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 | 1297.4 | ||
Root | \(-1.30724 - 1.29485i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.1297 |
Dual form | 1512.2.s.o.865.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.70873 | − | 2.95960i | 0.764166 | − | 1.32357i | −0.176521 | − | 0.984297i | \(-0.556484\pi\) |
0.940687 | − | 0.339277i | \(-0.110182\pi\) | |||||||
\(6\) | 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 | −0.814971 | − | 0.579502i | \(-0.803247\pi\) |
−0.0943778 | − | 0.995536i | \(-0.530086\pi\) | |||||||
\(12\) | 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 | \(-0.266738\pi\) |
−0.978194 | + | 0.207691i | \(0.933405\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.74274 | + | 3.01852i | −0.399813 | + | 0.692496i | −0.993703 | − | 0.112050i | \(-0.964258\pi\) |
0.593890 | + | 0.804546i | \(0.297592\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.54822 | + | 7.87774i | −0.948369 | + | 1.64262i | −0.199508 | + | 0.979896i | \(0.563934\pi\) |
−0.748861 | + | 0.662727i | \(0.769399\pi\) | |||||||
\(24\) | 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 | \(-0.450176\pi\) | ||||
0.155890 | + | 0.987774i | \(0.450176\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.82321 | − | 6.62200i | −0.686669 | − | 1.18935i | −0.972909 | − | 0.231188i | \(-0.925739\pi\) |
0.286240 | − | 0.958158i | \(-0.407594\pi\) | |||||||
\(32\) | 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 | 0.165344 | + | 0.986236i | \(0.447127\pi\) |
−0.936777 | + | 0.349926i | \(0.886207\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.13253 | 0.333046 | 0.166523 | − | 0.986038i | \(-0.446746\pi\) | ||||
0.166523 | + | 0.986038i | \(0.446746\pi\) | |||||||
\(42\) | 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 | −0.419795 | − | 0.907619i | \(-0.637898\pi\) |
0.995919 | − | 0.0902560i | \(-0.0287685\pi\) | |||||||
\(48\) | 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 | \(-0.209105\pi\) |
−0.924805 | + | 0.380441i | \(0.875772\pi\) | |||||||
\(54\) | 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 | 0.999930 | + | 0.0118637i | \(0.00377642\pi\) |
−0.489691 | + | 0.871896i | \(0.662890\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.67648 | + | 8.09990i | −0.598762 | + | 1.03709i | 0.394243 | + | 0.919006i | \(0.371007\pi\) |
−0.993004 | + | 0.118079i | \(0.962326\pi\) | |||||||
\(62\) | 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 | 0.832764 | − | 0.553628i | \(-0.186757\pi\) |
−0.895838 | + | 0.444381i | \(0.853424\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.650582 | 0.0772099 | 0.0386049 | − | 0.999255i | \(-0.487709\pi\) | ||||
0.0386049 | + | 0.999255i | \(0.487709\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.642460 | − | 1.11277i | −0.0751942 | − | 0.130240i | 0.825976 | − | 0.563705i | \(-0.190624\pi\) |
−0.901171 | + | 0.433464i | \(0.857291\pi\) | |||||||
\(74\) | 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 | 0.129079 | − | 0.991634i | \(-0.458798\pi\) |
0.794241 | − | 0.607603i | \(-0.207869\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.1645 | −1.55475 | −0.777376 | − | 0.629036i | \(-0.783450\pi\) | ||||
−0.777376 | + | 0.629036i | \(0.783450\pi\) | |||||||
\(84\) | 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 | −0.253358 | − | 0.967373i | \(-0.581535\pi\) |
0.964448 | − | 0.264272i | \(-0.0851317\pi\) | |||||||
\(90\) | 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 | \(-0.148407\pi\) |
−0.835934 | + | 0.548830i | \(0.815074\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.32352 | + | 4.02446i | −0.228944 | + | 0.396542i | −0.957495 | − | 0.288449i | \(-0.906860\pi\) |
0.728552 | + | 0.684991i | \(0.240194\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.50177 | + | 4.33319i | −0.241855 | + | 0.418905i | −0.961243 | − | 0.275704i | \(-0.911089\pi\) |
0.719388 | + | 0.694609i | \(0.244423\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.54999 | − | 11.3449i | −0.627375 | − | 1.08665i | −0.988076 | − | 0.153964i | \(-0.950796\pi\) |
0.360702 | − | 0.932681i | \(-0.382537\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.3169 | −1.53496 | −0.767480 | − | 0.641072i | \(-0.778490\pi\) | ||||
−0.767480 | + | 0.641072i | \(0.778490\pi\) | |||||||
\(114\) | 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 | \(-0.848260\pi\) |
0.841635 | + | 0.540046i | \(0.181593\pi\) | |||||||
\(132\) | 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 | −0.993509 | − | 0.113754i | \(-0.963712\pi\) |
0.398240 | − | 0.917281i | \(-0.369621\pi\) | |||||||
\(138\) | 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 | \(-0.689304\pi\) |
0.997472 | + | 0.0710588i | \(0.0226378\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.69245 | − | 15.0558i | −0.707381 | − | 1.22522i | −0.965825 | − | 0.259194i | \(-0.916543\pi\) |
0.258444 | − | 0.966026i | \(-0.416790\pi\) | |||||||
\(152\) | 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 | −0.921804 | − | 0.387655i | \(-0.873285\pi\) |
0.125183 | − | 0.992134i | \(-0.460048\pi\) | |||||||
\(158\) | 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 | −0.857092 | − | 0.515164i | \(-0.827731\pi\) |
0.874691 | + | 0.484681i | \(0.161064\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.15946 | 0.167104 | 0.0835520 | − | 0.996503i | \(-0.473374\pi\) | ||||
0.0835520 | + | 0.996503i | \(0.473374\pi\) | |||||||
\(168\) | 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 | −0.400200 | − | 0.916428i | \(-0.631059\pi\) |
0.993750 | − | 0.111631i | \(-0.0356074\pi\) | |||||||
\(174\) | 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 | \(-0.273025\pi\) |
−0.982105 | + | 0.188332i | \(0.939692\pi\) | |||||||
\(180\) | 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 | \(-0.786735\pi\) |
0.929697 | + | 0.368324i | \(0.120068\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.93373 | − | 5.08138i | −0.211175 | − | 0.365765i | 0.740908 | − | 0.671607i | \(-0.234396\pi\) |
−0.952082 | + | 0.305841i | \(0.901062\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.711544 | 0.0506954 | 0.0253477 | − | 0.999679i | \(-0.491931\pi\) | ||||
0.0253477 | + | 0.999679i | \(0.491931\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.11448 | − | 8.85855i | −0.362556 | − | 0.627966i | 0.625825 | − | 0.779964i | \(-0.284763\pi\) |
−0.988381 | + | 0.151998i | \(0.951429\pi\) | |||||||
\(200\) | 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 | \(-0.288587\pi\) |
−0.990136 | + | 0.140112i | \(0.955254\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5132 | + | 18.2093i | −0.694729 | + | 1.20331i | 0.275544 | + | 0.961289i | \(0.411142\pi\) |
−0.970272 | + | 0.242017i | \(0.922191\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.80901 | − | 11.7936i | 0.446073 | − | 0.772621i | −0.552053 | − | 0.833809i | \(-0.686155\pi\) |
0.998126 | + | 0.0611876i | \(0.0194888\pi\) | |||||||
\(234\) | 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 | \(-0.276918\pi\) | ||||
0.644854 | + | 0.764305i | \(0.276918\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.39940 | + | 11.0841i | 0.412222 | + | 0.713989i | 0.995132 | − | 0.0985472i | \(-0.0314195\pi\) |
−0.582911 | + | 0.812536i | \(0.698086\pi\) | |||||||
\(242\) | 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 | \(-0.449235\pi\) | ||||
0.158807 | + | 0.987310i | \(0.449235\pi\) | |||||||
\(252\) | 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 | \(-0.938282\pi\) |
0.657496 | + | 0.753458i | \(0.271616\pi\) | |||||||
\(258\) | 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 | \(-0.0742588\pi\) |
−0.686664 | + | 0.726975i | \(0.740926\pi\) | |||||||
\(264\) | 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 | \(-0.0528067\pi\) |
−0.636148 | + | 0.771567i | \(0.719473\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.142148 | − | 0.246207i | 0.00863486 | − | 0.0149560i | −0.861676 | − | 0.507459i | \(-0.830585\pi\) |
0.870311 | + | 0.492503i | \(0.163918\pi\) | |||||||
\(272\) | 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 | 0.912183 | + | 0.409783i | \(0.134396\pi\) |
−0.101209 | + | 0.994865i | \(0.532271\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.6145 | −0.931482 | −0.465741 | − | 0.884921i | \(-0.654212\pi\) | ||||
−0.465741 | + | 0.884921i | \(0.654212\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.0504 | + | 27.8001i | 0.954098 | + | 1.65255i | 0.736419 | + | 0.676526i | \(0.236515\pi\) |
0.217679 | + | 0.976020i | \(0.430151\pi\) | |||||||
\(284\) | 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 | \(-0.342078\pi\) | ||||
0.476022 | + | 0.879433i | \(0.342078\pi\) | |||||||
\(294\) | 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 | 0.978539 | + | 0.206060i | \(0.0660642\pi\) |
−0.310817 | + | 0.950470i | \(0.600603\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.08255 | + | 3.60708i | −0.117713 | + | 0.203884i | −0.918861 | − | 0.394582i | \(-0.870889\pi\) |
0.801148 | + | 0.598466i | \(0.204223\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.82321 | − | 4.88994i | 0.158567 | − | 0.274647i | −0.775785 | − | 0.630997i | \(-0.782646\pi\) |
0.934352 | + | 0.356351i | \(0.115979\pi\) | |||||||
\(318\) | 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 | −0.726965 | − | 0.686674i | \(-0.759070\pi\) |
0.958160 | + | 0.286233i | \(0.0924032\pi\) | |||||||
\(332\) | 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 | \(-0.248899\pi\) |
−0.965025 | + | 0.262157i | \(0.915566\pi\) | |||||||
\(348\) | 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 | −0.978270 | − | 0.207333i | \(-0.933522\pi\) |
0.309579 | − | 0.950874i | \(-0.399812\pi\) | |||||||
\(354\) | 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 | −0.362763 | − | 0.931882i | \(-0.618166\pi\) |
0.988414 | − | 0.151779i | \(-0.0485003\pi\) | |||||||
\(360\) | 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 | 0.950951 | + | 0.309341i | \(0.100109\pi\) |
−0.207578 | + | 0.978218i | \(0.566558\pi\) | |||||||
\(368\) | 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 | −0.570441 | − | 0.821339i | \(-0.693228\pi\) |
0.996521 | + | 0.0833468i | \(0.0265609\pi\) | |||||||
\(374\) | 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 | 0.173504 | − | 0.984833i | \(-0.444491\pi\) |
0.766139 | − | 0.642675i | \(-0.222176\pi\) | |||||||
\(384\) | 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 | −0.999986 | − | 0.00525463i | \(-0.998327\pi\) |
0.495442 | − | 0.868641i | \(-0.335006\pi\) | |||||||
\(390\) | 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 | 0.331443 | + | 0.943475i | \(0.392465\pi\) |
−0.982795 | + | 0.184700i | \(0.940869\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.2506 | − | 26.4148i | 0.761578 | − | 1.31909i | −0.180459 | − | 0.983583i | \(-0.557758\pi\) |
0.942037 | − | 0.335509i | \(-0.108908\pi\) | |||||||
\(402\) | 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 | 0.942764 | − | 0.333462i | \(-0.108217\pi\) |
−0.760168 | + | 0.649726i | \(0.774884\pi\) | |||||||
\(410\) | 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 | \(-0.681289\pi\) | ||||
−0.539241 | + | 0.842152i | \(0.681289\pi\) | |||||||
\(420\) | 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 | \(-0.200121\pi\) |
−0.913700 | + | 0.406389i | \(0.866788\pi\) | |||||||
\(432\) | 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 | −0.837667 | − | 0.546181i | \(-0.816081\pi\) |
0.891840 | + | 0.452351i | \(0.149415\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.95932 | − | 12.0539i | 0.330647 | − | 0.572698i | −0.651992 | − | 0.758226i | \(-0.726066\pi\) |
0.982639 | + | 0.185528i | \(0.0593997\pi\) | |||||||
\(444\) | 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 | \(-0.337859\pi\) | ||||
0.487636 | + | 0.873047i | \(0.337859\pi\) | |||||||
\(450\) | 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 | −0.973573 | − | 0.228377i | \(-0.926658\pi\) |
0.684567 | + | 0.728950i | \(0.259991\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.4304 | −1.13784 | −0.568918 | − | 0.822394i | \(-0.692638\pi\) | ||||
−0.568918 | + | 0.822394i | \(0.692638\pi\) | |||||||
\(462\) | 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 | \(-0.932290\pi\) |
0.671562 | + | 0.740948i | \(0.265623\pi\) | |||||||
\(468\) | 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 | −0.872277 | − | 0.489012i | \(-0.837357\pi\) |
0.0126417 | − | 0.999920i | \(-0.495976\pi\) | |||||||
\(480\) | 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 | 0.600938 | − | 0.799295i | \(-0.294794\pi\) |
−0.992679 | + | 0.120780i | \(0.961460\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.1837 | 0.459584 | 0.229792 | − | 0.973240i | \(-0.426195\pi\) | ||||
0.229792 | + | 0.973240i | \(0.426195\pi\) | |||||||
\(492\) | 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 | −0.436210 | − | 0.899845i | \(-0.643679\pi\) |
0.997394 | − | 0.0721540i | \(-0.0229873\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.2887 | 1.43968 | 0.719841 | − | 0.694139i | \(-0.244215\pi\) | ||||
0.719841 | + | 0.694139i | \(0.244215\pi\) | |||||||
\(504\) | 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 | 0.420684 | + | 0.907207i | \(0.361790\pi\) |
−0.996006 | + | 0.0892808i | \(0.971543\pi\) | |||||||
\(510\) | 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 | \(-0.234378\pi\) |
−0.952066 | + | 0.305893i | \(0.901045\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.48372 | + | 14.6942i | −0.370967 | + | 0.642534i | −0.989715 | − | 0.143056i | \(-0.954307\pi\) |
0.618747 | + | 0.785590i | \(0.287640\pi\) | |||||||
\(524\) | 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 | −0.793947 | − | 0.607987i | \(-0.791977\pi\) |
0.923506 | + | 0.383585i | \(0.125311\pi\) | |||||||
\(542\) | 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 | \(-0.135206\pi\) |
−0.812461 | + | 0.583015i | \(0.801873\pi\) | |||||||
\(558\) | 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 | \(-0.304224\pi\) |
−0.995821 | + | 0.0913216i | \(0.970891\pi\) | |||||||
\(564\) | 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 | 0.222546 | + | 0.974922i | \(0.428563\pi\) |
−0.955580 | + | 0.294731i | \(0.904770\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.21049 | − | 9.02484i | −0.218052 | − | 0.377678i | 0.736160 | − | 0.676807i | \(-0.236637\pi\) |
−0.954212 | + | 0.299130i | \(0.903304\pi\) | |||||||
\(572\) | 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 | 0.937945 | + | 0.346784i | \(0.112726\pi\) |
−0.168649 | + | 0.985676i | \(0.553940\pi\) | |||||||
\(578\) | 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 | \(-0.685104\pi\) | ||||
−0.549296 | + | 0.835628i | \(0.685104\pi\) | |||||||
\(588\) | 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 | \(-0.866041\pi\) |
0.810171 | + | 0.586193i | \(0.199374\pi\) | |||||||
\(594\) | 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 | −0.985024 | − | 0.172416i | \(-0.944843\pi\) |
0.343196 | − | 0.939264i | \(-0.388491\pi\) | |||||||
\(600\) | 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 | −0.796267 | − | 0.604946i | \(-0.793195\pi\) |
0.922032 | + | 0.387114i | \(0.126528\pi\) | |||||||
\(608\) | 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 | 0.970445 | − | 0.241322i | \(-0.0775809\pi\) |
−0.694213 | + | 0.719769i | \(0.744248\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.8071 | −0.636371 | −0.318186 | − | 0.948028i | \(-0.603073\pi\) | ||||
−0.318186 | + | 0.948028i | \(0.603073\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.6961 | − | 30.6505i | −0.711266 | − | 1.23195i | −0.964382 | − | 0.264513i | \(-0.914789\pi\) |
0.253116 | − | 0.967436i | \(-0.418545\pi\) | |||||||
\(620\) | 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 | \(-0.140445\pi\) |
−0.821947 | + | 0.569565i | \(0.807112\pi\) | |||||||
\(642\) | 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 | \(-0.236046\pi\) |
−0.953655 | + | 0.300901i | \(0.902713\pi\) | |||||||
\(648\) | 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 | \(-0.917192\pi\) |
0.705939 | + | 0.708273i | \(0.250525\pi\) | |||||||
\(654\) | 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 | \(-0.318410\pi\) | ||||
0.540036 | + | 0.841642i | \(0.318410\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.65561 | + | 13.2599i | 0.297769 | + | 0.515751i | 0.975625 | − | 0.219444i | \(-0.0704242\pi\) |
−0.677856 | + | 0.735194i | \(0.737091\pi\) | |||||||
\(662\) | 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 | \(-0.858881\pi\) |
0.823150 | + | 0.567824i | \(0.192214\pi\) | |||||||
\(678\) | 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 | \(-0.0226976\pi\) |
−0.560430 | + | 0.828201i | \(0.689364\pi\) | |||||||
\(684\) | 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 | −0.997980 | − | 0.0635214i | \(-0.979767\pi\) |
0.554001 | + | 0.832516i | \(0.313100\pi\) | |||||||
\(692\) | 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 | \(-0.551411\pi\) | ||||
−0.160810 | + | 0.986985i | \(0.551411\pi\) | |||||||
\(702\) | 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 | −0.998005 | − | 0.0631380i | \(-0.979889\pi\) |
0.553681 | + | 0.832729i | \(0.313223\pi\) | |||||||
\(710\) | 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 | \(-0.892216\pi\) |
0.759285 | + | 0.650759i | \(0.225549\pi\) | |||||||
\(720\) | 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 | −0.975891 | − | 0.218258i | \(-0.929963\pi\) |
0.676962 | + | 0.736018i | \(0.263296\pi\) | |||||||
\(734\) | 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 | 0.718976 | − | 0.695035i | \(-0.244611\pi\) |
−0.961406 | + | 0.275134i | \(0.911278\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.9733 | −1.13630 | −0.568149 | − | 0.822925i | \(-0.692340\pi\) | ||||
−0.568149 | + | 0.822925i | \(0.692340\pi\) | |||||||
\(744\) | 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 | −0.105258 | + | 0.994445i | \(0.533567\pi\) |
−0.808585 | + | 0.588379i | \(0.799766\pi\) | |||||||
\(752\) | 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 | \(-0.812129\pi\) |
0.897387 | + | 0.441244i | \(0.145463\pi\) | |||||||
\(762\) | 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 | \(-0.133057\pi\) |
−0.808506 | + | 0.588487i | \(0.799724\pi\) | |||||||
\(774\) | 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 | 0.711444 | − | 0.702743i | \(-0.248042\pi\) |
−0.964315 | + | 0.264757i | \(0.914708\pi\) | |||||||
\(788\) | 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 | \(-0.469018\pi\) | ||||
0.0971791 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(798\) | 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 | \(-0.0995799\pi\) |
−0.742261 | + | 0.670111i | \(0.766247\pi\) | |||||||
\(810\) | 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 | \(-0.827889\pi\) |
0.874451 | + | 0.485115i | \(0.161222\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.15458 | − | 14.1241i | −0.284251 | − | 0.492337i | 0.688176 | − | 0.725543i | \(-0.258412\pi\) |
−0.972427 | + | 0.233207i | \(0.925078\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.8944 | 1.21340 | 0.606698 | − | 0.794932i | \(-0.292494\pi\) | ||||
0.606698 | + | 0.794932i | \(0.292494\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.62014 | + | 6.27026i | 0.125733 | + | 0.217775i | 0.922019 | − | 0.387145i | \(-0.126539\pi\) |
−0.796286 | + | 0.604920i | \(0.793205\pi\) | |||||||
\(830\) | 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 | \(-0.582599\pi\) | ||||
−0.256591 | + | 0.966520i | \(0.582599\pi\) | |||||||
\(840\) | 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 | 0.984773 | + | 0.173847i | \(0.0556198\pi\) |
−0.341831 | + | 0.939762i | \(0.611047\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.1571 | + | 36.6451i | −0.721870 | + | 1.25032i | 0.238380 | + | 0.971172i | \(0.423384\pi\) |
−0.960250 | + | 0.279143i | \(0.909950\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.30163 | − | 14.3788i | 0.282591 | − | 0.489461i | −0.689431 | − | 0.724351i | \(-0.742140\pi\) |
0.972022 | + | 0.234890i | \(0.0754729\pi\) | |||||||
\(864\) | 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 | −0.699662 | − | 0.714474i | \(-0.746666\pi\) |
0.968584 | + | 0.248688i | \(0.0799993\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.32330 | −0.111965 | −0.0559825 | − | 0.998432i | \(-0.517829\pi\) | ||||
−0.0559825 | + | 0.998432i | \(0.517829\pi\) | |||||||
\(882\) | 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 | 0.125118 | − | 0.992142i | \(-0.460069\pi\) |
0.796661 | − | 0.604426i | \(-0.206598\pi\) | |||||||
\(888\) | 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 | 0.628253 | − | 0.778009i | \(-0.283770\pi\) |
−0.987902 | + | 0.155078i | \(0.950437\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.5771 | −0.681751 | −0.340876 | − | 0.940108i | \(-0.610723\pi\) | ||||
−0.340876 | + | 0.940108i | \(0.610723\pi\) | |||||||
\(912\) | 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 | −0.651402 | − | 0.758733i | \(-0.725819\pi\) |
0.982783 | + | 0.184764i | \(0.0591520\pi\) | |||||||
\(920\) | 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 | \(-0.700351\pi\) |
0.994406 | + | 0.105625i | \(0.0336844\pi\) | |||||||
\(930\) | 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 | 0.937949 | + | 0.346774i | \(0.112723\pi\) |
−0.168659 | + | 0.985674i | \(0.553944\pi\) | |||||||
\(942\) | 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 | \(-0.696278\pi\) |
0.995676 | + | 0.0928925i | \(0.0296113\pi\) | |||||||
\(948\) | 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 | \(-0.579695\pi\) | ||||
−0.247760 | + | 0.968821i | \(0.579695\pi\) | |||||||
\(954\) | 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 | \(-0.923042\pi\) |
0.692803 | + | 0.721127i | \(0.256376\pi\) | |||||||
\(972\) | 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 | −0.970431 | − | 0.241380i | \(-0.922400\pi\) |
0.276174 | − | 0.961108i | \(-0.410933\pi\) | |||||||
\(978\) | 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 | \(-0.277028\pi\) |
−0.984396 | + | 0.175968i | \(0.943694\pi\) | |||||||
\(984\) | 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 | 0.917634 | − | 0.397426i | \(-0.130097\pi\) |
−0.802998 | + | 0.595981i | \(0.796763\pi\) | |||||||
\(992\) | 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 | 0.701161 | − | 0.713003i | \(-0.252665\pi\) |
−0.968059 | + | 0.250722i | \(0.919332\pi\) | |||||||
\(998\) | 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.o.1297.4 | yes | 8 | |
3.2 | odd | 2 | 1512.2.s.n.1297.1 | yes | 8 | ||
7.4 | even | 3 | inner | 1512.2.s.o.865.4 | yes | 8 | |
21.11 | odd | 6 | 1512.2.s.n.865.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.s.n.865.1 | ✓ | 8 | 21.11 | odd | 6 | ||
1512.2.s.n.1297.1 | yes | 8 | 3.2 | odd | 2 | ||
1512.2.s.o.865.4 | yes | 8 | 7.4 | even | 3 | inner | |
1512.2.s.o.1297.4 | yes | 8 | 1.1 | even | 1 | trivial |