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.g.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 | −0.320328 | − | 0.947307i | \(-0.603793\pi\) |
0.947307 | + | 0.320328i | \(0.103793\pi\) | |||||||
\(6\) | 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 | 0.946977 | − | 0.321302i | \(-0.104120\pi\) |
−0.321302 | + | 0.946977i | \(0.604120\pi\) | |||||||
\(14\) | 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 | \(-0.891542\pi\) | ||
0.942511 | − | 0.334175i | \(-0.108458\pi\) | |||||||
\(24\) | 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 | 0.608443 | − | 0.793598i | \(-0.291795\pi\) |
−0.793598 | + | 0.608443i | \(0.791795\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.34435 | 0.959874 | 0.479937 | − | 0.877303i | \(-0.340660\pi\) | ||||
0.479937 | + | 0.877303i | \(0.340660\pi\) | |||||||
\(32\) | 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 | −0.519788 | − | 0.854295i | \(-0.673989\pi\) |
0.854295 | + | 0.519788i | \(0.173989\pi\) | |||||||
\(38\) | 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 | \(-0.249617\pi\) | ||||
0.707958 | + | 0.706255i | \(0.249617\pi\) | |||||||
\(48\) | 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 | \(-0.483651\pi\) |
0.998681 | − | 0.0513390i | \(-0.0163489\pi\) | |||||||
\(54\) | 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 | 0.586769 | − | 0.809754i | \(-0.300399\pi\) |
−0.809754 | + | 0.586769i | \(0.800399\pi\) | |||||||
\(62\) | 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 | \(0.140171\pi\) | ||||
−0.904598 | + | 0.426266i | \(0.859829\pi\) | |||||||
\(72\) | 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 | \(-0.318662\pi\) | ||||
0.539370 | + | 0.842069i | \(0.318662\pi\) | |||||||
\(80\) | 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 | −0.963767 | − | 0.266745i | \(-0.914052\pi\) |
0.266745 | + | 0.963767i | \(0.414052\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.10887i | − | 0.798991i | −0.916735 | − | 0.399496i | \(-0.869185\pi\) | ||
0.916735 | − | 0.399496i | \(-0.130815\pi\) | |||||||
\(104\) | 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 | 0.721301 | − | 0.692622i | \(-0.243545\pi\) |
−0.692622 | + | 0.721301i | \(0.743545\pi\) | |||||||
\(110\) | 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 | \(-0.290965\pi\) | ||||
0.610509 | + | 0.792009i | \(0.290965\pi\) | |||||||
\(128\) | 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 | \(-0.402237\pi\) |
0.953205 | − | 0.302325i | \(-0.0977628\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 21.5070i | − | 1.75022i | −0.483925 | − | 0.875109i | \(-0.660789\pi\) | ||
0.483925 | − | 0.875109i | \(-0.339211\pi\) | |||||||
\(152\) | 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 | 0.944664 | − | 0.328041i | \(-0.106388\pi\) |
−0.328041 | + | 0.944664i | \(0.606388\pi\) | |||||||
\(158\) | 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 | \(-0.892329\pi\) | ||
0.943334 | − | 0.331846i | \(-0.107671\pi\) | |||||||
\(168\) | 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 | 0.469378 | − | 0.882997i | \(-0.344478\pi\) |
−0.882997 | + | 0.469378i | \(0.844478\pi\) | |||||||
\(174\) | 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 | −0.899940 | − | 0.436014i | \(-0.856390\pi\) |
0.436014 | + | 0.899940i | \(0.356390\pi\) | |||||||
\(182\) | 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 | \(-0.518150\pi\) | ||||
−0.0569893 | + | 0.998375i | \(0.518150\pi\) | |||||||
\(192\) | 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 | −0.747512 | − | 0.664249i | \(-0.768752\pi\) |
0.664249 | + | 0.747512i | \(0.268752\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.09013i | − | 0.289942i | −0.989436 | − | 0.144971i | \(-0.953691\pi\) | ||
0.989436 | − | 0.144971i | \(-0.0463088\pi\) | |||||||
\(200\) | 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 | \(-0.836496\pi\) | ||||
−0.870950 | + | 0.491372i | \(0.836496\pi\) | |||||||
\(224\) | 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 | −0.729205 | − | 0.684296i | \(-0.760110\pi\) |
0.684296 | + | 0.729205i | \(0.260110\pi\) | |||||||
\(230\) | 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 | \(-0.401148\pi\) | ||||
0.305585 | + | 0.952165i | \(0.401148\pi\) | |||||||
\(240\) | 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 | \(0.0920538\pi\) | ||||
−0.958474 | + | 0.285181i | \(0.907946\pi\) | |||||||
\(264\) | 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 | 0.914550 | − | 0.404474i | \(-0.132545\pi\) |
−0.404474 | + | 0.914550i | \(0.632545\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.15740 | 0.0703071 | 0.0351535 | − | 0.999382i | \(-0.488808\pi\) | ||||
0.0351535 | + | 0.999382i | \(0.488808\pi\) | |||||||
\(272\) | 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 | \(0.500942\pi\) |
−0.999996 | + | 0.00295975i | \(0.999058\pi\) | |||||||
\(278\) | 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 | \(0.546873\pi\) |
−0.989178 | + | 0.146723i | \(0.953127\pi\) | |||||||
\(294\) | 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 | \(0.245599\pi\) | ||||
−0.716815 | + | 0.697263i | \(0.754401\pi\) | |||||||
\(312\) | 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 | 0.925013 | − | 0.379935i | \(-0.124054\pi\) |
−0.379935 | + | 0.925013i | \(0.624054\pi\) | |||||||
\(318\) | 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 | \(0.141423\pi\) |
0.429821 | + | 0.902914i | \(0.358577\pi\) | |||||||
\(350\) | 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 | \(0.232671\pi\) | ||||
−0.744536 | + | 0.667582i | \(0.767329\pi\) | |||||||
\(360\) | 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 | \(-0.619016\pi\) | ||||
−0.365250 | + | 0.930910i | \(0.619016\pi\) | |||||||
\(368\) | 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 | −0.853943 | − | 0.520367i | \(-0.825795\pi\) |
0.520367 | + | 0.853943i | \(0.325795\pi\) | |||||||
\(374\) | 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 | \(-0.432545\pi\) | ||||
0.210332 | + | 0.977630i | \(0.432545\pi\) | |||||||
\(384\) | 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 | \(0.555000\pi\) |
−0.985109 | + | 0.171930i | \(0.945000\pi\) | |||||||
\(390\) | 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 | \(-0.994698\pi\) |
−0.0166562 | − | 0.999861i | \(-0.505302\pi\) | |||||||
\(398\) | 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 | −0.796378 | − | 0.604799i | \(-0.793253\pi\) |
0.604799 | + | 0.796378i | \(0.293253\pi\) | |||||||
\(422\) | 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 | \(-0.766589\pi\) | ||||
−0.742981 | + | 0.669313i | \(0.766589\pi\) | |||||||
\(432\) | 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 | \(0.162698\pi\) | ||||
−0.872192 | + | 0.489164i | \(0.837302\pi\) | |||||||
\(440\) | 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 | \(0.0728964\pi\) |
0.227014 | + | 0.973891i | \(0.427104\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.56380 | 0.0726760 | 0.0363380 | − | 0.999340i | \(-0.488431\pi\) | ||||
0.0363380 | + | 0.999340i | \(0.488431\pi\) | |||||||
\(464\) | 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 | \(-0.700678\pi\) | ||||
−0.589508 | + | 0.807762i | \(0.700678\pi\) | |||||||
\(480\) | 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 | \(0.0185425\pi\) | ||||
−0.998304 | + | 0.0582201i | \(0.981457\pi\) | |||||||
\(488\) | 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 | \(-0.686894\pi\) | ||
0.553987 | − | 0.832525i | \(-0.313106\pi\) | |||||||
\(504\) | 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 | 0.999346 | − | 0.0361674i | \(-0.0115150\pi\) |
−0.0361674 | + | 0.999346i | \(0.511515\pi\) | |||||||
\(510\) | 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 | 0.127551 | − | 0.991832i | \(-0.459288\pi\) |
−0.991832 | + | 0.127551i | \(0.959288\pi\) | |||||||
\(542\) | 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 | 0.998280 | − | 0.0586254i | \(-0.0186717\pi\) |
−0.0586254 | + | 0.998280i | \(0.518672\pi\) | |||||||
\(558\) | 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 | \(0.308696\pi\) | ||||
−0.565468 | + | 0.824770i | \(0.691304\pi\) | |||||||
\(600\) | 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 | \(-0.436144\pi\) | ||||
0.199265 | + | 0.979946i | \(0.436144\pi\) | |||||||
\(608\) | 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 | −0.801792 | − | 0.597603i | \(-0.796120\pi\) |
0.597603 | + | 0.801792i | \(0.296120\pi\) | |||||||
\(614\) | 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 | \(0.00873184\pi\) | ||||
−0.999624 | + | 0.0274285i | \(0.991268\pi\) | |||||||
\(632\) | 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 | \(-0.814219\pi\) | ||
0.834458 | − | 0.551071i | \(-0.185781\pi\) | |||||||
\(648\) | 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 | 0.243561 | − | 0.969886i | \(-0.421684\pi\) |
−0.969886 | + | 0.243561i | \(0.921684\pi\) | |||||||
\(654\) | 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 | −0.728785 | − | 0.684742i | \(-0.759915\pi\) |
0.684742 | + | 0.728785i | \(0.259915\pi\) | |||||||
\(662\) | 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 | −0.834466 | − | 0.551059i | \(-0.814224\pi\) |
0.551059 | + | 0.834466i | \(0.314224\pi\) | |||||||
\(678\) | 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 | 0.785568 | − | 0.618775i | \(-0.212371\pi\) |
−0.618775 | + | 0.785568i | \(0.712371\pi\) | |||||||
\(702\) | 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 | −0.654400 | − | 0.756148i | \(-0.727079\pi\) |
0.756148 | + | 0.654400i | \(0.227079\pi\) | |||||||
\(710\) | 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 | \(-0.446358\pi\) | ||||
0.167726 | + | 0.985834i | \(0.446358\pi\) | |||||||
\(720\) | 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 | \(-0.785402\pi\) | ||
0.781219 | − | 0.624256i | \(-0.214598\pi\) | |||||||
\(728\) | 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 | \(-0.975773\pi\) |
−0.0760379 | − | 0.997105i | \(-0.524227\pi\) | |||||||
\(734\) | 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 | \(0.170121\pi\) | ||||
−0.860548 | + | 0.509369i | \(0.829879\pi\) | |||||||
\(744\) | 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 | \(-0.188106\pi\) | ||||
0.830410 | + | 0.557153i | \(0.188106\pi\) | |||||||
\(752\) | 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 | −0.220676 | − | 0.975347i | \(-0.570826\pi\) |
0.975347 | + | 0.220676i | \(0.0708263\pi\) | |||||||
\(758\) | 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 | −0.733444 | − | 0.679750i | \(-0.762088\pi\) |
0.679750 | + | 0.733444i | \(0.262088\pi\) | |||||||
\(774\) | 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 | 0.983987 | − | 0.178238i | \(-0.0570396\pi\) |
−0.178238 | + | 0.983987i | \(0.557040\pi\) | |||||||
\(798\) | 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 | −0.384063 | − | 0.923307i | \(-0.625475\pi\) |
0.923307 | + | 0.384063i | \(0.125475\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 22.4104i | − | 0.781178i | −0.920565 | − | 0.390589i | \(-0.872271\pi\) | ||
0.920565 | − | 0.390589i | \(-0.127729\pi\) | |||||||
\(824\) | 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 | 0.577433 | − | 0.816438i | \(-0.304054\pi\) |
−0.816438 | + | 0.577433i | \(0.804054\pi\) | |||||||
\(830\) | 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 | \(0.136916\pi\) | ||||
−0.908910 | + | 0.416993i | \(0.863084\pi\) | |||||||
\(840\) | 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 | −0.971642 | − | 0.236458i | \(-0.924013\pi\) |
0.236458 | + | 0.971642i | \(0.424013\pi\) | |||||||
\(854\) | 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 | \(-0.395295\pi\) | ||||
0.323040 | + | 0.946385i | \(0.395295\pi\) | |||||||
\(864\) | 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 | 0.587898 | − | 0.808935i | \(-0.299956\pi\) |
−0.808935 | + | 0.587898i | \(0.799956\pi\) | |||||||
\(878\) | 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 | \(0.0182275\pi\) | ||||
−0.998361 | + | 0.0572321i | \(0.981773\pi\) | |||||||
\(888\) | 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 | \(-0.371578\pi\) | ||||
0.392593 | + | 0.919712i | \(0.371578\pi\) | |||||||
\(912\) | 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 | \(0.163350\pi\) | ||||
−0.871189 | + | 0.490949i | \(0.836650\pi\) | |||||||
\(920\) | 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 | 0.893060 | − | 0.449938i | \(-0.148554\pi\) |
−0.449938 | + | 0.893060i | \(0.648554\pi\) | |||||||
\(942\) | 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 | \(0.0981427\pi\) | ||||
−0.952843 | + | 0.303462i | \(0.901857\pi\) | |||||||
\(968\) | 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 | \(0.178826\pi\) | ||||
−0.846298 | + | 0.532710i | \(0.821174\pi\) | |||||||
\(984\) | 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 | \(-0.368013\pi\) | ||||
0.402870 | + | 0.915257i | \(0.368013\pi\) | |||||||
\(992\) | 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 | −0.508336 | − | 0.861159i | \(-0.669739\pi\) |
0.861159 | + | 0.508336i | \(0.169739\pi\) | |||||||
\(998\) | 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.g.1345.4 | yes | 16 | |
4.3 | odd | 2 | 1792.2.m.e.1345.5 | yes | 16 | ||
8.3 | odd | 2 | 1792.2.m.h.1345.4 | yes | 16 | ||
8.5 | even | 2 | 1792.2.m.f.1345.5 | yes | 16 | ||
16.3 | odd | 4 | 1792.2.m.h.449.4 | yes | 16 | ||
16.5 | even | 4 | inner | 1792.2.m.g.449.4 | yes | 16 | |
16.11 | odd | 4 | 1792.2.m.e.449.5 | ✓ | 16 | ||
16.13 | even | 4 | 1792.2.m.f.449.5 | yes | 16 | ||
32.5 | even | 8 | 7168.2.a.ba.1.5 | 8 | |||
32.11 | odd | 8 | 7168.2.a.bf.1.5 | 8 | |||
32.21 | even | 8 | 7168.2.a.be.1.4 | 8 | |||
32.27 | odd | 8 | 7168.2.a.bb.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1792.2.m.e.449.5 | ✓ | 16 | 16.11 | odd | 4 | ||
1792.2.m.e.1345.5 | yes | 16 | 4.3 | odd | 2 | ||
1792.2.m.f.449.5 | yes | 16 | 16.13 | even | 4 | ||
1792.2.m.f.1345.5 | yes | 16 | 8.5 | even | 2 | ||
1792.2.m.g.449.4 | yes | 16 | 16.5 | even | 4 | inner | |
1792.2.m.g.1345.4 | yes | 16 | 1.1 | even | 1 | trivial | |
1792.2.m.h.449.4 | yes | 16 | 16.3 | odd | 4 | ||
1792.2.m.h.1345.4 | yes | 16 | 8.3 | odd | 2 | ||
7168.2.a.ba.1.5 | 8 | 32.5 | even | 8 | |||
7168.2.a.bb.1.4 | 8 | 32.27 | odd | 8 | |||
7168.2.a.be.1.4 | 8 | 32.21 | even | 8 | |||
7168.2.a.bf.1.5 | 8 | 32.11 | odd | 8 |