Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(151,1050)]
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, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.151");
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.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: | \(8.38429221223\) |
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 | 751.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.751 |
Dual form | 1050.2.i.r.151.1 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −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 | \(0.627296\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | −0.500000 | + | 2.59808i | −0.133631 | + | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −3.00000 | + | 5.19615i | −0.688247 | + | 1.19208i | 0.284157 | + | 0.958778i | \(0.408286\pi\) |
−0.972404 | + | 0.233301i | \(0.925047\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | − | 1.73205i | −0.436436 | − | 0.377964i | ||||
\(22\) | 4.00000 | 0.852803 | ||||||||
\(23\) | −3.50000 | + | 6.06218i | −0.729800 | + | 1.26405i | 0.227167 | + | 0.973856i | \(0.427054\pi\) |
−0.956967 | + | 0.290196i | \(0.906280\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000 | − | 3.46410i | 0.392232 | − | 0.679366i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.00000 | + | 1.73205i | 0.377964 | + | 0.327327i | ||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.50000 | + | 4.33013i | 0.449013 | + | 0.777714i | 0.998322 | − | 0.0579057i | \(-0.0184423\pi\) |
−0.549309 | + | 0.835619i | \(0.685109\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −2.00000 | + | 3.46410i | −0.348155 | + | 0.603023i | ||||
\(34\) | −3.00000 | −0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.00000 | + | 1.73205i | −0.164399 | + | 0.284747i | −0.936442 | − | 0.350823i | \(-0.885902\pi\) |
0.772043 | + | 0.635571i | \(0.219235\pi\) | |||||||
\(38\) | 3.00000 | + | 5.19615i | 0.486664 | + | 0.842927i | ||||
\(39\) | 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 | \(0.315919\pi\) | |||||||
\(42\) | −2.50000 | + | 0.866025i | −0.385758 | + | 0.133631i | ||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 2.00000 | − | 3.46410i | 0.301511 | − | 0.522233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.50000 | + | 6.06218i | 0.516047 | + | 0.893819i | ||||
\(47\) | −0.500000 | + | 0.866025i | −0.0729325 | + | 0.126323i | −0.900185 | − | 0.435507i | \(-0.856569\pi\) |
0.827253 | + | 0.561830i | \(0.189902\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.50000 | − | 2.59808i | 0.210042 | − | 0.363803i | ||||
\(52\) | −2.00000 | − | 3.46410i | −0.277350 | − | 0.480384i | ||||
\(53\) | 1.00000 | + | 1.73205i | 0.137361 | + | 0.237915i | 0.926497 | − | 0.376303i | \(-0.122805\pi\) |
−0.789136 | + | 0.614218i | \(0.789471\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.50000 | − | 0.866025i | 0.334077 | − | 0.115728i | ||||
\(57\) | −6.00000 | −0.794719 | ||||||||
\(58\) | 2.00000 | − | 3.46410i | 0.262613 | − | 0.454859i | ||||
\(59\) | 7.00000 | + | 12.1244i | 0.911322 | + | 1.57846i | 0.812198 | + | 0.583382i | \(0.198271\pi\) |
0.0991242 | + | 0.995075i | \(0.468396\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | + | 10.3923i | −0.768221 | + | 1.33060i | 0.170305 | + | 0.985391i | \(0.445525\pi\) |
−0.938527 | + | 0.345207i | \(0.887809\pi\) | |||||||
\(62\) | 5.00000 | 0.635001 | ||||||||
\(63\) | 0.500000 | − | 2.59808i | 0.0629941 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.00000 | + | 3.46410i | 0.246183 | + | 0.426401i | ||||
\(67\) | −6.00000 | − | 10.3923i | −0.733017 | − | 1.26962i | −0.955588 | − | 0.294706i | \(-0.904778\pi\) |
0.222571 | − | 0.974916i | \(-0.428555\pi\) | |||||||
\(68\) | −1.50000 | + | 2.59808i | −0.181902 | + | 0.315063i | ||||
\(69\) | −7.00000 | −0.842701 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.00000 | −1.06810 | −0.534052 | − | 0.845452i | \(-0.679331\pi\) | ||||
−0.534052 | + | 0.845452i | \(0.679331\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −3.00000 | − | 5.19615i | −0.351123 | − | 0.608164i | 0.635323 | − | 0.772246i | \(-0.280867\pi\) |
−0.986447 | + | 0.164083i | \(0.947534\pi\) | |||||||
\(74\) | 1.00000 | + | 1.73205i | 0.116248 | + | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | −8.00000 | − | 6.92820i | −0.911685 | − | 0.789542i | ||||
\(78\) | 4.00000 | 0.452911 | ||||||||
\(79\) | 8.50000 | − | 14.7224i | 0.956325 | − | 1.65640i | 0.225018 | − | 0.974355i | \(-0.427756\pi\) |
0.731307 | − | 0.682048i | \(-0.238911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 3.50000 | − | 6.06218i | 0.386510 | − | 0.669456i | ||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | −0.500000 | + | 2.59808i | −0.0545545 | + | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.00000 | − | 1.73205i | 0.107833 | − | 0.186772i | ||||
\(87\) | 2.00000 | + | 3.46410i | 0.214423 | + | 0.371391i | ||||
\(88\) | −2.00000 | − | 3.46410i | −0.213201 | − | 0.369274i | ||||
\(89\) | 3.50000 | − | 6.06218i | 0.370999 | − | 0.642590i | −0.618720 | − | 0.785611i | \(-0.712349\pi\) |
0.989720 | + | 0.143022i | \(0.0456819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0000 | + | 3.46410i | −1.04828 | + | 0.363137i | ||||
\(92\) | 7.00000 | 0.729800 | ||||||||
\(93\) | −2.50000 | + | 4.33013i | −0.259238 | + | 0.449013i | ||||
\(94\) | 0.500000 | + | 0.866025i | 0.0515711 | + | 0.0893237i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | −7.00000 | −0.710742 | −0.355371 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355371 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(98\) | −1.00000 | − | 6.92820i | −0.101015 | − | 0.699854i | ||||
\(99\) | −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 | \(0.480128\pi\) | |||||||
\(102\) | −1.50000 | − | 2.59808i | −0.148522 | − | 0.257248i | ||||
\(103\) | 3.50000 | − | 6.06218i | 0.344865 | − | 0.597324i | −0.640464 | − | 0.767988i | \(-0.721258\pi\) |
0.985329 | + | 0.170664i | \(0.0545913\pi\) | |||||||
\(104\) | −4.00000 | −0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | −7.00000 | + | 12.1244i | −0.676716 | + | 1.17211i | 0.299249 | + | 0.954175i | \(0.403264\pi\) |
−0.975964 | + | 0.217931i | \(0.930069\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | −3.00000 | − | 5.19615i | −0.287348 | − | 0.497701i | 0.685828 | − | 0.727764i | \(-0.259440\pi\) |
−0.973176 | + | 0.230063i | \(0.926107\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | 0.500000 | − | 2.59808i | 0.0472456 | − | 0.245495i | ||||
\(113\) | −3.00000 | −0.282216 | −0.141108 | − | 0.989994i | \(-0.545067\pi\) | ||||
−0.141108 | + | 0.989994i | \(0.545067\pi\) | |||||||
\(114\) | −3.00000 | + | 5.19615i | −0.280976 | + | 0.486664i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.00000 | − | 3.46410i | −0.185695 | − | 0.321634i | ||||
\(117\) | −2.00000 | + | 3.46410i | −0.184900 | + | 0.320256i | ||||
\(118\) | 14.0000 | 1.28880 | ||||||||
\(119\) | 6.00000 | + | 5.19615i | 0.550019 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | 6.00000 | + | 10.3923i | 0.543214 | + | 0.940875i | ||||
\(123\) | 3.50000 | + | 6.06218i | 0.315584 | + | 0.546608i | ||||
\(124\) | 2.50000 | − | 4.33013i | 0.224507 | − | 0.388857i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | − | 1.73205i | −0.178174 | − | 0.154303i | ||||
\(127\) | 16.0000 | 1.41977 | 0.709885 | − | 0.704317i | \(-0.248747\pi\) | ||||
0.709885 | + | 0.704317i | \(0.248747\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 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 | \(0.0530244\pi\) | |||||||
\(132\) | 4.00000 | 0.348155 | ||||||||
\(133\) | 3.00000 | − | 15.5885i | 0.260133 | − | 1.35169i | ||||
\(134\) | −12.0000 | −1.03664 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.50000 | + | 2.59808i | 0.128624 | + | 0.222783i | ||||
\(137\) | −7.50000 | − | 12.9904i | −0.640768 | − | 1.10984i | −0.985262 | − | 0.171054i | \(-0.945283\pi\) |
0.344493 | − | 0.938789i | \(-0.388051\pi\) | |||||||
\(138\) | −3.50000 | + | 6.06218i | −0.297940 | + | 0.516047i | ||||
\(139\) | 2.00000 | 0.169638 | 0.0848189 | − | 0.996396i | \(-0.472969\pi\) | ||||
0.0848189 | + | 0.996396i | \(0.472969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.00000 | −0.0842152 | ||||||||
\(142\) | −4.50000 | + | 7.79423i | −0.377632 | + | 0.654077i | ||||
\(143\) | 8.00000 | + | 13.8564i | 0.668994 | + | 1.15873i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.00000 | −0.496564 | ||||||||
\(147\) | 6.50000 | + | 2.59808i | 0.536111 | + | 0.214286i | ||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | − | 20.7846i | −0.976546 | − | 1.69143i | −0.674735 | − | 0.738060i | \(-0.735742\pi\) |
−0.301811 | − | 0.953368i | \(-0.597591\pi\) | |||||||
\(152\) | 3.00000 | − | 5.19615i | 0.243332 | − | 0.421464i | ||||
\(153\) | 3.00000 | 0.242536 | ||||||||
\(154\) | −10.0000 | + | 3.46410i | −0.805823 | + | 0.279145i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | − | 3.46410i | 0.160128 | − | 0.277350i | ||||
\(157\) | 2.00000 | + | 3.46410i | 0.159617 | + | 0.276465i | 0.934731 | − | 0.355357i | \(-0.115641\pi\) |
−0.775113 | + | 0.631822i | \(0.782307\pi\) | |||||||
\(158\) | −8.50000 | − | 14.7224i | −0.676224 | − | 1.17125i | ||||
\(159\) | −1.00000 | + | 1.73205i | −0.0793052 | + | 0.137361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.50000 | − | 18.1865i | 0.275839 | − | 1.43330i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 4.00000 | − | 6.92820i | 0.313304 | − | 0.542659i | −0.665771 | − | 0.746156i | \(-0.731897\pi\) |
0.979076 | + | 0.203497i | \(0.0652307\pi\) | |||||||
\(164\) | −3.50000 | − | 6.06218i | −0.273304 | − | 0.473377i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.00000 | + | 3.46410i | −0.155230 | + | 0.268866i | ||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 2.00000 | + | 1.73205i | 0.154303 | + | 0.133631i | ||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | − | 5.19615i | −0.229416 | − | 0.397360i | ||||
\(172\) | −1.00000 | − | 1.73205i | −0.0762493 | − | 0.132068i | ||||
\(173\) | −3.00000 | + | 5.19615i | −0.228086 | + | 0.395056i | −0.957241 | − | 0.289292i | \(-0.906580\pi\) |
0.729155 | + | 0.684349i | \(0.239913\pi\) | |||||||
\(174\) | 4.00000 | 0.303239 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | −7.00000 | + | 12.1244i | −0.526152 | + | 0.911322i | ||||
\(178\) | −3.50000 | − | 6.06218i | −0.262336 | − | 0.454379i | ||||
\(179\) | −1.00000 | − | 1.73205i | −0.0747435 | − | 0.129460i | 0.826231 | − | 0.563331i | \(-0.190480\pi\) |
−0.900975 | + | 0.433872i | \(0.857147\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0000 | 0.891953 | 0.445976 | − | 0.895045i | \(-0.352856\pi\) | ||||
0.445976 | + | 0.895045i | \(0.352856\pi\) | |||||||
\(182\) | −2.00000 | + | 10.3923i | −0.148250 | + | 0.770329i | ||||
\(183\) | −12.0000 | −0.887066 | ||||||||
\(184\) | 3.50000 | − | 6.06218i | 0.258023 | − | 0.446910i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.50000 | + | 4.33013i | 0.183309 | + | 0.317500i | ||||
\(187\) | 6.00000 | − | 10.3923i | 0.438763 | − | 0.759961i | ||||
\(188\) | 1.00000 | 0.0729325 | ||||||||
\(189\) | 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 | \(0.984076\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −12.5000 | − | 21.6506i | −0.899770 | − | 1.55845i | −0.827788 | − | 0.561041i | \(-0.810401\pi\) |
−0.0719816 | − | 0.997406i | \(-0.522932\pi\) | |||||||
\(194\) | −3.50000 | + | 6.06218i | −0.251285 | + | 0.435239i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | 20.0000 | 1.42494 | 0.712470 | − | 0.701702i | \(-0.247576\pi\) | ||||
0.712470 | + | 0.701702i | \(0.247576\pi\) | |||||||
\(198\) | −2.00000 | + | 3.46410i | −0.142134 | + | 0.246183i | ||||
\(199\) | −7.50000 | − | 12.9904i | −0.531661 | − | 0.920864i | −0.999317 | − | 0.0369532i | \(-0.988235\pi\) |
0.467656 | − | 0.883911i | \(-0.345099\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.00000 | − | 10.3923i | 0.423207 | − | 0.733017i | ||||
\(202\) | 18.0000 | 1.26648 | ||||||||
\(203\) | −10.0000 | + | 3.46410i | −0.701862 | + | 0.243132i | ||||
\(204\) | −3.00000 | −0.210042 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.50000 | − | 6.06218i | −0.243857 | − | 0.422372i | ||||
\(207\) | −3.50000 | − | 6.06218i | −0.243267 | − | 0.421350i | ||||
\(208\) | −2.00000 | + | 3.46410i | −0.138675 | + | 0.240192i | ||||
\(209\) | −24.0000 | −1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.0000 | −1.51454 | −0.757271 | − | 0.653101i | \(-0.773468\pi\) | ||||
−0.757271 | + | 0.653101i | \(0.773468\pi\) | |||||||
\(212\) | 1.00000 | − | 1.73205i | 0.0686803 | − | 0.118958i | ||||
\(213\) | −4.50000 | − | 7.79423i | −0.308335 | − | 0.534052i | ||||
\(214\) | 7.00000 | + | 12.1244i | 0.478510 | + | 0.828804i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −10.0000 | − | 8.66025i | −0.678844 | − | 0.587896i | ||||
\(218\) | −6.00000 | −0.406371 | ||||||||
\(219\) | 3.00000 | − | 5.19615i | 0.202721 | − | 0.351123i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | − | 10.3923i | −0.403604 | − | 0.699062i | ||||
\(222\) | −1.00000 | + | 1.73205i | −0.0671156 | + | 0.116248i | ||||
\(223\) | 9.00000 | 0.602685 | 0.301342 | − | 0.953516i | \(-0.402565\pi\) | ||||
0.301342 | + | 0.953516i | \(0.402565\pi\) | |||||||
\(224\) | −2.00000 | − | 1.73205i | −0.133631 | − | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.50000 | + | 2.59808i | −0.0997785 | + | 0.172821i | ||||
\(227\) | 11.0000 | + | 19.0526i | 0.730096 | + | 1.26456i | 0.956842 | + | 0.290609i | \(0.0938578\pi\) |
−0.226746 | + | 0.973954i | \(0.572809\pi\) | |||||||
\(228\) | 3.00000 | + | 5.19615i | 0.198680 | + | 0.344124i | ||||
\(229\) | −4.00000 | + | 6.92820i | −0.264327 | + | 0.457829i | −0.967387 | − | 0.253302i | \(-0.918483\pi\) |
0.703060 | + | 0.711131i | \(0.251817\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.00000 | − | 10.3923i | 0.131590 | − | 0.683763i | ||||
\(232\) | −4.00000 | −0.262613 | ||||||||
\(233\) | 3.00000 | − | 5.19615i | 0.196537 | − | 0.340411i | −0.750867 | − | 0.660454i | \(-0.770364\pi\) |
0.947403 | + | 0.320043i | \(0.103697\pi\) | |||||||
\(234\) | 2.00000 | + | 3.46410i | 0.130744 | + | 0.226455i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.00000 | − | 12.1244i | 0.455661 | − | 0.789228i | ||||
\(237\) | 17.0000 | 1.10427 | ||||||||
\(238\) | 7.50000 | − | 2.59808i | 0.486153 | − | 0.168408i | ||||
\(239\) | 3.00000 | 0.194054 | 0.0970269 | − | 0.995282i | \(-0.469067\pi\) | ||||
0.0970269 | + | 0.995282i | \(0.469067\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | + | 1.73205i | 0.0644157 | + | 0.111571i | 0.896435 | − | 0.443176i | \(-0.146148\pi\) |
−0.832019 | + | 0.554747i | \(0.812815\pi\) | |||||||
\(242\) | 2.50000 | + | 4.33013i | 0.160706 | + | 0.278351i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 12.0000 | 0.768221 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.00000 | 0.446304 | ||||||||
\(247\) | −12.0000 | + | 20.7846i | −0.763542 | + | 1.32249i | ||||
\(248\) | −2.50000 | − | 4.33013i | −0.158750 | − | 0.274963i | ||||
\(249\) | −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 | \(0.459709\pi\) | |||||||
\(252\) | −2.50000 | + | 0.866025i | −0.157485 | + | 0.0545545i | ||||
\(253\) | −28.0000 | −1.76034 | ||||||||
\(254\) | 8.00000 | − | 13.8564i | 0.501965 | − | 0.869428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.00000 | − | 1.73205i | 0.0623783 | − | 0.108042i | −0.833150 | − | 0.553047i | \(-0.813465\pi\) |
0.895528 | + | 0.445005i | \(0.146798\pi\) | |||||||
\(258\) | 2.00000 | 0.124515 | ||||||||
\(259\) | 1.00000 | − | 5.19615i | 0.0621370 | − | 0.322873i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | + | 3.46410i | −0.123797 | + | 0.214423i | ||||
\(262\) | −4.00000 | − | 6.92820i | −0.247121 | − | 0.428026i | ||||
\(263\) | 13.5000 | + | 23.3827i | 0.832446 | + | 1.44184i | 0.896093 | + | 0.443866i | \(0.146393\pi\) |
−0.0636476 | + | 0.997972i | \(0.520273\pi\) | |||||||
\(264\) | 2.00000 | − | 3.46410i | 0.123091 | − | 0.213201i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −12.0000 | − | 10.3923i | −0.735767 | − | 0.637193i | ||||
\(267\) | 7.00000 | 0.428393 | ||||||||
\(268\) | −6.00000 | + | 10.3923i | −0.366508 | + | 0.634811i | ||||
\(269\) | 5.00000 | + | 8.66025i | 0.304855 | + | 0.528025i | 0.977229 | − | 0.212187i | \(-0.0680585\pi\) |
−0.672374 | + | 0.740212i | \(0.734725\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.50000 | + | 4.33013i | −0.151864 | + | 0.263036i | −0.931913 | − | 0.362682i | \(-0.881861\pi\) |
0.780049 | + | 0.625719i | \(0.215194\pi\) | |||||||
\(272\) | 3.00000 | 0.181902 | ||||||||
\(273\) | −8.00000 | − | 6.92820i | −0.484182 | − | 0.419314i | ||||
\(274\) | −15.0000 | −0.906183 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.50000 | + | 6.06218i | 0.210675 | + | 0.364900i | ||||
\(277\) | 8.00000 | + | 13.8564i | 0.480673 | + | 0.832551i | 0.999754 | − | 0.0221745i | \(-0.00705893\pi\) |
−0.519081 | + | 0.854725i | \(0.673726\pi\) | |||||||
\(278\) | 1.00000 | − | 1.73205i | 0.0599760 | − | 0.103882i | ||||
\(279\) | −5.00000 | −0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.0000 | 1.01413 | 0.507067 | − | 0.861906i | \(-0.330729\pi\) | ||||
0.507067 | + | 0.861906i | \(0.330729\pi\) | |||||||
\(282\) | −0.500000 | + | 0.866025i | −0.0297746 | + | 0.0515711i | ||||
\(283\) | 4.00000 | + | 6.92820i | 0.237775 | + | 0.411839i | 0.960076 | − | 0.279741i | \(-0.0902485\pi\) |
−0.722300 | + | 0.691580i | \(0.756915\pi\) | |||||||
\(284\) | 4.50000 | + | 7.79423i | 0.267026 | + | 0.462502i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.0000 | 0.946100 | ||||||||
\(287\) | −17.5000 | + | 6.06218i | −1.03299 | + | 0.357839i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.50000 | − | 6.06218i | −0.205174 | − | 0.355371i | ||||
\(292\) | −3.00000 | + | 5.19615i | −0.175562 | + | 0.304082i | ||||
\(293\) | −12.0000 | −0.701047 | −0.350524 | − | 0.936554i | \(-0.613996\pi\) | ||||
−0.350524 | + | 0.936554i | \(0.613996\pi\) | |||||||
\(294\) | 5.50000 | − | 4.33013i | 0.320767 | − | 0.252538i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.00000 | − | 1.73205i | 0.0581238 | − | 0.100673i | ||||
\(297\) | −2.00000 | − | 3.46410i | −0.116052 | − | 0.201008i | ||||
\(298\) | −3.00000 | − | 5.19615i | −0.173785 | − | 0.301005i | ||||
\(299\) | −14.0000 | + | 24.2487i | −0.809641 | + | 1.40234i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.00000 | + | 1.73205i | −0.288195 | + | 0.0998337i | ||||
\(302\) | −24.0000 | −1.38104 | ||||||||
\(303\) | −9.00000 | + | 15.5885i | −0.517036 | + | 0.895533i | ||||
\(304\) | −3.00000 | − | 5.19615i | −0.172062 | − | 0.298020i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.50000 | − | 2.59808i | 0.0857493 | − | 0.148522i | ||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | −2.00000 | + | 10.3923i | −0.113961 | + | 0.592157i | ||||
\(309\) | 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 | \(-0.369673\pi\) | |||||||
\(312\) | −2.00000 | − | 3.46410i | −0.113228 | − | 0.196116i | ||||
\(313\) | 13.5000 | − | 23.3827i | 0.763065 | − | 1.32167i | −0.178198 | − | 0.983995i | \(-0.557027\pi\) |
0.941263 | − | 0.337673i | \(-0.109640\pi\) | |||||||
\(314\) | 4.00000 | 0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.0000 | −0.956325 | ||||||||
\(317\) | −9.00000 | + | 15.5885i | −0.505490 | + | 0.875535i | 0.494489 | + | 0.869184i | \(0.335355\pi\) |
−0.999980 | + | 0.00635137i | \(0.997978\pi\) | |||||||
\(318\) | 1.00000 | + | 1.73205i | 0.0560772 | + | 0.0971286i | ||||
\(319\) | 8.00000 | + | 13.8564i | 0.447914 | + | 0.775810i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.0000 | −0.781404 | ||||||||
\(322\) | −14.0000 | − | 12.1244i | −0.780189 | − | 0.675664i | ||||
\(323\) | 18.0000 | 1.00155 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.00000 | − | 6.92820i | −0.221540 | − | 0.383718i | ||||
\(327\) | 3.00000 | − | 5.19615i | 0.165900 | − | 0.287348i | ||||
\(328\) | −7.00000 | −0.386510 | ||||||||
\(329\) | 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 | \(-0.217401\pi\) | |||||||
\(332\) | 2.00000 | + | 3.46410i | 0.109764 | + | 0.190117i | ||||
\(333\) | −1.00000 | − | 1.73205i | −0.0547997 | − | 0.0949158i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.50000 | − | 0.866025i | 0.136386 | − | 0.0472456i | ||||
\(337\) | 3.00000 | 0.163420 | 0.0817102 | − | 0.996656i | \(-0.473962\pi\) | ||||
0.0817102 | + | 0.996656i | \(0.473962\pi\) | |||||||
\(338\) | 1.50000 | − | 2.59808i | 0.0815892 | − | 0.141317i | ||||
\(339\) | −1.50000 | − | 2.59808i | −0.0814688 | − | 0.141108i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.0000 | + | 17.3205i | −0.541530 | + | 0.937958i | ||||
\(342\) | −6.00000 | −0.324443 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | + | 5.19615i | 0.161281 | + | 0.279347i | ||||
\(347\) | −16.0000 | − | 27.7128i | −0.858925 | − | 1.48770i | −0.872955 | − | 0.487800i | \(-0.837799\pi\) |
0.0140303 | − | 0.999902i | \(-0.495534\pi\) | |||||||
\(348\) | 2.00000 | − | 3.46410i | 0.107211 | − | 0.185695i | ||||
\(349\) | −18.0000 | −0.963518 | −0.481759 | − | 0.876304i | \(-0.660002\pi\) | ||||
−0.481759 | + | 0.876304i | \(0.660002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | −2.00000 | + | 3.46410i | −0.106600 | + | 0.184637i | ||||
\(353\) | 7.50000 | + | 12.9904i | 0.399185 | + | 0.691408i | 0.993626 | − | 0.112731i | \(-0.0359599\pi\) |
−0.594441 | + | 0.804139i | \(0.702627\pi\) | |||||||
\(354\) | 7.00000 | + | 12.1244i | 0.372046 | + | 0.644402i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.00000 | −0.370999 | ||||||||
\(357\) | −1.50000 | + | 7.79423i | −0.0793884 | + | 0.412514i | ||||
\(358\) | −2.00000 | −0.105703 | ||||||||
\(359\) | −2.00000 | + | 3.46410i | −0.105556 | + | 0.182828i | −0.913965 | − | 0.405793i | \(-0.866996\pi\) |
0.808409 | + | 0.588621i | \(0.200329\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | 6.00000 | − | 10.3923i | 0.315353 | − | 0.546207i | ||||
\(363\) | −5.00000 | −0.262432 | ||||||||
\(364\) | 8.00000 | + | 6.92820i | 0.419314 | + | 0.363137i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.00000 | + | 10.3923i | −0.313625 | + | 0.543214i | ||||
\(367\) | 16.0000 | + | 27.7128i | 0.835193 | + | 1.44660i | 0.893873 | + | 0.448320i | \(0.147978\pi\) |
−0.0586798 | + | 0.998277i | \(0.518689\pi\) | |||||||
\(368\) | −3.50000 | − | 6.06218i | −0.182450 | − | 0.316013i | ||||
\(369\) | −3.50000 | + | 6.06218i | −0.182203 | + | 0.315584i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.00000 | − | 3.46410i | −0.207670 | − | 0.179847i | ||||
\(372\) | 5.00000 | 0.259238 | ||||||||
\(373\) | −6.00000 | + | 10.3923i | −0.310668 | + | 0.538093i | −0.978507 | − | 0.206213i | \(-0.933886\pi\) |
0.667839 | + | 0.744306i | \(0.267219\pi\) | |||||||
\(374\) | −6.00000 | − | 10.3923i | −0.310253 | − | 0.537373i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.500000 | − | 0.866025i | 0.0257855 | − | 0.0446619i | ||||
\(377\) | 16.0000 | 0.824042 | ||||||||
\(378\) | 0.500000 | − | 2.59808i | 0.0257172 | − | 0.133631i | ||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | + | 13.8564i | 0.409852 | + | 0.709885i | ||||
\(382\) | 7.50000 | + | 12.9904i | 0.383733 | + | 0.664646i | ||||
\(383\) | 15.5000 | − | 26.8468i | 0.792013 | − | 1.37181i | −0.132706 | − | 0.991155i | \(-0.542367\pi\) |
0.924719 | − | 0.380651i | \(-0.124300\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.0000 | −1.27247 | ||||||||
\(387\) | −1.00000 | + | 1.73205i | −0.0508329 | + | 0.0880451i | ||||
\(388\) | 3.50000 | + | 6.06218i | 0.177686 | + | 0.307760i | ||||
\(389\) | −5.00000 | − | 8.66025i | −0.253510 | − | 0.439092i | 0.710980 | − | 0.703213i | \(-0.248252\pi\) |
−0.964490 | + | 0.264120i | \(0.914918\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.0000 | 1.06202 | ||||||||
\(392\) | −5.50000 | + | 4.33013i | −0.277792 | + | 0.218704i | ||||
\(393\) | 8.00000 | 0.403547 | ||||||||
\(394\) | 10.0000 | − | 17.3205i | 0.503793 | − | 0.872595i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.00000 | + | 3.46410i | 0.100504 | + | 0.174078i | ||||
\(397\) | 11.0000 | − | 19.0526i | 0.552074 | − | 0.956221i | −0.446051 | − | 0.895008i | \(-0.647170\pi\) |
0.998125 | − | 0.0612128i | \(-0.0194968\pi\) | |||||||
\(398\) | −15.0000 | −0.751882 | ||||||||
\(399\) | 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 | \(0.843908\pi\) | |||||||
\(402\) | −6.00000 | − | 10.3923i | −0.299253 | − | 0.518321i | ||||
\(403\) | 10.0000 | + | 17.3205i | 0.498135 | + | 0.862796i | ||||
\(404\) | 9.00000 | − | 15.5885i | 0.447767 | − | 0.775555i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.00000 | + | 10.3923i | −0.0992583 | + | 0.515761i | ||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | −1.50000 | + | 2.59808i | −0.0742611 | + | 0.128624i | ||||
\(409\) | −14.5000 | − | 25.1147i | −0.716979 | − | 1.24184i | −0.962191 | − | 0.272374i | \(-0.912191\pi\) |
0.245212 | − | 0.969469i | \(-0.421142\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.50000 | − | 12.9904i | 0.369948 | − | 0.640768i | ||||
\(412\) | −7.00000 | −0.344865 | ||||||||
\(413\) | −28.0000 | − | 24.2487i | −1.37779 | − | 1.19320i | ||||
\(414\) | −7.00000 | −0.344031 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.00000 | + | 3.46410i | 0.0980581 | + | 0.169842i | ||||
\(417\) | 1.00000 | + | 1.73205i | 0.0489702 | + | 0.0848189i | ||||
\(418\) | −12.0000 | + | 20.7846i | −0.586939 | + | 1.01661i | ||||
\(419\) | −26.0000 | −1.27018 | −0.635092 | − | 0.772437i | \(-0.719038\pi\) | ||||
−0.635092 | + | 0.772437i | \(0.719038\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0000 | 0.779792 | 0.389896 | − | 0.920859i | \(-0.372511\pi\) | ||||
0.389896 | + | 0.920859i | \(0.372511\pi\) | |||||||
\(422\) | −11.0000 | + | 19.0526i | −0.535472 | + | 0.927464i | ||||
\(423\) | −0.500000 | − | 0.866025i | −0.0243108 | − | 0.0421076i | ||||
\(424\) | −1.00000 | − | 1.73205i | −0.0485643 | − | 0.0841158i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.00000 | −0.436051 | ||||||||
\(427\) | 6.00000 | − | 31.1769i | 0.290360 | − | 1.50876i | ||||
\(428\) | 14.0000 | 0.676716 | ||||||||
\(429\) | −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 | \(0.444826\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 37.0000 | 1.77811 | 0.889053 | − | 0.457804i | \(-0.151364\pi\) | ||||
0.889053 | + | 0.457804i | \(0.151364\pi\) | |||||||
\(434\) | −12.5000 | + | 4.33013i | −0.600019 | + | 0.207853i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.00000 | + | 5.19615i | −0.143674 | + | 0.248851i | ||||
\(437\) | −21.0000 | − | 36.3731i | −1.00457 | − | 1.73996i | ||||
\(438\) | −3.00000 | − | 5.19615i | −0.143346 | − | 0.248282i | ||||
\(439\) | −8.50000 | + | 14.7224i | −0.405683 | + | 0.702663i | −0.994401 | − | 0.105675i | \(-0.966300\pi\) |
0.588718 | + | 0.808339i | \(0.299633\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | 13.0000 | − | 22.5167i | 0.617649 | − | 1.06980i | −0.372265 | − | 0.928126i | \(-0.621419\pi\) |
0.989914 | − | 0.141672i | \(-0.0452479\pi\) | |||||||
\(444\) | 1.00000 | + | 1.73205i | 0.0474579 | + | 0.0821995i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.50000 | − | 7.79423i | 0.213081 | − | 0.369067i | ||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | −2.50000 | + | 0.866025i | −0.118114 | + | 0.0409159i | ||||
\(449\) | −13.0000 | −0.613508 | −0.306754 | − | 0.951789i | \(-0.599243\pi\) | ||||
−0.306754 | + | 0.951789i | \(0.599243\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.0000 | + | 24.2487i | 0.659234 | + | 1.14183i | ||||
\(452\) | 1.50000 | + | 2.59808i | 0.0705541 | + | 0.122203i | ||||
\(453\) | 12.0000 | − | 20.7846i | 0.563809 | − | 0.976546i | ||||
\(454\) | 22.0000 | 1.03251 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | −9.00000 | + | 15.5885i | −0.421002 | + | 0.729197i | −0.996038 | − | 0.0889312i | \(-0.971655\pi\) |
0.575036 | + | 0.818128i | \(0.304988\pi\) | |||||||
\(458\) | 4.00000 | + | 6.92820i | 0.186908 | + | 0.323734i | ||||
\(459\) | 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 | \(0.183524\pi\) | |||||||
\(462\) | −8.00000 | − | 6.92820i | −0.372194 | − | 0.322329i | ||||
\(463\) | −7.00000 | −0.325318 | −0.162659 | − | 0.986682i | \(-0.552007\pi\) | ||||
−0.162659 | + | 0.986682i | \(0.552007\pi\) | |||||||
\(464\) | −2.00000 | + | 3.46410i | −0.0928477 | + | 0.160817i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | − | 5.19615i | −0.138972 | − | 0.240707i | ||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | 4.00000 | 0.184900 | ||||||||
\(469\) | 24.0000 | + | 20.7846i | 1.10822 | + | 0.959744i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.00000 | + | 3.46410i | −0.0921551 | + | 0.159617i | ||||
\(472\) | −7.00000 | − | 12.1244i | −0.322201 | − | 0.558069i | ||||
\(473\) | 4.00000 | + | 6.92820i | 0.183920 | + | 0.318559i | ||||
\(474\) | 8.50000 | − | 14.7224i | 0.390418 | − | 0.676224i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.50000 | − | 7.79423i | 0.0687524 | − | 0.357248i | ||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 1.50000 | − | 2.59808i | 0.0686084 | − | 0.118833i | ||||
\(479\) | −0.500000 | − | 0.866025i | −0.0228456 | − | 0.0395697i | 0.854377 | − | 0.519654i | \(-0.173939\pi\) |
−0.877222 | + | 0.480085i | \(0.840606\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | + | 6.92820i | −0.182384 | + | 0.315899i | ||||
\(482\) | 2.00000 | 0.0910975 | ||||||||
\(483\) | 17.5000 | − | 6.06218i | 0.796278 | − | 0.275839i | ||||
\(484\) | 5.00000 | 0.227273 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −2.50000 | − | 4.33013i | −0.113286 | − | 0.196217i | 0.803807 | − | 0.594890i | \(-0.202804\pi\) |
−0.917093 | + | 0.398673i | \(0.869471\pi\) | |||||||
\(488\) | 6.00000 | − | 10.3923i | 0.271607 | − | 0.470438i | ||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.0000 | 1.71492 | 0.857458 | − | 0.514554i | \(-0.172042\pi\) | ||||
0.857458 | + | 0.514554i | \(0.172042\pi\) | |||||||
\(492\) | 3.50000 | − | 6.06218i | 0.157792 | − | 0.273304i | ||||
\(493\) | −6.00000 | − | 10.3923i | −0.270226 | − | 0.468046i | ||||
\(494\) | 12.0000 | + | 20.7846i | 0.539906 | + | 0.935144i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.00000 | −0.224507 | ||||||||
\(497\) | 22.5000 | − | 7.79423i | 1.00926 | − | 0.349619i | ||||
\(498\) | −4.00000 | −0.179244 | ||||||||
\(499\) | −14.0000 | + | 24.2487i | −0.626726 | + | 1.08552i | 0.361478 | + | 0.932381i | \(0.382272\pi\) |
−0.988204 | + | 0.153141i | \(0.951061\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.00000 | − | 3.46410i | 0.0892644 | − | 0.154610i | ||||
\(503\) | 36.0000 | 1.60516 | 0.802580 | − | 0.596544i | \(-0.203460\pi\) | ||||
0.802580 | + | 0.596544i | \(0.203460\pi\) | |||||||
\(504\) | −0.500000 | + | 2.59808i | −0.0222718 | + | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −14.0000 | + | 24.2487i | −0.622376 | + | 1.07799i | ||||
\(507\) | 1.50000 | + | 2.59808i | 0.0666173 | + | 0.115385i | ||||
\(508\) | −8.00000 | − | 13.8564i | −0.354943 | − | 0.614779i | ||||
\(509\) | 8.00000 | − | 13.8564i | 0.354594 | − | 0.614174i | −0.632455 | − | 0.774597i | \(-0.717953\pi\) |
0.987048 | + | 0.160423i | \(0.0512858\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | + | 10.3923i | 0.530849 | + | 0.459728i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.00000 | − | 5.19615i | 0.132453 | − | 0.229416i | ||||
\(514\) | −1.00000 | − | 1.73205i | −0.0441081 | − | 0.0763975i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.00000 | − | 1.73205i | 0.0440225 | − | 0.0762493i | ||||
\(517\) | −4.00000 | −0.175920 | ||||||||
\(518\) | −4.00000 | − | 3.46410i | −0.175750 | − | 0.152204i | ||||
\(519\) | −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 | \(0.770165\pi\) | |||||||
\(522\) | 2.00000 | + | 3.46410i | 0.0875376 | + | 0.151620i | ||||
\(523\) | −22.0000 | + | 38.1051i | −0.961993 | + | 1.66622i | −0.244507 | + | 0.969648i | \(0.578626\pi\) |
−0.717486 | + | 0.696573i | \(0.754707\pi\) | |||||||
\(524\) | −8.00000 | −0.349482 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.0000 | 1.17726 | ||||||||
\(527\) | 7.50000 | − | 12.9904i | 0.326705 | − | 0.565870i | ||||
\(528\) | −2.00000 | − | 3.46410i | −0.0870388 | − | 0.150756i | ||||
\(529\) | −13.0000 | − | 22.5167i | −0.565217 | − | 0.978985i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.0000 | −0.607548 | ||||||||
\(532\) | −15.0000 | + | 5.19615i | −0.650332 | + | 0.225282i | ||||
\(533\) | 28.0000 | 1.21281 | ||||||||
\(534\) | 3.50000 | − | 6.06218i | 0.151460 | − | 0.262336i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.00000 | + | 10.3923i | 0.259161 | + | 0.448879i | ||||
\(537\) | 1.00000 | − | 1.73205i | 0.0431532 | − | 0.0747435i | ||||
\(538\) | 10.0000 | 0.431131 | ||||||||
\(539\) | 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 | \(0.925202\pi\) | |||||||
\(542\) | 2.50000 | + | 4.33013i | 0.107384 | + | 0.185995i | ||||
\(543\) | 6.00000 | + | 10.3923i | 0.257485 | + | 0.445976i | ||||
\(544\) | 1.50000 | − | 2.59808i | 0.0643120 | − | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10.0000 | + | 3.46410i | −0.427960 | + | 0.148250i | ||||
\(547\) | 22.0000 | 0.940652 | 0.470326 | − | 0.882493i | \(-0.344136\pi\) | ||||
0.470326 | + | 0.882493i | \(0.344136\pi\) | |||||||
\(548\) | −7.50000 | + | 12.9904i | −0.320384 | + | 0.554922i | ||||
\(549\) | −6.00000 | − | 10.3923i | −0.256074 | − | 0.443533i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | + | 20.7846i | −0.511217 | + | 0.885454i | ||||
\(552\) | 7.00000 | 0.297940 | ||||||||
\(553\) | −8.50000 | + | 44.1673i | −0.361457 | + | 1.87818i | ||||
\(554\) | 16.0000 | 0.679775 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00000 | − | 1.73205i | −0.0424094 | − | 0.0734553i | ||||
\(557\) | −15.0000 | − | 25.9808i | −0.635570 | − | 1.10084i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) |
0.350824 | − | 0.936442i | \(-0.385902\pi\) | |||||||
\(558\) | −2.50000 | + | 4.33013i | −0.105833 | + | 0.183309i | ||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0000 | 0.506640 | ||||||||
\(562\) | 8.50000 | − | 14.7224i | 0.358551 | − | 0.621028i | ||||
\(563\) | 1.00000 | + | 1.73205i | 0.0421450 | + | 0.0729972i | 0.886328 | − | 0.463057i | \(-0.153248\pi\) |
−0.844183 | + | 0.536054i | \(0.819914\pi\) | |||||||
\(564\) | 0.500000 | + | 0.866025i | 0.0210538 | + | 0.0364662i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.00000 | 0.336265 | ||||||||
\(567\) | 2.00000 | + | 1.73205i | 0.0839921 | + | 0.0727393i | ||||
\(568\) | 9.00000 | 0.377632 | ||||||||
\(569\) | 22.5000 | − | 38.9711i | 0.943249 | − | 1.63376i | 0.184030 | − | 0.982921i | \(-0.441086\pi\) |
0.759220 | − | 0.650835i | \(-0.225581\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | − | 34.6410i | −0.836974 | − | 1.44968i | −0.892413 | − | 0.451219i | \(-0.850989\pi\) |
0.0554391 | − | 0.998462i | \(-0.482344\pi\) | |||||||
\(572\) | 8.00000 | − | 13.8564i | 0.334497 | − | 0.579365i | ||||
\(573\) | −15.0000 | −0.626634 | ||||||||
\(574\) | −3.50000 | + | 18.1865i | −0.146087 | + | 0.759091i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 1.00000 | + | 1.73205i | 0.0416305 | + | 0.0721062i | 0.886090 | − | 0.463513i | \(-0.153411\pi\) |
−0.844459 | + | 0.535620i | \(0.820078\pi\) | |||||||
\(578\) | −4.00000 | − | 6.92820i | −0.166378 | − | 0.288175i | ||||
\(579\) | 12.5000 | − | 21.6506i | 0.519482 | − | 0.899770i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.0000 | − | 3.46410i | 0.414870 | − | 0.143715i | ||||
\(582\) | −7.00000 | −0.290159 | ||||||||
\(583\) | −4.00000 | + | 6.92820i | −0.165663 | + | 0.286937i | ||||
\(584\) | 3.00000 | + | 5.19615i | 0.124141 | + | 0.215018i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | + | 10.3923i | −0.247858 | + | 0.429302i | ||||
\(587\) | 42.0000 | 1.73353 | 0.866763 | − | 0.498721i | \(-0.166197\pi\) | ||||
0.866763 | + | 0.498721i | \(0.166197\pi\) | |||||||
\(588\) | −1.00000 | − | 6.92820i | −0.0412393 | − | 0.285714i | ||||
\(589\) | −30.0000 | −1.23613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0000 | + | 17.3205i | 0.411345 | + | 0.712470i | ||||
\(592\) | −1.00000 | − | 1.73205i | −0.0410997 | − | 0.0711868i | ||||
\(593\) | −6.50000 | + | 11.2583i | −0.266923 | + | 0.462324i | −0.968066 | − | 0.250697i | \(-0.919340\pi\) |
0.701143 | + | 0.713021i | \(0.252674\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 7.50000 | − | 12.9904i | 0.306955 | − | 0.531661i | ||||
\(598\) | 14.0000 | + | 24.2487i | 0.572503 | + | 0.991604i | ||||
\(599\) | 15.5000 | + | 26.8468i | 0.633313 | + | 1.09693i | 0.986870 | + | 0.161517i | \(0.0516387\pi\) |
−0.353557 | + | 0.935413i | \(0.615028\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.0000 | 1.87638 | 0.938190 | − | 0.346122i | \(-0.112502\pi\) | ||||
0.938190 | + | 0.346122i | \(0.112502\pi\) | |||||||
\(602\) | −1.00000 | + | 5.19615i | −0.0407570 | + | 0.211779i | ||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | −12.0000 | + | 20.7846i | −0.488273 | + | 0.845714i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.00000 | + | 15.5885i | 0.365600 | + | 0.633238i | ||||
\(607\) | −14.5000 | + | 25.1147i | −0.588537 | + | 1.01938i | 0.405887 | + | 0.913923i | \(0.366962\pi\) |
−0.994424 | + | 0.105453i | \(0.966371\pi\) | |||||||
\(608\) | −6.00000 | −0.243332 | ||||||||
\(609\) | −8.00000 | − | 6.92820i | −0.324176 | − | 0.280745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.00000 | + | 3.46410i | −0.0809113 | + | 0.140143i | ||||
\(612\) | −1.50000 | − | 2.59808i | −0.0606339 | − | 0.105021i | ||||
\(613\) | −2.00000 | − | 3.46410i | −0.0807792 | − | 0.139914i | 0.822806 | − | 0.568323i | \(-0.192408\pi\) |
−0.903585 | + | 0.428409i | \(0.859074\pi\) | |||||||
\(614\) | 10.0000 | − | 17.3205i | 0.403567 | − | 0.698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.00000 | + | 6.92820i | 0.322329 | + | 0.279145i | ||||
\(617\) | 1.00000 | 0.0402585 | 0.0201292 | − | 0.999797i | \(-0.493592\pi\) | ||||
0.0201292 | + | 0.999797i | \(0.493592\pi\) | |||||||
\(618\) | 3.50000 | − | 6.06218i | 0.140791 | − | 0.243857i | ||||
\(619\) | 8.00000 | + | 13.8564i | 0.321547 | + | 0.556936i | 0.980807 | − | 0.194979i | \(-0.0624638\pi\) |
−0.659260 | + | 0.751915i | \(0.729130\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.50000 | − | 6.06218i | 0.140450 | − | 0.243267i | ||||
\(622\) | −21.0000 | −0.842023 | ||||||||
\(623\) | −3.50000 | + | 18.1865i | −0.140225 | + | 0.728628i | ||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −13.5000 | − | 23.3827i | −0.539569 | − | 0.934560i | ||||
\(627\) | −12.0000 | − | 20.7846i | −0.479234 | − | 0.830057i | ||||
\(628\) | 2.00000 | − | 3.46410i | 0.0798087 | − | 0.138233i | ||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.00000 | 0.278666 | 0.139333 | − | 0.990246i | \(-0.455504\pi\) | ||||
0.139333 | + | 0.990246i | \(0.455504\pi\) | |||||||
\(632\) | −8.50000 | + | 14.7224i | −0.338112 | + | 0.585627i | ||||
\(633\) | −11.0000 | − | 19.0526i | −0.437211 | − | 0.757271i | ||||
\(634\) | 9.00000 | + | 15.5885i | 0.357436 | + | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.00000 | 0.0793052 | ||||||||
\(637\) | 22.0000 | − | 17.3205i | 0.871672 | − | 0.686264i | ||||
\(638\) | 16.0000 | 0.633446 | ||||||||
\(639\) | 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 | \(0.776455\pi\) | |||||||
\(642\) | −7.00000 | + | 12.1244i | −0.276268 | + | 0.478510i | ||||
\(643\) | 14.0000 | 0.552106 | 0.276053 | − | 0.961142i | \(-0.410973\pi\) | ||||
0.276053 | + | 0.961142i | \(0.410973\pi\) | |||||||
\(644\) | −17.5000 | + | 6.06218i | −0.689597 | + | 0.238883i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.00000 | − | 15.5885i | 0.354100 | − | 0.613320i | ||||
\(647\) | 16.0000 | + | 27.7128i | 0.629025 | + | 1.08950i | 0.987748 | + | 0.156059i | \(0.0498790\pi\) |
−0.358723 | + | 0.933444i | \(0.616788\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −28.0000 | + | 48.4974i | −1.09910 | + | 1.90369i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.50000 | − | 12.9904i | 0.0979827 | − | 0.509133i | ||||
\(652\) | −8.00000 | −0.313304 | ||||||||
\(653\) | −8.00000 | + | 13.8564i | −0.313064 | + | 0.542243i | −0.979024 | − | 0.203744i | \(-0.934689\pi\) |
0.665960 | + | 0.745988i | \(0.268022\pi\) | |||||||
\(654\) | −3.00000 | − | 5.19615i | −0.117309 | − | 0.203186i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.50000 | + | 6.06218i | −0.136652 | + | 0.236688i | ||||
\(657\) | 6.00000 | 0.234082 | ||||||||
\(658\) | −2.00000 | − | 1.73205i | −0.0779681 | − | 0.0675224i | ||||
\(659\) | 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 | \(-0.364957\pi\) | |||||||
\(662\) | −17.0000 | − | 29.4449i | −0.660724 | − | 1.14441i | ||||
\(663\) | 6.00000 | − | 10.3923i | 0.233021 | − | 0.403604i | ||||
\(664\) | 4.00000 | 0.155230 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.00000 | −0.0774984 | ||||||||
\(667\) | −14.0000 | + | 24.2487i | −0.542082 | + | 0.938914i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.50000 | + | 7.79423i | 0.173980 | + | 0.301342i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −48.0000 | −1.85302 | ||||||||
\(672\) | 0.500000 | − | 2.59808i | 0.0192879 | − | 0.100223i | ||||
\(673\) | −11.0000 | −0.424019 | −0.212009 | − | 0.977268i | \(-0.568001\pi\) | ||||
−0.212009 | + | 0.977268i | \(0.568001\pi\) | |||||||
\(674\) | 1.50000 | − | 2.59808i | 0.0577778 | − | 0.100074i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.50000 | − | 2.59808i | −0.0576923 | − | 0.0999260i | ||||
\(677\) | −16.0000 | + | 27.7128i | −0.614930 | + | 1.06509i | 0.375467 | + | 0.926836i | \(0.377482\pi\) |
−0.990397 | + | 0.138254i | \(0.955851\pi\) | |||||||
\(678\) | −3.00000 | −0.115214 | ||||||||
\(679\) | 17.5000 | − | 6.06218i | 0.671588 | − | 0.232645i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.0000 | + | 19.0526i | −0.421521 | + | 0.730096i | ||||
\(682\) | 10.0000 | + | 17.3205i | 0.382920 | + | 0.663237i | ||||
\(683\) | −11.0000 | − | 19.0526i | −0.420903 | − | 0.729026i | 0.575125 | − | 0.818066i | \(-0.304953\pi\) |
−0.996028 | + | 0.0890398i | \(0.971620\pi\) | |||||||
\(684\) | −3.00000 | + | 5.19615i | −0.114708 | + | 0.198680i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.50000 | + | 16.4545i | 0.324532 | + | 0.628235i | ||||
\(687\) | −8.00000 | −0.305219 | ||||||||
\(688\) | −1.00000 | + | 1.73205i | −0.0381246 | + | 0.0660338i | ||||
\(689\) | 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 | \(0.0157690\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 10.0000 | − | 3.46410i | 0.379869 | − | 0.131590i | ||||
\(694\) | −32.0000 | −1.21470 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.00000 | − | 3.46410i | −0.0758098 | − | 0.131306i | ||||
\(697\) | −10.5000 | − | 18.1865i | −0.397716 | − | 0.688864i | ||||
\(698\) | −9.00000 | + | 15.5885i | −0.340655 | + | 0.590032i | ||||
\(699\) | 6.00000 | 0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.0000 | 0.453234 | 0.226617 | − | 0.973984i | \(-0.427233\pi\) | ||||
0.226617 | + | 0.973984i | \(0.427233\pi\) | |||||||
\(702\) | −2.00000 | + | 3.46410i | −0.0754851 | + | 0.130744i | ||||
\(703\) | −6.00000 | − | 10.3923i | −0.226294 | − | 0.391953i | ||||
\(704\) | 2.00000 | + | 3.46410i | 0.0753778 | + | 0.130558i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.0000 | 0.564532 | ||||||||
\(707\) | −36.0000 | − | 31.1769i | −1.35392 | − | 1.17253i | ||||
\(708\) | 14.0000 | 0.526152 | ||||||||
\(709\) | −7.00000 | + | 12.1244i | −0.262891 | + | 0.455340i | −0.967009 | − | 0.254743i | \(-0.918009\pi\) |
0.704118 | + | 0.710083i | \(0.251342\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.50000 | + | 14.7224i | 0.318775 | + | 0.552134i | ||||
\(712\) | −3.50000 | + | 6.06218i | −0.131168 | + | 0.227190i | ||||
\(713\) | −35.0000 | −1.31076 | ||||||||
\(714\) | 6.00000 | + | 5.19615i | 0.224544 | + | 0.194461i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.00000 | + | 1.73205i | −0.0373718 | + | 0.0647298i | ||||
\(717\) | 1.50000 | + | 2.59808i | 0.0560185 | + | 0.0970269i | ||||
\(718\) | 2.00000 | + | 3.46410i | 0.0746393 | + | 0.129279i | ||||
\(719\) | 3.50000 | − | 6.06218i | 0.130528 | − | 0.226081i | −0.793352 | − | 0.608763i | \(-0.791666\pi\) |
0.923880 | + | 0.382682i | \(0.124999\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.50000 | + | 18.1865i | −0.130347 | + | 0.677302i | ||||
\(722\) | −17.0000 | −0.632674 | ||||||||
\(723\) | −1.00000 | + | 1.73205i | −0.0371904 | + | 0.0644157i | ||||
\(724\) | −6.00000 | − | 10.3923i | −0.222988 | − | 0.386227i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.50000 | + | 4.33013i | −0.0927837 | + | 0.160706i | ||||
\(727\) | −49.0000 | −1.81731 | −0.908655 | − | 0.417548i | \(-0.862889\pi\) | ||||
−0.908655 | + | 0.417548i | \(0.862889\pi\) | |||||||
\(728\) | 10.0000 | − | 3.46410i | 0.370625 | − | 0.128388i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.00000 | − | 5.19615i | −0.110959 | − | 0.192187i | ||||
\(732\) | 6.00000 | + | 10.3923i | 0.221766 | + | 0.384111i | ||||
\(733\) | 5.00000 | − | 8.66025i | 0.184679 | − | 0.319874i | −0.758789 | − | 0.651336i | \(-0.774209\pi\) |
0.943468 | + | 0.331463i | \(0.107542\pi\) | |||||||
\(734\) | 32.0000 | 1.18114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.00000 | −0.258023 | ||||||||
\(737\) | 24.0000 | − | 41.5692i | 0.884051 | − | 1.53122i | ||||
\(738\) | 3.50000 | + | 6.06218i | 0.128837 | + | 0.223152i | ||||
\(739\) | −7.00000 | − | 12.1244i | −0.257499 | − | 0.446002i | 0.708072 | − | 0.706140i | \(-0.249565\pi\) |
−0.965571 | + | 0.260138i | \(0.916232\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.0000 | −0.881662 | ||||||||
\(742\) | −5.00000 | + | 1.73205i | −0.183556 | + | 0.0635856i | ||||
\(743\) | 1.00000 | 0.0366864 | 0.0183432 | − | 0.999832i | \(-0.494161\pi\) | ||||
0.0183432 | + | 0.999832i | \(0.494161\pi\) | |||||||
\(744\) | 2.50000 | − | 4.33013i | 0.0916544 | − | 0.158750i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.00000 | + | 10.3923i | 0.219676 | + | 0.380489i | ||||
\(747\) | 2.00000 | − | 3.46410i | 0.0731762 | − | 0.126745i | ||||
\(748\) | −12.0000 | −0.438763 | ||||||||
\(749\) | 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 | \(0.0723712\pi\) | |||||||
\(752\) | −0.500000 | − | 0.866025i | −0.0182331 | − | 0.0315807i | ||||
\(753\) | 2.00000 | + | 3.46410i | 0.0728841 | + | 0.126239i | ||||
\(754\) | 8.00000 | − | 13.8564i | 0.291343 | − | 0.504621i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.00000 | − | 1.73205i | −0.0727393 | − | 0.0629941i | ||||
\(757\) | −16.0000 | −0.581530 | −0.290765 | − | 0.956795i | \(-0.593910\pi\) | ||||
−0.290765 | + | 0.956795i | \(0.593910\pi\) | |||||||
\(758\) | 10.0000 | − | 17.3205i | 0.363216 | − | 0.629109i | ||||
\(759\) | −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 | \(0.0423756\pi\) | |||||||
\(762\) | 16.0000 | 0.579619 | ||||||||
\(763\) | 12.0000 | + | 10.3923i | 0.434429 | + | 0.376227i | ||||
\(764\) | 15.0000 | 0.542681 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.5000 | − | 26.8468i | −0.560038 | − | 0.970014i | ||||
\(767\) | 28.0000 | + | 48.4974i | 1.01102 | + | 1.75114i | ||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | 10.0000 | 0.360609 | 0.180305 | − | 0.983611i | \(-0.442292\pi\) | ||||
0.180305 | + | 0.983611i | \(0.442292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.00000 | 0.0720282 | ||||||||
\(772\) | −12.5000 | + | 21.6506i | −0.449885 | + | 0.779223i | ||||
\(773\) | 9.00000 | + | 15.5885i | 0.323708 | + | 0.560678i | 0.981250 | − | 0.192740i | \(-0.0617373\pi\) |
−0.657542 | + | 0.753418i | \(0.728404\pi\) | |||||||
\(774\) | 1.00000 | + | 1.73205i | 0.0359443 | + | 0.0622573i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.00000 | 0.251285 | ||||||||
\(777\) | 5.00000 | − | 1.73205i | 0.179374 | − | 0.0621370i | ||||
\(778\) | −10.0000 | −0.358517 | ||||||||
\(779\) | −21.0000 | + | 36.3731i | −0.752403 | + | 1.30320i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | − | 31.1769i | −0.644091 | − | 1.11560i | ||||
\(782\) | 10.5000 | − | 18.1865i | 0.375479 | − | 0.650349i | ||||
\(783\) | −4.00000 | −0.142948 | ||||||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.00000 | − | 6.92820i | 0.142675 | − | 0.247121i | ||||
\(787\) | −11.0000 | − | 19.0526i | −0.392108 | − | 0.679150i | 0.600620 | − | 0.799535i | \(-0.294921\pi\) |
−0.992727 | + | 0.120384i | \(0.961587\pi\) | |||||||
\(788\) | −10.0000 | − | 17.3205i | −0.356235 | − | 0.617018i | ||||
\(789\) | −13.5000 | + | 23.3827i | −0.480613 | + | 0.832446i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.50000 | − | 2.59808i | 0.266669 | − | 0.0923770i | ||||
\(792\) | 4.00000 | 0.142134 | ||||||||
\(793\) | −24.0000 | + | 41.5692i | −0.852265 | + | 1.47617i | ||||
\(794\) | −11.0000 | − | 19.0526i | −0.390375 | − | 0.676150i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.50000 | + | 12.9904i | −0.265830 | + | 0.460432i | ||||
\(797\) | −12.0000 | −0.425062 | −0.212531 | − | 0.977154i | \(-0.568171\pi\) | ||||
−0.212531 | + | 0.977154i | \(0.568171\pi\) | |||||||
\(798\) | 3.00000 | − | 15.5885i | 0.106199 | − | 0.551825i | ||||
\(799\) | 3.00000 | 0.106132 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.50000 | + | 6.06218i | 0.123666 | + | 0.214197i | ||||
\(802\) | 17.0000 | + | 29.4449i | 0.600291 | + | 1.03973i | ||||
\(803\) | 12.0000 | − | 20.7846i | 0.423471 | − | 0.733473i | ||||
\(804\) | −12.0000 | −0.423207 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.0000 | 0.704470 | ||||||||
\(807\) | −5.00000 | + | 8.66025i | −0.176008 | + | 0.304855i | ||||
\(808\) | −9.00000 | − | 15.5885i | −0.316619 | − | 0.548400i | ||||
\(809\) | −27.0000 | − | 46.7654i | −0.949269 | − | 1.64418i | −0.746968 | − | 0.664860i | \(-0.768491\pi\) |
−0.202301 | − | 0.979323i | \(-0.564842\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 8.00000 | + | 6.92820i | 0.280745 | + | 0.243132i | ||||
\(813\) | −5.00000 | −0.175358 | ||||||||
\(814\) | −4.00000 | + | 6.92820i | −0.140200 | + | 0.242833i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.50000 | + | 2.59808i | 0.0525105 | + | 0.0909509i | ||||
\(817\) | −6.00000 | + | 10.3923i | −0.209913 | + | 0.363581i | ||||
\(818\) | −29.0000 | −1.01396 | ||||||||
\(819\) | 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 | \(0.200055\pi\) | |||||||
\(822\) | −7.50000 | − | 12.9904i | −0.261593 | − | 0.453092i | ||||
\(823\) | 12.0000 | + | 20.7846i | 0.418294 | + | 0.724506i | 0.995768 | − | 0.0919029i | \(-0.0292950\pi\) |
−0.577474 | + | 0.816409i | \(0.695962\pi\) | |||||||
\(824\) | −3.50000 | + | 6.06218i | −0.121928 | + | 0.211186i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −35.0000 | + | 12.1244i | −1.21781 | + | 0.421860i | ||||
\(827\) | 20.0000 | 0.695468 | 0.347734 | − | 0.937593i | \(-0.386951\pi\) | ||||
0.347734 | + | 0.937593i | \(0.386951\pi\) | |||||||
\(828\) | −3.50000 | + | 6.06218i | −0.121633 | + | 0.210675i | ||||
\(829\) | 19.0000 | + | 32.9090i | 0.659897 | + | 1.14298i | 0.980642 | + | 0.195810i | \(0.0627335\pi\) |
−0.320745 | + | 0.947166i | \(0.603933\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.00000 | + | 13.8564i | −0.277517 | + | 0.480673i | ||||
\(832\) | 4.00000 | 0.138675 | ||||||||
\(833\) | −19.5000 | − | 7.79423i | −0.675635 | − | 0.270054i | ||||
\(834\) | 2.00000 | 0.0692543 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.0000 | + | 20.7846i | 0.415029 | + | 0.718851i | ||||
\(837\) | −2.50000 | − | 4.33013i | −0.0864126 | − | 0.149671i | ||||
\(838\) | −13.0000 | + | 22.5167i | −0.449078 | + | 0.777825i | ||||
\(839\) | −25.0000 | −0.863096 | −0.431548 | − | 0.902090i | \(-0.642032\pi\) | ||||
−0.431548 | + | 0.902090i | \(0.642032\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 8.00000 | − | 13.8564i | 0.275698 | − | 0.477523i | ||||
\(843\) | 8.50000 | + | 14.7224i | 0.292756 | + | 0.507067i | ||||
\(844\) | 11.0000 | + | 19.0526i | 0.378636 | + | 0.655816i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.00000 | −0.0343807 | ||||||||
\(847\) | 2.50000 | − | 12.9904i | 0.0859010 | − | 0.446355i | ||||
\(848\) | −2.00000 | −0.0686803 | ||||||||
\(849\) | −4.00000 | + | 6.92820i | −0.137280 | + | 0.237775i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.00000 | − | 12.1244i | −0.239957 | − | 0.415618i | ||||
\(852\) | −4.50000 | + | 7.79423i | −0.154167 | + | 0.267026i | ||||
\(853\) | −2.00000 | −0.0684787 | −0.0342393 | − | 0.999414i | \(-0.510901\pi\) | ||||
−0.0342393 | + | 0.999414i | \(0.510901\pi\) | |||||||
\(854\) | −24.0000 | − | 20.7846i | −0.821263 | − | 0.711235i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.00000 | − | 12.1244i | 0.239255 | − | 0.414402i | ||||
\(857\) | 13.0000 | + | 22.5167i | 0.444072 | + | 0.769154i | 0.997987 | − | 0.0634184i | \(-0.0202003\pi\) |
−0.553915 | + | 0.832573i | \(0.686867\pi\) | |||||||
\(858\) | 8.00000 | + | 13.8564i | 0.273115 | + | 0.473050i | ||||
\(859\) | −12.0000 | + | 20.7846i | −0.409435 | + | 0.709162i | −0.994826 | − | 0.101589i | \(-0.967607\pi\) |
0.585392 | + | 0.810751i | \(0.300941\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.0000 | − | 12.1244i | −0.477119 | − | 0.413197i | ||||
\(862\) | 39.0000 | 1.32835 | ||||||||
\(863\) | 5.50000 | − | 9.52628i | 0.187222 | − | 0.324278i | −0.757101 | − | 0.653298i | \(-0.773385\pi\) |
0.944323 | + | 0.329020i | \(0.106718\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.5000 | − | 32.0429i | 0.628656 | − | 1.08886i | ||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | −2.50000 | + | 12.9904i | −0.0848555 | + | 0.440922i | ||||
\(869\) | 68.0000 | 2.30674 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0000 | − | 41.5692i | −0.813209 | − | 1.40852i | ||||
\(872\) | 3.00000 | + | 5.19615i | 0.101593 | + | 0.175964i | ||||
\(873\) | 3.50000 | − | 6.06218i | 0.118457 | − | 0.205174i | ||||
\(874\) | −42.0000 | −1.42067 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.00000 | −0.202721 | ||||||||
\(877\) | −19.0000 | + | 32.9090i | −0.641584 | + | 1.11126i | 0.343495 | + | 0.939155i | \(0.388389\pi\) |
−0.985079 | + | 0.172102i | \(0.944944\pi\) | |||||||
\(878\) | 8.50000 | + | 14.7224i | 0.286861 | + | 0.496858i | ||||
\(879\) | −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 | \(0.700711\pi\) | |||||||
\(882\) | 6.50000 | + | 2.59808i | 0.218866 | + | 0.0874818i | ||||
\(883\) | 6.00000 | 0.201916 | 0.100958 | − | 0.994891i | \(-0.467809\pi\) | ||||
0.100958 | + | 0.994891i | \(0.467809\pi\) | |||||||
\(884\) | −6.00000 | + | 10.3923i | −0.201802 | + | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.0000 | − | 22.5167i | −0.436744 | − | 0.756462i | ||||
\(887\) | −28.0000 | + | 48.4974i | −0.940148 | + | 1.62838i | −0.174962 | + | 0.984575i | \(0.555980\pi\) |
−0.765186 | + | 0.643809i | \(0.777353\pi\) | |||||||
\(888\) | 2.00000 | 0.0671156 | ||||||||
\(889\) | −40.0000 | + | 13.8564i | −1.34156 | + | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00000 | − | 3.46410i | 0.0670025 | − | 0.116052i | ||||
\(892\) | −4.50000 | − | 7.79423i | −0.150671 | − | 0.260970i | ||||
\(893\) | −3.00000 | − | 5.19615i | −0.100391 | − | 0.173883i | ||||
\(894\) | 3.00000 | − | 5.19615i | 0.100335 | − | 0.173785i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.500000 | + | 2.59808i | −0.0167038 | + | 0.0867956i | ||||
\(897\) | −28.0000 | −0.934893 | ||||||||
\(898\) | −6.50000 | + | 11.2583i | −0.216908 | + | 0.375695i | ||||
\(899\) | 10.0000 | + | 17.3205i | 0.333519 | + | 0.577671i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.00000 | − | 5.19615i | 0.0999445 | − | 0.173109i | ||||
\(902\) | 28.0000 | 0.932298 | ||||||||
\(903\) | −4.00000 | − | 3.46410i | −0.133112 | − | 0.115278i | ||||
\(904\) | 3.00000 | 0.0997785 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −12.0000 | − | 20.7846i | −0.398673 | − | 0.690522i | ||||
\(907\) | 14.0000 | + | 24.2487i | 0.464862 | + | 0.805165i | 0.999195 | − | 0.0401089i | \(-0.0127705\pi\) |
−0.534333 | + | 0.845274i | \(0.679437\pi\) | |||||||
\(908\) | 11.0000 | − | 19.0526i | 0.365048 | − | 0.632281i | ||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.0000 | 0.629498 | 0.314749 | − | 0.949175i | \(-0.398080\pi\) | ||||
0.314749 | + | 0.949175i | \(0.398080\pi\) | |||||||
\(912\) | 3.00000 | − | 5.19615i | 0.0993399 | − | 0.172062i | ||||
\(913\) | −8.00000 | − | 13.8564i | −0.264761 | − | 0.458580i | ||||
\(914\) | 9.00000 | + | 15.5885i | 0.297694 | + | 0.515620i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.00000 | 0.264327 | ||||||||
\(917\) | −4.00000 | + | 20.7846i | −0.132092 | + | 0.686368i | ||||
\(918\) | 3.00000 | 0.0990148 | ||||||||
\(919\) | 19.5000 | − | 33.7750i | 0.643246 | − | 1.11413i | −0.341458 | − | 0.939897i | \(-0.610921\pi\) |
0.984704 | − | 0.174237i | \(-0.0557459\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0000 | + | 17.3205i | 0.329511 | + | 0.570730i | ||||
\(922\) | 18.0000 | − | 31.1769i | 0.592798 | − | 1.02676i | ||||
\(923\) | −36.0000 | −1.18495 | ||||||||
\(924\) | −10.0000 | + | 3.46410i | −0.328976 | + | 0.113961i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.50000 | + | 6.06218i | −0.115017 | + | 0.199216i | ||||
\(927\) | 3.50000 | + | 6.06218i | 0.114955 | + | 0.199108i | ||||
\(928\) | 2.00000 | + | 3.46410i | 0.0656532 | + | 0.113715i | ||||
\(929\) | 15.0000 | − | 25.9808i | 0.492134 | − | 0.852401i | −0.507825 | − | 0.861460i | \(-0.669550\pi\) |
0.999959 | + | 0.00905914i | \(0.00288365\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000 | + | 41.5692i | 0.196642 | + | 1.36238i | ||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | 10.5000 | − | 18.1865i | 0.343755 | − | 0.595400i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | − | 3.46410i | 0.0653720 | − | 0.113228i | ||||
\(937\) | −6.00000 | −0.196011 | −0.0980057 | − | 0.995186i | \(-0.531246\pi\) | ||||
−0.0980057 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(938\) | 30.0000 | − | 10.3923i | 0.979535 | − | 0.339321i | ||||
\(939\) | 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 | \(-0.406681\pi\) | |||||||
\(942\) | 2.00000 | + | 3.46410i | 0.0651635 | + | 0.112867i | ||||
\(943\) | −24.5000 | + | 42.4352i | −0.797830 | + | 1.38188i | ||||
\(944\) | −14.0000 | −0.455661 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.00000 | 0.260102 | ||||||||
\(947\) | 16.0000 | − | 27.7128i | 0.519930 | − | 0.900545i | −0.479801 | − | 0.877377i | \(-0.659291\pi\) |
0.999732 | − | 0.0231683i | \(-0.00737536\pi\) | |||||||
\(948\) | −8.50000 | − | 14.7224i | −0.276067 | − | 0.478162i | ||||
\(949\) | −12.0000 | − | 20.7846i | −0.389536 | − | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | −6.00000 | − | 5.19615i | −0.194461 | − | 0.168408i | ||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | −1.00000 | + | 1.73205i | −0.0323762 | + | 0.0560772i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.50000 | − | 2.59808i | −0.0485135 | − | 0.0840278i | ||||
\(957\) | −8.00000 | + | 13.8564i | −0.258603 | + | 0.447914i | ||||
\(958\) | −1.00000 | −0.0323085 | ||||||||
\(959\) | 30.0000 | + | 25.9808i | 0.968751 | + | 0.838963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | − | 5.19615i | 0.0967742 | − | 0.167618i | ||||
\(962\) | 4.00000 | + | 6.92820i | 0.128965 | + | 0.223374i | ||||
\(963\) | −7.00000 | − | 12.1244i | −0.225572 | − | 0.390702i | ||||
\(964\) | 1.00000 | − | 1.73205i | 0.0322078 | − | 0.0557856i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.50000 | − | 18.1865i | 0.112611 | − | 0.585142i | ||||
\(967\) | −29.0000 | −0.932577 | −0.466289 | − | 0.884633i | \(-0.654409\pi\) | ||||
−0.466289 | + | 0.884633i | \(0.654409\pi\) | |||||||
\(968\) | 2.50000 | − | 4.33013i | 0.0803530 | − | 0.139176i | ||||
\(969\) | 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 | \(0.0408342\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −5.00000 | + | 1.73205i | −0.160293 | + | 0.0555270i | ||||
\(974\) | −5.00000 | −0.160210 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.00000 | − | 10.3923i | −0.192055 | − | 0.332650i | ||||
\(977\) | −1.50000 | − | 2.59808i | −0.0479893 | − | 0.0831198i | 0.841033 | − | 0.540984i | \(-0.181948\pi\) |
−0.889022 | + | 0.457864i | \(0.848615\pi\) | |||||||
\(978\) | 4.00000 | − | 6.92820i | 0.127906 | − | 0.221540i | ||||
\(979\) | 28.0000 | 0.894884 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.00000 | 0.191565 | ||||||||
\(982\) | 19.0000 | − | 32.9090i | 0.606314 | − | 1.05017i | ||||
\(983\) | −14.0000 | − | 24.2487i | −0.446531 | − | 0.773414i | 0.551627 | − | 0.834091i | \(-0.314007\pi\) |
−0.998157 | + | 0.0606773i | \(0.980674\pi\) | |||||||
\(984\) | −3.50000 | − | 6.06218i | −0.111576 | − | 0.193255i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12.0000 | −0.382158 | ||||||||
\(987\) | 2.50000 | − | 0.866025i | 0.0795759 | − | 0.0275659i | ||||
\(988\) | 24.0000 | 0.763542 | ||||||||
\(989\) | −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 | \(0.868797\pi\) | |||||||
\(992\) | −2.50000 | + | 4.33013i | −0.0793751 | + | 0.137482i | ||||
\(993\) | 34.0000 | 1.07896 | ||||||||
\(994\) | 4.50000 | − | 23.3827i | 0.142731 | − | 0.741654i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.00000 | + | 3.46410i | −0.0633724 | + | 0.109764i | ||||
\(997\) | 8.00000 | + | 13.8564i | 0.253363 | + | 0.438837i | 0.964449 | − | 0.264267i | \(-0.0851301\pi\) |
−0.711087 | + | 0.703104i | \(0.751797\pi\) | |||||||
\(998\) | 14.0000 | + | 24.2487i | 0.443162 | + | 0.767580i | ||||
\(999\) | 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.i.r.751.1 | yes | 2 | |
5.2 | odd | 4 | 1050.2.o.l.499.2 | 4 | |||
5.3 | odd | 4 | 1050.2.o.l.499.1 | 4 | |||
5.4 | even | 2 | 1050.2.i.d.751.1 | yes | 2 | ||
7.2 | even | 3 | 7350.2.a.e.1.1 | 1 | |||
7.4 | even | 3 | inner | 1050.2.i.r.151.1 | yes | 2 | |
7.5 | odd | 6 | 7350.2.a.v.1.1 | 1 | |||
35.4 | even | 6 | 1050.2.i.d.151.1 | ✓ | 2 | ||
35.9 | even | 6 | 7350.2.a.ci.1.1 | 1 | |||
35.18 | odd | 12 | 1050.2.o.l.949.2 | 4 | |||
35.19 | odd | 6 | 7350.2.a.bs.1.1 | 1 | |||
35.32 | odd | 12 | 1050.2.o.l.949.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.i.d.151.1 | ✓ | 2 | 35.4 | even | 6 | ||
1050.2.i.d.751.1 | yes | 2 | 5.4 | even | 2 | ||
1050.2.i.r.151.1 | yes | 2 | 7.4 | even | 3 | inner | |
1050.2.i.r.751.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1050.2.o.l.499.1 | 4 | 5.3 | odd | 4 | |||
1050.2.o.l.499.2 | 4 | 5.2 | odd | 4 | |||
1050.2.o.l.949.1 | 4 | 35.32 | odd | 12 | |||
1050.2.o.l.949.2 | 4 | 35.18 | odd | 12 | |||
7350.2.a.e.1.1 | 1 | 7.2 | even | 3 | |||
7350.2.a.v.1.1 | 1 | 7.5 | odd | 6 | |||
7350.2.a.bs.1.1 | 1 | 35.19 | odd | 6 | |||
7350.2.a.ci.1.1 | 1 | 35.9 | even | 6 |