Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(2177,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.2177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.w (of order \(4\), degree \(2\), not 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: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 27x^{8} + 107x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 1440) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2753.4 | ||
Root | \(-1.04736 + 1.04736i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.2753 |
Dual form | 2880.2.w.p.2177.4 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 0.137134 | − | 2.23186i | 0.0613281 | − | 0.998118i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.806063 | + | 0.806063i | −0.304663 | + | 0.304663i | −0.842835 | − | 0.538172i | \(-0.819115\pi\) |
0.538172 | + | 0.842835i | \(0.319115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.87793i | 1.77226i | 0.463434 | + | 0.886132i | \(0.346617\pi\) | ||||
−0.463434 | + | 0.886132i | \(0.653383\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.193937 | + | 0.193937i | 0.0537883 | + | 0.0537883i | 0.733489 | − | 0.679701i | \(-0.237890\pi\) |
−0.679701 | + | 0.733489i | \(0.737890\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.50894 | − | 3.50894i | −0.851043 | − | 0.851043i | 0.139219 | − | 0.990262i | \(-0.455541\pi\) |
−0.990262 | + | 0.139219i | \(0.955541\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.38787i | 0.547816i | 0.961756 | + | 0.273908i | \(0.0883163\pi\) | ||||
−0.961756 | + | 0.273908i | \(0.911684\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.18945 | − | 4.18945i | 0.873561 | − | 0.873561i | −0.119298 | − | 0.992859i | \(-0.538064\pi\) |
0.992859 | + | 0.119298i | \(0.0380643\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96239 | − | 0.612127i | −0.992478 | − | 0.122425i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.29214 | −1.35412 | −0.677059 | − | 0.735929i | \(-0.736746\pi\) | ||||
−0.677059 | + | 0.735929i | \(0.736746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.31265 | 0.774575 | 0.387287 | − | 0.921959i | \(-0.373412\pi\) | ||||
0.387287 | + | 0.921959i | \(0.373412\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.68848 | + | 1.90956i | 0.285405 | + | 0.322774i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.54420 | + | 1.54420i | −0.253865 | + | 0.253865i | −0.822553 | − | 0.568688i | \(-0.807451\pi\) |
0.568688 | + | 0.822553i | \(0.307451\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.32377i | − | 0.519086i | −0.965732 | − | 0.259543i | \(-0.916428\pi\) | ||
0.965732 | − | 0.259543i | \(-0.0835719\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.31265 | − | 8.31265i | −1.26767 | − | 1.26767i | −0.947290 | − | 0.320377i | \(-0.896190\pi\) |
−0.320377 | − | 0.947290i | \(-0.603810\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.42647 | − | 6.42647i | −0.937397 | − | 0.937397i | 0.0607561 | − | 0.998153i | \(-0.480649\pi\) |
−0.998153 | + | 0.0607561i | \(0.980649\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.70052i | 0.814360i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.64888 | − | 4.64888i | 0.638573 | − | 0.638573i | −0.311630 | − | 0.950203i | \(-0.600875\pi\) |
0.950203 | + | 0.311630i | \(0.100875\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.1187 | + | 0.806063i | 1.76893 | + | 0.108690i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.4377 | −1.35887 | −0.679437 | − | 0.733734i | \(-0.737776\pi\) | ||||
−0.679437 | + | 0.733734i | \(0.737776\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.53690 | −0.965002 | −0.482501 | − | 0.875896i | \(-0.660271\pi\) | ||||
−0.482501 | + | 0.875896i | \(0.660271\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.459434 | − | 0.406244i | 0.0569858 | − | 0.0503883i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.31265 | + | 4.31265i | −0.526874 | + | 0.526874i | −0.919639 | − | 0.392765i | \(-0.871519\pi\) |
0.392765 | + | 0.919639i | \(0.371519\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.47597i | − | 1.12459i | −0.826936 | − | 0.562295i | \(-0.809918\pi\) | ||
0.826936 | − | 0.562295i | \(-0.190082\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0376114 | + | 0.0376114i | 0.00440208 | + | 0.00440208i | 0.709304 | − | 0.704902i | \(-0.249009\pi\) |
−0.704902 | + | 0.709304i | \(0.749009\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.73799 | − | 4.73799i | −0.539944 | − | 0.539944i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.68735i | − | 0.414859i | −0.978250 | − | 0.207430i | \(-0.933490\pi\) | ||
0.978250 | − | 0.207430i | \(-0.0665098\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.221077 | + | 0.221077i | −0.0242664 | + | 0.0242664i | −0.719136 | − | 0.694869i | \(-0.755462\pi\) |
0.694869 | + | 0.719136i | \(0.255462\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.31265 | + | 7.35026i | −0.901634 | + | 0.797248i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.52916 | −1.01009 | −0.505045 | − | 0.863093i | \(-0.668524\pi\) | ||||
−0.505045 | + | 0.863093i | \(0.668524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.312650 | −0.0327747 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.32940 | + | 0.327458i | 0.546784 | + | 0.0335965i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.27504 | + | 8.27504i | −0.840203 | + | 0.840203i | −0.988885 | − | 0.148682i | \(-0.952497\pi\) |
0.148682 | + | 0.988885i | \(0.452497\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 5.82474i | − | 0.579583i | −0.957090 | − | 0.289792i | \(-0.906414\pi\) | ||
0.957090 | − | 0.289792i | \(-0.0935860\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.41819 | + | 2.41819i | 0.238271 | + | 0.238271i | 0.816134 | − | 0.577863i | \(-0.196113\pi\) |
−0.577863 | + | 0.816134i | \(0.696113\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.5348 | + | 11.5348i | 1.11511 | + | 1.11511i | 0.992449 | + | 0.122661i | \(0.0391429\pi\) |
0.122661 | + | 0.992449i | \(0.460857\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0132i | 1.05487i | 0.849595 | + | 0.527435i | \(0.176846\pi\) | ||||
−0.849595 | + | 0.527435i | \(0.823154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.20304 | − | 7.20304i | 0.677605 | − | 0.677605i | −0.281852 | − | 0.959458i | \(-0.590949\pi\) |
0.959458 | + | 0.281852i | \(0.0909489\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.77575 | − | 9.92478i | −0.818343 | − | 0.925490i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.65685 | 0.518563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −23.5501 | −2.14092 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.04669 | + | 10.9914i | −0.183062 | + | 0.983101i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.80606 | + | 8.80606i | −0.781412 | + | 0.781412i | −0.980069 | − | 0.198657i | \(-0.936342\pi\) |
0.198657 | + | 0.980069i | \(0.436342\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.8147i | 1.20699i | 0.797365 | + | 0.603497i | \(0.206226\pi\) | ||||
−0.797365 | + | 0.603497i | \(0.793774\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.92478 | − | 1.92478i | −0.166899 | − | 0.166899i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.64326 | − | 2.64326i | −0.225829 | − | 0.225829i | 0.585119 | − | 0.810948i | \(-0.301048\pi\) |
−0.810948 | + | 0.585119i | \(0.801048\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.7005i | 1.58616i | 0.609119 | + | 0.793079i | \(0.291523\pi\) | ||||
−0.609119 | + | 0.793079i | \(0.708477\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.13995 | + | 1.13995i | −0.0953271 | + | 0.0953271i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.00000 | + | 16.2750i | −0.0830455 | + | 1.35157i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.55610 | 0.619020 | 0.309510 | − | 0.950896i | \(-0.399835\pi\) | ||||
0.309510 | + | 0.950896i | \(0.399835\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.1490 | −1.39557 | −0.697784 | − | 0.716308i | \(-0.745831\pi\) | ||||
−0.697784 | + | 0.716308i | \(0.745831\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.591410 | − | 9.62523i | 0.0475032 | − | 0.773117i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.69323 | + | 8.69323i | −0.693795 | + | 0.693795i | −0.963065 | − | 0.269270i | \(-0.913218\pi\) |
0.269270 | + | 0.963065i | \(0.413218\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.75393i | 0.532284i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.31265 | + | 4.31265i | 0.337793 | + | 0.337793i | 0.855536 | − | 0.517743i | \(-0.173228\pi\) |
−0.517743 | + | 0.855536i | \(0.673228\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.90956 | + | 1.90956i | 0.147766 | + | 0.147766i | 0.777119 | − | 0.629353i | \(-0.216680\pi\) |
−0.629353 | + | 0.777119i | \(0.716680\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.9248i | − | 0.994214i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.17586 | + | 1.17586i | −0.0893987 | + | 0.0893987i | −0.750392 | − | 0.660993i | \(-0.770135\pi\) |
0.660993 | + | 0.750392i | \(0.270135\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.49341 | − | 3.50659i | 0.339670 | − | 0.265073i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.81274 | −0.658695 | −0.329348 | − | 0.944209i | \(-0.606829\pi\) | ||||
−0.329348 | + | 0.944209i | \(0.606829\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.7889 | −1.17358 | −0.586791 | − | 0.809739i | \(-0.699609\pi\) | ||||
−0.586791 | + | 0.809739i | \(0.699609\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.23467 | + | 3.65819i | 0.237818 | + | 0.268956i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.6253 | − | 20.6253i | 1.50827 | − | 1.50827i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.83774i | − | 0.132974i | −0.997787 | − | 0.0664870i | \(-0.978821\pi\) | ||
0.997787 | − | 0.0664870i | \(-0.0211791\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0884 | + | 10.0884i | 0.726179 | + | 0.726179i | 0.969856 | − | 0.243678i | \(-0.0783539\pi\) |
−0.243678 | + | 0.969856i | \(0.578354\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.5979 | − | 17.5979i | −1.25380 | − | 1.25380i | −0.954004 | − | 0.299793i | \(-0.903082\pi\) |
−0.299793 | − | 0.954004i | \(-0.596918\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 21.9248i | − | 1.55421i | −0.629373 | − | 0.777103i | \(-0.716688\pi\) | ||
0.629373 | − | 0.777103i | \(-0.283312\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.87793 | − | 5.87793i | 0.412550 | − | 0.412550i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.41819 | − | 0.455802i | −0.518109 | − | 0.0318346i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.0358 | −0.970873 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4763 | 1.06543 | 0.532715 | − | 0.846295i | \(-0.321172\pi\) | ||||
0.532715 | + | 0.846295i | \(0.321172\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.6926 | + | 17.4127i | −1.34302 | + | 1.18754i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.47627 | + | 3.47627i | −0.235985 | + | 0.235985i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.36102i | − | 0.0915523i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.2823 | + | 16.2823i | 1.09035 | + | 1.09035i | 0.995491 | + | 0.0948545i | \(0.0302386\pi\) |
0.0948545 | + | 0.995491i | \(0.469761\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.09901 | − | 6.09901i | −0.404805 | − | 0.404805i | 0.475117 | − | 0.879923i | \(-0.342406\pi\) |
−0.879923 | + | 0.475117i | \(0.842406\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 21.0738i | − | 1.39260i | −0.717753 | − | 0.696298i | \(-0.754829\pi\) | ||
0.717753 | − | 0.696298i | \(-0.245171\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.5428 | − | 12.5428i | 0.821703 | − | 0.821703i | −0.164649 | − | 0.986352i | \(-0.552649\pi\) |
0.986352 | + | 0.164649i | \(0.0526491\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.2243 | + | 13.4617i | −0.993121 | + | 0.878143i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.4108 | 0.802787 | 0.401393 | − | 0.915906i | \(-0.368526\pi\) | ||||
0.401393 | + | 0.915906i | \(0.368526\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.47627 | 0.0950949 | 0.0475474 | − | 0.998869i | \(-0.484859\pi\) | ||||
0.0475474 | + | 0.998869i | \(0.484859\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.7228 | + | 0.781735i | 0.812828 | + | 0.0499432i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.463096 | + | 0.463096i | −0.0294661 | + | 0.0294661i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 26.0127i | − | 1.64191i | −0.570995 | − | 0.820953i | \(-0.693443\pi\) | ||
0.570995 | − | 0.820953i | \(-0.306557\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.6253 | + | 24.6253i | 1.54818 | + | 1.54818i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.1464 | − | 18.1464i | −1.13194 | − | 1.13194i | −0.989854 | − | 0.142089i | \(-0.954618\pi\) |
−0.142089 | − | 0.989854i | \(-0.545382\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.48944i | − | 0.154686i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.3223 | + | 19.3223i | −1.19146 | + | 1.19146i | −0.214806 | + | 0.976657i | \(0.568912\pi\) |
−0.976657 | + | 0.214806i | \(0.931088\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.73813 | − | 11.0132i | −0.598209 | − | 0.676534i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.6257 | −1.86728 | −0.933640 | − | 0.358213i | \(-0.883386\pi\) | ||||
−0.933640 | + | 0.358213i | \(0.883386\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.2520 | −0.744257 | −0.372128 | − | 0.928181i | \(-0.621372\pi\) | ||||
−0.372128 | + | 0.928181i | \(0.621372\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.59804 | − | 29.1686i | 0.216970 | − | 1.75893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.80606 | − | 1.80606i | 0.108516 | − | 0.108516i | −0.650764 | − | 0.759280i | \(-0.725551\pi\) |
0.759280 | + | 0.650764i | \(0.225551\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 16.8110i | − | 1.00286i | −0.865198 | − | 0.501430i | \(-0.832808\pi\) | ||
0.865198 | − | 0.501430i | \(-0.167192\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.62530 | + | 4.62530i | 0.274946 | + | 0.274946i | 0.831087 | − | 0.556142i | \(-0.187719\pi\) |
−0.556142 | + | 0.831087i | \(0.687719\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.67917 | + | 2.67917i | 0.158146 | + | 0.158146i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.62530i | 0.448547i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.5141 | − | 22.5141i | 1.31529 | − | 1.31529i | 0.397825 | − | 0.917461i | \(-0.369765\pi\) |
0.917461 | − | 0.397825i | \(-0.130235\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.43136 | + | 23.2955i | −0.0833372 | + | 1.35632i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.62498 | 0.0939747 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.4010 | 0.772424 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.03356 | + | 16.8213i | −0.0591817 | + | 0.963185i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.3879 | − | 10.3879i | 0.592867 | − | 0.592867i | −0.345538 | − | 0.938405i | \(-0.612303\pi\) |
0.938405 | + | 0.345538i | \(0.112303\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.82105i | 0.500196i | 0.968221 | + | 0.250098i | \(0.0804629\pi\) | ||||
−0.968221 | + | 0.250098i | \(0.919537\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.23743 | − | 3.23743i | −0.182990 | − | 0.182990i | 0.609667 | − | 0.792657i | \(-0.291303\pi\) |
−0.792657 | + | 0.609667i | \(0.791303\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.0891011 | + | 0.0891011i | 0.00500442 | + | 0.00500442i | 0.709605 | − | 0.704600i | \(-0.248874\pi\) |
−0.704600 | + | 0.709605i | \(0.748874\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 42.8627i | − | 2.39985i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.37890 | − | 8.37890i | 0.466214 | − | 0.466214i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.843675 | − | 1.08110i | −0.0467987 | − | 0.0599688i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.3603 | 0.571181 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.6859 | 1.13700 | 0.568501 | − | 0.822683i | \(-0.307524\pi\) | ||||
0.568501 | + | 0.822683i | \(0.307524\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.03382 | + | 10.2166i | 0.493570 | + | 0.558195i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.4387 | − | 23.4387i | 1.27679 | − | 1.27679i | 0.334328 | − | 0.942457i | \(-0.391491\pi\) |
0.942457 | − | 0.334328i | \(-0.108509\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.3495i | 1.37275i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.2374 | − | 10.2374i | −0.552769 | − | 0.552769i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.55978 | + | 4.55978i | 0.244782 | + | 0.244782i | 0.818825 | − | 0.574043i | \(-0.194626\pi\) |
−0.574043 | + | 0.818825i | \(0.694626\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8.46310i | − | 0.453019i | −0.974009 | − | 0.226510i | \(-0.927269\pi\) | ||
0.974009 | − | 0.226510i | \(-0.0727315\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.9690 | + | 10.9690i | −0.583819 | + | 0.583819i | −0.935951 | − | 0.352131i | \(-0.885457\pi\) |
0.352131 | + | 0.935951i | \(0.385457\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.1490 | − | 1.29948i | −1.12247 | − | 0.0689691i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.9073 | 1.31456 | 0.657279 | − | 0.753648i | \(-0.271707\pi\) | ||||
0.657279 | + | 0.753648i | \(0.271707\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.2981 | 0.699898 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.0891011 | − | 0.0787855i | 0.00466377 | − | 0.00412382i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.7440 | + | 21.7440i | −1.13503 | + | 1.13503i | −0.145699 | + | 0.989329i | \(0.546543\pi\) |
−0.989329 | + | 0.145699i | \(0.953457\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.49459i | 0.389100i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.1695 | − | 16.1695i | −0.837225 | − | 0.837225i | 0.151268 | − | 0.988493i | \(-0.451664\pi\) |
−0.988493 | + | 0.151268i | \(0.951664\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.41421 | − | 1.41421i | −0.0728357 | − | 0.0728357i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.7005i | 0.960581i | 0.877109 | + | 0.480291i | \(0.159469\pi\) | ||||
−0.877109 | + | 0.480291i | \(0.840531\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.0220 | + | 25.0220i | −1.27856 | + | 1.27856i | −0.337094 | + | 0.941471i | \(0.609444\pi\) |
−0.941471 | + | 0.337094i | \(0.890556\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.2243 | + | 9.92478i | −0.572041 | + | 0.505813i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.1478 | −0.818724 | −0.409362 | − | 0.912372i | \(-0.634249\pi\) | ||||
−0.409362 | + | 0.912372i | \(0.634249\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.4010 | −1.48687 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.22964 | − | 0.505660i | −0.414078 | − | 0.0254425i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.4690 | − | 15.4690i | 0.776366 | − | 0.776366i | −0.202845 | − | 0.979211i | \(-0.565019\pi\) |
0.979211 | + | 0.202845i | \(0.0650188\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.1181i | 1.25434i | 0.778884 | + | 0.627168i | \(0.215786\pi\) | ||||
−0.778884 | + | 0.627168i | \(0.784214\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.836381 | + | 0.836381i | 0.0416631 | + | 0.0416631i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.07669 | − | 9.07669i | −0.449915 | − | 0.449915i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 9.92478i | − | 0.490749i | −0.969428 | − | 0.245374i | \(-0.921089\pi\) | ||
0.969428 | − | 0.245374i | \(-0.0789109\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.41346 | − | 8.41346i | 0.413999 | − | 0.413999i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.463096 | + | 0.523730i | 0.0227325 | + | 0.0257089i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.06075 | 0.344940 | 0.172470 | − | 0.985015i | \(-0.444825\pi\) | ||||
0.172470 | + | 0.985015i | \(0.444825\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.7757 | −0.525178 | −0.262589 | − | 0.964908i | \(-0.584576\pi\) | ||||
−0.262589 | + | 0.964908i | \(0.584576\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.2648 | + | 19.5606i | 0.740452 | + | 0.948830i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.07522 | − | 6.07522i | 0.294001 | − | 0.294001i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.19414i | 0.105688i | 0.998603 | + | 0.0528440i | \(0.0168286\pi\) | ||||
−0.998603 | + | 0.0528440i | \(0.983171\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.4617 | + | 16.4617i | 0.791098 | + | 0.791098i | 0.981673 | − | 0.190575i | \(-0.0610352\pi\) |
−0.190575 | + | 0.981673i | \(0.561035\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.0039 | + | 10.0039i | 0.478550 | + | 0.478550i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.3996i | 1.25999i | 0.776601 | + | 0.629993i | \(0.216942\pi\) | ||||
−0.776601 | + | 0.629993i | \(0.783058\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.37696 | − | 3.37696i | 0.160444 | − | 0.160444i | −0.622319 | − | 0.782764i | \(-0.713809\pi\) |
0.782764 | + | 0.622319i | \(0.213809\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.30677 | + | 21.2677i | −0.0619469 | + | 1.00819i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.5490 | −1.01696 | −0.508480 | − | 0.861074i | \(-0.669792\pi\) | ||||
−0.508480 | + | 0.861074i | \(0.669792\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.5369 | 0.919957 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0428749 | + | 0.697791i | −0.00201001 | + | 0.0327130i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.9003 | − | 14.9003i | 0.697008 | − | 0.697008i | −0.266756 | − | 0.963764i | \(-0.585952\pi\) |
0.963764 | + | 0.266756i | \(0.0859517\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.0208i | 0.606440i | 0.952921 | + | 0.303220i | \(0.0980617\pi\) | ||||
−0.952921 | + | 0.303220i | \(0.901938\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.28233 | − | 8.28233i | −0.384913 | − | 0.384913i | 0.487956 | − | 0.872868i | \(-0.337743\pi\) |
−0.872868 | + | 0.487956i | \(0.837743\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.25489 | + | 9.25489i | 0.428265 | + | 0.428265i | 0.888037 | − | 0.459772i | \(-0.152069\pi\) |
−0.459772 | + | 0.888037i | \(0.652069\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.95254i | − | 0.321038i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 48.8612 | − | 48.8612i | 2.24664 | − | 2.24664i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.46168 | − | 11.8496i | 0.0670665 | − | 0.543695i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.0358 | 0.641310 | 0.320655 | − | 0.947196i | \(-0.396097\pi\) | ||||
0.320655 | + | 0.947196i | \(0.396097\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.598953 | −0.0273099 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.3339 | + | 19.6035i | 0.787093 | + | 0.890149i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.0435 | − | 11.0435i | 0.500428 | − | 0.500428i | −0.411143 | − | 0.911571i | \(-0.634870\pi\) |
0.911571 | + | 0.411143i | \(0.134870\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.07207i | 0.364288i | 0.983272 | + | 0.182144i | \(0.0583036\pi\) | ||||
−0.983272 | + | 0.182144i | \(0.941696\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.5877 | + | 25.5877i | 1.15241 | + | 1.15241i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.63823 | + | 7.63823i | 0.342622 | + | 0.342622i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 42.0870i | 1.88407i | 0.335512 | + | 0.942036i | \(0.391091\pi\) | ||||
−0.335512 | + | 0.942036i | \(0.608909\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.1191 | − | 26.1191i | 1.16459 | − | 1.16459i | 0.181134 | − | 0.983459i | \(-0.442023\pi\) |
0.983459 | − | 0.181134i | \(-0.0579766\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.0000 | − | 0.798769i | −0.578492 | − | 0.0355448i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.7362 | 0.564524 | 0.282262 | − | 0.959337i | \(-0.408915\pi\) | ||||
0.282262 | + | 0.959337i | \(0.408915\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0606343 | −0.00268231 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.72868 | − | 5.06544i | 0.252436 | − | 0.223210i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 37.7743 | − | 37.7743i | 1.66131 | − | 1.66131i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.9279i | 1.31116i | 0.755124 | + | 0.655582i | \(0.227577\pi\) | ||||
−0.755124 | + | 0.655582i | \(0.772423\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.3733 | − | 16.3733i | −0.715954 | − | 0.715954i | 0.251820 | − | 0.967774i | \(-0.418971\pi\) |
−0.967774 | + | 0.251820i | \(0.918971\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.1328 | − | 15.1328i | −0.659196 | − | 0.659196i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 12.1030i | − | 0.526217i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.644601 | − | 0.644601i | 0.0279208 | − | 0.0279208i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.3258 | − | 24.1622i | 1.18140 | − | 1.04462i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −33.5073 | −1.44326 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.6385 | 0.844324 | 0.422162 | − | 0.906520i | \(-0.361271\pi\) | ||||
0.422162 | + | 0.906520i | \(0.361271\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.5799 | + | 1.51028i | 1.05289 | + | 0.0646932i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.0738 | − | 15.0738i | 0.644509 | − | 0.644509i | −0.307151 | − | 0.951661i | \(-0.599376\pi\) |
0.951661 | + | 0.307151i | \(0.0993757\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 17.4127i | − | 0.741807i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.97224 | + | 2.97224i | 0.126392 | + | 0.126392i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.8609 | + | 13.8609i | 0.587305 | + | 0.587305i | 0.936901 | − | 0.349595i | \(-0.113681\pi\) |
−0.349595 | + | 0.936901i | \(0.613681\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.22425i | − | 0.136371i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.81912 | + | 3.81912i | −0.160957 | + | 0.160957i | −0.782990 | − | 0.622034i | \(-0.786307\pi\) |
0.622034 | + | 0.782990i | \(0.286307\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.0884 | − | 17.0640i | −0.634774 | − | 0.717886i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.3735 | −0.602570 | −0.301285 | − | 0.953534i | \(-0.597415\pi\) | ||||
−0.301285 | + | 0.953534i | \(0.597415\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.3112 | −0.891847 | −0.445924 | − | 0.895071i | \(-0.647125\pi\) | ||||
−0.445924 | + | 0.895071i | \(0.647125\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.3542 | + | 18.2252i | −0.973936 | + | 0.760044i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.55149 | − | 8.55149i | 0.356003 | − | 0.356003i | −0.506334 | − | 0.862337i | \(-0.669000\pi\) |
0.862337 | + | 0.506334i | \(0.169000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 0.356404i | − | 0.0147861i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.3258 | + | 27.3258i | 1.13172 | + | 1.13172i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.7176 | − | 12.7176i | −0.524912 | − | 0.524912i | 0.394139 | − | 0.919051i | \(-0.371043\pi\) |
−0.919051 | + | 0.394139i | \(0.871043\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.2981i | 0.424324i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.5905 | + | 23.5905i | −0.968746 | + | 0.968746i | −0.999526 | − | 0.0307800i | \(-0.990201\pi\) |
0.0307800 | + | 0.999526i | \(0.490201\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.775746 | − | 12.6253i | 0.0318025 | − | 0.517587i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.7059 | −1.05031 | −0.525157 | − | 0.851006i | \(-0.675993\pi\) | ||||
−0.525157 | + | 0.851006i | \(0.675993\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.74798 | 0.316047 | 0.158023 | − | 0.987435i | \(-0.449488\pi\) | ||||
0.158023 | + | 0.987435i | \(0.449488\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.22951 | + | 52.5605i | −0.131298 | + | 2.13689i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.04349 | − | 3.04349i | 0.123531 | − | 0.123531i | −0.642638 | − | 0.766170i | \(-0.722160\pi\) |
0.766170 | + | 0.642638i | \(0.222160\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 2.49265i | − | 0.100842i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.24472 | − | 8.24472i | −0.333001 | − | 0.333001i | 0.520724 | − | 0.853725i | \(-0.325662\pi\) |
−0.853725 | + | 0.520724i | \(0.825662\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.4628 | + | 27.4628i | 1.10561 | + | 1.10561i | 0.993720 | + | 0.111891i | \(0.0356907\pi\) |
0.111891 | + | 0.993720i | \(0.464309\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 24.7269i | − | 0.993857i | −0.867792 | − | 0.496928i | \(-0.834461\pi\) | ||
0.867792 | − | 0.496928i | \(-0.165539\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.68111 | − | 7.68111i | 0.307737 | − | 0.307737i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2506 | + | 6.07522i | 0.970024 | + | 0.243009i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.8370 | 0.432099 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.7875 | 1.62372 | 0.811862 | − | 0.583849i | \(-0.198454\pi\) | ||||
0.811862 | + | 0.583849i | \(0.198454\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.4463 | + | 20.8615i | 0.732018 | + | 0.827863i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.10554 | + | 1.10554i | −0.0438031 | + | 0.0438031i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.0747i | 1.66185i | 0.556384 | + | 0.830925i | \(0.312188\pi\) | ||||
−0.556384 | + | 0.830925i | \(0.687812\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.8496 | − | 15.8496i | −0.625045 | − | 0.625045i | 0.321772 | − | 0.946817i | \(-0.395722\pi\) |
−0.946817 | + | 0.321772i | \(0.895722\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.95243 | + | 1.95243i | 0.0767581 | + | 0.0767581i | 0.744444 | − | 0.667685i | \(-0.232715\pi\) |
−0.667685 | + | 0.744444i | \(0.732715\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 61.3522i | − | 2.40828i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.1587 | − | 23.1587i | 0.906269 | − | 0.906269i | −0.0896999 | − | 0.995969i | \(-0.528591\pi\) |
0.995969 | + | 0.0896999i | \(0.0285908\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.8324 | + | 1.89446i | 1.20472 | + | 0.0740227i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.12594 | −0.160724 | −0.0803620 | − | 0.996766i | \(-0.525608\pi\) | ||||
−0.0803620 | + | 0.996766i | \(0.525608\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9116 | −0.579994 | −0.289997 | − | 0.957028i | \(-0.593654\pi\) | ||||
−0.289997 | + | 0.957028i | \(0.593654\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.55978 | + | 4.03188i | −0.176821 | + | 0.156350i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.5501 | + | 30.5501i | −1.18290 | + | 1.18290i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 44.3014i | − | 1.71024i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.9380 | + | 29.9380i | 1.15402 | + | 1.15402i | 0.985738 | + | 0.168285i | \(0.0538228\pi\) |
0.168285 | + | 0.985738i | \(0.446177\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.9964 | − | 24.9964i | −0.960690 | − | 0.960690i | 0.0385660 | − | 0.999256i | \(-0.487721\pi\) |
−0.999256 | + | 0.0385660i | \(0.987721\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 13.3404i | − | 0.511958i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.34064 | + | 9.34064i | −0.357410 | + | 0.357410i | −0.862857 | − | 0.505448i | \(-0.831327\pi\) |
0.505448 | + | 0.862857i | \(0.331327\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.26187 | + | 5.53690i | −0.239254 | + | 0.211554i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.80318 | 0.0686956 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.2374 | −0.845952 | −0.422976 | − | 0.906141i | \(-0.639014\pi\) | ||||
−0.422976 | + | 0.906141i | \(0.639014\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41.7369 | + | 2.56447i | 1.58317 | + | 0.0972761i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.6629 | + | 11.6629i | −0.441764 | + | 0.441764i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.1358i | 0.798287i | 0.916888 | + | 0.399143i | \(0.130692\pi\) | ||||
−0.916888 | + | 0.399143i | \(0.869308\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.68735 | − | 3.68735i | −0.139071 | − | 0.139071i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.69511 | + | 4.69511i | 0.176578 | + | 0.176578i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 38.4749i | − | 1.44495i | −0.691395 | − | 0.722477i | \(-0.743004\pi\) | ||
0.691395 | − | 0.722477i | \(-0.256996\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.0676 | − | 18.0676i | 0.676638 | − | 0.676638i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.38787 | + | 2.70052i | 0.0893014 | + | 0.100994i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.81912 | −0.142429 | −0.0712145 | − | 0.997461i | \(-0.522687\pi\) | ||||
−0.0712145 | + | 0.997461i | \(0.522687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.89843 | −0.145185 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 36.1865 | + | 4.46372i | 1.34393 | + | 0.165778i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.8930 | + | 30.8930i | −1.14576 | + | 1.14576i | −0.158382 | + | 0.987378i | \(0.550628\pi\) |
−0.987378 | + | 0.158382i | \(0.949372\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 58.3372i | 2.15768i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.6556 | + | 25.6556i | 0.947612 | + | 0.947612i | 0.998694 | − | 0.0510826i | \(-0.0162672\pi\) |
−0.0510826 | + | 0.998694i | \(0.516267\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.3495 | − | 25.3495i | −0.933759 | − | 0.933759i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.9657i | 0.955164i | 0.878587 | + | 0.477582i | \(0.158487\pi\) | ||||
−0.878587 | + | 0.477582i | \(0.841513\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.4284 | − | 11.4284i | 0.419268 | − | 0.419268i | −0.465684 | − | 0.884951i | \(-0.654192\pi\) |
0.884951 | + | 0.465684i | \(0.154192\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.03620 | − | 16.8641i | 0.0379633 | − | 0.617854i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.5955 | −0.679466 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.9380 | 0.764037 | 0.382018 | − | 0.924155i | \(-0.375229\pi\) | ||||
0.382018 | + | 0.924155i | \(0.375229\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.35171 | + | 38.2742i | −0.0855876 | + | 1.39294i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.1187 | − | 16.1187i | 0.585845 | − | 0.585845i | −0.350659 | − | 0.936503i | \(-0.614042\pi\) |
0.936503 | + | 0.350659i | \(0.114042\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 31.4877i | − | 1.14143i | −0.821148 | − | 0.570715i | \(-0.806666\pi\) | ||
0.821148 | − | 0.570715i | \(-0.193334\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.87732 | − | 8.87732i | −0.321380 | − | 0.321380i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.02425 | − | 2.02425i | −0.0730916 | − | 0.0730916i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.47627i | 0.125357i | 0.998034 | + | 0.0626787i | \(0.0199644\pi\) | ||||
−0.998034 | + | 0.0626787i | \(0.980036\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.1089 | + | 12.1089i | −0.435527 | + | 0.435527i | −0.890504 | − | 0.454976i | \(-0.849648\pi\) |
0.454976 | + | 0.890504i | \(0.349648\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.4010 | − | 2.63989i | −0.768748 | − | 0.0948276i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.93675 | 0.284363 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 55.6991 | 1.99307 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.2099 | + | 20.5942i | 0.649940 | + | 0.735038i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.7889 | + | 19.7889i | −0.705399 | + | 0.705399i | −0.965564 | − | 0.260165i | \(-0.916223\pi\) |
0.260165 | + | 0.965564i | \(0.416223\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.6122i | 0.412883i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.46168 | − | 1.46168i | −0.0519058 | − | 0.0519058i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.4896 | − | 12.4896i | −0.442403 | − | 0.442403i | 0.450416 | − | 0.892819i | \(-0.351276\pi\) |
−0.892819 | + | 0.450416i | \(0.851276\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.1002i | 1.59553i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.221077 | + | 0.221077i | −0.00780164 | + | 0.00780164i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.0738 | + | 0.926192i | 0.531282 | + | 0.0326440i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.50860 | 0.228830 | 0.114415 | − | 0.993433i | \(-0.463501\pi\) | ||||
0.114415 | + | 0.993433i | \(0.463501\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.3733 | 0.715403 | 0.357701 | − | 0.933836i | \(-0.383561\pi\) | ||||
0.357701 | + | 0.933836i | \(0.383561\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.2166 | − | 9.03382i | 0.357873 | − | 0.316441i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.8496 | − | 19.8496i | 0.694448 | − | 0.694448i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.7867i | 0.516061i | 0.966137 | + | 0.258030i | \(0.0830735\pi\) | ||||
−0.966137 | + | 0.258030i | \(0.916927\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.5198 | − | 18.5198i | −0.645558 | − | 0.645558i | 0.306358 | − | 0.951916i | \(-0.400890\pi\) |
−0.951916 | + | 0.306358i | \(0.900890\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.6294 | + | 27.6294i | 0.960767 | + | 0.960767i | 0.999259 | − | 0.0384921i | \(-0.0122554\pi\) |
−0.0384921 | + | 0.999259i | \(0.512255\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 49.4617i | − | 1.71788i | −0.512080 | − | 0.858938i | \(-0.671125\pi\) | ||
0.512080 | − | 0.858938i | \(-0.328875\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.0028 | − | 20.0028i | 0.693055 | − | 0.693055i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.52373 | − | 4.00000i | 0.156550 | − | 0.138426i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.39558 | −0.0481809 | −0.0240904 | − | 0.999710i | \(-0.507669\pi\) | ||||
−0.0240904 | + | 0.999710i | \(0.507669\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.1754 | 0.833634 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.8463 | − | 1.77242i | −0.992342 | − | 0.0609733i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.9829 | − | 18.9829i | 0.652259 | − | 0.652259i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.9387i | 0.443532i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.9927 | + | 15.9927i | 0.547580 | + | 0.547580i | 0.925740 | − | 0.378160i | \(-0.123443\pi\) |
−0.378160 | + | 0.925740i | \(0.623443\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.1829 | − | 25.1829i | −0.860232 | − | 0.860232i | 0.131132 | − | 0.991365i | \(-0.458139\pi\) |
−0.991365 | + | 0.131132i | \(0.958139\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 14.9722i | − | 0.510846i | −0.966829 | − | 0.255423i | \(-0.917785\pi\) | ||
0.966829 | − | 0.255423i | \(-0.0822148\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.4757 | − | 37.4757i | 1.27569 | − | 1.27569i | 0.332628 | − | 0.943058i | \(-0.392065\pi\) |
0.943058 | − | 0.332628i | \(-0.107935\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.46310 | + | 2.78560i | 0.0837478 | + | 0.0947131i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.6740 | 0.735240 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.67276 | −0.0566794 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.21001 | − | 10.5095i | −0.243743 | − | 0.355287i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.60483 | + | 9.60483i | −0.324332 | + | 0.324332i | −0.850426 | − | 0.526094i | \(-0.823656\pi\) |
0.526094 | + | 0.850426i | \(0.323656\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.23802i | 0.109092i | 0.998511 | + | 0.0545459i | \(0.0173711\pi\) | ||||
−0.998511 | + | 0.0545459i | \(0.982629\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.5369 | − | 15.5369i | −0.522858 | − | 0.522858i | 0.395575 | − | 0.918434i | \(-0.370545\pi\) |
−0.918434 | + | 0.395575i | \(0.870545\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.7644 | − | 19.7644i | −0.663625 | − | 0.663625i | 0.292608 | − | 0.956233i | \(-0.405477\pi\) |
−0.956233 | + | 0.292608i | \(0.905477\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 14.1965i | − | 0.476135i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.3456 | − | 15.3456i | 0.513521 | − | 0.513521i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.20853 | + | 19.6688i | −0.0403965 | + | 0.657455i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31.4485 | −1.04887 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.6253 | −1.08691 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.16520 | + | 35.2386i | −0.0719735 | + | 1.17137i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.836381 | − | 0.836381i | 0.0277716 | − | 0.0277716i | −0.693085 | − | 0.720856i | \(-0.743749\pi\) |
0.720856 | + | 0.693085i | \(0.243749\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.90487i | 0.129374i | 0.997906 | + | 0.0646870i | \(0.0206049\pi\) | ||||
−0.997906 | + | 0.0646870i | \(0.979395\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.29948 | − | 1.29948i | −0.0430064 | − | 0.0430064i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.1355 | − | 11.1355i | −0.367727 | − | 0.367727i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 19.3865i | − | 0.639500i | −0.947502 | − | 0.319750i | \(-0.896401\pi\) | ||
0.947502 | − | 0.319750i | \(-0.103599\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.83774 | − | 1.83774i | 0.0604899 | − | 0.0604899i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.60816 | − | 6.71767i | 0.283034 | − | 0.220876i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.6328 | −0.545704 | −0.272852 | − | 0.962056i | \(-0.587967\pi\) | ||||
−0.272852 | + | 0.962056i | \(0.587967\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.6121 | −0.446119 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −43.2043 | − | 48.8612i | −1.41293 | − | 1.59793i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.1754 | − | 40.1754i | 1.31247 | − | 1.31247i | 0.392885 | − | 0.919588i | \(-0.371477\pi\) |
0.919588 | − | 0.392885i | \(-0.128523\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 10.2988i | − | 0.335730i | −0.985810 | − | 0.167865i | \(-0.946313\pi\) | ||
0.985810 | − | 0.167865i | \(-0.0536873\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.9248 | − | 13.9248i | −0.453453 | − | 0.453453i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.90487 | + | 3.90487i | 0.126891 | + | 0.126891i | 0.767700 | − | 0.640809i | \(-0.221401\pi\) |
−0.640809 | + | 0.767700i | \(0.721401\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.0145884i | 0.000473561i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.2815 | + | 10.2815i | −0.333050 | + | 0.333050i | −0.853744 | − | 0.520693i | \(-0.825673\pi\) |
0.520693 | + | 0.853744i | \(0.325673\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.10157 | − | 0.252016i | −0.132724 | − | 0.00815505i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.26127 | 0.137604 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.4010 | −0.400034 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.8993 | − | 21.1324i | 0.769347 | − | 0.680277i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.8945 | − | 25.8945i | 0.832710 | − | 0.832710i | −0.155177 | − | 0.987887i | \(-0.549595\pi\) |
0.987887 | + | 0.155177i | \(0.0495948\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 43.1960i | − | 1.38623i | −0.720829 | − | 0.693113i | \(-0.756239\pi\) | ||
0.720829 | − | 0.693113i | \(-0.243761\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.0738 | − | 15.0738i | −0.483244 | − | 0.483244i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.5766 | − | 21.5766i | −0.690296 | − | 0.690296i | 0.272001 | − | 0.962297i | \(-0.412315\pi\) |
−0.962297 | + | 0.272001i | \(0.912315\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 56.0118i | − | 1.79014i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.9230 | + | 18.9230i | −0.603550 | + | 0.603550i | −0.941253 | − | 0.337703i | \(-0.890350\pi\) |
0.337703 | + | 0.941253i | \(0.390350\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41.6893 | + | 36.8627i | −1.32833 | + | 1.17454i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −69.6509 | −2.21477 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.6531 | −0.560768 | −0.280384 | − | 0.959888i | \(-0.590462\pi\) | ||||
−0.280384 | + | 0.959888i | \(0.590462\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −48.9330 | − | 3.00663i | −1.55128 | − | 0.0953166i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.38058 | + | 2.38058i | −0.0753937 | + | 0.0753937i | −0.743798 | − | 0.668404i | \(-0.766978\pi\) |
0.668404 | + | 0.743798i | \(0.266978\pi\) | |||||||
\(998\) | 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 | 2880.2.w.p.2753.4 | 12 | ||
3.2 | odd | 2 | inner | 2880.2.w.p.2753.3 | 12 | ||
4.3 | odd | 2 | 2880.2.w.q.2753.4 | 12 | |||
5.2 | odd | 4 | inner | 2880.2.w.p.2177.3 | 12 | ||
8.3 | odd | 2 | 1440.2.w.g.1313.3 | yes | 12 | ||
8.5 | even | 2 | 1440.2.w.f.1313.3 | yes | 12 | ||
12.11 | even | 2 | 2880.2.w.q.2753.3 | 12 | |||
15.2 | even | 4 | inner | 2880.2.w.p.2177.4 | 12 | ||
20.7 | even | 4 | 2880.2.w.q.2177.3 | 12 | |||
24.5 | odd | 2 | 1440.2.w.f.1313.4 | yes | 12 | ||
24.11 | even | 2 | 1440.2.w.g.1313.4 | yes | 12 | ||
40.27 | even | 4 | 1440.2.w.g.737.4 | yes | 12 | ||
40.37 | odd | 4 | 1440.2.w.f.737.4 | yes | 12 | ||
60.47 | odd | 4 | 2880.2.w.q.2177.4 | 12 | |||
120.77 | even | 4 | 1440.2.w.f.737.3 | ✓ | 12 | ||
120.107 | odd | 4 | 1440.2.w.g.737.3 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.2.w.f.737.3 | ✓ | 12 | 120.77 | even | 4 | ||
1440.2.w.f.737.4 | yes | 12 | 40.37 | odd | 4 | ||
1440.2.w.f.1313.3 | yes | 12 | 8.5 | even | 2 | ||
1440.2.w.f.1313.4 | yes | 12 | 24.5 | odd | 2 | ||
1440.2.w.g.737.3 | yes | 12 | 120.107 | odd | 4 | ||
1440.2.w.g.737.4 | yes | 12 | 40.27 | even | 4 | ||
1440.2.w.g.1313.3 | yes | 12 | 8.3 | odd | 2 | ||
1440.2.w.g.1313.4 | yes | 12 | 24.11 | even | 2 | ||
2880.2.w.p.2177.3 | 12 | 5.2 | odd | 4 | inner | ||
2880.2.w.p.2177.4 | 12 | 15.2 | even | 4 | inner | ||
2880.2.w.p.2753.3 | 12 | 3.2 | odd | 2 | inner | ||
2880.2.w.p.2753.4 | 12 | 1.1 | even | 1 | trivial | ||
2880.2.w.q.2177.3 | 12 | 20.7 | even | 4 | |||
2880.2.w.q.2177.4 | 12 | 60.47 | odd | 4 | |||
2880.2.w.q.2753.3 | 12 | 12.11 | even | 2 | |||
2880.2.w.q.2753.4 | 12 | 4.3 | odd | 2 |