Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(31,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.s (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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 18 x^{10} - 18 x^{9} + 11 x^{8} - 36 x^{7} + 180 x^{6} - 120 x^{5} + 31 x^{4} + 18 x^{3} + 162 x^{2} - 54 x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(0.836844 + 0.836844i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.31 |
Dual form | 1216.2.s.g.863.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | −1.96854 | + | 1.13654i | −1.13654 | + | 0.656180i | −0.945571 | − | 0.325417i | \(-0.894495\pi\) |
−0.190966 | + | 0.981597i | \(0.561162\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.50000 | + | 0.866025i | −0.670820 | + | 0.387298i | −0.796387 | − | 0.604787i | \(-0.793258\pi\) |
0.125567 | + | 0.992085i | \(0.459925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.00000i | − | 0.755929i | −0.925820 | − | 0.377964i | \(-0.876624\pi\) | ||
0.925820 | − | 0.377964i | \(-0.123376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.08343 | − | 1.87656i | 0.361143 | − | 0.625519i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.85650 | + | 4.94761i | −0.792251 | + | 1.37222i | 0.132319 | + | 0.991207i | \(0.457758\pi\) |
−0.924570 | + | 0.381012i | \(0.875576\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.96854 | − | 3.40961i | 0.508275 | − | 0.880357i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.583430 | − | 1.01053i | −0.141503 | − | 0.245090i | 0.786560 | − | 0.617514i | \(-0.211860\pi\) |
−0.928063 | + | 0.372424i | \(0.878527\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.144505 | − | 4.35650i | 0.0331518 | − | 0.999450i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.27307 | + | 3.93708i | 0.496025 | + | 0.859141i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.31807 | − | 2.49304i | −0.900380 | − | 0.519835i | −0.0230566 | − | 0.999734i | \(-0.507340\pi\) |
−0.877323 | + | 0.479900i | \(0.840673\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.89379i | − | 0.364460i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.583430 | − | 1.01053i | 0.108340 | − | 0.187651i | −0.806758 | − | 0.590882i | \(-0.798780\pi\) |
0.915098 | + | 0.403232i | \(0.132113\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.289010 | −0.0519078 | −0.0259539 | − | 0.999663i | \(-0.508262\pi\) | ||||
−0.0259539 | + | 0.999663i | \(0.508262\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.73205 | + | 3.00000i | 0.292770 | + | 0.507093i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.71301 | 0.446015 | 0.223008 | − | 0.974817i | \(-0.428412\pi\) | ||||
0.223008 | + | 0.974817i | \(0.428412\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 12.9861i | − | 2.07944i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.56951 | − | 4.94761i | 1.33833 | − | 0.772687i | 0.351772 | − | 0.936086i | \(-0.385579\pi\) |
0.986560 | + | 0.163399i | \(0.0522458\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.380993 | − | 0.659900i | −0.0581009 | − | 0.100634i | 0.835512 | − | 0.549472i | \(-0.185171\pi\) |
−0.893613 | + | 0.448838i | \(0.851838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.75311i | 0.559481i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.90562 | + | 3.40961i | 0.861423 | + | 0.497343i | 0.864488 | − | 0.502653i | \(-0.167643\pi\) |
−0.00306575 | + | 0.999995i | \(0.500976\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.29701 | + | 1.32618i | 0.321646 | + | 0.185702i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.333140 | + | 0.577015i | −0.0457603 | + | 0.0792591i | −0.887998 | − | 0.459847i | \(-0.847904\pi\) |
0.842238 | + | 0.539106i | \(0.181238\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.66686 | + | 8.74018i | 0.618141 | + | 1.15767i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.51422 | − | 5.49304i | 1.23865 | − | 0.715133i | 0.269829 | − | 0.962908i | \(-0.413033\pi\) |
0.968817 | + | 0.247775i | \(0.0796995\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.31922 | − | 3.07105i | −0.681056 | − | 0.393208i | 0.119197 | − | 0.992871i | \(-0.461968\pi\) |
−0.800253 | + | 0.599663i | \(0.795301\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.75311 | − | 2.16686i | −0.472848 | − | 0.272999i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 9.89522i | − | 1.22735i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.18575 | + | 5.30340i | 1.12222 | + | 0.647913i | 0.941966 | − | 0.335707i | \(-0.108975\pi\) |
0.180252 | + | 0.983620i | \(0.442309\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.3337 | 1.36442 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.57715 | − | 9.65990i | −0.661885 | − | 1.14642i | −0.980120 | − | 0.198407i | \(-0.936423\pi\) |
0.318234 | − | 0.948012i | \(-0.396910\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.50000 | + | 4.33013i | 0.292603 | + | 0.506803i | 0.974424 | − | 0.224716i | \(-0.0721453\pi\) |
−0.681822 | + | 0.731519i | \(0.738812\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 4.54615i | − | 0.524944i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.84509 | + | 6.65990i | 0.432607 | + | 0.749297i | 0.997097 | − | 0.0761427i | \(-0.0242604\pi\) |
−0.564490 | + | 0.825440i | \(0.690927\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.40265 | + | 9.35766i | 0.600294 | + | 1.03974i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.289010 | −0.0317230 | −0.0158615 | − | 0.999874i | \(-0.505049\pi\) | ||||
−0.0158615 | + | 0.999874i | \(0.505049\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.75029 | + | 1.01053i | 0.189846 | + | 0.109607i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.65236i | 0.284363i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.0689 | + | 8.12270i | 1.49130 | + | 0.861004i | 0.999950 | − | 0.00995611i | \(-0.00316918\pi\) |
0.491353 | + | 0.870961i | \(0.336503\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.89522 | + | 5.71301i | 1.03730 | + | 0.598886i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.568928 | − | 0.328471i | 0.0589951 | − | 0.0340608i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.55608 | + | 6.65990i | 0.364847 | + | 0.683291i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.56951 | − | 4.94761i | 0.870102 | − | 0.502354i | 0.00271974 | − | 0.999996i | \(-0.499134\pi\) |
0.867382 | + | 0.497643i | \(0.165801\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.75029 | + | 4.47463i | 0.771183 | + | 0.445243i | 0.833296 | − | 0.552827i | \(-0.186451\pi\) |
−0.0621136 | + | 0.998069i | \(0.519784\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.41005 | −0.434536 | −0.217268 | − | 0.976112i | \(-0.569714\pi\) | ||||
−0.217268 | + | 0.976112i | \(0.569714\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.81922 | − | 3.93708i | −0.665488 | − | 0.384219i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.33372i | 0.225609i | 0.993617 | + | 0.112805i | \(0.0359834\pi\) | ||||
−0.993617 | + | 0.112805i | \(0.964017\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.96272 | − | 17.2559i | −0.954255 | − | 1.65282i | −0.736064 | − | 0.676912i | \(-0.763318\pi\) |
−0.218191 | − | 0.975906i | \(-0.570016\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.34066 | + | 3.08343i | −0.506913 | + | 0.292666i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.5732i | − | 1.18279i | −0.806382 | − | 0.591395i | \(-0.798578\pi\) | ||
0.806382 | − | 0.591395i | \(-0.201422\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.63614 | 0.805324 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.18964 | + | 10.7208i | 0.572233 | + | 0.991136i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.02106 | + | 1.16686i | −0.185270 | + | 0.106966i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.2463 | + | 19.4791i | −1.01404 | + | 1.75637i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.1244i | − | 1.08444i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.31807 | − | 7.47912i | 0.383167 | − | 0.663664i | −0.608346 | − | 0.793672i | \(-0.708167\pi\) |
0.991513 | + | 0.130007i | \(0.0415001\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.50000 | + | 0.866025i | 0.132068 | + | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.19463 | − | 10.7294i | −0.541227 | − | 0.937433i | −0.998834 | − | 0.0482781i | \(-0.984627\pi\) |
0.457607 | − | 0.889155i | \(-0.348707\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.71301 | − | 0.289010i | −0.755513 | − | 0.0250604i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.64007 | + | 2.84068i | 0.141155 | + | 0.244487i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.41657 | − | 9.38177i | 0.462769 | − | 0.801539i | −0.536329 | − | 0.844009i | \(-0.680189\pi\) |
0.999098 | + | 0.0424700i | \(0.0135227\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0919828 | − | 0.159319i | 0.00780188 | − | 0.0135133i | −0.862098 | − | 0.506741i | \(-0.830850\pi\) |
0.869900 | + | 0.493228i | \(0.164183\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.5006 | −1.30538 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.02106i | 0.167840i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.90562 | + | 3.40961i | −0.487087 | + | 0.281220i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.75029 | − | 4.47463i | 0.634929 | − | 0.366576i | −0.147730 | − | 0.989028i | \(-0.547197\pi\) |
0.782658 | + | 0.622452i | \(0.213863\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.2665 | −1.48650 | −0.743252 | − | 0.669012i | \(-0.766718\pi\) | ||||
−0.743252 | + | 0.669012i | \(0.766718\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.52842 | −0.204411 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.433516 | − | 0.250290i | 0.0348208 | − | 0.0201038i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.81980 | + | 3.36006i | −0.464471 | + | 0.268162i | −0.713922 | − | 0.700225i | \(-0.753083\pi\) |
0.249452 | + | 0.968387i | \(0.419750\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 1.51450i | − | 0.120108i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.98608 | + | 8.63614i | −0.392958 | + | 0.680623i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.3383 | −0.888081 | −0.444040 | − | 0.896007i | \(-0.646455\pi\) | ||||
−0.444040 | + | 0.896007i | \(0.646455\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.96854 | − | 3.40961i | 0.152330 | − | 0.263843i | −0.779754 | − | 0.626087i | \(-0.784656\pi\) |
0.932084 | + | 0.362243i | \(0.117989\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.81922 | − | 17.0074i | −0.755325 | − | 1.30826i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.01866 | − | 4.99114i | −0.613202 | − | 0.381682i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.50000 | + | 2.59808i | 0.114043 | + | 0.197528i | 0.917397 | − | 0.397974i | \(-0.130287\pi\) |
−0.803354 | + | 0.595502i | \(0.796953\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.46410 | + | 2.00000i | 0.261861 | + | 0.151186i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.4861 | + | 21.6265i | −0.938511 | + | 1.62555i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 25.6384i | − | 1.91631i | −0.286255 | − | 0.958153i | \(-0.592411\pi\) | ||
0.286255 | − | 0.958153i | \(-0.407589\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.21301 | − | 7.29714i | 0.313150 | − | 0.542392i | −0.665892 | − | 0.746048i | \(-0.731949\pi\) |
0.979043 | + | 0.203656i | \(0.0652823\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.9615 | 1.03206 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.06951 | + | 2.34953i | −0.299196 | + | 0.172741i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.78757 | −0.275506 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 17.3047i | − | 1.25213i | −0.779773 | − | 0.626063i | \(-0.784665\pi\) | ||
0.779773 | − | 0.626063i | \(-0.215335\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.1384 | + | 7.00813i | −0.873744 | + | 0.504456i | −0.868591 | − | 0.495530i | \(-0.834974\pi\) |
−0.00515328 | + | 0.999987i | \(0.501640\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.2463 | + | 19.4791i | 0.805362 | + | 1.39493i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.17509i | 0.226216i | 0.993583 | + | 0.113108i | \(0.0360806\pi\) | ||||
−0.993583 | + | 0.113108i | \(0.963919\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.4489 | + | 11.2288i | 1.37870 | + | 0.795991i | 0.992003 | − | 0.126218i | \(-0.0402838\pi\) |
0.386693 | + | 0.922208i | \(0.373617\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −24.1100 | −1.70059 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.02106 | − | 1.16686i | −0.141851 | − | 0.0818975i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.56951 | + | 14.8428i | −0.598520 | + | 1.03667i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.35666 | + | 5.40207i | −0.650333 | + | 0.375470i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.40853 | + | 3.12262i | −0.372338 | + | 0.214970i | −0.674480 | − | 0.738294i | \(-0.735632\pi\) |
0.302141 | + | 0.953263i | \(0.402299\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.9577 | + | 12.6773i | 1.50451 | + | 0.868631i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.14298 | + | 0.659900i | 0.0779506 | + | 0.0450048i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.578021i | 0.0392386i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.84269 | − | 5.68268i | −0.665108 | − | 0.384000i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.66628 | 0.448422 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.65873 | + | 16.7294i | 0.646796 | + | 1.12028i | 0.983884 | + | 0.178811i | \(0.0572249\pi\) |
−0.337087 | + | 0.941473i | \(0.609442\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.16686 | + | 3.75311i | 0.144457 | + | 0.250207i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 9.66628i | − | 0.641574i | −0.947151 | − | 0.320787i | \(-0.896053\pi\) | ||
0.947151 | − | 0.320787i | \(-0.103947\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.9234i | 1.25049i | 0.780427 | + | 0.625247i | \(0.215002\pi\) | ||||
−0.780427 | + | 0.625247i | \(0.784998\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.56951 | − | 14.8428i | −0.561407 | − | 0.972386i | −0.997374 | − | 0.0724230i | \(-0.976927\pi\) |
0.435967 | − | 0.899963i | \(-0.356407\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.8112 | −0.770480 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.1384 | − | 8.74018i | −0.983347 | − | 0.567736i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.4727i | 1.45364i | 0.686828 | + | 0.726820i | \(0.259003\pi\) | ||||
−0.686828 | + | 0.726820i | \(0.740997\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.3887 | + | 10.6167i | 1.18452 | + | 0.683884i | 0.957056 | − | 0.289902i | \(-0.0936227\pi\) |
0.227466 | + | 0.973786i | \(0.426956\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.3504 | − | 9.43993i | −1.04888 | − | 0.605572i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.50000 | + | 2.59808i | −0.287494 | + | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.1415 | + | 13.1593i | 1.34520 | + | 0.837307i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.568928 | − | 0.328471i | 0.0360544 | − | 0.0208160i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.58602 | − | 4.47912i | 0.163228 | − | 0.282719i | −0.772797 | − | 0.634654i | \(-0.781143\pi\) |
0.936025 | + | 0.351934i | \(0.114476\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.59402 | −0.287689 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.3192 | − | 11.7313i | −1.26748 | − | 0.731779i | −0.292968 | − | 0.956122i | \(-0.594643\pi\) |
−0.974510 | + | 0.224343i | \(0.927976\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 5.42601i | − | 0.337156i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.26421 | − | 2.18968i | −0.0782527 | − | 0.135538i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.2979 | + | 9.40961i | −1.00497 | + | 0.580221i | −0.909716 | − | 0.415231i | \(-0.863701\pi\) |
−0.0952570 | + | 0.995453i | \(0.530367\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.15403i | − | 0.0708915i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −36.9270 | −2.25989 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.56951 | − | 9.64667i | −0.339579 | − | 0.588168i | 0.644775 | − | 0.764373i | \(-0.276951\pi\) |
−0.984354 | + | 0.176205i | \(0.943618\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.50470 | − | 4.91019i | 0.516624 | − | 0.298273i | −0.218929 | − | 0.975741i | \(-0.570256\pi\) |
0.735552 | + | 0.677468i | \(0.236923\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −25.9722 | −1.57191 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 30.8397i | − | 1.85298i | −0.376323 | − | 0.926488i | \(-0.622812\pi\) | ||
0.376323 | − | 0.926488i | \(-0.377188\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.313123 | + | 0.542344i | −0.0187462 | + | 0.0324693i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.13844 | + | 5.27608i | 0.545153 | + | 0.314744i | 0.747165 | − | 0.664639i | \(-0.231415\pi\) |
−0.202011 | + | 0.979383i | \(0.564748\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.92668 | + | 13.7294i | 0.471192 | + | 0.816129i | 0.999457 | − | 0.0329510i | \(-0.0104905\pi\) |
−0.528265 | + | 0.849080i | \(0.677157\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.5695 | − | 9.06865i | −0.863023 | − | 0.537181i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.89522 | − | 17.1390i | −0.584096 | − | 1.01168i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.81922 | − | 13.5433i | 0.459954 | − | 0.796664i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.2463 | + | 19.4791i | −0.659268 | + | 1.14189i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.1112 | 1.40859 | 0.704295 | − | 0.709907i | \(-0.251263\pi\) | ||||
0.704295 | + | 0.709907i | \(0.251263\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.51422 | + | 16.4791i | −0.553939 | + | 0.959451i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 24.6692 | − | 14.2427i | 1.42665 | − | 0.823679i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.31980 | + | 0.761986i | −0.0760720 | + | 0.0439202i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −20.3423 | −1.16864 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.6384 | 0.609155 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.2285 | + | 9.94689i | −0.983284 | + | 0.567699i | −0.903260 | − | 0.429094i | \(-0.858833\pi\) |
−0.0800239 | + | 0.996793i | \(0.525500\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.68136 | − | 5.01219i | 0.493865 | − | 0.285133i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.4727i | 0.593855i | 0.954900 | + | 0.296927i | \(0.0959619\pi\) | ||||
−0.954900 | + | 0.296927i | \(0.904038\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.3887 | + | 28.3861i | −0.926346 | + | 1.60448i | −0.136963 | + | 0.990576i | \(0.543734\pi\) |
−0.789383 | + | 0.613902i | \(0.789599\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.50622 | 0.422928 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.40265 | + | 2.42946i | −0.0787806 | + | 0.136452i | −0.902724 | − | 0.430220i | \(-0.858436\pi\) |
0.823943 | + | 0.566672i | \(0.191769\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.65236 | − | 4.59402i | −0.148040 | − | 0.256413i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.48669 | + | 2.39569i | −0.249646 | + | 0.133300i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.71301 | − | 9.89522i | −0.316901 | − | 0.548888i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 39.2240 | + | 22.6460i | 2.16909 | + | 1.25233i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.81922 | − | 11.8112i | 0.375956 | − | 0.651174i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 22.4249i | − | 1.23258i | −0.787519 | − | 0.616291i | \(-0.788635\pi\) | ||
0.787519 | − | 0.616291i | \(-0.211365\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.93935 | − | 5.09111i | 0.161076 | − | 0.278991i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.3715 | −1.00374 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.0689 | + | 6.39065i | −0.602963 | + | 0.348121i | −0.770206 | − | 0.637795i | \(-0.779847\pi\) |
0.167243 | + | 0.985916i | \(0.446513\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.2899 | + | 24.7509i | 0.776122 | + | 1.34428i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.0000i | − | 1.07990i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17.0006 | + | 9.81529i | −0.915280 | + | 0.528437i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.7104 | + | 25.4791i | 0.789694 | + | 1.36779i | 0.926154 | + | 0.377145i | \(0.123094\pi\) |
−0.136460 | + | 0.990646i | \(0.543572\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 19.5014i | − | 1.04389i | −0.852980 | − | 0.521944i | \(-0.825207\pi\) | ||
0.852980 | − | 0.521944i | \(-0.174793\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.36972 | + | 5.40961i | 0.500119 | + | 0.288744i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.83314 | 0.416916 | 0.208458 | − | 0.978031i | \(-0.433156\pi\) | ||||
0.208458 | + | 0.978031i | \(0.433156\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.7314 | + | 9.65990i | 0.888012 | + | 0.512694i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.65236 | − | 4.59402i | 0.140378 | − | 0.243141i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.9972 | + | 17.8963i | −1.63597 | + | 0.944529i | −0.653772 | + | 0.756692i | \(0.726814\pi\) |
−0.982200 | + | 0.187837i | \(0.939852\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9582 | − | 1.25907i | −0.997802 | − | 0.0662671i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.6539 | − | 12.5019i | 1.13654 | − | 0.656180i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.50000 | − | 4.33013i | −0.392568 | − | 0.226649i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.44151 | + | 1.40961i | 0.127446 | + | 0.0735810i | 0.562368 | − | 0.826887i | \(-0.309891\pi\) |
−0.434922 | + | 0.900468i | \(0.643224\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 21.4416i | − | 1.11620i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.15403 | + | 0.666280i | 0.0599143 | + | 0.0345915i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.21243 | 0.425223 | 0.212612 | − | 0.977137i | \(-0.431803\pi\) | ||||
0.212612 | + | 0.977137i | \(0.431803\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.7798 | + | 23.8673i | 0.711584 | + | 1.23250i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.33314 | + | 5.77317i | 0.171665 | + | 0.297333i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.8520i | − | 0.865630i | −0.901483 | − | 0.432815i | \(-0.857520\pi\) | ||
0.901483 | − | 0.432815i | \(-0.142480\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.6306i | 1.00571i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.7104 | − | 25.4791i | −0.751665 | − | 1.30192i | −0.947015 | − | 0.321189i | \(-0.895918\pi\) |
0.195350 | − | 0.980734i | \(-0.437416\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.65112 | −0.0839311 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.4582 | − | 11.2342i | −0.986572 | − | 0.569597i | −0.0823240 | − | 0.996606i | \(-0.526234\pi\) |
−0.904248 | + | 0.427008i | \(0.859568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.81806i | 0.294232i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.3887 | + | 14.0808i | 1.23025 | + | 0.710284i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.5353 | − | 6.65990i | −0.580403 | − | 0.335096i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.3192 | − | 11.7313i | 1.01979 | − | 0.588777i | 0.105749 | − | 0.994393i | \(-0.466276\pi\) |
0.914044 | + | 0.405616i | \(0.132943\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.4804 | − | 9.33372i | 0.875113 | − | 0.467270i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.74913 | − | 2.16456i | 0.187223 | − | 0.108093i | −0.403459 | − | 0.914998i | \(-0.632192\pi\) |
0.590682 | + | 0.806905i | \(0.298859\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.825559 | − | 1.42991i | 0.0411240 | − | 0.0712289i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.2079 | − | 9.35766i | −0.805379 | − | 0.464986i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.8198 | + | 13.7524i | 1.17781 | + | 0.680011i | 0.955508 | − | 0.294966i | \(-0.0953084\pi\) |
0.222306 | + | 0.974977i | \(0.428642\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.6245i | 1.21464i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.9861 | − | 19.0284i | −0.540590 | − | 0.936329i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.433516 | − | 0.250290i | 0.0212804 | − | 0.0122863i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.418167i | 0.0204777i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.6646 | 1.35150 | 0.675752 | − | 0.737129i | \(-0.263819\pi\) | ||||
0.675752 | + | 0.737129i | \(0.263819\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.2130 | + | 28.0818i | 0.790174 | + | 1.36862i | 0.925859 | + | 0.377869i | \(0.123343\pi\) |
−0.135686 | + | 0.990752i | \(0.543324\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.7966 | − | 7.38815i | 0.622194 | − | 0.359224i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.33372 | 0.113202 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.14210 | + | 10.6384i | −0.297237 | + | 0.514830i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.53502 | − | 2.65874i | 0.0739395 | − | 0.128067i | −0.826685 | − | 0.562665i | \(-0.809776\pi\) |
0.900625 | + | 0.434598i | \(0.143110\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.9577 | + | 10.9452i | 0.911047 | + | 0.525993i | 0.880768 | − | 0.473548i | \(-0.157027\pi\) |
0.0302790 | + | 0.999541i | \(0.490360\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.29701 | − | 3.97854i | −0.110133 | − | 0.190756i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.4849 | + | 18.4514i | −0.549398 | + | 0.882652i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.564959 | − | 0.978538i | −0.0269640 | − | 0.0467030i | 0.852229 | − | 0.523170i | \(-0.175251\pi\) |
−0.879193 | + | 0.476467i | \(0.841917\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.25029 | − | 5.62967i | 0.154776 | − | 0.268079i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.20415 | + | 12.4780i | −0.342280 | + | 0.592846i | −0.984856 | − | 0.173376i | \(-0.944532\pi\) |
0.642576 | + | 0.766222i | \(0.277866\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.1379 | −1.33386 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.1712 | + | 17.6170i | −0.481080 | + | 0.833254i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 29.5258i | − | 1.39341i | −0.717358 | − | 0.696704i | \(-0.754649\pi\) | ||
0.717358 | − | 0.696704i | \(-0.245351\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 35.9582 | − | 20.7605i | 1.68947 | − | 0.975413i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −19.7904 | −0.927790 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.63960 | 0.310587 | 0.155294 | − | 0.987868i | \(-0.450368\pi\) | ||||
0.155294 | + | 0.987868i | \(0.450368\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.91373 | + | 1.10489i | −0.0893253 | + | 0.0515720i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.7085 | − | 18.3069i | 1.47681 | − | 0.852639i | 0.477156 | − | 0.878819i | \(-0.341668\pi\) |
0.999657 | + | 0.0261800i | \(0.00833430\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 18.1390i | − | 0.842992i | −0.906830 | − | 0.421496i | \(-0.861505\pi\) | ||
0.906830 | − | 0.421496i | \(-0.138495\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.568928 | + | 0.985413i | −0.0263834 | + | 0.0456974i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.87998 | −0.318367 | −0.159184 | − | 0.987249i | \(-0.550886\pi\) | ||||
−0.159184 | + | 0.987249i | \(0.550886\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.6068 | − | 18.3715i | 0.489776 | − | 0.848317i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.63767 | − | 13.2288i | 0.351925 | − | 0.609552i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.40118 | + | 4.60679i | 0.339589 | + | 0.211374i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.721867 | + | 1.25031i | 0.0330520 | + | 0.0572478i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.1092 | − | 16.2288i | −1.28434 | − | 0.741514i | −0.306701 | − | 0.951806i | \(-0.599225\pi\) |
−0.977639 | + | 0.210292i | \(0.932559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.74971 | + | 13.4229i | −0.353356 | + | 0.612031i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 22.6674i | − | 1.03140i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.56951 | + | 14.8428i | −0.389121 | + | 0.673978i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.8326 | 1.07996 | 0.539978 | − | 0.841679i | \(-0.318433\pi\) | ||||
0.539978 | + | 0.841679i | \(0.318433\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.3198 | − | 12.8863i | 1.00934 | − | 0.582741i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.48364 | − | 11.2300i | −0.292602 | − | 0.506802i | 0.681822 | − | 0.731518i | \(-0.261188\pi\) |
−0.974424 | + | 0.224716i | \(0.927855\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.36156 | −0.0613217 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.3198 | + | 11.1543i | −0.866611 | + | 0.500338i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.380993 | − | 0.659900i | −0.0170556 | − | 0.0295412i | 0.857372 | − | 0.514698i | \(-0.172096\pi\) |
−0.874427 | + | 0.485157i | \(0.838763\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.94926i | 0.399824i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.36019 | − | 4.82676i | −0.372763 | − | 0.215215i | 0.301902 | − | 0.953339i | \(-0.402378\pi\) |
−0.674665 | + | 0.738124i | \(0.735712\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.5006 | −0.689767 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 38.6590 | + | 22.3198i | 1.71691 | + | 0.991257i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.0689 | + | 29.5643i | −0.756567 | + | 1.31041i | 0.188025 | + | 0.982164i | \(0.439792\pi\) |
−0.944592 | + | 0.328248i | \(0.893542\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.66025 | − | 5.00000i | 0.383107 | − | 0.221187i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.25029 | − | 0.273662i | −0.364259 | − | 0.0120825i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.61508 | − | 3.81922i | 0.291495 | − | 0.168295i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.90562 | − | 3.40961i | −0.259228 | − | 0.149665i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 39.5809i | − | 1.73407i | −0.498248 | − | 0.867035i | \(-0.666023\pi\) | ||
0.498248 | − | 0.867035i | \(-0.333977\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.4733 | − | 17.0164i | −1.28878 | − | 0.744075i | −0.310340 | − | 0.950626i | \(-0.600443\pi\) |
−0.978436 | + | 0.206550i | \(0.933776\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.09229 | −0.396820 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.168617 | + | 0.292054i | 0.00734509 | + | 0.0127221i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.930491 | + | 1.61166i | 0.0404561 | + | 0.0700721i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 23.8053i | − | 1.03306i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 56.5314i | 2.44865i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.02106 | − | 3.50058i | −0.0873781 | − | 0.151343i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 29.1390 | + | 50.4703i | 1.25744 | + | 2.17795i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.931072 | − | 0.537555i | −0.0400299 | − | 0.0231113i | 0.479851 | − | 0.877350i | \(-0.340691\pi\) |
−0.519881 | + | 0.854238i | \(0.674024\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.1529i | 0.821931i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.8881 | + | 17.2559i | 1.28027 | + | 0.739163i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0324 | − | 6.94689i | −0.514467 | − | 0.297028i | 0.220201 | − | 0.975455i | \(-0.429329\pi\) |
−0.734668 | + | 0.678427i | \(0.762662\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.5260 | + | 6.65454i | −0.491918 | + | 0.284009i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.31807 | − | 2.68774i | −0.183956 | − | 0.114502i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.3198 | − | 7.69019i | 0.566415 | − | 0.327020i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.34066 | − | 9.25029i | 0.226698 | − | 0.392653i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.4571 | + | 19.3165i | 1.41762 | + | 0.818464i | 0.996090 | − | 0.0883491i | \(-0.0281591\pi\) |
0.421532 | + | 0.906813i | \(0.361492\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.35323 | 0.184122 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 2.63960i | − | 0.111246i | −0.998452 | − | 0.0556229i | \(-0.982286\pi\) | ||
0.998452 | − | 0.0556229i | \(-0.0177145\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.8887 | + | 18.8598i | 0.458092 | + | 0.793439i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.7153 | − | 10.8053i | 0.785970 | − | 0.453780i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 41.4421i | − | 1.73734i | −0.495389 | − | 0.868671i | \(-0.664975\pi\) | ||
0.495389 | − | 0.868671i | \(-0.335025\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.45828 | −0.186573 | −0.0932866 | − | 0.995639i | \(-0.529737\pi\) | ||||
−0.0932866 | + | 0.995639i | \(0.529737\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.6674 | + | 34.0650i | 0.821619 | + | 1.42309i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.63614 | − | 4.98608i | 0.360152 | − | 0.207934i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.1379 | −0.463675 | −0.231838 | − | 0.972755i | \(-0.574474\pi\) | ||||
−0.231838 | + | 0.972755i | \(0.574474\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.9300 | − | 27.5916i | 0.662028 | − | 1.14667i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.578021i | 0.0239803i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −18.5689 | − | 10.7208i | −0.767731 | − | 0.443250i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.8338 | − | 22.2288i | −0.529708 | − | 0.917482i | −0.999399 | − | 0.0346511i | \(-0.988968\pi\) |
0.469691 | − | 0.882831i | \(-0.344365\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0417635 | + | 1.25907i | −0.00172084 | + | 0.0518793i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.60861 | − | 6.25029i | −0.148438 | − | 0.257103i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.5695 | − | 20.0390i | 0.475103 | − | 0.822902i | −0.524491 | − | 0.851416i | \(-0.675744\pi\) |
0.999593 | + | 0.0285141i | \(0.00907754\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.02106 | − | 3.50058i | 0.0828554 | − | 0.143510i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −51.0479 | −2.08925 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.75224 | − | 15.1593i | 0.357607 | − | 0.619393i | −0.629954 | − | 0.776633i | \(-0.716926\pi\) |
0.987560 | + | 0.157240i | \(0.0502595\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0315i | 0.694729i | 0.937730 | + | 0.347365i | \(0.112923\pi\) | ||||
−0.937730 | + | 0.347365i | \(0.887077\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.9042 | − | 11.4917i | 0.810563 | − | 0.467979i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.5000 | − | 9.52628i | 0.670820 | − | 0.387298i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.6047 | 1.20162 | 0.600809 | − | 0.799392i | \(-0.294845\pi\) | ||||
0.600809 | + | 0.799392i | \(0.294845\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.30472 | 0.214958 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.7388 | + | 19.4791i | −1.36493 | + | 0.788041i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.2497 | − | 11.1138i | 0.777488 | − | 0.448883i | −0.0580510 | − | 0.998314i | \(-0.518489\pi\) |
0.835539 | + | 0.549430i | \(0.185155\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 38.9582i | − | 1.57095i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.06893 | + | 13.9758i | −0.324843 | + | 0.562644i | −0.981481 | − | 0.191562i | \(-0.938645\pi\) |
0.656638 | + | 0.754206i | \(0.271978\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.97615 | −0.400975 | −0.200488 | − | 0.979696i | \(-0.564253\pi\) | ||||
−0.200488 | + | 0.979696i | \(0.564253\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.72129 | + | 8.17751i | −0.189459 | + | 0.328152i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.2454 | − | 28.1379i | 0.650858 | − | 1.12732i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.58285 | − | 2.74158i | −0.0631123 | − | 0.109314i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.6631 | − | 16.5486i | −1.14106 | − | 0.658790i | −0.194366 | − | 0.980929i | \(-0.562265\pi\) |
−0.946693 | + | 0.322139i | \(0.895598\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.09793 | − | 12.2940i | 0.282117 | − | 0.488642i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.9582i | 0.593600i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.56951 | + | 14.8428i | −0.339536 | + | 0.588094i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.1698 | −0.956142 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.18020 | − | 1.83609i | 0.125610 | − | 0.0725212i | −0.435878 | − | 0.900006i | \(-0.643562\pi\) |
0.561489 | + | 0.827484i | \(0.310229\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.8015 | + | 34.2972i | 0.780894 | + | 1.35255i | 0.931421 | + | 0.363943i | \(0.118570\pi\) |
−0.150527 | + | 0.988606i | \(0.548097\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.00000 | −0.118125 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 41.6106i | − | 1.63588i | −0.575303 | − | 0.817941i | \(-0.695116\pi\) | ||
0.575303 | − | 0.817941i | \(-0.304884\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.656942 | − | 1.13786i | −0.0257476 | − | 0.0445961i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.1181i | 1.72647i | 0.504799 | + | 0.863237i | \(0.331566\pi\) | ||||
−0.504799 | + | 0.863237i | \(0.668434\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.5839 | + | 10.7294i | 0.726132 | + | 0.419233i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.8343 | 0.422686 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.2769 | + | 8.24275i | 0.556148 | + | 0.321092i | 0.751598 | − | 0.659622i | \(-0.229283\pi\) |
−0.195450 | + | 0.980714i | \(0.562617\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.962716 | − | 1.66747i | 0.0374453 | − | 0.0648572i | −0.846695 | − | 0.532078i | \(-0.821411\pi\) |
0.884141 | + | 0.467221i | \(0.154745\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.1228 | + | 7.57647i | −0.509648 | + | 0.294246i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.3198 | − | 7.11217i | 0.516520 | − | 0.275798i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.03859 | + | 2.90903i | −0.195095 | + | 0.112638i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −38.0272 | − | 21.9550i | −1.47022 | − | 0.848829i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 19.5496i | − | 0.753584i | −0.926298 | − | 0.376792i | \(-0.877027\pi\) | ||
0.926298 | − | 0.376792i | \(-0.122973\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.28014 | + | 1.89379i | 0.126252 | + | 0.0728919i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.1947 | −0.468680 | −0.234340 | − | 0.972155i | \(-0.575293\pi\) | ||||
−0.234340 | + | 0.972155i | \(0.575293\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.89522 | − | 17.1390i | −0.379744 | − | 0.657735i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.9861 | + | 19.0284i | 0.420987 | + | 0.729172i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.13902i | 0.0818472i | 0.999162 | + | 0.0409236i | \(0.0130300\pi\) | ||||
−0.999162 | + | 0.0409236i | \(0.986970\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.7635i | 0.716918i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.5071 | − | 37.2515i | −0.820548 | − | 1.42123i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.90323 | − | 3.29649i | −0.0725073 | − | 0.125586i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.7846 | −0.790684 | −0.395342 | − | 0.918534i | \(-0.629374\pi\) | ||||
−0.395342 | + | 0.918534i | \(0.629374\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.318638i | 0.0120866i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.99942 | − | 5.77317i | −0.378755 | − | 0.218674i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 33.7388 | + | 19.4791i | 1.27612 | + | 0.736768i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.1662 | − | 24.9220i | 1.63036 | − | 0.941291i | 0.646384 | − | 0.763012i | \(-0.276280\pi\) |
0.983980 | − | 0.178279i | \(-0.0570530\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.392043 | − | 11.8192i | 0.0147862 | − | 0.445770i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.2509 | − | 13.4239i | 0.875678 | − | 0.505573i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.94926 | − | 15.5006i | 0.336572 | − | 0.582959i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.8198 | − | 6.82416i | −0.443902 | − | 0.256287i | 0.261349 | − | 0.965244i | \(-0.415833\pi\) |
−0.705251 | + | 0.708957i | \(0.749166\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.6636 | 0.624933 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.24797 | + | 0.720514i | 0.0467367 | + | 0.0269835i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25.5411 | − | 44.2385i | −0.953849 | − | 1.65212i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.94774 | + | 5.74333i | −0.370988 | + | 0.214190i | −0.673890 | − | 0.738832i | \(-0.735378\pi\) |
0.302902 | + | 0.953022i | \(0.402045\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.82011i | 0.328478i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −48.2652 | −1.79500 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.16686 | + | 2.02106i | 0.0433361 | + | 0.0750603i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.4669 | + | 13.5486i | −0.870340 | + | 0.502491i | −0.867461 | − | 0.497505i | \(-0.834250\pi\) |
−0.00287848 | + | 0.999996i | \(0.500916\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.4994 | 0.388867 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.444566 | + | 0.770011i | −0.0164429 | + | 0.0284799i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.2741i | 1.67224i | 0.548549 | + | 0.836119i | \(0.315181\pi\) | ||||
−0.548549 | + | 0.836119i | \(0.684819\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.90562 | − | 10.2288i | 0.217832 | − | 0.377296i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.7944 | + | 22.1605i | 0.470648 | + | 0.815186i | 0.999436 | − | 0.0335673i | \(-0.0106868\pi\) |
−0.528788 | + | 0.848754i | \(0.677353\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −56.5739 | − | 1.87656i | −2.07829 | − | 0.0689370i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.3608 | − | 21.4096i | −0.453475 | − | 0.785442i | 0.545124 | − | 0.838356i | \(-0.316483\pi\) |
−0.998599 | + | 0.0529132i | \(0.983149\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.75029 | + | 13.4239i | −0.283949 | + | 0.491814i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.313123 | + | 0.542344i | −0.0114566 | + | 0.0198433i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.66744 | 0.170545 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.4812 | − | 21.6181i | 0.455447 | − | 0.788857i | −0.543267 | − | 0.839560i | \(-0.682813\pi\) |
0.998714 | + | 0.0507030i | \(0.0161462\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.7564i | 0.428428i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27.3997 | − | 15.8192i | 0.997177 | − | 0.575720i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.6402 | + | 9.60721i | −0.604798 | + | 0.349180i | −0.770927 | − | 0.636924i | \(-0.780207\pi\) |
0.166129 | + | 0.986104i | \(0.446873\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.8065 | −1.33423 | −0.667117 | − | 0.744953i | \(-0.732472\pi\) | ||||
−0.667117 | + | 0.744953i | \(0.732472\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.5119 | + | 19.9254i | −1.24941 | + | 0.721349i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.79263 | − | 2.18968i | 0.137123 | − | 0.0791680i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 62.7635i | 2.26626i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.819799 | − | 1.41993i | 0.0295627 | − | 0.0512041i | −0.850866 | − | 0.525384i | \(-0.823922\pi\) |
0.880428 | + | 0.474179i | \(0.157255\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 53.3322 | 1.92071 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.1663 | − | 19.3406i | 0.401623 | − | 0.695632i | −0.592299 | − | 0.805718i | \(-0.701780\pi\) |
0.993922 | + | 0.110087i | \(0.0351128\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.289010 | − | 0.500581i | 0.0103816 | − | 0.0179814i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.16686 | + | 10.6813i | 0.221235 | + | 0.383190i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.3159 | − | 38.0480i | −0.727894 | − | 1.36321i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.91373 | − | 1.10489i | −0.0683911 | − | 0.0394856i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.81980 | − | 10.0802i | 0.207718 | − | 0.359777i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 20.2124i | − | 0.720495i | −0.932857 | − | 0.360248i | \(-0.882692\pi\) | ||
0.932857 | − | 0.360248i | \(-0.117308\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.3887 | − | 37.0464i | 0.761459 | − | 1.31889i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.1464 | −0.894104 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.3887 | − | 17.5449i | 1.07914 | − | 0.623039i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.31160 | + | 2.27175i | 0.0465176 | + | 0.0805708i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 48.8065 | 1.72881 | 0.864407 | − | 0.502793i | \(-0.167694\pi\) | ||||
0.864407 | + | 0.502793i | \(0.167694\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 7.95708i | − | 0.281501i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 30.4854 | − | 17.6008i | 1.07715 | − | 0.621892i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 17.2723i | − | 0.608768i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.9276 | + | 12.6599i | 0.771888 | + | 0.445650i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.8053 | 0.836950 | 0.418475 | − | 0.908228i | \(-0.362565\pi\) | ||||
0.418475 | + | 0.908228i | \(0.362565\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.1947 | + | 25.5158i | 1.55189 | + | 0.895982i | 0.997988 | + | 0.0633968i | \(0.0201934\pi\) |
0.553897 | + | 0.832585i | \(0.313140\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.1612 | + | 19.3318i | −0.391441 | + | 0.677996i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.0074 | − | 9.81922i | 0.595743 | − | 0.343952i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.92991 | + | 1.56444i | −0.102505 | + | 0.0547328i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.4416 | − | 12.3793i | 0.749228 | − | 0.432567i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.70853 | + | 0.986418i | 0.0596280 | + | 0.0344262i | 0.529518 | − | 0.848299i | \(-0.322373\pi\) |
−0.469890 | + | 0.882725i | \(0.655706\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.3431 | − | 10.5904i | −0.639400 | − | 0.369158i | 0.144983 | − | 0.989434i | \(-0.453687\pi\) |
−0.784383 | + | 0.620276i | \(0.787020\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.5904 | + | 12.4652i | 0.750770 | + | 0.433457i | 0.825972 | − | 0.563711i | \(-0.190627\pi\) |
−0.0752019 | + | 0.997168i | \(0.523960\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.8520 | 0.585295 | 0.292647 | − | 0.956220i | \(-0.405464\pi\) | ||||
0.292647 | + | 0.956220i | \(0.405464\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 35.0504 | + | 60.7091i | 1.21589 | + | 2.10598i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.75029 | − | 3.03159i | −0.0606440 | − | 0.105038i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.81922i | 0.235989i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.547324i | 0.0189183i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.444566 | − | 0.770011i | −0.0153481 | − | 0.0265837i | 0.858249 | − | 0.513233i | \(-0.171552\pi\) |
−0.873597 | + | 0.486649i | \(0.838219\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.8192 | + | 23.9356i | 0.476525 | + | 0.825365i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.9858 | −0.826116 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29.4577 | + | 17.0074i | 1.01337 | + | 0.585072i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.0000i | 0.755929i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.2079 | − | 18.0179i | −1.07105 | − | 0.618373i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.7150 | − | 6.76363i | −0.401583 | − | 0.231854i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.680781 | − | 0.393049i | 0.0233095 | − | 0.0134578i | −0.488300 | − | 0.872676i | \(-0.662383\pi\) |
0.511609 | + | 0.859218i | \(0.329049\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.3504 | + | 0.542344i | 0.559173 | + | 0.0185478i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.50000 | + | 2.59808i | −0.153717 | + | 0.0887486i | −0.574886 | − | 0.818234i | \(-0.694953\pi\) |
0.421168 | + | 0.906982i | \(0.361620\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.236488 | − | 0.409609i | 0.00806887 | − | 0.0139757i | −0.861963 | − | 0.506972i | \(-0.830765\pi\) |
0.870032 | + | 0.492996i | \(0.164098\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 38.9582 | + | 22.4925i | 1.32769 | + | 0.766544i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.9655 | 0.781756 | 0.390878 | − | 0.920443i | \(-0.372172\pi\) | ||||
0.390878 | + | 0.920443i | \(0.372172\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.50000 | − | 2.59808i | −0.153005 | − | 0.0883372i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 35.5473i | 1.20725i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −52.4783 | + | 30.2983i | −1.77816 | + | 1.02662i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 21.4416i | − | 0.725687i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.2487 | −0.819756 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.78193 | − | 3.08640i | −0.0601716 | − | 0.104220i | 0.834370 | − | 0.551204i | \(-0.185831\pi\) |
−0.894542 | + | 0.446984i | \(0.852498\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −47.4638 | + | 27.4032i | −1.60091 | + | 0.924288i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.4159 | 1.59748 | 0.798741 | − | 0.601675i | \(-0.205500\pi\) | ||||
0.798741 | + | 0.601675i | \(0.205500\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.52615 | − | 7.83952i | 0.152317 | − | 0.263821i | −0.779762 | − | 0.626076i | \(-0.784660\pi\) |
0.932079 | + | 0.362255i | \(0.117993\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 43.2530i | − | 1.45394i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.5149 | + | 23.4084i | −0.453785 | + | 0.785979i | −0.998617 | − | 0.0525662i | \(-0.983260\pi\) |
0.544832 | + | 0.838545i | \(0.316593\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.9582 | − | 8.63614i | −0.501683 | − | 0.289647i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.7074 | − | 25.2351i | 0.525627 | − | 0.844461i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.2035 | + | 38.4577i | 0.742182 | + | 1.28550i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −32.3748 | + | 56.0748i | −1.08096 | + | 1.87228i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.168617 | + | 0.292054i | −0.00562370 | + | 0.00974054i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.777455 | 0.0259008 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.73205 | − | 3.00000i | 0.0576390 | − | 0.0998337i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.5943i | 0.485130i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.5576 | − | 12.4463i | 0.715810 | − | 0.413273i | −0.0973986 | − | 0.995245i | \(-0.531052\pi\) |
0.813209 | + | 0.581972i | \(0.197719\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.7938 | − | 9.69590i | 0.557015 | − | 0.321593i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.0511 | 1.29382 | 0.646910 | − | 0.762567i | \(-0.276061\pi\) | ||||
0.646910 | + | 0.762567i | \(0.276061\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20.9422 | + | 12.0910i | −0.692327 | + | 0.399715i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.4588 | + | 12.3893i | −0.708633 | + | 0.409129i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18.3616i | − | 0.605692i | −0.953039 | − | 0.302846i | \(-0.902063\pi\) | ||
0.953039 | − | 0.302846i | \(-0.0979368\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.6100 | − | 39.1617i | 0.745025 | − | 1.29042i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 63.7245 | 2.09752 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.71301 | + | 4.69906i | −0.0892031 | + | 0.154504i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.77799 | + | 8.27571i | −0.156930 | + | 0.271810i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.6529 | + | 18.4514i | 0.349512 | + | 0.605372i | 0.986163 | − | 0.165780i | \(-0.0530142\pi\) |
−0.636651 | + | 0.771152i | \(0.719681\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.433516 | − | 13.0695i | 0.0142079 | − | 0.428336i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.9026 | − | 20.6160i | −0.389675 | − | 0.674937i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.1396 | + | 41.8110i | −0.788606 | + | 1.36591i | 0.138215 | + | 0.990402i | \(0.455864\pi\) |
−0.926821 | + | 0.375504i | \(0.877470\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 74.5055i | − | 2.43140i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.9727 | − | 20.7374i | 0.390300 | − | 0.676020i | −0.602189 | − | 0.798354i | \(-0.705705\pi\) |
0.992489 | + | 0.122334i | \(0.0390379\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −49.3383 | −1.60668 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.68136 | − | 3.28014i | 0.184815 | − | 0.106703i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.3496 | + | 36.9785i | 0.693768 | + | 1.20164i | 0.970594 | + | 0.240721i | \(0.0773839\pi\) |
−0.276827 | + | 0.960920i | \(0.589283\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.5650 | −0.927260 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 6.37665i | − | 0.206777i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.4571 | + | 12.3882i | −0.695063 | + | 0.401295i | −0.805506 | − | 0.592588i | \(-0.798106\pi\) |
0.110443 | + | 0.993882i | \(0.464773\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.9863 | + | 25.9571i | 0.484946 | + | 0.839951i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.7635 | − | 10.8331i | −0.605907 | − | 0.349820i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9165 | −0.997306 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.37936 | + | 2.52842i | 0.141123 | + | 0.0814773i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.1384 | − | 21.0244i | 0.390750 | − | 0.676799i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.3453 | − | 30.7989i | 1.71547 | − | 0.990426i | 0.788714 | − | 0.614761i | \(-0.210747\pi\) |
0.926755 | − | 0.375666i | \(-0.122586\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.10943 | − | 9.81529i | 0.196263 | − | 0.315313i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.6399 | + | 24.6181i | −1.36838 | + | 0.790034i | −0.990721 | − | 0.135912i | \(-0.956604\pi\) |
−0.377657 | + | 0.925945i | \(0.623270\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.318638 | − | 0.183966i | −0.0102151 | − | 0.00589767i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 22.4925 | + | 12.9861i | 0.720338 | + | 0.415887i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.70489i | 0.118530i | 0.998242 | + | 0.0592649i | \(0.0188757\pi\) | ||||
−0.998242 | + | 0.0592649i | \(0.981124\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −43.1756 | −1.37849 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.01714 | − | 15.6181i | −0.287602 | − | 0.498141i | 0.685635 | − | 0.727946i | \(-0.259525\pi\) |
−0.973237 | + | 0.229804i | \(0.926191\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.74971 | − | 4.76264i | −0.0876130 | − | 0.151750i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 31.0012i | 0.986778i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.79932i | 0.120811i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.5023 | + | 25.1187i | 0.460681 | + | 0.797922i | 0.998995 | − | 0.0448218i | \(-0.0142720\pi\) |
−0.538314 | + | 0.842744i | \(0.680939\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.4867 | + | 44.1442i | 0.808795 | + | 1.40087i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38.8978 | −1.23314 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.1384 | − | 15.6684i | −0.859483 | − | 0.496223i | 0.00435617 | − | 0.999991i | \(-0.498613\pi\) |
−0.863839 | + | 0.503768i | \(0.831947\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 5.13786i | − | 0.162555i |
(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 | 1216.2.s.g.31.2 | ✓ | 12 | |
4.3 | odd | 2 | inner | 1216.2.s.g.31.5 | yes | 12 | |
8.3 | odd | 2 | 1216.2.s.h.31.2 | yes | 12 | ||
8.5 | even | 2 | 1216.2.s.h.31.5 | yes | 12 | ||
19.8 | odd | 6 | 1216.2.s.h.863.2 | yes | 12 | ||
76.27 | even | 6 | 1216.2.s.h.863.5 | yes | 12 | ||
152.27 | even | 6 | inner | 1216.2.s.g.863.2 | yes | 12 | |
152.141 | odd | 6 | inner | 1216.2.s.g.863.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.s.g.31.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
1216.2.s.g.31.5 | yes | 12 | 4.3 | odd | 2 | inner | |
1216.2.s.g.863.2 | yes | 12 | 152.27 | even | 6 | inner | |
1216.2.s.g.863.5 | yes | 12 | 152.141 | odd | 6 | inner | |
1216.2.s.h.31.2 | yes | 12 | 8.3 | odd | 2 | ||
1216.2.s.h.31.5 | yes | 12 | 8.5 | even | 2 | ||
1216.2.s.h.863.2 | yes | 12 | 19.8 | odd | 6 | ||
1216.2.s.h.863.5 | yes | 12 | 76.27 | even | 6 |