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 | 949.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.949 |
Dual form | 1050.2.o.h.499.1 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 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 | ||||||||
\(11\) | −3.00000 | + | 5.19615i | −0.904534 | + | 1.56670i | −0.0829925 | + | 0.996550i | \(0.526448\pi\) |
−0.821541 | + | 0.570149i | \(0.806886\pi\) | |||||||
\(12\) | −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 | \(-0.451855\pi\) |
−0.780801 | + | 0.624780i | \(0.785189\pi\) | |||||||
\(18\) | −0.866025 | − | 0.500000i | −0.204124 | − | 0.117851i | ||||
\(19\) | −2.00000 | − | 3.46410i | −0.458831 | − | 0.794719i | 0.540068 | − | 0.841621i | \(-0.318398\pi\) |
−0.998899 | + | 0.0469020i | \(0.985065\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | + | 1.73205i | −0.436436 | + | 0.377964i | ||||
\(22\) | − | 6.00000i | − | 1.27920i | ||||||
\(23\) | 2.59808 | − | 1.50000i | 0.541736 | − | 0.312772i | −0.204046 | − | 0.978961i | \(-0.565409\pi\) |
0.745782 | + | 0.666190i | \(0.232076\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 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 | ||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | + | 4.33013i | −0.449013 | + | 0.777714i | −0.998322 | − | 0.0579057i | \(-0.981558\pi\) |
0.549309 | + | 0.835619i | \(0.314891\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 5.19615 | − | 3.00000i | 0.904534 | − | 0.522233i | ||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.92820 | + | 4.00000i | −1.13899 | + | 0.657596i | −0.946180 | − | 0.323640i | \(-0.895093\pi\) |
−0.192809 | + | 0.981236i | \(0.561760\pi\) | |||||||
\(38\) | 3.46410 | + | 2.00000i | 0.561951 | + | 0.324443i | ||||
\(39\) | −2.00000 | + | 3.46410i | −0.320256 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | 0.866025 | − | 2.50000i | 0.133631 | − | 0.385758i | ||||
\(43\) | 8.00000i | 1.21999i | 0.792406 | + | 0.609994i | \(0.208828\pi\) | ||||
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | 3.00000 | + | 5.19615i | 0.452267 | + | 0.783349i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.50000 | + | 2.59808i | −0.221163 | + | 0.383065i | ||||
\(47\) | −7.79423 | + | 4.50000i | −1.13691 | + | 0.656392i | −0.945662 | − | 0.325150i | \(-0.894585\pi\) |
−0.191243 | + | 0.981543i | \(0.561252\pi\) | |||||||
\(48\) | 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 | ||||
\(53\) | −10.3923 | − | 6.00000i | −1.42749 | − | 0.824163i | −0.430570 | − | 0.902557i | \(-0.641688\pi\) |
−0.996922 | + | 0.0783936i | \(0.975021\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.50000 | + | 0.866025i | 0.334077 | + | 0.115728i | ||||
\(57\) | 4.00000i | 0.529813i | ||||||||
\(58\) | −5.19615 | + | 3.00000i | −0.682288 | + | 0.393919i | ||||
\(59\) | 3.00000 | − | 5.19615i | 0.390567 | − | 0.676481i | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.992524 | + | 0.122047i | \(0.0389457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | − | 1.73205i | −0.128037 | − | 0.221766i | 0.794879 | − | 0.606768i | \(-0.207534\pi\) |
−0.922916 | + | 0.385002i | \(0.874201\pi\) | |||||||
\(62\) | − | 5.00000i | − | 0.635001i | ||||||
\(63\) | 2.59808 | − | 0.500000i | 0.327327 | − | 0.0629941i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.00000 | + | 5.19615i | −0.369274 | + | 0.639602i | ||||
\(67\) | 6.92820 | + | 4.00000i | 0.846415 | + | 0.488678i | 0.859440 | − | 0.511237i | \(-0.170813\pi\) |
−0.0130248 | + | 0.999915i | \(0.504146\pi\) | |||||||
\(68\) | −2.59808 | + | 1.50000i | −0.315063 | + | 0.181902i | ||||
\(69\) | −3.00000 | −0.361158 | ||||||||
\(70\) | 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 | ||||
\(73\) | −12.1244 | − | 7.00000i | −1.41905 | − | 0.819288i | −0.422833 | − | 0.906208i | \(-0.638964\pi\) |
−0.996215 | + | 0.0869195i | \(0.972298\pi\) | |||||||
\(74\) | 4.00000 | − | 6.92820i | 0.464991 | − | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | 10.3923 | + | 12.0000i | 1.18431 | + | 1.36753i | ||||
\(78\) | − | 4.00000i | − | 0.452911i | ||||||
\(79\) | −3.50000 | − | 6.06218i | −0.393781 | − | 0.682048i | 0.599164 | − | 0.800626i | \(-0.295500\pi\) |
−0.992945 | + | 0.118578i | \(0.962166\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 2.59808 | − | 1.50000i | 0.286910 | − | 0.165647i | ||||
\(83\) | − | 6.00000i | − | 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | 0.500000 | + | 2.59808i | 0.0545545 | + | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | − | 6.92820i | −0.431331 | − | 0.747087i | ||||
\(87\) | −5.19615 | − | 3.00000i | −0.557086 | − | 0.321634i | ||||
\(88\) | −5.19615 | − | 3.00000i | −0.553912 | − | 0.319801i | ||||
\(89\) | 1.50000 | + | 2.59808i | 0.159000 | + | 0.275396i | 0.934508 | − | 0.355942i | \(-0.115840\pi\) |
−0.775509 | + | 0.631337i | \(0.782506\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0000 | − | 3.46410i | −1.04828 | − | 0.363137i | ||||
\(92\) | − | 3.00000i | − | 0.312772i | ||||||
\(93\) | 4.33013 | − | 2.50000i | 0.449013 | − | 0.259238i | ||||
\(94\) | 4.50000 | − | 7.79423i | 0.464140 | − | 0.803913i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | − | 17.0000i | − | 1.72609i | −0.505128 | − | 0.863044i | \(-0.668555\pi\) | ||
0.505128 | − | 0.863044i | \(-0.331445\pi\) | |||||||
\(98\) | 6.92820 | + | 1.00000i | 0.699854 | + | 0.101015i | ||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | + | 10.3923i | −0.597022 | + | 1.03407i | 0.396236 | + | 0.918149i | \(0.370316\pi\) |
−0.993258 | + | 0.115924i | \(0.963017\pi\) | |||||||
\(102\) | −2.59808 | − | 1.50000i | −0.257248 | − | 0.148522i | ||||
\(103\) | −11.2583 | + | 6.50000i | −1.10932 | + | 0.640464i | −0.938652 | − | 0.344865i | \(-0.887925\pi\) |
−0.170664 | + | 0.985329i | \(0.554591\pi\) | |||||||
\(104\) | 4.00000 | 0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.0000 | 1.16554 | ||||||||
\(107\) | −5.19615 | + | 3.00000i | −0.502331 | + | 0.290021i | −0.729676 | − | 0.683793i | \(-0.760329\pi\) |
0.227345 | + | 0.973814i | \(0.426996\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | −2.00000 | + | 3.46410i | −0.191565 | + | 0.331801i | −0.945769 | − | 0.324840i | \(-0.894690\pi\) |
0.754204 | + | 0.656640i | \(0.228023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | 0.759326 | ||||||||
\(112\) | −2.59808 | + | 0.500000i | −0.245495 | + | 0.0472456i | ||||
\(113\) | 3.00000i | 0.282216i | 0.989994 | + | 0.141108i | \(0.0450665\pi\) | ||||
−0.989994 | + | 0.141108i | \(0.954933\pi\) | |||||||
\(114\) | −2.00000 | − | 3.46410i | −0.187317 | − | 0.324443i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.00000 | − | 5.19615i | 0.278543 | − | 0.482451i | ||||
\(117\) | 3.46410 | − | 2.00000i | 0.320256 | − | 0.184900i | ||||
\(118\) | 6.00000i | 0.552345i | ||||||||
\(119\) | −6.00000 | + | 5.19615i | −0.550019 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | − | 21.6506i | −1.13636 | − | 1.96824i | ||||
\(122\) | 1.73205 | + | 1.00000i | 0.156813 | + | 0.0905357i | ||||
\(123\) | 2.59808 | + | 1.50000i | 0.234261 | + | 0.135250i | ||||
\(124\) | 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 | ||||
\(129\) | 4.00000 | − | 6.92820i | 0.352180 | − | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.00000 | + | 15.5885i | 0.786334 | + | 1.36197i | 0.928199 | + | 0.372084i | \(0.121357\pi\) |
−0.141865 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(132\) | − | 6.00000i | − | 0.522233i | ||||||
\(133\) | −10.3923 | + | 2.00000i | −0.901127 | + | 0.173422i | ||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.50000 | − | 2.59808i | 0.128624 | − | 0.222783i | ||||
\(137\) | −12.9904 | − | 7.50000i | −1.10984 | − | 0.640768i | −0.171054 | − | 0.985262i | \(-0.554717\pi\) |
−0.938789 | + | 0.344493i | \(0.888051\pi\) | |||||||
\(138\) | 2.59808 | − | 1.50000i | 0.221163 | − | 0.127688i | ||||
\(139\) | −2.00000 | −0.169638 | −0.0848189 | − | 0.996396i | \(-0.527031\pi\) | ||||
−0.0848189 | + | 0.996396i | \(0.527031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.00000 | 0.757937 | ||||||||
\(142\) | 7.79423 | − | 4.50000i | 0.654077 | − | 0.377632i | ||||
\(143\) | 20.7846 | + | 12.0000i | 1.73810 | + | 1.00349i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 14.0000 | 1.15865 | ||||||||
\(147\) | 2.59808 | + | 6.50000i | 0.214286 | + | 0.536111i | ||||
\(148\) | 8.00000i | 0.657596i | ||||||||
\(149\) | −3.00000 | − | 5.19615i | −0.245770 | − | 0.425685i | 0.716578 | − | 0.697507i | \(-0.245707\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | − | 13.8564i | 0.651031 | − | 1.12762i | −0.331842 | − | 0.943335i | \(-0.607670\pi\) |
0.982873 | − | 0.184284i | \(-0.0589965\pi\) | |||||||
\(152\) | 3.46410 | − | 2.00000i | 0.280976 | − | 0.162221i | ||||
\(153\) | − | 3.00000i | − | 0.242536i | ||||||
\(154\) | −15.0000 | − | 5.19615i | −1.20873 | − | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | + | 3.46410i | 0.160128 | + | 0.277350i | ||||
\(157\) | 12.1244 | + | 7.00000i | 0.967629 | + | 0.558661i | 0.898513 | − | 0.438948i | \(-0.144649\pi\) |
0.0691164 | + | 0.997609i | \(0.477982\pi\) | |||||||
\(158\) | 6.06218 | + | 3.50000i | 0.482281 | + | 0.278445i | ||||
\(159\) | 6.00000 | + | 10.3923i | 0.475831 | + | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.50000 | − | 7.79423i | −0.118217 | − | 0.614271i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 6.92820 | − | 4.00000i | 0.542659 | − | 0.313304i | −0.203497 | − | 0.979076i | \(-0.565231\pi\) |
0.746156 | + | 0.665771i | \(0.231897\pi\) | |||||||
\(164\) | −1.50000 | + | 2.59808i | −0.117130 | + | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | + | 5.19615i | 0.232845 | + | 0.403300i | ||||
\(167\) | 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 | ||||||||
\(171\) | 2.00000 | − | 3.46410i | 0.152944 | − | 0.264906i | ||||
\(172\) | 6.92820 | + | 4.00000i | 0.528271 | + | 0.304997i | ||||
\(173\) | −5.19615 | + | 3.00000i | −0.395056 | + | 0.228086i | −0.684349 | − | 0.729155i | \(-0.739913\pi\) |
0.289292 | + | 0.957241i | \(0.406580\pi\) | |||||||
\(174\) | 6.00000 | 0.454859 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.00000 | 0.452267 | ||||||||
\(177\) | −5.19615 | + | 3.00000i | −0.390567 | + | 0.225494i | ||||
\(178\) | −2.59808 | − | 1.50000i | −0.194734 | − | 0.112430i | ||||
\(179\) | −9.00000 | + | 15.5885i | −0.672692 | + | 1.16514i | 0.304446 | + | 0.952529i | \(0.401529\pi\) |
−0.977138 | + | 0.212607i | \(0.931805\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 10.3923 | − | 2.00000i | 0.770329 | − | 0.148250i | ||||
\(183\) | 2.00000i | 0.147844i | ||||||||
\(184\) | 1.50000 | + | 2.59808i | 0.110581 | + | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.50000 | + | 4.33013i | −0.183309 | + | 0.317500i | ||||
\(187\) | 15.5885 | − | 9.00000i | 1.13994 | − | 0.658145i | ||||
\(188\) | 9.00000i | 0.656392i | ||||||||
\(189\) | −2.50000 | − | 0.866025i | −0.181848 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.50000 | − | 12.9904i | −0.542681 | − | 0.939951i | −0.998749 | − | 0.0500060i | \(-0.984076\pi\) |
0.456068 | − | 0.889945i | \(-0.349257\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | −4.33013 | − | 2.50000i | −0.311689 | − | 0.179954i | 0.335993 | − | 0.941865i | \(-0.390928\pi\) |
−0.647682 | + | 0.761911i | \(0.724262\pi\) | |||||||
\(194\) | 8.50000 | + | 14.7224i | 0.610264 | + | 1.05701i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | + | 2.59808i | −0.464286 | + | 0.185577i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 5.19615 | − | 3.00000i | 0.369274 | − | 0.213201i | ||||
\(199\) | 2.50000 | − | 4.33013i | 0.177220 | − | 0.306955i | −0.763707 | − | 0.645563i | \(-0.776623\pi\) |
0.940927 | + | 0.338608i | \(0.109956\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | − | 6.92820i | −0.282138 | − | 0.488678i | ||||
\(202\) | − | 12.0000i | − | 0.844317i | ||||||
\(203\) | 5.19615 | − | 15.0000i | 0.364698 | − | 1.05279i | ||||
\(204\) | 3.00000 | 0.210042 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.50000 | − | 11.2583i | 0.452876 | − | 0.784405i | ||||
\(207\) | 2.59808 | + | 1.50000i | 0.180579 | + | 0.104257i | ||||
\(208\) | −3.46410 | + | 2.00000i | −0.240192 | + | 0.138675i | ||||
\(209\) | 24.0000 | 1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | −10.3923 | + | 6.00000i | −0.713746 | + | 0.412082i | ||||
\(213\) | 7.79423 | + | 4.50000i | 0.534052 | + | 0.308335i | ||||
\(214\) | 3.00000 | − | 5.19615i | 0.205076 | − | 0.355202i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 8.66025 | + | 10.0000i | 0.587896 | + | 0.678844i | ||||
\(218\) | − | 4.00000i | − | 0.270914i | ||||||
\(219\) | 7.00000 | + | 12.1244i | 0.473016 | + | 0.819288i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | + | 10.3923i | −0.403604 | + | 0.699062i | ||||
\(222\) | −6.92820 | + | 4.00000i | −0.464991 | + | 0.268462i | ||||
\(223\) | 11.0000i | 0.736614i | 0.929704 | + | 0.368307i | \(0.120063\pi\) | ||||
−0.929704 | + | 0.368307i | \(0.879937\pi\) | |||||||
\(224\) | 2.00000 | − | 1.73205i | 0.133631 | − | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.50000 | − | 2.59808i | −0.0997785 | − | 0.172821i | ||||
\(227\) | −15.5885 | − | 9.00000i | −1.03464 | − | 0.597351i | −0.116331 | − | 0.993210i | \(-0.537113\pi\) |
−0.918311 | + | 0.395860i | \(0.870447\pi\) | |||||||
\(228\) | 3.46410 | + | 2.00000i | 0.229416 | + | 0.132453i | ||||
\(229\) | −11.0000 | − | 19.0526i | −0.726900 | − | 1.25903i | −0.958187 | − | 0.286143i | \(-0.907627\pi\) |
0.231287 | − | 0.972886i | \(-0.425707\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | − | 15.5885i | −0.197386 | − | 1.02565i | ||||
\(232\) | 6.00000i | 0.393919i | ||||||||
\(233\) | 5.19615 | − | 3.00000i | 0.340411 | − | 0.196537i | −0.320043 | − | 0.947403i | \(-0.603697\pi\) |
0.660454 | + | 0.750867i | \(0.270364\pi\) | |||||||
\(234\) | −2.00000 | + | 3.46410i | −0.130744 | + | 0.226455i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.00000 | − | 5.19615i | −0.195283 | − | 0.338241i | ||||
\(237\) | 7.00000i | 0.454699i | ||||||||
\(238\) | 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 | ||||||||
\(241\) | 11.0000 | − | 19.0526i | 0.708572 | − | 1.22728i | −0.256814 | − | 0.966461i | \(-0.582673\pi\) |
0.965387 | − | 0.260822i | \(-0.0839937\pi\) | |||||||
\(242\) | 21.6506 | + | 12.5000i | 1.39176 | + | 0.803530i | ||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.00000 | −0.191273 | ||||||||
\(247\) | −13.8564 | + | 8.00000i | −0.881662 | + | 0.509028i | ||||
\(248\) | −4.33013 | − | 2.50000i | −0.274963 | − | 0.158750i | ||||
\(249\) | −3.00000 | + | 5.19615i | −0.190117 | + | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0.866025 | − | 2.50000i | 0.0545545 | − | 0.157485i | ||||
\(253\) | 18.0000i | 1.13165i | ||||||||
\(254\) | −8.00000 | − | 13.8564i | −0.501965 | − | 0.869428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 15.5885 | − | 9.00000i | 0.972381 | − | 0.561405i | 0.0724199 | − | 0.997374i | \(-0.476928\pi\) |
0.899961 | + | 0.435970i | \(0.143595\pi\) | |||||||
\(258\) | 8.00000i | 0.498058i | ||||||||
\(259\) | 4.00000 | + | 20.7846i | 0.248548 | + | 1.29149i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | + | 5.19615i | 0.185695 | + | 0.321634i | ||||
\(262\) | −15.5885 | − | 9.00000i | −0.963058 | − | 0.556022i | ||||
\(263\) | 2.59808 | + | 1.50000i | 0.160204 | + | 0.0924940i | 0.577959 | − | 0.816066i | \(-0.303849\pi\) |
−0.417755 | + | 0.908560i | \(0.637183\pi\) | |||||||
\(264\) | 3.00000 | + | 5.19615i | 0.184637 | + | 0.319801i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.00000 | − | 6.92820i | 0.490511 | − | 0.424795i | ||||
\(267\) | − | 3.00000i | − | 0.183597i | ||||||
\(268\) | 6.92820 | − | 4.00000i | 0.423207 | − | 0.244339i | ||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5000 | + | 21.6506i | 0.759321 | + | 1.31518i | 0.943197 | + | 0.332233i | \(0.107802\pi\) |
−0.183876 | + | 0.982949i | \(0.558865\pi\) | |||||||
\(272\) | 3.00000i | 0.181902i | ||||||||
\(273\) | 6.92820 | + | 8.00000i | 0.419314 | + | 0.484182i | ||||
\(274\) | 15.0000 | 0.906183 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.50000 | + | 2.59808i | −0.0902894 | + | 0.156386i | ||||
\(277\) | 22.5167 | + | 13.0000i | 1.35290 | + | 0.781094i | 0.988654 | − | 0.150210i | \(-0.0479951\pi\) |
0.364241 | + | 0.931305i | \(0.381328\pi\) | |||||||
\(278\) | 1.73205 | − | 1.00000i | 0.103882 | − | 0.0599760i | ||||
\(279\) | −5.00000 | −0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.0000 | 1.61068 | 0.805342 | − | 0.592810i | \(-0.201981\pi\) | ||||
0.805342 | + | 0.592810i | \(0.201981\pi\) | |||||||
\(282\) | −7.79423 | + | 4.50000i | −0.464140 | + | 0.267971i | ||||
\(283\) | 19.0526 | + | 11.0000i | 1.13256 | + | 0.653882i | 0.944577 | − | 0.328291i | \(-0.106473\pi\) |
0.187980 | + | 0.982173i | \(0.439806\pi\) | |||||||
\(284\) | −4.50000 | + | 7.79423i | −0.267026 | + | 0.462502i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24.0000 | −1.41915 | ||||||||
\(287\) | −2.59808 | + | 7.50000i | −0.153360 | + | 0.442711i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −4.00000 | − | 6.92820i | −0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.50000 | + | 14.7224i | −0.498279 | + | 0.863044i | ||||
\(292\) | −12.1244 | + | 7.00000i | −0.709524 | + | 0.409644i | ||||
\(293\) | − | 18.0000i | − | 1.05157i | −0.850617 | − | 0.525786i | \(-0.823771\pi\) | ||
0.850617 | − | 0.525786i | \(-0.176229\pi\) | |||||||
\(294\) | −5.50000 | − | 4.33013i | −0.320767 | − | 0.252538i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.00000 | − | 6.92820i | −0.232495 | − | 0.402694i | ||||
\(297\) | 5.19615 | + | 3.00000i | 0.301511 | + | 0.174078i | ||||
\(298\) | 5.19615 | + | 3.00000i | 0.301005 | + | 0.173785i | ||||
\(299\) | −6.00000 | − | 10.3923i | −0.346989 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0000 | + | 6.92820i | 1.15278 | + | 0.399335i | ||||
\(302\) | 16.0000i | 0.920697i | ||||||||
\(303\) | 10.3923 | − | 6.00000i | 0.597022 | − | 0.344691i | ||||
\(304\) | −2.00000 | + | 3.46410i | −0.114708 | + | 0.198680i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.50000 | + | 2.59808i | 0.0857493 | + | 0.148522i | ||||
\(307\) | − | 20.0000i | − | 1.14146i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) | ||
0.821138 | − | 0.570730i | \(-0.193340\pi\) | |||||||
\(308\) | 15.5885 | − | 3.00000i | 0.888235 | − | 0.170941i | ||||
\(309\) | 13.0000 | 0.739544 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.5000 | + | 18.1865i | −0.595400 | + | 1.03126i | 0.398090 | + | 0.917346i | \(0.369673\pi\) |
−0.993490 | + | 0.113917i | \(0.963660\pi\) | |||||||
\(312\) | −3.46410 | − | 2.00000i | −0.196116 | − | 0.113228i | ||||
\(313\) | 14.7224 | − | 8.50000i | 0.832161 | − | 0.480448i | −0.0224310 | − | 0.999748i | \(-0.507141\pi\) |
0.854592 | + | 0.519300i | \(0.173807\pi\) | |||||||
\(314\) | −14.0000 | −0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.00000 | −0.393781 | ||||||||
\(317\) | −10.3923 | + | 6.00000i | −0.583690 | + | 0.336994i | −0.762598 | − | 0.646872i | \(-0.776077\pi\) |
0.178908 | + | 0.983866i | \(0.442743\pi\) | |||||||
\(318\) | −10.3923 | − | 6.00000i | −0.582772 | − | 0.336463i | ||||
\(319\) | −18.0000 | + | 31.1769i | −1.00781 | + | 1.74557i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.00000 | 0.334887 | ||||||||
\(322\) | 5.19615 | + | 6.00000i | 0.289570 | + | 0.334367i | ||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.00000 | + | 6.92820i | −0.221540 | + | 0.383718i | ||||
\(327\) | 3.46410 | − | 2.00000i | 0.191565 | − | 0.110600i | ||||
\(328\) | − | 3.00000i | − | 0.165647i | ||||||
\(329\) | 4.50000 | + | 23.3827i | 0.248093 | + | 1.28913i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0000 | − | 22.5167i | −0.714545 | − | 1.23763i | −0.963135 | − | 0.269019i | \(-0.913301\pi\) |
0.248590 | − | 0.968609i | \(-0.420033\pi\) | |||||||
\(332\) | −5.19615 | − | 3.00000i | −0.285176 | − | 0.164646i | ||||
\(333\) | −6.92820 | − | 4.00000i | −0.379663 | − | 0.219199i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.50000 | + | 0.866025i | 0.136386 | + | 0.0472456i | ||||
\(337\) | 13.0000i | 0.708155i | 0.935216 | + | 0.354078i | \(0.115205\pi\) | ||||
−0.935216 | + | 0.354078i | \(0.884795\pi\) | |||||||
\(338\) | 2.59808 | − | 1.50000i | 0.141317 | − | 0.0815892i | ||||
\(339\) | 1.50000 | − | 2.59808i | 0.0814688 | − | 0.141108i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.0000 | − | 25.9808i | −0.812296 | − | 1.40694i | ||||
\(342\) | 4.00000i | 0.216295i | ||||||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | − | 5.19615i | 0.161281 | − | 0.279347i | ||||
\(347\) | 15.5885 | + | 9.00000i | 0.836832 | + | 0.483145i | 0.856186 | − | 0.516667i | \(-0.172828\pi\) |
−0.0193540 | + | 0.999813i | \(0.506161\pi\) | |||||||
\(348\) | −5.19615 | + | 3.00000i | −0.278543 | + | 0.160817i | ||||
\(349\) | 28.0000 | 1.49881 | 0.749403 | − | 0.662114i | \(-0.230341\pi\) | ||||
0.749403 | + | 0.662114i | \(0.230341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | −5.19615 | + | 3.00000i | −0.276956 | + | 0.159901i | ||||
\(353\) | −12.9904 | − | 7.50000i | −0.691408 | − | 0.399185i | 0.112731 | − | 0.993626i | \(-0.464040\pi\) |
−0.804139 | + | 0.594441i | \(0.797373\pi\) | |||||||
\(354\) | 3.00000 | − | 5.19615i | 0.159448 | − | 0.276172i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.00000 | 0.159000 | ||||||||
\(357\) | 7.79423 | − | 1.50000i | 0.412514 | − | 0.0793884i | ||||
\(358\) | − | 18.0000i | − | 0.951330i | ||||||
\(359\) | −18.0000 | − | 31.1769i | −0.950004 | − | 1.64545i | −0.745409 | − | 0.666608i | \(-0.767746\pi\) |
−0.204595 | − | 0.978847i | \(-0.565588\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | −1.73205 | + | 1.00000i | −0.0910346 | + | 0.0525588i | ||||
\(363\) | 25.0000i | 1.31216i | ||||||||
\(364\) | −8.00000 | + | 6.92820i | −0.419314 | + | 0.363137i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.00000 | − | 1.73205i | −0.0522708 | − | 0.0905357i | ||||
\(367\) | −24.2487 | − | 14.0000i | −1.26577 | − | 0.730794i | −0.291587 | − | 0.956544i | \(-0.594183\pi\) |
−0.974185 | + | 0.225750i | \(0.927517\pi\) | |||||||
\(368\) | −2.59808 | − | 1.50000i | −0.135434 | − | 0.0781929i | ||||
\(369\) | −1.50000 | − | 2.59808i | −0.0780869 | − | 0.135250i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.0000 | + | 20.7846i | −1.24602 | + | 1.07908i | ||||
\(372\) | − | 5.00000i | − | 0.259238i | ||||||
\(373\) | 6.92820 | − | 4.00000i | 0.358729 | − | 0.207112i | −0.309794 | − | 0.950804i | \(-0.600260\pi\) |
0.668523 | + | 0.743691i | \(0.266927\pi\) | |||||||
\(374\) | −9.00000 | + | 15.5885i | −0.465379 | + | 0.806060i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.50000 | − | 7.79423i | −0.232070 | − | 0.401957i | ||||
\(377\) | − | 24.0000i | − | 1.23606i | ||||||
\(378\) | 2.59808 | − | 0.500000i | 0.133631 | − | 0.0257172i | ||||
\(379\) | 10.0000 | 0.513665 | 0.256833 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256833 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | − | 13.8564i | 0.409852 | − | 0.709885i | ||||
\(382\) | 12.9904 | + | 7.50000i | 0.664646 | + | 0.383733i | ||||
\(383\) | 18.1865 | − | 10.5000i | 0.929288 | − | 0.536525i | 0.0427020 | − | 0.999088i | \(-0.486403\pi\) |
0.886586 | + | 0.462563i | \(0.153070\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.00000 | 0.254493 | ||||||||
\(387\) | −6.92820 | + | 4.00000i | −0.352180 | + | 0.203331i | ||||
\(388\) | −14.7224 | − | 8.50000i | −0.747418 | − | 0.431522i | ||||
\(389\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | −0.455150 | ||||||||
\(392\) | 4.33013 | − | 5.50000i | 0.218704 | − | 0.277792i | ||||
\(393\) | − | 18.0000i | − | 0.907980i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.00000 | + | 5.19615i | −0.150756 | + | 0.261116i | ||||
\(397\) | −1.73205 | + | 1.00000i | −0.0869291 | + | 0.0501886i | −0.542834 | − | 0.839840i | \(-0.682649\pi\) |
0.455905 | + | 0.890028i | \(0.349316\pi\) | |||||||
\(398\) | 5.00000i | 0.250627i | ||||||||
\(399\) | 10.0000 | + | 3.46410i | 0.500626 | + | 0.173422i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00000 | + | 5.19615i | 0.149813 | + | 0.259483i | 0.931158 | − | 0.364615i | \(-0.118800\pi\) |
−0.781345 | + | 0.624099i | \(0.785466\pi\) | |||||||
\(402\) | 6.92820 | + | 4.00000i | 0.345547 | + | 0.199502i | ||||
\(403\) | 17.3205 | + | 10.0000i | 0.862796 | + | 0.498135i | ||||
\(404\) | 6.00000 | + | 10.3923i | 0.298511 | + | 0.517036i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.00000 | + | 15.5885i | 0.148888 | + | 0.773642i | ||||
\(407\) | − | 48.0000i | − | 2.37927i | ||||||
\(408\) | −2.59808 | + | 1.50000i | −0.128624 | + | 0.0742611i | ||||
\(409\) | 14.5000 | − | 25.1147i | 0.716979 | − | 1.24184i | −0.245212 | − | 0.969469i | \(-0.578858\pi\) |
0.962191 | − | 0.272374i | \(-0.0878089\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.50000 | + | 12.9904i | 0.369948 | + | 0.640768i | ||||
\(412\) | 13.0000i | 0.640464i | ||||||||
\(413\) | −10.3923 | − | 12.0000i | −0.511372 | − | 0.590481i | ||||
\(414\) | −3.00000 | −0.147442 | ||||||||
\(415\) | 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 | ||||
\(419\) | −24.0000 | −1.17248 | −0.586238 | − | 0.810139i | \(-0.699392\pi\) | ||||
−0.586238 | + | 0.810139i | \(0.699392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | −0.194948 | −0.0974740 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974740 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(422\) | −6.92820 | + | 4.00000i | −0.337260 | + | 0.194717i | ||||
\(423\) | −7.79423 | − | 4.50000i | −0.378968 | − | 0.218797i | ||||
\(424\) | 6.00000 | − | 10.3923i | 0.291386 | − | 0.504695i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.00000 | −0.436051 | ||||||||
\(427\) | −5.19615 | + | 1.00000i | −0.251459 | + | 0.0483934i | ||||
\(428\) | 6.00000i | 0.290021i | ||||||||
\(429\) | −12.0000 | − | 20.7846i | −0.579365 | − | 1.00349i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.5000 | + | 18.1865i | −0.505767 | + | 0.876014i | 0.494211 | + | 0.869342i | \(0.335457\pi\) |
−0.999978 | + | 0.00667224i | \(0.997876\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 7.00000i | − | 0.336399i | −0.985753 | − | 0.168199i | \(-0.946205\pi\) | ||
0.985753 | − | 0.168199i | \(-0.0537952\pi\) | |||||||
\(434\) | −12.5000 | − | 4.33013i | −0.600019 | − | 0.207853i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | + | 3.46410i | 0.0957826 | + | 0.165900i | ||||
\(437\) | −10.3923 | − | 6.00000i | −0.497131 | − | 0.287019i | ||||
\(438\) | −12.1244 | − | 7.00000i | −0.579324 | − | 0.334473i | ||||
\(439\) | −6.50000 | − | 11.2583i | −0.310228 | − | 0.537331i | 0.668184 | − | 0.743996i | \(-0.267072\pi\) |
−0.978412 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | − | 6.92820i | 0.0476190 | − | 0.329914i | ||||
\(442\) | − | 12.0000i | − | 0.570782i | ||||||
\(443\) | −20.7846 | + | 12.0000i | −0.987507 | + | 0.570137i | −0.904528 | − | 0.426414i | \(-0.859777\pi\) |
−0.0829786 | + | 0.996551i | \(0.526443\pi\) | |||||||
\(444\) | 4.00000 | − | 6.92820i | 0.189832 | − | 0.328798i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.50000 | − | 9.52628i | −0.260433 | − | 0.451082i | ||||
\(447\) | 6.00000i | 0.283790i | ||||||||
\(448\) | −0.866025 | + | 2.50000i | −0.0409159 | + | 0.118114i | ||||
\(449\) | 3.00000 | 0.141579 | 0.0707894 | − | 0.997491i | \(-0.477448\pi\) | ||||
0.0707894 | + | 0.997491i | \(0.477448\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | − | 15.5885i | 0.423793 | − | 0.734032i | ||||
\(452\) | 2.59808 | + | 1.50000i | 0.122203 | + | 0.0705541i | ||||
\(453\) | −13.8564 | + | 8.00000i | −0.651031 | + | 0.375873i | ||||
\(454\) | 18.0000 | 0.844782 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.00000 | −0.187317 | ||||||||
\(457\) | −1.73205 | + | 1.00000i | −0.0810219 | + | 0.0467780i | −0.539964 | − | 0.841688i | \(-0.681562\pi\) |
0.458942 | + | 0.888466i | \(0.348229\pi\) | |||||||
\(458\) | 19.0526 | + | 11.0000i | 0.890268 | + | 0.513996i | ||||
\(459\) | −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 | \(0.183524\pi\) | |||||||
\(462\) | 10.3923 | + | 12.0000i | 0.483494 | + | 0.558291i | ||||
\(463\) | − | 13.0000i | − | 0.604161i | −0.953282 | − | 0.302081i | \(-0.902319\pi\) | ||
0.953282 | − | 0.302081i | \(-0.0976812\pi\) | |||||||
\(464\) | −3.00000 | − | 5.19615i | −0.139272 | − | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | + | 5.19615i | −0.138972 | + | 0.240707i | ||||
\(467\) | 25.9808 | − | 15.0000i | 1.20225 | − | 0.694117i | 0.241192 | − | 0.970477i | \(-0.422462\pi\) |
0.961054 | + | 0.276360i | \(0.0891283\pi\) | |||||||
\(468\) | − | 4.00000i | − | 0.184900i | ||||||
\(469\) | 16.0000 | − | 13.8564i | 0.738811 | − | 0.639829i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.00000 | − | 12.1244i | −0.322543 | − | 0.558661i | ||||
\(472\) | 5.19615 | + | 3.00000i | 0.239172 | + | 0.138086i | ||||
\(473\) | −41.5692 | − | 24.0000i | −1.91135 | − | 1.10352i | ||||
\(474\) | −3.50000 | − | 6.06218i | −0.160760 | − | 0.278445i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.50000 | + | 7.79423i | 0.0687524 | + | 0.357248i | ||||
\(477\) | − | 12.0000i | − | 0.549442i | ||||||
\(478\) | 2.59808 | − | 1.50000i | 0.118833 | − | 0.0686084i | ||||
\(479\) | 10.5000 | − | 18.1865i | 0.479757 | − | 0.830964i | −0.519973 | − | 0.854183i | \(-0.674058\pi\) |
0.999730 | + | 0.0232187i | \(0.00739140\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0000 | + | 27.7128i | 0.729537 | + | 1.26360i | ||||
\(482\) | 22.0000i | 1.00207i | ||||||||
\(483\) | −2.59808 | + | 7.50000i | −0.118217 | + | 0.341262i | ||||
\(484\) | −25.0000 | −1.13636 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | −21.6506 | − | 12.5000i | −0.981084 | − | 0.566429i | −0.0784867 | − | 0.996915i | \(-0.525009\pi\) |
−0.902597 | + | 0.430486i | \(0.858342\pi\) | |||||||
\(488\) | 1.73205 | − | 1.00000i | 0.0784063 | − | 0.0452679i | ||||
\(489\) | −8.00000 | −0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 2.59808 | − | 1.50000i | 0.117130 | − | 0.0676252i | ||||
\(493\) | −15.5885 | − | 9.00000i | −0.702069 | − | 0.405340i | ||||
\(494\) | 8.00000 | − | 13.8564i | 0.359937 | − | 0.623429i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.00000 | 0.224507 | ||||||||
\(497\) | −7.79423 | + | 22.5000i | −0.349619 | + | 1.00926i | ||||
\(498\) | − | 6.00000i | − | 0.268866i | ||||||
\(499\) | 19.0000 | + | 32.9090i | 0.850557 | + | 1.47321i | 0.880707 | + | 0.473662i | \(0.157068\pi\) |
−0.0301498 | + | 0.999545i | \(0.509598\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −20.7846 | + | 12.0000i | −0.927663 | + | 0.535586i | ||||
\(503\) | 24.0000i | 1.07011i | 0.844818 | + | 0.535054i | \(0.179709\pi\) | ||||
−0.844818 | + | 0.535054i | \(0.820291\pi\) | |||||||
\(504\) | 0.500000 | + | 2.59808i | 0.0222718 | + | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.00000 | − | 15.5885i | −0.400099 | − | 0.692991i | ||||
\(507\) | 2.59808 | + | 1.50000i | 0.115385 | + | 0.0666173i | ||||
\(508\) | 13.8564 | + | 8.00000i | 0.614779 | + | 0.354943i | ||||
\(509\) | −3.00000 | − | 5.19615i | −0.132973 | − | 0.230315i | 0.791849 | − | 0.610718i | \(-0.209119\pi\) |
−0.924821 | + | 0.380402i | \(0.875786\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.0000 | + | 24.2487i | −1.23865 | + | 1.07270i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −3.46410 | + | 2.00000i | −0.152944 | + | 0.0883022i | ||||
\(514\) | −9.00000 | + | 15.5885i | −0.396973 | + | 0.687577i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.00000 | − | 6.92820i | −0.176090 | − | 0.304997i | ||||
\(517\) | − | 54.0000i | − | 2.37492i | ||||||
\(518\) | −13.8564 | − | 16.0000i | −0.608816 | − | 0.703000i | ||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.5000 | + | 18.1865i | −0.460013 | + | 0.796766i | −0.998961 | − | 0.0455727i | \(-0.985489\pi\) |
0.538948 | + | 0.842339i | \(0.318822\pi\) | |||||||
\(522\) | −5.19615 | − | 3.00000i | −0.227429 | − | 0.131306i | ||||
\(523\) | −29.4449 | + | 17.0000i | −1.28753 | + | 0.743358i | −0.978214 | − | 0.207600i | \(-0.933435\pi\) |
−0.309320 | + | 0.950958i | \(0.600101\pi\) | |||||||
\(524\) | 18.0000 | 0.786334 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.00000 | −0.130806 | ||||||||
\(527\) | 12.9904 | − | 7.50000i | 0.565870 | − | 0.326705i | ||||
\(528\) | −5.19615 | − | 3.00000i | −0.226134 | − | 0.130558i | ||||
\(529\) | −7.00000 | + | 12.1244i | −0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.00000 | 0.260378 | ||||||||
\(532\) | −3.46410 | + | 10.0000i | −0.150188 | + | 0.433555i | ||||
\(533\) | 12.0000i | 0.519778i | ||||||||
\(534\) | 1.50000 | + | 2.59808i | 0.0649113 | + | 0.112430i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.00000 | + | 6.92820i | −0.172774 | + | 0.299253i | ||||
\(537\) | 15.5885 | − | 9.00000i | 0.672692 | − | 0.388379i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 39.0000 | − | 15.5885i | 1.67985 | − | 0.671442i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.0000 | + | 24.2487i | 0.601907 | + | 1.04253i | 0.992532 | + | 0.121984i | \(0.0389256\pi\) |
−0.390625 | + | 0.920550i | \(0.627741\pi\) | |||||||
\(542\) | −21.6506 | − | 12.5000i | −0.929974 | − | 0.536921i | ||||
\(543\) | −1.73205 | − | 1.00000i | −0.0743294 | − | 0.0429141i | ||||
\(544\) | −1.50000 | − | 2.59808i | −0.0643120 | − | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10.0000 | − | 3.46410i | −0.427960 | − | 0.148250i | ||||
\(547\) | − | 8.00000i | − | 0.342055i | −0.985266 | − | 0.171028i | \(-0.945291\pi\) | ||
0.985266 | − | 0.171028i | \(-0.0547087\pi\) | |||||||
\(548\) | −12.9904 | + | 7.50000i | −0.554922 | + | 0.320384i | ||||
\(549\) | 1.00000 | − | 1.73205i | 0.0426790 | − | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | − | 20.7846i | −0.511217 | − | 0.885454i | ||||
\(552\) | − | 3.00000i | − | 0.127688i | ||||||
\(553\) | −18.1865 | + | 3.50000i | −0.773370 | + | 0.148835i | ||||
\(554\) | −26.0000 | −1.10463 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00000 | + | 1.73205i | −0.0424094 | + | 0.0734553i | ||||
\(557\) | −25.9808 | − | 15.0000i | −1.10084 | − | 0.635570i | −0.164399 | − | 0.986394i | \(-0.552568\pi\) |
−0.936442 | + | 0.350824i | \(0.885902\pi\) | |||||||
\(558\) | 4.33013 | − | 2.50000i | 0.183309 | − | 0.105833i | ||||
\(559\) | 32.0000 | 1.35346 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.0000 | −0.759961 | ||||||||
\(562\) | −23.3827 | + | 13.5000i | −0.986339 | + | 0.569463i | ||||
\(563\) | −10.3923 | − | 6.00000i | −0.437983 | − | 0.252870i | 0.264758 | − | 0.964315i | \(-0.414708\pi\) |
−0.702742 | + | 0.711445i | \(0.748041\pi\) | |||||||
\(564\) | 4.50000 | − | 7.79423i | 0.189484 | − | 0.328196i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −22.0000 | −0.924729 | ||||||||
\(567\) | 1.73205 | + | 2.00000i | 0.0727393 | + | 0.0839921i | ||||
\(568\) | − | 9.00000i | − | 0.377632i | ||||||
\(569\) | −7.50000 | − | 12.9904i | −0.314416 | − | 0.544585i | 0.664897 | − | 0.746935i | \(-0.268475\pi\) |
−0.979313 | + | 0.202350i | \(0.935142\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 20.7846 | − | 12.0000i | 0.869048 | − | 0.501745i | ||||
\(573\) | 15.0000i | 0.626634i | ||||||||
\(574\) | −1.50000 | − | 7.79423i | −0.0626088 | − | 0.325325i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 1.73205 | + | 1.00000i | 0.0721062 | + | 0.0416305i | 0.535620 | − | 0.844459i | \(-0.320078\pi\) |
−0.463513 | + | 0.886090i | \(0.653411\pi\) | |||||||
\(578\) | 6.92820 | + | 4.00000i | 0.288175 | + | 0.166378i | ||||
\(579\) | 2.50000 | + | 4.33013i | 0.103896 | + | 0.179954i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.0000 | − | 5.19615i | −0.622305 | − | 0.215573i | ||||
\(582\) | − | 17.0000i | − | 0.704673i | ||||||
\(583\) | 62.3538 | − | 36.0000i | 2.58243 | − | 1.49097i | ||||
\(584\) | 7.00000 | − | 12.1244i | 0.289662 | − | 0.501709i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.00000 | + | 15.5885i | 0.371787 | + | 0.643953i | ||||
\(587\) | − | 18.0000i | − | 0.742940i | −0.928445 | − | 0.371470i | \(-0.878854\pi\) | ||
0.928445 | − | 0.371470i | \(-0.121146\pi\) | |||||||
\(588\) | 6.92820 | + | 1.00000i | 0.285714 | + | 0.0412393i | ||||
\(589\) | 20.0000 | 0.824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.92820 | + | 4.00000i | 0.284747 | + | 0.164399i | ||||
\(593\) | −28.5788 | + | 16.5000i | −1.17359 | + | 0.677574i | −0.954524 | − | 0.298136i | \(-0.903635\pi\) |
−0.219069 | + | 0.975709i | \(0.570302\pi\) | |||||||
\(594\) | −6.00000 | −0.246183 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | −4.33013 | + | 2.50000i | −0.177220 | + | 0.102318i | ||||
\(598\) | 10.3923 | + | 6.00000i | 0.424973 | + | 0.245358i | ||||
\(599\) | 4.50000 | − | 7.79423i | 0.183865 | − | 0.318464i | −0.759328 | − | 0.650708i | \(-0.774472\pi\) |
0.943193 | + | 0.332244i | \(0.107806\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.0000 | −1.38689 | −0.693444 | − | 0.720510i | \(-0.743908\pi\) | ||||
−0.693444 | + | 0.720510i | \(0.743908\pi\) | |||||||
\(602\) | −20.7846 | + | 4.00000i | −0.847117 | + | 0.163028i | ||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | −8.00000 | − | 13.8564i | −0.325515 | − | 0.563809i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.00000 | + | 10.3923i | −0.243733 | + | 0.422159i | ||||
\(607\) | −9.52628 | + | 5.50000i | −0.386660 | + | 0.223238i | −0.680712 | − | 0.732551i | \(-0.738329\pi\) |
0.294052 | + | 0.955789i | \(0.404996\pi\) | |||||||
\(608\) | − | 4.00000i | − | 0.162221i | ||||||
\(609\) | −12.0000 | + | 10.3923i | −0.486265 | + | 0.421117i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0000 | + | 31.1769i | 0.728202 | + | 1.26128i | ||||
\(612\) | −2.59808 | − | 1.50000i | −0.105021 | − | 0.0606339i | ||||
\(613\) | 29.4449 | + | 17.0000i | 1.18927 | + | 0.686624i | 0.958140 | − | 0.286300i | \(-0.0924254\pi\) |
0.231127 | + | 0.972924i | \(0.425759\pi\) | |||||||
\(614\) | 10.0000 | + | 17.3205i | 0.403567 | + | 0.698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.0000 | + | 10.3923i | −0.483494 | + | 0.418718i | ||||
\(617\) | 21.0000i | 0.845428i | 0.906263 | + | 0.422714i | \(0.138923\pi\) | ||||
−0.906263 | + | 0.422714i | \(0.861077\pi\) | |||||||
\(618\) | −11.2583 | + | 6.50000i | −0.452876 | + | 0.261468i | ||||
\(619\) | −23.0000 | + | 39.8372i | −0.924448 | + | 1.60119i | −0.132002 | + | 0.991250i | \(0.542140\pi\) |
−0.792446 | + | 0.609941i | \(0.791193\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.50000 | − | 2.59808i | −0.0601929 | − | 0.104257i | ||||
\(622\) | − | 21.0000i | − | 0.842023i | ||||||
\(623\) | 7.79423 | − | 1.50000i | 0.312269 | − | 0.0600962i | ||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.50000 | + | 14.7224i | −0.339728 | + | 0.588427i | ||||
\(627\) | −20.7846 | − | 12.0000i | −0.830057 | − | 0.479234i | ||||
\(628\) | 12.1244 | − | 7.00000i | 0.483814 | − | 0.279330i | ||||
\(629\) | 24.0000 | 0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.0000 | 0.676759 | 0.338380 | − | 0.941010i | \(-0.390121\pi\) | ||||
0.338380 | + | 0.941010i | \(0.390121\pi\) | |||||||
\(632\) | 6.06218 | − | 3.50000i | 0.241140 | − | 0.139223i | ||||
\(633\) | −6.92820 | − | 4.00000i | −0.275371 | − | 0.158986i | ||||
\(634\) | 6.00000 | − | 10.3923i | 0.238290 | − | 0.412731i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 12.0000 | 0.475831 | ||||||||
\(637\) | −17.3205 | + | 22.0000i | −0.686264 | + | 0.871672i | ||||
\(638\) | − | 36.0000i | − | 1.42525i | ||||||
\(639\) | −4.50000 | − | 7.79423i | −0.178017 | − | 0.308335i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.5000 | − | 33.7750i | 0.770204 | − | 1.33403i | −0.167247 | − | 0.985915i | \(-0.553488\pi\) |
0.937451 | − | 0.348117i | \(-0.113179\pi\) | |||||||
\(642\) | −5.19615 | + | 3.00000i | −0.205076 | + | 0.118401i | ||||
\(643\) | − | 34.0000i | − | 1.34083i | −0.741987 | − | 0.670415i | \(-0.766116\pi\) | ||
0.741987 | − | 0.670415i | \(-0.233884\pi\) | |||||||
\(644\) | −7.50000 | − | 2.59808i | −0.295541 | − | 0.102379i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | 10.3923 | + | 6.00000i | 0.408564 | + | 0.235884i | 0.690172 | − | 0.723645i | \(-0.257535\pi\) |
−0.281609 | + | 0.959529i | \(0.590868\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 18.0000 | + | 31.1769i | 0.706562 | + | 1.22380i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.50000 | − | 12.9904i | −0.0979827 | − | 0.509133i | ||||
\(652\) | − | 8.00000i | − | 0.313304i | ||||||
\(653\) | −31.1769 | + | 18.0000i | −1.22005 | + | 0.704394i | −0.964928 | − | 0.262515i | \(-0.915448\pi\) |
−0.255119 | + | 0.966910i | \(0.582115\pi\) | |||||||
\(654\) | −2.00000 | + | 3.46410i | −0.0782062 | + | 0.135457i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.50000 | + | 2.59808i | 0.0585652 | + | 0.101438i | ||||
\(657\) | − | 14.0000i | − | 0.546192i | ||||||
\(658\) | −15.5885 | − | 18.0000i | −0.607701 | − | 0.701713i | ||||
\(659\) | 30.0000 | 1.16863 | 0.584317 | − | 0.811525i | \(-0.301362\pi\) | ||||
0.584317 | + | 0.811525i | \(0.301362\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00000 | − | 8.66025i | 0.194477 | − | 0.336845i | −0.752252 | − | 0.658876i | \(-0.771032\pi\) |
0.946729 | + | 0.322031i | \(0.104366\pi\) | |||||||
\(662\) | 22.5167 | + | 13.0000i | 0.875135 | + | 0.505259i | ||||
\(663\) | 10.3923 | − | 6.00000i | 0.403604 | − | 0.233021i | ||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.00000 | 0.309994 | ||||||||
\(667\) | 15.5885 | − | 9.00000i | 0.603587 | − | 0.348481i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.50000 | − | 9.52628i | 0.212642 | − | 0.368307i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | −2.59808 | + | 0.500000i | −0.100223 | + | 0.0192879i | ||||
\(673\) | − | 19.0000i | − | 0.732396i | −0.930537 | − | 0.366198i | \(-0.880659\pi\) | ||
0.930537 | − | 0.366198i | \(-0.119341\pi\) | |||||||
\(674\) | −6.50000 | − | 11.2583i | −0.250371 | − | 0.433655i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.50000 | + | 2.59808i | −0.0576923 | + | 0.0999260i | ||||
\(677\) | −15.5885 | + | 9.00000i | −0.599113 | + | 0.345898i | −0.768693 | − | 0.639618i | \(-0.779092\pi\) |
0.169580 | + | 0.985517i | \(0.445759\pi\) | |||||||
\(678\) | 3.00000i | 0.115214i | ||||||||
\(679\) | −42.5000 | − | 14.7224i | −1.63100 | − | 0.564995i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.00000 | + | 15.5885i | 0.344881 | + | 0.597351i | ||||
\(682\) | 25.9808 | + | 15.0000i | 0.994855 | + | 0.574380i | ||||
\(683\) | −15.5885 | − | 9.00000i | −0.596476 | − | 0.344375i | 0.171178 | − | 0.985240i | \(-0.445243\pi\) |
−0.767654 | + | 0.640865i | \(0.778576\pi\) | |||||||
\(684\) | −2.00000 | − | 3.46410i | −0.0764719 | − | 0.132453i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.50000 | − | 16.4545i | 0.324532 | − | 0.628235i | ||||
\(687\) | 22.0000i | 0.839352i | ||||||||
\(688\) | 6.92820 | − | 4.00000i | 0.264135 | − | 0.152499i | ||||
\(689\) | −24.0000 | + | 41.5692i | −0.914327 | + | 1.58366i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.0000 | + | 29.4449i | 0.646710 | + | 1.12014i | 0.983904 | + | 0.178700i | \(0.0571891\pi\) |
−0.337193 | + | 0.941435i | \(0.609478\pi\) | |||||||
\(692\) | 6.00000i | 0.228086i | ||||||||
\(693\) | −5.19615 | + | 15.0000i | −0.197386 | + | 0.569803i | ||||
\(694\) | −18.0000 | −0.683271 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.00000 | − | 5.19615i | 0.113715 | − | 0.196960i | ||||
\(697\) | 7.79423 | + | 4.50000i | 0.295227 | + | 0.170450i | ||||
\(698\) | −24.2487 | + | 14.0000i | −0.917827 | + | 0.529908i | ||||
\(699\) | −6.00000 | −0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.0000 | −1.81293 | −0.906467 | − | 0.422276i | \(-0.861231\pi\) | ||||
−0.906467 | + | 0.422276i | \(0.861231\pi\) | |||||||
\(702\) | 3.46410 | − | 2.00000i | 0.130744 | − | 0.0754851i | ||||
\(703\) | 27.7128 | + | 16.0000i | 1.04521 | + | 0.603451i | ||||
\(704\) | 3.00000 | − | 5.19615i | 0.113067 | − | 0.195837i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.0000 | 0.564532 | ||||||||
\(707\) | 20.7846 | + | 24.0000i | 0.781686 | + | 0.902613i | ||||
\(708\) | 6.00000i | 0.225494i | ||||||||
\(709\) | −23.0000 | − | 39.8372i | −0.863783 | − | 1.49612i | −0.868250 | − | 0.496126i | \(-0.834755\pi\) |
0.00446726 | − | 0.999990i | \(-0.498578\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.50000 | − | 6.06218i | 0.131260 | − | 0.227349i | ||||
\(712\) | −2.59808 | + | 1.50000i | −0.0973670 | + | 0.0562149i | ||||
\(713\) | 15.0000i | 0.561754i | ||||||||
\(714\) | −6.00000 | + | 5.19615i | −0.224544 | + | 0.194461i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.00000 | + | 15.5885i | 0.336346 | + | 0.582568i | ||||
\(717\) | 2.59808 | + | 1.50000i | 0.0970269 | + | 0.0560185i | ||||
\(718\) | 31.1769 | + | 18.0000i | 1.16351 | + | 0.671754i | ||||
\(719\) | −13.5000 | − | 23.3827i | −0.503465 | − | 0.872027i | −0.999992 | − | 0.00400572i | \(-0.998725\pi\) |
0.496527 | − | 0.868021i | \(-0.334608\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.50000 | + | 33.7750i | 0.242073 | + | 1.25785i | ||||
\(722\) | 3.00000i | 0.111648i | ||||||||
\(723\) | −19.0526 | + | 11.0000i | −0.708572 | + | 0.409094i | ||||
\(724\) | 1.00000 | − | 1.73205i | 0.0371647 | − | 0.0643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −12.5000 | − | 21.6506i | −0.463919 | − | 0.803530i | ||||
\(727\) | 31.0000i | 1.14973i | 0.818250 | + | 0.574863i | \(0.194945\pi\) | ||||
−0.818250 | + | 0.574863i | \(0.805055\pi\) | |||||||
\(728\) | 3.46410 | − | 10.0000i | 0.128388 | − | 0.370625i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0000 | − | 20.7846i | 0.443836 | − | 0.768747i | ||||
\(732\) | 1.73205 | + | 1.00000i | 0.0640184 | + | 0.0369611i | ||||
\(733\) | 43.3013 | − | 25.0000i | 1.59937 | − | 0.923396i | 0.607760 | − | 0.794121i | \(-0.292068\pi\) |
0.991609 | − | 0.129275i | \(-0.0412651\pi\) | |||||||
\(734\) | 28.0000 | 1.03350 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | 0.110581 | ||||||||
\(737\) | −41.5692 | + | 24.0000i | −1.53122 | + | 0.884051i | ||||
\(738\) | 2.59808 | + | 1.50000i | 0.0956365 | + | 0.0552158i | ||||
\(739\) | −8.00000 | + | 13.8564i | −0.294285 | + | 0.509716i | −0.974818 | − | 0.223001i | \(-0.928415\pi\) |
0.680534 | + | 0.732717i | \(0.261748\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.0000 | 0.587775 | ||||||||
\(742\) | 10.3923 | − | 30.0000i | 0.381514 | − | 1.10133i | ||||
\(743\) | 9.00000i | 0.330178i | 0.986279 | + | 0.165089i | \(0.0527911\pi\) | ||||
−0.986279 | + | 0.165089i | \(0.947209\pi\) | |||||||
\(744\) | 2.50000 | + | 4.33013i | 0.0916544 | + | 0.158750i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.00000 | + | 6.92820i | −0.146450 | + | 0.253660i | ||||
\(747\) | 5.19615 | − | 3.00000i | 0.190117 | − | 0.109764i | ||||
\(748\) | − | 18.0000i | − | 0.658145i | ||||||
\(749\) | 3.00000 | + | 15.5885i | 0.109618 | + | 0.569590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | + | 13.8564i | 0.291924 | + | 0.505627i | 0.974265 | − | 0.225407i | \(-0.0723712\pi\) |
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(752\) | 7.79423 | + | 4.50000i | 0.284226 | + | 0.164098i | ||||
\(753\) | −20.7846 | − | 12.0000i | −0.757433 | − | 0.437304i | ||||
\(754\) | 12.0000 | + | 20.7846i | 0.437014 | + | 0.756931i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.00000 | + | 1.73205i | −0.0727393 | + | 0.0629941i | ||||
\(757\) | 4.00000i | 0.145382i | 0.997354 | + | 0.0726912i | \(0.0231588\pi\) | ||||
−0.997354 | + | 0.0726912i | \(0.976841\pi\) | |||||||
\(758\) | −8.66025 | + | 5.00000i | −0.314555 | + | 0.181608i | ||||
\(759\) | 9.00000 | − | 15.5885i | 0.326679 | − | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.50000 | − | 7.79423i | −0.163125 | − | 0.282541i | 0.772863 | − | 0.634573i | \(-0.218824\pi\) |
−0.935988 | + | 0.352032i | \(0.885491\pi\) | |||||||
\(762\) | 16.0000i | 0.579619i | ||||||||
\(763\) | 6.92820 | + | 8.00000i | 0.250818 | + | 0.289619i | ||||
\(764\) | −15.0000 | −0.542681 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.5000 | + | 18.1865i | −0.379380 | + | 0.657106i | ||||
\(767\) | −20.7846 | − | 12.0000i | −0.750489 | − | 0.433295i | ||||
\(768\) | 0.866025 | − | 0.500000i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | −50.0000 | −1.80305 | −0.901523 | − | 0.432731i | \(-0.857550\pi\) | ||||
−0.901523 | + | 0.432731i | \(0.857550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | −4.33013 | + | 2.50000i | −0.155845 | + | 0.0899770i | ||||
\(773\) | 10.3923 | + | 6.00000i | 0.373785 | + | 0.215805i | 0.675111 | − | 0.737716i | \(-0.264096\pi\) |
−0.301326 | + | 0.953521i | \(0.597429\pi\) | |||||||
\(774\) | 4.00000 | − | 6.92820i | 0.143777 | − | 0.249029i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.0000 | 0.610264 | ||||||||
\(777\) | 6.92820 | − | 20.0000i | 0.248548 | − | 0.717496i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.00000 | + | 10.3923i | 0.214972 | + | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.0000 | − | 46.7654i | 0.966136 | − | 1.67340i | ||||
\(782\) | 7.79423 | − | 4.50000i | 0.278721 | − | 0.160920i | ||||
\(783\) | − | 6.00000i | − | 0.214423i | ||||||
\(784\) | −1.00000 | + | 6.92820i | −0.0357143 | + | 0.247436i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.00000 | + | 15.5885i | 0.321019 | + | 0.556022i | ||||
\(787\) | 6.92820 | + | 4.00000i | 0.246964 | + | 0.142585i | 0.618373 | − | 0.785885i | \(-0.287792\pi\) |
−0.371409 | + | 0.928469i | \(0.621125\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.50000 | − | 2.59808i | −0.0534014 | − | 0.0924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.50000 | + | 2.59808i | 0.266669 | + | 0.0923770i | ||||
\(792\) | − | 6.00000i | − | 0.213201i | ||||||
\(793\) | −6.92820 | + | 4.00000i | −0.246028 | + | 0.142044i | ||||
\(794\) | 1.00000 | − | 1.73205i | 0.0354887 | − | 0.0614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.50000 | − | 4.33013i | −0.0886102 | − | 0.153477i | ||||
\(797\) | 18.0000i | 0.637593i | 0.947823 | + | 0.318796i | \(0.103279\pi\) | ||||
−0.947823 | + | 0.318796i | \(0.896721\pi\) | |||||||
\(798\) | −10.3923 | + | 2.00000i | −0.367884 | + | 0.0707992i | ||||
\(799\) | 27.0000 | 0.955191 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.50000 | + | 2.59808i | −0.0529999 | + | 0.0917985i | ||||
\(802\) | −5.19615 | − | 3.00000i | −0.183483 | − | 0.105934i | ||||
\(803\) | 72.7461 | − | 42.0000i | 2.56716 | − | 1.48215i | ||||
\(804\) | −8.00000 | −0.282138 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.0000 | −0.704470 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.3923 | − | 6.00000i | −0.365600 | − | 0.211079i | ||||
\(809\) | −3.00000 | + | 5.19615i | −0.105474 | + | 0.182687i | −0.913932 | − | 0.405868i | \(-0.866969\pi\) |
0.808458 | + | 0.588555i | \(0.200303\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.0000 | −1.40459 | −0.702295 | − | 0.711886i | \(-0.747841\pi\) | ||||
−0.702295 | + | 0.711886i | \(0.747841\pi\) | |||||||
\(812\) | −10.3923 | − | 12.0000i | −0.364698 | − | 0.421117i | ||||
\(813\) | − | 25.0000i | − | 0.876788i | ||||||
\(814\) | 24.0000 | + | 41.5692i | 0.841200 | + | 1.45700i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.50000 | − | 2.59808i | 0.0525105 | − | 0.0909509i | ||||
\(817\) | 27.7128 | − | 16.0000i | 0.969549 | − | 0.559769i | ||||
\(818\) | 29.0000i | 1.01396i | ||||||||
\(819\) | −2.00000 | − | 10.3923i | −0.0698857 | − | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.0000 | − | 31.1769i | −0.628204 | − | 1.08808i | −0.987912 | − | 0.155017i | \(-0.950457\pi\) |
0.359708 | − | 0.933065i | \(-0.382876\pi\) | |||||||
\(822\) | −12.9904 | − | 7.50000i | −0.453092 | − | 0.261593i | ||||
\(823\) | −38.1051 | − | 22.0000i | −1.32826 | − | 0.766872i | −0.343230 | − | 0.939251i | \(-0.611521\pi\) |
−0.985031 | + | 0.172379i | \(0.944854\pi\) | |||||||
\(824\) | −6.50000 | − | 11.2583i | −0.226438 | − | 0.392203i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.0000 | + | 5.19615i | 0.521917 | + | 0.180797i | ||||
\(827\) | − | 30.0000i | − | 1.04320i | −0.853189 | − | 0.521601i | \(-0.825335\pi\) | ||
0.853189 | − | 0.521601i | \(-0.174665\pi\) | |||||||
\(828\) | 2.59808 | − | 1.50000i | 0.0902894 | − | 0.0521286i | ||||
\(829\) | 1.00000 | − | 1.73205i | 0.0347314 | − | 0.0601566i | −0.848137 | − | 0.529777i | \(-0.822276\pi\) |
0.882869 | + | 0.469620i | \(0.155609\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.0000 | − | 22.5167i | −0.450965 | − | 0.781094i | ||||
\(832\) | 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 | ||||
\(838\) | 20.7846 | − | 12.0000i | 0.717992 | − | 0.414533i | ||||
\(839\) | −15.0000 | −0.517858 | −0.258929 | − | 0.965896i | \(-0.583369\pi\) | ||||
−0.258929 | + | 0.965896i | \(0.583369\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 3.46410 | − | 2.00000i | 0.119381 | − | 0.0689246i | ||||
\(843\) | −23.3827 | − | 13.5000i | −0.805342 | − | 0.464965i | ||||
\(844\) | 4.00000 | − | 6.92820i | 0.137686 | − | 0.238479i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.00000 | 0.309426 | ||||||||
\(847\) | −64.9519 | + | 12.5000i | −2.23177 | + | 0.429505i | ||||
\(848\) | 12.0000i | 0.412082i | ||||||||
\(849\) | −11.0000 | − | 19.0526i | −0.377519 | − | 0.653882i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.0000 | + | 20.7846i | −0.411355 | + | 0.712487i | ||||
\(852\) | 7.79423 | − | 4.50000i | 0.267026 | − | 0.154167i | ||||
\(853\) | − | 28.0000i | − | 0.958702i | −0.877623 | − | 0.479351i | \(-0.840872\pi\) | ||
0.877623 | − | 0.479351i | \(-0.159128\pi\) | |||||||
\(854\) | 4.00000 | − | 3.46410i | 0.136877 | − | 0.118539i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | − | 5.19615i | −0.102538 | − | 0.177601i | ||||
\(857\) | 5.19615 | + | 3.00000i | 0.177497 | + | 0.102478i | 0.586116 | − | 0.810227i | \(-0.300656\pi\) |
−0.408619 | + | 0.912705i | \(0.633990\pi\) | |||||||
\(858\) | 20.7846 | + | 12.0000i | 0.709575 | + | 0.409673i | ||||
\(859\) | 7.00000 | + | 12.1244i | 0.238837 | + | 0.413678i | 0.960381 | − | 0.278691i | \(-0.0899005\pi\) |
−0.721544 | + | 0.692369i | \(0.756567\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.00000 | − | 5.19615i | 0.204479 | − | 0.177084i | ||||
\(862\) | − | 21.0000i | − | 0.715263i | ||||||
\(863\) | 18.1865 | − | 10.5000i | 0.619077 | − | 0.357424i | −0.157433 | − | 0.987530i | \(-0.550322\pi\) |
0.776509 | + | 0.630106i | \(0.216988\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.50000 | + | 6.06218i | 0.118935 | + | 0.206001i | ||||
\(867\) | 8.00000i | 0.271694i | ||||||||
\(868\) | 12.9904 | − | 2.50000i | 0.440922 | − | 0.0848555i | ||||
\(869\) | 42.0000 | 1.42475 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.0000 | − | 27.7128i | 0.542139 | − | 0.939013i | ||||
\(872\) | −3.46410 | − | 2.00000i | −0.117309 | − | 0.0677285i | ||||
\(873\) | 14.7224 | − | 8.50000i | 0.498279 | − | 0.287681i | ||||
\(874\) | 12.0000 | 0.405906 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.0000 | 0.473016 | ||||||||
\(877\) | −1.73205 | + | 1.00000i | −0.0584872 | + | 0.0337676i | −0.528958 | − | 0.848648i | \(-0.677417\pi\) |
0.470471 | + | 0.882415i | \(0.344084\pi\) | |||||||
\(878\) | 11.2583 | + | 6.50000i | 0.379950 | + | 0.219364i | ||||
\(879\) | −9.00000 | + | 15.5885i | −0.303562 | + | 0.525786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.0000 | 0.505363 | 0.252681 | − | 0.967550i | \(-0.418688\pi\) | ||||
0.252681 | + | 0.967550i | \(0.418688\pi\) | |||||||
\(882\) | 2.59808 | + | 6.50000i | 0.0874818 | + | 0.218866i | ||||
\(883\) | 14.0000i | 0.471138i | 0.971858 | + | 0.235569i | \(0.0756953\pi\) | ||||
−0.971858 | + | 0.235569i | \(0.924305\pi\) | |||||||
\(884\) | 6.00000 | + | 10.3923i | 0.201802 | + | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0000 | − | 20.7846i | 0.403148 | − | 0.698273i | ||||
\(887\) | −20.7846 | + | 12.0000i | −0.697879 | + | 0.402921i | −0.806557 | − | 0.591156i | \(-0.798672\pi\) |
0.108678 | + | 0.994077i | \(0.465338\pi\) | |||||||
\(888\) | 8.00000i | 0.268462i | ||||||||
\(889\) | 40.0000 | + | 13.8564i | 1.34156 | + | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.00000 | − | 5.19615i | −0.100504 | − | 0.174078i | ||||
\(892\) | 9.52628 | + | 5.50000i | 0.318963 | + | 0.184154i | ||||
\(893\) | 31.1769 | + | 18.0000i | 1.04330 | + | 0.602347i | ||||
\(894\) | −3.00000 | − | 5.19615i | −0.100335 | − | 0.173785i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.500000 | − | 2.59808i | −0.0167038 | − | 0.0867956i | ||||
\(897\) | 12.0000i | 0.400668i | ||||||||
\(898\) | −2.59808 | + | 1.50000i | −0.0866989 | + | 0.0500556i | ||||
\(899\) | −15.0000 | + | 25.9808i | −0.500278 | + | 0.866507i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.0000 | + | 31.1769i | 0.599667 | + | 1.03865i | ||||
\(902\) | 18.0000i | 0.599334i | ||||||||
\(903\) | −13.8564 | − | 16.0000i | −0.461112 | − | 0.532447i | ||||
\(904\) | −3.00000 | −0.0997785 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.00000 | − | 13.8564i | 0.265782 | − | 0.460348i | ||||
\(907\) | 32.9090 | + | 19.0000i | 1.09272 | + | 0.630885i | 0.934300 | − | 0.356487i | \(-0.116025\pi\) |
0.158424 | + | 0.987371i | \(0.449359\pi\) | |||||||
\(908\) | −15.5885 | + | 9.00000i | −0.517321 | + | 0.298675i | ||||
\(909\) | −12.0000 | −0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.0000 | −0.695761 | −0.347881 | − | 0.937539i | \(-0.613099\pi\) | ||||
−0.347881 | + | 0.937539i | \(0.613099\pi\) | |||||||
\(912\) | 3.46410 | − | 2.00000i | 0.114708 | − | 0.0662266i | ||||
\(913\) | 31.1769 | + | 18.0000i | 1.03181 | + | 0.595713i | ||||
\(914\) | 1.00000 | − | 1.73205i | 0.0330771 | − | 0.0572911i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.0000 | −0.726900 | ||||||||
\(917\) | 46.7654 | − | 9.00000i | 1.54433 | − | 0.297206i | ||||
\(918\) | − | 3.00000i | − | 0.0990148i | ||||||
\(919\) | 5.50000 | + | 9.52628i | 0.181428 | + | 0.314243i | 0.942367 | − | 0.334581i | \(-0.108595\pi\) |
−0.760939 | + | 0.648824i | \(0.775261\pi\) | |||||||
\(920\) | 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 | ||||||||
\(924\) | −15.0000 | − | 5.19615i | −0.493464 | − | 0.170941i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.50000 | + | 11.2583i | 0.213603 | + | 0.369972i | ||||
\(927\) | −11.2583 | − | 6.50000i | −0.369772 | − | 0.213488i | ||||
\(928\) | 5.19615 | + | 3.00000i | 0.170572 | + | 0.0984798i | ||||
\(929\) | −15.0000 | − | 25.9808i | −0.492134 | − | 0.852401i | 0.507825 | − | 0.861460i | \(-0.330450\pi\) |
−0.999959 | + | 0.00905914i | \(0.997116\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00000 | + | 27.7128i | −0.131095 | + | 0.908251i | ||||
\(932\) | − | 6.00000i | − | 0.196537i | ||||||
\(933\) | 18.1865 | − | 10.5000i | 0.595400 | − | 0.343755i | ||||
\(934\) | −15.0000 | + | 25.9808i | −0.490815 | + | 0.850117i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | + | 3.46410i | 0.0653720 | + | 0.113228i | ||||
\(937\) | 34.0000i | 1.11073i | 0.831606 | + | 0.555366i | \(0.187422\pi\) | ||||
−0.831606 | + | 0.555366i | \(0.812578\pi\) | |||||||
\(938\) | −6.92820 | + | 20.0000i | −0.226214 | + | 0.653023i | ||||
\(939\) | −17.0000 | −0.554774 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.00000 | + | 10.3923i | −0.195594 | + | 0.338779i | −0.947095 | − | 0.320953i | \(-0.895997\pi\) |
0.751501 | + | 0.659732i | \(0.229330\pi\) | |||||||
\(942\) | 12.1244 | + | 7.00000i | 0.395033 | + | 0.228072i | ||||
\(943\) | −7.79423 | + | 4.50000i | −0.253815 | + | 0.146540i | ||||
\(944\) | −6.00000 | −0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 48.0000 | 1.56061 | ||||||||
\(947\) | 41.5692 | − | 24.0000i | 1.35082 | − | 0.779895i | 0.362454 | − | 0.932002i | \(-0.381939\pi\) |
0.988364 | + | 0.152106i | \(0.0486057\pi\) | |||||||
\(948\) | 6.06218 | + | 3.50000i | 0.196890 | + | 0.113675i | ||||
\(949\) | −28.0000 | + | 48.4974i | −0.908918 | + | 1.57429i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.0000 | 0.389127 | ||||||||
\(952\) | −5.19615 | − | 6.00000i | −0.168408 | − | 0.194461i | ||||
\(953\) | 6.00000i | 0.194359i | 0.995267 | + | 0.0971795i | \(0.0309821\pi\) | ||||
−0.995267 | + | 0.0971795i | \(0.969018\pi\) | |||||||
\(954\) | 6.00000 | + | 10.3923i | 0.194257 | + | 0.336463i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.50000 | + | 2.59808i | −0.0485135 | + | 0.0840278i | ||||
\(957\) | 31.1769 | − | 18.0000i | 1.00781 | − | 0.581857i | ||||
\(958\) | 21.0000i | 0.678479i | ||||||||
\(959\) | −30.0000 | + | 25.9808i | −0.968751 | + | 0.838963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | + | 5.19615i | 0.0967742 | + | 0.167618i | ||||
\(962\) | −27.7128 | − | 16.0000i | −0.893497 | − | 0.515861i | ||||
\(963\) | −5.19615 | − | 3.00000i | −0.167444 | − | 0.0966736i | ||||
\(964\) | −11.0000 | − | 19.0526i | −0.354286 | − | 0.613642i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.50000 | − | 7.79423i | −0.0482617 | − | 0.250775i | ||||
\(967\) | 31.0000i | 0.996893i | 0.866921 | + | 0.498446i | \(0.166096\pi\) | ||||
−0.866921 | + | 0.498446i | \(0.833904\pi\) | |||||||
\(968\) | 21.6506 | − | 12.5000i | 0.695878 | − | 0.401765i | ||||
\(969\) | 6.00000 | − | 10.3923i | 0.192748 | − | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.00000 | − | 5.19615i | −0.0962746 | − | 0.166752i | 0.813865 | − | 0.581054i | \(-0.197359\pi\) |
−0.910140 | + | 0.414301i | \(0.864026\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | −1.73205 | + | 5.00000i | −0.0555270 | + | 0.160293i | ||||
\(974\) | 25.0000 | 0.801052 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.00000 | + | 1.73205i | −0.0320092 | + | 0.0554416i | ||||
\(977\) | 49.3634 | + | 28.5000i | 1.57928 | + | 0.911796i | 0.994960 | + | 0.100270i | \(0.0319706\pi\) |
0.584316 | + | 0.811526i | \(0.301363\pi\) | |||||||
\(978\) | 6.92820 | − | 4.00000i | 0.221540 | − | 0.127906i | ||||
\(979\) | −18.0000 | −0.575282 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.00000 | −0.127710 | ||||||||
\(982\) | 10.3923 | − | 6.00000i | 0.331632 | − | 0.191468i | ||||
\(983\) | 41.5692 | + | 24.0000i | 1.32585 | + | 0.765481i | 0.984655 | − | 0.174511i | \(-0.0558344\pi\) |
0.341197 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(984\) | −1.50000 | + | 2.59808i | −0.0478183 | + | 0.0828236i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18.0000 | 0.573237 | ||||||||
\(987\) | 7.79423 | − | 22.5000i | 0.248093 | − | 0.716183i | ||||
\(988\) | 16.0000i | 0.509028i | ||||||||
\(989\) | 12.0000 | + | 20.7846i | 0.381578 | + | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5000 | − | 37.2391i | 0.682970 | − | 1.18294i | −0.291100 | − | 0.956693i | \(-0.594021\pi\) |
0.974070 | − | 0.226246i | \(-0.0726454\pi\) | |||||||
\(992\) | −4.33013 | + | 2.50000i | −0.137482 | + | 0.0793751i | ||||
\(993\) | 26.0000i | 0.825085i | ||||||||
\(994\) | −4.50000 | − | 23.3827i | −0.142731 | − | 0.741654i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.00000 | + | 5.19615i | 0.0950586 | + | 0.164646i | ||||
\(997\) | −3.46410 | − | 2.00000i | −0.109709 | − | 0.0633406i | 0.444141 | − | 0.895957i | \(-0.353509\pi\) |
−0.553851 | + | 0.832616i | \(0.686842\pi\) | |||||||
\(998\) | −32.9090 | − | 19.0000i | −1.04172 | − | 0.601434i | ||||
\(999\) | 4.00000 | + | 6.92820i | 0.126554 | + | 0.219199i |
(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.h.949.1 | 4 | ||
5.2 | odd | 4 | 1050.2.i.c.151.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1050.2.i.q.151.1 | yes | 2 | ||
5.4 | even | 2 | inner | 1050.2.o.h.949.2 | 4 | ||
7.2 | even | 3 | inner | 1050.2.o.h.499.2 | 4 | ||
35.2 | odd | 12 | 1050.2.i.c.751.1 | yes | 2 | ||
35.3 | even | 12 | 7350.2.a.bm.1.1 | 1 | |||
35.9 | even | 6 | inner | 1050.2.o.h.499.1 | 4 | ||
35.17 | even | 12 | 7350.2.a.cg.1.1 | 1 | |||
35.18 | odd | 12 | 7350.2.a.s.1.1 | 1 | |||
35.23 | odd | 12 | 1050.2.i.q.751.1 | yes | 2 | ||
35.32 | odd | 12 | 7350.2.a.cy.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.i.c.151.1 | ✓ | 2 | 5.2 | odd | 4 | ||
1050.2.i.c.751.1 | yes | 2 | 35.2 | odd | 12 | ||
1050.2.i.q.151.1 | yes | 2 | 5.3 | odd | 4 | ||
1050.2.i.q.751.1 | yes | 2 | 35.23 | odd | 12 | ||
1050.2.o.h.499.1 | 4 | 35.9 | even | 6 | inner | ||
1050.2.o.h.499.2 | 4 | 7.2 | even | 3 | inner | ||
1050.2.o.h.949.1 | 4 | 1.1 | even | 1 | trivial | ||
1050.2.o.h.949.2 | 4 | 5.4 | even | 2 | inner | ||
7350.2.a.s.1.1 | 1 | 35.18 | odd | 12 | |||
7350.2.a.bm.1.1 | 1 | 35.3 | even | 12 | |||
7350.2.a.cg.1.1 | 1 | 35.17 | even | 12 | |||
7350.2.a.cy.1.1 | 1 | 35.32 | odd | 12 |