Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(499,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.499");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 499.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.499 |
Dual form | 1050.2.o.l.949.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.866025 | − | 2.50000i | −0.327327 | − | 0.944911i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | + | 3.46410i | 0.603023 | + | 1.04447i | 0.992361 | + | 0.123371i | \(0.0393705\pi\) |
−0.389338 | + | 0.921095i | \(0.627296\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | − | 4.00000i | − | 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | 0.500000 | − | 2.59808i | 0.133631 | − | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.59808 | − | 1.50000i | 0.630126 | − | 0.363803i | −0.150675 | − | 0.988583i | \(-0.548145\pi\) |
0.780801 | + | 0.624780i | \(0.214811\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | 3.00000 | − | 5.19615i | 0.688247 | − | 1.19208i | −0.284157 | − | 0.958778i | \(-0.591714\pi\) |
0.972404 | − | 0.233301i | \(-0.0749529\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | − | 1.73205i | −0.436436 | − | 0.377964i | ||||
\(22\) | 4.00000i | 0.852803i | ||||||||
\(23\) | 6.06218 | + | 3.50000i | 1.26405 | + | 0.729800i | 0.973856 | − | 0.227167i | \(-0.0729463\pi\) |
0.290196 | + | 0.956967i | \(0.406280\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000 | − | 3.46410i | 0.392232 | − | 0.679366i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 1.73205 | − | 2.00000i | 0.327327 | − | 0.377964i | ||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.50000 | + | 4.33013i | 0.449013 | + | 0.777714i | 0.998322 | − | 0.0579057i | \(-0.0184423\pi\) |
−0.549309 | + | 0.835619i | \(0.685109\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 3.46410 | + | 2.00000i | 0.603023 | + | 0.348155i | ||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.73205 | − | 1.00000i | −0.284747 | − | 0.164399i | 0.350823 | − | 0.936442i | \(-0.385902\pi\) |
−0.635571 | + | 0.772043i | \(0.719235\pi\) | |||||||
\(38\) | 5.19615 | − | 3.00000i | 0.842927 | − | 0.486664i | ||||
\(39\) | −2.00000 | − | 3.46410i | −0.320256 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.00000 | 1.09322 | 0.546608 | − | 0.837389i | \(-0.315919\pi\) | ||||
0.546608 | + | 0.837389i | \(0.315919\pi\) | |||||||
\(42\) | −0.866025 | − | 2.50000i | −0.133631 | − | 0.385758i | ||||
\(43\) | − | 2.00000i | − | 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | −2.00000 | + | 3.46410i | −0.301511 | + | 0.522233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.50000 | + | 6.06218i | 0.516047 | + | 0.893819i | ||||
\(47\) | −0.866025 | − | 0.500000i | −0.126323 | − | 0.0729325i | 0.435507 | − | 0.900185i | \(-0.356569\pi\) |
−0.561830 | + | 0.827253i | \(0.689902\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −5.50000 | + | 4.33013i | −0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.50000 | − | 2.59808i | 0.210042 | − | 0.363803i | ||||
\(52\) | 3.46410 | − | 2.00000i | 0.480384 | − | 0.277350i | ||||
\(53\) | 1.73205 | − | 1.00000i | 0.237915 | − | 0.137361i | −0.376303 | − | 0.926497i | \(-0.622805\pi\) |
0.614218 | + | 0.789136i | \(0.289471\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.50000 | − | 0.866025i | 0.334077 | − | 0.115728i | ||||
\(57\) | − | 6.00000i | − | 0.794719i | ||||||
\(58\) | −3.46410 | − | 2.00000i | −0.454859 | − | 0.262613i | ||||
\(59\) | −7.00000 | − | 12.1244i | −0.911322 | − | 1.57846i | −0.812198 | − | 0.583382i | \(-0.801729\pi\) |
−0.0991242 | − | 0.995075i | \(-0.531604\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | + | 10.3923i | −0.768221 | + | 1.33060i | 0.170305 | + | 0.985391i | \(0.445525\pi\) |
−0.938527 | + | 0.345207i | \(0.887809\pi\) | |||||||
\(62\) | 5.00000i | 0.635001i | ||||||||
\(63\) | −2.59808 | − | 0.500000i | −0.327327 | − | 0.0629941i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.00000 | + | 3.46410i | 0.246183 | + | 0.426401i | ||||
\(67\) | 10.3923 | − | 6.00000i | 1.26962 | − | 0.733017i | 0.294706 | − | 0.955588i | \(-0.404778\pi\) |
0.974916 | + | 0.222571i | \(0.0714450\pi\) | |||||||
\(68\) | 2.59808 | + | 1.50000i | 0.315063 | + | 0.181902i | ||||
\(69\) | 7.00000 | 0.842701 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.00000 | −1.06810 | −0.534052 | − | 0.845452i | \(-0.679331\pi\) | ||||
−0.534052 | + | 0.845452i | \(0.679331\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | −5.19615 | + | 3.00000i | −0.608164 | + | 0.351123i | −0.772246 | − | 0.635323i | \(-0.780867\pi\) |
0.164083 | + | 0.986447i | \(0.447534\pi\) | |||||||
\(74\) | −1.00000 | − | 1.73205i | −0.116248 | − | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | 6.92820 | − | 8.00000i | 0.789542 | − | 0.911685i | ||||
\(78\) | − | 4.00000i | − | 0.452911i | ||||||
\(79\) | −8.50000 | + | 14.7224i | −0.956325 | + | 1.65640i | −0.225018 | + | 0.974355i | \(0.572244\pi\) |
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 6.06218 | + | 3.50000i | 0.669456 | + | 0.386510i | ||||
\(83\) | 4.00000i | 0.439057i | 0.975606 | + | 0.219529i | \(0.0704519\pi\) | ||||
−0.975606 | + | 0.219529i | \(0.929548\pi\) | |||||||
\(84\) | 0.500000 | − | 2.59808i | 0.0545545 | − | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.00000 | − | 1.73205i | 0.107833 | − | 0.186772i | ||||
\(87\) | −3.46410 | + | 2.00000i | −0.371391 | + | 0.214423i | ||||
\(88\) | −3.46410 | + | 2.00000i | −0.369274 | + | 0.213201i | ||||
\(89\) | −3.50000 | + | 6.06218i | −0.370999 | + | 0.642590i | −0.989720 | − | 0.143022i | \(-0.954318\pi\) |
0.618720 | + | 0.785611i | \(0.287651\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0000 | + | 3.46410i | −1.04828 | + | 0.363137i | ||||
\(92\) | 7.00000i | 0.729800i | ||||||||
\(93\) | 4.33013 | + | 2.50000i | 0.449013 | + | 0.259238i | ||||
\(94\) | −0.500000 | − | 0.866025i | −0.0515711 | − | 0.0893237i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | − | 7.00000i | − | 0.710742i | −0.934725 | − | 0.355371i | \(-0.884354\pi\) | ||
0.934725 | − | 0.355371i | \(-0.115646\pi\) | |||||||
\(98\) | −6.92820 | + | 1.00000i | −0.699854 | + | 0.101015i | ||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.00000 | + | 15.5885i | 0.895533 | + | 1.55111i | 0.833143 | + | 0.553058i | \(0.186539\pi\) |
0.0623905 | + | 0.998052i | \(0.480128\pi\) | |||||||
\(102\) | 2.59808 | − | 1.50000i | 0.257248 | − | 0.148522i | ||||
\(103\) | −6.06218 | − | 3.50000i | −0.597324 | − | 0.344865i | 0.170664 | − | 0.985329i | \(-0.445409\pi\) |
−0.767988 | + | 0.640464i | \(0.778742\pi\) | |||||||
\(104\) | 4.00000 | 0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | −12.1244 | − | 7.00000i | −1.17211 | − | 0.676716i | −0.217931 | − | 0.975964i | \(-0.569931\pi\) |
−0.954175 | + | 0.299249i | \(0.903264\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 3.00000 | + | 5.19615i | 0.287348 | + | 0.497701i | 0.973176 | − | 0.230063i | \(-0.0738931\pi\) |
−0.685828 | + | 0.727764i | \(0.740560\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | 2.59808 | + | 0.500000i | 0.245495 | + | 0.0472456i | ||||
\(113\) | 3.00000i | 0.282216i | 0.989994 | + | 0.141108i | \(0.0450665\pi\) | ||||
−0.989994 | + | 0.141108i | \(0.954933\pi\) | |||||||
\(114\) | 3.00000 | − | 5.19615i | 0.280976 | − | 0.486664i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.00000 | − | 3.46410i | −0.185695 | − | 0.321634i | ||||
\(117\) | −3.46410 | − | 2.00000i | −0.320256 | − | 0.184900i | ||||
\(118\) | − | 14.0000i | − | 1.28880i | ||||||
\(119\) | −6.00000 | − | 5.19615i | −0.550019 | − | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | −10.3923 | + | 6.00000i | −0.940875 | + | 0.543214i | ||||
\(123\) | 6.06218 | − | 3.50000i | 0.546608 | − | 0.315584i | ||||
\(124\) | −2.50000 | + | 4.33013i | −0.224507 | + | 0.388857i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | − | 1.73205i | −0.178174 | − | 0.154303i | ||||
\(127\) | 16.0000i | 1.41977i | 0.704317 | + | 0.709885i | \(0.251253\pi\) | ||||
−0.704317 | + | 0.709885i | \(0.748747\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −1.00000 | − | 1.73205i | −0.0880451 | − | 0.152499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | − | 6.92820i | 0.349482 | − | 0.605320i | −0.636676 | − | 0.771132i | \(-0.719691\pi\) |
0.986157 | + | 0.165812i | \(0.0530244\pi\) | |||||||
\(132\) | 4.00000i | 0.348155i | ||||||||
\(133\) | −15.5885 | − | 3.00000i | −1.35169 | − | 0.260133i | ||||
\(134\) | 12.0000 | 1.03664 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.50000 | + | 2.59808i | 0.128624 | + | 0.222783i | ||||
\(137\) | 12.9904 | − | 7.50000i | 1.10984 | − | 0.640768i | 0.171054 | − | 0.985262i | \(-0.445283\pi\) |
0.938789 | + | 0.344493i | \(0.111949\pi\) | |||||||
\(138\) | 6.06218 | + | 3.50000i | 0.516047 | + | 0.297940i | ||||
\(139\) | −2.00000 | −0.169638 | −0.0848189 | − | 0.996396i | \(-0.527031\pi\) | ||||
−0.0848189 | + | 0.996396i | \(0.527031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.00000 | −0.0842152 | ||||||||
\(142\) | −7.79423 | − | 4.50000i | −0.654077 | − | 0.377632i | ||||
\(143\) | 13.8564 | − | 8.00000i | 1.15873 | − | 0.668994i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.00000 | −0.496564 | ||||||||
\(147\) | −2.59808 | + | 6.50000i | −0.214286 | + | 0.536111i | ||||
\(148\) | − | 2.00000i | − | 0.164399i | ||||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | − | 20.7846i | −0.976546 | − | 1.69143i | −0.674735 | − | 0.738060i | \(-0.735742\pi\) |
−0.301811 | − | 0.953368i | \(-0.597591\pi\) | |||||||
\(152\) | 5.19615 | + | 3.00000i | 0.421464 | + | 0.243332i | ||||
\(153\) | − | 3.00000i | − | 0.242536i | ||||||
\(154\) | 10.0000 | − | 3.46410i | 0.805823 | − | 0.279145i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | − | 3.46410i | 0.160128 | − | 0.277350i | ||||
\(157\) | −3.46410 | + | 2.00000i | −0.276465 | + | 0.159617i | −0.631822 | − | 0.775113i | \(-0.717693\pi\) |
0.355357 | + | 0.934731i | \(0.384359\pi\) | |||||||
\(158\) | −14.7224 | + | 8.50000i | −1.17125 | + | 0.676224i | ||||
\(159\) | 1.00000 | − | 1.73205i | 0.0793052 | − | 0.137361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.50000 | − | 18.1865i | 0.275839 | − | 1.43330i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −6.92820 | − | 4.00000i | −0.542659 | − | 0.313304i | 0.203497 | − | 0.979076i | \(-0.434769\pi\) |
−0.746156 | + | 0.665771i | \(0.768103\pi\) | |||||||
\(164\) | 3.50000 | + | 6.06218i | 0.273304 | + | 0.473377i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.00000 | + | 3.46410i | −0.155230 | + | 0.268866i | ||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 1.73205 | − | 2.00000i | 0.133631 | − | 0.154303i | ||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | − | 5.19615i | −0.229416 | − | 0.397360i | ||||
\(172\) | 1.73205 | − | 1.00000i | 0.132068 | − | 0.0762493i | ||||
\(173\) | 5.19615 | + | 3.00000i | 0.395056 | + | 0.228086i | 0.684349 | − | 0.729155i | \(-0.260087\pi\) |
−0.289292 | + | 0.957241i | \(0.593420\pi\) | |||||||
\(174\) | −4.00000 | −0.303239 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | −12.1244 | − | 7.00000i | −0.911322 | − | 0.526152i | ||||
\(178\) | −6.06218 | + | 3.50000i | −0.454379 | + | 0.262336i | ||||
\(179\) | 1.00000 | + | 1.73205i | 0.0747435 | + | 0.129460i | 0.900975 | − | 0.433872i | \(-0.142853\pi\) |
−0.826231 | + | 0.563331i | \(0.809520\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0000 | 0.891953 | 0.445976 | − | 0.895045i | \(-0.352856\pi\) | ||||
0.445976 | + | 0.895045i | \(0.352856\pi\) | |||||||
\(182\) | −10.3923 | − | 2.00000i | −0.770329 | − | 0.148250i | ||||
\(183\) | 12.0000i | 0.887066i | ||||||||
\(184\) | −3.50000 | + | 6.06218i | −0.258023 | + | 0.446910i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.50000 | + | 4.33013i | 0.183309 | + | 0.317500i | ||||
\(187\) | 10.3923 | + | 6.00000i | 0.759961 | + | 0.438763i | ||||
\(188\) | − | 1.00000i | − | 0.0729325i | ||||||
\(189\) | −2.50000 | + | 0.866025i | −0.181848 | + | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.50000 | + | 12.9904i | −0.542681 | + | 0.939951i | 0.456068 | + | 0.889945i | \(0.349257\pi\) |
−0.998749 | + | 0.0500060i | \(0.984076\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −21.6506 | + | 12.5000i | −1.55845 | + | 0.899770i | −0.561041 | + | 0.827788i | \(0.689599\pi\) |
−0.997406 | + | 0.0719816i | \(0.977068\pi\) | |||||||
\(194\) | 3.50000 | − | 6.06218i | 0.251285 | − | 0.435239i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | 20.0000i | 1.42494i | 0.701702 | + | 0.712470i | \(0.252424\pi\) | ||||
−0.701702 | + | 0.712470i | \(0.747576\pi\) | |||||||
\(198\) | 3.46410 | + | 2.00000i | 0.246183 | + | 0.142134i | ||||
\(199\) | 7.50000 | + | 12.9904i | 0.531661 | + | 0.920864i | 0.999317 | + | 0.0369532i | \(0.0117652\pi\) |
−0.467656 | + | 0.883911i | \(0.654901\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.00000 | − | 10.3923i | 0.423207 | − | 0.733017i | ||||
\(202\) | 18.0000i | 1.26648i | ||||||||
\(203\) | 3.46410 | + | 10.0000i | 0.243132 | + | 0.701862i | ||||
\(204\) | 3.00000 | 0.210042 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.50000 | − | 6.06218i | −0.243857 | − | 0.422372i | ||||
\(207\) | 6.06218 | − | 3.50000i | 0.421350 | − | 0.243267i | ||||
\(208\) | 3.46410 | + | 2.00000i | 0.240192 | + | 0.138675i | ||||
\(209\) | 24.0000 | 1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.0000 | −1.51454 | −0.757271 | − | 0.653101i | \(-0.773468\pi\) | ||||
−0.757271 | + | 0.653101i | \(0.773468\pi\) | |||||||
\(212\) | 1.73205 | + | 1.00000i | 0.118958 | + | 0.0686803i | ||||
\(213\) | −7.79423 | + | 4.50000i | −0.534052 | + | 0.308335i | ||||
\(214\) | −7.00000 | − | 12.1244i | −0.478510 | − | 0.828804i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 8.66025 | − | 10.0000i | 0.587896 | − | 0.678844i | ||||
\(218\) | 6.00000i | 0.406371i | ||||||||
\(219\) | −3.00000 | + | 5.19615i | −0.202721 | + | 0.351123i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | − | 10.3923i | −0.403604 | − | 0.699062i | ||||
\(222\) | −1.73205 | − | 1.00000i | −0.116248 | − | 0.0671156i | ||||
\(223\) | − | 9.00000i | − | 0.602685i | −0.953516 | − | 0.301342i | \(-0.902565\pi\) | ||
0.953516 | − | 0.301342i | \(-0.0974347\pi\) | |||||||
\(224\) | 2.00000 | + | 1.73205i | 0.133631 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.50000 | + | 2.59808i | −0.0997785 | + | 0.172821i | ||||
\(227\) | −19.0526 | + | 11.0000i | −1.26456 | + | 0.730096i | −0.973954 | − | 0.226746i | \(-0.927191\pi\) |
−0.290609 | + | 0.956842i | \(0.593858\pi\) | |||||||
\(228\) | 5.19615 | − | 3.00000i | 0.344124 | − | 0.198680i | ||||
\(229\) | 4.00000 | − | 6.92820i | 0.264327 | − | 0.457829i | −0.703060 | − | 0.711131i | \(-0.748183\pi\) |
0.967387 | + | 0.253302i | \(0.0815167\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.00000 | − | 10.3923i | 0.131590 | − | 0.683763i | ||||
\(232\) | − | 4.00000i | − | 0.262613i | ||||||
\(233\) | −5.19615 | − | 3.00000i | −0.340411 | − | 0.196537i | 0.320043 | − | 0.947403i | \(-0.396303\pi\) |
−0.660454 | + | 0.750867i | \(0.729636\pi\) | |||||||
\(234\) | −2.00000 | − | 3.46410i | −0.130744 | − | 0.226455i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.00000 | − | 12.1244i | 0.455661 | − | 0.789228i | ||||
\(237\) | 17.0000i | 1.10427i | ||||||||
\(238\) | −2.59808 | − | 7.50000i | −0.168408 | − | 0.486153i | ||||
\(239\) | −3.00000 | −0.194054 | −0.0970269 | − | 0.995282i | \(-0.530933\pi\) | ||||
−0.0970269 | + | 0.995282i | \(0.530933\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | + | 1.73205i | 0.0644157 | + | 0.111571i | 0.896435 | − | 0.443176i | \(-0.146148\pi\) |
−0.832019 | + | 0.554747i | \(0.812815\pi\) | |||||||
\(242\) | −4.33013 | + | 2.50000i | −0.278351 | + | 0.160706i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −12.0000 | −0.768221 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.00000 | 0.446304 | ||||||||
\(247\) | −20.7846 | − | 12.0000i | −1.32249 | − | 0.763542i | ||||
\(248\) | −4.33013 | + | 2.50000i | −0.274963 | + | 0.158750i | ||||
\(249\) | 2.00000 | + | 3.46410i | 0.126745 | + | 0.219529i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.00000 | 0.252478 | 0.126239 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126239 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(252\) | −0.866025 | − | 2.50000i | −0.0545545 | − | 0.157485i | ||||
\(253\) | 28.0000i | 1.76034i | ||||||||
\(254\) | −8.00000 | + | 13.8564i | −0.501965 | + | 0.869428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.73205 | + | 1.00000i | 0.108042 | + | 0.0623783i | 0.553047 | − | 0.833150i | \(-0.313465\pi\) |
−0.445005 | + | 0.895528i | \(0.646798\pi\) | |||||||
\(258\) | − | 2.00000i | − | 0.124515i | ||||||
\(259\) | −1.00000 | + | 5.19615i | −0.0621370 | + | 0.322873i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | + | 3.46410i | −0.123797 | + | 0.214423i | ||||
\(262\) | 6.92820 | − | 4.00000i | 0.428026 | − | 0.247121i | ||||
\(263\) | 23.3827 | − | 13.5000i | 1.44184 | − | 0.832446i | 0.443866 | − | 0.896093i | \(-0.353607\pi\) |
0.997972 | + | 0.0636476i | \(0.0202734\pi\) | |||||||
\(264\) | −2.00000 | + | 3.46410i | −0.123091 | + | 0.213201i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −12.0000 | − | 10.3923i | −0.735767 | − | 0.637193i | ||||
\(267\) | 7.00000i | 0.428393i | ||||||||
\(268\) | 10.3923 | + | 6.00000i | 0.634811 | + | 0.366508i | ||||
\(269\) | −5.00000 | − | 8.66025i | −0.304855 | − | 0.528025i | 0.672374 | − | 0.740212i | \(-0.265275\pi\) |
−0.977229 | + | 0.212187i | \(0.931941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.50000 | + | 4.33013i | −0.151864 | + | 0.263036i | −0.931913 | − | 0.362682i | \(-0.881861\pi\) |
0.780049 | + | 0.625719i | \(0.215194\pi\) | |||||||
\(272\) | 3.00000i | 0.181902i | ||||||||
\(273\) | −6.92820 | + | 8.00000i | −0.419314 | + | 0.484182i | ||||
\(274\) | 15.0000 | 0.906183 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.50000 | + | 6.06218i | 0.210675 | + | 0.364900i | ||||
\(277\) | −13.8564 | + | 8.00000i | −0.832551 | + | 0.480673i | −0.854725 | − | 0.519081i | \(-0.826274\pi\) |
0.0221745 | + | 0.999754i | \(0.492941\pi\) | |||||||
\(278\) | −1.73205 | − | 1.00000i | −0.103882 | − | 0.0599760i | ||||
\(279\) | 5.00000 | 0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.0000 | 1.01413 | 0.507067 | − | 0.861906i | \(-0.330729\pi\) | ||||
0.507067 | + | 0.861906i | \(0.330729\pi\) | |||||||
\(282\) | −0.866025 | − | 0.500000i | −0.0515711 | − | 0.0297746i | ||||
\(283\) | 6.92820 | − | 4.00000i | 0.411839 | − | 0.237775i | −0.279741 | − | 0.960076i | \(-0.590248\pi\) |
0.691580 | + | 0.722300i | \(0.256915\pi\) | |||||||
\(284\) | −4.50000 | − | 7.79423i | −0.267026 | − | 0.462502i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.0000 | 0.946100 | ||||||||
\(287\) | −6.06218 | − | 17.5000i | −0.357839 | − | 1.03299i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.50000 | − | 6.06218i | −0.205174 | − | 0.355371i | ||||
\(292\) | −5.19615 | − | 3.00000i | −0.304082 | − | 0.175562i | ||||
\(293\) | 12.0000i | 0.701047i | 0.936554 | + | 0.350524i | \(0.113996\pi\) | ||||
−0.936554 | + | 0.350524i | \(0.886004\pi\) | |||||||
\(294\) | −5.50000 | + | 4.33013i | −0.320767 | + | 0.252538i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.00000 | − | 1.73205i | 0.0581238 | − | 0.100673i | ||||
\(297\) | 3.46410 | − | 2.00000i | 0.201008 | − | 0.116052i | ||||
\(298\) | −5.19615 | + | 3.00000i | −0.301005 | + | 0.173785i | ||||
\(299\) | 14.0000 | − | 24.2487i | 0.809641 | − | 1.40234i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.00000 | + | 1.73205i | −0.288195 | + | 0.0998337i | ||||
\(302\) | − | 24.0000i | − | 1.38104i | ||||||
\(303\) | 15.5885 | + | 9.00000i | 0.895533 | + | 0.517036i | ||||
\(304\) | 3.00000 | + | 5.19615i | 0.172062 | + | 0.298020i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.50000 | − | 2.59808i | 0.0857493 | − | 0.148522i | ||||
\(307\) | 20.0000i | 1.14146i | 0.821138 | + | 0.570730i | \(0.193340\pi\) | ||||
−0.821138 | + | 0.570730i | \(0.806660\pi\) | |||||||
\(308\) | 10.3923 | + | 2.00000i | 0.592157 | + | 0.113961i | ||||
\(309\) | −7.00000 | −0.398216 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.5000 | − | 18.1865i | −0.595400 | − | 1.03126i | −0.993490 | − | 0.113917i | \(-0.963660\pi\) |
0.398090 | − | 0.917346i | \(-0.369673\pi\) | |||||||
\(312\) | 3.46410 | − | 2.00000i | 0.196116 | − | 0.113228i | ||||
\(313\) | −23.3827 | − | 13.5000i | −1.32167 | − | 0.763065i | −0.337673 | − | 0.941263i | \(-0.609640\pi\) |
−0.983995 | + | 0.178198i | \(0.942973\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.0000 | −0.956325 | ||||||||
\(317\) | −15.5885 | − | 9.00000i | −0.875535 | − | 0.505490i | −0.00635137 | − | 0.999980i | \(-0.502022\pi\) |
−0.869184 | + | 0.494489i | \(0.835355\pi\) | |||||||
\(318\) | 1.73205 | − | 1.00000i | 0.0971286 | − | 0.0560772i | ||||
\(319\) | −8.00000 | − | 13.8564i | −0.447914 | − | 0.775810i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.0000 | −0.781404 | ||||||||
\(322\) | 12.1244 | − | 14.0000i | 0.675664 | − | 0.780189i | ||||
\(323\) | − | 18.0000i | − | 1.00155i | ||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.00000 | − | 6.92820i | −0.221540 | − | 0.383718i | ||||
\(327\) | 5.19615 | + | 3.00000i | 0.287348 | + | 0.165900i | ||||
\(328\) | 7.00000i | 0.386510i | ||||||||
\(329\) | −0.500000 | + | 2.59808i | −0.0275659 | + | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.0000 | − | 29.4449i | 0.934405 | − | 1.61844i | 0.158712 | − | 0.987325i | \(-0.449266\pi\) |
0.775692 | − | 0.631111i | \(-0.217401\pi\) | |||||||
\(332\) | −3.46410 | + | 2.00000i | −0.190117 | + | 0.109764i | ||||
\(333\) | −1.73205 | + | 1.00000i | −0.0949158 | + | 0.0547997i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.50000 | − | 0.866025i | 0.136386 | − | 0.0472456i | ||||
\(337\) | 3.00000i | 0.163420i | 0.996656 | + | 0.0817102i | \(0.0260382\pi\) | ||||
−0.996656 | + | 0.0817102i | \(0.973962\pi\) | |||||||
\(338\) | −2.59808 | − | 1.50000i | −0.141317 | − | 0.0815892i | ||||
\(339\) | 1.50000 | + | 2.59808i | 0.0814688 | + | 0.141108i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.0000 | + | 17.3205i | −0.541530 | + | 0.937958i | ||||
\(342\) | − | 6.00000i | − | 0.324443i | ||||||
\(343\) | 15.5885 | + | 10.0000i | 0.841698 | + | 0.539949i | ||||
\(344\) | 2.00000 | 0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | + | 5.19615i | 0.161281 | + | 0.279347i | ||||
\(347\) | 27.7128 | − | 16.0000i | 1.48770 | − | 0.858925i | 0.487800 | − | 0.872955i | \(-0.337799\pi\) |
0.999902 | + | 0.0140303i | \(0.00446613\pi\) | |||||||
\(348\) | −3.46410 | − | 2.00000i | −0.185695 | − | 0.107211i | ||||
\(349\) | 18.0000 | 0.963518 | 0.481759 | − | 0.876304i | \(-0.339998\pi\) | ||||
0.481759 | + | 0.876304i | \(0.339998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | −3.46410 | − | 2.00000i | −0.184637 | − | 0.106600i | ||||
\(353\) | 12.9904 | − | 7.50000i | 0.691408 | − | 0.399185i | −0.112731 | − | 0.993626i | \(-0.535960\pi\) |
0.804139 | + | 0.594441i | \(0.202627\pi\) | |||||||
\(354\) | −7.00000 | − | 12.1244i | −0.372046 | − | 0.644402i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.00000 | −0.370999 | ||||||||
\(357\) | −7.79423 | − | 1.50000i | −0.412514 | − | 0.0793884i | ||||
\(358\) | 2.00000i | 0.105703i | ||||||||
\(359\) | 2.00000 | − | 3.46410i | 0.105556 | − | 0.182828i | −0.808409 | − | 0.588621i | \(-0.799671\pi\) |
0.913965 | + | 0.405793i | \(0.133004\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | 10.3923 | + | 6.00000i | 0.546207 | + | 0.315353i | ||||
\(363\) | 5.00000i | 0.262432i | ||||||||
\(364\) | −8.00000 | − | 6.92820i | −0.419314 | − | 0.363137i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.00000 | + | 10.3923i | −0.313625 | + | 0.543214i | ||||
\(367\) | −27.7128 | + | 16.0000i | −1.44660 | + | 0.835193i | −0.998277 | − | 0.0586798i | \(-0.981311\pi\) |
−0.448320 | + | 0.893873i | \(0.647978\pi\) | |||||||
\(368\) | −6.06218 | + | 3.50000i | −0.316013 | + | 0.182450i | ||||
\(369\) | 3.50000 | − | 6.06218i | 0.182203 | − | 0.315584i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.00000 | − | 3.46410i | −0.207670 | − | 0.179847i | ||||
\(372\) | 5.00000i | 0.259238i | ||||||||
\(373\) | 10.3923 | + | 6.00000i | 0.538093 | + | 0.310668i | 0.744306 | − | 0.667839i | \(-0.232781\pi\) |
−0.206213 | + | 0.978507i | \(0.566114\pi\) | |||||||
\(374\) | 6.00000 | + | 10.3923i | 0.310253 | + | 0.537373i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.500000 | − | 0.866025i | 0.0257855 | − | 0.0446619i | ||||
\(377\) | 16.0000i | 0.824042i | ||||||||
\(378\) | −2.59808 | − | 0.500000i | −0.133631 | − | 0.0257172i | ||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | + | 13.8564i | 0.409852 | + | 0.709885i | ||||
\(382\) | −12.9904 | + | 7.50000i | −0.664646 | + | 0.383733i | ||||
\(383\) | −26.8468 | − | 15.5000i | −1.37181 | − | 0.792013i | −0.380651 | − | 0.924719i | \(-0.624300\pi\) |
−0.991155 | + | 0.132706i | \(0.957633\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.0000 | −1.27247 | ||||||||
\(387\) | −1.73205 | − | 1.00000i | −0.0880451 | − | 0.0508329i | ||||
\(388\) | 6.06218 | − | 3.50000i | 0.307760 | − | 0.177686i | ||||
\(389\) | 5.00000 | + | 8.66025i | 0.253510 | + | 0.439092i | 0.964490 | − | 0.264120i | \(-0.0850816\pi\) |
−0.710980 | + | 0.703213i | \(0.751748\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.0000 | 1.06202 | ||||||||
\(392\) | −4.33013 | − | 5.50000i | −0.218704 | − | 0.277792i | ||||
\(393\) | − | 8.00000i | − | 0.403547i | ||||||
\(394\) | −10.0000 | + | 17.3205i | −0.503793 | + | 0.872595i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.00000 | + | 3.46410i | 0.100504 | + | 0.174078i | ||||
\(397\) | 19.0526 | + | 11.0000i | 0.956221 | + | 0.552074i | 0.895008 | − | 0.446051i | \(-0.147170\pi\) |
0.0612128 | + | 0.998125i | \(0.480503\pi\) | |||||||
\(398\) | 15.0000i | 0.751882i | ||||||||
\(399\) | −15.0000 | + | 5.19615i | −0.750939 | + | 0.260133i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.0000 | + | 29.4449i | −0.848939 | + | 1.47041i | 0.0332161 | + | 0.999448i | \(0.489425\pi\) |
−0.882156 | + | 0.470958i | \(0.843908\pi\) | |||||||
\(402\) | 10.3923 | − | 6.00000i | 0.518321 | − | 0.299253i | ||||
\(403\) | 17.3205 | − | 10.0000i | 0.862796 | − | 0.498135i | ||||
\(404\) | −9.00000 | + | 15.5885i | −0.447767 | + | 0.775555i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.00000 | + | 10.3923i | −0.0992583 | + | 0.515761i | ||||
\(407\) | − | 8.00000i | − | 0.396545i | ||||||
\(408\) | 2.59808 | + | 1.50000i | 0.128624 | + | 0.0742611i | ||||
\(409\) | 14.5000 | + | 25.1147i | 0.716979 | + | 1.24184i | 0.962191 | + | 0.272374i | \(0.0878089\pi\) |
−0.245212 | + | 0.969469i | \(0.578858\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.50000 | − | 12.9904i | 0.369948 | − | 0.640768i | ||||
\(412\) | − | 7.00000i | − | 0.344865i | ||||||
\(413\) | −24.2487 | + | 28.0000i | −1.19320 | + | 1.37779i | ||||
\(414\) | 7.00000 | 0.344031 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.00000 | + | 3.46410i | 0.0980581 | + | 0.169842i | ||||
\(417\) | −1.73205 | + | 1.00000i | −0.0848189 | + | 0.0489702i | ||||
\(418\) | 20.7846 | + | 12.0000i | 1.01661 | + | 0.586939i | ||||
\(419\) | 26.0000 | 1.27018 | 0.635092 | − | 0.772437i | \(-0.280962\pi\) | ||||
0.635092 | + | 0.772437i | \(0.280962\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0000 | 0.779792 | 0.389896 | − | 0.920859i | \(-0.372511\pi\) | ||||
0.389896 | + | 0.920859i | \(0.372511\pi\) | |||||||
\(422\) | −19.0526 | − | 11.0000i | −0.927464 | − | 0.535472i | ||||
\(423\) | −0.866025 | + | 0.500000i | −0.0421076 | + | 0.0243108i | ||||
\(424\) | 1.00000 | + | 1.73205i | 0.0485643 | + | 0.0841158i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.00000 | −0.436051 | ||||||||
\(427\) | 31.1769 | + | 6.00000i | 1.50876 | + | 0.290360i | ||||
\(428\) | − | 14.0000i | − | 0.676716i | ||||||
\(429\) | 8.00000 | − | 13.8564i | 0.386244 | − | 0.668994i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.5000 | + | 33.7750i | 0.939282 | + | 1.62688i | 0.766814 | + | 0.641869i | \(0.221841\pi\) |
0.172468 | + | 0.985015i | \(0.444826\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 37.0000i | − | 1.77811i | −0.457804 | − | 0.889053i | \(-0.651364\pi\) | ||
0.457804 | − | 0.889053i | \(-0.348636\pi\) | |||||||
\(434\) | 12.5000 | − | 4.33013i | 0.600019 | − | 0.207853i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.00000 | + | 5.19615i | −0.143674 | + | 0.248851i | ||||
\(437\) | 36.3731 | − | 21.0000i | 1.73996 | − | 1.00457i | ||||
\(438\) | −5.19615 | + | 3.00000i | −0.248282 | + | 0.143346i | ||||
\(439\) | 8.50000 | − | 14.7224i | 0.405683 | − | 0.702663i | −0.588718 | − | 0.808339i | \(-0.700367\pi\) |
0.994401 | + | 0.105675i | \(0.0337004\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | − | 12.0000i | − | 0.570782i | ||||||
\(443\) | −22.5167 | − | 13.0000i | −1.06980 | − | 0.617649i | −0.141672 | − | 0.989914i | \(-0.545248\pi\) |
−0.928126 | + | 0.372265i | \(0.878581\pi\) | |||||||
\(444\) | −1.00000 | − | 1.73205i | −0.0474579 | − | 0.0821995i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.50000 | − | 7.79423i | 0.213081 | − | 0.369067i | ||||
\(447\) | 6.00000i | 0.283790i | ||||||||
\(448\) | 0.866025 | + | 2.50000i | 0.0409159 | + | 0.118114i | ||||
\(449\) | 13.0000 | 0.613508 | 0.306754 | − | 0.951789i | \(-0.400757\pi\) | ||||
0.306754 | + | 0.951789i | \(0.400757\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.0000 | + | 24.2487i | 0.659234 | + | 1.14183i | ||||
\(452\) | −2.59808 | + | 1.50000i | −0.122203 | + | 0.0705541i | ||||
\(453\) | −20.7846 | − | 12.0000i | −0.976546 | − | 0.563809i | ||||
\(454\) | −22.0000 | −1.03251 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | −15.5885 | − | 9.00000i | −0.729197 | − | 0.421002i | 0.0889312 | − | 0.996038i | \(-0.471655\pi\) |
−0.818128 | + | 0.575036i | \(0.804988\pi\) | |||||||
\(458\) | 6.92820 | − | 4.00000i | 0.323734 | − | 0.186908i | ||||
\(459\) | −1.50000 | − | 2.59808i | −0.0700140 | − | 0.121268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.0000 | 1.67669 | 0.838344 | − | 0.545142i | \(-0.183524\pi\) | ||||
0.838344 | + | 0.545142i | \(0.183524\pi\) | |||||||
\(462\) | 6.92820 | − | 8.00000i | 0.322329 | − | 0.372194i | ||||
\(463\) | 7.00000i | 0.325318i | 0.986682 | + | 0.162659i | \(0.0520070\pi\) | ||||
−0.986682 | + | 0.162659i | \(0.947993\pi\) | |||||||
\(464\) | 2.00000 | − | 3.46410i | 0.0928477 | − | 0.160817i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | − | 5.19615i | −0.138972 | − | 0.240707i | ||||
\(467\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(468\) | − | 4.00000i | − | 0.184900i | ||||||
\(469\) | −24.0000 | − | 20.7846i | −1.10822 | − | 0.959744i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.00000 | + | 3.46410i | −0.0921551 | + | 0.159617i | ||||
\(472\) | 12.1244 | − | 7.00000i | 0.558069 | − | 0.322201i | ||||
\(473\) | 6.92820 | − | 4.00000i | 0.318559 | − | 0.183920i | ||||
\(474\) | −8.50000 | + | 14.7224i | −0.390418 | + | 0.676224i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.50000 | − | 7.79423i | 0.0687524 | − | 0.357248i | ||||
\(477\) | − | 2.00000i | − | 0.0915737i | ||||||
\(478\) | −2.59808 | − | 1.50000i | −0.118833 | − | 0.0686084i | ||||
\(479\) | 0.500000 | + | 0.866025i | 0.0228456 | + | 0.0395697i | 0.877222 | − | 0.480085i | \(-0.159394\pi\) |
−0.854377 | + | 0.519654i | \(0.826061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | + | 6.92820i | −0.182384 | + | 0.315899i | ||||
\(482\) | 2.00000i | 0.0910975i | ||||||||
\(483\) | −6.06218 | − | 17.5000i | −0.275839 | − | 0.796278i | ||||
\(484\) | −5.00000 | −0.227273 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 4.33013 | − | 2.50000i | 0.196217 | − | 0.113286i | −0.398673 | − | 0.917093i | \(-0.630529\pi\) |
0.594890 | + | 0.803807i | \(0.297196\pi\) | |||||||
\(488\) | −10.3923 | − | 6.00000i | −0.470438 | − | 0.271607i | ||||
\(489\) | −8.00000 | −0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.0000 | 1.71492 | 0.857458 | − | 0.514554i | \(-0.172042\pi\) | ||||
0.857458 | + | 0.514554i | \(0.172042\pi\) | |||||||
\(492\) | 6.06218 | + | 3.50000i | 0.273304 | + | 0.157792i | ||||
\(493\) | −10.3923 | + | 6.00000i | −0.468046 | + | 0.270226i | ||||
\(494\) | −12.0000 | − | 20.7846i | −0.539906 | − | 0.935144i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.00000 | −0.224507 | ||||||||
\(497\) | 7.79423 | + | 22.5000i | 0.349619 | + | 1.00926i | ||||
\(498\) | 4.00000i | 0.179244i | ||||||||
\(499\) | 14.0000 | − | 24.2487i | 0.626726 | − | 1.08552i | −0.361478 | − | 0.932381i | \(-0.617728\pi\) |
0.988204 | − | 0.153141i | \(-0.0489388\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.46410 | + | 2.00000i | 0.154610 | + | 0.0892644i | ||||
\(503\) | − | 36.0000i | − | 1.60516i | −0.596544 | − | 0.802580i | \(-0.703460\pi\) | ||
0.596544 | − | 0.802580i | \(-0.296540\pi\) | |||||||
\(504\) | 0.500000 | − | 2.59808i | 0.0222718 | − | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −14.0000 | + | 24.2487i | −0.622376 | + | 1.07799i | ||||
\(507\) | −2.59808 | + | 1.50000i | −0.115385 | + | 0.0666173i | ||||
\(508\) | −13.8564 | + | 8.00000i | −0.614779 | + | 0.354943i | ||||
\(509\) | −8.00000 | + | 13.8564i | −0.354594 | + | 0.614174i | −0.987048 | − | 0.160423i | \(-0.948714\pi\) |
0.632455 | + | 0.774597i | \(0.282047\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | + | 10.3923i | 0.530849 | + | 0.459728i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −5.19615 | − | 3.00000i | −0.229416 | − | 0.132453i | ||||
\(514\) | 1.00000 | + | 1.73205i | 0.0441081 | + | 0.0763975i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.00000 | − | 1.73205i | 0.0440225 | − | 0.0762493i | ||||
\(517\) | − | 4.00000i | − | 0.175920i | ||||||
\(518\) | −3.46410 | + | 4.00000i | −0.152204 | + | 0.175750i | ||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.50000 | + | 7.79423i | 0.197149 | + | 0.341471i | 0.947603 | − | 0.319451i | \(-0.103499\pi\) |
−0.750454 | + | 0.660922i | \(0.770165\pi\) | |||||||
\(522\) | −3.46410 | + | 2.00000i | −0.151620 | + | 0.0875376i | ||||
\(523\) | 38.1051 | + | 22.0000i | 1.66622 | + | 0.961993i | 0.969648 | + | 0.244507i | \(0.0786260\pi\) |
0.696573 | + | 0.717486i | \(0.254707\pi\) | |||||||
\(524\) | 8.00000 | 0.349482 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.0000 | 1.17726 | ||||||||
\(527\) | 12.9904 | + | 7.50000i | 0.565870 | + | 0.326705i | ||||
\(528\) | −3.46410 | + | 2.00000i | −0.150756 | + | 0.0870388i | ||||
\(529\) | 13.0000 | + | 22.5167i | 0.565217 | + | 0.978985i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.0000 | −0.607548 | ||||||||
\(532\) | −5.19615 | − | 15.0000i | −0.225282 | − | 0.650332i | ||||
\(533\) | − | 28.0000i | − | 1.21281i | ||||||
\(534\) | −3.50000 | + | 6.06218i | −0.151460 | + | 0.262336i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.00000 | + | 10.3923i | 0.259161 | + | 0.448879i | ||||
\(537\) | 1.73205 | + | 1.00000i | 0.0747435 | + | 0.0431532i | ||||
\(538\) | − | 10.0000i | − | 0.431131i | ||||||
\(539\) | −26.0000 | − | 10.3923i | −1.11990 | − | 0.447628i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.0000 | + | 27.7128i | −0.687894 | + | 1.19147i | 0.284624 | + | 0.958639i | \(0.408131\pi\) |
−0.972518 | + | 0.232828i | \(0.925202\pi\) | |||||||
\(542\) | −4.33013 | + | 2.50000i | −0.185995 | + | 0.107384i | ||||
\(543\) | 10.3923 | − | 6.00000i | 0.445976 | − | 0.257485i | ||||
\(544\) | −1.50000 | + | 2.59808i | −0.0643120 | + | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10.0000 | + | 3.46410i | −0.427960 | + | 0.148250i | ||||
\(547\) | 22.0000i | 0.940652i | 0.882493 | + | 0.470326i | \(0.155864\pi\) | ||||
−0.882493 | + | 0.470326i | \(0.844136\pi\) | |||||||
\(548\) | 12.9904 | + | 7.50000i | 0.554922 | + | 0.320384i | ||||
\(549\) | 6.00000 | + | 10.3923i | 0.256074 | + | 0.443533i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | + | 20.7846i | −0.511217 | + | 0.885454i | ||||
\(552\) | 7.00000i | 0.297940i | ||||||||
\(553\) | 44.1673 | + | 8.50000i | 1.87818 | + | 0.361457i | ||||
\(554\) | −16.0000 | −0.679775 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00000 | − | 1.73205i | −0.0424094 | − | 0.0734553i | ||||
\(557\) | 25.9808 | − | 15.0000i | 1.10084 | − | 0.635570i | 0.164399 | − | 0.986394i | \(-0.447432\pi\) |
0.936442 | + | 0.350824i | \(0.114098\pi\) | |||||||
\(558\) | 4.33013 | + | 2.50000i | 0.183309 | + | 0.105833i | ||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0000 | 0.506640 | ||||||||
\(562\) | 14.7224 | + | 8.50000i | 0.621028 | + | 0.358551i | ||||
\(563\) | 1.73205 | − | 1.00000i | 0.0729972 | − | 0.0421450i | −0.463057 | − | 0.886328i | \(-0.653248\pi\) |
0.536054 | + | 0.844183i | \(0.319914\pi\) | |||||||
\(564\) | −0.500000 | − | 0.866025i | −0.0210538 | − | 0.0364662i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.00000 | 0.336265 | ||||||||
\(567\) | −1.73205 | + | 2.00000i | −0.0727393 | + | 0.0839921i | ||||
\(568\) | − | 9.00000i | − | 0.377632i | ||||||
\(569\) | −22.5000 | + | 38.9711i | −0.943249 | + | 1.63376i | −0.184030 | + | 0.982921i | \(0.558914\pi\) |
−0.759220 | + | 0.650835i | \(0.774419\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | − | 34.6410i | −0.836974 | − | 1.44968i | −0.892413 | − | 0.451219i | \(-0.850989\pi\) |
0.0554391 | − | 0.998462i | \(-0.482344\pi\) | |||||||
\(572\) | 13.8564 | + | 8.00000i | 0.579365 | + | 0.334497i | ||||
\(573\) | 15.0000i | 0.626634i | ||||||||
\(574\) | 3.50000 | − | 18.1865i | 0.146087 | − | 0.759091i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −1.73205 | + | 1.00000i | −0.0721062 | + | 0.0416305i | −0.535620 | − | 0.844459i | \(-0.679922\pi\) |
0.463513 | + | 0.886090i | \(0.346589\pi\) | |||||||
\(578\) | −6.92820 | + | 4.00000i | −0.288175 | + | 0.166378i | ||||
\(579\) | −12.5000 | + | 21.6506i | −0.519482 | + | 0.899770i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.0000 | − | 3.46410i | 0.414870 | − | 0.143715i | ||||
\(582\) | − | 7.00000i | − | 0.290159i | ||||||
\(583\) | 6.92820 | + | 4.00000i | 0.286937 | + | 0.165663i | ||||
\(584\) | −3.00000 | − | 5.19615i | −0.124141 | − | 0.215018i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | + | 10.3923i | −0.247858 | + | 0.429302i | ||||
\(587\) | 42.0000i | 1.73353i | 0.498721 | + | 0.866763i | \(0.333803\pi\) | ||||
−0.498721 | + | 0.866763i | \(0.666197\pi\) | |||||||
\(588\) | −6.92820 | + | 1.00000i | −0.285714 | + | 0.0412393i | ||||
\(589\) | 30.0000 | 1.23613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0000 | + | 17.3205i | 0.411345 | + | 0.712470i | ||||
\(592\) | 1.73205 | − | 1.00000i | 0.0711868 | − | 0.0410997i | ||||
\(593\) | 11.2583 | + | 6.50000i | 0.462324 | + | 0.266923i | 0.713021 | − | 0.701143i | \(-0.247326\pi\) |
−0.250697 | + | 0.968066i | \(0.580660\pi\) | |||||||
\(594\) | 4.00000 | 0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 12.9904 | + | 7.50000i | 0.531661 | + | 0.306955i | ||||
\(598\) | 24.2487 | − | 14.0000i | 0.991604 | − | 0.572503i | ||||
\(599\) | −15.5000 | − | 26.8468i | −0.633313 | − | 1.09693i | −0.986870 | − | 0.161517i | \(-0.948361\pi\) |
0.353557 | − | 0.935413i | \(-0.384972\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.0000 | 1.87638 | 0.938190 | − | 0.346122i | \(-0.112502\pi\) | ||||
0.938190 | + | 0.346122i | \(0.112502\pi\) | |||||||
\(602\) | −5.19615 | − | 1.00000i | −0.211779 | − | 0.0407570i | ||||
\(603\) | − | 12.0000i | − | 0.488678i | ||||||
\(604\) | 12.0000 | − | 20.7846i | 0.488273 | − | 0.845714i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.00000 | + | 15.5885i | 0.365600 | + | 0.633238i | ||||
\(607\) | −25.1147 | − | 14.5000i | −1.01938 | − | 0.588537i | −0.105453 | − | 0.994424i | \(-0.533629\pi\) |
−0.913923 | + | 0.405887i | \(0.866962\pi\) | |||||||
\(608\) | 6.00000i | 0.243332i | ||||||||
\(609\) | 8.00000 | + | 6.92820i | 0.324176 | + | 0.280745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.00000 | + | 3.46410i | −0.0809113 | + | 0.140143i | ||||
\(612\) | 2.59808 | − | 1.50000i | 0.105021 | − | 0.0606339i | ||||
\(613\) | −3.46410 | + | 2.00000i | −0.139914 | + | 0.0807792i | −0.568323 | − | 0.822806i | \(-0.692408\pi\) |
0.428409 | + | 0.903585i | \(0.359074\pi\) | |||||||
\(614\) | −10.0000 | + | 17.3205i | −0.403567 | + | 0.698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.00000 | + | 6.92820i | 0.322329 | + | 0.279145i | ||||
\(617\) | 1.00000i | 0.0402585i | 0.999797 | + | 0.0201292i | \(0.00640777\pi\) | ||||
−0.999797 | + | 0.0201292i | \(0.993592\pi\) | |||||||
\(618\) | −6.06218 | − | 3.50000i | −0.243857 | − | 0.140791i | ||||
\(619\) | −8.00000 | − | 13.8564i | −0.321547 | − | 0.556936i | 0.659260 | − | 0.751915i | \(-0.270870\pi\) |
−0.980807 | + | 0.194979i | \(0.937536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.50000 | − | 6.06218i | 0.140450 | − | 0.243267i | ||||
\(622\) | − | 21.0000i | − | 0.842023i | ||||||
\(623\) | 18.1865 | + | 3.50000i | 0.728628 | + | 0.140225i | ||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −13.5000 | − | 23.3827i | −0.539569 | − | 0.934560i | ||||
\(627\) | 20.7846 | − | 12.0000i | 0.830057 | − | 0.479234i | ||||
\(628\) | −3.46410 | − | 2.00000i | −0.138233 | − | 0.0798087i | ||||
\(629\) | −6.00000 | −0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.00000 | 0.278666 | 0.139333 | − | 0.990246i | \(-0.455504\pi\) | ||||
0.139333 | + | 0.990246i | \(0.455504\pi\) | |||||||
\(632\) | −14.7224 | − | 8.50000i | −0.585627 | − | 0.338112i | ||||
\(633\) | −19.0526 | + | 11.0000i | −0.757271 | + | 0.437211i | ||||
\(634\) | −9.00000 | − | 15.5885i | −0.357436 | − | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.00000 | 0.0793052 | ||||||||
\(637\) | 17.3205 | + | 22.0000i | 0.686264 | + | 0.871672i | ||||
\(638\) | − | 16.0000i | − | 0.633446i | ||||||
\(639\) | −4.50000 | + | 7.79423i | −0.178017 | + | 0.308335i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.50000 | + | 7.79423i | 0.177739 | + | 0.307854i | 0.941106 | − | 0.338112i | \(-0.109788\pi\) |
−0.763367 | + | 0.645966i | \(0.776455\pi\) | |||||||
\(642\) | −12.1244 | − | 7.00000i | −0.478510 | − | 0.276268i | ||||
\(643\) | − | 14.0000i | − | 0.552106i | −0.961142 | − | 0.276053i | \(-0.910973\pi\) | ||
0.961142 | − | 0.276053i | \(-0.0890266\pi\) | |||||||
\(644\) | 17.5000 | − | 6.06218i | 0.689597 | − | 0.238883i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.00000 | − | 15.5885i | 0.354100 | − | 0.613320i | ||||
\(647\) | −27.7128 | + | 16.0000i | −1.08950 | + | 0.629025i | −0.933444 | − | 0.358723i | \(-0.883212\pi\) |
−0.156059 | + | 0.987748i | \(0.549879\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 28.0000 | − | 48.4974i | 1.09910 | − | 1.90369i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.50000 | − | 12.9904i | 0.0979827 | − | 0.509133i | ||||
\(652\) | − | 8.00000i | − | 0.313304i | ||||||
\(653\) | 13.8564 | + | 8.00000i | 0.542243 | + | 0.313064i | 0.745988 | − | 0.665960i | \(-0.231978\pi\) |
−0.203744 | + | 0.979024i | \(0.565311\pi\) | |||||||
\(654\) | 3.00000 | + | 5.19615i | 0.117309 | + | 0.203186i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.50000 | + | 6.06218i | −0.136652 | + | 0.236688i | ||||
\(657\) | 6.00000i | 0.234082i | ||||||||
\(658\) | −1.73205 | + | 2.00000i | −0.0675224 | + | 0.0779681i | ||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.0000 | − | 25.9808i | −0.583432 | − | 1.01053i | −0.995069 | − | 0.0991864i | \(-0.968376\pi\) |
0.411636 | − | 0.911348i | \(-0.364957\pi\) | |||||||
\(662\) | 29.4449 | − | 17.0000i | 1.14441 | − | 0.660724i | ||||
\(663\) | −10.3923 | − | 6.00000i | −0.403604 | − | 0.233021i | ||||
\(664\) | −4.00000 | −0.155230 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.00000 | −0.0774984 | ||||||||
\(667\) | −24.2487 | − | 14.0000i | −0.938914 | − | 0.542082i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.50000 | − | 7.79423i | −0.173980 | − | 0.301342i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −48.0000 | −1.85302 | ||||||||
\(672\) | 2.59808 | + | 0.500000i | 0.100223 | + | 0.0192879i | ||||
\(673\) | 11.0000i | 0.424019i | 0.977268 | + | 0.212009i | \(0.0680008\pi\) | ||||
−0.977268 | + | 0.212009i | \(0.931999\pi\) | |||||||
\(674\) | −1.50000 | + | 2.59808i | −0.0577778 | + | 0.100074i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.50000 | − | 2.59808i | −0.0576923 | − | 0.0999260i | ||||
\(677\) | −27.7128 | − | 16.0000i | −1.06509 | − | 0.614930i | −0.138254 | − | 0.990397i | \(-0.544149\pi\) |
−0.926836 | + | 0.375467i | \(0.877482\pi\) | |||||||
\(678\) | 3.00000i | 0.115214i | ||||||||
\(679\) | −17.5000 | + | 6.06218i | −0.671588 | + | 0.232645i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.0000 | + | 19.0526i | −0.421521 | + | 0.730096i | ||||
\(682\) | −17.3205 | + | 10.0000i | −0.663237 | + | 0.382920i | ||||
\(683\) | −19.0526 | + | 11.0000i | −0.729026 | + | 0.420903i | −0.818066 | − | 0.575125i | \(-0.804953\pi\) |
0.0890398 | + | 0.996028i | \(0.471620\pi\) | |||||||
\(684\) | 3.00000 | − | 5.19615i | 0.114708 | − | 0.198680i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.50000 | + | 16.4545i | 0.324532 | + | 0.628235i | ||||
\(687\) | − | 8.00000i | − | 0.305219i | ||||||
\(688\) | 1.73205 | + | 1.00000i | 0.0660338 | + | 0.0381246i | ||||
\(689\) | −4.00000 | − | 6.92820i | −0.152388 | − | 0.263944i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.0000 | − | 20.7846i | 0.456502 | − | 0.790684i | −0.542272 | − | 0.840203i | \(-0.682436\pi\) |
0.998773 | + | 0.0495194i | \(0.0157690\pi\) | |||||||
\(692\) | 6.00000i | 0.228086i | ||||||||
\(693\) | −3.46410 | − | 10.0000i | −0.131590 | − | 0.379869i | ||||
\(694\) | 32.0000 | 1.21470 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.00000 | − | 3.46410i | −0.0758098 | − | 0.131306i | ||||
\(697\) | 18.1865 | − | 10.5000i | 0.688864 | − | 0.397716i | ||||
\(698\) | 15.5885 | + | 9.00000i | 0.590032 | + | 0.340655i | ||||
\(699\) | −6.00000 | −0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.0000 | 0.453234 | 0.226617 | − | 0.973984i | \(-0.427233\pi\) | ||||
0.226617 | + | 0.973984i | \(0.427233\pi\) | |||||||
\(702\) | −3.46410 | − | 2.00000i | −0.130744 | − | 0.0754851i | ||||
\(703\) | −10.3923 | + | 6.00000i | −0.391953 | + | 0.226294i | ||||
\(704\) | −2.00000 | − | 3.46410i | −0.0753778 | − | 0.130558i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.0000 | 0.564532 | ||||||||
\(707\) | 31.1769 | − | 36.0000i | 1.17253 | − | 1.35392i | ||||
\(708\) | − | 14.0000i | − | 0.526152i | ||||||
\(709\) | 7.00000 | − | 12.1244i | 0.262891 | − | 0.455340i | −0.704118 | − | 0.710083i | \(-0.748658\pi\) |
0.967009 | + | 0.254743i | \(0.0819909\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.50000 | + | 14.7224i | 0.318775 | + | 0.552134i | ||||
\(712\) | −6.06218 | − | 3.50000i | −0.227190 | − | 0.131168i | ||||
\(713\) | 35.0000i | 1.31076i | ||||||||
\(714\) | −6.00000 | − | 5.19615i | −0.224544 | − | 0.194461i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.00000 | + | 1.73205i | −0.0373718 | + | 0.0647298i | ||||
\(717\) | −2.59808 | + | 1.50000i | −0.0970269 | + | 0.0560185i | ||||
\(718\) | 3.46410 | − | 2.00000i | 0.129279 | − | 0.0746393i | ||||
\(719\) | −3.50000 | + | 6.06218i | −0.130528 | + | 0.226081i | −0.923880 | − | 0.382682i | \(-0.875001\pi\) |
0.793352 | + | 0.608763i | \(0.208334\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.50000 | + | 18.1865i | −0.130347 | + | 0.677302i | ||||
\(722\) | − | 17.0000i | − | 0.632674i | ||||||
\(723\) | 1.73205 | + | 1.00000i | 0.0644157 | + | 0.0371904i | ||||
\(724\) | 6.00000 | + | 10.3923i | 0.222988 | + | 0.386227i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.50000 | + | 4.33013i | −0.0927837 | + | 0.160706i | ||||
\(727\) | − | 49.0000i | − | 1.81731i | −0.417548 | − | 0.908655i | \(-0.637111\pi\) | ||
0.417548 | − | 0.908655i | \(-0.362889\pi\) | |||||||
\(728\) | −3.46410 | − | 10.0000i | −0.128388 | − | 0.370625i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.00000 | − | 5.19615i | −0.110959 | − | 0.192187i | ||||
\(732\) | −10.3923 | + | 6.00000i | −0.384111 | + | 0.221766i | ||||
\(733\) | −8.66025 | − | 5.00000i | −0.319874 | − | 0.184679i | 0.331463 | − | 0.943468i | \(-0.392458\pi\) |
−0.651336 | + | 0.758789i | \(0.725791\pi\) | |||||||
\(734\) | −32.0000 | −1.18114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.00000 | −0.258023 | ||||||||
\(737\) | 41.5692 | + | 24.0000i | 1.53122 | + | 0.884051i | ||||
\(738\) | 6.06218 | − | 3.50000i | 0.223152 | − | 0.128837i | ||||
\(739\) | 7.00000 | + | 12.1244i | 0.257499 | + | 0.446002i | 0.965571 | − | 0.260138i | \(-0.0837682\pi\) |
−0.708072 | + | 0.706140i | \(0.750435\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.0000 | −0.881662 | ||||||||
\(742\) | −1.73205 | − | 5.00000i | −0.0635856 | − | 0.183556i | ||||
\(743\) | − | 1.00000i | − | 0.0366864i | −0.999832 | − | 0.0183432i | \(-0.994161\pi\) | ||
0.999832 | − | 0.0183432i | \(-0.00583916\pi\) | |||||||
\(744\) | −2.50000 | + | 4.33013i | −0.0916544 | + | 0.158750i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.00000 | + | 10.3923i | 0.219676 | + | 0.380489i | ||||
\(747\) | 3.46410 | + | 2.00000i | 0.126745 | + | 0.0731762i | ||||
\(748\) | 12.0000i | 0.438763i | ||||||||
\(749\) | −7.00000 | + | 36.3731i | −0.255774 | + | 1.32904i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | − | 13.8564i | 0.291924 | − | 0.505627i | −0.682341 | − | 0.731034i | \(-0.739038\pi\) |
0.974265 | + | 0.225407i | \(0.0723712\pi\) | |||||||
\(752\) | 0.866025 | − | 0.500000i | 0.0315807 | − | 0.0182331i | ||||
\(753\) | 3.46410 | − | 2.00000i | 0.126239 | − | 0.0728841i | ||||
\(754\) | −8.00000 | + | 13.8564i | −0.291343 | + | 0.504621i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.00000 | − | 1.73205i | −0.0727393 | − | 0.0629941i | ||||
\(757\) | − | 16.0000i | − | 0.581530i | −0.956795 | − | 0.290765i | \(-0.906090\pi\) | ||
0.956795 | − | 0.290765i | \(-0.0939098\pi\) | |||||||
\(758\) | −17.3205 | − | 10.0000i | −0.629109 | − | 0.363216i | ||||
\(759\) | 14.0000 | + | 24.2487i | 0.508168 | + | 0.880172i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.5000 | − | 18.1865i | 0.380625 | − | 0.659261i | −0.610527 | − | 0.791995i | \(-0.709042\pi\) |
0.991152 | + | 0.132734i | \(0.0423756\pi\) | |||||||
\(762\) | 16.0000i | 0.579619i | ||||||||
\(763\) | 10.3923 | − | 12.0000i | 0.376227 | − | 0.434429i | ||||
\(764\) | −15.0000 | −0.542681 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.5000 | − | 26.8468i | −0.560038 | − | 0.970014i | ||||
\(767\) | −48.4974 | + | 28.0000i | −1.75114 | + | 1.01102i | ||||
\(768\) | −0.866025 | − | 0.500000i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | −10.0000 | −0.360609 | −0.180305 | − | 0.983611i | \(-0.557708\pi\) | ||||
−0.180305 | + | 0.983611i | \(0.557708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.00000 | 0.0720282 | ||||||||
\(772\) | −21.6506 | − | 12.5000i | −0.779223 | − | 0.449885i | ||||
\(773\) | 15.5885 | − | 9.00000i | 0.560678 | − | 0.323708i | −0.192740 | − | 0.981250i | \(-0.561737\pi\) |
0.753418 | + | 0.657542i | \(0.228404\pi\) | |||||||
\(774\) | −1.00000 | − | 1.73205i | −0.0359443 | − | 0.0622573i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.00000 | 0.251285 | ||||||||
\(777\) | 1.73205 | + | 5.00000i | 0.0621370 | + | 0.179374i | ||||
\(778\) | 10.0000i | 0.358517i | ||||||||
\(779\) | 21.0000 | − | 36.3731i | 0.752403 | − | 1.30320i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | − | 31.1769i | −0.644091 | − | 1.11560i | ||||
\(782\) | 18.1865 | + | 10.5000i | 0.650349 | + | 0.375479i | ||||
\(783\) | 4.00000i | 0.142948i | ||||||||
\(784\) | −1.00000 | − | 6.92820i | −0.0357143 | − | 0.247436i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.00000 | − | 6.92820i | 0.142675 | − | 0.247121i | ||||
\(787\) | 19.0526 | − | 11.0000i | 0.679150 | − | 0.392108i | −0.120384 | − | 0.992727i | \(-0.538413\pi\) |
0.799535 | + | 0.600620i | \(0.205079\pi\) | |||||||
\(788\) | −17.3205 | + | 10.0000i | −0.617018 | + | 0.356235i | ||||
\(789\) | 13.5000 | − | 23.3827i | 0.480613 | − | 0.832446i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.50000 | − | 2.59808i | 0.266669 | − | 0.0923770i | ||||
\(792\) | 4.00000i | 0.142134i | ||||||||
\(793\) | 41.5692 | + | 24.0000i | 1.47617 | + | 0.852265i | ||||
\(794\) | 11.0000 | + | 19.0526i | 0.390375 | + | 0.676150i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.50000 | + | 12.9904i | −0.265830 | + | 0.460432i | ||||
\(797\) | − | 12.0000i | − | 0.425062i | −0.977154 | − | 0.212531i | \(-0.931829\pi\) | ||
0.977154 | − | 0.212531i | \(-0.0681706\pi\) | |||||||
\(798\) | −15.5885 | − | 3.00000i | −0.551825 | − | 0.106199i | ||||
\(799\) | −3.00000 | −0.106132 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.50000 | + | 6.06218i | 0.123666 | + | 0.214197i | ||||
\(802\) | −29.4449 | + | 17.0000i | −1.03973 | + | 0.600291i | ||||
\(803\) | −20.7846 | − | 12.0000i | −0.733473 | − | 0.423471i | ||||
\(804\) | 12.0000 | 0.423207 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.0000 | 0.704470 | ||||||||
\(807\) | −8.66025 | − | 5.00000i | −0.304855 | − | 0.176008i | ||||
\(808\) | −15.5885 | + | 9.00000i | −0.548400 | + | 0.316619i | ||||
\(809\) | 27.0000 | + | 46.7654i | 0.949269 | + | 1.64418i | 0.746968 | + | 0.664860i | \(0.231509\pi\) |
0.202301 | + | 0.979323i | \(0.435158\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | −6.92820 | + | 8.00000i | −0.243132 | + | 0.280745i | ||||
\(813\) | 5.00000i | 0.175358i | ||||||||
\(814\) | 4.00000 | − | 6.92820i | 0.140200 | − | 0.242833i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.50000 | + | 2.59808i | 0.0525105 | + | 0.0909509i | ||||
\(817\) | −10.3923 | − | 6.00000i | −0.363581 | − | 0.209913i | ||||
\(818\) | 29.0000i | 1.01396i | ||||||||
\(819\) | −2.00000 | + | 10.3923i | −0.0698857 | + | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.00000 | + | 5.19615i | −0.104701 | + | 0.181347i | −0.913616 | − | 0.406578i | \(-0.866722\pi\) |
0.808915 | + | 0.587925i | \(0.200055\pi\) | |||||||
\(822\) | 12.9904 | − | 7.50000i | 0.453092 | − | 0.261593i | ||||
\(823\) | 20.7846 | − | 12.0000i | 0.724506 | − | 0.418294i | −0.0919029 | − | 0.995768i | \(-0.529295\pi\) |
0.816409 | + | 0.577474i | \(0.195962\pi\) | |||||||
\(824\) | 3.50000 | − | 6.06218i | 0.121928 | − | 0.211186i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −35.0000 | + | 12.1244i | −1.21781 | + | 0.421860i | ||||
\(827\) | 20.0000i | 0.695468i | 0.937593 | + | 0.347734i | \(0.113049\pi\) | ||||
−0.937593 | + | 0.347734i | \(0.886951\pi\) | |||||||
\(828\) | 6.06218 | + | 3.50000i | 0.210675 | + | 0.121633i | ||||
\(829\) | −19.0000 | − | 32.9090i | −0.659897 | − | 1.14298i | −0.980642 | − | 0.195810i | \(-0.937266\pi\) |
0.320745 | − | 0.947166i | \(-0.396067\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.00000 | + | 13.8564i | −0.277517 | + | 0.480673i | ||||
\(832\) | 4.00000i | 0.138675i | ||||||||
\(833\) | −7.79423 | + | 19.5000i | −0.270054 | + | 0.675635i | ||||
\(834\) | −2.00000 | −0.0692543 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.0000 | + | 20.7846i | 0.415029 | + | 0.718851i | ||||
\(837\) | 4.33013 | − | 2.50000i | 0.149671 | − | 0.0864126i | ||||
\(838\) | 22.5167 | + | 13.0000i | 0.777825 | + | 0.449078i | ||||
\(839\) | 25.0000 | 0.863096 | 0.431548 | − | 0.902090i | \(-0.357968\pi\) | ||||
0.431548 | + | 0.902090i | \(0.357968\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 13.8564 | + | 8.00000i | 0.477523 | + | 0.275698i | ||||
\(843\) | 14.7224 | − | 8.50000i | 0.507067 | − | 0.292756i | ||||
\(844\) | −11.0000 | − | 19.0526i | −0.378636 | − | 0.655816i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.00000 | −0.0343807 | ||||||||
\(847\) | 12.9904 | + | 2.50000i | 0.446355 | + | 0.0859010i | ||||
\(848\) | 2.00000i | 0.0686803i | ||||||||
\(849\) | 4.00000 | − | 6.92820i | 0.137280 | − | 0.237775i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.00000 | − | 12.1244i | −0.239957 | − | 0.415618i | ||||
\(852\) | −7.79423 | − | 4.50000i | −0.267026 | − | 0.154167i | ||||
\(853\) | 2.00000i | 0.0684787i | 0.999414 | + | 0.0342393i | \(0.0109009\pi\) | ||||
−0.999414 | + | 0.0342393i | \(0.989099\pi\) | |||||||
\(854\) | 24.0000 | + | 20.7846i | 0.821263 | + | 0.711235i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.00000 | − | 12.1244i | 0.239255 | − | 0.414402i | ||||
\(857\) | −22.5167 | + | 13.0000i | −0.769154 | + | 0.444072i | −0.832573 | − | 0.553915i | \(-0.813133\pi\) |
0.0634184 | + | 0.997987i | \(0.479800\pi\) | |||||||
\(858\) | 13.8564 | − | 8.00000i | 0.473050 | − | 0.273115i | ||||
\(859\) | 12.0000 | − | 20.7846i | 0.409435 | − | 0.709162i | −0.585392 | − | 0.810751i | \(-0.699059\pi\) |
0.994826 | + | 0.101589i | \(0.0323926\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.0000 | − | 12.1244i | −0.477119 | − | 0.413197i | ||||
\(862\) | 39.0000i | 1.32835i | ||||||||
\(863\) | −9.52628 | − | 5.50000i | −0.324278 | − | 0.187222i | 0.329020 | − | 0.944323i | \(-0.393282\pi\) |
−0.653298 | + | 0.757101i | \(0.726615\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.5000 | − | 32.0429i | 0.628656 | − | 1.08886i | ||||
\(867\) | 8.00000i | 0.271694i | ||||||||
\(868\) | 12.9904 | + | 2.50000i | 0.440922 | + | 0.0848555i | ||||
\(869\) | −68.0000 | −2.30674 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0000 | − | 41.5692i | −0.813209 | − | 1.40852i | ||||
\(872\) | −5.19615 | + | 3.00000i | −0.175964 | + | 0.101593i | ||||
\(873\) | −6.06218 | − | 3.50000i | −0.205174 | − | 0.118457i | ||||
\(874\) | 42.0000 | 1.42067 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.00000 | −0.202721 | ||||||||
\(877\) | −32.9090 | − | 19.0000i | −1.11126 | − | 0.641584i | −0.172102 | − | 0.985079i | \(-0.555056\pi\) |
−0.939155 | + | 0.343495i | \(0.888389\pi\) | |||||||
\(878\) | 14.7224 | − | 8.50000i | 0.496858 | − | 0.286861i | ||||
\(879\) | 6.00000 | + | 10.3923i | 0.202375 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.0000 | −1.17918 | −0.589590 | − | 0.807703i | \(-0.700711\pi\) | ||||
−0.589590 | + | 0.807703i | \(0.700711\pi\) | |||||||
\(882\) | −2.59808 | + | 6.50000i | −0.0874818 | + | 0.218866i | ||||
\(883\) | − | 6.00000i | − | 0.201916i | −0.994891 | − | 0.100958i | \(-0.967809\pi\) | ||
0.994891 | − | 0.100958i | \(-0.0321908\pi\) | |||||||
\(884\) | 6.00000 | − | 10.3923i | 0.201802 | − | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.0000 | − | 22.5167i | −0.436744 | − | 0.756462i | ||||
\(887\) | −48.4974 | − | 28.0000i | −1.62838 | − | 0.940148i | −0.984575 | − | 0.174962i | \(-0.944020\pi\) |
−0.643809 | − | 0.765186i | \(-0.722647\pi\) | |||||||
\(888\) | − | 2.00000i | − | 0.0671156i | ||||||
\(889\) | 40.0000 | − | 13.8564i | 1.34156 | − | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00000 | − | 3.46410i | 0.0670025 | − | 0.116052i | ||||
\(892\) | 7.79423 | − | 4.50000i | 0.260970 | − | 0.150671i | ||||
\(893\) | −5.19615 | + | 3.00000i | −0.173883 | + | 0.100391i | ||||
\(894\) | −3.00000 | + | 5.19615i | −0.100335 | + | 0.173785i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.500000 | + | 2.59808i | −0.0167038 | + | 0.0867956i | ||||
\(897\) | − | 28.0000i | − | 0.934893i | ||||||
\(898\) | 11.2583 | + | 6.50000i | 0.375695 | + | 0.216908i | ||||
\(899\) | −10.0000 | − | 17.3205i | −0.333519 | − | 0.577671i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.00000 | − | 5.19615i | 0.0999445 | − | 0.173109i | ||||
\(902\) | 28.0000i | 0.932298i | ||||||||
\(903\) | −3.46410 | + | 4.00000i | −0.115278 | + | 0.133112i | ||||
\(904\) | −3.00000 | −0.0997785 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −12.0000 | − | 20.7846i | −0.398673 | − | 0.690522i | ||||
\(907\) | −24.2487 | + | 14.0000i | −0.805165 | + | 0.464862i | −0.845274 | − | 0.534333i | \(-0.820563\pi\) |
0.0401089 | + | 0.999195i | \(0.487230\pi\) | |||||||
\(908\) | −19.0526 | − | 11.0000i | −0.632281 | − | 0.365048i | ||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.0000 | 0.629498 | 0.314749 | − | 0.949175i | \(-0.398080\pi\) | ||||
0.314749 | + | 0.949175i | \(0.398080\pi\) | |||||||
\(912\) | 5.19615 | + | 3.00000i | 0.172062 | + | 0.0993399i | ||||
\(913\) | −13.8564 | + | 8.00000i | −0.458580 | + | 0.264761i | ||||
\(914\) | −9.00000 | − | 15.5885i | −0.297694 | − | 0.515620i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.00000 | 0.264327 | ||||||||
\(917\) | −20.7846 | − | 4.00000i | −0.686368 | − | 0.132092i | ||||
\(918\) | − | 3.00000i | − | 0.0990148i | ||||||
\(919\) | −19.5000 | + | 33.7750i | −0.643246 | + | 1.11413i | 0.341458 | + | 0.939897i | \(0.389079\pi\) |
−0.984704 | + | 0.174237i | \(0.944254\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0000 | + | 17.3205i | 0.329511 | + | 0.570730i | ||||
\(922\) | 31.1769 | + | 18.0000i | 1.02676 | + | 0.592798i | ||||
\(923\) | 36.0000i | 1.18495i | ||||||||
\(924\) | 10.0000 | − | 3.46410i | 0.328976 | − | 0.113961i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.50000 | + | 6.06218i | −0.115017 | + | 0.199216i | ||||
\(927\) | −6.06218 | + | 3.50000i | −0.199108 | + | 0.114955i | ||||
\(928\) | 3.46410 | − | 2.00000i | 0.113715 | − | 0.0656532i | ||||
\(929\) | −15.0000 | + | 25.9808i | −0.492134 | + | 0.852401i | −0.999959 | − | 0.00905914i | \(-0.997116\pi\) |
0.507825 | + | 0.861460i | \(0.330450\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000 | + | 41.5692i | 0.196642 | + | 1.36238i | ||||
\(932\) | − | 6.00000i | − | 0.196537i | ||||||
\(933\) | −18.1865 | − | 10.5000i | −0.595400 | − | 0.343755i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | − | 3.46410i | 0.0653720 | − | 0.113228i | ||||
\(937\) | − | 6.00000i | − | 0.196011i | −0.995186 | − | 0.0980057i | \(-0.968754\pi\) | ||
0.995186 | − | 0.0980057i | \(-0.0312463\pi\) | |||||||
\(938\) | −10.3923 | − | 30.0000i | −0.339321 | − | 0.979535i | ||||
\(939\) | −27.0000 | −0.881112 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.0000 | − | 36.3731i | −0.684580 | − | 1.18573i | −0.973568 | − | 0.228395i | \(-0.926652\pi\) |
0.288988 | − | 0.957333i | \(-0.406681\pi\) | |||||||
\(942\) | −3.46410 | + | 2.00000i | −0.112867 | + | 0.0651635i | ||||
\(943\) | 42.4352 | + | 24.5000i | 1.38188 | + | 0.797830i | ||||
\(944\) | 14.0000 | 0.455661 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.00000 | 0.260102 | ||||||||
\(947\) | 27.7128 | + | 16.0000i | 0.900545 | + | 0.519930i | 0.877377 | − | 0.479801i | \(-0.159291\pi\) |
0.0231683 | + | 0.999732i | \(0.492625\pi\) | |||||||
\(948\) | −14.7224 | + | 8.50000i | −0.478162 | + | 0.276067i | ||||
\(949\) | 12.0000 | + | 20.7846i | 0.389536 | + | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 5.19615 | − | 6.00000i | 0.168408 | − | 0.194461i | ||||
\(953\) | 26.0000i | 0.842223i | 0.907009 | + | 0.421111i | \(0.138360\pi\) | ||||
−0.907009 | + | 0.421111i | \(0.861640\pi\) | |||||||
\(954\) | 1.00000 | − | 1.73205i | 0.0323762 | − | 0.0560772i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.50000 | − | 2.59808i | −0.0485135 | − | 0.0840278i | ||||
\(957\) | −13.8564 | − | 8.00000i | −0.447914 | − | 0.258603i | ||||
\(958\) | 1.00000i | 0.0323085i | ||||||||
\(959\) | −30.0000 | − | 25.9808i | −0.968751 | − | 0.838963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | − | 5.19615i | 0.0967742 | − | 0.167618i | ||||
\(962\) | −6.92820 | + | 4.00000i | −0.223374 | + | 0.128965i | ||||
\(963\) | −12.1244 | + | 7.00000i | −0.390702 | + | 0.225572i | ||||
\(964\) | −1.00000 | + | 1.73205i | −0.0322078 | + | 0.0557856i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.50000 | − | 18.1865i | 0.112611 | − | 0.585142i | ||||
\(967\) | − | 29.0000i | − | 0.932577i | −0.884633 | − | 0.466289i | \(-0.845591\pi\) | ||
0.884633 | − | 0.466289i | \(-0.154409\pi\) | |||||||
\(968\) | −4.33013 | − | 2.50000i | −0.139176 | − | 0.0803530i | ||||
\(969\) | −9.00000 | − | 15.5885i | −0.289122 | − | 0.500773i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | − | 20.7846i | 0.385098 | − | 0.667010i | −0.606685 | − | 0.794943i | \(-0.707501\pi\) |
0.991783 | + | 0.127933i | \(0.0408342\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 1.73205 | + | 5.00000i | 0.0555270 | + | 0.160293i | ||||
\(974\) | 5.00000 | 0.160210 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.00000 | − | 10.3923i | −0.192055 | − | 0.332650i | ||||
\(977\) | 2.59808 | − | 1.50000i | 0.0831198 | − | 0.0479893i | −0.457864 | − | 0.889022i | \(-0.651385\pi\) |
0.540984 | + | 0.841033i | \(0.318052\pi\) | |||||||
\(978\) | −6.92820 | − | 4.00000i | −0.221540 | − | 0.127906i | ||||
\(979\) | −28.0000 | −0.894884 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.00000 | 0.191565 | ||||||||
\(982\) | 32.9090 | + | 19.0000i | 1.05017 | + | 0.606314i | ||||
\(983\) | −24.2487 | + | 14.0000i | −0.773414 | + | 0.446531i | −0.834091 | − | 0.551627i | \(-0.814007\pi\) |
0.0606773 | + | 0.998157i | \(0.480674\pi\) | |||||||
\(984\) | 3.50000 | + | 6.06218i | 0.111576 | + | 0.193255i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12.0000 | −0.382158 | ||||||||
\(987\) | 0.866025 | + | 2.50000i | 0.0275659 | + | 0.0795759i | ||||
\(988\) | − | 24.0000i | − | 0.763542i | ||||||
\(989\) | 7.00000 | − | 12.1244i | 0.222587 | − | 0.385532i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.50000 | − | 6.06218i | −0.111181 | − | 0.192571i | 0.805066 | − | 0.593186i | \(-0.202130\pi\) |
−0.916247 | + | 0.400614i | \(0.868797\pi\) | |||||||
\(992\) | −4.33013 | − | 2.50000i | −0.137482 | − | 0.0793751i | ||||
\(993\) | − | 34.0000i | − | 1.07896i | ||||||
\(994\) | −4.50000 | + | 23.3827i | −0.142731 | + | 0.741654i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.00000 | + | 3.46410i | −0.0633724 | + | 0.109764i | ||||
\(997\) | −13.8564 | + | 8.00000i | −0.438837 | + | 0.253363i | −0.703104 | − | 0.711087i | \(-0.748203\pi\) |
0.264267 | + | 0.964449i | \(0.414870\pi\) | |||||||
\(998\) | 24.2487 | − | 14.0000i | 0.767580 | − | 0.443162i | ||||
\(999\) | −1.00000 | + | 1.73205i | −0.0316386 | + | 0.0547997i |
(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 | 1050.2.o.l.499.2 | 4 | ||
5.2 | odd | 4 | 1050.2.i.d.751.1 | yes | 2 | ||
5.3 | odd | 4 | 1050.2.i.r.751.1 | yes | 2 | ||
5.4 | even | 2 | inner | 1050.2.o.l.499.1 | 4 | ||
7.4 | even | 3 | inner | 1050.2.o.l.949.1 | 4 | ||
35.2 | odd | 12 | 7350.2.a.ci.1.1 | 1 | |||
35.4 | even | 6 | inner | 1050.2.o.l.949.2 | 4 | ||
35.12 | even | 12 | 7350.2.a.bs.1.1 | 1 | |||
35.18 | odd | 12 | 1050.2.i.r.151.1 | yes | 2 | ||
35.23 | odd | 12 | 7350.2.a.e.1.1 | 1 | |||
35.32 | odd | 12 | 1050.2.i.d.151.1 | ✓ | 2 | ||
35.33 | even | 12 | 7350.2.a.v.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.i.d.151.1 | ✓ | 2 | 35.32 | odd | 12 | ||
1050.2.i.d.751.1 | yes | 2 | 5.2 | odd | 4 | ||
1050.2.i.r.151.1 | yes | 2 | 35.18 | odd | 12 | ||
1050.2.i.r.751.1 | yes | 2 | 5.3 | odd | 4 | ||
1050.2.o.l.499.1 | 4 | 5.4 | even | 2 | inner | ||
1050.2.o.l.499.2 | 4 | 1.1 | even | 1 | trivial | ||
1050.2.o.l.949.1 | 4 | 7.4 | even | 3 | inner | ||
1050.2.o.l.949.2 | 4 | 35.4 | even | 6 | inner | ||
7350.2.a.e.1.1 | 1 | 35.23 | odd | 12 | |||
7350.2.a.v.1.1 | 1 | 35.33 | even | 12 | |||
7350.2.a.bs.1.1 | 1 | 35.12 | even | 12 | |||
7350.2.a.ci.1.1 | 1 | 35.2 | odd | 12 |