Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(109,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.u (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: | \(5.03057532734\) |
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 | 289.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.289 |
Dual form | 630.2.u.c.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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0.133975 | − | 2.23205i | 0.0599153 | − | 0.998203i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | − | 2.00000i | 0.654654 | − | 0.755929i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.23205 | − | 1.86603i | 0.389609 | − | 0.590089i | ||||
\(11\) | −2.50000 | − | 4.33013i | −0.753778 | − | 1.30558i | −0.945979 | − | 0.324227i | \(-0.894896\pi\) |
0.192201 | − | 0.981356i | \(-0.438437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | 0.990338 | + | 0.138675i | \(0.0442844\pi\) | ||||
−0.990338 | + | 0.138675i | \(0.955716\pi\) | |||||||
\(14\) | 2.50000 | − | 0.866025i | 0.668153 | − | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −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 | 0 | ||||||||
\(19\) | 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 | 0 | ||||||||
\(22\) | − | 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 | 0 | ||||||||
\(25\) | −4.96410 | − | 0.598076i | −0.992820 | − | 0.119615i | ||||
\(26\) | −0.500000 | + | 0.866025i | −0.0980581 | + | 0.169842i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.59808 | + | 0.500000i | 0.490990 | + | 0.0944911i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 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 | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | −4.23205 | − | 4.13397i | −0.715347 | − | 0.698769i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.33013 | − | 2.50000i | −0.711868 | − | 0.410997i | 0.0998840 | − | 0.994999i | \(-0.468153\pi\) |
−0.811752 | + | 0.584002i | \(0.801486\pi\) | |||||||
\(38\) | 6.06218 | − | 3.50000i | 0.983415 | − | 0.567775i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.23205 | + | 0.133975i | 0.352918 | + | 0.0211832i | ||||
\(41\) | 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 | 0 | ||||||||
\(46\) | 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 | \(0.269646\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | −4.00000 | − | 3.00000i | −0.565685 | − | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −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 | 0 | ||||||||
\(55\) | −10.0000 | + | 5.00000i | −1.34840 | + | 0.674200i | ||||
\(56\) | 2.00000 | + | 1.73205i | 0.267261 | + | 0.231455i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | − | 3.46410i | −0.260378 | − | 0.450988i | 0.705965 | − | 0.708247i | \(-0.250514\pi\) |
−0.966342 | + | 0.257260i | \(0.917180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 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 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.23205 | + | 0.133975i | 0.276852 | + | 0.0166175i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.19615 | + | 3.00000i | −0.634811 | + | 0.366508i | −0.782613 | − | 0.622509i | \(-0.786114\pi\) |
0.147802 | + | 0.989017i | \(0.452780\pi\) | |||||||
\(68\) | −1.73205 | − | 1.00000i | −0.210042 | − | 0.121268i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.59808 | − | 5.69615i | −0.191007 | − | 0.680820i | ||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.46410 | − | 2.00000i | 0.405442 | − | 0.234082i | −0.283387 | − | 0.959006i | \(-0.591458\pi\) |
0.688830 | + | 0.724923i | \(0.258125\pi\) | |||||||
\(74\) | −2.50000 | − | 4.33013i | −0.290619 | − | 0.503367i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.00000 | 0.802955 | ||||||||
\(77\) | −12.9904 | − | 2.50000i | −1.48039 | − | 0.284901i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.00000 | + | 12.1244i | −0.787562 | + | 1.36410i | 0.139895 | + | 0.990166i | \(0.455323\pi\) |
−0.927457 | + | 0.373930i | \(0.878010\pi\) | |||||||
\(80\) | 1.86603 | + | 1.23205i | 0.208628 | + | 0.137747i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | 0.469389 | + | 0.882992i | \(0.344474\pi\) |
−0.999388 | + | 0.0349934i | \(0.988859\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | + | 1.73205i | 0.209657 | + | 0.181568i | ||||
\(92\) | 3.00000i | 0.312772i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.50000 | + | 11.2583i | 0.670424 | + | 1.16121i | ||||
\(95\) | −13.0622 | − | 8.62436i | −1.34015 | − | 0.884840i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.00000i | − | 0.812277i | −0.913812 | − | 0.406138i | \(-0.866875\pi\) | ||
0.913812 | − | 0.406138i | \(-0.133125\pi\) | |||||||
\(98\) | 2.59808 | − | 6.50000i | 0.262445 | − | 0.656599i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.96410 | − | 4.59808i | −0.196410 | − | 0.459808i | ||||
\(101\) | 4.00000 | + | 6.92820i | 0.398015 | + | 0.689382i | 0.993481 | − | 0.113998i | \(-0.0363659\pi\) |
−0.595466 | + | 0.803380i | \(0.703033\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 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 | 0 | ||||||||
\(109\) | −9.00000 | − | 15.5885i | −0.862044 | − | 1.49310i | −0.869953 | − | 0.493135i | \(-0.835851\pi\) |
0.00790932 | − | 0.999969i | \(-0.497482\pi\) | |||||||
\(110\) | −11.1603 | − | 0.669873i | −1.06409 | − | 0.0638699i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.866025 | + | 2.50000i | 0.0818317 | + | 0.236228i | ||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.69615 | − | 5.59808i | 0.344668 | − | 0.522023i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 4.00000i | − | 0.368230i | ||||||
\(119\) | −1.00000 | + | 5.19615i | −0.0916698 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 1.73205 | − | 1.00000i | 0.156813 | − | 0.0905357i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −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 | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.86603 | + | 1.23205i | 0.163661 | + | 0.108058i | ||||
\(131\) | −8.50000 | + | 14.7224i | −0.742648 | + | 1.28630i | 0.208637 | + | 0.977993i | \(0.433097\pi\) |
−0.951285 | + | 0.308312i | \(0.900236\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.06218 | − | 17.5000i | −0.525657 | − | 1.51744i | ||||
\(134\) | −6.00000 | −0.518321 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −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 | \(0.387992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | 1.46410 | − | 5.73205i | 0.123739 | − | 0.484447i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.73205 | + | 1.00000i | 0.145350 | + | 0.0839181i | ||||
\(143\) | 4.33013 | − | 2.50000i | 0.362103 | − | 0.209061i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 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 | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 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 | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.0000 | − | 8.66025i | −0.805823 | − | 0.697863i | ||||
\(155\) | 12.0000 | − | 6.00000i | 0.963863 | − | 0.481932i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.2583 | + | 6.50000i | −0.898513 | + | 0.518756i | −0.876717 | − | 0.481006i | \(-0.840272\pi\) |
−0.0217953 | + | 0.999762i | \(0.506938\pi\) | |||||||
\(158\) | −12.1244 | + | 7.00000i | −0.964562 | + | 0.556890i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | + | 2.00000i | 0.0790569 | + | 0.158114i | ||||
\(161\) | 7.50000 | − | 2.59808i | 0.591083 | − | 0.204757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3923 | + | 6.00000i | 0.813988 | + | 0.469956i | 0.848339 | − | 0.529454i | \(-0.177603\pi\) |
−0.0343508 | + | 0.999410i | \(0.510936\pi\) | |||||||
\(164\) | 4.50000 | + | 7.79423i | 0.351391 | + | 0.608627i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −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 | ||||||||
\(170\) | −0.267949 | + | 4.46410i | −0.0205508 | + | 0.342381i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −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 | ||||||||
\(175\) | −9.79423 | + | 8.89230i | −0.740374 | + | 0.672195i | ||||
\(176\) | 5.00000 | 0.376889 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.66025 | + | 5.00000i | −0.649113 | + | 0.374766i | ||||
\(179\) | 5.50000 | + | 9.52628i | 0.411089 | + | 0.712028i | 0.995009 | − | 0.0997838i | \(-0.0318151\pi\) |
−0.583920 | + | 0.811811i | \(0.698482\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −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 | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.50000 | + | 2.59808i | −0.110581 | + | 0.191533i | ||||
\(185\) | −6.16025 | + | 9.33013i | −0.452911 | + | 0.685965i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 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 | 0.416751 | + | 0.909021i | \(0.363169\pi\) |
−0.995610 | + | 0.0935936i | \(0.970165\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.5885 | + | 9.00000i | −1.12208 | + | 0.647834i | −0.941932 | − | 0.335805i | \(-0.890992\pi\) |
−0.180150 | + | 0.983639i | \(0.557658\pi\) | |||||||
\(194\) | 4.00000 | − | 6.92820i | 0.287183 | − | 0.497416i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | − | 4.33013i | 0.392857 | − | 0.309295i | ||||
\(197\) | − | 27.0000i | − | 1.92367i | −0.273629 | − | 0.961835i | \(-0.588224\pi\) | ||
0.273629 | − | 0.961835i | \(-0.411776\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.00000 | − | 12.1244i | −0.496217 | − | 0.859473i | 0.503774 | − | 0.863836i | \(-0.331945\pi\) |
−0.999990 | + | 0.00436292i | \(0.998611\pi\) | |||||||
\(200\) | 0.598076 | − | 4.96410i | 0.0422904 | − | 0.351015i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.00000i | 0.562878i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.20577 | − | 20.0885i | 0.0842147 | − | 1.40304i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −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 | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.00000 | − | 10.3923i | −0.410152 | − | 0.710403i | ||||
\(215\) | 22.3205 | + | 1.33975i | 1.52225 | + | 0.0913699i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.5885 | + | 3.00000i | 1.05821 | + | 0.203653i | ||||
\(218\) | − | 18.0000i | − | 1.21911i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.33013 | − | 6.16025i | −0.629037 | − | 0.415324i | ||||
\(221\) | −1.00000 | − | 1.73205i | −0.0672673 | − | 0.116510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000i | 1.07144i | 0.844396 | + | 0.535720i | \(0.179960\pi\) | ||||
−0.844396 | + | 0.535720i | \(0.820040\pi\) | |||||||
\(224\) | −0.500000 | + | 2.59808i | −0.0334077 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 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 | \(0.179529\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −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 | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0167 | − | 24.2583i | 1.04481 | − | 1.58244i | ||||
\(236\) | 2.00000 | − | 3.46410i | 0.130189 | − | 0.225494i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.46410 | + | 4.00000i | −0.224544 | + | 0.259281i | ||||
\(239\) | 20.0000 | 1.29369 | 0.646846 | − | 0.762620i | \(-0.276088\pi\) | ||||
0.646846 | + | 0.762620i | \(0.276088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 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 | 0 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | −15.5981 | + | 1.30385i | −0.996525 | + | 0.0832998i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.06218 | + | 3.50000i | 0.385727 | + | 0.222700i | ||||
\(248\) | −5.19615 | + | 3.00000i | −0.329956 | + | 0.190500i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.23205 | + | 8.52628i | −0.457395 | + | 0.539249i | ||||
\(251\) | 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 | 0 | ||||||||
\(256\) | −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 | \(0.565704\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −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 | \(0.598485\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.00000 | − | 2.00000i | −0.0614295 | − | 0.122859i | ||||
\(266\) | 3.50000 | − | 18.1865i | 0.214599 | − | 1.11509i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.19615 | − | 3.00000i | −0.317406 | − | 0.183254i | ||||
\(269\) | −7.00000 | − | 12.1244i | −0.426798 | − | 0.739235i | 0.569789 | − | 0.821791i | \(-0.307025\pi\) |
−0.996586 | + | 0.0825561i | \(0.973692\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −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 | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.00000 | −0.241649 | ||||||||
\(275\) | 9.82051 | + | 22.9904i | 0.592199 | + | 1.38637i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.73205 | + | 1.00000i | −0.104069 | + | 0.0600842i | −0.551131 | − | 0.834419i | \(-0.685804\pi\) |
0.447062 | + | 0.894503i | \(0.352470\pi\) | |||||||
\(278\) | 6.92820 | + | 4.00000i | 0.415526 | + | 0.239904i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.13397 | − | 4.23205i | 0.247052 | − | 0.252913i | ||||
\(281\) | 11.0000 | 0.656205 | 0.328102 | − | 0.944642i | \(-0.393591\pi\) | ||||
0.328102 | + | 0.944642i | \(0.393591\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.5167 | − | 13.0000i | 1.33848 | − | 0.772770i | 0.351895 | − | 0.936039i | \(-0.385537\pi\) |
0.986581 | + | 0.163270i | \(0.0522041\pi\) | |||||||
\(284\) | 1.00000 | + | 1.73205i | 0.0593391 | + | 0.102778i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.00000 | 0.295656 | ||||||||
\(287\) | 15.5885 | − | 18.0000i | 0.920158 | − | 1.06251i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.50000 | + | 11.2583i | −0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 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 | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.19615 | − | 3.00000i | 0.301005 | − | 0.173785i | ||||
\(299\) | −1.50000 | + | 2.59808i | −0.0867472 | + | 0.150251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0000 | + | 17.3205i | 1.15278 | + | 0.998337i | ||||
\(302\) | 22.0000i | 1.26596i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.50000 | + | 6.06218i | 0.200739 | + | 0.347690i | ||||
\(305\) | −3.73205 | − | 2.46410i | −0.213697 | − | 0.141094i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.00000i | − | 0.114146i | −0.998370 | − | 0.0570730i | \(-0.981823\pi\) | ||
0.998370 | − | 0.0570730i | \(-0.0181768\pi\) | |||||||
\(308\) | −4.33013 | − | 12.5000i | −0.246732 | − | 0.712254i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.3923 | + | 0.803848i | 0.760632 | + | 0.0456555i | ||||
\(311\) | −13.0000 | − | 22.5167i | −0.737162 | − | 1.27680i | −0.953768 | − | 0.300544i | \(-0.902832\pi\) |
0.216606 | − | 0.976259i | \(-0.430501\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.66025 | + | 5.00000i | 0.489506 | + | 0.282617i | 0.724370 | − | 0.689412i | \(-0.242131\pi\) |
−0.234863 | + | 0.972028i | \(0.575464\pi\) | |||||||
\(314\) | −13.0000 | −0.733632 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −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 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.133975 | + | 2.23205i | −0.00748941 | + | 0.124775i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.79423 | + | 1.50000i | 0.434355 | + | 0.0835917i | ||||
\(323\) | 14.0000i | 0.778981i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.598076 | − | 4.96410i | 0.0331753 | − | 0.275359i | ||||
\(326\) | 6.00000 | + | 10.3923i | 0.332309 | + | 0.575577i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.00000i | 0.496942i | ||||||||
\(329\) | 32.5000 | − | 11.2583i | 1.79178 | − | 0.620692i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 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 | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.46410 | + | 3.73205i | −0.133635 | + | 0.202399i | ||||
\(341\) | 15.0000 | − | 25.9808i | 0.812296 | − | 1.40694i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | −10.0000 | −0.539164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 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 | \(0.277962\pi\) | |||||||
\(350\) | −12.9282 | + | 2.80385i | −0.691042 | + | 0.149872i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.33013 | + | 2.50000i | 0.230797 | + | 0.133250i | ||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.267949 | − | 4.46410i | 0.0142213 | − | 0.236930i | ||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.0000i | 0.581368i | ||||||||
\(359\) | 14.0000 | − | 24.2487i | 0.738892 | − | 1.27980i | −0.214103 | − | 0.976811i | \(-0.568683\pi\) |
0.952995 | − | 0.302987i | \(-0.0979839\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | − | 25.9808i | −0.789474 | − | 1.36741i | ||||
\(362\) | −1.73205 | − | 1.00000i | −0.0910346 | − | 0.0525588i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.500000 | + | 2.59808i | −0.0262071 | + | 0.136176i | ||||
\(365\) | −4.00000 | − | 8.00000i | −0.209370 | − | 0.418739i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.0429 | − | 18.5000i | 1.67263 | − | 0.965692i | 0.706469 | − | 0.707744i | \(-0.250287\pi\) |
0.966159 | − | 0.257948i | \(-0.0830464\pi\) | |||||||
\(368\) | −2.59808 | + | 1.50000i | −0.135434 | + | 0.0781929i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.0000 | + | 5.00000i | −0.519875 | + | 0.259938i | ||||
\(371\) | 0.500000 | − | 2.59808i | 0.0259587 | − | 0.134885i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.19615 | − | 3.00000i | −0.269047 | − | 0.155334i | 0.359408 | − | 0.933181i | \(-0.382979\pi\) |
−0.628454 | + | 0.777847i | \(0.716312\pi\) | |||||||
\(374\) | 5.00000 | + | 8.66025i | 0.258544 | + | 0.447811i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −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 | \(0.491824\pi\) | |||||||
\(380\) | 0.937822 | − | 15.6244i | 0.0481093 | − | 0.801513i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −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 | \(0.740519\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.32051 | + | 28.6603i | −0.373088 | + | 1.46066i | ||||
\(386\) | −18.0000 | −0.916176 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.92820 | − | 4.00000i | 0.351726 | − | 0.203069i | ||||
\(389\) | −3.00000 | − | 5.19615i | −0.152106 | − | 0.263455i | 0.779895 | − | 0.625910i | \(-0.215272\pi\) |
−0.932002 | + | 0.362454i | \(0.881939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.00000 | −0.303433 | ||||||||
\(392\) | 6.92820 | − | 1.00000i | 0.349927 | − | 0.0505076i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.5000 | − | 23.3827i | 0.680120 | − | 1.17800i | ||||
\(395\) | 26.1244 | + | 17.2487i | 1.31446 | + | 0.867877i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.73205 | − | 1.00000i | −0.0869291 | − | 0.0501886i | 0.455905 | − | 0.890028i | \(-0.349316\pi\) |
−0.542834 | + | 0.839840i | \(0.682649\pi\) | |||||||
\(398\) | − | 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 | 0.302556 | + | 0.953131i | \(0.402160\pi\) |
−0.976714 | + | 0.214544i | \(0.931173\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.19615 | + | 3.00000i | −0.258839 | + | 0.149441i | ||||
\(404\) | −4.00000 | + | 6.92820i | −0.199007 | + | 0.344691i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.0000i | 1.23920i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00000 | + | 8.66025i | 0.247234 | + | 0.428222i | 0.962757 | − | 0.270367i | \(-0.0871450\pi\) |
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(410\) | 11.0885 | − | 16.7942i | 0.547620 | − | 0.829408i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.3923 | − | 2.00000i | −0.511372 | − | 0.0984136i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.3205 | + | 1.33975i | 1.09567 | + | 0.0657655i | ||||
\(416\) | −0.500000 | − | 0.866025i | −0.0245145 | − | 0.0424604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −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 | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.500000 | + | 0.866025i | 0.0242821 | + | 0.0420579i | ||||
\(425\) | 9.19615 | − | 3.92820i | 0.446079 | − | 0.190546i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.73205 | − | 5.00000i | −0.0838198 | − | 0.241967i | ||||
\(428\) | − | 12.0000i | − | 0.580042i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.6603 | + | 12.3205i | 0.899877 | + | 0.594148i | ||||
\(431\) | 9.00000 | + | 15.5885i | 0.433515 | + | 0.750870i | 0.997173 | − | 0.0751385i | \(-0.0239399\pi\) |
−0.563658 | + | 0.826008i | \(0.690607\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.00000i | 0.192228i | 0.995370 | + | 0.0961139i | \(0.0306413\pi\) | ||||
−0.995370 | + | 0.0961139i | \(0.969359\pi\) | |||||||
\(434\) | 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 | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 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 | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 2.00000i | − | 0.0951303i | ||||||
\(443\) | −5.19615 | − | 3.00000i | −0.246877 | − | 0.142534i | 0.371457 | − | 0.928450i | \(-0.378858\pi\) |
−0.618333 | + | 0.785916i | \(0.712192\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.6603 | + | 12.3205i | 0.884581 | + | 0.584048i | ||||
\(446\) | −8.00000 | + | 13.8564i | −0.378811 | + | 0.656120i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.73205 | + | 2.00000i | −0.0818317 | + | 0.0944911i | ||||
\(449\) | 9.00000 | 0.424736 | 0.212368 | − | 0.977190i | \(-0.431882\pi\) | ||||
0.212368 | + | 0.977190i | \(0.431882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.5000 | − | 38.9711i | −1.05948 | − | 1.83508i | ||||
\(452\) | 5.19615 | − | 3.00000i | 0.244406 | − | 0.141108i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.0000 | 0.657053 | ||||||||
\(455\) | 4.13397 | − | 4.23205i | 0.193804 | − | 0.198402i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.9090 | − | 19.0000i | −1.53942 | − | 0.888783i | −0.998873 | − | 0.0474665i | \(-0.984885\pi\) |
−0.540544 | − | 0.841316i | \(-0.681781\pi\) | |||||||
\(458\) | −3.46410 | + | 2.00000i | −0.161867 | + | 0.0934539i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.69615 | + | 0.401924i | 0.312210 | + | 0.0187398i | ||||
\(461\) | 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 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.73205 | − | 1.00000i | −0.0801498 | − | 0.0462745i | 0.459390 | − | 0.888235i | \(-0.348068\pi\) |
−0.539539 | + | 0.841960i | \(0.681402\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.00000 | + | 15.5885i | −0.138527 | + | 0.719808i | ||||
\(470\) | 26.0000 | − | 13.0000i | 1.19929 | − | 0.599645i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.46410 | − | 2.00000i | 0.159448 | − | 0.0920575i | ||||
\(473\) | 43.3013 | − | 25.0000i | 1.99099 | − | 1.14950i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.0000 | + | 28.0000i | −0.963546 | + | 1.28473i | ||||
\(476\) | −5.00000 | + | 1.73205i | −0.229175 | + | 0.0793884i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17.3205 | + | 10.0000i | 0.792222 | + | 0.457389i | ||||
\(479\) | −4.00000 | − | 6.92820i | −0.182765 | − | 0.316558i | 0.760056 | − | 0.649857i | \(-0.225171\pi\) |
−0.942821 | + | 0.333300i | \(0.891838\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.50000 | − | 4.33013i | 0.113990 | − | 0.197437i | ||||
\(482\) | 1.00000i | 0.0455488i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.0000 | −0.636364 | ||||||||
\(485\) | −17.8564 | − | 1.07180i | −0.810818 | − | 0.0486678i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.7846 | + | 12.0000i | −0.941841 | + | 0.543772i | −0.890537 | − | 0.454911i | \(-0.849671\pi\) |
−0.0513038 | + | 0.998683i | \(0.516338\pi\) | |||||||
\(488\) | 1.73205 | + | 1.00000i | 0.0784063 | + | 0.0452679i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −14.1603 | − | 6.66987i | −0.639695 | − | 0.301314i | ||||
\(491\) | −24.0000 | −1.08310 | −0.541552 | − | 0.840667i | \(-0.682163\pi\) | ||||
−0.541552 | + | 0.840667i | \(0.682163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 3.50000 | + | 6.06218i | 0.157472 | + | 0.272750i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | 3.46410 | − | 4.00000i | 0.155386 | − | 0.179425i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0000 | + | 24.2487i | −0.626726 | + | 1.08552i | 0.361478 | + | 0.932381i | \(0.382272\pi\) |
−0.988204 | + | 0.153141i | \(0.951061\pi\) | |||||||
\(500\) | −10.5263 | + | 3.76795i | −0.470750 | + | 0.168508i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.79423 | − | 4.50000i | 0.345813 | − | 0.199655i | ||||
\(509\) | −7.00000 | + | 12.1244i | −0.310270 | + | 0.537403i | −0.978421 | − | 0.206623i | \(-0.933753\pi\) |
0.668151 | + | 0.744026i | \(0.267086\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | − | 10.3923i | 0.0884748 | − | 0.459728i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.00000 | + | 8.66025i | 0.220541 | + | 0.381987i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 65.0000i | − | 2.85870i | ||||||
\(518\) | −12.9904 | − | 2.50000i | −0.570765 | − | 0.109844i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.133975 | + | 2.23205i | −0.00587517 | + | 0.0978819i | ||||
\(521\) | −7.50000 | − | 12.9904i | −0.328581 | − | 0.569119i | 0.653650 | − | 0.756797i | \(-0.273237\pi\) |
−0.982231 | + | 0.187678i | \(0.939904\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.3923 | − | 6.00000i | −0.454424 | − | 0.262362i | 0.255273 | − | 0.966869i | \(-0.417835\pi\) |
−0.709697 | + | 0.704507i | \(0.751168\pi\) | |||||||
\(524\) | −17.0000 | −0.742648 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | −10.3923 | − | 6.00000i | −0.452696 | − | 0.261364i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | − | 12.1244i | −0.304348 | − | 0.527146i | ||||
\(530\) | 0.133975 | − | 2.23205i | 0.00581948 | − | 0.0969541i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.1244 | − | 14.0000i | 0.525657 | − | 0.606977i | ||||
\(533\) | 9.00000i | 0.389833i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.7846 | + | 22.3923i | −0.639194 | + | 0.968104i | ||||
\(536\) | −3.00000 | − | 5.19615i | −0.129580 | − | 0.224440i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 14.0000i | − | 0.603583i | ||||||
\(539\) | −27.5000 | + | 21.6506i | −1.18451 | + | 0.932559i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −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 | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 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 | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.99038 | + | 24.8205i | −0.127510 | + | 1.05835i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.1244 | + | 35.0000i | 0.515580 | + | 1.48835i | ||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 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 | \(0.642859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.0000 | −0.422955 | ||||||||
\(560\) | 5.69615 | − | 1.59808i | 0.240706 | − | 0.0675310i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 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 | \(0.551171\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.3923 | − | 0.803848i | −0.563418 | − | 0.0338181i | ||||
\(566\) | 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 | \(-0.813304\pi\) |
0.895753 | + | 0.444552i | \(0.146637\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 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 | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 22.5000 | − | 7.79423i | 0.939132 | − | 0.325325i | ||||
\(575\) | −12.0000 | − | 9.00000i | −0.500435 | − | 0.375326i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.7846 | + | 12.0000i | −0.865275 | + | 0.499567i | −0.865775 | − | 0.500433i | \(-0.833174\pi\) |
0.000500448 | 1.00000i | \(0.499841\pi\) | ||||||||
\(578\) | −11.2583 | + | 6.50000i | −0.468285 | + | 0.270364i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.0000 | + | 17.3205i | 0.829740 | + | 0.718576i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.33013 | − | 2.50000i | −0.179336 | − | 0.103539i | ||||
\(584\) | 2.00000 | + | 3.46410i | 0.0827606 | + | 0.143346i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 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 | ||||||||
\(590\) | −8.92820 | − | 0.535898i | −0.367568 | − | 0.0220626i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 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 | \(0.912640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.4641 | + | 2.92820i | 0.469982 | + | 0.120045i | ||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.59808 | + | 1.50000i | −0.106243 | + | 0.0613396i | ||||
\(599\) | 14.0000 | + | 24.2487i | 0.572024 | + | 0.990775i | 0.996358 | + | 0.0852695i | \(0.0271751\pi\) |
−0.424333 | + | 0.905506i | \(0.639492\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −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 | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.0000 | + | 19.0526i | −0.447584 | + | 0.775238i | ||||
\(605\) | 26.1244 | + | 17.2487i | 1.06211 | + | 0.701260i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.2583 | + | 6.50000i | 0.456962 | + | 0.263827i | 0.710766 | − | 0.703429i | \(-0.248349\pi\) |
−0.253804 | + | 0.967256i | \(0.581682\pi\) | |||||||
\(608\) | 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 | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.4545 | − | 9.50000i | 0.664590 | − | 0.383701i | −0.129433 | − | 0.991588i | \(-0.541316\pi\) |
0.794024 | + | 0.607887i | \(0.207983\pi\) | |||||||
\(614\) | 1.00000 | − | 1.73205i | 0.0403567 | − | 0.0698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 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 | \(0.735863\pi\) | |||||||
\(620\) | 11.1962 | + | 7.39230i | 0.449648 | + | 0.296882i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 26.0000i | − | 1.04251i | ||||||
\(623\) | 8.66025 | + | 25.0000i | 0.346966 | + | 1.00160i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2846 | + | 5.93782i | 0.971384 | + | 0.237513i | ||||
\(626\) | 5.00000 | + | 8.66025i | 0.199840 | + | 0.346133i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.00000 | − | 1.73205i | −0.0397151 | − | 0.0687885i | ||||
\(635\) | −20.0885 | − | 1.20577i | −0.797186 | − | 0.0478496i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.92820 | − | 1.00000i | 0.274505 | − | 0.0396214i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.23205 | + | 1.86603i | −0.0487011 | + | 0.0737611i | ||||
\(641\) | −16.5000 | − | 28.5788i | −0.651711 | − | 1.12880i | −0.982708 | − | 0.185164i | \(-0.940718\pi\) |
0.330997 | − | 0.943632i | \(-0.392615\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.0000i | 1.49857i | 0.662246 | + | 0.749287i | \(0.269604\pi\) | ||||
−0.662246 | + | 0.749287i | \(0.730396\pi\) | |||||||
\(644\) | 6.00000 | + | 5.19615i | 0.236433 | + | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −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 | 0 | ||||||||
\(649\) | −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 | 0.582327 | − | 0.812955i | \(-0.302142\pi\) |
−0.412876 | + | 0.910787i | \(0.635476\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.7224 | + | 20.9449i | 1.23950 | + | 0.818384i | ||||
\(656\) | −4.50000 | + | 7.79423i | −0.175695 | + | 0.304314i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 33.7750 | + | 6.50000i | 1.31669 | + | 0.253396i | ||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −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 | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.0000 | −0.388075 | ||||||||
\(665\) | −39.8731 | + | 11.1865i | −1.54621 | + | 0.433795i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 16.4545 | − | 9.50000i | 0.636643 | − | 0.367566i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.803848 | + | 13.3923i | −0.0310553 | + | 0.517390i | ||||
\(671\) | −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 | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 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 | \(0.885315\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.0000 | − | 13.8564i | −0.614024 | − | 0.531760i | ||||
\(680\) | −4.00000 | + | 2.00000i | −0.153393 | + | 0.0766965i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 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 | \(0.308950\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.00000 | + | 8.00000i | 0.152832 | + | 0.305664i | ||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.66025 | − | 5.00000i | −0.330169 | − | 0.190623i | ||||
\(689\) | 0.500000 | + | 0.866025i | 0.0190485 | + | 0.0329929i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.0000 | −0.607352 | ||||||||
\(695\) | 1.07180 | − | 17.8564i | 0.0406556 | − | 0.677332i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.5885 | + | 9.00000i | −0.590455 | + | 0.340899i | ||||
\(698\) | 20.7846 | + | 12.0000i | 0.786709 | + | 0.454207i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.5981 | − | 4.03590i | −0.476163 | − | 0.152543i | ||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.3109 | + | 17.5000i | −1.14320 | + | 0.660025i | ||||
\(704\) | 2.50000 | + | 4.33013i | 0.0942223 | + | 0.163198i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.7846 | + | 4.00000i | 0.781686 | + | 0.150435i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.00000 | − | 13.8564i | 0.300446 | − | 0.520388i | −0.675791 | − | 0.737093i | \(-0.736198\pi\) |
0.976237 | + | 0.216705i | \(0.0695310\pi\) | |||||||
\(710\) | 2.46410 | − | 3.73205i | 0.0924761 | − | 0.140061i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −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 | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.2487 | − | 14.0000i | 0.904954 | − | 0.522475i | ||||
\(719\) | 1.00000 | − | 1.73205i | 0.0372937 | − | 0.0645946i | −0.846776 | − | 0.531949i | \(-0.821460\pi\) |
0.884070 | + | 0.467355i | \(0.154793\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 30.0000i | − | 1.11648i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.00000 | − | 1.73205i | −0.0371647 | − | 0.0643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 53.0000i | − | 1.96566i | −0.184510 | − | 0.982831i | \(-0.559070\pi\) | ||
0.184510 | − | 0.982831i | \(-0.440930\pi\) | |||||||
\(728\) | −1.73205 | + | 2.00000i | −0.0641941 | + | 0.0741249i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.535898 | − | 8.92820i | 0.0198345 | − | 0.330448i | ||||
\(731\) | −10.0000 | − | 17.3205i | −0.369863 | − | 0.640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.1865 | + | 10.5000i | 0.671735 | + | 0.387826i | 0.796734 | − | 0.604331i | \(-0.206559\pi\) |
−0.124999 | + | 0.992157i | \(0.539893\pi\) | |||||||
\(734\) | 37.0000 | 1.36569 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | −0.110581 | ||||||||
\(737\) | 25.9808 | + | 15.0000i | 0.957014 | + | 0.552532i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.5000 | + | 40.7032i | 0.864461 | + | 1.49729i | 0.867581 | + | 0.497296i | \(0.165674\pi\) |
−0.00311943 | + | 0.999995i | \(0.500993\pi\) | |||||||
\(740\) | −11.1603 | − | 0.669873i | −0.410259 | − | 0.0246250i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.73205 | − | 2.00000i | 0.0635856 | − | 0.0734223i | ||||
\(743\) | 31.0000i | 1.13728i | 0.822587 | + | 0.568640i | \(0.192530\pi\) | ||||
−0.822587 | + | 0.568640i | \(0.807470\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.1962 | − | 7.39230i | −0.410195 | − | 0.270833i | ||||
\(746\) | −3.00000 | − | 5.19615i | −0.109838 | − | 0.190245i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.0000i | 0.365636i | ||||||||
\(749\) | −30.0000 | + | 10.3923i | −1.09618 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −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 | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.62436 | − | 13.0622i | 0.312838 | − | 0.473815i | ||||
\(761\) | −1.50000 | + | 2.59808i | −0.0543750 | + | 0.0941802i | −0.891932 | − | 0.452170i | \(-0.850650\pi\) |
0.837557 | + | 0.546350i | \(0.183983\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.7654 | − | 9.00000i | −1.69302 | − | 0.325822i | ||||
\(764\) | −16.0000 | −0.578860 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.50000 | − | 7.79423i | −0.162592 | − | 0.281617i | ||||
\(767\) | 3.46410 | − | 2.00000i | 0.125081 | − | 0.0722158i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −51.0000 | −1.83911 | −0.919554 | − | 0.392965i | \(-0.871449\pi\) | ||||
−0.919554 | + | 0.392965i | \(0.871449\pi\) | |||||||
\(770\) | −20.6699 | + | 21.1603i | −0.744891 | + | 0.762563i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −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 | \(0.101595\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.7846 | − | 27.5885i | −0.423316 | − | 0.991007i | ||||
\(776\) | 8.00000 | 0.287183 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 6.00000i | − | 0.215110i | ||||||
\(779\) | 31.5000 | − | 54.5596i | 1.12860 | − | 1.95480i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −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 | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.9090 | + | 19.0000i | −1.17308 | + | 0.677277i | −0.954403 | − | 0.298521i | \(-0.903507\pi\) |
−0.218675 | + | 0.975798i | \(0.570173\pi\) | |||||||
\(788\) | 23.3827 | − | 13.5000i | 0.832974 | − | 0.480918i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14.0000 | + | 28.0000i | 0.498098 | + | 0.996195i | ||||
\(791\) | −12.0000 | − | 10.3923i | −0.426671 | − | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.73205 | + | 1.00000i | 0.0615069 | + | 0.0355110i | ||||
\(794\) | −1.00000 | − | 1.73205i | −0.0354887 | − | 0.0614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 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 | ||||||||
\(800\) | 4.59808 | − | 1.96410i | 0.162567 | − | 0.0694415i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.3827 | + | 13.5000i | −0.825671 | + | 0.476702i | ||||
\(803\) | −17.3205 | − | 10.0000i | −0.611227 | − | 0.352892i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.79423 | − | 17.0885i | −0.168974 | − | 0.602289i | ||||
\(806\) | −6.00000 | −0.211341 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.92820 | + | 4.00000i | −0.243733 | + | 0.140720i | ||||
\(809\) | 4.50000 | + | 7.79423i | 0.158212 | + | 0.274030i | 0.934224 | − | 0.356687i | \(-0.116094\pi\) |
−0.776012 | + | 0.630718i | \(0.782761\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0000 | 0.386262 | 0.193131 | − | 0.981173i | \(-0.438136\pi\) | ||||
0.193131 | + | 0.981173i | \(0.438136\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12.5000 | + | 21.6506i | −0.438125 | + | 0.758854i | ||||
\(815\) | 14.7846 | − | 22.3923i | 0.517882 | − | 0.784368i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 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 | \(-0.799945\pi\) |
0.913616 | + | 0.406578i | \(0.133278\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.92820 | + | 4.00000i | −0.241502 | + | 0.139431i | −0.615867 | − | 0.787850i | \(-0.711194\pi\) |
0.374365 | + | 0.927281i | \(0.377861\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | − | 6.92820i | −0.278356 | − | 0.241063i | ||||
\(827\) | − | 42.0000i | − | 1.46048i | −0.683189 | − | 0.730242i | \(-0.739408\pi\) | ||
0.683189 | − | 0.730242i | \(-0.260592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.00000 | + | 1.73205i | 0.0347314 | + | 0.0601566i | 0.882869 | − | 0.469620i | \(-0.155609\pi\) |
−0.848137 | + | 0.529777i | \(0.822276\pi\) | |||||||
\(830\) | 18.6603 | + | 12.3205i | 0.647707 | + | 0.427651i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 1.00000i | − | 0.0346688i | ||||||
\(833\) | 8.66025 | + | 11.0000i | 0.300060 | + | 0.381127i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −42.4090 | − | 2.54552i | −1.46762 | − | 0.0880913i | ||||
\(836\) | −17.5000 | − | 30.3109i | −0.605250 | − | 1.04832i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 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 | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.50000 | + | 16.4545i | 0.327003 | + | 0.566387i | ||||
\(845\) | 1.60770 | − | 26.7846i | 0.0553064 | − | 0.921419i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.1244 | + | 35.0000i | 0.416598 | + | 1.20261i | ||||
\(848\) | 1.00000i | 0.0343401i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.92820 | + | 1.19615i | 0.340535 | + | 0.0410277i | ||||
\(851\) | −7.50000 | − | 12.9904i | −0.257097 | − | 0.445305i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 49.0000i | − | 1.67773i | −0.544341 | − | 0.838864i | \(-0.683220\pi\) | ||
0.544341 | − | 0.838864i | \(-0.316780\pi\) | |||||||
\(854\) | 1.00000 | − | 5.19615i | 0.0342193 | − | 0.177809i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 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 | \(0.927607\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 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 | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 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 | 0 | ||||||||
\(865\) | 8.62436 | − | 13.0622i | 0.293237 | − | 0.444127i | ||||
\(866\) | −2.00000 | + | 3.46410i | −0.0679628 | + | 0.117715i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 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 | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 21.0000 | 0.710336 | ||||||||
\(875\) | 18.5359 | + | 23.0526i | 0.626628 | + | 0.779319i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.3827 | − | 13.5000i | −0.789577 | − | 0.455863i | 0.0502365 | − | 0.998737i | \(-0.484002\pi\) |
−0.839814 | + | 0.542875i | \(0.817336\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.669873 | − | 11.1603i | 0.0225814 | − | 0.376212i | ||||
\(881\) | 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 | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −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 | \(0.602098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.0000 | − | 15.5885i | −0.603701 | − | 0.522820i | ||||
\(890\) | 10.0000 | + | 20.0000i | 0.335201 | + | 0.670402i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.8564 | + | 8.00000i | −0.463947 | + | 0.267860i | ||||
\(893\) | 78.8083 | − | 45.5000i | 2.63722 | − | 1.52260i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.0000 | − | 11.0000i | 0.735379 | − | 0.367689i | ||||
\(896\) | −2.50000 | + | 0.866025i | −0.0835191 | + | 0.0289319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.79423 | + | 4.50000i | 0.260097 | + | 0.150167i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.00000 | + | 1.73205i | −0.0333148 | + | 0.0577030i | ||||
\(902\) | − | 45.0000i | − | 1.49834i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | −0.267949 | + | 4.46410i | −0.00890693 | + | 0.148392i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.8564 | − | 8.00000i | 0.460094 | − | 0.265636i | −0.251990 | − | 0.967730i | \(-0.581085\pi\) |
0.712084 | + | 0.702094i | \(0.247752\pi\) | |||||||
\(908\) | 12.1244 | + | 7.00000i | 0.402361 | + | 0.232303i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.69615 | − | 1.59808i | 0.188826 | − | 0.0529757i | ||||
\(911\) | 6.00000 | 0.198789 | 0.0993944 | − | 0.995048i | \(-0.468309\pi\) | ||||
0.0993944 | + | 0.995048i | \(0.468309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.3013 | − | 25.0000i | 1.43306 | − | 0.827379i | ||||
\(914\) | −19.0000 | − | 32.9090i | −0.628464 | − | 1.08853i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.00000 | −0.132164 | ||||||||
\(917\) | 14.7224 | + | 42.5000i | 0.486178 | + | 1.40347i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.0000 | − | 48.4974i | 0.923635 | − | 1.59978i | 0.129893 | − | 0.991528i | \(-0.458537\pi\) |
0.793742 | − | 0.608254i | \(-0.208130\pi\) | |||||||
\(920\) | 5.59808 | + | 3.69615i | 0.184563 | + | 0.121859i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 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 | 0.457480 | + | 0.889220i | \(0.348752\pi\) |
−0.998827 | + | 0.0484211i | \(0.984581\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.5000 | − | 18.1865i | −1.49120 | − | 0.596040i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.00000 | − | 1.73205i | −0.0327210 | − | 0.0566744i | ||||
\(935\) | 12.3205 | − | 18.6603i | 0.402924 | − | 0.610256i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.0000i | 1.11073i | 0.831606 | + | 0.555366i | \(0.187422\pi\) | ||||
−0.831606 | + | 0.555366i | \(0.812578\pi\) | |||||||
\(938\) | −10.3923 | + | 12.0000i | −0.339321 | + | 0.391814i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 29.0167 | + | 1.74167i | 0.946419 | + | 0.0568070i | ||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 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 | 0.321552 | − | 0.946892i | \(-0.395796\pi\) |
−0.659256 | + | 0.751918i | \(0.729129\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.00000 | + | 3.46410i | 0.0649227 | + | 0.112449i | ||||
\(950\) | −32.1865 | + | 13.7487i | −1.04427 | + | 0.446067i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −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 | 0 | ||||||||
\(955\) | 29.8564 | + | 19.7128i | 0.966131 | + | 0.637892i | ||||
\(956\) | 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 | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50000 | + | 4.33013i | −0.0806452 | + | 0.139682i | ||||
\(962\) | 4.33013 | − | 2.50000i | 0.139609 | − | 0.0806032i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −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 | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.9282 | − | 9.85641i | −0.479316 | − | 0.316470i | ||||
\(971\) | 19.5000 | − | 33.7750i | 0.625785 | − | 1.08389i | −0.362604 | − | 0.931943i | \(-0.618112\pi\) |
0.988389 | − | 0.151948i | \(-0.0485545\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.8564 | − | 16.0000i | 0.444216 | − | 0.512936i | ||||
\(974\) | −24.0000 | −0.769010 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 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 | \(0.0988335\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 50.0000 | 1.59801 | ||||||||
\(980\) | −8.92820 | − | 12.8564i | −0.285201 | − | 0.410683i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −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 | \(0.509743\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −60.2654 | − | 3.61731i | −1.92021 | − | 0.115257i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.00000i | 0.222700i | ||||||||
\(989\) | −15.0000 | + | 25.9808i | −0.476972 | + | 0.826140i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.00000 | − | 1.73205i | 0.158590 | − | 0.0549373i | ||||
\(995\) | −28.0000 | + | 14.0000i | −0.887660 | + | 0.443830i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.66025 | − | 5.00000i | 0.274273 | − | 0.158352i | −0.356555 | − | 0.934274i | \(-0.616049\pi\) |
0.630828 | + | 0.775923i | \(0.282715\pi\) | |||||||
\(998\) | −24.2487 | + | 14.0000i | −0.767580 | + | 0.443162i | ||||
\(999\) | 0 | 0 |
(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 | 630.2.u.c.289.2 | 4 | ||
3.2 | odd | 2 | 210.2.n.a.79.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 630.2.u.c.289.1 | 4 | ||
7.4 | even | 3 | inner | 630.2.u.c.109.1 | 4 | ||
12.11 | even | 2 | 1680.2.di.a.289.1 | 4 | |||
15.2 | even | 4 | 1050.2.i.o.751.1 | 2 | |||
15.8 | even | 4 | 1050.2.i.f.751.1 | 2 | |||
15.14 | odd | 2 | 210.2.n.a.79.2 | yes | 4 | ||
21.2 | odd | 6 | 1470.2.g.f.589.2 | 2 | |||
21.5 | even | 6 | 1470.2.g.a.589.2 | 2 | |||
21.11 | odd | 6 | 210.2.n.a.109.2 | yes | 4 | ||
21.17 | even | 6 | 1470.2.n.i.949.2 | 4 | |||
21.20 | even | 2 | 1470.2.n.i.79.1 | 4 | |||
35.4 | even | 6 | inner | 630.2.u.c.109.2 | 4 | ||
60.59 | even | 2 | 1680.2.di.a.289.2 | 4 | |||
84.11 | even | 6 | 1680.2.di.a.529.2 | 4 | |||
105.2 | even | 12 | 7350.2.a.t.1.1 | 1 | |||
105.23 | even | 12 | 7350.2.a.bn.1.1 | 1 | |||
105.32 | even | 12 | 1050.2.i.o.151.1 | 2 | |||
105.44 | odd | 6 | 1470.2.g.f.589.1 | 2 | |||
105.47 | odd | 12 | 7350.2.a.b.1.1 | 1 | |||
105.53 | even | 12 | 1050.2.i.f.151.1 | 2 | |||
105.59 | even | 6 | 1470.2.n.i.949.1 | 4 | |||
105.68 | odd | 12 | 7350.2.a.ch.1.1 | 1 | |||
105.74 | odd | 6 | 210.2.n.a.109.1 | yes | 4 | ||
105.89 | even | 6 | 1470.2.g.a.589.1 | 2 | |||
105.104 | even | 2 | 1470.2.n.i.79.2 | 4 | |||
420.179 | even | 6 | 1680.2.di.a.529.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.n.a.79.1 | ✓ | 4 | 3.2 | odd | 2 | ||
210.2.n.a.79.2 | yes | 4 | 15.14 | odd | 2 | ||
210.2.n.a.109.1 | yes | 4 | 105.74 | odd | 6 | ||
210.2.n.a.109.2 | yes | 4 | 21.11 | odd | 6 | ||
630.2.u.c.109.1 | 4 | 7.4 | even | 3 | inner | ||
630.2.u.c.109.2 | 4 | 35.4 | even | 6 | inner | ||
630.2.u.c.289.1 | 4 | 5.4 | even | 2 | inner | ||
630.2.u.c.289.2 | 4 | 1.1 | even | 1 | trivial | ||
1050.2.i.f.151.1 | 2 | 105.53 | even | 12 | |||
1050.2.i.f.751.1 | 2 | 15.8 | even | 4 | |||
1050.2.i.o.151.1 | 2 | 105.32 | even | 12 | |||
1050.2.i.o.751.1 | 2 | 15.2 | even | 4 | |||
1470.2.g.a.589.1 | 2 | 105.89 | even | 6 | |||
1470.2.g.a.589.2 | 2 | 21.5 | even | 6 | |||
1470.2.g.f.589.1 | 2 | 105.44 | odd | 6 | |||
1470.2.g.f.589.2 | 2 | 21.2 | odd | 6 | |||
1470.2.n.i.79.1 | 4 | 21.20 | even | 2 | |||
1470.2.n.i.79.2 | 4 | 105.104 | even | 2 | |||
1470.2.n.i.949.1 | 4 | 105.59 | even | 6 | |||
1470.2.n.i.949.2 | 4 | 21.17 | even | 6 | |||
1680.2.di.a.289.1 | 4 | 12.11 | even | 2 | |||
1680.2.di.a.289.2 | 4 | 60.59 | even | 2 | |||
1680.2.di.a.529.1 | 4 | 420.179 | even | 6 | |||
1680.2.di.a.529.2 | 4 | 84.11 | even | 6 | |||
7350.2.a.b.1.1 | 1 | 105.47 | odd | 12 | |||
7350.2.a.t.1.1 | 1 | 105.2 | even | 12 | |||
7350.2.a.bn.1.1 | 1 | 105.23 | even | 12 | |||
7350.2.a.ch.1.1 | 1 | 105.68 | odd | 12 |