Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(79,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.n (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: | \(1.67685844245\) |
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 | 79.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.79 |
Dual form | 210.2.n.a.109.2 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.86603 | + | 1.23205i | −0.834512 | + | 0.550990i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.73205 | + | 2.00000i | −0.654654 | + | 0.755929i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −2.23205 | + | 0.133975i | −0.705836 | + | 0.0423665i | ||||
\(11\) | 2.50000 | + | 4.33013i | 0.753778 | + | 1.30558i | 0.945979 | + | 0.324227i | \(0.105104\pi\) |
−0.192201 | + | 0.981356i | \(0.561563\pi\) | |||||||
\(12\) | −0.866025 | − | 0.500000i | −0.250000 | − | 0.144338i | ||||
\(13\) | − | 1.00000i | − | 0.277350i | −0.990338 | − | 0.138675i | \(-0.955716\pi\) | ||
0.990338 | − | 0.138675i | \(-0.0442844\pi\) | |||||||
\(14\) | −2.50000 | + | 0.866025i | −0.668153 | + | 0.231455i | ||||
\(15\) | 1.00000 | − | 2.00000i | 0.258199 | − | 0.516398i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.73205 | + | 1.00000i | −0.420084 | + | 0.242536i | −0.695113 | − | 0.718900i | \(-0.744646\pi\) |
0.275029 | + | 0.961436i | \(0.411312\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | 3.50000 | − | 6.06218i | 0.802955 | − | 1.39076i | −0.114708 | − | 0.993399i | \(-0.536593\pi\) |
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | −2.00000 | − | 1.00000i | −0.447214 | − | 0.223607i | ||||
\(21\) | 0.500000 | − | 2.59808i | 0.109109 | − | 0.566947i | ||||
\(22\) | 5.00000i | 1.06600i | ||||||||
\(23\) | 2.59808 | + | 1.50000i | 0.541736 | + | 0.312772i | 0.745782 | − | 0.666190i | \(-0.232076\pi\) |
−0.204046 | + | 0.978961i | \(0.565409\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 1.96410 | − | 4.59808i | 0.392820 | − | 0.919615i | ||||
\(26\) | 0.500000 | − | 0.866025i | 0.0980581 | − | 0.169842i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −2.59808 | − | 0.500000i | −0.490990 | − | 0.0944911i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 1.86603 | − | 1.23205i | 0.340688 | − | 0.224941i | ||||
\(31\) | 3.00000 | + | 5.19615i | 0.538816 | + | 0.933257i | 0.998968 | + | 0.0454165i | \(0.0144615\pi\) |
−0.460152 | + | 0.887840i | \(0.652205\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −4.33013 | − | 2.50000i | −0.753778 | − | 0.435194i | ||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0.767949 | − | 5.86603i | 0.129807 | − | 0.991539i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.33013 | + | 2.50000i | 0.711868 | + | 0.410997i | 0.811752 | − | 0.584002i | \(-0.198514\pi\) |
−0.0998840 | + | 0.994999i | \(0.531847\pi\) | |||||||
\(38\) | 6.06218 | − | 3.50000i | 0.983415 | − | 0.567775i | ||||
\(39\) | 0.500000 | + | 0.866025i | 0.0800641 | + | 0.138675i | ||||
\(40\) | −1.23205 | − | 1.86603i | −0.194804 | − | 0.295045i | ||||
\(41\) | −9.00000 | −1.40556 | −0.702782 | − | 0.711405i | \(-0.748059\pi\) | ||||
−0.702782 | + | 0.711405i | \(0.748059\pi\) | |||||||
\(42\) | 1.73205 | − | 2.00000i | 0.267261 | − | 0.308607i | ||||
\(43\) | − | 10.0000i | − | 1.52499i | −0.646997 | − | 0.762493i | \(-0.723975\pi\) | ||
0.646997 | − | 0.762493i | \(-0.276025\pi\) | |||||||
\(44\) | −2.50000 | + | 4.33013i | −0.376889 | + | 0.652791i | ||||
\(45\) | 0.133975 | + | 2.23205i | 0.0199718 | + | 0.332734i | ||||
\(46\) | 1.50000 | + | 2.59808i | 0.221163 | + | 0.383065i | ||||
\(47\) | 11.2583 | + | 6.50000i | 1.64220 | + | 0.948122i | 0.980051 | + | 0.198747i | \(0.0636872\pi\) |
0.662145 | + | 0.749375i | \(0.269646\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | 4.00000 | − | 3.00000i | 0.565685 | − | 0.424264i | ||||
\(51\) | 1.00000 | − | 1.73205i | 0.140028 | − | 0.242536i | ||||
\(52\) | 0.866025 | − | 0.500000i | 0.120096 | − | 0.0693375i | ||||
\(53\) | 0.866025 | − | 0.500000i | 0.118958 | − | 0.0686803i | −0.439340 | − | 0.898321i | \(-0.644788\pi\) |
0.558298 | + | 0.829640i | \(0.311454\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −10.0000 | − | 5.00000i | −1.34840 | − | 0.674200i | ||||
\(56\) | −2.00000 | − | 1.73205i | −0.267261 | − | 0.231455i | ||||
\(57\) | 7.00000i | 0.927173i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.00000 | + | 3.46410i | 0.260378 | + | 0.450988i | 0.966342 | − | 0.257260i | \(-0.0828195\pi\) |
−0.705965 | + | 0.708247i | \(0.749486\pi\) | |||||||
\(60\) | 2.23205 | − | 0.133975i | 0.288157 | − | 0.0172960i | ||||
\(61\) | 1.00000 | − | 1.73205i | 0.128037 | − | 0.221766i | −0.794879 | − | 0.606768i | \(-0.792466\pi\) |
0.922916 | + | 0.385002i | \(0.125799\pi\) | |||||||
\(62\) | 6.00000i | 0.762001i | ||||||||
\(63\) | 0.866025 | + | 2.50000i | 0.109109 | + | 0.314970i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.23205 | + | 1.86603i | 0.152817 | + | 0.231452i | ||||
\(66\) | −2.50000 | − | 4.33013i | −0.307729 | − | 0.533002i | ||||
\(67\) | 5.19615 | − | 3.00000i | 0.634811 | − | 0.366508i | −0.147802 | − | 0.989017i | \(-0.547220\pi\) |
0.782613 | + | 0.622509i | \(0.213886\pi\) | |||||||
\(68\) | −1.73205 | − | 1.00000i | −0.210042 | − | 0.121268i | ||||
\(69\) | −3.00000 | −0.361158 | ||||||||
\(70\) | 3.59808 | − | 4.69615i | 0.430052 | − | 0.561298i | ||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | −3.46410 | + | 2.00000i | −0.405442 | + | 0.234082i | −0.688830 | − | 0.724923i | \(-0.741875\pi\) |
0.283387 | + | 0.959006i | \(0.408542\pi\) | |||||||
\(74\) | 2.50000 | + | 4.33013i | 0.290619 | + | 0.503367i | ||||
\(75\) | 0.598076 | + | 4.96410i | 0.0690599 | + | 0.573205i | ||||
\(76\) | 7.00000 | 0.802955 | ||||||||
\(77\) | −12.9904 | − | 2.50000i | −1.48039 | − | 0.284901i | ||||
\(78\) | 1.00000i | 0.113228i | ||||||||
\(79\) | −7.00000 | + | 12.1244i | −0.787562 | + | 1.36410i | 0.139895 | + | 0.990166i | \(0.455323\pi\) |
−0.927457 | + | 0.373930i | \(0.878010\pi\) | |||||||
\(80\) | −0.133975 | − | 2.23205i | −0.0149788 | − | 0.249551i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −7.79423 | − | 4.50000i | −0.860729 | − | 0.496942i | ||||
\(83\) | 10.0000i | 1.09764i | 0.835940 | + | 0.548821i | \(0.184923\pi\) | ||||
−0.835940 | + | 0.548821i | \(0.815077\pi\) | |||||||
\(84\) | 2.50000 | − | 0.866025i | 0.272772 | − | 0.0944911i | ||||
\(85\) | 2.00000 | − | 4.00000i | 0.216930 | − | 0.433861i | ||||
\(86\) | 5.00000 | − | 8.66025i | 0.539164 | − | 0.933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.33013 | + | 2.50000i | −0.461593 | + | 0.266501i | ||||
\(89\) | 5.00000 | − | 8.66025i | 0.529999 | − | 0.917985i | −0.469389 | − | 0.882992i | \(-0.655526\pi\) |
0.999388 | − | 0.0349934i | \(-0.0111410\pi\) | |||||||
\(90\) | −1.00000 | + | 2.00000i | −0.105409 | + | 0.210819i | ||||
\(91\) | 2.00000 | + | 1.73205i | 0.209657 | + | 0.181568i | ||||
\(92\) | 3.00000i | 0.312772i | ||||||||
\(93\) | −5.19615 | − | 3.00000i | −0.538816 | − | 0.311086i | ||||
\(94\) | 6.50000 | + | 11.2583i | 0.670424 | + | 1.16121i | ||||
\(95\) | 0.937822 | + | 15.6244i | 0.0962185 | + | 1.60303i | ||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 8.00000i | 0.812277i | 0.913812 | + | 0.406138i | \(0.133125\pi\) | ||||
−0.913812 | + | 0.406138i | \(0.866875\pi\) | |||||||
\(98\) | 2.59808 | − | 6.50000i | 0.262445 | − | 0.656599i | ||||
\(99\) | 5.00000 | 0.502519 | ||||||||
\(100\) | 4.96410 | − | 0.598076i | 0.496410 | − | 0.0598076i | ||||
\(101\) | −4.00000 | − | 6.92820i | −0.398015 | − | 0.689382i | 0.595466 | − | 0.803380i | \(-0.296967\pi\) |
−0.993481 | + | 0.113998i | \(0.963634\pi\) | |||||||
\(102\) | 1.73205 | − | 1.00000i | 0.171499 | − | 0.0990148i | ||||
\(103\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 2.26795 | + | 5.46410i | 0.221329 | + | 0.533242i | ||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | −10.3923 | − | 6.00000i | −1.00466 | − | 0.580042i | −0.0950377 | − | 0.995474i | \(-0.530297\pi\) |
−0.909624 | + | 0.415432i | \(0.863630\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | −9.00000 | − | 15.5885i | −0.862044 | − | 1.49310i | −0.869953 | − | 0.493135i | \(-0.835851\pi\) |
0.00790932 | − | 0.999969i | \(-0.497482\pi\) | |||||||
\(110\) | −6.16025 | − | 9.33013i | −0.587357 | − | 0.889593i | ||||
\(111\) | −5.00000 | −0.474579 | ||||||||
\(112\) | −0.866025 | − | 2.50000i | −0.0818317 | − | 0.236228i | ||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | −3.50000 | + | 6.06218i | −0.327805 | + | 0.567775i | ||||
\(115\) | −6.69615 | + | 0.401924i | −0.624419 | + | 0.0374796i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.866025 | − | 0.500000i | −0.0800641 | − | 0.0462250i | ||||
\(118\) | 4.00000i | 0.368230i | ||||||||
\(119\) | 1.00000 | − | 5.19615i | 0.0916698 | − | 0.476331i | ||||
\(120\) | 2.00000 | + | 1.00000i | 0.182574 | + | 0.0912871i | ||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 1.73205 | − | 1.00000i | 0.156813 | − | 0.0905357i | ||||
\(123\) | 7.79423 | − | 4.50000i | 0.702782 | − | 0.405751i | ||||
\(124\) | −3.00000 | + | 5.19615i | −0.269408 | + | 0.466628i | ||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | −0.500000 | + | 2.59808i | −0.0445435 | + | 0.231455i | ||||
\(127\) | 9.00000i | 0.798621i | 0.916816 | + | 0.399310i | \(0.130750\pi\) | ||||
−0.916816 | + | 0.399310i | \(0.869250\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 5.00000 | + | 8.66025i | 0.440225 | + | 0.762493i | ||||
\(130\) | 0.133975 | + | 2.23205i | 0.0117503 | + | 0.195764i | ||||
\(131\) | 8.50000 | − | 14.7224i | 0.742648 | − | 1.28630i | −0.208637 | − | 0.977993i | \(-0.566903\pi\) |
0.951285 | − | 0.308312i | \(-0.0997640\pi\) | |||||||
\(132\) | − | 5.00000i | − | 0.435194i | ||||||
\(133\) | 6.06218 | + | 17.5000i | 0.525657 | + | 1.51744i | ||||
\(134\) | 6.00000 | 0.518321 | ||||||||
\(135\) | −1.23205 | − | 1.86603i | −0.106038 | − | 0.160602i | ||||
\(136\) | −1.00000 | − | 1.73205i | −0.0857493 | − | 0.148522i | ||||
\(137\) | −3.46410 | + | 2.00000i | −0.295958 | + | 0.170872i | −0.640626 | − | 0.767853i | \(-0.721325\pi\) |
0.344668 | + | 0.938725i | \(0.387992\pi\) | |||||||
\(138\) | −2.59808 | − | 1.50000i | −0.221163 | − | 0.127688i | ||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | 5.46410 | − | 2.26795i | 0.461801 | − | 0.191677i | ||||
\(141\) | −13.0000 | −1.09480 | ||||||||
\(142\) | −1.73205 | − | 1.00000i | −0.145350 | − | 0.0839181i | ||||
\(143\) | 4.33013 | − | 2.50000i | 0.362103 | − | 0.209061i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | 4.33013 | + | 5.50000i | 0.357143 | + | 0.453632i | ||||
\(148\) | 5.00000i | 0.410997i | ||||||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | −1.96410 | + | 4.59808i | −0.160368 | + | 0.375431i | ||||
\(151\) | 11.0000 | + | 19.0526i | 0.895167 | + | 1.55048i | 0.833597 | + | 0.552372i | \(0.186277\pi\) |
0.0615699 | + | 0.998103i | \(0.480389\pi\) | |||||||
\(152\) | 6.06218 | + | 3.50000i | 0.491708 | + | 0.283887i | ||||
\(153\) | 2.00000i | 0.161690i | ||||||||
\(154\) | −10.0000 | − | 8.66025i | −0.805823 | − | 0.697863i | ||||
\(155\) | −12.0000 | − | 6.00000i | −0.963863 | − | 0.481932i | ||||
\(156\) | −0.500000 | + | 0.866025i | −0.0400320 | + | 0.0693375i | ||||
\(157\) | 11.2583 | − | 6.50000i | 0.898513 | − | 0.518756i | 0.0217953 | − | 0.999762i | \(-0.493062\pi\) |
0.876717 | + | 0.481006i | \(0.159728\pi\) | |||||||
\(158\) | −12.1244 | + | 7.00000i | −0.964562 | + | 0.556890i | ||||
\(159\) | −0.500000 | + | 0.866025i | −0.0396526 | + | 0.0686803i | ||||
\(160\) | 1.00000 | − | 2.00000i | 0.0790569 | − | 0.158114i | ||||
\(161\) | −7.50000 | + | 2.59808i | −0.591083 | + | 0.204757i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −10.3923 | − | 6.00000i | −0.813988 | − | 0.469956i | 0.0343508 | − | 0.999410i | \(-0.489064\pi\) |
−0.848339 | + | 0.529454i | \(0.822397\pi\) | |||||||
\(164\) | −4.50000 | − | 7.79423i | −0.351391 | − | 0.608627i | ||||
\(165\) | 11.1603 | − | 0.669873i | 0.868825 | − | 0.0521495i | ||||
\(166\) | −5.00000 | + | 8.66025i | −0.388075 | + | 0.672166i | ||||
\(167\) | − | 19.0000i | − | 1.47026i | −0.677924 | − | 0.735132i | \(-0.737120\pi\) | ||
0.677924 | − | 0.735132i | \(-0.262880\pi\) | |||||||
\(168\) | 2.59808 | + | 0.500000i | 0.200446 | + | 0.0385758i | ||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 3.73205 | − | 2.46410i | 0.286235 | − | 0.188988i | ||||
\(171\) | −3.50000 | − | 6.06218i | −0.267652 | − | 0.463586i | ||||
\(172\) | 8.66025 | − | 5.00000i | 0.660338 | − | 0.381246i | ||||
\(173\) | 6.06218 | + | 3.50000i | 0.460899 | + | 0.266100i | 0.712422 | − | 0.701751i | \(-0.247598\pi\) |
−0.251523 | + | 0.967851i | \(0.580932\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.79423 | + | 11.8923i | 0.438003 | + | 0.898974i | ||||
\(176\) | −5.00000 | −0.376889 | ||||||||
\(177\) | −3.46410 | − | 2.00000i | −0.260378 | − | 0.150329i | ||||
\(178\) | 8.66025 | − | 5.00000i | 0.649113 | − | 0.374766i | ||||
\(179\) | −5.50000 | − | 9.52628i | −0.411089 | − | 0.712028i | 0.583920 | − | 0.811811i | \(-0.301518\pi\) |
−0.995009 | + | 0.0997838i | \(0.968185\pi\) | |||||||
\(180\) | −1.86603 | + | 1.23205i | −0.139085 | + | 0.0918316i | ||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0.866025 | + | 2.50000i | 0.0641941 | + | 0.185312i | ||||
\(183\) | 2.00000i | 0.147844i | ||||||||
\(184\) | −1.50000 | + | 2.59808i | −0.110581 | + | 0.191533i | ||||
\(185\) | −11.1603 | + | 0.669873i | −0.820518 | + | 0.0492500i | ||||
\(186\) | −3.00000 | − | 5.19615i | −0.219971 | − | 0.381000i | ||||
\(187\) | −8.66025 | − | 5.00000i | −0.633300 | − | 0.365636i | ||||
\(188\) | 13.0000i | 0.948122i | ||||||||
\(189\) | −2.00000 | − | 1.73205i | −0.145479 | − | 0.125988i | ||||
\(190\) | −7.00000 | + | 14.0000i | −0.507833 | + | 1.01567i | ||||
\(191\) | 8.00000 | − | 13.8564i | 0.578860 | − | 1.00261i | −0.416751 | − | 0.909021i | \(-0.636831\pi\) |
0.995610 | − | 0.0935936i | \(-0.0298354\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | 15.5885 | − | 9.00000i | 1.12208 | − | 0.647834i | 0.180150 | − | 0.983639i | \(-0.442342\pi\) |
0.941932 | + | 0.335805i | \(0.109008\pi\) | |||||||
\(194\) | −4.00000 | + | 6.92820i | −0.287183 | + | 0.497416i | ||||
\(195\) | −2.00000 | − | 1.00000i | −0.143223 | − | 0.0716115i | ||||
\(196\) | 5.50000 | − | 4.33013i | 0.392857 | − | 0.309295i | ||||
\(197\) | − | 27.0000i | − | 1.92367i | −0.273629 | − | 0.961835i | \(-0.588224\pi\) | ||
0.273629 | − | 0.961835i | \(-0.411776\pi\) | |||||||
\(198\) | 4.33013 | + | 2.50000i | 0.307729 | + | 0.177667i | ||||
\(199\) | −7.00000 | − | 12.1244i | −0.496217 | − | 0.859473i | 0.503774 | − | 0.863836i | \(-0.331945\pi\) |
−0.999990 | + | 0.00436292i | \(0.998611\pi\) | |||||||
\(200\) | 4.59808 | + | 1.96410i | 0.325133 | + | 0.138883i | ||||
\(201\) | −3.00000 | + | 5.19615i | −0.211604 | + | 0.366508i | ||||
\(202\) | − | 8.00000i | − | 0.562878i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.00000 | 0.140028 | ||||||||
\(205\) | 16.7942 | − | 11.0885i | 1.17296 | − | 0.774451i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.59808 | − | 1.50000i | 0.180579 | − | 0.104257i | ||||
\(208\) | 0.866025 | + | 0.500000i | 0.0600481 | + | 0.0346688i | ||||
\(209\) | 35.0000 | 2.42100 | ||||||||
\(210\) | −0.767949 | + | 5.86603i | −0.0529935 | + | 0.404794i | ||||
\(211\) | 19.0000 | 1.30801 | 0.654007 | − | 0.756489i | \(-0.273087\pi\) | ||||
0.654007 | + | 0.756489i | \(0.273087\pi\) | |||||||
\(212\) | 0.866025 | + | 0.500000i | 0.0594789 | + | 0.0343401i | ||||
\(213\) | 1.73205 | − | 1.00000i | 0.118678 | − | 0.0685189i | ||||
\(214\) | −6.00000 | − | 10.3923i | −0.410152 | − | 0.710403i | ||||
\(215\) | 12.3205 | + | 18.6603i | 0.840252 | + | 1.27262i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −15.5885 | − | 3.00000i | −1.05821 | − | 0.203653i | ||||
\(218\) | − | 18.0000i | − | 1.21911i | ||||||
\(219\) | 2.00000 | − | 3.46410i | 0.135147 | − | 0.234082i | ||||
\(220\) | −0.669873 | − | 11.1603i | −0.0451628 | − | 0.752424i | ||||
\(221\) | 1.00000 | + | 1.73205i | 0.0672673 | + | 0.116510i | ||||
\(222\) | −4.33013 | − | 2.50000i | −0.290619 | − | 0.167789i | ||||
\(223\) | − | 16.0000i | − | 1.07144i | −0.844396 | − | 0.535720i | \(-0.820040\pi\) | ||
0.844396 | − | 0.535720i | \(-0.179960\pi\) | |||||||
\(224\) | 0.500000 | − | 2.59808i | 0.0334077 | − | 0.173591i | ||||
\(225\) | −3.00000 | − | 4.00000i | −0.200000 | − | 0.266667i | ||||
\(226\) | 3.00000 | − | 5.19615i | 0.199557 | − | 0.345643i | ||||
\(227\) | 12.1244 | − | 7.00000i | 0.804722 | − | 0.464606i | −0.0403978 | − | 0.999184i | \(-0.512863\pi\) |
0.845120 | + | 0.534577i | \(0.179529\pi\) | |||||||
\(228\) | −6.06218 | + | 3.50000i | −0.401478 | + | 0.231793i | ||||
\(229\) | −2.00000 | + | 3.46410i | −0.132164 | + | 0.228914i | −0.924510 | − | 0.381157i | \(-0.875526\pi\) |
0.792347 | + | 0.610071i | \(0.208859\pi\) | |||||||
\(230\) | −6.00000 | − | 3.00000i | −0.395628 | − | 0.197814i | ||||
\(231\) | 12.5000 | − | 4.33013i | 0.822440 | − | 0.284901i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | −0.500000 | − | 0.866025i | −0.0326860 | − | 0.0566139i | ||||
\(235\) | −29.0167 | + | 1.74167i | −1.89284 | + | 0.113614i | ||||
\(236\) | −2.00000 | + | 3.46410i | −0.130189 | + | 0.225494i | ||||
\(237\) | − | 14.0000i | − | 0.909398i | ||||||
\(238\) | 3.46410 | − | 4.00000i | 0.224544 | − | 0.259281i | ||||
\(239\) | −20.0000 | −1.29369 | −0.646846 | − | 0.762620i | \(-0.723912\pi\) | ||||
−0.646846 | + | 0.762620i | \(0.723912\pi\) | |||||||
\(240\) | 1.23205 | + | 1.86603i | 0.0795285 | + | 0.120451i | ||||
\(241\) | 0.500000 | + | 0.866025i | 0.0322078 | + | 0.0557856i | 0.881680 | − | 0.471848i | \(-0.156413\pi\) |
−0.849472 | + | 0.527633i | \(0.823079\pi\) | |||||||
\(242\) | −12.1244 | + | 7.00000i | −0.779383 | + | 0.449977i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 10.4019 | + | 11.6962i | 0.664555 | + | 0.747240i | ||||
\(246\) | 9.00000 | 0.573819 | ||||||||
\(247\) | −6.06218 | − | 3.50000i | −0.385727 | − | 0.222700i | ||||
\(248\) | −5.19615 | + | 3.00000i | −0.329956 | + | 0.190500i | ||||
\(249\) | −5.00000 | − | 8.66025i | −0.316862 | − | 0.548821i | ||||
\(250\) | −3.76795 | + | 10.5263i | −0.238306 | + | 0.665740i | ||||
\(251\) | −3.00000 | −0.189358 | −0.0946792 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946792 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(252\) | −1.73205 | + | 2.00000i | −0.109109 | + | 0.125988i | ||||
\(253\) | 15.0000i | 0.943042i | ||||||||
\(254\) | −4.50000 | + | 7.79423i | −0.282355 | + | 0.489053i | ||||
\(255\) | 0.267949 | + | 4.46410i | 0.0167796 | + | 0.279553i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 8.66025 | + | 5.00000i | 0.540212 | + | 0.311891i | 0.745165 | − | 0.666880i | \(-0.232371\pi\) |
−0.204953 | + | 0.978772i | \(0.565704\pi\) | |||||||
\(258\) | 10.0000i | 0.622573i | ||||||||
\(259\) | −12.5000 | + | 4.33013i | −0.776712 | + | 0.269061i | ||||
\(260\) | −1.00000 | + | 2.00000i | −0.0620174 | + | 0.124035i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.7224 | − | 8.50000i | 0.909555 | − | 0.525132i | ||||
\(263\) | −20.7846 | + | 12.0000i | −1.28163 | + | 0.739952i | −0.977147 | − | 0.212565i | \(-0.931818\pi\) |
−0.304487 | + | 0.952517i | \(0.598485\pi\) | |||||||
\(264\) | 2.50000 | − | 4.33013i | 0.153864 | − | 0.266501i | ||||
\(265\) | −1.00000 | + | 2.00000i | −0.0614295 | + | 0.122859i | ||||
\(266\) | −3.50000 | + | 18.1865i | −0.214599 | + | 1.11509i | ||||
\(267\) | 10.0000i | 0.611990i | ||||||||
\(268\) | 5.19615 | + | 3.00000i | 0.317406 | + | 0.183254i | ||||
\(269\) | 7.00000 | + | 12.1244i | 0.426798 | + | 0.739235i | 0.996586 | − | 0.0825561i | \(-0.0263084\pi\) |
−0.569789 | + | 0.821791i | \(0.692975\pi\) | |||||||
\(270\) | −0.133975 | − | 2.23205i | −0.00815343 | − | 0.135838i | ||||
\(271\) | −4.00000 | + | 6.92820i | −0.242983 | + | 0.420858i | −0.961563 | − | 0.274586i | \(-0.911459\pi\) |
0.718580 | + | 0.695444i | \(0.244792\pi\) | |||||||
\(272\) | − | 2.00000i | − | 0.121268i | ||||||
\(273\) | −2.59808 | − | 0.500000i | −0.157243 | − | 0.0302614i | ||||
\(274\) | −4.00000 | −0.241649 | ||||||||
\(275\) | 24.8205 | − | 2.99038i | 1.49673 | − | 0.180327i | ||||
\(276\) | −1.50000 | − | 2.59808i | −0.0902894 | − | 0.156386i | ||||
\(277\) | 1.73205 | − | 1.00000i | 0.104069 | − | 0.0600842i | −0.447062 | − | 0.894503i | \(-0.647530\pi\) |
0.551131 | + | 0.834419i | \(0.314196\pi\) | |||||||
\(278\) | 6.92820 | + | 4.00000i | 0.415526 | + | 0.239904i | ||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 5.86603 | + | 0.767949i | 0.350562 | + | 0.0458937i | ||||
\(281\) | −11.0000 | −0.656205 | −0.328102 | − | 0.944642i | \(-0.606409\pi\) | ||||
−0.328102 | + | 0.944642i | \(0.606409\pi\) | |||||||
\(282\) | −11.2583 | − | 6.50000i | −0.670424 | − | 0.387069i | ||||
\(283\) | −22.5167 | + | 13.0000i | −1.33848 | + | 0.772770i | −0.986581 | − | 0.163270i | \(-0.947796\pi\) |
−0.351895 | + | 0.936039i | \(0.614463\pi\) | |||||||
\(284\) | −1.00000 | − | 1.73205i | −0.0593391 | − | 0.102778i | ||||
\(285\) | −8.62436 | − | 13.0622i | −0.510863 | − | 0.773737i | ||||
\(286\) | 5.00000 | 0.295656 | ||||||||
\(287\) | 15.5885 | − | 18.0000i | 0.920158 | − | 1.06251i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −6.50000 | + | 11.2583i | −0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.00000 | − | 6.92820i | −0.234484 | − | 0.406138i | ||||
\(292\) | −3.46410 | − | 2.00000i | −0.202721 | − | 0.117041i | ||||
\(293\) | − | 1.00000i | − | 0.0584206i | −0.999573 | − | 0.0292103i | \(-0.990701\pi\) | ||
0.999573 | − | 0.0292103i | \(-0.00929925\pi\) | |||||||
\(294\) | 1.00000 | + | 6.92820i | 0.0583212 | + | 0.404061i | ||||
\(295\) | −8.00000 | − | 4.00000i | −0.465778 | − | 0.232889i | ||||
\(296\) | −2.50000 | + | 4.33013i | −0.145310 | + | 0.251684i | ||||
\(297\) | −4.33013 | + | 2.50000i | −0.251259 | + | 0.145065i | ||||
\(298\) | −5.19615 | + | 3.00000i | −0.301005 | + | 0.173785i | ||||
\(299\) | 1.50000 | − | 2.59808i | 0.0867472 | − | 0.150251i | ||||
\(300\) | −4.00000 | + | 3.00000i | −0.230940 | + | 0.173205i | ||||
\(301\) | 20.0000 | + | 17.3205i | 1.15278 | + | 0.998337i | ||||
\(302\) | 22.0000i | 1.26596i | ||||||||
\(303\) | 6.92820 | + | 4.00000i | 0.398015 | + | 0.229794i | ||||
\(304\) | 3.50000 | + | 6.06218i | 0.200739 | + | 0.347690i | ||||
\(305\) | 0.267949 | + | 4.46410i | 0.0153427 | + | 0.255614i | ||||
\(306\) | −1.00000 | + | 1.73205i | −0.0571662 | + | 0.0990148i | ||||
\(307\) | 2.00000i | 0.114146i | 0.998370 | + | 0.0570730i | \(0.0181768\pi\) | ||||
−0.998370 | + | 0.0570730i | \(0.981823\pi\) | |||||||
\(308\) | −4.33013 | − | 12.5000i | −0.246732 | − | 0.712254i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.39230 | − | 11.1962i | −0.419855 | − | 0.635899i | ||||
\(311\) | 13.0000 | + | 22.5167i | 0.737162 | + | 1.27680i | 0.953768 | + | 0.300544i | \(0.0971681\pi\) |
−0.216606 | + | 0.976259i | \(0.569499\pi\) | |||||||
\(312\) | −0.866025 | + | 0.500000i | −0.0490290 | + | 0.0283069i | ||||
\(313\) | −8.66025 | − | 5.00000i | −0.489506 | − | 0.282617i | 0.234863 | − | 0.972028i | \(-0.424536\pi\) |
−0.724370 | + | 0.689412i | \(0.757869\pi\) | |||||||
\(314\) | 13.0000 | 0.733632 | ||||||||
\(315\) | −4.69615 | − | 3.59808i | −0.264598 | − | 0.202729i | ||||
\(316\) | −14.0000 | −0.787562 | ||||||||
\(317\) | −1.73205 | − | 1.00000i | −0.0972817 | − | 0.0561656i | 0.450570 | − | 0.892741i | \(-0.351221\pi\) |
−0.547852 | + | 0.836576i | \(0.684554\pi\) | |||||||
\(318\) | −0.866025 | + | 0.500000i | −0.0485643 | + | 0.0280386i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.86603 | − | 1.23205i | 0.104314 | − | 0.0688737i | ||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | −7.79423 | − | 1.50000i | −0.434355 | − | 0.0835917i | ||||
\(323\) | 14.0000i | 0.778981i | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | −4.59808 | − | 1.96410i | −0.255055 | − | 0.108949i | ||||
\(326\) | −6.00000 | − | 10.3923i | −0.332309 | − | 0.575577i | ||||
\(327\) | 15.5885 | + | 9.00000i | 0.862044 | + | 0.497701i | ||||
\(328\) | − | 9.00000i | − | 0.496942i | ||||||
\(329\) | −32.5000 | + | 11.2583i | −1.79178 | + | 0.620692i | ||||
\(330\) | 10.0000 | + | 5.00000i | 0.550482 | + | 0.275241i | ||||
\(331\) | 7.50000 | − | 12.9904i | 0.412237 | − | 0.714016i | −0.582897 | − | 0.812546i | \(-0.698081\pi\) |
0.995134 | + | 0.0985303i | \(0.0314141\pi\) | |||||||
\(332\) | −8.66025 | + | 5.00000i | −0.475293 | + | 0.274411i | ||||
\(333\) | 4.33013 | − | 2.50000i | 0.237289 | − | 0.136999i | ||||
\(334\) | 9.50000 | − | 16.4545i | 0.519817 | − | 0.900349i | ||||
\(335\) | −6.00000 | + | 12.0000i | −0.327815 | + | 0.655630i | ||||
\(336\) | 2.00000 | + | 1.73205i | 0.109109 | + | 0.0944911i | ||||
\(337\) | − | 14.0000i | − | 0.762629i | −0.924445 | − | 0.381314i | \(-0.875472\pi\) | ||
0.924445 | − | 0.381314i | \(-0.124528\pi\) | |||||||
\(338\) | 10.3923 | + | 6.00000i | 0.565267 | + | 0.326357i | ||||
\(339\) | 3.00000 | + | 5.19615i | 0.162938 | + | 0.282216i | ||||
\(340\) | 4.46410 | − | 0.267949i | 0.242100 | − | 0.0145316i | ||||
\(341\) | −15.0000 | + | 25.9808i | −0.812296 | + | 1.40694i | ||||
\(342\) | − | 7.00000i | − | 0.378517i | ||||||
\(343\) | 15.5885 | + | 10.0000i | 0.841698 | + | 0.539949i | ||||
\(344\) | 10.0000 | 0.539164 | ||||||||
\(345\) | 5.59808 | − | 3.69615i | 0.301390 | − | 0.198994i | ||||
\(346\) | 3.50000 | + | 6.06218i | 0.188161 | + | 0.325905i | ||||
\(347\) | −13.8564 | + | 8.00000i | −0.743851 | + | 0.429463i | −0.823468 | − | 0.567363i | \(-0.807964\pi\) |
0.0796169 | + | 0.996826i | \(0.474630\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.0000 | 1.28469 | 0.642345 | − | 0.766415i | \(-0.277962\pi\) | ||||
0.642345 | + | 0.766415i | \(0.277962\pi\) | |||||||
\(350\) | −0.928203 | + | 13.1962i | −0.0496145 | + | 0.705364i | ||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −4.33013 | − | 2.50000i | −0.230797 | − | 0.133250i | ||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | −2.00000 | − | 3.46410i | −0.106299 | − | 0.184115i | ||||
\(355\) | 3.73205 | − | 2.46410i | 0.198077 | − | 0.130781i | ||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | 1.73205 | + | 5.00000i | 0.0916698 | + | 0.264628i | ||||
\(358\) | − | 11.0000i | − | 0.581368i | ||||||
\(359\) | −14.0000 | + | 24.2487i | −0.738892 | + | 1.27980i | 0.214103 | + | 0.976811i | \(0.431317\pi\) |
−0.952995 | + | 0.302987i | \(0.902016\pi\) | |||||||
\(360\) | −2.23205 | + | 0.133975i | −0.117639 | + | 0.00706108i | ||||
\(361\) | −15.0000 | − | 25.9808i | −0.789474 | − | 1.36741i | ||||
\(362\) | −1.73205 | − | 1.00000i | −0.0910346 | − | 0.0525588i | ||||
\(363\) | − | 14.0000i | − | 0.734809i | ||||||
\(364\) | −0.500000 | + | 2.59808i | −0.0262071 | + | 0.136176i | ||||
\(365\) | 4.00000 | − | 8.00000i | 0.209370 | − | 0.418739i | ||||
\(366\) | −1.00000 | + | 1.73205i | −0.0522708 | + | 0.0905357i | ||||
\(367\) | −32.0429 | + | 18.5000i | −1.67263 | + | 0.965692i | −0.706469 | + | 0.707744i | \(0.749713\pi\) |
−0.966159 | + | 0.257948i | \(0.916954\pi\) | |||||||
\(368\) | −2.59808 | + | 1.50000i | −0.135434 | + | 0.0781929i | ||||
\(369\) | −4.50000 | + | 7.79423i | −0.234261 | + | 0.405751i | ||||
\(370\) | −10.0000 | − | 5.00000i | −0.519875 | − | 0.259938i | ||||
\(371\) | −0.500000 | + | 2.59808i | −0.0259587 | + | 0.134885i | ||||
\(372\) | − | 6.00000i | − | 0.311086i | ||||||
\(373\) | 5.19615 | + | 3.00000i | 0.269047 | + | 0.155334i | 0.628454 | − | 0.777847i | \(-0.283688\pi\) |
−0.359408 | + | 0.933181i | \(0.617021\pi\) | |||||||
\(374\) | −5.00000 | − | 8.66025i | −0.258544 | − | 0.447811i | ||||
\(375\) | −7.23205 | − | 8.52628i | −0.373461 | − | 0.440295i | ||||
\(376\) | −6.50000 | + | 11.2583i | −0.335212 | + | 0.580604i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.866025 | − | 2.50000i | −0.0445435 | − | 0.128586i | ||||
\(379\) | 1.00000 | 0.0513665 | 0.0256833 | − | 0.999670i | \(-0.491824\pi\) | ||||
0.0256833 | + | 0.999670i | \(0.491824\pi\) | |||||||
\(380\) | −13.0622 | + | 8.62436i | −0.670076 | + | 0.442420i | ||||
\(381\) | −4.50000 | − | 7.79423i | −0.230542 | − | 0.399310i | ||||
\(382\) | 13.8564 | − | 8.00000i | 0.708955 | − | 0.409316i | ||||
\(383\) | −7.79423 | − | 4.50000i | −0.398266 | − | 0.229939i | 0.287469 | − | 0.957790i | \(-0.407186\pi\) |
−0.685736 | + | 0.727851i | \(0.740519\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 27.3205 | − | 11.3397i | 1.39238 | − | 0.577927i | ||||
\(386\) | 18.0000 | 0.916176 | ||||||||
\(387\) | −8.66025 | − | 5.00000i | −0.440225 | − | 0.254164i | ||||
\(388\) | −6.92820 | + | 4.00000i | −0.351726 | + | 0.203069i | ||||
\(389\) | 3.00000 | + | 5.19615i | 0.152106 | + | 0.263455i | 0.932002 | − | 0.362454i | \(-0.118061\pi\) |
−0.779895 | + | 0.625910i | \(0.784728\pi\) | |||||||
\(390\) | −1.23205 | − | 1.86603i | −0.0623873 | − | 0.0944899i | ||||
\(391\) | −6.00000 | −0.303433 | ||||||||
\(392\) | 6.92820 | − | 1.00000i | 0.349927 | − | 0.0505076i | ||||
\(393\) | 17.0000i | 0.857537i | ||||||||
\(394\) | 13.5000 | − | 23.3827i | 0.680120 | − | 1.17800i | ||||
\(395\) | −1.87564 | − | 31.2487i | −0.0943739 | − | 1.57229i | ||||
\(396\) | 2.50000 | + | 4.33013i | 0.125630 | + | 0.217597i | ||||
\(397\) | 1.73205 | + | 1.00000i | 0.0869291 | + | 0.0501886i | 0.542834 | − | 0.839840i | \(-0.317351\pi\) |
−0.455905 | + | 0.890028i | \(0.650684\pi\) | |||||||
\(398\) | − | 14.0000i | − | 0.701757i | ||||||
\(399\) | −14.0000 | − | 12.1244i | −0.700877 | − | 0.606977i | ||||
\(400\) | 3.00000 | + | 4.00000i | 0.150000 | + | 0.200000i | ||||
\(401\) | 13.5000 | − | 23.3827i | 0.674158 | − | 1.16768i | −0.302556 | − | 0.953131i | \(-0.597840\pi\) |
0.976714 | − | 0.214544i | \(-0.0688266\pi\) | |||||||
\(402\) | −5.19615 | + | 3.00000i | −0.259161 | + | 0.149626i | ||||
\(403\) | 5.19615 | − | 3.00000i | 0.258839 | − | 0.149441i | ||||
\(404\) | 4.00000 | − | 6.92820i | 0.199007 | − | 0.344691i | ||||
\(405\) | 2.00000 | + | 1.00000i | 0.0993808 | + | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.0000i | 1.23920i | ||||||||
\(408\) | 1.73205 | + | 1.00000i | 0.0857493 | + | 0.0495074i | ||||
\(409\) | 5.00000 | + | 8.66025i | 0.247234 | + | 0.428222i | 0.962757 | − | 0.270367i | \(-0.0871450\pi\) |
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(410\) | 20.0885 | − | 1.20577i | 0.992098 | − | 0.0595488i | ||||
\(411\) | 2.00000 | − | 3.46410i | 0.0986527 | − | 0.170872i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.3923 | − | 2.00000i | −0.511372 | − | 0.0984136i | ||||
\(414\) | 3.00000 | 0.147442 | ||||||||
\(415\) | −12.3205 | − | 18.6603i | −0.604790 | − | 0.915996i | ||||
\(416\) | 0.500000 | + | 0.866025i | 0.0245145 | + | 0.0424604i | ||||
\(417\) | −6.92820 | + | 4.00000i | −0.339276 | + | 0.195881i | ||||
\(418\) | 30.3109 | + | 17.5000i | 1.48255 | + | 0.855953i | ||||
\(419\) | −3.00000 | −0.146560 | −0.0732798 | − | 0.997311i | \(-0.523347\pi\) | ||||
−0.0732798 | + | 0.997311i | \(0.523347\pi\) | |||||||
\(420\) | −3.59808 | + | 4.69615i | −0.175568 | + | 0.229149i | ||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | 16.4545 | + | 9.50000i | 0.800992 | + | 0.462453i | ||||
\(423\) | 11.2583 | − | 6.50000i | 0.547399 | − | 0.316041i | ||||
\(424\) | 0.500000 | + | 0.866025i | 0.0242821 | + | 0.0420579i | ||||
\(425\) | 1.19615 | + | 9.92820i | 0.0580219 | + | 0.481589i | ||||
\(426\) | 2.00000 | 0.0969003 | ||||||||
\(427\) | 1.73205 | + | 5.00000i | 0.0838198 | + | 0.241967i | ||||
\(428\) | − | 12.0000i | − | 0.580042i | ||||||
\(429\) | −2.50000 | + | 4.33013i | −0.120701 | + | 0.209061i | ||||
\(430\) | 1.33975 | + | 22.3205i | 0.0646083 | + | 1.07639i | ||||
\(431\) | −9.00000 | − | 15.5885i | −0.433515 | − | 0.750870i | 0.563658 | − | 0.826008i | \(-0.309393\pi\) |
−0.997173 | + | 0.0751385i | \(0.976060\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | − | 4.00000i | − | 0.192228i | −0.995370 | − | 0.0961139i | \(-0.969359\pi\) | ||
0.995370 | − | 0.0961139i | \(-0.0306413\pi\) | |||||||
\(434\) | −12.0000 | − | 10.3923i | −0.576018 | − | 0.498847i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.00000 | − | 15.5885i | 0.431022 | − | 0.746552i | ||||
\(437\) | 18.1865 | − | 10.5000i | 0.869980 | − | 0.502283i | ||||
\(438\) | 3.46410 | − | 2.00000i | 0.165521 | − | 0.0955637i | ||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | 5.00000 | − | 10.0000i | 0.238366 | − | 0.476731i | ||||
\(441\) | −6.50000 | − | 2.59808i | −0.309524 | − | 0.123718i | ||||
\(442\) | 2.00000i | 0.0951303i | ||||||||
\(443\) | −5.19615 | − | 3.00000i | −0.246877 | − | 0.142534i | 0.371457 | − | 0.928450i | \(-0.378858\pi\) |
−0.618333 | + | 0.785916i | \(0.712192\pi\) | |||||||
\(444\) | −2.50000 | − | 4.33013i | −0.118645 | − | 0.205499i | ||||
\(445\) | 1.33975 | + | 22.3205i | 0.0635100 | + | 1.05809i | ||||
\(446\) | 8.00000 | − | 13.8564i | 0.378811 | − | 0.656120i | ||||
\(447\) | − | 6.00000i | − | 0.283790i | ||||||
\(448\) | 1.73205 | − | 2.00000i | 0.0818317 | − | 0.0944911i | ||||
\(449\) | −9.00000 | −0.424736 | −0.212368 | − | 0.977190i | \(-0.568118\pi\) | ||||
−0.212368 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(450\) | −0.598076 | − | 4.96410i | −0.0281936 | − | 0.234010i | ||||
\(451\) | −22.5000 | − | 38.9711i | −1.05948 | − | 1.83508i | ||||
\(452\) | 5.19615 | − | 3.00000i | 0.244406 | − | 0.141108i | ||||
\(453\) | −19.0526 | − | 11.0000i | −0.895167 | − | 0.516825i | ||||
\(454\) | 14.0000 | 0.657053 | ||||||||
\(455\) | −5.86603 | − | 0.767949i | −0.275004 | − | 0.0360020i | ||||
\(456\) | −7.00000 | −0.327805 | ||||||||
\(457\) | 32.9090 | + | 19.0000i | 1.53942 | + | 0.888783i | 0.998873 | + | 0.0474665i | \(0.0151147\pi\) |
0.540544 | + | 0.841316i | \(0.318219\pi\) | |||||||
\(458\) | −3.46410 | + | 2.00000i | −0.161867 | + | 0.0934539i | ||||
\(459\) | −1.00000 | − | 1.73205i | −0.0466760 | − | 0.0808452i | ||||
\(460\) | −3.69615 | − | 5.59808i | −0.172334 | − | 0.261012i | ||||
\(461\) | −12.0000 | −0.558896 | −0.279448 | − | 0.960161i | \(-0.590151\pi\) | ||||
−0.279448 | + | 0.960161i | \(0.590151\pi\) | |||||||
\(462\) | 12.9904 | + | 2.50000i | 0.604367 | + | 0.116311i | ||||
\(463\) | 15.0000i | 0.697109i | 0.937288 | + | 0.348555i | \(0.113327\pi\) | ||||
−0.937288 | + | 0.348555i | \(0.886673\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.3923 | − | 0.803848i | 0.621053 | − | 0.0372775i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.73205 | − | 1.00000i | −0.0801498 | − | 0.0462745i | 0.459390 | − | 0.888235i | \(-0.348068\pi\) |
−0.539539 | + | 0.841960i | \(0.681402\pi\) | |||||||
\(468\) | − | 1.00000i | − | 0.0462250i | ||||||
\(469\) | −3.00000 | + | 15.5885i | −0.138527 | + | 0.719808i | ||||
\(470\) | −26.0000 | − | 13.0000i | −1.19929 | − | 0.599645i | ||||
\(471\) | −6.50000 | + | 11.2583i | −0.299504 | + | 0.518756i | ||||
\(472\) | −3.46410 | + | 2.00000i | −0.159448 | + | 0.0920575i | ||||
\(473\) | 43.3013 | − | 25.0000i | 1.99099 | − | 1.14950i | ||||
\(474\) | 7.00000 | − | 12.1244i | 0.321521 | − | 0.556890i | ||||
\(475\) | −21.0000 | − | 28.0000i | −0.963546 | − | 1.28473i | ||||
\(476\) | 5.00000 | − | 1.73205i | 0.229175 | − | 0.0793884i | ||||
\(477\) | − | 1.00000i | − | 0.0457869i | ||||||
\(478\) | −17.3205 | − | 10.0000i | −0.792222 | − | 0.457389i | ||||
\(479\) | 4.00000 | + | 6.92820i | 0.182765 | + | 0.316558i | 0.942821 | − | 0.333300i | \(-0.108162\pi\) |
−0.760056 | + | 0.649857i | \(0.774829\pi\) | |||||||
\(480\) | 0.133975 | + | 2.23205i | 0.00611508 | + | 0.101879i | ||||
\(481\) | 2.50000 | − | 4.33013i | 0.113990 | − | 0.197437i | ||||
\(482\) | 1.00000i | 0.0455488i | ||||||||
\(483\) | 5.19615 | − | 6.00000i | 0.236433 | − | 0.273009i | ||||
\(484\) | −14.0000 | −0.636364 | ||||||||
\(485\) | −9.85641 | − | 14.9282i | −0.447556 | − | 0.677855i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 20.7846 | − | 12.0000i | 0.941841 | − | 0.543772i | 0.0513038 | − | 0.998683i | \(-0.483662\pi\) |
0.890537 | + | 0.454911i | \(0.150329\pi\) | |||||||
\(488\) | 1.73205 | + | 1.00000i | 0.0784063 | + | 0.0452679i | ||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | 3.16025 | + | 15.3301i | 0.142766 | + | 0.692545i | ||||
\(491\) | 24.0000 | 1.08310 | 0.541552 | − | 0.840667i | \(-0.317837\pi\) | ||||
0.541552 | + | 0.840667i | \(0.317837\pi\) | |||||||
\(492\) | 7.79423 | + | 4.50000i | 0.351391 | + | 0.202876i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −3.50000 | − | 6.06218i | −0.157472 | − | 0.272750i | ||||
\(495\) | −9.33013 | + | 6.16025i | −0.419358 | + | 0.276883i | ||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | 3.46410 | − | 4.00000i | 0.155386 | − | 0.179425i | ||||
\(498\) | − | 10.0000i | − | 0.448111i | ||||||
\(499\) | −14.0000 | + | 24.2487i | −0.626726 | + | 1.08552i | 0.361478 | + | 0.932381i | \(0.382272\pi\) |
−0.988204 | + | 0.153141i | \(0.951061\pi\) | |||||||
\(500\) | −8.52628 | + | 7.23205i | −0.381307 | + | 0.323427i | ||||
\(501\) | 9.50000 | + | 16.4545i | 0.424429 | + | 0.735132i | ||||
\(502\) | −2.59808 | − | 1.50000i | −0.115958 | − | 0.0669483i | ||||
\(503\) | − | 24.0000i | − | 1.07011i | −0.844818 | − | 0.535054i | \(-0.820291\pi\) | ||
0.844818 | − | 0.535054i | \(-0.179709\pi\) | |||||||
\(504\) | −2.50000 | + | 0.866025i | −0.111359 | + | 0.0385758i | ||||
\(505\) | 16.0000 | + | 8.00000i | 0.711991 | + | 0.355995i | ||||
\(506\) | −7.50000 | + | 12.9904i | −0.333416 | + | 0.577493i | ||||
\(507\) | −10.3923 | + | 6.00000i | −0.461538 | + | 0.266469i | ||||
\(508\) | −7.79423 | + | 4.50000i | −0.345813 | + | 0.199655i | ||||
\(509\) | 7.00000 | − | 12.1244i | 0.310270 | − | 0.537403i | −0.668151 | − | 0.744026i | \(-0.732914\pi\) |
0.978421 | + | 0.206623i | \(0.0662474\pi\) | |||||||
\(510\) | −2.00000 | + | 4.00000i | −0.0885615 | + | 0.177123i | ||||
\(511\) | 2.00000 | − | 10.3923i | 0.0884748 | − | 0.459728i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 6.06218 | + | 3.50000i | 0.267652 | + | 0.154529i | ||||
\(514\) | 5.00000 | + | 8.66025i | 0.220541 | + | 0.381987i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.00000 | + | 8.66025i | −0.220113 | + | 0.381246i | ||||
\(517\) | 65.0000i | 2.85870i | ||||||||
\(518\) | −12.9904 | − | 2.50000i | −0.570765 | − | 0.109844i | ||||
\(519\) | −7.00000 | −0.307266 | ||||||||
\(520\) | −1.86603 | + | 1.23205i | −0.0818306 | + | 0.0540290i | ||||
\(521\) | 7.50000 | + | 12.9904i | 0.328581 | + | 0.569119i | 0.982231 | − | 0.187678i | \(-0.0600963\pi\) |
−0.653650 | + | 0.756797i | \(0.726763\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.3923 | + | 6.00000i | 0.454424 | + | 0.262362i | 0.709697 | − | 0.704507i | \(-0.248832\pi\) |
−0.255273 | + | 0.966869i | \(0.582165\pi\) | |||||||
\(524\) | 17.0000 | 0.742648 | ||||||||
\(525\) | −10.9641 | − | 7.40192i | −0.478513 | − | 0.323046i | ||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | −10.3923 | − | 6.00000i | −0.452696 | − | 0.261364i | ||||
\(528\) | 4.33013 | − | 2.50000i | 0.188445 | − | 0.108799i | ||||
\(529\) | −7.00000 | − | 12.1244i | −0.304348 | − | 0.527146i | ||||
\(530\) | −1.86603 | + | 1.23205i | −0.0810550 | + | 0.0535169i | ||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | −12.1244 | + | 14.0000i | −0.525657 | + | 0.606977i | ||||
\(533\) | 9.00000i | 0.389833i | ||||||||
\(534\) | −5.00000 | + | 8.66025i | −0.216371 | + | 0.374766i | ||||
\(535\) | 26.7846 | − | 1.60770i | 1.15800 | − | 0.0695067i | ||||
\(536\) | 3.00000 | + | 5.19615i | 0.129580 | + | 0.224440i | ||||
\(537\) | 9.52628 | + | 5.50000i | 0.411089 | + | 0.237343i | ||||
\(538\) | 14.0000i | 0.603583i | ||||||||
\(539\) | 27.5000 | − | 21.6506i | 1.18451 | − | 0.932559i | ||||
\(540\) | 1.00000 | − | 2.00000i | 0.0430331 | − | 0.0860663i | ||||
\(541\) | −2.00000 | + | 3.46410i | −0.0859867 | + | 0.148933i | −0.905811 | − | 0.423681i | \(-0.860738\pi\) |
0.819825 | + | 0.572615i | \(0.194071\pi\) | |||||||
\(542\) | −6.92820 | + | 4.00000i | −0.297592 | + | 0.171815i | ||||
\(543\) | 1.73205 | − | 1.00000i | 0.0743294 | − | 0.0429141i | ||||
\(544\) | 1.00000 | − | 1.73205i | 0.0428746 | − | 0.0742611i | ||||
\(545\) | 36.0000 | + | 18.0000i | 1.54207 | + | 0.771035i | ||||
\(546\) | −2.00000 | − | 1.73205i | −0.0855921 | − | 0.0741249i | ||||
\(547\) | − | 14.0000i | − | 0.598597i | −0.954160 | − | 0.299298i | \(-0.903247\pi\) | ||
0.954160 | − | 0.299298i | \(-0.0967526\pi\) | |||||||
\(548\) | −3.46410 | − | 2.00000i | −0.147979 | − | 0.0854358i | ||||
\(549\) | −1.00000 | − | 1.73205i | −0.0426790 | − | 0.0739221i | ||||
\(550\) | 22.9904 | + | 9.82051i | 0.980313 | + | 0.418748i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | − | 3.00000i | − | 0.127688i | ||||||
\(553\) | −12.1244 | − | 35.0000i | −0.515580 | − | 1.48835i | ||||
\(554\) | 2.00000 | 0.0849719 | ||||||||
\(555\) | 9.33013 | − | 6.16025i | 0.396042 | − | 0.261488i | ||||
\(556\) | 4.00000 | + | 6.92820i | 0.169638 | + | 0.293821i | ||||
\(557\) | −33.7750 | + | 19.5000i | −1.43109 | + | 0.826242i | −0.997204 | − | 0.0747252i | \(-0.976192\pi\) |
−0.433888 | + | 0.900967i | \(0.642859\pi\) | |||||||
\(558\) | 5.19615 | + | 3.00000i | 0.219971 | + | 0.127000i | ||||
\(559\) | −10.0000 | −0.422955 | ||||||||
\(560\) | 4.69615 | + | 3.59808i | 0.198449 | + | 0.152046i | ||||
\(561\) | 10.0000 | 0.422200 | ||||||||
\(562\) | −9.52628 | − | 5.50000i | −0.401842 | − | 0.232003i | ||||
\(563\) | −25.9808 | + | 15.0000i | −1.09496 | + | 0.632175i | −0.934892 | − | 0.354932i | \(-0.884504\pi\) |
−0.160066 | + | 0.987106i | \(0.551171\pi\) | |||||||
\(564\) | −6.50000 | − | 11.2583i | −0.273699 | − | 0.474061i | ||||
\(565\) | 7.39230 | + | 11.1962i | 0.310997 | + | 0.471026i | ||||
\(566\) | −26.0000 | −1.09286 | ||||||||
\(567\) | 2.59808 | + | 0.500000i | 0.109109 | + | 0.0209980i | ||||
\(568\) | − | 2.00000i | − | 0.0839181i | ||||||
\(569\) | −1.50000 | + | 2.59808i | −0.0628833 | + | 0.108917i | −0.895753 | − | 0.444552i | \(-0.853363\pi\) |
0.832870 | + | 0.553469i | \(0.186696\pi\) | |||||||
\(570\) | −0.937822 | − | 15.6244i | −0.0392810 | − | 0.654432i | ||||
\(571\) | 4.00000 | + | 6.92820i | 0.167395 | + | 0.289936i | 0.937503 | − | 0.347977i | \(-0.113131\pi\) |
−0.770108 | + | 0.637913i | \(0.779798\pi\) | |||||||
\(572\) | 4.33013 | + | 2.50000i | 0.181052 | + | 0.104530i | ||||
\(573\) | 16.0000i | 0.668410i | ||||||||
\(574\) | 22.5000 | − | 7.79423i | 0.939132 | − | 0.325325i | ||||
\(575\) | 12.0000 | − | 9.00000i | 0.500435 | − | 0.375326i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 20.7846 | − | 12.0000i | 0.865275 | − | 0.499567i | −0.000500448 | − | 1.00000i | \(-0.500159\pi\) |
0.865775 | + | 0.500433i | \(0.166826\pi\) | |||||||
\(578\) | −11.2583 | + | 6.50000i | −0.468285 | + | 0.270364i | ||||
\(579\) | −9.00000 | + | 15.5885i | −0.374027 | + | 0.647834i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.0000 | − | 17.3205i | −0.829740 | − | 0.718576i | ||||
\(582\) | − | 8.00000i | − | 0.331611i | ||||||
\(583\) | 4.33013 | + | 2.50000i | 0.179336 | + | 0.103539i | ||||
\(584\) | −2.00000 | − | 3.46410i | −0.0827606 | − | 0.143346i | ||||
\(585\) | 2.23205 | − | 0.133975i | 0.0922839 | − | 0.00553917i | ||||
\(586\) | 0.500000 | − | 0.866025i | 0.0206548 | − | 0.0357752i | ||||
\(587\) | 2.00000i | 0.0825488i | 0.999148 | + | 0.0412744i | \(0.0131418\pi\) | ||||
−0.999148 | + | 0.0412744i | \(0.986858\pi\) | |||||||
\(588\) | −2.59808 | + | 6.50000i | −0.107143 | + | 0.268055i | ||||
\(589\) | 42.0000 | 1.73058 | ||||||||
\(590\) | −4.92820 | − | 7.46410i | −0.202891 | − | 0.307292i | ||||
\(591\) | 13.5000 | + | 23.3827i | 0.555316 | + | 0.961835i | ||||
\(592\) | −4.33013 | + | 2.50000i | −0.177967 | + | 0.102749i | ||||
\(593\) | −29.4449 | − | 17.0000i | −1.20916 | − | 0.698106i | −0.246581 | − | 0.969122i | \(-0.579307\pi\) |
−0.962575 | + | 0.271016i | \(0.912640\pi\) | |||||||
\(594\) | −5.00000 | −0.205152 | ||||||||
\(595\) | 4.53590 | + | 10.9282i | 0.185954 | + | 0.448013i | ||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 12.1244 | + | 7.00000i | 0.496217 | + | 0.286491i | ||||
\(598\) | 2.59808 | − | 1.50000i | 0.106243 | − | 0.0613396i | ||||
\(599\) | −14.0000 | − | 24.2487i | −0.572024 | − | 0.990775i | −0.996358 | − | 0.0852695i | \(-0.972825\pi\) |
0.424333 | − | 0.905506i | \(-0.360508\pi\) | |||||||
\(600\) | −4.96410 | + | 0.598076i | −0.202659 | + | 0.0244164i | ||||
\(601\) | −30.0000 | −1.22373 | −0.611863 | − | 0.790964i | \(-0.709580\pi\) | ||||
−0.611863 | + | 0.790964i | \(0.709580\pi\) | |||||||
\(602\) | 8.66025 | + | 25.0000i | 0.352966 | + | 1.01892i | ||||
\(603\) | − | 6.00000i | − | 0.244339i | ||||||
\(604\) | −11.0000 | + | 19.0526i | −0.447584 | + | 0.775238i | ||||
\(605\) | −1.87564 | − | 31.2487i | −0.0762558 | − | 1.27044i | ||||
\(606\) | 4.00000 | + | 6.92820i | 0.162489 | + | 0.281439i | ||||
\(607\) | −11.2583 | − | 6.50000i | −0.456962 | − | 0.263827i | 0.253804 | − | 0.967256i | \(-0.418318\pi\) |
−0.710766 | + | 0.703429i | \(0.751651\pi\) | |||||||
\(608\) | 7.00000i | 0.283887i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.00000 | + | 4.00000i | −0.0809776 | + | 0.161955i | ||||
\(611\) | 6.50000 | − | 11.2583i | 0.262962 | − | 0.455463i | ||||
\(612\) | −1.73205 | + | 1.00000i | −0.0700140 | + | 0.0404226i | ||||
\(613\) | −16.4545 | + | 9.50000i | −0.664590 | + | 0.383701i | −0.794024 | − | 0.607887i | \(-0.792017\pi\) |
0.129433 | + | 0.991588i | \(0.458684\pi\) | |||||||
\(614\) | −1.00000 | + | 1.73205i | −0.0403567 | + | 0.0698999i | ||||
\(615\) | −9.00000 | + | 18.0000i | −0.362915 | + | 0.725830i | ||||
\(616\) | 2.50000 | − | 12.9904i | 0.100728 | − | 0.523397i | ||||
\(617\) | 30.0000i | 1.20775i | 0.797077 | + | 0.603877i | \(0.206378\pi\) | ||||
−0.797077 | + | 0.603877i | \(0.793622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.50000 | + | 12.9904i | 0.301450 | + | 0.522127i | 0.976465 | − | 0.215677i | \(-0.0691959\pi\) |
−0.675014 | + | 0.737805i | \(0.735863\pi\) | |||||||
\(620\) | −0.803848 | − | 13.3923i | −0.0322833 | − | 0.537848i | ||||
\(621\) | −1.50000 | + | 2.59808i | −0.0601929 | + | 0.104257i | ||||
\(622\) | 26.0000i | 1.04251i | ||||||||
\(623\) | 8.66025 | + | 25.0000i | 0.346966 | + | 1.00160i | ||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −17.2846 | − | 18.0622i | −0.691384 | − | 0.722487i | ||||
\(626\) | −5.00000 | − | 8.66025i | −0.199840 | − | 0.346133i | ||||
\(627\) | −30.3109 | + | 17.5000i | −1.21050 | + | 0.698883i | ||||
\(628\) | 11.2583 | + | 6.50000i | 0.449256 | + | 0.259378i | ||||
\(629\) | −10.0000 | −0.398726 | ||||||||
\(630\) | −2.26795 | − | 5.46410i | −0.0903573 | − | 0.217695i | ||||
\(631\) | 18.0000 | 0.716569 | 0.358284 | − | 0.933613i | \(-0.383362\pi\) | ||||
0.358284 | + | 0.933613i | \(0.383362\pi\) | |||||||
\(632\) | −12.1244 | − | 7.00000i | −0.482281 | − | 0.278445i | ||||
\(633\) | −16.4545 | + | 9.50000i | −0.654007 | + | 0.377591i | ||||
\(634\) | −1.00000 | − | 1.73205i | −0.0397151 | − | 0.0687885i | ||||
\(635\) | −11.0885 | − | 16.7942i | −0.440032 | − | 0.666459i | ||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | −6.92820 | + | 1.00000i | −0.274505 | + | 0.0396214i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.00000 | + | 1.73205i | −0.0395594 | + | 0.0685189i | ||||
\(640\) | 2.23205 | − | 0.133975i | 0.0882296 | − | 0.00529581i | ||||
\(641\) | 16.5000 | + | 28.5788i | 0.651711 | + | 1.12880i | 0.982708 | + | 0.185164i | \(0.0592817\pi\) |
−0.330997 | + | 0.943632i | \(0.607385\pi\) | |||||||
\(642\) | 10.3923 | + | 6.00000i | 0.410152 | + | 0.236801i | ||||
\(643\) | − | 38.0000i | − | 1.49857i | −0.662246 | − | 0.749287i | \(-0.730396\pi\) | ||
0.662246 | − | 0.749287i | \(-0.269604\pi\) | |||||||
\(644\) | −6.00000 | − | 5.19615i | −0.236433 | − | 0.204757i | ||||
\(645\) | −20.0000 | − | 10.0000i | −0.787499 | − | 0.393750i | ||||
\(646\) | −7.00000 | + | 12.1244i | −0.275411 | + | 0.477026i | ||||
\(647\) | −0.866025 | + | 0.500000i | −0.0340470 | + | 0.0196570i | −0.516927 | − | 0.856030i | \(-0.672924\pi\) |
0.482880 | + | 0.875687i | \(0.339591\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −10.0000 | + | 17.3205i | −0.392534 | + | 0.679889i | ||||
\(650\) | −3.00000 | − | 4.00000i | −0.117670 | − | 0.156893i | ||||
\(651\) | 15.0000 | − | 5.19615i | 0.587896 | − | 0.203653i | ||||
\(652\) | − | 12.0000i | − | 0.469956i | ||||||
\(653\) | 4.33013 | + | 2.50000i | 0.169451 | + | 0.0978326i | 0.582327 | − | 0.812955i | \(-0.302142\pi\) |
−0.412876 | + | 0.910787i | \(0.635476\pi\) | |||||||
\(654\) | 9.00000 | + | 15.5885i | 0.351928 | + | 0.609557i | ||||
\(655\) | 2.27757 | + | 37.9449i | 0.0889920 | + | 1.48263i | ||||
\(656\) | 4.50000 | − | 7.79423i | 0.175695 | − | 0.304314i | ||||
\(657\) | 4.00000i | 0.156055i | ||||||||
\(658\) | −33.7750 | − | 6.50000i | −1.31669 | − | 0.253396i | ||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 6.16025 | + | 9.33013i | 0.239788 | + | 0.363175i | ||||
\(661\) | −20.0000 | − | 34.6410i | −0.777910 | − | 1.34738i | −0.933144 | − | 0.359502i | \(-0.882947\pi\) |
0.155235 | − | 0.987878i | \(-0.450387\pi\) | |||||||
\(662\) | 12.9904 | − | 7.50000i | 0.504885 | − | 0.291496i | ||||
\(663\) | −1.73205 | − | 1.00000i | −0.0672673 | − | 0.0388368i | ||||
\(664\) | −10.0000 | −0.388075 | ||||||||
\(665\) | −32.8731 | − | 25.1865i | −1.27476 | − | 0.976692i | ||||
\(666\) | 5.00000 | 0.193746 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 16.4545 | − | 9.50000i | 0.636643 | − | 0.367566i | ||||
\(669\) | 8.00000 | + | 13.8564i | 0.309298 | + | 0.535720i | ||||
\(670\) | −11.1962 | + | 7.39230i | −0.432545 | + | 0.285590i | ||||
\(671\) | 10.0000 | 0.386046 | ||||||||
\(672\) | 0.866025 | + | 2.50000i | 0.0334077 | + | 0.0964396i | ||||
\(673\) | − | 36.0000i | − | 1.38770i | −0.720121 | − | 0.693849i | \(-0.755914\pi\) | ||
0.720121 | − | 0.693849i | \(-0.244086\pi\) | |||||||
\(674\) | 7.00000 | − | 12.1244i | 0.269630 | − | 0.467013i | ||||
\(675\) | 4.59808 | + | 1.96410i | 0.176980 | + | 0.0755983i | ||||
\(676\) | 6.00000 | + | 10.3923i | 0.230769 | + | 0.399704i | ||||
\(677\) | −28.5788 | − | 16.5000i | −1.09837 | − | 0.634147i | −0.162581 | − | 0.986695i | \(-0.551982\pi\) |
−0.935793 | + | 0.352549i | \(0.885315\pi\) | |||||||
\(678\) | 6.00000i | 0.230429i | ||||||||
\(679\) | −16.0000 | − | 13.8564i | −0.614024 | − | 0.531760i | ||||
\(680\) | 4.00000 | + | 2.00000i | 0.153393 | + | 0.0766965i | ||||
\(681\) | −7.00000 | + | 12.1244i | −0.268241 | + | 0.464606i | ||||
\(682\) | −25.9808 | + | 15.0000i | −0.994855 | + | 0.574380i | ||||
\(683\) | 3.46410 | − | 2.00000i | 0.132550 | − | 0.0765279i | −0.432259 | − | 0.901750i | \(-0.642283\pi\) |
0.564809 | + | 0.825222i | \(0.308950\pi\) | |||||||
\(684\) | 3.50000 | − | 6.06218i | 0.133826 | − | 0.231793i | ||||
\(685\) | 4.00000 | − | 8.00000i | 0.152832 | − | 0.305664i | ||||
\(686\) | 8.50000 | + | 16.4545i | 0.324532 | + | 0.628235i | ||||
\(687\) | − | 4.00000i | − | 0.152610i | ||||||
\(688\) | 8.66025 | + | 5.00000i | 0.330169 | + | 0.190623i | ||||
\(689\) | −0.500000 | − | 0.866025i | −0.0190485 | − | 0.0329929i | ||||
\(690\) | 6.69615 | − | 0.401924i | 0.254918 | − | 0.0153010i | ||||
\(691\) | 10.0000 | − | 17.3205i | 0.380418 | − | 0.658903i | −0.610704 | − | 0.791859i | \(-0.709113\pi\) |
0.991122 | + | 0.132956i | \(0.0424468\pi\) | |||||||
\(692\) | 7.00000i | 0.266100i | ||||||||
\(693\) | −8.66025 | + | 10.0000i | −0.328976 | + | 0.379869i | ||||
\(694\) | −16.0000 | −0.607352 | ||||||||
\(695\) | −14.9282 | + | 9.85641i | −0.566259 | + | 0.373875i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.5885 | − | 9.00000i | 0.590455 | − | 0.340899i | ||||
\(698\) | 20.7846 | + | 12.0000i | 0.786709 | + | 0.454207i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.40192 | + | 10.9641i | −0.279766 | + | 0.414404i | ||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0.866025 | + | 0.500000i | 0.0326860 | + | 0.0188713i | ||||
\(703\) | 30.3109 | − | 17.5000i | 1.14320 | − | 0.660025i | ||||
\(704\) | −2.50000 | − | 4.33013i | −0.0942223 | − | 0.163198i | ||||
\(705\) | 24.2583 | − | 16.0167i | 0.913622 | − | 0.603222i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.7846 | + | 4.00000i | 0.781686 | + | 0.150435i | ||||
\(708\) | − | 4.00000i | − | 0.150329i | ||||||
\(709\) | 8.00000 | − | 13.8564i | 0.300446 | − | 0.520388i | −0.675791 | − | 0.737093i | \(-0.736198\pi\) |
0.976237 | + | 0.216705i | \(0.0695310\pi\) | |||||||
\(710\) | 4.46410 | − | 0.267949i | 0.167535 | − | 0.0100560i | ||||
\(711\) | 7.00000 | + | 12.1244i | 0.262521 | + | 0.454699i | ||||
\(712\) | 8.66025 | + | 5.00000i | 0.324557 | + | 0.187383i | ||||
\(713\) | 18.0000i | 0.674105i | ||||||||
\(714\) | −1.00000 | + | 5.19615i | −0.0374241 | + | 0.194461i | ||||
\(715\) | −5.00000 | + | 10.0000i | −0.186989 | + | 0.373979i | ||||
\(716\) | 5.50000 | − | 9.52628i | 0.205545 | − | 0.356014i | ||||
\(717\) | 17.3205 | − | 10.0000i | 0.646846 | − | 0.373457i | ||||
\(718\) | −24.2487 | + | 14.0000i | −0.904954 | + | 0.522475i | ||||
\(719\) | −1.00000 | + | 1.73205i | −0.0372937 | + | 0.0645946i | −0.884070 | − | 0.467355i | \(-0.845207\pi\) |
0.846776 | + | 0.531949i | \(0.178540\pi\) | |||||||
\(720\) | −2.00000 | − | 1.00000i | −0.0745356 | − | 0.0372678i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 30.0000i | − | 1.11648i | ||||||
\(723\) | −0.866025 | − | 0.500000i | −0.0322078 | − | 0.0185952i | ||||
\(724\) | −1.00000 | − | 1.73205i | −0.0371647 | − | 0.0643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.00000 | − | 12.1244i | 0.259794 | − | 0.449977i | ||||
\(727\) | 53.0000i | 1.96566i | 0.184510 | + | 0.982831i | \(0.440930\pi\) | ||||
−0.184510 | + | 0.982831i | \(0.559070\pi\) | |||||||
\(728\) | −1.73205 | + | 2.00000i | −0.0641941 | + | 0.0741249i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 7.46410 | − | 4.92820i | 0.276259 | − | 0.182401i | ||||
\(731\) | 10.0000 | + | 17.3205i | 0.369863 | + | 0.640622i | ||||
\(732\) | −1.73205 | + | 1.00000i | −0.0640184 | + | 0.0369611i | ||||
\(733\) | −18.1865 | − | 10.5000i | −0.671735 | − | 0.387826i | 0.124999 | − | 0.992157i | \(-0.460107\pi\) |
−0.796734 | + | 0.604331i | \(0.793441\pi\) | |||||||
\(734\) | −37.0000 | −1.36569 | ||||||||
\(735\) | −14.8564 | − | 4.92820i | −0.547987 | − | 0.181780i | ||||
\(736\) | −3.00000 | −0.110581 | ||||||||
\(737\) | 25.9808 | + | 15.0000i | 0.957014 | + | 0.552532i | ||||
\(738\) | −7.79423 | + | 4.50000i | −0.286910 | + | 0.165647i | ||||
\(739\) | 23.5000 | + | 40.7032i | 0.864461 | + | 1.49729i | 0.867581 | + | 0.497296i | \(0.165674\pi\) |
−0.00311943 | + | 0.999995i | \(0.500993\pi\) | |||||||
\(740\) | −6.16025 | − | 9.33013i | −0.226455 | − | 0.342982i | ||||
\(741\) | 7.00000 | 0.257151 | ||||||||
\(742\) | −1.73205 | + | 2.00000i | −0.0635856 | + | 0.0734223i | ||||
\(743\) | 31.0000i | 1.13728i | 0.822587 | + | 0.568640i | \(0.192530\pi\) | ||||
−0.822587 | + | 0.568640i | \(0.807470\pi\) | |||||||
\(744\) | 3.00000 | − | 5.19615i | 0.109985 | − | 0.190500i | ||||
\(745\) | −0.803848 | − | 13.3923i | −0.0294507 | − | 0.490656i | ||||
\(746\) | 3.00000 | + | 5.19615i | 0.109838 | + | 0.190245i | ||||
\(747\) | 8.66025 | + | 5.00000i | 0.316862 | + | 0.182940i | ||||
\(748\) | − | 10.0000i | − | 0.365636i | ||||||
\(749\) | 30.0000 | − | 10.3923i | 1.09618 | − | 0.379727i | ||||
\(750\) | −2.00000 | − | 11.0000i | −0.0730297 | − | 0.401663i | ||||
\(751\) | −2.00000 | + | 3.46410i | −0.0729810 | + | 0.126407i | −0.900207 | − | 0.435463i | \(-0.856585\pi\) |
0.827225 | + | 0.561870i | \(0.189918\pi\) | |||||||
\(752\) | −11.2583 | + | 6.50000i | −0.410549 | + | 0.237031i | ||||
\(753\) | 2.59808 | − | 1.50000i | 0.0946792 | − | 0.0546630i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −44.0000 | − | 22.0000i | −1.60132 | − | 0.800662i | ||||
\(756\) | 0.500000 | − | 2.59808i | 0.0181848 | − | 0.0944911i | ||||
\(757\) | − | 26.0000i | − | 0.944986i | −0.881334 | − | 0.472493i | \(-0.843354\pi\) | ||
0.881334 | − | 0.472493i | \(-0.156646\pi\) | |||||||
\(758\) | 0.866025 | + | 0.500000i | 0.0314555 | + | 0.0181608i | ||||
\(759\) | −7.50000 | − | 12.9904i | −0.272233 | − | 0.471521i | ||||
\(760\) | −15.6244 | + | 0.937822i | −0.566755 | + | 0.0340184i | ||||
\(761\) | 1.50000 | − | 2.59808i | 0.0543750 | − | 0.0941802i | −0.837557 | − | 0.546350i | \(-0.816017\pi\) |
0.891932 | + | 0.452170i | \(0.149350\pi\) | |||||||
\(762\) | − | 9.00000i | − | 0.326036i | ||||||
\(763\) | 46.7654 | + | 9.00000i | 1.69302 | + | 0.325822i | ||||
\(764\) | 16.0000 | 0.578860 | ||||||||
\(765\) | −2.46410 | − | 3.73205i | −0.0890898 | − | 0.134933i | ||||
\(766\) | −4.50000 | − | 7.79423i | −0.162592 | − | 0.281617i | ||||
\(767\) | 3.46410 | − | 2.00000i | 0.125081 | − | 0.0722158i | ||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | −51.0000 | −1.83911 | −0.919554 | − | 0.392965i | \(-0.871449\pi\) | ||||
−0.919554 | + | 0.392965i | \(0.871449\pi\) | |||||||
\(770\) | 29.3301 | + | 3.83975i | 1.05698 | + | 0.138375i | ||||
\(771\) | −10.0000 | −0.360141 | ||||||||
\(772\) | 15.5885 | + | 9.00000i | 0.561041 | + | 0.323917i | ||||
\(773\) | 32.0429 | − | 18.5000i | 1.15250 | − | 0.665399i | 0.203008 | − | 0.979177i | \(-0.434928\pi\) |
0.949496 | + | 0.313778i | \(0.101595\pi\) | |||||||
\(774\) | −5.00000 | − | 8.66025i | −0.179721 | − | 0.311286i | ||||
\(775\) | 29.7846 | − | 3.58846i | 1.06989 | − | 0.128901i | ||||
\(776\) | −8.00000 | −0.287183 | ||||||||
\(777\) | 8.66025 | − | 10.0000i | 0.310685 | − | 0.358748i | ||||
\(778\) | 6.00000i | 0.215110i | ||||||||
\(779\) | −31.5000 | + | 54.5596i | −1.12860 | + | 1.95480i | ||||
\(780\) | −0.133975 | − | 2.23205i | −0.00479706 | − | 0.0799202i | ||||
\(781\) | −5.00000 | − | 8.66025i | −0.178914 | − | 0.309888i | ||||
\(782\) | −5.19615 | − | 3.00000i | −0.185814 | − | 0.107280i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.50000 | + | 2.59808i | 0.232143 | + | 0.0927884i | ||||
\(785\) | −13.0000 | + | 26.0000i | −0.463990 | + | 0.927980i | ||||
\(786\) | −8.50000 | + | 14.7224i | −0.303185 | + | 0.525132i | ||||
\(787\) | 32.9090 | − | 19.0000i | 1.17308 | − | 0.677277i | 0.218675 | − | 0.975798i | \(-0.429827\pi\) |
0.954403 | + | 0.298521i | \(0.0964933\pi\) | |||||||
\(788\) | 23.3827 | − | 13.5000i | 0.832974 | − | 0.480918i | ||||
\(789\) | 12.0000 | − | 20.7846i | 0.427211 | − | 0.739952i | ||||
\(790\) | 14.0000 | − | 28.0000i | 0.498098 | − | 0.996195i | ||||
\(791\) | 12.0000 | + | 10.3923i | 0.426671 | + | 0.369508i | ||||
\(792\) | 5.00000i | 0.177667i | ||||||||
\(793\) | −1.73205 | − | 1.00000i | −0.0615069 | − | 0.0355110i | ||||
\(794\) | 1.00000 | + | 1.73205i | 0.0354887 | + | 0.0614682i | ||||
\(795\) | −0.133975 | − | 2.23205i | −0.00475159 | − | 0.0791627i | ||||
\(796\) | 7.00000 | − | 12.1244i | 0.248108 | − | 0.429736i | ||||
\(797\) | − | 30.0000i | − | 1.06265i | −0.847167 | − | 0.531327i | \(-0.821693\pi\) | ||
0.847167 | − | 0.531327i | \(-0.178307\pi\) | |||||||
\(798\) | −6.06218 | − | 17.5000i | −0.214599 | − | 0.619493i | ||||
\(799\) | −26.0000 | −0.919814 | ||||||||
\(800\) | 0.598076 | + | 4.96410i | 0.0211452 | + | 0.175507i | ||||
\(801\) | −5.00000 | − | 8.66025i | −0.176666 | − | 0.305995i | ||||
\(802\) | 23.3827 | − | 13.5000i | 0.825671 | − | 0.476702i | ||||
\(803\) | −17.3205 | − | 10.0000i | −0.611227 | − | 0.352892i | ||||
\(804\) | −6.00000 | −0.211604 | ||||||||
\(805\) | 10.7942 | − | 14.0885i | 0.380447 | − | 0.496553i | ||||
\(806\) | 6.00000 | 0.211341 | ||||||||
\(807\) | −12.1244 | − | 7.00000i | −0.426798 | − | 0.246412i | ||||
\(808\) | 6.92820 | − | 4.00000i | 0.243733 | − | 0.140720i | ||||
\(809\) | −4.50000 | − | 7.79423i | −0.158212 | − | 0.274030i | 0.776012 | − | 0.630718i | \(-0.217239\pi\) |
−0.934224 | + | 0.356687i | \(0.883906\pi\) | |||||||
\(810\) | 1.23205 | + | 1.86603i | 0.0432899 | + | 0.0655654i | ||||
\(811\) | 11.0000 | 0.386262 | 0.193131 | − | 0.981173i | \(-0.438136\pi\) | ||||
0.193131 | + | 0.981173i | \(0.438136\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 8.00000i | − | 0.280572i | ||||||
\(814\) | −12.5000 | + | 21.6506i | −0.438125 | + | 0.758854i | ||||
\(815\) | 26.7846 | − | 1.60770i | 0.938224 | − | 0.0563151i | ||||
\(816\) | 1.00000 | + | 1.73205i | 0.0350070 | + | 0.0606339i | ||||
\(817\) | −60.6218 | − | 35.0000i | −2.12089 | − | 1.22449i | ||||
\(818\) | 10.0000i | 0.349642i | ||||||||
\(819\) | 2.50000 | − | 0.866025i | 0.0873571 | − | 0.0302614i | ||||
\(820\) | 18.0000 | + | 9.00000i | 0.628587 | + | 0.314294i | ||||
\(821\) | −3.00000 | + | 5.19615i | −0.104701 | + | 0.181347i | −0.913616 | − | 0.406578i | \(-0.866722\pi\) |
0.808915 | + | 0.587925i | \(0.200055\pi\) | |||||||
\(822\) | 3.46410 | − | 2.00000i | 0.120824 | − | 0.0697580i | ||||
\(823\) | 6.92820 | − | 4.00000i | 0.241502 | − | 0.139431i | −0.374365 | − | 0.927281i | \(-0.622139\pi\) |
0.615867 | + | 0.787850i | \(0.288806\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −20.0000 | + | 15.0000i | −0.696311 | + | 0.522233i | ||||
\(826\) | −8.00000 | − | 6.92820i | −0.278356 | − | 0.241063i | ||||
\(827\) | − | 42.0000i | − | 1.46048i | −0.683189 | − | 0.730242i | \(-0.739408\pi\) | ||
0.683189 | − | 0.730242i | \(-0.260592\pi\) | |||||||
\(828\) | 2.59808 | + | 1.50000i | 0.0902894 | + | 0.0521286i | ||||
\(829\) | 1.00000 | + | 1.73205i | 0.0347314 | + | 0.0601566i | 0.882869 | − | 0.469620i | \(-0.155609\pi\) |
−0.848137 | + | 0.529777i | \(0.822276\pi\) | |||||||
\(830\) | −1.33975 | − | 22.3205i | −0.0465033 | − | 0.774756i | ||||
\(831\) | −1.00000 | + | 1.73205i | −0.0346896 | + | 0.0600842i | ||||
\(832\) | 1.00000i | 0.0346688i | ||||||||
\(833\) | 8.66025 | + | 11.0000i | 0.300060 | + | 0.381127i | ||||
\(834\) | −8.00000 | −0.277017 | ||||||||
\(835\) | 23.4090 | + | 35.4545i | 0.810101 | + | 1.22695i | ||||
\(836\) | 17.5000 | + | 30.3109i | 0.605250 | + | 1.04832i | ||||
\(837\) | −5.19615 | + | 3.00000i | −0.179605 | + | 0.103695i | ||||
\(838\) | −2.59808 | − | 1.50000i | −0.0897491 | − | 0.0518166i | ||||
\(839\) | −2.00000 | −0.0690477 | −0.0345238 | − | 0.999404i | \(-0.510991\pi\) | ||||
−0.0345238 | + | 0.999404i | \(0.510991\pi\) | |||||||
\(840\) | −5.46410 | + | 2.26795i | −0.188529 | + | 0.0782517i | ||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | −17.3205 | − | 10.0000i | −0.596904 | − | 0.344623i | ||||
\(843\) | 9.52628 | − | 5.50000i | 0.328102 | − | 0.189430i | ||||
\(844\) | 9.50000 | + | 16.4545i | 0.327003 | + | 0.566387i | ||||
\(845\) | −22.3923 | + | 14.7846i | −0.770319 | + | 0.508606i | ||||
\(846\) | 13.0000 | 0.446949 | ||||||||
\(847\) | −12.1244 | − | 35.0000i | −0.416598 | − | 1.20261i | ||||
\(848\) | 1.00000i | 0.0343401i | ||||||||
\(849\) | 13.0000 | − | 22.5167i | 0.446159 | − | 0.772770i | ||||
\(850\) | −3.92820 | + | 9.19615i | −0.134736 | + | 0.315425i | ||||
\(851\) | 7.50000 | + | 12.9904i | 0.257097 | + | 0.445305i | ||||
\(852\) | 1.73205 | + | 1.00000i | 0.0593391 | + | 0.0342594i | ||||
\(853\) | 49.0000i | 1.67773i | 0.544341 | + | 0.838864i | \(0.316780\pi\) | ||||
−0.544341 | + | 0.838864i | \(0.683220\pi\) | |||||||
\(854\) | −1.00000 | + | 5.19615i | −0.0342193 | + | 0.177809i | ||||
\(855\) | 14.0000 | + | 7.00000i | 0.478790 | + | 0.239395i | ||||
\(856\) | 6.00000 | − | 10.3923i | 0.205076 | − | 0.355202i | ||||
\(857\) | −48.4974 | + | 28.0000i | −1.65664 | + | 0.956462i | −0.682391 | + | 0.730987i | \(0.739060\pi\) |
−0.974249 | + | 0.225475i | \(0.927607\pi\) | |||||||
\(858\) | −4.33013 | + | 2.50000i | −0.147828 | + | 0.0853486i | ||||
\(859\) | 18.0000 | − | 31.1769i | 0.614152 | − | 1.06374i | −0.376381 | − | 0.926465i | \(-0.622831\pi\) |
0.990533 | − | 0.137277i | \(-0.0438352\pi\) | |||||||
\(860\) | −10.0000 | + | 20.0000i | −0.340997 | + | 0.681994i | ||||
\(861\) | −4.50000 | + | 23.3827i | −0.153360 | + | 0.796880i | ||||
\(862\) | − | 18.0000i | − | 0.613082i | ||||||
\(863\) | 12.9904 | + | 7.50000i | 0.442198 | + | 0.255303i | 0.704529 | − | 0.709675i | \(-0.251158\pi\) |
−0.262332 | + | 0.964978i | \(0.584491\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −15.6244 | + | 0.937822i | −0.531244 | + | 0.0318869i | ||||
\(866\) | 2.00000 | − | 3.46410i | 0.0679628 | − | 0.117715i | ||||
\(867\) | − | 13.0000i | − | 0.441503i | ||||||
\(868\) | −5.19615 | − | 15.0000i | −0.176369 | − | 0.509133i | ||||
\(869\) | −70.0000 | −2.37459 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.00000 | − | 5.19615i | −0.101651 | − | 0.176065i | ||||
\(872\) | 15.5885 | − | 9.00000i | 0.527892 | − | 0.304778i | ||||
\(873\) | 6.92820 | + | 4.00000i | 0.234484 | + | 0.135379i | ||||
\(874\) | 21.0000 | 0.710336 | ||||||||
\(875\) | −25.4641 | − | 15.0526i | −0.860844 | − | 0.508869i | ||||
\(876\) | 4.00000 | 0.135147 | ||||||||
\(877\) | 23.3827 | + | 13.5000i | 0.789577 | + | 0.455863i | 0.839814 | − | 0.542875i | \(-0.182664\pi\) |
−0.0502365 | + | 0.998737i | \(0.515998\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.500000 | + | 0.866025i | 0.0168646 | + | 0.0292103i | ||||
\(880\) | 9.33013 | − | 6.16025i | 0.314519 | − | 0.207662i | ||||
\(881\) | −3.00000 | −0.101073 | −0.0505363 | − | 0.998722i | \(-0.516093\pi\) | ||||
−0.0505363 | + | 0.998722i | \(0.516093\pi\) | |||||||
\(882\) | −4.33013 | − | 5.50000i | −0.145803 | − | 0.185195i | ||||
\(883\) | 52.0000i | 1.74994i | 0.484178 | + | 0.874970i | \(0.339119\pi\) | ||||
−0.484178 | + | 0.874970i | \(0.660881\pi\) | |||||||
\(884\) | −1.00000 | + | 1.73205i | −0.0336336 | + | 0.0582552i | ||||
\(885\) | 8.92820 | − | 0.535898i | 0.300118 | − | 0.0180140i | ||||
\(886\) | −3.00000 | − | 5.19615i | −0.100787 | − | 0.174568i | ||||
\(887\) | 10.3923 | + | 6.00000i | 0.348939 | + | 0.201460i | 0.664218 | − | 0.747539i | \(-0.268765\pi\) |
−0.315279 | + | 0.948999i | \(0.602098\pi\) | |||||||
\(888\) | − | 5.00000i | − | 0.167789i | ||||||
\(889\) | −18.0000 | − | 15.5885i | −0.603701 | − | 0.522820i | ||||
\(890\) | −10.0000 | + | 20.0000i | −0.335201 | + | 0.670402i | ||||
\(891\) | 2.50000 | − | 4.33013i | 0.0837532 | − | 0.145065i | ||||
\(892\) | 13.8564 | − | 8.00000i | 0.463947 | − | 0.267860i | ||||
\(893\) | 78.8083 | − | 45.5000i | 2.63722 | − | 1.52260i | ||||
\(894\) | 3.00000 | − | 5.19615i | 0.100335 | − | 0.173785i | ||||
\(895\) | 22.0000 | + | 11.0000i | 0.735379 | + | 0.367689i | ||||
\(896\) | 2.50000 | − | 0.866025i | 0.0835191 | − | 0.0289319i | ||||
\(897\) | 3.00000i | 0.100167i | ||||||||
\(898\) | −7.79423 | − | 4.50000i | −0.260097 | − | 0.150167i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.96410 | − | 4.59808i | 0.0654701 | − | 0.153269i | ||||
\(901\) | −1.00000 | + | 1.73205i | −0.0333148 | + | 0.0577030i | ||||
\(902\) | − | 45.0000i | − | 1.49834i | ||||||
\(903\) | −25.9808 | − | 5.00000i | −0.864586 | − | 0.166390i | ||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | 3.73205 | − | 2.46410i | 0.124058 | − | 0.0819095i | ||||
\(906\) | −11.0000 | − | 19.0526i | −0.365451 | − | 0.632979i | ||||
\(907\) | −13.8564 | + | 8.00000i | −0.460094 | + | 0.265636i | −0.712084 | − | 0.702094i | \(-0.752248\pi\) |
0.251990 | + | 0.967730i | \(0.418915\pi\) | |||||||
\(908\) | 12.1244 | + | 7.00000i | 0.402361 | + | 0.232303i | ||||
\(909\) | −8.00000 | −0.265343 | ||||||||
\(910\) | −4.69615 | − | 3.59808i | −0.155676 | − | 0.119275i | ||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | −6.06218 | − | 3.50000i | −0.200739 | − | 0.115897i | ||||
\(913\) | −43.3013 | + | 25.0000i | −1.43306 | + | 0.827379i | ||||
\(914\) | 19.0000 | + | 32.9090i | 0.628464 | + | 1.08853i | ||||
\(915\) | −2.46410 | − | 3.73205i | −0.0814607 | − | 0.123378i | ||||
\(916\) | −4.00000 | −0.132164 | ||||||||
\(917\) | 14.7224 | + | 42.5000i | 0.486178 | + | 1.40347i | ||||
\(918\) | − | 2.00000i | − | 0.0660098i | ||||||
\(919\) | 28.0000 | − | 48.4974i | 0.923635 | − | 1.59978i | 0.129893 | − | 0.991528i | \(-0.458537\pi\) |
0.793742 | − | 0.608254i | \(-0.208130\pi\) | |||||||
\(920\) | −0.401924 | − | 6.69615i | −0.0132510 | − | 0.220766i | ||||
\(921\) | −1.00000 | − | 1.73205i | −0.0329511 | − | 0.0570730i | ||||
\(922\) | −10.3923 | − | 6.00000i | −0.342252 | − | 0.197599i | ||||
\(923\) | 2.00000i | 0.0658308i | ||||||||
\(924\) | 10.0000 | + | 8.66025i | 0.328976 | + | 0.284901i | ||||
\(925\) | 20.0000 | − | 15.0000i | 0.657596 | − | 0.493197i | ||||
\(926\) | −7.50000 | + | 12.9904i | −0.246465 | + | 0.426890i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.5000 | − | 28.5788i | 0.541347 | − | 0.937641i | −0.457480 | − | 0.889220i | \(-0.651248\pi\) |
0.998827 | − | 0.0484211i | \(-0.0154190\pi\) | |||||||
\(930\) | 12.0000 | + | 6.00000i | 0.393496 | + | 0.196748i | ||||
\(931\) | −45.5000 | − | 18.1865i | −1.49120 | − | 0.596040i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.5167 | − | 13.0000i | −0.737162 | − | 0.425601i | ||||
\(934\) | −1.00000 | − | 1.73205i | −0.0327210 | − | 0.0566744i | ||||
\(935\) | 22.3205 | − | 1.33975i | 0.729959 | − | 0.0438144i | ||||
\(936\) | 0.500000 | − | 0.866025i | 0.0163430 | − | 0.0283069i | ||||
\(937\) | − | 34.0000i | − | 1.11073i | −0.831606 | − | 0.555366i | \(-0.812578\pi\) | ||
0.831606 | − | 0.555366i | \(-0.187422\pi\) | |||||||
\(938\) | −10.3923 | + | 12.0000i | −0.339321 | + | 0.391814i | ||||
\(939\) | 10.0000 | 0.326338 | ||||||||
\(940\) | −16.0167 | − | 24.2583i | −0.522406 | − | 0.791219i | ||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | −11.2583 | + | 6.50000i | −0.366816 | + | 0.211781i | ||||
\(943\) | −23.3827 | − | 13.5000i | −0.761445 | − | 0.439620i | ||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | 5.86603 | + | 0.767949i | 0.190822 | + | 0.0249814i | ||||
\(946\) | 50.0000 | 1.62564 | ||||||||
\(947\) | −10.3923 | − | 6.00000i | −0.337705 | − | 0.194974i | 0.321552 | − | 0.946892i | \(-0.395796\pi\) |
−0.659256 | + | 0.751918i | \(0.729129\pi\) | |||||||
\(948\) | 12.1244 | − | 7.00000i | 0.393781 | − | 0.227349i | ||||
\(949\) | 2.00000 | + | 3.46410i | 0.0649227 | + | 0.112449i | ||||
\(950\) | −4.18653 | − | 34.7487i | −0.135829 | − | 1.12740i | ||||
\(951\) | 2.00000 | 0.0648544 | ||||||||
\(952\) | 5.19615 | + | 1.00000i | 0.168408 | + | 0.0324102i | ||||
\(953\) | 24.0000i | 0.777436i | 0.921357 | + | 0.388718i | \(0.127082\pi\) | ||||
−0.921357 | + | 0.388718i | \(0.872918\pi\) | |||||||
\(954\) | 0.500000 | − | 0.866025i | 0.0161881 | − | 0.0280386i | ||||
\(955\) | 2.14359 | + | 35.7128i | 0.0693651 | + | 1.15564i | ||||
\(956\) | −10.0000 | − | 17.3205i | −0.323423 | − | 0.560185i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.00000i | 0.258468i | ||||||||
\(959\) | 2.00000 | − | 10.3923i | 0.0645834 | − | 0.335585i | ||||
\(960\) | −1.00000 | + | 2.00000i | −0.0322749 | + | 0.0645497i | ||||
\(961\) | −2.50000 | + | 4.33013i | −0.0806452 | + | 0.139682i | ||||
\(962\) | 4.33013 | − | 2.50000i | 0.139609 | − | 0.0806032i | ||||
\(963\) | −10.3923 | + | 6.00000i | −0.334887 | + | 0.193347i | ||||
\(964\) | −0.500000 | + | 0.866025i | −0.0161039 | + | 0.0278928i | ||||
\(965\) | −18.0000 | + | 36.0000i | −0.579441 | + | 1.15888i | ||||
\(966\) | 7.50000 | − | 2.59808i | 0.241309 | − | 0.0835917i | ||||
\(967\) | − | 24.0000i | − | 0.771788i | −0.922543 | − | 0.385894i | \(-0.873893\pi\) | ||
0.922543 | − | 0.385894i | \(-0.126107\pi\) | |||||||
\(968\) | −12.1244 | − | 7.00000i | −0.389692 | − | 0.224989i | ||||
\(969\) | −7.00000 | − | 12.1244i | −0.224872 | − | 0.389490i | ||||
\(970\) | −1.07180 | − | 17.8564i | −0.0344133 | − | 0.573335i | ||||
\(971\) | −19.5000 | + | 33.7750i | −0.625785 | + | 1.08389i | 0.362604 | + | 0.931943i | \(0.381888\pi\) |
−0.988389 | + | 0.151948i | \(0.951445\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | −13.8564 | + | 16.0000i | −0.444216 | + | 0.512936i | ||||
\(974\) | 24.0000 | 0.769010 | ||||||||
\(975\) | 4.96410 | − | 0.598076i | 0.158978 | − | 0.0191538i | ||||
\(976\) | 1.00000 | + | 1.73205i | 0.0320092 | + | 0.0554416i | ||||
\(977\) | 36.3731 | − | 21.0000i | 1.16368 | − | 0.671850i | 0.211495 | − | 0.977379i | \(-0.432167\pi\) |
0.952183 | + | 0.305530i | \(0.0988335\pi\) | |||||||
\(978\) | 10.3923 | + | 6.00000i | 0.332309 | + | 0.191859i | ||||
\(979\) | 50.0000 | 1.59801 | ||||||||
\(980\) | −4.92820 | + | 14.8564i | −0.157426 | + | 0.474570i | ||||
\(981\) | −18.0000 | −0.574696 | ||||||||
\(982\) | 20.7846 | + | 12.0000i | 0.663264 | + | 0.382935i | ||||
\(983\) | −28.5788 | + | 16.5000i | −0.911523 | + | 0.526268i | −0.880921 | − | 0.473263i | \(-0.843076\pi\) |
−0.0306024 | + | 0.999532i | \(0.509743\pi\) | |||||||
\(984\) | 4.50000 | + | 7.79423i | 0.143455 | + | 0.248471i | ||||
\(985\) | 33.2654 | + | 50.3827i | 1.05992 | + | 1.60533i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.5167 | − | 26.0000i | 0.716713 | − | 0.827589i | ||||
\(988\) | − | 7.00000i | − | 0.222700i | ||||||
\(989\) | 15.0000 | − | 25.9808i | 0.476972 | − | 0.826140i | ||||
\(990\) | −11.1603 | + | 0.669873i | −0.354696 | + | 0.0212900i | ||||
\(991\) | 18.0000 | + | 31.1769i | 0.571789 | + | 0.990367i | 0.996382 | + | 0.0849833i | \(0.0270837\pi\) |
−0.424594 | + | 0.905384i | \(0.639583\pi\) | |||||||
\(992\) | −5.19615 | − | 3.00000i | −0.164978 | − | 0.0952501i | ||||
\(993\) | 15.0000i | 0.476011i | ||||||||
\(994\) | 5.00000 | − | 1.73205i | 0.158590 | − | 0.0549373i | ||||
\(995\) | 28.0000 | + | 14.0000i | 0.887660 | + | 0.443830i | ||||
\(996\) | 5.00000 | − | 8.66025i | 0.158431 | − | 0.274411i | ||||
\(997\) | −8.66025 | + | 5.00000i | −0.274273 | + | 0.158352i | −0.630828 | − | 0.775923i | \(-0.717285\pi\) |
0.356555 | + | 0.934274i | \(0.383951\pi\) | |||||||
\(998\) | −24.2487 | + | 14.0000i | −0.767580 | + | 0.443162i | ||||
\(999\) | −2.50000 | + | 4.33013i | −0.0790965 | + | 0.136999i |
(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 | 210.2.n.a.79.2 | yes | 4 | |
3.2 | odd | 2 | 630.2.u.c.289.1 | 4 | |||
4.3 | odd | 2 | 1680.2.di.a.289.2 | 4 | |||
5.2 | odd | 4 | 1050.2.i.f.751.1 | 2 | |||
5.3 | odd | 4 | 1050.2.i.o.751.1 | 2 | |||
5.4 | even | 2 | inner | 210.2.n.a.79.1 | ✓ | 4 | |
7.2 | even | 3 | 1470.2.g.f.589.1 | 2 | |||
7.3 | odd | 6 | 1470.2.n.i.949.1 | 4 | |||
7.4 | even | 3 | inner | 210.2.n.a.109.1 | yes | 4 | |
7.5 | odd | 6 | 1470.2.g.a.589.1 | 2 | |||
7.6 | odd | 2 | 1470.2.n.i.79.2 | 4 | |||
15.14 | odd | 2 | 630.2.u.c.289.2 | 4 | |||
20.19 | odd | 2 | 1680.2.di.a.289.1 | 4 | |||
21.11 | odd | 6 | 630.2.u.c.109.2 | 4 | |||
28.11 | odd | 6 | 1680.2.di.a.529.1 | 4 | |||
35.2 | odd | 12 | 7350.2.a.bn.1.1 | 1 | |||
35.4 | even | 6 | inner | 210.2.n.a.109.2 | yes | 4 | |
35.9 | even | 6 | 1470.2.g.f.589.2 | 2 | |||
35.12 | even | 12 | 7350.2.a.ch.1.1 | 1 | |||
35.18 | odd | 12 | 1050.2.i.o.151.1 | 2 | |||
35.19 | odd | 6 | 1470.2.g.a.589.2 | 2 | |||
35.23 | odd | 12 | 7350.2.a.t.1.1 | 1 | |||
35.24 | odd | 6 | 1470.2.n.i.949.2 | 4 | |||
35.32 | odd | 12 | 1050.2.i.f.151.1 | 2 | |||
35.33 | even | 12 | 7350.2.a.b.1.1 | 1 | |||
35.34 | odd | 2 | 1470.2.n.i.79.1 | 4 | |||
105.74 | odd | 6 | 630.2.u.c.109.1 | 4 | |||
140.39 | odd | 6 | 1680.2.di.a.529.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.n.a.79.1 | ✓ | 4 | 5.4 | even | 2 | inner | |
210.2.n.a.79.2 | yes | 4 | 1.1 | even | 1 | trivial | |
210.2.n.a.109.1 | yes | 4 | 7.4 | even | 3 | inner | |
210.2.n.a.109.2 | yes | 4 | 35.4 | even | 6 | inner | |
630.2.u.c.109.1 | 4 | 105.74 | odd | 6 | |||
630.2.u.c.109.2 | 4 | 21.11 | odd | 6 | |||
630.2.u.c.289.1 | 4 | 3.2 | odd | 2 | |||
630.2.u.c.289.2 | 4 | 15.14 | odd | 2 | |||
1050.2.i.f.151.1 | 2 | 35.32 | odd | 12 | |||
1050.2.i.f.751.1 | 2 | 5.2 | odd | 4 | |||
1050.2.i.o.151.1 | 2 | 35.18 | odd | 12 | |||
1050.2.i.o.751.1 | 2 | 5.3 | odd | 4 | |||
1470.2.g.a.589.1 | 2 | 7.5 | odd | 6 | |||
1470.2.g.a.589.2 | 2 | 35.19 | odd | 6 | |||
1470.2.g.f.589.1 | 2 | 7.2 | even | 3 | |||
1470.2.g.f.589.2 | 2 | 35.9 | even | 6 | |||
1470.2.n.i.79.1 | 4 | 35.34 | odd | 2 | |||
1470.2.n.i.79.2 | 4 | 7.6 | odd | 2 | |||
1470.2.n.i.949.1 | 4 | 7.3 | odd | 6 | |||
1470.2.n.i.949.2 | 4 | 35.24 | odd | 6 | |||
1680.2.di.a.289.1 | 4 | 20.19 | odd | 2 | |||
1680.2.di.a.289.2 | 4 | 4.3 | odd | 2 | |||
1680.2.di.a.529.1 | 4 | 28.11 | odd | 6 | |||
1680.2.di.a.529.2 | 4 | 140.39 | odd | 6 | |||
7350.2.a.b.1.1 | 1 | 35.33 | even | 12 | |||
7350.2.a.t.1.1 | 1 | 35.23 | odd | 12 | |||
7350.2.a.bn.1.1 | 1 | 35.2 | odd | 12 | |||
7350.2.a.ch.1.1 | 1 | 35.12 | even | 12 |