Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1690,2,Mod(361,1690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1690, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1690.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1690 = 2 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1690.l (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: | \(13.4947179416\) |
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 130) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1690.361 |
Dual form | 1690.2.l.a.1161.2 |
$q$-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 \(\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||
\(3\) | −1.00000 | − | 1.73205i | −0.577350 | − | 1.00000i | −0.995782 | − | 0.0917517i | \(-0.970753\pi\) |
0.418432 | − | 0.908248i | \(-0.362580\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | −1.73205 | − | 1.00000i | −0.707107 | − | 0.408248i | ||||
\(7\) | −3.46410 | − | 2.00000i | −1.30931 | − | 0.755929i | −0.327327 | − | 0.944911i | \(-0.606148\pi\) |
−0.981981 | + | 0.188982i | \(0.939481\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | 1.73205 | − | 1.00000i | 0.522233 | − | 0.301511i | −0.215615 | − | 0.976478i | \(-0.569176\pi\) |
0.737848 | + | 0.674967i | \(0.235842\pi\) | |||||||
\(12\) | −2.00000 | −0.577350 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −4.00000 | −1.06904 | ||||||||
\(15\) | −1.73205 | + | 1.00000i | −0.447214 | + | 0.258199i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −5.19615 | − | 3.00000i | −1.19208 | − | 0.688247i | −0.233301 | − | 0.972404i | \(-0.574953\pi\) |
−0.958778 | + | 0.284157i | \(0.908286\pi\) | |||||||
\(20\) | −0.866025 | − | 0.500000i | −0.193649 | − | 0.111803i | ||||
\(21\) | 8.00000i | 1.74574i | ||||||||
\(22\) | 1.00000 | − | 1.73205i | 0.213201 | − | 0.369274i | ||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | −1.73205 | + | 1.00000i | −0.353553 | + | 0.204124i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | −3.46410 | + | 2.00000i | −0.654654 | + | 0.377964i | ||||
\(29\) | −1.00000 | − | 1.73205i | −0.185695 | − | 0.321634i | 0.758115 | − | 0.652121i | \(-0.226120\pi\) |
−0.943811 | + | 0.330487i | \(0.892787\pi\) | |||||||
\(30\) | −1.00000 | + | 1.73205i | −0.182574 | + | 0.316228i | ||||
\(31\) | − | 6.00000i | − | 1.07763i | −0.842424 | − | 0.538816i | \(-0.818872\pi\) | ||
0.842424 | − | 0.538816i | \(-0.181128\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −3.46410 | − | 2.00000i | −0.603023 | − | 0.348155i | ||||
\(34\) | − | 2.00000i | − | 0.342997i | ||||||
\(35\) | −2.00000 | + | 3.46410i | −0.338062 | + | 0.585540i | ||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | 1.73205 | − | 1.00000i | 0.284747 | − | 0.164399i | −0.350823 | − | 0.936442i | \(-0.614098\pi\) |
0.635571 | + | 0.772043i | \(0.280765\pi\) | |||||||
\(38\) | −6.00000 | −0.973329 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 8.66025 | − | 5.00000i | 1.35250 | − | 0.780869i | 0.363905 | − | 0.931436i | \(-0.381443\pi\) |
0.988600 | + | 0.150567i | \(0.0481100\pi\) | |||||||
\(42\) | 4.00000 | + | 6.92820i | 0.617213 | + | 1.06904i | ||||
\(43\) | −5.00000 | + | 8.66025i | −0.762493 | + | 1.32068i | 0.179069 | + | 0.983836i | \(0.442691\pi\) |
−0.941562 | + | 0.336840i | \(0.890642\pi\) | |||||||
\(44\) | − | 2.00000i | − | 0.301511i | ||||||
\(45\) | 0.866025 | + | 0.500000i | 0.129099 | + | 0.0745356i | ||||
\(46\) | 5.19615 | + | 3.00000i | 0.766131 | + | 0.442326i | ||||
\(47\) | 12.0000i | 1.75038i | 0.483779 | + | 0.875190i | \(0.339264\pi\) | ||||
−0.483779 | + | 0.875190i | \(0.660736\pi\) | |||||||
\(48\) | −1.00000 | + | 1.73205i | −0.144338 | + | 0.250000i | ||||
\(49\) | 4.50000 | + | 7.79423i | 0.642857 | + | 1.11346i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | −3.46410 | + | 2.00000i | −0.471405 | + | 0.272166i | ||||
\(55\) | −1.00000 | − | 1.73205i | −0.134840 | − | 0.233550i | ||||
\(56\) | −2.00000 | + | 3.46410i | −0.267261 | + | 0.462910i | ||||
\(57\) | 12.0000i | 1.58944i | ||||||||
\(58\) | −1.73205 | − | 1.00000i | −0.227429 | − | 0.131306i | ||||
\(59\) | 8.66025 | + | 5.00000i | 1.12747 | + | 0.650945i | 0.943297 | − | 0.331949i | \(-0.107706\pi\) |
0.184172 | + | 0.982894i | \(0.441040\pi\) | |||||||
\(60\) | 2.00000i | 0.258199i | ||||||||
\(61\) | −1.00000 | + | 1.73205i | −0.128037 | + | 0.221766i | −0.922916 | − | 0.385002i | \(-0.874201\pi\) |
0.794879 | + | 0.606768i | \(0.207534\pi\) | |||||||
\(62\) | −3.00000 | − | 5.19615i | −0.381000 | − | 0.659912i | ||||
\(63\) | 3.46410 | − | 2.00000i | 0.436436 | − | 0.251976i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.00000 | −0.492366 | ||||||||
\(67\) | −10.3923 | + | 6.00000i | −1.26962 | + | 0.733017i | −0.974916 | − | 0.222571i | \(-0.928555\pi\) |
−0.294706 | + | 0.955588i | \(0.595222\pi\) | |||||||
\(68\) | −1.00000 | − | 1.73205i | −0.121268 | − | 0.210042i | ||||
\(69\) | 6.00000 | − | 10.3923i | 0.722315 | − | 1.25109i | ||||
\(70\) | 4.00000i | 0.478091i | ||||||||
\(71\) | −8.66025 | − | 5.00000i | −1.02778 | − | 0.593391i | −0.111434 | − | 0.993772i | \(-0.535544\pi\) |
−0.916349 | + | 0.400381i | \(0.868878\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | − | 10.0000i | − | 1.17041i | −0.810885 | − | 0.585206i | \(-0.801014\pi\) | ||
0.810885 | − | 0.585206i | \(-0.198986\pi\) | |||||||
\(74\) | 1.00000 | − | 1.73205i | 0.116248 | − | 0.201347i | ||||
\(75\) | 1.00000 | + | 1.73205i | 0.115470 | + | 0.200000i | ||||
\(76\) | −5.19615 | + | 3.00000i | −0.596040 | + | 0.344124i | ||||
\(77\) | −8.00000 | −0.911685 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | −0.866025 | + | 0.500000i | −0.0968246 | + | 0.0559017i | ||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | 5.00000 | − | 8.66025i | 0.552158 | − | 0.956365i | ||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 6.92820 | + | 4.00000i | 0.755929 | + | 0.436436i | ||||
\(85\) | −1.73205 | − | 1.00000i | −0.187867 | − | 0.108465i | ||||
\(86\) | 10.0000i | 1.07833i | ||||||||
\(87\) | −2.00000 | + | 3.46410i | −0.214423 | + | 0.371391i | ||||
\(88\) | −1.00000 | − | 1.73205i | −0.106600 | − | 0.184637i | ||||
\(89\) | 12.1244 | − | 7.00000i | 1.28518 | − | 0.741999i | 0.307389 | − | 0.951584i | \(-0.400545\pi\) |
0.977790 | + | 0.209585i | \(0.0672115\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | −10.3923 | + | 6.00000i | −1.07763 | + | 0.622171i | ||||
\(94\) | 6.00000 | + | 10.3923i | 0.618853 | + | 1.07188i | ||||
\(95\) | −3.00000 | + | 5.19615i | −0.307794 | + | 0.533114i | ||||
\(96\) | 2.00000i | 0.204124i | ||||||||
\(97\) | −12.1244 | − | 7.00000i | −1.23104 | − | 0.710742i | −0.263795 | − | 0.964579i | \(-0.584974\pi\) |
−0.967247 | + | 0.253837i | \(0.918307\pi\) | |||||||
\(98\) | 7.79423 | + | 4.50000i | 0.787336 | + | 0.454569i | ||||
\(99\) | 2.00000i | 0.201008i | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 7.00000 | + | 12.1244i | 0.696526 | + | 1.20642i | 0.969664 | + | 0.244443i | \(0.0786053\pi\) |
−0.273138 | + | 0.961975i | \(0.588061\pi\) | |||||||
\(102\) | −3.46410 | + | 2.00000i | −0.342997 | + | 0.198030i | ||||
\(103\) | 18.0000 | 1.77359 | 0.886796 | − | 0.462160i | \(-0.152926\pi\) | ||||
0.886796 | + | 0.462160i | \(0.152926\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.00000 | 0.780720 | ||||||||
\(106\) | 1.73205 | − | 1.00000i | 0.168232 | − | 0.0971286i | ||||
\(107\) | −3.00000 | − | 5.19615i | −0.290021 | − | 0.502331i | 0.683793 | − | 0.729676i | \(-0.260329\pi\) |
−0.973814 | + | 0.227345i | \(0.926996\pi\) | |||||||
\(108\) | −2.00000 | + | 3.46410i | −0.192450 | + | 0.333333i | ||||
\(109\) | − | 6.00000i | − | 0.574696i | −0.957826 | − | 0.287348i | \(-0.907226\pi\) | ||
0.957826 | − | 0.287348i | \(-0.0927736\pi\) | |||||||
\(110\) | −1.73205 | − | 1.00000i | −0.165145 | − | 0.0953463i | ||||
\(111\) | −3.46410 | − | 2.00000i | −0.328798 | − | 0.189832i | ||||
\(112\) | 4.00000i | 0.377964i | ||||||||
\(113\) | −1.00000 | + | 1.73205i | −0.0940721 | + | 0.162938i | −0.909221 | − | 0.416314i | \(-0.863322\pi\) |
0.815149 | + | 0.579252i | \(0.196655\pi\) | |||||||
\(114\) | 6.00000 | + | 10.3923i | 0.561951 | + | 0.973329i | ||||
\(115\) | 5.19615 | − | 3.00000i | 0.484544 | − | 0.279751i | ||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.0000 | 0.920575 | ||||||||
\(119\) | −6.92820 | + | 4.00000i | −0.635107 | + | 0.366679i | ||||
\(120\) | 1.00000 | + | 1.73205i | 0.0912871 | + | 0.158114i | ||||
\(121\) | −3.50000 | + | 6.06218i | −0.318182 | + | 0.551107i | ||||
\(122\) | 2.00000i | 0.181071i | ||||||||
\(123\) | −17.3205 | − | 10.0000i | −1.56174 | − | 0.901670i | ||||
\(124\) | −5.19615 | − | 3.00000i | −0.466628 | − | 0.269408i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 2.00000 | − | 3.46410i | 0.178174 | − | 0.308607i | ||||
\(127\) | −7.00000 | − | 12.1244i | −0.621150 | − | 1.07586i | −0.989272 | − | 0.146085i | \(-0.953333\pi\) |
0.368122 | − | 0.929777i | \(-0.380001\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 20.0000 | 1.76090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | −3.46410 | + | 2.00000i | −0.301511 | + | 0.174078i | ||||
\(133\) | 12.0000 | + | 20.7846i | 1.04053 | + | 1.80225i | ||||
\(134\) | −6.00000 | + | 10.3923i | −0.518321 | + | 0.897758i | ||||
\(135\) | 4.00000i | 0.344265i | ||||||||
\(136\) | −1.73205 | − | 1.00000i | −0.148522 | − | 0.0857493i | ||||
\(137\) | −15.5885 | − | 9.00000i | −1.33181 | − | 0.768922i | −0.346235 | − | 0.938148i | \(-0.612540\pi\) |
−0.985577 | + | 0.169226i | \(0.945873\pi\) | |||||||
\(138\) | − | 12.0000i | − | 1.02151i | ||||||
\(139\) | 4.00000 | − | 6.92820i | 0.339276 | − | 0.587643i | −0.645021 | − | 0.764165i | \(-0.723151\pi\) |
0.984297 | + | 0.176522i | \(0.0564848\pi\) | |||||||
\(140\) | 2.00000 | + | 3.46410i | 0.169031 | + | 0.292770i | ||||
\(141\) | 20.7846 | − | 12.0000i | 1.75038 | − | 1.01058i | ||||
\(142\) | −10.0000 | −0.839181 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.73205 | + | 1.00000i | −0.143839 | + | 0.0830455i | ||||
\(146\) | −5.00000 | − | 8.66025i | −0.413803 | − | 0.716728i | ||||
\(147\) | 9.00000 | − | 15.5885i | 0.742307 | − | 1.28571i | ||||
\(148\) | − | 2.00000i | − | 0.164399i | ||||||
\(149\) | −1.73205 | − | 1.00000i | −0.141895 | − | 0.0819232i | 0.427372 | − | 0.904076i | \(-0.359440\pi\) |
−0.569267 | + | 0.822153i | \(0.692773\pi\) | |||||||
\(150\) | 1.73205 | + | 1.00000i | 0.141421 | + | 0.0816497i | ||||
\(151\) | − | 6.00000i | − | 0.488273i | −0.969741 | − | 0.244137i | \(-0.921495\pi\) | ||
0.969741 | − | 0.244137i | \(-0.0785045\pi\) | |||||||
\(152\) | −3.00000 | + | 5.19615i | −0.243332 | + | 0.421464i | ||||
\(153\) | 1.00000 | + | 1.73205i | 0.0808452 | + | 0.140028i | ||||
\(154\) | −6.92820 | + | 4.00000i | −0.558291 | + | 0.322329i | ||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | −3.46410 | + | 2.00000i | −0.275589 | + | 0.159111i | ||||
\(159\) | −2.00000 | − | 3.46410i | −0.158610 | − | 0.274721i | ||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | − | 24.0000i | − | 1.89146i | ||||||
\(162\) | 9.52628 | + | 5.50000i | 0.748455 | + | 0.432121i | ||||
\(163\) | −3.46410 | − | 2.00000i | −0.271329 | − | 0.156652i | 0.358162 | − | 0.933659i | \(-0.383403\pi\) |
−0.629492 | + | 0.777007i | \(0.716737\pi\) | |||||||
\(164\) | − | 10.0000i | − | 0.780869i | ||||||
\(165\) | −2.00000 | + | 3.46410i | −0.155700 | + | 0.269680i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.3205 | + | 10.0000i | −1.34030 | + | 0.773823i | −0.986851 | − | 0.161630i | \(-0.948325\pi\) |
−0.353450 | + | 0.935454i | \(0.614991\pi\) | |||||||
\(168\) | 8.00000 | 0.617213 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.00000 | −0.153393 | ||||||||
\(171\) | 5.19615 | − | 3.00000i | 0.397360 | − | 0.229416i | ||||
\(172\) | 5.00000 | + | 8.66025i | 0.381246 | + | 0.660338i | ||||
\(173\) | 5.00000 | − | 8.66025i | 0.380143 | − | 0.658427i | −0.610939 | − | 0.791677i | \(-0.709208\pi\) |
0.991082 | + | 0.133250i | \(0.0425415\pi\) | |||||||
\(174\) | 4.00000i | 0.303239i | ||||||||
\(175\) | 3.46410 | + | 2.00000i | 0.261861 | + | 0.151186i | ||||
\(176\) | −1.73205 | − | 1.00000i | −0.130558 | − | 0.0753778i | ||||
\(177\) | − | 20.0000i | − | 1.50329i | ||||||
\(178\) | 7.00000 | − | 12.1244i | 0.524672 | − | 0.908759i | ||||
\(179\) | −2.00000 | − | 3.46410i | −0.149487 | − | 0.258919i | 0.781551 | − | 0.623841i | \(-0.214429\pi\) |
−0.931038 | + | 0.364922i | \(0.881096\pi\) | |||||||
\(180\) | 0.866025 | − | 0.500000i | 0.0645497 | − | 0.0372678i | ||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.00000 | 0.295689 | ||||||||
\(184\) | 5.19615 | − | 3.00000i | 0.383065 | − | 0.221163i | ||||
\(185\) | −1.00000 | − | 1.73205i | −0.0735215 | − | 0.127343i | ||||
\(186\) | −6.00000 | + | 10.3923i | −0.439941 | + | 0.762001i | ||||
\(187\) | − | 4.00000i | − | 0.292509i | ||||||
\(188\) | 10.3923 | + | 6.00000i | 0.757937 | + | 0.437595i | ||||
\(189\) | 13.8564 | + | 8.00000i | 1.00791 | + | 0.581914i | ||||
\(190\) | 6.00000i | 0.435286i | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | 1.00000 | + | 1.73205i | 0.0721688 | + | 0.125000i | ||||
\(193\) | −12.1244 | + | 7.00000i | −0.872730 | + | 0.503871i | −0.868255 | − | 0.496119i | \(-0.834758\pi\) |
−0.00447566 | + | 0.999990i | \(0.501425\pi\) | |||||||
\(194\) | −14.0000 | −1.00514 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.00000 | 0.642857 | ||||||||
\(197\) | −5.19615 | + | 3.00000i | −0.370211 | + | 0.213741i | −0.673550 | − | 0.739141i | \(-0.735232\pi\) |
0.303340 | + | 0.952882i | \(0.401898\pi\) | |||||||
\(198\) | 1.00000 | + | 1.73205i | 0.0710669 | + | 0.123091i | ||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 20.7846 | + | 12.0000i | 1.46603 | + | 0.846415i | ||||
\(202\) | 12.1244 | + | 7.00000i | 0.853067 | + | 0.492518i | ||||
\(203\) | 8.00000i | 0.561490i | ||||||||
\(204\) | −2.00000 | + | 3.46410i | −0.140028 | + | 0.242536i | ||||
\(205\) | −5.00000 | − | 8.66025i | −0.349215 | − | 0.604858i | ||||
\(206\) | 15.5885 | − | 9.00000i | 1.08610 | − | 0.627060i | ||||
\(207\) | −6.00000 | −0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 6.92820 | − | 4.00000i | 0.478091 | − | 0.276026i | ||||
\(211\) | −14.0000 | − | 24.2487i | −0.963800 | − | 1.66935i | −0.712806 | − | 0.701361i | \(-0.752576\pi\) |
−0.250994 | − | 0.967989i | \(-0.580757\pi\) | |||||||
\(212\) | 1.00000 | − | 1.73205i | 0.0686803 | − | 0.118958i | ||||
\(213\) | 20.0000i | 1.37038i | ||||||||
\(214\) | −5.19615 | − | 3.00000i | −0.355202 | − | 0.205076i | ||||
\(215\) | 8.66025 | + | 5.00000i | 0.590624 | + | 0.340997i | ||||
\(216\) | 4.00000i | 0.272166i | ||||||||
\(217\) | −12.0000 | + | 20.7846i | −0.814613 | + | 1.41095i | ||||
\(218\) | −3.00000 | − | 5.19615i | −0.203186 | − | 0.351928i | ||||
\(219\) | −17.3205 | + | 10.0000i | −1.17041 | + | 0.675737i | ||||
\(220\) | −2.00000 | −0.134840 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.00000 | −0.268462 | ||||||||
\(223\) | 3.46410 | − | 2.00000i | 0.231973 | − | 0.133930i | −0.379509 | − | 0.925188i | \(-0.623907\pi\) |
0.611482 | + | 0.791258i | \(0.290574\pi\) | |||||||
\(224\) | 2.00000 | + | 3.46410i | 0.133631 | + | 0.231455i | ||||
\(225\) | 0.500000 | − | 0.866025i | 0.0333333 | − | 0.0577350i | ||||
\(226\) | 2.00000i | 0.133038i | ||||||||
\(227\) | 3.46410 | + | 2.00000i | 0.229920 | + | 0.132745i | 0.610535 | − | 0.791989i | \(-0.290954\pi\) |
−0.380615 | + | 0.924734i | \(0.624288\pi\) | |||||||
\(228\) | 10.3923 | + | 6.00000i | 0.688247 | + | 0.397360i | ||||
\(229\) | − | 10.0000i | − | 0.660819i | −0.943838 | − | 0.330409i | \(-0.892813\pi\) | ||
0.943838 | − | 0.330409i | \(-0.107187\pi\) | |||||||
\(230\) | 3.00000 | − | 5.19615i | 0.197814 | − | 0.342624i | ||||
\(231\) | 8.00000 | + | 13.8564i | 0.526361 | + | 0.911685i | ||||
\(232\) | −1.73205 | + | 1.00000i | −0.113715 | + | 0.0656532i | ||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0000 | 0.782794 | ||||||||
\(236\) | 8.66025 | − | 5.00000i | 0.563735 | − | 0.325472i | ||||
\(237\) | 4.00000 | + | 6.92820i | 0.259828 | + | 0.450035i | ||||
\(238\) | −4.00000 | + | 6.92820i | −0.259281 | + | 0.449089i | ||||
\(239\) | − | 26.0000i | − | 1.68180i | −0.541190 | − | 0.840900i | \(-0.682026\pi\) | ||
0.541190 | − | 0.840900i | \(-0.317974\pi\) | |||||||
\(240\) | 1.73205 | + | 1.00000i | 0.111803 | + | 0.0645497i | ||||
\(241\) | −19.0526 | − | 11.0000i | −1.22728 | − | 0.708572i | −0.260822 | − | 0.965387i | \(-0.583994\pi\) |
−0.966461 | + | 0.256814i | \(0.917327\pi\) | |||||||
\(242\) | 7.00000i | 0.449977i | ||||||||
\(243\) | 5.00000 | − | 8.66025i | 0.320750 | − | 0.555556i | ||||
\(244\) | 1.00000 | + | 1.73205i | 0.0640184 | + | 0.110883i | ||||
\(245\) | 7.79423 | − | 4.50000i | 0.497955 | − | 0.287494i | ||||
\(246\) | −20.0000 | −1.27515 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(252\) | − | 4.00000i | − | 0.251976i | ||||||
\(253\) | 10.3923 | + | 6.00000i | 0.653359 | + | 0.377217i | ||||
\(254\) | −12.1244 | − | 7.00000i | −0.760750 | − | 0.439219i | ||||
\(255\) | 4.00000i | 0.250490i | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −15.0000 | − | 25.9808i | −0.935674 | − | 1.62064i | −0.773427 | − | 0.633885i | \(-0.781459\pi\) |
−0.162247 | − | 0.986750i | \(-0.551874\pi\) | |||||||
\(258\) | 17.3205 | − | 10.0000i | 1.07833 | − | 0.622573i | ||||
\(259\) | −8.00000 | −0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 3.46410 | − | 2.00000i | 0.214013 | − | 0.123560i | ||||
\(263\) | −1.00000 | − | 1.73205i | −0.0616626 | − | 0.106803i | 0.833546 | − | 0.552450i | \(-0.186307\pi\) |
−0.895209 | + | 0.445647i | \(0.852974\pi\) | |||||||
\(264\) | −2.00000 | + | 3.46410i | −0.123091 | + | 0.213201i | ||||
\(265\) | − | 2.00000i | − | 0.122859i | ||||||
\(266\) | 20.7846 | + | 12.0000i | 1.27439 | + | 0.735767i | ||||
\(267\) | −24.2487 | − | 14.0000i | −1.48400 | − | 0.856786i | ||||
\(268\) | 12.0000i | 0.733017i | ||||||||
\(269\) | −3.00000 | + | 5.19615i | −0.182913 | + | 0.316815i | −0.942871 | − | 0.333157i | \(-0.891886\pi\) |
0.759958 | + | 0.649972i | \(0.225219\pi\) | |||||||
\(270\) | 2.00000 | + | 3.46410i | 0.121716 | + | 0.210819i | ||||
\(271\) | 1.73205 | − | 1.00000i | 0.105215 | − | 0.0607457i | −0.446469 | − | 0.894799i | \(-0.647319\pi\) |
0.551684 | + | 0.834053i | \(0.313985\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.0000 | −1.08742 | ||||||||
\(275\) | −1.73205 | + | 1.00000i | −0.104447 | + | 0.0603023i | ||||
\(276\) | −6.00000 | − | 10.3923i | −0.361158 | − | 0.625543i | ||||
\(277\) | 1.00000 | − | 1.73205i | 0.0600842 | − | 0.104069i | −0.834419 | − | 0.551131i | \(-0.814196\pi\) |
0.894503 | + | 0.447062i | \(0.147530\pi\) | |||||||
\(278\) | − | 8.00000i | − | 0.479808i | ||||||
\(279\) | 5.19615 | + | 3.00000i | 0.311086 | + | 0.179605i | ||||
\(280\) | 3.46410 | + | 2.00000i | 0.207020 | + | 0.119523i | ||||
\(281\) | 6.00000i | 0.357930i | 0.983855 | + | 0.178965i | \(0.0572749\pi\) | ||||
−0.983855 | + | 0.178965i | \(0.942725\pi\) | |||||||
\(282\) | 12.0000 | − | 20.7846i | 0.714590 | − | 1.23771i | ||||
\(283\) | 7.00000 | + | 12.1244i | 0.416107 | + | 0.720718i | 0.995544 | − | 0.0942988i | \(-0.0300609\pi\) |
−0.579437 | + | 0.815017i | \(0.696728\pi\) | |||||||
\(284\) | −8.66025 | + | 5.00000i | −0.513892 | + | 0.296695i | ||||
\(285\) | 12.0000 | 0.710819 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −40.0000 | −2.36113 | ||||||||
\(288\) | 0.866025 | − | 0.500000i | 0.0510310 | − | 0.0294628i | ||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | −1.00000 | + | 1.73205i | −0.0587220 | + | 0.101710i | ||||
\(291\) | 28.0000i | 1.64139i | ||||||||
\(292\) | −8.66025 | − | 5.00000i | −0.506803 | − | 0.292603i | ||||
\(293\) | 19.0526 | + | 11.0000i | 1.11306 | + | 0.642627i | 0.939621 | − | 0.342217i | \(-0.111178\pi\) |
0.173442 | + | 0.984844i | \(0.444511\pi\) | |||||||
\(294\) | − | 18.0000i | − | 1.04978i | ||||||
\(295\) | 5.00000 | − | 8.66025i | 0.291111 | − | 0.504219i | ||||
\(296\) | −1.00000 | − | 1.73205i | −0.0581238 | − | 0.100673i | ||||
\(297\) | −6.92820 | + | 4.00000i | −0.402015 | + | 0.232104i | ||||
\(298\) | −2.00000 | −0.115857 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.00000 | 0.115470 | ||||||||
\(301\) | 34.6410 | − | 20.0000i | 1.99667 | − | 1.15278i | ||||
\(302\) | −3.00000 | − | 5.19615i | −0.172631 | − | 0.299005i | ||||
\(303\) | 14.0000 | − | 24.2487i | 0.804279 | − | 1.39305i | ||||
\(304\) | 6.00000i | 0.344124i | ||||||||
\(305\) | 1.73205 | + | 1.00000i | 0.0991769 | + | 0.0572598i | ||||
\(306\) | 1.73205 | + | 1.00000i | 0.0990148 | + | 0.0571662i | ||||
\(307\) | − | 24.0000i | − | 1.36975i | −0.728659 | − | 0.684876i | \(-0.759856\pi\) | ||
0.728659 | − | 0.684876i | \(-0.240144\pi\) | |||||||
\(308\) | −4.00000 | + | 6.92820i | −0.227921 | + | 0.394771i | ||||
\(309\) | −18.0000 | − | 31.1769i | −1.02398 | − | 1.77359i | ||||
\(310\) | −5.19615 | + | 3.00000i | −0.295122 | + | 0.170389i | ||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | 8.66025 | − | 5.00000i | 0.488726 | − | 0.282166i | ||||
\(315\) | −2.00000 | − | 3.46410i | −0.112687 | − | 0.195180i | ||||
\(316\) | −2.00000 | + | 3.46410i | −0.112509 | + | 0.194871i | ||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | −3.46410 | − | 2.00000i | −0.194257 | − | 0.112154i | ||||
\(319\) | −3.46410 | − | 2.00000i | −0.193952 | − | 0.111979i | ||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −6.00000 | + | 10.3923i | −0.334887 | + | 0.580042i | ||||
\(322\) | −12.0000 | − | 20.7846i | −0.668734 | − | 1.15828i | ||||
\(323\) | −10.3923 | + | 6.00000i | −0.578243 | + | 0.333849i | ||||
\(324\) | 11.0000 | 0.611111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | −10.3923 | + | 6.00000i | −0.574696 | + | 0.331801i | ||||
\(328\) | −5.00000 | − | 8.66025i | −0.276079 | − | 0.478183i | ||||
\(329\) | 24.0000 | − | 41.5692i | 1.32316 | − | 2.29179i | ||||
\(330\) | 4.00000i | 0.220193i | ||||||||
\(331\) | 12.1244 | + | 7.00000i | 0.666415 | + | 0.384755i | 0.794717 | − | 0.606980i | \(-0.207619\pi\) |
−0.128302 | + | 0.991735i | \(0.540953\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.00000i | 0.109599i | ||||||||
\(334\) | −10.0000 | + | 17.3205i | −0.547176 | + | 0.947736i | ||||
\(335\) | 6.00000 | + | 10.3923i | 0.327815 | + | 0.567792i | ||||
\(336\) | 6.92820 | − | 4.00000i | 0.377964 | − | 0.218218i | ||||
\(337\) | 22.0000 | 1.19842 | 0.599208 | − | 0.800593i | \(-0.295482\pi\) | ||||
0.599208 | + | 0.800593i | \(0.295482\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.00000 | 0.217250 | ||||||||
\(340\) | −1.73205 | + | 1.00000i | −0.0939336 | + | 0.0542326i | ||||
\(341\) | −6.00000 | − | 10.3923i | −0.324918 | − | 0.562775i | ||||
\(342\) | 3.00000 | − | 5.19615i | 0.162221 | − | 0.280976i | ||||
\(343\) | − | 8.00000i | − | 0.431959i | ||||||
\(344\) | 8.66025 | + | 5.00000i | 0.466930 | + | 0.269582i | ||||
\(345\) | −10.3923 | − | 6.00000i | −0.559503 | − | 0.323029i | ||||
\(346\) | − | 10.0000i | − | 0.537603i | ||||||
\(347\) | −3.00000 | + | 5.19615i | −0.161048 | + | 0.278944i | −0.935245 | − | 0.354001i | \(-0.884821\pi\) |
0.774197 | + | 0.632945i | \(0.218154\pi\) | |||||||
\(348\) | 2.00000 | + | 3.46410i | 0.107211 | + | 0.185695i | ||||
\(349\) | −1.73205 | + | 1.00000i | −0.0927146 | + | 0.0535288i | −0.545640 | − | 0.838019i | \(-0.683714\pi\) |
0.452926 | + | 0.891548i | \(0.350380\pi\) | |||||||
\(350\) | 4.00000 | 0.213809 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.00000 | −0.106600 | ||||||||
\(353\) | 29.4449 | − | 17.0000i | 1.56719 | − | 0.904819i | 0.570697 | − | 0.821160i | \(-0.306673\pi\) |
0.996495 | − | 0.0836583i | \(-0.0266604\pi\) | |||||||
\(354\) | −10.0000 | − | 17.3205i | −0.531494 | − | 0.920575i | ||||
\(355\) | −5.00000 | + | 8.66025i | −0.265372 | + | 0.459639i | ||||
\(356\) | − | 14.0000i | − | 0.741999i | ||||||
\(357\) | 13.8564 | + | 8.00000i | 0.733359 | + | 0.423405i | ||||
\(358\) | −3.46410 | − | 2.00000i | −0.183083 | − | 0.105703i | ||||
\(359\) | 6.00000i | 0.316668i | 0.987386 | + | 0.158334i | \(0.0506123\pi\) | ||||
−0.987386 | + | 0.158334i | \(0.949388\pi\) | |||||||
\(360\) | 0.500000 | − | 0.866025i | 0.0263523 | − | 0.0456435i | ||||
\(361\) | 8.50000 | + | 14.7224i | 0.447368 | + | 0.774865i | ||||
\(362\) | −8.66025 | + | 5.00000i | −0.455173 | + | 0.262794i | ||||
\(363\) | 14.0000 | 0.734809 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.0000 | −0.523424 | ||||||||
\(366\) | 3.46410 | − | 2.00000i | 0.181071 | − | 0.104542i | ||||
\(367\) | −15.0000 | − | 25.9808i | −0.782994 | − | 1.35618i | −0.930190 | − | 0.367078i | \(-0.880358\pi\) |
0.147197 | − | 0.989107i | \(-0.452975\pi\) | |||||||
\(368\) | 3.00000 | − | 5.19615i | 0.156386 | − | 0.270868i | ||||
\(369\) | 10.0000i | 0.520579i | ||||||||
\(370\) | −1.73205 | − | 1.00000i | −0.0900450 | − | 0.0519875i | ||||
\(371\) | −6.92820 | − | 4.00000i | −0.359694 | − | 0.207670i | ||||
\(372\) | 12.0000i | 0.622171i | ||||||||
\(373\) | 7.00000 | − | 12.1244i | 0.362446 | − | 0.627775i | −0.625917 | − | 0.779890i | \(-0.715275\pi\) |
0.988363 | + | 0.152115i | \(0.0486083\pi\) | |||||||
\(374\) | −2.00000 | − | 3.46410i | −0.103418 | − | 0.179124i | ||||
\(375\) | 1.73205 | − | 1.00000i | 0.0894427 | − | 0.0516398i | ||||
\(376\) | 12.0000 | 0.618853 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 16.0000 | 0.822951 | ||||||||
\(379\) | 5.19615 | − | 3.00000i | 0.266908 | − | 0.154100i | −0.360573 | − | 0.932731i | \(-0.617419\pi\) |
0.627482 | + | 0.778631i | \(0.284086\pi\) | |||||||
\(380\) | 3.00000 | + | 5.19615i | 0.153897 | + | 0.266557i | ||||
\(381\) | −14.0000 | + | 24.2487i | −0.717242 | + | 1.24230i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.3923 | − | 6.00000i | −0.531022 | − | 0.306586i | 0.210411 | − | 0.977613i | \(-0.432520\pi\) |
−0.741433 | + | 0.671027i | \(0.765853\pi\) | |||||||
\(384\) | 1.73205 | + | 1.00000i | 0.0883883 | + | 0.0510310i | ||||
\(385\) | 8.00000i | 0.407718i | ||||||||
\(386\) | −7.00000 | + | 12.1244i | −0.356291 | + | 0.617113i | ||||
\(387\) | −5.00000 | − | 8.66025i | −0.254164 | − | 0.440225i | ||||
\(388\) | −12.1244 | + | 7.00000i | −0.615521 | + | 0.355371i | ||||
\(389\) | 10.0000 | 0.507020 | 0.253510 | − | 0.967333i | \(-0.418415\pi\) | ||||
0.253510 | + | 0.967333i | \(0.418415\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 7.79423 | − | 4.50000i | 0.393668 | − | 0.227284i | ||||
\(393\) | −4.00000 | − | 6.92820i | −0.201773 | − | 0.349482i | ||||
\(394\) | −3.00000 | + | 5.19615i | −0.151138 | + | 0.261778i | ||||
\(395\) | 4.00000i | 0.201262i | ||||||||
\(396\) | 1.73205 | + | 1.00000i | 0.0870388 | + | 0.0502519i | ||||
\(397\) | 32.9090 | + | 19.0000i | 1.65165 | + | 0.953583i | 0.976392 | + | 0.216004i | \(0.0693024\pi\) |
0.675261 | + | 0.737579i | \(0.264031\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 24.0000 | − | 41.5692i | 1.20150 | − | 2.08106i | ||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | 5.19615 | − | 3.00000i | 0.259483 | − | 0.149813i | −0.364615 | − | 0.931158i | \(-0.618800\pi\) |
0.624099 | + | 0.781345i | \(0.285466\pi\) | |||||||
\(402\) | 24.0000 | 1.19701 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 14.0000 | 0.696526 | ||||||||
\(405\) | 9.52628 | − | 5.50000i | 0.473365 | − | 0.273297i | ||||
\(406\) | 4.00000 | + | 6.92820i | 0.198517 | + | 0.343841i | ||||
\(407\) | 2.00000 | − | 3.46410i | 0.0991363 | − | 0.171709i | ||||
\(408\) | 4.00000i | 0.198030i | ||||||||
\(409\) | −29.4449 | − | 17.0000i | −1.45595 | − | 0.840596i | −0.457146 | − | 0.889392i | \(-0.651128\pi\) |
−0.998809 | + | 0.0487958i | \(0.984462\pi\) | |||||||
\(410\) | −8.66025 | − | 5.00000i | −0.427699 | − | 0.246932i | ||||
\(411\) | 36.0000i | 1.77575i | ||||||||
\(412\) | 9.00000 | − | 15.5885i | 0.443398 | − | 0.767988i | ||||
\(413\) | −20.0000 | − | 34.6410i | −0.984136 | − | 1.70457i | ||||
\(414\) | −5.19615 | + | 3.00000i | −0.255377 | + | 0.147442i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.0000 | −0.783523 | ||||||||
\(418\) | −10.3923 | + | 6.00000i | −0.508304 | + | 0.293470i | ||||
\(419\) | −8.00000 | − | 13.8564i | −0.390826 | − | 0.676930i | 0.601733 | − | 0.798697i | \(-0.294477\pi\) |
−0.992559 | + | 0.121768i | \(0.961144\pi\) | |||||||
\(420\) | 4.00000 | − | 6.92820i | 0.195180 | − | 0.338062i | ||||
\(421\) | 10.0000i | 0.487370i | 0.969854 | + | 0.243685i | \(0.0783563\pi\) | ||||
−0.969854 | + | 0.243685i | \(0.921644\pi\) | |||||||
\(422\) | −24.2487 | − | 14.0000i | −1.18041 | − | 0.681509i | ||||
\(423\) | −10.3923 | − | 6.00000i | −0.505291 | − | 0.291730i | ||||
\(424\) | − | 2.00000i | − | 0.0971286i | ||||||
\(425\) | −1.00000 | + | 1.73205i | −0.0485071 | + | 0.0840168i | ||||
\(426\) | 10.0000 | + | 17.3205i | 0.484502 | + | 0.839181i | ||||
\(427\) | 6.92820 | − | 4.00000i | 0.335279 | − | 0.193574i | ||||
\(428\) | −6.00000 | −0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.0000 | 0.482243 | ||||||||
\(431\) | 15.5885 | − | 9.00000i | 0.750870 | − | 0.433515i | −0.0751385 | − | 0.997173i | \(-0.523940\pi\) |
0.826008 | + | 0.563658i | \(0.190607\pi\) | |||||||
\(432\) | 2.00000 | + | 3.46410i | 0.0962250 | + | 0.166667i | ||||
\(433\) | −19.0000 | + | 32.9090i | −0.913082 | + | 1.58150i | −0.103396 | + | 0.994640i | \(0.532971\pi\) |
−0.809686 | + | 0.586864i | \(0.800362\pi\) | |||||||
\(434\) | 24.0000i | 1.15204i | ||||||||
\(435\) | 3.46410 | + | 2.00000i | 0.166091 | + | 0.0958927i | ||||
\(436\) | −5.19615 | − | 3.00000i | −0.248851 | − | 0.143674i | ||||
\(437\) | − | 36.0000i | − | 1.72211i | ||||||
\(438\) | −10.0000 | + | 17.3205i | −0.477818 | + | 0.827606i | ||||
\(439\) | −16.0000 | − | 27.7128i | −0.763638 | − | 1.32266i | −0.940963 | − | 0.338508i | \(-0.890078\pi\) |
0.177325 | − | 0.984152i | \(-0.443256\pi\) | |||||||
\(440\) | −1.73205 | + | 1.00000i | −0.0825723 | + | 0.0476731i | ||||
\(441\) | −9.00000 | −0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.0000 | −0.665160 | −0.332580 | − | 0.943075i | \(-0.607919\pi\) | ||||
−0.332580 | + | 0.943075i | \(0.607919\pi\) | |||||||
\(444\) | −3.46410 | + | 2.00000i | −0.164399 | + | 0.0949158i | ||||
\(445\) | −7.00000 | − | 12.1244i | −0.331832 | − | 0.574750i | ||||
\(446\) | 2.00000 | − | 3.46410i | 0.0947027 | − | 0.164030i | ||||
\(447\) | 4.00000i | 0.189194i | ||||||||
\(448\) | 3.46410 | + | 2.00000i | 0.163663 | + | 0.0944911i | ||||
\(449\) | −5.19615 | − | 3.00000i | −0.245222 | − | 0.141579i | 0.372353 | − | 0.928091i | \(-0.378551\pi\) |
−0.617574 | + | 0.786513i | \(0.711885\pi\) | |||||||
\(450\) | − | 1.00000i | − | 0.0471405i | ||||||
\(451\) | 10.0000 | − | 17.3205i | 0.470882 | − | 0.815591i | ||||
\(452\) | 1.00000 | + | 1.73205i | 0.0470360 | + | 0.0814688i | ||||
\(453\) | −10.3923 | + | 6.00000i | −0.488273 | + | 0.281905i | ||||
\(454\) | 4.00000 | 0.187729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.0000 | 0.561951 | ||||||||
\(457\) | −8.66025 | + | 5.00000i | −0.405110 | + | 0.233890i | −0.688686 | − | 0.725059i | \(-0.741812\pi\) |
0.283577 | + | 0.958950i | \(0.408479\pi\) | |||||||
\(458\) | −5.00000 | − | 8.66025i | −0.233635 | − | 0.404667i | ||||
\(459\) | −4.00000 | + | 6.92820i | −0.186704 | + | 0.323381i | ||||
\(460\) | − | 6.00000i | − | 0.279751i | ||||||
\(461\) | 5.19615 | + | 3.00000i | 0.242009 | + | 0.139724i | 0.616100 | − | 0.787668i | \(-0.288712\pi\) |
−0.374091 | + | 0.927392i | \(0.622045\pi\) | |||||||
\(462\) | 13.8564 | + | 8.00000i | 0.644658 | + | 0.372194i | ||||
\(463\) | − | 16.0000i | − | 0.743583i | −0.928316 | − | 0.371792i | \(-0.878744\pi\) | ||
0.928316 | − | 0.371792i | \(-0.121256\pi\) | |||||||
\(464\) | −1.00000 | + | 1.73205i | −0.0464238 | + | 0.0804084i | ||||
\(465\) | 6.00000 | + | 10.3923i | 0.278243 | + | 0.481932i | ||||
\(466\) | 5.19615 | − | 3.00000i | 0.240707 | − | 0.138972i | ||||
\(467\) | −10.0000 | −0.462745 | −0.231372 | − | 0.972865i | \(-0.574322\pi\) | ||||
−0.231372 | + | 0.972865i | \(0.574322\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 48.0000 | 2.21643 | ||||||||
\(470\) | 10.3923 | − | 6.00000i | 0.479361 | − | 0.276759i | ||||
\(471\) | −10.0000 | − | 17.3205i | −0.460776 | − | 0.798087i | ||||
\(472\) | 5.00000 | − | 8.66025i | 0.230144 | − | 0.398621i | ||||
\(473\) | 20.0000i | 0.919601i | ||||||||
\(474\) | 6.92820 | + | 4.00000i | 0.318223 | + | 0.183726i | ||||
\(475\) | 5.19615 | + | 3.00000i | 0.238416 | + | 0.137649i | ||||
\(476\) | 8.00000i | 0.366679i | ||||||||
\(477\) | −1.00000 | + | 1.73205i | −0.0457869 | + | 0.0793052i | ||||
\(478\) | −13.0000 | − | 22.5167i | −0.594606 | − | 1.02989i | ||||
\(479\) | −1.73205 | + | 1.00000i | −0.0791394 | + | 0.0456912i | −0.539048 | − | 0.842275i | \(-0.681216\pi\) |
0.459908 | + | 0.887967i | \(0.347882\pi\) | |||||||
\(480\) | 2.00000 | 0.0912871 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −22.0000 | −1.00207 | ||||||||
\(483\) | −41.5692 | + | 24.0000i | −1.89146 | + | 1.09204i | ||||
\(484\) | 3.50000 | + | 6.06218i | 0.159091 | + | 0.275554i | ||||
\(485\) | −7.00000 | + | 12.1244i | −0.317854 | + | 0.550539i | ||||
\(486\) | − | 10.0000i | − | 0.453609i | ||||||
\(487\) | 13.8564 | + | 8.00000i | 0.627894 | + | 0.362515i | 0.779936 | − | 0.625859i | \(-0.215252\pi\) |
−0.152042 | + | 0.988374i | \(0.548585\pi\) | |||||||
\(488\) | 1.73205 | + | 1.00000i | 0.0784063 | + | 0.0452679i | ||||
\(489\) | 8.00000i | 0.361773i | ||||||||
\(490\) | 4.50000 | − | 7.79423i | 0.203289 | − | 0.352107i | ||||
\(491\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(492\) | −17.3205 | + | 10.0000i | −0.780869 | + | 0.450835i | ||||
\(493\) | −4.00000 | −0.180151 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.00000 | 0.0898933 | ||||||||
\(496\) | −5.19615 | + | 3.00000i | −0.233314 | + | 0.134704i | ||||
\(497\) | 20.0000 | + | 34.6410i | 0.897123 | + | 1.55386i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.0000i | 1.70111i | 0.525883 | + | 0.850557i | \(0.323735\pi\) | ||||
−0.525883 | + | 0.850557i | \(0.676265\pi\) | |||||||
\(500\) | 0.866025 | + | 0.500000i | 0.0387298 | + | 0.0223607i | ||||
\(501\) | 34.6410 | + | 20.0000i | 1.54765 | + | 0.893534i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.00000 | − | 12.1244i | 0.312115 | − | 0.540598i | −0.666705 | − | 0.745321i | \(-0.732296\pi\) |
0.978820 | + | 0.204723i | \(0.0656294\pi\) | |||||||
\(504\) | −2.00000 | − | 3.46410i | −0.0890871 | − | 0.154303i | ||||
\(505\) | 12.1244 | − | 7.00000i | 0.539527 | − | 0.311496i | ||||
\(506\) | 12.0000 | 0.533465 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.0000 | −0.621150 | ||||||||
\(509\) | −5.19615 | + | 3.00000i | −0.230315 | + | 0.132973i | −0.610718 | − | 0.791849i | \(-0.709119\pi\) |
0.380402 | + | 0.924821i | \(0.375786\pi\) | |||||||
\(510\) | 2.00000 | + | 3.46410i | 0.0885615 | + | 0.153393i | ||||
\(511\) | −20.0000 | + | 34.6410i | −0.884748 | + | 1.53243i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 20.7846 | + | 12.0000i | 0.917663 | + | 0.529813i | ||||
\(514\) | −25.9808 | − | 15.0000i | −1.14596 | − | 0.661622i | ||||
\(515\) | − | 18.0000i | − | 0.793175i | ||||||
\(516\) | 10.0000 | − | 17.3205i | 0.440225 | − | 0.762493i | ||||
\(517\) | 12.0000 | + | 20.7846i | 0.527759 | + | 0.914106i | ||||
\(518\) | −6.92820 | + | 4.00000i | −0.304408 | + | 0.175750i | ||||
\(519\) | −20.0000 | −0.877903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.0000 | −1.13908 | −0.569540 | − | 0.821963i | \(-0.692879\pi\) | ||||
−0.569540 | + | 0.821963i | \(0.692879\pi\) | |||||||
\(522\) | 1.73205 | − | 1.00000i | 0.0758098 | − | 0.0437688i | ||||
\(523\) | 3.00000 | + | 5.19615i | 0.131181 | + | 0.227212i | 0.924132 | − | 0.382073i | \(-0.124790\pi\) |
−0.792951 | + | 0.609285i | \(0.791456\pi\) | |||||||
\(524\) | 2.00000 | − | 3.46410i | 0.0873704 | − | 0.151330i | ||||
\(525\) | − | 8.00000i | − | 0.349149i | ||||||
\(526\) | −1.73205 | − | 1.00000i | −0.0755210 | − | 0.0436021i | ||||
\(527\) | −10.3923 | − | 6.00000i | −0.452696 | − | 0.261364i | ||||
\(528\) | 4.00000i | 0.174078i | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | −1.00000 | − | 1.73205i | −0.0434372 | − | 0.0752355i | ||||
\(531\) | −8.66025 | + | 5.00000i | −0.375823 | + | 0.216982i | ||||
\(532\) | 24.0000 | 1.04053 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −28.0000 | −1.21168 | ||||||||
\(535\) | −5.19615 | + | 3.00000i | −0.224649 | + | 0.129701i | ||||
\(536\) | 6.00000 | + | 10.3923i | 0.259161 | + | 0.448879i | ||||
\(537\) | −4.00000 | + | 6.92820i | −0.172613 | + | 0.298974i | ||||
\(538\) | 6.00000i | 0.258678i | ||||||||
\(539\) | 15.5885 | + | 9.00000i | 0.671442 | + | 0.387657i | ||||
\(540\) | 3.46410 | + | 2.00000i | 0.149071 | + | 0.0860663i | ||||
\(541\) | 38.0000i | 1.63375i | 0.576816 | + | 0.816874i | \(0.304295\pi\) | ||||
−0.576816 | + | 0.816874i | \(0.695705\pi\) | |||||||
\(542\) | 1.00000 | − | 1.73205i | 0.0429537 | − | 0.0743980i | ||||
\(543\) | 10.0000 | + | 17.3205i | 0.429141 | + | 0.743294i | ||||
\(544\) | −1.73205 | + | 1.00000i | −0.0742611 | + | 0.0428746i | ||||
\(545\) | −6.00000 | −0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.0000 | 0.940652 | 0.470326 | − | 0.882493i | \(-0.344136\pi\) | ||||
0.470326 | + | 0.882493i | \(0.344136\pi\) | |||||||
\(548\) | −15.5885 | + | 9.00000i | −0.665906 | + | 0.384461i | ||||
\(549\) | −1.00000 | − | 1.73205i | −0.0426790 | − | 0.0739221i | ||||
\(550\) | −1.00000 | + | 1.73205i | −0.0426401 | + | 0.0738549i | ||||
\(551\) | 12.0000i | 0.511217i | ||||||||
\(552\) | −10.3923 | − | 6.00000i | −0.442326 | − | 0.255377i | ||||
\(553\) | 13.8564 | + | 8.00000i | 0.589234 | + | 0.340195i | ||||
\(554\) | − | 2.00000i | − | 0.0849719i | ||||||
\(555\) | −2.00000 | + | 3.46410i | −0.0848953 | + | 0.147043i | ||||
\(556\) | −4.00000 | − | 6.92820i | −0.169638 | − | 0.293821i | ||||
\(557\) | −32.9090 | + | 19.0000i | −1.39440 | + | 0.805056i | −0.993798 | − | 0.111198i | \(-0.964531\pi\) |
−0.400599 | + | 0.916253i | \(0.631198\pi\) | |||||||
\(558\) | 6.00000 | 0.254000 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4.00000 | 0.169031 | ||||||||
\(561\) | −6.92820 | + | 4.00000i | −0.292509 | + | 0.168880i | ||||
\(562\) | 3.00000 | + | 5.19615i | 0.126547 | + | 0.219186i | ||||
\(563\) | 3.00000 | − | 5.19615i | 0.126435 | − | 0.218992i | −0.795858 | − | 0.605483i | \(-0.792980\pi\) |
0.922293 | + | 0.386492i | \(0.126313\pi\) | |||||||
\(564\) | − | 24.0000i | − | 1.01058i | ||||||
\(565\) | 1.73205 | + | 1.00000i | 0.0728679 | + | 0.0420703i | ||||
\(566\) | 12.1244 | + | 7.00000i | 0.509625 | + | 0.294232i | ||||
\(567\) | − | 44.0000i | − | 1.84783i | ||||||
\(568\) | −5.00000 | + | 8.66025i | −0.209795 | + | 0.363376i | ||||
\(569\) | 3.00000 | + | 5.19615i | 0.125767 | + | 0.217834i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | 10.3923 | − | 6.00000i | 0.435286 | − | 0.251312i | ||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −34.6410 | + | 20.0000i | −1.44589 | + | 0.834784i | ||||
\(575\) | −3.00000 | − | 5.19615i | −0.125109 | − | 0.216695i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 18.0000i | 0.749350i | 0.927156 | + | 0.374675i | \(0.122246\pi\) | ||||
−0.927156 | + | 0.374675i | \(0.877754\pi\) | |||||||
\(578\) | 11.2583 | + | 6.50000i | 0.468285 | + | 0.270364i | ||||
\(579\) | 24.2487 | + | 14.0000i | 1.00774 | + | 0.581820i | ||||
\(580\) | 2.00000i | 0.0830455i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 14.0000 | + | 24.2487i | 0.580319 | + | 1.00514i | ||||
\(583\) | 3.46410 | − | 2.00000i | 0.143468 | − | 0.0828315i | ||||
\(584\) | −10.0000 | −0.413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.0000 | 0.908812 | ||||||||
\(587\) | 10.3923 | − | 6.00000i | 0.428936 | − | 0.247647i | −0.269957 | − | 0.962872i | \(-0.587010\pi\) |
0.698893 | + | 0.715226i | \(0.253676\pi\) | |||||||
\(588\) | −9.00000 | − | 15.5885i | −0.371154 | − | 0.642857i | ||||
\(589\) | −18.0000 | + | 31.1769i | −0.741677 | + | 1.28462i | ||||
\(590\) | − | 10.0000i | − | 0.411693i | ||||||
\(591\) | 10.3923 | + | 6.00000i | 0.427482 | + | 0.246807i | ||||
\(592\) | −1.73205 | − | 1.00000i | −0.0711868 | − | 0.0410997i | ||||
\(593\) | 2.00000i | 0.0821302i | 0.999156 | + | 0.0410651i | \(0.0130751\pi\) | ||||
−0.999156 | + | 0.0410651i | \(0.986925\pi\) | |||||||
\(594\) | −4.00000 | + | 6.92820i | −0.164122 | + | 0.284268i | ||||
\(595\) | 4.00000 | + | 6.92820i | 0.163984 | + | 0.284029i | ||||
\(596\) | −1.73205 | + | 1.00000i | −0.0709476 | + | 0.0409616i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.0000 | −0.490307 | −0.245153 | − | 0.969484i | \(-0.578838\pi\) | ||||
−0.245153 | + | 0.969484i | \(0.578838\pi\) | |||||||
\(600\) | 1.73205 | − | 1.00000i | 0.0707107 | − | 0.0408248i | ||||
\(601\) | −5.00000 | − | 8.66025i | −0.203954 | − | 0.353259i | 0.745845 | − | 0.666120i | \(-0.232046\pi\) |
−0.949799 | + | 0.312861i | \(0.898713\pi\) | |||||||
\(602\) | 20.0000 | − | 34.6410i | 0.815139 | − | 1.41186i | ||||
\(603\) | − | 12.0000i | − | 0.488678i | ||||||
\(604\) | −5.19615 | − | 3.00000i | −0.211428 | − | 0.122068i | ||||
\(605\) | 6.06218 | + | 3.50000i | 0.246463 | + | 0.142295i | ||||
\(606\) | − | 28.0000i | − | 1.13742i | ||||||
\(607\) | 17.0000 | − | 29.4449i | 0.690009 | − | 1.19513i | −0.281826 | − | 0.959466i | \(-0.590940\pi\) |
0.971834 | − | 0.235665i | \(-0.0757267\pi\) | |||||||
\(608\) | 3.00000 | + | 5.19615i | 0.121666 | + | 0.210732i | ||||
\(609\) | 13.8564 | − | 8.00000i | 0.561490 | − | 0.324176i | ||||
\(610\) | 2.00000 | 0.0809776 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.00000 | 0.0808452 | ||||||||
\(613\) | 22.5167 | − | 13.0000i | 0.909439 | − | 0.525065i | 0.0291886 | − | 0.999574i | \(-0.490708\pi\) |
0.880251 | + | 0.474509i | \(0.157374\pi\) | |||||||
\(614\) | −12.0000 | − | 20.7846i | −0.484281 | − | 0.838799i | ||||
\(615\) | −10.0000 | + | 17.3205i | −0.403239 | + | 0.698430i | ||||
\(616\) | 8.00000i | 0.322329i | ||||||||
\(617\) | −5.19615 | − | 3.00000i | −0.209189 | − | 0.120775i | 0.391745 | − | 0.920074i | \(-0.371871\pi\) |
−0.600935 | + | 0.799298i | \(0.705205\pi\) | |||||||
\(618\) | −31.1769 | − | 18.0000i | −1.25412 | − | 0.724066i | ||||
\(619\) | 46.0000i | 1.84890i | 0.381308 | + | 0.924448i | \(0.375474\pi\) | ||||
−0.381308 | + | 0.924448i | \(0.624526\pi\) | |||||||
\(620\) | −3.00000 | + | 5.19615i | −0.120483 | + | 0.208683i | ||||
\(621\) | −12.0000 | − | 20.7846i | −0.481543 | − | 0.834058i | ||||
\(622\) | 10.3923 | − | 6.00000i | 0.416693 | − | 0.240578i | ||||
\(623\) | −56.0000 | −2.24359 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.19615 | + | 3.00000i | −0.207680 | + | 0.119904i | ||||
\(627\) | 12.0000 | + | 20.7846i | 0.479234 | + | 0.830057i | ||||
\(628\) | 5.00000 | − | 8.66025i | 0.199522 | − | 0.345582i | ||||
\(629\) | − | 4.00000i | − | 0.159490i | ||||||
\(630\) | −3.46410 | − | 2.00000i | −0.138013 | − | 0.0796819i | ||||
\(631\) | 25.9808 | + | 15.0000i | 1.03428 | + | 0.597141i | 0.918207 | − | 0.396100i | \(-0.129637\pi\) |
0.116071 | + | 0.993241i | \(0.462970\pi\) | |||||||
\(632\) | 4.00000i | 0.159111i | ||||||||
\(633\) | −28.0000 | + | 48.4974i | −1.11290 | + | 1.92760i | ||||
\(634\) | −9.00000 | − | 15.5885i | −0.357436 | − | 0.619097i | ||||
\(635\) | −12.1244 | + | 7.00000i | −0.481140 | + | 0.277787i | ||||
\(636\) | −4.00000 | −0.158610 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.00000 | −0.158362 | ||||||||
\(639\) | 8.66025 | − | 5.00000i | 0.342594 | − | 0.197797i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | 9.00000 | − | 15.5885i | 0.355479 | − | 0.615707i | −0.631721 | − | 0.775196i | \(-0.717651\pi\) |
0.987200 | + | 0.159489i | \(0.0509845\pi\) | |||||||
\(642\) | 12.0000i | 0.473602i | ||||||||
\(643\) | 13.8564 | + | 8.00000i | 0.546443 | + | 0.315489i | 0.747686 | − | 0.664052i | \(-0.231165\pi\) |
−0.201243 | + | 0.979541i | \(0.564498\pi\) | |||||||
\(644\) | −20.7846 | − | 12.0000i | −0.819028 | − | 0.472866i | ||||
\(645\) | − | 20.0000i | − | 0.787499i | ||||||
\(646\) | −6.00000 | + | 10.3923i | −0.236067 | + | 0.408880i | ||||
\(647\) | 21.0000 | + | 36.3731i | 0.825595 | + | 1.42997i | 0.901464 | + | 0.432855i | \(0.142494\pi\) |
−0.0758684 | + | 0.997118i | \(0.524173\pi\) | |||||||
\(648\) | 9.52628 | − | 5.50000i | 0.374228 | − | 0.216060i | ||||
\(649\) | 20.0000 | 0.785069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 48.0000 | 1.88127 | ||||||||
\(652\) | −3.46410 | + | 2.00000i | −0.135665 | + | 0.0783260i | ||||
\(653\) | 3.00000 | + | 5.19615i | 0.117399 | + | 0.203341i | 0.918736 | − | 0.394872i | \(-0.129211\pi\) |
−0.801337 | + | 0.598213i | \(0.795878\pi\) | |||||||
\(654\) | −6.00000 | + | 10.3923i | −0.234619 | + | 0.406371i | ||||
\(655\) | − | 4.00000i | − | 0.156293i | ||||||
\(656\) | −8.66025 | − | 5.00000i | −0.338126 | − | 0.195217i | ||||
\(657\) | 8.66025 | + | 5.00000i | 0.337869 | + | 0.195069i | ||||
\(658\) | − | 48.0000i | − | 1.87123i | ||||||
\(659\) | −4.00000 | + | 6.92820i | −0.155818 | + | 0.269884i | −0.933357 | − | 0.358951i | \(-0.883135\pi\) |
0.777539 | + | 0.628835i | \(0.216468\pi\) | |||||||
\(660\) | 2.00000 | + | 3.46410i | 0.0778499 | + | 0.134840i | ||||
\(661\) | 25.9808 | − | 15.0000i | 1.01053 | − | 0.583432i | 0.0991864 | − | 0.995069i | \(-0.468376\pi\) |
0.911348 | + | 0.411636i | \(0.135043\pi\) | |||||||
\(662\) | 14.0000 | 0.544125 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.7846 | − | 12.0000i | 0.805993 | − | 0.465340i | ||||
\(666\) | 1.00000 | + | 1.73205i | 0.0387492 | + | 0.0671156i | ||||
\(667\) | 6.00000 | − | 10.3923i | 0.232321 | − | 0.402392i | ||||
\(668\) | 20.0000i | 0.773823i | ||||||||
\(669\) | −6.92820 | − | 4.00000i | −0.267860 | − | 0.154649i | ||||
\(670\) | 10.3923 | + | 6.00000i | 0.401490 | + | 0.231800i | ||||
\(671\) | 4.00000i | 0.154418i | ||||||||
\(672\) | 4.00000 | − | 6.92820i | 0.154303 | − | 0.267261i | ||||
\(673\) | 1.00000 | + | 1.73205i | 0.0385472 | + | 0.0667657i | 0.884655 | − | 0.466246i | \(-0.154394\pi\) |
−0.846108 | + | 0.533011i | \(0.821060\pi\) | |||||||
\(674\) | 19.0526 | − | 11.0000i | 0.733877 | − | 0.423704i | ||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.00000 | −0.230599 | −0.115299 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115299 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(678\) | 3.46410 | − | 2.00000i | 0.133038 | − | 0.0768095i | ||||
\(679\) | 28.0000 | + | 48.4974i | 1.07454 | + | 1.86116i | ||||
\(680\) | −1.00000 | + | 1.73205i | −0.0383482 | + | 0.0664211i | ||||
\(681\) | − | 8.00000i | − | 0.306561i | ||||||
\(682\) | −10.3923 | − | 6.00000i | −0.397942 | − | 0.229752i | ||||
\(683\) | −38.1051 | − | 22.0000i | −1.45805 | − | 0.841807i | −0.459136 | − | 0.888366i | \(-0.651841\pi\) |
−0.998916 | + | 0.0465592i | \(0.985174\pi\) | |||||||
\(684\) | − | 6.00000i | − | 0.229416i | ||||||
\(685\) | −9.00000 | + | 15.5885i | −0.343872 | + | 0.595604i | ||||
\(686\) | −4.00000 | − | 6.92820i | −0.152721 | − | 0.264520i | ||||
\(687\) | −17.3205 | + | 10.0000i | −0.660819 | + | 0.381524i | ||||
\(688\) | 10.0000 | 0.381246 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −12.0000 | −0.456832 | ||||||||
\(691\) | −32.9090 | + | 19.0000i | −1.25192 | + | 0.722794i | −0.971490 | − | 0.237082i | \(-0.923809\pi\) |
−0.280426 | + | 0.959876i | \(0.590476\pi\) | |||||||
\(692\) | −5.00000 | − | 8.66025i | −0.190071 | − | 0.329213i | ||||
\(693\) | 4.00000 | − | 6.92820i | 0.151947 | − | 0.263181i | ||||
\(694\) | 6.00000i | 0.227757i | ||||||||
\(695\) | −6.92820 | − | 4.00000i | −0.262802 | − | 0.151729i | ||||
\(696\) | 3.46410 | + | 2.00000i | 0.131306 | + | 0.0758098i | ||||
\(697\) | − | 20.0000i | − | 0.757554i | ||||||
\(698\) | −1.00000 | + | 1.73205i | −0.0378506 | + | 0.0655591i | ||||
\(699\) | −6.00000 | − | 10.3923i | −0.226941 | − | 0.393073i | ||||
\(700\) | 3.46410 | − | 2.00000i | 0.130931 | − | 0.0755929i | ||||
\(701\) | −38.0000 | −1.43524 | −0.717620 | − | 0.696435i | \(-0.754769\pi\) | ||||
−0.717620 | + | 0.696435i | \(0.754769\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0000 | −0.452589 | ||||||||
\(704\) | −1.73205 | + | 1.00000i | −0.0652791 | + | 0.0376889i | ||||
\(705\) | −12.0000 | − | 20.7846i | −0.451946 | − | 0.782794i | ||||
\(706\) | 17.0000 | − | 29.4449i | 0.639803 | − | 1.10817i | ||||
\(707\) | − | 56.0000i | − | 2.10610i | ||||||
\(708\) | −17.3205 | − | 10.0000i | −0.650945 | − | 0.375823i | ||||
\(709\) | −19.0526 | − | 11.0000i | −0.715534 | − | 0.413114i | 0.0975728 | − | 0.995228i | \(-0.468892\pi\) |
−0.813107 | + | 0.582115i | \(0.802225\pi\) | |||||||
\(710\) | 10.0000i | 0.375293i | ||||||||
\(711\) | 2.00000 | − | 3.46410i | 0.0750059 | − | 0.129914i | ||||
\(712\) | −7.00000 | − | 12.1244i | −0.262336 | − | 0.454379i | ||||
\(713\) | 31.1769 | − | 18.0000i | 1.16758 | − | 0.674105i | ||||
\(714\) | 16.0000 | 0.598785 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.00000 | −0.149487 | ||||||||
\(717\) | −45.0333 | + | 26.0000i | −1.68180 | + | 0.970988i | ||||
\(718\) | 3.00000 | + | 5.19615i | 0.111959 | + | 0.193919i | ||||
\(719\) | 24.0000 | − | 41.5692i | 0.895049 | − | 1.55027i | 0.0613050 | − | 0.998119i | \(-0.480474\pi\) |
0.833744 | − | 0.552151i | \(-0.186193\pi\) | |||||||
\(720\) | − | 1.00000i | − | 0.0372678i | ||||||
\(721\) | −62.3538 | − | 36.0000i | −2.32218 | − | 1.34071i | ||||
\(722\) | 14.7224 | + | 8.50000i | 0.547912 | + | 0.316337i | ||||
\(723\) | 44.0000i | 1.63638i | ||||||||
\(724\) | −5.00000 | + | 8.66025i | −0.185824 | + | 0.321856i | ||||
\(725\) | 1.00000 | + | 1.73205i | 0.0371391 | + | 0.0643268i | ||||
\(726\) | 12.1244 | − | 7.00000i | 0.449977 | − | 0.259794i | ||||
\(727\) | 14.0000 | 0.519231 | 0.259616 | − | 0.965712i | \(-0.416404\pi\) | ||||
0.259616 | + | 0.965712i | \(0.416404\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −8.66025 | + | 5.00000i | −0.320530 | + | 0.185058i | ||||
\(731\) | 10.0000 | + | 17.3205i | 0.369863 | + | 0.640622i | ||||
\(732\) | 2.00000 | − | 3.46410i | 0.0739221 | − | 0.128037i | ||||
\(733\) | 2.00000i | 0.0738717i | 0.999318 | + | 0.0369358i | \(0.0117597\pi\) | ||||
−0.999318 | + | 0.0369358i | \(0.988240\pi\) | |||||||
\(734\) | −25.9808 | − | 15.0000i | −0.958967 | − | 0.553660i | ||||
\(735\) | −15.5885 | − | 9.00000i | −0.574989 | − | 0.331970i | ||||
\(736\) | − | 6.00000i | − | 0.221163i | ||||||
\(737\) | −12.0000 | + | 20.7846i | −0.442026 | + | 0.765611i | ||||
\(738\) | 5.00000 | + | 8.66025i | 0.184053 | + | 0.318788i | ||||
\(739\) | −36.3731 | + | 21.0000i | −1.33800 | + | 0.772497i | −0.986511 | − | 0.163693i | \(-0.947659\pi\) |
−0.351494 | + | 0.936190i | \(0.614326\pi\) | |||||||
\(740\) | −2.00000 | −0.0735215 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.00000 | −0.293689 | ||||||||
\(743\) | −10.3923 | + | 6.00000i | −0.381257 | + | 0.220119i | −0.678365 | − | 0.734725i | \(-0.737311\pi\) |
0.297108 | + | 0.954844i | \(0.403978\pi\) | |||||||
\(744\) | 6.00000 | + | 10.3923i | 0.219971 | + | 0.381000i | ||||
\(745\) | −1.00000 | + | 1.73205i | −0.0366372 | + | 0.0634574i | ||||
\(746\) | − | 14.0000i | − | 0.512576i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.46410 | − | 2.00000i | −0.126660 | − | 0.0731272i | ||||
\(749\) | 24.0000i | 0.876941i | ||||||||
\(750\) | 1.00000 | − | 1.73205i | 0.0365148 | − | 0.0632456i | ||||
\(751\) | 22.0000 | + | 38.1051i | 0.802791 | + | 1.39048i | 0.917772 | + | 0.397108i | \(0.129986\pi\) |
−0.114981 | + | 0.993368i | \(0.536681\pi\) | |||||||
\(752\) | 10.3923 | − | 6.00000i | 0.378968 | − | 0.218797i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.00000 | −0.218362 | ||||||||
\(756\) | 13.8564 | − | 8.00000i | 0.503953 | − | 0.290957i | ||||
\(757\) | −9.00000 | − | 15.5885i | −0.327111 | − | 0.566572i | 0.654827 | − | 0.755779i | \(-0.272742\pi\) |
−0.981937 | + | 0.189207i | \(0.939408\pi\) | |||||||
\(758\) | 3.00000 | − | 5.19615i | 0.108965 | − | 0.188733i | ||||
\(759\) | − | 24.0000i | − | 0.871145i | ||||||
\(760\) | 5.19615 | + | 3.00000i | 0.188484 | + | 0.108821i | ||||
\(761\) | −12.1244 | − | 7.00000i | −0.439508 | − | 0.253750i | 0.263881 | − | 0.964555i | \(-0.414997\pi\) |
−0.703389 | + | 0.710805i | \(0.748331\pi\) | |||||||
\(762\) | 28.0000i | 1.01433i | ||||||||
\(763\) | −12.0000 | + | 20.7846i | −0.434429 | + | 0.752453i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.73205 | − | 1.00000i | 0.0626224 | − | 0.0361551i | ||||
\(766\) | −12.0000 | −0.433578 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.00000 | 0.0721688 | ||||||||
\(769\) | 8.66025 | − | 5.00000i | 0.312297 | − | 0.180305i | −0.335657 | − | 0.941984i | \(-0.608958\pi\) |
0.647954 | + | 0.761680i | \(0.275625\pi\) | |||||||
\(770\) | 4.00000 | + | 6.92820i | 0.144150 | + | 0.249675i | ||||
\(771\) | −30.0000 | + | 51.9615i | −1.08042 | + | 1.87135i | ||||
\(772\) | 14.0000i | 0.503871i | ||||||||
\(773\) | 29.4449 | + | 17.0000i | 1.05906 | + | 0.611448i | 0.925172 | − | 0.379549i | \(-0.123921\pi\) |
0.133887 | + | 0.990997i | \(0.457254\pi\) | |||||||
\(774\) | −8.66025 | − | 5.00000i | −0.311286 | − | 0.179721i | ||||
\(775\) | 6.00000i | 0.215526i | ||||||||
\(776\) | −7.00000 | + | 12.1244i | −0.251285 | + | 0.435239i | ||||
\(777\) | 8.00000 | + | 13.8564i | 0.286998 | + | 0.497096i | ||||
\(778\) | 8.66025 | − | 5.00000i | 0.310485 | − | 0.179259i | ||||
\(779\) | −60.0000 | −2.14972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.0000 | −0.715656 | ||||||||
\(782\) | 10.3923 | − | 6.00000i | 0.371628 | − | 0.214560i | ||||
\(783\) | 4.00000 | + | 6.92820i | 0.142948 | + | 0.247594i | ||||
\(784\) | 4.50000 | − | 7.79423i | 0.160714 | − | 0.278365i | ||||
\(785\) | − | 10.0000i | − | 0.356915i | ||||||
\(786\) | −6.92820 | − | 4.00000i | −0.247121 | − | 0.142675i | ||||
\(787\) | −6.92820 | − | 4.00000i | −0.246964 | − | 0.142585i | 0.371409 | − | 0.928469i | \(-0.378875\pi\) |
−0.618373 | + | 0.785885i | \(0.712208\pi\) | |||||||
\(788\) | 6.00000i | 0.213741i | ||||||||
\(789\) | −2.00000 | + | 3.46410i | −0.0712019 | + | 0.123325i | ||||
\(790\) | 2.00000 | + | 3.46410i | 0.0711568 | + | 0.123247i | ||||
\(791\) | 6.92820 | − | 4.00000i | 0.246339 | − | 0.142224i | ||||
\(792\) | 2.00000 | 0.0710669 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 38.0000 | 1.34857 | ||||||||
\(795\) | −3.46410 | + | 2.00000i | −0.122859 | + | 0.0709327i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.0000 | + | 19.0526i | −0.389640 | + | 0.674876i | −0.992401 | − | 0.123045i | \(-0.960734\pi\) |
0.602761 | + | 0.797922i | \(0.294067\pi\) | |||||||
\(798\) | − | 48.0000i | − | 1.69918i | ||||||
\(799\) | 20.7846 | + | 12.0000i | 0.735307 | + | 0.424529i | ||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | 14.0000i | 0.494666i | ||||||||
\(802\) | 3.00000 | − | 5.19615i | 0.105934 | − | 0.183483i | ||||
\(803\) | −10.0000 | − | 17.3205i | −0.352892 | − | 0.611227i | ||||
\(804\) | 20.7846 | − | 12.0000i | 0.733017 | − | 0.423207i | ||||
\(805\) | −24.0000 | −0.845889 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.0000 | 0.422420 | ||||||||
\(808\) | 12.1244 | − | 7.00000i | 0.426533 | − | 0.246259i | ||||
\(809\) | 17.0000 | + | 29.4449i | 0.597688 | + | 1.03523i | 0.993161 | + | 0.116749i | \(0.0372472\pi\) |
−0.395473 | + | 0.918477i | \(0.629419\pi\) | |||||||
\(810\) | 5.50000 | − | 9.52628i | 0.193250 | − | 0.334719i | ||||
\(811\) | − | 38.0000i | − | 1.33436i | −0.744896 | − | 0.667180i | \(-0.767501\pi\) | ||
0.744896 | − | 0.667180i | \(-0.232499\pi\) | |||||||
\(812\) | 6.92820 | + | 4.00000i | 0.243132 | + | 0.140372i | ||||
\(813\) | −3.46410 | − | 2.00000i | −0.121491 | − | 0.0701431i | ||||
\(814\) | − | 4.00000i | − | 0.140200i | ||||||
\(815\) | −2.00000 | + | 3.46410i | −0.0700569 | + | 0.121342i | ||||
\(816\) | 2.00000 | + | 3.46410i | 0.0700140 | + | 0.121268i | ||||
\(817\) | 51.9615 | − | 30.0000i | 1.81790 | − | 1.04957i | ||||
\(818\) | −34.0000 | −1.18878 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.0000 | −0.349215 | ||||||||
\(821\) | 43.3013 | − | 25.0000i | 1.51122 | − | 0.872506i | 0.511311 | − | 0.859396i | \(-0.329160\pi\) |
0.999914 | − | 0.0131101i | \(-0.00417319\pi\) | |||||||
\(822\) | 18.0000 | + | 31.1769i | 0.627822 | + | 1.08742i | ||||
\(823\) | 7.00000 | − | 12.1244i | 0.244005 | − | 0.422628i | −0.717847 | − | 0.696201i | \(-0.754872\pi\) |
0.961851 | + | 0.273573i | \(0.0882054\pi\) | |||||||
\(824\) | − | 18.0000i | − | 0.627060i | ||||||
\(825\) | 3.46410 | + | 2.00000i | 0.120605 | + | 0.0696311i | ||||
\(826\) | −34.6410 | − | 20.0000i | −1.20532 | − | 0.695889i | ||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | −3.00000 | + | 5.19615i | −0.104257 | + | 0.180579i | ||||
\(829\) | 1.00000 | + | 1.73205i | 0.0347314 | + | 0.0601566i | 0.882869 | − | 0.469620i | \(-0.155609\pi\) |
−0.848137 | + | 0.529777i | \(0.822276\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.00000 | −0.138758 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0000 | 0.623663 | ||||||||
\(834\) | −13.8564 | + | 8.00000i | −0.479808 | + | 0.277017i | ||||
\(835\) | 10.0000 | + | 17.3205i | 0.346064 | + | 0.599401i | ||||
\(836\) | −6.00000 | + | 10.3923i | −0.207514 | + | 0.359425i | ||||
\(837\) | 24.0000i | 0.829561i | ||||||||
\(838\) | −13.8564 | − | 8.00000i | −0.478662 | − | 0.276355i | ||||
\(839\) | 22.5167 | + | 13.0000i | 0.777361 | + | 0.448810i | 0.835494 | − | 0.549499i | \(-0.185181\pi\) |
−0.0581329 | + | 0.998309i | \(0.518515\pi\) | |||||||
\(840\) | − | 8.00000i | − | 0.276026i | ||||||
\(841\) | 12.5000 | − | 21.6506i | 0.431034 | − | 0.746574i | ||||
\(842\) | 5.00000 | + | 8.66025i | 0.172311 | + | 0.298452i | ||||
\(843\) | 10.3923 | − | 6.00000i | 0.357930 | − | 0.206651i | ||||
\(844\) | −28.0000 | −0.963800 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.0000 | −0.412568 | ||||||||
\(847\) | 24.2487 | − | 14.0000i | 0.833196 | − | 0.481046i | ||||
\(848\) | −1.00000 | − | 1.73205i | −0.0343401 | − | 0.0594789i | ||||
\(849\) | 14.0000 | − | 24.2487i | 0.480479 | − | 0.832214i | ||||
\(850\) | 2.00000i | 0.0685994i | ||||||||
\(851\) | 10.3923 | + | 6.00000i | 0.356244 | + | 0.205677i | ||||
\(852\) | 17.3205 | + | 10.0000i | 0.593391 | + | 0.342594i | ||||
\(853\) | 26.0000i | 0.890223i | 0.895475 | + | 0.445112i | \(0.146836\pi\) | ||||
−0.895475 | + | 0.445112i | \(0.853164\pi\) | |||||||
\(854\) | 4.00000 | − | 6.92820i | 0.136877 | − | 0.237078i | ||||
\(855\) | −3.00000 | − | 5.19615i | −0.102598 | − | 0.177705i | ||||
\(856\) | −5.19615 | + | 3.00000i | −0.177601 | + | 0.102538i | ||||
\(857\) | 14.0000 | 0.478231 | 0.239115 | − | 0.970991i | \(-0.423143\pi\) | ||||
0.239115 | + | 0.970991i | \(0.423143\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | 8.66025 | − | 5.00000i | 0.295312 | − | 0.170499i | ||||
\(861\) | 40.0000 | + | 69.2820i | 1.36320 | + | 2.36113i | ||||
\(862\) | 9.00000 | − | 15.5885i | 0.306541 | − | 0.530945i | ||||
\(863\) | − | 36.0000i | − | 1.22545i | −0.790295 | − | 0.612727i | \(-0.790072\pi\) | ||
0.790295 | − | 0.612727i | \(-0.209928\pi\) | |||||||
\(864\) | 3.46410 | + | 2.00000i | 0.117851 | + | 0.0680414i | ||||
\(865\) | −8.66025 | − | 5.00000i | −0.294457 | − | 0.170005i | ||||
\(866\) | 38.0000i | 1.29129i | ||||||||
\(867\) | 13.0000 | − | 22.5167i | 0.441503 | − | 0.764706i | ||||
\(868\) | 12.0000 | + | 20.7846i | 0.407307 | + | 0.705476i | ||||
\(869\) | −6.92820 | + | 4.00000i | −0.235023 | + | 0.135691i | ||||
\(870\) | 4.00000 | 0.135613 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.00000 | −0.203186 | ||||||||
\(873\) | 12.1244 | − | 7.00000i | 0.410347 | − | 0.236914i | ||||
\(874\) | −18.0000 | − | 31.1769i | −0.608859 | − | 1.05457i | ||||
\(875\) | 2.00000 | − | 3.46410i | 0.0676123 | − | 0.117108i | ||||
\(876\) | 20.0000i | 0.675737i | ||||||||
\(877\) | 12.1244 | + | 7.00000i | 0.409410 | + | 0.236373i | 0.690536 | − | 0.723298i | \(-0.257375\pi\) |
−0.281126 | + | 0.959671i | \(0.590708\pi\) | |||||||
\(878\) | −27.7128 | − | 16.0000i | −0.935262 | − | 0.539974i | ||||
\(879\) | − | 44.0000i | − | 1.48408i | ||||||
\(880\) | −1.00000 | + | 1.73205i | −0.0337100 | + | 0.0583874i | ||||
\(881\) | 3.00000 | + | 5.19615i | 0.101073 | + | 0.175063i | 0.912127 | − | 0.409908i | \(-0.134439\pi\) |
−0.811054 | + | 0.584971i | \(0.801106\pi\) | |||||||
\(882\) | −7.79423 | + | 4.50000i | −0.262445 | + | 0.151523i | ||||
\(883\) | −38.0000 | −1.27880 | −0.639401 | − | 0.768874i | \(-0.720818\pi\) | ||||
−0.639401 | + | 0.768874i | \(0.720818\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.0000 | −0.672293 | ||||||||
\(886\) | −12.1244 | + | 7.00000i | −0.407326 | + | 0.235170i | ||||
\(887\) | −11.0000 | − | 19.0526i | −0.369344 | − | 0.639722i | 0.620119 | − | 0.784508i | \(-0.287084\pi\) |
−0.989463 | + | 0.144785i | \(0.953751\pi\) | |||||||
\(888\) | −2.00000 | + | 3.46410i | −0.0671156 | + | 0.116248i | ||||
\(889\) | 56.0000i | 1.87818i | ||||||||
\(890\) | −12.1244 | − | 7.00000i | −0.406409 | − | 0.234641i | ||||
\(891\) | 19.0526 | + | 11.0000i | 0.638285 | + | 0.368514i | ||||
\(892\) | − | 4.00000i | − | 0.133930i | ||||||
\(893\) | 36.0000 | − | 62.3538i | 1.20469 | − | 2.08659i | ||||
\(894\) | 2.00000 | + | 3.46410i | 0.0668900 | + | 0.115857i | ||||
\(895\) | −3.46410 | + | 2.00000i | −0.115792 | + | 0.0668526i | ||||
\(896\) | 4.00000 | 0.133631 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.00000 | −0.200223 | ||||||||
\(899\) | −10.3923 | + | 6.00000i | −0.346603 | + | 0.200111i | ||||
\(900\) | −0.500000 | − | 0.866025i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | 2.00000 | − | 3.46410i | 0.0666297 | − | 0.115406i | ||||
\(902\) | − | 20.0000i | − | 0.665927i | ||||||
\(903\) | −69.2820 | − | 40.0000i | −2.30556 | − | 1.33112i | ||||
\(904\) | 1.73205 | + | 1.00000i | 0.0576072 | + | 0.0332595i | ||||
\(905\) | 10.0000i | 0.332411i | ||||||||
\(906\) | −6.00000 | + | 10.3923i | −0.199337 | + | 0.345261i | ||||
\(907\) | −7.00000 | − | 12.1244i | −0.232431 | − | 0.402583i | 0.726092 | − | 0.687598i | \(-0.241335\pi\) |
−0.958523 | + | 0.285015i | \(0.908001\pi\) | |||||||
\(908\) | 3.46410 | − | 2.00000i | 0.114960 | − | 0.0663723i | ||||
\(909\) | −14.0000 | −0.464351 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0000 | 0.530104 | 0.265052 | − | 0.964234i | \(-0.414611\pi\) | ||||
0.265052 | + | 0.964234i | \(0.414611\pi\) | |||||||
\(912\) | 10.3923 | − | 6.00000i | 0.344124 | − | 0.198680i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −5.00000 | + | 8.66025i | −0.165385 | + | 0.286456i | ||||
\(915\) | − | 4.00000i | − | 0.132236i | ||||||
\(916\) | −8.66025 | − | 5.00000i | −0.286143 | − | 0.165205i | ||||
\(917\) | −13.8564 | − | 8.00000i | −0.457579 | − | 0.264183i | ||||
\(918\) | 8.00000i | 0.264039i | ||||||||
\(919\) | −2.00000 | + | 3.46410i | −0.0659739 | + | 0.114270i | −0.897126 | − | 0.441776i | \(-0.854349\pi\) |
0.831152 | + | 0.556046i | \(0.187682\pi\) | |||||||
\(920\) | −3.00000 | − | 5.19615i | −0.0989071 | − | 0.171312i | ||||
\(921\) | −41.5692 | + | 24.0000i | −1.36975 | + | 0.790827i | ||||
\(922\) | 6.00000 | 0.197599 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 16.0000 | 0.526361 | ||||||||
\(925\) | −1.73205 | + | 1.00000i | −0.0569495 | + | 0.0328798i | ||||
\(926\) | −8.00000 | − | 13.8564i | −0.262896 | − | 0.455350i | ||||
\(927\) | −9.00000 | + | 15.5885i | −0.295599 | + | 0.511992i | ||||
\(928\) | 2.00000i | 0.0656532i | ||||||||
\(929\) | 5.19615 | + | 3.00000i | 0.170480 | + | 0.0984268i | 0.582812 | − | 0.812607i | \(-0.301952\pi\) |
−0.412332 | + | 0.911034i | \(0.635286\pi\) | |||||||
\(930\) | 10.3923 | + | 6.00000i | 0.340777 | + | 0.196748i | ||||
\(931\) | − | 54.0000i | − | 1.76978i | ||||||
\(932\) | 3.00000 | − | 5.19615i | 0.0982683 | − | 0.170206i | ||||
\(933\) | −12.0000 | − | 20.7846i | −0.392862 | − | 0.680458i | ||||
\(934\) | −8.66025 | + | 5.00000i | −0.283372 | + | 0.163605i | ||||
\(935\) | −4.00000 | −0.130814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.0000 | 0.588034 | 0.294017 | − | 0.955800i | \(-0.405008\pi\) | ||||
0.294017 | + | 0.955800i | \(0.405008\pi\) | |||||||
\(938\) | 41.5692 | − | 24.0000i | 1.35728 | − | 0.783628i | ||||
\(939\) | 6.00000 | + | 10.3923i | 0.195803 | + | 0.339140i | ||||
\(940\) | 6.00000 | − | 10.3923i | 0.195698 | − | 0.338960i | ||||
\(941\) | 50.0000i | 1.62995i | 0.579494 | + | 0.814977i | \(0.303250\pi\) | ||||
−0.579494 | + | 0.814977i | \(0.696750\pi\) | |||||||
\(942\) | −17.3205 | − | 10.0000i | −0.564333 | − | 0.325818i | ||||
\(943\) | 51.9615 | + | 30.0000i | 1.69210 | + | 0.976934i | ||||
\(944\) | − | 10.0000i | − | 0.325472i | ||||||
\(945\) | 8.00000 | − | 13.8564i | 0.260240 | − | 0.450749i | ||||
\(946\) | 10.0000 | + | 17.3205i | 0.325128 | + | 0.563138i | ||||
\(947\) | 6.92820 | − | 4.00000i | 0.225136 | − | 0.129983i | −0.383190 | − | 0.923670i | \(-0.625175\pi\) |
0.608326 | + | 0.793687i | \(0.291841\pi\) | |||||||
\(948\) | 8.00000 | 0.259828 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 6.00000 | 0.194666 | ||||||||
\(951\) | −31.1769 | + | 18.0000i | −1.01098 | + | 0.583690i | ||||
\(952\) | 4.00000 | + | 6.92820i | 0.129641 | + | 0.224544i | ||||
\(953\) | 9.00000 | − | 15.5885i | 0.291539 | − | 0.504960i | −0.682635 | − | 0.730759i | \(-0.739166\pi\) |
0.974174 | + | 0.225800i | \(0.0724995\pi\) | |||||||
\(954\) | 2.00000i | 0.0647524i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −22.5167 | − | 13.0000i | −0.728241 | − | 0.420450i | ||||
\(957\) | 8.00000i | 0.258603i | ||||||||
\(958\) | −1.00000 | + | 1.73205i | −0.0323085 | + | 0.0559600i | ||||
\(959\) | 36.0000 | + | 62.3538i | 1.16250 | + | 2.01351i | ||||
\(960\) | 1.73205 | − | 1.00000i | 0.0559017 | − | 0.0322749i | ||||
\(961\) | −5.00000 | −0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.00000 | 0.193347 | ||||||||
\(964\) | −19.0526 | + | 11.0000i | −0.613642 | + | 0.354286i | ||||
\(965\) | 7.00000 | + | 12.1244i | 0.225338 | + | 0.390297i | ||||
\(966\) | −24.0000 | + | 41.5692i | −0.772187 | + | 1.33747i | ||||
\(967\) | − | 32.0000i | − | 1.02905i | −0.857475 | − | 0.514525i | \(-0.827968\pi\) | ||
0.857475 | − | 0.514525i | \(-0.172032\pi\) | |||||||
\(968\) | 6.06218 | + | 3.50000i | 0.194846 | + | 0.112494i | ||||
\(969\) | 20.7846 | + | 12.0000i | 0.667698 | + | 0.385496i | ||||
\(970\) | 14.0000i | 0.449513i | ||||||||
\(971\) | −10.0000 | + | 17.3205i | −0.320915 | + | 0.555842i | −0.980677 | − | 0.195633i | \(-0.937324\pi\) |
0.659762 | + | 0.751475i | \(0.270657\pi\) | |||||||
\(972\) | −5.00000 | − | 8.66025i | −0.160375 | − | 0.277778i | ||||
\(973\) | −27.7128 | + | 16.0000i | −0.888432 | + | 0.512936i | ||||
\(974\) | 16.0000 | 0.512673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | −25.9808 | + | 15.0000i | −0.831198 | + | 0.479893i | −0.854263 | − | 0.519841i | \(-0.825991\pi\) |
0.0230645 | + | 0.999734i | \(0.492658\pi\) | |||||||
\(978\) | 4.00000 | + | 6.92820i | 0.127906 | + | 0.221540i | ||||
\(979\) | 14.0000 | − | 24.2487i | 0.447442 | − | 0.774992i | ||||
\(980\) | − | 9.00000i | − | 0.287494i | ||||||
\(981\) | 5.19615 | + | 3.00000i | 0.165900 | + | 0.0957826i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.0000i | 0.510321i | 0.966899 | + | 0.255160i | \(0.0821283\pi\) | ||||
−0.966899 | + | 0.255160i | \(0.917872\pi\) | |||||||
\(984\) | −10.0000 | + | 17.3205i | −0.318788 | + | 0.552158i | ||||
\(985\) | 3.00000 | + | 5.19615i | 0.0955879 | + | 0.165563i | ||||
\(986\) | −3.46410 | + | 2.00000i | −0.110319 | + | 0.0636930i | ||||
\(987\) | −96.0000 | −3.05571 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −60.0000 | −1.90789 | ||||||||
\(990\) | 1.73205 | − | 1.00000i | 0.0550482 | − | 0.0317821i | ||||
\(991\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(992\) | −3.00000 | + | 5.19615i | −0.0952501 | + | 0.164978i | ||||
\(993\) | − | 28.0000i | − | 0.888553i | ||||||
\(994\) | 34.6410 | + | 20.0000i | 1.09875 | + | 0.634361i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.00000 | + | 8.66025i | −0.158352 | + | 0.274273i | −0.934274 | − | 0.356555i | \(-0.883951\pi\) |
0.775923 | + | 0.630828i | \(0.217285\pi\) | |||||||
\(998\) | 19.0000 | + | 32.9090i | 0.601434 | + | 1.04172i | ||||
\(999\) | −6.92820 | + | 4.00000i | −0.219199 | + | 0.126554i |
(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 | 1690.2.l.a.361.2 | 4 | ||
13.2 | odd | 12 | 130.2.a.c.1.1 | ✓ | 1 | ||
13.3 | even | 3 | 1690.2.d.e.1351.2 | 2 | |||
13.4 | even | 6 | inner | 1690.2.l.a.1161.2 | 4 | ||
13.5 | odd | 4 | 1690.2.e.a.991.1 | 2 | |||
13.6 | odd | 12 | 1690.2.e.a.191.1 | 2 | |||
13.7 | odd | 12 | 1690.2.e.g.191.1 | 2 | |||
13.8 | odd | 4 | 1690.2.e.g.991.1 | 2 | |||
13.9 | even | 3 | inner | 1690.2.l.a.1161.1 | 4 | ||
13.10 | even | 6 | 1690.2.d.e.1351.1 | 2 | |||
13.11 | odd | 12 | 1690.2.a.e.1.1 | 1 | |||
13.12 | even | 2 | inner | 1690.2.l.a.361.1 | 4 | ||
39.2 | even | 12 | 1170.2.a.d.1.1 | 1 | |||
52.15 | even | 12 | 1040.2.a.b.1.1 | 1 | |||
65.2 | even | 12 | 650.2.b.g.599.2 | 2 | |||
65.24 | odd | 12 | 8450.2.a.n.1.1 | 1 | |||
65.28 | even | 12 | 650.2.b.g.599.1 | 2 | |||
65.54 | odd | 12 | 650.2.a.c.1.1 | 1 | |||
91.41 | even | 12 | 6370.2.a.l.1.1 | 1 | |||
104.67 | even | 12 | 4160.2.a.t.1.1 | 1 | |||
104.93 | odd | 12 | 4160.2.a.c.1.1 | 1 | |||
156.119 | odd | 12 | 9360.2.a.by.1.1 | 1 | |||
195.2 | odd | 12 | 5850.2.e.u.5149.1 | 2 | |||
195.119 | even | 12 | 5850.2.a.cb.1.1 | 1 | |||
195.158 | odd | 12 | 5850.2.e.u.5149.2 | 2 | |||
260.119 | even | 12 | 5200.2.a.bd.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.a.c.1.1 | ✓ | 1 | 13.2 | odd | 12 | ||
650.2.a.c.1.1 | 1 | 65.54 | odd | 12 | |||
650.2.b.g.599.1 | 2 | 65.28 | even | 12 | |||
650.2.b.g.599.2 | 2 | 65.2 | even | 12 | |||
1040.2.a.b.1.1 | 1 | 52.15 | even | 12 | |||
1170.2.a.d.1.1 | 1 | 39.2 | even | 12 | |||
1690.2.a.e.1.1 | 1 | 13.11 | odd | 12 | |||
1690.2.d.e.1351.1 | 2 | 13.10 | even | 6 | |||
1690.2.d.e.1351.2 | 2 | 13.3 | even | 3 | |||
1690.2.e.a.191.1 | 2 | 13.6 | odd | 12 | |||
1690.2.e.a.991.1 | 2 | 13.5 | odd | 4 | |||
1690.2.e.g.191.1 | 2 | 13.7 | odd | 12 | |||
1690.2.e.g.991.1 | 2 | 13.8 | odd | 4 | |||
1690.2.l.a.361.1 | 4 | 13.12 | even | 2 | inner | ||
1690.2.l.a.361.2 | 4 | 1.1 | even | 1 | trivial | ||
1690.2.l.a.1161.1 | 4 | 13.9 | even | 3 | inner | ||
1690.2.l.a.1161.2 | 4 | 13.4 | even | 6 | inner | ||
4160.2.a.c.1.1 | 1 | 104.93 | odd | 12 | |||
4160.2.a.t.1.1 | 1 | 104.67 | even | 12 | |||
5200.2.a.bd.1.1 | 1 | 260.119 | even | 12 | |||
5850.2.a.cb.1.1 | 1 | 195.119 | even | 12 | |||
5850.2.e.u.5149.1 | 2 | 195.2 | odd | 12 | |||
5850.2.e.u.5149.2 | 2 | 195.158 | odd | 12 | |||
6370.2.a.l.1.1 | 1 | 91.41 | even | 12 | |||
8450.2.a.n.1.1 | 1 | 65.24 | odd | 12 | |||
9360.2.a.by.1.1 | 1 | 156.119 | odd | 12 |