Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(449,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.m (of order \(4\), 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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1345.4 | ||
Root | \(0.277956 - 0.213283i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1345 |
Dual form | 1792.2.m.h.449.4 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −0.328027 | − | 0.328027i | −0.189386 | − | 0.189386i | 0.606044 | − | 0.795431i | \(-0.292755\pi\) |
−0.795431 | + | 0.606044i | \(0.792755\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.40197 | + | 1.40197i | −0.626979 | + | 0.626979i | −0.947307 | − | 0.320328i | \(-0.896207\pi\) |
0.320328 | + | 0.947307i | \(0.396207\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.78480i | − | 0.928266i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.444087 | + | 0.444087i | −0.133897 | + | 0.133897i | −0.770879 | − | 0.636982i | \(-0.780183\pi\) |
0.636982 | + | 0.770879i | \(0.280183\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.25590 | − | 2.25590i | −0.625675 | − | 0.625675i | 0.321302 | − | 0.946977i | \(-0.395880\pi\) |
−0.946977 | + | 0.321302i | \(0.895880\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.919765 | 0.237482 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.85578 | 1.17770 | 0.588849 | − | 0.808243i | \(-0.299581\pi\) | ||||
0.588849 | + | 0.808243i | \(0.299581\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.114004 | + | 0.114004i | 0.0261543 | + | 0.0261543i | 0.720063 | − | 0.693909i | \(-0.244113\pi\) |
−0.693909 | + | 0.720063i | \(0.744113\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.328027 | + | 0.328027i | −0.0715813 | + | 0.0715813i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.20529i | 0.668350i | 0.942511 | + | 0.334175i | \(0.108458\pi\) | ||||
−0.942511 | + | 0.334175i | \(0.891542\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.06898i | 0.213795i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.89757 | + | 1.89757i | −0.365187 | + | 0.365187i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.997091 | + | 0.997091i | 0.185155 | + | 0.185155i | 0.793598 | − | 0.608443i | \(-0.208205\pi\) |
−0.608443 | + | 0.793598i | \(0.708205\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.34435 | −0.959874 | −0.479937 | − | 0.877303i | \(-0.659340\pi\) | ||||
−0.479937 | + | 0.877303i | \(0.659340\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.291345 | 0.0507167 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.40197 | + | 1.40197i | 0.236976 | + | 0.236976i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.03472 | + | 2.03472i | −0.334507 | + | 0.334507i | −0.854295 | − | 0.519788i | \(-0.826011\pi\) |
0.519788 | + | 0.854295i | \(0.326011\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.47999i | 0.236989i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.57673i | − | 1.49563i | −0.663905 | − | 0.747817i | \(-0.731102\pi\) | ||
0.663905 | − | 0.747817i | \(-0.268898\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.86758 | + | 6.86758i | −1.04730 | + | 1.04730i | −0.0484714 | + | 0.998825i | \(0.515435\pi\) |
−0.998825 | + | 0.0484714i | \(0.984565\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.90419 | + | 3.90419i | 0.582003 | + | 0.582003i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.70703 | −1.41592 | −0.707958 | − | 0.706255i | \(-0.750383\pi\) | ||||
−0.707958 | + | 0.706255i | \(0.750383\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.59282 | − | 1.59282i | −0.223040 | − | 0.223040i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.64426 | + | 7.64426i | −1.05002 | + | 1.05002i | −0.0513390 | + | 0.998681i | \(0.516349\pi\) |
−0.998681 | + | 0.0513390i | \(0.983651\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.24519i | − | 0.167902i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.0747927i | − | 0.00990653i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.50266 | + | 1.50266i | −0.195630 | + | 0.195630i | −0.798123 | − | 0.602494i | \(-0.794174\pi\) |
0.602494 | + | 0.798123i | \(0.294174\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.74157 | + | 1.74157i | 0.222985 | + | 0.222985i | 0.809754 | − | 0.586769i | \(-0.199601\pi\) |
−0.586769 | + | 0.809754i | \(0.699601\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.78480 | −0.350851 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.32541 | 0.784571 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.96491 | − | 8.96491i | −1.09524 | − | 1.09524i | −0.994959 | − | 0.100279i | \(-0.968027\pi\) |
−0.100279 | − | 0.994959i | \(-0.531973\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.05142 | − | 1.05142i | 0.126576 | − | 0.126576i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.18356i | − | 0.852532i | −0.904598 | − | 0.426266i | \(-0.859829\pi\) | ||
0.904598 | − | 0.426266i | \(-0.140171\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.04029i | − | 1.05809i | −0.848595 | − | 0.529043i | \(-0.822551\pi\) | ||
0.848595 | − | 0.529043i | \(-0.177449\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.350652 | − | 0.350652i | 0.0404898 | − | 0.0404898i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.444087 | + | 0.444087i | 0.0506085 | + | 0.0506085i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.58806 | −1.07874 | −0.539370 | − | 0.842069i | \(-0.681338\pi\) | ||||
−0.539370 | + | 0.842069i | \(0.681338\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.10949 | −0.789943 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.30245 | − | 5.30245i | −0.582020 | − | 0.582020i | 0.353438 | − | 0.935458i | \(-0.385012\pi\) |
−0.935458 | + | 0.353438i | \(0.885012\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.80764 | + | 6.80764i | −0.738392 | + | 0.738392i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 0.654145i | − | 0.0701317i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.49938i | 0.264934i | 0.991187 | + | 0.132467i | \(0.0422898\pi\) | ||||
−0.991187 | + | 0.132467i | \(0.957710\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.25590 | + | 2.25590i | −0.236483 | + | 0.236483i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.75309 | + | 1.75309i | 0.181787 | + | 0.181787i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.319660 | −0.0327964 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.89073 | 0.598113 | 0.299057 | − | 0.954235i | \(-0.403328\pi\) | ||||
0.299057 | + | 0.954235i | \(0.403328\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.23669 | + | 1.23669i | 0.124292 | + | 0.124292i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.00499 | − | 7.00499i | 0.697022 | − | 0.697022i | −0.266745 | − | 0.963767i | \(-0.585948\pi\) |
0.963767 | + | 0.266745i | \(0.0859482\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.10887i | 0.798991i | 0.916735 | + | 0.399496i | \(0.130815\pi\) | ||||
−0.916735 | + | 0.399496i | \(0.869185\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 0.919765i | − | 0.0897599i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.24367 | − | 2.24367i | 0.216904 | − | 0.216904i | −0.590288 | − | 0.807192i | \(-0.700986\pi\) |
0.807192 | + | 0.590288i | \(0.200986\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.299413 | − | 0.299413i | −0.0286786 | − | 0.0286786i | 0.692622 | − | 0.721301i | \(-0.256455\pi\) |
−0.721301 | + | 0.692622i | \(0.756455\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.33489 | 0.126702 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.67432 | 0.439723 | 0.219862 | − | 0.975531i | \(-0.429439\pi\) | ||||
0.219862 | + | 0.975531i | \(0.429439\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.49372 | − | 4.49372i | −0.419041 | − | 0.419041i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.28224 | + | 6.28224i | −0.580793 | + | 0.580793i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 4.85578i | − | 0.445128i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6056i | 0.964143i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.14142 | + | 3.14142i | −0.283252 | + | 0.283252i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.50850 | − | 8.50850i | −0.761024 | − | 0.761024i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.7602 | −1.22102 | −0.610509 | − | 0.792009i | \(-0.709035\pi\) | ||||
−0.610509 | + | 0.792009i | \(0.709035\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.50550 | 0.396687 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.91851 | − | 6.91851i | −0.604473 | − | 0.604473i | 0.337023 | − | 0.941496i | \(-0.390580\pi\) |
−0.941496 | + | 0.337023i | \(0.890580\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.114004 | − | 0.114004i | 0.00988539 | − | 0.00988539i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 5.32066i | − | 0.457929i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 7.10937i | − | 0.607395i | −0.952769 | − | 0.303697i | \(-0.901779\pi\) | ||
0.952769 | − | 0.303697i | \(-0.0982211\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.8171 | + | 10.8171i | −0.917496 | + | 0.917496i | −0.996847 | − | 0.0793508i | \(-0.974715\pi\) |
0.0793508 | + | 0.996847i | \(0.474715\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.18416 | + | 3.18416i | 0.268155 | + | 0.268155i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00364 | 0.167553 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.79578 | −0.232177 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.328027 | + | 0.328027i | 0.0270552 | + | 0.0270552i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.3257 | + | 15.3257i | −1.25553 | + | 1.25553i | −0.302325 | + | 0.953205i | \(0.597763\pi\) |
−0.953205 | + | 0.302325i | \(0.902237\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.5070i | 1.75022i | 0.483925 | + | 0.875109i | \(0.339211\pi\) | ||||
−0.483925 | + | 0.875109i | \(0.660789\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 13.5224i | − | 1.09322i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.49260 | − | 7.49260i | 0.601821 | − | 0.601821i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.72626 | − | 7.72626i | −0.616623 | − | 0.616623i | 0.328041 | − | 0.944664i | \(-0.393612\pi\) |
−0.944664 | + | 0.328041i | \(0.893612\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.01504 | 0.397719 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.20529 | 0.252612 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.9336 | + | 16.9336i | 1.32634 | + | 1.32634i | 0.908538 | + | 0.417802i | \(0.137199\pi\) |
0.417802 | + | 0.908538i | \(0.362801\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.408456 | + | 0.408456i | −0.0317983 | + | 0.0317983i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.57678i | 0.663691i | 0.943334 | + | 0.331846i | \(0.107671\pi\) | ||||
−0.943334 | + | 0.331846i | \(0.892329\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2.82179i | − | 0.217061i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.317478 | − | 0.317478i | 0.0242781 | − | 0.0242781i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.44032 | + | 5.44032i | 0.413620 | + | 0.413620i | 0.882997 | − | 0.469378i | \(-0.155522\pi\) |
−0.469378 | + | 0.882997i | \(0.655522\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.06898 | 0.0808069 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.985825 | 0.0740991 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.32748 | − | 8.32748i | −0.622425 | − | 0.622425i | 0.323726 | − | 0.946151i | \(-0.395064\pi\) |
−0.946151 | + | 0.323726i | \(0.895064\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.24148 | − | 6.24148i | 0.463926 | − | 0.463926i | −0.436014 | − | 0.899940i | \(-0.643610\pi\) |
0.899940 | + | 0.436014i | \(0.143610\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.14256i | − | 0.0844605i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5.70524i | − | 0.419457i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.15639 | + | 2.15639i | −0.157691 | + | 0.157691i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.89757 | + | 1.89757i | 0.138028 | + | 0.138028i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.57521 | 0.113979 | 0.0569893 | − | 0.998375i | \(-0.481850\pi\) | ||||
0.0569893 | + | 0.998375i | \(0.481850\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.649369 | 0.0467426 | 0.0233713 | − | 0.999727i | \(-0.492560\pi\) | ||||
0.0233713 | + | 0.999727i | \(0.492560\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.07490 | − | 2.07490i | −0.148587 | − | 0.148587i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.16865 | − | 1.16865i | 0.0832632 | − | 0.0832632i | −0.664249 | − | 0.747512i | \(-0.731248\pi\) |
0.747512 | + | 0.664249i | \(0.231248\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.09013i | 0.289942i | 0.989436 | + | 0.144971i | \(0.0463088\pi\) | ||||
−0.989436 | + | 0.144971i | \(0.953691\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.88146i | 0.414846i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.997091 | − | 0.997091i | 0.0699821 | − | 0.0699821i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.4263 | + | 13.4263i | 0.937731 | + | 0.937731i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.92609 | 0.620406 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.101255 | −0.00700398 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0421 | + | 19.0421i | 1.31091 | + | 1.31091i | 0.920745 | + | 0.390164i | \(0.127582\pi\) |
0.390164 | + | 0.920745i | \(0.372418\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.35640 | + | 2.35640i | −0.161458 | + | 0.161458i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 19.2562i | − | 1.31326i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.34435i | 0.362798i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.96546 | + | 2.96546i | −0.200387 | + | 0.200387i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.9542 | − | 10.9542i | −0.736857 | − | 0.736857i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.0121 | 1.74190 | 0.870950 | − | 0.491372i | \(-0.163504\pi\) | ||||
0.870950 | + | 0.491372i | \(0.163504\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.97688 | 0.198459 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.181612 | − | 0.181612i | −0.0120540 | − | 0.0120540i | 0.701054 | − | 0.713108i | \(-0.252713\pi\) |
−0.713108 | + | 0.701054i | \(0.752713\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.679595 | − | 0.679595i | 0.0449089 | − | 0.0449089i | −0.684296 | − | 0.729205i | \(-0.739890\pi\) |
0.729205 | + | 0.684296i | \(0.239890\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 0.291345i | − | 0.0191691i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.6676i | 1.28847i | 0.764828 | + | 0.644235i | \(0.222824\pi\) | ||||
−0.764828 | + | 0.644235i | \(0.777176\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.6089 | − | 13.6089i | 0.887749 | − | 0.887749i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.14514 | + | 3.14514i | 0.204299 | + | 0.204299i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.44846 | −0.611170 | −0.305585 | − | 0.952165i | \(-0.598852\pi\) | ||||
−0.305585 | + | 0.952165i | \(0.598852\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.8233 | −1.47018 | −0.735088 | − | 0.677971i | \(-0.762859\pi\) | ||||
−0.735088 | + | 0.677971i | \(0.762859\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.02480 | + | 8.02480i | 0.514791 | + | 0.514791i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.40197 | − | 1.40197i | 0.0895684 | − | 0.0895684i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.514364i | − | 0.0327282i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.47869i | 0.220453i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.2670 | − | 12.2670i | 0.774287 | − | 0.774287i | −0.204566 | − | 0.978853i | \(-0.565578\pi\) |
0.978853 | + | 0.204566i | \(0.0655782\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.42343 | − | 1.42343i | −0.0894903 | − | 0.0894903i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.46618 | 0.279683 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.71213 | 0.481070 | 0.240535 | − | 0.970641i | \(-0.422677\pi\) | ||||
0.240535 | + | 0.970641i | \(0.422677\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.03472 | + | 2.03472i | 0.126432 | + | 0.126432i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.77670 | − | 2.77670i | 0.171873 | − | 0.171873i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 9.24972i | − | 0.570362i | −0.958474 | − | 0.285181i | \(-0.907946\pi\) | ||
0.958474 | − | 0.285181i | \(-0.0920538\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 21.4340i | − | 1.31668i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.819863 | − | 0.819863i | 0.0501748 | − | 0.0501748i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.36587 | − | 8.36587i | −0.510076 | − | 0.510076i | 0.404474 | − | 0.914550i | \(-0.367455\pi\) |
−0.914550 | + | 0.404474i | \(0.867455\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.15740 | −0.0703071 | −0.0351535 | − | 0.999382i | \(-0.511192\pi\) | ||||
−0.0351535 | + | 0.999382i | \(0.511192\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.47999 | 0.0895733 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.474718 | − | 0.474718i | −0.0286266 | − | 0.0286266i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.6925 | − | 16.6925i | 1.00296 | − | 1.00296i | 0.00295975 | − | 0.999996i | \(-0.499058\pi\) |
0.999996 | − | 0.00295975i | \(-0.000942120\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.8829i | 0.891018i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.3656i | 1.75180i | 0.482490 | + | 0.875902i | \(0.339732\pi\) | ||||
−0.482490 | + | 0.875902i | \(0.660268\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0502 | + | 13.0502i | −0.775752 | + | 0.775752i | −0.979105 | − | 0.203354i | \(-0.934816\pi\) |
0.203354 | + | 0.979105i | \(0.434816\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.104857 | + | 0.104857i | 0.00621118 | + | 0.00621118i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.57673 | −0.565296 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.57857 | 0.386975 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.93232 | − | 1.93232i | −0.113274 | − | 0.113274i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.4435 | − | 19.4435i | 1.13590 | − | 1.13590i | 0.146723 | − | 0.989178i | \(-0.453127\pi\) |
0.989178 | − | 0.146723i | \(-0.0468727\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.21336i | − | 0.245311i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.68537i | − | 0.0977952i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.23084 | − | 7.23084i | 0.418170 | − | 0.418170i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.86758 | + | 6.86758i | 0.395841 | + | 0.395841i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.59564 | −0.264013 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.88324 | −0.279613 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.5562 | − | 19.5562i | −1.11613 | − | 1.11613i | −0.992303 | − | 0.123830i | \(-0.960482\pi\) |
−0.123830 | − | 0.992303i | \(-0.539518\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.65993 | − | 2.65993i | 0.151318 | − | 0.151318i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 24.5927i | − | 1.39453i | −0.716815 | − | 0.697263i | \(-0.754401\pi\) | ||
0.716815 | − | 0.697263i | \(-0.245599\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.0125i | 1.01812i | 0.860730 | + | 0.509062i | \(0.170008\pi\) | ||||
−0.860730 | + | 0.509062i | \(0.829992\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.90419 | − | 3.90419i | 0.219976 | − | 0.219976i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.70483 | − | 9.70483i | −0.545078 | − | 0.545078i | 0.379935 | − | 0.925013i | \(-0.375946\pi\) |
−0.925013 | + | 0.379935i | \(0.875946\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.885591 | −0.0495836 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.47197 | −0.0821573 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.553578 | + | 0.553578i | 0.0308019 | + | 0.0308019i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.41151 | − | 2.41151i | 0.133766 | − | 0.133766i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.196431i | 0.0108627i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.70703i | 0.535166i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.50341 | + | 1.50341i | −0.0826349 | + | 0.0826349i | −0.747216 | − | 0.664581i | \(-0.768610\pi\) |
0.664581 | + | 0.747216i | \(0.268610\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.66630 | + | 5.66630i | 0.310511 | + | 0.310511i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.1370 | 1.37338 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.7244 | −0.965512 | −0.482756 | − | 0.875755i | \(-0.660364\pi\) | ||||
−0.482756 | + | 0.875755i | \(0.660364\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.53330 | − | 1.53330i | −0.0832776 | − | 0.0832776i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.37336 | − | 2.37336i | 0.128525 | − | 0.128525i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.94812i | 0.158721i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.92098 | + | 4.92098i | −0.264172 | + | 0.264172i | −0.826747 | − | 0.562574i | \(-0.809811\pi\) |
0.562574 | + | 0.826747i | \(0.309811\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.8975 | − | 24.8975i | −1.33274 | − | 1.33274i | −0.902914 | − | 0.429821i | \(-0.858577\pi\) |
−0.429821 | − | 0.902914i | \(-0.641423\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.56146 | 0.456977 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.71306 | −0.304075 | −0.152038 | − | 0.988375i | \(-0.548584\pi\) | ||||
−0.152038 | + | 0.988375i | \(0.548584\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.0711 | + | 10.0711i | 0.534519 | + | 0.534519i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.59282 | + | 1.59282i | −0.0843012 | + | 0.0843012i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 25.2978i | − | 1.33516i | −0.744536 | − | 0.667582i | \(-0.767329\pi\) | ||
0.744536 | − | 0.667582i | \(-0.232671\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.9740i | − | 0.998632i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.47891 | − | 3.47891i | 0.182595 | − | 0.182595i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.6742 | + | 12.6742i | 0.663398 | + | 0.663398i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.9944 | 0.730499 | 0.365250 | − | 0.930910i | \(-0.380984\pi\) | ||||
0.365250 | + | 0.930910i | \(0.380984\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −26.6692 | −1.38835 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.64426 | + | 7.64426i | 0.396870 | + | 0.396870i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.44242 | − | 6.44242i | 0.333576 | − | 0.333576i | −0.520367 | − | 0.853943i | \(-0.674205\pi\) |
0.853943 | + | 0.520367i | \(0.174205\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.58203i | 0.288255i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.49869i | − | 0.231694i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0039 | − | 20.0039i | 1.02753 | − | 1.02753i | 0.0279235 | − | 0.999610i | \(-0.491111\pi\) |
0.999610 | − | 0.0279235i | \(-0.00888948\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.51371 | + | 4.51371i | 0.231244 | + | 0.231244i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.23256 | −0.420664 | −0.210332 | − | 0.977630i | \(-0.567455\pi\) | ||||
−0.210332 | + | 0.977630i | \(0.567455\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.24519 | −0.0634609 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 19.1248 | + | 19.1248i | 0.972169 | + | 0.972169i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.8204 | − | 22.8204i | 1.15704 | − | 1.15704i | 0.171930 | − | 0.985109i | \(-0.445000\pi\) |
0.985109 | − | 0.171930i | \(-0.0550003\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.5642i | 0.787115i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.53891i | 0.228958i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.4421 | − | 13.4421i | 0.676348 | − | 0.676348i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.2540 | + | 20.2540i | 1.01652 | + | 1.01652i | 0.999861 | + | 0.0166562i | \(0.00530208\pi\) |
0.0166562 | + | 0.999861i | \(0.494698\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0747927 | −0.00374432 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.9844 | −1.04791 | −0.523956 | − | 0.851745i | \(-0.675544\pi\) | ||||
−0.523956 | + | 0.851745i | \(0.675544\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0563 | + | 12.0563i | 0.600569 | + | 0.600569i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.96727 | − | 9.96727i | 0.495277 | − | 0.495277i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.80719i | − | 0.0895791i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.9268i | 1.13366i | 0.823836 | + | 0.566828i | \(0.191830\pi\) | ||||
−0.823836 | + | 0.566828i | \(0.808170\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.33206 | + | 2.33206i | −0.115032 | + | 0.115032i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.50266 | + | 1.50266i | 0.0739410 | + | 0.0739410i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.8677 | 0.729828 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.09661 | 0.347522 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.8867 | − | 27.8867i | −1.36235 | − | 1.36235i | −0.870909 | − | 0.491444i | \(-0.836469\pi\) |
−0.491444 | − | 0.870909i | \(-0.663531\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.93087 | − | 3.93087i | 0.191579 | − | 0.191579i | −0.604799 | − | 0.796378i | \(-0.706747\pi\) |
0.796378 | + | 0.604799i | \(0.206747\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 27.0321i | 1.31435i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.19071i | 0.251786i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.74157 | − | 1.74157i | 0.0842803 | − | 0.0842803i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.657247 | − | 0.657247i | −0.0317322 | − | 0.0317322i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.8494 | 1.48596 | 0.742981 | − | 0.669313i | \(-0.233411\pi\) | ||||
0.742981 | + | 0.669313i | \(0.233411\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.5480 | −1.08359 | −0.541794 | − | 0.840511i | \(-0.682255\pi\) | ||||
−0.541794 | + | 0.840511i | \(0.682255\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.917090 | + | 0.917090i | 0.0439711 | + | 0.0439711i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.365416 | + | 0.365416i | −0.0174802 | + | 0.0174802i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 20.4983i | − | 0.978329i | −0.872192 | − | 0.489164i | \(-0.837302\pi\) | ||
0.872192 | − | 0.489164i | \(-0.162698\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.78480i | 0.132609i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.8801 | − | 15.8801i | 0.754485 | − | 0.754485i | −0.220828 | − | 0.975313i | \(-0.570876\pi\) |
0.975313 | + | 0.220828i | \(0.0708758\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.50405 | − | 3.50405i | −0.166108 | − | 0.166108i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.0545 | 0.475560 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.3273 | 1.33685 | 0.668423 | − | 0.743781i | \(-0.266969\pi\) | ||||
0.668423 | + | 0.743781i | \(0.266969\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.25290 | + | 4.25290i | 0.200261 | + | 0.200261i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.05488 | − | 7.05488i | 0.331467 | − | 0.331467i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 6.32541i | − | 0.296540i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.979734i | 0.0458300i | 0.999737 | + | 0.0229150i | \(0.00729472\pi\) | ||||
−0.999737 | + | 0.0229150i | \(0.992705\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.21417 | + | 9.21417i | −0.430080 | + | 0.430080i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.7845 | − | 25.7845i | −1.20091 | − | 1.20091i | −0.973891 | − | 0.227014i | \(-0.927104\pi\) |
−0.227014 | − | 0.973891i | \(-0.572896\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.56380 | −0.0726760 | −0.0363380 | − | 0.999340i | \(-0.511569\pi\) | ||||
−0.0363380 | + | 0.999340i | \(0.511569\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.91555 | −0.227953 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.6856 | + | 28.6856i | 1.32741 | + | 1.32741i | 0.907620 | + | 0.419792i | \(0.137897\pi\) |
0.419792 | + | 0.907620i | \(0.362103\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.96491 | + | 8.96491i | −0.413961 | + | 0.413961i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.06884i | 0.233560i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6.09961i | − | 0.280460i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.121867 | + | 0.121867i | −0.00559166 | + | 0.00559166i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.2877 | + | 21.2877i | 0.974698 | + | 0.974698i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.8040 | 1.17902 | 0.589508 | − | 0.807762i | \(-0.299322\pi\) | ||||
0.589508 | + | 0.807762i | \(0.299322\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.18029 | 0.418585 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.05142 | − | 1.05142i | −0.0478413 | − | 0.0478413i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.25861 | + | 8.25861i | −0.375004 | + | 0.375004i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.56961i | − | 0.116440i | −0.998304 | − | 0.0582201i | \(-0.981457\pi\) | ||
0.998304 | − | 0.0582201i | \(-0.0185425\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 11.1093i | − | 0.502381i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.11127 | + | 2.11127i | −0.0952804 | + | 0.0952804i | −0.753140 | − | 0.657860i | \(-0.771462\pi\) |
0.657860 | + | 0.753140i | \(0.271462\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.84165 | + | 4.84165i | 0.218057 | + | 0.218057i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.46761 | −0.155857 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.18356 | −0.322227 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.30410 | + | 5.30410i | 0.237444 | + | 0.237444i | 0.815791 | − | 0.578347i | \(-0.196302\pi\) |
−0.578347 | + | 0.815791i | \(0.696302\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.81341 | − | 2.81341i | 0.125694 | − | 0.125694i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.3432i | 1.66505i | 0.553987 | + | 0.832525i | \(0.313106\pi\) | ||||
−0.553987 | + | 0.832525i | \(0.686894\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.6415i | 0.874036i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.925621 | + | 0.925621i | −0.0411083 | + | 0.0411083i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.7303 | − | 21.7303i | −0.963178 | − | 0.963178i | 0.0361674 | − | 0.999346i | \(-0.488485\pi\) |
−0.999346 | + | 0.0361674i | \(0.988485\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.04029 | −0.399919 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.432660 | −0.0191024 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.3684 | − | 11.3684i | −0.500951 | − | 0.500951i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.31077 | − | 4.31077i | 0.189587 | − | 0.189587i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 3.56914i | − | 0.156668i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.96517i | 0.217528i | 0.994068 | + | 0.108764i | \(0.0346893\pi\) | ||||
−0.994068 | + | 0.108764i | \(0.965311\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.922937 | + | 0.922937i | −0.0403572 | + | 0.0403572i | −0.726997 | − | 0.686640i | \(-0.759085\pi\) |
0.686640 | + | 0.726997i | \(0.259085\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.350652 | − | 0.350652i | −0.0153037 | − | 0.0153037i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.9510 | −1.13044 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.7261 | 0.553309 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.18460 | + | 4.18460i | 0.181596 | + | 0.181596i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.6042 | + | 21.6042i | −0.935781 | + | 0.935781i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.29111i | 0.271989i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.46327i | 0.235757i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.444087 | − | 0.444087i | 0.0191282 | − | 0.0191282i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.1027 | + | 20.1027i | 0.864281 | + | 0.864281i | 0.991832 | − | 0.127551i | \(-0.0407116\pi\) |
−0.127551 | + | 0.991832i | \(0.540712\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.09474 | −0.175722 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.839535 | 0.0359617 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.7415 | + | 16.7415i | 0.715813 | + | 0.715813i | 0.967745 | − | 0.251932i | \(-0.0810659\pi\) |
−0.251932 | + | 0.967745i | \(0.581066\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.84991 | − | 4.84991i | 0.206989 | − | 0.206989i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.227345i | 0.00968521i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.58806i | 0.407726i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.87147 | + | 1.87147i | −0.0794394 | + | 0.0794394i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.1766 | − | 22.1766i | −0.939655 | − | 0.939655i | 0.0586254 | − | 0.998280i | \(-0.481328\pi\) |
−0.998280 | + | 0.0586254i | \(0.981328\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.9852 | 1.31053 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.41471 | 0.0597290 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.2669 | − | 24.2669i | −1.02273 | − | 1.02273i | −0.999736 | − | 0.0229924i | \(-0.992681\pi\) |
−0.0229924 | − | 0.999736i | \(-0.507319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.55325 | + | 6.55325i | −0.275697 | + | 0.275697i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.10949i | 0.298570i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.8086i | 1.79463i | 0.441392 | + | 0.897315i | \(0.354485\pi\) | ||||
−0.441392 | + | 0.897315i | \(0.645515\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.89908 | − | 6.89908i | 0.288717 | − | 0.288717i | −0.547856 | − | 0.836573i | \(-0.684556\pi\) |
0.836573 | + | 0.547856i | \(0.184556\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.516712 | − | 0.516712i | −0.0215860 | − | 0.0215860i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.42638 | −0.142890 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.38332 | −0.0992189 | −0.0496094 | − | 0.998769i | \(-0.515798\pi\) | ||||
−0.0496094 | + | 0.998769i | \(0.515798\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.213010 | − | 0.213010i | −0.00885240 | − | 0.00885240i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.30245 | + | 5.30245i | −0.219983 | + | 0.219983i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6.78944i | − | 0.281190i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 17.6150i | − | 0.728290i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.70993 | − | 2.70993i | 0.111851 | − | 0.111851i | −0.648966 | − | 0.760817i | \(-0.724798\pi\) |
0.760817 | + | 0.648966i | \(0.224798\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.609277 | − | 0.609277i | −0.0251048 | − | 0.0251048i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.766700 | −0.0315378 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.3573 | 1.20556 | 0.602780 | − | 0.797907i | \(-0.294060\pi\) | ||||
0.602780 | + | 0.797907i | \(0.294060\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.80764 | + | 6.80764i | 0.279086 | + | 0.279086i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.34167 | − | 1.34167i | 0.0549110 | − | 0.0549110i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 40.3716i | − | 1.64954i | −0.565468 | − | 0.824770i | \(-0.691304\pi\) | ||
0.565468 | − | 0.824770i | \(-0.308696\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 30.9931i | − | 1.26424i | −0.774872 | − | 0.632118i | \(-0.782186\pi\) | ||
0.774872 | − | 0.632118i | \(-0.217814\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.9655 | + | 24.9655i | −1.01667 | + | 1.01667i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.8687 | − | 14.8687i | −0.604497 | − | 0.604497i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.81876 | −0.398531 | −0.199265 | − | 0.979946i | \(-0.563856\pi\) | ||||
−0.199265 | + | 0.979946i | \(0.563856\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.654145 | −0.0265073 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.8981 | + | 21.8981i | 0.885904 | + | 0.885904i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.05548 | − | 5.05548i | 0.204189 | − | 0.204189i | −0.597603 | − | 0.801792i | \(-0.703880\pi\) |
0.801792 | + | 0.597603i | \(0.203880\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 8.80834i | − | 0.355187i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.8190i | 1.40176i | 0.713279 | + | 0.700881i | \(0.247209\pi\) | ||||
−0.713279 | + | 0.700881i | \(0.752791\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.1722 | − | 34.1722i | 1.37350 | − | 1.37350i | 0.518294 | − | 0.855203i | \(-0.326567\pi\) |
0.855203 | − | 0.518294i | \(-0.173433\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.08226 | − | 6.08226i | −0.244073 | − | 0.244073i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.49938 | 0.100135 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.5124 | 0.740497 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0332145 | + | 0.0332145i | 0.00132646 | + | 0.00132646i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.88017 | + | 9.88017i | −0.393948 | + | 0.393948i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.37799i | − | 0.0548569i | −0.999624 | − | 0.0274285i | \(-0.991268\pi\) | ||
0.999624 | − | 0.0274285i | \(-0.00873184\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 12.4926i | − | 0.496537i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.2913 | − | 19.2913i | 0.765553 | − | 0.765553i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.25590 | + | 2.25590i | 0.0893822 | + | 0.0893822i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −20.0048 | −0.791376 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.24423 | −0.0491440 | −0.0245720 | − | 0.999698i | \(-0.507822\pi\) | ||||
−0.0245720 | + | 0.999698i | \(0.507822\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.0773 | − | 25.0773i | −0.988954 | − | 0.988954i | 0.0109861 | − | 0.999940i | \(-0.496503\pi\) |
−0.999940 | + | 0.0109861i | \(0.996503\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.31656 | + | 6.31656i | −0.248714 | + | 0.248714i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.0343i | 1.10214i | 0.834458 | + | 0.551071i | \(0.185781\pi\) | ||||
−0.834458 | + | 0.551071i | \(0.814219\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.33462i | − | 0.0523886i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.75309 | − | 1.75309i | 0.0687090 | − | 0.0687090i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.5604 | + | 18.5604i | 0.726324 | + | 0.726324i | 0.969886 | − | 0.243561i | \(-0.0783157\pi\) |
−0.243561 | + | 0.969886i | \(0.578316\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.3991 | 0.757984 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −25.1754 | −0.982185 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.92378 | − | 2.92378i | −0.113894 | − | 0.113894i | 0.647863 | − | 0.761757i | \(-0.275663\pi\) |
−0.761757 | + | 0.647863i | \(0.775663\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.13234 | − | 1.13234i | 0.0440428 | − | 0.0440428i | −0.684742 | − | 0.728785i | \(-0.740085\pi\) |
0.728785 | + | 0.684742i | \(0.240085\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.18652i | 0.279101i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.319660i | 0.0123959i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.19597 | + | 3.19597i | −0.123748 | + | 0.123748i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.53267 | − | 8.53267i | −0.329892 | − | 0.329892i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.54681 | −0.0597141 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.3603 | −1.94125 | −0.970623 | − | 0.240607i | \(-0.922654\pi\) | ||||
−0.970623 | + | 0.240607i | \(0.922654\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.02845 | − | 2.02845i | −0.0780752 | − | 0.0780752i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.37404 | − | 7.37404i | 0.283407 | − | 0.283407i | −0.551059 | − | 0.834466i | \(-0.685776\pi\) |
0.834466 | + | 0.551059i | \(0.185776\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 5.89073i | − | 0.226065i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.119147i | 0.00456573i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.3569 | + | 23.3569i | −0.893726 | + | 0.893726i | −0.994872 | − | 0.101146i | \(-0.967749\pi\) |
0.101146 | + | 0.994872i | \(0.467749\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.96711 | + | 9.96711i | 0.380824 | + | 0.380824i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.445851 | −0.0170103 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.4895 | 1.31394 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.1302 | − | 12.1302i | −0.461453 | − | 0.461453i | 0.437679 | − | 0.899132i | \(-0.355801\pi\) |
−0.899132 | + | 0.437679i | \(0.855801\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.23669 | − | 1.23669i | 0.0469781 | − | 0.0469781i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 30.3305i | − | 1.15050i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 46.5025i | − | 1.76141i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.45151 | − | 6.45151i | 0.244019 | − | 0.244019i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.41607 | − | 4.41607i | −0.166793 | − | 0.166793i | 0.618775 | − | 0.785568i | \(-0.287629\pi\) |
−0.785568 | + | 0.618775i | \(0.787629\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.463933 | −0.0174976 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.92819 | −0.336255 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.00499 | − | 7.00499i | −0.263450 | − | 0.263450i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.70925 | + | 2.70925i | −0.101748 | + | 0.101748i | −0.756148 | − | 0.654400i | \(-0.772921\pi\) |
0.654400 | + | 0.756148i | \(0.272921\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.7008i | 1.00136i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 17.1302i | − | 0.641531i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.80903 | + | 2.80903i | −0.105052 | + | 0.105052i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.09935 | + | 3.09935i | 0.115747 | + | 0.115747i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.99485 | −0.335451 | −0.167726 | − | 0.985834i | \(-0.553642\pi\) | ||||
−0.167726 | + | 0.985834i | \(0.553642\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.10887 | 0.301990 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.48664 | + | 7.48664i | 0.278431 | + | 0.278431i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.06587 | + | 1.06587i | −0.0395853 | + | 0.0395853i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.6636i | 1.24851i | 0.781219 | + | 0.624256i | \(0.214598\pi\) | ||||
−0.781219 | + | 0.624256i | \(0.785402\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.0638i | 0.594954i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −33.3474 | + | 33.3474i | −1.23340 | + | 1.23340i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.0542 | + | 29.0542i | 1.07314 | + | 1.07314i | 0.997105 | + | 0.0760379i | \(0.0242270\pi\) |
0.0760379 | + | 0.997105i | \(0.475773\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.919765 | −0.0339261 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.96241 | 0.293299 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.63034 | − | 5.63034i | −0.207115 | − | 0.207115i | 0.595925 | − | 0.803040i | \(-0.296786\pi\) |
−0.803040 | + | 0.595925i | \(0.796786\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.168725 | + | 0.168725i | −0.00619827 | + | 0.00619827i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 27.7688i | − | 1.01874i | −0.860548 | − | 0.509369i | \(-0.829879\pi\) | ||
0.860548 | − | 0.509369i | \(-0.170121\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 42.9723i | − | 1.57438i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.7663 | + | 14.7663i | −0.540269 | + | 0.540269i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.24367 | − | 2.24367i | −0.0819820 | − | 0.0819820i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.5138 | −1.66082 | −0.830410 | − | 0.557153i | \(-0.811894\pi\) | ||||
−0.830410 | + | 0.557153i | \(0.811894\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.04781 | −0.293279 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −30.1522 | − | 30.1522i | −1.09735 | − | 1.09735i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.7637 | + | 20.7637i | −0.754671 | + | 0.754671i | −0.975347 | − | 0.220676i | \(-0.929174\pi\) |
0.220676 | + | 0.975347i | \(0.429174\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.933846i | 0.0338965i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3.64393i | − | 0.132092i | −0.997817 | − | 0.0660461i | \(-0.978962\pi\) | ||
0.997817 | − | 0.0660461i | \(-0.0210384\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.299413 | + | 0.299413i | −0.0108395 | + | 0.0108395i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.9579 | + | 18.9579i | 0.685424 | + | 0.685424i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.77971 | 0.244801 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.23588 | −0.224872 | −0.112436 | − | 0.993659i | \(-0.535865\pi\) | ||||
−0.112436 | + | 0.993659i | \(0.535865\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.52979 | − | 2.52979i | −0.0911080 | − | 0.0911080i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.49286 | − | 1.49286i | 0.0536943 | − | 0.0536943i | −0.679750 | − | 0.733444i | \(-0.737912\pi\) |
0.733444 | + | 0.679750i | \(0.237912\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 5.71298i | − | 0.205216i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 1.33489i | − | 0.0478888i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.09178 | − | 1.09178i | 0.0391172 | − | 0.0391172i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.19013 | + | 3.19013i | 0.114152 | + | 0.114152i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.78410 | −0.135233 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.6639 | 0.773219 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.76929 | − | 8.76929i | −0.312591 | − | 0.312591i | 0.533321 | − | 0.845913i | \(-0.320944\pi\) |
−0.845913 | + | 0.533321i | \(0.820944\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.03416 | + | 3.03416i | −0.108019 | + | 0.108019i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 4.67432i | − | 0.166200i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 7.85761i | − | 0.279032i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.03093 | + | 7.03093i | −0.249361 | + | 0.249361i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.7473 | − | 22.7473i | −0.805750 | − | 0.805750i | 0.178238 | − | 0.983987i | \(-0.442960\pi\) |
−0.983987 | + | 0.178238i | \(0.942960\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47.1352 | −1.66752 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.96026 | 0.245929 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.01468 | + | 4.01468i | 0.141675 | + | 0.141675i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.49372 | + | 4.49372i | −0.158383 | + | 0.158383i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.48846i | 0.193203i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 2.69445i | − | 0.0947319i | −0.998878 | − | 0.0473660i | \(-0.984917\pi\) | ||
0.998878 | − | 0.0473660i | \(-0.0150827\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.5311 | + | 30.5311i | −1.07209 | + | 1.07209i | −0.0749015 | + | 0.997191i | \(0.523864\pi\) |
−0.997191 | + | 0.0749015i | \(0.976136\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.379658 | + | 0.379658i | 0.0133152 | + | 0.0133152i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −47.4806 | −1.66317 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.56586 | −0.0547826 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.28224 | + | 6.28224i | 0.219519 | + | 0.219519i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.4510 | + | 15.4510i | −0.539244 | + | 0.539244i | −0.923307 | − | 0.384063i | \(-0.874525\pi\) |
0.384063 | + | 0.923307i | \(0.374525\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.4104i | 0.781178i | 0.920565 | + | 0.390589i | \(0.127729\pi\) | ||||
−0.920565 | + | 0.390589i | \(0.872271\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.311441i | 0.0108430i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.9620 | − | 15.9620i | 0.555052 | − | 0.555052i | −0.372842 | − | 0.927895i | \(-0.621617\pi\) |
0.927895 | + | 0.372842i | \(0.121617\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.88152 | + | 6.88152i | 0.239005 | + | 0.239005i | 0.816438 | − | 0.577433i | \(-0.195946\pi\) |
−0.577433 | + | 0.816438i | \(0.695946\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.9512 | −0.379892 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.85578 | −0.168243 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.0244 | − | 12.0244i | −0.416120 | − | 0.416120i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.1413 | − | 10.1413i | 0.350533 | − | 0.350533i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 24.1568i | − | 0.833986i | −0.908910 | − | 0.416993i | \(-0.863084\pi\) | ||
0.908910 | − | 0.416993i | \(-0.136916\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 27.0116i | − | 0.931435i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.63269 | − | 9.63269i | 0.331767 | − | 0.331767i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.95605 | + | 3.95605i | 0.136092 | + | 0.136092i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.6056 | 0.364412 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.56160 | 0.293833 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.52189 | − | 6.52189i | −0.223567 | − | 0.223567i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.4719 | − | 21.4719i | 0.735183 | − | 0.735183i | −0.236458 | − | 0.971642i | \(-0.575987\pi\) |
0.971642 | + | 0.236458i | \(0.0759867\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.890187i | 0.0304438i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 3.52721i | − | 0.120487i | −0.998184 | − | 0.0602436i | \(-0.980812\pi\) | ||
0.998184 | − | 0.0602436i | \(-0.0191877\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.9597 | + | 38.9597i | −1.32929 | + | 1.32929i | −0.423294 | + | 0.905992i | \(0.639126\pi\) |
−0.905992 | + | 0.423294i | \(0.860874\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.14142 | + | 3.14142i | 0.107059 | + | 0.107059i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.9798 | −0.646081 | −0.323040 | − | 0.946385i | \(-0.604705\pi\) | ||||
−0.323040 | + | 0.946385i | \(0.604705\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.2543 | −0.518662 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.15795 | − | 2.15795i | −0.0732877 | − | 0.0732877i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.25794 | − | 4.25794i | 0.144441 | − | 0.144441i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.4480i | 1.37053i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 16.4045i | − | 0.555208i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.50850 | + | 8.50850i | −0.287640 | + | 0.287640i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.54582 | + | 6.54582i | 0.221037 | + | 0.221037i | 0.808935 | − | 0.587898i | \(-0.200044\pi\) |
−0.587898 | + | 0.808935i | \(0.700044\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.7560 | −0.430248 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.2370 | 0.883946 | 0.441973 | − | 0.897028i | \(-0.354279\pi\) | ||||
0.441973 | + | 0.897028i | \(0.354279\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.3060 | + | 19.3060i | 0.649700 | + | 0.649700i | 0.952920 | − | 0.303221i | \(-0.0980620\pi\) |
−0.303221 | + | 0.952920i | \(0.598062\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.38209 | + | 1.38209i | −0.0464586 | + | 0.0464586i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 3.40903i | − | 0.114464i | −0.998361 | − | 0.0572321i | \(-0.981773\pi\) | ||
0.998361 | − | 0.0572321i | \(-0.0182275\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.7602i | 0.461502i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.15723 | − | 3.15723i | 0.105771 | − | 0.105771i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.10664 | − | 1.10664i | −0.0370323 | − | 0.0370323i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.3497 | 0.780494 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.74381 | −0.158391 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.32880 | − | 5.32880i | −0.177726 | − | 0.177726i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.1188 | + | 37.1188i | −1.23661 | + | 1.23661i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 4.50550i | − | 0.149934i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.5007i | 0.581743i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.9095 | + | 17.9095i | −0.594675 | + | 0.594675i | −0.938891 | − | 0.344216i | \(-0.888145\pi\) |
0.344216 | + | 0.938891i | \(0.388145\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.5075 | − | 19.5075i | −0.647022 | − | 0.647022i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.6991 | −0.785186 | −0.392593 | − | 0.919712i | \(-0.628422\pi\) | ||||
−0.392593 | + | 0.919712i | \(0.628422\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.70950 | 0.155862 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.60183 | + | 1.60183i | 0.0529549 | + | 0.0529549i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.91851 | + | 6.91851i | −0.228469 | + | 0.228469i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 29.7662i | − | 0.981897i | −0.871189 | − | 0.490949i | \(-0.836650\pi\) | ||
0.871189 | − | 0.490949i | \(-0.163350\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.8299i | 0.422761i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.2054 | + | 16.2054i | −0.533408 | + | 0.533408i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.17507 | − | 2.17507i | −0.0715159 | − | 0.0715159i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.5816 | 0.741676 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.6355 | 1.53006 | 0.765031 | − | 0.643993i | \(-0.222723\pi\) | ||||
0.765031 | + | 0.643993i | \(0.222723\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.114004 | − | 0.114004i | −0.00373633 | − | 0.00373633i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.06707 | + | 8.06707i | −0.264104 | + | 0.264104i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 6.04638i | − | 0.197738i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 13.5471i | − | 0.442564i | −0.975210 | − | 0.221282i | \(-0.928976\pi\) | ||
0.975210 | − | 0.221282i | \(-0.0710241\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.90856 | − | 5.90856i | 0.192819 | − | 0.192819i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.5931 | − | 13.5931i | −0.443121 | − | 0.443121i | 0.449938 | − | 0.893060i | \(-0.351446\pi\) |
−0.893060 | + | 0.449938i | \(0.851446\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.6962 | 0.999606 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.32066 | −0.173081 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.7780 | − | 28.7780i | −0.935159 | − | 0.935159i | 0.0628630 | − | 0.998022i | \(-0.479977\pi\) |
−0.998022 | + | 0.0628630i | \(0.979977\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.3940 | + | 20.3940i | −0.662019 | + | 0.662019i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.36689i | 0.206460i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 30.3026i | − | 0.981598i | −0.871273 | − | 0.490799i | \(-0.836705\pi\) | ||
0.871273 | − | 0.490799i | \(-0.163295\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.20840 | + | 2.20840i | −0.0714621 | + | 0.0714621i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.290498 | + | 0.290498i | 0.00939045 | + | 0.00939045i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.10937 | −0.229574 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.43792 | −0.0786425 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.24818 | − | 6.24818i | −0.201345 | − | 0.201345i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.910393 | + | 0.910393i | −0.0293066 | + | 0.0293066i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 18.8733i | − | 0.606925i | −0.952843 | − | 0.303462i | \(-0.901857\pi\) | ||
0.952843 | − | 0.303462i | \(-0.0981427\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 0.363176i | − | 0.0116669i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.5680 | − | 28.5680i | 0.916790 | − | 0.916790i | −0.0800042 | − | 0.996795i | \(-0.525493\pi\) |
0.996795 | + | 0.0800042i | \(0.0254934\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.8171 | + | 10.8171i | 0.346781 | + | 0.346781i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.58208 | −0.0506670 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.4828 | 0.527331 | 0.263666 | − | 0.964614i | \(-0.415068\pi\) | ||||
0.263666 | + | 0.964614i | \(0.415068\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.10994 | − | 1.10994i | −0.0354739 | − | 0.0354739i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.833805 | + | 0.833805i | −0.0266213 | + | 0.0266213i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 33.4039i | − | 1.06542i | −0.846298 | − | 0.532710i | \(-0.821174\pi\) | ||
0.846298 | − | 0.532710i | \(-0.178826\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.27683i | 0.104408i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.18416 | − | 3.18416i | 0.101353 | − | 0.101353i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.0126 | − | 22.0126i | −0.699960 | − | 0.699960i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.3648 | −0.805740 | −0.402870 | − | 0.915257i | \(-0.631987\pi\) | ||||
−0.402870 | + | 0.915257i | \(0.631987\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.986318 | 0.0312998 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.73423 | − | 5.73423i | −0.181787 | − | 0.181787i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.1405 | + | 11.1405i | −0.352824 | + | 0.352824i | −0.861159 | − | 0.508336i | \(-0.830261\pi\) |
0.508336 | + | 0.861159i | \(0.330261\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 7.72206i | − | 0.244315i |
(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 | 1792.2.m.h.1345.4 | yes | 16 | |
4.3 | odd | 2 | 1792.2.m.f.1345.5 | yes | 16 | ||
8.3 | odd | 2 | 1792.2.m.g.1345.4 | yes | 16 | ||
8.5 | even | 2 | 1792.2.m.e.1345.5 | yes | 16 | ||
16.3 | odd | 4 | 1792.2.m.g.449.4 | yes | 16 | ||
16.5 | even | 4 | inner | 1792.2.m.h.449.4 | yes | 16 | |
16.11 | odd | 4 | 1792.2.m.f.449.5 | yes | 16 | ||
16.13 | even | 4 | 1792.2.m.e.449.5 | ✓ | 16 | ||
32.5 | even | 8 | 7168.2.a.bf.1.5 | 8 | |||
32.11 | odd | 8 | 7168.2.a.ba.1.5 | 8 | |||
32.21 | even | 8 | 7168.2.a.bb.1.4 | 8 | |||
32.27 | odd | 8 | 7168.2.a.be.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1792.2.m.e.449.5 | ✓ | 16 | 16.13 | even | 4 | ||
1792.2.m.e.1345.5 | yes | 16 | 8.5 | even | 2 | ||
1792.2.m.f.449.5 | yes | 16 | 16.11 | odd | 4 | ||
1792.2.m.f.1345.5 | yes | 16 | 4.3 | odd | 2 | ||
1792.2.m.g.449.4 | yes | 16 | 16.3 | odd | 4 | ||
1792.2.m.g.1345.4 | yes | 16 | 8.3 | odd | 2 | ||
1792.2.m.h.449.4 | yes | 16 | 16.5 | even | 4 | inner | |
1792.2.m.h.1345.4 | yes | 16 | 1.1 | even | 1 | trivial | |
7168.2.a.ba.1.5 | 8 | 32.11 | odd | 8 | |||
7168.2.a.bb.1.4 | 8 | 32.21 | even | 8 | |||
7168.2.a.be.1.4 | 8 | 32.27 | odd | 8 | |||
7168.2.a.bf.1.5 | 8 | 32.5 | even | 8 |