Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(961,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.bg (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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.38363328.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 3x^{4} - 2x^{3} - 21x^{2} - 49x + 343 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1201.2 | ||
Root | \(2.59174 + 0.531877i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.1201 |
Dual form | 1680.2.bg.u.961.2 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.835250 | + | 2.51045i | 0.315695 | + | 0.948861i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.335250 | − | 0.580670i | 0.101082 | − | 0.175079i | −0.811049 | − | 0.584978i | \(-0.801103\pi\) |
0.912131 | + | 0.409900i | \(0.134436\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.51298 | −0.974324 | −0.487162 | − | 0.873312i | \(-0.661968\pi\) | ||||
−0.487162 | + | 0.873312i | \(0.661968\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.25649 | + | 5.64040i | −0.789814 | + | 1.36800i | 0.136266 | + | 0.990672i | \(0.456490\pi\) |
−0.926080 | + | 0.377326i | \(0.876844\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.01298 | − | 6.95068i | −0.920640 | − | 1.59459i | −0.798427 | − | 0.602091i | \(-0.794334\pi\) |
−0.122212 | − | 0.992504i | \(-0.538999\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.59174 | + | 0.531877i | 0.565564 | + | 0.116065i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.84823 | − | 4.93327i | −0.593896 | − | 1.02866i | −0.993702 | − | 0.112058i | \(-0.964256\pi\) |
0.399805 | − | 0.916600i | \(-0.369078\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.85398 | −1.08706 | −0.543528 | − | 0.839391i | \(-0.682912\pi\) | ||||
−0.543528 | + | 0.839391i | \(0.682912\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.09174 | − | 5.35505i | 0.555293 | − | 0.961795i | −0.442588 | − | 0.896725i | \(-0.645940\pi\) |
0.997881 | − | 0.0650699i | \(-0.0207270\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.335250 | − | 0.580670i | −0.0583596 | − | 0.101082i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.75649 | − | 1.97857i | 0.296901 | − | 0.334440i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.42699 | − | 9.39982i | −0.892191 | − | 1.54532i | −0.837243 | − | 0.546832i | \(-0.815834\pi\) |
−0.0549488 | − | 0.998489i | \(-0.517500\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.75649 | + | 3.04233i | −0.281263 | + | 0.487162i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.35545 | 1.30490 | 0.652451 | − | 0.757831i | \(-0.273741\pi\) | ||||
0.652451 | + | 0.757831i | \(0.273741\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.67050 | 0.254749 | 0.127374 | − | 0.991855i | \(-0.459345\pi\) | ||||
0.127374 | + | 0.991855i | \(0.459345\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.591738 | + | 1.02492i | 0.0863139 | + | 0.149500i | 0.905950 | − | 0.423384i | \(-0.139158\pi\) |
−0.819636 | + | 0.572884i | \(0.805825\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.60471 | + | 4.19371i | −0.800673 | + | 0.599101i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.25649 | + | 5.64040i | 0.456000 | + | 0.789814i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.10471 | + | 10.5737i | −0.838547 | + | 1.45241i | 0.0525625 | + | 0.998618i | \(0.483261\pi\) |
−0.891109 | + | 0.453788i | \(0.850072\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.670500 | −0.0904103 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.02595 | −1.06306 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.92699 | − | 8.53379i | 0.641439 | − | 1.11101i | −0.343672 | − | 0.939090i | \(-0.611671\pi\) |
0.985112 | − | 0.171916i | \(-0.0549957\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.51298 | − | 7.81670i | −0.577827 | − | 1.00083i | −0.995728 | − | 0.0923337i | \(-0.970567\pi\) |
0.417901 | − | 0.908493i | \(-0.362766\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.75649 | − | 1.97857i | 0.221297 | − | 0.249277i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.75649 | + | 3.04233i | 0.217866 | + | 0.377354i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.67773 | − | 2.90591i | 0.204967 | − | 0.355013i | −0.745155 | − | 0.666891i | \(-0.767625\pi\) |
0.950122 | + | 0.311878i | \(0.100958\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.69645 | −0.685772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.8799 | −1.52857 | −0.764283 | − | 0.644881i | \(-0.776907\pi\) | ||||
−0.764283 | + | 0.644881i | \(0.776907\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.34823 | − | 7.53135i | 0.508921 | − | 0.881478i | −0.491025 | − | 0.871145i | \(-0.663378\pi\) |
0.999947 | − | 0.0103323i | \(-0.00328895\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.73776 | + | 0.356624i | 0.198036 | + | 0.0406410i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.42124 | + | 7.65781i | 0.497428 | + | 0.861571i | 0.999996 | − | 0.00296721i | \(-0.000944493\pi\) |
−0.502567 | + | 0.864538i | \(0.667611\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.17198 | −0.348170 | −0.174085 | − | 0.984731i | \(-0.555697\pi\) | ||||
−0.174085 | + | 0.984731i | \(0.555697\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.51298 | 0.706431 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.92699 | + | 5.06969i | −0.313806 | + | 0.543528i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.74351 | − | 3.01985i | −0.184812 | − | 0.320104i | 0.758701 | − | 0.651439i | \(-0.225834\pi\) |
−0.943513 | + | 0.331335i | \(0.892501\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.93421 | − | 8.81915i | −0.307589 | − | 0.924498i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.09174 | − | 5.35505i | −0.320598 | − | 0.555293i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.01298 | + | 6.95068i | −0.411723 | + | 0.713125i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.02595 | −0.510308 | −0.255154 | − | 0.966900i | \(-0.582126\pi\) | ||||
−0.255154 | + | 0.966900i | \(0.582126\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.670500 | −0.0673878 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.25649 | + | 16.0327i | −0.921055 | + | 1.59531i | −0.123269 | + | 0.992373i | \(0.539338\pi\) |
−0.797786 | + | 0.602941i | \(0.793996\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.322274 | − | 0.558195i | −0.0317546 | − | 0.0550006i | 0.849711 | − | 0.527248i | \(-0.176776\pi\) |
−0.881466 | + | 0.472248i | \(0.843443\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.835250 | − | 2.51045i | −0.0815121 | − | 0.244995i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.92699 | + | 10.2658i | 0.572984 | + | 0.992437i | 0.996257 | + | 0.0864349i | \(0.0275475\pi\) |
−0.423274 | + | 0.906002i | \(0.639119\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.76224 | − | 4.78434i | 0.264574 | − | 0.458256i | −0.702878 | − | 0.711311i | \(-0.748102\pi\) |
0.967452 | + | 0.253054i | \(0.0814352\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.8540 | −1.03021 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.84823 | + | 4.93327i | −0.265598 | + | 0.460030i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.75649 | + | 3.04233i | 0.162387 | + | 0.281263i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.8799 | − | 3.46410i | −1.54738 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.27521 | + | 9.13694i | 0.479565 | + | 0.830631i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.17773 | − | 7.23603i | 0.376693 | − | 0.652451i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.53893 | 0.580236 | 0.290118 | − | 0.956991i | \(-0.406305\pi\) | ||||
0.290118 | + | 0.956991i | \(0.406305\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.835250 | − | 1.44670i | 0.0735397 | − | 0.127374i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.4457 | − | 18.0925i | −0.912646 | − | 1.58075i | −0.810311 | − | 0.586000i | \(-0.800702\pi\) |
−0.102335 | − | 0.994750i | \(-0.532631\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.0975 | − | 15.8799i | 1.22241 | − | 1.37696i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.585988 | − | 1.01496i | 0.0500643 | − | 0.0867139i | −0.839907 | − | 0.542730i | \(-0.817391\pi\) |
0.889972 | + | 0.456016i | \(0.150724\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.50147 | −0.466629 | −0.233315 | − | 0.972401i | \(-0.574957\pi\) | ||||
−0.233315 | + | 0.972401i | \(0.574957\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.18348 | 0.0996667 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.17773 | + | 2.03988i | −0.0984864 | + | 0.170583i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.92699 | + | 5.06969i | 0.243073 | + | 0.421015i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.829500 | + | 6.95068i | 0.0684160 | + | 0.573282i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00000 | + | 3.46410i | 0.163846 | + | 0.283790i | 0.936245 | − | 0.351348i | \(-0.114277\pi\) |
−0.772399 | + | 0.635138i | \(0.780943\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.51298 | + | 13.0129i | −0.611397 | + | 1.05897i | 0.379608 | + | 0.925147i | \(0.376059\pi\) |
−0.991005 | + | 0.133824i | \(0.957274\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.51298 | 0.526543 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.18348 | −0.496669 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.92124 | + | 17.1841i | −0.791801 | + | 1.37144i | 0.133050 | + | 0.991109i | \(0.457523\pi\) |
−0.924851 | + | 0.380330i | \(0.875810\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.10471 | + | 10.5737i | 0.484135 | + | 0.838547i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.0058 | − | 11.2708i | 0.788564 | − | 0.888267i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00000 | + | 13.8564i | 0.626608 | + | 1.08532i | 0.988227 | + | 0.152992i | \(0.0488907\pi\) |
−0.361619 | + | 0.932326i | \(0.617776\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.335250 | + | 0.580670i | −0.0260992 | + | 0.0452051i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.0145 | 1.00709 | 0.503544 | − | 0.863969i | \(-0.332029\pi\) | ||||
0.503544 | + | 0.863969i | \(0.332029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.658999 | −0.0506923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.01298 | + | 6.95068i | −0.306880 | + | 0.531532i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.07876 | − | 5.33257i | −0.234074 | − | 0.405428i | 0.724929 | − | 0.688823i | \(-0.241872\pi\) |
−0.959003 | + | 0.283395i | \(0.908539\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.59174 | − | 0.531877i | −0.195917 | − | 0.0402061i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.92699 | − | 8.53379i | −0.370335 | − | 0.641439i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.40826 | + | 5.90328i | −0.254745 | + | 0.441232i | −0.964826 | − | 0.262888i | \(-0.915325\pi\) |
0.710081 | + | 0.704120i | \(0.248658\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.5504 | 1.52750 | 0.763751 | − | 0.645511i | \(-0.223356\pi\) | ||||
0.763751 | + | 0.645511i | \(0.223356\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.02595 | −0.667218 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.42699 | + | 9.39982i | −0.399000 | + | 0.691088i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.18348 | + | 3.78189i | 0.159672 | + | 0.276559i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.835250 | − | 2.51045i | −0.0607555 | − | 0.182608i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.341001 | − | 0.590631i | −0.0246739 | − | 0.0427365i | 0.853425 | − | 0.521216i | \(-0.174521\pi\) |
−0.878099 | + | 0.478480i | \(0.841188\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0447 | − | 19.1299i | 0.795013 | − | 1.37700i | −0.127817 | − | 0.991798i | \(-0.540797\pi\) |
0.922831 | − | 0.385206i | \(-0.125870\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.51298 | 0.251569 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.35545 | 0.310313 | 0.155157 | − | 0.987890i | \(-0.450412\pi\) | ||||
0.155157 | + | 0.987890i | \(0.450412\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.32950 | − | 7.49891i | 0.306910 | − | 0.531584i | −0.670775 | − | 0.741661i | \(-0.734038\pi\) |
0.977685 | + | 0.210077i | \(0.0673716\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.67773 | − | 2.90591i | −0.118338 | − | 0.204967i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.88954 | − | 14.6961i | −0.343178 | − | 1.03146i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.17773 | − | 7.23603i | −0.291785 | − | 0.505386i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.84823 | + | 4.93327i | −0.197965 | + | 0.342886i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.38140 | −0.372239 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.5245 | 0.999906 | 0.499953 | − | 0.866052i | \(-0.333351\pi\) | ||||
0.499953 | + | 0.866052i | \(0.333351\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.43996 | + | 11.1543i | −0.441259 | + | 0.764283i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.835250 | − | 1.44670i | −0.0569636 | − | 0.0986638i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0260 | + | 3.28885i | 1.08791 | + | 0.223262i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.34823 | − | 7.53135i | −0.293826 | − | 0.508921i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.4400 | − | 19.8146i | 0.769535 | − | 1.33287i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.7080 | −1.05188 | −0.525941 | − | 0.850521i | \(-0.676287\pi\) | ||||
−0.525941 | + | 0.850521i | \(0.676287\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.58599 | − | 9.67521i | 0.370755 | − | 0.642167i | −0.618927 | − | 0.785449i | \(-0.712432\pi\) |
0.989682 | + | 0.143282i | \(0.0457656\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.2752 | − | 22.9933i | −0.877251 | − | 1.51944i | −0.854346 | − | 0.519705i | \(-0.826042\pi\) |
−0.0229054 | − | 0.999738i | \(-0.507292\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.17773 | − | 1.32663i | 0.0774887 | − | 0.0872861i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.48702 | + | 7.77175i | 0.293955 | + | 0.509144i | 0.974741 | − | 0.223337i | \(-0.0716952\pi\) |
−0.680786 | + | 0.732482i | \(0.738362\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.591738 | − | 1.02492i | 0.0386007 | − | 0.0668585i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.84248 | 0.574381 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.43421 | − | 9.41233i | 0.350048 | − | 0.606302i | −0.636209 | − | 0.771517i | \(-0.719498\pi\) |
0.986258 | + | 0.165215i | \(0.0528318\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.43421 | + | 2.75697i | 0.411067 | + | 0.176136i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.0975 | + | 24.4176i | 0.897002 | + | 1.55365i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.58599 | + | 2.74701i | −0.100508 | + | 0.174085i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.69645 | −0.233318 | −0.116659 | − | 0.993172i | \(-0.537218\pi\) | ||||
−0.116659 | + | 0.993172i | \(0.537218\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.81947 | −0.240128 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.25649 | − | 5.64040i | 0.203929 | − | 0.353216i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.414012 | − | 0.717090i | −0.0258254 | − | 0.0447309i | 0.852824 | − | 0.522199i | \(-0.174888\pi\) |
−0.878649 | + | 0.477468i | \(0.841555\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.0649 | − | 21.4754i | 1.18463 | − | 1.33442i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.92699 | + | 5.06969i | 0.181176 | + | 0.313806i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.51298 | + | 11.2808i | −0.401607 | + | 0.695604i | −0.993920 | − | 0.110104i | \(-0.964882\pi\) |
0.592313 | + | 0.805708i | \(0.298215\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.2094 | 0.750019 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.48702 | −0.213402 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.69645 | − | 4.67039i | 0.164406 | − | 0.284759i | −0.772038 | − | 0.635576i | \(-0.780763\pi\) |
0.936444 | + | 0.350817i | \(0.114096\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.3555 | − | 19.6682i | −0.689795 | − | 1.19476i | −0.971904 | − | 0.235377i | \(-0.924368\pi\) |
0.282110 | − | 0.959382i | \(-0.408966\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.10471 | − | 1.86847i | −0.551042 | − | 0.113085i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.335250 | + | 0.580670i | 0.0202163 | + | 0.0350157i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.53170 | + | 14.7773i | −0.512620 | + | 0.887884i | 0.487273 | + | 0.873250i | \(0.337992\pi\) |
−0.999893 | + | 0.0146345i | \(0.995342\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.18348 | −0.370195 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.81652 | −0.287330 | −0.143665 | − | 0.989626i | \(-0.545889\pi\) | ||||
−0.143665 | + | 0.989626i | \(0.545889\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.8872 | − | 27.5174i | 0.944393 | − | 1.63574i | 0.187432 | − | 0.982278i | \(-0.439984\pi\) |
0.756961 | − | 0.653460i | \(-0.226683\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.01298 | + | 6.95068i | 0.237708 | + | 0.411723i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.97889 | + | 20.9759i | 0.411951 | + | 1.23817i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.7094 | − | 22.0134i | −0.747613 | − | 1.29490i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.51298 | + | 4.35260i | −0.147313 | + | 0.255154i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.18348 | −0.419663 | −0.209832 | − | 0.977738i | \(-0.567292\pi\) | ||||
−0.209832 | + | 0.977738i | \(0.567292\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.85398 | −0.573721 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.335250 | + | 0.580670i | −0.0194532 | + | 0.0336939i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.0058 | + | 17.3305i | 0.578647 | + | 1.00225i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.39529 | + | 4.19371i | 0.0804229 | + | 0.241721i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.25649 | + | 16.0327i | 0.531771 | + | 0.921055i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.51298 | + | 7.81670i | −0.258412 | + | 0.447583i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.4044 | 0.822103 | 0.411051 | − | 0.911612i | \(-0.365162\pi\) | ||||
0.411051 | + | 0.911612i | \(0.365162\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.644548 | −0.0366671 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.7954 | + | 22.1623i | −0.725561 | + | 1.25671i | 0.233181 | + | 0.972433i | \(0.425087\pi\) |
−0.958742 | + | 0.284276i | \(0.908247\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.16475 | − | 2.01741i | −0.0658356 | − | 0.114031i | 0.831229 | − | 0.555931i | \(-0.187638\pi\) |
−0.897064 | + | 0.441900i | \(0.854305\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.59174 | − | 0.531877i | −0.146028 | − | 0.0299679i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.2939 | + | 24.7578i | 0.802828 | + | 1.39054i | 0.917748 | + | 0.397164i | \(0.130005\pi\) |
−0.114920 | + | 0.993375i | \(0.536661\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.96255 | + | 3.39923i | −0.109882 | + | 0.190320i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.8540 | 0.661624 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 52.2728 | 2.90854 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.75649 | − | 3.04233i | 0.0974324 | − | 0.168758i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.76224 | − | 4.78434i | −0.152752 | − | 0.264574i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.07876 | + | 2.34159i | −0.114606 | + | 0.129096i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.85545 | − | 10.1419i | −0.321845 | − | 0.557451i | 0.659024 | − | 0.752122i | \(-0.270970\pi\) |
−0.980869 | + | 0.194671i | \(0.937636\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.42699 | + | 9.39982i | −0.297397 | + | 0.515107i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.35545 | −0.183328 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.673450 | 0.0366852 | 0.0183426 | − | 0.999832i | \(-0.494161\pi\) | ||||
0.0183426 | + | 0.999832i | \(0.494161\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.00000 | + | 5.19615i | −0.162938 | + | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.07301 | − | 3.59056i | −0.112260 | − | 0.194440i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.2094 | − | 10.5676i | −0.821232 | − | 0.570595i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.84823 | + | 4.93327i | 0.153343 | + | 0.265598i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.15752 | + | 7.20104i | −0.223188 | + | 0.386572i | −0.955774 | − | 0.294102i | \(-0.904980\pi\) |
0.732587 | + | 0.680674i | \(0.238313\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36.3670 | 1.94668 | 0.973339 | − | 0.229371i | \(-0.0736668\pi\) | ||||
0.973339 | + | 0.229371i | \(0.0736668\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.51298 | 0.187509 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.414012 | − | 0.717090i | 0.0220357 | − | 0.0381669i | −0.854797 | − | 0.518962i | \(-0.826319\pi\) |
0.876833 | + | 0.480795i | \(0.159652\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.43996 | + | 11.1543i | 0.341798 | + | 0.592011i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.4400 | + | 12.8864i | −0.605467 | + | 0.682020i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.07301 | − | 12.2508i | −0.373299 | − | 0.646573i | 0.616772 | − | 0.787142i | \(-0.288440\pi\) |
−0.990071 | + | 0.140569i | \(0.955107\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.7080 | + | 39.3313i | −1.19516 | + | 2.07007i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.5504 | 0.553754 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.69645 | −0.455193 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.24351 | − | 10.8141i | 0.325909 | − | 0.564490i | −0.655787 | − | 0.754946i | \(-0.727663\pi\) |
0.981696 | + | 0.190455i | \(0.0609965\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.17773 | − | 7.23603i | −0.217484 | − | 0.376693i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.6436 | − | 6.49391i | −1.64286 | − | 0.337147i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.83525 | + | 3.17875i | 0.0950257 | + | 0.164589i | 0.909619 | − | 0.415443i | \(-0.136373\pi\) |
−0.814594 | + | 0.580032i | \(0.803040\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.5649 | 1.05915 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.6820 | 0.908263 | 0.454132 | − | 0.890935i | \(-0.349950\pi\) | ||||
0.454132 | + | 0.890935i | \(0.349950\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.26946 | − | 5.66288i | 0.167500 | − | 0.290118i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.10471 | − | 10.5737i | −0.311936 | − | 0.540290i | 0.666845 | − | 0.745196i | \(-0.267644\pi\) |
−0.978782 | + | 0.204907i | \(0.934311\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.560036 | − | 1.68326i | −0.0285421 | − | 0.0857867i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.835250 | − | 1.44670i | −0.0424582 | − | 0.0735397i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.41401 | − | 12.8414i | 0.375905 | − | 0.651087i | −0.614557 | − | 0.788873i | \(-0.710665\pi\) |
0.990462 | + | 0.137785i | \(0.0439984\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.1009 | 1.87627 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.8914 | −1.05383 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.42124 | − | 7.65781i | 0.222457 | − | 0.385306i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.49425 | − | 7.78427i | −0.225560 | − | 0.390681i | 0.730927 | − | 0.682455i | \(-0.239088\pi\) |
−0.956487 | + | 0.291774i | \(0.905754\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.70368 | − | 20.1487i | −0.335604 | − | 1.00870i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.44571 | − | 9.43226i | −0.271946 | − | 0.471024i | 0.697414 | − | 0.716668i | \(-0.254334\pi\) |
−0.969360 | + | 0.245644i | \(0.921001\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.8612 | + | 18.8122i | −0.541035 | + | 0.937100i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.27760 | −0.360737 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.27521 | + | 2.20874i | −0.0630553 | + | 0.109215i | −0.895830 | − | 0.444398i | \(-0.853418\pi\) |
0.832774 | + | 0.553613i | \(0.186751\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.585988 | − | 1.01496i | −0.0289046 | − | 0.0500643i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 25.5389 | + | 5.24110i | 1.25669 | + | 0.257898i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.58599 | + | 2.74701i | 0.0778531 | + | 0.134845i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.75074 | + | 4.76442i | −0.134704 | + | 0.233315i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.2094 | 1.47583 | 0.737914 | − | 0.674895i | \(-0.235811\pi\) | ||||
0.737914 | + | 0.674895i | \(0.235811\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.790571 | −0.0385301 | −0.0192650 | − | 0.999814i | \(-0.506133\pi\) | ||||
−0.0192650 | + | 0.999814i | \(0.506133\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.591738 | − | 1.02492i | 0.0287713 | − | 0.0498333i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.25649 | − | 5.64040i | −0.157963 | − | 0.273600i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.8540 | − | 17.8585i | 0.767228 | − | 0.864233i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.17773 | + | 2.03988i | 0.0568611 | + | 0.0984864i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.01445 | − | 10.4173i | 0.289706 | − | 0.501785i | −0.684034 | − | 0.729451i | \(-0.739776\pi\) |
0.973739 | + | 0.227665i | \(0.0731092\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.6705 | 0.656962 | 0.328481 | − | 0.944511i | \(-0.393463\pi\) | ||||
0.328481 | + | 0.944511i | \(0.393463\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.85398 | 0.280677 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.8597 | + | 39.5942i | −1.09353 | + | 1.89405i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.183476 | − | 0.317790i | −0.00875685 | − | 0.0151673i | 0.861614 | − | 0.507564i | \(-0.169454\pi\) |
−0.870371 | + | 0.492397i | \(0.836121\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.43421 | + | 2.75697i | 0.306391 | + | 0.131284i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.85398 | + | 13.6035i | 0.373154 | + | 0.646321i | 0.990049 | − | 0.140724i | \(-0.0449431\pi\) |
−0.616895 | + | 0.787045i | \(0.711610\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.74351 | + | 3.01985i | −0.0826504 | + | 0.143155i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.00000 | 0.189194 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.5015 | −0.495595 | −0.247798 | − | 0.968812i | \(-0.579707\pi\) | ||||
−0.247798 | + | 0.968812i | \(0.579707\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.80117 | − | 4.85176i | 0.131902 | − | 0.228461i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.51298 | + | 13.0129i | 0.352990 | + | 0.611397i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.17050 | + | 6.95068i | −0.289278 | + | 0.325853i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.55765 | + | 16.5543i | 0.447088 | + | 0.774380i | 0.998195 | − | 0.0600552i | \(-0.0191277\pi\) |
−0.551107 | + | 0.834435i | \(0.685794\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.25649 | − | 5.64040i | 0.152000 | − | 0.263271i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.9318 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.9318 | −0.833363 | −0.416681 | − | 0.909053i | \(-0.636807\pi\) | ||||
−0.416681 | + | 0.909053i | \(0.636807\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.09174 | + | 5.35505i | −0.143376 | + | 0.248334i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.5504 | + | 18.2739i | 0.488216 | + | 0.845614i | 0.999908 | − | 0.0135544i | \(-0.00431462\pi\) |
−0.511692 | + | 0.859169i | \(0.670981\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.69645 | + | 1.78469i | 0.401565 | + | 0.0824092i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.92124 | + | 17.1841i | 0.457147 | + | 0.791801i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.560036 | − | 0.970010i | 0.0257505 | − | 0.0446011i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.02595 | 0.368256 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.2094 | 0.559031 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.8684 | − | 18.8247i | 0.496591 | − | 0.860121i | −0.503401 | − | 0.864053i | \(-0.667918\pi\) |
0.999992 | + | 0.00393175i | \(0.00125152\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.0649 | + | 33.0213i | 0.869284 | + | 1.50564i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.75796 | − | 14.3007i | −0.216495 | − | 0.650702i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.51298 | + | 4.35260i | 0.114108 | + | 0.197641i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.17625 | + | 3.76938i | −0.0986153 | + | 0.170807i | −0.911112 | − | 0.412159i | \(-0.864775\pi\) |
0.812496 | + | 0.582966i | \(0.198108\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.0000 | 0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.70795 | −0.347855 | −0.173928 | − | 0.984758i | \(-0.555646\pi\) | ||||
−0.173928 | + | 0.984758i | \(0.555646\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.0634 | − | 33.0188i | 0.858573 | − | 1.48709i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.335250 | + | 0.580670i | 0.0150684 | + | 0.0260992i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.7580 | − | 32.3344i | −0.482561 | − | 1.45040i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.8026 | − | 32.5671i | −0.841722 | − | 1.45790i | −0.888438 | − | 0.458997i | \(-0.848209\pi\) |
0.0467161 | − | 0.998908i | \(-0.485124\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.50723 | − | 11.2708i | 0.290721 | − | 0.503544i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.658999 | 0.0293833 | 0.0146917 | − | 0.999892i | \(-0.495323\pi\) | ||||
0.0146917 | + | 0.999892i | \(0.495323\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.5130 | 0.823817 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.329500 | + | 0.570710i | −0.0146336 | + | 0.0253461i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.1979 | − | 26.3236i | −0.673636 | − | 1.16677i | −0.976865 | − | 0.213855i | \(-0.931398\pi\) |
0.303229 | − | 0.952918i | \(-0.401935\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.5389 | + | 4.62544i | 0.997063 | + | 0.204618i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.01298 | + | 6.95068i | 0.177177 | + | 0.306880i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.322274 | + | 0.558195i | −0.0142011 | + | 0.0245970i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.793521 | 0.0348990 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.15752 | −0.270285 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.76371 | + | 15.1792i | −0.383945 | + | 0.665013i | −0.991622 | − | 0.129172i | \(-0.958768\pi\) |
0.607677 | + | 0.794184i | \(0.292102\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.16475 | − | 7.21356i | −0.182112 | − | 0.315427i | 0.760488 | − | 0.649352i | \(-0.224960\pi\) |
−0.942599 | + | 0.333925i | \(0.891627\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.75649 | + | 1.97857i | −0.0766594 | + | 0.0863520i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.1364 | + | 34.8773i | 0.877156 | + | 1.51928i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.72479 | + | 8.18357i | −0.205425 | + | 0.355807i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.85398 | −0.427626 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.3525 | −1.27140 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.92699 | − | 10.2658i | 0.256246 | − | 0.443831i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.40826 | + | 5.90328i | 0.147077 | + | 0.254745i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.556180 | + | 4.66043i | 0.0239564 | + | 0.200739i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.27521 | − | 16.0651i | −0.398773 | − | 0.690694i | 0.594802 | − | 0.803872i | \(-0.297230\pi\) |
−0.993575 | + | 0.113178i | \(0.963897\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.2752 | − | 17.7972i | 0.440952 | − | 0.763751i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.52448 | −0.236643 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.7599 | −1.44347 | −0.721734 | − | 0.692171i | \(-0.756654\pi\) | ||||
−0.721734 | + | 0.692171i | \(0.756654\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.51298 | + | 7.81670i | −0.192609 | + | 0.333609i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.4919 | + | 40.6891i | 1.00079 | + | 1.73341i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.5317 | + | 17.4955i | −0.660475 | + | 0.743984i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.42699 | + | 9.39982i | 0.230363 | + | 0.399000i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.4602 | − | 19.8496i | 0.485583 | − | 0.841054i | −0.514280 | − | 0.857622i | \(-0.671941\pi\) |
0.999863 | + | 0.0165683i | \(0.00527409\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.86843 | −0.248208 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.36695 | 0.184373 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.0259521 | − | 0.0449504i | 0.00109375 | − | 0.00189443i | −0.865478 | − | 0.500947i | \(-0.832985\pi\) |
0.866572 | + | 0.499052i | \(0.166319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.00000 | + | 5.19615i | 0.126211 | + | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.59174 | − | 0.531877i | −0.108843 | − | 0.0223367i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.1777 | + | 17.6283i | 0.426672 | + | 0.739018i | 0.996575 | − | 0.0826939i | \(-0.0263524\pi\) |
−0.569903 | + | 0.821712i | \(0.693019\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.9717 | − | 25.9317i | 0.626545 | − | 1.08521i | −0.361695 | − | 0.932296i | \(-0.617802\pi\) |
0.988240 | − | 0.152911i | \(-0.0488648\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.682001 | −0.0284910 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.69645 | 0.237558 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.5317 | + | 18.2414i | −0.438441 | + | 0.759401i | −0.997569 | − | 0.0696795i | \(-0.977802\pi\) |
0.559129 | + | 0.829081i | \(0.311136\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.0447 | − | 19.1299i | −0.459001 | − | 0.795013i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.64939 | − | 7.96308i | −0.109915 | − | 0.330364i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.09321 | + | 7.08965i | 0.169524 | + | 0.293623i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.75649 | − | 3.04233i | 0.0726218 | − | 0.125785i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.1720 | 1.53425 | 0.767126 | − | 0.641497i | \(-0.221686\pi\) | ||||
0.767126 | + | 0.641497i | \(0.221686\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −49.6283 | −2.04490 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.17773 | − | 3.77193i | 0.0895797 | − | 0.155157i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.4659 | − | 21.5916i | −0.511914 | − | 0.886661i | −0.999905 | − | 0.0138120i | \(-0.995603\pi\) |
0.487991 | − | 0.872849i | \(-0.337730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.43996 | + | 16.3505i | 0.223017 | + | 0.670305i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.32950 | − | 7.49891i | −0.177195 | − | 0.306910i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.32950 | + | 5.76686i | −0.136040 | + | 0.235628i | −0.925994 | − | 0.377538i | \(-0.876771\pi\) |
0.789954 | + | 0.613166i | \(0.210104\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.8914 | −0.566643 | −0.283322 | − | 0.959025i | \(-0.591436\pi\) | ||||
−0.283322 | + | 0.959025i | \(0.591436\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.35545 | −0.136645 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.27521 | − | 9.13694i | 0.214468 | − | 0.371469i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.5990 | − | 33.9464i | −0.795497 | − | 1.37784i | −0.922523 | − | 0.385942i | \(-0.873876\pi\) |
0.127025 | − | 0.991899i | \(-0.459457\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.1720 | − | 3.11360i | −0.614799 | − | 0.126169i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.07876 | − | 3.60052i | −0.0840977 | − | 0.145662i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.89529 | + | 3.28273i | −0.0765499 | + | 0.132588i | −0.901759 | − | 0.432239i | \(-0.857724\pi\) |
0.825209 | + | 0.564827i | \(0.191057\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.35545 | −0.336924 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0230 | 0.725579 | 0.362789 | − | 0.931871i | \(-0.381824\pi\) | ||||
0.362789 | + | 0.931871i | \(0.381824\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.6979 | + | 23.7255i | −0.550566 | + | 0.953609i | 0.447668 | + | 0.894200i | \(0.352255\pi\) |
−0.998234 | + | 0.0594085i | \(0.981079\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.84823 | + | 4.93327i | 0.114295 | + | 0.197965i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.12492 | − | 6.89933i | 0.245390 | − | 0.276416i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.69070 | + | 4.66043i | −0.107456 | + | 0.186120i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 70.6917 | 2.81866 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.1528 | 1.47903 | 0.739514 | − | 0.673141i | \(-0.235055\pi\) | ||||
0.739514 | + | 0.673141i | \(0.235055\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.26224 | − | 12.5786i | 0.288648 | − | 0.499953i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.26946 | − | 5.66288i | −0.129745 | − | 0.224724i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.6892 | − | 14.7324i | 0.780116 | − | 0.583719i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.43996 | + | 11.1543i | 0.254761 | + | 0.441259i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.8597 | − | 24.0058i | 0.547426 | − | 0.948170i | −0.451024 | − | 0.892512i | \(-0.648941\pi\) |
0.998450 | − | 0.0556582i | \(-0.0177257\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.0115 | −1.06523 | −0.532615 | − | 0.846358i | \(-0.678791\pi\) | ||||
−0.532615 | + | 0.846358i | \(0.678791\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.67050 | −0.0657759 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.85973 | + | 13.6134i | −0.308998 | + | 0.535200i | −0.978143 | − | 0.207931i | \(-0.933327\pi\) |
0.669146 | + | 0.743131i | \(0.266660\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.30355 | − | 5.72191i | −0.129676 | − | 0.224605i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.8612 | − | 12.2345i | 0.425684 | − | 0.479506i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.81077 | + | 8.33250i | 0.188260 | + | 0.326076i | 0.944670 | − | 0.328022i | \(-0.106382\pi\) |
−0.756410 | + | 0.654098i | \(0.773049\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.4457 | + | 18.0925i | −0.408148 | + | 0.706933i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.69645 | −0.339281 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.05190 | −0.235749 | −0.117874 | − | 0.993029i | \(-0.537608\pi\) | ||||
−0.117874 | + | 0.993029i | \(0.537608\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.11769 | + | 8.86410i | −0.199055 | + | 0.344774i | −0.948222 | − | 0.317607i | \(-0.897121\pi\) |
0.749167 | + | 0.662381i | \(0.230454\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.4400 | − | 19.8146i | −0.444291 | − | 0.769535i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.8012 | − | 4.26882i | −0.806635 | − | 0.165538i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.6735 | + | 28.8793i | 0.645599 | + | 1.11821i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.85398 | + | 13.6035i | −0.303652 | + | 0.525941i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.05190 | −0.233631 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.69645 | 0.258129 | 0.129065 | − | 0.991636i | \(-0.458803\pi\) | ||||
0.129065 | + | 0.991636i | \(0.458803\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.2411 | + | 38.5228i | 0.854796 | + | 1.48055i | 0.876834 | + | 0.480793i | \(0.159651\pi\) |
−0.0220379 | + | 0.999757i | \(0.507015\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.19793 | − | 12.6174i | −0.161102 | − | 0.484211i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.58599 | − | 9.67521i | −0.214056 | − | 0.370755i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.743512 | + | 1.28780i | −0.0284497 | + | 0.0492763i | −0.879900 | − | 0.475159i | \(-0.842390\pi\) |
0.851450 | + | 0.524436i | \(0.175724\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.17198 | −0.0447789 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.5504 | −1.01296 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.4457 | − | 37.1451i | 0.817017 | − | 1.41511i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.73629 | − | 4.73939i | −0.104093 | − | 0.180295i | 0.809274 | − | 0.587431i | \(-0.199861\pi\) |
−0.913367 | + | 0.407136i | \(0.866527\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.560036 | − | 1.68326i | −0.0212740 | − | 0.0639417i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.75074 | + | 4.76442i | 0.104341 | + | 0.180725i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.2094 | + | 47.1281i | −1.03063 | + | 1.78510i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.97405 | 0.339430 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.5649 | −1.45658 | −0.728288 | − | 0.685271i | \(-0.759684\pi\) | ||||
−0.728288 | + | 0.685271i | \(0.759684\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −43.5567 | + | 75.4425i | −1.64277 | + | 2.84537i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.591738 | − | 1.02492i | −0.0222862 | − | 0.0386007i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −47.9808 | − | 9.84662i | −1.80450 | − | 0.370320i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.48702 | − | 6.03970i | −0.130958 | − | 0.226826i | 0.793088 | − | 0.609107i | \(-0.208472\pi\) |
−0.924046 | + | 0.382281i | \(0.875139\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.42124 | − | 7.65781i | 0.165809 | − | 0.287190i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.2239 | −1.31914 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.35545 | 0.0880889 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.00000 | − | 5.19615i | 0.112037 | − | 0.194054i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.48702 | + | 4.30765i | 0.0927503 | + | 0.160648i | 0.908667 | − | 0.417521i | \(-0.137101\pi\) |
−0.815917 | + | 0.578169i | \(0.803767\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.13214 | − | 1.27529i | 0.0421631 | − | 0.0474941i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.43421 | − | 9.41233i | −0.202101 | − | 0.350048i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.92699 | − | 5.06969i | 0.108706 | − | 0.188284i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.9548 | −1.33349 | −0.666746 | − | 0.745285i | \(-0.732313\pi\) | ||||
−0.666746 | + | 0.745285i | \(0.732313\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.43996 | + | 9.42229i | −0.201204 | + | 0.348496i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.9400 | − | 20.6806i | −0.441013 | − | 0.763856i | 0.556752 | − | 0.830679i | \(-0.312047\pi\) |
−0.997765 | + | 0.0668223i | \(0.978714\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.60471 | − | 4.19371i | 0.206733 | − | 0.154687i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.12492 | − | 1.94841i | −0.0414368 | − | 0.0717707i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.5260 | + | 18.2315i | −0.387203 | + | 0.670656i | −0.992072 | − | 0.125669i | \(-0.959892\pi\) |
0.604869 | + | 0.796325i | \(0.293226\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.1950 | 1.03577 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.7973 | −1.42334 | −0.711668 | − | 0.702516i | \(-0.752060\pi\) | ||||
−0.711668 | + | 0.702516i | \(0.752060\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.00000 | − | 3.46410i | 0.0732743 | − | 0.126915i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.58599 | + | 2.74701i | 0.0580283 | + | 0.100508i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.8214 | + | 23.4540i | −0.760796 | + | 0.856989i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.08024 | − | 7.06718i | −0.148890 | − | 0.257885i | 0.781928 | − | 0.623369i | \(-0.214237\pi\) |
−0.930817 | + | 0.365484i | \(0.880903\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.84823 | + | 3.20122i | −0.0673531 | + | 0.116659i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.0260 | 0.546850 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.2661 | 0.482164 | 0.241082 | − | 0.970505i | \(-0.422498\pi\) | ||||
0.241082 | + | 0.970505i | \(0.422498\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.90974 | + | 3.30776i | −0.0693191 | + | 0.120064i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.3727 | − | 21.4302i | −0.448510 | − | 0.776842i | 0.549779 | − | 0.835310i | \(-0.314712\pi\) |
−0.998289 | + | 0.0584677i | \(0.981379\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.3180 | + | 2.93834i | 0.518346 | + | 0.106375i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.25649 | − | 5.64040i | −0.117739 | − | 0.203929i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.3084 | + | 29.9790i | −0.624970 | + | 1.08248i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.3150 | 0.624397 | 0.312198 | − | 0.950017i | \(-0.398935\pi\) | ||||
0.312198 | + | 0.950017i | \(0.398935\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.828025 | −0.0298206 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.85973 | + | 13.6134i | −0.282695 | + | 0.489642i | −0.972048 | − | 0.234784i | \(-0.924562\pi\) |
0.689353 | + | 0.724426i | \(0.257895\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.09174 | + | 5.35505i | 0.111059 | + | 0.192359i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.06579 | − | 27.2484i | −0.325233 | − | 0.977530i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33.5302 | − | 58.0761i | −1.20135 | − | 2.08079i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.31800 | + | 7.47899i | −0.154510 | + | 0.267619i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.85398 | 0.209204 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.8425 | 0.708208 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.64455 | − | 9.77664i | 0.201206 | − | 0.348500i | −0.747711 | − | 0.664024i | \(-0.768847\pi\) |
0.948917 | + | 0.315525i | \(0.102180\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.51298 | + | 11.2808i | 0.231868 | + | 0.401607i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.01150 | − | 15.0627i | −0.178188 | − | 0.535568i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.8540 | + | 27.4599i | 0.562991 | + | 0.975129i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.10471 | − | 10.5737i | 0.216512 | − | 0.375010i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.51003 | 0.0534879 | 0.0267439 | − | 0.999642i | \(-0.491486\pi\) | ||||
0.0267439 | + | 0.999642i | \(0.491486\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.70795 | −0.272688 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.74351 | + | 3.01985i | −0.0616040 | + | 0.106701i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.91549 | − | 5.04977i | −0.102885 | − | 0.178203i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.7637 | − | 3.02981i | −0.520353 | − | 0.106787i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.69645 | − | 4.67039i | −0.0949196 | − | 0.164406i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.11917 | − | 14.0628i | 0.285455 | − | 0.494422i | −0.687265 | − | 0.726407i | \(-0.741189\pi\) |
0.972719 | + | 0.231985i | \(0.0745221\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.91738 | −0.348246 | −0.174123 | − | 0.984724i | \(-0.555709\pi\) | ||||
−0.174123 | + | 0.984724i | \(0.555709\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.7109 | −0.796506 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.00000 | − | 13.8564i | 0.280228 | − | 0.485369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.70368 | − | 11.6111i | −0.234532 | − | 0.406221i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.17050 | + | 6.95068i | −0.215615 | + | 0.242876i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.29394 | − | 7.43732i | −0.149860 | − | 0.259564i | 0.781316 | − | 0.624136i | \(-0.214549\pi\) |
−0.931175 | + | 0.364571i | \(0.881215\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.81652 | + | 6.61041i | −0.133036 | + | 0.230425i | −0.924845 | − | 0.380343i | \(-0.875806\pi\) |
0.791810 | + | 0.610768i | \(0.209139\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.670500 | 0.0233438 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.2920 | −0.775170 | −0.387585 | − | 0.921834i | \(-0.626691\pi\) | ||||
−0.387585 | + | 0.921834i | \(0.626691\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.61917 | + | 14.9288i | −0.299356 | + | 0.518500i | −0.975989 | − | 0.217821i | \(-0.930105\pi\) |
0.676633 | + | 0.736321i | \(0.263438\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.53170 | + | 14.7773i | 0.295961 | + | 0.512620i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.40251 | − | 45.2696i | −0.187186 | − | 1.56850i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.50723 | − | 11.2708i | −0.225192 | − | 0.390044i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.09174 | + | 5.35505i | −0.106866 | + | 0.185098i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.1460 | 0.764566 | 0.382283 | − | 0.924045i | \(-0.375138\pi\) | ||||
0.382283 | + | 0.924045i | \(0.375138\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.26904 | 0.181691 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.40826 | + | 4.17123i | −0.0829449 | + | 0.143665i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.329500 | + | 0.570710i | 0.0113351 | + | 0.0196330i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.5317 | + | 20.8748i | −0.636757 | + | 0.717266i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.8872 | − | 27.5174i | −0.545246 | − | 0.944393i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.9146 | + | 53.5456i | −1.05974 | + | 1.83552i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.2699 | 1.03642 | 0.518211 | − | 0.855253i | \(-0.326598\pi\) | ||||
0.518211 | + | 0.855253i | \(0.326598\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.02595 | 0.274482 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.0048 | − | 43.3097i | 0.854149 | − | 1.47943i | −0.0232828 | − | 0.999729i | \(-0.507412\pi\) |
0.877432 | − | 0.479701i | \(-0.159255\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.8655 | − | 22.2837i | −0.438964 | − | 0.760309i | 0.558645 | − | 0.829407i | \(-0.311321\pi\) |
−0.997610 | + | 0.0690979i | \(0.977988\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.6551 | + | 4.44407i | 0.738005 | + | 0.151454i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.3401 | − | 42.1583i | −0.828546 | − | 1.43508i | −0.899178 | − | 0.437582i | \(-0.855835\pi\) |
0.0706320 | − | 0.997502i | \(-0.477498\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.07876 | + | 5.33257i | −0.104681 | + | 0.181313i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.4189 | −0.863270 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.92888 | 0.201124 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.89381 | + | 10.2084i | −0.199704 | + | 0.345898i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.51298 | + | 4.35260i | 0.0850514 | + | 0.147313i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.835250 | + | 2.51045i | 0.0282366 | + | 0.0848687i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.7752 | − | 48.1081i | −0.937902 | − | 1.62449i | −0.769375 | − | 0.638798i | \(-0.779432\pi\) |
−0.168528 | − | 0.985697i | \(-0.553901\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.59174 | + | 6.22107i | −0.121146 | + | 0.209832i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.9203 | −1.51340 | −0.756702 | − | 0.653760i | \(-0.773191\pi\) | ||||
−0.756702 | + | 0.653760i | \(0.773191\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.3324 | 0.515978 | 0.257989 | − | 0.966148i | \(-0.416940\pi\) | ||||
0.257989 | + | 0.966148i | \(0.416940\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.92699 | + | 8.53379i | −0.165619 | + | 0.286860i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.26799 | − | 14.3206i | −0.277612 | − | 0.480838i | 0.693179 | − | 0.720766i | \(-0.256210\pi\) |
−0.970791 | + | 0.239928i | \(0.922876\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.46164 | + | 16.4156i | 0.183178 | + | 0.550563i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.335250 | + | 0.580670i | 0.0112313 | + | 0.0194532i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.74926 | − | 8.22596i | 0.158928 | − | 0.275271i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.81652 | 0.227851 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.0115 | 0.668165 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.0990 | + | 31.3483i | −0.603634 | + | 1.04553i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.7599 | − | 68.8661i | −1.32459 | − | 2.29426i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.32950 | + | 0.888501i | 0.144077 | + | 0.0295674i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.2752 | − | 17.7972i | −0.341560 | − | 0.591599i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.0332 | + | 20.8421i | −0.399555 | + | 0.692050i | −0.993671 | − | 0.112330i | \(-0.964169\pi\) |
0.594116 | + | 0.804379i | \(0.297502\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.5130 | 0.614037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.8310 | −0.590767 | −0.295383 | − | 0.955379i | \(-0.595447\pi\) | ||||
−0.295383 | + | 0.955379i | \(0.595447\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.06341 | + | 1.84187i | −0.0351936 | + | 0.0609571i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.51298 | + | 7.81670i | 0.149194 | + | 0.258412i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.6955 | − | 41.3352i | 1.21179 | − | 1.36501i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.7622 | − | 34.2292i | −0.651896 | − | 1.12912i | −0.982662 | − | 0.185404i | \(-0.940640\pi\) |
0.330766 | − | 0.943713i | \(-0.392693\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.20220 | − | 12.4746i | 0.237321 | − | 0.411051i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45.2469 | 1.48932 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.8540 | 0.356877 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.322274 | + | 0.558195i | −0.0105849 | + | 0.0183335i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.70220 | − | 11.6086i | −0.219892 | − | 0.380864i | 0.734883 | − | 0.678194i | \(-0.237237\pi\) |
−0.954775 | + | 0.297330i | \(0.903904\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.6407 | + | 22.1273i | 1.69246 | + | 0.725194i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.7954 | + | 22.1623i | 0.418903 | + | 0.725561i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.18348 | − | 3.78189i | 0.0714073 | − | 0.123681i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.40736 | 0.0459763 | 0.0229882 | − | 0.999736i | \(-0.492682\pi\) | ||||
0.0229882 | + | 0.999736i | \(0.492682\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.32950 | −0.0760203 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.9414 | + | 20.6832i | −0.389280 | + | 0.674252i | −0.992353 | − | 0.123434i | \(-0.960609\pi\) |
0.603073 | + | 0.797686i | \(0.293943\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.7982 | − | 41.2197i | −0.774977 | − | 1.34230i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.75649 | + | 1.97857i | −0.0571386 | + | 0.0643630i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.9644 | − | 44.9717i | −0.843731 | − | 1.46138i | −0.886719 | − | 0.462309i | \(-0.847021\pi\) |
0.0429877 | − | 0.999076i | \(-0.486312\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.2752 | + | 26.4574i | −0.495854 | + | 0.858845i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.5879 | 0.927026 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.8118 | 1.67835 | 0.839174 | − | 0.543863i | \(-0.183039\pi\) | ||||
0.839174 | + | 0.543863i | \(0.183039\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.341001 | + | 0.590631i | −0.0110345 | + | 0.0191124i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.96255 | + | 3.39923i | 0.0634401 | + | 0.109882i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.03745 | + | 0.623347i | 0.0980845 | + | 0.0201289i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.61769 | − | 6.26602i | −0.116700 | − | 0.202130i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.92699 | − | 10.2658i | 0.190995 | − | 0.330812i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.0894 | −0.711082 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.67050 | −0.0537197 | −0.0268598 | − | 0.999639i | \(-0.508551\pi\) | ||||
−0.0268598 | + | 0.999639i | \(0.508551\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 26.1364 | − | 45.2696i | 0.839623 | − | 1.45427i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.77521 | − | 8.27091i | −0.153244 | − | 0.265426i | 0.779174 | − | 0.626807i | \(-0.215639\pi\) |
−0.932418 | + | 0.361381i | \(0.882305\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.59511 | − | 13.8112i | −0.147312 | − | 0.442766i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.75649 | − | 3.04233i | −0.0562526 | − | 0.0974324i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.3343 | + | 50.8086i | −0.938489 | + | 1.62551i | −0.170198 | + | 0.985410i | \(0.554441\pi\) |
−0.768291 | + | 0.640100i | \(0.778893\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.33805 | −0.0747244 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.52448 | −0.176383 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.2152 | − | 40.2099i | 0.740449 | − | 1.28250i | −0.211842 | − | 0.977304i | \(-0.567946\pi\) |
0.952291 | − | 0.305192i | \(-0.0987205\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.17773 | − | 3.77193i | −0.0693881 | − | 0.120184i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.988499 | + | 2.97106i | 0.0314643 | + | 0.0945698i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.75796 | − | 8.24103i | −0.151294 | − | 0.262050i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.08024 | − | 7.06718i | 0.129613 | − | 0.224496i | −0.793914 | − | 0.608030i | \(-0.791960\pi\) |
0.923527 | + | 0.383534i | \(0.125293\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.7109 | −0.371634 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.65900 | −0.274509 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.4683 | + | 19.8637i | −0.363205 | + | 0.629089i | −0.988486 | − | 0.151310i | \(-0.951651\pi\) |
0.625282 | + | 0.780399i | \(0.284984\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.42699 | + | 9.39982i | 0.171702 | + | 0.297397i |
(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 | 1680.2.bg.u.1201.2 | 6 | ||
4.3 | odd | 2 | 840.2.bg.i.361.2 | yes | 6 | ||
7.2 | even | 3 | inner | 1680.2.bg.u.961.2 | 6 | ||
12.11 | even | 2 | 2520.2.bi.o.361.2 | 6 | |||
28.3 | even | 6 | 5880.2.a.bt.1.2 | 3 | |||
28.11 | odd | 6 | 5880.2.a.bw.1.2 | 3 | |||
28.23 | odd | 6 | 840.2.bg.i.121.2 | ✓ | 6 | ||
84.23 | even | 6 | 2520.2.bi.o.1801.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.bg.i.121.2 | ✓ | 6 | 28.23 | odd | 6 | ||
840.2.bg.i.361.2 | yes | 6 | 4.3 | odd | 2 | ||
1680.2.bg.u.961.2 | 6 | 7.2 | even | 3 | inner | ||
1680.2.bg.u.1201.2 | 6 | 1.1 | even | 1 | trivial | ||
2520.2.bi.o.361.2 | 6 | 12.11 | even | 2 | |||
2520.2.bi.o.1801.2 | 6 | 84.23 | even | 6 | |||
5880.2.a.bt.1.2 | 3 | 28.3 | even | 6 | |||
5880.2.a.bw.1.2 | 3 | 28.11 | odd | 6 |