Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,3,Mod(325,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.325");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.z (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.0655186332\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 114x^{12} - 336x^{10} + 755x^{8} - 336x^{6} + 114x^{4} - 12x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{6}\cdot 7^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.1 | ||
Root | \(-1.45341 + 0.839125i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.901 |
Dual form | 1764.3.z.n.325.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.33147 | − | 3.07813i | −1.06629 | − | 0.615626i | −0.139128 | − | 0.990274i | \(-0.544430\pi\) |
−0.927167 | + | 0.374649i | \(0.877763\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.975845 | − | 1.69021i | −0.0887132 | − | 0.153656i | 0.818254 | − | 0.574856i | \(-0.194942\pi\) |
−0.906967 | + | 0.421201i | \(0.861609\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.317025i | 0.0243866i | 0.999926 | + | 0.0121933i | \(0.00388134\pi\) | ||||
−0.999926 | + | 0.0121933i | \(0.996119\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −15.9944 | + | 9.23438i | −0.940848 | + | 0.543199i | −0.890226 | − | 0.455519i | \(-0.849454\pi\) |
−0.0506223 | + | 0.998718i | \(0.516120\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.01255 | + | 3.47135i | 0.316450 | + | 0.182702i | 0.649809 | − | 0.760097i | \(-0.274849\pi\) |
−0.333359 | + | 0.942800i | \(0.608182\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 18.4430 | − | 31.9442i | 0.801868 | − | 1.38888i | −0.116517 | − | 0.993189i | \(-0.537173\pi\) |
0.918385 | − | 0.395688i | \(-0.129494\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.44975 | + | 11.1713i | 0.257990 | + | 0.446852i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −40.7893 | −1.40653 | −0.703264 | − | 0.710929i | \(-0.748275\pi\) | ||||
−0.703264 | + | 0.710929i | \(0.748275\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −26.2190 | + | 15.1376i | −0.845775 | + | 0.488308i | −0.859223 | − | 0.511601i | \(-0.829053\pi\) |
0.0134481 | + | 0.999910i | \(0.495719\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.84924 | − | 11.8632i | 0.185115 | − | 0.320628i | −0.758500 | − | 0.651672i | \(-0.774068\pi\) |
0.943615 | + | 0.331044i | \(0.107401\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 30.1625i | 0.735672i | 0.929891 | + | 0.367836i | \(0.119901\pi\) | ||||
−0.929891 | + | 0.367836i | \(0.880099\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 41.7990 | 0.972070 | 0.486035 | − | 0.873939i | \(-0.338443\pi\) | ||||
0.486035 | + | 0.873939i | \(0.338443\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −42.1160 | − | 24.3157i | −0.896084 | − | 0.517354i | −0.0201565 | − | 0.999797i | \(-0.506416\pi\) |
−0.875928 | + | 0.482442i | \(0.839750\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.95169 | + | 3.38043i | 0.0368243 | + | 0.0637816i | 0.883850 | − | 0.467770i | \(-0.154942\pi\) |
−0.847026 | + | 0.531552i | \(0.821609\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.0151i | 0.218456i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −20.7901 | + | 12.0031i | −0.352374 | + | 0.203443i | −0.665730 | − | 0.746192i | \(-0.731880\pi\) |
0.313356 | + | 0.949636i | \(0.398547\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 69.1305 | + | 39.9125i | 1.13329 | + | 0.654304i | 0.944760 | − | 0.327764i | \(-0.106295\pi\) |
0.188528 | + | 0.982068i | \(0.439628\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.975845 | − | 1.69021i | 0.0150130 | − | 0.0260033i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 45.6985 | + | 79.1521i | 0.682067 | + | 1.18137i | 0.974349 | + | 0.225042i | \(0.0722521\pi\) |
−0.292282 | + | 0.956332i | \(0.594415\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 75.7236 | 1.06653 | 0.533265 | − | 0.845948i | \(-0.320965\pi\) | ||||
0.533265 | + | 0.845948i | \(0.320965\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −114.430 | + | 66.0663i | −1.56754 | + | 0.905018i | −0.571082 | + | 0.820893i | \(0.693476\pi\) |
−0.996455 | + | 0.0841251i | \(0.973190\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.5980 | − | 21.8203i | 0.159468 | − | 0.276207i | −0.775209 | − | 0.631705i | \(-0.782355\pi\) |
0.934677 | + | 0.355498i | \(0.115689\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 84.9501i | − | 1.02350i | −0.859136 | − | 0.511748i | \(-0.828998\pi\) | ||
0.859136 | − | 0.511748i | \(-0.171002\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 113.698 | 1.33763 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 110.889 | + | 64.0220i | 1.24595 | + | 0.719348i | 0.970299 | − | 0.241911i | \(-0.0777741\pi\) |
0.275649 | + | 0.961259i | \(0.411107\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.3705 | − | 37.0148i | −0.224953 | − | 0.389629i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.05760i | − | 0.0418310i | −0.999781 | − | 0.0209155i | \(-0.993342\pi\) | ||
0.999781 | − | 0.0209155i | \(-0.00665809\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 131.679 | − | 76.0251i | 1.30376 | − | 0.752724i | 0.322710 | − | 0.946498i | \(-0.395406\pi\) |
0.981046 | + | 0.193774i | \(0.0620729\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 82.0069 | + | 47.3467i | 0.796183 | + | 0.459677i | 0.842135 | − | 0.539267i | \(-0.181299\pi\) |
−0.0459515 | + | 0.998944i | \(0.514632\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −94.1665 | + | 163.101i | −0.880061 | + | 1.52431i | −0.0287895 | + | 0.999585i | \(0.509165\pi\) |
−0.851272 | + | 0.524725i | \(0.824168\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 59.4472 | + | 102.966i | 0.545387 | + | 0.944639i | 0.998582 | + | 0.0532272i | \(0.0169508\pi\) |
−0.453195 | + | 0.891411i | \(0.649716\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.3207 | −0.170980 | −0.0854900 | − | 0.996339i | \(-0.527246\pi\) | ||||
−0.0854900 | + | 0.996339i | \(0.527246\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −196.656 | + | 113.540i | −1.71006 | + | 0.987301i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 58.5955 | − | 101.490i | 0.484260 | − | 0.838763i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 74.4938i | 0.595951i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 174.995 | 1.37791 | 0.688956 | − | 0.724803i | \(-0.258069\pi\) | ||||
0.688956 | + | 0.724803i | \(0.258069\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 30.9172 | + | 17.8500i | 0.236009 | + | 0.136260i | 0.613341 | − | 0.789818i | \(-0.289825\pi\) |
−0.377332 | + | 0.926078i | \(0.623158\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 100.022 | + | 173.243i | 0.730085 | + | 1.26454i | 0.956847 | + | 0.290594i | \(0.0938528\pi\) |
−0.226762 | + | 0.973950i | \(0.572814\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 92.8231i | 0.667792i | 0.942610 | + | 0.333896i | \(0.108363\pi\) | ||||
−0.942610 | + | 0.333896i | \(0.891637\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.535840 | − | 0.309367i | 0.00374713 | − | 0.00216341i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 217.467 | + | 125.555i | 1.49977 | + | 0.865895i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −42.7410 | + | 74.0296i | −0.286852 | + | 0.496843i | −0.973057 | − | 0.230566i | \(-0.925942\pi\) |
0.686204 | + | 0.727409i | \(0.259276\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 122.296 | + | 211.824i | 0.809910 | + | 1.40281i | 0.912926 | + | 0.408126i | \(0.133818\pi\) |
−0.103015 | + | 0.994680i | \(0.532849\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 186.381 | 1.20246 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −196.327 | + | 113.349i | −1.25049 | + | 0.721970i | −0.971207 | − | 0.238239i | \(-0.923430\pi\) |
−0.279282 | + | 0.960209i | \(0.590096\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.5025 | + | 38.9755i | −0.138052 | + | 0.239114i | −0.926759 | − | 0.375656i | \(-0.877418\pi\) |
0.788707 | + | 0.614769i | \(0.210751\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 86.8063i | − | 0.519798i | −0.965636 | − | 0.259899i | \(-0.916311\pi\) | ||
0.965636 | − | 0.259899i | \(-0.0836893\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 168.899 | 0.999405 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.18811 | − | 1.84066i | −0.0184284 | − | 0.0106396i | 0.490757 | − | 0.871296i | \(-0.336720\pi\) |
−0.509186 | + | 0.860657i | \(0.670053\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −148.520 | − | 257.244i | −0.829719 | − | 1.43711i | −0.898259 | − | 0.439466i | \(-0.855168\pi\) |
0.0685406 | − | 0.997648i | \(-0.478166\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 119.483i | − | 0.660130i | −0.943958 | − | 0.330065i | \(-0.892929\pi\) | ||
0.943958 | − | 0.330065i | \(-0.107071\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −73.0331 | + | 42.1657i | −0.394774 | + | 0.227923i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.2161 | + | 18.0227i | 0.166931 | + | 0.0963778i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 168.037 | − | 291.048i | 0.879772 | − | 1.52381i | 0.0281817 | − | 0.999603i | \(-0.491028\pi\) |
0.851591 | − | 0.524207i | \(-0.175638\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.7990 | + | 42.9531i | 0.128492 | + | 0.222555i | 0.923093 | − | 0.384578i | \(-0.125653\pi\) |
−0.794600 | + | 0.607133i | \(0.792320\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −217.608 | −1.10461 | −0.552306 | − | 0.833642i | \(-0.686252\pi\) | ||||
−0.552306 | + | 0.833642i | \(0.686252\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −251.868 | + | 145.416i | −1.26567 | + | 0.730733i | −0.974165 | − | 0.225838i | \(-0.927488\pi\) |
−0.291501 | + | 0.956570i | \(0.594155\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 92.8442 | − | 160.811i | 0.452898 | − | 0.784443i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 13.5500i | − | 0.0648325i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 237.990 | 1.12791 | 0.563957 | − | 0.825804i | \(-0.309278\pi\) | ||||
0.563957 | + | 0.825804i | \(0.309278\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −222.850 | − | 128.663i | −1.03651 | − | 0.598431i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.92753 | − | 5.07064i | −0.0132468 | − | 0.0229441i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 179.242i | 0.803776i | 0.915689 | + | 0.401888i | \(0.131646\pi\) | ||||
−0.915689 | + | 0.401888i | \(0.868354\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −75.1765 | + | 43.4032i | −0.331174 | + | 0.191203i | −0.656362 | − | 0.754446i | \(-0.727906\pi\) |
0.325188 | + | 0.945649i | \(0.394572\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 274.024 | + | 158.208i | 1.19661 | + | 0.690863i | 0.959798 | − | 0.280693i | \(-0.0905642\pi\) |
0.236812 | + | 0.971556i | \(0.423898\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 74.6497 | − | 129.297i | 0.320385 | − | 0.554923i | −0.660183 | − | 0.751105i | \(-0.729521\pi\) |
0.980567 | + | 0.196182i | \(0.0628545\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 149.693 | + | 259.277i | 0.636993 | + | 1.10330i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −196.140 | −0.820669 | −0.410334 | − | 0.911935i | \(-0.634588\pi\) | ||||
−0.410334 | + | 0.911935i | \(0.634588\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −110.559 | + | 63.8312i | −0.458751 | + | 0.264860i | −0.711519 | − | 0.702667i | \(-0.751992\pi\) |
0.252768 | + | 0.967527i | \(0.418659\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.10051 | + | 1.90613i | −0.00445549 | + | 0.00771713i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 329.344i | 1.31213i | 0.754705 | + | 0.656064i | \(0.227780\pi\) | ||||
−0.754705 | + | 0.656064i | \(0.772220\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −71.9899 | −0.284545 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −80.5080 | − | 46.4813i | −0.313261 | − | 0.180861i | 0.335124 | − | 0.942174i | \(-0.391222\pi\) |
−0.648385 | + | 0.761313i | \(0.724555\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 247.467 | + | 428.626i | 0.940940 | + | 1.62976i | 0.763683 | + | 0.645592i | \(0.223389\pi\) |
0.177258 | + | 0.984164i | \(0.443277\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 24.0302i | − | 0.0906800i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −335.347 | + | 193.613i | −1.24664 | + | 0.719750i | −0.970438 | − | 0.241349i | \(-0.922410\pi\) |
−0.276205 | + | 0.961099i | \(0.589077\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −192.813 | − | 111.320i | −0.711486 | − | 0.410777i | 0.100125 | − | 0.994975i | \(-0.468076\pi\) |
−0.811611 | + | 0.584198i | \(0.801409\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.5879 | − | 21.8029i | 0.0457742 | − | 0.0792832i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −69.6985 | − | 120.721i | −0.251619 | − | 0.435817i | 0.712353 | − | 0.701822i | \(-0.247630\pi\) |
−0.963972 | + | 0.266005i | \(0.914296\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −91.1409 | −0.324345 | −0.162172 | − | 0.986762i | \(-0.551850\pi\) | ||||
−0.162172 | + | 0.986762i | \(0.551850\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.0275939 | + | 0.0159313i | −9.75048e−5 | + | 5.62944e-5i | −0.500049 | − | 0.865997i | \(-0.666685\pi\) |
0.499951 | + | 0.866054i | \(0.333351\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.0477 | − | 45.1160i | 0.0901305 | − | 0.156111i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.6375i | 0.111391i | 0.998448 | + | 0.0556954i | \(0.0177376\pi\) | ||||
−0.998448 | + | 0.0556954i | \(0.982262\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 147.789 | 0.500979 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.1271 | + | 5.84689i | 0.0338699 | + | 0.0195548i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −245.712 | − | 425.585i | −0.805612 | − | 1.39536i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 93.2341i | − | 0.303694i | −0.988404 | − | 0.151847i | \(-0.951478\pi\) | ||
0.988404 | − | 0.151847i | \(-0.0485221\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 157.265 | − | 90.7970i | 0.505675 | − | 0.291952i | −0.225379 | − | 0.974271i | \(-0.572362\pi\) |
0.731054 | + | 0.682319i | \(0.239029\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 257.523 | + | 148.681i | 0.822757 | + | 0.475019i | 0.851366 | − | 0.524572i | \(-0.175775\pi\) |
−0.0286095 | + | 0.999591i | \(0.509108\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 73.8700 | − | 127.947i | 0.233028 | − | 0.403617i | −0.725670 | − | 0.688043i | \(-0.758470\pi\) |
0.958698 | + | 0.284427i | \(0.0918032\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 39.8040 | + | 68.9426i | 0.124778 | + | 0.216121i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −128.223 | −0.396975 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.54158 | + | 2.04473i | −0.0108972 | + | 0.00629149i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −160.593 | + | 278.155i | −0.485175 | + | 0.840348i | −0.999855 | − | 0.0170346i | \(-0.994577\pi\) |
0.514680 | + | 0.857382i | \(0.327911\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 562.663i | − | 1.67959i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −44.8944 | −0.133218 | −0.0666090 | − | 0.997779i | \(-0.521218\pi\) | ||||
−0.0666090 | + | 0.997779i | \(0.521218\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 51.1714 | + | 29.5438i | 0.150063 | + | 0.0866387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −72.6980 | − | 125.917i | −0.209504 | − | 0.362872i | 0.742054 | − | 0.670340i | \(-0.233852\pi\) |
−0.951558 | + | 0.307468i | \(0.900518\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 187.199i | − | 0.536388i | −0.963365 | − | 0.268194i | \(-0.913573\pi\) | ||
0.963365 | − | 0.268194i | \(-0.0864268\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 400.396 | − | 231.169i | 1.13427 | − | 0.654870i | 0.189263 | − | 0.981926i | \(-0.439390\pi\) |
0.945005 | + | 0.327057i | \(0.106057\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −403.718 | − | 233.087i | −1.13723 | − | 0.656583i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −177.697 | + | 307.780i | −0.494977 | + | 0.857326i | −0.999983 | − | 0.00578996i | \(-0.998157\pi\) |
0.505006 | + | 0.863116i | \(0.331490\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −156.399 | − | 270.892i | −0.433240 | − | 0.750393i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 813.442 | 2.22861 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 285.636 | − | 164.912i | 0.778300 | − | 0.449352i | −0.0575274 | − | 0.998344i | \(-0.518322\pi\) |
0.835827 | + | 0.548992i | \(0.184988\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 203.296 | − | 352.120i | 0.545031 | − | 0.944021i | −0.453574 | − | 0.891218i | \(-0.649851\pi\) |
0.998605 | − | 0.0528024i | \(-0.0168154\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.9312i | − | 0.0343004i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −435.196 | −1.14827 | −0.574137 | − | 0.818759i | \(-0.694662\pi\) | ||||
−0.574137 | + | 0.818759i | \(0.694662\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 407.335 | + | 235.175i | 1.06354 | + | 0.614035i | 0.926409 | − | 0.376519i | \(-0.122879\pi\) |
0.137130 | + | 0.990553i | \(0.456212\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 117.587 | + | 203.666i | 0.302280 | + | 0.523564i | 0.976652 | − | 0.214828i | \(-0.0689190\pi\) |
−0.674372 | + | 0.738392i | \(0.735586\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 681.238i | 1.74230i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −134.332 | + | 77.5564i | −0.340080 | + | 0.196345i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 54.1392 | + | 31.2573i | 0.136371 | + | 0.0787336i | 0.566633 | − | 0.823970i | \(-0.308246\pi\) |
−0.430263 | + | 0.902704i | \(0.641579\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −255.176 | + | 441.978i | −0.636349 | + | 1.10219i | 0.349879 | + | 0.936795i | \(0.386223\pi\) |
−0.986228 | + | 0.165394i | \(0.947110\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.79899 | − | 8.31209i | −0.0119082 | − | 0.0206255i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26.7352 | −0.0656884 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 529.213 | − | 305.541i | 1.29392 | − | 0.747045i | 0.314574 | − | 0.949233i | \(-0.398139\pi\) |
0.979347 | + | 0.202188i | \(0.0648052\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −261.487 | + | 452.909i | −0.630090 | + | 1.09135i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 639.632i | 1.52657i | 0.646063 | + | 0.763284i | \(0.276414\pi\) | ||||
−0.646063 | + | 0.763284i | \(0.723586\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −369.186 | −0.876926 | −0.438463 | − | 0.898749i | \(-0.644477\pi\) | ||||
−0.438463 | + | 0.898749i | \(0.644477\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −206.320 | − | 119.119i | −0.485459 | − | 0.280280i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 230.294 | + | 398.882i | 0.534326 | + | 0.925479i | 0.999196 | + | 0.0401004i | \(0.0127678\pi\) |
−0.464870 | + | 0.885379i | \(0.653899\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 801.072i | − | 1.85005i | −0.379905 | − | 0.925025i | \(-0.624043\pi\) | ||
0.379905 | − | 0.925025i | \(-0.375957\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 221.779 | − | 128.044i | 0.507502 | − | 0.293007i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −632.057 | − | 364.918i | −1.43977 | − | 0.831249i | −0.441933 | − | 0.897048i | \(-0.645707\pi\) |
−0.997833 | + | 0.0657988i | \(0.979040\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −191.457 | + | 331.613i | −0.432182 | + | 0.748562i | −0.997061 | − | 0.0766122i | \(-0.975590\pi\) |
0.564879 | + | 0.825174i | \(0.308923\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −394.136 | − | 682.663i | −0.885698 | − | 1.53407i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 271.863 | 0.605486 | 0.302743 | − | 0.953072i | \(-0.402098\pi\) | ||||
0.302743 | + | 0.953072i | \(0.402098\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 50.9811 | − | 29.4340i | 0.113040 | − | 0.0652638i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 98.9045 | − | 171.308i | 0.216421 | − | 0.374853i | −0.737290 | − | 0.675576i | \(-0.763895\pi\) |
0.953711 | + | 0.300724i | \(0.0972282\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 486.344i | − | 1.05498i | −0.849562 | − | 0.527488i | \(-0.823134\pi\) | ||
0.849562 | − | 0.527488i | \(-0.176866\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 73.1859 | 0.158069 | 0.0790344 | − | 0.996872i | \(-0.474816\pi\) | ||||
0.0790344 | + | 0.996872i | \(0.474816\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 676.535 | + | 390.597i | 1.44868 | + | 0.836397i | 0.998403 | − | 0.0564910i | \(-0.0179912\pi\) |
0.450279 | + | 0.892888i | \(0.351325\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −40.7893 | − | 70.6492i | −0.0862354 | − | 0.149364i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 89.5573i | 0.188542i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 613.628 | − | 354.279i | 1.28106 | − | 0.739621i | 0.304019 | − | 0.952666i | \(-0.401671\pi\) |
0.977042 | + | 0.213045i | \(0.0683380\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.76095 | + | 2.17138i | 0.00781902 | + | 0.00451431i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.4898 | + | 21.6330i | −0.0257522 | + | 0.0446042i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.1005 | + | 40.0112i | 0.0474343 | + | 0.0821586i | 0.888768 | − | 0.458358i | \(-0.151562\pi\) |
−0.841333 | + | 0.540516i | \(0.818229\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −627.453 | −1.27791 | −0.638955 | − | 0.769245i | \(-0.720633\pi\) | ||||
−0.638955 | + | 0.769245i | \(0.720633\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 652.402 | − | 376.664i | 1.32333 | − | 0.764025i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −205.784 | + | 356.428i | −0.412392 | + | 0.714285i | −0.995151 | − | 0.0983608i | \(-0.968640\pi\) |
0.582758 | + | 0.812645i | \(0.301973\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 137.913i | 0.274180i | 0.990559 | + | 0.137090i | \(0.0437750\pi\) | ||||
−0.990559 | + | 0.137090i | \(0.956225\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −936.060 | −1.85358 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −229.789 | − | 132.669i | −0.451452 | − | 0.260646i | 0.256991 | − | 0.966414i | \(-0.417269\pi\) |
−0.708443 | + | 0.705768i | \(0.750602\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −291.478 | − | 504.855i | −0.565977 | − | 0.980302i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 94.9132i | 0.183585i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −315.093 | + | 181.919i | −0.604785 | + | 0.349173i | −0.770922 | − | 0.636930i | \(-0.780204\pi\) |
0.166137 | + | 0.986103i | \(0.446871\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −679.391 | − | 392.246i | −1.29903 | − | 0.749993i | −0.318790 | − | 0.947825i | \(-0.603276\pi\) |
−0.980236 | + | 0.197832i | \(0.936610\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 279.572 | − | 484.233i | 0.530497 | − | 0.918848i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −415.786 | − | 720.163i | −0.785986 | − | 1.36137i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.56229 | −0.0179405 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1004.09 | − | 579.713i | 1.87681 | − | 1.08358i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −201.090 | + | 348.299i | −0.371701 | + | 0.643806i | −0.989827 | − | 0.142273i | \(-0.954559\pi\) |
0.618126 | + | 0.786079i | \(0.287892\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 731.945i | − | 1.34302i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −411.206 | −0.751748 | −0.375874 | − | 0.926671i | \(-0.622657\pi\) | ||||
−0.375874 | + | 0.926671i | \(0.622657\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −245.248 | − | 141.594i | −0.445096 | − | 0.256976i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −103.145 | − | 178.653i | −0.185180 | − | 0.320741i | 0.758457 | − | 0.651723i | \(-0.225954\pi\) |
−0.943637 | + | 0.330982i | \(0.892620\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.2513i | 0.0237054i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −841.837 | + | 486.035i | −1.49527 | + | 0.863295i | −0.999985 | − | 0.00543587i | \(-0.998270\pi\) |
−0.495285 | + | 0.868731i | \(0.664936\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 103.008 | + | 59.4717i | 0.182315 | + | 0.105260i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 284.451 | − | 492.684i | 0.499914 | − | 0.865877i | −0.500086 | − | 0.865976i | \(-0.666698\pi\) |
1.00000 | 9.87795e-5i | \(3.14425e-5\pi\) | ||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.6934 | − | 37.5741i | −0.0379920 | − | 0.0658041i | 0.846404 | − | 0.532541i | \(-0.178763\pi\) |
−0.884396 | + | 0.466737i | \(0.845429\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 475.810 | 0.827496 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 215.380 | − | 124.350i | 0.373275 | − | 0.215511i | −0.301613 | − | 0.953430i | \(-0.597525\pi\) |
0.674888 | + | 0.737920i | \(0.264192\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.80909 | − | 6.59754i | 0.00653360 | − | 0.0113165i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 804.582i | 1.37067i | 0.728229 | + | 0.685334i | \(0.240344\pi\) | ||||
−0.728229 | + | 0.685334i | \(0.759656\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −210.191 | −0.356861 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −503.275 | − | 290.566i | −0.848693 | − | 0.489993i | 0.0115165 | − | 0.999934i | \(-0.496334\pi\) |
−0.860210 | + | 0.509940i | \(0.829667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 358.125 | + | 620.291i | 0.597872 | + | 1.03554i | 0.993135 | + | 0.116976i | \(0.0373201\pi\) |
−0.395263 | + | 0.918568i | \(0.629347\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 135.622i | − | 0.225660i | −0.993614 | − | 0.112830i | \(-0.964008\pi\) | ||
0.993614 | − | 0.112830i | \(-0.0359915\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −624.800 | + | 360.729i | −1.03273 | + | 0.596246i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −865.749 | − | 499.841i | −1.42628 | − | 0.823461i | −0.429451 | − | 0.903090i | \(-0.641293\pi\) |
−0.996825 | + | 0.0796296i | \(0.974626\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.70868 | − | 13.3518i | 0.0126165 | − | 0.0218524i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −407.246 | − | 705.371i | −0.664349 | − | 1.15069i | −0.979461 | − | 0.201632i | \(-0.935375\pi\) |
0.315112 | − | 0.949055i | \(-0.397958\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −417.848 | −0.677225 | −0.338612 | − | 0.940926i | \(-0.609958\pi\) | ||||
−0.338612 | + | 0.940926i | \(0.609958\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 249.395 | − | 143.988i | 0.402900 | − | 0.232615i | −0.284834 | − | 0.958577i | \(-0.591939\pi\) |
0.687735 | + | 0.725962i | \(0.258605\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390.545 | − | 676.444i | 0.624872 | − | 1.08231i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 252.994i | 0.402216i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −474.412 | −0.751842 | −0.375921 | − | 0.926652i | \(-0.622674\pi\) | ||||
−0.375921 | + | 0.926652i | \(0.622674\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −932.981 | − | 538.657i | −1.46926 | − | 0.848279i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.8120 | − | 62.0282i | −0.0558690 | − | 0.0967679i | 0.836738 | − | 0.547603i | \(-0.184460\pi\) |
−0.892607 | + | 0.450835i | \(0.851126\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 256.561i | 0.399006i | 0.979897 | + | 0.199503i | \(0.0639328\pi\) | ||||
−0.979897 | + | 0.199503i | \(0.936067\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 614.700 | − | 354.897i | 0.950078 | − | 0.548528i | 0.0569725 | − | 0.998376i | \(-0.481855\pi\) |
0.893105 | + | 0.449848i | \(0.148522\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.5757 | + | 23.4264i | 0.0625204 | + | 0.0360962i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 208.532 | − | 361.187i | 0.319344 | − | 0.553120i | −0.661007 | − | 0.750379i | \(-0.729871\pi\) |
0.980351 | + | 0.197259i | \(0.0632041\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −109.889 | − | 190.334i | −0.167770 | − | 0.290586i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −755.676 | −1.14670 | −0.573351 | − | 0.819310i | \(-0.694357\pi\) | ||||
−0.573351 | + | 0.819310i | \(0.694357\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 746.681 | − | 431.096i | 1.12962 | − | 0.652188i | 0.185783 | − | 0.982591i | \(-0.440518\pi\) |
0.943840 | + | 0.330403i | \(0.107185\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −752.276 | + | 1302.98i | −1.12785 | + | 1.95349i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 155.794i | − | 0.232181i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −529.266 | −0.786428 | −0.393214 | − | 0.919447i | \(-0.628637\pi\) | ||||
−0.393214 | + | 0.919447i | \(0.628637\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 390.269 | + | 225.322i | 0.576469 | + | 0.332824i | 0.759729 | − | 0.650240i | \(-0.225332\pi\) |
−0.183260 | + | 0.983064i | \(0.558665\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −60.8897 | − | 105.464i | −0.0891504 | − | 0.154413i | 0.818002 | − | 0.575216i | \(-0.195082\pi\) |
−0.907152 | + | 0.420803i | \(0.861749\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1231.52i | − | 1.79784i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.07168 | + | 0.618735i | −0.00155541 | + | 0.000898019i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −933.123 | − | 538.739i | −1.35040 | − | 0.779651i | −0.362091 | − | 0.932143i | \(-0.617937\pi\) |
−0.988305 | + | 0.152491i | \(0.951270\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 285.721 | − | 494.884i | 0.411110 | − | 0.712063i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −278.533 | − | 482.433i | −0.399616 | − | 0.692156i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −770.701 | −1.09943 | −0.549716 | − | 0.835352i | \(-0.685264\pi\) | ||||
−0.549716 | + | 0.835352i | \(0.685264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 82.3628 | − | 47.5522i | 0.117159 | − | 0.0676418i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 124.251 | − | 215.209i | 0.175249 | − | 0.303539i | −0.764999 | − | 0.644032i | \(-0.777260\pi\) |
0.940247 | + | 0.340492i | \(0.110594\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1116.73i | 1.56624i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.80909 | −0.00532740 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 261.269 | + | 150.844i | 0.363379 | + | 0.209797i | 0.670562 | − | 0.741854i | \(-0.266053\pi\) |
−0.307183 | + | 0.951650i | \(0.599386\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −263.081 | − | 455.669i | −0.362870 | − | 0.628509i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1082.52i | 1.48902i | 0.667610 | + | 0.744511i | \(0.267317\pi\) | ||||
−0.667610 | + | 0.744511i | \(0.732683\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −668.551 | + | 385.988i | −0.914570 | + | 0.528027i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 813.779 | + | 469.835i | 1.11020 | + | 0.640976i | 0.938882 | − | 0.344239i | \(-0.111863\pi\) |
0.171321 | + | 0.985215i | \(0.445196\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 89.1892 | − | 154.480i | 0.121017 | − | 0.209607i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 281.176 | + | 487.011i | 0.380481 | + | 0.659013i | 0.991131 | − | 0.132888i | \(-0.0424250\pi\) |
−0.610650 | + | 0.791901i | \(0.709092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −52.3033 | −0.0703948 | −0.0351974 | − | 0.999380i | \(-0.511206\pi\) | ||||
−0.0351974 | + | 0.999380i | \(0.511206\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 455.745 | − | 263.125i | 0.611739 | − | 0.353187i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 159.709 | − | 276.623i | 0.212661 | − | 0.368340i | −0.739885 | − | 0.672733i | \(-0.765120\pi\) |
0.952547 | + | 0.304393i | \(0.0984536\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1505.78i | − | 1.99441i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −784.060 | −1.03575 | −0.517873 | − | 0.855457i | \(-0.673276\pi\) | ||||
−0.517873 | + | 0.855457i | \(0.673276\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 793.318 | + | 458.022i | 1.04247 | + | 0.601869i | 0.920531 | − | 0.390669i | \(-0.127756\pi\) |
0.121937 | + | 0.992538i | \(0.461090\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.80530 | − | 6.59098i | −0.00496128 | − | 0.00859319i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 452.414i | 0.588315i | 0.955757 | + | 0.294157i | \(0.0950390\pi\) | ||||
−0.955757 | + | 0.294157i | \(0.904961\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 717.606 | − | 414.310i | 0.928339 | − | 0.535977i | 0.0420528 | − | 0.999115i | \(-0.486610\pi\) |
0.886286 | + | 0.463139i | \(0.153277\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −338.212 | − | 195.267i | −0.436403 | − | 0.251957i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −104.705 | + | 181.354i | −0.134409 | + | 0.232803i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −73.8944 | − | 127.989i | −0.0946152 | − | 0.163878i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1395.61 | 1.77785 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 213.430 | − | 123.224i | 0.271195 | − | 0.156574i | −0.358236 | − | 0.933631i | \(-0.616622\pi\) |
0.629431 | + | 0.777057i | \(0.283288\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.6533 | + | 21.9161i | −0.0159562 | + | 0.0276370i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 426.638i | 0.535305i | 0.963516 | + | 0.267652i | \(0.0862479\pi\) | ||||
−0.963516 | + | 0.267652i | \(0.913752\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 898.161 | 1.12411 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 223.332 | + | 128.941i | 0.278122 | + | 0.160574i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 553.289 | + | 958.325i | 0.683917 | + | 1.18458i | 0.973776 | + | 0.227510i | \(0.0730585\pi\) |
−0.289858 | + | 0.957070i | \(0.593608\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1002.47i | − | 1.23609i | −0.786143 | − | 0.618045i | \(-0.787925\pi\) | ||
0.786143 | − | 0.618045i | \(-0.212075\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 239.943 | − | 138.531i | 0.294409 | − | 0.169977i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 251.319 | + | 145.099i | 0.307611 | + | 0.177600i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −765.337 | + | 1325.60i | −0.932201 | + | 1.61462i | −0.152649 | + | 0.988280i | \(0.548781\pi\) |
−0.779551 | + | 0.626338i | \(0.784553\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −252.276 | − | 436.955i | −0.306533 | − | 0.530930i | 0.671069 | − | 0.741395i | \(-0.265835\pi\) |
−0.977601 | + | 0.210465i | \(0.932502\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1105.22 | 1.33641 | 0.668207 | − | 0.743975i | \(-0.267062\pi\) | ||||
0.668207 | + | 0.743975i | \(0.267062\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −717.661 | + | 414.342i | −0.865695 | + | 0.499809i | −0.865915 | − | 0.500191i | \(-0.833263\pi\) |
0.000220471 | 1.00000i | \(0.499930\pi\) | ||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −267.201 | + | 462.806i | −0.320001 | + | 0.554258i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 594.032i | − | 0.708024i | −0.935241 | − | 0.354012i | \(-0.884817\pi\) | ||
0.935241 | − | 0.354012i | \(-0.115183\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 822.769 | 0.978322 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −900.483 | − | 519.894i | −1.06566 | − | 0.615260i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −252.641 | − | 437.587i | −0.296875 | − | 0.514203i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 481.329i | − | 0.564278i | −0.959374 | − | 0.282139i | \(-0.908956\pi\) | ||
0.959374 | − | 0.282139i | \(-0.0910439\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −332.722 | + | 192.097i | −0.388240 | + | 0.224150i | −0.681397 | − | 0.731914i | \(-0.738627\pi\) |
0.293157 | + | 0.956064i | \(0.405294\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −348.973 | − | 201.480i | −0.406255 | − | 0.234552i | 0.282924 | − | 0.959142i | \(-0.408696\pi\) |
−0.689180 | + | 0.724591i | \(0.742029\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −297.721 | + | 515.668i | −0.344984 | + | 0.597529i | −0.985351 | − | 0.170540i | \(-0.945449\pi\) |
0.640367 | + | 0.768069i | \(0.278782\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.3316 | + | 19.6268i | 0.0131001 | + | 0.0226900i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −49.1747 | −0.0565877 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.0932 | + | 14.4876i | −0.0288097 | + | 0.0166333i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 499.829 | − | 865.729i | 0.569930 | − | 0.987149i | −0.426642 | − | 0.904421i | \(-0.640303\pi\) |
0.996572 | − | 0.0827278i | \(-0.0263632\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.4436i | 0.0447714i | 0.999749 | + | 0.0223857i | \(0.00712618\pi\) | ||||
−0.999749 | + | 0.0223857i | \(0.992874\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1168.75 | −1.32362 | −0.661808 | − | 0.749673i | \(-0.730211\pi\) | ||||
−0.661808 | + | 0.749673i | \(0.730211\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −367.363 | − | 212.097i | −0.414163 | − | 0.239117i | 0.278414 | − | 0.960461i | \(-0.410191\pi\) |
−0.692577 | + | 0.721344i | \(0.743525\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −168.816 | − | 292.398i | −0.189044 | − | 0.327434i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1828.65i | 2.04318i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1069.46 | − | 617.451i | 1.18961 | − | 0.686820i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −62.4323 | − | 36.0453i | −0.0692922 | − | 0.0400059i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −367.785 | + | 637.023i | −0.406393 | + | 0.703893i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 629.080 | + | 1089.60i | 0.693584 | + | 1.20132i | 0.970656 | + | 0.240473i | \(0.0773025\pi\) |
−0.277072 | + | 0.960849i | \(0.589364\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 467.611 | 0.513294 | 0.256647 | − | 0.966505i | \(-0.417382\pi\) | ||||
0.256647 | + | 0.966505i | \(0.417382\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −143.584 | + | 82.8981i | −0.157266 | + | 0.0907975i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −111.302 | + | 192.780i | −0.121112 | + | 0.209771i | −0.920206 | − | 0.391434i | \(-0.871979\pi\) |
0.799095 | + | 0.601205i | \(0.205313\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.0063i | 0.0260090i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 176.704 | 0.191031 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1362.69 | + | 786.748i | 1.46683 | + | 0.846876i | 0.999311 | − | 0.0371060i | \(-0.0118139\pi\) |
0.467521 | + | 0.883982i | \(0.345147\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −110.952 | − | 192.175i | −0.118665 | − | 0.205534i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1165.80i | − | 1.24418i | −0.782945 | − | 0.622090i | \(-0.786284\pi\) | ||
0.782945 | − | 0.622090i | \(-0.213716\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1227.82 | − | 708.882i | 1.30480 | − | 0.753328i | 0.323579 | − | 0.946201i | \(-0.395114\pi\) |
0.981224 | + | 0.192873i | \(0.0617804\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 963.517 | + | 556.287i | 1.02176 | + | 0.589912i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −630.283 | + | 1091.68i | −0.665557 | + | 1.15278i | 0.313577 | + | 0.949563i | \(0.398473\pi\) |
−0.979134 | + | 0.203216i | \(0.934861\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.9447 | − | 36.2773i | −0.0220703 | − | 0.0382268i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1479.73 | −1.55271 | −0.776355 | − | 0.630295i | \(-0.782934\pi\) | ||||
−0.776355 | + | 0.630295i | \(0.782934\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1791.76 | + | 1034.48i | −1.87619 | + | 1.08322i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.2086 | + | 38.4664i | −0.0231099 | + | 0.0400275i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 305.338i | − | 0.316412i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1725.53 | 1.78441 | 0.892206 | − | 0.451628i | \(-0.149156\pi\) | ||||
0.892206 | + | 0.451628i | \(0.149156\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 781.610 | + | 451.263i | 0.804954 | + | 0.464740i | 0.845200 | − | 0.534449i | \(-0.179481\pi\) |
−0.0402465 | + | 0.999190i | \(0.512814\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 599.448 | + | 1038.27i | 0.613560 | + | 1.06272i | 0.990635 | + | 0.136534i | \(0.0435964\pi\) |
−0.377075 | + | 0.926183i | \(0.623070\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 249.902i | − | 0.255262i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −937.268 | + | 541.132i | −0.953477 | + | 0.550490i | −0.894159 | − | 0.447749i | \(-0.852226\pi\) |
−0.0593177 | + | 0.998239i | \(0.518892\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1160.17 | + | 669.827i | 1.17784 | + | 0.680027i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 770.898 | − | 1335.23i | 0.779472 | − | 1.35008i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 824.377 | + | 1427.86i | 0.831864 | + | 1.44083i | 0.896559 | + | 0.442925i | \(0.146059\pi\) |
−0.0646952 | + | 0.997905i | \(0.520608\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1790.43 | 1.79943 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −340.518 | + | 196.598i | −0.341542 | + | 0.197189i | −0.660954 | − | 0.750427i | \(-0.729848\pi\) |
0.319412 | + | 0.947616i | \(0.396515\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1764.3.z.n.901.1 | 16 | ||
3.2 | odd | 2 | inner | 1764.3.z.n.901.8 | 16 | ||
7.2 | even | 3 | 1764.3.d.g.685.8 | yes | 8 | ||
7.3 | odd | 6 | inner | 1764.3.z.n.325.1 | 16 | ||
7.4 | even | 3 | inner | 1764.3.z.n.325.7 | 16 | ||
7.5 | odd | 6 | 1764.3.d.g.685.2 | yes | 8 | ||
7.6 | odd | 2 | inner | 1764.3.z.n.901.7 | 16 | ||
21.2 | odd | 6 | 1764.3.d.g.685.1 | ✓ | 8 | ||
21.5 | even | 6 | 1764.3.d.g.685.7 | yes | 8 | ||
21.11 | odd | 6 | inner | 1764.3.z.n.325.2 | 16 | ||
21.17 | even | 6 | inner | 1764.3.z.n.325.8 | 16 | ||
21.20 | even | 2 | inner | 1764.3.z.n.901.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.3.d.g.685.1 | ✓ | 8 | 21.2 | odd | 6 | ||
1764.3.d.g.685.2 | yes | 8 | 7.5 | odd | 6 | ||
1764.3.d.g.685.7 | yes | 8 | 21.5 | even | 6 | ||
1764.3.d.g.685.8 | yes | 8 | 7.2 | even | 3 | ||
1764.3.z.n.325.1 | 16 | 7.3 | odd | 6 | inner | ||
1764.3.z.n.325.2 | 16 | 21.11 | odd | 6 | inner | ||
1764.3.z.n.325.7 | 16 | 7.4 | even | 3 | inner | ||
1764.3.z.n.325.8 | 16 | 21.17 | even | 6 | inner | ||
1764.3.z.n.901.1 | 16 | 1.1 | even | 1 | trivial | ||
1764.3.z.n.901.2 | 16 | 21.20 | even | 2 | inner | ||
1764.3.z.n.901.7 | 16 | 7.6 | odd | 2 | inner | ||
1764.3.z.n.901.8 | 16 | 3.2 | odd | 2 | inner |