Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(221,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.i (of order \(3\), 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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 331.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.331 |
Dual form | 770.2.i.a.221.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | 0.684819 | − | 0.728714i | \(-0.259881\pi\) |
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.50000 | − | 0.866025i | 0.944911 | − | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | −0.500000 | + | 2.59808i | −0.133631 | + | 0.694365i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 1.00000 | + | 1.73205i | 0.235702 | + | 0.408248i | ||||
\(19\) | −1.00000 | + | 1.73205i | −0.229416 | + | 0.397360i | −0.957635 | − | 0.287984i | \(-0.907015\pi\) |
0.728219 | + | 0.685344i | \(0.240348\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −2.00000 | − | 1.73205i | −0.436436 | − | 0.377964i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 3.00000 | − | 5.19615i | 0.625543 | − | 1.08347i | −0.362892 | − | 0.931831i | \(-0.618211\pi\) |
0.988436 | − | 0.151642i | \(-0.0484560\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0.500000 | − | 0.866025i | 0.0980581 | − | 0.169842i | ||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | −2.00000 | − | 1.73205i | −0.377964 | − | 0.327327i | ||||
\(29\) | −9.00000 | −1.67126 | −0.835629 | − | 0.549294i | \(-0.814897\pi\) | ||||
−0.835629 | + | 0.549294i | \(0.814897\pi\) | |||||||
\(30\) | 0.500000 | − | 0.866025i | 0.0912871 | − | 0.158114i | ||||
\(31\) | 2.00000 | + | 3.46410i | 0.359211 | + | 0.622171i | 0.987829 | − | 0.155543i | \(-0.0497126\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −0.500000 | + | 0.866025i | −0.0870388 | + | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.500000 | − | 2.59808i | 0.0845154 | − | 0.439155i | ||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | 2.00000 | − | 3.46410i | 0.328798 | − | 0.569495i | −0.653476 | − | 0.756948i | \(-0.726690\pi\) |
0.982274 | + | 0.187453i | \(0.0600231\pi\) | |||||||
\(38\) | −1.00000 | − | 1.73205i | −0.162221 | − | 0.280976i | ||||
\(39\) | 0.500000 | + | 0.866025i | 0.0800641 | + | 0.138675i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | 12.0000 | 1.87409 | 0.937043 | − | 0.349215i | \(-0.113552\pi\) | ||||
0.937043 | + | 0.349215i | \(0.113552\pi\) | |||||||
\(42\) | 2.50000 | − | 0.866025i | 0.385758 | − | 0.133631i | ||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | −1.00000 | − | 1.73205i | −0.149071 | − | 0.258199i | ||||
\(46\) | 3.00000 | + | 5.19615i | 0.442326 | + | 0.766131i | ||||
\(47\) | 6.00000 | − | 10.3923i | 0.875190 | − | 1.51587i | 0.0186297 | − | 0.999826i | \(-0.494070\pi\) |
0.856560 | − | 0.516047i | \(-0.172597\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.500000 | + | 0.866025i | 0.0693375 | + | 0.120096i | ||||
\(53\) | −3.00000 | − | 5.19615i | −0.412082 | − | 0.713746i | 0.583036 | − | 0.812447i | \(-0.301865\pi\) |
−0.995117 | + | 0.0987002i | \(0.968532\pi\) | |||||||
\(54\) | 2.50000 | − | 4.33013i | 0.340207 | − | 0.589256i | ||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 2.50000 | − | 0.866025i | 0.334077 | − | 0.115728i | ||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | 4.50000 | − | 7.79423i | 0.590879 | − | 1.02343i | ||||
\(59\) | −1.50000 | − | 2.59808i | −0.195283 | − | 0.338241i | 0.751710 | − | 0.659494i | \(-0.229229\pi\) |
−0.946993 | + | 0.321253i | \(0.895896\pi\) | |||||||
\(60\) | 0.500000 | + | 0.866025i | 0.0645497 | + | 0.111803i | ||||
\(61\) | 3.50000 | − | 6.06218i | 0.448129 | − | 0.776182i | −0.550135 | − | 0.835076i | \(-0.685424\pi\) |
0.998264 | + | 0.0588933i | \(0.0187572\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 1.00000 | − | 5.19615i | 0.125988 | − | 0.654654i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.500000 | + | 0.866025i | −0.0620174 | + | 0.107417i | ||||
\(66\) | −0.500000 | − | 0.866025i | −0.0615457 | − | 0.106600i | ||||
\(67\) | 6.50000 | + | 11.2583i | 0.794101 | + | 1.37542i | 0.923408 | + | 0.383819i | \(0.125391\pi\) |
−0.129307 | + | 0.991605i | \(0.541275\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 2.00000 | + | 1.73205i | 0.239046 | + | 0.207020i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 1.00000 | − | 1.73205i | 0.117851 | − | 0.204124i | ||||
\(73\) | −7.00000 | − | 12.1244i | −0.819288 | − | 1.41905i | −0.906208 | − | 0.422833i | \(-0.861036\pi\) |
0.0869195 | − | 0.996215i | \(-0.472298\pi\) | |||||||
\(74\) | 2.00000 | + | 3.46410i | 0.232495 | + | 0.402694i | ||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | −2.00000 | − | 1.73205i | −0.227921 | − | 0.197386i | ||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −8.50000 | + | 14.7224i | −0.956325 | + | 1.65640i | −0.225018 | + | 0.974355i | \(0.572244\pi\) |
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −6.00000 | + | 10.3923i | −0.662589 | + | 1.14764i | ||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | −0.500000 | + | 2.59808i | −0.0545545 | + | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.00000 | − | 8.66025i | 0.539164 | − | 0.933859i | ||||
\(87\) | 4.50000 | + | 7.79423i | 0.482451 | + | 0.835629i | ||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | 2.00000 | 0.210819 | ||||||||
\(91\) | −2.50000 | + | 0.866025i | −0.262071 | + | 0.0907841i | ||||
\(92\) | −6.00000 | −0.625543 | ||||||||
\(93\) | 2.00000 | − | 3.46410i | 0.207390 | − | 0.359211i | ||||
\(94\) | 6.00000 | + | 10.3923i | 0.618853 | + | 1.07188i | ||||
\(95\) | 1.00000 | + | 1.73205i | 0.102598 | + | 0.177705i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 5.00000 | 0.507673 | 0.253837 | − | 0.967247i | \(-0.418307\pi\) | ||||
0.253837 | + | 0.967247i | \(0.418307\pi\) | |||||||
\(98\) | 1.00000 | + | 6.92820i | 0.101015 | + | 0.699854i | ||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 4.50000 | + | 7.79423i | 0.447767 | + | 0.775555i | 0.998240 | − | 0.0592978i | \(-0.0188862\pi\) |
−0.550474 | + | 0.834853i | \(0.685553\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | − | 3.46410i | 0.197066 | − | 0.341328i | −0.750510 | − | 0.660859i | \(-0.770192\pi\) |
0.947576 | + | 0.319531i | \(0.103525\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −2.50000 | + | 0.866025i | −0.243975 | + | 0.0845154i | ||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 3.00000 | − | 5.19615i | 0.290021 | − | 0.502331i | −0.683793 | − | 0.729676i | \(-0.739671\pi\) |
0.973814 | + | 0.227345i | \(0.0730044\pi\) | |||||||
\(108\) | 2.50000 | + | 4.33013i | 0.240563 | + | 0.416667i | ||||
\(109\) | 5.00000 | + | 8.66025i | 0.478913 | + | 0.829502i | 0.999708 | − | 0.0241802i | \(-0.00769755\pi\) |
−0.520794 | + | 0.853682i | \(0.674364\pi\) | |||||||
\(110\) | 0.500000 | − | 0.866025i | 0.0476731 | − | 0.0825723i | ||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | −0.500000 | + | 2.59808i | −0.0472456 | + | 0.245495i | ||||
\(113\) | −9.00000 | −0.846649 | −0.423324 | − | 0.905978i | \(-0.639137\pi\) | ||||
−0.423324 | + | 0.905978i | \(0.639137\pi\) | |||||||
\(114\) | −1.00000 | + | 1.73205i | −0.0936586 | + | 0.162221i | ||||
\(115\) | −3.00000 | − | 5.19615i | −0.279751 | − | 0.484544i | ||||
\(116\) | 4.50000 | + | 7.79423i | 0.417815 | + | 0.723676i | ||||
\(117\) | −1.00000 | + | 1.73205i | −0.0924500 | + | 0.160128i | ||||
\(118\) | 3.00000 | 0.276172 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 3.50000 | + | 6.06218i | 0.316875 | + | 0.548844i | ||||
\(123\) | −6.00000 | − | 10.3923i | −0.541002 | − | 0.937043i | ||||
\(124\) | 2.00000 | − | 3.46410i | 0.179605 | − | 0.311086i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 4.00000 | + | 3.46410i | 0.356348 | + | 0.308607i | ||||
\(127\) | −13.0000 | −1.15356 | −0.576782 | − | 0.816898i | \(-0.695692\pi\) | ||||
−0.576782 | + | 0.816898i | \(0.695692\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 5.00000 | + | 8.66025i | 0.440225 | + | 0.762493i | ||||
\(130\) | −0.500000 | − | 0.866025i | −0.0438529 | − | 0.0759555i | ||||
\(131\) | −9.00000 | + | 15.5885i | −0.786334 | + | 1.36197i | 0.141865 | + | 0.989886i | \(0.454690\pi\) |
−0.928199 | + | 0.372084i | \(0.878643\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | −1.00000 | + | 5.19615i | −0.0867110 | + | 0.450564i | ||||
\(134\) | −13.0000 | −1.12303 | ||||||||
\(135\) | −2.50000 | + | 4.33013i | −0.215166 | + | 0.372678i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.50000 | − | 7.79423i | −0.384461 | − | 0.665906i | 0.607233 | − | 0.794524i | \(-0.292279\pi\) |
−0.991694 | + | 0.128618i | \(0.958946\pi\) | |||||||
\(138\) | 3.00000 | − | 5.19615i | 0.255377 | − | 0.442326i | ||||
\(139\) | 20.0000 | 1.69638 | 0.848189 | − | 0.529694i | \(-0.177693\pi\) | ||||
0.848189 | + | 0.529694i | \(0.177693\pi\) | |||||||
\(140\) | −2.50000 | + | 0.866025i | −0.211289 | + | 0.0731925i | ||||
\(141\) | −12.0000 | −1.01058 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.500000 | + | 0.866025i | 0.0418121 | + | 0.0724207i | ||||
\(144\) | 1.00000 | + | 1.73205i | 0.0833333 | + | 0.144338i | ||||
\(145\) | −4.50000 | + | 7.79423i | −0.373705 | + | 0.647275i | ||||
\(146\) | 14.0000 | 1.15865 | ||||||||
\(147\) | −6.50000 | − | 2.59808i | −0.536111 | − | 0.214286i | ||||
\(148\) | −4.00000 | −0.328798 | ||||||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | 9.50000 | + | 16.4545i | 0.773099 | + | 1.33905i | 0.935857 | + | 0.352381i | \(0.114628\pi\) |
−0.162758 | + | 0.986666i | \(0.552039\pi\) | |||||||
\(152\) | −1.00000 | + | 1.73205i | −0.0811107 | + | 0.140488i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.50000 | − | 0.866025i | 0.201456 | − | 0.0697863i | ||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0.500000 | − | 0.866025i | 0.0400320 | − | 0.0693375i | ||||
\(157\) | 5.00000 | + | 8.66025i | 0.399043 | + | 0.691164i | 0.993608 | − | 0.112884i | \(-0.0360089\pi\) |
−0.594565 | + | 0.804048i | \(0.702676\pi\) | |||||||
\(158\) | −8.50000 | − | 14.7224i | −0.676224 | − | 1.17125i | ||||
\(159\) | −3.00000 | + | 5.19615i | −0.237915 | + | 0.412082i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 3.00000 | − | 15.5885i | 0.236433 | − | 1.22854i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −2.50000 | + | 4.33013i | −0.195815 | + | 0.339162i | −0.947167 | − | 0.320740i | \(-0.896069\pi\) |
0.751352 | + | 0.659901i | \(0.229402\pi\) | |||||||
\(164\) | −6.00000 | − | 10.3923i | −0.468521 | − | 0.811503i | ||||
\(165\) | 0.500000 | + | 0.866025i | 0.0389249 | + | 0.0674200i | ||||
\(166\) | −3.00000 | + | 5.19615i | −0.232845 | + | 0.403300i | ||||
\(167\) | −3.00000 | −0.232147 | −0.116073 | − | 0.993241i | \(-0.537031\pi\) | ||||
−0.116073 | + | 0.993241i | \(0.537031\pi\) | |||||||
\(168\) | −2.00000 | − | 1.73205i | −0.154303 | − | 0.133631i | ||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | + | 3.46410i | 0.152944 | + | 0.264906i | ||||
\(172\) | 5.00000 | + | 8.66025i | 0.381246 | + | 0.660338i | ||||
\(173\) | 10.5000 | − | 18.1865i | 0.798300 | − | 1.38270i | −0.122422 | − | 0.992478i | \(-0.539066\pi\) |
0.920722 | − | 0.390218i | \(-0.127601\pi\) | |||||||
\(174\) | −9.00000 | −0.682288 | ||||||||
\(175\) | −2.00000 | − | 1.73205i | −0.151186 | − | 0.130931i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −1.50000 | + | 2.59808i | −0.112747 | + | 0.195283i | ||||
\(178\) | 3.00000 | + | 5.19615i | 0.224860 | + | 0.389468i | ||||
\(179\) | 10.5000 | + | 18.1865i | 0.784807 | + | 1.35933i | 0.929114 | + | 0.369792i | \(0.120571\pi\) |
−0.144308 | + | 0.989533i | \(0.546095\pi\) | |||||||
\(180\) | −1.00000 | + | 1.73205i | −0.0745356 | + | 0.129099i | ||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | 0.500000 | − | 2.59808i | 0.0370625 | − | 0.192582i | ||||
\(183\) | −7.00000 | −0.517455 | ||||||||
\(184\) | 3.00000 | − | 5.19615i | 0.221163 | − | 0.383065i | ||||
\(185\) | −2.00000 | − | 3.46410i | −0.147043 | − | 0.254686i | ||||
\(186\) | 2.00000 | + | 3.46410i | 0.146647 | + | 0.254000i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −12.0000 | −0.875190 | ||||||||
\(189\) | −12.5000 | + | 4.33013i | −0.909241 | + | 0.314970i | ||||
\(190\) | −2.00000 | −0.145095 | ||||||||
\(191\) | −6.00000 | + | 10.3923i | −0.434145 | + | 0.751961i | −0.997225 | − | 0.0744412i | \(-0.976283\pi\) |
0.563081 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 2.00000 | + | 3.46410i | 0.143963 | + | 0.249351i | 0.928986 | − | 0.370116i | \(-0.120682\pi\) |
−0.785022 | + | 0.619467i | \(0.787349\pi\) | |||||||
\(194\) | −2.50000 | + | 4.33013i | −0.179490 | + | 0.310885i | ||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | 9.00000 | 0.641223 | 0.320612 | − | 0.947211i | \(-0.396112\pi\) | ||||
0.320612 | + | 0.947211i | \(0.396112\pi\) | |||||||
\(198\) | 1.00000 | − | 1.73205i | 0.0710669 | − | 0.123091i | ||||
\(199\) | 5.00000 | + | 8.66025i | 0.354441 | + | 0.613909i | 0.987022 | − | 0.160585i | \(-0.0513380\pi\) |
−0.632581 | + | 0.774494i | \(0.718005\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 6.50000 | − | 11.2583i | 0.458475 | − | 0.794101i | ||||
\(202\) | −9.00000 | −0.633238 | ||||||||
\(203\) | −22.5000 | + | 7.79423i | −1.57919 | + | 0.547048i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | − | 10.3923i | 0.419058 | − | 0.725830i | ||||
\(206\) | 2.00000 | + | 3.46410i | 0.139347 | + | 0.241355i | ||||
\(207\) | −6.00000 | − | 10.3923i | −0.417029 | − | 0.722315i | ||||
\(208\) | 0.500000 | − | 0.866025i | 0.0346688 | − | 0.0600481i | ||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0.500000 | − | 2.59808i | 0.0345033 | − | 0.179284i | ||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | −3.00000 | + | 5.19615i | −0.206041 | + | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.00000 | + | 5.19615i | 0.205076 | + | 0.355202i | ||||
\(215\) | −5.00000 | + | 8.66025i | −0.340997 | + | 0.590624i | ||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | 8.00000 | + | 6.92820i | 0.543075 | + | 0.470317i | ||||
\(218\) | −10.0000 | −0.677285 | ||||||||
\(219\) | −7.00000 | + | 12.1244i | −0.473016 | + | 0.819288i | ||||
\(220\) | 0.500000 | + | 0.866025i | 0.0337100 | + | 0.0583874i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.00000 | − | 3.46410i | 0.134231 | − | 0.232495i | ||||
\(223\) | 20.0000 | 1.33930 | 0.669650 | − | 0.742677i | \(-0.266444\pi\) | ||||
0.669650 | + | 0.742677i | \(0.266444\pi\) | |||||||
\(224\) | −2.00000 | − | 1.73205i | −0.133631 | − | 0.115728i | ||||
\(225\) | −2.00000 | −0.133333 | ||||||||
\(226\) | 4.50000 | − | 7.79423i | 0.299336 | − | 0.518464i | ||||
\(227\) | 6.00000 | + | 10.3923i | 0.398234 | + | 0.689761i | 0.993508 | − | 0.113761i | \(-0.0362899\pi\) |
−0.595274 | + | 0.803523i | \(0.702957\pi\) | |||||||
\(228\) | −1.00000 | − | 1.73205i | −0.0662266 | − | 0.114708i | ||||
\(229\) | 5.00000 | − | 8.66025i | 0.330409 | − | 0.572286i | −0.652183 | − | 0.758062i | \(-0.726147\pi\) |
0.982592 | + | 0.185776i | \(0.0594799\pi\) | |||||||
\(230\) | 6.00000 | 0.395628 | ||||||||
\(231\) | −0.500000 | + | 2.59808i | −0.0328976 | + | 0.170941i | ||||
\(232\) | −9.00000 | −0.590879 | ||||||||
\(233\) | 6.00000 | − | 10.3923i | 0.393073 | − | 0.680823i | −0.599780 | − | 0.800165i | \(-0.704745\pi\) |
0.992853 | + | 0.119342i | \(0.0380786\pi\) | |||||||
\(234\) | −1.00000 | − | 1.73205i | −0.0653720 | − | 0.113228i | ||||
\(235\) | −6.00000 | − | 10.3923i | −0.391397 | − | 0.677919i | ||||
\(236\) | −1.50000 | + | 2.59808i | −0.0976417 | + | 0.169120i | ||||
\(237\) | 17.0000 | 1.10427 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.00000 | 0.194054 | 0.0970269 | − | 0.995282i | \(-0.469067\pi\) | ||||
0.0970269 | + | 0.995282i | \(0.469067\pi\) | |||||||
\(240\) | 0.500000 | − | 0.866025i | 0.0322749 | − | 0.0559017i | ||||
\(241\) | 5.00000 | + | 8.66025i | 0.322078 | + | 0.557856i | 0.980917 | − | 0.194429i | \(-0.0622852\pi\) |
−0.658838 | + | 0.752285i | \(0.728952\pi\) | |||||||
\(242\) | −0.500000 | − | 0.866025i | −0.0321412 | − | 0.0556702i | ||||
\(243\) | −8.00000 | + | 13.8564i | −0.513200 | + | 0.888889i | ||||
\(244\) | −7.00000 | −0.448129 | ||||||||
\(245\) | −1.00000 | − | 6.92820i | −0.0638877 | − | 0.442627i | ||||
\(246\) | 12.0000 | 0.765092 | ||||||||
\(247\) | 1.00000 | − | 1.73205i | 0.0636285 | − | 0.110208i | ||||
\(248\) | 2.00000 | + | 3.46410i | 0.127000 | + | 0.219971i | ||||
\(249\) | −3.00000 | − | 5.19615i | −0.190117 | − | 0.329293i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | −5.00000 | + | 1.73205i | −0.314970 | + | 0.109109i | ||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 6.50000 | − | 11.2583i | 0.407846 | − | 0.706410i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −4.50000 | + | 7.79423i | −0.280702 | + | 0.486191i | −0.971558 | − | 0.236802i | \(-0.923901\pi\) |
0.690856 | + | 0.722993i | \(0.257234\pi\) | |||||||
\(258\) | −10.0000 | −0.622573 | ||||||||
\(259\) | 2.00000 | − | 10.3923i | 0.124274 | − | 0.645746i | ||||
\(260\) | 1.00000 | 0.0620174 | ||||||||
\(261\) | −9.00000 | + | 15.5885i | −0.557086 | + | 0.964901i | ||||
\(262\) | −9.00000 | − | 15.5885i | −0.556022 | − | 0.963058i | ||||
\(263\) | −4.50000 | − | 7.79423i | −0.277482 | − | 0.480613i | 0.693276 | − | 0.720672i | \(-0.256167\pi\) |
−0.970758 | + | 0.240059i | \(0.922833\pi\) | |||||||
\(264\) | −0.500000 | + | 0.866025i | −0.0307729 | + | 0.0533002i | ||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | −4.00000 | − | 3.46410i | −0.245256 | − | 0.212398i | ||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 6.50000 | − | 11.2583i | 0.397051 | − | 0.687712i | ||||
\(269\) | −3.00000 | − | 5.19615i | −0.182913 | − | 0.316815i | 0.759958 | − | 0.649972i | \(-0.225219\pi\) |
−0.942871 | + | 0.333157i | \(0.891886\pi\) | |||||||
\(270\) | −2.50000 | − | 4.33013i | −0.152145 | − | 0.263523i | ||||
\(271\) | −14.5000 | + | 25.1147i | −0.880812 | + | 1.52561i | −0.0303728 | + | 0.999539i | \(0.509669\pi\) |
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.00000 | + | 1.73205i | 0.121046 | + | 0.104828i | ||||
\(274\) | 9.00000 | 0.543710 | ||||||||
\(275\) | −0.500000 | + | 0.866025i | −0.0301511 | + | 0.0522233i | ||||
\(276\) | 3.00000 | + | 5.19615i | 0.180579 | + | 0.312772i | ||||
\(277\) | 9.50000 | + | 16.4545i | 0.570800 | + | 0.988654i | 0.996484 | + | 0.0837823i | \(0.0267000\pi\) |
−0.425684 | + | 0.904872i | \(0.639967\pi\) | |||||||
\(278\) | −10.0000 | + | 17.3205i | −0.599760 | + | 1.03882i | ||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | 0.500000 | − | 2.59808i | 0.0298807 | − | 0.155265i | ||||
\(281\) | 24.0000 | 1.43172 | 0.715860 | − | 0.698244i | \(-0.246035\pi\) | ||||
0.715860 | + | 0.698244i | \(0.246035\pi\) | |||||||
\(282\) | 6.00000 | − | 10.3923i | 0.357295 | − | 0.618853i | ||||
\(283\) | 11.0000 | + | 19.0526i | 0.653882 | + | 1.13256i | 0.982173 | + | 0.187980i | \(0.0601941\pi\) |
−0.328291 | + | 0.944577i | \(0.606473\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00000 | − | 1.73205i | 0.0592349 | − | 0.102598i | ||||
\(286\) | −1.00000 | −0.0591312 | ||||||||
\(287\) | 30.0000 | − | 10.3923i | 1.77084 | − | 0.613438i | ||||
\(288\) | −2.00000 | −0.117851 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | −4.50000 | − | 7.79423i | −0.264249 | − | 0.457693i | ||||
\(291\) | −2.50000 | − | 4.33013i | −0.146553 | − | 0.253837i | ||||
\(292\) | −7.00000 | + | 12.1244i | −0.409644 | + | 0.709524i | ||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 5.50000 | − | 4.33013i | 0.320767 | − | 0.252538i | ||||
\(295\) | −3.00000 | −0.174667 | ||||||||
\(296\) | 2.00000 | − | 3.46410i | 0.116248 | − | 0.201347i | ||||
\(297\) | 2.50000 | + | 4.33013i | 0.145065 | + | 0.251259i | ||||
\(298\) | 3.00000 | + | 5.19615i | 0.173785 | + | 0.301005i | ||||
\(299\) | −3.00000 | + | 5.19615i | −0.173494 | + | 0.300501i | ||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −25.0000 | + | 8.66025i | −1.44098 | + | 0.499169i | ||||
\(302\) | −19.0000 | −1.09333 | ||||||||
\(303\) | 4.50000 | − | 7.79423i | 0.258518 | − | 0.447767i | ||||
\(304\) | −1.00000 | − | 1.73205i | −0.0573539 | − | 0.0993399i | ||||
\(305\) | −3.50000 | − | 6.06218i | −0.200409 | − | 0.347119i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.00000 | 0.114146 | 0.0570730 | − | 0.998370i | \(-0.481823\pi\) | ||||
0.0570730 | + | 0.998370i | \(0.481823\pi\) | |||||||
\(308\) | −0.500000 | + | 2.59808i | −0.0284901 | + | 0.148039i | ||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | −2.00000 | + | 3.46410i | −0.113592 | + | 0.196748i | ||||
\(311\) | −12.0000 | − | 20.7846i | −0.680458 | − | 1.17859i | −0.974841 | − | 0.222900i | \(-0.928448\pi\) |
0.294384 | − | 0.955687i | \(-0.404886\pi\) | |||||||
\(312\) | 0.500000 | + | 0.866025i | 0.0283069 | + | 0.0490290i | ||||
\(313\) | 0.500000 | − | 0.866025i | 0.0282617 | − | 0.0489506i | −0.851549 | − | 0.524276i | \(-0.824336\pi\) |
0.879810 | + | 0.475325i | \(0.157669\pi\) | |||||||
\(314\) | −10.0000 | −0.564333 | ||||||||
\(315\) | −4.00000 | − | 3.46410i | −0.225374 | − | 0.195180i | ||||
\(316\) | 17.0000 | 0.956325 | ||||||||
\(317\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(318\) | −3.00000 | − | 5.19615i | −0.168232 | − | 0.291386i | ||||
\(319\) | 4.50000 | + | 7.79423i | 0.251952 | + | 0.436393i | ||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | −6.00000 | −0.334887 | ||||||||
\(322\) | 12.0000 | + | 10.3923i | 0.668734 | + | 0.579141i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 0.500000 | + | 0.866025i | 0.0277350 | + | 0.0480384i | ||||
\(326\) | −2.50000 | − | 4.33013i | −0.138462 | − | 0.239824i | ||||
\(327\) | 5.00000 | − | 8.66025i | 0.276501 | − | 0.478913i | ||||
\(328\) | 12.0000 | 0.662589 | ||||||||
\(329\) | 6.00000 | − | 31.1769i | 0.330791 | − | 1.71884i | ||||
\(330\) | −1.00000 | −0.0550482 | ||||||||
\(331\) | 3.50000 | − | 6.06218i | 0.192377 | − | 0.333207i | −0.753660 | − | 0.657264i | \(-0.771714\pi\) |
0.946038 | + | 0.324057i | \(0.105047\pi\) | |||||||
\(332\) | −3.00000 | − | 5.19615i | −0.164646 | − | 0.285176i | ||||
\(333\) | −4.00000 | − | 6.92820i | −0.219199 | − | 0.379663i | ||||
\(334\) | 1.50000 | − | 2.59808i | 0.0820763 | − | 0.142160i | ||||
\(335\) | 13.0000 | 0.710266 | ||||||||
\(336\) | 2.50000 | − | 0.866025i | 0.136386 | − | 0.0472456i | ||||
\(337\) | 32.0000 | 1.74315 | 0.871576 | − | 0.490261i | \(-0.163099\pi\) | ||||
0.871576 | + | 0.490261i | \(0.163099\pi\) | |||||||
\(338\) | 6.00000 | − | 10.3923i | 0.326357 | − | 0.565267i | ||||
\(339\) | 4.50000 | + | 7.79423i | 0.244406 | + | 0.423324i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | − | 3.46410i | 0.108306 | − | 0.187592i | ||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | −10.0000 | −0.539164 | ||||||||
\(345\) | −3.00000 | + | 5.19615i | −0.161515 | + | 0.279751i | ||||
\(346\) | 10.5000 | + | 18.1865i | 0.564483 | + | 0.977714i | ||||
\(347\) | −9.00000 | − | 15.5885i | −0.483145 | − | 0.836832i | 0.516667 | − | 0.856186i | \(-0.327172\pi\) |
−0.999813 | + | 0.0193540i | \(0.993839\pi\) | |||||||
\(348\) | 4.50000 | − | 7.79423i | 0.241225 | − | 0.417815i | ||||
\(349\) | 26.0000 | 1.39175 | 0.695874 | − | 0.718164i | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(350\) | 2.50000 | − | 0.866025i | 0.133631 | − | 0.0462910i | ||||
\(351\) | 5.00000 | 0.266880 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | 3.00000 | + | 5.19615i | 0.159674 | + | 0.276563i | 0.934751 | − | 0.355303i | \(-0.115622\pi\) |
−0.775077 | + | 0.631867i | \(0.782289\pi\) | |||||||
\(354\) | −1.50000 | − | 2.59808i | −0.0797241 | − | 0.138086i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.0000 | −1.10988 | ||||||||
\(359\) | 13.5000 | − | 23.3827i | 0.712503 | − | 1.23409i | −0.251412 | − | 0.967880i | \(-0.580895\pi\) |
0.963915 | − | 0.266211i | \(-0.0857717\pi\) | |||||||
\(360\) | −1.00000 | − | 1.73205i | −0.0527046 | − | 0.0912871i | ||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | 8.00000 | − | 13.8564i | 0.420471 | − | 0.728277i | ||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 2.00000 | + | 1.73205i | 0.104828 | + | 0.0907841i | ||||
\(365\) | −14.0000 | −0.732793 | ||||||||
\(366\) | 3.50000 | − | 6.06218i | 0.182948 | − | 0.316875i | ||||
\(367\) | 14.0000 | + | 24.2487i | 0.730794 | + | 1.26577i | 0.956544 | + | 0.291587i | \(0.0941834\pi\) |
−0.225750 | + | 0.974185i | \(0.572483\pi\) | |||||||
\(368\) | 3.00000 | + | 5.19615i | 0.156386 | + | 0.270868i | ||||
\(369\) | 12.0000 | − | 20.7846i | 0.624695 | − | 1.08200i | ||||
\(370\) | 4.00000 | 0.207950 | ||||||||
\(371\) | −12.0000 | − | 10.3923i | −0.623009 | − | 0.539542i | ||||
\(372\) | −4.00000 | −0.207390 | ||||||||
\(373\) | −14.5000 | + | 25.1147i | −0.750782 | + | 1.30039i | 0.196663 | + | 0.980471i | \(0.436990\pi\) |
−0.947444 | + | 0.319921i | \(0.896344\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | 6.00000 | − | 10.3923i | 0.309426 | − | 0.535942i | ||||
\(377\) | 9.00000 | 0.463524 | ||||||||
\(378\) | 2.50000 | − | 12.9904i | 0.128586 | − | 0.668153i | ||||
\(379\) | 5.00000 | 0.256833 | 0.128416 | − | 0.991720i | \(-0.459011\pi\) | ||||
0.128416 | + | 0.991720i | \(0.459011\pi\) | |||||||
\(380\) | 1.00000 | − | 1.73205i | 0.0512989 | − | 0.0888523i | ||||
\(381\) | 6.50000 | + | 11.2583i | 0.333005 | + | 0.576782i | ||||
\(382\) | −6.00000 | − | 10.3923i | −0.306987 | − | 0.531717i | ||||
\(383\) | −18.0000 | + | 31.1769i | −0.919757 | + | 1.59307i | −0.119974 | + | 0.992777i | \(0.538281\pi\) |
−0.799783 | + | 0.600289i | \(0.795052\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −2.50000 | + | 0.866025i | −0.127412 | + | 0.0441367i | ||||
\(386\) | −4.00000 | −0.203595 | ||||||||
\(387\) | −10.0000 | + | 17.3205i | −0.508329 | + | 0.880451i | ||||
\(388\) | −2.50000 | − | 4.33013i | −0.126918 | − | 0.219829i | ||||
\(389\) | −6.00000 | − | 10.3923i | −0.304212 | − | 0.526911i | 0.672874 | − | 0.739758i | \(-0.265060\pi\) |
−0.977086 | + | 0.212847i | \(0.931726\pi\) | |||||||
\(390\) | −0.500000 | + | 0.866025i | −0.0253185 | + | 0.0438529i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 5.50000 | − | 4.33013i | 0.277792 | − | 0.218704i | ||||
\(393\) | 18.0000 | 0.907980 | ||||||||
\(394\) | −4.50000 | + | 7.79423i | −0.226707 | + | 0.392668i | ||||
\(395\) | 8.50000 | + | 14.7224i | 0.427681 | + | 0.740766i | ||||
\(396\) | 1.00000 | + | 1.73205i | 0.0502519 | + | 0.0870388i | ||||
\(397\) | −1.00000 | + | 1.73205i | −0.0501886 | + | 0.0869291i | −0.890028 | − | 0.455905i | \(-0.849316\pi\) |
0.839840 | + | 0.542834i | \(0.182649\pi\) | |||||||
\(398\) | −10.0000 | −0.501255 | ||||||||
\(399\) | 5.00000 | − | 1.73205i | 0.250313 | − | 0.0867110i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −7.50000 | + | 12.9904i | −0.374532 | + | 0.648709i | −0.990257 | − | 0.139253i | \(-0.955530\pi\) |
0.615725 | + | 0.787961i | \(0.288863\pi\) | |||||||
\(402\) | 6.50000 | + | 11.2583i | 0.324191 | + | 0.561514i | ||||
\(403\) | −2.00000 | − | 3.46410i | −0.0996271 | − | 0.172559i | ||||
\(404\) | 4.50000 | − | 7.79423i | 0.223883 | − | 0.387777i | ||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 4.50000 | − | 23.3827i | 0.223331 | − | 1.16046i | ||||
\(407\) | −4.00000 | −0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0000 | − | 17.3205i | −0.494468 | − | 0.856444i | 0.505511 | − | 0.862820i | \(-0.331304\pi\) |
−0.999980 | + | 0.00637586i | \(0.997970\pi\) | |||||||
\(410\) | 6.00000 | + | 10.3923i | 0.296319 | + | 0.513239i | ||||
\(411\) | −4.50000 | + | 7.79423i | −0.221969 | + | 0.384461i | ||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | −6.00000 | − | 5.19615i | −0.295241 | − | 0.255686i | ||||
\(414\) | 12.0000 | 0.589768 | ||||||||
\(415\) | 3.00000 | − | 5.19615i | 0.147264 | − | 0.255069i | ||||
\(416\) | 0.500000 | + | 0.866025i | 0.0245145 | + | 0.0424604i | ||||
\(417\) | −10.0000 | − | 17.3205i | −0.489702 | − | 0.848189i | ||||
\(418\) | −1.00000 | + | 1.73205i | −0.0489116 | + | 0.0847174i | ||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 2.00000 | + | 1.73205i | 0.0975900 | + | 0.0845154i | ||||
\(421\) | 32.0000 | 1.55958 | 0.779792 | − | 0.626038i | \(-0.215325\pi\) | ||||
0.779792 | + | 0.626038i | \(0.215325\pi\) | |||||||
\(422\) | 8.00000 | − | 13.8564i | 0.389434 | − | 0.674519i | ||||
\(423\) | −12.0000 | − | 20.7846i | −0.583460 | − | 1.01058i | ||||
\(424\) | −3.00000 | − | 5.19615i | −0.145693 | − | 0.252347i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.50000 | − | 18.1865i | 0.169377 | − | 0.880108i | ||||
\(428\) | −6.00000 | −0.290021 | ||||||||
\(429\) | 0.500000 | − | 0.866025i | 0.0241402 | − | 0.0418121i | ||||
\(430\) | −5.00000 | − | 8.66025i | −0.241121 | − | 0.417635i | ||||
\(431\) | 7.50000 | + | 12.9904i | 0.361262 | + | 0.625725i | 0.988169 | − | 0.153370i | \(-0.0490126\pi\) |
−0.626907 | + | 0.779094i | \(0.715679\pi\) | |||||||
\(432\) | 2.50000 | − | 4.33013i | 0.120281 | − | 0.208333i | ||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | −10.0000 | + | 3.46410i | −0.480015 | + | 0.166282i | ||||
\(435\) | 9.00000 | 0.431517 | ||||||||
\(436\) | 5.00000 | − | 8.66025i | 0.239457 | − | 0.414751i | ||||
\(437\) | 6.00000 | + | 10.3923i | 0.287019 | + | 0.497131i | ||||
\(438\) | −7.00000 | − | 12.1244i | −0.334473 | − | 0.579324i | ||||
\(439\) | 6.50000 | − | 11.2583i | 0.310228 | − | 0.537331i | −0.668184 | − | 0.743996i | \(-0.732928\pi\) |
0.978412 | + | 0.206666i | \(0.0662612\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | −2.00000 | − | 13.8564i | −0.0952381 | − | 0.659829i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0000 | − | 20.7846i | 0.570137 | − | 0.987507i | −0.426414 | − | 0.904528i | \(-0.640223\pi\) |
0.996551 | − | 0.0829786i | \(-0.0264433\pi\) | |||||||
\(444\) | 2.00000 | + | 3.46410i | 0.0949158 | + | 0.164399i | ||||
\(445\) | −3.00000 | − | 5.19615i | −0.142214 | − | 0.246321i | ||||
\(446\) | −10.0000 | + | 17.3205i | −0.473514 | + | 0.820150i | ||||
\(447\) | −6.00000 | −0.283790 | ||||||||
\(448\) | 2.50000 | − | 0.866025i | 0.118114 | − | 0.0409159i | ||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 1.00000 | − | 1.73205i | 0.0471405 | − | 0.0816497i | ||||
\(451\) | −6.00000 | − | 10.3923i | −0.282529 | − | 0.489355i | ||||
\(452\) | 4.50000 | + | 7.79423i | 0.211662 | + | 0.366610i | ||||
\(453\) | 9.50000 | − | 16.4545i | 0.446349 | − | 0.773099i | ||||
\(454\) | −12.0000 | −0.563188 | ||||||||
\(455\) | −0.500000 | + | 2.59808i | −0.0234404 | + | 0.121800i | ||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | 2.00000 | − | 3.46410i | 0.0935561 | − | 0.162044i | −0.815449 | − | 0.578829i | \(-0.803510\pi\) |
0.909005 | + | 0.416785i | \(0.136843\pi\) | |||||||
\(458\) | 5.00000 | + | 8.66025i | 0.233635 | + | 0.404667i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.00000 | + | 5.19615i | −0.139876 | + | 0.242272i | ||||
\(461\) | 15.0000 | 0.698620 | 0.349310 | − | 0.937007i | \(-0.386416\pi\) | ||||
0.349310 | + | 0.937007i | \(0.386416\pi\) | |||||||
\(462\) | −2.00000 | − | 1.73205i | −0.0930484 | − | 0.0805823i | ||||
\(463\) | 20.0000 | 0.929479 | 0.464739 | − | 0.885448i | \(-0.346148\pi\) | ||||
0.464739 | + | 0.885448i | \(0.346148\pi\) | |||||||
\(464\) | 4.50000 | − | 7.79423i | 0.208907 | − | 0.361838i | ||||
\(465\) | −2.00000 | − | 3.46410i | −0.0927478 | − | 0.160644i | ||||
\(466\) | 6.00000 | + | 10.3923i | 0.277945 | + | 0.481414i | ||||
\(467\) | −6.00000 | + | 10.3923i | −0.277647 | + | 0.480899i | −0.970799 | − | 0.239892i | \(-0.922888\pi\) |
0.693153 | + | 0.720791i | \(0.256221\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | 26.0000 | + | 22.5167i | 1.20057 | + | 1.03972i | ||||
\(470\) | 12.0000 | 0.553519 | ||||||||
\(471\) | 5.00000 | − | 8.66025i | 0.230388 | − | 0.399043i | ||||
\(472\) | −1.50000 | − | 2.59808i | −0.0690431 | − | 0.119586i | ||||
\(473\) | 5.00000 | + | 8.66025i | 0.229900 | + | 0.398199i | ||||
\(474\) | −8.50000 | + | 14.7224i | −0.390418 | + | 0.676224i | ||||
\(475\) | 2.00000 | 0.0917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.0000 | −0.549442 | ||||||||
\(478\) | −1.50000 | + | 2.59808i | −0.0686084 | + | 0.118833i | ||||
\(479\) | 10.5000 | + | 18.1865i | 0.479757 | + | 0.830964i | 0.999730 | − | 0.0232187i | \(-0.00739140\pi\) |
−0.519973 | + | 0.854183i | \(0.674058\pi\) | |||||||
\(480\) | 0.500000 | + | 0.866025i | 0.0228218 | + | 0.0395285i | ||||
\(481\) | −2.00000 | + | 3.46410i | −0.0911922 | + | 0.157949i | ||||
\(482\) | −10.0000 | −0.455488 | ||||||||
\(483\) | −15.0000 | + | 5.19615i | −0.682524 | + | 0.236433i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 2.50000 | − | 4.33013i | 0.113519 | − | 0.196621i | ||||
\(486\) | −8.00000 | − | 13.8564i | −0.362887 | − | 0.628539i | ||||
\(487\) | −1.00000 | − | 1.73205i | −0.0453143 | − | 0.0784867i | 0.842479 | − | 0.538730i | \(-0.181096\pi\) |
−0.887793 | + | 0.460243i | \(0.847762\pi\) | |||||||
\(488\) | 3.50000 | − | 6.06218i | 0.158438 | − | 0.274422i | ||||
\(489\) | 5.00000 | 0.226108 | ||||||||
\(490\) | 6.50000 | + | 2.59808i | 0.293640 | + | 0.117369i | ||||
\(491\) | −24.0000 | −1.08310 | −0.541552 | − | 0.840667i | \(-0.682163\pi\) | ||||
−0.541552 | + | 0.840667i | \(0.682163\pi\) | |||||||
\(492\) | −6.00000 | + | 10.3923i | −0.270501 | + | 0.468521i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 1.00000 | + | 1.73205i | 0.0449921 | + | 0.0779287i | ||||
\(495\) | −1.00000 | + | 1.73205i | −0.0449467 | + | 0.0778499i | ||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.00000 | 0.268866 | ||||||||
\(499\) | −10.0000 | + | 17.3205i | −0.447661 | + | 0.775372i | −0.998233 | − | 0.0594153i | \(-0.981076\pi\) |
0.550572 | + | 0.834788i | \(0.314410\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | 1.50000 | + | 2.59808i | 0.0670151 | + | 0.116073i | ||||
\(502\) | −6.00000 | + | 10.3923i | −0.267793 | + | 0.463831i | ||||
\(503\) | −3.00000 | −0.133763 | −0.0668817 | − | 0.997761i | \(-0.521305\pi\) | ||||
−0.0668817 | + | 0.997761i | \(0.521305\pi\) | |||||||
\(504\) | 1.00000 | − | 5.19615i | 0.0445435 | − | 0.231455i | ||||
\(505\) | 9.00000 | 0.400495 | ||||||||
\(506\) | 3.00000 | − | 5.19615i | 0.133366 | − | 0.230997i | ||||
\(507\) | 6.00000 | + | 10.3923i | 0.266469 | + | 0.461538i | ||||
\(508\) | 6.50000 | + | 11.2583i | 0.288391 | + | 0.499508i | ||||
\(509\) | 3.00000 | − | 5.19615i | 0.132973 | − | 0.230315i | −0.791849 | − | 0.610718i | \(-0.790881\pi\) |
0.924821 | + | 0.380402i | \(0.124214\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.0000 | − | 24.2487i | −1.23865 | − | 1.07270i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.00000 | − | 8.66025i | 0.220755 | − | 0.382360i | ||||
\(514\) | −4.50000 | − | 7.79423i | −0.198486 | − | 0.343789i | ||||
\(515\) | −2.00000 | − | 3.46410i | −0.0881305 | − | 0.152647i | ||||
\(516\) | 5.00000 | − | 8.66025i | 0.220113 | − | 0.381246i | ||||
\(517\) | −12.0000 | −0.527759 | ||||||||
\(518\) | 8.00000 | + | 6.92820i | 0.351500 | + | 0.304408i | ||||
\(519\) | −21.0000 | −0.921798 | ||||||||
\(520\) | −0.500000 | + | 0.866025i | −0.0219265 | + | 0.0379777i | ||||
\(521\) | −3.00000 | − | 5.19615i | −0.131432 | − | 0.227648i | 0.792797 | − | 0.609486i | \(-0.208624\pi\) |
−0.924229 | + | 0.381839i | \(0.875291\pi\) | |||||||
\(522\) | −9.00000 | − | 15.5885i | −0.393919 | − | 0.682288i | ||||
\(523\) | −1.00000 | + | 1.73205i | −0.0437269 | + | 0.0757373i | −0.887061 | − | 0.461653i | \(-0.847256\pi\) |
0.843334 | + | 0.537390i | \(0.180590\pi\) | |||||||
\(524\) | 18.0000 | 0.786334 | ||||||||
\(525\) | −0.500000 | + | 2.59808i | −0.0218218 | + | 0.113389i | ||||
\(526\) | 9.00000 | 0.392419 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.500000 | − | 0.866025i | −0.0217597 | − | 0.0376889i | ||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 3.00000 | − | 5.19615i | 0.130312 | − | 0.225706i | ||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | 5.00000 | − | 1.73205i | 0.216777 | − | 0.0750939i | ||||
\(533\) | −12.0000 | −0.519778 | ||||||||
\(534\) | 3.00000 | − | 5.19615i | 0.129823 | − | 0.224860i | ||||
\(535\) | −3.00000 | − | 5.19615i | −0.129701 | − | 0.224649i | ||||
\(536\) | 6.50000 | + | 11.2583i | 0.280757 | + | 0.486286i | ||||
\(537\) | 10.5000 | − | 18.1865i | 0.453108 | − | 0.784807i | ||||
\(538\) | 6.00000 | 0.258678 | ||||||||
\(539\) | −6.50000 | − | 2.59808i | −0.279975 | − | 0.111907i | ||||
\(540\) | 5.00000 | 0.215166 | ||||||||
\(541\) | −2.50000 | + | 4.33013i | −0.107483 | + | 0.186167i | −0.914750 | − | 0.404020i | \(-0.867613\pi\) |
0.807267 | + | 0.590187i | \(0.200946\pi\) | |||||||
\(542\) | −14.5000 | − | 25.1147i | −0.622828 | − | 1.07877i | ||||
\(543\) | 8.00000 | + | 13.8564i | 0.343313 | + | 0.594635i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.0000 | 0.428353 | ||||||||
\(546\) | −2.50000 | + | 0.866025i | −0.106990 | + | 0.0370625i | ||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | −4.50000 | + | 7.79423i | −0.192230 | + | 0.332953i | ||||
\(549\) | −7.00000 | − | 12.1244i | −0.298753 | − | 0.517455i | ||||
\(550\) | −0.500000 | − | 0.866025i | −0.0213201 | − | 0.0369274i | ||||
\(551\) | 9.00000 | − | 15.5885i | 0.383413 | − | 0.664091i | ||||
\(552\) | −6.00000 | −0.255377 | ||||||||
\(553\) | −8.50000 | + | 44.1673i | −0.361457 | + | 1.87818i | ||||
\(554\) | −19.0000 | −0.807233 | ||||||||
\(555\) | −2.00000 | + | 3.46410i | −0.0848953 | + | 0.147043i | ||||
\(556\) | −10.0000 | − | 17.3205i | −0.424094 | − | 0.734553i | ||||
\(557\) | −9.00000 | − | 15.5885i | −0.381342 | − | 0.660504i | 0.609912 | − | 0.792469i | \(-0.291205\pi\) |
−0.991254 | + | 0.131965i | \(0.957871\pi\) | |||||||
\(558\) | −4.00000 | + | 6.92820i | −0.169334 | + | 0.293294i | ||||
\(559\) | 10.0000 | 0.422955 | ||||||||
\(560\) | 2.00000 | + | 1.73205i | 0.0845154 | + | 0.0731925i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.0000 | + | 20.7846i | −0.506189 | + | 0.876746i | ||||
\(563\) | −3.00000 | − | 5.19615i | −0.126435 | − | 0.218992i | 0.795858 | − | 0.605483i | \(-0.207020\pi\) |
−0.922293 | + | 0.386492i | \(0.873687\pi\) | |||||||
\(564\) | 6.00000 | + | 10.3923i | 0.252646 | + | 0.437595i | ||||
\(565\) | −4.50000 | + | 7.79423i | −0.189316 | + | 0.327906i | ||||
\(566\) | −22.0000 | −0.924729 | ||||||||
\(567\) | −2.00000 | − | 1.73205i | −0.0839921 | − | 0.0727393i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.0000 | + | 36.3731i | −0.880366 | + | 1.52484i | −0.0294311 | + | 0.999567i | \(0.509370\pi\) |
−0.850935 | + | 0.525271i | \(0.823964\pi\) | |||||||
\(570\) | 1.00000 | + | 1.73205i | 0.0418854 | + | 0.0725476i | ||||
\(571\) | −10.0000 | − | 17.3205i | −0.418487 | − | 0.724841i | 0.577301 | − | 0.816532i | \(-0.304106\pi\) |
−0.995788 | + | 0.0916910i | \(0.970773\pi\) | |||||||
\(572\) | 0.500000 | − | 0.866025i | 0.0209061 | − | 0.0362103i | ||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | −6.00000 | + | 31.1769i | −0.250435 | + | 1.30130i | ||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | 1.00000 | − | 1.73205i | 0.0416667 | − | 0.0721688i | ||||
\(577\) | −5.50000 | − | 9.52628i | −0.228968 | − | 0.396584i | 0.728535 | − | 0.685009i | \(-0.240202\pi\) |
−0.957503 | + | 0.288425i | \(0.906868\pi\) | |||||||
\(578\) | 8.50000 | + | 14.7224i | 0.353553 | + | 0.612372i | ||||
\(579\) | 2.00000 | − | 3.46410i | 0.0831172 | − | 0.143963i | ||||
\(580\) | 9.00000 | 0.373705 | ||||||||
\(581\) | 15.0000 | − | 5.19615i | 0.622305 | − | 0.215573i | ||||
\(582\) | 5.00000 | 0.207257 | ||||||||
\(583\) | −3.00000 | + | 5.19615i | −0.124247 | + | 0.215203i | ||||
\(584\) | −7.00000 | − | 12.1244i | −0.289662 | − | 0.501709i | ||||
\(585\) | 1.00000 | + | 1.73205i | 0.0413449 | + | 0.0716115i | ||||
\(586\) | −3.00000 | + | 5.19615i | −0.123929 | + | 0.214651i | ||||
\(587\) | −15.0000 | −0.619116 | −0.309558 | − | 0.950881i | \(-0.600181\pi\) | ||||
−0.309558 | + | 0.950881i | \(0.600181\pi\) | |||||||
\(588\) | 1.00000 | + | 6.92820i | 0.0412393 | + | 0.285714i | ||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 1.50000 | − | 2.59808i | 0.0617540 | − | 0.106961i | ||||
\(591\) | −4.50000 | − | 7.79423i | −0.185105 | − | 0.320612i | ||||
\(592\) | 2.00000 | + | 3.46410i | 0.0821995 | + | 0.142374i | ||||
\(593\) | −21.0000 | + | 36.3731i | −0.862367 | + | 1.49366i | 0.00727173 | + | 0.999974i | \(0.497685\pi\) |
−0.869638 | + | 0.493689i | \(0.835648\pi\) | |||||||
\(594\) | −5.00000 | −0.205152 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 5.00000 | − | 8.66025i | 0.204636 | − | 0.354441i | ||||
\(598\) | −3.00000 | − | 5.19615i | −0.122679 | − | 0.212486i | ||||
\(599\) | −12.0000 | − | 20.7846i | −0.490307 | − | 0.849236i | 0.509631 | − | 0.860393i | \(-0.329782\pi\) |
−0.999938 | + | 0.0111569i | \(0.996449\pi\) | |||||||
\(600\) | −0.500000 | + | 0.866025i | −0.0204124 | + | 0.0353553i | ||||
\(601\) | −28.0000 | −1.14214 | −0.571072 | − | 0.820900i | \(-0.693472\pi\) | ||||
−0.571072 | + | 0.820900i | \(0.693472\pi\) | |||||||
\(602\) | 5.00000 | − | 25.9808i | 0.203785 | − | 1.05890i | ||||
\(603\) | 26.0000 | 1.05880 | ||||||||
\(604\) | 9.50000 | − | 16.4545i | 0.386550 | − | 0.669523i | ||||
\(605\) | 0.500000 | + | 0.866025i | 0.0203279 | + | 0.0352089i | ||||
\(606\) | 4.50000 | + | 7.79423i | 0.182800 | + | 0.316619i | ||||
\(607\) | 8.00000 | − | 13.8564i | 0.324710 | − | 0.562414i | −0.656744 | − | 0.754114i | \(-0.728067\pi\) |
0.981454 | + | 0.191700i | \(0.0614000\pi\) | |||||||
\(608\) | 2.00000 | 0.0811107 | ||||||||
\(609\) | 18.0000 | + | 15.5885i | 0.729397 | + | 0.631676i | ||||
\(610\) | 7.00000 | 0.283422 | ||||||||
\(611\) | −6.00000 | + | 10.3923i | −0.242734 | + | 0.420428i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00000 | − | 1.73205i | −0.0403896 | − | 0.0699569i | 0.845124 | − | 0.534570i | \(-0.179527\pi\) |
−0.885514 | + | 0.464614i | \(0.846193\pi\) | |||||||
\(614\) | −1.00000 | + | 1.73205i | −0.0403567 | + | 0.0698999i | ||||
\(615\) | −12.0000 | −0.483887 | ||||||||
\(616\) | −2.00000 | − | 1.73205i | −0.0805823 | − | 0.0697863i | ||||
\(617\) | 15.0000 | 0.603877 | 0.301939 | − | 0.953327i | \(-0.402366\pi\) | ||||
0.301939 | + | 0.953327i | \(0.402366\pi\) | |||||||
\(618\) | 2.00000 | − | 3.46410i | 0.0804518 | − | 0.139347i | ||||
\(619\) | −4.00000 | − | 6.92820i | −0.160774 | − | 0.278468i | 0.774373 | − | 0.632730i | \(-0.218066\pi\) |
−0.935146 | + | 0.354262i | \(0.884732\pi\) | |||||||
\(620\) | −2.00000 | − | 3.46410i | −0.0803219 | − | 0.139122i | ||||
\(621\) | −15.0000 | + | 25.9808i | −0.601929 | + | 1.04257i | ||||
\(622\) | 24.0000 | 0.962312 | ||||||||
\(623\) | 3.00000 | − | 15.5885i | 0.120192 | − | 0.624538i | ||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0.500000 | + | 0.866025i | 0.0199840 | + | 0.0346133i | ||||
\(627\) | −1.00000 | − | 1.73205i | −0.0399362 | − | 0.0691714i | ||||
\(628\) | 5.00000 | − | 8.66025i | 0.199522 | − | 0.345582i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 5.00000 | − | 1.73205i | 0.199205 | − | 0.0690066i | ||||
\(631\) | 2.00000 | 0.0796187 | 0.0398094 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398094 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(632\) | −8.50000 | + | 14.7224i | −0.338112 | + | 0.585627i | ||||
\(633\) | 8.00000 | + | 13.8564i | 0.317971 | + | 0.550743i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.50000 | + | 11.2583i | −0.257945 | + | 0.446773i | ||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | −5.50000 | + | 4.33013i | −0.217918 | + | 0.171566i | ||||
\(638\) | −9.00000 | −0.356313 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | −4.50000 | − | 7.79423i | −0.177739 | − | 0.307854i | 0.763367 | − | 0.645966i | \(-0.223545\pi\) |
−0.941106 | + | 0.338112i | \(0.890212\pi\) | |||||||
\(642\) | 3.00000 | − | 5.19615i | 0.118401 | − | 0.205076i | ||||
\(643\) | −19.0000 | −0.749287 | −0.374643 | − | 0.927169i | \(-0.622235\pi\) | ||||
−0.374643 | + | 0.927169i | \(0.622235\pi\) | |||||||
\(644\) | −15.0000 | + | 5.19615i | −0.591083 | + | 0.204757i | ||||
\(645\) | 10.0000 | 0.393750 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.0000 | + | 36.3731i | 0.825595 | + | 1.42997i | 0.901464 | + | 0.432855i | \(0.142494\pi\) |
−0.0758684 | + | 0.997118i | \(0.524173\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −1.50000 | + | 2.59808i | −0.0588802 | + | 0.101983i | ||||
\(650\) | −1.00000 | −0.0392232 | ||||||||
\(651\) | 2.00000 | − | 10.3923i | 0.0783862 | − | 0.407307i | ||||
\(652\) | 5.00000 | 0.195815 | ||||||||
\(653\) | −9.00000 | + | 15.5885i | −0.352197 | + | 0.610023i | −0.986634 | − | 0.162951i | \(-0.947899\pi\) |
0.634437 | + | 0.772975i | \(0.281232\pi\) | |||||||
\(654\) | 5.00000 | + | 8.66025i | 0.195515 | + | 0.338643i | ||||
\(655\) | 9.00000 | + | 15.5885i | 0.351659 | + | 0.609091i | ||||
\(656\) | −6.00000 | + | 10.3923i | −0.234261 | + | 0.405751i | ||||
\(657\) | −28.0000 | −1.09238 | ||||||||
\(658\) | 24.0000 | + | 20.7846i | 0.935617 | + | 0.810268i | ||||
\(659\) | −6.00000 | −0.233727 | −0.116863 | − | 0.993148i | \(-0.537284\pi\) | ||||
−0.116863 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(660\) | 0.500000 | − | 0.866025i | 0.0194625 | − | 0.0337100i | ||||
\(661\) | −13.0000 | − | 22.5167i | −0.505641 | − | 0.875797i | −0.999979 | − | 0.00652642i | \(-0.997923\pi\) |
0.494337 | − | 0.869270i | \(-0.335411\pi\) | |||||||
\(662\) | 3.50000 | + | 6.06218i | 0.136031 | + | 0.235613i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 4.00000 | + | 3.46410i | 0.155113 | + | 0.134332i | ||||
\(666\) | 8.00000 | 0.309994 | ||||||||
\(667\) | −27.0000 | + | 46.7654i | −1.04544 | + | 1.81076i | ||||
\(668\) | 1.50000 | + | 2.59808i | 0.0580367 | + | 0.100523i | ||||
\(669\) | −10.0000 | − | 17.3205i | −0.386622 | − | 0.669650i | ||||
\(670\) | −6.50000 | + | 11.2583i | −0.251117 | + | 0.434947i | ||||
\(671\) | −7.00000 | −0.270232 | ||||||||
\(672\) | −0.500000 | + | 2.59808i | −0.0192879 | + | 0.100223i | ||||
\(673\) | −34.0000 | −1.31060 | −0.655302 | − | 0.755367i | \(-0.727459\pi\) | ||||
−0.655302 | + | 0.755367i | \(0.727459\pi\) | |||||||
\(674\) | −16.0000 | + | 27.7128i | −0.616297 | + | 1.06746i | ||||
\(675\) | 2.50000 | + | 4.33013i | 0.0962250 | + | 0.166667i | ||||
\(676\) | 6.00000 | + | 10.3923i | 0.230769 | + | 0.399704i | ||||
\(677\) | 21.0000 | − | 36.3731i | 0.807096 | − | 1.39793i | −0.107772 | − | 0.994176i | \(-0.534372\pi\) |
0.914867 | − | 0.403755i | \(-0.132295\pi\) | |||||||
\(678\) | −9.00000 | −0.345643 | ||||||||
\(679\) | 12.5000 | − | 4.33013i | 0.479706 | − | 0.166175i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | − | 10.3923i | 0.229920 | − | 0.398234i | ||||
\(682\) | 2.00000 | + | 3.46410i | 0.0765840 | + | 0.132647i | ||||
\(683\) | −19.5000 | − | 33.7750i | −0.746147 | − | 1.29236i | −0.949657 | − | 0.313291i | \(-0.898568\pi\) |
0.203510 | − | 0.979073i | \(-0.434765\pi\) | |||||||
\(684\) | 2.00000 | − | 3.46410i | 0.0764719 | − | 0.132453i | ||||
\(685\) | −9.00000 | −0.343872 | ||||||||
\(686\) | 8.50000 | + | 16.4545i | 0.324532 | + | 0.628235i | ||||
\(687\) | −10.0000 | −0.381524 | ||||||||
\(688\) | 5.00000 | − | 8.66025i | 0.190623 | − | 0.330169i | ||||
\(689\) | 3.00000 | + | 5.19615i | 0.114291 | + | 0.197958i | ||||
\(690\) | −3.00000 | − | 5.19615i | −0.114208 | − | 0.197814i | ||||
\(691\) | −8.50000 | + | 14.7224i | −0.323355 | + | 0.560068i | −0.981178 | − | 0.193105i | \(-0.938144\pi\) |
0.657823 | + | 0.753173i | \(0.271478\pi\) | |||||||
\(692\) | −21.0000 | −0.798300 | ||||||||
\(693\) | −5.00000 | + | 1.73205i | −0.189934 | + | 0.0657952i | ||||
\(694\) | 18.0000 | 0.683271 | ||||||||
\(695\) | 10.0000 | − | 17.3205i | 0.379322 | − | 0.657004i | ||||
\(696\) | 4.50000 | + | 7.79423i | 0.170572 | + | 0.295439i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −13.0000 | + | 22.5167i | −0.492057 | + | 0.852268i | ||||
\(699\) | −12.0000 | −0.453882 | ||||||||
\(700\) | −0.500000 | + | 2.59808i | −0.0188982 | + | 0.0981981i | ||||
\(701\) | 21.0000 | 0.793159 | 0.396580 | − | 0.918000i | \(-0.370197\pi\) | ||||
0.396580 | + | 0.918000i | \(0.370197\pi\) | |||||||
\(702\) | −2.50000 | + | 4.33013i | −0.0943564 | + | 0.163430i | ||||
\(703\) | 4.00000 | + | 6.92820i | 0.150863 | + | 0.261302i | ||||
\(704\) | −0.500000 | − | 0.866025i | −0.0188445 | − | 0.0326396i | ||||
\(705\) | −6.00000 | + | 10.3923i | −0.225973 | + | 0.391397i | ||||
\(706\) | −6.00000 | −0.225813 | ||||||||
\(707\) | 18.0000 | + | 15.5885i | 0.676960 | + | 0.586264i | ||||
\(708\) | 3.00000 | 0.112747 | ||||||||
\(709\) | 5.00000 | − | 8.66025i | 0.187779 | − | 0.325243i | −0.756730 | − | 0.653727i | \(-0.773204\pi\) |
0.944509 | + | 0.328484i | \(0.106538\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.0000 | + | 29.4449i | 0.637550 | + | 1.10427i | ||||
\(712\) | 3.00000 | − | 5.19615i | 0.112430 | − | 0.194734i | ||||
\(713\) | 24.0000 | 0.898807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.00000 | 0.0373979 | ||||||||
\(716\) | 10.5000 | − | 18.1865i | 0.392403 | − | 0.679663i | ||||
\(717\) | −1.50000 | − | 2.59808i | −0.0560185 | − | 0.0970269i | ||||
\(718\) | 13.5000 | + | 23.3827i | 0.503816 | + | 0.872634i | ||||
\(719\) | −12.0000 | + | 20.7846i | −0.447524 | + | 0.775135i | −0.998224 | − | 0.0595683i | \(-0.981028\pi\) |
0.550700 | + | 0.834703i | \(0.314361\pi\) | |||||||
\(720\) | 2.00000 | 0.0745356 | ||||||||
\(721\) | 2.00000 | − | 10.3923i | 0.0744839 | − | 0.387030i | ||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | 5.00000 | − | 8.66025i | 0.185952 | − | 0.322078i | ||||
\(724\) | 8.00000 | + | 13.8564i | 0.297318 | + | 0.514969i | ||||
\(725\) | 4.50000 | + | 7.79423i | 0.167126 | + | 0.289470i | ||||
\(726\) | −0.500000 | + | 0.866025i | −0.0185567 | + | 0.0321412i | ||||
\(727\) | −34.0000 | −1.26099 | −0.630495 | − | 0.776193i | \(-0.717148\pi\) | ||||
−0.630495 | + | 0.776193i | \(0.717148\pi\) | |||||||
\(728\) | −2.50000 | + | 0.866025i | −0.0926562 | + | 0.0320970i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 7.00000 | − | 12.1244i | 0.259082 | − | 0.448743i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 3.50000 | + | 6.06218i | 0.129364 | + | 0.224065i | ||||
\(733\) | −5.50000 | + | 9.52628i | −0.203147 | + | 0.351861i | −0.949541 | − | 0.313644i | \(-0.898450\pi\) |
0.746394 | + | 0.665505i | \(0.231784\pi\) | |||||||
\(734\) | −28.0000 | −1.03350 | ||||||||
\(735\) | −5.50000 | + | 4.33013i | −0.202871 | + | 0.159719i | ||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | 6.50000 | − | 11.2583i | 0.239431 | − | 0.414706i | ||||
\(738\) | 12.0000 | + | 20.7846i | 0.441726 | + | 0.765092i | ||||
\(739\) | 8.00000 | + | 13.8564i | 0.294285 | + | 0.509716i | 0.974818 | − | 0.223001i | \(-0.0715853\pi\) |
−0.680534 | + | 0.732717i | \(0.738252\pi\) | |||||||
\(740\) | −2.00000 | + | 3.46410i | −0.0735215 | + | 0.127343i | ||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | 15.0000 | − | 5.19615i | 0.550667 | − | 0.190757i | ||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | 2.00000 | − | 3.46410i | 0.0733236 | − | 0.127000i | ||||
\(745\) | −3.00000 | − | 5.19615i | −0.109911 | − | 0.190372i | ||||
\(746\) | −14.5000 | − | 25.1147i | −0.530883 | − | 0.919516i | ||||
\(747\) | 6.00000 | − | 10.3923i | 0.219529 | − | 0.380235i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.00000 | − | 15.5885i | 0.109618 | − | 0.569590i | ||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 23.0000 | − | 39.8372i | 0.839282 | − | 1.45368i | −0.0512140 | − | 0.998688i | \(-0.516309\pi\) |
0.890496 | − | 0.454991i | \(-0.150358\pi\) | |||||||
\(752\) | 6.00000 | + | 10.3923i | 0.218797 | + | 0.378968i | ||||
\(753\) | −6.00000 | − | 10.3923i | −0.218652 | − | 0.378717i | ||||
\(754\) | −4.50000 | + | 7.79423i | −0.163880 | + | 0.283849i | ||||
\(755\) | 19.0000 | 0.691481 | ||||||||
\(756\) | 10.0000 | + | 8.66025i | 0.363696 | + | 0.314970i | ||||
\(757\) | −46.0000 | −1.67190 | −0.835949 | − | 0.548807i | \(-0.815082\pi\) | ||||
−0.835949 | + | 0.548807i | \(0.815082\pi\) | |||||||
\(758\) | −2.50000 | + | 4.33013i | −0.0908041 | + | 0.157277i | ||||
\(759\) | 3.00000 | + | 5.19615i | 0.108893 | + | 0.188608i | ||||
\(760\) | 1.00000 | + | 1.73205i | 0.0362738 | + | 0.0628281i | ||||
\(761\) | −9.00000 | + | 15.5885i | −0.326250 | + | 0.565081i | −0.981764 | − | 0.190101i | \(-0.939118\pi\) |
0.655515 | + | 0.755182i | \(0.272452\pi\) | |||||||
\(762\) | −13.0000 | −0.470940 | ||||||||
\(763\) | 20.0000 | + | 17.3205i | 0.724049 | + | 0.627044i | ||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.0000 | − | 31.1769i | −0.650366 | − | 1.12647i | ||||
\(767\) | 1.50000 | + | 2.59808i | 0.0541619 | + | 0.0938111i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | −4.00000 | −0.144244 | −0.0721218 | − | 0.997396i | \(-0.522977\pi\) | ||||
−0.0721218 | + | 0.997396i | \(0.522977\pi\) | |||||||
\(770\) | 0.500000 | − | 2.59808i | 0.0180187 | − | 0.0936282i | ||||
\(771\) | 9.00000 | 0.324127 | ||||||||
\(772\) | 2.00000 | − | 3.46410i | 0.0719816 | − | 0.124676i | ||||
\(773\) | 27.0000 | + | 46.7654i | 0.971123 | + | 1.68203i | 0.692179 | + | 0.721726i | \(0.256651\pi\) |
0.278944 | + | 0.960307i | \(0.410016\pi\) | |||||||
\(774\) | −10.0000 | − | 17.3205i | −0.359443 | − | 0.622573i | ||||
\(775\) | 2.00000 | − | 3.46410i | 0.0718421 | − | 0.124434i | ||||
\(776\) | 5.00000 | 0.179490 | ||||||||
\(777\) | −10.0000 | + | 3.46410i | −0.358748 | + | 0.124274i | ||||
\(778\) | 12.0000 | 0.430221 | ||||||||
\(779\) | −12.0000 | + | 20.7846i | −0.429945 | + | 0.744686i | ||||
\(780\) | −0.500000 | − | 0.866025i | −0.0179029 | − | 0.0310087i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 45.0000 | 1.60817 | ||||||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | 10.0000 | 0.356915 | ||||||||
\(786\) | −9.00000 | + | 15.5885i | −0.321019 | + | 0.556022i | ||||
\(787\) | −7.00000 | − | 12.1244i | −0.249523 | − | 0.432187i | 0.713871 | − | 0.700278i | \(-0.246941\pi\) |
−0.963394 | + | 0.268091i | \(0.913607\pi\) | |||||||
\(788\) | −4.50000 | − | 7.79423i | −0.160306 | − | 0.277658i | ||||
\(789\) | −4.50000 | + | 7.79423i | −0.160204 | + | 0.277482i | ||||
\(790\) | −17.0000 | −0.604833 | ||||||||
\(791\) | −22.5000 | + | 7.79423i | −0.800008 | + | 0.277131i | ||||
\(792\) | −2.00000 | −0.0710669 | ||||||||
\(793\) | −3.50000 | + | 6.06218i | −0.124289 | + | 0.215274i | ||||
\(794\) | −1.00000 | − | 1.73205i | −0.0354887 | − | 0.0614682i | ||||
\(795\) | 3.00000 | + | 5.19615i | 0.106399 | + | 0.184289i | ||||
\(796\) | 5.00000 | − | 8.66025i | 0.177220 | − | 0.306955i | ||||
\(797\) | 24.0000 | 0.850124 | 0.425062 | − | 0.905164i | \(-0.360252\pi\) | ||||
0.425062 | + | 0.905164i | \(0.360252\pi\) | |||||||
\(798\) | −1.00000 | + | 5.19615i | −0.0353996 | + | 0.183942i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | −6.00000 | − | 10.3923i | −0.212000 | − | 0.367194i | ||||
\(802\) | −7.50000 | − | 12.9904i | −0.264834 | − | 0.458706i | ||||
\(803\) | −7.00000 | + | 12.1244i | −0.247025 | + | 0.427859i | ||||
\(804\) | −13.0000 | −0.458475 | ||||||||
\(805\) | −12.0000 | − | 10.3923i | −0.422944 | − | 0.366281i | ||||
\(806\) | 4.00000 | 0.140894 | ||||||||
\(807\) | −3.00000 | + | 5.19615i | −0.105605 | + | 0.182913i | ||||
\(808\) | 4.50000 | + | 7.79423i | 0.158309 | + | 0.274200i | ||||
\(809\) | −6.00000 | − | 10.3923i | −0.210949 | − | 0.365374i | 0.741063 | − | 0.671436i | \(-0.234322\pi\) |
−0.952012 | + | 0.306062i | \(0.900989\pi\) | |||||||
\(810\) | 0.500000 | − | 0.866025i | 0.0175682 | − | 0.0304290i | ||||
\(811\) | −28.0000 | −0.983213 | −0.491606 | − | 0.870817i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870817i | \(0.663590\pi\) | |||||||
\(812\) | 18.0000 | + | 15.5885i | 0.631676 | + | 0.547048i | ||||
\(813\) | 29.0000 | 1.01707 | ||||||||
\(814\) | 2.00000 | − | 3.46410i | 0.0701000 | − | 0.121417i | ||||
\(815\) | 2.50000 | + | 4.33013i | 0.0875712 | + | 0.151678i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.0000 | − | 17.3205i | 0.349856 | − | 0.605968i | ||||
\(818\) | 20.0000 | 0.699284 | ||||||||
\(819\) | −1.00000 | + | 5.19615i | −0.0349428 | + | 0.181568i | ||||
\(820\) | −12.0000 | −0.419058 | ||||||||
\(821\) | −1.50000 | + | 2.59808i | −0.0523504 | + | 0.0906735i | −0.891013 | − | 0.453978i | \(-0.850005\pi\) |
0.838663 | + | 0.544651i | \(0.183338\pi\) | |||||||
\(822\) | −4.50000 | − | 7.79423i | −0.156956 | − | 0.271855i | ||||
\(823\) | 8.00000 | + | 13.8564i | 0.278862 | + | 0.483004i | 0.971102 | − | 0.238664i | \(-0.0767093\pi\) |
−0.692240 | + | 0.721668i | \(0.743376\pi\) | |||||||
\(824\) | 2.00000 | − | 3.46410i | 0.0696733 | − | 0.120678i | ||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | 7.50000 | − | 2.59808i | 0.260958 | − | 0.0903986i | ||||
\(827\) | −6.00000 | −0.208640 | −0.104320 | − | 0.994544i | \(-0.533267\pi\) | ||||
−0.104320 | + | 0.994544i | \(0.533267\pi\) | |||||||
\(828\) | −6.00000 | + | 10.3923i | −0.208514 | + | 0.361158i | ||||
\(829\) | −10.0000 | − | 17.3205i | −0.347314 | − | 0.601566i | 0.638457 | − | 0.769657i | \(-0.279573\pi\) |
−0.985771 | + | 0.168091i | \(0.946240\pi\) | |||||||
\(830\) | 3.00000 | + | 5.19615i | 0.104132 | + | 0.180361i | ||||
\(831\) | 9.50000 | − | 16.4545i | 0.329551 | − | 0.570800i | ||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 20.0000 | 0.692543 | ||||||||
\(835\) | −1.50000 | + | 2.59808i | −0.0519096 | + | 0.0899101i | ||||
\(836\) | −1.00000 | − | 1.73205i | −0.0345857 | − | 0.0599042i | ||||
\(837\) | −10.0000 | − | 17.3205i | −0.345651 | − | 0.598684i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.0000 | 1.45000 | 0.725001 | − | 0.688748i | \(-0.241839\pi\) | ||||
0.725001 | + | 0.688748i | \(0.241839\pi\) | |||||||
\(840\) | −2.50000 | + | 0.866025i | −0.0862582 | + | 0.0298807i | ||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | −16.0000 | + | 27.7128i | −0.551396 | + | 0.955047i | ||||
\(843\) | −12.0000 | − | 20.7846i | −0.413302 | − | 0.715860i | ||||
\(844\) | 8.00000 | + | 13.8564i | 0.275371 | + | 0.476957i | ||||
\(845\) | −6.00000 | + | 10.3923i | −0.206406 | + | 0.357506i | ||||
\(846\) | 24.0000 | 0.825137 | ||||||||
\(847\) | −0.500000 | + | 2.59808i | −0.0171802 | + | 0.0892710i | ||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 11.0000 | − | 19.0526i | 0.377519 | − | 0.653882i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.0000 | − | 20.7846i | −0.411355 | − | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.0000 | 0.890223 | 0.445112 | − | 0.895475i | \(-0.353164\pi\) | ||||
0.445112 | + | 0.895475i | \(0.353164\pi\) | |||||||
\(854\) | 14.0000 | + | 12.1244i | 0.479070 | + | 0.414887i | ||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | 3.00000 | − | 5.19615i | 0.102538 | − | 0.177601i | ||||
\(857\) | 21.0000 | + | 36.3731i | 0.717346 | + | 1.24248i | 0.962048 | + | 0.272882i | \(0.0879768\pi\) |
−0.244701 | + | 0.969599i | \(0.578690\pi\) | |||||||
\(858\) | 0.500000 | + | 0.866025i | 0.0170697 | + | 0.0295656i | ||||
\(859\) | −2.50000 | + | 4.33013i | −0.0852989 | + | 0.147742i | −0.905519 | − | 0.424307i | \(-0.860518\pi\) |
0.820220 | + | 0.572049i | \(0.193851\pi\) | |||||||
\(860\) | 10.0000 | 0.340997 | ||||||||
\(861\) | −24.0000 | − | 20.7846i | −0.817918 | − | 0.708338i | ||||
\(862\) | −15.0000 | −0.510902 | ||||||||
\(863\) | −18.0000 | + | 31.1769i | −0.612727 | + | 1.06127i | 0.378052 | + | 0.925785i | \(0.376594\pi\) |
−0.990779 | + | 0.135490i | \(0.956739\pi\) | |||||||
\(864\) | 2.50000 | + | 4.33013i | 0.0850517 | + | 0.147314i | ||||
\(865\) | −10.5000 | − | 18.1865i | −0.357011 | − | 0.618361i | ||||
\(866\) | −1.00000 | + | 1.73205i | −0.0339814 | + | 0.0588575i | ||||
\(867\) | −17.0000 | −0.577350 | ||||||||
\(868\) | 2.00000 | − | 10.3923i | 0.0678844 | − | 0.352738i | ||||
\(869\) | 17.0000 | 0.576686 | ||||||||
\(870\) | −4.50000 | + | 7.79423i | −0.152564 | + | 0.264249i | ||||
\(871\) | −6.50000 | − | 11.2583i | −0.220244 | − | 0.381474i | ||||
\(872\) | 5.00000 | + | 8.66025i | 0.169321 | + | 0.293273i | ||||
\(873\) | 5.00000 | − | 8.66025i | 0.169224 | − | 0.293105i | ||||
\(874\) | −12.0000 | −0.405906 | ||||||||
\(875\) | −2.50000 | + | 0.866025i | −0.0845154 | + | 0.0292770i | ||||
\(876\) | 14.0000 | 0.473016 | ||||||||
\(877\) | −8.50000 | + | 14.7224i | −0.287025 | + | 0.497141i | −0.973098 | − | 0.230391i | \(-0.925999\pi\) |
0.686074 | + | 0.727532i | \(0.259333\pi\) | |||||||
\(878\) | 6.50000 | + | 11.2583i | 0.219364 | + | 0.379950i | ||||
\(879\) | −3.00000 | − | 5.19615i | −0.101187 | − | 0.175262i | ||||
\(880\) | 0.500000 | − | 0.866025i | 0.0168550 | − | 0.0291937i | ||||
\(881\) | −51.0000 | −1.71823 | −0.859117 | − | 0.511780i | \(-0.828986\pi\) | ||||
−0.859117 | + | 0.511780i | \(0.828986\pi\) | |||||||
\(882\) | 13.0000 | + | 5.19615i | 0.437733 | + | 0.174964i | ||||
\(883\) | −19.0000 | −0.639401 | −0.319700 | − | 0.947519i | \(-0.603582\pi\) | ||||
−0.319700 | + | 0.947519i | \(0.603582\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.50000 | + | 2.59808i | 0.0504219 | + | 0.0873334i | ||||
\(886\) | 12.0000 | + | 20.7846i | 0.403148 | + | 0.698273i | ||||
\(887\) | 7.50000 | − | 12.9904i | 0.251825 | − | 0.436174i | −0.712203 | − | 0.701974i | \(-0.752302\pi\) |
0.964028 | + | 0.265799i | \(0.0856358\pi\) | |||||||
\(888\) | −4.00000 | −0.134231 | ||||||||
\(889\) | −32.5000 | + | 11.2583i | −1.09002 | + | 0.377592i | ||||
\(890\) | 6.00000 | 0.201120 | ||||||||
\(891\) | −0.500000 | + | 0.866025i | −0.0167506 | + | 0.0290129i | ||||
\(892\) | −10.0000 | − | 17.3205i | −0.334825 | − | 0.579934i | ||||
\(893\) | 12.0000 | + | 20.7846i | 0.401565 | + | 0.695530i | ||||
\(894\) | 3.00000 | − | 5.19615i | 0.100335 | − | 0.173785i | ||||
\(895\) | 21.0000 | 0.701953 | ||||||||
\(896\) | −0.500000 | + | 2.59808i | −0.0167038 | + | 0.0867956i | ||||
\(897\) | 6.00000 | 0.200334 | ||||||||
\(898\) | 15.0000 | − | 25.9808i | 0.500556 | − | 0.866989i | ||||
\(899\) | −18.0000 | − | 31.1769i | −0.600334 | − | 1.03981i | ||||
\(900\) | 1.00000 | + | 1.73205i | 0.0333333 | + | 0.0577350i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 12.0000 | 0.399556 | ||||||||
\(903\) | 20.0000 | + | 17.3205i | 0.665558 | + | 0.576390i | ||||
\(904\) | −9.00000 | −0.299336 | ||||||||
\(905\) | −8.00000 | + | 13.8564i | −0.265929 | + | 0.460603i | ||||
\(906\) | 9.50000 | + | 16.4545i | 0.315616 | + | 0.546664i | ||||
\(907\) | −10.0000 | − | 17.3205i | −0.332045 | − | 0.575118i | 0.650868 | − | 0.759191i | \(-0.274405\pi\) |
−0.982913 | + | 0.184073i | \(0.941072\pi\) | |||||||
\(908\) | 6.00000 | − | 10.3923i | 0.199117 | − | 0.344881i | ||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | −2.00000 | − | 1.73205i | −0.0662994 | − | 0.0574169i | ||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | −1.00000 | + | 1.73205i | −0.0331133 | + | 0.0573539i | ||||
\(913\) | −3.00000 | − | 5.19615i | −0.0992855 | − | 0.171968i | ||||
\(914\) | 2.00000 | + | 3.46410i | 0.0661541 | + | 0.114582i | ||||
\(915\) | −3.50000 | + | 6.06218i | −0.115706 | + | 0.200409i | ||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | −9.00000 | + | 46.7654i | −0.297206 | + | 1.54433i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.00000 | − | 13.8564i | 0.263896 | − | 0.457081i | −0.703378 | − | 0.710816i | \(-0.748326\pi\) |
0.967274 | + | 0.253735i | \(0.0816592\pi\) | |||||||
\(920\) | −3.00000 | − | 5.19615i | −0.0989071 | − | 0.171312i | ||||
\(921\) | −1.00000 | − | 1.73205i | −0.0329511 | − | 0.0570730i | ||||
\(922\) | −7.50000 | + | 12.9904i | −0.246999 | + | 0.427815i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.50000 | − | 0.866025i | 0.0822440 | − | 0.0284901i | ||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | −10.0000 | + | 17.3205i | −0.328620 | + | 0.569187i | ||||
\(927\) | −4.00000 | − | 6.92820i | −0.131377 | − | 0.227552i | ||||
\(928\) | 4.50000 | + | 7.79423i | 0.147720 | + | 0.255858i | ||||
\(929\) | 10.5000 | − | 18.1865i | 0.344494 | − | 0.596681i | −0.640768 | − | 0.767735i | \(-0.721384\pi\) |
0.985262 | + | 0.171054i | \(0.0547172\pi\) | |||||||
\(930\) | 4.00000 | 0.131165 | ||||||||
\(931\) | 2.00000 | + | 13.8564i | 0.0655474 | + | 0.454125i | ||||
\(932\) | −12.0000 | −0.393073 | ||||||||
\(933\) | −12.0000 | + | 20.7846i | −0.392862 | + | 0.680458i | ||||
\(934\) | −6.00000 | − | 10.3923i | −0.196326 | − | 0.340047i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.00000 | + | 1.73205i | −0.0326860 | + | 0.0566139i | ||||
\(937\) | −52.0000 | −1.69877 | −0.849383 | − | 0.527777i | \(-0.823026\pi\) | ||||
−0.849383 | + | 0.527777i | \(0.823026\pi\) | |||||||
\(938\) | −32.5000 | + | 11.2583i | −1.06116 | + | 0.367598i | ||||
\(939\) | −1.00000 | −0.0326338 | ||||||||
\(940\) | −6.00000 | + | 10.3923i | −0.195698 | + | 0.338960i | ||||
\(941\) | 1.50000 | + | 2.59808i | 0.0488986 | + | 0.0846949i | 0.889439 | − | 0.457054i | \(-0.151096\pi\) |
−0.840540 | + | 0.541749i | \(0.817762\pi\) | |||||||
\(942\) | 5.00000 | + | 8.66025i | 0.162909 | + | 0.282166i | ||||
\(943\) | 36.0000 | − | 62.3538i | 1.17232 | − | 2.03052i | ||||
\(944\) | 3.00000 | 0.0976417 | ||||||||
\(945\) | −2.50000 | + | 12.9904i | −0.0813250 | + | 0.422577i | ||||
\(946\) | −10.0000 | −0.325128 | ||||||||
\(947\) | 24.0000 | − | 41.5692i | 0.779895 | − | 1.35082i | −0.152106 | − | 0.988364i | \(-0.548606\pi\) |
0.932002 | − | 0.362454i | \(-0.118061\pi\) | |||||||
\(948\) | −8.50000 | − | 14.7224i | −0.276067 | − | 0.478162i | ||||
\(949\) | 7.00000 | + | 12.1244i | 0.227230 | + | 0.393573i | ||||
\(950\) | −1.00000 | + | 1.73205i | −0.0324443 | + | 0.0561951i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.0000 | 0.583077 | 0.291539 | − | 0.956559i | \(-0.405833\pi\) | ||||
0.291539 | + | 0.956559i | \(0.405833\pi\) | |||||||
\(954\) | 6.00000 | − | 10.3923i | 0.194257 | − | 0.336463i | ||||
\(955\) | 6.00000 | + | 10.3923i | 0.194155 | + | 0.336287i | ||||
\(956\) | −1.50000 | − | 2.59808i | −0.0485135 | − | 0.0840278i | ||||
\(957\) | 4.50000 | − | 7.79423i | 0.145464 | − | 0.251952i | ||||
\(958\) | −21.0000 | −0.678479 | ||||||||
\(959\) | −18.0000 | − | 15.5885i | −0.581250 | − | 0.503378i | ||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | −2.00000 | − | 3.46410i | −0.0644826 | − | 0.111687i | ||||
\(963\) | −6.00000 | − | 10.3923i | −0.193347 | − | 0.334887i | ||||
\(964\) | 5.00000 | − | 8.66025i | 0.161039 | − | 0.278928i | ||||
\(965\) | 4.00000 | 0.128765 | ||||||||
\(966\) | 3.00000 | − | 15.5885i | 0.0965234 | − | 0.501550i | ||||
\(967\) | 8.00000 | 0.257263 | 0.128631 | − | 0.991692i | \(-0.458942\pi\) | ||||
0.128631 | + | 0.991692i | \(0.458942\pi\) | |||||||
\(968\) | −0.500000 | + | 0.866025i | −0.0160706 | + | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.50000 | + | 4.33013i | 0.0802702 | + | 0.139032i | ||||
\(971\) | 7.50000 | − | 12.9904i | 0.240686 | − | 0.416881i | −0.720224 | − | 0.693742i | \(-0.755961\pi\) |
0.960910 | + | 0.276861i | \(0.0892941\pi\) | |||||||
\(972\) | 16.0000 | 0.513200 | ||||||||
\(973\) | 50.0000 | − | 17.3205i | 1.60293 | − | 0.555270i | ||||
\(974\) | 2.00000 | 0.0640841 | ||||||||
\(975\) | 0.500000 | − | 0.866025i | 0.0160128 | − | 0.0277350i | ||||
\(976\) | 3.50000 | + | 6.06218i | 0.112032 | + | 0.194046i | ||||
\(977\) | −15.0000 | − | 25.9808i | −0.479893 | − | 0.831198i | 0.519841 | − | 0.854263i | \(-0.325991\pi\) |
−0.999734 | + | 0.0230645i | \(0.992658\pi\) | |||||||
\(978\) | −2.50000 | + | 4.33013i | −0.0799412 | + | 0.138462i | ||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | −5.50000 | + | 4.33013i | −0.175691 | + | 0.138321i | ||||
\(981\) | 20.0000 | 0.638551 | ||||||||
\(982\) | 12.0000 | − | 20.7846i | 0.382935 | − | 0.663264i | ||||
\(983\) | −15.0000 | − | 25.9808i | −0.478426 | − | 0.828658i | 0.521268 | − | 0.853393i | \(-0.325459\pi\) |
−0.999694 | + | 0.0247352i | \(0.992126\pi\) | |||||||
\(984\) | −6.00000 | − | 10.3923i | −0.191273 | − | 0.331295i | ||||
\(985\) | 4.50000 | − | 7.79423i | 0.143382 | − | 0.248345i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −30.0000 | + | 10.3923i | −0.954911 | + | 0.330791i | ||||
\(988\) | −2.00000 | −0.0636285 | ||||||||
\(989\) | −30.0000 | + | 51.9615i | −0.953945 | + | 1.65228i | ||||
\(990\) | −1.00000 | − | 1.73205i | −0.0317821 | − | 0.0550482i | ||||
\(991\) | −10.0000 | − | 17.3205i | −0.317660 | − | 0.550204i | 0.662339 | − | 0.749204i | \(-0.269564\pi\) |
−0.979999 | + | 0.199000i | \(0.936231\pi\) | |||||||
\(992\) | 2.00000 | − | 3.46410i | 0.0635001 | − | 0.109985i | ||||
\(993\) | −7.00000 | −0.222138 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0000 | 0.317021 | ||||||||
\(996\) | −3.00000 | + | 5.19615i | −0.0950586 | + | 0.164646i | ||||
\(997\) | 5.00000 | + | 8.66025i | 0.158352 | + | 0.274273i | 0.934274 | − | 0.356555i | \(-0.116049\pi\) |
−0.775923 | + | 0.630828i | \(0.782715\pi\) | |||||||
\(998\) | −10.0000 | − | 17.3205i | −0.316544 | − | 0.548271i | ||||
\(999\) | −10.0000 | + | 17.3205i | −0.316386 | + | 0.547997i |
(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 | 770.2.i.a.331.1 | yes | 2 | |
7.2 | even | 3 | 5390.2.a.be.1.1 | 1 | |||
7.4 | even | 3 | inner | 770.2.i.a.221.1 | ✓ | 2 | |
7.5 | odd | 6 | 5390.2.a.z.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.i.a.221.1 | ✓ | 2 | 7.4 | even | 3 | inner | |
770.2.i.a.331.1 | yes | 2 | 1.1 | even | 1 | trivial | |
5390.2.a.z.1.1 | 1 | 7.5 | odd | 6 | |||
5390.2.a.be.1.1 | 1 | 7.2 | even | 3 |