Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(79,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.n (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 949.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.949 |
Dual form | 1470.2.n.i.79.2 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 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 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 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 | −0.192201 | − | 0.981356i | \(-0.561563\pi\) |
0.945979 | − | 0.324227i | \(-0.105104\pi\) | |||||||
\(12\) | 0.866025 | − | 0.500000i | 0.250000 | − | 0.144338i | ||||
\(13\) | − | 1.00000i | − | 0.277350i | −0.990338 | − | 0.138675i | \(-0.955716\pi\) | ||
0.990338 | − | 0.138675i | \(-0.0442844\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 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 | \(-0.255354\pi\) |
−0.275029 | + | 0.961436i | \(0.588688\pi\) | |||||||
\(18\) | 0.866025 | + | 0.500000i | 0.204124 | + | 0.117851i | ||||
\(19\) | −3.50000 | − | 6.06218i | −0.802955 | − | 1.39076i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.114708 | − | 0.993399i | \(-0.463407\pi\) | |||||||
\(20\) | 2.00000 | − | 1.00000i | 0.447214 | − | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 5.00000i | − | 1.06600i | ||||||
\(23\) | 2.59808 | − | 1.50000i | 0.541736 | − | 0.312772i | −0.204046 | − | 0.978961i | \(-0.565409\pi\) |
0.745782 | + | 0.666190i | \(0.232076\pi\) | |||||||
\(24\) | 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 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 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 | 0.460152 | + | 0.887840i | \(0.347795\pi\) |
−0.998968 | + | 0.0454165i | \(0.985539\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 4.33013 | − | 2.50000i | 0.753778 | − | 0.435194i | ||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.33013 | − | 2.50000i | 0.711868 | − | 0.410997i | −0.0998840 | − | 0.994999i | \(-0.531847\pi\) |
0.811752 | + | 0.584002i | \(0.198514\pi\) | |||||||
\(38\) | −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 | \(-0.251941\pi\) | ||||
0.702782 | + | 0.711405i | \(0.251941\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0000i | 1.52499i | 0.646997 | + | 0.762493i | \(0.276025\pi\) | ||||
−0.646997 | + | 0.762493i | \(0.723975\pi\) | |||||||
\(44\) | −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 | −0.662145 | + | 0.749375i | \(0.730354\pi\) |
−0.980051 | + | 0.198747i | \(0.936313\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 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 | 0.558298 | − | 0.829640i | \(-0.311454\pi\) |
−0.439340 | + | 0.898321i | \(0.644788\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 10.0000 | − | 5.00000i | 1.34840 | − | 0.674200i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.00000i | − | 0.927173i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | 2.23205 | + | 0.133975i | 0.288157 | + | 0.0172960i | ||||
\(61\) | −1.00000 | − | 1.73205i | −0.128037 | − | 0.221766i | 0.794879 | − | 0.606768i | \(-0.207534\pi\) |
−0.922916 | + | 0.385002i | \(0.874201\pi\) | |||||||
\(62\) | 6.00000i | 0.762001i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −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 | 0.782613 | − | 0.622509i | \(-0.213886\pi\) |
−0.147802 | + | 0.989017i | \(0.547220\pi\) | |||||||
\(68\) | 1.73205 | − | 1.00000i | 0.210042 | − | 0.121268i | ||||
\(69\) | 3.00000 | 0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −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 | \(-0.258125\pi\) |
−0.283387 | + | 0.959006i | \(0.591458\pi\) | |||||||
\(74\) | 2.50000 | − | 4.33013i | 0.290619 | − | 0.503367i | ||||
\(75\) | −0.598076 | + | 4.96410i | −0.0690599 | + | 0.573205i | ||||
\(76\) | −7.00000 | −0.802955 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 1.00000i | − | 0.113228i | ||||||
\(79\) | −7.00000 | − | 12.1244i | −0.787562 | − | 1.36410i | −0.927457 | − | 0.373930i | \(-0.878010\pi\) |
0.139895 | − | 0.990166i | \(-0.455323\pi\) | |||||||
\(80\) | 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 | \(0.815077\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 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 | −0.999388 | − | 0.0349934i | \(-0.988859\pi\) |
0.469389 | − | 0.882992i | \(-0.344474\pi\) | |||||||
\(90\) | 1.00000 | + | 2.00000i | 0.105409 | + | 0.210819i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 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 | \(0.866875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 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 | \(-0.703033\pi\) |
0.993481 | + | 0.113998i | \(0.0363659\pi\) | |||||||
\(102\) | 1.73205 | + | 1.00000i | 0.171499 | + | 0.0990148i | ||||
\(103\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | −10.3923 | + | 6.00000i | −1.00466 | + | 0.580042i | −0.909624 | − | 0.415432i | \(-0.863630\pi\) |
−0.0950377 | + | 0.995474i | \(0.530297\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | −9.00000 | + | 15.5885i | −0.862044 | + | 1.49310i | 0.00790932 | + | 0.999969i | \(0.497482\pi\) |
−0.869953 | + | 0.493135i | \(0.835851\pi\) | |||||||
\(110\) | 6.16025 | − | 9.33013i | 0.587357 | − | 0.889593i | ||||
\(111\) | 5.00000 | 0.474579 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | −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 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 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 | 0 | ||||||||
\(127\) | − | 9.00000i | − | 0.798621i | −0.916816 | − | 0.399310i | \(-0.869250\pi\) | ||
0.916816 | − | 0.399310i | \(-0.130750\pi\) | |||||||
\(128\) | −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 | −0.951285 | − | 0.308312i | \(-0.900236\pi\) |
0.208637 | − | 0.977993i | \(-0.433097\pi\) | |||||||
\(132\) | − | 5.00000i | − | 0.435194i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 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 | 0.344668 | − | 0.938725i | \(-0.387992\pi\) |
−0.640626 | + | 0.767853i | \(0.721325\pi\) | |||||||
\(138\) | 2.59808 | − | 1.50000i | 0.221163 | − | 0.127688i | ||||
\(139\) | −8.00000 | −0.678551 | −0.339276 | − | 0.940687i | \(-0.610182\pi\) | ||||
−0.339276 | + | 0.940687i | \(0.610182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −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 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 5.00000i | − | 0.410997i | ||||||
\(149\) | −3.00000 | − | 5.19615i | −0.245770 | − | 0.425685i | 0.716578 | − | 0.697507i | \(-0.245707\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | 1.96410 | + | 4.59808i | 0.160368 | + | 0.375431i | ||||
\(151\) | 11.0000 | − | 19.0526i | 0.895167 | − | 1.55048i | 0.0615699 | − | 0.998103i | \(-0.480389\pi\) |
0.833597 | − | 0.552372i | \(-0.186277\pi\) | |||||||
\(152\) | −6.06218 | + | 3.50000i | −0.491708 | + | 0.283887i | ||||
\(153\) | 2.00000i | 0.161690i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −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 | \(-0.506938\pi\) |
−0.876717 | + | 0.481006i | \(0.840272\pi\) | |||||||
\(158\) | −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 | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | −10.3923 | + | 6.00000i | −0.813988 | + | 0.469956i | −0.848339 | − | 0.529454i | \(-0.822397\pi\) |
0.0343508 | + | 0.999410i | \(0.489064\pi\) | |||||||
\(164\) | 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 | \(-0.262880\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 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 | \(-0.752402\pi\) |
0.251523 | + | 0.967851i | \(0.419068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −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 | −0.995009 | − | 0.0997838i | \(-0.968185\pi\) |
0.583920 | + | 0.811811i | \(0.301518\pi\) | |||||||
\(180\) | 1.86603 | + | 1.23205i | 0.139085 | + | 0.0918316i | ||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 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 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.00000 | − | 14.0000i | −0.507833 | − | 1.01567i | ||||
\(191\) | 8.00000 | + | 13.8564i | 0.578860 | + | 1.00261i | 0.995610 | + | 0.0935936i | \(0.0298354\pi\) |
−0.416751 | + | 0.909021i | \(0.636831\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | 15.5885 | + | 9.00000i | 1.12208 | + | 0.647834i | 0.941932 | − | 0.335805i | \(-0.109008\pi\) |
0.180150 | + | 0.983639i | \(0.442342\pi\) | |||||||
\(194\) | 4.00000 | + | 6.92820i | 0.287183 | + | 0.497416i | ||||
\(195\) | 2.00000 | − | 1.00000i | 0.143223 | − | 0.0716115i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 27.0000i | 1.92367i | 0.273629 | + | 0.961835i | \(0.411776\pi\) | ||||
−0.273629 | + | 0.961835i | \(0.588224\pi\) | |||||||
\(198\) | 4.33013 | − | 2.50000i | 0.307729 | − | 0.177667i | ||||
\(199\) | 7.00000 | − | 12.1244i | 0.496217 | − | 0.859473i | −0.503774 | − | 0.863836i | \(-0.668055\pi\) |
0.999990 | + | 0.00436292i | \(0.00138876\pi\) | |||||||
\(200\) | 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 | 0 | ||||||||
\(211\) | 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 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 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 | 0 | ||||||||
\(225\) | −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 | \(-0.487137\pi\) |
−0.845120 | + | 0.534577i | \(0.820471\pi\) | |||||||
\(228\) | −6.06218 | − | 3.50000i | −0.401478 | − | 0.231793i | ||||
\(229\) | 2.00000 | + | 3.46410i | 0.132164 | + | 0.228914i | 0.924510 | − | 0.381157i | \(-0.124474\pi\) |
−0.792347 | + | 0.610071i | \(0.791141\pi\) | |||||||
\(230\) | 6.00000 | − | 3.00000i | 0.395628 | − | 0.197814i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(234\) | 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 | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −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 | \(-0.843587\pi\) |
0.849472 | + | 0.527633i | \(0.176921\pi\) | |||||||
\(242\) | −12.1244 | − | 7.00000i | −0.779383 | − | 0.449977i | ||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 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 | \(-0.469817\pi\) | ||||
0.0946792 | + | 0.995508i | \(0.469817\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 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 | \(-0.767629\pi\) |
0.204953 | + | 0.978772i | \(0.434296\pi\) | |||||||
\(258\) | 10.0000i | 0.622573i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −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 | −0.304487 | − | 0.952517i | \(-0.598485\pi\) |
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(264\) | −2.50000 | − | 4.33013i | −0.153864 | − | 0.266501i | ||||
\(265\) | 1.00000 | + | 2.00000i | 0.0614295 | + | 0.122859i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 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 | \(-0.973692\pi\) |
0.569789 | + | 0.821791i | \(0.307025\pi\) | |||||||
\(270\) | −0.133975 | + | 2.23205i | −0.00815343 | + | 0.135838i | ||||
\(271\) | 4.00000 | + | 6.92820i | 0.242983 | + | 0.420858i | 0.961563 | − | 0.274586i | \(-0.0885408\pi\) |
−0.718580 | + | 0.695444i | \(0.755208\pi\) | |||||||
\(272\) | − | 2.00000i | − | 0.121268i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −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 | 0.551131 | − | 0.834419i | \(-0.314196\pi\) |
−0.447062 | + | 0.894503i | \(0.647530\pi\) | |||||||
\(278\) | −6.92820 | + | 4.00000i | −0.415526 | + | 0.239904i | ||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −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 | \(-0.0522041\pi\) |
0.351895 | + | 0.936039i | \(0.385537\pi\) | |||||||
\(284\) | −1.00000 | + | 1.73205i | −0.0593391 | + | 0.102778i | ||||
\(285\) | 8.62436 | − | 13.0622i | 0.510863 | − | 0.773737i | ||||
\(286\) | −5.00000 | −0.295656 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 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 | \(-0.00929925\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −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 | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 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 | \(0.981823\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.39230 | + | 11.1962i | −0.419855 | + | 0.635899i | ||||
\(311\) | −13.0000 | + | 22.5167i | −0.737162 | + | 1.27680i | 0.216606 | + | 0.976259i | \(0.430501\pi\) |
−0.953768 | + | 0.300544i | \(0.902832\pi\) | |||||||
\(312\) | −0.866025 | − | 0.500000i | −0.0490290 | − | 0.0283069i | ||||
\(313\) | 8.66025 | − | 5.00000i | 0.489506 | − | 0.282617i | −0.234863 | − | 0.972028i | \(-0.575464\pi\) |
0.724370 | + | 0.689412i | \(0.242131\pi\) | |||||||
\(314\) | −13.0000 | −0.733632 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.0000 | −0.787562 | ||||||||
\(317\) | −1.73205 | + | 1.00000i | −0.0972817 | + | 0.0561656i | −0.547852 | − | 0.836576i | \(-0.684554\pi\) |
0.450570 | + | 0.892741i | \(0.351221\pi\) | |||||||
\(318\) | 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 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 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 | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 10.0000 | − | 5.00000i | 0.550482 | − | 0.275241i | ||||
\(331\) | 7.50000 | + | 12.9904i | 0.412237 | + | 0.714016i | 0.995134 | − | 0.0985303i | \(-0.0314141\pi\) |
−0.582897 | + | 0.812546i | \(0.698081\pi\) | |||||||
\(332\) | 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 | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000i | 0.762629i | 0.924445 | + | 0.381314i | \(0.124528\pi\) | ||||
−0.924445 | + | 0.381314i | \(0.875472\pi\) | |||||||
\(338\) | 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 | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 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 | 0.0796169 | − | 0.996826i | \(-0.474630\pi\) |
−0.823468 | + | 0.567363i | \(0.807964\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.0000 | −1.28469 | −0.642345 | − | 0.766415i | \(-0.722038\pi\) | ||||
−0.642345 | + | 0.766415i | \(0.722038\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −4.33013 | + | 2.50000i | −0.230797 | + | 0.133250i | ||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | −2.00000 | + | 3.46410i | −0.106299 | + | 0.184115i | ||||
\(355\) | −3.73205 | − | 2.46410i | −0.198077 | − | 0.130781i | ||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.0000i | 0.581368i | ||||||||
\(359\) | −14.0000 | − | 24.2487i | −0.738892 | − | 1.27980i | −0.952995 | − | 0.302987i | \(-0.902016\pi\) |
0.214103 | − | 0.976811i | \(-0.431317\pi\) | |||||||
\(360\) | 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 | 0 | ||||||||
\(365\) | 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 | 0.966159 | + | 0.257948i | \(0.0830464\pi\) |
0.706469 | + | 0.707744i | \(0.250287\pi\) | |||||||
\(368\) | −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 | 0 | ||||||||
\(372\) | 6.00000i | 0.311086i | ||||||||
\(373\) | 5.19615 | − | 3.00000i | 0.269047 | − | 0.155334i | −0.359408 | − | 0.933181i | \(-0.617021\pi\) |
0.628454 | + | 0.777847i | \(0.283688\pi\) | |||||||
\(374\) | 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 | 0 | ||||||||
\(379\) | 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 | \(-0.592814\pi\) |
0.685736 | + | 0.727851i | \(0.259481\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 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 | −0.779895 | − | 0.625910i | \(-0.784728\pi\) |
0.932002 | + | 0.362454i | \(0.118061\pi\) | |||||||
\(390\) | 1.23205 | − | 1.86603i | 0.0623873 | − | 0.0944899i | ||||
\(391\) | 6.00000 | 0.303433 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 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 | \(-0.682649\pi\) |
0.455905 | + | 0.890028i | \(0.349316\pi\) | |||||||
\(398\) | − | 14.0000i | − | 0.701757i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | − | 4.00000i | 0.150000 | − | 0.200000i | ||||
\(401\) | 13.5000 | + | 23.3827i | 0.674158 | + | 1.16768i | 0.976714 | + | 0.214544i | \(0.0688266\pi\) |
−0.302556 | + | 0.953131i | \(0.597840\pi\) | |||||||
\(402\) | 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 | \(-0.912855\pi\) |
0.715523 | + | 0.698589i | \(0.246188\pi\) | |||||||
\(410\) | 20.0885 | + | 1.20577i | 0.992098 | + | 0.0595488i | ||||
\(411\) | −2.00000 | − | 3.46410i | −0.0986527 | − | 0.170872i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 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 | \(-0.476653\pi\) | ||||
0.0732798 | + | 0.997311i | \(0.476653\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −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 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 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 | −0.997173 | − | 0.0751385i | \(-0.976060\pi\) |
0.563658 | + | 0.826008i | \(0.309393\pi\) | |||||||
\(432\) | 0.866025 | − | 0.500000i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | − | 4.00000i | − | 0.192228i | −0.995370 | − | 0.0961139i | \(-0.969359\pi\) | ||
0.995370 | − | 0.0961139i | \(-0.0306413\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | −5.00000 | − | 10.0000i | −0.238366 | − | 0.476731i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 2.00000i | − | 0.0951303i | ||||||
\(443\) | −5.19615 | + | 3.00000i | −0.246877 | + | 0.142534i | −0.618333 | − | 0.785916i | \(-0.712192\pi\) |
0.371457 | + | 0.928450i | \(0.378858\pi\) | |||||||
\(444\) | 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 | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −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 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.00000 | −0.327805 | ||||||||
\(457\) | 32.9090 | − | 19.0000i | 1.53942 | − | 0.888783i | 0.540544 | − | 0.841316i | \(-0.318219\pi\) |
0.998873 | − | 0.0474665i | \(-0.0151147\pi\) | |||||||
\(458\) | 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 | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15.0000i | − | 0.697109i | −0.937288 | − | 0.348555i | \(-0.886673\pi\) | ||
0.937288 | − | 0.348555i | \(-0.113327\pi\) | |||||||
\(464\) | 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 | \(-0.651932\pi\) |
0.539539 | + | 0.841960i | \(0.318598\pi\) | |||||||
\(468\) | − | 1.00000i | − | 0.0462250i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −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 | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 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 | \(-0.891838\pi\) |
0.760056 | + | 0.649857i | \(0.225171\pi\) | |||||||
\(480\) | 0.133975 | − | 2.23205i | 0.00611508 | − | 0.101879i | ||||
\(481\) | −2.50000 | − | 4.33013i | −0.113990 | − | 0.197437i | ||||
\(482\) | 1.00000i | 0.0455488i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −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 | 0.890537 | − | 0.454911i | \(-0.150329\pi\) |
0.0513038 | + | 0.998683i | \(0.483662\pi\) | |||||||
\(488\) | −1.73205 | + | 1.00000i | −0.0784063 | + | 0.0452679i | ||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 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 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 10.0000i | 0.448111i | ||||||||
\(499\) | −14.0000 | − | 24.2487i | −0.626726 | − | 1.08552i | −0.988204 | − | 0.153141i | \(-0.951061\pi\) |
0.361478 | − | 0.932381i | \(-0.382272\pi\) | |||||||
\(500\) | 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 | \(-0.179709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 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 | \(-0.267086\pi\) |
−0.978421 | + | 0.206623i | \(0.933753\pi\) | |||||||
\(510\) | 2.00000 | + | 4.00000i | 0.0885615 | + | 0.177123i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 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 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −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 | \(-0.939904\pi\) |
0.653650 | + | 0.756797i | \(0.273237\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.3923 | + | 6.00000i | −0.454424 | + | 0.262362i | −0.709697 | − | 0.704507i | \(-0.751168\pi\) |
0.255273 | + | 0.966869i | \(0.417835\pi\) | |||||||
\(524\) | −17.0000 | −0.742648 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −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 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 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 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000 | + | 2.00000i | 0.0430331 | + | 0.0860663i | ||||
\(541\) | −2.00000 | − | 3.46410i | −0.0859867 | − | 0.148933i | 0.819825 | − | 0.572615i | \(-0.194071\pi\) |
−0.905811 | + | 0.423681i | \(0.860738\pi\) | |||||||
\(542\) | 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 | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0000i | 0.598597i | 0.954160 | + | 0.299298i | \(0.0967526\pi\) | ||||
−0.954160 | + | 0.299298i | \(0.903247\pi\) | |||||||
\(548\) | −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 | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 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 | −0.433888 | − | 0.900967i | \(-0.642859\pi\) |
−0.997204 | + | 0.0747252i | \(0.976192\pi\) | |||||||
\(558\) | −5.19615 | + | 3.00000i | −0.219971 | + | 0.127000i | ||||
\(559\) | 10.0000 | 0.422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 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 | \(-0.115496\pi\) |
0.160066 | + | 0.987106i | \(0.448829\pi\) | |||||||
\(564\) | −6.50000 | + | 11.2583i | −0.273699 | + | 0.474061i | ||||
\(565\) | −7.39230 | + | 11.1962i | −0.310997 | + | 0.471026i | ||||
\(566\) | 26.0000 | 1.09286 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.00000i | 0.0839181i | ||||||||
\(569\) | −1.50000 | − | 2.59808i | −0.0628833 | − | 0.108917i | 0.832870 | − | 0.553469i | \(-0.186696\pi\) |
−0.895753 | + | 0.444552i | \(0.853363\pi\) | |||||||
\(570\) | 0.937822 | − | 15.6244i | 0.0392810 | − | 0.654432i | ||||
\(571\) | 4.00000 | − | 6.92820i | 0.167395 | − | 0.289936i | −0.770108 | − | 0.637913i | \(-0.779798\pi\) |
0.937503 | + | 0.347977i | \(0.113131\pi\) | |||||||
\(572\) | −4.33013 | + | 2.50000i | −0.181052 | + | 0.104530i | ||||
\(573\) | 16.0000i | 0.668410i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 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 | \(-0.499841\pi\) |
−0.865775 | + | 0.500433i | \(0.833174\pi\) | |||||||
\(578\) | −11.2583 | − | 6.50000i | −0.468285 | − | 0.270364i | ||||
\(579\) | 9.00000 | + | 15.5885i | 0.374027 | + | 0.647834i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 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 | \(0.986858\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 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 | \(-0.420693\pi\) |
0.962575 | + | 0.271016i | \(0.0873596\pi\) | |||||||
\(594\) | 5.00000 | 0.205152 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −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 | 0.424333 | + | 0.905506i | \(0.360508\pi\) |
−0.996358 | + | 0.0852695i | \(0.972825\pi\) | |||||||
\(600\) | 4.96410 | + | 0.598076i | 0.202659 | + | 0.0244164i | ||||
\(601\) | 30.0000 | 1.22373 | 0.611863 | − | 0.790964i | \(-0.290420\pi\) | ||||
0.611863 | + | 0.790964i | \(0.290420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 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 | \(-0.581682\pi\) |
0.710766 | + | 0.703429i | \(0.248349\pi\) | |||||||
\(608\) | 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 | 0.129433 | − | 0.991588i | \(-0.458684\pi\) |
−0.794024 | + | 0.607887i | \(0.792017\pi\) | |||||||
\(614\) | 1.00000 | + | 1.73205i | 0.0403567 | + | 0.0698999i | ||||
\(615\) | 9.00000 | + | 18.0000i | 0.362915 | + | 0.725830i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 30.0000i | − | 1.20775i | −0.797077 | − | 0.603877i | \(-0.793622\pi\) | ||
0.797077 | − | 0.603877i | \(-0.206378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.50000 | + | 12.9904i | −0.301450 | + | 0.522127i | −0.976465 | − | 0.215677i | \(-0.930804\pi\) |
0.675014 | + | 0.737805i | \(0.264137\pi\) | |||||||
\(620\) | −0.803848 | + | 13.3923i | −0.0322833 | + | 0.537848i | ||||
\(621\) | 1.50000 | + | 2.59808i | 0.0601929 | + | 0.104257i | ||||
\(622\) | 26.0000i | 1.04251i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −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 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 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 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 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 | −0.330997 | − | 0.943632i | \(-0.607385\pi\) |
0.982708 | − | 0.185164i | \(-0.0592817\pi\) | |||||||
\(642\) | −10.3923 | + | 6.00000i | −0.410152 | + | 0.236801i | ||||
\(643\) | − | 38.0000i | − | 1.49857i | −0.662246 | − | 0.749287i | \(-0.730396\pi\) | ||
0.662246 | − | 0.749287i | \(-0.269604\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −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 | \(-0.327076\pi\) |
−0.482880 | + | 0.875687i | \(0.660409\pi\) | |||||||
\(648\) | 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 | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.0000i | 0.469956i | ||||||||
\(653\) | 4.33013 | − | 2.50000i | 0.169451 | − | 0.0978326i | −0.412876 | − | 0.910787i | \(-0.635476\pi\) |
0.582327 | + | 0.812955i | \(0.302142\pi\) | |||||||
\(654\) | −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 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 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 | −0.155235 | − | 0.987878i | \(-0.549613\pi\) |
0.933144 | − | 0.359502i | \(-0.117053\pi\) | |||||||
\(662\) | 12.9904 | + | 7.50000i | 0.504885 | + | 0.291496i | ||||
\(663\) | 1.73205 | − | 1.00000i | 0.0672673 | − | 0.0388368i | ||||
\(664\) | 10.0000 | 0.388075 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 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 | 0 | ||||||||
\(673\) | 36.0000i | 1.38770i | 0.720121 | + | 0.693849i | \(0.244086\pi\) | ||||
−0.720121 | + | 0.693849i | \(0.755914\pi\) | |||||||
\(674\) | 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 | \(-0.448018\pi\) |
0.935793 | + | 0.352549i | \(0.114685\pi\) | |||||||
\(678\) | 6.00000i | 0.230429i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 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 | 0.564809 | − | 0.825222i | \(-0.308950\pi\) |
−0.432259 | + | 0.901750i | \(0.642283\pi\) | |||||||
\(684\) | −3.50000 | − | 6.06218i | −0.133826 | − | 0.231793i | ||||
\(685\) | −4.00000 | − | 8.00000i | −0.152832 | − | 0.305664i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 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 | \(-0.290887\pi\) |
−0.991122 | + | 0.132956i | \(0.957553\pi\) | |||||||
\(692\) | 7.00000i | 0.266100i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −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 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 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 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.00000i | 0.150329i | ||||||||
\(709\) | 8.00000 | + | 13.8564i | 0.300446 | + | 0.520388i | 0.976237 | − | 0.216705i | \(-0.0695310\pi\) |
−0.675791 | + | 0.737093i | \(0.736198\pi\) | |||||||
\(710\) | −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 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −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 | \(-0.154793\pi\) |
−0.846776 | + | 0.531949i | \(0.821460\pi\) | |||||||
\(720\) | 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 | \(0.559070\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −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 | \(-0.539893\pi\) |
0.796734 | + | 0.604331i | \(0.206559\pi\) | |||||||
\(734\) | 37.0000 | 1.36569 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −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 | −0.00311943 | − | 0.999995i | \(-0.500993\pi\) |
0.867581 | − | 0.497296i | \(-0.165674\pi\) | |||||||
\(740\) | 6.16025 | − | 9.33013i | 0.226455 | − | 0.342982i | ||||
\(741\) | −7.00000 | −0.257151 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 31.0000i | − | 1.13728i | −0.822587 | − | 0.568640i | \(-0.807470\pi\) | ||
0.822587 | − | 0.568640i | \(-0.192530\pi\) | |||||||
\(744\) | 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 | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.00000 | + | 11.0000i | −0.0730297 | + | 0.401663i | ||||
\(751\) | −2.00000 | − | 3.46410i | −0.0729810 | − | 0.126407i | 0.827225 | − | 0.561870i | \(-0.189918\pi\) |
−0.900207 | + | 0.435463i | \(0.856585\pi\) | |||||||
\(752\) | 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 | 0 | ||||||||
\(757\) | 26.0000i | 0.944986i | 0.881334 | + | 0.472493i | \(0.156646\pi\) | ||||
−0.881334 | + | 0.472493i | \(0.843354\pi\) | |||||||
\(758\) | 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 | \(-0.183983\pi\) |
−0.891932 | + | 0.452170i | \(0.850650\pi\) | |||||||
\(762\) | − | 9.00000i | − | 0.326036i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 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 | \(-0.128551\pi\) | ||||
0.919554 | + | 0.392965i | \(0.128551\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −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 | \(-0.565072\pi\) |
−0.949496 | + | 0.313778i | \(0.898405\pi\) | |||||||
\(774\) | −5.00000 | + | 8.66025i | −0.179721 | + | 0.311286i | ||||
\(775\) | −29.7846 | − | 3.58846i | −1.06989 | − | 0.128901i | ||||
\(776\) | 8.00000 | 0.287183 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 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 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −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 | \(-0.570173\pi\) |
−0.954403 | + | 0.298521i | \(0.903507\pi\) | |||||||
\(788\) | 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 | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 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 | \(-0.178307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −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 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 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 | −0.934224 | − | 0.356687i | \(-0.883906\pi\) |
0.776012 | + | 0.630718i | \(0.217239\pi\) | |||||||
\(810\) | −1.23205 | + | 1.86603i | −0.0432899 | + | 0.0655654i | ||||
\(811\) | −11.0000 | −0.386262 | −0.193131 | − | 0.981173i | \(-0.561864\pi\) | ||||
−0.193131 | + | 0.981173i | \(0.561864\pi\) | |||||||
\(812\) | 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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18.0000 | − | 9.00000i | 0.628587 | − | 0.314294i | ||||
\(821\) | −3.00000 | − | 5.19615i | −0.104701 | − | 0.181347i | 0.808915 | − | 0.587925i | \(-0.200055\pi\) |
−0.913616 | + | 0.406578i | \(0.866722\pi\) | |||||||
\(822\) | −3.46410 | − | 2.00000i | −0.120824 | − | 0.0697580i | ||||
\(823\) | 6.92820 | + | 4.00000i | 0.241502 | + | 0.139431i | 0.615867 | − | 0.787850i | \(-0.288806\pi\) |
−0.374365 | + | 0.927281i | \(0.622139\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20.0000 | + | 15.0000i | 0.696311 | + | 0.522233i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.0000i | 1.46048i | 0.683189 | + | 0.730242i | \(0.260592\pi\) | ||||
−0.683189 | + | 0.730242i | \(0.739408\pi\) | |||||||
\(828\) | 2.59808 | − | 1.50000i | 0.0902894 | − | 0.0521286i | ||||
\(829\) | −1.00000 | + | 1.73205i | −0.0347314 | + | 0.0601566i | −0.882869 | − | 0.469620i | \(-0.844391\pi\) |
0.848137 | + | 0.529777i | \(0.177724\pi\) | |||||||
\(830\) | −1.33975 | + | 22.3205i | −0.0465033 | + | 0.774756i | ||||
\(831\) | 1.00000 | + | 1.73205i | 0.0346896 | + | 0.0600842i | ||||
\(832\) | 1.00000i | 0.0346688i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −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 | \(-0.489009\pi\) | ||||
0.0345238 | + | 0.999404i | \(0.489009\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −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 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 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 | \(0.683220\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 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 | 0.974249 | + | 0.225475i | \(0.0723933\pi\) |
0.682391 | + | 0.730987i | \(0.260940\pi\) | |||||||
\(858\) | −4.33013 | − | 2.50000i | −0.147828 | − | 0.0853486i | ||||
\(859\) | −18.0000 | − | 31.1769i | −0.614152 | − | 1.06374i | −0.990533 | − | 0.137277i | \(-0.956165\pi\) |
0.376381 | − | 0.926465i | \(-0.377169\pi\) | |||||||
\(860\) | 10.0000 | + | 20.0000i | 0.340997 | + | 0.681994i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.0000i | 0.613082i | ||||||||
\(863\) | 12.9904 | − | 7.50000i | 0.442198 | − | 0.255303i | −0.262332 | − | 0.964978i | \(-0.584491\pi\) |
0.704529 | + | 0.709675i | \(0.251158\pi\) | |||||||
\(864\) | 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 | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −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 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.00000 | 0.135147 | ||||||||
\(877\) | 23.3827 | − | 13.5000i | 0.789577 | − | 0.455863i | −0.0502365 | − | 0.998737i | \(-0.515998\pi\) |
0.839814 | + | 0.542875i | \(0.182664\pi\) | |||||||
\(878\) | 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 | \(-0.483907\pi\) | ||||
0.0505363 | + | 0.998722i | \(0.483907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 52.0000i | − | 1.74994i | −0.484178 | − | 0.874970i | \(-0.660881\pi\) | ||
0.484178 | − | 0.874970i | \(-0.339119\pi\) | |||||||
\(884\) | −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 | \(-0.731235\pi\) |
0.315279 | + | 0.948999i | \(0.397902\pi\) | |||||||
\(888\) | − | 5.00000i | − | 0.167789i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −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 | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 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 | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 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 | 0.251990 | − | 0.967730i | \(-0.418915\pi\) |
−0.712084 | + | 0.702094i | \(0.752248\pi\) | |||||||
\(908\) | −12.1244 | + | 7.00000i | −0.402361 | + | 0.232303i | ||||
\(909\) | 8.00000 | 0.265343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −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 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.00000i | 0.0660098i | ||||||||
\(919\) | 28.0000 | + | 48.4974i | 0.923635 | + | 1.59978i | 0.793742 | + | 0.608254i | \(0.208130\pi\) |
0.129893 | + | 0.991528i | \(0.458537\pi\) | |||||||
\(920\) | 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 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 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 | −0.998827 | − | 0.0484211i | \(-0.984581\pi\) |
0.457480 | − | 0.889220i | \(-0.348752\pi\) | |||||||
\(930\) | −12.0000 | + | 6.00000i | −0.393496 | + | 0.196748i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 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 | \(-0.187422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.0000 | 0.326338 | ||||||||
\(940\) | −16.0167 | + | 24.2583i | −0.522406 | + | 0.791219i | ||||
\(941\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(942\) | −11.2583 | − | 6.50000i | −0.366816 | − | 0.211781i | ||||
\(943\) | 23.3827 | − | 13.5000i | 0.761445 | − | 0.439620i | ||||
\(944\) | 4.00000 | 0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 50.0000 | 1.62564 | ||||||||
\(947\) | −10.3923 | + | 6.00000i | −0.337705 | + | 0.194974i | −0.659256 | − | 0.751918i | \(-0.729129\pi\) |
0.321552 | + | 0.946892i | \(0.395796\pi\) | |||||||
\(948\) | −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 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 24.0000i | − | 0.777436i | −0.921357 | − | 0.388718i | \(-0.872918\pi\) | ||
0.921357 | − | 0.388718i | \(-0.127082\pi\) | |||||||
\(954\) | 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 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −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 | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.0000i | 0.771788i | 0.922543 | + | 0.385894i | \(0.126107\pi\) | ||||
−0.922543 | + | 0.385894i | \(0.873893\pi\) | |||||||
\(968\) | −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 | 0.988389 | + | 0.151948i | \(0.0485545\pi\) |
−0.362604 | + | 0.931943i | \(0.618112\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 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 | 0.952183 | − | 0.305530i | \(-0.0988335\pi\) |
0.211495 | + | 0.977379i | \(0.432167\pi\) | |||||||
\(978\) | −10.3923 | + | 6.00000i | −0.332309 | + | 0.191859i | ||||
\(979\) | −50.0000 | −1.59801 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −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 | \(-0.156924\pi\) |
0.0306024 | + | 0.999532i | \(0.490257\pi\) | |||||||
\(984\) | 4.50000 | − | 7.79423i | 0.143455 | − | 0.248471i | ||||
\(985\) | −33.2654 | + | 50.3827i | −1.05992 | + | 1.60533i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | −0.424594 | − | 0.905384i | \(-0.639583\pi\) |
0.996382 | − | 0.0849833i | \(-0.0270837\pi\) | |||||||
\(992\) | 5.19615 | − | 3.00000i | 0.164978 | − | 0.0952501i | ||||
\(993\) | 15.0000i | 0.476011i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 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 | \(-0.282715\pi\) |
−0.356555 | + | 0.934274i | \(0.616049\pi\) | |||||||
\(998\) | −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 | 1470.2.n.i.949.2 | 4 | ||
5.4 | even | 2 | inner | 1470.2.n.i.949.1 | 4 | ||
7.2 | even | 3 | inner | 1470.2.n.i.79.1 | 4 | ||
7.3 | odd | 6 | 1470.2.g.f.589.2 | 2 | |||
7.4 | even | 3 | 1470.2.g.a.589.2 | 2 | |||
7.5 | odd | 6 | 210.2.n.a.79.1 | ✓ | 4 | ||
7.6 | odd | 2 | 210.2.n.a.109.2 | yes | 4 | ||
21.5 | even | 6 | 630.2.u.c.289.2 | 4 | |||
21.20 | even | 2 | 630.2.u.c.109.1 | 4 | |||
28.19 | even | 6 | 1680.2.di.a.289.1 | 4 | |||
28.27 | even | 2 | 1680.2.di.a.529.2 | 4 | |||
35.3 | even | 12 | 7350.2.a.bn.1.1 | 1 | |||
35.4 | even | 6 | 1470.2.g.a.589.1 | 2 | |||
35.9 | even | 6 | inner | 1470.2.n.i.79.2 | 4 | ||
35.12 | even | 12 | 1050.2.i.o.751.1 | 2 | |||
35.13 | even | 4 | 1050.2.i.f.151.1 | 2 | |||
35.17 | even | 12 | 7350.2.a.t.1.1 | 1 | |||
35.18 | odd | 12 | 7350.2.a.ch.1.1 | 1 | |||
35.19 | odd | 6 | 210.2.n.a.79.2 | yes | 4 | ||
35.24 | odd | 6 | 1470.2.g.f.589.1 | 2 | |||
35.27 | even | 4 | 1050.2.i.o.151.1 | 2 | |||
35.32 | odd | 12 | 7350.2.a.b.1.1 | 1 | |||
35.33 | even | 12 | 1050.2.i.f.751.1 | 2 | |||
35.34 | odd | 2 | 210.2.n.a.109.1 | yes | 4 | ||
105.89 | even | 6 | 630.2.u.c.289.1 | 4 | |||
105.104 | even | 2 | 630.2.u.c.109.2 | 4 | |||
140.19 | even | 6 | 1680.2.di.a.289.2 | 4 | |||
140.139 | even | 2 | 1680.2.di.a.529.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.n.a.79.1 | ✓ | 4 | 7.5 | odd | 6 | ||
210.2.n.a.79.2 | yes | 4 | 35.19 | odd | 6 | ||
210.2.n.a.109.1 | yes | 4 | 35.34 | odd | 2 | ||
210.2.n.a.109.2 | yes | 4 | 7.6 | odd | 2 | ||
630.2.u.c.109.1 | 4 | 21.20 | even | 2 | |||
630.2.u.c.109.2 | 4 | 105.104 | even | 2 | |||
630.2.u.c.289.1 | 4 | 105.89 | even | 6 | |||
630.2.u.c.289.2 | 4 | 21.5 | even | 6 | |||
1050.2.i.f.151.1 | 2 | 35.13 | even | 4 | |||
1050.2.i.f.751.1 | 2 | 35.33 | even | 12 | |||
1050.2.i.o.151.1 | 2 | 35.27 | even | 4 | |||
1050.2.i.o.751.1 | 2 | 35.12 | even | 12 | |||
1470.2.g.a.589.1 | 2 | 35.4 | even | 6 | |||
1470.2.g.a.589.2 | 2 | 7.4 | even | 3 | |||
1470.2.g.f.589.1 | 2 | 35.24 | odd | 6 | |||
1470.2.g.f.589.2 | 2 | 7.3 | odd | 6 | |||
1470.2.n.i.79.1 | 4 | 7.2 | even | 3 | inner | ||
1470.2.n.i.79.2 | 4 | 35.9 | even | 6 | inner | ||
1470.2.n.i.949.1 | 4 | 5.4 | even | 2 | inner | ||
1470.2.n.i.949.2 | 4 | 1.1 | even | 1 | trivial | ||
1680.2.di.a.289.1 | 4 | 28.19 | even | 6 | |||
1680.2.di.a.289.2 | 4 | 140.19 | even | 6 | |||
1680.2.di.a.529.1 | 4 | 140.139 | even | 2 | |||
1680.2.di.a.529.2 | 4 | 28.27 | even | 2 | |||
7350.2.a.b.1.1 | 1 | 35.32 | odd | 12 | |||
7350.2.a.t.1.1 | 1 | 35.17 | even | 12 | |||
7350.2.a.bn.1.1 | 1 | 35.3 | even | 12 | |||
7350.2.a.ch.1.1 | 1 | 35.18 | odd | 12 |