.615725 | − | 0.787961i | \(-0.711137\pi\) |
0.990257 | + | 0.139253i | \(0.0444700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.00000 | + | 3.46410i | 0.0996271 | + | 0.172559i | ||||
\(404\) | −7.50000 | + | 12.9904i | −0.373139 | + | 0.646296i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.500000 | + | 2.59808i | −0.0248146 | + | 0.128940i | ||||
\(407\) | −2.00000 | −0.0991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.0000 | + | 27.7128i | 0.791149 | + | 1.37031i | 0.925256 | + | 0.379344i | \(0.123850\pi\) |
−0.134107 | + | 0.990967i | \(0.542817\pi\) | |||||||
\(410\) | −4.00000 | − | 6.92820i | −0.197546 | − | 0.342160i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.0000 | 0.591198 | ||||||||
\(413\) | −18.0000 | − | 15.5885i | −0.885722 | − | 0.767058i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | + | 20.7846i | −0.589057 | + | 1.02028i | ||||
\(416\) | 0.500000 | + | 0.866025i | 0.0245145 | + | 0.0424604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.00000 | + | 5.19615i | −0.146735 | + | 0.254152i | ||||
\(419\) | 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 | \(0.662044\pi\) | |||||||
\(422\) | 7.00000 | − | 12.1244i | 0.340755 | − | 0.590204i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | − | 10.3923i | −0.291386 | − | 0.504695i | ||||
\(425\) | 11.0000 | − | 19.0526i | 0.533578 | − | 0.924185i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.50000 | + | 12.9904i | −0.120983 | + | 0.628649i | ||||
\(428\) | −8.00000 | −0.386695 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | − | 13.8564i | −0.385794 | − | 0.668215i | ||||
\(431\) | 0.500000 | + | 0.866025i | 0.0240842 | + | 0.0417150i | 0.877816 | − | 0.478997i | \(-0.159000\pi\) |
−0.853732 | + | 0.520712i | \(0.825666\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0000 | −0.480569 | −0.240285 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240285 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(434\) | −10.0000 | + | 3.46410i | −0.480015 | + | 0.166282i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.00000 | + | 8.66025i | −0.239457 | + | 0.414751i | ||||
\(437\) | −6.00000 | − | 10.3923i | −0.287019 | − | 0.497131i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.50000 | − | 4.33013i | 0.119318 | − | 0.206666i | −0.800179 | − | 0.599761i | \(-0.795262\pi\) |
0.919498 | + | 0.393095i | \(0.128596\pi\) | |||||||
\(440\) | 4.00000 | 0.190693 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.00000 | 0.0951303 | ||||||||
\(443\) | −6.00000 | + | 10.3923i | −0.285069 | + | 0.493753i | −0.972626 | − | 0.232377i | \(-0.925350\pi\) |
0.687557 | + | 0.726130i | \(0.258683\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0000 | + | 20.7846i | 0.568855 | + | 0.985285i | ||||
\(446\) | 13.0000 | − | 22.5167i | 0.615568 | − | 1.06619i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.50000 | + | 0.866025i | −0.118114 | + | 0.0409159i | ||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.00000 | − | 1.73205i | −0.0470882 | − | 0.0815591i | ||||
\(452\) | 8.50000 | + | 14.7224i | 0.399806 | + | 0.692485i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.0000 | −0.469323 | ||||||||
\(455\) | −2.00000 | + | 10.3923i | −0.0937614 | + | 0.487199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | + | 1.73205i | −0.0467780 | + | 0.0810219i | −0.888466 | − | 0.458942i | \(-0.848229\pi\) |
0.841688 | + | 0.539964i | \(0.181562\pi\) | |||||||
\(458\) | 8.00000 | + | 13.8564i | 0.373815 | + | 0.647467i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.00000 | + | 6.92820i | −0.186501 | + | 0.323029i | ||||
\(461\) | 3.00000 | 0.139724 | 0.0698620 | − | 0.997557i | \(-0.477744\pi\) | ||||
0.0698620 | + | 0.997557i | \(0.477744\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0000 | −0.650635 | −0.325318 | − | 0.945605i | \(-0.605471\pi\) | ||||
−0.325318 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(464\) | 0.500000 | − | 0.866025i | 0.0232119 | − | 0.0402042i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.00000 | + | 5.19615i | 0.138972 | + | 0.240707i | ||||
\(467\) | −6.00000 | + | 10.3923i | −0.277647 | + | 0.480899i | −0.970799 | − | 0.239892i | \(-0.922888\pi\) |
0.693153 | + | 0.720791i | \(0.256221\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.0000 | − | 15.5885i | −0.831163 | − | 0.719808i | ||||
\(470\) | −8.00000 | −0.369012 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.50000 | + | 7.79423i | 0.207129 | + | 0.358758i | ||||
\(473\) | −2.00000 | − | 3.46410i | −0.0919601 | − | 0.159280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 66.0000 | 3.02829 | ||||||||
\(476\) | −1.00000 | + | 5.19615i | −0.0458349 | + | 0.238165i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.50000 | − | 16.4545i | 0.434520 | − | 0.752611i | ||||
\(479\) | −18.5000 | − | 32.0429i | −0.845287 | − | 1.46408i | −0.885372 | − | 0.464883i | \(-0.846096\pi\) |
0.0400855 | − | 0.999196i | \(-0.487237\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.00000 | + | 1.73205i | −0.0455961 | + | 0.0789747i | ||||
\(482\) | 30.0000 | 1.36646 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 10.0000 | − | 17.3205i | 0.454077 | − | 0.786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.00000 | + | 3.46410i | 0.0906287 | + | 0.156973i | 0.907776 | − | 0.419456i | \(-0.137779\pi\) |
−0.817147 | + | 0.576429i | \(0.804446\pi\) | |||||||
\(488\) | 2.50000 | − | 4.33013i | 0.113170 | − | 0.196016i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −26.0000 | − | 10.3923i | −1.17456 | − | 0.469476i | ||||
\(491\) | −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 | ||||
\(494\) | 3.00000 | + | 5.19615i | 0.134976 | + | 0.233786i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | 10.0000 | − | 3.46410i | 0.448561 | − | 0.155386i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.00000 | − | 13.8564i | 0.358129 | − | 0.620298i | −0.629519 | − | 0.776985i | \(-0.716748\pi\) |
0.987648 | + | 0.156687i | \(0.0500814\pi\) | |||||||
\(500\) | −12.0000 | − | 20.7846i | −0.536656 | − | 0.929516i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.00000 | − | 10.3923i | 0.267793 | − | 0.463831i | ||||
\(503\) | 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 | ||||||||
\(506\) | −1.00000 | + | 1.73205i | −0.0444554 | + | 0.0769991i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.50000 | − | 4.33013i | −0.110920 | − | 0.192118i | ||||
\(509\) | 1.00000 | − | 1.73205i | 0.0443242 | − | 0.0767718i | −0.843012 | − | 0.537895i | \(-0.819220\pi\) |
0.887336 | + | 0.461123i | \(0.152553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.00000 | − | 3.46410i | −0.176950 | − | 0.153243i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.5000 | − | 18.1865i | −0.463135 | − | 0.802174i | ||||
\(515\) | −24.0000 | − | 41.5692i | −1.05757 | − | 1.83176i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.00000 | −0.0879599 | ||||||||
\(518\) | −4.00000 | − | 3.46410i | −0.175750 | − | 0.152204i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.00000 | − | 3.46410i | 0.0877058 | − | 0.151911i | ||||
\(521\) | −13.0000 | − | 22.5167i | −0.569540 | − | 0.986473i | −0.996611 | − | 0.0822547i | \(-0.973788\pi\) |
0.427071 | − | 0.904218i | \(-0.359545\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.0000 | + | 17.3205i | −0.437269 | + | 0.757373i | −0.997478 | − | 0.0709788i | \(-0.977388\pi\) |
0.560208 | + | 0.828352i | \(0.310721\pi\) | |||||||
\(524\) | 18.0000 | 0.786334 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.00000 | −0.130806 | ||||||||
\(527\) | 4.00000 | − | 6.92820i | 0.174243 | − | 0.301797i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.50000 | + | 16.4545i | 0.413043 | + | 0.715412i | ||||
\(530\) | −24.0000 | + | 41.5692i | −1.04249 | + | 1.80565i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −15.0000 | + | 5.19615i | −0.650332 | + | 0.225282i | ||||
\(533\) | −2.00000 | −0.0866296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.0000 | + | 27.7128i | 0.691740 | + | 1.19813i | ||||
\(536\) | 4.50000 | + | 7.79423i | 0.194370 | + | 0.336659i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.0000 | −0.517357 | ||||||||
\(539\) | −6.50000 | − | 2.59808i | −0.279975 | − | 0.111907i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5000 | − | 21.6506i | 0.537417 | − | 0.930834i | −0.461625 | − | 0.887075i | \(-0.652733\pi\) |
0.999042 | − | 0.0437584i | \(-0.0139332\pi\) | |||||||
\(542\) | −12.5000 | − | 21.6506i | −0.536921 | − | 0.929974i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.00000 | − | 1.73205i | 0.0428746 | − | 0.0742611i | ||||
\(545\) | 40.0000 | 1.71341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(548\) | −4.50000 | + | 7.79423i | −0.192230 | + | 0.332953i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.50000 | − | 9.52628i | −0.234521 | − | 0.406202i | ||||
\(551\) | 3.00000 | − | 5.19615i | 0.127804 | − | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.50000 | + | 38.9711i | −0.318932 | + | 1.65722i | ||||
\(554\) | −3.00000 | −0.127458 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.00000 | − | 6.92820i | −0.169638 | − | 0.293821i | ||||
\(557\) | 19.0000 | + | 32.9090i | 0.805056 | + | 1.39440i | 0.916253 | + | 0.400599i | \(0.131198\pi\) |
−0.111198 | + | 0.993798i | \(0.535469\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 8.00000 | + | 6.92820i | 0.338062 | + | 0.292770i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.00000 | + | 8.66025i | −0.210912 | + | 0.365311i | ||||
\(563\) | 13.0000 | + | 22.5167i | 0.547885 | + | 0.948964i | 0.998419 | + | 0.0562051i | \(0.0179001\pi\) |
−0.450535 | + | 0.892759i | \(0.648767\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 34.0000 | − | 58.8897i | 1.43039 | − | 2.47751i | ||||
\(566\) | −6.00000 | −0.252199 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | 18.0000 | − | 31.1769i | 0.754599 | − | 1.30700i | −0.190974 | − | 0.981595i | \(-0.561165\pi\) |
0.945573 | − | 0.325409i | \(-0.105502\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.0000 | + | 17.3205i | 0.418487 | + | 0.724841i | 0.995788 | − | 0.0916910i | \(-0.0292272\pi\) |
−0.577301 | + | 0.816532i | \(0.695894\pi\) | |||||||
\(572\) | 0.500000 | − | 0.866025i | 0.0209061 | − | 0.0362103i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.00000 | − | 5.19615i | 0.0417392 | − | 0.216883i | ||||
\(575\) | 22.0000 | 0.917463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.50000 | + | 6.06218i | 0.145707 | + | 0.252372i | 0.929636 | − | 0.368478i | \(-0.120121\pi\) |
−0.783930 | + | 0.620850i | \(0.786788\pi\) | |||||||
\(578\) | 6.50000 | + | 11.2583i | 0.270364 | + | 0.468285i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.00000 | −0.166091 | ||||||||
\(581\) | −15.0000 | + | 5.19615i | −0.622305 | + | 0.215573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.00000 | + | 10.3923i | −0.248495 | + | 0.430405i | ||||
\(584\) | 1.00000 | + | 1.73205i | 0.0413803 | + | 0.0716728i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.00000 | + | 5.19615i | −0.123929 | + | 0.214651i | ||||
\(587\) | 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 | ||||||||
\(590\) | 18.0000 | − | 31.1769i | 0.741048 | − | 1.28353i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000 | + | 1.73205i | 0.0410997 | + | 0.0711868i | ||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.0000 | − | 6.92820i | 0.819920 | − | 0.284029i | ||||
\(596\) | 10.0000 | 0.409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.00000 | + | 1.73205i | 0.0408930 | + | 0.0708288i | ||||
\(599\) | −12.0000 | − | 20.7846i | −0.490307 | − | 0.849236i | 0.509631 | − | 0.860393i | \(-0.329782\pi\) |
−0.999938 | + | 0.0111569i | \(0.996449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | 2.00000 | − | 10.3923i | 0.0815139 | − | 0.423559i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.50000 | + | 7.79423i | −0.183102 | + | 0.317143i | ||||
\(605\) | −2.00000 | − | 3.46410i | −0.0813116 | − | 0.140836i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.00000 | − | 13.8564i | 0.324710 | − | 0.562414i | −0.656744 | − | 0.754114i | \(-0.728067\pi\) |
0.981454 | + | 0.191700i | \(0.0614000\pi\) | |||||||
\(608\) | 6.00000 | 0.243332 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.0000 | −0.809776 | ||||||||
\(611\) | −1.00000 | + | 1.73205i | −0.0404557 | + | 0.0700713i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.0000 | − | 19.0526i | −0.444286 | − | 0.769526i | 0.553716 | − | 0.832705i | \(-0.313209\pi\) |
−0.998002 | + | 0.0631797i | \(0.979876\pi\) | |||||||
\(614\) | −16.0000 | + | 27.7128i | −0.645707 | + | 1.11840i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | + | 1.73205i | 0.0805823 | + | 0.0697863i | ||||
\(617\) | 27.0000 | 1.08698 | 0.543490 | − | 0.839416i | \(-0.317103\pi\) | ||||
0.543490 | + | 0.839416i | \(0.317103\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0000 | − | 17.3205i | −0.401934 | − | 0.696170i | 0.592025 | − | 0.805919i | \(-0.298329\pi\) |
−0.993959 | + | 0.109749i | \(0.964995\pi\) | |||||||
\(620\) | −8.00000 | − | 13.8564i | −0.321288 | − | 0.556487i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 28.0000 | 1.12270 | ||||||||
\(623\) | −3.00000 | + | 15.5885i | −0.120192 | + | 0.624538i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.5000 | + | 35.5070i | −0.820000 | + | 1.42028i | ||||
\(626\) | −0.500000 | − | 0.866025i | −0.0199840 | − | 0.0346133i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.00000 | + | 3.46410i | −0.0798087 | + | 0.138233i | ||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 7.50000 | − | 12.9904i | 0.298334 | − | 0.516730i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.00000 | − | 10.3923i | −0.238290 | − | 0.412731i | ||||
\(635\) | −10.0000 | + | 17.3205i | −0.396838 | + | 0.687343i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.50000 | + | 4.33013i | −0.217918 | + | 0.171566i | ||||
\(638\) | −1.00000 | −0.0395904 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.00000 | − | 3.46410i | −0.0790569 | − | 0.136931i | ||||
\(641\) | 4.50000 | + | 7.79423i | 0.177739 | + | 0.307854i | 0.941106 | − | 0.338112i | \(-0.109788\pi\) |
−0.763367 | + | 0.645966i | \(0.776455\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.00000 | 0.0394362 | 0.0197181 | − | 0.999806i | \(-0.493723\pi\) | ||||
0.0197181 | + | 0.999806i | \(0.493723\pi\) | |||||||
\(644\) | −5.00000 | + | 1.73205i | −0.197028 | + | 0.0682524i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.00000 | − | 10.3923i | 0.236067 | − | 0.408880i | ||||
\(647\) | 12.0000 | + | 20.7846i | 0.471769 | + | 0.817127i | 0.999478 | − | 0.0322975i | \(-0.0102824\pi\) |
−0.527710 | + | 0.849425i | \(0.676949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.50000 | − | 7.79423i | 0.176640 | − | 0.305950i | ||||
\(650\) | −11.0000 | −0.431455 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.0000 | 0.509119 | ||||||||
\(653\) | 11.0000 | − | 19.0526i | 0.430463 | − | 0.745584i | −0.566450 | − | 0.824096i | \(-0.691684\pi\) |
0.996913 | + | 0.0785119i | \(0.0250169\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.0000 | − | 62.3538i | −1.40664 | − | 2.43637i | ||||
\(656\) | −1.00000 | + | 1.73205i | −0.0390434 | + | 0.0676252i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.00000 | − | 3.46410i | −0.155936 | − | 0.135045i | ||||
\(659\) | 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 | 0.946729 | − | 0.322031i | \(-0.104366\pi\) |
−0.752252 | + | 0.658876i | \(0.771032\pi\) | |||||||
\(662\) | −3.50000 | − | 6.06218i | −0.136031 | − | 0.235613i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 48.0000 | + | 41.5692i | 1.86136 | + | 1.61199i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | − | 1.73205i | 0.0387202 | − | 0.0670653i | ||||
\(668\) | −8.50000 | − | 14.7224i | −0.328875 | − | 0.569628i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.0000 | − | 31.1769i | 0.695401 | − | 1.20447i | ||||
\(671\) | −5.00000 | −0.193023 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.0000 | 0.616755 | 0.308377 | − | 0.951264i | \(-0.400214\pi\) | ||||
0.308377 | + | 0.951264i | \(0.400214\pi\) | |||||||
\(674\) | 15.0000 | − | 25.9808i | 0.577778 | − | 1.00074i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.00000 | + | 10.3923i | 0.230769 | + | 0.399704i | ||||
\(677\) | 19.0000 | − | 32.9090i | 0.730229 | − | 1.26479i | −0.226556 | − | 0.973998i | \(-0.572747\pi\) |
0.956785 | − | 0.290796i | \(-0.0939201\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.5000 | − | 4.33013i | 0.479706 | − | 0.166175i | ||||
\(680\) | −8.00000 | −0.306786 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.00000 | − | 3.46410i | −0.0765840 | − | 0.132647i | ||||
\(683\) | −16.5000 | − | 28.5788i | −0.631355 | − | 1.09354i | −0.987275 | − | 0.159022i | \(-0.949166\pi\) |
0.355920 | − | 0.934516i | \(-0.384168\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.0000 | 1.37549 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.00000 | + | 3.46410i | −0.0762493 | + | 0.132068i | ||||
\(689\) | 6.00000 | + | 10.3923i | 0.228582 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.50000 | + | 12.9904i | −0.285313 | + | 0.494177i | −0.972685 | − | 0.232128i | \(-0.925431\pi\) |
0.687372 | + | 0.726306i | \(0.258764\pi\) | |||||||
\(692\) | 5.00000 | 0.190071 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.0000 | 1.06287 | ||||||||
\(695\) | −16.0000 | + | 27.7128i | −0.606915 | + | 1.05121i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.00000 | + | 3.46410i | 0.0757554 | + | 0.131212i | ||||
\(698\) | −1.00000 | + | 1.73205i | −0.0378506 | + | 0.0655591i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.50000 | − | 28.5788i | 0.207880 | − | 1.08018i | ||||
\(701\) | −39.0000 | −1.47301 | −0.736505 | − | 0.676432i | \(-0.763525\pi\) | ||||
−0.736505 | + | 0.676432i | \(0.763525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.00000 | + | 10.3923i | 0.226294 | + | 0.391953i | ||||
\(704\) | −0.500000 | − | 0.866025i | −0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.0000 | 0.677439 | ||||||||
\(707\) | 30.0000 | + | 25.9808i | 1.12827 | + | 0.977107i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.00000 | + | 5.19615i | −0.112667 | + | 0.195146i | −0.916845 | − | 0.399244i | \(-0.869273\pi\) |
0.804178 | + | 0.594389i | \(0.202606\pi\) | |||||||
\(710\) | 8.00000 | + | 13.8564i | 0.300235 | + | 0.520022i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.00000 | − | 5.19615i | 0.112430 | − | 0.194734i | ||||
\(713\) | 8.00000 | 0.299602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.00000 | −0.149592 | ||||||||
\(716\) | 6.50000 | − | 11.2583i | 0.242916 | − | 0.420744i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.5000 | − | 26.8468i | −0.578455 | − | 1.00191i | ||||
\(719\) | −13.0000 | + | 22.5167i | −0.484818 | + | 0.839730i | −0.999848 | − | 0.0174426i | \(-0.994448\pi\) |
0.515030 | + | 0.857172i | \(0.327781\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | − | 31.1769i | 0.223452 | − | 1.16109i | ||||
\(722\) | 17.0000 | 0.632674 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.0000 | + | 19.0526i | 0.408812 | + | 0.708083i | ||||
\(725\) | 5.50000 | + | 9.52628i | 0.204265 | + | 0.353797i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.0000 | −1.26099 | −0.630495 | − | 0.776193i | \(-0.717148\pi\) | ||||
−0.630495 | + | 0.776193i | \(0.717148\pi\) | |||||||
\(728\) | 2.50000 | − | 0.866025i | 0.0926562 | − | 0.0320970i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.00000 | − | 6.92820i | 0.148047 | − | 0.256424i | ||||
\(731\) | 4.00000 | + | 6.92820i | 0.147945 | + | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.500000 | − | 0.866025i | 0.0184679 | − | 0.0319874i | −0.856644 | − | 0.515908i | \(-0.827454\pi\) |
0.875112 | + | 0.483921i | \(0.160788\pi\) | |||||||
\(734\) | −14.0000 | −0.516749 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.00000 | 0.0737210 | ||||||||
\(737\) | 4.50000 | − | 7.79423i | 0.165760 | − | 0.287104i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.00000 | − | 15.5885i | −0.331070 | − | 0.573431i | 0.651652 | − | 0.758518i | \(-0.274076\pi\) |
−0.982722 | + | 0.185088i | \(0.940743\pi\) | |||||||
\(740\) | 4.00000 | − | 6.92820i | 0.147043 | − | 0.254686i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −30.0000 | + | 10.3923i | −1.10133 | + | 0.381514i | ||||
\(743\) | −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 | ||||
\(746\) | 3.50000 | + | 6.06218i | 0.128144 | + | 0.221952i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.00000 | −0.0731272 | ||||||||
\(749\) | −4.00000 | + | 20.7846i | −0.146157 | + | 0.759453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.0000 | − | 38.1051i | 0.802791 | − | 1.39048i | −0.114981 | − | 0.993368i | \(-0.536681\pi\) |
0.917772 | − | 0.397108i | \(-0.129986\pi\) | |||||||
\(752\) | 1.00000 | + | 1.73205i | 0.0364662 | + | 0.0631614i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.500000 | + | 0.866025i | −0.0182089 | + | 0.0315388i | ||||
\(755\) | 36.0000 | 1.31017 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | 14.5000 | − | 25.1147i | 0.526664 | − | 0.912208i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.0000 | − | 20.7846i | −0.435286 | − | 0.753937i | ||||
\(761\) | 27.0000 | − | 46.7654i | 0.978749 | − | 1.69524i | 0.311787 | − | 0.950152i | \(-0.399073\pi\) |
0.666962 | − | 0.745091i | \(-0.267594\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.0000 | + | 17.3205i | 0.724049 | + | 0.627044i | ||||
\(764\) | −14.0000 | −0.506502 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.00000 | + | 6.92820i | 0.144526 | + | 0.250326i | ||||
\(767\) | −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 | \(0.740267\pi\) | |||||||
\(770\) | 2.00000 | − | 10.3923i | 0.0720750 | − | 0.374513i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.0000 | − | 19.0526i | 0.395899 | − | 0.685717i | ||||
\(773\) | −12.0000 | − | 20.7846i | −0.431610 | − | 0.747570i | 0.565402 | − | 0.824815i | \(-0.308721\pi\) |
−0.997012 | + | 0.0772449i | \(0.975388\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.0000 | + | 38.1051i | −0.790263 | + | 1.36878i | ||||
\(776\) | −5.00000 | −0.179490 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.00000 | + | 10.3923i | −0.214972 | + | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | + | 3.46410i | 0.0715656 | + | 0.123955i | ||||
\(782\) | 2.00000 | − | 3.46410i | 0.0715199 | − | 0.123876i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | 16.0000 | 0.571064 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.0000 | + | 19.0526i | 0.392108 | + | 0.679150i | 0.992727 | − | 0.120384i | \(-0.0384127\pi\) |
−0.600620 | + | 0.799535i | \(0.705079\pi\) | |||||||
\(788\) | −1.50000 | − | 2.59808i | −0.0534353 | − | 0.0925526i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −60.0000 | −2.13470 | ||||||||
\(791\) | 42.5000 | − | 14.7224i | 1.51113 | − | 0.523469i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.50000 | + | 4.33013i | −0.0887776 | + | 0.153767i | ||||
\(794\) | 15.0000 | + | 25.9808i | 0.532330 | + | 0.922023i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.00000 | + | 8.66025i | −0.177220 | + | 0.306955i | ||||
\(797\) | −38.0000 | −1.34603 | −0.673015 | − | 0.739629i | \(-0.735001\pi\) | ||||
−0.673015 | + | 0.739629i | \(0.735001\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.00000 | 0.141510 | ||||||||
\(800\) | −5.50000 | + | 9.52628i | −0.194454 | + | 0.336805i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.50000 | + | 12.9904i | 0.264834 | + | 0.458706i | ||||
\(803\) | 1.00000 | − | 1.73205i | 0.0352892 | − | 0.0611227i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0000 | + | 13.8564i | 0.563926 | + | 0.488374i | ||||
\(806\) | −4.00000 | −0.140894 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.50000 | − | 12.9904i | −0.263849 | − | 0.457000i | ||||
\(809\) | −24.0000 | − | 41.5692i | −0.843795 | − | 1.46150i | −0.886664 | − | 0.462415i | \(-0.846983\pi\) |
0.0428684 | − | 0.999081i | \(-0.486350\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.0000 | −0.983213 | −0.491606 | − | 0.870817i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870817i | \(0.663590\pi\) | |||||||
\(812\) | −2.00000 | − | 1.73205i | −0.0701862 | − | 0.0607831i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.00000 | − | 1.73205i | 0.0350500 | − | 0.0607083i | ||||
\(815\) | −26.0000 | − | 45.0333i | −0.910740 | − | 1.57745i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0000 | + | 20.7846i | −0.419827 | + | 0.727161i | ||||
\(818\) | −32.0000 | −1.11885 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.00000 | 0.279372 | ||||||||
\(821\) | −7.50000 | + | 12.9904i | −0.261752 | + | 0.453367i | −0.966708 | − | 0.255884i | \(-0.917634\pi\) |
0.704956 | + | 0.709251i | \(0.250967\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.0000 | − | 32.9090i | −0.662298 | − | 1.14713i | −0.980010 | − | 0.198947i | \(-0.936248\pi\) |
0.317712 | − | 0.948187i | \(-0.397086\pi\) | |||||||
\(824\) | −6.00000 | + | 10.3923i | −0.209020 | + | 0.362033i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 22.5000 | − | 7.79423i | 0.782875 | − | 0.271196i | ||||
\(827\) | 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 | 0.692999 | − | 0.720938i | \(-0.256289\pi\) |
−0.970851 | + | 0.239686i | \(0.922956\pi\) | |||||||
\(830\) | −12.0000 | − | 20.7846i | −0.416526 | − | 0.721444i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 13.0000 | + | 5.19615i | 0.450423 | + | 0.180036i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.0000 | + | 58.8897i | −1.17662 | + | 2.03796i | ||||
\(836\) | −3.00000 | − | 5.19615i | −0.103757 | − | 0.179713i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.0000 | + | 17.3205i | −0.345444 | + | 0.598327i | ||||
\(839\) | −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 | ||||||||
\(842\) | 10.0000 | − | 17.3205i | 0.344623 | − | 0.596904i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.00000 | + | 12.1244i | 0.240950 | + | 0.417338i | ||||
\(845\) | 24.0000 | − | 41.5692i | 0.825625 | − | 1.43002i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.500000 | − | 2.59808i | 0.0171802 | − | 0.0892710i | ||||
\(848\) | 12.0000 | 0.412082 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 11.0000 | + | 19.0526i | 0.377297 | + | 0.653497i | ||||
\(851\) | 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 | \(0.172952\pi\) | |||||||
\(854\) | −10.0000 | − | 8.66025i | −0.342193 | − | 0.296348i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.00000 | − | 6.92820i | 0.136717 | − | 0.236801i | ||||
\(857\) | −2.00000 | − | 3.46410i | −0.0683187 | − | 0.118331i | 0.829843 | − | 0.557998i | \(-0.188430\pi\) |
−0.898161 | + | 0.439666i | \(0.855097\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.50000 | − | 14.7224i | 0.290016 | − | 0.502323i | −0.683797 | − | 0.729672i | \(-0.739673\pi\) |
0.973813 | + | 0.227349i | \(0.0730059\pi\) | |||||||
\(860\) | 16.0000 | 0.545595 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | 5.00000 | − | 8.66025i | 0.170202 | − | 0.294798i | −0.768288 | − | 0.640104i | \(-0.778891\pi\) |
0.938490 | + | 0.345305i | \(0.112225\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0000 | − | 17.3205i | −0.340010 | − | 0.588915i | ||||
\(866\) | 5.00000 | − | 8.66025i | 0.169907 | − | 0.294287i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.00000 | − | 10.3923i | 0.0678844 | − | 0.352738i | ||||
\(869\) | −15.0000 | −0.508840 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.50000 | − | 7.79423i | −0.152477 | − | 0.264097i | ||||
\(872\) | −5.00000 | − | 8.66025i | −0.169321 | − | 0.293273i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.0000 | 0.405906 | ||||||||
\(875\) | −60.0000 | + | 20.7846i | −2.02837 | + | 0.702648i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.5000 | + | 21.6506i | −0.422095 | + | 0.731090i | −0.996144 | − | 0.0877308i | \(-0.972038\pi\) |
0.574049 | + | 0.818821i | \(0.305372\pi\) | |||||||
\(878\) | 2.50000 | + | 4.33013i | 0.0843709 | + | 0.146135i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.00000 | + | 3.46410i | −0.0674200 | + | 0.116775i | ||||
\(881\) | −9.00000 | −0.303218 | −0.151609 | − | 0.988441i | \(-0.548445\pi\) | ||||
−0.151609 | + | 0.988441i | \(0.548445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.00000 | 0.0336527 | 0.0168263 | − | 0.999858i | \(-0.494644\pi\) | ||||
0.0168263 | + | 0.999858i | \(0.494644\pi\) | |||||||
\(884\) | −1.00000 | + | 1.73205i | −0.0336336 | + | 0.0582552i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.00000 | − | 10.3923i | −0.201574 | − | 0.349136i | ||||
\(887\) | −8.50000 | + | 14.7224i | −0.285402 | + | 0.494331i | −0.972707 | − | 0.232038i | \(-0.925460\pi\) |
0.687305 | + | 0.726369i | \(0.258794\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.5000 | + | 4.33013i | −0.419237 | + | 0.145228i | ||||
\(890\) | −24.0000 | −0.804482 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.0000 | + | 22.5167i | 0.435272 | + | 0.753914i | ||||
\(893\) | 6.00000 | + | 10.3923i | 0.200782 | + | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −52.0000 | −1.73817 | ||||||||
\(896\) | 0.500000 | − | 2.59808i | 0.0167038 | − | 0.0867956i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.0000 | − | 25.9808i | 0.500556 | − | 0.866989i | ||||
\(899\) | 2.00000 | + | 3.46410i | 0.0667037 | + | 0.115534i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | − | 20.7846i | 0.399778 | − | 0.692436i | ||||
\(902\) | 2.00000 | 0.0665927 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.0000 | −0.565412 | ||||||||
\(905\) | 44.0000 | − | 76.2102i | 1.46261 | − | 2.53331i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.0000 | − | 38.1051i | −0.730498 | − | 1.26526i | −0.956671 | − | 0.291172i | \(-0.905955\pi\) |
0.226173 | − | 0.974087i | \(-0.427379\pi\) | |||||||
\(908\) | 5.00000 | − | 8.66025i | 0.165931 | − | 0.287401i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.00000 | − | 6.92820i | −0.265197 | − | 0.229668i | ||||
\(911\) | 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 | ||||
\(914\) | −1.00000 | − | 1.73205i | −0.0330771 | − | 0.0572911i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.0000 | −0.528655 | ||||||||
\(917\) | 9.00000 | − | 46.7654i | 0.297206 | − | 1.54433i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.0000 | − | 20.7846i | 0.395843 | − | 0.685621i | −0.597365 | − | 0.801970i | \(-0.703786\pi\) |
0.993208 | + | 0.116348i | \(0.0371189\pi\) | |||||||
\(920\) | −4.00000 | − | 6.92820i | −0.131876 | − | 0.228416i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.50000 | + | 2.59808i | −0.0493999 | + | 0.0855631i | ||||
\(923\) | 4.00000 | 0.131662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.0000 | −0.723356 | ||||||||
\(926\) | 7.00000 | − | 12.1244i | 0.230034 | − | 0.398431i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.500000 | + | 0.866025i | 0.0164133 | + | 0.0284287i | ||||
\(929\) | −16.5000 | + | 28.5788i | −0.541347 | + | 0.937641i | 0.457480 | + | 0.889220i | \(0.348752\pi\) |
−0.998827 | + | 0.0484211i | \(0.984581\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000 | + | 41.5692i | 0.196642 | + | 1.36238i | ||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.00000 | − | 10.3923i | −0.196326 | − | 0.340047i | ||||
\(935\) | 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 | \(0.562799\pi\) | |||||||
\(938\) | 22.5000 | − | 7.79423i | 0.734651 | − | 0.254491i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.00000 | − | 6.92820i | 0.130466 | − | 0.225973i | ||||
\(941\) | 27.5000 | + | 47.6314i | 0.896474 | + | 1.55274i | 0.831969 | + | 0.554822i | \(0.187214\pi\) |
0.0645052 | + | 0.997917i | \(0.479453\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.00000 | + | 3.46410i | −0.0651290 | + | 0.112807i | ||||
\(944\) | −9.00000 | −0.292925 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | −8.00000 | + | 13.8564i | −0.259965 | + | 0.450273i | −0.966232 | − | 0.257673i | \(-0.917044\pi\) |
0.706267 | + | 0.707945i | \(0.250378\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.00000 | − | 1.73205i | −0.0324614 | − | 0.0562247i | ||||
\(950\) | −33.0000 | + | 57.1577i | −1.07066 | + | 1.85444i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.00000 | − | 3.46410i | −0.129641 | − | 0.112272i | ||||
\(953\) | −56.0000 | −1.81402 | −0.907009 | − | 0.421111i | \(-0.861640\pi\) | ||||
−0.907009 | + | 0.421111i | \(0.861640\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.0000 | + | 48.4974i | 0.906059 | + | 1.56934i | ||||
\(956\) | 9.50000 | + | 16.4545i | 0.307252 | + | 0.532176i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 37.0000 | 1.19542 | ||||||||
\(959\) | 18.0000 | + | 15.5885i | 0.581250 | + | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | −1.00000 | − | 1.73205i | −0.0322413 | − | 0.0558436i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.0000 | + | 25.9808i | −0.483117 | + | 0.836784i | ||||
\(965\) | −88.0000 | −2.83282 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.0000 | 1.80084 | 0.900419 | − | 0.435023i | \(-0.143260\pi\) | ||||
0.900419 | + | 0.435023i | \(0.143260\pi\) | |||||||
\(968\) | −0.500000 | + | 0.866025i | −0.0160706 | + | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.0000 | + | 17.3205i | 0.321081 | + | 0.556128i | ||||
\(971\) | −6.50000 | + | 11.2583i | −0.208595 | + | 0.361297i | −0.951272 | − | 0.308353i | \(-0.900222\pi\) |
0.742677 | + | 0.669650i | \(0.233556\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.0000 | + | 6.92820i | −0.641171 | + | 0.222108i | ||||
\(974\) | −4.00000 | −0.128168 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.50000 | + | 4.33013i | 0.0800230 | + | 0.138604i | ||||
\(977\) | 7.00000 | + | 12.1244i | 0.223950 | + | 0.387893i | 0.956004 | − | 0.293354i | \(-0.0947715\pi\) |
−0.732054 | + | 0.681247i | \(0.761438\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | 22.0000 | − | 17.3205i | 0.702764 | − | 0.553283i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.00000 | − | 15.5885i | 0.287202 | − | 0.497448i | ||||
\(983\) | 9.00000 | + | 15.5885i | 0.287055 | + | 0.497195i | 0.973106 | − | 0.230360i | \(-0.0739903\pi\) |
−0.686050 | + | 0.727554i | \(0.740657\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | + | 10.3923i | −0.191176 | + | 0.331126i | ||||
\(986\) | 2.00000 | 0.0636930 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.00000 | −0.190885 | ||||||||
\(989\) | −4.00000 | + | 6.92820i | −0.127193 | + | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.0000 | + | 17.3205i | 0.317660 | + | 0.550204i | 0.979999 | − | 0.199000i | \(-0.0637695\pi\) |
−0.662339 | + | 0.749204i | \(0.730436\pi\) | |||||||
\(992\) | −2.00000 | + | 3.46410i | −0.0635001 | + | 0.109985i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.00000 | + | 10.3923i | −0.0634361 | + | 0.329624i | ||||
\(995\) | 40.0000 | 1.26809 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.0000 | + | 36.3731i | 0.665077 | + | 1.15195i | 0.979265 | + | 0.202586i | \(0.0649345\pi\) |
−0.314188 | + | 0.949361i | \(0.601732\pi\) | |||||||
\(998\) | 8.00000 | + | 13.8564i | 0.253236 | + | 0.438617i | ||||
\(999\) | 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 | 1386.2.k.a.793.1 | 2 | ||
3.2 | odd | 2 | 154.2.e.d.23.1 | ✓ | 2 | ||
7.2 | even | 3 | 9702.2.a.cg.1.1 | 1 | |||
7.4 | even | 3 | inner | 1386.2.k.a.991.1 | 2 | ||
7.5 | odd | 6 | 9702.2.a.bb.1.1 | 1 | |||
12.11 | even | 2 | 1232.2.q.a.177.1 | 2 | |||
21.2 | odd | 6 | 1078.2.a.a.1.1 | 1 | |||
21.5 | even | 6 | 1078.2.a.f.1.1 | 1 | |||
21.11 | odd | 6 | 154.2.e.d.67.1 | yes | 2 | ||
21.17 | even | 6 | 1078.2.e.g.67.1 | 2 | |||
21.20 | even | 2 | 1078.2.e.g.177.1 | 2 | |||
84.11 | even | 6 | 1232.2.q.a.529.1 | 2 | |||
84.23 | even | 6 | 8624.2.a.bd.1.1 | 1 | |||
84.47 | odd | 6 | 8624.2.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.d.23.1 | ✓ | 2 | 3.2 | odd | 2 | ||
154.2.e.d.67.1 | yes | 2 | 21.11 | odd | 6 | ||
1078.2.a.a.1.1 | 1 | 21.2 | odd | 6 | |||
1078.2.a.f.1.1 | 1 | 21.5 | even | 6 | |||
1078.2.e.g.67.1 | 2 | 21.17 | even | 6 | |||
1078.2.e.g.177.1 | 2 | 21.20 | even | 2 | |||
1232.2.q.a.177.1 | 2 | 12.11 | even | 2 | |||
1232.2.q.a.529.1 | 2 | 84.11 | even | 6 | |||
1386.2.k.a.793.1 | 2 | 1.1 | even | 1 | trivial | ||
1386.2.k.a.991.1 | 2 | 7.4 | even | 3 | inner | ||
8624.2.a.d.1.1 | 1 | 84.47 | odd | 6 | |||
8624.2.a.bd.1.1 | 1 | 84.23 | even | 6 | |||
9702.2.a.bb.1.1 | 1 | 7.5 | odd | 6 | |||
9702.2.a.cg.1.1 | 1 | 7.2 | even | 3 |