Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(121,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.bb (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.11416567883\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.361 |
Dual form | 390.2.bb.a.121.2 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | 2.59808 | + | 1.50000i | 0.981981 | + | 0.566947i | 0.902867 | − | 0.429919i | \(-0.141458\pi\) |
0.0791130 | + | 0.996866i | \(0.474791\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | 0.232051 | − | 0.133975i | 0.0699660 | − | 0.0403949i | −0.464609 | − | 0.885516i | \(-0.653805\pi\) |
0.534575 | + | 0.845121i | \(0.320472\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0.866025 | − | 3.50000i | 0.240192 | − | 0.970725i | ||||
\(14\) | 3.00000 | 0.801784 | ||||||||
\(15\) | 0.866025 | − | 0.500000i | 0.223607 | − | 0.129099i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.00000 | + | 3.46410i | −0.485071 | + | 0.840168i | −0.999853 | − | 0.0171533i | \(-0.994540\pi\) |
0.514782 | + | 0.857321i | \(0.327873\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 4.96410 | + | 2.86603i | 1.13884 | + | 0.657511i | 0.946144 | − | 0.323747i | \(-0.104943\pi\) |
0.192699 | + | 0.981258i | \(0.438276\pi\) | |||||||
\(20\) | −0.866025 | − | 0.500000i | −0.193649 | − | 0.111803i | ||||
\(21\) | 3.00000i | 0.654654i | ||||||||
\(22\) | 0.133975 | − | 0.232051i | 0.0285635 | − | 0.0494734i | ||||
\(23\) | −1.73205 | − | 3.00000i | −0.361158 | − | 0.625543i | 0.626994 | − | 0.779024i | \(-0.284285\pi\) |
−0.988152 | + | 0.153481i | \(0.950952\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −1.00000 | − | 3.46410i | −0.196116 | − | 0.679366i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.59808 | − | 1.50000i | 0.490990 | − | 0.283473i | ||||
\(29\) | −0.732051 | − | 1.26795i | −0.135938 | − | 0.235452i | 0.790017 | − | 0.613085i | \(-0.210072\pi\) |
−0.925956 | + | 0.377633i | \(0.876738\pi\) | |||||||
\(30\) | 0.500000 | − | 0.866025i | 0.0912871 | − | 0.158114i | ||||
\(31\) | − | 4.92820i | − | 0.885131i | −0.896736 | − | 0.442566i | \(-0.854068\pi\) | ||
0.896736 | − | 0.442566i | \(-0.145932\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0.232051 | + | 0.133975i | 0.0403949 | + | 0.0233220i | ||||
\(34\) | 4.00000i | 0.685994i | ||||||||
\(35\) | 1.50000 | − | 2.59808i | 0.253546 | − | 0.439155i | ||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | −5.13397 | + | 2.96410i | −0.844020 | + | 0.487295i | −0.858629 | − | 0.512598i | \(-0.828683\pi\) |
0.0146085 | + | 0.999893i | \(0.495350\pi\) | |||||||
\(38\) | 5.73205 | 0.929861 | ||||||||
\(39\) | 3.46410 | − | 1.00000i | 0.554700 | − | 0.160128i | ||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −3.46410 | + | 2.00000i | −0.541002 | + | 0.312348i | −0.745485 | − | 0.666523i | \(-0.767782\pi\) |
0.204483 | + | 0.978870i | \(0.434449\pi\) | |||||||
\(42\) | 1.50000 | + | 2.59808i | 0.231455 | + | 0.400892i | ||||
\(43\) | −3.00000 | + | 5.19615i | −0.457496 | + | 0.792406i | −0.998828 | − | 0.0484030i | \(-0.984587\pi\) |
0.541332 | + | 0.840809i | \(0.317920\pi\) | |||||||
\(44\) | − | 0.267949i | − | 0.0403949i | ||||||
\(45\) | 0.866025 | + | 0.500000i | 0.129099 | + | 0.0745356i | ||||
\(46\) | −3.00000 | − | 1.73205i | −0.442326 | − | 0.255377i | ||||
\(47\) | 6.46410i | 0.942886i | 0.881897 | + | 0.471443i | \(0.156267\pi\) | ||||
−0.881897 | + | 0.471443i | \(0.843733\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | 1.00000 | + | 1.73205i | 0.142857 | + | 0.247436i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | −2.59808 | − | 2.50000i | −0.360288 | − | 0.346688i | ||||
\(53\) | −0.267949 | −0.0368057 | −0.0184028 | − | 0.999831i | \(-0.505858\pi\) | ||||
−0.0184028 | + | 0.999831i | \(0.505858\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | −0.133975 | − | 0.232051i | −0.0180651 | − | 0.0312897i | ||||
\(56\) | 1.50000 | − | 2.59808i | 0.200446 | − | 0.347183i | ||||
\(57\) | 5.73205i | 0.759229i | ||||||||
\(58\) | −1.26795 | − | 0.732051i | −0.166490 | − | 0.0961230i | ||||
\(59\) | −9.92820 | − | 5.73205i | −1.29254 | − | 0.746249i | −0.313438 | − | 0.949609i | \(-0.601481\pi\) |
−0.979104 | + | 0.203359i | \(0.934814\pi\) | |||||||
\(60\) | − | 1.00000i | − | 0.129099i | ||||||
\(61\) | 0.267949 | − | 0.464102i | 0.0343074 | − | 0.0594221i | −0.848362 | − | 0.529417i | \(-0.822411\pi\) |
0.882669 | + | 0.469995i | \(0.155744\pi\) | |||||||
\(62\) | −2.46410 | − | 4.26795i | −0.312941 | − | 0.542030i | ||||
\(63\) | −2.59808 | + | 1.50000i | −0.327327 | + | 0.188982i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −3.50000 | − | 0.866025i | −0.434122 | − | 0.107417i | ||||
\(66\) | 0.267949 | 0.0329823 | ||||||||
\(67\) | 1.26795 | − | 0.732051i | 0.154905 | − | 0.0894342i | −0.420544 | − | 0.907272i | \(-0.638161\pi\) |
0.575449 | + | 0.817838i | \(0.304827\pi\) | |||||||
\(68\) | 2.00000 | + | 3.46410i | 0.242536 | + | 0.420084i | ||||
\(69\) | 1.73205 | − | 3.00000i | 0.208514 | − | 0.361158i | ||||
\(70\) | − | 3.00000i | − | 0.358569i | ||||||
\(71\) | −11.1962 | − | 6.46410i | −1.32874 | − | 0.767148i | −0.343634 | − | 0.939104i | \(-0.611658\pi\) |
−0.985105 | + | 0.171956i | \(0.944991\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | 6.92820i | 0.810885i | 0.914121 | + | 0.405442i | \(0.132883\pi\) | ||||
−0.914121 | + | 0.405442i | \(0.867117\pi\) | |||||||
\(74\) | −2.96410 | + | 5.13397i | −0.344570 | + | 0.596812i | ||||
\(75\) | −0.500000 | − | 0.866025i | −0.0577350 | − | 0.100000i | ||||
\(76\) | 4.96410 | − | 2.86603i | 0.569422 | − | 0.328756i | ||||
\(77\) | 0.803848 | 0.0916069 | ||||||||
\(78\) | 2.50000 | − | 2.59808i | 0.283069 | − | 0.294174i | ||||
\(79\) | 3.07180 | 0.345604 | 0.172802 | − | 0.984957i | \(-0.444718\pi\) | ||||
0.172802 | + | 0.984957i | \(0.444718\pi\) | |||||||
\(80\) | −0.866025 | + | 0.500000i | −0.0968246 | + | 0.0559017i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.00000 | + | 3.46410i | −0.220863 | + | 0.382546i | ||||
\(83\) | − | 9.46410i | − | 1.03882i | −0.854525 | − | 0.519410i | \(-0.826152\pi\) | ||
0.854525 | − | 0.519410i | \(-0.173848\pi\) | |||||||
\(84\) | 2.59808 | + | 1.50000i | 0.283473 | + | 0.163663i | ||||
\(85\) | 3.46410 | + | 2.00000i | 0.375735 | + | 0.216930i | ||||
\(86\) | 6.00000i | 0.646997i | ||||||||
\(87\) | 0.732051 | − | 1.26795i | 0.0784841 | − | 0.135938i | ||||
\(88\) | −0.133975 | − | 0.232051i | −0.0142817 | − | 0.0247367i | ||||
\(89\) | −12.2321 | + | 7.06218i | −1.29659 | + | 0.748589i | −0.979814 | − | 0.199910i | \(-0.935935\pi\) |
−0.316780 | + | 0.948499i | \(0.602602\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 7.50000 | − | 7.79423i | 0.786214 | − | 0.817057i | ||||
\(92\) | −3.46410 | −0.361158 | ||||||||
\(93\) | 4.26795 | − | 2.46410i | 0.442566 | − | 0.255515i | ||||
\(94\) | 3.23205 | + | 5.59808i | 0.333361 | + | 0.577397i | ||||
\(95\) | 2.86603 | − | 4.96410i | 0.294048 | − | 0.509306i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 7.26795 | + | 4.19615i | 0.737948 | + | 0.426055i | 0.821323 | − | 0.570464i | \(-0.193236\pi\) |
−0.0833745 | + | 0.996518i | \(0.526570\pi\) | |||||||
\(98\) | 1.73205 | + | 1.00000i | 0.174964 | + | 0.101015i | ||||
\(99\) | 0.267949i | 0.0269299i | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −6.19615 | − | 10.7321i | −0.616540 | − | 1.06788i | −0.990112 | − | 0.140278i | \(-0.955200\pi\) |
0.373572 | − | 0.927601i | \(-0.378133\pi\) | |||||||
\(102\) | −3.46410 | + | 2.00000i | −0.342997 | + | 0.198030i | ||||
\(103\) | −11.5885 | −1.14184 | −0.570922 | − | 0.821004i | \(-0.693414\pi\) | ||||
−0.570922 | + | 0.821004i | \(0.693414\pi\) | |||||||
\(104\) | −3.50000 | − | 0.866025i | −0.343203 | − | 0.0849208i | ||||
\(105\) | 3.00000 | 0.292770 | ||||||||
\(106\) | −0.232051 | + | 0.133975i | −0.0225388 | + | 0.0130128i | ||||
\(107\) | 6.46410 | + | 11.1962i | 0.624908 | + | 1.08237i | 0.988559 | + | 0.150837i | \(0.0481970\pi\) |
−0.363650 | + | 0.931536i | \(0.618470\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | 10.3923i | 0.995402i | 0.867349 | + | 0.497701i | \(0.165822\pi\) | ||||
−0.867349 | + | 0.497701i | \(0.834178\pi\) | |||||||
\(110\) | −0.232051 | − | 0.133975i | −0.0221252 | − | 0.0127740i | ||||
\(111\) | −5.13397 | − | 2.96410i | −0.487295 | − | 0.281340i | ||||
\(112\) | − | 3.00000i | − | 0.283473i | ||||||
\(113\) | 6.00000 | − | 10.3923i | 0.564433 | − | 0.977626i | −0.432670 | − | 0.901553i | \(-0.642428\pi\) |
0.997102 | − | 0.0760733i | \(-0.0242383\pi\) | |||||||
\(114\) | 2.86603 | + | 4.96410i | 0.268428 | + | 0.464931i | ||||
\(115\) | −3.00000 | + | 1.73205i | −0.279751 | + | 0.161515i | ||||
\(116\) | −1.46410 | −0.135938 | ||||||||
\(117\) | 2.59808 | + | 2.50000i | 0.240192 | + | 0.231125i | ||||
\(118\) | −11.4641 | −1.05536 | ||||||||
\(119\) | −10.3923 | + | 6.00000i | −0.952661 | + | 0.550019i | ||||
\(120\) | −0.500000 | − | 0.866025i | −0.0456435 | − | 0.0790569i | ||||
\(121\) | −5.46410 | + | 9.46410i | −0.496737 | + | 0.860373i | ||||
\(122\) | − | 0.535898i | − | 0.0485180i | ||||||
\(123\) | −3.46410 | − | 2.00000i | −0.312348 | − | 0.180334i | ||||
\(124\) | −4.26795 | − | 2.46410i | −0.383273 | − | 0.221283i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −1.50000 | + | 2.59808i | −0.133631 | + | 0.231455i | ||||
\(127\) | 6.33013 | + | 10.9641i | 0.561708 | + | 0.972907i | 0.997348 | + | 0.0727855i | \(0.0231889\pi\) |
−0.435640 | + | 0.900121i | \(0.643478\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −6.00000 | −0.528271 | ||||||||
\(130\) | −3.46410 | + | 1.00000i | −0.303822 | + | 0.0877058i | ||||
\(131\) | 14.3205 | 1.25119 | 0.625594 | − | 0.780149i | \(-0.284857\pi\) | ||||
0.625594 | + | 0.780149i | \(0.284857\pi\) | |||||||
\(132\) | 0.232051 | − | 0.133975i | 0.0201974 | − | 0.0116610i | ||||
\(133\) | 8.59808 | + | 14.8923i | 0.745548 | + | 1.29133i | ||||
\(134\) | 0.732051 | − | 1.26795i | 0.0632396 | − | 0.109534i | ||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 3.46410 | + | 2.00000i | 0.297044 | + | 0.171499i | ||||
\(137\) | 11.6603 | + | 6.73205i | 0.996203 | + | 0.575158i | 0.907123 | − | 0.420867i | \(-0.138274\pi\) |
0.0890802 | + | 0.996024i | \(0.471607\pi\) | |||||||
\(138\) | − | 3.46410i | − | 0.294884i | ||||||
\(139\) | 9.89230 | − | 17.1340i | 0.839054 | − | 1.45328i | −0.0516319 | − | 0.998666i | \(-0.516442\pi\) |
0.890686 | − | 0.454619i | \(-0.150224\pi\) | |||||||
\(140\) | −1.50000 | − | 2.59808i | −0.126773 | − | 0.219578i | ||||
\(141\) | −5.59808 | + | 3.23205i | −0.471443 | + | 0.272188i | ||||
\(142\) | −12.9282 | −1.08491 | ||||||||
\(143\) | −0.267949 | − | 0.928203i | −0.0224070 | − | 0.0776203i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.26795 | + | 0.732051i | −0.105297 | + | 0.0607935i | ||||
\(146\) | 3.46410 | + | 6.00000i | 0.286691 | + | 0.496564i | ||||
\(147\) | −1.00000 | + | 1.73205i | −0.0824786 | + | 0.142857i | ||||
\(148\) | 5.92820i | 0.487295i | ||||||||
\(149\) | 16.2679 | + | 9.39230i | 1.33272 | + | 0.769448i | 0.985716 | − | 0.168415i | \(-0.0538649\pi\) |
0.347006 | + | 0.937863i | \(0.387198\pi\) | |||||||
\(150\) | −0.866025 | − | 0.500000i | −0.0707107 | − | 0.0408248i | ||||
\(151\) | − | 22.7846i | − | 1.85419i | −0.374832 | − | 0.927093i | \(-0.622300\pi\) | ||
0.374832 | − | 0.927093i | \(-0.377700\pi\) | |||||||
\(152\) | 2.86603 | − | 4.96410i | 0.232465 | − | 0.402642i | ||||
\(153\) | −2.00000 | − | 3.46410i | −0.161690 | − | 0.280056i | ||||
\(154\) | 0.696152 | − | 0.401924i | 0.0560976 | − | 0.0323879i | ||||
\(155\) | −4.92820 | −0.395843 | ||||||||
\(156\) | 0.866025 | − | 3.50000i | 0.0693375 | − | 0.280224i | ||||
\(157\) | 21.1962 | 1.69164 | 0.845819 | − | 0.533471i | \(-0.179113\pi\) | ||||
0.845819 | + | 0.533471i | \(0.179113\pi\) | |||||||
\(158\) | 2.66025 | − | 1.53590i | 0.211638 | − | 0.122190i | ||||
\(159\) | −0.133975 | − | 0.232051i | −0.0106249 | − | 0.0184028i | ||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | − | 10.3923i | − | 0.819028i | ||||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | −2.53590 | − | 1.46410i | −0.198627 | − | 0.114677i | 0.397388 | − | 0.917651i | \(-0.369917\pi\) |
−0.596015 | + | 0.802973i | \(0.703250\pi\) | |||||||
\(164\) | 4.00000i | 0.312348i | ||||||||
\(165\) | 0.133975 | − | 0.232051i | 0.0104299 | − | 0.0180651i | ||||
\(166\) | −4.73205 | − | 8.19615i | −0.367278 | − | 0.636145i | ||||
\(167\) | −0.401924 | + | 0.232051i | −0.0311018 | + | 0.0179566i | −0.515470 | − | 0.856907i | \(-0.672383\pi\) |
0.484368 | + | 0.874864i | \(0.339049\pi\) | |||||||
\(168\) | 3.00000 | 0.231455 | ||||||||
\(169\) | −11.5000 | − | 6.06218i | −0.884615 | − | 0.466321i | ||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | −4.96410 | + | 2.86603i | −0.379614 | + | 0.219170i | ||||
\(172\) | 3.00000 | + | 5.19615i | 0.228748 | + | 0.396203i | ||||
\(173\) | 1.06218 | − | 1.83975i | 0.0807559 | − | 0.139873i | −0.822819 | − | 0.568304i | \(-0.807600\pi\) |
0.903575 | + | 0.428430i | \(0.140933\pi\) | |||||||
\(174\) | − | 1.46410i | − | 0.110993i | ||||||
\(175\) | −2.59808 | − | 1.50000i | −0.196396 | − | 0.113389i | ||||
\(176\) | −0.232051 | − | 0.133975i | −0.0174915 | − | 0.0100987i | ||||
\(177\) | − | 11.4641i | − | 0.861695i | ||||||
\(178\) | −7.06218 | + | 12.2321i | −0.529333 | + | 0.916831i | ||||
\(179\) | −4.53590 | − | 7.85641i | −0.339029 | − | 0.587215i | 0.645221 | − | 0.763996i | \(-0.276765\pi\) |
−0.984250 | + | 0.176780i | \(0.943432\pi\) | |||||||
\(180\) | 0.866025 | − | 0.500000i | 0.0645497 | − | 0.0372678i | ||||
\(181\) | 16.9282 | 1.25826 | 0.629132 | − | 0.777299i | \(-0.283411\pi\) | ||||
0.629132 | + | 0.777299i | \(0.283411\pi\) | |||||||
\(182\) | 2.59808 | − | 10.5000i | 0.192582 | − | 0.778312i | ||||
\(183\) | 0.535898 | 0.0396147 | ||||||||
\(184\) | −3.00000 | + | 1.73205i | −0.221163 | + | 0.127688i | ||||
\(185\) | 2.96410 | + | 5.13397i | 0.217925 | + | 0.377457i | ||||
\(186\) | 2.46410 | − | 4.26795i | 0.180677 | − | 0.312941i | ||||
\(187\) | 1.07180i | 0.0783775i | ||||||||
\(188\) | 5.59808 | + | 3.23205i | 0.408282 | + | 0.235722i | ||||
\(189\) | −2.59808 | − | 1.50000i | −0.188982 | − | 0.109109i | ||||
\(190\) | − | 5.73205i | − | 0.415847i | ||||||
\(191\) | 8.66025 | − | 15.0000i | 0.626634 | − | 1.08536i | −0.361588 | − | 0.932338i | \(-0.617765\pi\) |
0.988222 | − | 0.153024i | \(-0.0489012\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −8.53590 | + | 4.92820i | −0.614427 | + | 0.354740i | −0.774696 | − | 0.632334i | \(-0.782097\pi\) |
0.160269 | + | 0.987073i | \(0.448764\pi\) | |||||||
\(194\) | 8.39230 | 0.602532 | ||||||||
\(195\) | −1.00000 | − | 3.46410i | −0.0716115 | − | 0.248069i | ||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | −9.86603 | + | 5.69615i | −0.702925 | + | 0.405834i | −0.808436 | − | 0.588584i | \(-0.799686\pi\) |
0.105511 | + | 0.994418i | \(0.466352\pi\) | |||||||
\(198\) | 0.133975 | + | 0.232051i | 0.00952116 | + | 0.0164911i | ||||
\(199\) | 12.4641 | − | 21.5885i | 0.883557 | − | 1.53037i | 0.0361978 | − | 0.999345i | \(-0.488475\pi\) |
0.847359 | − | 0.531021i | \(-0.178191\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 1.26795 | + | 0.732051i | 0.0894342 | + | 0.0516349i | ||||
\(202\) | −10.7321 | − | 6.19615i | −0.755104 | − | 0.435960i | ||||
\(203\) | − | 4.39230i | − | 0.308279i | ||||||
\(204\) | −2.00000 | + | 3.46410i | −0.140028 | + | 0.242536i | ||||
\(205\) | 2.00000 | + | 3.46410i | 0.139686 | + | 0.241943i | ||||
\(206\) | −10.0359 | + | 5.79423i | −0.699234 | + | 0.403703i | ||||
\(207\) | 3.46410 | 0.240772 | ||||||||
\(208\) | −3.46410 | + | 1.00000i | −0.240192 | + | 0.0693375i | ||||
\(209\) | 1.53590 | 0.106240 | ||||||||
\(210\) | 2.59808 | − | 1.50000i | 0.179284 | − | 0.103510i | ||||
\(211\) | 4.03590 | + | 6.99038i | 0.277843 | + | 0.481238i | 0.970848 | − | 0.239694i | \(-0.0770473\pi\) |
−0.693006 | + | 0.720932i | \(0.743714\pi\) | |||||||
\(212\) | −0.133975 | + | 0.232051i | −0.00920141 | + | 0.0159373i | ||||
\(213\) | − | 12.9282i | − | 0.885826i | ||||||
\(214\) | 11.1962 | + | 6.46410i | 0.765353 | + | 0.441877i | ||||
\(215\) | 5.19615 | + | 3.00000i | 0.354375 | + | 0.204598i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 7.39230 | − | 12.8038i | 0.501822 | − | 0.869182i | ||||
\(218\) | 5.19615 | + | 9.00000i | 0.351928 | + | 0.609557i | ||||
\(219\) | −6.00000 | + | 3.46410i | −0.405442 | + | 0.234082i | ||||
\(220\) | −0.267949 | −0.0180651 | ||||||||
\(221\) | 10.3923 | + | 10.0000i | 0.699062 | + | 0.672673i | ||||
\(222\) | −5.92820 | −0.397875 | ||||||||
\(223\) | −16.3301 | + | 9.42820i | −1.09355 | + | 0.631359i | −0.934518 | − | 0.355915i | \(-0.884169\pi\) |
−0.159028 | + | 0.987274i | \(0.550836\pi\) | |||||||
\(224\) | −1.50000 | − | 2.59808i | −0.100223 | − | 0.173591i | ||||
\(225\) | 0.500000 | − | 0.866025i | 0.0333333 | − | 0.0577350i | ||||
\(226\) | − | 12.0000i | − | 0.798228i | ||||||
\(227\) | 5.66025 | + | 3.26795i | 0.375684 | + | 0.216901i | 0.675939 | − | 0.736958i | \(-0.263738\pi\) |
−0.300255 | + | 0.953859i | \(0.597072\pi\) | |||||||
\(228\) | 4.96410 | + | 2.86603i | 0.328756 | + | 0.189807i | ||||
\(229\) | − | 4.53590i | − | 0.299741i | −0.988706 | − | 0.149870i | \(-0.952114\pi\) | ||
0.988706 | − | 0.149870i | \(-0.0478856\pi\) | |||||||
\(230\) | −1.73205 | + | 3.00000i | −0.114208 | + | 0.197814i | ||||
\(231\) | 0.401924 | + | 0.696152i | 0.0264446 | + | 0.0458035i | ||||
\(232\) | −1.26795 | + | 0.732051i | −0.0832449 | + | 0.0480615i | ||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 3.50000 | + | 0.866025i | 0.228802 | + | 0.0566139i | ||||
\(235\) | 6.46410 | 0.421671 | ||||||||
\(236\) | −9.92820 | + | 5.73205i | −0.646271 | + | 0.373125i | ||||
\(237\) | 1.53590 | + | 2.66025i | 0.0997673 | + | 0.172802i | ||||
\(238\) | −6.00000 | + | 10.3923i | −0.388922 | + | 0.673633i | ||||
\(239\) | 3.46410i | 0.224074i | 0.993704 | + | 0.112037i | \(0.0357375\pi\) | ||||
−0.993704 | + | 0.112037i | \(0.964262\pi\) | |||||||
\(240\) | −0.866025 | − | 0.500000i | −0.0559017 | − | 0.0322749i | ||||
\(241\) | −21.8205 | − | 12.5981i | −1.40558 | − | 0.811513i | −0.410624 | − | 0.911805i | \(-0.634689\pi\) |
−0.994958 | + | 0.100291i | \(0.968023\pi\) | |||||||
\(242\) | 10.9282i | 0.702492i | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −0.267949 | − | 0.464102i | −0.0171537 | − | 0.0297111i | ||||
\(245\) | 1.73205 | − | 1.00000i | 0.110657 | − | 0.0638877i | ||||
\(246\) | −4.00000 | −0.255031 | ||||||||
\(247\) | 14.3301 | − | 14.8923i | 0.911804 | − | 0.947575i | ||||
\(248\) | −4.92820 | −0.312941 | ||||||||
\(249\) | 8.19615 | − | 4.73205i | 0.519410 | − | 0.299882i | ||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | −9.76795 | + | 16.9186i | −0.616547 | + | 1.06789i | 0.373563 | + | 0.927605i | \(0.378136\pi\) |
−0.990111 | + | 0.140287i | \(0.955198\pi\) | |||||||
\(252\) | 3.00000i | 0.188982i | ||||||||
\(253\) | −0.803848 | − | 0.464102i | −0.0505375 | − | 0.0291778i | ||||
\(254\) | 10.9641 | + | 6.33013i | 0.687949 | + | 0.397187i | ||||
\(255\) | 4.00000i | 0.250490i | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −7.26795 | − | 12.5885i | −0.453362 | − | 0.785246i | 0.545230 | − | 0.838286i | \(-0.316442\pi\) |
−0.998592 | + | 0.0530400i | \(0.983109\pi\) | |||||||
\(258\) | −5.19615 | + | 3.00000i | −0.323498 | + | 0.186772i | ||||
\(259\) | −17.7846 | −1.10508 | ||||||||
\(260\) | −2.50000 | + | 2.59808i | −0.155043 | + | 0.161126i | ||||
\(261\) | 1.46410 | 0.0906256 | ||||||||
\(262\) | 12.4019 | − | 7.16025i | 0.766193 | − | 0.442362i | ||||
\(263\) | 12.2583 | + | 21.2321i | 0.755881 | + | 1.30922i | 0.944935 | + | 0.327258i | \(0.106125\pi\) |
−0.189054 | + | 0.981967i | \(0.560542\pi\) | |||||||
\(264\) | 0.133975 | − | 0.232051i | 0.00824557 | − | 0.0142817i | ||||
\(265\) | 0.267949i | 0.0164600i | ||||||||
\(266\) | 14.8923 | + | 8.59808i | 0.913106 | + | 0.527182i | ||||
\(267\) | −12.2321 | − | 7.06218i | −0.748589 | − | 0.432198i | ||||
\(268\) | − | 1.46410i | − | 0.0894342i | ||||||
\(269\) | 8.53590 | − | 14.7846i | 0.520443 | − | 0.901434i | −0.479275 | − | 0.877665i | \(-0.659100\pi\) |
0.999717 | − | 0.0237685i | \(-0.00756648\pi\) | |||||||
\(270\) | 0.500000 | + | 0.866025i | 0.0304290 | + | 0.0527046i | ||||
\(271\) | 21.1244 | − | 12.1962i | 1.28321 | − | 0.740863i | 0.305779 | − | 0.952103i | \(-0.401083\pi\) |
0.977434 | + | 0.211239i | \(0.0677499\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | 10.5000 | + | 2.59808i | 0.635489 | + | 0.157243i | ||||
\(274\) | 13.4641 | 0.813396 | ||||||||
\(275\) | −0.232051 | + | 0.133975i | −0.0139932 | + | 0.00807897i | ||||
\(276\) | −1.73205 | − | 3.00000i | −0.104257 | − | 0.180579i | ||||
\(277\) | −5.79423 | + | 10.0359i | −0.348141 | + | 0.602999i | −0.985919 | − | 0.167222i | \(-0.946520\pi\) |
0.637778 | + | 0.770220i | \(0.279854\pi\) | |||||||
\(278\) | − | 19.7846i | − | 1.18660i | ||||||
\(279\) | 4.26795 | + | 2.46410i | 0.255515 | + | 0.147522i | ||||
\(280\) | −2.59808 | − | 1.50000i | −0.155265 | − | 0.0896421i | ||||
\(281\) | 6.92820i | 0.413302i | 0.978415 | + | 0.206651i | \(0.0662565\pi\) | ||||
−0.978415 | + | 0.206651i | \(0.933744\pi\) | |||||||
\(282\) | −3.23205 | + | 5.59808i | −0.192466 | + | 0.333361i | ||||
\(283\) | 3.19615 | + | 5.53590i | 0.189992 | + | 0.329075i | 0.945247 | − | 0.326355i | \(-0.105821\pi\) |
−0.755256 | + | 0.655430i | \(0.772487\pi\) | |||||||
\(284\) | −11.1962 | + | 6.46410i | −0.664369 | + | 0.383574i | ||||
\(285\) | 5.73205 | 0.339537 | ||||||||
\(286\) | −0.696152 | − | 0.669873i | −0.0411644 | − | 0.0396104i | ||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | 0.866025 | − | 0.500000i | 0.0510310 | − | 0.0294628i | ||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | −0.732051 | + | 1.26795i | −0.0429875 | + | 0.0744565i | ||||
\(291\) | 8.39230i | 0.491966i | ||||||||
\(292\) | 6.00000 | + | 3.46410i | 0.351123 | + | 0.202721i | ||||
\(293\) | 25.3301 | + | 14.6244i | 1.47980 | + | 0.854364i | 0.999738 | − | 0.0228698i | \(-0.00728033\pi\) |
0.480063 | + | 0.877234i | \(0.340614\pi\) | |||||||
\(294\) | 2.00000i | 0.116642i | ||||||||
\(295\) | −5.73205 | + | 9.92820i | −0.333733 | + | 0.578042i | ||||
\(296\) | 2.96410 | + | 5.13397i | 0.172285 | + | 0.298406i | ||||
\(297\) | −0.232051 | + | 0.133975i | −0.0134650 | + | 0.00777399i | ||||
\(298\) | 18.7846 | 1.08816 | ||||||||
\(299\) | −12.0000 | + | 3.46410i | −0.693978 | + | 0.200334i | ||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −15.5885 | + | 9.00000i | −0.898504 | + | 0.518751i | ||||
\(302\) | −11.3923 | − | 19.7321i | −0.655553 | − | 1.13545i | ||||
\(303\) | 6.19615 | − | 10.7321i | 0.355960 | − | 0.616540i | ||||
\(304\) | − | 5.73205i | − | 0.328756i | ||||||
\(305\) | −0.464102 | − | 0.267949i | −0.0265744 | − | 0.0153427i | ||||
\(306\) | −3.46410 | − | 2.00000i | −0.198030 | − | 0.114332i | ||||
\(307\) | − | 28.2487i | − | 1.61224i | −0.591753 | − | 0.806120i | \(-0.701564\pi\) | ||
0.591753 | − | 0.806120i | \(-0.298436\pi\) | |||||||
\(308\) | 0.401924 | − | 0.696152i | 0.0229017 | − | 0.0396670i | ||||
\(309\) | −5.79423 | − | 10.0359i | −0.329622 | − | 0.570922i | ||||
\(310\) | −4.26795 | + | 2.46410i | −0.242403 | + | 0.139952i | ||||
\(311\) | 18.9282 | 1.07332 | 0.536660 | − | 0.843799i | \(-0.319686\pi\) | ||||
0.536660 | + | 0.843799i | \(0.319686\pi\) | |||||||
\(312\) | −1.00000 | − | 3.46410i | −0.0566139 | − | 0.196116i | ||||
\(313\) | −33.3205 | −1.88339 | −0.941693 | − | 0.336473i | \(-0.890766\pi\) | ||||
−0.941693 | + | 0.336473i | \(0.890766\pi\) | |||||||
\(314\) | 18.3564 | − | 10.5981i | 1.03591 | − | 0.598084i | ||||
\(315\) | 1.50000 | + | 2.59808i | 0.0845154 | + | 0.146385i | ||||
\(316\) | 1.53590 | − | 2.66025i | 0.0864010 | − | 0.149651i | ||||
\(317\) | 30.4641i | 1.71103i | 0.517774 | + | 0.855517i | \(0.326761\pi\) | ||||
−0.517774 | + | 0.855517i | \(0.673239\pi\) | |||||||
\(318\) | −0.232051 | − | 0.133975i | −0.0130128 | − | 0.00751292i | ||||
\(319\) | −0.339746 | − | 0.196152i | −0.0190221 | − | 0.0109824i | ||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −6.46410 | + | 11.1962i | −0.360791 | + | 0.624908i | ||||
\(322\) | −5.19615 | − | 9.00000i | −0.289570 | − | 0.501550i | ||||
\(323\) | −19.8564 | + | 11.4641i | −1.10484 | + | 0.637880i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −0.866025 | + | 3.50000i | −0.0480384 | + | 0.194145i | ||||
\(326\) | −2.92820 | −0.162178 | ||||||||
\(327\) | −9.00000 | + | 5.19615i | −0.497701 | + | 0.287348i | ||||
\(328\) | 2.00000 | + | 3.46410i | 0.110432 | + | 0.191273i | ||||
\(329\) | −9.69615 | + | 16.7942i | −0.534566 | + | 0.925896i | ||||
\(330\) | − | 0.267949i | − | 0.0147501i | ||||||
\(331\) | 12.4641 | + | 7.19615i | 0.685089 | + | 0.395536i | 0.801770 | − | 0.597633i | \(-0.203892\pi\) |
−0.116681 | + | 0.993169i | \(0.537225\pi\) | |||||||
\(332\) | −8.19615 | − | 4.73205i | −0.449822 | − | 0.259705i | ||||
\(333\) | − | 5.92820i | − | 0.324864i | ||||||
\(334\) | −0.232051 | + | 0.401924i | −0.0126973 | + | 0.0219923i | ||||
\(335\) | −0.732051 | − | 1.26795i | −0.0399962 | − | 0.0692755i | ||||
\(336\) | 2.59808 | − | 1.50000i | 0.141737 | − | 0.0818317i | ||||
\(337\) | −26.3923 | −1.43768 | −0.718840 | − | 0.695175i | \(-0.755327\pi\) | ||||
−0.718840 | + | 0.695175i | \(0.755327\pi\) | |||||||
\(338\) | −12.9904 | + | 0.500000i | −0.706584 | + | 0.0271964i | ||||
\(339\) | 12.0000 | 0.651751 | ||||||||
\(340\) | 3.46410 | − | 2.00000i | 0.187867 | − | 0.108465i | ||||
\(341\) | −0.660254 | − | 1.14359i | −0.0357548 | − | 0.0619291i | ||||
\(342\) | −2.86603 | + | 4.96410i | −0.154977 | + | 0.268428i | ||||
\(343\) | − | 15.0000i | − | 0.809924i | ||||||
\(344\) | 5.19615 | + | 3.00000i | 0.280158 | + | 0.161749i | ||||
\(345\) | −3.00000 | − | 1.73205i | −0.161515 | − | 0.0932505i | ||||
\(346\) | − | 2.12436i | − | 0.114206i | ||||||
\(347\) | −2.19615 | + | 3.80385i | −0.117896 | + | 0.204201i | −0.918934 | − | 0.394412i | \(-0.870948\pi\) |
0.801038 | + | 0.598614i | \(0.204281\pi\) | |||||||
\(348\) | −0.732051 | − | 1.26795i | −0.0392420 | − | 0.0679692i | ||||
\(349\) | −9.12436 | + | 5.26795i | −0.488416 | + | 0.281987i | −0.723917 | − | 0.689887i | \(-0.757660\pi\) |
0.235501 | + | 0.971874i | \(0.424327\pi\) | |||||||
\(350\) | −3.00000 | −0.160357 | ||||||||
\(351\) | −0.866025 | + | 3.50000i | −0.0462250 | + | 0.186816i | ||||
\(352\) | −0.267949 | −0.0142817 | ||||||||
\(353\) | 6.58846 | − | 3.80385i | 0.350668 | − | 0.202458i | −0.314311 | − | 0.949320i | \(-0.601774\pi\) |
0.664980 | + | 0.746862i | \(0.268440\pi\) | |||||||
\(354\) | −5.73205 | − | 9.92820i | −0.304655 | − | 0.527678i | ||||
\(355\) | −6.46410 | + | 11.1962i | −0.343079 | + | 0.594230i | ||||
\(356\) | 14.1244i | 0.748589i | ||||||||
\(357\) | −10.3923 | − | 6.00000i | −0.550019 | − | 0.317554i | ||||
\(358\) | −7.85641 | − | 4.53590i | −0.415224 | − | 0.239730i | ||||
\(359\) | 0.928203i | 0.0489887i | 0.999700 | + | 0.0244943i | \(0.00779757\pi\) | ||||
−0.999700 | + | 0.0244943i | \(0.992202\pi\) | |||||||
\(360\) | 0.500000 | − | 0.866025i | 0.0263523 | − | 0.0456435i | ||||
\(361\) | 6.92820 | + | 12.0000i | 0.364642 | + | 0.631579i | ||||
\(362\) | 14.6603 | − | 8.46410i | 0.770526 | − | 0.444863i | ||||
\(363\) | −10.9282 | −0.573582 | ||||||||
\(364\) | −3.00000 | − | 10.3923i | −0.157243 | − | 0.544705i | ||||
\(365\) | 6.92820 | 0.362639 | ||||||||
\(366\) | 0.464102 | − | 0.267949i | 0.0242590 | − | 0.0140059i | ||||
\(367\) | −10.6603 | − | 18.4641i | −0.556461 | − | 0.963818i | −0.997788 | − | 0.0664722i | \(-0.978826\pi\) |
0.441328 | − | 0.897346i | \(-0.354508\pi\) | |||||||
\(368\) | −1.73205 | + | 3.00000i | −0.0902894 | + | 0.156386i | ||||
\(369\) | − | 4.00000i | − | 0.208232i | ||||||
\(370\) | 5.13397 | + | 2.96410i | 0.266903 | + | 0.154096i | ||||
\(371\) | −0.696152 | − | 0.401924i | −0.0361424 | − | 0.0208668i | ||||
\(372\) | − | 4.92820i | − | 0.255515i | ||||||
\(373\) | −4.53590 | + | 7.85641i | −0.234860 | + | 0.406789i | −0.959232 | − | 0.282620i | \(-0.908796\pi\) |
0.724372 | + | 0.689409i | \(0.242130\pi\) | |||||||
\(374\) | 0.535898 | + | 0.928203i | 0.0277106 | + | 0.0479962i | ||||
\(375\) | −0.866025 | + | 0.500000i | −0.0447214 | + | 0.0258199i | ||||
\(376\) | 6.46410 | 0.333361 | ||||||||
\(377\) | −5.07180 | + | 1.46410i | −0.261211 | + | 0.0754051i | ||||
\(378\) | −3.00000 | −0.154303 | ||||||||
\(379\) | −8.42820 | + | 4.86603i | −0.432928 | + | 0.249951i | −0.700593 | − | 0.713561i | \(-0.747081\pi\) |
0.267665 | + | 0.963512i | \(0.413748\pi\) | |||||||
\(380\) | −2.86603 | − | 4.96410i | −0.147024 | − | 0.254653i | ||||
\(381\) | −6.33013 | + | 10.9641i | −0.324302 | + | 0.561708i | ||||
\(382\) | − | 17.3205i | − | 0.886194i | ||||||
\(383\) | 4.14359 | + | 2.39230i | 0.211728 | + | 0.122241i | 0.602114 | − | 0.798410i | \(-0.294325\pi\) |
−0.390386 | + | 0.920651i | \(0.627659\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | − | 0.803848i | − | 0.0409679i | ||||||
\(386\) | −4.92820 | + | 8.53590i | −0.250839 | + | 0.434466i | ||||
\(387\) | −3.00000 | − | 5.19615i | −0.152499 | − | 0.264135i | ||||
\(388\) | 7.26795 | − | 4.19615i | 0.368974 | − | 0.213027i | ||||
\(389\) | 17.8564 | 0.905356 | 0.452678 | − | 0.891674i | \(-0.350469\pi\) | ||||
0.452678 | + | 0.891674i | \(0.350469\pi\) | |||||||
\(390\) | −2.59808 | − | 2.50000i | −0.131559 | − | 0.126592i | ||||
\(391\) | 13.8564 | 0.700749 | ||||||||
\(392\) | 1.73205 | − | 1.00000i | 0.0874818 | − | 0.0505076i | ||||
\(393\) | 7.16025 | + | 12.4019i | 0.361187 | + | 0.625594i | ||||
\(394\) | −5.69615 | + | 9.86603i | −0.286968 | + | 0.497043i | ||||
\(395\) | − | 3.07180i | − | 0.154559i | ||||||
\(396\) | 0.232051 | + | 0.133975i | 0.0116610 | + | 0.00673248i | ||||
\(397\) | −5.13397 | − | 2.96410i | −0.257667 | − | 0.148764i | 0.365603 | − | 0.930771i | \(-0.380863\pi\) |
−0.623270 | + | 0.782007i | \(0.714196\pi\) | |||||||
\(398\) | − | 24.9282i | − | 1.24954i | ||||||
\(399\) | −8.59808 | + | 14.8923i | −0.430442 | + | 0.745548i | ||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | −19.1603 | + | 11.0622i | −0.956817 | + | 0.552419i | −0.895192 | − | 0.445681i | \(-0.852962\pi\) |
−0.0616254 | + | 0.998099i | \(0.519628\pi\) | |||||||
\(402\) | 1.46410 | 0.0730228 | ||||||||
\(403\) | −17.2487 | − | 4.26795i | −0.859220 | − | 0.212602i | ||||
\(404\) | −12.3923 | −0.616540 | ||||||||
\(405\) | −0.866025 | + | 0.500000i | −0.0430331 | + | 0.0248452i | ||||
\(406\) | −2.19615 | − | 3.80385i | −0.108993 | − | 0.188782i | ||||
\(407\) | −0.794229 | + | 1.37564i | −0.0393685 | + | 0.0681882i | ||||
\(408\) | 4.00000i | 0.198030i | ||||||||
\(409\) | −33.8205 | − | 19.5263i | −1.67232 | − | 0.965512i | −0.966337 | − | 0.257280i | \(-0.917174\pi\) |
−0.705980 | − | 0.708232i | \(-0.749493\pi\) | |||||||
\(410\) | 3.46410 | + | 2.00000i | 0.171080 | + | 0.0987730i | ||||
\(411\) | 13.4641i | 0.664135i | ||||||||
\(412\) | −5.79423 | + | 10.0359i | −0.285461 | + | 0.494433i | ||||
\(413\) | −17.1962 | − | 29.7846i | −0.846167 | − | 1.46560i | ||||
\(414\) | 3.00000 | − | 1.73205i | 0.147442 | − | 0.0851257i | ||||
\(415\) | −9.46410 | −0.464574 | ||||||||
\(416\) | −2.50000 | + | 2.59808i | −0.122573 | + | 0.127381i | ||||
\(417\) | 19.7846 | 0.968857 | ||||||||
\(418\) | 1.33013 | − | 0.767949i | 0.0650586 | − | 0.0375616i | ||||
\(419\) | −4.92820 | − | 8.53590i | −0.240758 | − | 0.417006i | 0.720172 | − | 0.693795i | \(-0.244063\pi\) |
−0.960931 | + | 0.276790i | \(0.910730\pi\) | |||||||
\(420\) | 1.50000 | − | 2.59808i | 0.0731925 | − | 0.126773i | ||||
\(421\) | 21.8564i | 1.06522i | 0.846362 | + | 0.532608i | \(0.178788\pi\) | ||||
−0.846362 | + | 0.532608i | \(0.821212\pi\) | |||||||
\(422\) | 6.99038 | + | 4.03590i | 0.340286 | + | 0.196464i | ||||
\(423\) | −5.59808 | − | 3.23205i | −0.272188 | − | 0.157148i | ||||
\(424\) | 0.267949i | 0.0130128i | ||||||||
\(425\) | 2.00000 | − | 3.46410i | 0.0970143 | − | 0.168034i | ||||
\(426\) | −6.46410 | − | 11.1962i | −0.313187 | − | 0.542455i | ||||
\(427\) | 1.39230 | − | 0.803848i | 0.0673784 | − | 0.0389009i | ||||
\(428\) | 12.9282 | 0.624908 | ||||||||
\(429\) | 0.669873 | − | 0.696152i | 0.0323418 | − | 0.0336106i | ||||
\(430\) | 6.00000 | 0.289346 | ||||||||
\(431\) | −12.0000 | + | 6.92820i | −0.578020 | + | 0.333720i | −0.760346 | − | 0.649518i | \(-0.774971\pi\) |
0.182326 | + | 0.983238i | \(0.441637\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 4.39230 | − | 7.60770i | 0.211081 | − | 0.365602i | −0.740972 | − | 0.671536i | \(-0.765635\pi\) |
0.952053 | + | 0.305933i | \(0.0989684\pi\) | |||||||
\(434\) | − | 14.7846i | − | 0.709684i | ||||||
\(435\) | −1.26795 | − | 0.732051i | −0.0607935 | − | 0.0350991i | ||||
\(436\) | 9.00000 | + | 5.19615i | 0.431022 | + | 0.248851i | ||||
\(437\) | − | 19.8564i | − | 0.949861i | ||||||
\(438\) | −3.46410 | + | 6.00000i | −0.165521 | + | 0.286691i | ||||
\(439\) | 6.66025 | + | 11.5359i | 0.317877 | + | 0.550578i | 0.980045 | − | 0.198777i | \(-0.0636969\pi\) |
−0.662168 | + | 0.749355i | \(0.730364\pi\) | |||||||
\(440\) | −0.232051 | + | 0.133975i | −0.0110626 | + | 0.00638699i | ||||
\(441\) | −2.00000 | −0.0952381 | ||||||||
\(442\) | 14.0000 | + | 3.46410i | 0.665912 | + | 0.164771i | ||||
\(443\) | −19.8564 | −0.943406 | −0.471703 | − | 0.881757i | \(-0.656361\pi\) | ||||
−0.471703 | + | 0.881757i | \(0.656361\pi\) | |||||||
\(444\) | −5.13397 | + | 2.96410i | −0.243648 | + | 0.140670i | ||||
\(445\) | 7.06218 | + | 12.2321i | 0.334779 | + | 0.579855i | ||||
\(446\) | −9.42820 | + | 16.3301i | −0.446438 | + | 0.773254i | ||||
\(447\) | 18.7846i | 0.888482i | ||||||||
\(448\) | −2.59808 | − | 1.50000i | −0.122748 | − | 0.0708683i | ||||
\(449\) | −5.30385 | − | 3.06218i | −0.250304 | − | 0.144513i | 0.369599 | − | 0.929191i | \(-0.379495\pi\) |
−0.619903 | + | 0.784678i | \(0.712828\pi\) | |||||||
\(450\) | − | 1.00000i | − | 0.0471405i | ||||||
\(451\) | −0.535898 | + | 0.928203i | −0.0252345 | + | 0.0437074i | ||||
\(452\) | −6.00000 | − | 10.3923i | −0.282216 | − | 0.488813i | ||||
\(453\) | 19.7321 | − | 11.3923i | 0.927093 | − | 0.535257i | ||||
\(454\) | 6.53590 | 0.306745 | ||||||||
\(455\) | −7.79423 | − | 7.50000i | −0.365399 | − | 0.351605i | ||||
\(456\) | 5.73205 | 0.268428 | ||||||||
\(457\) | −6.46410 | + | 3.73205i | −0.302378 | + | 0.174578i | −0.643511 | − | 0.765437i | \(-0.722523\pi\) |
0.341133 | + | 0.940015i | \(0.389189\pi\) | |||||||
\(458\) | −2.26795 | − | 3.92820i | −0.105974 | − | 0.183553i | ||||
\(459\) | 2.00000 | − | 3.46410i | 0.0933520 | − | 0.161690i | ||||
\(460\) | 3.46410i | 0.161515i | ||||||||
\(461\) | −10.0526 | − | 5.80385i | −0.468194 | − | 0.270312i | 0.247289 | − | 0.968942i | \(-0.420460\pi\) |
−0.715484 | + | 0.698630i | \(0.753794\pi\) | |||||||
\(462\) | 0.696152 | + | 0.401924i | 0.0323879 | + | 0.0186992i | ||||
\(463\) | − | 40.7846i | − | 1.89542i | −0.319131 | − | 0.947711i | \(-0.603391\pi\) | ||
0.319131 | − | 0.947711i | \(-0.396609\pi\) | |||||||
\(464\) | −0.732051 | + | 1.26795i | −0.0339846 | + | 0.0588631i | ||||
\(465\) | −2.46410 | − | 4.26795i | −0.114270 | − | 0.197921i | ||||
\(466\) | 15.5885 | − | 9.00000i | 0.722121 | − | 0.416917i | ||||
\(467\) | 24.3923 | 1.12874 | 0.564371 | − | 0.825522i | \(-0.309119\pi\) | ||||
0.564371 | + | 0.825522i | \(0.309119\pi\) | |||||||
\(468\) | 3.46410 | − | 1.00000i | 0.160128 | − | 0.0462250i | ||||
\(469\) | 4.39230 | 0.202818 | ||||||||
\(470\) | 5.59808 | − | 3.23205i | 0.258220 | − | 0.149083i | ||||
\(471\) | 10.5981 | + | 18.3564i | 0.488334 | + | 0.845819i | ||||
\(472\) | −5.73205 | + | 9.92820i | −0.263839 | + | 0.456983i | ||||
\(473\) | 1.60770i | 0.0739219i | ||||||||
\(474\) | 2.66025 | + | 1.53590i | 0.122190 | + | 0.0705461i | ||||
\(475\) | −4.96410 | − | 2.86603i | −0.227769 | − | 0.131502i | ||||
\(476\) | 12.0000i | 0.550019i | ||||||||
\(477\) | 0.133975 | − | 0.232051i | 0.00613428 | − | 0.0106249i | ||||
\(478\) | 1.73205 | + | 3.00000i | 0.0792222 | + | 0.137217i | ||||
\(479\) | −19.2679 | + | 11.1244i | −0.880375 | + | 0.508285i | −0.870782 | − | 0.491669i | \(-0.836387\pi\) |
−0.00959301 | + | 0.999954i | \(0.503054\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 5.92820 | + | 20.5359i | 0.270303 | + | 0.936356i | ||||
\(482\) | −25.1962 | −1.14765 | ||||||||
\(483\) | 9.00000 | − | 5.19615i | 0.409514 | − | 0.236433i | ||||
\(484\) | 5.46410 | + | 9.46410i | 0.248368 | + | 0.430186i | ||||
\(485\) | 4.19615 | − | 7.26795i | 0.190537 | − | 0.330021i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 18.1865 | + | 10.5000i | 0.824110 | + | 0.475800i | 0.851832 | − | 0.523815i | \(-0.175492\pi\) |
−0.0277214 | + | 0.999616i | \(0.508825\pi\) | |||||||
\(488\) | −0.464102 | − | 0.267949i | −0.0210089 | − | 0.0121295i | ||||
\(489\) | − | 2.92820i | − | 0.132418i | ||||||
\(490\) | 1.00000 | − | 1.73205i | 0.0451754 | − | 0.0782461i | ||||
\(491\) | −2.69615 | − | 4.66987i | −0.121676 | − | 0.210748i | 0.798753 | − | 0.601659i | \(-0.205493\pi\) |
−0.920429 | + | 0.390911i | \(0.872160\pi\) | |||||||
\(492\) | −3.46410 | + | 2.00000i | −0.156174 | + | 0.0901670i | ||||
\(493\) | 5.85641 | 0.263759 | ||||||||
\(494\) | 4.96410 | − | 20.0622i | 0.223345 | − | 0.902640i | ||||
\(495\) | 0.267949 | 0.0120434 | ||||||||
\(496\) | −4.26795 | + | 2.46410i | −0.191637 | + | 0.110641i | ||||
\(497\) | −19.3923 | − | 33.5885i | −0.869864 | − | 1.50665i | ||||
\(498\) | 4.73205 | − | 8.19615i | 0.212048 | − | 0.367278i | ||||
\(499\) | 33.3205i | 1.49163i | 0.666153 | + | 0.745815i | \(0.267940\pi\) | ||||
−0.666153 | + | 0.745815i | \(0.732060\pi\) | |||||||
\(500\) | 0.866025 | + | 0.500000i | 0.0387298 | + | 0.0223607i | ||||
\(501\) | −0.401924 | − | 0.232051i | −0.0179566 | − | 0.0103673i | ||||
\(502\) | 19.5359i | 0.871930i | ||||||||
\(503\) | −1.86603 | + | 3.23205i | −0.0832020 | + | 0.144110i | −0.904624 | − | 0.426211i | \(-0.859848\pi\) |
0.821422 | + | 0.570321i | \(0.193181\pi\) | |||||||
\(504\) | 1.50000 | + | 2.59808i | 0.0668153 | + | 0.115728i | ||||
\(505\) | −10.7321 | + | 6.19615i | −0.477570 | + | 0.275725i | ||||
\(506\) | −0.928203 | −0.0412637 | ||||||||
\(507\) | −0.500000 | − | 12.9904i | −0.0222058 | − | 0.576923i | ||||
\(508\) | 12.6603 | 0.561708 | ||||||||
\(509\) | 25.3923 | − | 14.6603i | 1.12549 | − | 0.649804i | 0.182696 | − | 0.983169i | \(-0.441517\pi\) |
0.942798 | + | 0.333365i | \(0.108184\pi\) | |||||||
\(510\) | 2.00000 | + | 3.46410i | 0.0885615 | + | 0.153393i | ||||
\(511\) | −10.3923 | + | 18.0000i | −0.459728 | + | 0.796273i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −4.96410 | − | 2.86603i | −0.219170 | − | 0.126538i | ||||
\(514\) | −12.5885 | − | 7.26795i | −0.555253 | − | 0.320575i | ||||
\(515\) | 11.5885i | 0.510648i | ||||||||
\(516\) | −3.00000 | + | 5.19615i | −0.132068 | + | 0.228748i | ||||
\(517\) | 0.866025 | + | 1.50000i | 0.0380878 | + | 0.0659699i | ||||
\(518\) | −15.4019 | + | 8.89230i | −0.676722 | + | 0.390705i | ||||
\(519\) | 2.12436 | 0.0932489 | ||||||||
\(520\) | −0.866025 | + | 3.50000i | −0.0379777 | + | 0.153485i | ||||
\(521\) | −6.60770 | −0.289488 | −0.144744 | − | 0.989469i | \(-0.546236\pi\) | ||||
−0.144744 | + | 0.989469i | \(0.546236\pi\) | |||||||
\(522\) | 1.26795 | − | 0.732051i | 0.0554966 | − | 0.0320410i | ||||
\(523\) | 20.8564 | + | 36.1244i | 0.911987 | + | 1.57961i | 0.811254 | + | 0.584694i | \(0.198786\pi\) |
0.100733 | + | 0.994913i | \(0.467881\pi\) | |||||||
\(524\) | 7.16025 | − | 12.4019i | 0.312797 | − | 0.541781i | ||||
\(525\) | − | 3.00000i | − | 0.130931i | ||||||
\(526\) | 21.2321 | + | 12.2583i | 0.925761 | + | 0.534489i | ||||
\(527\) | 17.0718 | + | 9.85641i | 0.743659 | + | 0.429352i | ||||
\(528\) | − | 0.267949i | − | 0.0116610i | ||||||
\(529\) | 5.50000 | − | 9.52628i | 0.239130 | − | 0.414186i | ||||
\(530\) | 0.133975 | + | 0.232051i | 0.00581948 | + | 0.0100796i | ||||
\(531\) | 9.92820 | − | 5.73205i | 0.430847 | − | 0.248750i | ||||
\(532\) | 17.1962 | 0.745548 | ||||||||
\(533\) | 4.00000 | + | 13.8564i | 0.173259 | + | 0.600188i | ||||
\(534\) | −14.1244 | −0.611221 | ||||||||
\(535\) | 11.1962 | − | 6.46410i | 0.484052 | − | 0.279467i | ||||
\(536\) | −0.732051 | − | 1.26795i | −0.0316198 | − | 0.0547671i | ||||
\(537\) | 4.53590 | − | 7.85641i | 0.195738 | − | 0.339029i | ||||
\(538\) | − | 17.0718i | − | 0.736017i | ||||||
\(539\) | 0.464102 | + | 0.267949i | 0.0199903 | + | 0.0115414i | ||||
\(540\) | 0.866025 | + | 0.500000i | 0.0372678 | + | 0.0215166i | ||||
\(541\) | 14.7846i | 0.635640i | 0.948151 | + | 0.317820i | \(0.102951\pi\) | ||||
−0.948151 | + | 0.317820i | \(0.897049\pi\) | |||||||
\(542\) | 12.1962 | − | 21.1244i | 0.523870 | − | 0.907369i | ||||
\(543\) | 8.46410 | + | 14.6603i | 0.363229 | + | 0.629132i | ||||
\(544\) | 3.46410 | − | 2.00000i | 0.148522 | − | 0.0857493i | ||||
\(545\) | 10.3923 | 0.445157 | ||||||||
\(546\) | 10.3923 | − | 3.00000i | 0.444750 | − | 0.128388i | ||||
\(547\) | −5.32051 | −0.227488 | −0.113744 | − | 0.993510i | \(-0.536284\pi\) | ||||
−0.113744 | + | 0.993510i | \(0.536284\pi\) | |||||||
\(548\) | 11.6603 | − | 6.73205i | 0.498101 | − | 0.287579i | ||||
\(549\) | 0.267949 | + | 0.464102i | 0.0114358 | + | 0.0198074i | ||||
\(550\) | −0.133975 | + | 0.232051i | −0.00571270 | + | 0.00989468i | ||||
\(551\) | − | 8.39230i | − | 0.357524i | ||||||
\(552\) | −3.00000 | − | 1.73205i | −0.127688 | − | 0.0737210i | ||||
\(553\) | 7.98076 | + | 4.60770i | 0.339377 | + | 0.195939i | ||||
\(554\) | 11.5885i | 0.492346i | ||||||||
\(555\) | −2.96410 | + | 5.13397i | −0.125819 | + | 0.217925i | ||||
\(556\) | −9.89230 | − | 17.1340i | −0.419527 | − | 0.726642i | ||||
\(557\) | −19.5788 | + | 11.3038i | −0.829582 | + | 0.478959i | −0.853710 | − | 0.520749i | \(-0.825653\pi\) |
0.0241275 | + | 0.999709i | \(0.492319\pi\) | |||||||
\(558\) | 4.92820 | 0.208627 | ||||||||
\(559\) | 15.5885 | + | 15.0000i | 0.659321 | + | 0.634432i | ||||
\(560\) | −3.00000 | −0.126773 | ||||||||
\(561\) | −0.928203 | + | 0.535898i | −0.0391888 | + | 0.0226256i | ||||
\(562\) | 3.46410 | + | 6.00000i | 0.146124 | + | 0.253095i | ||||
\(563\) | 7.66025 | − | 13.2679i | 0.322841 | − | 0.559177i | −0.658232 | − | 0.752815i | \(-0.728695\pi\) |
0.981073 | + | 0.193638i | \(0.0620287\pi\) | |||||||
\(564\) | 6.46410i | 0.272188i | ||||||||
\(565\) | −10.3923 | − | 6.00000i | −0.437208 | − | 0.252422i | ||||
\(566\) | 5.53590 | + | 3.19615i | 0.232691 | + | 0.134344i | ||||
\(567\) | − | 3.00000i | − | 0.125988i | ||||||
\(568\) | −6.46410 | + | 11.1962i | −0.271228 | + | 0.469780i | ||||
\(569\) | 8.16025 | + | 14.1340i | 0.342096 | + | 0.592527i | 0.984822 | − | 0.173569i | \(-0.0555300\pi\) |
−0.642726 | + | 0.766096i | \(0.722197\pi\) | |||||||
\(570\) | 4.96410 | − | 2.86603i | 0.207923 | − | 0.120045i | ||||
\(571\) | 10.8564 | 0.454326 | 0.227163 | − | 0.973857i | \(-0.427055\pi\) | ||||
0.227163 | + | 0.973857i | \(0.427055\pi\) | |||||||
\(572\) | −0.937822 | − | 0.232051i | −0.0392123 | − | 0.00970253i | ||||
\(573\) | 17.3205 | 0.723575 | ||||||||
\(574\) | −10.3923 | + | 6.00000i | −0.433766 | + | 0.250435i | ||||
\(575\) | 1.73205 | + | 3.00000i | 0.0722315 | + | 0.125109i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | − | 9.32051i | − | 0.388018i | −0.981000 | − | 0.194009i | \(-0.937851\pi\) | ||
0.981000 | − | 0.194009i | \(-0.0621491\pi\) | |||||||
\(578\) | 0.866025 | + | 0.500000i | 0.0360219 | + | 0.0207973i | ||||
\(579\) | −8.53590 | − | 4.92820i | −0.354740 | − | 0.204809i | ||||
\(580\) | 1.46410i | 0.0607935i | ||||||||
\(581\) | 14.1962 | − | 24.5885i | 0.588956 | − | 1.02010i | ||||
\(582\) | 4.19615 | + | 7.26795i | 0.173936 | + | 0.301266i | ||||
\(583\) | −0.0621778 | + | 0.0358984i | −0.00257514 | + | 0.00148676i | ||||
\(584\) | 6.92820 | 0.286691 | ||||||||
\(585\) | 2.50000 | − | 2.59808i | 0.103362 | − | 0.107417i | ||||
\(586\) | 29.2487 | 1.20825 | ||||||||
\(587\) | −7.73205 | + | 4.46410i | −0.319136 | + | 0.184253i | −0.651007 | − | 0.759071i | \(-0.725653\pi\) |
0.331871 | + | 0.943325i | \(0.392320\pi\) | |||||||
\(588\) | 1.00000 | + | 1.73205i | 0.0412393 | + | 0.0714286i | ||||
\(589\) | 14.1244 | − | 24.4641i | 0.581984 | − | 1.00803i | ||||
\(590\) | 11.4641i | 0.471970i | ||||||||
\(591\) | −9.86603 | − | 5.69615i | −0.405834 | − | 0.234308i | ||||
\(592\) | 5.13397 | + | 2.96410i | 0.211005 | + | 0.121824i | ||||
\(593\) | − | 44.7846i | − | 1.83908i | −0.392992 | − | 0.919542i | \(-0.628560\pi\) | ||
0.392992 | − | 0.919542i | \(-0.371440\pi\) | |||||||
\(594\) | −0.133975 | + | 0.232051i | −0.00549704 | + | 0.00952116i | ||||
\(595\) | 6.00000 | + | 10.3923i | 0.245976 | + | 0.426043i | ||||
\(596\) | 16.2679 | − | 9.39230i | 0.666361 | − | 0.384724i | ||||
\(597\) | 24.9282 | 1.02024 | ||||||||
\(598\) | −8.66025 | + | 9.00000i | −0.354144 | + | 0.368037i | ||||
\(599\) | 28.9282 | 1.18197 | 0.590987 | − | 0.806681i | \(-0.298738\pi\) | ||||
0.590987 | + | 0.806681i | \(0.298738\pi\) | |||||||
\(600\) | −0.866025 | + | 0.500000i | −0.0353553 | + | 0.0204124i | ||||
\(601\) | −15.3564 | − | 26.5981i | −0.626401 | − | 1.08496i | −0.988268 | − | 0.152729i | \(-0.951194\pi\) |
0.361867 | − | 0.932230i | \(-0.382139\pi\) | |||||||
\(602\) | −9.00000 | + | 15.5885i | −0.366813 | + | 0.635338i | ||||
\(603\) | 1.46410i | 0.0596228i | ||||||||
\(604\) | −19.7321 | − | 11.3923i | −0.802886 | − | 0.463546i | ||||
\(605\) | 9.46410 | + | 5.46410i | 0.384770 | + | 0.222147i | ||||
\(606\) | − | 12.3923i | − | 0.503403i | ||||||
\(607\) | 10.7224 | − | 18.5718i | 0.435210 | − | 0.753806i | −0.562103 | − | 0.827067i | \(-0.690007\pi\) |
0.997313 | + | 0.0732615i | \(0.0233408\pi\) | |||||||
\(608\) | −2.86603 | − | 4.96410i | −0.116233 | − | 0.201321i | ||||
\(609\) | 3.80385 | − | 2.19615i | 0.154140 | − | 0.0889926i | ||||
\(610\) | −0.535898 | −0.0216979 | ||||||||
\(611\) | 22.6244 | + | 5.59808i | 0.915283 | + | 0.226474i | ||||
\(612\) | −4.00000 | −0.161690 | ||||||||
\(613\) | 38.9711 | − | 22.5000i | 1.57403 | − | 0.908766i | 0.578362 | − | 0.815780i | \(-0.303692\pi\) |
0.995667 | − | 0.0929864i | \(-0.0296413\pi\) | |||||||
\(614\) | −14.1244 | − | 24.4641i | −0.570013 | − | 0.987291i | ||||
\(615\) | −2.00000 | + | 3.46410i | −0.0806478 | + | 0.139686i | ||||
\(616\) | − | 0.803848i | − | 0.0323879i | ||||||
\(617\) | −30.7128 | − | 17.7321i | −1.23645 | − | 0.713865i | −0.268084 | − | 0.963395i | \(-0.586391\pi\) |
−0.968367 | + | 0.249530i | \(0.919724\pi\) | |||||||
\(618\) | −10.0359 | − | 5.79423i | −0.403703 | − | 0.233078i | ||||
\(619\) | 2.51666i | 0.101153i | 0.998720 | + | 0.0505766i | \(0.0161059\pi\) | ||||
−0.998720 | + | 0.0505766i | \(0.983894\pi\) | |||||||
\(620\) | −2.46410 | + | 4.26795i | −0.0989607 | + | 0.171405i | ||||
\(621\) | 1.73205 | + | 3.00000i | 0.0695048 | + | 0.120386i | ||||
\(622\) | 16.3923 | − | 9.46410i | 0.657272 | − | 0.379476i | ||||
\(623\) | −42.3731 | −1.69764 | ||||||||
\(624\) | −2.59808 | − | 2.50000i | −0.104006 | − | 0.100080i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −28.8564 | + | 16.6603i | −1.15333 | + | 0.665878i | ||||
\(627\) | 0.767949 | + | 1.33013i | 0.0306689 | + | 0.0531202i | ||||
\(628\) | 10.5981 | − | 18.3564i | 0.422909 | − | 0.732500i | ||||
\(629\) | − | 23.7128i | − | 0.945492i | ||||||
\(630\) | 2.59808 | + | 1.50000i | 0.103510 | + | 0.0597614i | ||||
\(631\) | −6.92820 | − | 4.00000i | −0.275807 | − | 0.159237i | 0.355716 | − | 0.934594i | \(-0.384237\pi\) |
−0.631524 | + | 0.775356i | \(0.717570\pi\) | |||||||
\(632\) | − | 3.07180i | − | 0.122190i | ||||||
\(633\) | −4.03590 | + | 6.99038i | −0.160413 | + | 0.277843i | ||||
\(634\) | 15.2321 | + | 26.3827i | 0.604942 | + | 1.04779i | ||||
\(635\) | 10.9641 | − | 6.33013i | 0.435097 | − | 0.251203i | ||||
\(636\) | −0.267949 | −0.0106249 | ||||||||
\(637\) | 6.92820 | − | 2.00000i | 0.274505 | − | 0.0792429i | ||||
\(638\) | −0.392305 | −0.0155315 | ||||||||
\(639\) | 11.1962 | − | 6.46410i | 0.442913 | − | 0.255716i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | −7.23205 | + | 12.5263i | −0.285649 | + | 0.494758i | −0.972766 | − | 0.231788i | \(-0.925542\pi\) |
0.687117 | + | 0.726546i | \(0.258876\pi\) | |||||||
\(642\) | 12.9282i | 0.510235i | ||||||||
\(643\) | 11.0718 | + | 6.39230i | 0.436629 | + | 0.252088i | 0.702167 | − | 0.712013i | \(-0.252216\pi\) |
−0.265538 | + | 0.964100i | \(0.585549\pi\) | |||||||
\(644\) | −9.00000 | − | 5.19615i | −0.354650 | − | 0.204757i | ||||
\(645\) | 6.00000i | 0.236250i | ||||||||
\(646\) | −11.4641 | + | 19.8564i | −0.451049 | + | 0.781240i | ||||
\(647\) | 17.8660 | + | 30.9449i | 0.702386 | + | 1.21657i | 0.967627 | + | 0.252386i | \(0.0812152\pi\) |
−0.265241 | + | 0.964182i | \(0.585451\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | −3.07180 | −0.120579 | ||||||||
\(650\) | 1.00000 | + | 3.46410i | 0.0392232 | + | 0.135873i | ||||
\(651\) | 14.7846 | 0.579455 | ||||||||
\(652\) | −2.53590 | + | 1.46410i | −0.0993134 | + | 0.0573386i | ||||
\(653\) | 0.794229 | + | 1.37564i | 0.0310806 | + | 0.0538331i | 0.881147 | − | 0.472842i | \(-0.156772\pi\) |
−0.850067 | + | 0.526675i | \(0.823438\pi\) | |||||||
\(654\) | −5.19615 | + | 9.00000i | −0.203186 | + | 0.351928i | ||||
\(655\) | − | 14.3205i | − | 0.559549i | ||||||
\(656\) | 3.46410 | + | 2.00000i | 0.135250 | + | 0.0780869i | ||||
\(657\) | −6.00000 | − | 3.46410i | −0.234082 | − | 0.135147i | ||||
\(658\) | 19.3923i | 0.755991i | ||||||||
\(659\) | 19.8564 | − | 34.3923i | 0.773496 | − | 1.33973i | −0.162140 | − | 0.986768i | \(-0.551840\pi\) |
0.935636 | − | 0.352966i | \(-0.114827\pi\) | |||||||
\(660\) | −0.133975 | − | 0.232051i | −0.00521495 | − | 0.00903257i | ||||
\(661\) | −18.7128 | + | 10.8038i | −0.727844 | + | 0.420221i | −0.817633 | − | 0.575740i | \(-0.804714\pi\) |
0.0897889 | + | 0.995961i | \(0.471381\pi\) | |||||||
\(662\) | 14.3923 | 0.559373 | ||||||||
\(663\) | −3.46410 | + | 14.0000i | −0.134535 | + | 0.543715i | ||||
\(664\) | −9.46410 | −0.367278 | ||||||||
\(665\) | 14.8923 | − | 8.59808i | 0.577499 | − | 0.333419i | ||||
\(666\) | −2.96410 | − | 5.13397i | −0.114857 | − | 0.198937i | ||||
\(667\) | −2.53590 | + | 4.39230i | −0.0981904 | + | 0.170071i | ||||
\(668\) | 0.464102i | 0.0179566i | ||||||||
\(669\) | −16.3301 | − | 9.42820i | −0.631359 | − | 0.364515i | ||||
\(670\) | −1.26795 | − | 0.732051i | −0.0489852 | − | 0.0282816i | ||||
\(671\) | − | 0.143594i | − | 0.00554337i | ||||||
\(672\) | 1.50000 | − | 2.59808i | 0.0578638 | − | 0.100223i | ||||
\(673\) | 8.39230 | + | 14.5359i | 0.323500 | + | 0.560318i | 0.981208 | − | 0.192955i | \(-0.0618072\pi\) |
−0.657708 | + | 0.753273i | \(0.728474\pi\) | |||||||
\(674\) | −22.8564 | + | 13.1962i | −0.880396 | + | 0.508297i | ||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −11.0000 | + | 6.92820i | −0.423077 | + | 0.266469i | ||||
\(677\) | 10.9282 | 0.420005 | 0.210002 | − | 0.977701i | \(-0.432653\pi\) | ||||
0.210002 | + | 0.977701i | \(0.432653\pi\) | |||||||
\(678\) | 10.3923 | − | 6.00000i | 0.399114 | − | 0.230429i | ||||
\(679\) | 12.5885 | + | 21.8038i | 0.483101 | + | 0.836755i | ||||
\(680\) | 2.00000 | − | 3.46410i | 0.0766965 | − | 0.132842i | ||||
\(681\) | 6.53590i | 0.250456i | ||||||||
\(682\) | −1.14359 | − | 0.660254i | −0.0437905 | − | 0.0252824i | ||||
\(683\) | 35.7846 | + | 20.6603i | 1.36926 | + | 0.790543i | 0.990834 | − | 0.135089i | \(-0.0431319\pi\) |
0.378427 | + | 0.925631i | \(0.376465\pi\) | |||||||
\(684\) | 5.73205i | 0.219170i | ||||||||
\(685\) | 6.73205 | − | 11.6603i | 0.257218 | − | 0.445515i | ||||
\(686\) | −7.50000 | − | 12.9904i | −0.286351 | − | 0.495975i | ||||
\(687\) | 3.92820 | − | 2.26795i | 0.149870 | − | 0.0865277i | ||||
\(688\) | 6.00000 | 0.228748 | ||||||||
\(689\) | −0.232051 | + | 0.937822i | −0.00884043 | + | 0.0357282i | ||||
\(690\) | −3.46410 | −0.131876 | ||||||||
\(691\) | 13.0359 | − | 7.52628i | 0.495909 | − | 0.286313i | −0.231114 | − | 0.972927i | \(-0.574237\pi\) |
0.727023 | + | 0.686614i | \(0.240904\pi\) | |||||||
\(692\) | −1.06218 | − | 1.83975i | −0.0403779 | − | 0.0699366i | ||||
\(693\) | −0.401924 | + | 0.696152i | −0.0152678 | + | 0.0264446i | ||||
\(694\) | 4.39230i | 0.166730i | ||||||||
\(695\) | −17.1340 | − | 9.89230i | −0.649929 | − | 0.375237i | ||||
\(696\) | −1.26795 | − | 0.732051i | −0.0480615 | − | 0.0277483i | ||||
\(697\) | − | 16.0000i | − | 0.606043i | ||||||
\(698\) | −5.26795 | + | 9.12436i | −0.199395 | + | 0.345362i | ||||
\(699\) | 9.00000 | + | 15.5885i | 0.340411 | + | 0.589610i | ||||
\(700\) | −2.59808 | + | 1.50000i | −0.0981981 | + | 0.0566947i | ||||
\(701\) | −4.39230 | −0.165895 | −0.0829475 | − | 0.996554i | \(-0.526433\pi\) | ||||
−0.0829475 | + | 0.996554i | \(0.526433\pi\) | |||||||
\(702\) | 1.00000 | + | 3.46410i | 0.0377426 | + | 0.130744i | ||||
\(703\) | −33.9808 | −1.28161 | ||||||||
\(704\) | −0.232051 | + | 0.133975i | −0.00874574 | + | 0.00504936i | ||||
\(705\) | 3.23205 | + | 5.59808i | 0.121726 | + | 0.210836i | ||||
\(706\) | 3.80385 | − | 6.58846i | 0.143160 | − | 0.247960i | ||||
\(707\) | − | 37.1769i | − | 1.39818i | ||||||
\(708\) | −9.92820 | − | 5.73205i | −0.373125 | − | 0.215424i | ||||
\(709\) | −23.6603 | − | 13.6603i | −0.888579 | − | 0.513022i | −0.0151019 | − | 0.999886i | \(-0.504807\pi\) |
−0.873478 | + | 0.486864i | \(0.838141\pi\) | |||||||
\(710\) | 12.9282i | 0.485187i | ||||||||
\(711\) | −1.53590 | + | 2.66025i | −0.0576007 | + | 0.0997673i | ||||
\(712\) | 7.06218 | + | 12.2321i | 0.264666 | + | 0.458415i | ||||
\(713\) | −14.7846 | + | 8.53590i | −0.553688 | + | 0.319672i | ||||
\(714\) | −12.0000 | −0.449089 | ||||||||
\(715\) | −0.928203 | + | 0.267949i | −0.0347128 | + | 0.0100207i | ||||
\(716\) | −9.07180 | −0.339029 | ||||||||
\(717\) | −3.00000 | + | 1.73205i | −0.112037 | + | 0.0646846i | ||||
\(718\) | 0.464102 | + | 0.803848i | 0.0173201 | + | 0.0299993i | ||||
\(719\) | −8.00000 | + | 13.8564i | −0.298350 | + | 0.516757i | −0.975759 | − | 0.218850i | \(-0.929769\pi\) |
0.677409 | + | 0.735607i | \(0.263103\pi\) | |||||||
\(720\) | − | 1.00000i | − | 0.0372678i | ||||||
\(721\) | −30.1077 | − | 17.3827i | −1.12127 | − | 0.647365i | ||||
\(722\) | 12.0000 | + | 6.92820i | 0.446594 | + | 0.257841i | ||||
\(723\) | − | 25.1962i | − | 0.937055i | ||||||
\(724\) | 8.46410 | − | 14.6603i | 0.314566 | − | 0.544844i | ||||
\(725\) | 0.732051 | + | 1.26795i | 0.0271877 | + | 0.0470905i | ||||
\(726\) | −9.46410 | + | 5.46410i | −0.351246 | + | 0.202792i | ||||
\(727\) | −4.66025 | −0.172839 | −0.0864196 | − | 0.996259i | \(-0.527543\pi\) | ||||
−0.0864196 | + | 0.996259i | \(0.527543\pi\) | |||||||
\(728\) | −7.79423 | − | 7.50000i | −0.288873 | − | 0.277968i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.00000 | − | 3.46410i | 0.222070 | − | 0.128212i | ||||
\(731\) | −12.0000 | − | 20.7846i | −0.443836 | − | 0.768747i | ||||
\(732\) | 0.267949 | − | 0.464102i | 0.00990369 | − | 0.0171537i | ||||
\(733\) | 20.8564i | 0.770349i | 0.922844 | + | 0.385174i | \(0.125859\pi\) | ||||
−0.922844 | + | 0.385174i | \(0.874141\pi\) | |||||||
\(734\) | −18.4641 | − | 10.6603i | −0.681522 | − | 0.393477i | ||||
\(735\) | 1.73205 | + | 1.00000i | 0.0638877 | + | 0.0368856i | ||||
\(736\) | 3.46410i | 0.127688i | ||||||||
\(737\) | 0.196152 | − | 0.339746i | 0.00722537 | − | 0.0125147i | ||||
\(738\) | −2.00000 | − | 3.46410i | −0.0736210 | − | 0.127515i | ||||
\(739\) | 31.0359 | − | 17.9186i | 1.14167 | − | 0.659146i | 0.194829 | − | 0.980837i | \(-0.437585\pi\) |
0.946845 | + | 0.321691i | \(0.104251\pi\) | |||||||
\(740\) | 5.92820 | 0.217925 | ||||||||
\(741\) | 20.0622 | + | 4.96410i | 0.737003 | + | 0.182361i | ||||
\(742\) | −0.803848 | −0.0295102 | ||||||||
\(743\) | −9.46410 | + | 5.46410i | −0.347204 | + | 0.200458i | −0.663453 | − | 0.748218i | \(-0.730910\pi\) |
0.316249 | + | 0.948676i | \(0.397576\pi\) | |||||||
\(744\) | −2.46410 | − | 4.26795i | −0.0903383 | − | 0.156471i | ||||
\(745\) | 9.39230 | − | 16.2679i | 0.344107 | − | 0.596012i | ||||
\(746\) | 9.07180i | 0.332142i | ||||||||
\(747\) | 8.19615 | + | 4.73205i | 0.299882 | + | 0.173137i | ||||
\(748\) | 0.928203 | + | 0.535898i | 0.0339385 | + | 0.0195944i | ||||
\(749\) | 38.7846i | 1.41716i | ||||||||
\(750\) | −0.500000 | + | 0.866025i | −0.0182574 | + | 0.0316228i | ||||
\(751\) | 10.5885 | + | 18.3397i | 0.386378 | + | 0.669227i | 0.991959 | − | 0.126557i | \(-0.0403926\pi\) |
−0.605581 | + | 0.795784i | \(0.707059\pi\) | |||||||
\(752\) | 5.59808 | − | 3.23205i | 0.204141 | − | 0.117861i | ||||
\(753\) | −19.5359 | −0.711928 | ||||||||
\(754\) | −3.66025 | + | 3.80385i | −0.133299 | + | 0.138528i | ||||
\(755\) | −22.7846 | −0.829217 | ||||||||
\(756\) | −2.59808 | + | 1.50000i | −0.0944911 | + | 0.0545545i | ||||
\(757\) | −10.8660 | − | 18.8205i | −0.394932 | − | 0.684043i | 0.598160 | − | 0.801377i | \(-0.295899\pi\) |
−0.993093 | + | 0.117334i | \(0.962565\pi\) | |||||||
\(758\) | −4.86603 | + | 8.42820i | −0.176742 | + | 0.306126i | ||||
\(759\) | − | 0.928203i | − | 0.0336916i | ||||||
\(760\) | −4.96410 | − | 2.86603i | −0.180067 | − | 0.103962i | ||||
\(761\) | 6.91154 | + | 3.99038i | 0.250543 | + | 0.144651i | 0.620013 | − | 0.784592i | \(-0.287127\pi\) |
−0.369470 | + | 0.929243i | \(0.620461\pi\) | |||||||
\(762\) | 12.6603i | 0.458633i | ||||||||
\(763\) | −15.5885 | + | 27.0000i | −0.564340 | + | 0.977466i | ||||
\(764\) | −8.66025 | − | 15.0000i | −0.313317 | − | 0.542681i | ||||
\(765\) | −3.46410 | + | 2.00000i | −0.125245 | + | 0.0723102i | ||||
\(766\) | 4.78461 | 0.172875 | ||||||||
\(767\) | −28.6603 | + | 29.7846i | −1.03486 | + | 1.07546i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 13.6077 | − | 7.85641i | 0.490706 | − | 0.283309i | −0.234161 | − | 0.972198i | \(-0.575234\pi\) |
0.724867 | + | 0.688889i | \(0.241901\pi\) | |||||||
\(770\) | −0.401924 | − | 0.696152i | −0.0144843 | − | 0.0250876i | ||||
\(771\) | 7.26795 | − | 12.5885i | 0.261749 | − | 0.453362i | ||||
\(772\) | 9.85641i | 0.354740i | ||||||||
\(773\) | −28.2391 | − | 16.3038i | −1.01569 | − | 0.586409i | −0.102837 | − | 0.994698i | \(-0.532792\pi\) |
−0.912852 | + | 0.408290i | \(0.866125\pi\) | |||||||
\(774\) | −5.19615 | − | 3.00000i | −0.186772 | − | 0.107833i | ||||
\(775\) | 4.92820i | 0.177026i | ||||||||
\(776\) | 4.19615 | − | 7.26795i | 0.150633 | − | 0.260904i | ||||
\(777\) | −8.89230 | − | 15.4019i | −0.319010 | − | 0.552541i | ||||
\(778\) | 15.4641 | − | 8.92820i | 0.554415 | − | 0.320092i | ||||
\(779\) | −22.9282 | −0.821488 | ||||||||
\(780\) | −3.50000 | − | 0.866025i | −0.125320 | − | 0.0310087i | ||||
\(781\) | −3.46410 | −0.123955 | ||||||||
\(782\) | 12.0000 | − | 6.92820i | 0.429119 | − | 0.247752i | ||||
\(783\) | 0.732051 | + | 1.26795i | 0.0261614 | + | 0.0453128i | ||||
\(784\) | 1.00000 | − | 1.73205i | 0.0357143 | − | 0.0618590i | ||||
\(785\) | − | 21.1962i | − | 0.756523i | ||||||
\(786\) | 12.4019 | + | 7.16025i | 0.442362 | + | 0.255398i | ||||
\(787\) | 1.26795 | + | 0.732051i | 0.0451975 | + | 0.0260948i | 0.522428 | − | 0.852683i | \(-0.325026\pi\) |
−0.477231 | + | 0.878778i | \(0.658359\pi\) | |||||||
\(788\) | 11.3923i | 0.405834i | ||||||||
\(789\) | −12.2583 | + | 21.2321i | −0.436408 | + | 0.755881i | ||||
\(790\) | −1.53590 | − | 2.66025i | −0.0546448 | − | 0.0946476i | ||||
\(791\) | 31.1769 | − | 18.0000i | 1.10852 | − | 0.640006i | ||||
\(792\) | 0.267949 | 0.00952116 | ||||||||
\(793\) | −1.39230 | − | 1.33975i | −0.0494422 | − | 0.0475758i | ||||
\(794\) | −5.92820 | −0.210384 | ||||||||
\(795\) | −0.232051 | + | 0.133975i | −0.00822999 | + | 0.00475159i | ||||
\(796\) | −12.4641 | − | 21.5885i | −0.441778 | − | 0.765183i | ||||
\(797\) | 5.07180 | − | 8.78461i | 0.179652 | − | 0.311167i | −0.762109 | − | 0.647449i | \(-0.775836\pi\) |
0.941761 | + | 0.336282i | \(0.109169\pi\) | |||||||
\(798\) | 17.1962i | 0.608737i | ||||||||
\(799\) | −22.3923 | − | 12.9282i | −0.792183 | − | 0.457367i | ||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | − | 14.1244i | − | 0.499060i | ||||||
\(802\) | −11.0622 | + | 19.1603i | −0.390619 | + | 0.676572i | ||||
\(803\) | 0.928203 | + | 1.60770i | 0.0327556 | + | 0.0567343i | ||||
\(804\) | 1.26795 | − | 0.732051i | 0.0447171 | − | 0.0258174i | ||||
\(805\) | −10.3923 | −0.366281 | ||||||||
\(806\) | −17.0718 | + | 4.92820i | −0.601328 | + | 0.173589i | ||||
\(807\) | 17.0718 | 0.600956 | ||||||||
\(808\) | −10.7321 | + | 6.19615i | −0.377552 | + | 0.217980i | ||||
\(809\) | 3.39230 | + | 5.87564i | 0.119267 | + | 0.206577i | 0.919477 | − | 0.393143i | \(-0.128612\pi\) |
−0.800210 | + | 0.599719i | \(0.795279\pi\) | |||||||
\(810\) | −0.500000 | + | 0.866025i | −0.0175682 | + | 0.0304290i | ||||
\(811\) | 23.5885i | 0.828303i | 0.910208 | + | 0.414151i | \(0.135922\pi\) | ||||
−0.910208 | + | 0.414151i | \(0.864078\pi\) | |||||||
\(812\) | −3.80385 | − | 2.19615i | −0.133489 | − | 0.0770698i | ||||
\(813\) | 21.1244 | + | 12.1962i | 0.740863 | + | 0.427738i | ||||
\(814\) | 1.58846i | 0.0556754i | ||||||||
\(815\) | −1.46410 | + | 2.53590i | −0.0512852 | + | 0.0888286i | ||||
\(816\) | 2.00000 | + | 3.46410i | 0.0700140 | + | 0.121268i | ||||
\(817\) | −29.7846 | + | 17.1962i | −1.04203 | + | 0.601617i | ||||
\(818\) | −39.0526 | −1.36544 | ||||||||
\(819\) | 3.00000 | + | 10.3923i | 0.104828 | + | 0.363137i | ||||
\(820\) | 4.00000 | 0.139686 | ||||||||
\(821\) | −12.7128 | + | 7.33975i | −0.443680 | + | 0.256159i | −0.705157 | − | 0.709051i | \(-0.749124\pi\) |
0.261477 | + | 0.965210i | \(0.415790\pi\) | |||||||
\(822\) | 6.73205 | + | 11.6603i | 0.234807 | + | 0.406698i | ||||
\(823\) | 4.20577 | − | 7.28461i | 0.146604 | − | 0.253926i | −0.783366 | − | 0.621560i | \(-0.786499\pi\) |
0.929970 | + | 0.367635i | \(0.119832\pi\) | |||||||
\(824\) | 11.5885i | 0.403703i | ||||||||
\(825\) | −0.232051 | − | 0.133975i | −0.00807897 | − | 0.00466440i | ||||
\(826\) | −29.7846 | − | 17.1962i | −1.03634 | − | 0.598331i | ||||
\(827\) | 46.4974i | 1.61687i | 0.588583 | + | 0.808437i | \(0.299686\pi\) | ||||
−0.588583 | + | 0.808437i | \(0.700314\pi\) | |||||||
\(828\) | 1.73205 | − | 3.00000i | 0.0601929 | − | 0.104257i | ||||
\(829\) | 2.33975 | + | 4.05256i | 0.0812627 | + | 0.140751i | 0.903793 | − | 0.427971i | \(-0.140771\pi\) |
−0.822530 | + | 0.568722i | \(0.807438\pi\) | |||||||
\(830\) | −8.19615 | + | 4.73205i | −0.284493 | + | 0.164252i | ||||
\(831\) | −11.5885 | −0.401999 | ||||||||
\(832\) | −0.866025 | + | 3.50000i | −0.0300240 | + | 0.121341i | ||||
\(833\) | −8.00000 | −0.277184 | ||||||||
\(834\) | 17.1340 | − | 9.89230i | 0.593301 | − | 0.342543i | ||||
\(835\) | 0.232051 | + | 0.401924i | 0.00803045 | + | 0.0139091i | ||||
\(836\) | 0.767949 | − | 1.33013i | 0.0265601 | − | 0.0460034i | ||||
\(837\) | 4.92820i | 0.170344i | ||||||||
\(838\) | −8.53590 | − | 4.92820i | −0.294868 | − | 0.170242i | ||||
\(839\) | 16.6077 | + | 9.58846i | 0.573361 | + | 0.331030i | 0.758491 | − | 0.651684i | \(-0.225937\pi\) |
−0.185129 | + | 0.982714i | \(0.559270\pi\) | |||||||
\(840\) | − | 3.00000i | − | 0.103510i | ||||||
\(841\) | 13.4282 | − | 23.2583i | 0.463041 | − | 0.802011i | ||||
\(842\) | 10.9282 | + | 18.9282i | 0.376611 | + | 0.652309i | ||||
\(843\) | −6.00000 | + | 3.46410i | −0.206651 | + | 0.119310i | ||||
\(844\) | 8.07180 | 0.277843 | ||||||||
\(845\) | −6.06218 | + | 11.5000i | −0.208545 | + | 0.395612i | ||||
\(846\) | −6.46410 | −0.222240 | ||||||||
\(847\) | −28.3923 | + | 16.3923i | −0.975571 | + | 0.563246i | ||||
\(848\) | 0.133975 | + | 0.232051i | 0.00460071 | + | 0.00796866i | ||||
\(849\) | −3.19615 | + | 5.53590i | −0.109692 | + | 0.189992i | ||||
\(850\) | − | 4.00000i | − | 0.137199i | ||||||
\(851\) | 17.7846 | + | 10.2679i | 0.609649 | + | 0.351981i | ||||
\(852\) | −11.1962 | − | 6.46410i | −0.383574 | − | 0.221456i | ||||
\(853\) | − | 24.6410i | − | 0.843692i | −0.906667 | − | 0.421846i | \(-0.861382\pi\) | ||
0.906667 | − | 0.421846i | \(-0.138618\pi\) | |||||||
\(854\) | 0.803848 | − | 1.39230i | 0.0275071 | − | 0.0476437i | ||||
\(855\) | 2.86603 | + | 4.96410i | 0.0980160 | + | 0.169769i | ||||
\(856\) | 11.1962 | − | 6.46410i | 0.382677 | − | 0.220938i | ||||
\(857\) | −28.9282 | −0.988169 | −0.494084 | − | 0.869414i | \(-0.664497\pi\) | ||||
−0.494084 | + | 0.869414i | \(0.664497\pi\) | |||||||
\(858\) | 0.232051 | − | 0.937822i | 0.00792208 | − | 0.0320167i | ||||
\(859\) | −6.07180 | −0.207167 | −0.103584 | − | 0.994621i | \(-0.533031\pi\) | ||||
−0.103584 | + | 0.994621i | \(0.533031\pi\) | |||||||
\(860\) | 5.19615 | − | 3.00000i | 0.177187 | − | 0.102299i | ||||
\(861\) | −6.00000 | − | 10.3923i | −0.204479 | − | 0.354169i | ||||
\(862\) | −6.92820 | + | 12.0000i | −0.235976 | + | 0.408722i | ||||
\(863\) | 2.92820i | 0.0996772i | 0.998757 | + | 0.0498386i | \(0.0158707\pi\) | ||||
−0.998757 | + | 0.0498386i | \(0.984129\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | −1.83975 | − | 1.06218i | −0.0625532 | − | 0.0361151i | ||||
\(866\) | − | 8.78461i | − | 0.298513i | ||||||
\(867\) | −0.500000 | + | 0.866025i | −0.0169809 | + | 0.0294118i | ||||
\(868\) | −7.39230 | − | 12.8038i | −0.250911 | − | 0.434591i | ||||
\(869\) | 0.712813 | − | 0.411543i | 0.0241805 | − | 0.0139606i | ||||
\(870\) | −1.46410 | −0.0496377 | ||||||||
\(871\) | −1.46410 | − | 5.07180i | −0.0496092 | − | 0.171851i | ||||
\(872\) | 10.3923 | 0.351928 | ||||||||
\(873\) | −7.26795 | + | 4.19615i | −0.245983 | + | 0.142018i | ||||
\(874\) | −9.92820 | − | 17.1962i | −0.335826 | − | 0.581669i | ||||
\(875\) | −1.50000 | + | 2.59808i | −0.0507093 | + | 0.0878310i | ||||
\(876\) | 6.92820i | 0.234082i | ||||||||
\(877\) | 18.8038 | + | 10.8564i | 0.634961 | + | 0.366595i | 0.782671 | − | 0.622436i | \(-0.213857\pi\) |
−0.147710 | + | 0.989031i | \(0.547190\pi\) | |||||||
\(878\) | 11.5359 | + | 6.66025i | 0.389318 | + | 0.224773i | ||||
\(879\) | 29.2487i | 0.986535i | ||||||||
\(880\) | −0.133975 | + | 0.232051i | −0.00451628 | + | 0.00782243i | ||||
\(881\) | −19.5526 | − | 33.8660i | −0.658742 | − | 1.14098i | −0.980941 | − | 0.194303i | \(-0.937755\pi\) |
0.322199 | − | 0.946672i | \(-0.395578\pi\) | |||||||
\(882\) | −1.73205 | + | 1.00000i | −0.0583212 | + | 0.0336718i | ||||
\(883\) | −13.3205 | −0.448271 | −0.224135 | − | 0.974558i | \(-0.571956\pi\) | ||||
−0.224135 | + | 0.974558i | \(0.571956\pi\) | |||||||
\(884\) | 13.8564 | − | 4.00000i | 0.466041 | − | 0.134535i | ||||
\(885\) | −11.4641 | −0.385362 | ||||||||
\(886\) | −17.1962 | + | 9.92820i | −0.577716 | + | 0.333545i | ||||
\(887\) | −27.8660 | − | 48.2654i | −0.935650 | − | 1.62059i | −0.773472 | − | 0.633831i | \(-0.781481\pi\) |
−0.162178 | − | 0.986762i | \(-0.551852\pi\) | |||||||
\(888\) | −2.96410 | + | 5.13397i | −0.0994687 | + | 0.172285i | ||||
\(889\) | 37.9808i | 1.27383i | ||||||||
\(890\) | 12.2321 | + | 7.06218i | 0.410019 | + | 0.236725i | ||||
\(891\) | −0.232051 | − | 0.133975i | −0.00777399 | − | 0.00448832i | ||||
\(892\) | 18.8564i | 0.631359i | ||||||||
\(893\) | −18.5263 | + | 32.0885i | −0.619958 | + | 1.07380i | ||||
\(894\) | 9.39230 | + | 16.2679i | 0.314126 | + | 0.544082i | ||||
\(895\) | −7.85641 | + | 4.53590i | −0.262611 | + | 0.151618i | ||||
\(896\) | −3.00000 | −0.100223 | ||||||||
\(897\) | −9.00000 | − | 8.66025i | −0.300501 | − | 0.289157i | ||||
\(898\) | −6.12436 | −0.204372 | ||||||||
\(899\) | −6.24871 | + | 3.60770i | −0.208406 | + | 0.120323i | ||||
\(900\) | −0.500000 | − | 0.866025i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | 0.535898 | − | 0.928203i | 0.0178534 | − | 0.0309229i | ||||
\(902\) | 1.07180i | 0.0356869i | ||||||||
\(903\) | −15.5885 | − | 9.00000i | −0.518751 | − | 0.299501i | ||||
\(904\) | −10.3923 | − | 6.00000i | −0.345643 | − | 0.199557i | ||||
\(905\) | − | 16.9282i | − | 0.562713i | ||||||
\(906\) | 11.3923 | − | 19.7321i | 0.378484 | − | 0.655553i | ||||
\(907\) | −10.4641 | − | 18.1244i | −0.347455 | − | 0.601809i | 0.638342 | − | 0.769753i | \(-0.279621\pi\) |
−0.985797 | + | 0.167944i | \(0.946287\pi\) | |||||||
\(908\) | 5.66025 | − | 3.26795i | 0.187842 | − | 0.108451i | ||||
\(909\) | 12.3923 | 0.411027 | ||||||||
\(910\) | −10.5000 | − | 2.59808i | −0.348072 | − | 0.0861254i | ||||
\(911\) | 12.7846 | 0.423573 | 0.211787 | − | 0.977316i | \(-0.432072\pi\) | ||||
0.211787 | + | 0.977316i | \(0.432072\pi\) | |||||||
\(912\) | 4.96410 | − | 2.86603i | 0.164378 | − | 0.0949036i | ||||
\(913\) | −1.26795 | − | 2.19615i | −0.0419630 | − | 0.0726820i | ||||
\(914\) | −3.73205 | + | 6.46410i | −0.123445 | + | 0.213813i | ||||
\(915\) | − | 0.535898i | − | 0.0177163i | ||||||
\(916\) | −3.92820 | − | 2.26795i | −0.129791 | − | 0.0749352i | ||||
\(917\) | 37.2058 | + | 21.4808i | 1.22864 | + | 0.709357i | ||||
\(918\) | − | 4.00000i | − | 0.132020i | ||||||
\(919\) | 23.9808 | − | 41.5359i | 0.791052 | − | 1.37014i | −0.134264 | − | 0.990946i | \(-0.542867\pi\) |
0.925316 | − | 0.379197i | \(-0.123800\pi\) | |||||||
\(920\) | 1.73205 | + | 3.00000i | 0.0571040 | + | 0.0989071i | ||||
\(921\) | 24.4641 | − | 14.1244i | 0.806120 | − | 0.465413i | ||||
\(922\) | −11.6077 | −0.382279 | ||||||||
\(923\) | −32.3205 | + | 33.5885i | −1.06384 | + | 1.10558i | ||||
\(924\) | 0.803848 | 0.0264446 | ||||||||
\(925\) | 5.13397 | − | 2.96410i | 0.168804 | − | 0.0974591i | ||||
\(926\) | −20.3923 | − | 35.3205i | −0.670133 | − | 1.16070i | ||||
\(927\) | 5.79423 | − | 10.0359i | 0.190307 | − | 0.329622i | ||||
\(928\) | 1.46410i | 0.0480615i | ||||||||
\(929\) | 50.1051 | + | 28.9282i | 1.64390 | + | 0.949104i | 0.979430 | + | 0.201785i | \(0.0646742\pi\) |
0.664466 | + | 0.747319i | \(0.268659\pi\) | |||||||
\(930\) | −4.26795 | − | 2.46410i | −0.139952 | − | 0.0808011i | ||||
\(931\) | 11.4641i | 0.375721i | ||||||||
\(932\) | 9.00000 | − | 15.5885i | 0.294805 | − | 0.510617i | ||||
\(933\) | 9.46410 | + | 16.3923i | 0.309841 | + | 0.536660i | ||||
\(934\) | 21.1244 | − | 12.1962i | 0.691210 | − | 0.399070i | ||||
\(935\) | 1.07180 | 0.0350515 | ||||||||
\(936\) | 2.50000 | − | 2.59808i | 0.0817151 | − | 0.0849208i | ||||
\(937\) | −21.7128 | −0.709327 | −0.354663 | − | 0.934994i | \(-0.615405\pi\) | ||||
−0.354663 | + | 0.934994i | \(0.615405\pi\) | |||||||
\(938\) | 3.80385 | − | 2.19615i | 0.124200 | − | 0.0717069i | ||||
\(939\) | −16.6603 | − | 28.8564i | −0.543687 | − | 0.941693i | ||||
\(940\) | 3.23205 | − | 5.59808i | 0.105418 | − | 0.182589i | ||||
\(941\) | − | 60.4974i | − | 1.97216i | −0.166273 | − | 0.986080i | \(-0.553173\pi\) | ||
0.166273 | − | 0.986080i | \(-0.446827\pi\) | |||||||
\(942\) | 18.3564 | + | 10.5981i | 0.598084 | + | 0.345304i | ||||
\(943\) | 12.0000 | + | 6.92820i | 0.390774 | + | 0.225613i | ||||
\(944\) | 11.4641i | 0.373125i | ||||||||
\(945\) | −1.50000 | + | 2.59808i | −0.0487950 | + | 0.0845154i | ||||
\(946\) | 0.803848 | + | 1.39230i | 0.0261353 | + | 0.0452677i | ||||
\(947\) | 29.7846 | − | 17.1962i | 0.967870 | − | 0.558800i | 0.0692836 | − | 0.997597i | \(-0.477929\pi\) |
0.898586 | + | 0.438797i | \(0.144595\pi\) | |||||||
\(948\) | 3.07180 | 0.0997673 | ||||||||
\(949\) | 24.2487 | + | 6.00000i | 0.787146 | + | 0.194768i | ||||
\(950\) | −5.73205 | −0.185972 | ||||||||
\(951\) | −26.3827 | + | 15.2321i | −0.855517 | + | 0.493933i | ||||
\(952\) | 6.00000 | + | 10.3923i | 0.194461 | + | 0.336817i | ||||
\(953\) | 26.6603 | − | 46.1769i | 0.863610 | − | 1.49582i | −0.00481009 | − | 0.999988i | \(-0.501531\pi\) |
0.868420 | − | 0.495829i | \(-0.165136\pi\) | |||||||
\(954\) | − | 0.267949i | − | 0.00867518i | ||||||
\(955\) | −15.0000 | − | 8.66025i | −0.485389 | − | 0.280239i | ||||
\(956\) | 3.00000 | + | 1.73205i | 0.0970269 | + | 0.0560185i | ||||
\(957\) | − | 0.392305i | − | 0.0126814i | ||||||
\(958\) | −11.1244 | + | 19.2679i | −0.359412 | + | 0.622519i | ||||
\(959\) | 20.1962 | + | 34.9808i | 0.652168 | + | 1.12959i | ||||
\(960\) | −0.866025 | + | 0.500000i | −0.0279508 | + | 0.0161374i | ||||
\(961\) | 6.71281 | 0.216542 | ||||||||
\(962\) | 15.4019 | + | 14.8205i | 0.496578 | + | 0.477832i | ||||
\(963\) | −12.9282 | −0.416606 | ||||||||
\(964\) | −21.8205 | + | 12.5981i | −0.702791 | + | 0.405757i | ||||
\(965\) | 4.92820 | + | 8.53590i | 0.158644 | + | 0.274780i | ||||
\(966\) | 5.19615 | − | 9.00000i | 0.167183 | − | 0.289570i | ||||
\(967\) | − | 1.14359i | − | 0.0367755i | −0.999831 | − | 0.0183877i | \(-0.994147\pi\) | ||
0.999831 | − | 0.0183877i | \(-0.00585333\pi\) | |||||||
\(968\) | 9.46410 | + | 5.46410i | 0.304188 | + | 0.175623i | ||||
\(969\) | −19.8564 | − | 11.4641i | −0.637880 | − | 0.368280i | ||||
\(970\) | − | 8.39230i | − | 0.269461i | ||||||
\(971\) | 20.6962 | − | 35.8468i | 0.664171 | − | 1.15038i | −0.315338 | − | 0.948979i | \(-0.602118\pi\) |
0.979509 | − | 0.201399i | \(-0.0645487\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | 51.4019 | − | 29.6769i | 1.64787 | − | 0.951398i | ||||
\(974\) | 21.0000 | 0.672883 | ||||||||
\(975\) | −3.46410 | + | 1.00000i | −0.110940 | + | 0.0320256i | ||||
\(976\) | −0.535898 | −0.0171537 | ||||||||
\(977\) | −4.73205 | + | 2.73205i | −0.151392 | + | 0.0874060i | −0.573782 | − | 0.819008i | \(-0.694524\pi\) |
0.422391 | + | 0.906414i | \(0.361191\pi\) | |||||||
\(978\) | −1.46410 | − | 2.53590i | −0.0468168 | − | 0.0810891i | ||||
\(979\) | −1.89230 | + | 3.27757i | −0.0604783 | + | 0.104752i | ||||
\(980\) | − | 2.00000i | − | 0.0638877i | ||||||
\(981\) | −9.00000 | − | 5.19615i | −0.287348 | − | 0.165900i | ||||
\(982\) | −4.66987 | − | 2.69615i | −0.149022 | − | 0.0860377i | ||||
\(983\) | 46.1769i | 1.47281i | 0.676538 | + | 0.736407i | \(0.263479\pi\) | ||||
−0.676538 | + | 0.736407i | \(0.736521\pi\) | |||||||
\(984\) | −2.00000 | + | 3.46410i | −0.0637577 | + | 0.110432i | ||||
\(985\) | 5.69615 | + | 9.86603i | 0.181495 | + | 0.314358i | ||||
\(986\) | 5.07180 | − | 2.92820i | 0.161519 | − | 0.0932530i | ||||
\(987\) | −19.3923 | −0.617264 | ||||||||
\(988\) | −5.73205 | − | 19.8564i | −0.182361 | − | 0.631716i | ||||
\(989\) | 20.7846 | 0.660912 | ||||||||
\(990\) | 0.232051 | − | 0.133975i | 0.00737506 | − | 0.00425799i | ||||
\(991\) | −19.5885 | − | 33.9282i | −0.622248 | − | 1.07776i | −0.989066 | − | 0.147472i | \(-0.952886\pi\) |
0.366818 | − | 0.930293i | \(-0.380447\pi\) | |||||||
\(992\) | −2.46410 | + | 4.26795i | −0.0782353 | + | 0.135508i | ||||
\(993\) | 14.3923i | 0.456726i | ||||||||
\(994\) | −33.5885 | − | 19.3923i | −1.06536 | − | 0.615087i | ||||
\(995\) | −21.5885 | − | 12.4641i | −0.684400 | − | 0.395139i | ||||
\(996\) | − | 9.46410i | − | 0.299882i | ||||||
\(997\) | −30.9904 | + | 53.6769i | −0.981475 | + | 1.69996i | −0.324817 | + | 0.945777i | \(0.605303\pi\) |
−0.656659 | + | 0.754188i | \(0.728031\pi\) | |||||||
\(998\) | 16.6603 | + | 28.8564i | 0.527371 | + | 0.913434i | ||||
\(999\) | 5.13397 | − | 2.96410i | 0.162432 | − | 0.0937800i |
(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 | 390.2.bb.a.361.2 | yes | 4 | |
3.2 | odd | 2 | 1170.2.bs.d.361.1 | 4 | |||
5.2 | odd | 4 | 1950.2.y.e.49.2 | 4 | |||
5.3 | odd | 4 | 1950.2.y.d.49.1 | 4 | |||
5.4 | even | 2 | 1950.2.bc.a.751.1 | 4 | |||
13.2 | odd | 12 | 5070.2.a.be.1.2 | 2 | |||
13.3 | even | 3 | 5070.2.b.p.1351.3 | 4 | |||
13.4 | even | 6 | inner | 390.2.bb.a.121.2 | ✓ | 4 | |
13.10 | even | 6 | 5070.2.b.p.1351.2 | 4 | |||
13.11 | odd | 12 | 5070.2.a.ba.1.1 | 2 | |||
39.17 | odd | 6 | 1170.2.bs.d.901.1 | 4 | |||
65.4 | even | 6 | 1950.2.bc.a.901.1 | 4 | |||
65.17 | odd | 12 | 1950.2.y.d.199.1 | 4 | |||
65.43 | odd | 12 | 1950.2.y.e.199.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.a.121.2 | ✓ | 4 | 13.4 | even | 6 | inner | |
390.2.bb.a.361.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1170.2.bs.d.361.1 | 4 | 3.2 | odd | 2 | |||
1170.2.bs.d.901.1 | 4 | 39.17 | odd | 6 | |||
1950.2.y.d.49.1 | 4 | 5.3 | odd | 4 | |||
1950.2.y.d.199.1 | 4 | 65.17 | odd | 12 | |||
1950.2.y.e.49.2 | 4 | 5.2 | odd | 4 | |||
1950.2.y.e.199.2 | 4 | 65.43 | odd | 12 | |||
1950.2.bc.a.751.1 | 4 | 5.4 | even | 2 | |||
1950.2.bc.a.901.1 | 4 | 65.4 | even | 6 | |||
5070.2.a.ba.1.1 | 2 | 13.11 | odd | 12 | |||
5070.2.a.be.1.2 | 2 | 13.2 | odd | 12 | |||
5070.2.b.p.1351.2 | 4 | 13.10 | even | 6 | |||
5070.2.b.p.1351.3 | 4 | 13.3 | even | 3 |