Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(751,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.751");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.bc (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 751.4 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.751 |
Dual form | 1950.2.bc.f.901.4 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | −0.417738 | − | 0.241181i | −0.157890 | − | 0.0911578i | 0.418973 | − | 0.907999i | \(-0.362390\pi\) |
−0.576863 | + | 0.816841i | \(0.695723\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00731 | + | 1.15892i | −0.605226 | + | 0.349427i | −0.771095 | − | 0.636721i | \(-0.780290\pi\) |
0.165869 | + | 0.986148i | \(0.446957\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.08725 | − | 1.86250i | 0.856248 | − | 0.516565i | ||||
\(14\) | −0.482362 | −0.128917 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.39778 | + | 5.88512i | −0.824082 | + | 1.42735i | 0.0785367 | + | 0.996911i | \(0.474975\pi\) |
−0.902619 | + | 0.430441i | \(0.858358\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 4.39778 | + | 2.53906i | 1.00892 | + | 0.582500i | 0.910875 | − | 0.412682i | \(-0.135408\pi\) |
0.0980443 | + | 0.995182i | \(0.468741\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.482362i | − | 0.105260i | ||||||
\(22\) | −1.15892 | + | 2.00731i | −0.247082 | + | 0.427959i | ||||
\(23\) | 3.45327 | + | 5.98124i | 0.720057 | + | 1.24718i | 0.960976 | + | 0.276630i | \(0.0892177\pi\) |
−0.240920 | + | 0.970545i | \(0.577449\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.74238 | − | 3.15660i | 0.341709 | − | 0.619060i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.417738 | + | 0.241181i | −0.0789450 | + | 0.0455789i | ||||
\(29\) | 4.20478 | + | 7.28290i | 0.780809 | + | 1.35240i | 0.931471 | + | 0.363815i | \(0.118526\pi\) |
−0.150662 | + | 0.988585i | \(0.548141\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.952516i | 0.171077i | 0.996335 | + | 0.0855385i | \(0.0272611\pi\) | ||||
−0.996335 | + | 0.0855385i | \(0.972739\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −2.00731 | − | 1.15892i | −0.349427 | − | 0.201742i | ||||
\(34\) | 6.79555i | 1.16543i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | 5.35948 | − | 3.09429i | 0.881092 | − | 0.508699i | 0.0100739 | − | 0.999949i | \(-0.496793\pi\) |
0.871018 | + | 0.491250i | \(0.163460\pi\) | |||||||
\(38\) | 5.07812 | 0.823779 | ||||||||
\(39\) | 3.15660 | + | 1.74238i | 0.505460 | + | 0.279005i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.55607 | − | 4.36250i | 1.18006 | − | 0.681308i | 0.224032 | − | 0.974582i | \(-0.428078\pi\) |
0.956029 | + | 0.293274i | \(0.0947447\pi\) | |||||||
\(42\) | −0.241181 | − | 0.417738i | −0.0372150 | − | 0.0644583i | ||||
\(43\) | 5.64747 | − | 9.78170i | 0.861231 | − | 1.49170i | −0.00951136 | − | 0.999955i | \(-0.503028\pi\) |
0.870742 | − | 0.491740i | \(-0.163639\pi\) | |||||||
\(44\) | 2.31784i | 0.349427i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.98124 | + | 3.45327i | 0.881886 | + | 0.509157i | ||||
\(47\) | − | 5.77729i | − | 0.842705i | −0.906897 | − | 0.421353i | \(-0.861556\pi\) | ||
0.906897 | − | 0.421353i | \(-0.138444\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −3.38366 | − | 5.86068i | −0.483380 | − | 0.837240i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.79555 | −0.951568 | ||||||||
\(52\) | −0.0693504 | − | 3.60488i | −0.00961716 | − | 0.499908i | ||||
\(53\) | −5.81017 | −0.798088 | −0.399044 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399044 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.241181 | + | 0.417738i | −0.0322292 | + | 0.0558225i | ||||
\(57\) | 5.07812i | 0.672613i | ||||||||
\(58\) | 7.28290 | + | 4.20478i | 0.956292 | + | 0.552115i | ||||
\(59\) | 10.2397 | + | 5.91189i | 1.33309 | + | 0.769663i | 0.985773 | − | 0.168083i | \(-0.0537577\pi\) |
0.347322 | + | 0.937746i | \(0.387091\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.68764 | + | 8.11924i | −0.600191 | + | 1.03956i | 0.392600 | + | 0.919709i | \(0.371576\pi\) |
−0.992792 | + | 0.119853i | \(0.961758\pi\) | |||||||
\(62\) | 0.476258 | + | 0.824903i | 0.0604848 | + | 0.104763i | ||||
\(63\) | 0.417738 | − | 0.241181i | 0.0526300 | − | 0.0303859i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.31784 | −0.285306 | ||||||||
\(67\) | −6.40300 | + | 3.69677i | −0.782251 | + | 0.451633i | −0.837227 | − | 0.546855i | \(-0.815825\pi\) |
0.0549764 | + | 0.998488i | \(0.482492\pi\) | |||||||
\(68\) | 3.39778 | + | 5.88512i | 0.412041 | + | 0.713676i | ||||
\(69\) | −3.45327 | + | 5.98124i | −0.415725 | + | 0.720057i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.01876 | + | 1.74288i | 0.358261 | + | 0.206842i | 0.668318 | − | 0.743876i | \(-0.267015\pi\) |
−0.310057 | + | 0.950718i | \(0.600348\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | 8.53465i | 0.998906i | 0.866341 | + | 0.499453i | \(0.166466\pi\) | ||||
−0.866341 | + | 0.499453i | \(0.833534\pi\) | |||||||
\(74\) | 3.09429 | − | 5.35948i | 0.359704 | − | 0.623026i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.39778 | − | 2.53906i | 0.504460 | − | 0.291250i | ||||
\(77\) | 1.11804 | 0.127412 | ||||||||
\(78\) | 3.60488 | − | 0.0693504i | 0.408173 | − | 0.00785238i | ||||
\(79\) | 9.03820 | 1.01688 | 0.508438 | − | 0.861098i | \(-0.330223\pi\) | ||||
0.508438 | + | 0.861098i | \(0.330223\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 4.36250 | − | 7.55607i | 0.481758 | − | 0.834429i | ||||
\(83\) | 7.94887i | 0.872502i | 0.899825 | + | 0.436251i | \(0.143694\pi\) | ||||
−0.899825 | + | 0.436251i | \(0.856306\pi\) | |||||||
\(84\) | −0.417738 | − | 0.241181i | −0.0455789 | − | 0.0263150i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 11.2949i | − | 1.21796i | ||||||
\(87\) | −4.20478 | + | 7.28290i | −0.450800 | + | 0.780809i | ||||
\(88\) | 1.15892 | + | 2.00731i | 0.123541 | + | 0.213980i | ||||
\(89\) | 7.80941 | − | 4.50877i | 0.827796 | − | 0.477928i | −0.0253015 | − | 0.999680i | \(-0.508055\pi\) |
0.853097 | + | 0.521752i | \(0.174721\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.73886 | + | 0.0334520i | −0.182282 | + | 0.00350672i | ||||
\(92\) | 6.90654 | 0.720057 | ||||||||
\(93\) | −0.824903 | + | 0.476258i | −0.0855385 | + | 0.0493857i | ||||
\(94\) | −2.88865 | − | 5.00328i | −0.297941 | − | 0.516049i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | −7.95189 | − | 4.59103i | −0.807392 | − | 0.466148i | 0.0386571 | − | 0.999253i | \(-0.487692\pi\) |
−0.846050 | + | 0.533104i | \(0.821025\pi\) | |||||||
\(98\) | −5.86068 | − | 3.38366i | −0.592018 | − | 0.341802i | ||||
\(99\) | − | 2.31784i | − | 0.232951i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.34108 | − | 9.25102i | −0.531457 | − | 0.920511i | −0.999326 | − | 0.0367132i | \(-0.988311\pi\) |
0.467868 | − | 0.883798i | \(-0.345022\pi\) | |||||||
\(102\) | −5.88512 | + | 3.39778i | −0.582714 | + | 0.336430i | ||||
\(103\) | −9.17449 | −0.903990 | −0.451995 | − | 0.892021i | \(-0.649287\pi\) | ||||
−0.451995 | + | 0.892021i | \(0.649287\pi\) | |||||||
\(104\) | −1.86250 | − | 3.08725i | −0.182633 | − | 0.302729i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.03175 | + | 2.90508i | −0.488727 | + | 0.282167i | ||||
\(107\) | −1.60867 | − | 2.78629i | −0.155516 | − | 0.269361i | 0.777731 | − | 0.628597i | \(-0.216371\pi\) |
−0.933247 | + | 0.359236i | \(0.883037\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | 17.0669i | 1.63471i | 0.576132 | + | 0.817356i | \(0.304561\pi\) | ||||
−0.576132 | + | 0.817356i | \(0.695439\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.35948 | + | 3.09429i | 0.508699 | + | 0.293697i | ||||
\(112\) | 0.482362i | 0.0455789i | ||||||||
\(113\) | −0.828427 | + | 1.43488i | −0.0779319 | + | 0.134982i | −0.902357 | − | 0.430988i | \(-0.858165\pi\) |
0.824426 | + | 0.565970i | \(0.191498\pi\) | |||||||
\(114\) | 2.53906 | + | 4.39778i | 0.237805 | + | 0.411890i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.40957 | 0.780809 | ||||||||
\(117\) | 0.0693504 | + | 3.60488i | 0.00641144 | + | 0.333272i | ||||
\(118\) | 11.8238 | 1.08847 | ||||||||
\(119\) | 2.83876 | − | 1.63896i | 0.260229 | − | 0.150243i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.81382 | + | 4.87367i | −0.255801 | + | 0.443061i | ||||
\(122\) | 9.37529i | 0.848799i | ||||||||
\(123\) | 7.55607 | + | 4.36250i | 0.681308 | + | 0.393353i | ||||
\(124\) | 0.824903 | + | 0.476258i | 0.0740785 | + | 0.0427692i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.241181 | − | 0.417738i | 0.0214861 | − | 0.0372150i | ||||
\(127\) | −9.45946 | − | 16.3843i | −0.839391 | − | 1.45387i | −0.890405 | − | 0.455170i | \(-0.849578\pi\) |
0.0510134 | − | 0.998698i | \(-0.483755\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 11.2949 | 0.994463 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.96812 | −0.608808 | −0.304404 | − | 0.952543i | \(-0.598457\pi\) | ||||
−0.304404 | + | 0.952543i | \(0.598457\pi\) | |||||||
\(132\) | −2.00731 | + | 1.15892i | −0.174714 | + | 0.100871i | ||||
\(133\) | −1.22474 | − | 2.12132i | −0.106199 | − | 0.183942i | ||||
\(134\) | −3.69677 | + | 6.40300i | −0.319353 | + | 0.553135i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.88512 | + | 3.39778i | 0.504645 | + | 0.291357i | ||||
\(137\) | −17.7616 | − | 10.2547i | −1.51748 | − | 0.876116i | −0.999789 | − | 0.0205465i | \(-0.993459\pi\) |
−0.517688 | − | 0.855569i | \(-0.673207\pi\) | |||||||
\(138\) | 6.90654i | 0.587924i | ||||||||
\(139\) | 4.25467 | − | 7.36931i | 0.360877 | − | 0.625057i | −0.627229 | − | 0.778835i | \(-0.715811\pi\) |
0.988105 | + | 0.153778i | \(0.0491442\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.00328 | − | 2.88865i | 0.421353 | − | 0.243268i | ||||
\(142\) | 3.48576 | 0.292519 | ||||||||
\(143\) | −4.03856 | + | 7.31648i | −0.337721 | + | 0.611835i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.26733 | + | 7.39123i | 0.353166 | + | 0.611702i | ||||
\(147\) | 3.38366 | − | 5.86068i | 0.279080 | − | 0.483380i | ||||
\(148\) | − | 6.18859i | − | 0.508699i | ||||||
\(149\) | 6.27439 | + | 3.62252i | 0.514018 | + | 0.296769i | 0.734484 | − | 0.678626i | \(-0.237424\pi\) |
−0.220466 | + | 0.975395i | \(0.570758\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.82743i | 0.636987i | 0.947925 | + | 0.318494i | \(0.103177\pi\) | ||||
−0.947925 | + | 0.318494i | \(0.896823\pi\) | |||||||
\(152\) | 2.53906 | − | 4.39778i | 0.205945 | − | 0.356707i | ||||
\(153\) | −3.39778 | − | 5.88512i | −0.274694 | − | 0.475784i | ||||
\(154\) | 0.968248 | − | 0.559018i | 0.0780236 | − | 0.0450470i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.08725 | − | 1.86250i | 0.247178 | − | 0.149119i | ||||
\(157\) | −4.42267 | −0.352967 | −0.176484 | − | 0.984304i | \(-0.556472\pi\) | ||||
−0.176484 | + | 0.984304i | \(0.556472\pi\) | |||||||
\(158\) | 7.82731 | − | 4.51910i | 0.622707 | − | 0.359520i | ||||
\(159\) | −2.90508 | − | 5.03175i | −0.230388 | − | 0.399044i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.33145i | − | 0.262555i | ||||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | −9.72060 | − | 5.61219i | −0.761376 | − | 0.439581i | 0.0684135 | − | 0.997657i | \(-0.478206\pi\) |
−0.829790 | + | 0.558076i | \(0.811540\pi\) | |||||||
\(164\) | − | 8.72500i | − | 0.681308i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.97443 | + | 6.88392i | 0.308476 | + | 0.534296i | ||||
\(167\) | 13.0406 | − | 7.52898i | 1.00911 | − | 0.582610i | 0.0981794 | − | 0.995169i | \(-0.468698\pi\) |
0.910931 | + | 0.412558i | \(0.135365\pi\) | |||||||
\(168\) | −0.482362 | −0.0372150 | ||||||||
\(169\) | 6.06218 | − | 11.5000i | 0.466321 | − | 0.884615i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.39778 | + | 2.53906i | −0.336306 | + | 0.194167i | ||||
\(172\) | −5.64747 | − | 9.78170i | −0.430615 | − | 0.745848i | ||||
\(173\) | −7.37429 | + | 12.7727i | −0.560657 | + | 0.971087i | 0.436782 | + | 0.899567i | \(0.356118\pi\) |
−0.997439 | + | 0.0715193i | \(0.977215\pi\) | |||||||
\(174\) | 8.40957i | 0.637528i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00731 | + | 1.15892i | 0.151306 | + | 0.0873568i | ||||
\(177\) | 11.8238i | 0.888730i | ||||||||
\(178\) | 4.50877 | − | 7.80941i | 0.337946 | − | 0.585340i | ||||
\(179\) | 4.30589 | + | 7.45802i | 0.321837 | + | 0.557438i | 0.980867 | − | 0.194678i | \(-0.0623663\pi\) |
−0.659030 | + | 0.752117i | \(0.729033\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.84493 | 0.211462 | 0.105731 | − | 0.994395i | \(-0.466282\pi\) | ||||
0.105731 | + | 0.994395i | \(0.466282\pi\) | |||||||
\(182\) | −1.48917 | + | 0.898400i | −0.110385 | + | 0.0665938i | ||||
\(183\) | −9.37529 | −0.693041 | ||||||||
\(184\) | 5.98124 | − | 3.45327i | 0.440943 | − | 0.254579i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.476258 | + | 0.824903i | −0.0349209 | + | 0.0604848i | ||||
\(187\) | − | 15.7510i | − | 1.15183i | ||||||
\(188\) | −5.00328 | − | 2.88865i | −0.364902 | − | 0.210676i | ||||
\(189\) | 0.417738 | + | 0.241181i | 0.0303859 | + | 0.0175433i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.71794 | − | 2.97555i | 0.124306 | − | 0.215304i | −0.797156 | − | 0.603774i | \(-0.793663\pi\) |
0.921461 | + | 0.388470i | \(0.126996\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 2.30090 | − | 1.32843i | 0.165623 | − | 0.0956223i | −0.414898 | − | 0.909868i | \(-0.636183\pi\) |
0.580520 | + | 0.814246i | \(0.302849\pi\) | |||||||
\(194\) | −9.18206 | −0.659233 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.76733 | −0.483380 | ||||||||
\(197\) | −18.2868 | + | 10.5579i | −1.30288 | + | 0.752219i | −0.980897 | − | 0.194526i | \(-0.937683\pi\) |
−0.321984 | + | 0.946745i | \(0.604350\pi\) | |||||||
\(198\) | −1.15892 | − | 2.00731i | −0.0823608 | − | 0.142653i | ||||
\(199\) | 5.26941 | − | 9.12688i | 0.373538 | − | 0.646988i | −0.616569 | − | 0.787301i | \(-0.711478\pi\) |
0.990107 | + | 0.140314i | \(0.0448110\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.40300 | − | 3.69677i | −0.451633 | − | 0.260750i | ||||
\(202\) | −9.25102 | − | 5.34108i | −0.650900 | − | 0.375797i | ||||
\(203\) | − | 4.05646i | − | 0.284707i | ||||||
\(204\) | −3.39778 | + | 5.88512i | −0.237892 | + | 0.412041i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.94534 | + | 4.58725i | −0.553578 | + | 0.319609i | ||||
\(207\) | −6.90654 | −0.480038 | ||||||||
\(208\) | −3.15660 | − | 1.74238i | −0.218871 | − | 0.120813i | ||||
\(209\) | −11.7702 | −0.814165 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.74384 | + | 9.94863i | 0.395422 | + | 0.684892i | 0.993155 | − | 0.116804i | \(-0.0372649\pi\) |
−0.597733 | + | 0.801696i | \(0.703932\pi\) | |||||||
\(212\) | −2.90508 | + | 5.03175i | −0.199522 | + | 0.345582i | ||||
\(213\) | 3.48576i | 0.238840i | ||||||||
\(214\) | −2.78629 | − | 1.60867i | −0.190467 | − | 0.109966i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 0.229729 | − | 0.397902i | 0.0155950 | − | 0.0270113i | ||||
\(218\) | 8.53345 | + | 14.7804i | 0.577958 | + | 1.00105i | ||||
\(219\) | −7.39123 | + | 4.26733i | −0.499453 | + | 0.288359i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.471274 | + | 24.4972i | 0.0317013 | + | 1.64786i | ||||
\(222\) | 6.18859 | 0.415351 | ||||||||
\(223\) | 4.52739 | − | 2.61389i | 0.303176 | − | 0.175039i | −0.340693 | − | 0.940175i | \(-0.610662\pi\) |
0.643869 | + | 0.765136i | \(0.277328\pi\) | |||||||
\(224\) | 0.241181 | + | 0.417738i | 0.0161146 | + | 0.0279113i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.65685i | 0.110212i | ||||||||
\(227\) | 9.41271 | + | 5.43443i | 0.624744 | + | 0.360696i | 0.778714 | − | 0.627380i | \(-0.215873\pi\) |
−0.153970 | + | 0.988076i | \(0.549206\pi\) | |||||||
\(228\) | 4.39778 | + | 2.53906i | 0.291250 | + | 0.168153i | ||||
\(229\) | − | 21.1932i | − | 1.40048i | −0.713905 | − | 0.700242i | \(-0.753075\pi\) | ||
0.713905 | − | 0.700242i | \(-0.246925\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.559018 | + | 0.968248i | 0.0367807 | + | 0.0637060i | ||||
\(232\) | 7.28290 | − | 4.20478i | 0.478146 | − | 0.276058i | ||||
\(233\) | 21.8423 | 1.43094 | 0.715469 | − | 0.698645i | \(-0.246213\pi\) | ||||
0.715469 | + | 0.698645i | \(0.246213\pi\) | |||||||
\(234\) | 1.86250 | + | 3.08725i | 0.121756 | + | 0.201820i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.2397 | − | 5.91189i | 0.666547 | − | 0.384831i | ||||
\(237\) | 4.51910 | + | 7.82731i | 0.293547 | + | 0.508438i | ||||
\(238\) | 1.63896 | − | 2.83876i | 0.106238 | − | 0.184009i | ||||
\(239\) | 8.23027i | 0.532372i | 0.963922 | + | 0.266186i | \(0.0857635\pi\) | ||||
−0.963922 | + | 0.266186i | \(0.914236\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.68678 | − | 1.55121i | −0.173071 | − | 0.0999225i | 0.410962 | − | 0.911652i | \(-0.365193\pi\) |
−0.584033 | + | 0.811730i | \(0.698526\pi\) | |||||||
\(242\) | 5.62763i | 0.361758i | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 4.68764 | + | 8.11924i | 0.300096 | + | 0.519781i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.72500 | 0.556286 | ||||||||
\(247\) | 18.3060 | − | 0.352169i | 1.16478 | − | 0.0224080i | ||||
\(248\) | 0.952516 | 0.0604848 | ||||||||
\(249\) | −6.88392 | + | 3.97443i | −0.436251 | + | 0.251870i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.81042 | − | 13.5281i | 0.492990 | − | 0.853883i | −0.506978 | − | 0.861959i | \(-0.669237\pi\) |
0.999967 | + | 0.00807605i | \(0.00257072\pi\) | |||||||
\(252\) | − | 0.482362i | − | 0.0303859i | ||||||
\(253\) | −13.8635 | − | 8.00412i | −0.871594 | − | 0.503215i | ||||
\(254\) | −16.3843 | − | 9.45946i | −1.02804 | − | 0.593539i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1.76210 | + | 3.05205i | 0.109917 | + | 0.190382i | 0.915736 | − | 0.401780i | \(-0.131608\pi\) |
−0.805819 | + | 0.592161i | \(0.798275\pi\) | |||||||
\(258\) | 9.78170 | − | 5.64747i | 0.608982 | − | 0.351596i | ||||
\(259\) | −2.98514 | −0.185488 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.40957 | −0.520539 | ||||||||
\(262\) | −6.03457 | + | 3.48406i | −0.372817 | + | 0.215246i | ||||
\(263\) | −11.6415 | − | 20.1637i | −0.717845 | − | 1.24334i | −0.961852 | − | 0.273571i | \(-0.911795\pi\) |
0.244006 | − | 0.969774i | \(-0.421538\pi\) | |||||||
\(264\) | −1.15892 | + | 2.00731i | −0.0713265 | + | 0.123541i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.12132 | − | 1.22474i | −0.130066 | − | 0.0750939i | ||||
\(267\) | 7.80941 | + | 4.50877i | 0.477928 | + | 0.275932i | ||||
\(268\) | 7.39355i | 0.451633i | ||||||||
\(269\) | −4.90873 | + | 8.50217i | −0.299291 | + | 0.518387i | −0.975974 | − | 0.217888i | \(-0.930083\pi\) |
0.676683 | + | 0.736274i | \(0.263417\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.8862 | + | 10.9040i | −1.14726 | + | 0.662369i | −0.948217 | − | 0.317623i | \(-0.897115\pi\) |
−0.199039 | + | 0.979992i | \(0.563782\pi\) | |||||||
\(272\) | 6.79555 | 0.412041 | ||||||||
\(273\) | −0.898400 | − | 1.48917i | −0.0543736 | − | 0.0901287i | ||||
\(274\) | −20.5093 | −1.23901 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.45327 | + | 5.98124i | 0.207863 | + | 0.360028i | ||||
\(277\) | −6.73753 | + | 11.6697i | −0.404819 | + | 0.701167i | −0.994300 | − | 0.106615i | \(-0.965999\pi\) |
0.589481 | + | 0.807782i | \(0.299332\pi\) | |||||||
\(278\) | − | 8.50935i | − | 0.510357i | ||||||
\(279\) | −0.824903 | − | 0.476258i | −0.0493857 | − | 0.0285128i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 29.6167i | − | 1.76678i | −0.468635 | − | 0.883392i | \(-0.655254\pi\) | ||
0.468635 | − | 0.883392i | \(-0.344746\pi\) | |||||||
\(282\) | 2.88865 | − | 5.00328i | 0.172016 | − | 0.297941i | ||||
\(283\) | −6.09197 | − | 10.5516i | −0.362130 | − | 0.627228i | 0.626181 | − | 0.779678i | \(-0.284617\pi\) |
−0.988311 | + | 0.152450i | \(0.951284\pi\) | |||||||
\(284\) | 3.01876 | − | 1.74288i | 0.179130 | − | 0.103421i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.160743 | + | 8.35554i | 0.00950492 | + | 0.494073i | ||||
\(287\) | −4.20861 | −0.248426 | ||||||||
\(288\) | 0.866025 | − | 0.500000i | 0.0510310 | − | 0.0294628i | ||||
\(289\) | −14.5898 | − | 25.2702i | −0.858223 | − | 1.48649i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 9.18206i | − | 0.538262i | ||||||
\(292\) | 7.39123 | + | 4.26733i | 0.432539 | + | 0.249726i | ||||
\(293\) | −13.0085 | − | 7.51047i | −0.759965 | − | 0.438766i | 0.0693181 | − | 0.997595i | \(-0.477918\pi\) |
−0.829283 | + | 0.558829i | \(0.811251\pi\) | |||||||
\(294\) | − | 6.76733i | − | 0.394679i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.09429 | − | 5.35948i | −0.179852 | − | 0.311513i | ||||
\(297\) | 2.00731 | − | 1.15892i | 0.116476 | − | 0.0672473i | ||||
\(298\) | 7.24504 | 0.419694 | ||||||||
\(299\) | 21.8012 | + | 12.0338i | 1.26079 | + | 0.695935i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.71832 | + | 2.72412i | −0.271959 | + | 0.157016i | ||||
\(302\) | 3.91372 | + | 6.77875i | 0.225209 | + | 0.390073i | ||||
\(303\) | 5.34108 | − | 9.25102i | 0.306837 | − | 0.531457i | ||||
\(304\) | − | 5.07812i | − | 0.291250i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.88512 | − | 3.39778i | −0.336430 | − | 0.194238i | ||||
\(307\) | − | 27.9569i | − | 1.59558i | −0.602934 | − | 0.797791i | \(-0.706002\pi\) | ||
0.602934 | − | 0.797791i | \(-0.293998\pi\) | |||||||
\(308\) | 0.559018 | − | 0.968248i | 0.0318530 | − | 0.0551710i | ||||
\(309\) | −4.58725 | − | 7.94534i | −0.260959 | − | 0.451995i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.3067 | 0.811256 | 0.405628 | − | 0.914038i | \(-0.367053\pi\) | ||||
0.405628 | + | 0.914038i | \(0.367053\pi\) | |||||||
\(312\) | 1.74238 | − | 3.15660i | 0.0986430 | − | 0.178707i | ||||
\(313\) | −13.9895 | −0.790731 | −0.395366 | − | 0.918524i | \(-0.629382\pi\) | ||||
−0.395366 | + | 0.918524i | \(0.629382\pi\) | |||||||
\(314\) | −3.83014 | + | 2.21134i | −0.216148 | + | 0.124793i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.51910 | − | 7.82731i | 0.254219 | − | 0.440320i | ||||
\(317\) | − | 7.29868i | − | 0.409935i | −0.978769 | − | 0.204967i | \(-0.934291\pi\) | ||
0.978769 | − | 0.204967i | \(-0.0657089\pi\) | |||||||
\(318\) | −5.03175 | − | 2.90508i | −0.282167 | − | 0.162909i | ||||
\(319\) | −16.8806 | − | 9.74601i | −0.945131 | − | 0.545672i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.60867 | − | 2.78629i | 0.0897870 | − | 0.155516i | ||||
\(322\) | −1.66573 | − | 2.88512i | −0.0928273 | − | 0.160782i | ||||
\(323\) | −29.8853 | + | 17.2543i | −1.66286 | + | 0.960055i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.2244 | −0.621661 | ||||||||
\(327\) | −14.7804 | + | 8.53345i | −0.817356 | + | 0.471901i | ||||
\(328\) | −4.36250 | − | 7.55607i | −0.240879 | − | 0.417214i | ||||
\(329\) | −1.39337 | + | 2.41339i | −0.0768192 | + | 0.133055i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.8279 | + | 13.1797i | 1.25474 | + | 0.724423i | 0.972046 | − | 0.234788i | \(-0.0754397\pi\) |
0.282690 | + | 0.959211i | \(0.408773\pi\) | |||||||
\(332\) | 6.88392 | + | 3.97443i | 0.377804 | + | 0.218125i | ||||
\(333\) | 6.18859i | 0.339133i | ||||||||
\(334\) | 7.52898 | − | 13.0406i | 0.411968 | − | 0.713549i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.417738 | + | 0.241181i | −0.0227895 | + | 0.0131575i | ||||
\(337\) | 24.4240 | 1.33046 | 0.665229 | − | 0.746639i | \(-0.268334\pi\) | ||||
0.665229 | + | 0.746639i | \(0.268334\pi\) | |||||||
\(338\) | −0.500000 | − | 12.9904i | −0.0271964 | − | 0.706584i | ||||
\(339\) | −1.65685 | −0.0899880 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.10389 | − | 1.91199i | −0.0597789 | − | 0.103540i | ||||
\(342\) | −2.53906 | + | 4.39778i | −0.137297 | + | 0.237805i | ||||
\(343\) | 6.64083i | 0.358571i | ||||||||
\(344\) | −9.78170 | − | 5.64747i | −0.527394 | − | 0.304491i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.7486i | 0.792889i | ||||||||
\(347\) | 6.70818 | − | 11.6189i | 0.360114 | − | 0.623736i | −0.627865 | − | 0.778322i | \(-0.716071\pi\) |
0.987979 | + | 0.154586i | \(0.0494044\pi\) | |||||||
\(348\) | 4.20478 | + | 7.28290i | 0.225400 | + | 0.390404i | ||||
\(349\) | 0.824457 | − | 0.476000i | 0.0441322 | − | 0.0254797i | −0.477772 | − | 0.878484i | \(-0.658555\pi\) |
0.521904 | + | 0.853004i | \(0.325222\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.08725 | + | 1.86250i | −0.164785 | + | 0.0994130i | ||||
\(352\) | 2.31784 | 0.123541 | ||||||||
\(353\) | −12.5120 | + | 7.22380i | −0.665946 | + | 0.384484i | −0.794539 | − | 0.607213i | \(-0.792287\pi\) |
0.128593 | + | 0.991697i | \(0.458954\pi\) | |||||||
\(354\) | 5.91189 | + | 10.2397i | 0.314213 | + | 0.544234i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 9.01753i | − | 0.477928i | ||||||
\(357\) | 2.83876 | + | 1.63896i | 0.150243 | + | 0.0867429i | ||||
\(358\) | 7.45802 | + | 4.30589i | 0.394168 | + | 0.227573i | ||||
\(359\) | 8.11291i | 0.428183i | 0.976814 | + | 0.214092i | \(0.0686791\pi\) | ||||
−0.976814 | + | 0.214092i | \(0.931321\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.39363 | + | 5.87794i | 0.178612 | + | 0.309365i | ||||
\(362\) | 2.46378 | − | 1.42246i | 0.129493 | − | 0.0747630i | ||||
\(363\) | −5.62763 | −0.295374 | ||||||||
\(364\) | −0.840459 | + | 1.52262i | −0.0440520 | + | 0.0798071i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.11924 | + | 4.68764i | −0.424399 | + | 0.245027i | ||||
\(367\) | −11.9977 | − | 20.7806i | −0.626274 | − | 1.08474i | −0.988293 | − | 0.152568i | \(-0.951246\pi\) |
0.362019 | − | 0.932171i | \(-0.382088\pi\) | |||||||
\(368\) | 3.45327 | − | 5.98124i | 0.180014 | − | 0.311794i | ||||
\(369\) | 8.72500i | 0.454205i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.42713 | + | 1.40130i | 0.126010 | + | 0.0727520i | ||||
\(372\) | 0.952516i | 0.0493857i | ||||||||
\(373\) | 13.4288 | − | 23.2593i | 0.695316 | − | 1.20432i | −0.274758 | − | 0.961513i | \(-0.588598\pi\) |
0.970074 | − | 0.242809i | \(-0.0780689\pi\) | |||||||
\(374\) | −7.87550 | − | 13.6408i | −0.407232 | − | 0.705347i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.77729 | −0.297941 | ||||||||
\(377\) | 26.5456 | + | 14.6527i | 1.36717 | + | 0.754652i | ||||
\(378\) | 0.482362 | 0.0248100 | ||||||||
\(379\) | −13.2638 | + | 7.65785i | −0.681315 | + | 0.393357i | −0.800350 | − | 0.599533i | \(-0.795353\pi\) |
0.119035 | + | 0.992890i | \(0.462020\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.45946 | − | 16.3843i | 0.484623 | − | 0.839391i | ||||
\(382\) | − | 3.43587i | − | 0.175795i | ||||||
\(383\) | 30.5185 | + | 17.6198i | 1.55942 | + | 0.900332i | 0.997312 | + | 0.0732675i | \(0.0233427\pi\) |
0.562108 | + | 0.827064i | \(0.309991\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.32843 | − | 2.30090i | 0.0676152 | − | 0.117113i | ||||
\(387\) | 5.64747 | + | 9.78170i | 0.287077 | + | 0.497232i | ||||
\(388\) | −7.95189 | + | 4.59103i | −0.403696 | + | 0.233074i | ||||
\(389\) | −18.0946 | −0.917433 | −0.458717 | − | 0.888583i | \(-0.651691\pi\) | ||||
−0.458717 | + | 0.888583i | \(0.651691\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −46.9338 | −2.37354 | ||||||||
\(392\) | −5.86068 | + | 3.38366i | −0.296009 | + | 0.170901i | ||||
\(393\) | −3.48406 | − | 6.03457i | −0.175748 | − | 0.304404i | ||||
\(394\) | −10.5579 | + | 18.2868i | −0.531899 | + | 0.921276i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.00731 | − | 1.15892i | −0.100871 | − | 0.0582379i | ||||
\(397\) | −9.05105 | − | 5.22562i | −0.454259 | − | 0.262267i | 0.255368 | − | 0.966844i | \(-0.417803\pi\) |
−0.709627 | + | 0.704577i | \(0.751137\pi\) | |||||||
\(398\) | − | 10.5388i | − | 0.528263i | ||||||
\(399\) | 1.22474 | − | 2.12132i | 0.0613139 | − | 0.106199i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.21317 | + | 0.700423i | −0.0605827 | + | 0.0349775i | −0.529985 | − | 0.848007i | \(-0.677803\pi\) |
0.469403 | + | 0.882984i | \(0.344469\pi\) | |||||||
\(402\) | −7.39355 | −0.368757 | ||||||||
\(403\) | 1.77406 | + | 2.94065i | 0.0883723 | + | 0.146484i | ||||
\(404\) | −10.6822 | −0.531457 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.02823 | − | 3.51299i | −0.100659 | − | 0.174347i | ||||
\(407\) | −7.17207 | + | 12.4224i | −0.355506 | + | 0.615755i | ||||
\(408\) | 6.79555i | 0.336430i | ||||||||
\(409\) | 5.83817 | + | 3.37067i | 0.288679 | + | 0.166669i | 0.637346 | − | 0.770578i | \(-0.280032\pi\) |
−0.348667 | + | 0.937247i | \(0.613366\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 20.5093i | − | 1.01165i | ||||||
\(412\) | −4.58725 | + | 7.94534i | −0.225997 | + | 0.391439i | ||||
\(413\) | −2.85167 | − | 4.93924i | −0.140322 | − | 0.243044i | ||||
\(414\) | −5.98124 | + | 3.45327i | −0.293962 | + | 0.169719i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.60488 | + | 0.0693504i | −0.176744 | + | 0.00340018i | ||||
\(417\) | 8.50935 | 0.416704 | ||||||||
\(418\) | −10.1933 | + | 5.88512i | −0.498572 | + | 0.287851i | ||||
\(419\) | −18.2539 | − | 31.6166i | −0.891760 | − | 1.54457i | −0.837765 | − | 0.546032i | \(-0.816138\pi\) |
−0.0539949 | − | 0.998541i | \(-0.517195\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 40.8490i | − | 1.99086i | −0.0955005 | − | 0.995429i | \(-0.530445\pi\) | ||
0.0955005 | − | 0.995429i | \(-0.469555\pi\) | |||||||
\(422\) | 9.94863 | + | 5.74384i | 0.484292 | + | 0.279606i | ||||
\(423\) | 5.00328 | + | 2.88865i | 0.243268 | + | 0.140451i | ||||
\(424\) | 5.81017i | 0.282167i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.74288 | + | 3.01876i | 0.0844429 | + | 0.146259i | ||||
\(427\) | 3.91641 | − | 2.26114i | 0.189528 | − | 0.109424i | ||||
\(428\) | −3.21733 | −0.155516 | ||||||||
\(429\) | −8.35554 | + | 0.160743i | −0.403409 | + | 0.00776074i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.9145 | + | 9.18824i | −0.766575 | + | 0.442582i | −0.831651 | − | 0.555298i | \(-0.812604\pi\) |
0.0650767 | + | 0.997880i | \(0.479271\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 0.699097 | − | 1.21087i | 0.0335964 | − | 0.0581907i | −0.848738 | − | 0.528813i | \(-0.822637\pi\) |
0.882335 | + | 0.470622i | \(0.155971\pi\) | |||||||
\(434\) | − | 0.459457i | − | 0.0220547i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.7804 | + | 8.53345i | 0.707851 | + | 0.408678i | ||||
\(437\) | 35.0722i | 1.67773i | ||||||||
\(438\) | −4.26733 | + | 7.39123i | −0.203901 | + | 0.353166i | ||||
\(439\) | −7.65685 | − | 13.2621i | −0.365442 | − | 0.632964i | 0.623405 | − | 0.781899i | \(-0.285749\pi\) |
−0.988847 | + | 0.148935i | \(0.952415\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.76733 | 0.322254 | ||||||||
\(442\) | 12.6567 | + | 20.9796i | 0.602019 | + | 0.997895i | ||||
\(443\) | 33.1769 | 1.57628 | 0.788141 | − | 0.615495i | \(-0.211044\pi\) | ||||
0.788141 | + | 0.615495i | \(0.211044\pi\) | |||||||
\(444\) | 5.35948 | − | 3.09429i | 0.254349 | − | 0.146849i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.61389 | − | 4.52739i | 0.123771 | − | 0.214378i | ||||
\(447\) | 7.24504i | 0.342679i | ||||||||
\(448\) | 0.417738 | + | 0.241181i | 0.0197362 | + | 0.0113947i | ||||
\(449\) | 13.3408 | + | 7.70234i | 0.629593 | + | 0.363496i | 0.780595 | − | 0.625038i | \(-0.214916\pi\) |
−0.151001 | + | 0.988534i | \(0.548250\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.1116 | + | 17.5137i | −0.476135 | + | 0.824690i | ||||
\(452\) | 0.828427 | + | 1.43488i | 0.0389659 | + | 0.0674910i | ||||
\(453\) | −6.77875 | + | 3.91372i | −0.318494 | + | 0.183882i | ||||
\(454\) | 10.8689 | 0.510101 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.07812 | 0.237805 | ||||||||
\(457\) | −6.46224 | + | 3.73097i | −0.302291 | + | 0.174528i | −0.643471 | − | 0.765470i | \(-0.722506\pi\) |
0.341181 | + | 0.939998i | \(0.389173\pi\) | |||||||
\(458\) | −10.5966 | − | 18.3538i | −0.495146 | − | 0.857618i | ||||
\(459\) | 3.39778 | − | 5.88512i | 0.158595 | − | 0.274694i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.97457 | − | 2.29472i | −0.185114 | − | 0.106876i | 0.404579 | − | 0.914503i | \(-0.367418\pi\) |
−0.589693 | + | 0.807627i | \(0.700751\pi\) | |||||||
\(462\) | 0.968248 | + | 0.559018i | 0.0450470 | + | 0.0260079i | ||||
\(463\) | 9.20888i | 0.427973i | 0.976837 | + | 0.213986i | \(0.0686448\pi\) | ||||
−0.976837 | + | 0.213986i | \(0.931355\pi\) | |||||||
\(464\) | 4.20478 | − | 7.28290i | 0.195202 | − | 0.338100i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.9160 | − | 10.9212i | 0.876267 | − | 0.505913i | ||||
\(467\) | 0.219469 | 0.0101558 | 0.00507792 | − | 0.999987i | \(-0.498384\pi\) | ||||
0.00507792 | + | 0.999987i | \(0.498384\pi\) | |||||||
\(468\) | 3.15660 | + | 1.74238i | 0.145914 | + | 0.0805417i | ||||
\(469\) | 3.56637 | 0.164680 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.21134 | − | 3.83014i | −0.101893 | − | 0.176484i | ||||
\(472\) | 5.91189 | − | 10.2397i | 0.272117 | − | 0.471320i | ||||
\(473\) | 26.1798i | 1.20375i | ||||||||
\(474\) | 7.82731 | + | 4.51910i | 0.359520 | + | 0.207569i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 3.27792i | − | 0.150243i | ||||||
\(477\) | 2.90508 | − | 5.03175i | 0.133015 | − | 0.230388i | ||||
\(478\) | 4.11513 | + | 7.12762i | 0.188222 | + | 0.326010i | ||||
\(479\) | −5.49422 | + | 3.17209i | −0.251037 | + | 0.144936i | −0.620239 | − | 0.784413i | \(-0.712964\pi\) |
0.369202 | + | 0.929349i | \(0.379631\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.7829 | − | 19.5349i | 0.491658 | − | 0.890714i | ||||
\(482\) | −3.10243 | −0.141312 | ||||||||
\(483\) | 2.88512 | − | 1.66573i | 0.131278 | − | 0.0757932i | ||||
\(484\) | 2.81382 | + | 4.87367i | 0.127901 | + | 0.221530i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 32.2113 | + | 18.5972i | 1.45963 | + | 0.842720i | 0.998993 | − | 0.0448662i | \(-0.0142862\pi\) |
0.460641 | + | 0.887586i | \(0.347619\pi\) | |||||||
\(488\) | 8.11924 | + | 4.68764i | 0.367541 | + | 0.212200i | ||||
\(489\) | − | 11.2244i | − | 0.507584i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.99901 | + | 5.19444i | 0.135344 | + | 0.234422i | 0.925729 | − | 0.378188i | \(-0.123453\pi\) |
−0.790385 | + | 0.612610i | \(0.790120\pi\) | |||||||
\(492\) | 7.55607 | − | 4.36250i | 0.340654 | − | 0.196677i | ||||
\(493\) | −57.1477 | −2.57380 | ||||||||
\(494\) | 15.6774 | − | 9.45800i | 0.705359 | − | 0.425535i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.824903 | − | 0.476258i | 0.0370392 | − | 0.0213846i | ||||
\(497\) | −0.840699 | − | 1.45613i | −0.0377105 | − | 0.0653165i | ||||
\(498\) | −3.97443 | + | 6.88392i | −0.178099 | + | 0.308476i | ||||
\(499\) | − | 21.2908i | − | 0.953107i | −0.879145 | − | 0.476554i | \(-0.841886\pi\) | ||
0.879145 | − | 0.476554i | \(-0.158114\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.0406 | + | 7.52898i | 0.582610 | + | 0.336370i | ||||
\(502\) | − | 15.6208i | − | 0.697193i | ||||||
\(503\) | 9.52194 | − | 16.4925i | 0.424562 | − | 0.735363i | −0.571817 | − | 0.820381i | \(-0.693761\pi\) |
0.996379 | + | 0.0850178i | \(0.0270947\pi\) | |||||||
\(504\) | −0.241181 | − | 0.417738i | −0.0107431 | − | 0.0186075i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −16.0082 | −0.711653 | ||||||||
\(507\) | 12.9904 | − | 0.500000i | 0.576923 | − | 0.0222058i | ||||
\(508\) | −18.9189 | −0.839391 | ||||||||
\(509\) | −24.6679 | + | 14.2420i | −1.09339 | + | 0.631267i | −0.934476 | − | 0.356026i | \(-0.884132\pi\) |
−0.158911 | + | 0.987293i | \(0.550798\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.05840 | − | 3.56525i | 0.0910581 | − | 0.157717i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −4.39778 | − | 2.53906i | −0.194167 | − | 0.112102i | ||||
\(514\) | 3.05205 | + | 1.76210i | 0.134620 | + | 0.0777230i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.64747 | − | 9.78170i | 0.248616 | − | 0.430615i | ||||
\(517\) | 6.69541 | + | 11.5968i | 0.294464 | + | 0.510027i | ||||
\(518\) | −2.58521 | + | 1.49257i | −0.113587 | + | 0.0655797i | ||||
\(519\) | −14.7486 | −0.647391 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.6617 | −1.21188 | −0.605940 | − | 0.795511i | \(-0.707203\pi\) | ||||
−0.605940 | + | 0.795511i | \(0.707203\pi\) | |||||||
\(522\) | −7.28290 | + | 4.20478i | −0.318764 | + | 0.184038i | ||||
\(523\) | −8.44709 | − | 14.6308i | −0.369365 | − | 0.639759i | 0.620101 | − | 0.784522i | \(-0.287092\pi\) |
−0.989466 | + | 0.144762i | \(0.953758\pi\) | |||||||
\(524\) | −3.48406 | + | 6.03457i | −0.152202 | + | 0.263622i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.1637 | − | 11.6415i | −0.879177 | − | 0.507593i | ||||
\(527\) | −5.60567 | − | 3.23644i | −0.244187 | − | 0.140981i | ||||
\(528\) | 2.31784i | 0.100871i | ||||||||
\(529\) | −12.3502 | + | 21.3911i | −0.536964 | + | 0.930049i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.2397 | + | 5.91189i | −0.444365 | + | 0.256554i | ||||
\(532\) | −2.44949 | −0.106199 | ||||||||
\(533\) | 15.2023 | − | 27.5413i | 0.658485 | − | 1.19295i | ||||
\(534\) | 9.01753 | 0.390227 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.69677 | + | 6.40300i | 0.159676 | + | 0.276568i | ||||
\(537\) | −4.30589 | + | 7.45802i | −0.185813 | + | 0.321837i | ||||
\(538\) | 9.81746i | 0.423261i | ||||||||
\(539\) | 13.5841 | + | 7.84278i | 0.585108 | + | 0.337813i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 30.6639i | − | 1.31834i | −0.751993 | − | 0.659171i | \(-0.770907\pi\) | ||
0.751993 | − | 0.659171i | \(-0.229093\pi\) | |||||||
\(542\) | −10.9040 | + | 18.8862i | −0.468365 | + | 0.811233i | ||||
\(543\) | 1.42246 | + | 2.46378i | 0.0610438 | + | 0.105731i | ||||
\(544\) | 5.88512 | − | 3.39778i | 0.252323 | − | 0.145679i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.52262 | − | 0.840459i | −0.0651622 | − | 0.0359683i | ||||
\(547\) | 40.6726 | 1.73903 | 0.869517 | − | 0.493903i | \(-0.164430\pi\) | ||||
0.869517 | + | 0.493903i | \(0.164430\pi\) | |||||||
\(548\) | −17.7616 | + | 10.2547i | −0.758739 | + | 0.438058i | ||||
\(549\) | −4.68764 | − | 8.11924i | −0.200064 | − | 0.346521i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.7048i | 1.81928i | ||||||||
\(552\) | 5.98124 | + | 3.45327i | 0.254579 | + | 0.146981i | ||||
\(553\) | −3.77559 | − | 2.17984i | −0.160555 | − | 0.0926963i | ||||
\(554\) | 13.4751i | 0.572501i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.25467 | − | 7.36931i | −0.180438 | − | 0.312528i | ||||
\(557\) | −15.9822 | + | 9.22730i | −0.677186 | + | 0.390973i | −0.798794 | − | 0.601605i | \(-0.794528\pi\) |
0.121608 | + | 0.992578i | \(0.461195\pi\) | |||||||
\(558\) | −0.952516 | −0.0403232 | ||||||||
\(559\) | −0.783308 | − | 40.7169i | −0.0331304 | − | 1.72214i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.6408 | − | 7.87550i | 0.575913 | − | 0.332504i | ||||
\(562\) | −14.8083 | − | 25.6488i | −0.624652 | − | 1.08193i | ||||
\(563\) | 4.71770 | − | 8.17129i | 0.198827 | − | 0.344379i | −0.749321 | − | 0.662207i | \(-0.769620\pi\) |
0.948148 | + | 0.317828i | \(0.102953\pi\) | |||||||
\(564\) | − | 5.77729i | − | 0.243268i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.5516 | − | 6.09197i | −0.443517 | − | 0.256065i | ||||
\(567\) | 0.482362i | 0.0202573i | ||||||||
\(568\) | 1.74288 | − | 3.01876i | 0.0731297 | − | 0.126664i | ||||
\(569\) | 5.33503 | + | 9.24054i | 0.223656 | + | 0.387384i | 0.955915 | − | 0.293642i | \(-0.0948674\pi\) |
−0.732259 | + | 0.681026i | \(0.761534\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.532730 | 0.0222941 | 0.0111470 | − | 0.999938i | \(-0.496452\pi\) | ||||
0.0111470 | + | 0.999938i | \(0.496452\pi\) | |||||||
\(572\) | 4.31697 | + | 7.15573i | 0.180502 | + | 0.299196i | ||||
\(573\) | 3.43587 | 0.143536 | ||||||||
\(574\) | −3.64476 | + | 2.10430i | −0.152129 | + | 0.0878320i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 26.0683i | 1.08524i | 0.839978 | + | 0.542620i | \(0.182568\pi\) | ||||
−0.839978 | + | 0.542620i | \(0.817432\pi\) | |||||||
\(578\) | −25.2702 | − | 14.5898i | −1.05110 | − | 0.606855i | ||||
\(579\) | 2.30090 | + | 1.32843i | 0.0956223 | + | 0.0552075i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.91712 | − | 3.32054i | 0.0795354 | − | 0.137759i | ||||
\(582\) | −4.59103 | − | 7.95189i | −0.190304 | − | 0.329617i | ||||
\(583\) | 11.6628 | − | 6.73351i | 0.483023 | − | 0.278874i | ||||
\(584\) | 8.53465 | 0.353166 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.0209 | −0.620509 | ||||||||
\(587\) | 12.7739 | − | 7.37501i | 0.527235 | − | 0.304399i | −0.212655 | − | 0.977127i | \(-0.568211\pi\) |
0.739890 | + | 0.672728i | \(0.234878\pi\) | |||||||
\(588\) | −3.38366 | − | 5.86068i | −0.139540 | − | 0.241690i | ||||
\(589\) | −2.41849 | + | 4.18895i | −0.0996523 | + | 0.172603i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.2868 | − | 10.5579i | −0.752219 | − | 0.434294i | ||||
\(592\) | −5.35948 | − | 3.09429i | −0.220273 | − | 0.127175i | ||||
\(593\) | 23.4887i | 0.964566i | 0.876015 | + | 0.482283i | \(0.160192\pi\) | ||||
−0.876015 | + | 0.482283i | \(0.839808\pi\) | |||||||
\(594\) | 1.15892 | − | 2.00731i | 0.0475510 | − | 0.0823608i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.27439 | − | 3.62252i | 0.257009 | − | 0.148384i | ||||
\(597\) | 10.5388 | 0.431325 | ||||||||
\(598\) | 24.8973 | − | 0.478971i | 1.01813 | − | 0.0195866i | ||||
\(599\) | 3.72087 | 0.152031 | 0.0760154 | − | 0.997107i | \(-0.475780\pi\) | ||||
0.0760154 | + | 0.997107i | \(0.475780\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.1757 | + | 36.6773i | 0.863773 | + | 1.49610i | 0.868261 | + | 0.496109i | \(0.165238\pi\) |
−0.00448765 | + | 0.999990i | \(0.501428\pi\) | |||||||
\(602\) | −2.72412 | + | 4.71832i | −0.111027 | + | 0.192304i | ||||
\(603\) | − | 7.39355i | − | 0.301089i | ||||||
\(604\) | 6.77875 | + | 3.91372i | 0.275824 | + | 0.159247i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 10.6822i | − | 0.433933i | ||||||
\(607\) | 9.50853 | − | 16.4692i | 0.385939 | − | 0.668466i | −0.605960 | − | 0.795495i | \(-0.707211\pi\) |
0.991899 | + | 0.127029i | \(0.0405441\pi\) | |||||||
\(608\) | −2.53906 | − | 4.39778i | −0.102972 | − | 0.178353i | ||||
\(609\) | 3.51299 | − | 2.02823i | 0.142354 | − | 0.0821879i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.7602 | − | 17.8359i | −0.435312 | − | 0.721565i | ||||
\(612\) | −6.79555 | −0.274694 | ||||||||
\(613\) | 19.7672 | − | 11.4126i | 0.798390 | − | 0.460951i | −0.0445178 | − | 0.999009i | \(-0.514175\pi\) |
0.842908 | + | 0.538058i | \(0.180842\pi\) | |||||||
\(614\) | −13.9784 | − | 24.2114i | −0.564124 | − | 0.977091i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 1.11804i | − | 0.0450470i | ||||||
\(617\) | −15.0114 | − | 8.66682i | −0.604335 | − | 0.348913i | 0.166410 | − | 0.986057i | \(-0.446783\pi\) |
−0.770745 | + | 0.637144i | \(0.780116\pi\) | |||||||
\(618\) | −7.94534 | − | 4.58725i | −0.319609 | − | 0.184526i | ||||
\(619\) | 0.972021i | 0.0390688i | 0.999809 | + | 0.0195344i | \(0.00621839\pi\) | ||||
−0.999809 | + | 0.0195344i | \(0.993782\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.45327 | − | 5.98124i | −0.138575 | − | 0.240019i | ||||
\(622\) | 12.3899 | − | 7.15333i | 0.496791 | − | 0.286822i | ||||
\(623\) | −4.34971 | −0.174268 | ||||||||
\(624\) | −0.0693504 | − | 3.60488i | −0.00277624 | − | 0.144311i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.1152 | + | 6.99473i | −0.484222 | + | 0.279566i | ||||
\(627\) | −5.88512 | − | 10.1933i | −0.235029 | − | 0.407082i | ||||
\(628\) | −2.21134 | + | 3.83014i | −0.0882419 | + | 0.152839i | ||||
\(629\) | 42.0549i | 1.67684i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.53981 | + | 2.62106i | 0.180727 | + | 0.104343i | 0.587634 | − | 0.809127i | \(-0.300059\pi\) |
−0.406907 | + | 0.913470i | \(0.633393\pi\) | |||||||
\(632\) | − | 9.03820i | − | 0.359520i | ||||||
\(633\) | −5.74384 | + | 9.94863i | −0.228297 | + | 0.395422i | ||||
\(634\) | −3.64934 | − | 6.32085i | −0.144934 | − | 0.251033i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.81017 | −0.230388 | ||||||||
\(637\) | −21.3617 | − | 11.7913i | −0.846382 | − | 0.467187i | ||||
\(638\) | −19.4920 | −0.771696 | ||||||||
\(639\) | −3.01876 | + | 1.74288i | −0.119420 | + | 0.0689473i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.4075 | + | 28.4186i | −0.648057 | + | 1.12247i | 0.335529 | + | 0.942030i | \(0.391085\pi\) |
−0.983586 | + | 0.180439i | \(0.942248\pi\) | |||||||
\(642\) | − | 3.21733i | − | 0.126978i | ||||||
\(643\) | 10.0888 | + | 5.82478i | 0.397864 | + | 0.229707i | 0.685562 | − | 0.728014i | \(-0.259557\pi\) |
−0.287698 | + | 0.957721i | \(0.592890\pi\) | |||||||
\(644\) | −2.88512 | − | 1.66573i | −0.113690 | − | 0.0656388i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.2543 | + | 29.8853i | −0.678862 | + | 1.17582i | ||||
\(647\) | −11.0922 | − | 19.2123i | −0.436081 | − | 0.755314i | 0.561303 | − | 0.827611i | \(-0.310300\pi\) |
−0.997383 | + | 0.0722970i | \(0.976967\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | −27.4056 | −1.07576 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.459457 | 0.0180076 | ||||||||
\(652\) | −9.72060 | + | 5.61219i | −0.380688 | + | 0.219790i | ||||
\(653\) | 16.6764 | + | 28.8844i | 0.652598 | + | 1.13033i | 0.982490 | + | 0.186314i | \(0.0596542\pi\) |
−0.329892 | + | 0.944019i | \(0.607012\pi\) | |||||||
\(654\) | −8.53345 | + | 14.7804i | −0.333684 | + | 0.577958i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.55607 | − | 4.36250i | −0.295015 | − | 0.170327i | ||||
\(657\) | −7.39123 | − | 4.26733i | −0.288359 | − | 0.166484i | ||||
\(658\) | 2.78675i | 0.108639i | ||||||||
\(659\) | 12.2280 | − | 21.1796i | 0.476337 | − | 0.825039i | −0.523296 | − | 0.852151i | \(-0.675298\pi\) |
0.999632 | + | 0.0271118i | \(0.00863100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.8737 | − | 16.6702i | 1.12306 | − | 0.648396i | 0.180876 | − | 0.983506i | \(-0.442107\pi\) |
0.942179 | + | 0.335109i | \(0.108773\pi\) | |||||||
\(662\) | 26.3594 | 1.02449 | ||||||||
\(663\) | −20.9796 | + | 12.6567i | −0.814778 | + | 0.491547i | ||||
\(664\) | 7.94887 | 0.308476 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.09429 | + | 5.35948i | 0.119901 | + | 0.207675i | ||||
\(667\) | −29.0405 | + | 50.2997i | −1.12445 | + | 1.94761i | ||||
\(668\) | − | 15.0580i | − | 0.582610i | ||||||
\(669\) | 4.52739 | + | 2.61389i | 0.175039 | + | 0.101059i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 21.7304i | − | 0.838893i | ||||||
\(672\) | −0.241181 | + | 0.417738i | −0.00930376 | + | 0.0161146i | ||||
\(673\) | 16.9894 | + | 29.4265i | 0.654893 | + | 1.13431i | 0.981921 | + | 0.189293i | \(0.0606195\pi\) |
−0.327028 | + | 0.945015i | \(0.606047\pi\) | |||||||
\(674\) | 21.1518 | − | 12.2120i | 0.814736 | − | 0.470388i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.92820 | − | 11.0000i | −0.266469 | − | 0.423077i | ||||
\(677\) | 10.3145 | 0.396417 | 0.198208 | − | 0.980160i | \(-0.436488\pi\) | ||||
0.198208 | + | 0.980160i | \(0.436488\pi\) | |||||||
\(678\) | −1.43488 | + | 0.828427i | −0.0551062 | + | 0.0318156i | ||||
\(679\) | 2.21454 | + | 3.83569i | 0.0849861 | + | 0.147200i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.8689i | 0.416496i | ||||||||
\(682\) | −1.91199 | − | 1.10389i | −0.0732139 | − | 0.0422701i | ||||
\(683\) | −42.4682 | − | 24.5191i | −1.62500 | − | 0.938196i | −0.985554 | − | 0.169362i | \(-0.945829\pi\) |
−0.639448 | − | 0.768834i | \(-0.720837\pi\) | |||||||
\(684\) | 5.07812i | 0.194167i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.32042 | + | 5.75113i | 0.126774 | + | 0.219579i | ||||
\(687\) | 18.3538 | − | 10.5966i | 0.700242 | − | 0.404285i | ||||
\(688\) | −11.2949 | −0.430615 | ||||||||
\(689\) | −17.9374 | + | 10.8214i | −0.683361 | + | 0.412264i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.7340 | − | 17.1669i | 1.13113 | − | 0.653061i | 0.186914 | − | 0.982376i | \(-0.440151\pi\) |
0.944220 | + | 0.329315i | \(0.106818\pi\) | |||||||
\(692\) | 7.37429 | + | 12.7727i | 0.280329 | + | 0.485543i | ||||
\(693\) | −0.559018 | + | 0.968248i | −0.0212353 | + | 0.0367807i | ||||
\(694\) | − | 13.4164i | − | 0.509278i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.28290 | + | 4.20478i | 0.276058 | + | 0.159382i | ||||
\(697\) | 59.2912i | 2.24582i | ||||||||
\(698\) | 0.476000 | − | 0.824457i | 0.0180169 | − | 0.0312061i | ||||
\(699\) | 10.9212 | + | 18.9160i | 0.413076 | + | 0.715469i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.0303 | −1.20977 | −0.604885 | − | 0.796313i | \(-0.706781\pi\) | ||||
−0.604885 | + | 0.796313i | \(0.706781\pi\) | |||||||
\(702\) | −1.74238 | + | 3.15660i | −0.0657620 | + | 0.119138i | ||||
\(703\) | 31.4264 | 1.18527 | ||||||||
\(704\) | 2.00731 | − | 1.15892i | 0.0756532 | − | 0.0436784i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.22380 | + | 12.5120i | −0.271871 | + | 0.470895i | ||||
\(707\) | 5.15267i | 0.193786i | ||||||||
\(708\) | 10.2397 | + | 5.91189i | 0.384831 | + | 0.222182i | ||||
\(709\) | 27.0809 | + | 15.6352i | 1.01704 | + | 0.587190i | 0.913246 | − | 0.407408i | \(-0.133567\pi\) |
0.103797 | + | 0.994598i | \(0.466901\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.51910 | + | 7.82731i | −0.169479 | + | 0.293547i | ||||
\(712\) | −4.50877 | − | 7.80941i | −0.168973 | − | 0.292670i | ||||
\(713\) | −5.69723 | + | 3.28930i | −0.213363 | + | 0.123185i | ||||
\(714\) | 3.27792 | 0.122673 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.61177 | 0.321837 | ||||||||
\(717\) | −7.12762 | + | 4.11513i | −0.266186 | + | 0.153683i | ||||
\(718\) | 4.05646 | + | 7.02599i | 0.151386 | + | 0.262208i | ||||
\(719\) | −10.6716 | + | 18.4838i | −0.397984 | + | 0.689328i | −0.993477 | − | 0.114032i | \(-0.963623\pi\) |
0.595494 | + | 0.803360i | \(0.296957\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.83253 | + | 2.21271i | 0.142731 | + | 0.0824057i | ||||
\(722\) | 5.87794 | + | 3.39363i | 0.218754 | + | 0.126298i | ||||
\(723\) | − | 3.10243i | − | 0.115381i | ||||||
\(724\) | 1.42246 | − | 2.46378i | 0.0528655 | − | 0.0915656i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.87367 | + | 2.81382i | −0.180879 | + | 0.104430i | ||||
\(727\) | 8.80283 | 0.326479 | 0.163240 | − | 0.986586i | \(-0.447806\pi\) | ||||
0.163240 | + | 0.986586i | \(0.447806\pi\) | |||||||
\(728\) | 0.0334520 | + | 1.73886i | 0.00123981 | + | 0.0644464i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.3777 | + | 66.4721i | 1.41945 | + | 2.45856i | ||||
\(732\) | −4.68764 | + | 8.11924i | −0.173260 | + | 0.300096i | ||||
\(733\) | 7.86883i | 0.290642i | 0.989385 | + | 0.145321i | \(0.0464215\pi\) | ||||
−0.989385 | + | 0.145321i | \(0.953579\pi\) | |||||||
\(734\) | −20.7806 | − | 11.9977i | −0.767026 | − | 0.442843i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.90654i | − | 0.254579i | ||||||
\(737\) | 8.56852 | − | 14.8411i | 0.315626 | − | 0.546680i | ||||
\(738\) | 4.36250 | + | 7.55607i | 0.160586 | + | 0.278143i | ||||
\(739\) | 15.6988 | − | 9.06368i | 0.577488 | − | 0.333413i | −0.182646 | − | 0.983179i | \(-0.558466\pi\) |
0.760134 | + | 0.649766i | \(0.225133\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.45800 | + | 15.6774i | 0.347448 | + | 0.575923i | ||||
\(742\) | 2.80260 | 0.102887 | ||||||||
\(743\) | 1.19048 | − | 0.687322i | 0.0436744 | − | 0.0252154i | −0.478004 | − | 0.878358i | \(-0.658640\pi\) |
0.521678 | + | 0.853142i | \(0.325306\pi\) | |||||||
\(744\) | 0.476258 | + | 0.824903i | 0.0174605 | + | 0.0302424i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 26.8576i | − | 0.983325i | ||||||
\(747\) | −6.88392 | − | 3.97443i | −0.251870 | − | 0.145417i | ||||
\(748\) | −13.6408 | − | 7.87550i | −0.498756 | − | 0.287957i | ||||
\(749\) | 1.55192i | 0.0567059i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.0127 | − | 32.9310i | −0.693784 | − | 1.20167i | −0.970589 | − | 0.240743i | \(-0.922609\pi\) |
0.276805 | − | 0.960926i | \(-0.410724\pi\) | |||||||
\(752\) | −5.00328 | + | 2.88865i | −0.182451 | + | 0.105338i | ||||
\(753\) | 15.6208 | 0.569255 | ||||||||
\(754\) | 30.3155 | − | 0.583207i | 1.10403 | − | 0.0212391i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.417738 | − | 0.241181i | 0.0151930 | − | 0.00877167i | ||||
\(757\) | −18.4771 | − | 32.0033i | −0.671562 | − | 1.16318i | −0.977461 | − | 0.211115i | \(-0.932290\pi\) |
0.305899 | − | 0.952064i | \(-0.401043\pi\) | |||||||
\(758\) | −7.65785 | + | 13.2638i | −0.278146 | + | 0.481762i | ||||
\(759\) | − | 16.0082i | − | 0.581062i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.9967 | + | 15.0092i | 0.942380 | + | 0.544084i | 0.890706 | − | 0.454580i | \(-0.150211\pi\) |
0.0516746 | + | 0.998664i | \(0.483544\pi\) | |||||||
\(762\) | − | 18.9189i | − | 0.685360i | ||||||
\(763\) | 4.11621 | − | 7.12949i | 0.149017 | − | 0.258105i | ||||
\(764\) | −1.71794 | − | 2.97555i | −0.0621528 | − | 0.107652i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 35.2397 | 1.27326 | ||||||||
\(767\) | 42.6234 | − | 0.819984i | 1.53904 | − | 0.0296079i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −39.3038 | + | 22.6921i | −1.41733 | + | 0.818297i | −0.996064 | − | 0.0886391i | \(-0.971748\pi\) |
−0.421268 | + | 0.906936i | \(0.638415\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.76210 | + | 3.05205i | −0.0634606 | + | 0.109917i | ||||
\(772\) | − | 2.65685i | − | 0.0956223i | ||||||
\(773\) | 22.1132 | + | 12.7671i | 0.795358 | + | 0.459200i | 0.841845 | − | 0.539719i | \(-0.181469\pi\) |
−0.0464877 | + | 0.998919i | \(0.514803\pi\) | |||||||
\(774\) | 9.78170 | + | 5.64747i | 0.351596 | + | 0.202994i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.59103 | + | 7.95189i | −0.164808 | + | 0.285456i | ||||
\(777\) | −1.49257 | − | 2.58521i | −0.0535456 | − | 0.0927438i | ||||
\(778\) | −15.6704 | + | 9.04731i | −0.561811 | + | 0.324362i | ||||
\(779\) | 44.3066 | 1.58745 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.07943 | −0.289105 | ||||||||
\(782\) | −40.6459 | + | 23.4669i | −1.45349 | + | 0.839175i | ||||
\(783\) | −4.20478 | − | 7.28290i | −0.150267 | − | 0.260270i | ||||
\(784\) | −3.38366 | + | 5.86068i | −0.120845 | + | 0.209310i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.03457 | − | 3.48406i | −0.215246 | − | 0.124272i | ||||
\(787\) | −27.2796 | − | 15.7499i | −0.972413 | − | 0.561423i | −0.0724422 | − | 0.997373i | \(-0.523079\pi\) |
−0.899971 | + | 0.435949i | \(0.856413\pi\) | |||||||
\(788\) | 21.1158i | 0.752219i | ||||||||
\(789\) | 11.6415 | − | 20.1637i | 0.414448 | − | 0.717845i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.692130 | − | 0.399602i | 0.0246093 | − | 0.0142082i | ||||
\(792\) | −2.31784 | −0.0823608 | ||||||||
\(793\) | 0.650180 | + | 33.7968i | 0.0230886 | + | 1.20016i | ||||
\(794\) | −10.4512 | −0.370901 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.26941 | − | 9.12688i | −0.186769 | − | 0.323494i | ||||
\(797\) | −21.6986 | + | 37.5831i | −0.768605 | + | 1.33126i | 0.169715 | + | 0.985493i | \(0.445715\pi\) |
−0.938320 | + | 0.345769i | \(0.887618\pi\) | |||||||
\(798\) | − | 2.44949i | − | 0.0867110i | ||||||
\(799\) | 34.0001 | + | 19.6300i | 1.20284 | + | 0.694458i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.01753i | 0.318619i | ||||||||
\(802\) | −0.700423 | + | 1.21317i | −0.0247328 | + | 0.0428385i | ||||
\(803\) | −9.89097 | − | 17.1317i | −0.349045 | − | 0.604563i | ||||
\(804\) | −6.40300 | + | 3.69677i | −0.225816 | + | 0.130375i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.00671 | + | 1.65965i | 0.105907 | + | 0.0584586i | ||||
\(807\) | −9.81746 | −0.345591 | ||||||||
\(808\) | −9.25102 | + | 5.34108i | −0.325450 | + | 0.187899i | ||||
\(809\) | −16.3279 | − | 28.2807i | −0.574057 | − | 0.994296i | −0.996143 | − | 0.0877407i | \(-0.972035\pi\) |
0.422086 | − | 0.906556i | \(-0.361298\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.1669i | 1.05930i | 0.848216 | + | 0.529651i | \(0.177677\pi\) | ||||
−0.848216 | + | 0.529651i | \(0.822323\pi\) | |||||||
\(812\) | −3.51299 | − | 2.02823i | −0.123282 | − | 0.0711768i | ||||
\(813\) | −18.8862 | − | 10.9040i | −0.662369 | − | 0.382419i | ||||
\(814\) | 14.3441i | 0.502762i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.39778 | + | 5.88512i | 0.118946 | + | 0.206021i | ||||
\(817\) | 49.6726 | − | 28.6785i | 1.73782 | − | 1.00333i | ||||
\(818\) | 6.74134 | 0.235705 | ||||||||
\(819\) | 0.840459 | − | 1.52262i | 0.0293680 | − | 0.0532047i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.92648 | − | 3.99900i | 0.241736 | − | 0.139566i | −0.374238 | − | 0.927332i | \(-0.622096\pi\) |
0.615974 | + | 0.787766i | \(0.288763\pi\) | |||||||
\(822\) | −10.2547 | − | 17.7616i | −0.357673 | − | 0.619507i | ||||
\(823\) | 20.5022 | − | 35.5109i | 0.714663 | − | 1.23783i | −0.248426 | − | 0.968651i | \(-0.579913\pi\) |
0.963089 | − | 0.269182i | \(-0.0867534\pi\) | |||||||
\(824\) | 9.17449i | 0.319609i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.93924 | − | 2.85167i | −0.171858 | − | 0.0992223i | ||||
\(827\) | − | 32.0321i | − | 1.11386i | −0.830558 | − | 0.556932i | \(-0.811978\pi\) | ||
0.830558 | − | 0.556932i | \(-0.188022\pi\) | |||||||
\(828\) | −3.45327 | + | 5.98124i | −0.120009 | + | 0.207863i | ||||
\(829\) | −9.75006 | − | 16.8876i | −0.338634 | − | 0.586531i | 0.645542 | − | 0.763725i | \(-0.276631\pi\) |
−0.984176 | + | 0.177194i | \(0.943298\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.4751 | −0.467445 | ||||||||
\(832\) | −3.08725 | + | 1.86250i | −0.107031 | + | 0.0645706i | ||||
\(833\) | 45.9877 | 1.59338 | ||||||||
\(834\) | 7.36931 | − | 4.25467i | 0.255178 | − | 0.147327i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.88512 | + | 10.1933i | −0.203541 | + | 0.352544i | ||||
\(837\) | − | 0.952516i | − | 0.0329238i | ||||||
\(838\) | −31.6166 | − | 18.2539i | −1.09218 | − | 0.630569i | ||||
\(839\) | −7.55900 | − | 4.36419i | −0.260966 | − | 0.150669i | 0.363809 | − | 0.931473i | \(-0.381476\pi\) |
−0.624775 | + | 0.780805i | \(0.714809\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.8604 | + | 36.1313i | −0.719325 | + | 1.24591i | ||||
\(842\) | −20.4245 | − | 35.3763i | −0.703875 | − | 1.21915i | ||||
\(843\) | 25.6488 | − | 14.8083i | 0.883392 | − | 0.510026i | ||||
\(844\) | 11.4877 | 0.395422 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.77729 | 0.198627 | ||||||||
\(847\) | 2.35087 | − | 1.35728i | 0.0807770 | − | 0.0466366i | ||||
\(848\) | 2.90508 | + | 5.03175i | 0.0997610 | + | 0.172791i | ||||
\(849\) | 6.09197 | − | 10.5516i | 0.209076 | − | 0.362130i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.0154 | + | 21.3709i | 1.26887 | + | 0.732584i | ||||
\(852\) | 3.01876 | + | 1.74288i | 0.103421 | + | 0.0597101i | ||||
\(853\) | − | 25.1210i | − | 0.860125i | −0.902799 | − | 0.430063i | \(-0.858491\pi\) | ||
0.902799 | − | 0.430063i | \(-0.141509\pi\) | |||||||
\(854\) | 2.26114 | − | 3.91641i | 0.0773747 | − | 0.134017i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.78629 | + | 1.60867i | −0.0952335 | + | 0.0549831i | ||||
\(857\) | −48.1300 | −1.64409 | −0.822045 | − | 0.569423i | \(-0.807167\pi\) | ||||
−0.822045 | + | 0.569423i | \(0.807167\pi\) | |||||||
\(858\) | −7.15573 | + | 4.31697i | −0.244293 | + | 0.147379i | ||||
\(859\) | −47.1707 | −1.60944 | −0.804721 | − | 0.593653i | \(-0.797685\pi\) | ||||
−0.804721 | + | 0.593653i | \(0.797685\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.10430 | − | 3.64476i | −0.0717145 | − | 0.124213i | ||||
\(862\) | −9.18824 | + | 15.9145i | −0.312953 | + | 0.542050i | ||||
\(863\) | − | 26.6095i | − | 0.905799i | −0.891562 | − | 0.452900i | \(-0.850390\pi\) | ||
0.891562 | − | 0.452900i | \(-0.149610\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 1.39819i | − | 0.0475125i | ||||||
\(867\) | 14.5898 | − | 25.2702i | 0.495495 | − | 0.858223i | ||||
\(868\) | −0.229729 | − | 0.397902i | −0.00779750 | − | 0.0135057i | ||||
\(869\) | −18.1424 | + | 10.4745i | −0.615440 | + | 0.355324i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.8824 | + | 23.3385i | −0.436503 | + | 0.790793i | ||||
\(872\) | 17.0669 | 0.577958 | ||||||||
\(873\) | 7.95189 | − | 4.59103i | 0.269131 | − | 0.155383i | ||||
\(874\) | 17.5361 | + | 30.3734i | 0.593168 | + | 1.02740i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.53465i | 0.288359i | ||||||||
\(877\) | 5.80548 | + | 3.35180i | 0.196037 | + | 0.113182i | 0.594806 | − | 0.803870i | \(-0.297229\pi\) |
−0.398769 | + | 0.917052i | \(0.630562\pi\) | |||||||
\(878\) | −13.2621 | − | 7.65685i | −0.447573 | − | 0.258406i | ||||
\(879\) | − | 15.0209i | − | 0.506643i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.09215 | − | 8.81986i | −0.171559 | − | 0.297149i | 0.767406 | − | 0.641161i | \(-0.221547\pi\) |
−0.938965 | + | 0.344013i | \(0.888214\pi\) | |||||||
\(882\) | 5.86068 | − | 3.38366i | 0.197339 | − | 0.113934i | ||||
\(883\) | 45.3554 | 1.52633 | 0.763165 | − | 0.646204i | \(-0.223644\pi\) | ||||
0.763165 | + | 0.646204i | \(0.223644\pi\) | |||||||
\(884\) | 21.4508 | + | 11.8405i | 0.721469 | + | 0.398238i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.7320 | − | 16.5884i | 0.965272 | − | 0.557300i | ||||
\(887\) | −17.1908 | − | 29.7753i | −0.577210 | − | 0.999757i | −0.995798 | − | 0.0915805i | \(-0.970808\pi\) |
0.418588 | − | 0.908176i | \(-0.362525\pi\) | |||||||
\(888\) | 3.09429 | − | 5.35948i | 0.103838 | − | 0.179852i | ||||
\(889\) | 9.12576i | 0.306068i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00731 | + | 1.15892i | 0.0672473 | + | 0.0388252i | ||||
\(892\) | − | 5.22778i | − | 0.175039i | ||||||
\(893\) | 14.6689 | − | 25.4073i | 0.490876 | − | 0.850221i | ||||
\(894\) | 3.62252 | + | 6.27439i | 0.121155 | + | 0.209847i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.482362 | 0.0161146 | ||||||||
\(897\) | 0.478971 | + | 24.8973i | 0.0159924 | + | 0.831296i | ||||
\(898\) | 15.4047 | 0.514061 | ||||||||
\(899\) | −6.93708 | + | 4.00512i | −0.231365 | + | 0.133578i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.7417 | − | 34.1935i | 0.657690 | − | 1.13915i | ||||
\(902\) | 20.2231i | 0.673357i | ||||||||
\(903\) | −4.71832 | − | 2.72412i | −0.157016 | − | 0.0906531i | ||||
\(904\) | 1.43488 | + | 0.828427i | 0.0477233 | + | 0.0275531i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.91372 | + | 6.77875i | −0.130024 | + | 0.225209i | ||||
\(907\) | −16.9804 | − | 29.4110i | −0.563826 | − | 0.976575i | −0.997158 | − | 0.0753408i | \(-0.975996\pi\) |
0.433332 | − | 0.901234i | \(-0.357338\pi\) | |||||||
\(908\) | 9.41271 | − | 5.43443i | 0.312372 | − | 0.180348i | ||||
\(909\) | 10.6822 | 0.354305 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.0487 | 1.16121 | 0.580607 | − | 0.814184i | \(-0.302815\pi\) | ||||
0.580607 | + | 0.814184i | \(0.302815\pi\) | |||||||
\(912\) | 4.39778 | − | 2.53906i | 0.145625 | − | 0.0840766i | ||||
\(913\) | −9.21209 | − | 15.9558i | −0.304876 | − | 0.528060i | ||||
\(914\) | −3.73097 | + | 6.46224i | −0.123410 | + | 0.213752i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.3538 | − | 10.5966i | −0.606428 | − | 0.350121i | ||||
\(917\) | 2.91085 | + | 1.68058i | 0.0961247 | + | 0.0554976i | ||||
\(918\) | − | 6.79555i | − | 0.224287i | ||||||
\(919\) | 8.74038 | − | 15.1388i | 0.288319 | − | 0.499383i | −0.685090 | − | 0.728459i | \(-0.740237\pi\) |
0.973409 | + | 0.229076i | \(0.0735704\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.2114 | − | 13.9784i | 0.797791 | − | 0.460605i | ||||
\(922\) | −4.58943 | −0.151145 | ||||||||
\(923\) | 12.5658 | − | 0.241739i | 0.413607 | − | 0.00795693i | ||||
\(924\) | 1.11804 | 0.0367807 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.60444 | + | 7.97512i | 0.151311 | + | 0.262079i | ||||
\(927\) | 4.58725 | − | 7.94534i | 0.150665 | − | 0.260959i | ||||
\(928\) | − | 8.40957i | − | 0.276058i | ||||||
\(929\) | 6.74907 | + | 3.89658i | 0.221430 | + | 0.127842i | 0.606612 | − | 0.794998i | \(-0.292528\pi\) |
−0.385182 | + | 0.922840i | \(0.625861\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 34.3653i | − | 1.12628i | ||||||
\(932\) | 10.9212 | − | 18.9160i | 0.357734 | − | 0.619614i | ||||
\(933\) | 7.15333 | + | 12.3899i | 0.234190 | + | 0.405628i | ||||
\(934\) | 0.190066 | − | 0.109735i | 0.00621915 | − | 0.00359063i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.60488 | − | 0.0693504i | 0.117829 | − | 0.00226679i | ||||
\(937\) | −39.5690 | −1.29266 | −0.646331 | − | 0.763057i | \(-0.723697\pi\) | ||||
−0.646331 | + | 0.763057i | \(0.723697\pi\) | |||||||
\(938\) | 3.08856 | − | 1.78318i | 0.100845 | − | 0.0582230i | ||||
\(939\) | −6.99473 | − | 12.1152i | −0.228265 | − | 0.395366i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 23.6107i | − | 0.769687i | −0.922982 | − | 0.384844i | \(-0.874255\pi\) | ||
0.922982 | − | 0.384844i | \(-0.125745\pi\) | |||||||
\(942\) | −3.83014 | − | 2.21134i | −0.124793 | − | 0.0720492i | ||||
\(943\) | 52.1864 | + | 30.1298i | 1.69942 | + | 0.981161i | ||||
\(944\) | − | 11.8238i | − | 0.384831i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.0899 | + | 22.6724i | 0.425590 | + | 0.737143i | ||||
\(947\) | 16.6283 | − | 9.60036i | 0.540348 | − | 0.311970i | −0.204872 | − | 0.978789i | \(-0.565678\pi\) |
0.745220 | + | 0.666819i | \(0.232345\pi\) | |||||||
\(948\) | 9.03820 | 0.293547 | ||||||||
\(949\) | 15.8958 | + | 26.3486i | 0.516000 | + | 0.855311i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.32085 | − | 3.64934i | 0.204967 | − | 0.118338i | ||||
\(952\) | −1.63896 | − | 2.83876i | −0.0531189 | − | 0.0920047i | ||||
\(953\) | 0.303161 | − | 0.525090i | 0.00982035 | − | 0.0170093i | −0.861073 | − | 0.508481i | \(-0.830207\pi\) |
0.870894 | + | 0.491471i | \(0.163541\pi\) | |||||||
\(954\) | − | 5.81017i | − | 0.188111i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.12762 | + | 4.11513i | 0.230524 | + | 0.133093i | ||||
\(957\) | − | 19.4920i | − | 0.630087i | ||||||
\(958\) | −3.17209 | + | 5.49422i | −0.102486 | + | 0.177510i | ||||
\(959\) | 4.94646 | + | 8.56753i | 0.159730 | + | 0.276660i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.0927 | 0.970733 | ||||||||
\(962\) | −0.429181 | − | 22.3091i | −0.0138373 | − | 0.719276i | ||||
\(963\) | 3.21733 | 0.103677 | ||||||||
\(964\) | −2.68678 | + | 1.55121i | −0.0865354 | + | 0.0499613i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.66573 | − | 2.88512i | 0.0535939 | − | 0.0928273i | ||||
\(967\) | 1.49478i | 0.0480690i | 0.999711 | + | 0.0240345i | \(0.00765115\pi\) | ||||
−0.999711 | + | 0.0240345i | \(0.992349\pi\) | |||||||
\(968\) | 4.87367 | + | 2.81382i | 0.156646 | + | 0.0904394i | ||||
\(969\) | −29.8853 | − | 17.2543i | −0.960055 | − | 0.554288i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.72859 | + | 2.99401i | −0.0554731 | + | 0.0960823i | −0.892428 | − | 0.451189i | \(-0.851000\pi\) |
0.836955 | + | 0.547271i | \(0.184333\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | −3.55467 | + | 2.05229i | −0.113958 | + | 0.0657935i | ||||
\(974\) | 37.1944 | 1.19179 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.37529 | 0.300096 | ||||||||
\(977\) | −41.2109 | + | 23.7932i | −1.31845 | + | 0.761210i | −0.983480 | − | 0.181017i | \(-0.942061\pi\) |
−0.334975 | + | 0.942227i | \(0.608728\pi\) | |||||||
\(978\) | −5.61219 | − | 9.72060i | −0.179458 | − | 0.310830i | ||||
\(979\) | −10.4506 | + | 18.1009i | −0.334002 | + | 0.578509i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.7804 | − | 8.53345i | −0.471901 | − | 0.272452i | ||||
\(982\) | 5.19444 | + | 2.99901i | 0.165761 | + | 0.0957024i | ||||
\(983\) | 27.8101i | 0.887003i | 0.896274 | + | 0.443502i | \(0.146264\pi\) | ||||
−0.896274 | + | 0.443502i | \(0.853736\pi\) | |||||||
\(984\) | 4.36250 | − | 7.55607i | 0.139071 | − | 0.240879i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −49.4914 | + | 28.5738i | −1.57613 | + | 0.909977i | ||||
\(987\) | −2.78675 | −0.0887031 | ||||||||
\(988\) | 8.84802 | − | 16.0296i | 0.281493 | − | 0.509968i | ||||
\(989\) | 78.0089 | 2.48054 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.0369 | − | 41.6331i | −0.763557 | − | 1.32252i | −0.941006 | − | 0.338390i | \(-0.890118\pi\) |
0.177449 | − | 0.984130i | \(-0.443216\pi\) | |||||||
\(992\) | 0.476258 | − | 0.824903i | 0.0151212 | − | 0.0261907i | ||||
\(993\) | 26.3594i | 0.836491i | ||||||||
\(994\) | −1.45613 | − | 0.840699i | −0.0461858 | − | 0.0266654i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.94887i | 0.251870i | ||||||||
\(997\) | −8.40884 | + | 14.5645i | −0.266311 | + | 0.461264i | −0.967906 | − | 0.251312i | \(-0.919138\pi\) |
0.701596 | + | 0.712575i | \(0.252471\pi\) | |||||||
\(998\) | −10.6454 | − | 18.4384i | −0.336974 | − | 0.583657i | ||||
\(999\) | −5.35948 | + | 3.09429i | −0.169566 | + | 0.0978991i |
(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 | 1950.2.bc.f.751.4 | yes | 8 | |
5.2 | odd | 4 | 1950.2.y.l.49.3 | 8 | |||
5.3 | odd | 4 | 1950.2.y.i.49.2 | 8 | |||
5.4 | even | 2 | 1950.2.bc.e.751.1 | ✓ | 8 | ||
13.4 | even | 6 | inner | 1950.2.bc.f.901.4 | yes | 8 | |
65.4 | even | 6 | 1950.2.bc.e.901.1 | yes | 8 | ||
65.17 | odd | 12 | 1950.2.y.i.199.2 | 8 | |||
65.43 | odd | 12 | 1950.2.y.l.199.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.y.i.49.2 | 8 | 5.3 | odd | 4 | |||
1950.2.y.i.199.2 | 8 | 65.17 | odd | 12 | |||
1950.2.y.l.49.3 | 8 | 5.2 | odd | 4 | |||
1950.2.y.l.199.3 | 8 | 65.43 | odd | 12 | |||
1950.2.bc.e.751.1 | ✓ | 8 | 5.4 | even | 2 | ||
1950.2.bc.e.901.1 | yes | 8 | 65.4 | even | 6 | ||
1950.2.bc.f.751.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1950.2.bc.f.901.4 | yes | 8 | 13.4 | even | 6 | inner |