Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(79,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.n (of order \(6\), 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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 79.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.79 |
Dual form | 1470.2.n.g.949.1 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.23205 | − | 1.86603i | −0.550990 | − | 0.834512i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0.133975 | + | 2.23205i | 0.0423665 | + | 0.705836i | ||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | − | 2.00000i | − | 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | − | 1.00000i | −0.516398 | − | 0.258199i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 6.92820 | − | 4.00000i | 1.68034 | − | 0.970143i | 0.718900 | − | 0.695113i | \(-0.244646\pi\) |
0.961436 | − | 0.275029i | \(-0.0886875\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | −1.00000 | + | 1.73205i | −0.229416 | + | 0.397360i | −0.957635 | − | 0.287984i | \(-0.907015\pi\) |
0.728219 | + | 0.685344i | \(0.240348\pi\) | |||||||
\(20\) | 1.00000 | − | 2.00000i | 0.223607 | − | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −1.96410 | + | 4.59808i | −0.392820 | + | 0.919615i | ||||
\(26\) | −1.00000 | + | 1.73205i | −0.196116 | + | 0.339683i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 1.23205 | + | 1.86603i | 0.224941 | + | 0.340688i | ||||
\(31\) | −3.00000 | − | 5.19615i | −0.538816 | − | 0.933257i | −0.998968 | − | 0.0454165i | \(-0.985539\pi\) |
0.460152 | − | 0.887840i | \(-0.347795\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 1.73205 | + | 1.00000i | 0.301511 | + | 0.174078i | ||||
\(34\) | −8.00000 | −1.37199 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.92820 | − | 4.00000i | −1.13899 | − | 0.657596i | −0.192809 | − | 0.981236i | \(-0.561760\pi\) |
−0.946180 | + | 0.323640i | \(0.895093\pi\) | |||||||
\(38\) | 1.73205 | − | 1.00000i | 0.280976 | − | 0.162221i | ||||
\(39\) | −1.00000 | − | 1.73205i | −0.160128 | − | 0.277350i | ||||
\(40\) | −1.86603 | + | 1.23205i | −0.295045 | + | 0.194804i | ||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.00000i | − | 1.21999i | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||
0.792406 | − | 0.609994i | \(-0.208828\pi\) | |||||||
\(44\) | −1.00000 | + | 1.73205i | −0.150756 | + | 0.261116i | ||||
\(45\) | −2.23205 | + | 0.133975i | −0.332734 | + | 0.0199718i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.46410 | − | 2.00000i | −0.505291 | − | 0.291730i | 0.225605 | − | 0.974219i | \(-0.427564\pi\) |
−0.730896 | + | 0.682489i | \(0.760898\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.00000 | − | 3.00000i | 0.565685 | − | 0.424264i | ||||
\(51\) | 4.00000 | − | 6.92820i | 0.560112 | − | 0.970143i | ||||
\(52\) | 1.73205 | − | 1.00000i | 0.240192 | − | 0.138675i | ||||
\(53\) | 1.73205 | − | 1.00000i | 0.237915 | − | 0.137361i | −0.376303 | − | 0.926497i | \(-0.622805\pi\) |
0.614218 | + | 0.789136i | \(0.289471\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 2.00000 | − | 4.00000i | 0.269680 | − | 0.539360i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000i | 0.264906i | ||||||||
\(58\) | −5.19615 | − | 3.00000i | −0.682288 | − | 0.393919i | ||||
\(59\) | −4.00000 | − | 6.92820i | −0.520756 | − | 0.901975i | −0.999709 | − | 0.0241347i | \(-0.992317\pi\) |
0.478953 | − | 0.877841i | \(-0.341016\pi\) | |||||||
\(60\) | −0.133975 | − | 2.23205i | −0.0172960 | − | 0.288157i | ||||
\(61\) | −5.00000 | + | 8.66025i | −0.640184 | + | 1.10883i | 0.345207 | + | 0.938527i | \(0.387809\pi\) |
−0.985391 | + | 0.170305i | \(0.945525\pi\) | |||||||
\(62\) | 6.00000i | 0.762001i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −3.73205 | + | 2.46410i | −0.462904 | + | 0.305634i | ||||
\(66\) | −1.00000 | − | 1.73205i | −0.123091 | − | 0.213201i | ||||
\(67\) | −10.3923 | + | 6.00000i | −1.26962 | + | 0.733017i | −0.974916 | − | 0.222571i | \(-0.928555\pi\) |
−0.294706 | + | 0.955588i | \(0.595222\pi\) | |||||||
\(68\) | 6.92820 | + | 4.00000i | 0.840168 | + | 0.485071i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0000 | −1.66149 | −0.830747 | − | 0.556650i | \(-0.812086\pi\) | ||||
−0.830747 | + | 0.556650i | \(0.812086\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 8.66025 | − | 5.00000i | 1.01361 | − | 0.585206i | 0.101361 | − | 0.994850i | \(-0.467680\pi\) |
0.912245 | + | 0.409644i | \(0.134347\pi\) | |||||||
\(74\) | 4.00000 | + | 6.92820i | 0.464991 | + | 0.805387i | ||||
\(75\) | 0.598076 | + | 4.96410i | 0.0690599 | + | 0.573205i | ||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.00000i | 0.226455i | ||||||||
\(79\) | 2.00000 | − | 3.46410i | 0.225018 | − | 0.389742i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.956325 | + | 0.292306i | \(0.0944227\pi\) | |||||||
\(80\) | 2.23205 | − | 0.133975i | 0.249551 | − | 0.0149788i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −5.19615 | − | 3.00000i | −0.573819 | − | 0.331295i | ||||
\(83\) | − | 16.0000i | − | 1.75623i | −0.478451 | − | 0.878114i | \(-0.658802\pi\) | ||
0.478451 | − | 0.878114i | \(-0.341198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.0000 | − | 8.00000i | −1.73544 | − | 0.867722i | ||||
\(86\) | −4.00000 | + | 6.92820i | −0.431331 | + | 0.747087i | ||||
\(87\) | 5.19615 | − | 3.00000i | 0.557086 | − | 0.321634i | ||||
\(88\) | 1.73205 | − | 1.00000i | 0.184637 | − | 0.106600i | ||||
\(89\) | 5.00000 | − | 8.66025i | 0.529999 | − | 0.917985i | −0.469389 | − | 0.882992i | \(-0.655526\pi\) |
0.999388 | − | 0.0349934i | \(-0.0111410\pi\) | |||||||
\(90\) | 2.00000 | + | 1.00000i | 0.210819 | + | 0.105409i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.19615 | − | 3.00000i | −0.538816 | − | 0.311086i | ||||
\(94\) | 2.00000 | + | 3.46410i | 0.206284 | + | 0.357295i | ||||
\(95\) | 4.46410 | − | 0.267949i | 0.458007 | − | 0.0274910i | ||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | −4.96410 | + | 0.598076i | −0.496410 | + | 0.0598076i | ||||
\(101\) | 5.00000 | + | 8.66025i | 0.497519 | + | 0.861727i | 0.999996 | − | 0.00286291i | \(-0.000911295\pi\) |
−0.502477 | + | 0.864590i | \(0.667578\pi\) | |||||||
\(102\) | −6.92820 | + | 4.00000i | −0.685994 | + | 0.396059i | ||||
\(103\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | 10.3923 | + | 6.00000i | 1.00466 | + | 0.580042i | 0.909624 | − | 0.415432i | \(-0.136370\pi\) |
0.0950377 | + | 0.995474i | \(0.469703\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | −3.00000 | − | 5.19615i | −0.287348 | − | 0.497701i | 0.685828 | − | 0.727764i | \(-0.259440\pi\) |
−0.973176 | + | 0.230063i | \(0.926107\pi\) | |||||||
\(110\) | −3.73205 | + | 2.46410i | −0.355837 | + | 0.234943i | ||||
\(111\) | −8.00000 | −0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 1.00000 | − | 1.73205i | 0.0936586 | − | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.00000 | + | 5.19615i | 0.278543 | + | 0.482451i | ||||
\(117\) | −1.73205 | − | 1.00000i | −0.160128 | − | 0.0924500i | ||||
\(118\) | 8.00000i | 0.736460i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | + | 2.00000i | −0.0912871 | + | 0.182574i | ||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 8.66025 | − | 5.00000i | 0.784063 | − | 0.452679i | ||||
\(123\) | 5.19615 | − | 3.00000i | 0.468521 | − | 0.270501i | ||||
\(124\) | 3.00000 | − | 5.19615i | 0.269408 | − | 0.466628i | ||||
\(125\) | 11.0000 | − | 2.00000i | 0.983870 | − | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0000i | 1.06483i | 0.846484 | + | 0.532414i | \(0.178715\pi\) | ||||
−0.846484 | + | 0.532414i | \(0.821285\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −4.00000 | − | 6.92820i | −0.352180 | − | 0.609994i | ||||
\(130\) | 4.46410 | − | 0.267949i | 0.391528 | − | 0.0235007i | ||||
\(131\) | 10.0000 | − | 17.3205i | 0.873704 | − | 1.51330i | 0.0155672 | − | 0.999879i | \(-0.495045\pi\) |
0.858137 | − | 0.513421i | \(-0.171622\pi\) | |||||||
\(132\) | 2.00000i | 0.174078i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.0000 | 1.03664 | ||||||||
\(135\) | −1.86603 | + | 1.23205i | −0.160602 | + | 0.106038i | ||||
\(136\) | −4.00000 | − | 6.92820i | −0.342997 | − | 0.594089i | ||||
\(137\) | −12.1244 | + | 7.00000i | −1.03585 | + | 0.598050i | −0.918656 | − | 0.395058i | \(-0.870724\pi\) |
−0.117198 | + | 0.993109i | \(0.537391\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | 0.169638 | 0.0848189 | − | 0.996396i | \(-0.472969\pi\) | ||||
0.0848189 | + | 0.996396i | \(0.472969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.00000 | −0.336861 | ||||||||
\(142\) | 12.1244 | + | 7.00000i | 1.01745 | + | 0.587427i | ||||
\(143\) | 3.46410 | − | 2.00000i | 0.289683 | − | 0.167248i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −7.39230 | − | 11.1962i | −0.613898 | − | 0.929790i | ||||
\(146\) | −10.0000 | −0.827606 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 8.00000i | − | 0.657596i | ||||||
\(149\) | −9.00000 | + | 15.5885i | −0.737309 | + | 1.27706i | 0.216394 | + | 0.976306i | \(0.430570\pi\) |
−0.953703 | + | 0.300750i | \(0.902763\pi\) | |||||||
\(150\) | 1.96410 | − | 4.59808i | 0.160368 | − | 0.375431i | ||||
\(151\) | −4.00000 | − | 6.92820i | −0.325515 | − | 0.563809i | 0.656101 | − | 0.754673i | \(-0.272204\pi\) |
−0.981617 | + | 0.190864i | \(0.938871\pi\) | |||||||
\(152\) | 1.73205 | + | 1.00000i | 0.140488 | + | 0.0811107i | ||||
\(153\) | − | 8.00000i | − | 0.646762i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | + | 12.0000i | −0.481932 | + | 0.963863i | ||||
\(156\) | 1.00000 | − | 1.73205i | 0.0800641 | − | 0.138675i | ||||
\(157\) | −8.66025 | + | 5.00000i | −0.691164 | + | 0.399043i | −0.804048 | − | 0.594565i | \(-0.797324\pi\) |
0.112884 | + | 0.993608i | \(0.463991\pi\) | |||||||
\(158\) | −3.46410 | + | 2.00000i | −0.275589 | + | 0.159111i | ||||
\(159\) | 1.00000 | − | 1.73205i | 0.0793052 | − | 0.137361i | ||||
\(160\) | −2.00000 | − | 1.00000i | −0.158114 | − | 0.0790569i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(164\) | 3.00000 | + | 5.19615i | 0.234261 | + | 0.405751i | ||||
\(165\) | −0.267949 | − | 4.46410i | −0.0208598 | − | 0.347530i | ||||
\(166\) | −8.00000 | + | 13.8564i | −0.620920 | + | 1.07547i | ||||
\(167\) | − | 8.00000i | − | 0.619059i | −0.950890 | − | 0.309529i | \(-0.899829\pi\) | ||
0.950890 | − | 0.309529i | \(-0.100171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 9.85641 | + | 14.9282i | 0.755952 | + | 1.14494i | ||||
\(171\) | 1.00000 | + | 1.73205i | 0.0764719 | + | 0.132453i | ||||
\(172\) | 6.92820 | − | 4.00000i | 0.528271 | − | 0.304997i | ||||
\(173\) | −13.8564 | − | 8.00000i | −1.05348 | − | 0.608229i | −0.129861 | − | 0.991532i | \(-0.541453\pi\) |
−0.923622 | + | 0.383304i | \(0.874786\pi\) | |||||||
\(174\) | −6.00000 | −0.454859 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.00000 | −0.150756 | ||||||||
\(177\) | −6.92820 | − | 4.00000i | −0.520756 | − | 0.300658i | ||||
\(178\) | −8.66025 | + | 5.00000i | −0.649113 | + | 0.374766i | ||||
\(179\) | −1.00000 | − | 1.73205i | −0.0747435 | − | 0.129460i | 0.826231 | − | 0.563331i | \(-0.190480\pi\) |
−0.900975 | + | 0.433872i | \(0.857147\pi\) | |||||||
\(180\) | −1.23205 | − | 1.86603i | −0.0918316 | − | 0.139085i | ||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.0000i | 0.739221i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.07180 | + | 17.8564i | 0.0788001 | + | 1.31283i | ||||
\(186\) | 3.00000 | + | 5.19615i | 0.219971 | + | 0.381000i | ||||
\(187\) | 13.8564 | + | 8.00000i | 1.01328 | + | 0.585018i | ||||
\(188\) | − | 4.00000i | − | 0.291730i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.00000 | − | 2.00000i | −0.290191 | − | 0.145095i | ||||
\(191\) | −7.00000 | + | 12.1244i | −0.506502 | + | 0.877288i | 0.493469 | + | 0.869763i | \(0.335728\pi\) |
−0.999972 | + | 0.00752447i | \(0.997605\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(194\) | 5.00000 | − | 8.66025i | 0.358979 | − | 0.621770i | ||||
\(195\) | −2.00000 | + | 4.00000i | −0.143223 | + | 0.286446i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 6.00000i | − | 0.427482i | −0.976890 | − | 0.213741i | \(-0.931435\pi\) | ||
0.976890 | − | 0.213741i | \(-0.0685649\pi\) | |||||||
\(198\) | −1.73205 | − | 1.00000i | −0.123091 | − | 0.0710669i | ||||
\(199\) | −13.0000 | − | 22.5167i | −0.921546 | − | 1.59616i | −0.797025 | − | 0.603947i | \(-0.793594\pi\) |
−0.124521 | − | 0.992217i | \(-0.539739\pi\) | |||||||
\(200\) | 4.59808 | + | 1.96410i | 0.325133 | + | 0.138883i | ||||
\(201\) | −6.00000 | + | 10.3923i | −0.423207 | + | 0.733017i | ||||
\(202\) | − | 10.0000i | − | 0.703598i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 8.00000 | 0.560112 | ||||||||
\(205\) | −7.39230 | − | 11.1962i | −0.516301 | − | 0.781973i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.73205 | + | 1.00000i | 0.120096 | + | 0.0693375i | ||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 1.73205 | + | 1.00000i | 0.118958 | + | 0.0686803i | ||||
\(213\) | −12.1244 | + | 7.00000i | −0.830747 | + | 0.479632i | ||||
\(214\) | −6.00000 | − | 10.3923i | −0.410152 | − | 0.710403i | ||||
\(215\) | −14.9282 | + | 9.85641i | −1.01810 | + | 0.672201i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.00000i | 0.406371i | ||||||||
\(219\) | 5.00000 | − | 8.66025i | 0.337869 | − | 0.585206i | ||||
\(220\) | 4.46410 | − | 0.267949i | 0.300970 | − | 0.0180651i | ||||
\(221\) | −8.00000 | − | 13.8564i | −0.538138 | − | 0.932083i | ||||
\(222\) | 6.92820 | + | 4.00000i | 0.464991 | + | 0.268462i | ||||
\(223\) | 16.0000i | 1.07144i | 0.844396 | + | 0.535720i | \(0.179960\pi\) | ||||
−0.844396 | + | 0.535720i | \(0.820040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | + | 4.00000i | 0.200000 | + | 0.266667i | ||||
\(226\) | −3.00000 | + | 5.19615i | −0.199557 | + | 0.345643i | ||||
\(227\) | −6.92820 | + | 4.00000i | −0.459841 | + | 0.265489i | −0.711977 | − | 0.702202i | \(-0.752200\pi\) |
0.252136 | + | 0.967692i | \(0.418867\pi\) | |||||||
\(228\) | −1.73205 | + | 1.00000i | −0.114708 | + | 0.0662266i | ||||
\(229\) | 13.0000 | − | 22.5167i | 0.859064 | − | 1.48794i | −0.0137585 | − | 0.999905i | \(-0.504380\pi\) |
0.872823 | − | 0.488037i | \(-0.162287\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 6.00000i | − | 0.393919i | ||||||
\(233\) | 5.19615 | + | 3.00000i | 0.340411 | + | 0.196537i | 0.660454 | − | 0.750867i | \(-0.270364\pi\) |
−0.320043 | + | 0.947403i | \(0.603697\pi\) | |||||||
\(234\) | 1.00000 | + | 1.73205i | 0.0653720 | + | 0.113228i | ||||
\(235\) | 0.535898 | + | 8.92820i | 0.0349582 | + | 0.582412i | ||||
\(236\) | 4.00000 | − | 6.92820i | 0.260378 | − | 0.450988i | ||||
\(237\) | − | 4.00000i | − | 0.259828i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.0000 | 1.42306 | 0.711531 | − | 0.702655i | \(-0.248002\pi\) | ||||
0.711531 | + | 0.702655i | \(0.248002\pi\) | |||||||
\(240\) | 1.86603 | − | 1.23205i | 0.120451 | − | 0.0795285i | ||||
\(241\) | 5.00000 | + | 8.66025i | 0.322078 | + | 0.557856i | 0.980917 | − | 0.194429i | \(-0.0622852\pi\) |
−0.658838 | + | 0.752285i | \(0.728952\pi\) | |||||||
\(242\) | −6.06218 | + | 3.50000i | −0.389692 | + | 0.224989i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 3.46410 | + | 2.00000i | 0.220416 | + | 0.127257i | ||||
\(248\) | −5.19615 | + | 3.00000i | −0.329956 | + | 0.190500i | ||||
\(249\) | −8.00000 | − | 13.8564i | −0.506979 | − | 0.878114i | ||||
\(250\) | −10.5263 | − | 3.76795i | −0.665740 | − | 0.238306i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 6.00000 | − | 10.3923i | 0.376473 | − | 0.652071i | ||||
\(255\) | −17.8564 | + | 1.07180i | −1.11821 | + | 0.0671185i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 17.3205 | + | 10.0000i | 1.08042 | + | 0.623783i | 0.931011 | − | 0.364992i | \(-0.118928\pi\) |
0.149413 | + | 0.988775i | \(0.452262\pi\) | |||||||
\(258\) | 8.00000i | 0.498058i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.00000 | − | 2.00000i | −0.248069 | − | 0.124035i | ||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | −17.3205 | + | 10.0000i | −1.07006 | + | 0.617802i | ||||
\(263\) | 20.7846 | − | 12.0000i | 1.28163 | − | 0.739952i | 0.304487 | − | 0.952517i | \(-0.401515\pi\) |
0.977147 | + | 0.212565i | \(0.0681817\pi\) | |||||||
\(264\) | 1.00000 | − | 1.73205i | 0.0615457 | − | 0.106600i | ||||
\(265\) | −4.00000 | − | 2.00000i | −0.245718 | − | 0.122859i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 10.0000i | − | 0.611990i | ||||||
\(268\) | −10.3923 | − | 6.00000i | −0.634811 | − | 0.366508i | ||||
\(269\) | 7.00000 | + | 12.1244i | 0.426798 | + | 0.739235i | 0.996586 | − | 0.0825561i | \(-0.0263084\pi\) |
−0.569789 | + | 0.821791i | \(0.692975\pi\) | |||||||
\(270\) | 2.23205 | − | 0.133975i | 0.135838 | − | 0.00815343i | ||||
\(271\) | −1.00000 | + | 1.73205i | −0.0607457 | + | 0.105215i | −0.894799 | − | 0.446469i | \(-0.852681\pi\) |
0.834053 | + | 0.551684i | \(0.186015\pi\) | |||||||
\(272\) | 8.00000i | 0.485071i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.0000 | 0.845771 | ||||||||
\(275\) | −9.92820 | + | 1.19615i | −0.598693 | + | 0.0721307i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.92820 | + | 4.00000i | −0.416275 | + | 0.240337i | −0.693482 | − | 0.720473i | \(-0.743925\pi\) |
0.277207 | + | 0.960810i | \(0.410591\pi\) | |||||||
\(278\) | −1.73205 | − | 1.00000i | −0.103882 | − | 0.0599760i | ||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.0000 | 1.31241 | 0.656205 | − | 0.754583i | \(-0.272161\pi\) | ||||
0.656205 | + | 0.754583i | \(0.272161\pi\) | |||||||
\(282\) | 3.46410 | + | 2.00000i | 0.206284 | + | 0.119098i | ||||
\(283\) | −3.46410 | + | 2.00000i | −0.205919 | + | 0.118888i | −0.599414 | − | 0.800439i | \(-0.704600\pi\) |
0.393494 | + | 0.919327i | \(0.371266\pi\) | |||||||
\(284\) | −7.00000 | − | 12.1244i | −0.415374 | − | 0.719448i | ||||
\(285\) | 3.73205 | − | 2.46410i | 0.221068 | − | 0.145961i | ||||
\(286\) | −4.00000 | −0.236525 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 23.5000 | − | 40.7032i | 1.38235 | − | 2.39431i | ||||
\(290\) | 0.803848 | + | 13.3923i | 0.0472036 | + | 0.786423i | ||||
\(291\) | 5.00000 | + | 8.66025i | 0.293105 | + | 0.507673i | ||||
\(292\) | 8.66025 | + | 5.00000i | 0.506803 | + | 0.292603i | ||||
\(293\) | 16.0000i | 0.934730i | 0.884064 | + | 0.467365i | \(0.154797\pi\) | ||||
−0.884064 | + | 0.467365i | \(0.845203\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | + | 16.0000i | −0.465778 | + | 0.931556i | ||||
\(296\) | −4.00000 | + | 6.92820i | −0.232495 | + | 0.402694i | ||||
\(297\) | 1.73205 | − | 1.00000i | 0.100504 | − | 0.0580259i | ||||
\(298\) | 15.5885 | − | 9.00000i | 0.903015 | − | 0.521356i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.00000 | + | 3.00000i | −0.230940 | + | 0.173205i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.00000i | 0.460348i | ||||||||
\(303\) | 8.66025 | + | 5.00000i | 0.497519 | + | 0.287242i | ||||
\(304\) | −1.00000 | − | 1.73205i | −0.0573539 | − | 0.0993399i | ||||
\(305\) | 22.3205 | − | 1.33975i | 1.27807 | − | 0.0767136i | ||||
\(306\) | −4.00000 | + | 6.92820i | −0.228665 | + | 0.396059i | ||||
\(307\) | 28.0000i | 1.59804i | 0.601302 | + | 0.799022i | \(0.294649\pi\) | ||||
−0.601302 | + | 0.799022i | \(0.705351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11.1962 | − | 7.39230i | 0.635899 | − | 0.419855i | ||||
\(311\) | 4.00000 | + | 6.92820i | 0.226819 | + | 0.392862i | 0.956864 | − | 0.290537i | \(-0.0938340\pi\) |
−0.730044 | + | 0.683400i | \(0.760501\pi\) | |||||||
\(312\) | −1.73205 | + | 1.00000i | −0.0980581 | + | 0.0566139i | ||||
\(313\) | 8.66025 | + | 5.00000i | 0.489506 | + | 0.282617i | 0.724370 | − | 0.689412i | \(-0.242131\pi\) |
−0.234863 | + | 0.972028i | \(0.575464\pi\) | |||||||
\(314\) | 10.0000 | 0.564333 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | 1.73205 | + | 1.00000i | 0.0972817 | + | 0.0561656i | 0.547852 | − | 0.836576i | \(-0.315446\pi\) |
−0.450570 | + | 0.892741i | \(0.648779\pi\) | |||||||
\(318\) | −1.73205 | + | 1.00000i | −0.0971286 | + | 0.0560772i | ||||
\(319\) | 6.00000 | + | 10.3923i | 0.335936 | + | 0.581857i | ||||
\(320\) | 1.23205 | + | 1.86603i | 0.0688737 | + | 0.104314i | ||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.0000i | 0.890264i | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 9.19615 | + | 3.92820i | 0.510111 | + | 0.217898i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.19615 | − | 3.00000i | −0.287348 | − | 0.165900i | ||||
\(328\) | − | 6.00000i | − | 0.331295i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.00000 | + | 4.00000i | −0.110096 | + | 0.220193i | ||||
\(331\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(332\) | 13.8564 | − | 8.00000i | 0.760469 | − | 0.439057i | ||||
\(333\) | −6.92820 | + | 4.00000i | −0.379663 | + | 0.219199i | ||||
\(334\) | −4.00000 | + | 6.92820i | −0.218870 | + | 0.379094i | ||||
\(335\) | 24.0000 | + | 12.0000i | 1.31126 | + | 0.655630i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.0000i | 1.74315i | 0.490261 | + | 0.871576i | \(0.336901\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | −7.79423 | − | 4.50000i | −0.423950 | − | 0.244768i | ||||
\(339\) | −3.00000 | − | 5.19615i | −0.162938 | − | 0.282216i | ||||
\(340\) | −1.07180 | − | 17.8564i | −0.0581263 | − | 0.968400i | ||||
\(341\) | 6.00000 | − | 10.3923i | 0.324918 | − | 0.562775i | ||||
\(342\) | − | 2.00000i | − | 0.108148i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.00000 | + | 13.8564i | 0.430083 | + | 0.744925i | ||||
\(347\) | 3.46410 | − | 2.00000i | 0.185963 | − | 0.107366i | −0.404128 | − | 0.914702i | \(-0.632425\pi\) |
0.590091 | + | 0.807337i | \(0.299092\pi\) | |||||||
\(348\) | 5.19615 | + | 3.00000i | 0.278543 | + | 0.160817i | ||||
\(349\) | −18.0000 | −0.963518 | −0.481759 | − | 0.876304i | \(-0.660002\pi\) | ||||
−0.481759 | + | 0.876304i | \(0.660002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 1.73205 | + | 1.00000i | 0.0923186 | + | 0.0533002i | ||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 4.00000 | + | 6.92820i | 0.212598 | + | 0.368230i | ||||
\(355\) | 17.2487 | + | 26.1244i | 0.915467 | + | 1.38654i | ||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.00000i | 0.105703i | ||||||||
\(359\) | 7.00000 | − | 12.1244i | 0.369446 | − | 0.639899i | −0.620033 | − | 0.784576i | \(-0.712881\pi\) |
0.989479 | + | 0.144677i | \(0.0462142\pi\) | |||||||
\(360\) | 0.133975 | + | 2.23205i | 0.00706108 | + | 0.117639i | ||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | −19.0526 | − | 11.0000i | −1.00138 | − | 0.578147i | ||||
\(363\) | − | 7.00000i | − | 0.367405i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.0000 | − | 10.0000i | −1.04685 | − | 0.523424i | ||||
\(366\) | 5.00000 | − | 8.66025i | 0.261354 | − | 0.452679i | ||||
\(367\) | −27.7128 | + | 16.0000i | −1.44660 | + | 0.835193i | −0.998277 | − | 0.0586798i | \(-0.981311\pi\) |
−0.448320 | + | 0.893873i | \(0.647978\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.00000 | − | 5.19615i | 0.156174 | − | 0.270501i | ||||
\(370\) | 8.00000 | − | 16.0000i | 0.415900 | − | 0.831800i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 6.00000i | − | 0.311086i | ||||||
\(373\) | 31.1769 | + | 18.0000i | 1.61428 | + | 0.932005i | 0.988363 | + | 0.152115i | \(0.0486083\pi\) |
0.625917 | + | 0.779890i | \(0.284725\pi\) | |||||||
\(374\) | −8.00000 | − | 13.8564i | −0.413670 | − | 0.716498i | ||||
\(375\) | 8.52628 | − | 7.23205i | 0.440295 | − | 0.373461i | ||||
\(376\) | −2.00000 | + | 3.46410i | −0.103142 | + | 0.178647i | ||||
\(377\) | − | 12.0000i | − | 0.618031i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 2.46410 | + | 3.73205i | 0.126406 | + | 0.191450i | ||||
\(381\) | 6.00000 | + | 10.3923i | 0.307389 | + | 0.532414i | ||||
\(382\) | 12.1244 | − | 7.00000i | 0.620336 | − | 0.358151i | ||||
\(383\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.92820 | − | 4.00000i | −0.352180 | − | 0.203331i | ||||
\(388\) | −8.66025 | + | 5.00000i | −0.439658 | + | 0.253837i | ||||
\(389\) | 3.00000 | + | 5.19615i | 0.152106 | + | 0.263455i | 0.932002 | − | 0.362454i | \(-0.118061\pi\) |
−0.779895 | + | 0.625910i | \(0.784728\pi\) | |||||||
\(390\) | 3.73205 | − | 2.46410i | 0.188980 | − | 0.124775i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 20.0000i | − | 1.00887i | ||||||
\(394\) | −3.00000 | + | 5.19615i | −0.151138 | + | 0.261778i | ||||
\(395\) | −8.92820 | + | 0.535898i | −0.449227 | + | 0.0269640i | ||||
\(396\) | 1.00000 | + | 1.73205i | 0.0502519 | + | 0.0870388i | ||||
\(397\) | −1.73205 | − | 1.00000i | −0.0869291 | − | 0.0501886i | 0.455905 | − | 0.890028i | \(-0.349316\pi\) |
−0.542834 | + | 0.839840i | \(0.682649\pi\) | |||||||
\(398\) | 26.0000i | 1.30326i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | − | 4.00000i | −0.150000 | − | 0.200000i | ||||
\(401\) | −9.00000 | + | 15.5885i | −0.449439 | + | 0.778450i | −0.998350 | − | 0.0574304i | \(-0.981709\pi\) |
0.548911 | + | 0.835881i | \(0.315043\pi\) | |||||||
\(402\) | 10.3923 | − | 6.00000i | 0.518321 | − | 0.299253i | ||||
\(403\) | −10.3923 | + | 6.00000i | −0.517678 | + | 0.298881i | ||||
\(404\) | −5.00000 | + | 8.66025i | −0.248759 | + | 0.430864i | ||||
\(405\) | −1.00000 | + | 2.00000i | −0.0496904 | + | 0.0993808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 16.0000i | − | 0.793091i | ||||||
\(408\) | −6.92820 | − | 4.00000i | −0.342997 | − | 0.198030i | ||||
\(409\) | 5.00000 | + | 8.66025i | 0.247234 | + | 0.428222i | 0.962757 | − | 0.270367i | \(-0.0871450\pi\) |
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(410\) | 0.803848 | + | 13.3923i | 0.0396992 | + | 0.661399i | ||||
\(411\) | −7.00000 | + | 12.1244i | −0.345285 | + | 0.598050i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.8564 | + | 19.7128i | −1.46559 | + | 0.967664i | ||||
\(416\) | −1.00000 | − | 1.73205i | −0.0490290 | − | 0.0849208i | ||||
\(417\) | 1.73205 | − | 1.00000i | 0.0848189 | − | 0.0489702i | ||||
\(418\) | 3.46410 | + | 2.00000i | 0.169435 | + | 0.0978232i | ||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 6.92820 | + | 4.00000i | 0.337260 | + | 0.194717i | ||||
\(423\) | −3.46410 | + | 2.00000i | −0.168430 | + | 0.0972433i | ||||
\(424\) | −1.00000 | − | 1.73205i | −0.0485643 | − | 0.0841158i | ||||
\(425\) | 4.78461 | + | 39.7128i | 0.232088 | + | 1.92635i | ||||
\(426\) | 14.0000 | 0.678302 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.0000i | 0.580042i | ||||||||
\(429\) | 2.00000 | − | 3.46410i | 0.0965609 | − | 0.167248i | ||||
\(430\) | 17.8564 | − | 1.07180i | 0.861112 | − | 0.0516866i | ||||
\(431\) | 3.00000 | + | 5.19615i | 0.144505 | + | 0.250290i | 0.929188 | − | 0.369607i | \(-0.120508\pi\) |
−0.784683 | + | 0.619897i | \(0.787174\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 26.0000i | − | 1.24948i | −0.780833 | − | 0.624740i | \(-0.785205\pi\) | ||
0.780833 | − | 0.624740i | \(-0.214795\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.0000 | − | 6.00000i | −0.575356 | − | 0.287678i | ||||
\(436\) | 3.00000 | − | 5.19615i | 0.143674 | − | 0.248851i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −8.66025 | + | 5.00000i | −0.413803 | + | 0.238909i | ||||
\(439\) | 3.00000 | − | 5.19615i | 0.143182 | − | 0.247999i | −0.785511 | − | 0.618848i | \(-0.787600\pi\) |
0.928693 | + | 0.370849i | \(0.120933\pi\) | |||||||
\(440\) | −4.00000 | − | 2.00000i | −0.190693 | − | 0.0953463i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.0000i | 0.761042i | ||||||||
\(443\) | 31.1769 | + | 18.0000i | 1.48126 | + | 0.855206i | 0.999774 | − | 0.0212481i | \(-0.00676401\pi\) |
0.481486 | + | 0.876454i | \(0.340097\pi\) | |||||||
\(444\) | −4.00000 | − | 6.92820i | −0.189832 | − | 0.328798i | ||||
\(445\) | −22.3205 | + | 1.33975i | −1.05809 | + | 0.0635100i | ||||
\(446\) | 8.00000 | − | 13.8564i | 0.378811 | − | 0.656120i | ||||
\(447\) | 18.0000i | 0.851371i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | −0.598076 | − | 4.96410i | −0.0281936 | − | 0.234010i | ||||
\(451\) | 6.00000 | + | 10.3923i | 0.282529 | + | 0.489355i | ||||
\(452\) | 5.19615 | − | 3.00000i | 0.244406 | − | 0.141108i | ||||
\(453\) | −6.92820 | − | 4.00000i | −0.325515 | − | 0.187936i | ||||
\(454\) | 8.00000 | 0.375459 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | 24.2487 | + | 14.0000i | 1.13431 | + | 0.654892i | 0.945015 | − | 0.327028i | \(-0.106047\pi\) |
0.189292 | + | 0.981921i | \(0.439381\pi\) | |||||||
\(458\) | −22.5167 | + | 13.0000i | −1.05213 | + | 0.607450i | ||||
\(459\) | −4.00000 | − | 6.92820i | −0.186704 | − | 0.323381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0000 | 0.838344 | 0.419172 | − | 0.907907i | \(-0.362320\pi\) | ||||
0.419172 | + | 0.907907i | \(0.362320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.0000i | 0.557687i | 0.960337 | + | 0.278844i | \(0.0899511\pi\) | ||||
−0.960337 | + | 0.278844i | \(0.910049\pi\) | |||||||
\(464\) | −3.00000 | + | 5.19615i | −0.139272 | + | 0.241225i | ||||
\(465\) | 0.803848 | + | 13.3923i | 0.0372775 | + | 0.621053i | ||||
\(466\) | −3.00000 | − | 5.19615i | −0.138972 | − | 0.240707i | ||||
\(467\) | −13.8564 | − | 8.00000i | −0.641198 | − | 0.370196i | 0.143878 | − | 0.989595i | \(-0.454043\pi\) |
−0.785076 | + | 0.619400i | \(0.787376\pi\) | |||||||
\(468\) | − | 2.00000i | − | 0.0924500i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.00000 | − | 8.00000i | 0.184506 | − | 0.369012i | ||||
\(471\) | −5.00000 | + | 8.66025i | −0.230388 | + | 0.399043i | ||||
\(472\) | −6.92820 | + | 4.00000i | −0.318896 | + | 0.184115i | ||||
\(473\) | 13.8564 | − | 8.00000i | 0.637118 | − | 0.367840i | ||||
\(474\) | −2.00000 | + | 3.46410i | −0.0918630 | + | 0.159111i | ||||
\(475\) | −6.00000 | − | 8.00000i | −0.275299 | − | 0.367065i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 2.00000i | − | 0.0915737i | ||||||
\(478\) | −19.0526 | − | 11.0000i | −0.871444 | − | 0.503128i | ||||
\(479\) | 4.00000 | + | 6.92820i | 0.182765 | + | 0.316558i | 0.942821 | − | 0.333300i | \(-0.108162\pi\) |
−0.760056 | + | 0.649857i | \(0.774829\pi\) | |||||||
\(480\) | −2.23205 | + | 0.133975i | −0.101879 | + | 0.00611508i | ||||
\(481\) | −8.00000 | + | 13.8564i | −0.364769 | + | 0.631798i | ||||
\(482\) | − | 10.0000i | − | 0.455488i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 18.6603 | − | 12.3205i | 0.847318 | − | 0.559445i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 31.1769 | − | 18.0000i | 1.41276 | − | 0.815658i | 0.417113 | − | 0.908855i | \(-0.363042\pi\) |
0.995648 | + | 0.0931967i | \(0.0297085\pi\) | |||||||
\(488\) | 8.66025 | + | 5.00000i | 0.392031 | + | 0.226339i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −42.0000 | −1.89543 | −0.947717 | − | 0.319113i | \(-0.896615\pi\) | ||||
−0.947717 | + | 0.319113i | \(0.896615\pi\) | |||||||
\(492\) | 5.19615 | + | 3.00000i | 0.234261 | + | 0.135250i | ||||
\(493\) | 41.5692 | − | 24.0000i | 1.87218 | − | 1.08091i | ||||
\(494\) | −2.00000 | − | 3.46410i | −0.0899843 | − | 0.155857i | ||||
\(495\) | −2.46410 | − | 3.73205i | −0.110753 | − | 0.167743i | ||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 16.0000i | 0.716977i | ||||||||
\(499\) | −14.0000 | + | 24.2487i | −0.626726 | + | 1.08552i | 0.361478 | + | 0.932381i | \(0.382272\pi\) |
−0.988204 | + | 0.153141i | \(0.951061\pi\) | |||||||
\(500\) | 7.23205 | + | 8.52628i | 0.323427 | + | 0.381307i | ||||
\(501\) | −4.00000 | − | 6.92820i | −0.178707 | − | 0.309529i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 24.0000i | − | 1.07011i | −0.844818 | − | 0.535054i | \(-0.820291\pi\) | ||
0.844818 | − | 0.535054i | \(-0.179709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | − | 20.0000i | 0.444994 | − | 0.889988i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.79423 | − | 4.50000i | 0.346154 | − | 0.199852i | ||||
\(508\) | −10.3923 | + | 6.00000i | −0.461084 | + | 0.266207i | ||||
\(509\) | 1.00000 | − | 1.73205i | 0.0443242 | − | 0.0767718i | −0.843012 | − | 0.537895i | \(-0.819220\pi\) |
0.887336 | + | 0.461123i | \(0.152553\pi\) | |||||||
\(510\) | 16.0000 | + | 8.00000i | 0.708492 | + | 0.354246i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 1.73205 | + | 1.00000i | 0.0764719 | + | 0.0441511i | ||||
\(514\) | −10.0000 | − | 17.3205i | −0.441081 | − | 0.763975i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.00000 | − | 6.92820i | 0.176090 | − | 0.304997i | ||||
\(517\) | − | 8.00000i | − | 0.351840i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.0000 | −0.702322 | ||||||||
\(520\) | 2.46410 | + | 3.73205i | 0.108058 | + | 0.163661i | ||||
\(521\) | 3.00000 | + | 5.19615i | 0.131432 | + | 0.227648i | 0.924229 | − | 0.381839i | \(-0.124709\pi\) |
−0.792797 | + | 0.609486i | \(0.791376\pi\) | |||||||
\(522\) | −5.19615 | + | 3.00000i | −0.227429 | + | 0.131306i | ||||
\(523\) | −10.3923 | − | 6.00000i | −0.454424 | − | 0.262362i | 0.255273 | − | 0.966869i | \(-0.417835\pi\) |
−0.709697 | + | 0.704507i | \(0.751168\pi\) | |||||||
\(524\) | 20.0000 | 0.873704 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | −41.5692 | − | 24.0000i | −1.81078 | − | 1.04546i | ||||
\(528\) | −1.73205 | + | 1.00000i | −0.0753778 | + | 0.0435194i | ||||
\(529\) | −11.5000 | − | 19.9186i | −0.500000 | − | 0.866025i | ||||
\(530\) | 2.46410 | + | 3.73205i | 0.107034 | + | 0.162110i | ||||
\(531\) | −8.00000 | −0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 12.0000i | − | 0.519778i | ||||||
\(534\) | −5.00000 | + | 8.66025i | −0.216371 | + | 0.374766i | ||||
\(535\) | −1.60770 | − | 26.7846i | −0.0695067 | − | 1.15800i | ||||
\(536\) | 6.00000 | + | 10.3923i | 0.259161 | + | 0.448879i | ||||
\(537\) | −1.73205 | − | 1.00000i | −0.0747435 | − | 0.0431532i | ||||
\(538\) | − | 14.0000i | − | 0.603583i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.00000 | − | 1.00000i | −0.0860663 | − | 0.0430331i | ||||
\(541\) | 1.00000 | − | 1.73205i | 0.0429934 | − | 0.0744667i | −0.843728 | − | 0.536771i | \(-0.819644\pi\) |
0.886721 | + | 0.462304i | \(0.152977\pi\) | |||||||
\(542\) | 1.73205 | − | 1.00000i | 0.0743980 | − | 0.0429537i | ||||
\(543\) | 19.0526 | − | 11.0000i | 0.817624 | − | 0.472055i | ||||
\(544\) | 4.00000 | − | 6.92820i | 0.171499 | − | 0.297044i | ||||
\(545\) | −6.00000 | + | 12.0000i | −0.257012 | + | 0.514024i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000i | 0.855138i | 0.903983 | + | 0.427569i | \(0.140630\pi\) | ||||
−0.903983 | + | 0.427569i | \(0.859370\pi\) | |||||||
\(548\) | −12.1244 | − | 7.00000i | −0.517927 | − | 0.299025i | ||||
\(549\) | 5.00000 | + | 8.66025i | 0.213395 | + | 0.369611i | ||||
\(550\) | 9.19615 | + | 3.92820i | 0.392125 | + | 0.167499i | ||||
\(551\) | −6.00000 | + | 10.3923i | −0.255609 | + | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8.00000 | 0.339887 | ||||||||
\(555\) | 9.85641 | + | 14.9282i | 0.418381 | + | 0.633667i | ||||
\(556\) | 1.00000 | + | 1.73205i | 0.0424094 | + | 0.0734553i | ||||
\(557\) | 5.19615 | − | 3.00000i | 0.220168 | − | 0.127114i | −0.385860 | − | 0.922557i | \(-0.626095\pi\) |
0.606028 | + | 0.795443i | \(0.292762\pi\) | |||||||
\(558\) | 5.19615 | + | 3.00000i | 0.219971 | + | 0.127000i | ||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.0000 | 0.675521 | ||||||||
\(562\) | −19.0526 | − | 11.0000i | −0.803684 | − | 0.464007i | ||||
\(563\) | −10.3923 | + | 6.00000i | −0.437983 | + | 0.252870i | −0.702742 | − | 0.711445i | \(-0.748041\pi\) |
0.264758 | + | 0.964315i | \(0.414708\pi\) | |||||||
\(564\) | −2.00000 | − | 3.46410i | −0.0842152 | − | 0.145865i | ||||
\(565\) | −11.1962 | + | 7.39230i | −0.471026 | + | 0.310997i | ||||
\(566\) | 4.00000 | 0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.0000i | 0.587427i | ||||||||
\(569\) | 9.00000 | − | 15.5885i | 0.377300 | − | 0.653502i | −0.613369 | − | 0.789797i | \(-0.710186\pi\) |
0.990668 | + | 0.136295i | \(0.0435194\pi\) | |||||||
\(570\) | −4.46410 | + | 0.267949i | −0.186981 | + | 0.0112232i | ||||
\(571\) | 22.0000 | + | 38.1051i | 0.920671 | + | 1.59465i | 0.798379 | + | 0.602155i | \(0.205691\pi\) |
0.122292 | + | 0.992494i | \(0.460975\pi\) | |||||||
\(572\) | 3.46410 | + | 2.00000i | 0.144841 | + | 0.0836242i | ||||
\(573\) | 14.0000i | 0.584858i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 15.5885 | − | 9.00000i | 0.648956 | − | 0.374675i | −0.139100 | − | 0.990278i | \(-0.544421\pi\) |
0.788056 | + | 0.615603i | \(0.211088\pi\) | |||||||
\(578\) | −40.7032 | + | 23.5000i | −1.69303 | + | 0.977471i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.00000 | − | 12.0000i | 0.249136 | − | 0.498273i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 10.0000i | − | 0.414513i | ||||||
\(583\) | 3.46410 | + | 2.00000i | 0.143468 | + | 0.0828315i | ||||
\(584\) | −5.00000 | − | 8.66025i | −0.206901 | − | 0.358364i | ||||
\(585\) | 0.267949 | + | 4.46410i | 0.0110783 | + | 0.184568i | ||||
\(586\) | 8.00000 | − | 13.8564i | 0.330477 | − | 0.572403i | ||||
\(587\) | 4.00000i | 0.165098i | 0.996587 | + | 0.0825488i | \(0.0263060\pi\) | ||||
−0.996587 | + | 0.0825488i | \(0.973694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.0000 | 0.494451 | ||||||||
\(590\) | 14.9282 | − | 9.85641i | 0.614584 | − | 0.405782i | ||||
\(591\) | −3.00000 | − | 5.19615i | −0.123404 | − | 0.213741i | ||||
\(592\) | 6.92820 | − | 4.00000i | 0.284747 | − | 0.164399i | ||||
\(593\) | −27.7128 | − | 16.0000i | −1.13803 | − | 0.657041i | −0.192087 | − | 0.981378i | \(-0.561526\pi\) |
−0.945942 | + | 0.324337i | \(0.894859\pi\) | |||||||
\(594\) | −2.00000 | −0.0820610 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −18.0000 | −0.737309 | ||||||||
\(597\) | −22.5167 | − | 13.0000i | −0.921546 | − | 0.532055i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.00000 | + | 12.1244i | 0.286012 | + | 0.495388i | 0.972854 | − | 0.231419i | \(-0.0743369\pi\) |
−0.686842 | + | 0.726807i | \(0.741004\pi\) | |||||||
\(600\) | 4.96410 | − | 0.598076i | 0.202659 | − | 0.0244164i | ||||
\(601\) | −42.0000 | −1.71322 | −0.856608 | − | 0.515968i | \(-0.827432\pi\) | ||||
−0.856608 | + | 0.515968i | \(0.827432\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.0000i | 0.488678i | ||||||||
\(604\) | 4.00000 | − | 6.92820i | 0.162758 | − | 0.281905i | ||||
\(605\) | −15.6244 | + | 0.937822i | −0.635220 | + | 0.0381279i | ||||
\(606\) | −5.00000 | − | 8.66025i | −0.203111 | − | 0.351799i | ||||
\(607\) | 13.8564 | + | 8.00000i | 0.562414 | + | 0.324710i | 0.754114 | − | 0.656744i | \(-0.228067\pi\) |
−0.191700 | + | 0.981454i | \(0.561400\pi\) | |||||||
\(608\) | 2.00000i | 0.0811107i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.0000 | − | 10.0000i | −0.809776 | − | 0.404888i | ||||
\(611\) | −4.00000 | + | 6.92820i | −0.161823 | + | 0.280285i | ||||
\(612\) | 6.92820 | − | 4.00000i | 0.280056 | − | 0.161690i | ||||
\(613\) | −27.7128 | + | 16.0000i | −1.11931 | + | 0.646234i | −0.941225 | − | 0.337781i | \(-0.890324\pi\) |
−0.178085 | + | 0.984015i | \(0.556990\pi\) | |||||||
\(614\) | 14.0000 | − | 24.2487i | 0.564994 | − | 0.978598i | ||||
\(615\) | −12.0000 | − | 6.00000i | −0.483887 | − | 0.241943i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 18.0000i | − | 0.724653i | −0.932051 | − | 0.362326i | \(-0.881983\pi\) | ||
0.932051 | − | 0.362326i | \(-0.118017\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.00000 | − | 15.5885i | −0.361741 | − | 0.626553i | 0.626507 | − | 0.779416i | \(-0.284484\pi\) |
−0.988247 | + | 0.152863i | \(0.951151\pi\) | |||||||
\(620\) | −13.3923 | + | 0.803848i | −0.537848 | + | 0.0322833i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 8.00000i | − | 0.320771i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | −17.2846 | − | 18.0622i | −0.691384 | − | 0.722487i | ||||
\(626\) | −5.00000 | − | 8.66025i | −0.199840 | − | 0.346133i | ||||
\(627\) | −3.46410 | + | 2.00000i | −0.138343 | + | 0.0798723i | ||||
\(628\) | −8.66025 | − | 5.00000i | −0.345582 | − | 0.199522i | ||||
\(629\) | −64.0000 | −2.55185 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.0000 | 0.477712 | 0.238856 | − | 0.971055i | \(-0.423228\pi\) | ||||
0.238856 | + | 0.971055i | \(0.423228\pi\) | |||||||
\(632\) | −3.46410 | − | 2.00000i | −0.137795 | − | 0.0795557i | ||||
\(633\) | −6.92820 | + | 4.00000i | −0.275371 | + | 0.158986i | ||||
\(634\) | −1.00000 | − | 1.73205i | −0.0397151 | − | 0.0687885i | ||||
\(635\) | 22.3923 | − | 14.7846i | 0.888612 | − | 0.586709i | ||||
\(636\) | 2.00000 | 0.0793052 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 12.0000i | − | 0.475085i | ||||||
\(639\) | −7.00000 | + | 12.1244i | −0.276916 | + | 0.479632i | ||||
\(640\) | −0.133975 | − | 2.23205i | −0.00529581 | − | 0.0882296i | ||||
\(641\) | −15.0000 | − | 25.9808i | −0.592464 | − | 1.02618i | −0.993899 | − | 0.110291i | \(-0.964822\pi\) |
0.401435 | − | 0.915888i | \(-0.368512\pi\) | |||||||
\(642\) | −10.3923 | − | 6.00000i | −0.410152 | − | 0.236801i | ||||
\(643\) | 20.0000i | 0.788723i | 0.918955 | + | 0.394362i | \(0.129034\pi\) | ||||
−0.918955 | + | 0.394362i | \(0.870966\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.00000 | + | 16.0000i | −0.315000 | + | 0.629999i | ||||
\(646\) | 8.00000 | − | 13.8564i | 0.314756 | − | 0.545173i | ||||
\(647\) | 13.8564 | − | 8.00000i | 0.544752 | − | 0.314512i | −0.202251 | − | 0.979334i | \(-0.564826\pi\) |
0.747002 | + | 0.664821i | \(0.231492\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 8.00000 | − | 13.8564i | 0.314027 | − | 0.543912i | ||||
\(650\) | −6.00000 | − | 8.00000i | −0.235339 | − | 0.313786i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.1244 | − | 7.00000i | −0.474463 | − | 0.273931i | 0.243643 | − | 0.969865i | \(-0.421657\pi\) |
−0.718106 | + | 0.695934i | \(0.754991\pi\) | |||||||
\(654\) | 3.00000 | + | 5.19615i | 0.117309 | + | 0.203186i | ||||
\(655\) | −44.6410 | + | 2.67949i | −1.74427 | + | 0.104696i | ||||
\(656\) | −3.00000 | + | 5.19615i | −0.117130 | + | 0.202876i | ||||
\(657\) | − | 10.0000i | − | 0.390137i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.00000 | 0.233727 | 0.116863 | − | 0.993148i | \(-0.462716\pi\) | ||||
0.116863 | + | 0.993148i | \(0.462716\pi\) | |||||||
\(660\) | 3.73205 | − | 2.46410i | 0.145270 | − | 0.0959150i | ||||
\(661\) | −5.00000 | − | 8.66025i | −0.194477 | − | 0.336845i | 0.752252 | − | 0.658876i | \(-0.228968\pi\) |
−0.946729 | + | 0.322031i | \(0.895634\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.8564 | − | 8.00000i | −0.538138 | − | 0.310694i | ||||
\(664\) | −16.0000 | −0.620920 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.00000 | 0.309994 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 6.92820 | − | 4.00000i | 0.268060 | − | 0.154765i | ||||
\(669\) | 8.00000 | + | 13.8564i | 0.309298 | + | 0.535720i | ||||
\(670\) | −14.7846 | − | 22.3923i | −0.571179 | − | 0.865090i | ||||
\(671\) | −20.0000 | −0.772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 12.0000i | − | 0.462566i | −0.972887 | − | 0.231283i | \(-0.925708\pi\) | ||
0.972887 | − | 0.231283i | \(-0.0742923\pi\) | |||||||
\(674\) | 16.0000 | − | 27.7128i | 0.616297 | − | 1.06746i | ||||
\(675\) | 4.59808 | + | 1.96410i | 0.176980 | + | 0.0755983i | ||||
\(676\) | 4.50000 | + | 7.79423i | 0.173077 | + | 0.299778i | ||||
\(677\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(678\) | 6.00000i | 0.230429i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −8.00000 | + | 16.0000i | −0.306786 | + | 0.613572i | ||||
\(681\) | −4.00000 | + | 6.92820i | −0.153280 | + | 0.265489i | ||||
\(682\) | −10.3923 | + | 6.00000i | −0.397942 | + | 0.229752i | ||||
\(683\) | −24.2487 | + | 14.0000i | −0.927851 | + | 0.535695i | −0.886131 | − | 0.463434i | \(-0.846617\pi\) |
−0.0417198 | + | 0.999129i | \(0.513284\pi\) | |||||||
\(684\) | −1.00000 | + | 1.73205i | −0.0382360 | + | 0.0662266i | ||||
\(685\) | 28.0000 | + | 14.0000i | 1.06983 | + | 0.534913i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 26.0000i | − | 0.991962i | ||||||
\(688\) | 6.92820 | + | 4.00000i | 0.264135 | + | 0.152499i | ||||
\(689\) | −2.00000 | − | 3.46410i | −0.0761939 | − | 0.131972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.00000 | − | 12.1244i | 0.266293 | − | 0.461232i | −0.701609 | − | 0.712562i | \(-0.747535\pi\) |
0.967901 | + | 0.251330i | \(0.0808679\pi\) | |||||||
\(692\) | − | 16.0000i | − | 0.608229i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.00000 | −0.151838 | ||||||||
\(695\) | −2.46410 | − | 3.73205i | −0.0934687 | − | 0.141565i | ||||
\(696\) | −3.00000 | − | 5.19615i | −0.113715 | − | 0.196960i | ||||
\(697\) | 41.5692 | − | 24.0000i | 1.57455 | − | 0.909065i | ||||
\(698\) | 15.5885 | + | 9.00000i | 0.590032 | + | 0.340655i | ||||
\(699\) | 6.00000 | 0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | 1.73205 | + | 1.00000i | 0.0653720 | + | 0.0377426i | ||||
\(703\) | 13.8564 | − | 8.00000i | 0.522604 | − | 0.301726i | ||||
\(704\) | −1.00000 | − | 1.73205i | −0.0376889 | − | 0.0652791i | ||||
\(705\) | 4.92820 | + | 7.46410i | 0.185607 | + | 0.281114i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 8.00000i | − | 0.300658i | ||||||
\(709\) | −19.0000 | + | 32.9090i | −0.713560 | + | 1.23592i | 0.249952 | + | 0.968258i | \(0.419585\pi\) |
−0.963512 | + | 0.267664i | \(0.913748\pi\) | |||||||
\(710\) | −1.87564 | − | 31.2487i | −0.0703917 | − | 1.17274i | ||||
\(711\) | −2.00000 | − | 3.46410i | −0.0750059 | − | 0.129914i | ||||
\(712\) | −8.66025 | − | 5.00000i | −0.324557 | − | 0.187383i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.00000 | − | 4.00000i | −0.299183 | − | 0.149592i | ||||
\(716\) | 1.00000 | − | 1.73205i | 0.0373718 | − | 0.0647298i | ||||
\(717\) | 19.0526 | − | 11.0000i | 0.711531 | − | 0.410803i | ||||
\(718\) | −12.1244 | + | 7.00000i | −0.452477 | + | 0.261238i | ||||
\(719\) | −10.0000 | + | 17.3205i | −0.372937 | + | 0.645946i | −0.990016 | − | 0.140955i | \(-0.954983\pi\) |
0.617079 | + | 0.786901i | \(0.288316\pi\) | |||||||
\(720\) | 1.00000 | − | 2.00000i | 0.0372678 | − | 0.0745356i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 15.0000i | − | 0.558242i | ||||||
\(723\) | 8.66025 | + | 5.00000i | 0.322078 | + | 0.185952i | ||||
\(724\) | 11.0000 | + | 19.0526i | 0.408812 | + | 0.708083i | ||||
\(725\) | −11.7846 | + | 27.5885i | −0.437669 | + | 1.02461i | ||||
\(726\) | −3.50000 | + | 6.06218i | −0.129897 | + | 0.224989i | ||||
\(727\) | 16.0000i | 0.593407i | 0.954970 | + | 0.296704i | \(0.0958873\pi\) | ||||
−0.954970 | + | 0.296704i | \(0.904113\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 12.3205 | + | 18.6603i | 0.456002 | + | 0.690647i | ||||
\(731\) | −32.0000 | − | 55.4256i | −1.18356 | − | 2.04999i | ||||
\(732\) | −8.66025 | + | 5.00000i | −0.320092 | + | 0.184805i | ||||
\(733\) | −25.9808 | − | 15.0000i | −0.959621 | − | 0.554038i | −0.0635649 | − | 0.997978i | \(-0.520247\pi\) |
−0.896056 | + | 0.443940i | \(0.853580\pi\) | |||||||
\(734\) | 32.0000 | 1.18114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.7846 | − | 12.0000i | −0.765611 | − | 0.442026i | ||||
\(738\) | −5.19615 | + | 3.00000i | −0.191273 | + | 0.110432i | ||||
\(739\) | 10.0000 | + | 17.3205i | 0.367856 | + | 0.637145i | 0.989230 | − | 0.146369i | \(-0.0467586\pi\) |
−0.621374 | + | 0.783514i | \(0.713425\pi\) | |||||||
\(740\) | −14.9282 | + | 9.85641i | −0.548772 | + | 0.362329i | ||||
\(741\) | 4.00000 | 0.146944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 16.0000i | − | 0.586983i | −0.955962 | − | 0.293492i | \(-0.905183\pi\) | ||
0.955962 | − | 0.293492i | \(-0.0948173\pi\) | |||||||
\(744\) | −3.00000 | + | 5.19615i | −0.109985 | + | 0.190500i | ||||
\(745\) | 40.1769 | − | 2.41154i | 1.47197 | − | 0.0883521i | ||||
\(746\) | −18.0000 | − | 31.1769i | −0.659027 | − | 1.14147i | ||||
\(747\) | −13.8564 | − | 8.00000i | −0.506979 | − | 0.292705i | ||||
\(748\) | 16.0000i | 0.585018i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −11.0000 | + | 2.00000i | −0.401663 | + | 0.0730297i | ||||
\(751\) | −2.00000 | + | 3.46410i | −0.0729810 | + | 0.126407i | −0.900207 | − | 0.435463i | \(-0.856585\pi\) |
0.827225 | + | 0.561870i | \(0.189918\pi\) | |||||||
\(752\) | 3.46410 | − | 2.00000i | 0.126323 | − | 0.0729325i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.00000 | + | 10.3923i | −0.218507 | + | 0.378465i | ||||
\(755\) | −8.00000 | + | 16.0000i | −0.291150 | + | 0.582300i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 4.00000i | − | 0.145382i | −0.997354 | − | 0.0726912i | \(-0.976841\pi\) | ||
0.997354 | − | 0.0726912i | \(-0.0231588\pi\) | |||||||
\(758\) | −24.2487 | − | 14.0000i | −0.880753 | − | 0.508503i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.267949 | − | 4.46410i | −0.00971954 | − | 0.161930i | ||||
\(761\) | −3.00000 | + | 5.19615i | −0.108750 | + | 0.188360i | −0.915264 | − | 0.402854i | \(-0.868018\pi\) |
0.806514 | + | 0.591215i | \(0.201351\pi\) | |||||||
\(762\) | − | 12.0000i | − | 0.434714i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −14.0000 | −0.506502 | ||||||||
\(765\) | −14.9282 | + | 9.85641i | −0.539730 | + | 0.356359i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.8564 | + | 8.00000i | −0.500326 | + | 0.288863i | ||||
\(768\) | −0.866025 | − | 0.500000i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | 42.0000 | 1.51456 | 0.757279 | − | 0.653091i | \(-0.226528\pi\) | ||||
0.757279 | + | 0.653091i | \(0.226528\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.0000 | 0.720282 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.7128 | − | 16.0000i | 0.996761 | − | 0.575480i | 0.0894724 | − | 0.995989i | \(-0.471482\pi\) |
0.907288 | + | 0.420509i | \(0.138149\pi\) | |||||||
\(774\) | 4.00000 | + | 6.92820i | 0.143777 | + | 0.249029i | ||||
\(775\) | 29.7846 | − | 3.58846i | 1.06989 | − | 0.128901i | ||||
\(776\) | 10.0000 | 0.358979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 6.00000i | − | 0.215110i | ||||||
\(779\) | −6.00000 | + | 10.3923i | −0.214972 | + | 0.372343i | ||||
\(780\) | −4.46410 | + | 0.267949i | −0.159840 | + | 0.00959412i | ||||
\(781\) | −14.0000 | − | 24.2487i | −0.500959 | − | 0.867687i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 6.00000i | − | 0.214423i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.0000 | + | 10.0000i | 0.713831 | + | 0.356915i | ||||
\(786\) | −10.0000 | + | 17.3205i | −0.356688 | + | 0.617802i | ||||
\(787\) | −38.1051 | + | 22.0000i | −1.35830 | + | 0.784215i | −0.989395 | − | 0.145251i | \(-0.953601\pi\) |
−0.368906 | + | 0.929467i | \(0.620268\pi\) | |||||||
\(788\) | 5.19615 | − | 3.00000i | 0.185105 | − | 0.106871i | ||||
\(789\) | 12.0000 | − | 20.7846i | 0.427211 | − | 0.739952i | ||||
\(790\) | 8.00000 | + | 4.00000i | 0.284627 | + | 0.142314i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 2.00000i | − | 0.0710669i | ||||||
\(793\) | 17.3205 | + | 10.0000i | 0.615069 | + | 0.355110i | ||||
\(794\) | 1.00000 | + | 1.73205i | 0.0354887 | + | 0.0614682i | ||||
\(795\) | −4.46410 | + | 0.267949i | −0.158325 | + | 0.00950318i | ||||
\(796\) | 13.0000 | − | 22.5167i | 0.460773 | − | 0.798082i | ||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.0000 | −1.13208 | ||||||||
\(800\) | 0.598076 | + | 4.96410i | 0.0211452 | + | 0.175507i | ||||
\(801\) | −5.00000 | − | 8.66025i | −0.176666 | − | 0.305995i | ||||
\(802\) | 15.5885 | − | 9.00000i | 0.550448 | − | 0.317801i | ||||
\(803\) | 17.3205 | + | 10.0000i | 0.611227 | + | 0.352892i | ||||
\(804\) | −12.0000 | −0.423207 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.0000 | 0.422682 | ||||||||
\(807\) | 12.1244 | + | 7.00000i | 0.426798 | + | 0.246412i | ||||
\(808\) | 8.66025 | − | 5.00000i | 0.304667 | − | 0.175899i | ||||
\(809\) | 3.00000 | + | 5.19615i | 0.105474 | + | 0.182687i | 0.913932 | − | 0.405868i | \(-0.133031\pi\) |
−0.808458 | + | 0.588555i | \(0.799697\pi\) | |||||||
\(810\) | 1.86603 | − | 1.23205i | 0.0655654 | − | 0.0432899i | ||||
\(811\) | 14.0000 | 0.491606 | 0.245803 | − | 0.969320i | \(-0.420948\pi\) | ||||
0.245803 | + | 0.969320i | \(0.420948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.00000i | 0.0701431i | ||||||||
\(814\) | −8.00000 | + | 13.8564i | −0.280400 | + | 0.485667i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.00000 | + | 6.92820i | 0.140028 | + | 0.242536i | ||||
\(817\) | 13.8564 | + | 8.00000i | 0.484774 | + | 0.279885i | ||||
\(818\) | − | 10.0000i | − | 0.349642i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | − | 12.0000i | 0.209529 | − | 0.419058i | ||||
\(821\) | 3.00000 | − | 5.19615i | 0.104701 | − | 0.181347i | −0.808915 | − | 0.587925i | \(-0.799945\pi\) |
0.913616 | + | 0.406578i | \(0.133278\pi\) | |||||||
\(822\) | 12.1244 | − | 7.00000i | 0.422885 | − | 0.244153i | ||||
\(823\) | 3.46410 | − | 2.00000i | 0.120751 | − | 0.0697156i | −0.438408 | − | 0.898776i | \(-0.644457\pi\) |
0.559159 | + | 0.829060i | \(0.311124\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.00000 | + | 6.00000i | −0.278524 | + | 0.208893i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 36.0000i | − | 1.25184i | −0.779886 | − | 0.625921i | \(-0.784723\pi\) | ||
0.779886 | − | 0.625921i | \(-0.215277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.0000 | − | 29.4449i | −0.590434 | − | 1.02266i | −0.994174 | − | 0.107788i | \(-0.965623\pi\) |
0.403739 | − | 0.914874i | \(-0.367710\pi\) | |||||||
\(830\) | 35.7128 | − | 2.14359i | 1.23961 | − | 0.0744052i | ||||
\(831\) | −4.00000 | + | 6.92820i | −0.138758 | + | 0.240337i | ||||
\(832\) | 2.00000i | 0.0693375i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.00000 | −0.0692543 | ||||||||
\(835\) | −14.9282 | + | 9.85641i | −0.516612 | + | 0.341095i | ||||
\(836\) | −2.00000 | − | 3.46410i | −0.0691714 | − | 0.119808i | ||||
\(837\) | −5.19615 | + | 3.00000i | −0.179605 | + | 0.103695i | ||||
\(838\) | 10.3923 | + | 6.00000i | 0.358996 | + | 0.207267i | ||||
\(839\) | −44.0000 | −1.51905 | −0.759524 | − | 0.650479i | \(-0.774568\pi\) | ||||
−0.759524 | + | 0.650479i | \(0.774568\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −8.66025 | − | 5.00000i | −0.298452 | − | 0.172311i | ||||
\(843\) | 19.0526 | − | 11.0000i | 0.656205 | − | 0.378860i | ||||
\(844\) | −4.00000 | − | 6.92820i | −0.137686 | − | 0.238479i | ||||
\(845\) | −11.0885 | − | 16.7942i | −0.381455 | − | 0.577739i | ||||
\(846\) | 4.00000 | 0.137523 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.00000i | 0.0686803i | ||||||||
\(849\) | −2.00000 | + | 3.46410i | −0.0686398 | + | 0.118888i | ||||
\(850\) | 15.7128 | − | 36.7846i | 0.538945 | − | 1.26170i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −12.1244 | − | 7.00000i | −0.415374 | − | 0.239816i | ||||
\(853\) | − | 10.0000i | − | 0.342393i | −0.985237 | − | 0.171197i | \(-0.945237\pi\) | ||
0.985237 | − | 0.171197i | \(-0.0547634\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.00000 | − | 4.00000i | 0.0683986 | − | 0.136797i | ||||
\(856\) | 6.00000 | − | 10.3923i | 0.205076 | − | 0.355202i | ||||
\(857\) | 17.3205 | − | 10.0000i | 0.591657 | − | 0.341593i | −0.174095 | − | 0.984729i | \(-0.555700\pi\) |
0.765753 | + | 0.643135i | \(0.222367\pi\) | |||||||
\(858\) | −3.46410 | + | 2.00000i | −0.118262 | + | 0.0682789i | ||||
\(859\) | −3.00000 | + | 5.19615i | −0.102359 | + | 0.177290i | −0.912656 | − | 0.408729i | \(-0.865972\pi\) |
0.810297 | + | 0.586019i | \(0.199306\pi\) | |||||||
\(860\) | −16.0000 | − | 8.00000i | −0.545595 | − | 0.272798i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 6.00000i | − | 0.204361i | ||||||
\(863\) | 41.5692 | + | 24.0000i | 1.41503 | + | 0.816970i | 0.995857 | − | 0.0909355i | \(-0.0289857\pi\) |
0.419176 | + | 0.907905i | \(0.362319\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 2.14359 | + | 35.7128i | 0.0728844 | + | 1.21427i | ||||
\(866\) | −13.0000 | + | 22.5167i | −0.441758 | + | 0.765147i | ||||
\(867\) | − | 47.0000i | − | 1.59620i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.00000 | 0.271381 | ||||||||
\(870\) | 7.39230 | + | 11.1962i | 0.250623 | + | 0.379585i | ||||
\(871\) | 12.0000 | + | 20.7846i | 0.406604 | + | 0.704260i | ||||
\(872\) | −5.19615 | + | 3.00000i | −0.175964 | + | 0.101593i | ||||
\(873\) | 8.66025 | + | 5.00000i | 0.293105 | + | 0.169224i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.0000 | 0.337869 | ||||||||
\(877\) | 41.5692 | + | 24.0000i | 1.40369 | + | 0.810422i | 0.994769 | − | 0.102146i | \(-0.0325710\pi\) |
0.408923 | + | 0.912569i | \(0.365904\pi\) | |||||||
\(878\) | −5.19615 | + | 3.00000i | −0.175362 | + | 0.101245i | ||||
\(879\) | 8.00000 | + | 13.8564i | 0.269833 | + | 0.467365i | ||||
\(880\) | 2.46410 | + | 3.73205i | 0.0830648 | + | 0.125807i | ||||
\(881\) | −6.00000 | −0.202145 | −0.101073 | − | 0.994879i | \(-0.532227\pi\) | ||||
−0.101073 | + | 0.994879i | \(0.532227\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 52.0000i | − | 1.74994i | −0.484178 | − | 0.874970i | \(-0.660881\pi\) | ||
0.484178 | − | 0.874970i | \(-0.339119\pi\) | |||||||
\(884\) | 8.00000 | − | 13.8564i | 0.269069 | − | 0.466041i | ||||
\(885\) | 1.07180 | + | 17.8564i | 0.0360281 | + | 0.600237i | ||||
\(886\) | −18.0000 | − | 31.1769i | −0.604722 | − | 1.04741i | ||||
\(887\) | −31.1769 | − | 18.0000i | −1.04682 | − | 0.604381i | −0.125061 | − | 0.992149i | \(-0.539913\pi\) |
−0.921757 | + | 0.387768i | \(0.873246\pi\) | |||||||
\(888\) | 8.00000i | 0.268462i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 20.0000 | + | 10.0000i | 0.670402 | + | 0.335201i | ||||
\(891\) | 1.00000 | − | 1.73205i | 0.0335013 | − | 0.0580259i | ||||
\(892\) | −13.8564 | + | 8.00000i | −0.463947 | + | 0.267860i | ||||
\(893\) | 6.92820 | − | 4.00000i | 0.231843 | − | 0.133855i | ||||
\(894\) | 9.00000 | − | 15.5885i | 0.301005 | − | 0.521356i | ||||
\(895\) | −2.00000 | + | 4.00000i | −0.0668526 | + | 0.133705i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −25.9808 | − | 15.0000i | −0.866989 | − | 0.500556i | ||||
\(899\) | −18.0000 | − | 31.1769i | −0.600334 | − | 1.03981i | ||||
\(900\) | −1.96410 | + | 4.59808i | −0.0654701 | + | 0.153269i | ||||
\(901\) | 8.00000 | − | 13.8564i | 0.266519 | − | 0.461624i | ||||
\(902\) | − | 12.0000i | − | 0.399556i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | −27.1051 | − | 41.0526i | −0.901005 | − | 1.36463i | ||||
\(906\) | 4.00000 | + | 6.92820i | 0.132891 | + | 0.230174i | ||||
\(907\) | −38.1051 | + | 22.0000i | −1.26526 | + | 0.730498i | −0.974087 | − | 0.226173i | \(-0.927379\pi\) |
−0.291172 | + | 0.956671i | \(0.594045\pi\) | |||||||
\(908\) | −6.92820 | − | 4.00000i | −0.229920 | − | 0.132745i | ||||
\(909\) | 10.0000 | 0.331679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.00000 | 0.198789 | 0.0993944 | − | 0.995048i | \(-0.468309\pi\) | ||||
0.0993944 | + | 0.995048i | \(0.468309\pi\) | |||||||
\(912\) | −1.73205 | − | 1.00000i | −0.0573539 | − | 0.0331133i | ||||
\(913\) | 27.7128 | − | 16.0000i | 0.917160 | − | 0.529523i | ||||
\(914\) | −14.0000 | − | 24.2487i | −0.463079 | − | 0.802076i | ||||
\(915\) | 18.6603 | − | 12.3205i | 0.616889 | − | 0.407303i | ||||
\(916\) | 26.0000 | 0.859064 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 8.00000i | 0.264039i | ||||||||
\(919\) | −2.00000 | + | 3.46410i | −0.0659739 | + | 0.114270i | −0.897126 | − | 0.441776i | \(-0.854349\pi\) |
0.831152 | + | 0.556046i | \(0.187682\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0000 | + | 24.2487i | 0.461316 | + | 0.799022i | ||||
\(922\) | −15.5885 | − | 9.00000i | −0.513378 | − | 0.296399i | ||||
\(923\) | 28.0000i | 0.921631i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.0000 | − | 24.0000i | 1.05215 | − | 0.789115i | ||||
\(926\) | 6.00000 | − | 10.3923i | 0.197172 | − | 0.341512i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.19615 | − | 3.00000i | 0.170572 | − | 0.0984798i | ||||
\(929\) | −9.00000 | + | 15.5885i | −0.295280 | + | 0.511441i | −0.975050 | − | 0.221985i | \(-0.928746\pi\) |
0.679770 | + | 0.733426i | \(0.262080\pi\) | |||||||
\(930\) | 6.00000 | − | 12.0000i | 0.196748 | − | 0.393496i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.00000i | 0.196537i | ||||||||
\(933\) | 6.92820 | + | 4.00000i | 0.226819 | + | 0.130954i | ||||
\(934\) | 8.00000 | + | 13.8564i | 0.261768 | + | 0.453395i | ||||
\(935\) | −2.14359 | − | 35.7128i | −0.0701030 | − | 1.16793i | ||||
\(936\) | −1.00000 | + | 1.73205i | −0.0326860 | + | 0.0566139i | ||||
\(937\) | − | 26.0000i | − | 0.849383i | −0.905338 | − | 0.424691i | \(-0.860383\pi\) | ||
0.905338 | − | 0.424691i | \(-0.139617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.0000 | 0.326338 | ||||||||
\(940\) | −7.46410 | + | 4.92820i | −0.243452 | + | 0.160740i | ||||
\(941\) | 3.00000 | + | 5.19615i | 0.0977972 | + | 0.169390i | 0.910773 | − | 0.412908i | \(-0.135487\pi\) |
−0.812975 | + | 0.582298i | \(0.802154\pi\) | |||||||
\(942\) | 8.66025 | − | 5.00000i | 0.282166 | − | 0.162909i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 8.00000 | 0.260378 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.0000 | −0.520205 | ||||||||
\(947\) | −10.3923 | − | 6.00000i | −0.337705 | − | 0.194974i | 0.321552 | − | 0.946892i | \(-0.395796\pi\) |
−0.659256 | + | 0.751918i | \(0.729129\pi\) | |||||||
\(948\) | 3.46410 | − | 2.00000i | 0.112509 | − | 0.0649570i | ||||
\(949\) | −10.0000 | − | 17.3205i | −0.324614 | − | 0.562247i | ||||
\(950\) | 1.19615 | + | 9.92820i | 0.0388083 | + | 0.322113i | ||||
\(951\) | 2.00000 | 0.0648544 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.0000i | 0.583077i | 0.956559 | + | 0.291539i | \(0.0941672\pi\) | ||||
−0.956559 | + | 0.291539i | \(0.905833\pi\) | |||||||
\(954\) | −1.00000 | + | 1.73205i | −0.0323762 | + | 0.0560772i | ||||
\(955\) | 31.2487 | − | 1.87564i | 1.01118 | − | 0.0606944i | ||||
\(956\) | 11.0000 | + | 19.0526i | 0.355765 | + | 0.616204i | ||||
\(957\) | 10.3923 | + | 6.00000i | 0.335936 | + | 0.193952i | ||||
\(958\) | − | 8.00000i | − | 0.258468i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.00000 | + | 1.00000i | 0.0645497 | + | 0.0322749i | ||||
\(961\) | −2.50000 | + | 4.33013i | −0.0806452 | + | 0.139682i | ||||
\(962\) | 13.8564 | − | 8.00000i | 0.446748 | − | 0.257930i | ||||
\(963\) | 10.3923 | − | 6.00000i | 0.334887 | − | 0.193347i | ||||
\(964\) | −5.00000 | + | 8.66025i | −0.161039 | + | 0.278928i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 24.0000i | − | 0.771788i | −0.922543 | − | 0.385894i | \(-0.873893\pi\) | ||
0.922543 | − | 0.385894i | \(-0.126107\pi\) | |||||||
\(968\) | −6.06218 | − | 3.50000i | −0.194846 | − | 0.112494i | ||||
\(969\) | 8.00000 | + | 13.8564i | 0.256997 | + | 0.445132i | ||||
\(970\) | −22.3205 | + | 1.33975i | −0.716668 | + | 0.0430167i | ||||
\(971\) | −12.0000 | + | 20.7846i | −0.385098 | + | 0.667010i | −0.991783 | − | 0.127933i | \(-0.959166\pi\) |
0.606685 | + | 0.794943i | \(0.292499\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −36.0000 | −1.15351 | ||||||||
\(975\) | 9.92820 | − | 1.19615i | 0.317957 | − | 0.0383075i | ||||
\(976\) | −5.00000 | − | 8.66025i | −0.160046 | − | 0.277208i | ||||
\(977\) | −15.5885 | + | 9.00000i | −0.498719 | + | 0.287936i | −0.728184 | − | 0.685381i | \(-0.759636\pi\) |
0.229465 | + | 0.973317i | \(0.426302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0000 | 0.639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.00000 | −0.191565 | ||||||||
\(982\) | 36.3731 | + | 21.0000i | 1.16071 | + | 0.670137i | ||||
\(983\) | −10.3923 | + | 6.00000i | −0.331463 | + | 0.191370i | −0.656490 | − | 0.754334i | \(-0.727960\pi\) |
0.325027 | + | 0.945705i | \(0.394626\pi\) | |||||||
\(984\) | −3.00000 | − | 5.19615i | −0.0956365 | − | 0.165647i | ||||
\(985\) | −11.1962 | + | 7.39230i | −0.356739 | + | 0.235538i | ||||
\(986\) | −48.0000 | −1.52863 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.00000i | 0.127257i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0.267949 | + | 4.46410i | 0.00851598 | + | 0.141878i | ||||
\(991\) | 30.0000 | + | 51.9615i | 0.952981 | + | 1.65061i | 0.738921 | + | 0.673792i | \(0.235336\pi\) |
0.214060 | + | 0.976820i | \(0.431331\pi\) | |||||||
\(992\) | −5.19615 | − | 3.00000i | −0.164978 | − | 0.0952501i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26.0000 | + | 52.0000i | −0.824255 | + | 1.64851i | ||||
\(996\) | 8.00000 | − | 13.8564i | 0.253490 | − | 0.439057i | ||||
\(997\) | −32.9090 | + | 19.0000i | −1.04224 | + | 0.601736i | −0.920466 | − | 0.390822i | \(-0.872191\pi\) |
−0.121771 | + | 0.992558i | \(0.538857\pi\) | |||||||
\(998\) | 24.2487 | − | 14.0000i | 0.767580 | − | 0.443162i | ||||
\(999\) | −4.00000 | + | 6.92820i | −0.126554 | + | 0.219199i |
(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 | 1470.2.n.g.79.1 | 4 | ||
5.4 | even | 2 | inner | 1470.2.n.g.79.2 | 4 | ||
7.2 | even | 3 | 210.2.g.a.169.2 | yes | 2 | ||
7.3 | odd | 6 | 1470.2.n.c.949.2 | 4 | |||
7.4 | even | 3 | inner | 1470.2.n.g.949.2 | 4 | ||
7.5 | odd | 6 | 1470.2.g.e.589.2 | 2 | |||
7.6 | odd | 2 | 1470.2.n.c.79.1 | 4 | |||
21.2 | odd | 6 | 630.2.g.d.379.1 | 2 | |||
28.23 | odd | 6 | 1680.2.t.d.1009.1 | 2 | |||
35.2 | odd | 12 | 1050.2.a.g.1.1 | 1 | |||
35.4 | even | 6 | inner | 1470.2.n.g.949.1 | 4 | ||
35.9 | even | 6 | 210.2.g.a.169.1 | ✓ | 2 | ||
35.12 | even | 12 | 7350.2.a.g.1.1 | 1 | |||
35.19 | odd | 6 | 1470.2.g.e.589.1 | 2 | |||
35.23 | odd | 12 | 1050.2.a.m.1.1 | 1 | |||
35.24 | odd | 6 | 1470.2.n.c.949.1 | 4 | |||
35.33 | even | 12 | 7350.2.a.co.1.1 | 1 | |||
35.34 | odd | 2 | 1470.2.n.c.79.2 | 4 | |||
84.23 | even | 6 | 5040.2.t.k.1009.1 | 2 | |||
105.2 | even | 12 | 3150.2.a.be.1.1 | 1 | |||
105.23 | even | 12 | 3150.2.a.q.1.1 | 1 | |||
105.44 | odd | 6 | 630.2.g.d.379.2 | 2 | |||
140.23 | even | 12 | 8400.2.a.ca.1.1 | 1 | |||
140.79 | odd | 6 | 1680.2.t.d.1009.2 | 2 | |||
140.107 | even | 12 | 8400.2.a.bd.1.1 | 1 | |||
420.359 | even | 6 | 5040.2.t.k.1009.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.g.a.169.1 | ✓ | 2 | 35.9 | even | 6 | ||
210.2.g.a.169.2 | yes | 2 | 7.2 | even | 3 | ||
630.2.g.d.379.1 | 2 | 21.2 | odd | 6 | |||
630.2.g.d.379.2 | 2 | 105.44 | odd | 6 | |||
1050.2.a.g.1.1 | 1 | 35.2 | odd | 12 | |||
1050.2.a.m.1.1 | 1 | 35.23 | odd | 12 | |||
1470.2.g.e.589.1 | 2 | 35.19 | odd | 6 | |||
1470.2.g.e.589.2 | 2 | 7.5 | odd | 6 | |||
1470.2.n.c.79.1 | 4 | 7.6 | odd | 2 | |||
1470.2.n.c.79.2 | 4 | 35.34 | odd | 2 | |||
1470.2.n.c.949.1 | 4 | 35.24 | odd | 6 | |||
1470.2.n.c.949.2 | 4 | 7.3 | odd | 6 | |||
1470.2.n.g.79.1 | 4 | 1.1 | even | 1 | trivial | ||
1470.2.n.g.79.2 | 4 | 5.4 | even | 2 | inner | ||
1470.2.n.g.949.1 | 4 | 35.4 | even | 6 | inner | ||
1470.2.n.g.949.2 | 4 | 7.4 | even | 3 | inner | ||
1680.2.t.d.1009.1 | 2 | 28.23 | odd | 6 | |||
1680.2.t.d.1009.2 | 2 | 140.79 | odd | 6 | |||
3150.2.a.q.1.1 | 1 | 105.23 | even | 12 | |||
3150.2.a.be.1.1 | 1 | 105.2 | even | 12 | |||
5040.2.t.k.1009.1 | 2 | 84.23 | even | 6 | |||
5040.2.t.k.1009.2 | 2 | 420.359 | even | 6 | |||
7350.2.a.g.1.1 | 1 | 35.12 | even | 12 | |||
7350.2.a.co.1.1 | 1 | 35.33 | even | 12 | |||
8400.2.a.bd.1.1 | 1 | 140.107 | even | 12 | |||
8400.2.a.ca.1.1 | 1 | 140.23 | even | 12 |