Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [120,3,Mod(41,120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("120.41");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 120 = 2^{3} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 120.l (of order \(2\), degree \(1\), 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: | \(3.26976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.681615360000.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 2x^{6} + 20x^{5} + 49x^{4} - 136x^{3} + 168x^{2} - 96x + 864 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 41.8 | ||
Root | \(1.54294 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 120.41 |
Dual form | 120.3.l.a.41.7 |
$q$-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 \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(41\) | \(61\) | \(97\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.98254 | + | 0.323191i | 0.994180 | + | 0.107730i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.72640 | 0.675201 | 0.337600 | − | 0.941290i | \(-0.390385\pi\) | ||||
0.337600 | + | 0.941290i | \(0.390385\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.79110 | + | 1.92786i | 0.976788 | + | 0.214207i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.76442i | − | 0.433129i | −0.976268 | − | 0.216565i | \(-0.930515\pi\) | ||
0.976268 | − | 0.216565i | \(-0.0694852\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.06692 | −0.0820707 | −0.0410354 | − | 0.999158i | \(-0.513066\pi\) | ||||
−0.0410354 | + | 0.999158i | \(0.513066\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.722676 | − | 6.66916i | 0.0481784 | − | 0.444611i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 26.7847i | 1.57557i | 0.615950 | + | 0.787785i | \(0.288772\pi\) | ||||
−0.615950 | + | 0.787785i | \(0.711228\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.12938 | −0.427862 | −0.213931 | − | 0.976849i | \(-0.568627\pi\) | ||||
−0.213931 | + | 0.976849i | \(0.568627\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.0967 | + | 1.52753i | 0.671271 | + | 0.0727395i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 40.0468i | − | 1.74117i | −0.492021 | − | 0.870583i | \(-0.663742\pi\) | ||
0.492021 | − | 0.870583i | \(-0.336258\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 25.5967 | + | 8.59112i | 0.948027 | + | 0.318190i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 20.8744i | 0.719807i | 0.932990 | + | 0.359903i | \(0.117190\pi\) | ||||
−0.932990 | + | 0.359903i | \(0.882810\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −33.7860 | −1.08987 | −0.544936 | − | 0.838478i | \(-0.683446\pi\) | ||||
−0.544936 | + | 0.838478i | \(0.683446\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.53982 | − | 14.2101i | 0.0466611 | − | 0.430608i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 10.5686i | − | 0.301959i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −60.4351 | −1.63338 | −0.816691 | − | 0.577075i | \(-0.804194\pi\) | ||||
−0.816691 | + | 0.577075i | \(0.804194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.18213 | − | 0.344819i | −0.0815931 | − | 0.00884150i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 59.2611i | 1.44539i | 0.691166 | + | 0.722696i | \(0.257097\pi\) | ||||
−0.691166 | + | 0.722696i | \(0.742903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −56.4424 | −1.31261 | −0.656307 | − | 0.754494i | \(-0.727883\pi\) | ||||
−0.656307 | + | 0.754494i | \(0.727883\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.31082 | − | 19.6575i | 0.0957961 | − | 0.436833i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 9.68942i | − | 0.206158i | −0.994673 | − | 0.103079i | \(-0.967131\pi\) | ||
0.994673 | − | 0.103079i | \(-0.0328694\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −26.6611 | −0.544104 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.65657 | + | 79.8864i | −0.169737 | + | 1.56640i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 93.1378i | − | 1.75732i | −0.477451 | − | 0.878659i | \(-0.658439\pi\) | ||
0.477451 | − | 0.878659i | \(-0.341561\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.6536 | −0.193701 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −24.2462 | − | 2.62734i | −0.425372 | − | 0.0460937i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 17.4907i | 0.296453i | 0.988953 | + | 0.148227i | \(0.0473565\pi\) | ||||
−0.988953 | + | 0.148227i | \(0.952643\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 57.7400 | 0.946558 | 0.473279 | − | 0.880913i | \(-0.343070\pi\) | ||||
0.473279 | + | 0.880913i | \(0.343070\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 41.5503 | + | 9.11184i | 0.659528 | + | 0.144632i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.38570i | 0.0367032i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 101.531 | 1.51539 | 0.757695 | − | 0.652609i | \(-0.226325\pi\) | ||||
0.757695 | + | 0.652609i | \(0.226325\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.9428 | − | 119.441i | 0.187576 | − | 1.73103i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 90.1745i | 1.27006i | 0.772486 | + | 0.635032i | \(0.219013\pi\) | ||||
−0.772486 | + | 0.635032i | \(0.780987\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 40.0700 | 0.548904 | 0.274452 | − | 0.961601i | \(-0.411504\pi\) | ||||
0.274452 | + | 0.961601i | \(0.411504\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.9127 | − | 1.61595i | −0.198836 | − | 0.0215460i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 22.5186i | − | 0.292449i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 65.3727 | 0.827502 | 0.413751 | − | 0.910390i | \(-0.364218\pi\) | ||||
0.413751 | + | 0.910390i | \(0.364218\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 73.5667 | + | 33.8960i | 0.908231 | + | 0.418469i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 117.888i | − | 1.42033i | −0.704034 | − | 0.710166i | \(-0.748620\pi\) | ||
0.704034 | − | 0.710166i | \(-0.251380\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 59.8924 | 0.704617 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.74641 | + | 62.2587i | −0.0775450 | + | 0.715618i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 119.679i | 1.34471i | 0.740228 | + | 0.672356i | \(0.234718\pi\) | ||||
−0.740228 | + | 0.672356i | \(0.765282\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.04269 | −0.0554142 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −100.768 | − | 10.9193i | −1.08353 | − | 0.117412i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18.1779i | 0.191346i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.2522 | −0.157239 | −0.0786196 | − | 0.996905i | \(-0.525051\pi\) | ||||
−0.0786196 | + | 0.996905i | \(0.525051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.18513 | − | 41.8845i | 0.0927791 | − | 0.423075i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 72.0047i | − | 0.712918i | −0.934311 | − | 0.356459i | \(-0.883984\pi\) | ||
0.934311 | − | 0.356459i | \(-0.116016\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 110.950 | 1.07718 | 0.538591 | − | 0.842567i | \(-0.318957\pi\) | ||||
0.538591 | + | 0.842567i | \(0.318957\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.41566 | − | 31.5212i | 0.0325301 | − | 0.300202i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 30.6020i | − | 0.286000i | −0.989723 | − | 0.143000i | \(-0.954325\pi\) | ||
0.989723 | − | 0.143000i | \(-0.0456748\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.3694 | −0.159353 | −0.0796763 | − | 0.996821i | \(-0.525389\pi\) | ||||
−0.0796763 | + | 0.996821i | \(0.525389\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −180.250 | − | 19.5321i | −1.62388 | − | 0.175965i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.71526i | 0.0417280i | 0.999782 | + | 0.0208640i | \(0.00664170\pi\) | ||||
−0.999782 | + | 0.0208640i | \(0.993358\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −89.5474 | −0.778673 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.37939 | − | 2.05687i | −0.0801657 | − | 0.0175801i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 126.595i | 1.06383i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 98.3003 | 0.812399 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.1526 | + | 176.749i | −0.155712 | + | 1.43698i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.39528 | −0.0109865 | −0.00549325 | − | 0.999985i | \(-0.501749\pi\) | ||||
−0.00549325 | + | 0.999985i | \(0.501749\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −168.342 | − | 18.2417i | −1.30498 | − | 0.141408i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 226.220i | − | 1.72687i | −0.504460 | − | 0.863435i | \(-0.668308\pi\) | ||
0.504460 | − | 0.863435i | \(-0.331692\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −38.4227 | −0.288893 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 19.2103 | − | 57.2360i | 0.142299 | − | 0.423971i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 76.2589i | 0.556634i | 0.960489 | + | 0.278317i | \(0.0897766\pi\) | ||||
−0.960489 | + | 0.278317i | \(0.910223\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 127.660 | 0.918417 | 0.459208 | − | 0.888329i | \(-0.348133\pi\) | ||||
0.459208 | + | 0.888329i | \(0.348133\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.13153 | − | 28.8991i | 0.0222094 | − | 0.204958i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.08325i | 0.0355472i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 46.6766 | 0.321907 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −79.5178 | − | 8.61662i | −0.540938 | − | 0.0586165i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 63.3790i | 0.425362i | 0.977122 | + | 0.212681i | \(0.0682195\pi\) | ||||
−0.977122 | + | 0.212681i | \(0.931780\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −115.233 | −0.763134 | −0.381567 | − | 0.924341i | \(-0.624615\pi\) | ||||
−0.381567 | + | 0.924341i | \(0.624615\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −51.6371 | + | 235.467i | −0.337498 | + | 1.53900i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 75.5479i | 0.487406i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.3695 | −0.117003 | −0.0585017 | − | 0.998287i | \(-0.518632\pi\) | ||||
−0.0585017 | + | 0.998287i | \(0.518632\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 30.1013 | − | 277.787i | 0.189316 | − | 1.74709i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 189.278i | − | 1.17564i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −163.693 | −1.00425 | −0.502126 | − | 0.864794i | \(-0.667449\pi\) | ||||
−0.502126 | + | 0.864794i | \(0.667449\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −31.7747 | − | 3.44313i | −0.192574 | − | 0.0208675i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 48.7025i | 0.291632i | 0.989312 | + | 0.145816i | \(0.0465807\pi\) | ||||
−0.989312 | + | 0.145816i | \(0.953419\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −167.862 | −0.993264 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −71.4662 | − | 15.6723i | −0.417931 | − | 0.0916509i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 140.785i | 0.813787i | 0.913476 | + | 0.406894i | \(0.133388\pi\) | ||||
−0.913476 | + | 0.406894i | \(0.866612\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −23.6320 | −0.135040 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.65285 | + | 52.1669i | −0.0319370 | + | 0.294728i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.1350i | 0.0622065i | 0.999516 | + | 0.0311033i | \(0.00990207\pi\) | ||||
−0.999516 | + | 0.0311033i | \(0.990098\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −150.235 | −0.830028 | −0.415014 | − | 0.909815i | \(-0.636223\pi\) | ||||
−0.415014 | + | 0.909815i | \(0.636223\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 172.212 | + | 18.6610i | 0.941049 | + | 0.101973i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 135.137i | 0.730471i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 127.614 | 0.682425 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 120.981 | + | 40.6051i | 0.640108 | + | 0.214842i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 168.060i | − | 0.879895i | −0.898023 | − | 0.439948i | \(-0.854997\pi\) | ||
0.898023 | − | 0.439948i | \(-0.145003\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 312.926 | 1.62138 | 0.810688 | − | 0.585479i | \(-0.199093\pi\) | ||||
0.810688 | + | 0.585479i | \(0.199093\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.771038 | + | 7.11546i | −0.00395404 | + | 0.0364895i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 166.150i | − | 0.843400i | −0.906735 | − | 0.421700i | \(-0.861434\pi\) | ||
0.906735 | − | 0.421700i | \(-0.138566\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −105.535 | −0.530327 | −0.265163 | − | 0.964204i | \(-0.585426\pi\) | ||||
−0.265163 | + | 0.964204i | \(0.585426\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 302.821 | + | 32.8139i | 1.50657 | + | 0.163253i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 98.6608i | 0.486014i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 132.512 | 0.646399 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 77.2046 | − | 352.056i | 0.372969 | − | 1.70075i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 38.7318i | 0.185320i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 283.373 | 1.34300 | 0.671500 | − | 0.741004i | \(-0.265650\pi\) | ||||
0.671500 | + | 0.741004i | \(0.265650\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −29.1436 | + | 268.949i | −0.136824 | + | 1.26267i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 126.209i | 0.587019i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −159.686 | −0.735882 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 119.510 | + | 12.9503i | 0.545710 | + | 0.0591336i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 28.5771i | − | 0.129308i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −100.108 | −0.448915 | −0.224458 | − | 0.974484i | \(-0.572061\pi\) | ||||
−0.224458 | + | 0.974484i | \(0.572061\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −43.9555 | − | 9.63929i | −0.195358 | − | 0.0428413i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 239.794i | − | 1.05636i | −0.849132 | − | 0.528181i | \(-0.822874\pi\) | ||
0.849132 | − | 0.528181i | \(-0.177126\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 393.036 | 1.71632 | 0.858158 | − | 0.513386i | \(-0.171609\pi\) | ||||
0.858158 | + | 0.513386i | \(0.171609\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.27779 | − | 67.1626i | 0.0315056 | − | 0.290747i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 278.691i | − | 1.19610i | −0.801459 | − | 0.598050i | \(-0.795942\pi\) | ||
0.801459 | − | 0.598050i | \(-0.204058\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.6662 | −0.0921966 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 194.977 | + | 21.1278i | 0.822686 | + | 0.0891470i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 196.594i | 0.822570i | 0.911507 | + | 0.411285i | \(0.134920\pi\) | ||||
−0.911507 | + | 0.411285i | \(0.865080\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −231.153 | −0.959139 | −0.479570 | − | 0.877504i | \(-0.659207\pi\) | ||||
−0.479570 | + | 0.877504i | \(0.659207\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 208.461 | + | 124.872i | 0.857864 | + | 0.513877i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 59.6160i | 0.243331i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.67340 | 0.0351150 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 38.1002 | − | 351.604i | 0.153013 | − | 1.41207i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 243.442i | 0.969887i | 0.874545 | + | 0.484944i | \(0.161160\pi\) | ||||
−0.874545 | + | 0.484944i | \(0.838840\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −190.800 | −0.754150 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 178.632 | + | 19.3567i | 0.700516 | + | 0.0759085i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 358.482i | − | 1.39487i | −0.716646 | − | 0.697437i | \(-0.754324\pi\) | ||
0.716646 | − | 0.697437i | \(-0.245676\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −285.641 | −1.10286 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −40.2429 | + | 183.509i | −0.154187 | + | 0.703099i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 330.913i | 1.25823i | 0.777314 | + | 0.629113i | \(0.216582\pi\) | ||||
−0.777314 | + | 0.629113i | \(0.783418\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −208.262 | −0.785896 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −38.6793 | + | 356.949i | −0.144866 | + | 1.33689i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 97.0354i | − | 0.360727i | −0.983600 | − | 0.180363i | \(-0.942273\pi\) | ||
0.983600 | − | 0.180363i | \(-0.0577273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 67.1851 | 0.247915 | 0.123958 | − | 0.992288i | \(-0.460441\pi\) | ||||
0.123958 | + | 0.992288i | \(0.460441\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.0400 | − | 1.62975i | −0.0550917 | − | 0.00596979i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.8221i | 0.0866258i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −361.801 | −1.30614 | −0.653070 | − | 0.757298i | \(-0.726519\pi\) | ||||
−0.653070 | + | 0.757298i | \(0.726519\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −297.016 | − | 65.1347i | −1.06457 | − | 0.233458i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 288.193i | − | 1.02560i | −0.858509 | − | 0.512798i | \(-0.828609\pi\) | ||
0.858509 | − | 0.512798i | \(-0.171391\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −272.474 | −0.962805 | −0.481402 | − | 0.876500i | \(-0.659872\pi\) | ||||
−0.481402 | + | 0.876500i | \(0.659872\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.87491 | + | 54.2162i | −0.0206137 | + | 0.190232i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 280.092i | 0.975930i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −428.420 | −1.48242 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −45.4903 | − | 4.92937i | −0.156324 | − | 0.0169394i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 70.5674i | − | 0.240845i | −0.992723 | − | 0.120422i | \(-0.961575\pi\) | ||
0.992723 | − | 0.120422i | \(-0.0384248\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 39.1105 | 0.132578 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 40.9317 | − | 121.954i | 0.137817 | − | 0.410618i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 42.7267i | 0.142899i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −266.770 | −0.886278 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 23.2713 | − | 214.757i | 0.0768028 | − | 0.708769i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 129.111i | − | 0.423313i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −124.274 | −0.404801 | −0.202401 | − | 0.979303i | \(-0.564874\pi\) | ||||
−0.202401 | + | 0.979303i | \(0.564874\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 330.912 | + | 35.8580i | 1.07091 | + | 0.116045i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 229.006i | 0.736353i | 0.929756 | + | 0.368176i | \(0.120018\pi\) | ||||
−0.929756 | + | 0.368176i | \(0.879982\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 465.490 | 1.48719 | 0.743594 | − | 0.668631i | \(-0.233120\pi\) | ||||
0.743594 | + | 0.668631i | \(0.233120\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 20.3747 | − | 92.9092i | 0.0646816 | − | 0.294950i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 405.458i | 1.27905i | 0.768771 | + | 0.639524i | \(0.220869\pi\) | ||||
−0.768771 | + | 0.639524i | \(0.779131\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 99.4544 | 0.311769 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.89027 | − | 91.2716i | 0.0308108 | − | 0.284335i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 217.743i | − | 0.674127i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.33460 | 0.0164141 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −51.8051 | − | 5.61364i | −0.158425 | − | 0.0171671i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 45.7961i | − | 0.139198i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 45.9271 | 0.138753 | 0.0693763 | − | 0.997591i | \(-0.477899\pi\) | ||||
0.0693763 | + | 0.997591i | \(0.477899\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −531.291 | − | 116.510i | −1.59547 | − | 0.349881i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 227.031i | − | 0.677703i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 516.924 | 1.53390 | 0.766950 | − | 0.641707i | \(-0.221774\pi\) | ||||
0.766950 | + | 0.641707i | \(0.221774\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.52393 | + | 14.0635i | −0.00449537 | + | 0.0414852i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 160.971i | 0.472055i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −357.605 | −1.04258 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −267.079 | − | 28.9409i | −0.774142 | − | 0.0838867i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 5.39280i | − | 0.0155412i | −0.999970 | − | 0.00777061i | \(-0.997527\pi\) | ||
0.999970 | − | 0.00777061i | \(-0.00247349\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 284.894 | 0.816315 | 0.408157 | − | 0.912912i | \(-0.366171\pi\) | ||||
0.408157 | + | 0.912912i | \(0.366171\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.3097 | − | 9.16603i | −0.0778053 | − | 0.0261141i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 73.2882i | − | 0.207615i | −0.994597 | − | 0.103808i | \(-0.966897\pi\) | ||
0.994597 | − | 0.103808i | \(-0.0331026\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 201.636 | 0.567990 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −40.9144 | + | 377.576i | −0.114606 | + | 1.05763i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 361.674i | 1.00745i | 0.863865 | + | 0.503724i | \(0.168037\pi\) | ||||
−0.863865 | + | 0.503724i | \(0.831963\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −294.913 | −0.816934 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 293.185 | + | 31.7697i | 0.807671 | + | 0.0875200i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 89.5992i | − | 0.245477i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −131.432 | −0.358124 | −0.179062 | − | 0.983838i | \(-0.557306\pi\) | ||||
−0.179062 | + | 0.983838i | \(0.557306\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −114.247 | + | 520.970i | −0.309612 | + | 1.41184i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 440.207i | − | 1.18654i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 211.216 | 0.566262 | 0.283131 | − | 0.959081i | \(-0.408627\pi\) | ||||
0.283131 | + | 0.959081i | \(0.408627\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.61338 | + | 33.3458i | −0.00963569 | + | 0.0889222i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 22.2713i | − | 0.0590751i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 47.4989 | 0.125327 | 0.0626635 | − | 0.998035i | \(-0.480041\pi\) | ||||
0.0626635 | + | 0.998035i | \(0.480041\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.16149 | − | 0.450943i | −0.0109226 | − | 0.00118358i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 517.991i | − | 1.35246i | −0.736692 | − | 0.676228i | \(-0.763613\pi\) | ||
0.736692 | − | 0.676228i | \(-0.236387\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −50.3531 | −0.130787 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −496.191 | − | 108.813i | −1.28215 | − | 0.281171i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 253.951i | 0.652830i | 0.945227 | + | 0.326415i | \(0.105841\pi\) | ||||
−0.945227 | + | 0.326415i | \(0.894159\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1072.64 | 2.74333 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 73.1122 | − | 674.710i | 0.186036 | − | 1.71682i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 146.178i | − | 0.370070i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 527.905 | 1.32974 | 0.664868 | − | 0.746961i | \(-0.268488\pi\) | ||||
0.664868 | + | 0.746961i | \(0.268488\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −114.597 | − | 12.4179i | −0.287212 | − | 0.0311225i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 664.097i | 1.65610i | 0.560653 | + | 0.828051i | \(0.310550\pi\) | ||||
−0.560653 | + | 0.828051i | \(0.689450\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.0470 | 0.0894466 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 75.7937 | − | 164.500i | 0.187145 | − | 0.406173i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 287.938i | 0.707465i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 79.2471 | 0.193758 | 0.0968791 | − | 0.995296i | \(-0.469114\pi\) | ||||
0.0968791 | + | 0.995296i | \(0.469114\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.6462 | + | 227.445i | −0.0599664 | + | 0.553395i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 82.6683i | 0.200165i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −263.605 | −0.635192 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 380.751 | + | 41.2585i | 0.913072 | + | 0.0989413i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 666.530i | − | 1.59076i | −0.606109 | − | 0.795381i | \(-0.707271\pi\) | ||
0.606109 | − | 0.795381i | \(-0.292729\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −306.220 | −0.727364 | −0.363682 | − | 0.931523i | \(-0.618480\pi\) | ||||
−0.363682 | + | 0.931523i | \(0.618480\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.6798 | − | 85.1806i | 0.0441604 | − | 0.201373i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 133.923i | − | 0.315114i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 272.903 | 0.639116 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.64286 | + | 15.1610i | −0.00382951 | + | 0.0353403i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 254.551i | 0.590605i | 0.955404 | + | 0.295303i | \(0.0954205\pi\) | ||||
−0.955404 | + | 0.295303i | \(0.904579\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 442.391 | 1.02169 | 0.510845 | − | 0.859673i | \(-0.329333\pi\) | ||||
0.510845 | + | 0.859673i | \(0.329333\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 139.215 | + | 15.0854i | 0.320034 | + | 0.0346792i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 325.556i | 0.744979i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 561.568 | 1.27920 | 0.639599 | − | 0.768709i | \(-0.279101\pi\) | ||||
0.639599 | + | 0.768709i | \(0.279101\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −234.380 | − | 51.3988i | −0.531475 | − | 0.116551i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 564.841i | − | 1.27504i | −0.770436 | − | 0.637518i | \(-0.779961\pi\) | ||
0.770436 | − | 0.637518i | \(-0.220039\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 267.611 | 0.601374 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.4835 | + | 189.030i | −0.0458244 | + | 0.422887i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 512.215i | − | 1.14079i | −0.821370 | − | 0.570396i | \(-0.806790\pi\) | ||
0.821370 | − | 0.570396i | \(-0.193210\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 282.345 | 0.626041 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −343.688 | − | 37.2423i | −0.758692 | − | 0.0822126i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.2758i | 0.0247820i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 52.5358 | 0.114958 | 0.0574790 | − | 0.998347i | \(-0.481694\pi\) | ||||
0.0574790 | + | 0.998347i | \(0.481694\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −230.110 | + | 685.601i | −0.501330 | + | 1.49368i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 625.737i | 1.35735i | 0.734441 | + | 0.678673i | \(0.237445\pi\) | ||||
−0.734441 | + | 0.678673i | \(0.762555\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −49.8782 | −0.107728 | −0.0538641 | − | 0.998548i | \(-0.517154\pi\) | ||||
−0.0538641 | + | 0.998548i | \(0.517154\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −24.4164 | + | 225.325i | −0.0525083 | + | 0.484569i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 64.6312i | 0.138397i | 0.997603 | + | 0.0691983i | \(0.0220441\pi\) | ||||
−0.997603 | + | 0.0691983i | \(0.977956\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 479.877 | 1.02319 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −54.7879 | − | 5.93686i | −0.116322 | − | 0.0126048i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 268.915i | 0.568532i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 40.6469 | 0.0855724 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 179.557 | − | 818.783i | 0.376429 | − | 1.71653i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 872.673i | − | 1.82186i | −0.412556 | − | 0.910932i | \(-0.635364\pi\) | ||
0.412556 | − | 0.910932i | \(-0.364636\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 64.4794 | 0.134053 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 61.1727 | − | 564.528i | 0.126652 | − | 1.16879i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 34.1050i | 0.0703195i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −883.613 | −1.81440 | −0.907201 | − | 0.420698i | \(-0.861785\pi\) | ||||
−0.907201 | + | 0.420698i | \(0.861785\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −488.221 | − | 52.9041i | −0.998408 | − | 0.108188i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 596.247i | 1.21435i | 0.794567 | + | 0.607177i | \(0.207698\pi\) | ||||
−0.794567 | + | 0.607177i | \(0.792302\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −559.114 | −1.13411 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −93.6565 | − | 20.5386i | −0.189205 | − | 0.0414921i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 426.201i | 0.857548i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −560.109 | −1.12246 | −0.561231 | − | 0.827659i | \(-0.689672\pi\) | ||||
−0.561231 | + | 0.827659i | \(0.689672\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.7402 | + | 145.257i | −0.0314175 | + | 0.289934i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 505.038i | 1.00405i | 0.864853 | + | 0.502026i | \(0.167412\pi\) | ||||
−0.864853 | + | 0.502026i | \(0.832588\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −161.007 | −0.318827 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −500.654 | − | 54.2513i | −0.987484 | − | 0.107005i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.3027i | 0.0261350i | 0.999915 | + | 0.0130675i | \(0.00415963\pi\) | ||||
−0.999915 | + | 0.0130675i | \(0.995840\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 189.387 | 0.370620 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −208.086 | − | 69.8405i | −0.405625 | − | 0.136141i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 248.091i | − | 0.481731i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −46.1645 | −0.0892930 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −45.5005 | + | 419.898i | −0.0876695 | + | 0.809051i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 267.898i | 0.514200i | 0.966385 | + | 0.257100i | \(0.0827670\pi\) | ||||
−0.966385 | + | 0.257100i | \(0.917233\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 176.493 | 0.337463 | 0.168731 | − | 0.985662i | \(-0.446033\pi\) | ||||
0.168731 | + | 0.985662i | \(0.446033\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −70.4835 | − | 7.63765i | −0.134254 | − | 0.0145479i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 904.949i | − | 1.71717i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1074.75 | −2.03166 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −33.7197 | + | 153.763i | −0.0635022 | + | 0.289572i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 63.2268i | − | 0.118624i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −68.4281 | −0.127903 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.59872 | + | 33.2105i | −0.00670152 | + | 0.0618445i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 127.025i | 0.235667i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −790.757 | −1.46166 | −0.730829 | − | 0.682561i | \(-0.760866\pi\) | ||||
−0.730829 | + | 0.682561i | \(0.760866\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −448.082 | − | 48.5546i | −0.825198 | − | 0.0894191i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 38.8392i | 0.0712647i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.1668 | −0.0807436 | −0.0403718 | − | 0.999185i | \(-0.512854\pi\) | ||||
−0.0403718 | + | 0.999185i | \(0.512854\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 507.598 | + | 111.315i | 0.924587 | + | 0.202759i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 169.696i | − | 0.307978i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 308.978 | 0.558730 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −43.6751 | + | 403.052i | −0.0786938 | + | 0.726219i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 753.685i | − | 1.35312i | −0.736390 | − | 0.676558i | \(-0.763471\pi\) | ||
0.736390 | − | 0.676558i | \(-0.236529\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 60.2195 | 0.107727 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 380.613 | + | 41.2435i | 0.678454 | + | 0.0735179i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 609.590i | 1.08275i | 0.840780 | + | 0.541376i | \(0.182097\pi\) | ||||
−0.840780 | + | 0.541376i | \(0.817903\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.5437 | 0.0186613 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 347.706 | + | 160.206i | 0.613238 | + | 0.282550i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 528.082i | 0.928088i | 0.885812 | + | 0.464044i | \(0.153602\pi\) | ||||
−0.885812 | + | 0.464044i | \(0.846398\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −708.097 | −1.24010 | −0.620050 | − | 0.784562i | \(-0.712888\pi\) | ||||
−0.620050 | + | 0.784562i | \(0.712888\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 54.3154 | − | 501.246i | 0.0947913 | − | 0.874774i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 200.234i | 0.348233i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −55.0939 | −0.0954834 | −0.0477417 | − | 0.998860i | \(-0.515202\pi\) | ||||
−0.0477417 | + | 0.998860i | \(0.515202\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 933.313 | + | 101.135i | 1.61194 | + | 0.174671i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 557.184i | − | 0.959009i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −443.748 | −0.761145 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.59930 | + | 20.9730i | −0.00786206 | + | 0.0358512i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 596.377i | 1.01598i | 0.861364 | + | 0.507988i | \(0.169610\pi\) | ||||
−0.861364 | + | 0.507988i | \(0.830390\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 274.660 | 0.466315 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 53.6981 | − | 495.549i | 0.0908597 | − | 0.838492i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 269.915i | 0.455169i | 0.973758 | + | 0.227584i | \(0.0730828\pi\) | ||||
−0.973758 | + | 0.227584i | \(0.926917\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 283.076 | 0.475758 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −314.762 | − | 34.1079i | −0.527240 | − | 0.0571322i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 622.634i | − | 1.03946i | −0.854332 | − | 0.519728i | \(-0.826033\pi\) | ||
0.854332 | − | 0.519728i | \(-0.173967\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 865.760 | 1.44053 | 0.720266 | − | 0.693698i | \(-0.244020\pi\) | ||||
0.720266 | + | 0.693698i | \(0.244020\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 892.570 | + | 195.738i | 1.48022 | + | 0.324606i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 219.806i | − | 0.363316i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 390.780 | 0.643790 | 0.321895 | − | 0.946775i | \(-0.395680\pi\) | ||||
0.321895 | + | 0.946775i | \(0.395680\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −31.8863 | + | 294.260i | −0.0523584 | + | 0.483185i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.3378i | 0.0169195i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −398.441 | −0.649985 | −0.324993 | − | 0.945717i | \(-0.605362\pi\) | ||||
−0.324993 | + | 0.945717i | \(0.605362\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 395.222 | + | 42.8266i | 0.642637 | + | 0.0696367i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 178.765i | 0.289732i | 0.989451 | + | 0.144866i | \(0.0462752\pi\) | ||||
−0.989451 | + | 0.144866i | \(0.953725\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −224.867 | −0.363274 | −0.181637 | − | 0.983366i | \(-0.558140\pi\) | ||||
−0.181637 | + | 0.983366i | \(0.558140\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 344.047 | − | 1025.07i | 0.554021 | − | 1.65067i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 565.653i | 0.907950i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.5178 | + | 115.519i | −0.0199645 | + | 0.184241i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1618.74i | − | 2.57351i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.36019 | −0.0148339 | −0.00741695 | − | 0.999972i | \(-0.502361\pi\) | ||||
−0.00741695 | + | 0.999972i | \(0.502361\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 845.172 | + | 91.5836i | 1.33518 | + | 0.144682i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.11995i | 0.00491331i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.4453 | 0.0446550 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −173.844 | + | 792.733i | −0.272056 | + | 1.24058i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 785.281i | − | 1.22509i | −0.790437 | − | 0.612543i | \(-0.790146\pi\) | ||
0.790437 | − | 0.612543i | \(-0.209854\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 131.320 | 0.204230 | 0.102115 | − | 0.994773i | \(-0.467439\pi\) | ||||
0.102115 | + | 0.994773i | \(0.467439\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −40.7896 | + | 376.424i | −0.0632397 | + | 0.583603i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 155.225i | 0.239915i | 0.992779 | + | 0.119958i | \(0.0382759\pi\) | ||||
−0.992779 | + | 0.119958i | \(0.961724\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 83.3333 | 0.128403 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −476.271 | − | 51.6092i | −0.731599 | − | 0.0792768i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 668.464i | 1.02368i | 0.859080 | + | 0.511841i | \(0.171036\pi\) | ||||
−0.859080 | + | 0.511841i | \(0.828964\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −505.843 | −0.772280 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 352.259 | + | 77.2493i | 0.536163 | + | 0.117579i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 579.510i | 0.879377i | 0.898150 | + | 0.439689i | \(0.144911\pi\) | ||||
−0.898150 | + | 0.439689i | \(0.855089\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −307.070 | −0.464553 | −0.232277 | − | 0.972650i | \(-0.574617\pi\) | ||||
−0.232277 | + | 0.972650i | \(0.574617\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.23586 | − | 85.2324i | 0.0139304 | − | 0.128556i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 85.9159i | 0.129197i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 835.953 | 1.25330 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −298.576 | − | 32.3540i | −0.446302 | − | 0.0483617i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 275.098i | − | 0.409982i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.02018 | 0.0104312 | 0.00521559 | − | 0.999986i | \(-0.498340\pi\) | ||||
0.00521559 | + | 0.999986i | \(0.498340\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −127.984 | − | 42.9556i | −0.189605 | − | 0.0636379i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.21742i | − | 0.00179825i | −1.00000 | 0.000899127i | \(-0.999714\pi\) | |||
1.00000 | 0.000899127i | \(-0.000286201\pi\) | ||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −72.0881 | −0.106168 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 77.4993 | − | 715.196i | 0.113802 | − | 1.05021i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1261.23i | 1.84661i | 0.384067 | + | 0.923305i | \(0.374523\pi\) | ||||
−0.384067 | + | 0.923305i | \(0.625477\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 170.520 | 0.248934 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1172.25 | + | 127.026i | 1.70633 | + | 0.184899i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 99.3706i | 0.144224i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −158.177 | −0.228910 | −0.114455 | − | 0.993428i | \(-0.536512\pi\) | ||||
−0.114455 | + | 0.993428i | \(0.536512\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 43.4126 | − | 197.963i | 0.0626445 | − | 0.285661i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 285.456i | − | 0.410729i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1587.29 | −2.27732 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 90.0705 | − | 831.208i | 0.128856 | − | 1.18914i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 331.746i | − | 0.473247i | −0.971601 | − | 0.236623i | \(-0.923959\pi\) | ||
0.971601 | − | 0.236623i | \(-0.0760408\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 491.300 | 0.698863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −64.6203 | − | 7.00232i | −0.0916600 | − | 0.00993236i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 340.323i | − | 0.481363i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 854.366 | 1.20503 | 0.602515 | − | 0.798108i | \(-0.294165\pi\) | ||||
0.602515 | + | 0.798108i | \(0.294165\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 574.697 | + | 126.029i | 0.808295 | + | 0.177256i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1353.02i | 1.89765i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.3665 | 0.0158972 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −63.5374 | + | 586.350i | −0.0886156 | + | 0.817782i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 218.882i | 0.304426i | 0.988348 | + | 0.152213i | \(0.0486400\pi\) | ||||
−0.988348 | + | 0.152213i | \(0.951360\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 524.394 | 0.727314 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −689.422 | − | 74.7064i | −0.953557 | − | 0.103328i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 104.372i | − | 0.143961i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.2420 | 0.0168391 | 0.00841954 | − | 0.999965i | \(-0.497320\pi\) | ||||
0.00841954 | + | 0.999965i | \(0.497320\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 581.385 | + | 439.809i | 0.797511 | + | 0.603305i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1511.79i | − | 2.06812i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 86.8331 | 0.118463 | 0.0592313 | − | 0.998244i | \(-0.481135\pi\) | ||||
0.0592313 | + | 0.998244i | \(0.481135\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −19.2674 | + | 177.807i | −0.0262141 | + | 0.241915i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 483.737i | − | 0.656360i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −187.725 | −0.254026 | −0.127013 | − | 0.991901i | \(-0.540539\pi\) | ||||
−0.127013 | + | 0.991901i | \(0.540539\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.8688 | + | 2.80316i | 0.0349106 | + | 0.00378294i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 178.264i | − | 0.239925i | −0.992778 | − | 0.119963i | \(-0.961723\pi\) | ||
0.992778 | − | 0.119963i | \(-0.0382775\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 141.720 | 0.190228 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 227.271 | − | 1036.36i | 0.304244 | − | 1.38736i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 144.637i | − | 0.193107i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1328.32 | −1.76874 | −0.884370 | − | 0.466786i | \(-0.845412\pi\) | ||||
−0.884370 | + | 0.466786i | \(0.845412\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −78.6781 | + | 726.075i | −0.104486 | + | 0.964243i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 257.669i | 0.341284i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −545.957 | −0.721211 | −0.360606 | − | 0.932718i | \(-0.617430\pi\) | ||||
−0.360606 | + | 0.932718i | \(0.617430\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −569.068 | − | 61.6648i | −0.749761 | − | 0.0812448i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 828.655i | 1.08890i | 0.838793 | + | 0.544451i | \(0.183262\pi\) | ||||
−0.838793 | + | 0.544451i | \(0.816738\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −82.0950 | −0.107595 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 526.520 | + | 115.464i | 0.688261 | + | 0.150933i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 18.6612i | − | 0.0243301i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −303.757 | −0.395002 | −0.197501 | − | 0.980303i | \(-0.563283\pi\) | ||||
−0.197501 | + | 0.980303i | \(0.563283\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 115.858 | − | 1069.19i | 0.150270 | − | 1.38676i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 59.2137i | 0.0766025i | 0.999266 | + | 0.0383013i | \(0.0121947\pi\) | ||||
−0.999266 | + | 0.0383013i | \(0.987805\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 168.930 | 0.217974 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −851.936 | − | 92.3165i | −1.09644 | − | 0.118811i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 481.756i | − | 0.618429i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 429.629 | 0.550102 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −179.334 | + | 534.316i | −0.229035 | + | 0.682396i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 41.0755i | 0.0523255i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 214.281 | 0.272276 | 0.136138 | − | 0.990690i | \(-0.456531\pi\) | ||||
0.136138 | + | 0.990690i | \(0.456531\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −106.948 | + | 986.963i | −0.135549 | + | 1.25090i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.2862i | 0.0281748i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −61.6040 | −0.0776847 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −621.151 | − | 67.3085i | −0.781322 | − | 0.0846648i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 124.487i | 0.156195i | 0.996946 | + | 0.0780974i | \(0.0248845\pi\) | ||||
−0.996946 | + | 0.0780974i | \(0.975115\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 259.528 | 0.324816 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −230.725 | + | 1052.11i | −0.288046 | + | 1.31350i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 190.910i | − | 0.237746i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −423.237 | −0.525761 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.3610 | − | 289.412i | 0.0388612 | − | 0.358627i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.3423i | 0.0548113i | 0.999624 | + | 0.0274056i | \(0.00872458\pi\) | ||||
−0.999624 | + | 0.0274056i | \(0.991275\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −686.962 | −0.847056 | −0.423528 | − | 0.905883i | \(-0.639208\pi\) | ||||
−0.423528 | + | 0.905883i | \(0.639208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 200.382 | + | 21.7136i | 0.246473 | + | 0.0267080i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 366.029i | 0.449115i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 458.842 | 0.561618 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −44.3308 | − | 9.72160i | −0.0541280 | − | 0.0118701i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 865.772i | − | 1.05453i | −0.849700 | − | 0.527267i | \(-0.823217\pi\) | ||
0.849700 | − | 0.527267i | \(-0.176783\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −240.142 | −0.291789 | −0.145895 | − | 0.989300i | \(-0.546606\pi\) | ||||
−0.145895 | + | 0.989300i | \(0.546606\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.69908 | + | 71.0504i | −0.00933222 | + | 0.0861217i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 311.704i | − | 0.376910i | −0.982082 | − | 0.188455i | \(-0.939652\pi\) | ||
0.982082 | − | 0.188455i | \(-0.0603479\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1125.26 | −1.35737 | −0.678684 | − | 0.734430i | \(-0.737449\pi\) | ||||
−0.678684 | + | 0.734430i | \(0.737449\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1079.08 | − | 116.931i | −1.29854 | − | 0.140711i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 714.110i | − | 0.857274i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 108.902 | 0.130422 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −864.812 | − | 290.260i | −1.03323 | − | 0.346786i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 40.3794i | − | 0.0481280i | −0.999710 | − | 0.0240640i | \(-0.992339\pi\) | ||
0.999710 | − | 0.0240640i | \(-0.00766055\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 405.259 | 0.481878 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 93.1412 | − | 859.546i | 0.110488 | − | 1.01963i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 375.350i | 0.444201i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 464.607 | 0.548532 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −812.664 | − | 88.0610i | −0.957201 | − | 0.103723i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2420.24i | 2.84399i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −290.487 | −0.340547 | −0.170274 | − | 0.985397i | \(-0.554465\pi\) | ||||
−0.170274 | + | 0.985397i | \(0.554465\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −35.0443 | + | 159.803i | −0.0409875 | + | 0.186904i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1111.79i | 1.29731i | 0.761083 | + | 0.648655i | \(0.224668\pi\) | ||||
−0.761083 | + | 0.648655i | \(0.775332\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −159.069 | −0.185179 | −0.0925894 | − | 0.995704i | \(-0.529514\pi\) | ||||
−0.0925894 | + | 0.995704i | \(0.529514\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −90.5231 | + | 835.385i | −0.105137 | + | 0.970250i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 75.4630i | 0.0874426i | 0.999044 | + | 0.0437213i | \(0.0139214\pi\) | ||||
−0.999044 | + | 0.0437213i | \(0.986079\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 314.805 | 0.363937 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1277.78 | − | 138.461i | −1.47379 | − | 0.159702i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 311.463i | − | 0.358415i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −108.326 | −0.124369 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −134.084 | − | 29.4041i | −0.153589 | − | 0.0336817i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 52.8428i | 0.0603918i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −511.799 | −0.583579 | −0.291790 | − | 0.956483i | \(-0.594251\pi\) | ||||
−0.291790 | + | 0.956483i | \(0.594251\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.8067 | − | 210.470i | 0.0259462 | − | 0.239443i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 855.549i | − | 0.971111i | −0.874206 | − | 0.485556i | \(-0.838617\pi\) | ||
0.874206 | − | 0.485556i | \(-0.161383\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.2299 | 0.0127179 | 0.00635894 | − | 0.999980i | \(-0.497976\pi\) | ||||
0.00635894 | + | 0.999980i | \(0.497976\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 116.649 | + | 12.6401i | 0.131806 | + | 0.0142827i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 733.251i | − | 0.826664i | −0.910580 | − | 0.413332i | \(-0.864365\pi\) | ||
0.910580 | − | 0.413332i | \(-0.135635\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.59468 | −0.00741808 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 161.495 | − | 350.503i | 0.181251 | − | 0.393381i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 78.7690i | 0.0882072i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.8985 | 0.0278196 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.8089 | + | 127.434i | −0.0153945 | + | 0.142067i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 705.263i | − | 0.784497i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2494.67 | 2.76878 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −795.652 | − | 86.2175i | −0.881120 | − | 0.0954790i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 335.936i | 0.371200i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1141.39 | 1.25843 | 0.629214 | − | 0.777232i | \(-0.283377\pi\) | ||||
0.629214 | + | 0.777232i | \(0.283377\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 138.815 | − | 633.000i | 0.152712 | − | 0.696370i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 157.145i | 0.172497i | 0.996274 | + | 0.0862487i | \(0.0274880\pi\) | ||||
−0.996274 | + | 0.0862487i | \(0.972512\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −561.666 | −0.615187 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 41.7273 | − | 385.078i | 0.0456037 | − | 0.420850i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1069.21i | − | 1.16598i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1542.94 | 1.67893 | 0.839466 | − | 0.543412i | \(-0.182868\pi\) | ||||
0.839466 | + | 0.543412i | \(0.182868\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −370.652 | − | 40.1642i | −0.402446 | − | 0.0436094i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 96.2090i | − | 0.104235i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 302.176 | 0.326676 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 975.371 | + | 213.896i | 1.05218 | + | 0.230740i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 165.617i | − | 0.178274i | −0.996019 | − | 0.0891372i | \(-0.971589\pi\) | ||
0.996019 | − | 0.0891372i | \(-0.0284110\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 216.738 | 0.232802 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −74.0125 | + | 683.019i | −0.0793275 | + | 0.732067i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 285.353i | − | 0.305190i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1418.05 | 1.51339 | 0.756695 | − | 0.653768i | \(-0.226813\pi\) | ||||
0.756695 | + | 0.653768i | \(0.226813\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1388.34 | + | 150.442i | 1.47853 | + | 0.160215i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1274.33i | 1.35423i | 0.735878 | + | 0.677114i | \(0.236769\pi\) | ||||
−0.735878 | + | 0.677114i | \(0.763231\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2373.22 | 2.51667 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 90.7958 | − | 270.521i | 0.0960802 | − | 0.286265i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1406.16i | 1.48486i | 0.669926 | + | 0.742428i | \(0.266326\pi\) | ||||
−0.669926 | + | 0.742428i | \(0.733674\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.7515 | −0.0450490 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −131.040 | + | 1209.30i | −0.137792 | + | 1.27160i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1415.36i | − | 1.48516i | −0.669759 | − | 0.742579i | \(-0.733602\pi\) | ||
0.669759 | − | 0.742579i | \(-0.266398\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −375.794 | −0.393501 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 296.627 | + | 32.1427i | 0.309955 | + | 0.0335870i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 360.430i | 0.375840i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 180.496 | 0.187821 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 58.9963 | − | 269.025i | 0.0612630 | − | 0.279361i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 699.723i | − | 0.725101i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1662.07 | −1.71879 | −0.859394 | − | 0.511315i | \(-0.829159\pi\) | ||||
−0.859394 | + | 0.511315i | \(0.829159\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 70.3725 | − | 649.427i | 0.0726239 | − | 0.670204i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 868.901i | 0.894852i | 0.894321 | + | 0.447426i | \(0.147659\pi\) | ||||
−0.894321 | + | 0.447426i | \(0.852341\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 603.373 | 0.620116 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.9107 | + | 1.72409i | 0.0163186 | + | 0.00176830i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1336.81i | − | 1.36828i | −0.729350 | − | 0.684140i | \(-0.760178\pi\) | ||
0.729350 | − | 0.684140i | \(-0.239822\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 570.203 | 0.582434 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −152.696 | − | 33.4858i | −0.155654 | − | 0.0341344i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1193.86i | − | 1.21451i | −0.794508 | − | 0.607254i | \(-0.792271\pi\) | ||
0.794508 | − | 0.607254i | \(-0.207729\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −371.522 | −0.377180 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.8009 | − | 136.589i | 0.0149958 | − | 0.138388i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2260.34i | 2.28548i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −460.690 | −0.464874 | −0.232437 | − | 0.972611i | \(-0.574670\pi\) | ||||
−0.232437 | + | 0.972611i | \(0.574670\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 136.980 | + | 14.8432i | 0.137945 | + | 0.0149479i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 235.983i | 0.237169i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 673.924 | 0.675952 | 0.337976 | − | 0.941155i | \(-0.390258\pi\) | ||||
0.337976 | + | 0.941155i | \(0.390258\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1546.94 | − | 519.205i | −1.54849 | − | 0.519725i |
(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 | 120.3.l.a.41.8 | yes | 8 | |
3.2 | odd | 2 | inner | 120.3.l.a.41.7 | ✓ | 8 | |
4.3 | odd | 2 | 240.3.l.d.161.1 | 8 | |||
5.2 | odd | 4 | 600.3.c.d.449.9 | 16 | |||
5.3 | odd | 4 | 600.3.c.d.449.8 | 16 | |||
5.4 | even | 2 | 600.3.l.f.401.1 | 8 | |||
8.3 | odd | 2 | 960.3.l.g.641.8 | 8 | |||
8.5 | even | 2 | 960.3.l.h.641.1 | 8 | |||
12.11 | even | 2 | 240.3.l.d.161.2 | 8 | |||
15.2 | even | 4 | 600.3.c.d.449.7 | 16 | |||
15.8 | even | 4 | 600.3.c.d.449.10 | 16 | |||
15.14 | odd | 2 | 600.3.l.f.401.2 | 8 | |||
20.3 | even | 4 | 1200.3.c.m.449.9 | 16 | |||
20.7 | even | 4 | 1200.3.c.m.449.8 | 16 | |||
20.19 | odd | 2 | 1200.3.l.x.401.8 | 8 | |||
24.5 | odd | 2 | 960.3.l.h.641.2 | 8 | |||
24.11 | even | 2 | 960.3.l.g.641.7 | 8 | |||
60.23 | odd | 4 | 1200.3.c.m.449.7 | 16 | |||
60.47 | odd | 4 | 1200.3.c.m.449.10 | 16 | |||
60.59 | even | 2 | 1200.3.l.x.401.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.l.a.41.7 | ✓ | 8 | 3.2 | odd | 2 | inner | |
120.3.l.a.41.8 | yes | 8 | 1.1 | even | 1 | trivial | |
240.3.l.d.161.1 | 8 | 4.3 | odd | 2 | |||
240.3.l.d.161.2 | 8 | 12.11 | even | 2 | |||
600.3.c.d.449.7 | 16 | 15.2 | even | 4 | |||
600.3.c.d.449.8 | 16 | 5.3 | odd | 4 | |||
600.3.c.d.449.9 | 16 | 5.2 | odd | 4 | |||
600.3.c.d.449.10 | 16 | 15.8 | even | 4 | |||
600.3.l.f.401.1 | 8 | 5.4 | even | 2 | |||
600.3.l.f.401.2 | 8 | 15.14 | odd | 2 | |||
960.3.l.g.641.7 | 8 | 24.11 | even | 2 | |||
960.3.l.g.641.8 | 8 | 8.3 | odd | 2 | |||
960.3.l.h.641.1 | 8 | 8.5 | even | 2 | |||
960.3.l.h.641.2 | 8 | 24.5 | odd | 2 | |||
1200.3.c.m.449.7 | 16 | 60.23 | odd | 4 | |||
1200.3.c.m.449.8 | 16 | 20.7 | even | 4 | |||
1200.3.c.m.449.9 | 16 | 20.3 | even | 4 | |||
1200.3.c.m.449.10 | 16 | 60.47 | odd | 4 | |||
1200.3.l.x.401.7 | 8 | 60.59 | even | 2 | |||
1200.3.l.x.401.8 | 8 | 20.19 | odd | 2 |