Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(149,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("350.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.j (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: | \(2.79476407074\) |
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 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 249.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.249 |
Dual form | 350.2.j.f.149.1 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 | ||||
\(3\) | −2.59808 | − | 1.50000i | −1.50000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.00000 | 1.22474 | ||||||||
\(7\) | 2.59808 | − | 0.500000i | 0.981981 | − | 0.188982i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 3.00000 | + | 5.19615i | 1.00000 | + | 1.73205i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | −2.59808 | + | 1.50000i | −0.750000 | + | 0.433013i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | −2.00000 | + | 1.73205i | −0.534522 | + | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.46410 | − | 2.00000i | −0.840168 | − | 0.485071i | 0.0171533 | − | 0.999853i | \(-0.494540\pi\) |
−0.857321 | + | 0.514782i | \(0.827873\pi\) | |||||||
\(18\) | −5.19615 | − | 3.00000i | −1.22474 | − | 0.707107i | ||||
\(19\) | −3.00000 | − | 5.19615i | −0.688247 | − | 1.19208i | −0.972404 | − | 0.233301i | \(-0.925047\pi\) |
0.284157 | − | 0.958778i | \(-0.408286\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.50000 | − | 2.59808i | −1.63663 | − | 0.566947i | ||||
\(22\) | 2.00000i | 0.426401i | ||||||||
\(23\) | 2.59808 | − | 1.50000i | 0.541736 | − | 0.312772i | −0.204046 | − | 0.978961i | \(-0.565409\pi\) |
0.745782 | + | 0.666190i | \(0.232076\pi\) | |||||||
\(24\) | 1.50000 | − | 2.59808i | 0.306186 | − | 0.530330i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 9.00000i | − | 1.73205i | ||||||
\(28\) | 0.866025 | − | 2.50000i | 0.163663 | − | 0.472456i | ||||
\(29\) | −9.00000 | −1.67126 | −0.835629 | − | 0.549294i | \(-0.814897\pi\) | ||||
−0.835629 | + | 0.549294i | \(0.814897\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | − | 3.46410i | 0.359211 | − | 0.622171i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.987829 | + | 0.155543i | \(0.0497126\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −5.19615 | + | 3.00000i | −0.904534 | + | 0.522233i | ||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | 3.46410 | − | 2.00000i | 0.569495 | − | 0.328798i | −0.187453 | − | 0.982274i | \(-0.560023\pi\) |
0.756948 | + | 0.653476i | \(0.226690\pi\) | |||||||
\(38\) | 5.19615 | + | 3.00000i | 0.842927 | + | 0.486664i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.00000 | −1.09322 | −0.546608 | − | 0.837389i | \(-0.684081\pi\) | ||||
−0.546608 | + | 0.837389i | \(0.684081\pi\) | |||||||
\(42\) | 7.79423 | − | 1.50000i | 1.20268 | − | 0.231455i | ||||
\(43\) | − | 5.00000i | − | 0.762493i | −0.924473 | − | 0.381246i | \(-0.875495\pi\) | ||
0.924473 | − | 0.381246i | \(-0.124505\pi\) | |||||||
\(44\) | −1.00000 | − | 1.73205i | −0.150756 | − | 0.261116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.50000 | + | 2.59808i | −0.221163 | + | 0.383065i | ||||
\(47\) | −6.92820 | + | 4.00000i | −1.01058 | + | 0.583460i | −0.911362 | − | 0.411606i | \(-0.864968\pi\) |
−0.0992202 | + | 0.995066i | \(0.531635\pi\) | |||||||
\(48\) | 3.00000i | 0.433013i | ||||||||
\(49\) | 6.50000 | − | 2.59808i | 0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.00000 | + | 10.3923i | 0.840168 | + | 1.45521i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.73205 | + | 1.00000i | 0.237915 | + | 0.137361i | 0.614218 | − | 0.789136i | \(-0.289471\pi\) |
−0.376303 | + | 0.926497i | \(0.622805\pi\) | |||||||
\(54\) | 4.50000 | + | 7.79423i | 0.612372 | + | 1.06066i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.500000 | + | 2.59808i | 0.0668153 | + | 0.347183i | ||||
\(57\) | 18.0000i | 2.38416i | ||||||||
\(58\) | 7.79423 | − | 4.50000i | 1.02343 | − | 0.590879i | ||||
\(59\) | 5.00000 | − | 8.66025i | 0.650945 | − | 1.12747i | −0.331949 | − | 0.943297i | \(-0.607706\pi\) |
0.982894 | − | 0.184172i | \(-0.0589603\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.500000 | − | 0.866025i | −0.0640184 | − | 0.110883i | 0.832240 | − | 0.554416i | \(-0.187058\pi\) |
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 4.00000i | 0.508001i | ||||||||
\(63\) | 10.3923 | + | 12.0000i | 1.30931 | + | 1.51186i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.00000 | − | 5.19615i | 0.369274 | − | 0.639602i | ||||
\(67\) | −7.79423 | − | 4.50000i | −0.952217 | − | 0.549762i | −0.0584478 | − | 0.998290i | \(-0.518615\pi\) |
−0.893769 | + | 0.448528i | \(0.851948\pi\) | |||||||
\(68\) | −3.46410 | + | 2.00000i | −0.420084 | + | 0.242536i | ||||
\(69\) | −9.00000 | −1.08347 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | −5.19615 | + | 3.00000i | −0.612372 | + | 0.353553i | ||||
\(73\) | 3.46410 | + | 2.00000i | 0.405442 | + | 0.234082i | 0.688830 | − | 0.724923i | \(-0.258125\pi\) |
−0.283387 | + | 0.959006i | \(0.591458\pi\) | |||||||
\(74\) | −2.00000 | + | 3.46410i | −0.232495 | + | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.00000 | −0.688247 | ||||||||
\(77\) | 1.73205 | − | 5.00000i | 0.197386 | − | 0.569803i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.00000 | + | 8.66025i | 0.562544 | + | 0.974355i | 0.997274 | + | 0.0737937i | \(0.0235106\pi\) |
−0.434730 | + | 0.900561i | \(0.643156\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 6.06218 | − | 3.50000i | 0.669456 | − | 0.386510i | ||||
\(83\) | − | 7.00000i | − | 0.768350i | −0.923260 | − | 0.384175i | \(-0.874486\pi\) | ||
0.923260 | − | 0.384175i | \(-0.125514\pi\) | |||||||
\(84\) | −6.00000 | + | 5.19615i | −0.654654 | + | 0.566947i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.50000 | + | 4.33013i | 0.269582 | + | 0.466930i | ||||
\(87\) | 23.3827 | + | 13.5000i | 2.50689 | + | 1.44735i | ||||
\(88\) | 1.73205 | + | 1.00000i | 0.184637 | + | 0.106600i | ||||
\(89\) | 0.500000 | + | 0.866025i | 0.0529999 | + | 0.0917985i | 0.891308 | − | 0.453398i | \(-0.149788\pi\) |
−0.838308 | + | 0.545197i | \(0.816455\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 3.00000i | − | 0.312772i | ||||||
\(93\) | −10.3923 | + | 6.00000i | −1.07763 | + | 0.622171i | ||||
\(94\) | 4.00000 | − | 6.92820i | 0.412568 | − | 0.714590i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.50000 | − | 2.59808i | −0.153093 | − | 0.265165i | ||||
\(97\) | − | 14.0000i | − | 1.42148i | −0.703452 | − | 0.710742i | \(-0.748359\pi\) | ||
0.703452 | − | 0.710742i | \(-0.251641\pi\) | |||||||
\(98\) | −4.33013 | + | 5.50000i | −0.437409 | + | 0.555584i | ||||
\(99\) | 12.0000 | 1.20605 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.50000 | + | 2.59808i | −0.149256 | + | 0.258518i | −0.930953 | − | 0.365140i | \(-0.881021\pi\) |
0.781697 | + | 0.623658i | \(0.214354\pi\) | |||||||
\(102\) | −10.3923 | − | 6.00000i | −1.02899 | − | 0.594089i | ||||
\(103\) | 0.866025 | − | 0.500000i | 0.0853320 | − | 0.0492665i | −0.456727 | − | 0.889607i | \(-0.650978\pi\) |
0.542059 | + | 0.840341i | \(0.317645\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | −2.59808 | + | 1.50000i | −0.251166 | + | 0.145010i | −0.620298 | − | 0.784366i | \(-0.712988\pi\) |
0.369132 | + | 0.929377i | \(0.379655\pi\) | |||||||
\(108\) | −7.79423 | − | 4.50000i | −0.750000 | − | 0.433013i | ||||
\(109\) | −4.50000 | + | 7.79423i | −0.431022 | + | 0.746552i | −0.996962 | − | 0.0778949i | \(-0.975180\pi\) |
0.565940 | + | 0.824447i | \(0.308513\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.0000 | −1.13899 | ||||||||
\(112\) | −1.73205 | − | 2.00000i | −0.163663 | − | 0.188982i | ||||
\(113\) | 2.00000i | 0.188144i | 0.995565 | + | 0.0940721i | \(0.0299884\pi\) | ||||
−0.995565 | + | 0.0940721i | \(0.970012\pi\) | |||||||
\(114\) | −9.00000 | − | 15.5885i | −0.842927 | − | 1.45999i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.50000 | + | 7.79423i | −0.417815 | + | 0.723676i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.0000i | 0.920575i | ||||||||
\(119\) | −10.0000 | − | 3.46410i | −0.916698 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0.866025 | + | 0.500000i | 0.0784063 | + | 0.0452679i | ||||
\(123\) | 18.1865 | + | 10.5000i | 1.63982 | + | 0.946753i | ||||
\(124\) | −2.00000 | − | 3.46410i | −0.179605 | − | 0.311086i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −15.0000 | − | 5.19615i | −1.33631 | − | 0.462910i | ||||
\(127\) | − | 16.0000i | − | 1.41977i | −0.704317 | − | 0.709885i | \(-0.748747\pi\) | ||
0.704317 | − | 0.709885i | \(-0.251253\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −7.50000 | + | 12.9904i | −0.660338 | + | 1.14374i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | − | 6.92820i | −0.349482 | − | 0.605320i | 0.636676 | − | 0.771132i | \(-0.280309\pi\) |
−0.986157 | + | 0.165812i | \(0.946976\pi\) | |||||||
\(132\) | 6.00000i | 0.522233i | ||||||||
\(133\) | −10.3923 | − | 12.0000i | −0.901127 | − | 1.04053i | ||||
\(134\) | 9.00000 | 0.777482 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000 | − | 3.46410i | 0.171499 | − | 0.297044i | ||||
\(137\) | 10.3923 | + | 6.00000i | 0.887875 | + | 0.512615i | 0.873247 | − | 0.487278i | \(-0.162010\pi\) |
0.0146279 | + | 0.999893i | \(0.495344\pi\) | |||||||
\(138\) | 7.79423 | − | 4.50000i | 0.663489 | − | 0.383065i | ||||
\(139\) | 14.0000 | 1.18746 | 0.593732 | − | 0.804663i | \(-0.297654\pi\) | ||||
0.593732 | + | 0.804663i | \(0.297654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.0000 | 2.02116 | ||||||||
\(142\) | −1.73205 | + | 1.00000i | −0.145350 | + | 0.0839181i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000 | − | 5.19615i | 0.250000 | − | 0.433013i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | −20.7846 | − | 3.00000i | −1.71429 | − | 0.247436i | ||||
\(148\) | − | 4.00000i | − | 0.328798i | ||||||
\(149\) | 1.50000 | + | 2.59808i | 0.122885 | + | 0.212843i | 0.920904 | − | 0.389789i | \(-0.127452\pi\) |
−0.798019 | + | 0.602632i | \(0.794119\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | − | 13.8564i | 0.651031 | − | 1.12762i | −0.331842 | − | 0.943335i | \(-0.607670\pi\) |
0.982873 | − | 0.184284i | \(-0.0589965\pi\) | |||||||
\(152\) | 5.19615 | − | 3.00000i | 0.421464 | − | 0.243332i | ||||
\(153\) | − | 24.0000i | − | 1.94029i | ||||||
\(154\) | 1.00000 | + | 5.19615i | 0.0805823 | + | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.66025 | + | 5.00000i | 0.691164 | + | 0.399043i | 0.804048 | − | 0.594565i | \(-0.202676\pi\) |
−0.112884 | + | 0.993608i | \(0.536009\pi\) | |||||||
\(158\) | −8.66025 | − | 5.00000i | −0.688973 | − | 0.397779i | ||||
\(159\) | −3.00000 | − | 5.19615i | −0.237915 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | − | 5.19615i | 0.472866 | − | 0.409514i | ||||
\(162\) | − | 9.00000i | − | 0.707107i | ||||||
\(163\) | −3.46410 | + | 2.00000i | −0.271329 | + | 0.156652i | −0.629492 | − | 0.777007i | \(-0.716737\pi\) |
0.358162 | + | 0.933659i | \(0.383403\pi\) | |||||||
\(164\) | −3.50000 | + | 6.06218i | −0.273304 | + | 0.473377i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.50000 | + | 6.06218i | 0.271653 | + | 0.470516i | ||||
\(167\) | 21.0000i | 1.62503i | 0.582941 | + | 0.812514i | \(0.301902\pi\) | ||||
−0.582941 | + | 0.812514i | \(0.698098\pi\) | |||||||
\(168\) | 2.59808 | − | 7.50000i | 0.200446 | − | 0.578638i | ||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.0000 | − | 31.1769i | 1.37649 | − | 2.38416i | ||||
\(172\) | −4.33013 | − | 2.50000i | −0.330169 | − | 0.190623i | ||||
\(173\) | 6.92820 | − | 4.00000i | 0.526742 | − | 0.304114i | −0.212947 | − | 0.977064i | \(-0.568306\pi\) |
0.739689 | + | 0.672949i | \(0.234973\pi\) | |||||||
\(174\) | −27.0000 | −2.04686 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.00000 | −0.150756 | ||||||||
\(177\) | −25.9808 | + | 15.0000i | −1.95283 | + | 1.12747i | ||||
\(178\) | −0.866025 | − | 0.500000i | −0.0649113 | − | 0.0374766i | ||||
\(179\) | 6.00000 | − | 10.3923i | 0.448461 | − | 0.776757i | −0.549825 | − | 0.835280i | \(-0.685306\pi\) |
0.998286 | + | 0.0585225i | \(0.0186389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.00000 | 0.520306 | 0.260153 | − | 0.965567i | \(-0.416227\pi\) | ||||
0.260153 | + | 0.965567i | \(0.416227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.00000i | 0.221766i | ||||||||
\(184\) | 1.50000 | + | 2.59808i | 0.110581 | + | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.00000 | − | 10.3923i | 0.439941 | − | 0.762001i | ||||
\(187\) | −6.92820 | + | 4.00000i | −0.506640 | + | 0.292509i | ||||
\(188\) | 8.00000i | 0.583460i | ||||||||
\(189\) | −4.50000 | − | 23.3827i | −0.327327 | − | 1.70084i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | 2.59808 | + | 1.50000i | 0.187500 | + | 0.108253i | ||||
\(193\) | −22.5167 | − | 13.0000i | −1.62078 | − | 0.935760i | −0.986710 | − | 0.162488i | \(-0.948048\pi\) |
−0.634074 | − | 0.773272i | \(-0.718619\pi\) | |||||||
\(194\) | 7.00000 | + | 12.1244i | 0.502571 | + | 0.870478i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | − | 6.92820i | 0.0714286 | − | 0.494872i | ||||
\(197\) | − | 2.00000i | − | 0.142494i | −0.997459 | − | 0.0712470i | \(-0.977302\pi\) | ||
0.997459 | − | 0.0712470i | \(-0.0226979\pi\) | |||||||
\(198\) | −10.3923 | + | 6.00000i | −0.738549 | + | 0.426401i | ||||
\(199\) | −2.00000 | + | 3.46410i | −0.141776 | + | 0.245564i | −0.928166 | − | 0.372168i | \(-0.878615\pi\) |
0.786389 | + | 0.617731i | \(0.211948\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.5000 | + | 23.3827i | 0.952217 | + | 1.64929i | ||||
\(202\) | − | 3.00000i | − | 0.211079i | ||||||
\(203\) | −23.3827 | + | 4.50000i | −1.64114 | + | 0.315838i | ||||
\(204\) | 12.0000 | 0.840168 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.500000 | + | 0.866025i | −0.0348367 | + | 0.0603388i | ||||
\(207\) | 15.5885 | + | 9.00000i | 1.08347 | + | 0.625543i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.0000 | −1.78991 | −0.894957 | − | 0.446153i | \(-0.852794\pi\) | ||||
−0.894957 | + | 0.446153i | \(0.852794\pi\) | |||||||
\(212\) | 1.73205 | − | 1.00000i | 0.118958 | − | 0.0686803i | ||||
\(213\) | −5.19615 | − | 3.00000i | −0.356034 | − | 0.205557i | ||||
\(214\) | 1.50000 | − | 2.59808i | 0.102538 | − | 0.177601i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.00000 | 0.612372 | ||||||||
\(217\) | 3.46410 | − | 10.0000i | 0.235159 | − | 0.678844i | ||||
\(218\) | − | 9.00000i | − | 0.609557i | ||||||
\(219\) | −6.00000 | − | 10.3923i | −0.405442 | − | 0.702247i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 10.3923 | − | 6.00000i | 0.697486 | − | 0.402694i | ||||
\(223\) | 28.0000i | 1.87502i | 0.347960 | + | 0.937509i | \(0.386874\pi\) | ||||
−0.347960 | + | 0.937509i | \(0.613126\pi\) | |||||||
\(224\) | 2.50000 | + | 0.866025i | 0.167038 | + | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.00000 | − | 1.73205i | −0.0665190 | − | 0.115214i | ||||
\(227\) | −3.46410 | − | 2.00000i | −0.229920 | − | 0.132745i | 0.380615 | − | 0.924734i | \(-0.375712\pi\) |
−0.610535 | + | 0.791989i | \(0.709046\pi\) | |||||||
\(228\) | 15.5885 | + | 9.00000i | 1.03237 | + | 0.596040i | ||||
\(229\) | 11.0000 | + | 19.0526i | 0.726900 | + | 1.25903i | 0.958187 | + | 0.286143i | \(0.0923732\pi\) |
−0.231287 | + | 0.972886i | \(0.574293\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.0000 | + | 10.3923i | −0.789542 | + | 0.683763i | ||||
\(232\) | − | 9.00000i | − | 0.590879i | ||||||
\(233\) | 20.7846 | − | 12.0000i | 1.36165 | − | 0.786146i | 0.371802 | − | 0.928312i | \(-0.378740\pi\) |
0.989843 | + | 0.142166i | \(0.0454066\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.00000 | − | 8.66025i | −0.325472 | − | 0.563735i | ||||
\(237\) | − | 30.0000i | − | 1.94871i | ||||||
\(238\) | 10.3923 | − | 2.00000i | 0.673633 | − | 0.129641i | ||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00000 | + | 8.66025i | −0.322078 | + | 0.557856i | −0.980917 | − | 0.194429i | \(-0.937715\pi\) |
0.658838 | + | 0.752285i | \(0.271048\pi\) | |||||||
\(242\) | −6.06218 | − | 3.50000i | −0.389692 | − | 0.224989i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −21.0000 | −1.33891 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.46410 | + | 2.00000i | 0.219971 | + | 0.127000i | ||||
\(249\) | −10.5000 | + | 18.1865i | −0.665410 | + | 1.15252i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 15.5885 | − | 3.00000i | 0.981981 | − | 0.188982i | ||||
\(253\) | − | 6.00000i | − | 0.377217i | ||||||
\(254\) | 8.00000 | + | 13.8564i | 0.501965 | + | 0.869428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −6.92820 | + | 4.00000i | −0.432169 | + | 0.249513i | −0.700270 | − | 0.713878i | \(-0.746937\pi\) |
0.268101 | + | 0.963391i | \(0.413604\pi\) | |||||||
\(258\) | − | 15.0000i | − | 0.933859i | ||||||
\(259\) | 8.00000 | − | 6.92820i | 0.497096 | − | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.0000 | − | 46.7654i | −1.67126 | − | 2.89470i | ||||
\(262\) | 6.92820 | + | 4.00000i | 0.428026 | + | 0.247121i | ||||
\(263\) | −4.33013 | − | 2.50000i | −0.267007 | − | 0.154157i | 0.360520 | − | 0.932752i | \(-0.382599\pi\) |
−0.627527 | + | 0.778595i | \(0.715933\pi\) | |||||||
\(264\) | −3.00000 | − | 5.19615i | −0.184637 | − | 0.319801i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.0000 | + | 5.19615i | 0.919709 | + | 0.318597i | ||||
\(267\) | − | 3.00000i | − | 0.183597i | ||||||
\(268\) | −7.79423 | + | 4.50000i | −0.476108 | + | 0.274881i | ||||
\(269\) | 1.50000 | − | 2.59808i | 0.0914566 | − | 0.158408i | −0.816668 | − | 0.577108i | \(-0.804181\pi\) |
0.908124 | + | 0.418701i | \(0.137514\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.00000 | + | 5.19615i | 0.182237 | + | 0.315644i | 0.942642 | − | 0.333805i | \(-0.108333\pi\) |
−0.760405 | + | 0.649449i | \(0.775000\pi\) | |||||||
\(272\) | 4.00000i | 0.242536i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.50000 | + | 7.79423i | −0.270868 | + | 0.469157i | ||||
\(277\) | 10.3923 | + | 6.00000i | 0.624413 | + | 0.360505i | 0.778585 | − | 0.627539i | \(-0.215938\pi\) |
−0.154172 | + | 0.988044i | \(0.549271\pi\) | |||||||
\(278\) | −12.1244 | + | 7.00000i | −0.727171 | + | 0.419832i | ||||
\(279\) | 24.0000 | 1.43684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000 | 0.119310 | 0.0596550 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596550 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(282\) | −20.7846 | + | 12.0000i | −1.23771 | + | 0.714590i | ||||
\(283\) | 3.46410 | + | 2.00000i | 0.205919 | + | 0.118888i | 0.599414 | − | 0.800439i | \(-0.295400\pi\) |
−0.393494 | + | 0.919327i | \(0.628734\pi\) | |||||||
\(284\) | 1.00000 | − | 1.73205i | 0.0593391 | − | 0.102778i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.1865 | + | 3.50000i | −1.07352 | + | 0.206598i | ||||
\(288\) | 6.00000i | 0.353553i | ||||||||
\(289\) | −0.500000 | − | 0.866025i | −0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.0000 | + | 36.3731i | −1.23104 | + | 2.13223i | ||||
\(292\) | 3.46410 | − | 2.00000i | 0.202721 | − | 0.117041i | ||||
\(293\) | 28.0000i | 1.63578i | 0.575376 | + | 0.817889i | \(0.304856\pi\) | ||||
−0.575376 | + | 0.817889i | \(0.695144\pi\) | |||||||
\(294\) | 19.5000 | − | 7.79423i | 1.13726 | − | 0.454569i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.00000 | + | 3.46410i | 0.116248 | + | 0.201347i | ||||
\(297\) | −15.5885 | − | 9.00000i | −0.904534 | − | 0.522233i | ||||
\(298\) | −2.59808 | − | 1.50000i | −0.150503 | − | 0.0868927i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.50000 | − | 12.9904i | −0.144098 | − | 0.748753i | ||||
\(302\) | 16.0000i | 0.920697i | ||||||||
\(303\) | 7.79423 | − | 4.50000i | 0.447767 | − | 0.258518i | ||||
\(304\) | −3.00000 | + | 5.19615i | −0.172062 | + | 0.298020i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 12.0000 | + | 20.7846i | 0.685994 | + | 1.18818i | ||||
\(307\) | − | 7.00000i | − | 0.399511i | −0.979846 | − | 0.199756i | \(-0.935985\pi\) | ||
0.979846 | − | 0.199756i | \(-0.0640148\pi\) | |||||||
\(308\) | −3.46410 | − | 4.00000i | −0.197386 | − | 0.227921i | ||||
\(309\) | −3.00000 | −0.170664 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.00000 | − | 15.5885i | 0.510343 | − | 0.883940i | −0.489585 | − | 0.871956i | \(-0.662852\pi\) |
0.999928 | − | 0.0119847i | \(-0.00381495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.92820 | − | 4.00000i | 0.391605 | − | 0.226093i | −0.291250 | − | 0.956647i | \(-0.594071\pi\) |
0.682855 | + | 0.730554i | \(0.260738\pi\) | |||||||
\(314\) | −10.0000 | −0.564333 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | 27.7128 | − | 16.0000i | 1.55651 | − | 0.898650i | 0.558920 | − | 0.829222i | \(-0.311216\pi\) |
0.997587 | − | 0.0694277i | \(-0.0221173\pi\) | |||||||
\(318\) | 5.19615 | + | 3.00000i | 0.291386 | + | 0.168232i | ||||
\(319\) | −9.00000 | + | 15.5885i | −0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.00000 | 0.502331 | ||||||||
\(322\) | −2.59808 | + | 7.50000i | −0.144785 | + | 0.417959i | ||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | 4.50000 | + | 7.79423i | 0.250000 | + | 0.433013i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.00000 | − | 3.46410i | 0.110770 | − | 0.191859i | ||||
\(327\) | 23.3827 | − | 13.5000i | 1.29307 | − | 0.746552i | ||||
\(328\) | − | 7.00000i | − | 0.386510i | ||||||
\(329\) | −16.0000 | + | 13.8564i | −0.882109 | + | 0.763928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.0000 | + | 27.7128i | 0.879440 | + | 1.52323i | 0.851957 | + | 0.523612i | \(0.175416\pi\) |
0.0274825 | + | 0.999622i | \(0.491251\pi\) | |||||||
\(332\) | −6.06218 | − | 3.50000i | −0.332705 | − | 0.192087i | ||||
\(333\) | 20.7846 | + | 12.0000i | 1.13899 | + | 0.657596i | ||||
\(334\) | −10.5000 | − | 18.1865i | −0.574534 | − | 0.995123i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.50000 | + | 7.79423i | 0.0818317 | + | 0.425210i | ||||
\(337\) | 26.0000i | 1.41631i | 0.706057 | + | 0.708155i | \(0.250472\pi\) | ||||
−0.706057 | + | 0.708155i | \(0.749528\pi\) | |||||||
\(338\) | −11.2583 | + | 6.50000i | −0.612372 | + | 0.353553i | ||||
\(339\) | 3.00000 | − | 5.19615i | 0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.00000 | − | 6.92820i | −0.216612 | − | 0.375183i | ||||
\(342\) | 36.0000i | 1.94666i | ||||||||
\(343\) | 15.5885 | − | 10.0000i | 0.841698 | − | 0.539949i | ||||
\(344\) | 5.00000 | 0.269582 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.00000 | + | 6.92820i | −0.215041 | + | 0.372463i | ||||
\(347\) | 16.4545 | + | 9.50000i | 0.883323 | + | 0.509987i | 0.871753 | − | 0.489946i | \(-0.162984\pi\) |
0.0115703 | + | 0.999933i | \(0.496317\pi\) | |||||||
\(348\) | 23.3827 | − | 13.5000i | 1.25344 | − | 0.723676i | ||||
\(349\) | 35.0000 | 1.87351 | 0.936754 | − | 0.349990i | \(-0.113815\pi\) | ||||
0.936754 | + | 0.349990i | \(0.113815\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.73205 | − | 1.00000i | 0.0923186 | − | 0.0533002i | ||||
\(353\) | 15.5885 | + | 9.00000i | 0.829690 | + | 0.479022i | 0.853746 | − | 0.520689i | \(-0.174325\pi\) |
−0.0240566 | + | 0.999711i | \(0.507658\pi\) | |||||||
\(354\) | 15.0000 | − | 25.9808i | 0.797241 | − | 1.38086i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.00000 | 0.0529999 | ||||||||
\(357\) | 20.7846 | + | 24.0000i | 1.10004 | + | 1.27021i | ||||
\(358\) | 12.0000i | 0.634220i | ||||||||
\(359\) | −2.00000 | − | 3.46410i | −0.105556 | − | 0.182828i | 0.808409 | − | 0.588621i | \(-0.200329\pi\) |
−0.913965 | + | 0.405793i | \(0.866996\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | −6.06218 | + | 3.50000i | −0.318621 | + | 0.183956i | ||||
\(363\) | − | 21.0000i | − | 1.10221i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.50000 | − | 2.59808i | −0.0784063 | − | 0.135804i | ||||
\(367\) | −9.52628 | − | 5.50000i | −0.497268 | − | 0.287098i | 0.230317 | − | 0.973116i | \(-0.426024\pi\) |
−0.727585 | + | 0.686018i | \(0.759357\pi\) | |||||||
\(368\) | −2.59808 | − | 1.50000i | −0.135434 | − | 0.0781929i | ||||
\(369\) | −21.0000 | − | 36.3731i | −1.09322 | − | 1.89351i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.00000 | + | 1.73205i | 0.259587 | + | 0.0899236i | ||||
\(372\) | 12.0000i | 0.622171i | ||||||||
\(373\) | −3.46410 | + | 2.00000i | −0.179364 | + | 0.103556i | −0.586994 | − | 0.809591i | \(-0.699689\pi\) |
0.407630 | + | 0.913147i | \(0.366355\pi\) | |||||||
\(374\) | 4.00000 | − | 6.92820i | 0.206835 | − | 0.358249i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.00000 | − | 6.92820i | −0.206284 | − | 0.357295i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 15.5885 | + | 18.0000i | 0.801784 | + | 0.925820i | ||||
\(379\) | −30.0000 | −1.54100 | −0.770498 | − | 0.637442i | \(-0.779993\pi\) | ||||
−0.770498 | + | 0.637442i | \(0.779993\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.0000 | + | 41.5692i | −1.22956 | + | 2.12966i | ||||
\(382\) | −15.5885 | − | 9.00000i | −0.797575 | − | 0.460480i | ||||
\(383\) | 12.9904 | − | 7.50000i | 0.663777 | − | 0.383232i | −0.129937 | − | 0.991522i | \(-0.541478\pi\) |
0.793715 | + | 0.608290i | \(0.208144\pi\) | |||||||
\(384\) | −3.00000 | −0.153093 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.0000 | 1.32337 | ||||||||
\(387\) | 25.9808 | − | 15.0000i | 1.32068 | − | 0.762493i | ||||
\(388\) | −12.1244 | − | 7.00000i | −0.615521 | − | 0.355371i | ||||
\(389\) | 13.0000 | − | 22.5167i | 0.659126 | − | 1.14164i | −0.321716 | − | 0.946836i | \(-0.604260\pi\) |
0.980842 | − | 0.194804i | \(-0.0624070\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0000 | −0.606866 | ||||||||
\(392\) | 2.59808 | + | 6.50000i | 0.131223 | + | 0.328300i | ||||
\(393\) | 24.0000i | 1.21064i | ||||||||
\(394\) | 1.00000 | + | 1.73205i | 0.0503793 | + | 0.0872595i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.00000 | − | 10.3923i | 0.301511 | − | 0.522233i | ||||
\(397\) | −19.0526 | + | 11.0000i | −0.956221 | + | 0.552074i | −0.895008 | − | 0.446051i | \(-0.852830\pi\) |
−0.0612128 | + | 0.998125i | \(0.519497\pi\) | |||||||
\(398\) | − | 4.00000i | − | 0.200502i | ||||||
\(399\) | 9.00000 | + | 46.7654i | 0.450564 | + | 2.34120i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.5000 | − | 26.8468i | −0.774033 | − | 1.34066i | −0.935336 | − | 0.353760i | \(-0.884903\pi\) |
0.161303 | − | 0.986905i | \(-0.448430\pi\) | |||||||
\(402\) | −23.3827 | − | 13.5000i | −1.16622 | − | 0.673319i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.50000 | + | 2.59808i | 0.0746278 | + | 0.129259i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.0000 | − | 15.5885i | 0.893325 | − | 0.773642i | ||||
\(407\) | − | 8.00000i | − | 0.396545i | ||||||
\(408\) | −10.3923 | + | 6.00000i | −0.514496 | + | 0.297044i | ||||
\(409\) | 1.50000 | − | 2.59808i | 0.0741702 | − | 0.128467i | −0.826555 | − | 0.562856i | \(-0.809703\pi\) |
0.900725 | + | 0.434389i | \(0.143036\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.0000 | − | 31.1769i | −0.887875 | − | 1.53784i | ||||
\(412\) | − | 1.00000i | − | 0.0492665i | ||||||
\(413\) | 8.66025 | − | 25.0000i | 0.426143 | − | 1.23017i | ||||
\(414\) | −18.0000 | −0.884652 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −36.3731 | − | 21.0000i | −1.78120 | − | 1.02837i | ||||
\(418\) | 10.3923 | − | 6.00000i | 0.508304 | − | 0.293470i | ||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0000 | −0.926003 | −0.463002 | − | 0.886357i | \(-0.653228\pi\) | ||||
−0.463002 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(422\) | 22.5167 | − | 13.0000i | 1.09609 | − | 0.632830i | ||||
\(423\) | −41.5692 | − | 24.0000i | −2.02116 | − | 1.16692i | ||||
\(424\) | −1.00000 | + | 1.73205i | −0.0485643 | + | 0.0841158i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.00000 | 0.290701 | ||||||||
\(427\) | −1.73205 | − | 2.00000i | −0.0838198 | − | 0.0967868i | ||||
\(428\) | 3.00000i | 0.145010i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0000 | − | 25.9808i | 0.722525 | − | 1.25145i | −0.237460 | − | 0.971397i | \(-0.576315\pi\) |
0.959985 | − | 0.280052i | \(-0.0903517\pi\) | |||||||
\(432\) | −7.79423 | + | 4.50000i | −0.375000 | + | 0.216506i | ||||
\(433\) | 14.0000i | 0.672797i | 0.941720 | + | 0.336399i | \(0.109209\pi\) | ||||
−0.941720 | + | 0.336399i | \(0.890791\pi\) | |||||||
\(434\) | 2.00000 | + | 10.3923i | 0.0960031 | + | 0.498847i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.50000 | + | 7.79423i | 0.215511 | + | 0.373276i | ||||
\(437\) | −15.5885 | − | 9.00000i | −0.745697 | − | 0.430528i | ||||
\(438\) | 10.3923 | + | 6.00000i | 0.496564 | + | 0.286691i | ||||
\(439\) | −10.0000 | − | 17.3205i | −0.477274 | − | 0.826663i | 0.522387 | − | 0.852709i | \(-0.325042\pi\) |
−0.999661 | + | 0.0260459i | \(0.991708\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 33.0000 | + | 25.9808i | 1.57143 | + | 1.23718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.8468 | − | 15.5000i | 1.27553 | − | 0.736427i | 0.299506 | − | 0.954094i | \(-0.403178\pi\) |
0.976023 | + | 0.217667i | \(0.0698447\pi\) | |||||||
\(444\) | −6.00000 | + | 10.3923i | −0.284747 | + | 0.493197i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.0000 | − | 24.2487i | −0.662919 | − | 1.14821i | ||||
\(447\) | − | 9.00000i | − | 0.425685i | ||||||
\(448\) | −2.59808 | + | 0.500000i | −0.122748 | + | 0.0236228i | ||||
\(449\) | 33.0000 | 1.55737 | 0.778683 | − | 0.627417i | \(-0.215888\pi\) | ||||
0.778683 | + | 0.627417i | \(0.215888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.00000 | + | 12.1244i | −0.329617 | + | 0.570914i | ||||
\(452\) | 1.73205 | + | 1.00000i | 0.0814688 | + | 0.0470360i | ||||
\(453\) | −41.5692 | + | 24.0000i | −1.95309 | + | 1.12762i | ||||
\(454\) | 4.00000 | 0.187729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.0000 | −0.842927 | ||||||||
\(457\) | 27.7128 | − | 16.0000i | 1.29635 | − | 0.748448i | 0.316579 | − | 0.948566i | \(-0.397466\pi\) |
0.979772 | + | 0.200118i | \(0.0641325\pi\) | |||||||
\(458\) | −19.0526 | − | 11.0000i | −0.890268 | − | 0.513996i | ||||
\(459\) | −18.0000 | + | 31.1769i | −0.840168 | + | 1.45521i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 5.19615 | − | 15.0000i | 0.241747 | − | 0.697863i | ||||
\(463\) | − | 19.0000i | − | 0.883005i | −0.897260 | − | 0.441502i | \(-0.854446\pi\) | ||
0.897260 | − | 0.441502i | \(-0.145554\pi\) | |||||||
\(464\) | 4.50000 | + | 7.79423i | 0.208907 | + | 0.361838i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.0000 | + | 20.7846i | −0.555889 | + | 0.962828i | ||||
\(467\) | 11.2583 | − | 6.50000i | 0.520973 | − | 0.300784i | −0.216359 | − | 0.976314i | \(-0.569418\pi\) |
0.737333 | + | 0.675530i | \(0.236085\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.5000 | − | 7.79423i | −1.03895 | − | 0.359904i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.0000 | − | 25.9808i | −0.691164 | − | 1.19713i | ||||
\(472\) | 8.66025 | + | 5.00000i | 0.398621 | + | 0.230144i | ||||
\(473\) | −8.66025 | − | 5.00000i | −0.398199 | − | 0.229900i | ||||
\(474\) | 15.0000 | + | 25.9808i | 0.688973 | + | 1.19334i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.00000 | + | 6.92820i | −0.366679 | + | 0.317554i | ||||
\(477\) | 12.0000i | 0.549442i | ||||||||
\(478\) | 13.8564 | − | 8.00000i | 0.633777 | − | 0.365911i | ||||
\(479\) | 12.0000 | − | 20.7846i | 0.548294 | − | 0.949673i | −0.450098 | − | 0.892979i | \(-0.648611\pi\) |
0.998392 | − | 0.0566937i | \(-0.0180558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 10.0000i | − | 0.455488i | ||||||
\(483\) | −23.3827 | + | 4.50000i | −1.06395 | + | 0.204757i | ||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.8564 | − | 8.00000i | −0.627894 | − | 0.362515i | 0.152042 | − | 0.988374i | \(-0.451415\pi\) |
−0.779936 | + | 0.625859i | \(0.784748\pi\) | |||||||
\(488\) | 0.866025 | − | 0.500000i | 0.0392031 | − | 0.0226339i | ||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 18.1865 | − | 10.5000i | 0.819912 | − | 0.473377i | ||||
\(493\) | 31.1769 | + | 18.0000i | 1.40414 | + | 0.810679i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 5.19615 | − | 1.00000i | 0.233079 | − | 0.0448561i | ||||
\(498\) | − | 21.0000i | − | 0.941033i | ||||||
\(499\) | −9.00000 | − | 15.5885i | −0.402895 | − | 0.697835i | 0.591179 | − | 0.806541i | \(-0.298663\pi\) |
−0.994074 | + | 0.108705i | \(0.965329\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.5000 | − | 54.5596i | 1.40732 | − | 2.43754i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 21.0000i | − | 0.936344i | −0.883637 | − | 0.468172i | \(-0.844913\pi\) | ||
0.883637 | − | 0.468172i | \(-0.155087\pi\) | |||||||
\(504\) | −12.0000 | + | 10.3923i | −0.534522 | + | 0.462910i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.00000 | + | 5.19615i | 0.133366 | + | 0.230997i | ||||
\(507\) | −33.7750 | − | 19.5000i | −1.50000 | − | 0.866025i | ||||
\(508\) | −13.8564 | − | 8.00000i | −0.614779 | − | 0.354943i | ||||
\(509\) | 0.500000 | + | 0.866025i | 0.0221621 | + | 0.0383859i | 0.876894 | − | 0.480684i | \(-0.159612\pi\) |
−0.854732 | + | 0.519070i | \(0.826278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.0000 | + | 3.46410i | 0.442374 | + | 0.153243i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −46.7654 | + | 27.0000i | −2.06474 | + | 1.19208i | ||||
\(514\) | 4.00000 | − | 6.92820i | 0.176432 | − | 0.305590i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.50000 | + | 12.9904i | 0.330169 | + | 0.571870i | ||||
\(517\) | 16.0000i | 0.703679i | ||||||||
\(518\) | −3.46410 | + | 10.0000i | −0.152204 | + | 0.439375i | ||||
\(519\) | −24.0000 | −1.05348 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.0000 | + | 32.9090i | −0.832405 | + | 1.44177i | 0.0637207 | + | 0.997968i | \(0.479703\pi\) |
−0.896126 | + | 0.443800i | \(0.853630\pi\) | |||||||
\(522\) | 46.7654 | + | 27.0000i | 2.04686 | + | 1.18176i | ||||
\(523\) | −17.3205 | + | 10.0000i | −0.757373 | + | 0.437269i | −0.828352 | − | 0.560208i | \(-0.810721\pi\) |
0.0709788 | + | 0.997478i | \(0.477388\pi\) | |||||||
\(524\) | −8.00000 | −0.349482 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.00000 | 0.218010 | ||||||||
\(527\) | −13.8564 | + | 8.00000i | −0.603595 | + | 0.348485i | ||||
\(528\) | 5.19615 | + | 3.00000i | 0.226134 | + | 0.130558i | ||||
\(529\) | −7.00000 | + | 12.1244i | −0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 60.0000 | 2.60378 | ||||||||
\(532\) | −15.5885 | + | 3.00000i | −0.675845 | + | 0.130066i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 1.50000 | + | 2.59808i | 0.0649113 | + | 0.112430i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.50000 | − | 7.79423i | 0.194370 | − | 0.336659i | ||||
\(537\) | −31.1769 | + | 18.0000i | −1.34538 | + | 0.776757i | ||||
\(538\) | 3.00000i | 0.129339i | ||||||||
\(539\) | 2.00000 | − | 13.8564i | 0.0861461 | − | 0.596838i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.50000 | − | 2.59808i | −0.0644900 | − | 0.111700i | 0.831978 | − | 0.554809i | \(-0.187209\pi\) |
−0.896468 | + | 0.443109i | \(0.853875\pi\) | |||||||
\(542\) | −5.19615 | − | 3.00000i | −0.223194 | − | 0.128861i | ||||
\(543\) | −18.1865 | − | 10.5000i | −0.780459 | − | 0.450598i | ||||
\(544\) | −2.00000 | − | 3.46410i | −0.0857493 | − | 0.148522i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.0000i | 1.41098i | 0.708721 | + | 0.705489i | \(0.249273\pi\) | ||||
−0.708721 | + | 0.705489i | \(0.750727\pi\) | |||||||
\(548\) | 10.3923 | − | 6.00000i | 0.443937 | − | 0.256307i | ||||
\(549\) | 3.00000 | − | 5.19615i | 0.128037 | − | 0.221766i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.0000 | + | 46.7654i | 1.15024 | + | 1.99227i | ||||
\(552\) | − | 9.00000i | − | 0.383065i | ||||||
\(553\) | 17.3205 | + | 20.0000i | 0.736543 | + | 0.850487i | ||||
\(554\) | −12.0000 | −0.509831 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.00000 | − | 12.1244i | 0.296866 | − | 0.514187i | ||||
\(557\) | −1.73205 | − | 1.00000i | −0.0733893 | − | 0.0423714i | 0.462856 | − | 0.886433i | \(-0.346825\pi\) |
−0.536246 | + | 0.844062i | \(0.680158\pi\) | |||||||
\(558\) | −20.7846 | + | 12.0000i | −0.879883 | + | 0.508001i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | −1.73205 | + | 1.00000i | −0.0730622 | + | 0.0421825i | ||||
\(563\) | −14.7224 | − | 8.50000i | −0.620477 | − | 0.358232i | 0.156578 | − | 0.987666i | \(-0.449954\pi\) |
−0.777055 | + | 0.629433i | \(0.783287\pi\) | |||||||
\(564\) | 12.0000 | − | 20.7846i | 0.505291 | − | 0.875190i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | −7.79423 | + | 22.5000i | −0.327327 | + | 0.944911i | ||||
\(568\) | 2.00000i | 0.0839181i | ||||||||
\(569\) | −9.00000 | − | 15.5885i | −0.377300 | − | 0.653502i | 0.613369 | − | 0.789797i | \(-0.289814\pi\) |
−0.990668 | + | 0.136295i | \(0.956481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0000 | − | 25.9808i | 0.627730 | − | 1.08726i | −0.360276 | − | 0.932846i | \(-0.617317\pi\) |
0.988006 | − | 0.154415i | \(-0.0493493\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 54.0000i | − | 2.25588i | ||||||
\(574\) | 14.0000 | − | 12.1244i | 0.584349 | − | 0.506061i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.00000 | − | 5.19615i | −0.125000 | − | 0.216506i | ||||
\(577\) | 8.66025 | + | 5.00000i | 0.360531 | + | 0.208153i | 0.669314 | − | 0.742980i | \(-0.266588\pi\) |
−0.308783 | + | 0.951133i | \(0.599922\pi\) | |||||||
\(578\) | 0.866025 | + | 0.500000i | 0.0360219 | + | 0.0207973i | ||||
\(579\) | 39.0000 | + | 67.5500i | 1.62078 | + | 2.80728i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.50000 | − | 18.1865i | −0.145204 | − | 0.754505i | ||||
\(582\) | − | 42.0000i | − | 1.74096i | ||||||
\(583\) | 3.46410 | − | 2.00000i | 0.143468 | − | 0.0828315i | ||||
\(584\) | −2.00000 | + | 3.46410i | −0.0827606 | + | 0.143346i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.0000 | − | 24.2487i | −0.578335 | − | 1.00171i | ||||
\(587\) | 28.0000i | 1.15568i | 0.816149 | + | 0.577842i | \(0.196105\pi\) | ||||
−0.816149 | + | 0.577842i | \(0.803895\pi\) | |||||||
\(588\) | −12.9904 | + | 16.5000i | −0.535714 | + | 0.680449i | ||||
\(589\) | −24.0000 | −0.988903 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.00000 | + | 5.19615i | −0.123404 | + | 0.213741i | ||||
\(592\) | −3.46410 | − | 2.00000i | −0.142374 | − | 0.0821995i | ||||
\(593\) | −5.19615 | + | 3.00000i | −0.213380 | + | 0.123195i | −0.602881 | − | 0.797831i | \(-0.705981\pi\) |
0.389501 | + | 0.921026i | \(0.372647\pi\) | |||||||
\(594\) | 18.0000 | 0.738549 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.00000 | 0.122885 | ||||||||
\(597\) | 10.3923 | − | 6.00000i | 0.425329 | − | 0.245564i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.00000 | − | 10.3923i | 0.245153 | − | 0.424618i | −0.717021 | − | 0.697051i | \(-0.754495\pi\) |
0.962175 | + | 0.272433i | \(0.0878284\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.0000 | 1.71322 | 0.856608 | − | 0.515968i | \(-0.172568\pi\) | ||||
0.856608 | + | 0.515968i | \(0.172568\pi\) | |||||||
\(602\) | 8.66025 | + | 10.0000i | 0.352966 | + | 0.407570i | ||||
\(603\) | − | 54.0000i | − | 2.19905i | ||||||
\(604\) | −8.00000 | − | 13.8564i | −0.325515 | − | 0.563809i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.50000 | + | 7.79423i | −0.182800 | + | 0.316619i | ||||
\(607\) | −0.866025 | + | 0.500000i | −0.0351509 | + | 0.0202944i | −0.517472 | − | 0.855700i | \(-0.673127\pi\) |
0.482322 | + | 0.875994i | \(0.339794\pi\) | |||||||
\(608\) | − | 6.00000i | − | 0.243332i | ||||||
\(609\) | 67.5000 | + | 23.3827i | 2.73524 | + | 0.947514i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −20.7846 | − | 12.0000i | −0.840168 | − | 0.485071i | ||||
\(613\) | −10.3923 | − | 6.00000i | −0.419741 | − | 0.242338i | 0.275225 | − | 0.961380i | \(-0.411248\pi\) |
−0.694967 | + | 0.719042i | \(0.744581\pi\) | |||||||
\(614\) | 3.50000 | + | 6.06218i | 0.141249 | + | 0.244650i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.00000 | + | 1.73205i | 0.201456 | + | 0.0697863i | ||||
\(617\) | − | 44.0000i | − | 1.77137i | −0.464283 | − | 0.885687i | \(-0.653688\pi\) | ||
0.464283 | − | 0.885687i | \(-0.346312\pi\) | |||||||
\(618\) | 2.59808 | − | 1.50000i | 0.104510 | − | 0.0603388i | ||||
\(619\) | −23.0000 | + | 39.8372i | −0.924448 | + | 1.60119i | −0.132002 | + | 0.991250i | \(0.542140\pi\) |
−0.792446 | + | 0.609941i | \(0.791193\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.5000 | − | 23.3827i | −0.541736 | − | 0.938315i | ||||
\(622\) | 18.0000i | 0.721734i | ||||||||
\(623\) | 1.73205 | + | 2.00000i | 0.0693932 | + | 0.0801283i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.00000 | + | 6.92820i | −0.159872 | + | 0.276907i | ||||
\(627\) | 31.1769 | + | 18.0000i | 1.24509 | + | 0.718851i | ||||
\(628\) | 8.66025 | − | 5.00000i | 0.345582 | − | 0.199522i | ||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000 | 0.0796187 | 0.0398094 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398094 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(632\) | −8.66025 | + | 5.00000i | −0.344486 | + | 0.198889i | ||||
\(633\) | 67.5500 | + | 39.0000i | 2.68487 | + | 1.55011i | ||||
\(634\) | −16.0000 | + | 27.7128i | −0.635441 | + | 1.10062i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 18.0000i | − | 0.712627i | ||||||
\(639\) | 6.00000 | + | 10.3923i | 0.237356 | + | 0.411113i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.50000 | + | 4.33013i | −0.0987441 | + | 0.171030i | −0.911165 | − | 0.412042i | \(-0.864816\pi\) |
0.812421 | + | 0.583071i | \(0.198149\pi\) | |||||||
\(642\) | −7.79423 | + | 4.50000i | −0.307614 | + | 0.177601i | ||||
\(643\) | 28.0000i | 1.10421i | 0.833774 | + | 0.552106i | \(0.186176\pi\) | ||||
−0.833774 | + | 0.552106i | \(0.813824\pi\) | |||||||
\(644\) | −1.50000 | − | 7.79423i | −0.0591083 | − | 0.307136i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0000 | − | 20.7846i | −0.472134 | − | 0.817760i | ||||
\(647\) | −9.52628 | − | 5.50000i | −0.374517 | − | 0.216227i | 0.300913 | − | 0.953652i | \(-0.402709\pi\) |
−0.675430 | + | 0.737424i | \(0.736042\pi\) | |||||||
\(648\) | −7.79423 | − | 4.50000i | −0.306186 | − | 0.176777i | ||||
\(649\) | −10.0000 | − | 17.3205i | −0.392534 | − | 0.679889i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.0000 | + | 20.7846i | −0.940634 | + | 0.814613i | ||||
\(652\) | 4.00000i | 0.156652i | ||||||||
\(653\) | −3.46410 | + | 2.00000i | −0.135561 | + | 0.0782660i | −0.566247 | − | 0.824236i | \(-0.691605\pi\) |
0.430686 | + | 0.902502i | \(0.358272\pi\) | |||||||
\(654\) | −13.5000 | + | 23.3827i | −0.527892 | + | 0.914335i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.50000 | + | 6.06218i | 0.136652 | + | 0.236688i | ||||
\(657\) | 24.0000i | 0.936329i | ||||||||
\(658\) | 6.92820 | − | 20.0000i | 0.270089 | − | 0.779681i | ||||
\(659\) | 26.0000 | 1.01282 | 0.506408 | − | 0.862294i | \(-0.330973\pi\) | ||||
0.506408 | + | 0.862294i | \(0.330973\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.50000 | − | 9.52628i | 0.213925 | − | 0.370529i | −0.739014 | − | 0.673690i | \(-0.764708\pi\) |
0.952940 | + | 0.303160i | \(0.0980418\pi\) | |||||||
\(662\) | −27.7128 | − | 16.0000i | −1.07709 | − | 0.621858i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.00000 | 0.271653 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −24.0000 | −0.929981 | ||||||||
\(667\) | −23.3827 | + | 13.5000i | −0.905381 | + | 0.522722i | ||||
\(668\) | 18.1865 | + | 10.5000i | 0.703658 | + | 0.406257i | ||||
\(669\) | 42.0000 | − | 72.7461i | 1.62381 | − | 2.81253i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | −5.19615 | − | 6.00000i | −0.200446 | − | 0.231455i | ||||
\(673\) | 16.0000i | 0.616755i | 0.951264 | + | 0.308377i | \(0.0997859\pi\) | ||||
−0.951264 | + | 0.308377i | \(0.900214\pi\) | |||||||
\(674\) | −13.0000 | − | 22.5167i | −0.500741 | − | 0.867309i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.50000 | − | 11.2583i | 0.250000 | − | 0.433013i | ||||
\(677\) | 41.5692 | − | 24.0000i | 1.59763 | − | 0.922395i | 0.605693 | − | 0.795698i | \(-0.292896\pi\) |
0.991941 | − | 0.126697i | \(-0.0404375\pi\) | |||||||
\(678\) | 6.00000i | 0.230429i | ||||||||
\(679\) | −7.00000 | − | 36.3731i | −0.268635 | − | 1.39587i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | + | 10.3923i | 0.229920 | + | 0.398234i | ||||
\(682\) | 6.92820 | + | 4.00000i | 0.265295 | + | 0.153168i | ||||
\(683\) | 32.0429 | + | 18.5000i | 1.22609 | + | 0.707883i | 0.966209 | − | 0.257758i | \(-0.0829838\pi\) |
0.259880 | + | 0.965641i | \(0.416317\pi\) | |||||||
\(684\) | −18.0000 | − | 31.1769i | −0.688247 | − | 1.19208i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | + | 16.4545i | −0.324532 | + | 0.628235i | ||||
\(687\) | − | 66.0000i | − | 2.51806i | ||||||
\(688\) | −4.33013 | + | 2.50000i | −0.165085 | + | 0.0953116i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.0000 | − | 19.0526i | −0.418460 | − | 0.724793i | 0.577325 | − | 0.816514i | \(-0.304097\pi\) |
−0.995785 | + | 0.0917209i | \(0.970763\pi\) | |||||||
\(692\) | − | 8.00000i | − | 0.304114i | ||||||
\(693\) | 31.1769 | − | 6.00000i | 1.18431 | − | 0.227921i | ||||
\(694\) | −19.0000 | −0.721230 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −13.5000 | + | 23.3827i | −0.511716 | + | 0.886318i | ||||
\(697\) | 24.2487 | + | 14.0000i | 0.918485 | + | 0.530288i | ||||
\(698\) | −30.3109 | + | 17.5000i | −1.14728 | + | 0.662385i | ||||
\(699\) | −72.0000 | −2.72329 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −47.0000 | −1.77517 | −0.887583 | − | 0.460648i | \(-0.847617\pi\) | ||||
−0.887583 | + | 0.460648i | \(0.847617\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.7846 | − | 12.0000i | −0.783906 | − | 0.452589i | ||||
\(704\) | −1.00000 | + | 1.73205i | −0.0376889 | + | 0.0652791i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.0000 | −0.677439 | ||||||||
\(707\) | −2.59808 | + | 7.50000i | −0.0977107 | + | 0.282067i | ||||
\(708\) | 30.0000i | 1.12747i | ||||||||
\(709\) | −5.50000 | − | 9.52628i | −0.206557 | − | 0.357767i | 0.744071 | − | 0.668101i | \(-0.232892\pi\) |
−0.950628 | + | 0.310334i | \(0.899559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.0000 | + | 51.9615i | −1.12509 | + | 1.94871i | ||||
\(712\) | −0.866025 | + | 0.500000i | −0.0324557 | + | 0.0187383i | ||||
\(713\) | − | 12.0000i | − | 0.449404i | ||||||
\(714\) | −30.0000 | − | 10.3923i | −1.12272 | − | 0.388922i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.00000 | − | 10.3923i | −0.224231 | − | 0.388379i | ||||
\(717\) | 41.5692 | + | 24.0000i | 1.55243 | + | 0.896296i | ||||
\(718\) | 3.46410 | + | 2.00000i | 0.129279 | + | 0.0746393i | ||||
\(719\) | −3.00000 | − | 5.19615i | −0.111881 | − | 0.193784i | 0.804648 | − | 0.593753i | \(-0.202354\pi\) |
−0.916529 | + | 0.399969i | \(0.869021\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.00000 | − | 1.73205i | 0.0744839 | − | 0.0645049i | ||||
\(722\) | − | 17.0000i | − | 0.632674i | ||||||
\(723\) | 25.9808 | − | 15.0000i | 0.966235 | − | 0.557856i | ||||
\(724\) | 3.50000 | − | 6.06218i | 0.130076 | − | 0.225299i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.5000 | + | 18.1865i | 0.389692 | + | 0.674966i | ||||
\(727\) | 21.0000i | 0.778847i | 0.921059 | + | 0.389423i | \(0.127326\pi\) | ||||
−0.921059 | + | 0.389423i | \(0.872674\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.0000 | + | 17.3205i | −0.369863 | + | 0.640622i | ||||
\(732\) | 2.59808 | + | 1.50000i | 0.0960277 | + | 0.0554416i | ||||
\(733\) | 19.0526 | − | 11.0000i | 0.703722 | − | 0.406294i | −0.105010 | − | 0.994471i | \(-0.533487\pi\) |
0.808732 | + | 0.588177i | \(0.200154\pi\) | |||||||
\(734\) | 11.0000 | 0.406017 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | 0.110581 | ||||||||
\(737\) | −15.5885 | + | 9.00000i | −0.574208 | + | 0.331519i | ||||
\(738\) | 36.3731 | + | 21.0000i | 1.33891 | + | 0.773021i | ||||
\(739\) | −1.00000 | + | 1.73205i | −0.0367856 | + | 0.0637145i | −0.883832 | − | 0.467804i | \(-0.845045\pi\) |
0.847046 | + | 0.531519i | \(0.178379\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.19615 | + | 1.00000i | −0.190757 | + | 0.0367112i | ||||
\(743\) | 9.00000i | 0.330178i | 0.986279 | + | 0.165089i | \(0.0527911\pi\) | ||||
−0.986279 | + | 0.165089i | \(0.947209\pi\) | |||||||
\(744\) | −6.00000 | − | 10.3923i | −0.219971 | − | 0.381000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.00000 | − | 3.46410i | 0.0732252 | − | 0.126830i | ||||
\(747\) | 36.3731 | − | 21.0000i | 1.33082 | − | 0.768350i | ||||
\(748\) | 8.00000i | 0.292509i | ||||||||
\(749\) | −6.00000 | + | 5.19615i | −0.219235 | + | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00000 | + | 3.46410i | 0.0729810 | + | 0.126407i | 0.900207 | − | 0.435463i | \(-0.143415\pi\) |
−0.827225 | + | 0.561870i | \(0.810082\pi\) | |||||||
\(752\) | 6.92820 | + | 4.00000i | 0.252646 | + | 0.145865i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −22.5000 | − | 7.79423i | −0.818317 | − | 0.283473i | ||||
\(757\) | − | 16.0000i | − | 0.581530i | −0.956795 | − | 0.290765i | \(-0.906090\pi\) | ||
0.956795 | − | 0.290765i | \(-0.0939098\pi\) | |||||||
\(758\) | 25.9808 | − | 15.0000i | 0.943664 | − | 0.544825i | ||||
\(759\) | −9.00000 | + | 15.5885i | −0.326679 | + | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.00000 | + | 5.19615i | 0.108750 | + | 0.188360i | 0.915264 | − | 0.402854i | \(-0.131982\pi\) |
−0.806514 | + | 0.591215i | \(0.798649\pi\) | |||||||
\(762\) | − | 48.0000i | − | 1.73886i | ||||||
\(763\) | −7.79423 | + | 22.5000i | −0.282170 | + | 0.814555i | ||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.50000 | + | 12.9904i | −0.270986 | + | 0.469362i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.59808 | − | 1.50000i | 0.0937500 | − | 0.0541266i | ||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.0000 | 0.864339 | ||||||||
\(772\) | −22.5167 | + | 13.0000i | −0.810392 | + | 0.467880i | ||||
\(773\) | −20.7846 | − | 12.0000i | −0.747570 | − | 0.431610i | 0.0772449 | − | 0.997012i | \(-0.475388\pi\) |
−0.824815 | + | 0.565402i | \(0.808721\pi\) | |||||||
\(774\) | −15.0000 | + | 25.9808i | −0.539164 | + | 0.933859i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.0000 | 0.502571 | ||||||||
\(777\) | −31.1769 | + | 6.00000i | −1.11847 | + | 0.215249i | ||||
\(778\) | 26.0000i | 0.932145i | ||||||||
\(779\) | 21.0000 | + | 36.3731i | 0.752403 | + | 1.30320i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | − | 3.46410i | 0.0715656 | − | 0.123955i | ||||
\(782\) | 10.3923 | − | 6.00000i | 0.371628 | − | 0.214560i | ||||
\(783\) | 81.0000i | 2.89470i | ||||||||
\(784\) | −5.50000 | − | 4.33013i | −0.196429 | − | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −12.0000 | − | 20.7846i | −0.428026 | − | 0.741362i | ||||
\(787\) | 26.8468 | + | 15.5000i | 0.956985 | + | 0.552515i | 0.895244 | − | 0.445577i | \(-0.147001\pi\) |
0.0617409 | + | 0.998092i | \(0.480335\pi\) | |||||||
\(788\) | −1.73205 | − | 1.00000i | −0.0617018 | − | 0.0356235i | ||||
\(789\) | 7.50000 | + | 12.9904i | 0.267007 | + | 0.462470i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.00000 | + | 5.19615i | 0.0355559 | + | 0.184754i | ||||
\(792\) | 12.0000i | 0.426401i | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 11.0000 | − | 19.0526i | 0.390375 | − | 0.676150i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | −31.1769 | − | 36.0000i | −1.10365 | − | 1.27439i | ||||
\(799\) | 32.0000 | 1.13208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00000 | + | 5.19615i | −0.106000 | + | 0.183597i | ||||
\(802\) | 26.8468 | + | 15.5000i | 0.947993 | + | 0.547324i | ||||
\(803\) | 6.92820 | − | 4.00000i | 0.244491 | − | 0.141157i | ||||
\(804\) | 27.0000 | 0.952217 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.79423 | + | 4.50000i | −0.274370 | + | 0.158408i | ||||
\(808\) | −2.59808 | − | 1.50000i | −0.0914000 | − | 0.0527698i | ||||
\(809\) | −25.5000 | + | 44.1673i | −0.896532 | + | 1.55284i | −0.0646355 | + | 0.997909i | \(0.520588\pi\) |
−0.831897 | + | 0.554930i | \(0.812745\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.0000 | −0.983213 | −0.491606 | − | 0.870817i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870817i | \(0.663590\pi\) | |||||||
\(812\) | −7.79423 | + | 22.5000i | −0.273524 | + | 0.789595i | ||||
\(813\) | − | 18.0000i | − | 0.631288i | ||||||
\(814\) | 4.00000 | + | 6.92820i | 0.140200 | + | 0.242833i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.00000 | − | 10.3923i | 0.210042 | − | 0.363803i | ||||
\(817\) | −25.9808 | + | 15.0000i | −0.908952 | + | 0.524784i | ||||
\(818\) | 3.00000i | 0.104893i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.00000 | + | 15.5885i | 0.314102 | + | 0.544041i | 0.979246 | − | 0.202674i | \(-0.0649632\pi\) |
−0.665144 | + | 0.746715i | \(0.731630\pi\) | |||||||
\(822\) | 31.1769 | + | 18.0000i | 1.08742 | + | 0.627822i | ||||
\(823\) | −16.4545 | − | 9.50000i | −0.573567 | − | 0.331149i | 0.185006 | − | 0.982737i | \(-0.440770\pi\) |
−0.758573 | + | 0.651588i | \(0.774103\pi\) | |||||||
\(824\) | 0.500000 | + | 0.866025i | 0.0174183 | + | 0.0301694i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.00000 | + | 25.9808i | 0.173972 | + | 0.903986i | ||||
\(827\) | 19.0000i | 0.660695i | 0.943859 | + | 0.330347i | \(0.107166\pi\) | ||||
−0.943859 | + | 0.330347i | \(0.892834\pi\) | |||||||
\(828\) | 15.5885 | − | 9.00000i | 0.541736 | − | 0.312772i | ||||
\(829\) | −23.0000 | + | 39.8372i | −0.798823 | + | 1.38360i | 0.121560 | + | 0.992584i | \(0.461210\pi\) |
−0.920383 | + | 0.391018i | \(0.872123\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.0000 | − | 31.1769i | −0.624413 | − | 1.08152i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.7128 | − | 4.00000i | −0.960192 | − | 0.138592i | ||||
\(834\) | 42.0000 | 1.45434 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.00000 | + | 10.3923i | −0.207514 | + | 0.359425i | ||||
\(837\) | −31.1769 | − | 18.0000i | −1.07763 | − | 0.622171i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.0000 | −0.483334 | −0.241667 | − | 0.970359i | \(-0.577694\pi\) | ||||
−0.241667 | + | 0.970359i | \(0.577694\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | 16.4545 | − | 9.50000i | 0.567059 | − | 0.327392i | ||||
\(843\) | −5.19615 | − | 3.00000i | −0.178965 | − | 0.103325i | ||||
\(844\) | −13.0000 | + | 22.5167i | −0.447478 | + | 0.775055i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 48.0000 | 1.65027 | ||||||||
\(847\) | 12.1244 | + | 14.0000i | 0.416598 | + | 0.481046i | ||||
\(848\) | − | 2.00000i | − | 0.0686803i | ||||||
\(849\) | −6.00000 | − | 10.3923i | −0.205919 | − | 0.356663i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.00000 | − | 10.3923i | 0.205677 | − | 0.356244i | ||||
\(852\) | −5.19615 | + | 3.00000i | −0.178017 | + | 0.102778i | ||||
\(853\) | 14.0000i | 0.479351i | 0.970853 | + | 0.239675i | \(0.0770410\pi\) | ||||
−0.970853 | + | 0.239675i | \(0.922959\pi\) | |||||||
\(854\) | 2.50000 | + | 0.866025i | 0.0855482 | + | 0.0296348i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.50000 | − | 2.59808i | −0.0512689 | − | 0.0888004i | ||||
\(857\) | −15.5885 | − | 9.00000i | −0.532492 | − | 0.307434i | 0.209539 | − | 0.977800i | \(-0.432804\pi\) |
−0.742030 | + | 0.670366i | \(0.766137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.0000 | − | 41.5692i | −0.818869 | − | 1.41832i | −0.906516 | − | 0.422172i | \(-0.861268\pi\) |
0.0876464 | − | 0.996152i | \(-0.472065\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 52.5000 | + | 18.1865i | 1.78920 | + | 0.619795i | ||||
\(862\) | 30.0000i | 1.02180i | ||||||||
\(863\) | −9.52628 | + | 5.50000i | −0.324278 | + | 0.187222i | −0.653298 | − | 0.757101i | \(-0.726615\pi\) |
0.329020 | + | 0.944323i | \(0.393282\pi\) | |||||||
\(864\) | 4.50000 | − | 7.79423i | 0.153093 | − | 0.265165i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.00000 | − | 12.1244i | −0.237870 | − | 0.412002i | ||||
\(867\) | 3.00000i | 0.101885i | ||||||||
\(868\) | −6.92820 | − | 8.00000i | −0.235159 | − | 0.271538i | ||||
\(869\) | 20.0000 | 0.678454 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −7.79423 | − | 4.50000i | −0.263946 | − | 0.152389i | ||||
\(873\) | 72.7461 | − | 42.0000i | 2.46208 | − | 1.42148i | ||||
\(874\) | 18.0000 | 0.608859 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.0000 | −0.405442 | ||||||||
\(877\) | −32.9090 | + | 19.0000i | −1.11126 | + | 0.641584i | −0.939155 | − | 0.343495i | \(-0.888389\pi\) |
−0.172102 | + | 0.985079i | \(0.555056\pi\) | |||||||
\(878\) | 17.3205 | + | 10.0000i | 0.584539 | + | 0.337484i | ||||
\(879\) | 42.0000 | − | 72.7461i | 1.41662 | − | 2.45367i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.00000 | −0.235836 | −0.117918 | − | 0.993023i | \(-0.537622\pi\) | ||||
−0.117918 | + | 0.993023i | \(0.537622\pi\) | |||||||
\(882\) | −41.5692 | − | 6.00000i | −1.39971 | − | 0.202031i | ||||
\(883\) | − | 12.0000i | − | 0.403832i | −0.979403 | − | 0.201916i | \(-0.935283\pi\) | ||
0.979403 | − | 0.201916i | \(-0.0647168\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.5000 | + | 26.8468i | −0.520733 | + | 0.901935i | ||||
\(887\) | −25.1147 | + | 14.5000i | −0.843270 | + | 0.486862i | −0.858375 | − | 0.513024i | \(-0.828525\pi\) |
0.0151042 | + | 0.999886i | \(0.495192\pi\) | |||||||
\(888\) | − | 12.0000i | − | 0.402694i | ||||||
\(889\) | −8.00000 | − | 41.5692i | −0.268311 | − | 1.39419i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.00000 | + | 15.5885i | 0.301511 | + | 0.522233i | ||||
\(892\) | 24.2487 | + | 14.0000i | 0.811907 | + | 0.468755i | ||||
\(893\) | 41.5692 | + | 24.0000i | 1.39106 | + | 0.803129i | ||||
\(894\) | 4.50000 | + | 7.79423i | 0.150503 | + | 0.260678i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00000 | − | 1.73205i | 0.0668153 | − | 0.0578638i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28.5788 | + | 16.5000i | −0.953688 | + | 0.550612i | ||||
\(899\) | −18.0000 | + | 31.1769i | −0.600334 | + | 1.03981i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00000 | − | 6.92820i | −0.133259 | − | 0.230812i | ||||
\(902\) | − | 14.0000i | − | 0.466149i | ||||||
\(903\) | −12.9904 | + | 37.5000i | −0.432293 | + | 1.24792i | ||||
\(904\) | −2.00000 | −0.0665190 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 24.0000 | − | 41.5692i | 0.797347 | − | 1.38104i | ||||
\(907\) | 4.33013 | + | 2.50000i | 0.143780 | + | 0.0830111i | 0.570164 | − | 0.821531i | \(-0.306880\pi\) |
−0.426385 | + | 0.904542i | \(0.640213\pi\) | |||||||
\(908\) | −3.46410 | + | 2.00000i | −0.114960 | + | 0.0663723i | ||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | 15.5885 | − | 9.00000i | 0.516185 | − | 0.298020i | ||||
\(913\) | −12.1244 | − | 7.00000i | −0.401258 | − | 0.231666i | ||||
\(914\) | −16.0000 | + | 27.7128i | −0.529233 | + | 0.916658i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22.0000 | 0.726900 | ||||||||
\(917\) | −13.8564 | − | 16.0000i | −0.457579 | − | 0.528367i | ||||
\(918\) | − | 36.0000i | − | 1.18818i | ||||||
\(919\) | 19.0000 | + | 32.9090i | 0.626752 | + | 1.08557i | 0.988199 | + | 0.153174i | \(0.0489495\pi\) |
−0.361447 | + | 0.932393i | \(0.617717\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.5000 | + | 18.1865i | −0.345987 | + | 0.599267i | ||||
\(922\) | 12.1244 | − | 7.00000i | 0.399294 | − | 0.230533i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.00000 | + | 15.5885i | 0.0986928 | + | 0.512823i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.50000 | + | 16.4545i | 0.312189 | + | 0.540728i | ||||
\(927\) | 5.19615 | + | 3.00000i | 0.170664 | + | 0.0985329i | ||||
\(928\) | −7.79423 | − | 4.50000i | −0.255858 | − | 0.147720i | ||||
\(929\) | 21.5000 | + | 37.2391i | 0.705392 | + | 1.22177i | 0.966550 | + | 0.256479i | \(0.0825624\pi\) |
−0.261158 | + | 0.965296i | \(0.584104\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.0000 | − | 25.9808i | −1.08153 | − | 0.851485i | ||||
\(932\) | − | 24.0000i | − | 0.786146i | ||||||
\(933\) | −46.7654 | + | 27.0000i | −1.53103 | + | 0.883940i | ||||
\(934\) | −6.50000 | + | 11.2583i | −0.212686 | + | 0.368384i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.0000i | 0.914720i | 0.889282 | + | 0.457360i | \(0.151205\pi\) | ||||
−0.889282 | + | 0.457360i | \(0.848795\pi\) | |||||||
\(938\) | 23.3827 | − | 4.50000i | 0.763472 | − | 0.146930i | ||||
\(939\) | −24.0000 | −0.783210 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.0000 | − | 39.8372i | 0.749779 | − | 1.29865i | −0.198150 | − | 0.980172i | \(-0.563493\pi\) |
0.947929 | − | 0.318483i | \(-0.103173\pi\) | |||||||
\(942\) | 25.9808 | + | 15.0000i | 0.846499 | + | 0.488726i | ||||
\(943\) | −18.1865 | + | 10.5000i | −0.592235 | + | 0.341927i | ||||
\(944\) | −10.0000 | −0.325472 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.0000 | 0.325128 | ||||||||
\(947\) | 21.6506 | − | 12.5000i | 0.703551 | − | 0.406195i | −0.105118 | − | 0.994460i | \(-0.533522\pi\) |
0.808669 | + | 0.588264i | \(0.200189\pi\) | |||||||
\(948\) | −25.9808 | − | 15.0000i | −0.843816 | − | 0.487177i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −96.0000 | −3.11301 | ||||||||
\(952\) | 3.46410 | − | 10.0000i | 0.112272 | − | 0.324102i | ||||
\(953\) | − | 12.0000i | − | 0.388718i | −0.980930 | − | 0.194359i | \(-0.937737\pi\) | ||
0.980930 | − | 0.194359i | \(-0.0622627\pi\) | |||||||
\(954\) | −6.00000 | − | 10.3923i | −0.194257 | − | 0.336463i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8.00000 | + | 13.8564i | −0.258738 | + | 0.448148i | ||||
\(957\) | 46.7654 | − | 27.0000i | 1.51171 | − | 0.872786i | ||||
\(958\) | 24.0000i | 0.775405i | ||||||||
\(959\) | 30.0000 | + | 10.3923i | 0.968751 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.5885 | − | 9.00000i | −0.502331 | − | 0.290021i | ||||
\(964\) | 5.00000 | + | 8.66025i | 0.161039 | + | 0.278928i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 18.0000 | − | 15.5885i | 0.579141 | − | 0.501550i | ||||
\(967\) | − | 37.0000i | − | 1.18984i | −0.803785 | − | 0.594920i | \(-0.797184\pi\) | ||
0.803785 | − | 0.594920i | \(-0.202816\pi\) | |||||||
\(968\) | −6.06218 | + | 3.50000i | −0.194846 | + | 0.112494i | ||||
\(969\) | 36.0000 | − | 62.3538i | 1.15649 | − | 2.00309i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0000 | + | 41.5692i | 0.770197 | + | 1.33402i | 0.937455 | + | 0.348107i | \(0.113175\pi\) |
−0.167258 | + | 0.985913i | \(0.553491\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.3731 | − | 7.00000i | 1.16607 | − | 0.224410i | ||||
\(974\) | 16.0000 | 0.512673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.500000 | + | 0.866025i | −0.0160046 | + | 0.0277208i | ||||
\(977\) | −25.9808 | − | 15.0000i | −0.831198 | − | 0.479893i | 0.0230645 | − | 0.999734i | \(-0.492658\pi\) |
−0.854263 | + | 0.519841i | \(0.825991\pi\) | |||||||
\(978\) | −10.3923 | + | 6.00000i | −0.332309 | + | 0.191859i | ||||
\(979\) | 2.00000 | 0.0639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −54.0000 | −1.72409 | ||||||||
\(982\) | 10.3923 | − | 6.00000i | 0.331632 | − | 0.191468i | ||||
\(983\) | −14.7224 | − | 8.50000i | −0.469573 | − | 0.271108i | 0.246488 | − | 0.969146i | \(-0.420723\pi\) |
−0.716061 | + | 0.698038i | \(0.754057\pi\) | |||||||
\(984\) | −10.5000 | + | 18.1865i | −0.334728 | + | 0.579766i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −36.0000 | −1.14647 | ||||||||
\(987\) | 62.3538 | − | 12.0000i | 1.98474 | − | 0.381964i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.50000 | − | 12.9904i | −0.238486 | − | 0.413070i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.0000 | + | 34.6410i | −0.635321 | + | 1.10041i | 0.351126 | + | 0.936328i | \(0.385799\pi\) |
−0.986447 | + | 0.164080i | \(0.947534\pi\) | |||||||
\(992\) | 3.46410 | − | 2.00000i | 0.109985 | − | 0.0635001i | ||||
\(993\) | − | 96.0000i | − | 3.04647i | ||||||
\(994\) | −4.00000 | + | 3.46410i | −0.126872 | + | 0.109875i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 10.5000 | + | 18.1865i | 0.332705 | + | 0.576262i | ||||
\(997\) | −39.8372 | − | 23.0000i | −1.26166 | − | 0.728417i | −0.288261 | − | 0.957552i | \(-0.593077\pi\) |
−0.973395 | + | 0.229135i | \(0.926410\pi\) | |||||||
\(998\) | 15.5885 | + | 9.00000i | 0.493444 | + | 0.284890i | ||||
\(999\) | −18.0000 | − | 31.1769i | −0.569495 | − | 0.986394i |
(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 | 350.2.j.f.249.1 | 4 | ||
5.2 | odd | 4 | 70.2.e.a.11.1 | ✓ | 2 | ||
5.3 | odd | 4 | 350.2.e.l.151.1 | 2 | |||
5.4 | even | 2 | inner | 350.2.j.f.249.2 | 4 | ||
7.2 | even | 3 | inner | 350.2.j.f.149.2 | 4 | ||
7.3 | odd | 6 | 2450.2.c.a.99.1 | 2 | |||
7.4 | even | 3 | 2450.2.c.s.99.1 | 2 | |||
15.2 | even | 4 | 630.2.k.f.361.1 | 2 | |||
20.7 | even | 4 | 560.2.q.i.81.1 | 2 | |||
35.2 | odd | 12 | 70.2.e.a.51.1 | yes | 2 | ||
35.3 | even | 12 | 2450.2.a.q.1.1 | 1 | |||
35.4 | even | 6 | 2450.2.c.s.99.2 | 2 | |||
35.9 | even | 6 | inner | 350.2.j.f.149.1 | 4 | ||
35.12 | even | 12 | 490.2.e.f.471.1 | 2 | |||
35.17 | even | 12 | 490.2.a.e.1.1 | 1 | |||
35.18 | odd | 12 | 2450.2.a.b.1.1 | 1 | |||
35.23 | odd | 12 | 350.2.e.l.51.1 | 2 | |||
35.24 | odd | 6 | 2450.2.c.a.99.2 | 2 | |||
35.27 | even | 4 | 490.2.e.f.361.1 | 2 | |||
35.32 | odd | 12 | 490.2.a.k.1.1 | 1 | |||
105.2 | even | 12 | 630.2.k.f.541.1 | 2 | |||
105.17 | odd | 12 | 4410.2.a.h.1.1 | 1 | |||
105.32 | even | 12 | 4410.2.a.r.1.1 | 1 | |||
140.67 | even | 12 | 3920.2.a.b.1.1 | 1 | |||
140.87 | odd | 12 | 3920.2.a.bk.1.1 | 1 | |||
140.107 | even | 12 | 560.2.q.i.401.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.e.a.11.1 | ✓ | 2 | 5.2 | odd | 4 | ||
70.2.e.a.51.1 | yes | 2 | 35.2 | odd | 12 | ||
350.2.e.l.51.1 | 2 | 35.23 | odd | 12 | |||
350.2.e.l.151.1 | 2 | 5.3 | odd | 4 | |||
350.2.j.f.149.1 | 4 | 35.9 | even | 6 | inner | ||
350.2.j.f.149.2 | 4 | 7.2 | even | 3 | inner | ||
350.2.j.f.249.1 | 4 | 1.1 | even | 1 | trivial | ||
350.2.j.f.249.2 | 4 | 5.4 | even | 2 | inner | ||
490.2.a.e.1.1 | 1 | 35.17 | even | 12 | |||
490.2.a.k.1.1 | 1 | 35.32 | odd | 12 | |||
490.2.e.f.361.1 | 2 | 35.27 | even | 4 | |||
490.2.e.f.471.1 | 2 | 35.12 | even | 12 | |||
560.2.q.i.81.1 | 2 | 20.7 | even | 4 | |||
560.2.q.i.401.1 | 2 | 140.107 | even | 12 | |||
630.2.k.f.361.1 | 2 | 15.2 | even | 4 | |||
630.2.k.f.541.1 | 2 | 105.2 | even | 12 | |||
2450.2.a.b.1.1 | 1 | 35.18 | odd | 12 | |||
2450.2.a.q.1.1 | 1 | 35.3 | even | 12 | |||
2450.2.c.a.99.1 | 2 | 7.3 | odd | 6 | |||
2450.2.c.a.99.2 | 2 | 35.24 | odd | 6 | |||
2450.2.c.s.99.1 | 2 | 7.4 | even | 3 | |||
2450.2.c.s.99.2 | 2 | 35.4 | even | 6 | |||
3920.2.a.b.1.1 | 1 | 140.67 | even | 12 | |||
3920.2.a.bk.1.1 | 1 | 140.87 | odd | 12 | |||
4410.2.a.h.1.1 | 1 | 105.17 | odd | 12 | |||
4410.2.a.r.1.1 | 1 | 105.32 | even | 12 |