Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(559,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.559");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.bm (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.897122304.10 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 51x^{4} - 104x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 559.1 | ||
Root | \(1.30421 + 0.752986i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.559 |
Dual form | 2736.2.bm.q.1855.1 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.05719 | + | 3.56317i | −0.920006 | + | 1.59350i | −0.120603 | + | 0.992701i | \(0.538483\pi\) |
−0.799403 | + | 0.600795i | \(0.794851\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | −0.981981 | − | 0.188982i | \(-0.939481\pi\) | ||
0.981981 | − | 0.188982i | \(-0.0605189\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.11439i | 1.24054i | 0.784390 | + | 0.620268i | \(0.212976\pi\) | ||||
−0.784390 | + | 0.620268i | \(0.787024\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50000 | + | 0.866025i | −0.416025 | + | 0.240192i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50597 | + | 2.60842i | −0.365252 | + | 0.632634i | −0.988817 | − | 0.149137i | \(-0.952350\pi\) |
0.623565 | + | 0.781772i | \(0.285684\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.73205 | + | 4.00000i | −0.397360 | + | 0.917663i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.954747 | − | 0.551224i | 0.199079 | − | 0.114938i | −0.397147 | − | 0.917755i | \(-0.630000\pi\) |
0.596226 | + | 0.802817i | \(0.296666\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.96410 | − | 10.3301i | −1.19282 | − | 2.06603i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.51791 | + | 2.60842i | −0.838955 | + | 0.484371i | −0.856909 | − | 0.515468i | \(-0.827618\pi\) |
0.0179536 | + | 0.999839i | \(0.494285\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.26795 | 0.766546 | 0.383273 | − | 0.923635i | \(-0.374797\pi\) | ||||
0.383273 | + | 0.923635i | \(0.374797\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.56317 | + | 2.05719i | 0.602285 | + | 0.347729i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.26795i | − | 0.701647i | −0.936442 | − | 0.350823i | \(-0.885902\pi\) | ||
0.936442 | − | 0.350823i | \(-0.114098\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.59808 | − | 3.23205i | −0.853699 | − | 0.492883i | 0.00819845 | − | 0.999966i | \(-0.497390\pi\) |
−0.861897 | + | 0.507083i | \(0.830724\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.21684 | − | 3.01194i | 0.760954 | − | 0.439337i | −0.0686842 | − | 0.997638i | \(-0.521880\pi\) |
0.829638 | + | 0.558302i | \(0.188547\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.00000 | 0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.65367 | + | 0.954747i | −0.227149 | + | 0.131145i | −0.609256 | − | 0.792973i | \(-0.708532\pi\) |
0.382107 | + | 0.924118i | \(0.375199\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.6603 | − | 8.46410i | −1.97679 | − | 1.14130i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.954747 | + | 1.65367i | −0.124298 | + | 0.215290i | −0.921458 | − | 0.388478i | \(-0.873001\pi\) |
0.797161 | + | 0.603767i | \(0.206334\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.96410 | − | 3.40192i | −0.251477 | − | 0.435572i | 0.712455 | − | 0.701717i | \(-0.247583\pi\) |
−0.963933 | + | 0.266146i | \(0.914250\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 7.12633i | − | 0.883913i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.59808 | + | 9.69615i | 0.683914 | + | 1.18457i | 0.973777 | + | 0.227505i | \(0.0730569\pi\) |
−0.289863 | + | 0.957068i | \(0.593610\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.51791 | − | 7.82526i | 0.536178 | − | 0.928687i | −0.462928 | − | 0.886396i | \(-0.653201\pi\) |
0.999105 | − | 0.0422909i | \(-0.0134656\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.69615 | − | 4.66987i | 0.315561 | − | 0.546567i | −0.663996 | − | 0.747736i | \(-0.731141\pi\) |
0.979557 | + | 0.201169i | \(0.0644741\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.11439 | 0.468878 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.33013 | + | 12.6962i | −0.824704 | + | 1.42843i | 0.0774418 | + | 0.996997i | \(0.475325\pi\) |
−0.902146 | + | 0.431432i | \(0.858009\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.2407i | 1.23383i | 0.787030 | + | 0.616915i | \(0.211618\pi\) | ||||
−0.787030 | + | 0.616915i | \(0.788382\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.19615 | − | 10.7321i | −0.672067 | − | 1.16405i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.6895 | − | 6.17158i | 1.13308 | − | 0.654187i | 0.188376 | − | 0.982097i | \(-0.439678\pi\) |
0.944709 | + | 0.327910i | \(0.106344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.866025 | + | 1.50000i | 0.0907841 | + | 0.157243i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.6895 | − | 14.4004i | −1.09672 | − | 1.47745i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.19615 | − | 3.00000i | −0.527589 | − | 0.304604i | 0.212445 | − | 0.977173i | \(-0.431857\pi\) |
−0.740034 | + | 0.672569i | \(0.765191\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.62036 | − | 9.73475i | −0.559247 | − | 0.968644i | −0.997560 | − | 0.0698213i | \(-0.977757\pi\) |
0.438313 | − | 0.898823i | \(-0.355576\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.6603 | −1.44452 | −0.722259 | − | 0.691623i | \(-0.756896\pi\) | ||||
−0.722259 | + | 0.691623i | \(0.756896\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.4695 | −1.88219 | −0.941094 | − | 0.338145i | \(-0.890200\pi\) | ||||
−0.941094 | + | 0.338145i | \(0.890200\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.1962 | − | 6.46410i | −1.07240 | − | 0.619149i | −0.143562 | − | 0.989641i | \(-0.545856\pi\) |
−0.928835 | + | 0.370493i | \(0.879189\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.90949i | 0.179630i | 0.995958 | + | 0.0898151i | \(0.0286276\pi\) | ||||
−0.995958 | + | 0.0898151i | \(0.971372\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.53590i | 0.422975i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.60842 | + | 1.50597i | 0.239113 | + | 0.138052i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.92820 | −0.538928 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 28.5053 | 2.54959 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.92820 | − | 12.0000i | −0.614779 | − | 1.06483i | −0.990423 | − | 0.138064i | \(-0.955912\pi\) |
0.375645 | − | 0.926764i | \(-0.377421\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.60842 | − | 1.50597i | −0.227899 | − | 0.131577i | 0.381704 | − | 0.924285i | \(-0.375337\pi\) |
−0.609602 | + | 0.792707i | \(0.708671\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | + | 1.73205i | 0.346844 | + | 0.150188i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.403524 | − | 0.698924i | −0.0344754 | − | 0.0597131i | 0.848273 | − | 0.529559i | \(-0.177643\pi\) |
−0.882748 | + | 0.469846i | \(0.844309\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.86603 | − | 5.69615i | 0.836825 | − | 0.483141i | −0.0193585 | − | 0.999813i | \(-0.506162\pi\) |
0.856184 | + | 0.516671i | \(0.172829\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.56317 | − | 6.17158i | −0.297967 | − | 0.516094i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 21.4641i | − | 1.78250i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.15964 | − | 5.47266i | 0.258848 | − | 0.448338i | −0.707086 | − | 0.707128i | \(-0.749990\pi\) |
0.965934 | + | 0.258790i | \(0.0833238\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.07180 | 0.412737 | 0.206368 | − | 0.978474i | \(-0.433835\pi\) | ||||
0.206368 | + | 0.978474i | \(0.433835\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.78000 | + | 15.2074i | −0.705227 | + | 1.22149i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.69615 | − | 11.5981i | 0.534411 | − | 0.925627i | −0.464780 | − | 0.885426i | \(-0.653867\pi\) |
0.999192 | − | 0.0402013i | \(-0.0127999\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.551224 | − | 0.954747i | −0.0434425 | − | 0.0752446i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.00000i | 0.391630i | 0.980641 | + | 0.195815i | \(0.0627352\pi\) | ||||
−0.980641 | + | 0.195815i | \(0.937265\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.3884 | − | 19.7253i | −0.881263 | − | 1.52639i | −0.849938 | − | 0.526882i | \(-0.823361\pi\) |
−0.0313242 | − | 0.999509i | \(-0.509972\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | + | 8.66025i | −0.384615 | + | 0.666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.8611 | − | 9.73475i | −1.28192 | − | 0.740119i | −0.304724 | − | 0.952441i | \(-0.598564\pi\) |
−0.977200 | + | 0.212321i | \(0.931898\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.3301 | + | 5.96410i | −0.780884 | + | 0.450844i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.7768 | 1.70242 | 0.851211 | − | 0.524824i | \(-0.175869\pi\) | ||||
0.851211 | + | 0.524824i | \(0.175869\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.3923 | − | 11.1962i | 1.44142 | − | 0.832203i | 0.443474 | − | 0.896287i | \(-0.353746\pi\) |
0.997945 | + | 0.0640837i | \(0.0204125\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.2074 | + | 8.78000i | 1.11807 | + | 0.645519i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.7321 | − | 6.19615i | −0.784805 | − | 0.453108i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.31928i | 0.457247i | 0.973515 | + | 0.228624i | \(0.0734225\pi\) | ||||
−0.973515 | + | 0.228624i | \(0.926577\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8923 | − | 6.86603i | −0.856027 | − | 0.494227i | 0.00665294 | − | 0.999978i | \(-0.497882\pi\) |
−0.862680 | + | 0.505751i | \(0.831216\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.10245 | 0.0785461 | 0.0392731 | − | 0.999229i | \(-0.487496\pi\) | ||||
0.0392731 | + | 0.999229i | \(0.487496\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.401924 | − | 0.232051i | 0.0284916 | − | 0.0164496i | −0.485687 | − | 0.874133i | \(-0.661430\pi\) |
0.514178 | + | 0.857683i | \(0.328097\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.60842 | + | 4.51791i | 0.183075 | + | 0.317095i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.4576 | − | 7.12633i | −1.13839 | − | 0.492939i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.33013 | + | 12.6962i | −0.504627 | + | 0.874039i | 0.495359 | + | 0.868688i | \(0.335037\pi\) |
−0.999986 | + | 0.00535078i | \(0.998297\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23.0327 | − | 13.2979i | 1.57081 | − | 0.906910i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 4.26795i | − | 0.289727i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 5.21684i | − | 0.350922i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.86603 | − | 11.8923i | 0.459783 | − | 0.796368i | −0.539166 | − | 0.842199i | \(-0.681260\pi\) |
0.998949 | + | 0.0458318i | \(0.0145938\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.30734 | −0.219516 | −0.109758 | − | 0.993958i | \(-0.535008\pi\) | ||||
−0.109758 | + | 0.993958i | \(0.535008\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.3205 | −1.73931 | −0.869654 | − | 0.493662i | \(-0.835658\pi\) | ||||
−0.869654 | + | 0.493662i | \(0.835658\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.52986 | + | 13.0421i | −0.493297 | + | 0.854416i | −0.999970 | − | 0.00772244i | \(-0.997542\pi\) |
0.506673 | + | 0.862138i | \(0.330875\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.7846i | 1.61677i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.3909i | 1.57772i | 0.614574 | + | 0.788859i | \(0.289328\pi\) | ||||
−0.614574 | + | 0.788859i | \(0.710672\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.69615 | − | 5.59808i | 0.624584 | − | 0.360604i | −0.154068 | − | 0.988060i | \(-0.549237\pi\) |
0.778652 | + | 0.627457i | \(0.215904\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.3432 | + | 21.3790i | −0.788576 | + | 1.36585i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.866025 | − | 7.50000i | −0.0551039 | − | 0.477214i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.2527 | + | 8.22878i | −0.899620 | + | 0.519396i | −0.877077 | − | 0.480350i | \(-0.840510\pi\) |
−0.0225432 | + | 0.999746i | \(0.507176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.26795 | + | 3.92820i | 0.142585 | + | 0.246964i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.0327 | + | 13.2979i | −1.43674 | + | 0.829501i | −0.997622 | − | 0.0689288i | \(-0.978042\pi\) |
−0.439117 | + | 0.898430i | \(0.644709\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.26795 | −0.265197 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.0779 | + | 12.7467i | 1.36138 | + | 0.785995i | 0.989808 | − | 0.142408i | \(-0.0454846\pi\) |
0.371575 | + | 0.928403i | \(0.378818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 7.85641i | − | 0.482615i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.9968 | + | 8.08108i | 0.853402 | + | 0.492712i | 0.861797 | − | 0.507253i | \(-0.169339\pi\) |
−0.00839497 | + | 0.999965i | \(0.502672\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.39230 | − | 0.803848i | −0.0845765 | − | 0.0488303i | 0.457115 | − | 0.889407i | \(-0.348883\pi\) |
−0.541692 | + | 0.840577i | \(0.682216\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 42.5022 | − | 24.5386i | 2.56298 | − | 1.47974i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.4641 | −1.28965 | −0.644826 | − | 0.764329i | \(-0.723070\pi\) | ||||
−0.644826 | + | 0.764329i | \(0.723070\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.5506 | + | 15.9063i | −1.64353 | + | 0.948892i | −0.663965 | + | 0.747764i | \(0.731128\pi\) |
−0.979565 | + | 0.201129i | \(0.935539\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.58846 | + | 5.53590i | 0.569975 | + | 0.329075i | 0.757139 | − | 0.653254i | \(-0.226596\pi\) |
−0.187165 | + | 0.982329i | \(0.559930\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.96410 | + | 6.86603i | 0.233182 | + | 0.403884i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 14.2527i | − | 0.832650i | −0.909216 | − | 0.416325i | \(-0.863318\pi\) | ||
0.909216 | − | 0.416325i | \(-0.136682\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.92820 | − | 6.80385i | −0.228709 | − | 0.396135i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.954747 | + | 1.65367i | −0.0552145 | + | 0.0956343i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.23205 | + | 5.59808i | −0.186292 | + | 0.322668i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.1622 | 0.925443 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.2679 | − | 17.7846i | 0.586023 | − | 1.01502i | −0.408724 | − | 0.912658i | \(-0.634026\pi\) |
0.994747 | − | 0.102363i | \(-0.0326404\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.4029i | 1.55387i | 0.629578 | + | 0.776937i | \(0.283228\pi\) | ||||
−0.629578 | + | 0.776937i | \(0.716772\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.19615 | + | 14.1962i | 0.463274 | + | 0.802414i | 0.999122 | − | 0.0419006i | \(-0.0133413\pi\) |
−0.535848 | + | 0.844315i | \(0.680008\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.2074 | + | 8.78000i | −0.854133 | + | 0.493134i | −0.862043 | − | 0.506835i | \(-0.830815\pi\) |
0.00790998 | + | 0.999969i | \(0.497482\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.7321 | − | 18.5885i | −0.600879 | − | 1.04075i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.82526 | − | 10.5418i | −0.435409 | − | 0.586561i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.8923 | + | 10.3301i | 0.992487 | + | 0.573012i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.01194 | − | 5.21684i | −0.166054 | − | 0.287614i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.9808 | 1.42803 | 0.714016 | − | 0.700129i | \(-0.246874\pi\) | ||||
0.714016 | + | 0.700129i | \(0.246874\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −46.0653 | −2.51682 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.0885 | + | 15.0622i | 1.42113 | + | 0.820489i | 0.996395 | − | 0.0848294i | \(-0.0270345\pi\) |
0.424733 | + | 0.905319i | \(0.360368\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.5600i | 0.950928i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.0000i | − | 0.701934i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.47266 | + | 3.15964i | 0.293788 | + | 0.169618i | 0.639649 | − | 0.768667i | \(-0.279080\pi\) |
−0.345861 | + | 0.938286i | \(0.612413\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.0000 | 1.23116 | 0.615581 | − | 0.788074i | \(-0.288921\pi\) | ||||
0.615581 | + | 0.788074i | \(0.288921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.7530 | 0.891670 | 0.445835 | − | 0.895115i | \(-0.352907\pi\) | ||||
0.445835 | + | 0.895115i | \(0.352907\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.5885 | + | 32.1962i | 0.986573 | + | 1.70879i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.9453 | + | 6.31928i | 0.577672 | + | 0.333519i | 0.760208 | − | 0.649680i | \(-0.225097\pi\) |
−0.182536 | + | 0.983199i | \(0.558431\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0000 | − | 13.8564i | −0.684211 | − | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.0930 | + | 19.2137i | 0.580635 | + | 1.00569i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.9904 | + | 12.6962i | −1.14789 | + | 0.662734i | −0.948372 | − | 0.317161i | \(-0.897271\pi\) |
−0.199517 | + | 0.979894i | \(0.563937\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.954747 | + | 1.65367i | 0.0495680 | + | 0.0858543i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.5359i | 1.06331i | 0.846961 | + | 0.531654i | \(0.178429\pi\) | ||||
−0.846961 | + | 0.531654i | \(0.821571\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.51791 | − | 7.82526i | 0.232684 | − | 0.403021i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.5885 | 1.10892 | 0.554462 | − | 0.832209i | \(-0.312924\pi\) | ||||
0.554462 | + | 0.832209i | \(0.312924\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.8158 | + | 30.8579i | −0.910346 | + | 1.57677i | −0.0967711 | + | 0.995307i | \(0.530851\pi\) |
−0.813575 | + | 0.581460i | \(0.802482\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.46410 | + | 14.6603i | −0.431371 | + | 0.747156i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.0088 | − | 29.4601i | −0.862380 | − | 1.49369i | −0.869626 | − | 0.493711i | \(-0.835640\pi\) |
0.00724629 | − | 0.999974i | \(-0.497693\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.32051i | 0.167925i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −30.1590 | − | 52.2369i | −1.51746 | − | 2.62832i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.8923 | − | 22.3301i | 0.647046 | − | 1.12072i | −0.336779 | − | 0.941584i | \(-0.609337\pi\) |
0.983825 | − | 0.179133i | \(-0.0573293\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.9968 | − | 8.08108i | −0.698969 | − | 0.403550i | 0.107994 | − | 0.994152i | \(-0.465557\pi\) |
−0.806963 | + | 0.590602i | \(0.798890\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.40192 | + | 3.69615i | −0.318903 | + | 0.184118i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.5600 | 0.870417 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.9808 | + | 18.4641i | −1.58135 | + | 0.912991i | −0.586684 | + | 0.809816i | \(0.699567\pi\) |
−0.994663 | + | 0.103175i | \(0.967100\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.65367 | + | 0.954747i | 0.0813718 | + | 0.0469801i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −40.0526 | − | 23.1244i | −1.96610 | − | 1.13513i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 16.7530i | − | 0.818436i | −0.912437 | − | 0.409218i | \(-0.865802\pi\) | ||
0.912437 | − | 0.409218i | \(-0.134198\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.00000 | − | 5.19615i | −0.438633 | − | 0.253245i | 0.264385 | − | 0.964417i | \(-0.414831\pi\) |
−0.703018 | + | 0.711172i | \(0.748165\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 35.9271 | 1.74272 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.40192 | + | 1.96410i | −0.164631 | + | 0.0950495i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.21684 | + | 9.03583i | 0.251286 | + | 0.435240i | 0.963880 | − | 0.266336i | \(-0.0858131\pi\) |
−0.712594 | + | 0.701577i | \(0.752480\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.5000 | + | 11.2583i | −0.937110 | + | 0.541041i | −0.889053 | − | 0.457804i | \(-0.848636\pi\) |
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.551224 | + | 4.77374i | 0.0263686 | + | 0.228359i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.79423 | − | 3.10770i | 0.0856339 | − | 0.148322i | −0.820027 | − | 0.572324i | \(-0.806042\pi\) |
0.905661 | + | 0.424002i | \(0.139375\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.60842 | − | 1.50597i | 0.123930 | − | 0.0715509i | −0.436754 | − | 0.899581i | \(-0.643872\pi\) |
0.560683 | + | 0.828030i | \(0.310539\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 50.7846i | 2.40742i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.8548i | 0.606656i | 0.952886 | + | 0.303328i | \(0.0980978\pi\) | ||||
−0.952886 | + | 0.303328i | \(0.901902\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.12633 | −0.334088 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.3923 | 0.813578 | 0.406789 | − | 0.913522i | \(-0.366648\pi\) | ||||
0.406789 | + | 0.913522i | \(0.366648\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.37021 | − | 7.56943i | 0.203541 | − | 0.352544i | −0.746126 | − | 0.665805i | \(-0.768088\pi\) |
0.949667 | + | 0.313261i | \(0.101422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.3205i | 0.944374i | 0.881498 | + | 0.472187i | \(0.156535\pi\) | ||||
−0.881498 | + | 0.472187i | \(0.843465\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.84287i | 0.455474i | 0.973723 | + | 0.227737i | \(0.0731326\pi\) | ||||
−0.973723 | + | 0.227737i | \(0.926867\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.69615 | − | 5.59808i | 0.447727 | − | 0.258495i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.2979 | − | 23.0327i | 0.611439 | − | 1.05904i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 51.6506 | − | 5.96410i | 2.36989 | − | 0.273652i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.2948 | + | 15.7586i | −1.24713 | + | 0.720030i | −0.970536 | − | 0.240957i | \(-0.922539\pi\) |
−0.276593 | + | 0.960987i | \(0.589206\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.69615 | + | 6.40192i | 0.168530 | + | 0.291903i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.3790 | − | 12.3432i | 0.970770 | − | 0.560474i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.39230 | −0.199034 | −0.0995172 | − | 0.995036i | \(-0.531730\pi\) | ||||
−0.0995172 | + | 0.995036i | \(0.531730\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.00627 | + | 2.31302i | 0.180800 | + | 0.104385i | 0.587669 | − | 0.809102i | \(-0.300046\pi\) |
−0.406868 | + | 0.913487i | \(0.633379\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 15.7128i | − | 0.707670i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.82526 | − | 4.51791i | −0.351011 | − | 0.202656i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.3109 | + | 17.5000i | 1.35690 | + | 0.783408i | 0.989205 | − | 0.146538i | \(-0.0468131\pi\) |
0.367697 | + | 0.929946i | \(0.380146\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.2948 | − | 15.7586i | 1.21701 | − | 0.702643i | 0.252735 | − | 0.967535i | \(-0.418670\pi\) |
0.964278 | + | 0.264893i | \(0.0853365\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 46.2487 | 2.05804 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.3432 | + | 7.12633i | −0.547101 | + | 0.315869i | −0.747952 | − | 0.663753i | \(-0.768963\pi\) |
0.200851 | + | 0.979622i | \(0.435629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.66987 | − | 2.69615i | −0.206583 | − | 0.119271i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30.1590 | − | 52.2369i | 1.32896 | − | 2.30183i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.3923 | + | 21.4641i | 0.545013 | + | 0.943990i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 35.6317i | − | 1.56105i | −0.625124 | − | 0.780526i | \(-0.714951\pi\) | ||
0.625124 | − | 0.780526i | \(-0.285049\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.866025 | − | 1.50000i | −0.0378686 | − | 0.0655904i | 0.846470 | − | 0.532437i | \(-0.178724\pi\) |
−0.884339 | + | 0.466846i | \(0.845390\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.42741 | + | 11.1326i | −0.279982 | + | 0.484944i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.8923 | + | 18.8660i | −0.473578 | + | 0.820262i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 40.0526 | − | 69.3731i | 1.73162 | − | 2.99926i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.6863i | 1.06332i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.89230 | + | 13.6699i | 0.339317 | + | 0.587714i | 0.984304 | − | 0.176479i | \(-0.0564708\pi\) |
−0.644988 | + | 0.764193i | \(0.723138\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 46.0653 | − | 26.5958i | 1.97322 | − | 1.13924i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.79423 | + | 3.10770i | 0.0767157 | + | 0.132875i | 0.901831 | − | 0.432089i | \(-0.142223\pi\) |
−0.825115 | + | 0.564964i | \(0.808890\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.60842 | − | 22.5896i | −0.111122 | − | 0.962348i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.6962 | + | 7.33013i | 0.539895 | + | 0.311709i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.0540 | − | 27.8064i | −0.680231 | − | 1.17820i | −0.974910 | − | 0.222599i | \(-0.928546\pi\) |
0.294679 | − | 0.955596i | \(-0.404787\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.1962 | 0.473547 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.39785 | −0.0589122 | −0.0294561 | − | 0.999566i | \(-0.509378\pi\) | ||||
−0.0294561 | + | 0.999566i | \(0.509378\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.80385 | − | 3.92820i | −0.286240 | − | 0.165261i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.4337i | 0.437402i | 0.975792 | + | 0.218701i | \(0.0701820\pi\) | ||||
−0.975792 | + | 0.218701i | \(0.929818\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 17.7846i | − | 0.744263i | −0.928180 | − | 0.372131i | \(-0.878627\pi\) | ||
0.928180 | − | 0.372131i | \(-0.121373\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.3884 | − | 6.57511i | −0.474930 | − | 0.274201i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.3205 | 0.970845 | 0.485423 | − | 0.874280i | \(-0.338666\pi\) | ||||
0.485423 | + | 0.874280i | \(0.338666\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.2407 | 0.466344 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.92820 | − | 6.80385i | −0.162690 | − | 0.281787i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.4959 | − | 22.2256i | −1.58890 | − | 0.917350i | −0.993489 | − | 0.113925i | \(-0.963658\pi\) |
−0.595407 | − | 0.803425i | \(-0.703009\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.39230 | + | 17.0718i | −0.304595 | + | 0.703431i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.551224 | − | 0.954747i | −0.0226360 | − | 0.0392068i | 0.854485 | − | 0.519475i | \(-0.173873\pi\) |
−0.877122 | + | 0.480268i | \(0.840539\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.7321 | + | 6.19615i | −0.439971 | + | 0.254017i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.6895 | − | 18.5148i | −0.436761 | − | 0.756492i | 0.560676 | − | 0.828035i | \(-0.310541\pi\) |
−0.997438 | + | 0.0715426i | \(0.977208\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.7321i | 0.804887i | 0.915445 | + | 0.402444i | \(0.131839\pi\) | ||||
−0.915445 | + | 0.402444i | \(0.868161\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.1955 | − | 21.1232i | 0.495816 | − | 0.858779i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.3397 | 0.866154 | 0.433077 | − | 0.901357i | \(-0.357428\pi\) | ||||
0.433077 | + | 0.901357i | \(0.357428\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.21684 | + | 9.03583i | −0.211051 | + | 0.365550i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.46410 | − | 6.00000i | 0.139914 | − | 0.242338i | −0.787550 | − | 0.616251i | \(-0.788651\pi\) |
0.927464 | + | 0.373913i | \(0.121984\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.05719 | − | 3.56317i | −0.0828195 | − | 0.143448i | 0.821640 | − | 0.570006i | \(-0.193059\pi\) |
−0.904460 | + | 0.426558i | \(0.859726\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.39230i | 0.216735i | 0.994111 | + | 0.108368i | \(0.0345623\pi\) | ||||
−0.994111 | + | 0.108368i | \(0.965438\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.17158 | − | 10.6895i | −0.247259 | − | 0.428266i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.8205 | + | 49.9186i | −1.15282 | + | 1.99674i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.1326 | + | 6.42741i | 0.443886 | + | 0.256278i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.91858 | − | 1.10770i | 0.0763776 | − | 0.0440966i | −0.461325 | − | 0.887231i | \(-0.652626\pi\) |
0.537702 | + | 0.843135i | \(0.319292\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 57.0107 | 2.26240 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.00000 | + | 5.19615i | −0.356593 | + | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.30734 | + | 1.90949i | 0.130632 | + | 0.0754205i | 0.563892 | − | 0.825849i | \(-0.309303\pi\) |
−0.433260 | + | 0.901269i | \(0.642637\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.7750 | + | 17.7679i | 1.21365 | + | 0.700700i | 0.963552 | − | 0.267522i | \(-0.0862047\pi\) |
0.250095 | + | 0.968221i | \(0.419538\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.4934i | 1.00225i | 0.865375 | + | 0.501124i | \(0.167080\pi\) | ||||
−0.865375 | + | 0.501124i | \(0.832920\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.80385 | − | 3.92820i | −0.267074 | − | 0.154195i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.4934 | −0.997633 | −0.498817 | − | 0.866708i | \(-0.666232\pi\) | ||||
−0.498817 | + | 0.866708i | \(0.666232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.7321 | − | 6.19615i | 0.419336 | − | 0.242104i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.47266 | + | 9.47893i | 0.213185 | + | 0.369247i | 0.952709 | − | 0.303883i | \(-0.0982831\pi\) |
−0.739525 | + | 0.673129i | \(0.764950\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.7846 | + | 12.0000i | −0.808428 | + | 0.466746i | −0.846410 | − | 0.532533i | \(-0.821240\pi\) |
0.0379819 | + | 0.999278i | \(0.487907\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.4004 | + | 10.6895i | −0.558422 | + | 0.414521i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.87564 | + | 4.98076i | −0.111345 | + | 0.192856i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.9968 | − | 8.08108i | 0.540342 | − | 0.311967i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 24.3731i | − | 0.939513i | −0.882796 | − | 0.469756i | \(-0.844342\pi\) | ||
0.882796 | − | 0.469756i | \(-0.155658\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.8673i | 0.801997i | 0.916079 | + | 0.400999i | \(0.131337\pi\) | ||||
−0.916079 | + | 0.400999i | \(0.868663\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.00000 | + | 5.19615i | −0.115129 | + | 0.199410i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −49.8843 | −1.90877 | −0.954385 | − | 0.298578i | \(-0.903488\pi\) | ||||
−0.954385 | + | 0.298578i | \(0.903488\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.32051 | 0.126870 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.65367 | − | 2.86424i | 0.0629999 | − | 0.109119i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.2487i | 1.37897i | 0.724302 | + | 0.689483i | \(0.242162\pi\) | ||||
−0.724302 | + | 0.689483i | \(0.757838\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 46.8724i | 1.77797i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.4123 | + | 30.1590i | −0.657654 | + | 1.13909i | 0.323568 | + | 0.946205i | \(0.395118\pi\) |
−0.981221 | + | 0.192885i | \(0.938216\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.0718 | + | 7.39230i | 0.643875 | + | 0.278806i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.73475 | + | 5.62036i | −0.366113 | + | 0.211375i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.0885 | + | 33.0622i | 0.716882 | + | 1.24168i | 0.962229 | + | 0.272241i | \(0.0877647\pi\) |
−0.245347 | + | 0.969435i | \(0.578902\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.07481 | − | 2.35259i | 0.152603 | − | 0.0881054i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.3205 | 1.09652 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.1169 | + | 9.88245i | 0.638353 | + | 0.368553i | 0.783980 | − | 0.620786i | \(-0.213187\pi\) |
−0.145627 | + | 0.989340i | \(0.546520\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.6603i | 0.545976i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 53.8906 | + | 31.1137i | 2.00145 | + | 1.15554i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.7942 | − | 16.6244i | −1.06792 | − | 0.616563i | −0.140307 | − | 0.990108i | \(-0.544809\pi\) |
−0.927612 | + | 0.373545i | \(0.878142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.8611 | − | 9.73475i | 0.623630 | − | 0.360053i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.6077 | 0.576483 | 0.288242 | − | 0.957558i | \(-0.406929\pi\) | ||||
0.288242 | + | 0.957558i | \(0.406929\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −39.8938 | + | 23.0327i | −1.46951 | + | 0.848419i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.6699 | − | 13.0885i | −0.833925 | − | 0.481467i | 0.0212698 | − | 0.999774i | \(-0.493229\pi\) |
−0.855195 | + | 0.518307i | \(0.826562\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.56317 | + | 6.17158i | −0.130720 | + | 0.226413i | −0.923954 | − | 0.382503i | \(-0.875062\pi\) |
0.793234 | + | 0.608916i | \(0.208396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.0000 | + | 22.5167i | 0.476283 | + | 0.824947i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.4695i | 0.711400i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.06218 | + | 10.5000i | 0.221212 | + | 0.383150i | 0.955176 | − | 0.296038i | \(-0.0956654\pi\) |
−0.733964 | + | 0.679188i | \(0.762332\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.4337 | + | 18.0717i | −0.379720 | + | 0.657695i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.37564 | + | 2.38269i | −0.0499986 | + | 0.0866002i | −0.889942 | − | 0.456075i | \(-0.849255\pi\) |
0.839943 | + | 0.542675i | \(0.182588\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.4745 | −1.64845 | −0.824225 | − | 0.566262i | \(-0.808389\pi\) | ||||
−0.824225 | + | 0.566262i | \(0.808389\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.46410 | + | 11.1962i | −0.234016 | + | 0.405328i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.30734i | − | 0.119421i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.03590 | − | 12.1865i | −0.253721 | − | 0.439458i | 0.710826 | − | 0.703368i | \(-0.248321\pi\) |
−0.964547 | + | 0.263910i | \(0.914988\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.7222 | + | 19.4695i | −1.21290 | + | 0.700269i | −0.963390 | − | 0.268103i | \(-0.913603\pi\) |
−0.249512 | + | 0.968372i | \(0.580270\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.4545 | − | 44.0885i | −0.914352 | − | 1.58370i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.1962 | + | 18.5885i | 1.15207 | + | 0.665147i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.5506 | + | 47.7190i | 0.983322 | + | 1.70316i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −45.5885 | −1.62505 | −0.812526 | − | 0.582924i | \(-0.801908\pi\) | ||||
−0.812526 | + | 0.582924i | \(0.801908\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.90949 | 0.0678938 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.89230 | + | 3.40192i | 0.209242 | + | 0.120806i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 15.6505i | − | 0.554370i | −0.960817 | − | 0.277185i | \(-0.910599\pi\) | ||
0.960817 | − | 0.277185i | \(-0.0894014\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.1436i | 0.641874i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.2137 | + | 11.0930i | 0.678036 | + | 0.391464i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.53590 | 0.159869 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.0534 | −1.51368 | −0.756838 | − | 0.653602i | \(-0.773257\pi\) | ||||
−0.756838 | + | 0.653602i | \(0.773257\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.9282 | − | 32.7846i | −0.664659 | − | 1.15122i | −0.979378 | − | 0.202038i | \(-0.935243\pi\) |
0.314719 | − | 0.949185i | \(-0.398090\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.8158 | − | 10.2860i | −0.624061 | − | 0.360302i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.6244 | − | 16.7942i | 0.791526 | − | 0.587556i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.71087 | + | 6.42741i | 0.129510 | + | 0.224318i | 0.923487 | − | 0.383630i | \(-0.125326\pi\) |
−0.793977 | + | 0.607948i | \(0.791993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.7128 | − | 21.1962i | 1.27973 | − | 0.738851i | 0.302930 | − | 0.953013i | \(-0.402035\pi\) |
0.976798 | + | 0.214161i | \(0.0687019\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.6801 | + | 35.8189i | 0.719117 | + | 1.24555i | 0.961350 | + | 0.275329i | \(0.0887866\pi\) |
−0.242234 | + | 0.970218i | \(0.577880\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 4.26795i | − | 0.148232i | −0.997250 | − | 0.0741160i | \(-0.976386\pi\) | ||
0.997250 | − | 0.0741160i | \(-0.0236135\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.03583 | + | 15.6505i | −0.313073 | + | 0.542258i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 93.7128 | 3.24307 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.255824 | − | 0.443100i | 0.00883202 | − | 0.0152975i | −0.861576 | − | 0.507629i | \(-0.830522\pi\) |
0.870408 | + | 0.492332i | \(0.163855\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.892305 | + | 1.54552i | −0.0307691 | + | 0.0532937i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20.5719 | − | 35.6317i | −0.707697 | − | 1.22577i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.92820i | 0.203695i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.35259 | − | 4.07481i | −0.0806459 | − | 0.139683i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.8923 | + | 29.2583i | −0.578382 | + | 1.00179i | 0.417284 | + | 0.908776i | \(0.362982\pi\) |
−0.995665 | + | 0.0930099i | \(0.970351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.72848 | + | 3.30734i | 0.195681 | + | 0.112977i | 0.594639 | − | 0.803992i | \(-0.297295\pi\) |
−0.398958 | + | 0.916969i | \(0.630628\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.86603 | + | 5.69615i | −0.336624 | + | 0.194350i | −0.658778 | − | 0.752337i | \(-0.728926\pi\) |
0.322154 | + | 0.946687i | \(0.395593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.6863 | 0.840333 | 0.420166 | − | 0.907447i | \(-0.361972\pi\) | ||||
0.420166 | + | 0.907447i | \(0.361972\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 69.3731 | − | 40.0526i | 2.35876 | − | 1.36183i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −52.2369 | − | 30.1590i | −1.77202 | − | 1.02307i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.7942 | − | 9.69615i | −0.569051 | − | 0.328542i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 28.5053i | − | 0.963656i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.1077 | − | 12.1865i | −0.712756 | − | 0.411510i | 0.0993245 | − | 0.995055i | \(-0.468332\pi\) |
−0.812081 | + | 0.583545i | \(0.801665\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.8007 | 0.970321 | 0.485161 | − | 0.874425i | \(-0.338761\pi\) | ||||
0.485161 | + | 0.874425i | \(0.338761\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.6699 | − | 18.2846i | 1.06578 | − | 0.615326i | 0.138752 | − | 0.990327i | \(-0.455691\pi\) |
0.927024 | + | 0.375001i | \(0.122358\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.954747 | + | 1.65367i | 0.0320573 | + | 0.0555248i | 0.881609 | − | 0.471981i | \(-0.156461\pi\) |
−0.849552 | + | 0.527505i | \(0.823127\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.0000 | + | 6.92820i | −0.402467 | + | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.01194 | + | 26.0842i | 0.100791 | + | 0.872874i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46.8564 | + | 81.1577i | −1.56624 | + | 2.71280i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.2822 | + | 11.1326i | −0.643098 | + | 0.371293i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 5.75129i | − | 0.191603i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 92.1307i | 3.06253i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.5885 | − | 42.5885i | 0.816446 | − | 1.41413i | −0.0918384 | − | 0.995774i | \(-0.529274\pi\) |
0.908285 | − | 0.418353i | \(-0.137392\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.6863 | 0.817895 | 0.408947 | − | 0.912558i | \(-0.365896\pi\) | ||||
0.408947 | + | 0.912558i | \(0.365896\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −46.2487 | −1.53061 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.50597 | + | 2.60842i | −0.0497315 | + | 0.0861376i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.17691i | 0.269732i | 0.990864 | + | 0.134866i | \(0.0430603\pi\) | ||||
−0.990864 | + | 0.134866i | \(0.956940\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.6505i | 0.515143i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44.0885 | + | 25.4545i | −1.44962 | + | 0.836938i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.4123 | − | 30.1590i | 0.571279 | − | 0.989485i | −0.425156 | − | 0.905120i | \(-0.639781\pi\) |
0.996435 | − | 0.0843645i | \(-0.0268860\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.3923 | + | 24.0000i | −0.340594 | + | 0.786568i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 44.1558 | − | 25.4934i | 1.44405 | − | 0.833723i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.6962 | − | 18.5263i | −0.349428 | − | 0.605227i | 0.636720 | − | 0.771095i | \(-0.280291\pi\) |
−0.986148 | + | 0.165868i | \(0.946957\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.6505 | − | 9.03583i | 0.510192 | − | 0.294560i | −0.222721 | − | 0.974882i | \(-0.571494\pi\) |
0.732913 | + | 0.680323i | \(0.238160\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.1137 | + | 17.9635i | 1.01106 | + | 0.583736i | 0.911502 | − | 0.411295i | \(-0.134924\pi\) |
0.0995588 | + | 0.995032i | \(0.468257\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.33975i | 0.303181i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.8938 | − | 23.0327i | −1.29229 | − | 0.746101i | −0.313226 | − | 0.949678i | \(-0.601410\pi\) |
−0.979059 | + | 0.203577i | \(0.934743\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.5167 | − | 13.0000i | −0.728622 | − | 0.420670i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.698924 | + | 0.403524i | −0.0225694 | + | 0.0130305i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.7846 | −0.412407 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 48.9296 | − | 28.2495i | 1.57510 | − | 0.909384i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.9186 | − | 27.0885i | −1.50880 | − | 0.871106i | −0.999947 | − | 0.0102523i | \(-0.996737\pi\) |
−0.508853 | − | 0.860854i | \(-0.669930\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.3432 | + | 21.3790i | −0.396111 | + | 0.686085i | −0.993242 | − | 0.116059i | \(-0.962974\pi\) |
0.597131 | + | 0.802144i | \(0.296307\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.69615 | − | 9.86603i | −0.182610 | − | 0.316290i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 45.5537i | − | 1.45739i | −0.684838 | − | 0.728696i | \(-0.740127\pi\) | ||
0.684838 | − | 0.728696i | \(-0.259873\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.3923 | + | 43.9808i | 0.811542 | + | 1.40563i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.6895 | − | 18.5148i | 0.340942 | − | 0.590529i | −0.643666 | − | 0.765307i | \(-0.722587\pi\) |
0.984608 | + | 0.174778i | \(0.0559207\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.26795 | + | 3.92820i | −0.0722629 | + | 0.125163i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.12633 | −0.226604 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.99038 | + | 12.1077i | −0.222057 | + | 0.384614i | −0.955432 | − | 0.295210i | \(-0.904610\pi\) |
0.733376 | + | 0.679824i | \(0.237944\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.90949i | 0.0605351i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.1603 | − | 22.7942i | −0.416789 | − | 0.721900i | 0.578825 | − | 0.815452i | \(-0.303511\pi\) |
−0.995614 | + | 0.0935513i | \(0.970178\pi\) | |||||||
\(998\) | 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 | 2736.2.bm.q.559.1 | yes | 8 | |
3.2 | odd | 2 | inner | 2736.2.bm.q.559.4 | yes | 8 | |
4.3 | odd | 2 | 2736.2.bm.p.559.1 | ✓ | 8 | ||
12.11 | even | 2 | 2736.2.bm.p.559.4 | yes | 8 | ||
19.12 | odd | 6 | 2736.2.bm.p.1855.1 | yes | 8 | ||
57.50 | even | 6 | 2736.2.bm.p.1855.4 | yes | 8 | ||
76.31 | even | 6 | inner | 2736.2.bm.q.1855.1 | yes | 8 | |
228.107 | odd | 6 | inner | 2736.2.bm.q.1855.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.bm.p.559.1 | ✓ | 8 | 4.3 | odd | 2 | ||
2736.2.bm.p.559.4 | yes | 8 | 12.11 | even | 2 | ||
2736.2.bm.p.1855.1 | yes | 8 | 19.12 | odd | 6 | ||
2736.2.bm.p.1855.4 | yes | 8 | 57.50 | even | 6 | ||
2736.2.bm.q.559.1 | yes | 8 | 1.1 | even | 1 | trivial | |
2736.2.bm.q.559.4 | yes | 8 | 3.2 | odd | 2 | inner | |
2736.2.bm.q.1855.1 | yes | 8 | 76.31 | even | 6 | inner | |
2736.2.bm.q.1855.4 | yes | 8 | 228.107 | odd | 6 | inner |