Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(865,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.s (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 4x^{6} + 28x^{5} + 14x^{4} - 52x^{3} + 306x^{2} + 1052x + 1051 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 865.1 | ||
Root | \(-1.30724 + 1.29485i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.865 |
Dual form | 1512.2.s.n.1297.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.70873 | − | 2.95960i | −0.764166 | − | 1.32357i | −0.940687 | − | 0.339277i | \(-0.889818\pi\) |
0.176521 | − | 0.984297i | \(-0.443516\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.27499 | − | 1.35071i | −0.859867 | − | 0.510519i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.01597 | − | 5.22381i | 0.909349 | − | 1.57504i | 0.0943778 | − | 0.995536i | \(-0.469914\pi\) |
0.814971 | − | 0.579502i | \(-0.196753\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.417453 | 0.115781 | 0.0578903 | − | 0.998323i | \(-0.481563\pi\) | ||||
0.0578903 | + | 0.998323i | \(0.481563\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.27499 | − | 2.20835i | 0.309231 | − | 0.535604i | −0.668963 | − | 0.743296i | \(-0.733262\pi\) |
0.978194 | + | 0.207691i | \(0.0665950\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.74274 | − | 3.01852i | −0.399813 | − | 0.692496i | 0.593890 | − | 0.804546i | \(-0.297592\pi\) |
−0.993703 | + | 0.112050i | \(0.964258\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.54822 | + | 7.87774i | 0.948369 | + | 1.64262i | 0.748861 | + | 0.662727i | \(0.230601\pi\) |
0.199508 | + | 0.979896i | \(0.436066\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.33949 | + | 5.78417i | −0.667898 | + | 1.15683i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.67898 | −0.311779 | −0.155890 | − | 0.987774i | \(-0.549824\pi\) | ||||
−0.155890 | + | 0.987774i | \(0.549824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.82321 | + | 6.62200i | −0.686669 | + | 1.18935i | 0.286240 | + | 0.958158i | \(0.407594\pi\) |
−0.972909 | + | 0.231188i | \(0.925739\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.110210 | + | 9.04106i | −0.0186290 | + | 1.52822i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.69245 | − | 8.12755i | −0.771433 | − | 1.33616i | −0.936777 | − | 0.349926i | \(-0.886207\pi\) |
0.165344 | − | 0.986236i | \(-0.447127\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.13253 | −0.333046 | −0.166523 | − | 0.986038i | \(-0.553254\pi\) | ||||
−0.166523 | + | 0.986038i | \(0.553254\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.03194 | −0.919862 | −0.459931 | − | 0.887955i | \(-0.652126\pi\) | ||||
−0.459931 | + | 0.887955i | \(0.652126\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.94970 | − | 6.84108i | −0.576123 | − | 0.997875i | −0.995919 | − | 0.0902560i | \(-0.971231\pi\) |
0.419795 | − | 0.907619i | \(-0.362102\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.35119 | + | 6.14569i | 0.478741 | + | 0.877956i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.967751 | − | 1.67619i | 0.132931 | − | 0.230243i | −0.791874 | − | 0.610684i | \(-0.790895\pi\) |
0.924805 | + | 0.380441i | \(0.124228\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −20.6139 | −2.77957 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.91922 | + | 6.78829i | −0.510239 | + | 0.883760i | 0.489691 | + | 0.871896i | \(0.337110\pi\) |
−0.999930 | + | 0.0118637i | \(0.996224\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.67648 | − | 8.09990i | −0.598762 | − | 1.03709i | −0.993004 | − | 0.118079i | \(-0.962326\pi\) |
0.394243 | − | 0.919006i | \(-0.371007\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.713312 | − | 1.23549i | −0.0884755 | − | 0.153244i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.516281 | + | 0.894224i | −0.0630737 | + | 0.109247i | −0.895838 | − | 0.444381i | \(-0.853424\pi\) |
0.832764 | + | 0.553628i | \(0.186757\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.650582 | −0.0772099 | −0.0386049 | − | 0.999255i | \(-0.512291\pi\) | ||||
−0.0386049 | + | 0.999255i | \(0.512291\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.642460 | + | 1.11277i | −0.0751942 | + | 0.130240i | −0.901171 | − | 0.433464i | \(-0.857291\pi\) |
0.825976 | + | 0.563705i | \(0.190624\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.9171 | + | 7.81045i | −1.58601 | + | 0.890083i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.20665 | + | 14.2143i | 0.923320 | + | 1.59924i | 0.794241 | + | 0.607603i | \(0.207869\pi\) |
0.129079 | + | 0.991634i | \(0.458798\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.1645 | 1.55475 | 0.777376 | − | 0.629036i | \(-0.216550\pi\) | ||||
0.777376 | + | 0.629036i | \(0.216550\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.71446 | −0.945216 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.70841 | − | 11.6193i | −0.711090 | − | 1.23164i | −0.964448 | − | 0.264272i | \(-0.914868\pi\) |
0.253358 | − | 0.967373i | \(-0.418465\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.949702 | − | 0.563856i | −0.0995558 | − | 0.0591082i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.95574 | + | 10.3157i | −0.611046 | + | 1.05836i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.26507 | −0.229983 | −0.114991 | − | 0.993366i | \(-0.536684\pi\) | ||||
−0.114991 | + | 0.993366i | \(0.536684\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.576193 | + | 0.997996i | −0.0573334 | + | 0.0993043i | −0.893268 | − | 0.449525i | \(-0.851593\pi\) |
0.835934 | + | 0.548830i | \(0.184926\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.32352 | − | 4.02446i | −0.228944 | − | 0.396542i | 0.728552 | − | 0.684991i | \(-0.240194\pi\) |
−0.957495 | + | 0.288449i | \(0.906860\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.50177 | + | 4.33319i | 0.241855 | + | 0.418905i | 0.961243 | − | 0.275704i | \(-0.0889108\pi\) |
−0.719388 | + | 0.694609i | \(0.755577\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.54999 | + | 11.3449i | −0.627375 | + | 1.08665i | 0.360702 | + | 0.932681i | \(0.382537\pi\) |
−0.988076 | + | 0.153964i | \(0.950796\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.3169 | 1.53496 | 0.767480 | − | 0.641072i | \(-0.221510\pi\) | ||||
0.767480 | + | 0.641072i | \(0.221510\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.5433 | − | 26.9218i | 1.44942 | − | 2.51047i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.88344 | + | 3.30185i | −0.539334 | + | 0.302680i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.6921 | − | 21.9834i | −1.15383 | − | 1.99849i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.73785 | 0.513209 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.5373 | 1.28997 | 0.644987 | − | 0.764193i | \(-0.276863\pi\) | ||||
0.644987 | + | 0.764193i | \(0.276863\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.536523 | + | 0.929286i | 0.0468763 | + | 0.0811921i | 0.888512 | − | 0.458854i | \(-0.151740\pi\) |
−0.841635 | + | 0.540046i | \(0.818407\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.112405 | + | 9.22105i | −0.00974671 | + | 0.799566i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.96744 | − | 12.0680i | 0.595268 | − | 1.03104i | −0.398240 | − | 0.917281i | \(-0.630379\pi\) |
0.993509 | − | 0.113754i | \(-0.0362876\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.811516 | 0.0688319 | 0.0344160 | − | 0.999408i | \(-0.489043\pi\) | ||||
0.0344160 | + | 0.999408i | \(0.489043\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.25902 | − | 2.18069i | 0.105285 | − | 0.182359i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.86892 | + | 4.96912i | 0.238251 | + | 0.412663i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.33667 | − | 9.24339i | −0.437197 | − | 0.757248i | 0.560275 | − | 0.828307i | \(-0.310696\pi\) |
−0.997472 | + | 0.0710588i | \(0.977362\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.69245 | + | 15.0558i | −0.707381 | + | 1.22522i | 0.258444 | + | 0.966026i | \(0.416790\pi\) |
−0.965825 | + | 0.259194i | \(0.916543\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 26.1313 | 2.09892 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.98164 | + | 17.2887i | −0.796622 | + | 1.37979i | 0.125183 | + | 0.992134i | \(0.460048\pi\) |
−0.921804 | + | 0.387655i | \(0.873285\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.293354 | − | 24.0651i | 0.0231195 | − | 1.89660i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.224695 | + | 0.389183i | 0.0175995 | + | 0.0304832i | 0.874691 | − | 0.484681i | \(-0.161064\pi\) |
−0.857092 | + | 0.515164i | \(0.827731\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.15946 | −0.167104 | −0.0835520 | − | 0.996503i | \(-0.526626\pi\) | ||||
−0.0835520 | + | 0.996503i | \(0.526626\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8257 | −0.986595 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.80693 | − | 13.5220i | −0.593550 | − | 1.02806i | −0.993750 | − | 0.111631i | \(-0.964393\pi\) |
0.400200 | − | 0.916428i | \(-0.368941\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.4100 | − | 8.64827i | 1.16489 | − | 0.653748i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.38771 | − | 7.59974i | 0.327953 | − | 0.568031i | −0.654153 | − | 0.756363i | \(-0.726975\pi\) |
0.982105 | + | 0.188332i | \(0.0603080\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.7464 | 1.09609 | 0.548045 | − | 0.836449i | \(-0.315372\pi\) | ||||
0.548045 | + | 0.836449i | \(0.315372\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.0362 | + | 27.7755i | −1.17901 | + | 2.04210i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.69068 | − | 13.3206i | −0.562398 | − | 0.974102i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.01597 | − | 3.49176i | −0.145870 | − | 0.252655i | 0.783827 | − | 0.620979i | \(-0.213265\pi\) |
−0.929697 | + | 0.368324i | \(0.879932\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.93373 | + | 5.08138i | −0.211175 | + | 0.365765i | −0.952082 | − | 0.305841i | \(-0.901062\pi\) |
0.740908 | + | 0.671607i | \(0.234396\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.711544 | −0.0506954 | −0.0253477 | − | 0.999679i | \(-0.508069\pi\) | ||||
−0.0253477 | + | 0.999679i | \(0.508069\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.11448 | + | 8.85855i | −0.362556 | + | 0.627966i | −0.988381 | − | 0.151998i | \(-0.951429\pi\) |
0.625825 | + | 0.779964i | \(0.284763\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.81967 | + | 2.26781i | 0.268089 | + | 0.159169i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.64392 | + | 6.31145i | 0.254502 | + | 0.440811i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.0242 | −1.45428 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.5500 | 1.41472 | 0.707360 | − | 0.706854i | \(-0.249886\pi\) | ||||
0.707360 | + | 0.706854i | \(0.249886\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.3069 | + | 17.8521i | 0.702927 | + | 1.21750i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.6421 | − | 9.90096i | 1.19763 | − | 0.672121i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.532249 | − | 0.921883i | 0.0358030 | − | 0.0620125i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.8633 | −1.19622 | −0.598108 | − | 0.801416i | \(-0.704081\pi\) | ||||
−0.598108 | + | 0.801416i | \(0.704081\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.63077 | − | 9.75277i | 0.373727 | − | 0.647314i | −0.616409 | − | 0.787426i | \(-0.711413\pi\) |
0.990136 | + | 0.140112i | \(0.0447464\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5132 | − | 18.2093i | −0.694729 | − | 1.20331i | −0.970272 | − | 0.242017i | \(-0.922191\pi\) |
0.275544 | − | 0.961289i | \(-0.411142\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.80901 | − | 11.7936i | −0.446073 | − | 0.772621i | 0.552053 | − | 0.833809i | \(-0.313845\pi\) |
−0.998126 | + | 0.0611876i | \(0.980511\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.4979 | + | 23.3791i | −0.880507 | + | 1.52508i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.9384 | −1.28971 | −0.644854 | − | 0.764305i | \(-0.723082\pi\) | ||||
−0.644854 | + | 0.764305i | \(0.723082\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.39940 | − | 11.0841i | 0.412222 | − | 0.713989i | −0.582911 | − | 0.812536i | \(-0.698086\pi\) |
0.995132 | + | 0.0985472i | \(0.0314195\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.4625 | − | 20.4195i | 0.796203 | − | 1.30455i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.727513 | − | 1.26009i | −0.0462906 | − | 0.0801776i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.03194 | −0.317613 | −0.158807 | − | 0.987310i | \(-0.550765\pi\) | ||||
−0.158807 | + | 0.987310i | \(0.550765\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 54.8691 | 3.44959 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.19037 | + | 8.98998i | 0.323766 | + | 0.560779i | 0.981262 | − | 0.192679i | \(-0.0617176\pi\) |
−0.657496 | + | 0.753458i | \(0.728384\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.302656 | + | 24.8282i | −0.0188061 | + | 1.54275i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.64215 | + | 8.04044i | −0.286247 | + | 0.495795i | −0.972911 | − | 0.231181i | \(-0.925741\pi\) |
0.686664 | + | 0.726975i | \(0.259074\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.61448 | −0.406325 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.74243 | + | 9.94618i | −0.350122 | + | 0.606430i | −0.986271 | − | 0.165137i | \(-0.947193\pi\) |
0.636148 | + | 0.771567i | \(0.280527\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.142148 | + | 0.246207i | 0.00863486 | + | 0.0149560i | 0.870311 | − | 0.492503i | \(-0.163918\pi\) |
−0.861676 | + | 0.507459i | \(0.830585\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.1436 | + | 34.8897i | 1.21471 | + | 2.10393i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.4973 | − | 23.3780i | 0.810974 | − | 1.40465i | −0.101209 | − | 0.994865i | \(-0.532271\pi\) |
0.912183 | − | 0.409783i | \(-0.134396\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.6145 | 0.931482 | 0.465741 | − | 0.884921i | \(-0.345788\pi\) | ||||
0.465741 | + | 0.884921i | \(0.345788\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.0504 | − | 27.8001i | 0.954098 | − | 1.65255i | 0.217679 | − | 0.976020i | \(-0.430151\pi\) |
0.736419 | − | 0.676526i | \(-0.236515\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.85150 | + | 2.88043i | 0.286375 | + | 0.170026i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.24879 | + | 9.09116i | 0.308752 | + | 0.534774i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.2964 | −0.952045 | −0.476022 | − | 0.879433i | \(-0.657922\pi\) | ||||
−0.476022 | + | 0.879433i | \(0.657922\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.7875 | 1.55963 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.89867 | + | 3.28859i | 0.109803 | + | 0.190184i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.7226 | + | 8.14737i | 0.790958 | + | 0.469607i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.9816 | + | 27.6810i | −0.915106 | + | 1.58501i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.673971 | −0.0384656 | −0.0192328 | − | 0.999815i | \(-0.506122\pi\) | ||||
−0.0192328 | + | 0.999815i | \(0.506122\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.7754 | + | 20.3956i | −0.667723 | + | 1.15653i | 0.310817 | + | 0.950470i | \(0.399397\pi\) |
−0.978539 | + | 0.206060i | \(0.933936\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.08255 | − | 3.60708i | −0.117713 | − | 0.203884i | 0.801148 | − | 0.598466i | \(-0.204223\pi\) |
−0.918861 | + | 0.394582i | \(0.870889\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.82321 | − | 4.88994i | −0.158567 | − | 0.274647i | 0.775785 | − | 0.630997i | \(-0.217354\pi\) |
−0.934352 | + | 0.356351i | \(0.884021\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.06376 | + | 8.77069i | −0.283516 | + | 0.491064i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.88794 | −0.494538 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.39408 | + | 2.41462i | −0.0773296 | + | 0.133939i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.254750 | + | 20.8983i | −0.0140448 | + | 1.15216i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.20622 | + | 7.28539i | 0.231195 | + | 0.400441i | 0.958160 | − | 0.286233i | \(-0.0924032\pi\) |
−0.726965 | + | 0.686674i | \(0.759070\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.52873 | 0.192795 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0390 | 0.601333 | 0.300667 | − | 0.953729i | \(-0.402791\pi\) | ||||
0.300667 | + | 0.953729i | \(0.402791\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.0614 | + | 39.9435i | 1.24884 | + | 2.16306i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.677101 | − | 18.5079i | 0.0365600 | − | 0.999331i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.75902 | − | 8.24287i | 0.255478 | − | 0.442501i | −0.709547 | − | 0.704658i | \(-0.751101\pi\) |
0.965025 | + | 0.262157i | \(0.0844339\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.7053 | 0.840685 | 0.420342 | − | 0.907366i | \(-0.361910\pi\) | ||||
0.420342 | + | 0.907366i | \(0.361910\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.5636 | − | 21.7607i | 0.668691 | − | 1.15821i | −0.309579 | − | 0.950874i | \(-0.600188\pi\) |
0.978270 | − | 0.207333i | \(-0.0664784\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.11167 | + | 1.92546i | 0.0590011 | + | 0.102193i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.8544 | − | 20.5324i | −0.625652 | − | 1.08366i | −0.988414 | − | 0.151779i | \(-0.951500\pi\) |
0.362763 | − | 0.931882i | \(-0.381834\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.42569 | − | 5.93347i | 0.180299 | − | 0.312288i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.39115 | 0.229843 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.2410 | − | 24.6661i | 0.743373 | − | 1.28756i | −0.207578 | − | 0.978218i | \(-0.566558\pi\) |
0.950951 | − | 0.309341i | \(-0.100109\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.46567 | + | 2.50618i | −0.231846 | + | 0.130114i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.22897 | + | 14.2530i | 0.426080 | + | 0.737992i | 0.996521 | − | 0.0833468i | \(-0.0265609\pi\) |
−0.570441 | + | 0.821339i | \(0.693228\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.700896 | −0.0360980 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.4934 | −0.847210 | −0.423605 | − | 0.905847i | \(-0.639235\pi\) | ||||
−0.423605 | + | 0.905847i | \(0.639235\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.3892 | − | 31.8510i | −0.939642 | − | 1.62751i | −0.766139 | − | 0.642675i | \(-0.777824\pi\) |
−0.173504 | − | 0.984833i | \(-0.555509\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 46.8964 | + | 27.8433i | 2.39006 | + | 1.41902i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.95116 | − | 17.2359i | 0.504544 | − | 0.873895i | −0.495442 | − | 0.868641i | \(-0.664994\pi\) |
0.999986 | − | 0.00525463i | \(-0.00167261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.1958 | 1.17306 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.0458 | − | 48.5768i | 1.41114 | − | 2.44416i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.9781 | − | 22.4787i | −0.651352 | − | 1.12818i | −0.982795 | − | 0.184700i | \(-0.940869\pi\) |
0.331443 | − | 0.943475i | \(-0.392465\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.2506 | − | 26.4148i | −0.761578 | − | 1.31909i | −0.942037 | − | 0.335509i | \(-0.891092\pi\) |
0.180459 | − | 0.983583i | \(-0.442242\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.59601 | + | 2.76437i | −0.0795029 | + | 0.137703i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −56.6091 | −2.80601 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.69276 | − | 6.39604i | 0.182595 | − | 0.316264i | −0.760168 | − | 0.649726i | \(-0.774884\pi\) |
0.942764 | + | 0.333462i | \(0.108217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.0852 | − | 10.1496i | 0.889914 | − | 0.499429i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.2032 | − | 41.9212i | −1.18809 | − | 2.05783i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.0760 | 1.07848 | 0.539241 | − | 0.842152i | \(-0.318711\pi\) | ||||
0.539241 | + | 0.842152i | \(0.318711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.9952 | −0.584611 | −0.292306 | − | 0.956325i | \(-0.594422\pi\) | ||||
−0.292306 | + | 0.956325i | \(0.594422\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.51566 | + | 14.7495i | 0.413070 | + | 0.715458i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.301626 | + | 24.7438i | −0.0145967 | + | 1.19743i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.17793 | − | 3.77229i | 0.104907 | − | 0.181705i | −0.808793 | − | 0.588093i | \(-0.799879\pi\) |
0.913700 | + | 0.406389i | \(0.133212\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.6024 | −0.509519 | −0.254759 | − | 0.967004i | \(-0.581996\pi\) | ||||
−0.254759 | + | 0.967004i | \(0.581996\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.8528 | − | 27.4578i | 0.758340 | − | 1.31348i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.13504 | + | 1.96595i | 0.0541725 | + | 0.0938295i | 0.891840 | − | 0.452351i | \(-0.149415\pi\) |
−0.837667 | + | 0.546181i | \(0.816081\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.95932 | − | 12.0539i | −0.330647 | − | 0.572698i | 0.651992 | − | 0.758226i | \(-0.273934\pi\) |
−0.982639 | + | 0.185528i | \(0.940600\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.9257 | + | 39.7085i | −1.08678 | + | 1.88236i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.6657 | −0.975272 | −0.487636 | − | 0.873047i | \(-0.662141\pi\) | ||||
−0.487636 | + | 0.873047i | \(0.662141\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.43165 | + | 11.1400i | −0.302855 | + | 0.524560i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0460077 | + | 3.77421i | −0.00215687 | + | 0.176938i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.17825 | − | 10.7010i | −0.289006 | − | 0.500573i | 0.684567 | − | 0.728950i | \(-0.259991\pi\) |
−0.973573 | + | 0.228377i | \(0.926658\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.4304 | 1.13784 | 0.568918 | − | 0.822394i | \(-0.307362\pi\) | ||||
0.568918 | + | 0.822394i | \(0.307362\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.7458 | 1.70772 | 0.853860 | − | 0.520502i | \(-0.174255\pi\) | ||||
0.853860 | + | 0.520502i | \(0.174255\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.61052 | + | 11.4498i | 0.305898 | + | 0.529832i | 0.977461 | − | 0.211116i | \(-0.0677098\pi\) |
−0.671562 | + | 0.740948i | \(0.734377\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.38237 | − | 1.33701i | 0.110008 | − | 0.0617374i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.1921 | + | 31.5097i | −0.836475 | + | 1.44882i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.2795 | 1.06814 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.8140 | − | 32.5869i | 0.859635 | − | 1.48893i | −0.0126417 | − | 0.999920i | \(-0.504024\pi\) |
0.872277 | − | 0.489012i | \(-0.162643\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.95887 | − | 3.39287i | −0.0893170 | − | 0.154702i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.87038 | + | 6.70369i | 0.175745 | + | 0.304399i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.64497 | + | 14.9735i | −0.391741 | + | 0.678515i | −0.992679 | − | 0.120780i | \(-0.961460\pi\) |
0.600938 | + | 0.799295i | \(0.294794\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.1837 | −0.459584 | −0.229792 | − | 0.973240i | \(-0.573805\pi\) | ||||
−0.229792 | + | 0.973240i | \(0.573805\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.14069 | + | 3.70779i | −0.0964119 | + | 0.166990i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.48007 | + | 0.878745i | 0.0663902 | + | 0.0394171i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.5359 | + | 21.7128i | 0.561184 | + | 0.971999i | 0.997394 | + | 0.0721540i | \(0.0229873\pi\) |
−0.436210 | + | 0.899845i | \(0.643679\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.2887 | −1.43968 | −0.719841 | − | 0.694139i | \(-0.755785\pi\) | ||||
−0.719841 | + | 0.694139i | \(0.755785\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.93823 | 0.175249 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.9799 | + | 22.4818i | 0.575323 | + | 0.996488i | 0.996006 | + | 0.0892808i | \(0.0284568\pi\) |
−0.420684 | + | 0.907207i | \(0.638210\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.96462 | − | 1.66378i | 0.131147 | − | 0.0736011i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.94053 | + | 13.7534i | −0.349902 | + | 0.606047i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −47.6487 | −2.09559 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.81894 | − | 8.34664i | 0.211121 | − | 0.365673i | −0.740944 | − | 0.671566i | \(-0.765622\pi\) |
0.952066 | + | 0.305893i | \(0.0989551\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.48372 | − | 14.6942i | −0.370967 | − | 0.642534i | 0.618747 | − | 0.785590i | \(-0.287640\pi\) |
−0.989715 | + | 0.143056i | \(0.954307\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.74913 | + | 16.8860i | 0.424679 | + | 0.735566i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −29.8726 | + | 51.7408i | −1.29881 | + | 2.24960i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.890232 | −0.0385602 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.54967 | − | 14.8085i | 0.369635 | − | 0.640226i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 42.2110 | + | 1.02926i | 1.81816 | + | 0.0443332i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.01346 | + | 5.21947i | 0.129559 | + | 0.224403i | 0.923506 | − | 0.383585i | \(-0.125311\pi\) |
−0.793947 | + | 0.607987i | \(0.791977\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 44.7685 | 1.91767 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.6423 | −0.540544 | −0.270272 | − | 0.962784i | \(-0.587114\pi\) | ||||
−0.270272 | + | 0.962784i | \(0.587114\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.92604 | + | 5.06805i | 0.124653 | + | 0.215906i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.529317 | − | 43.4223i | 0.0225089 | − | 1.84650i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.32883 | + | 4.03365i | −0.0986756 | + | 0.170911i | −0.911137 | − | 0.412104i | \(-0.864794\pi\) |
0.812461 | + | 0.583015i | \(0.198127\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.51805 | −0.106502 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.93770 | − | 17.2126i | 0.418824 | − | 0.725424i | −0.576998 | − | 0.816746i | \(-0.695776\pi\) |
0.995821 | + | 0.0913216i | \(0.0291091\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.8810 | − | 48.2914i | −1.17296 | − | 2.03163i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.4856 | + | 30.2860i | 0.733035 | + | 1.26965i | 0.955580 | + | 0.294731i | \(0.0952300\pi\) |
−0.222546 | + | 0.974922i | \(0.571437\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.21049 | + | 9.02484i | −0.218052 | + | 0.377678i | −0.954212 | − | 0.299130i | \(-0.903304\pi\) |
0.736160 | + | 0.676807i | \(0.236637\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −60.7549 | −2.53366 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.4791 | − | 32.0068i | 0.769296 | − | 1.33246i | −0.168649 | − | 0.985676i | \(-0.553940\pi\) |
0.937945 | − | 0.346784i | \(-0.112726\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.2241 | − | 19.1320i | −1.33688 | − | 0.793731i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.83741 | − | 10.1107i | −0.241761 | − | 0.418742i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.6168 | 1.09859 | 0.549296 | − | 0.835628i | \(-0.314896\pi\) | ||||
0.549296 | + | 0.835628i | \(0.314896\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.6515 | 1.09816 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.49781 | + | 4.32633i | 0.102573 | + | 0.177661i | 0.912744 | − | 0.408532i | \(-0.133959\pi\) |
−0.810171 | + | 0.586193i | \(0.800626\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.8253 | + | 11.7707i | 0.812759 | + | 0.482550i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.7084 | − | 27.2078i | 0.641828 | − | 1.11168i | −0.343196 | − | 0.939264i | \(-0.611509\pi\) |
0.985024 | − | 0.172416i | \(-0.0551572\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.5402 | −0.797061 | −0.398530 | − | 0.917155i | \(-0.630480\pi\) | ||||
−0.398530 | + | 0.917155i | \(0.630480\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −43.3748 | + | 75.1273i | −1.76344 | + | 3.05436i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.09852 | + | 5.36679i | 0.125765 | + | 0.217831i | 0.922032 | − | 0.387114i | \(-0.126528\pi\) |
−0.796267 | + | 0.604946i | \(0.793195\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.64881 | − | 2.85583i | −0.0667039 | − | 0.115534i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.83918 | − | 11.8458i | 0.276232 | − | 0.478448i | −0.694213 | − | 0.719769i | \(-0.744248\pi\) |
0.970445 | + | 0.241322i | \(0.0775809\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.8071 | 0.636371 | 0.318186 | − | 0.948028i | \(-0.396927\pi\) | ||||
0.318186 | + | 0.948028i | \(0.396927\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.6961 | + | 30.6505i | −0.711266 | + | 1.23195i | 0.253116 | + | 0.967436i | \(0.418545\pi\) |
−0.964382 | + | 0.264513i | \(0.914789\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.432683 | + | 35.4950i | −0.0173351 | + | 1.42208i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.89305 | + | 11.9391i | 0.275722 | + | 0.477565i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23.9313 | −0.954205 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.9994 | 0.597116 | 0.298558 | − | 0.954392i | \(-0.403494\pi\) | ||||
0.298558 | + | 0.954392i | \(0.403494\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.8402 | − | 43.0245i | −0.985754 | − | 1.70738i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.39896 | + | 2.56554i | 0.0554289 | + | 0.101650i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.08327 | + | 3.60832i | −0.0822840 | + | 0.142520i | −0.904231 | − | 0.427044i | \(-0.859555\pi\) |
0.821947 | + | 0.569565i | \(0.192888\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.1973 | −1.38804 | −0.694022 | − | 0.719954i | \(-0.744163\pi\) | ||||
−0.694022 | + | 0.719954i | \(0.744163\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.50031 | − | 9.52682i | 0.216240 | − | 0.374538i | −0.737416 | − | 0.675439i | \(-0.763954\pi\) |
0.953655 | + | 0.300901i | \(0.0972874\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.6405 | + | 40.9465i | 0.927971 | + | 1.60729i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.65454 | + | 11.5260i | 0.260412 | + | 0.451048i | 0.966352 | − | 0.257225i | \(-0.0828081\pi\) |
−0.705939 | + | 0.708273i | \(0.749475\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.83354 | − | 3.17579i | 0.0716425 | − | 0.124088i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.7265 | −1.08007 | −0.540036 | − | 0.841642i | \(-0.681590\pi\) | ||||
−0.540036 | + | 0.841642i | \(0.681590\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.65561 | − | 13.2599i | 0.297769 | − | 0.515751i | −0.677856 | − | 0.735194i | \(-0.737091\pi\) |
0.975625 | + | 0.219444i | \(0.0704242\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 27.4827 | − | 15.4236i | 1.06573 | − | 0.598101i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.63638 | − | 13.2266i | −0.295682 | − | 0.512136i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −56.4164 | −2.17793 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.8109 | −1.11058 | −0.555289 | − | 0.831657i | \(-0.687392\pi\) | ||||
−0.555289 | + | 0.831657i | \(0.687392\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.08608 | + | 3.61320i | 0.0801747 | + | 0.138867i | 0.903325 | − | 0.428957i | \(-0.141119\pi\) |
−0.823150 | + | 0.567824i | \(0.807786\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.15301 | + | 3.05944i | 0.197754 | + | 0.117410i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.4214 | + | 19.7825i | −0.437028 | + | 0.756955i | −0.997459 | − | 0.0712463i | \(-0.977302\pi\) |
0.560430 | + | 0.828201i | \(0.310636\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −47.6218 | −1.81953 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.403990 | − | 0.699732i | 0.0153908 | − | 0.0266576i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.6708 | − | 20.2145i | −0.443979 | − | 0.768994i | 0.554001 | − | 0.832516i | \(-0.313100\pi\) |
−0.997980 | + | 0.0635214i | \(0.979767\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.38666 | − | 2.40176i | −0.0525990 | − | 0.0911041i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.71896 | + | 4.70939i | −0.102988 | + | 0.178381i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.51536 | 0.321621 | 0.160810 | − | 0.986985i | \(-0.448589\pi\) | ||||
0.160810 | + | 0.986985i | \(0.448589\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.3555 | + | 28.3285i | −0.616858 | + | 1.06843i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.65883 | − | 1.49217i | 0.0999958 | − | 0.0561187i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.8310 | − | 20.4919i | −0.444323 | − | 0.769591i | 0.553681 | − | 0.832729i | \(-0.313223\pi\) |
−0.998005 | + | 0.0631380i | \(0.979889\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −69.5552 | −2.60486 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.60531 | −0.321820 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.93197 | + | 8.54241i | 0.183931 | + | 0.318578i | 0.943216 | − | 0.332180i | \(-0.107784\pi\) |
−0.759285 | + | 0.650759i | \(0.774451\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.149864 | + | 12.2940i | −0.00558123 | + | 0.457853i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.60695 | − | 9.71152i | 0.208237 | − | 0.360677i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.37428 | 0.236409 | 0.118205 | − | 0.992989i | \(-0.462286\pi\) | ||||
0.118205 | + | 0.992989i | \(0.462286\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.69068 | + | 13.3206i | −0.284450 | + | 0.492682i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.09319 | − | 14.0178i | −0.298929 | − | 0.517760i | 0.676962 | − | 0.736018i | \(-0.263296\pi\) |
−0.975891 | + | 0.218258i | \(0.929963\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.11417 | + | 5.39391i | 0.114712 | + | 0.198687i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.59036 | + | 11.4148i | −0.242430 | + | 0.419901i | −0.961406 | − | 0.275134i | \(-0.911278\pi\) |
0.718976 | + | 0.695035i | \(0.244611\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.9733 | 1.13630 | 0.568149 | − | 0.822925i | \(-0.307660\pi\) | ||||
0.568149 | + | 0.822925i | \(0.307660\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.2378 | + | 31.5888i | −0.668182 | + | 1.15733i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.161361 | − | 13.2371i | 0.00589599 | − | 0.483674i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.0433 | − | 43.3763i | −0.913844 | − | 1.58282i | −0.808585 | − | 0.588379i | \(-0.799766\pi\) |
−0.105258 | − | 0.994445i | \(-0.533567\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 59.4120 | 2.16223 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.8647 | 0.721996 | 0.360998 | − | 0.932567i | \(-0.382436\pi\) | ||||
0.360998 | + | 0.932567i | \(0.382436\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.83627 | − | 3.18051i | −0.0665646 | − | 0.115293i | 0.830822 | − | 0.556538i | \(-0.187871\pi\) |
−0.897387 | + | 0.441244i | \(0.854537\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.2248 | − | 16.9625i | 1.09421 | − | 0.614083i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.63609 | + | 2.83379i | −0.0590758 | + | 0.102322i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.4494 | −0.593180 | −0.296590 | − | 0.955005i | \(-0.595850\pi\) | ||||
−0.296590 | + | 0.955005i | \(0.595850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.93020 | + | 5.07525i | −0.105392 | + | 0.182544i | −0.913898 | − | 0.405943i | \(-0.866943\pi\) |
0.808506 | + | 0.588487i | \(0.200276\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.5352 | − | 44.2282i | −0.917250 | − | 1.58872i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.71646 | + | 6.43710i | 0.133156 | + | 0.230633i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.96213 | + | 3.39852i | −0.0702107 | + | 0.121608i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 68.2236 | 2.43500 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.09393 | + | 12.2870i | −0.252871 | + | 0.437986i | −0.964315 | − | 0.264757i | \(-0.914708\pi\) |
0.711444 | + | 0.702743i | \(0.248042\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −37.1207 | − | 22.0393i | −1.31986 | − | 0.783627i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.95221 | − | 3.38132i | −0.0693249 | − | 0.120074i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.48696 | −0.194358 | −0.0971791 | − | 0.995267i | \(-0.530982\pi\) | ||||
−0.0971791 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.1434 | −0.712621 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.87528 | + | 6.71218i | 0.136756 | + | 0.236868i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −71.7244 | + | 40.2525i | −2.52795 | + | 1.41871i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.95033 | + | 10.3063i | −0.209202 | + | 0.362349i | −0.951463 | − | 0.307762i | \(-0.900420\pi\) |
0.742261 | + | 0.670111i | \(0.233753\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.3624 | −0.504330 | −0.252165 | − | 0.967684i | \(-0.581143\pi\) | ||||
−0.252165 | + | 0.967684i | \(0.581143\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.767885 | − | 1.33002i | 0.0268978 | − | 0.0465884i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.5121 | + | 18.2075i | 0.367773 | + | 0.637001i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.490073 | − | 0.848832i | −0.0171037 | − | 0.0296244i | 0.857347 | − | 0.514739i | \(-0.172111\pi\) |
−0.874451 | + | 0.485115i | \(0.838778\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.15458 | + | 14.1241i | −0.284251 | + | 0.492337i | −0.972427 | − | 0.233207i | \(-0.925078\pi\) |
0.688176 | + | 0.725543i | \(0.258412\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.8944 | −1.21340 | −0.606698 | − | 0.794932i | \(-0.707506\pi\) | ||||
−0.606698 | + | 0.794932i | \(0.707506\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.62014 | − | 6.27026i | 0.125733 | − | 0.217775i | −0.796286 | − | 0.604920i | \(-0.793205\pi\) |
0.922019 | + | 0.387145i | \(0.126539\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.8446 | + | 0.435116i | 0.618279 | + | 0.0150759i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.68992 | + | 6.39113i | 0.127695 | + | 0.221174i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.8646 | 0.513181 | 0.256591 | − | 0.966520i | \(-0.417401\pi\) | ||||
0.256591 | + | 0.966520i | \(0.417401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.1810 | −0.902794 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.9157 | + | 37.9591i | 0.753922 | + | 1.30583i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.818625 | + | 67.1555i | −0.0281283 | + | 2.30749i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 42.6845 | − | 73.9318i | 1.46321 | − | 2.53435i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.2313 | 1.61717 | 0.808584 | − | 0.588381i | \(-0.200235\pi\) | ||||
0.808584 | + | 0.588381i | \(0.200235\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.8218 | + | 32.6004i | −0.642942 | + | 1.11361i | 0.341831 | + | 0.939762i | \(0.388953\pi\) |
−0.984773 | + | 0.173847i | \(0.944380\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.1571 | − | 36.6451i | −0.721870 | − | 1.25032i | −0.960250 | − | 0.279143i | \(-0.909950\pi\) |
0.238380 | − | 0.971172i | \(-0.423384\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.30163 | − | 14.3788i | −0.282591 | − | 0.489461i | 0.689431 | − | 0.724351i | \(-0.257860\pi\) |
−0.972022 | + | 0.234890i | \(0.924527\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.6798 | + | 46.2108i | −0.907141 | + | 1.57121i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 99.0040 | 3.35848 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.215523 | + | 0.373296i | −0.00730271 | + | 0.0126487i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.0536 | − | 7.75014i | −0.441291 | − | 0.262003i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.96390 | + | 13.7939i | 0.268922 | + | 0.465786i | 0.968584 | − | 0.248688i | \(-0.0799993\pi\) |
−0.699662 | + | 0.714474i | \(0.746666\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.32330 | 0.111965 | 0.0559825 | − | 0.998432i | \(-0.482171\pi\) | ||||
0.0559825 | + | 0.998432i | \(0.482171\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.0603 | −1.14622 | −0.573111 | − | 0.819478i | \(-0.694264\pi\) | ||||
−0.573111 | + | 0.819478i | \(0.694264\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.4529 | − | 47.5499i | −0.921779 | − | 1.59657i | −0.796661 | − | 0.604426i | \(-0.793402\pi\) |
−0.125118 | − | 0.992142i | \(-0.539931\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33.0722 | − | 19.6356i | −1.10921 | − | 0.658557i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.7666 | + | 23.8445i | −0.460683 | + | 0.797926i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −29.9896 | −1.00244 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.41911 | − | 11.1182i | 0.214089 | − | 0.370813i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.46775 | − | 4.27427i | −0.0822127 | − | 0.142397i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.1976 | − | 43.6434i | −0.837595 | − | 1.45076i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.8314 | + | 18.7605i | −0.359650 | + | 0.622932i | −0.987902 | − | 0.155078i | \(-0.950437\pi\) |
0.628253 | + | 0.778009i | \(0.283770\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.5771 | 0.681751 | 0.340876 | − | 0.940108i | \(-0.389277\pi\) | ||||
0.340876 | + | 0.940108i | \(0.389277\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.7196 | − | 73.9925i | 1.41381 | − | 2.44879i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.0346050 | − | 2.83880i | 0.00114276 | − | 0.0937456i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.0458 | + | 17.3999i | 0.331381 | + | 0.573969i | 0.982783 | − | 0.184764i | \(-0.0591520\pi\) |
−0.651402 | + | 0.758733i | \(0.725819\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.271587 | −0.00893940 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 62.6815 | 2.06096 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.3664 | − | 21.4193i | −0.405729 | − | 0.702743i | 0.588677 | − | 0.808368i | \(-0.299649\pi\) |
−0.994406 | + | 0.105625i | \(0.966316\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.7106 | − | 20.8260i | 0.416575 | − | 0.682544i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −26.2825 | + | 45.5227i | −0.859531 | + | 1.48875i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.06826 | 0.263579 | 0.131789 | − | 0.991278i | \(-0.457928\pi\) | ||||
0.131789 | + | 0.991278i | \(0.457928\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.5985 | + | 40.8738i | −0.769290 | + | 1.33245i | 0.168659 | + | 0.985674i | \(0.446056\pi\) |
−0.937949 | + | 0.346774i | \(0.887277\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.69923 | − | 16.7996i | −0.315850 | − | 0.547069i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.8445 | − | 22.2474i | −0.417391 | − | 0.722942i | 0.578285 | − | 0.815835i | \(-0.303722\pi\) |
−0.995676 | + | 0.0928925i | \(0.970389\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.268197 | + | 0.464530i | −0.00870603 | + | 0.0150793i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.2971 | 0.495521 | 0.247760 | − | 0.968821i | \(-0.420305\pi\) | ||||
0.247760 | + | 0.968821i | \(0.420305\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.88948 | + | 11.9329i | −0.222938 | + | 0.386140i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.1511 | + | 18.0436i | −1.03821 | + | 0.582657i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.7339 | − | 23.7878i | −0.443028 | − | 0.767348i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.0518 | 0.645490 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.9754 | −1.18905 | −0.594524 | − | 0.804078i | \(-0.702659\pi\) | ||||
−0.594524 | + | 0.804078i | \(0.702659\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.66624 | + | 15.0104i | 0.278113 | + | 0.481706i | 0.970916 | − | 0.239421i | \(-0.0769578\pi\) |
−0.692803 | + | 0.721127i | \(0.743624\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.84619 | − | 1.09612i | −0.0591863 | − | 0.0351400i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.7004 | − | 37.5861i | 0.694256 | − | 1.20249i | −0.276174 | − | 0.961108i | \(-0.589067\pi\) |
0.970431 | − | 0.241380i | \(-0.0775999\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −80.9295 | −2.58652 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.6538 | − | 18.4530i | 0.339805 | − | 0.588559i | −0.644591 | − | 0.764528i | \(-0.722972\pi\) |
0.984396 | + | 0.175968i | \(0.0563057\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.21583 | + | 2.10589i | 0.0387397 | + | 0.0670992i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.4346 | − | 47.5181i | −0.872368 | − | 1.51099i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.60875 | − | 6.25055i | 0.114636 | − | 0.198555i | −0.802998 | − | 0.595981i | \(-0.796763\pi\) |
0.917634 | + | 0.397426i | \(0.130097\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34.9570 | 1.10821 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.42738 | + | 14.5966i | −0.266898 | + | 0.462281i | −0.968059 | − | 0.250722i | \(-0.919332\pi\) |
0.701161 | + | 0.713003i | \(0.252665\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1512.2.s.n.865.1 | ✓ | 8 | |
3.2 | odd | 2 | 1512.2.s.o.865.4 | yes | 8 | ||
7.2 | even | 3 | inner | 1512.2.s.n.1297.1 | yes | 8 | |
21.2 | odd | 6 | 1512.2.s.o.1297.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.s.n.865.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1512.2.s.n.1297.1 | yes | 8 | 7.2 | even | 3 | inner | |
1512.2.s.o.865.4 | yes | 8 | 3.2 | odd | 2 | ||
1512.2.s.o.1297.4 | yes | 8 | 21.2 | odd | 6 |