Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1301,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.d (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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.14786560000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 6x^{6} + 22x^{4} - 54x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1301.6 | ||
Root | \(1.30038 - 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1301 |
Dual form | 2100.2.d.k.1301.5 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.30038 | + | 1.14412i | 0.750774 | + | 0.660560i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.23607 | + | 1.41421i | −0.845154 | + | 0.534522i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.381966 | + | 2.97558i | 0.127322 | + | 0.991861i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.13657i | 0.342689i | 0.985211 | + | 0.171345i | \(0.0548112\pi\) | ||||
−0.985211 | + | 0.171345i | \(0.945189\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.333851i | − | 0.0925935i | −0.998928 | − | 0.0462967i | \(-0.985258\pi\) | ||
0.998928 | − | 0.0462967i | \(-0.0147420\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.20811 | −1.02062 | −0.510308 | − | 0.859991i | \(-0.670469\pi\) | ||||
−0.510308 | + | 0.859991i | \(0.670469\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.95440i | − | 0.448369i | −0.974547 | − | 0.224184i | \(-0.928028\pi\) | ||
0.974547 | − | 0.224184i | \(-0.0719718\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.52577 | − | 0.719324i | −0.987603 | − | 0.156969i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.54145i | − | 0.529929i | −0.964258 | − | 0.264965i | \(-0.914640\pi\) | ||
0.964258 | − | 0.264965i | \(-0.0853603\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.90773 | + | 4.30640i | −0.559594 | + | 0.828767i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.49262i | 1.57704i | 0.615009 | + | 0.788520i | \(0.289152\pi\) | ||||
−0.615009 | + | 0.788520i | \(0.710848\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.11667i | 0.918982i | 0.888183 | + | 0.459491i | \(0.151968\pi\) | ||||
−0.888183 | + | 0.459491i | \(0.848032\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.30038 | + | 1.47797i | −0.226367 | + | 0.257282i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.23607 | −0.367607 | −0.183804 | − | 0.982963i | \(-0.558841\pi\) | ||||
−0.183804 | + | 0.982963i | \(0.558841\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.381966 | − | 0.434132i | 0.0611635 | − | 0.0695167i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.81547 | −0.908223 | −0.454112 | − | 0.890945i | \(-0.650043\pi\) | ||||
−0.454112 | + | 0.890945i | \(0.650043\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.527864 | −0.0804985 | −0.0402493 | − | 0.999190i | \(-0.512815\pi\) | ||||
−0.0402493 | + | 0.999190i | \(0.512815\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.42282 | −1.08273 | −0.541365 | − | 0.840788i | \(-0.682092\pi\) | ||||
−0.541365 | + | 0.840788i | \(0.682092\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | − | 6.32456i | 0.428571 | − | 0.903508i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.47214 | − | 4.81460i | −0.766252 | − | 0.674178i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.22431i | − | 1.12970i | −0.825195 | − | 0.564848i | \(-0.808935\pi\) | ||
0.825195 | − | 0.564848i | \(-0.191065\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.23607 | − | 2.54145i | 0.296174 | − | 0.336624i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.59416 | −0.467919 | −0.233960 | − | 0.972246i | \(-0.575168\pi\) | ||||
−0.233960 | + | 0.972246i | \(0.575168\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4412i | 1.46490i | 0.680821 | + | 0.732450i | \(0.261623\pi\) | ||||
−0.680821 | + | 0.732450i | \(0.738377\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.06221 | − | 6.11343i | −0.637779 | − | 0.770219i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.70820 | −0.819538 | −0.409769 | − | 0.912189i | \(-0.634391\pi\) | ||||
−0.409769 | + | 0.912189i | \(0.634391\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.90773 | − | 3.30485i | 0.350050 | − | 0.397857i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.7658i | − | 1.27766i | −0.769347 | − | 0.638831i | \(-0.779418\pi\) | ||
0.769347 | − | 0.638831i | \(-0.220582\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.41421i | − | 0.165521i | −0.996569 | − | 0.0827606i | \(-0.973626\pi\) | ||
0.996569 | − | 0.0827606i | \(-0.0263737\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.60736 | − | 2.54145i | −0.183175 | − | 0.289625i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.47214 | 0.165628 | 0.0828141 | − | 0.996565i | \(-0.473609\pi\) | ||||
0.0828141 | + | 0.996565i | \(0.473609\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.70820 | + | 2.27314i | −0.967578 | + | 0.252572i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.81547 | −0.638330 | −0.319165 | − | 0.947699i | \(-0.603402\pi\) | ||||
−0.319165 | + | 0.947699i | \(0.603402\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.71660 | + | 11.0436i | −1.04173 | + | 1.18400i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.2251 | 1.61386 | 0.806928 | − | 0.590650i | \(-0.201128\pi\) | ||||
0.806928 | + | 0.590650i | \(0.201128\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.472136 | + | 0.746512i | 0.0494933 | + | 0.0782558i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.85410 | + | 6.65361i | −0.607042 | + | 0.689947i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.69316i | 0.984192i | 0.870541 | + | 0.492096i | \(0.163769\pi\) | ||||
−0.870541 | + | 0.492096i | \(0.836231\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.38197 | + | 0.434132i | −0.339900 | + | 0.0436319i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.2251 | −1.51495 | −0.757477 | − | 0.652862i | \(-0.773568\pi\) | ||||
−0.757477 | + | 0.652862i | \(0.773568\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.0162i | 1.47959i | 0.672834 | + | 0.739793i | \(0.265077\pi\) | ||||
−0.672834 | + | 0.739793i | \(0.734923\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 5.08290i | − | 0.491383i | −0.969348 | − | 0.245691i | \(-0.920985\pi\) | ||
0.969348 | − | 0.245691i | \(-0.0790150\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.47214 | 0.715701 | 0.357850 | − | 0.933779i | \(-0.383510\pi\) | ||||
0.357850 | + | 0.933779i | \(0.383510\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.90773 | − | 2.55834i | −0.275990 | − | 0.242827i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.9901i | 1.78644i | 0.449624 | + | 0.893218i | \(0.351558\pi\) | ||||
−0.449624 | + | 0.893218i | \(0.648442\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.993400 | − | 0.127520i | 0.0918399 | − | 0.0117892i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.40962 | − | 5.95117i | 0.862579 | − | 0.545543i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.70820 | 0.882564 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.56231 | − | 6.65361i | −0.681870 | − | 0.599936i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.7082 | −1.48261 | −0.741307 | − | 0.671166i | \(-0.765794\pi\) | ||||
−0.741307 | + | 0.671166i | \(0.765794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.686423 | − | 0.603941i | −0.0604362 | − | 0.0531741i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.40962 | 0.822123 | 0.411061 | − | 0.911608i | \(-0.365158\pi\) | ||||
0.411061 | + | 0.911608i | \(0.365158\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.76393 | + | 4.37016i | 0.239663 | + | 0.378941i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 21.5315i | − | 1.83956i | −0.392431 | − | 0.919781i | \(-0.628366\pi\) | ||
0.392431 | − | 0.919781i | \(-0.371634\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.746512i | 0.0633184i | 0.999499 | + | 0.0316592i | \(0.0100791\pi\) | ||||
−0.999499 | + | 0.0316592i | \(0.989921\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.65248 | − | 8.49262i | −0.812885 | − | 0.715208i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.379445 | 0.0317308 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.1372 | − | 4.79194i | 0.918581 | − | 0.395233i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.54145i | 0.208204i | 0.994567 | + | 0.104102i | \(0.0331968\pi\) | ||||
−0.994567 | + | 0.104102i | \(0.966803\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.65248 | 0.785507 | 0.392754 | − | 0.919644i | \(-0.371523\pi\) | ||||
0.392754 | + | 0.919644i | \(0.371523\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.60736 | − | 12.5216i | −0.129947 | − | 1.01231i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.61280i | 0.687376i | 0.939084 | + | 0.343688i | \(0.111676\pi\) | ||||
−0.939084 | + | 0.343688i | \(0.888324\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.40962 | − | 10.6947i | 0.746232 | − | 0.848146i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.59416 | + | 5.68286i | 0.283259 | + | 0.447872i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.94427 | 0.700569 | 0.350285 | − | 0.936643i | \(-0.386085\pi\) | ||||
0.350285 | + | 0.936643i | \(0.386085\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.0236 | −0.775648 | −0.387824 | − | 0.921733i | \(-0.626773\pi\) | ||||
−0.387824 | + | 0.921733i | \(0.626773\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8885 | 0.991426 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.81547 | − | 0.746512i | 0.444720 | − | 0.0570872i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.19491 | −0.470990 | −0.235495 | − | 0.971876i | \(-0.575671\pi\) | ||||
−0.235495 | + | 0.971876i | \(0.575671\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.67376 | − | 4.11216i | −0.351301 | − | 0.309089i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 13.3072i | − | 0.994628i | −0.867571 | − | 0.497314i | \(-0.834320\pi\) | ||
0.867571 | − | 0.497314i | \(-0.165680\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9799i | 0.816126i | 0.912954 | + | 0.408063i | \(0.133796\pi\) | ||||
−0.912954 | + | 0.408063i | \(0.866204\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.0902 | + | 14.8779i | −0.967653 | + | 1.09981i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.78282i | − | 0.349755i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.411720 | − | 13.7416i | 0.0299482 | − | 0.999551i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3.67802i | − | 0.266133i | −0.991107 | − | 0.133066i | \(-0.957518\pi\) | ||
0.991107 | − | 0.133066i | \(-0.0424823\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.0000 | 1.07972 | 0.539862 | − | 0.841754i | \(-0.318476\pi\) | ||||
0.539862 | + | 0.841754i | \(0.318476\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.7658i | 0.767029i | 0.923535 | + | 0.383515i | \(0.125286\pi\) | ||||
−0.923535 | + | 0.383515i | \(0.874714\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0903i | 1.70772i | 0.520504 | + | 0.853859i | \(0.325744\pi\) | ||||
−0.520504 | + | 0.853859i | \(0.674256\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.72320 | − | 7.67501i | −0.615287 | − | 0.541353i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.0104 | − | 18.9901i | −0.842963 | − | 1.33284i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.56231 | − | 0.970748i | 0.525617 | − | 0.0674717i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.22131 | 0.153651 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.70820 | 0.530655 | 0.265327 | − | 0.964158i | \(-0.414520\pi\) | ||||
0.265327 | + | 0.964158i | \(0.414520\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.3174 | − | 13.9996i | 0.843971 | − | 0.959234i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.23607 | − | 11.4412i | −0.491216 | − | 0.776681i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.61803 | − | 1.83901i | 0.109337 | − | 0.124269i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.40488i | 0.0945025i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.8918i | 1.13116i | 0.824695 | + | 0.565578i | \(0.191347\pi\) | ||||
−0.824695 | + | 0.565578i | \(0.808653\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.3964 | −0.756407 | −0.378204 | − | 0.925722i | \(-0.623458\pi\) | ||||
−0.378204 | + | 0.925722i | \(0.623458\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.2333i | − | 0.676239i | −0.941103 | − | 0.338119i | \(-0.890209\pi\) | ||
0.941103 | − | 0.338119i | \(-0.109791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.817564 | − | 5.14386i | 0.0537917 | − | 0.338441i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.8487i | 1.03828i | 0.854689 | + | 0.519140i | \(0.173748\pi\) | ||||
−0.854689 | + | 0.519140i | \(0.826252\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.91433 | + | 1.68430i | 0.124349 | + | 0.109407i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.4975i | 0.679024i | 0.940602 | + | 0.339512i | \(0.110262\pi\) | ||||
−0.940602 | + | 0.339512i | \(0.889738\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.4211i | 1.44427i | 0.691753 | + | 0.722135i | \(0.256839\pi\) | ||||
−0.691753 | + | 0.722135i | \(0.743161\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.9247 | − | 7.00731i | −0.893271 | − | 0.449519i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.652476 | −0.0415160 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.56231 | − | 6.65361i | −0.479242 | − | 0.421655i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.22131 | 0.140208 | 0.0701039 | − | 0.997540i | \(-0.477667\pi\) | ||||
0.0701039 | + | 0.997540i | \(0.477667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.88854 | 0.181601 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.6347 | 1.53667 | 0.768336 | − | 0.640047i | \(-0.221085\pi\) | ||||
0.768336 | + | 0.640047i | \(0.221085\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.00000 | − | 3.16228i | 0.310685 | − | 0.196494i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −25.2705 | + | 3.24389i | −1.56421 | + | 0.200792i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 15.8487i | − | 0.977271i | −0.872488 | − | 0.488635i | \(-0.837495\pi\) | ||
0.872488 | − | 0.488635i | \(-0.162505\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.7984 | + | 17.4194i | 1.21164 | + | 1.06605i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.8230 | −1.94028 | −0.970142 | − | 0.242537i | \(-0.922020\pi\) | ||||
−0.970142 | + | 0.242537i | \(0.922020\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.1359i | − | 1.34466i | −0.740250 | − | 0.672331i | \(-0.765293\pi\) | ||
0.740250 | − | 0.672331i | \(-0.234707\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.240147 | + | 1.51093i | −0.0145343 | + | 0.0914456i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.29180 | 0.498206 | 0.249103 | − | 0.968477i | \(-0.419864\pi\) | ||||
0.249103 | + | 0.968477i | \(0.419864\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.2251 | + | 1.95440i | −0.911502 | + | 0.117007i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.36088i | − | 0.558424i | −0.960230 | − | 0.279212i | \(-0.909927\pi\) | ||
0.960230 | − | 0.279212i | \(-0.0900732\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 5.91189i | − | 0.351426i | −0.984441 | − | 0.175713i | \(-0.943777\pi\) | ||
0.984441 | − | 0.175713i | \(-0.0562230\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.0038 | − | 8.22431i | 0.767589 | − | 0.485466i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.708204 | 0.0416591 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.0902 | + | 12.6048i | −0.650117 | + | 0.738905i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.6413 | 1.38114 | 0.690570 | − | 0.723265i | \(-0.257360\pi\) | ||||
0.690570 | + | 0.723265i | \(0.257360\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.89453 | − | 3.30485i | −0.284010 | − | 0.191767i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.848465 | −0.0490680 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.18034 | − | 0.746512i | 0.0680337 | − | 0.0430283i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.7984 | − | 17.4194i | −1.13739 | − | 1.00072i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 25.5046i | − | 1.45562i | −0.685778 | − | 0.727811i | \(-0.740538\pi\) | ||
0.685778 | − | 0.727811i | \(-0.259462\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.1803 | + | 19.5267i | −0.977355 | + | 1.11083i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.22131 | 0.125959 | 0.0629795 | − | 0.998015i | \(-0.479940\pi\) | ||||
0.0629795 | + | 0.998015i | \(0.479940\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.78282i | − | 0.270341i | −0.990822 | − | 0.135171i | \(-0.956842\pi\) | ||
0.990822 | − | 0.135171i | \(-0.0431582\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.1559i | 1.63756i | 0.574109 | + | 0.818779i | \(0.305349\pi\) | ||||
−0.574109 | + | 0.818779i | \(0.694651\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.65248 | −0.540435 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.81547 | − | 6.60970i | 0.324588 | − | 0.368917i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.22431i | 0.457613i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.71660 | + | 8.54904i | 0.537329 | + | 0.472763i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.5979 | − | 10.4975i | 0.915074 | − | 0.578744i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.1803 | 1.60390 | 0.801948 | − | 0.597393i | \(-0.203797\pi\) | ||||
0.801948 | + | 0.597393i | \(0.203797\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.854102 | − | 6.65361i | −0.0468045 | − | 0.364616i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0000 | −0.544735 | −0.272367 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272367 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.7270 | + | 24.6943i | −1.18005 | + | 1.34121i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.81547 | −0.314925 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.23607 | + | 18.3848i | 0.120736 | + | 0.992685i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.1559i | 1.56517i | 0.622544 | + | 0.782585i | \(0.286099\pi\) | ||||
−0.622544 | + | 0.782585i | \(0.713901\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.4211i | 1.20017i | 0.799935 | + | 0.600087i | \(0.204867\pi\) | ||||
−0.799935 | + | 0.600087i | \(0.795133\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.43769 | + | 0.970748i | 0.0767384 | + | 0.0518147i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.0509 | 1.75912 | 0.879562 | − | 0.475784i | \(-0.157836\pi\) | ||||
0.879562 | + | 0.475784i | \(0.157836\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.0449 | + | 3.02700i | 1.00796 | + | 0.160206i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.7658i | 0.568195i | 0.958795 | + | 0.284098i | \(0.0916940\pi\) | ||||
−0.958795 | + | 0.284098i | \(0.908306\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.1803 | 0.798965 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.6243 | + | 11.1074i | 0.662606 | + | 0.582986i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.5247i | 0.758183i | 0.925359 | + | 0.379091i | \(0.123763\pi\) | ||||
−0.925359 | + | 0.379091i | \(0.876237\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.22131 | − | 17.3044i | −0.115637 | − | 0.900832i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.6309 | + | 18.3901i | 0.603848 | + | 0.954768i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.6525 | 0.810454 | 0.405227 | − | 0.914216i | \(-0.367192\pi\) | ||||
0.405227 | + | 0.914216i | \(0.367192\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.83527 | 0.146024 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.18034 | −0.266096 | −0.133048 | − | 0.991110i | \(-0.542476\pi\) | ||||
−0.133048 | + | 0.991110i | \(0.542476\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.7270 | − | 19.1162i | −1.11311 | − | 0.979354i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.2251 | −0.777966 | −0.388983 | − | 0.921245i | \(-0.627173\pi\) | ||||
−0.388983 | + | 0.921245i | \(0.627173\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.201626 | − | 1.57070i | −0.0102492 | − | 0.0798434i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.1218i | 0.918812i | 0.888226 | + | 0.459406i | \(0.151938\pi\) | ||||
−0.888226 | + | 0.459406i | \(0.848062\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.6947i | 0.540855i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.2361 | + | 10.7658i | 0.617228 | + | 0.543061i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 39.1853i | − | 1.96665i | −0.181844 | − | 0.983327i | \(-0.558207\pi\) | ||
0.181844 | − | 0.983327i | \(-0.441793\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.40584 | + | 8.84514i | −0.0703802 | + | 0.442811i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3.94633i | − | 0.197070i | −0.995134 | − | 0.0985352i | \(-0.968584\pi\) | ||
0.995134 | − | 0.0985352i | \(-0.0314157\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.70820 | 0.0850917 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.54145i | − | 0.125975i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.8369i | 1.22810i | 0.789266 | + | 0.614052i | \(0.210461\pi\) | ||||
−0.789266 | + | 0.614052i | \(0.789539\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.6347 | − | 27.9991i | 1.21514 | − | 1.38110i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.03678 | − | 5.08290i | 0.395464 | − | 0.250113i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.854102 | + | 0.970748i | −0.0418256 | + | 0.0475378i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.2656 | −1.77169 | −0.885846 | − | 0.463979i | \(-0.846421\pi\) | ||||
−0.885846 | + | 0.463979i | \(0.846421\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.8885 | 0.920571 | 0.460286 | − | 0.887771i | \(-0.347747\pi\) | ||||
0.460286 | + | 0.887771i | \(0.347747\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.83527 | − | 22.0872i | −0.137855 | − | 1.07392i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.1803 | − | 25.5834i | −0.783022 | − | 1.23807i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.493422 | + | 0.434132i | 0.0238226 | + | 0.0209601i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.1607i | 1.50096i | 0.660894 | + | 0.750480i | \(0.270177\pi\) | ||||
−0.660894 | + | 0.750480i | \(0.729823\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 31.3677i | − | 1.50744i | −0.657197 | − | 0.753719i | \(-0.728258\pi\) | ||
0.657197 | − | 0.753719i | \(-0.271742\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.96700 | −0.237604 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 18.2272i | − | 0.869935i | −0.900446 | − | 0.434967i | \(-0.856760\pi\) | ||
0.900446 | − | 0.434967i | \(-0.143240\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.9651 | + | 6.51099i | 0.950721 | + | 0.310047i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.22431i | 0.390749i | 0.980729 | + | 0.195374i | \(0.0625922\pi\) | ||||
−0.980729 | + | 0.195374i | \(0.937408\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.90773 | + | 3.30485i | −0.137531 | + | 0.156314i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.35121i | − | 0.252539i | −0.991996 | − | 0.126270i | \(-0.959700\pi\) | ||
0.991996 | − | 0.126270i | \(-0.0403005\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6.60970i | − | 0.311239i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.5519 | + | 11.0436i | 0.589738 | + | 0.518874i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.3607 | 1.74766 | 0.873829 | − | 0.486233i | \(-0.161629\pi\) | ||||
0.873829 | + | 0.486233i | \(0.161629\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.2361 | − | 18.1218i | 0.571131 | − | 0.845854i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.2251 | 0.709103 | 0.354552 | − | 0.935036i | \(-0.384634\pi\) | ||||
0.354552 | + | 0.935036i | \(0.384634\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6525 | 0.495063 | 0.247531 | − | 0.968880i | \(-0.420381\pi\) | ||||
0.247531 | + | 0.968880i | \(0.420381\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.2487 | 1.16837 | 0.584185 | − | 0.811621i | \(-0.301414\pi\) | ||||
0.584185 | + | 0.811621i | \(0.301414\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.0000 | − | 9.48683i | 0.692636 | − | 0.438061i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.85410 | + | 11.1999i | −0.454053 | + | 0.516064i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 0.599956i | − | 0.0275860i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.4721 | − | 3.14141i | 1.12050 | − | 0.143835i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −41.2327 | −1.88397 | −0.941984 | − | 0.335658i | \(-0.891041\pi\) | ||||
−0.941984 | + | 0.335658i | \(0.891041\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.746512i | 0.0340380i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.82813 | + | 11.5020i | −0.0831827 | + | 0.523360i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.2361 | −0.554469 | −0.277235 | − | 0.960802i | \(-0.589418\pi\) | ||||
−0.277235 | + | 0.960802i | \(0.589418\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.6309 | + | 10.2333i | 0.525969 | + | 0.462768i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.4438i | 0.651839i | 0.945398 | + | 0.325920i | \(0.105674\pi\) | ||||
−0.945398 | + | 0.325920i | \(0.894326\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 35.7379i | − | 1.60955i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.2251 | + | 24.0730i | 0.682939 | + | 1.07982i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −42.6525 | −1.90939 | −0.954694 | − | 0.297591i | \(-0.903817\pi\) | ||||
−0.954694 | + | 0.297591i | \(0.903817\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.0344 | − | 11.4682i | −0.582336 | − | 0.512362i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.41622 | −0.375261 | −0.187630 | − | 0.982240i | \(-0.560081\pi\) | ||||
−0.187630 | + | 0.982240i | \(0.560081\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.7600 | + | 14.7461i | 0.744337 | + | 0.654896i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.4134 | 0.993457 | 0.496728 | − | 0.867906i | \(-0.334535\pi\) | ||||
0.496728 | + | 0.867906i | \(0.334535\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | + | 3.16228i | 0.0884748 | + | 0.139891i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.41641 | + | 5.68286i | 0.371593 | + | 0.250904i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8.43657i | − | 0.371040i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.05573 | − | 7.08774i | −0.353607 | − | 0.311117i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.44262 | 0.194635 | 0.0973174 | − | 0.995253i | \(-0.468974\pi\) | ||||
0.0973174 | + | 0.995253i | \(0.468974\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.48528i | 0.371035i | 0.982641 | + | 0.185518i | \(0.0593962\pi\) | ||||
−0.982641 | + | 0.185518i | \(0.940604\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 21.5315i | − | 0.937928i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.5410 | 0.719175 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.37285 | − | 10.6947i | −0.0595764 | − | 0.464111i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.94150i | 0.0840956i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.2251 | − | 17.3044i | 0.657011 | − | 0.746741i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.18831 | + | 3.40972i | 0.309623 | + | 0.146867i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.6525 | 0.844926 | 0.422463 | − | 0.906380i | \(-0.361166\pi\) | ||||
0.422463 | + | 0.906380i | \(0.361166\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.5623 | + | 14.2780i | −0.539100 | + | 0.612726i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.29180 | −0.140747 | −0.0703735 | − | 0.997521i | \(-0.522419\pi\) | ||||
−0.0703735 | + | 0.997521i | \(0.522419\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −34.0443 | + | 4.37016i | −1.45298 | + | 0.186514i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.5979 | 0.707096 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.29180 | + | 2.08191i | −0.139981 | + | 0.0885320i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 5.68286i | − | 0.240791i | −0.992726 | − | 0.120395i | \(-0.961584\pi\) | ||
0.992726 | − | 0.120395i | \(-0.0384162\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.176228i | 0.00745364i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.47214 | − | 6.21948i | 0.231034 | − | 0.262587i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.0076 | 1.09609 | 0.548044 | − | 0.836450i | \(-0.315373\pi\) | ||||
0.548044 | + | 0.836450i | \(0.315373\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.2574 | − | 17.3982i | 0.682748 | − | 0.730654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 29.1559i | − | 1.22228i | −0.791523 | − | 0.611139i | \(-0.790712\pi\) | ||
0.791523 | − | 0.611139i | \(-0.209288\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.00000 | 0.292941 | 0.146470 | − | 0.989215i | \(-0.453209\pi\) | ||||
0.146470 | + | 0.989215i | \(0.453209\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.20811 | − | 4.78282i | 0.175796 | − | 0.199805i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 7.45363i | − | 0.310299i | −0.987891 | − | 0.155149i | \(-0.950414\pi\) | ||
0.987891 | − | 0.155149i | \(-0.0495859\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.5057 | + | 17.1618i | 0.810628 | + | 0.713222i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.0038 | − | 8.22431i | 0.539488 | − | 0.341202i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.34752 | 0.387135 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.8560 | 1.10847 | 0.554233 | − | 0.832361i | \(-0.313012\pi\) | ||||
0.554233 | + | 0.832361i | \(0.313012\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0000 | 0.412043 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.3174 | + | 13.9996i | −0.506668 | + | 0.575865i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.7928 | −0.935990 | −0.467995 | − | 0.883731i | \(-0.655024\pi\) | ||||
−0.467995 | + | 0.883731i | \(0.655024\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −27.5623 | + | 31.3265i | −1.12805 | + | 1.28211i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 34.5704i | − | 1.41251i | −0.707958 | − | 0.706255i | \(-0.750383\pi\) | ||
0.707958 | − | 0.706255i | \(-0.249617\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.49302i | 0.0609018i | 0.999536 | + | 0.0304509i | \(0.00969431\pi\) | ||||
−0.999536 | + | 0.0304509i | \(0.990306\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.56231 | − | 19.9608i | −0.104345 | − | 0.812868i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.33695i | − | 0.0948540i | −0.998875 | − | 0.0474270i | \(-0.984898\pi\) | ||
0.998875 | − | 0.0474270i | \(-0.0151022\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.10895 | − | 38.4356i | 0.247547 | − | 1.55749i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.47811i | 0.100254i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.23607 | 0.0903139 | 0.0451570 | − | 0.998980i | \(-0.485621\pi\) | ||||
0.0451570 | + | 0.998980i | \(0.485621\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.54145i | 0.102315i | 0.998691 | + | 0.0511575i | \(0.0162911\pi\) | ||||
−0.998691 | + | 0.0511575i | \(0.983709\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 45.5887i | 1.83236i | 0.400763 | + | 0.916182i | \(0.368745\pi\) | ||||
−0.400763 | + | 0.916182i | \(0.631255\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.9445 | + | 7.38987i | 0.439188 | + | 0.296545i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −34.0443 | + | 21.5315i | −1.36396 | + | 0.862643i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.88854 | + | 2.54145i | 0.115357 | + | 0.101496i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.40962 | 0.375186 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.4721 | −1.01403 | −0.507015 | − | 0.861937i | \(-0.669251\pi\) | ||||
−0.507015 | + | 0.861937i | \(0.669251\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.0236 | + | 8.81913i | 0.398401 | + | 0.350529i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.11146 | − | 1.00155i | −0.0836589 | − | 0.0396829i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 32.0344 | − | 4.11216i | 1.26726 | − | 0.162674i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 37.3802i | − | 1.47643i | −0.674566 | − | 0.738215i | \(-0.735669\pi\) | ||
0.674566 | − | 0.738215i | \(-0.264331\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.40492i | 0.292021i | 0.989283 | + | 0.146011i | \(0.0466434\pi\) | ||||
−0.989283 | + | 0.146011i | \(0.953357\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.6385 | −1.47972 | −0.739861 | − | 0.672760i | \(-0.765109\pi\) | ||||
−0.739861 | + | 0.672760i | \(0.765109\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.08502i | − | 0.160351i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.68055 | − | 23.1569i | 0.144252 | − | 0.907589i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 13.3072i | − | 0.520752i | −0.965507 | − | 0.260376i | \(-0.916154\pi\) | ||
0.965507 | − | 0.260376i | \(-0.0838465\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.20811 | − | 0.540182i | 0.164174 | − | 0.0210745i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 26.9461i | − | 1.04967i | −0.851204 | − | 0.524835i | \(-0.824127\pi\) | ||
0.851204 | − | 0.524835i | \(-0.175873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.1877i | 0.474048i | 0.971504 | + | 0.237024i | \(0.0761720\pi\) | ||||
−0.971504 | + | 0.237024i | \(0.923828\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.60736 | + | 1.82688i | −0.0624245 | + | 0.0709500i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.5836 | 0.835720 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.3262 | + | 21.9657i | −0.747196 | + | 0.849242i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.0038 | −0.502005 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.3050 | −1.20672 | −0.603359 | − | 0.797470i | \(-0.706171\pi\) | ||||
−0.603359 | + | 0.797470i | \(0.706171\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.2091 | 1.19946 | 0.599731 | − | 0.800202i | \(-0.295274\pi\) | ||||
0.599731 | + | 0.800202i | \(0.295274\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.7082 | − | 21.6746i | −0.526073 | − | 0.831794i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.8197 | − | 13.0389i | −0.567891 | − | 0.499652i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.2973i | 1.23582i | 0.786248 | + | 0.617911i | \(0.212021\pi\) | ||||
−0.786248 | + | 0.617911i | \(0.787979\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.7082 | − | 13.3072i | 0.446696 | − | 0.507702i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.74569 | −0.104603 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 12.9343i | − | 0.492042i | −0.969264 | − | 0.246021i | \(-0.920877\pi\) | ||
0.969264 | − | 0.246021i | \(-0.0791232\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.94835 | − | 5.75357i | 0.263946 | − | 0.218560i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.4721 | 0.926948 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.1328 | + | 20.6093i | −0.685846 | + | 0.779514i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.48779i | − | 0.245040i | −0.992466 | − | 0.122520i | \(-0.960902\pi\) | ||
0.992466 | − | 0.122520i | \(-0.0390976\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.37016i | 0.164824i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 34.0443 | − | 21.5315i | 1.28037 | − | 0.809777i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.3050 | 0.875236 | 0.437618 | − | 0.899161i | \(-0.355822\pi\) | ||||
0.437618 | + | 0.899161i | \(0.355822\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.562306 | + | 4.38046i | 0.0210881 | + | 0.164280i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.0038 | 0.486995 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.0104 | + | 13.6507i | −0.448536 | + | 0.509793i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.8230 | 1.18680 | 0.593399 | − | 0.804908i | \(-0.297786\pi\) | ||||
0.593399 | + | 0.804908i | \(0.297786\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.2361 | − | 33.5772i | −0.790872 | − | 1.25048i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.6525 | + | 29.1559i | −0.954026 | + | 1.08432i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.0810i | 1.11564i | 0.829961 | + | 0.557822i | \(0.188363\pi\) | ||||
−0.829961 | + | 0.557822i | \(0.811637\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.0902 | − | 25.0437i | −0.373710 | − | 0.927546i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.22131 | 0.0821581 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.1189i | 1.29715i | 0.761152 | + | 0.648573i | \(0.224634\pi\) | ||||
−0.761152 | + | 0.648573i | \(0.775366\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 7.62436i | − | 0.280847i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.5967 | −1.34623 | −0.673117 | − | 0.739536i | \(-0.735045\pi\) | ||||
−0.673117 | + | 0.739536i | \(0.735045\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.848465 | − | 0.746512i | −0.0311691 | − | 0.0274238i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.3072i | − | 0.488194i | −0.969751 | − | 0.244097i | \(-0.921508\pi\) | ||
0.969751 | − | 0.244097i | \(-0.0784916\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.22131 | − | 17.3044i | −0.0812735 | − | 0.633135i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.18831 | + | 11.3657i | 0.262655 | + | 0.415294i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.12461 | −0.0410377 | −0.0205188 | − | 0.999789i | \(-0.506532\pi\) | ||||
−0.0205188 | + | 0.999789i | \(0.506532\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.88854 | + | 2.54145i | 0.105264 | + | 0.0926157i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.2361 | −0.808184 | −0.404092 | − | 0.914718i | \(-0.632412\pi\) | ||||
−0.404092 | + | 0.914718i | \(0.632412\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.75620 | + | 3.30485i | 0.136341 | + | 0.119958i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.18831 | −0.260576 | −0.130288 | − | 0.991476i | \(-0.541590\pi\) | ||||
−0.130288 | + | 0.991476i | \(0.541590\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.7082 | + | 10.5672i | −0.604878 | + | 0.382558i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.19991i | 0.0433263i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.62365i | 0.130672i | 0.997863 | + | 0.0653360i | \(0.0208119\pi\) | ||||
−0.997863 | + | 0.0653360i | \(0.979188\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.0344 | + | 28.1851i | 1.15369 | + | 1.01506i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.4068 | 0.841884 | 0.420942 | − | 0.907087i | \(-0.361700\pi\) | ||||
0.420942 | + | 0.907087i | \(0.361700\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.1199 | + | 1.60846i | 0.363050 | + | 0.0577031i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.3657i | 0.407219i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.2361 | 0.437841 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −36.5726 | − | 24.6943i | −1.30700 | − | 0.882502i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.32611i | 0.261148i | 0.991439 | + | 0.130574i | \(0.0416819\pi\) | ||||
−0.991439 | + | 0.130574i | \(0.958318\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.1328 | − | 20.6093i | 0.645546 | − | 0.733709i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.8560 | − | 42.4631i | −0.954890 | − | 1.50981i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.81966 | 0.135640 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.6583 | −1.22766 | −0.613830 | − | 0.789438i | \(-0.710372\pi\) | ||||
−0.613830 | + | 0.789438i | \(0.710372\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.2361 | 1.10505 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.81547 | + | 45.3035i | 0.205479 | + | 1.60072i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.60736 | 0.0567223 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −41.3820 | − | 36.4095i | −1.45671 | − | 1.28167i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.7998i | 0.766442i | 0.923657 | + | 0.383221i | \(0.125185\pi\) | ||||
−0.923657 | + | 0.383221i | \(0.874815\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.40182i | − | 0.189683i | −0.995492 | − | 0.0948417i | \(-0.969766\pi\) | ||
0.995492 | − | 0.0948417i | \(-0.0302345\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.3262 | − | 28.7851i | 0.888230 | − | 1.00954i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.03165i | 0.0360930i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.04097 | + | 1.69002i | −0.0713173 | + | 0.0590542i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.5753i | 1.27649i | 0.769835 | + | 0.638243i | \(0.220338\pi\) | ||||
−0.769835 | + | 0.638243i | \(0.779662\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.3607 | 0.605155 | 0.302578 | − | 0.953125i | \(-0.402153\pi\) | ||||
0.302578 | + | 0.953125i | \(0.402153\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.62436i | 0.265125i | 0.991175 | + | 0.132562i | \(0.0423205\pi\) | ||||
−0.991175 | + | 0.132562i | \(0.957679\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.5772i | 1.16618i | 0.812406 | + | 0.583092i | \(0.198157\pi\) | ||||
−0.812406 | + | 0.583092i | \(0.801843\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.7825 | + | 9.48683i | 0.374040 | + | 0.329095i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.6243 | + | 26.6144i | −0.437407 | + | 0.922136i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.0344 | − | 14.8779i | −0.761622 | − | 0.514256i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.6677 | 0.679005 | 0.339502 | − | 0.940605i | \(-0.389741\pi\) | ||||
0.339502 | + | 0.940605i | \(0.389741\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −43.1246 | −1.48706 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.7100 | − | 12.1727i | 0.368872 | − | 0.419250i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.7082 | + | 13.7295i | −0.745903 | + | 0.471750i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.76393 | − | 7.68770i | 0.232138 | − | 0.263841i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.68286i | 0.194806i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 23.1375i | − | 0.792213i | −0.918205 | − | 0.396106i | \(-0.870361\pi\) | ||
0.918205 | − | 0.396106i | \(-0.129639\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.6347 | −0.841506 | −0.420753 | − | 0.907175i | \(-0.638234\pi\) | ||||
−0.420753 | + | 0.907175i | \(0.638234\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 52.6598i | − | 1.79673i | −0.439252 | − | 0.898364i | \(-0.644757\pi\) | ||
0.439252 | − | 0.898364i | \(-0.355243\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.3195 | + | 4.18321i | 0.896965 | + | 0.142563i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 40.5216i | − | 1.37937i | −0.724109 | − | 0.689686i | \(-0.757749\pi\) | ||
0.724109 | − | 0.689686i | \(-0.242251\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.920933 | + | 0.810272i | 0.0312765 | + | 0.0275183i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.67319i | 0.0567590i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.23954i | 0.0758838i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −28.8428 | + | 3.70246i | −0.976182 | + | 0.125309i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.5279 | 0.524339 | 0.262169 | − | 0.965022i | \(-0.415562\pi\) | ||||
0.262169 | + | 0.965022i | \(0.415562\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.7426 | + | 27.0486i | 1.03692 | + | 0.912326i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.37285 | 0.0462523 | 0.0231262 | − | 0.999733i | \(-0.492638\pi\) | ||||
0.0231262 | + | 0.999733i | \(0.492638\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.11146 | 0.239320 | 0.119660 | − | 0.992815i | \(-0.461820\pi\) | ||||
0.119660 | + | 0.992815i | \(0.461820\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −47.8966 | −1.60821 | −0.804105 | − | 0.594487i | \(-0.797355\pi\) | ||||
−0.804105 | + | 0.594487i | \(0.797355\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.3607 | − | 23.6290i | 1.25304 | − | 0.792490i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.58359 | − | 9.89750i | −0.0865536 | − | 0.331579i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.5071i | 0.485463i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.10333 | − | 0.970748i | −0.0368390 | − | 0.0324123i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −43.4540 | −1.44927 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.6088i | 1.15299i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.38899 | + | 0.379705i | 0.0795006 | + | 0.0126358i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.3050 | 0.707419 | 0.353710 | − | 0.935355i | \(-0.384920\pi\) | ||||
0.353710 | + | 0.935355i | \(0.384920\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.81547 | − | 45.3035i | −0.192887 | − | 1.50262i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.4387i | 1.17414i | 0.809537 | + | 0.587068i | \(0.199718\pi\) | ||||
−0.809537 | + | 0.587068i | \(0.800282\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 6.60970i | − | 0.218749i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.0406 | + | 13.3072i | −0.694820 | + | 0.439443i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.3050 | −1.13162 | −0.565808 | − | 0.824537i | \(-0.691436\pi\) | ||||
−0.565808 | + | 0.824537i | \(0.691436\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.1803 | − | 33.1656i | 0.961525 | − | 1.09284i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.59416 | −0.118303 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −44.6819 | + | 5.73567i | −1.46755 | + | 0.188384i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.2251 | 0.499519 | 0.249760 | − | 0.968308i | \(-0.419648\pi\) | ||||
0.249760 | + | 0.968308i | \(0.419648\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.3607 | − | 5.86319i | −0.405105 | − | 0.192158i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.88854 | + | 2.54145i | 0.0945667 | + | 0.0832034i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.3020i | 1.44728i | 0.690176 | + | 0.723641i | \(0.257533\pi\) | ||||
−0.690176 | + | 0.723641i | \(0.742467\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.47214 | − | 6.21948i | 0.178576 | − | 0.202965i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.2656 | −1.18223 | −0.591113 | − | 0.806589i | \(-0.701311\pi\) | ||||
−0.591113 | + | 0.806589i | \(0.701311\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.7797i | 0.481294i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 6.28282i | − | 0.204164i | −0.994776 | − | 0.102082i | \(-0.967450\pi\) | ||
0.994776 | − | 0.102082i | \(-0.0325504\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.472136 | −0.0153262 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.3579 | + | 37.9137i | −1.08170 | + | 1.22944i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 47.5460i | − | 1.54017i | −0.637944 | − | 0.770083i | \(-0.720215\pi\) | ||
0.637944 | − | 0.770083i | \(-0.279785\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.5519 | − | 11.0436i | −0.405744 | − | 0.356989i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30.4502 | + | 48.1460i | 0.983288 | + | 1.55471i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.81966 | 0.155473 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.1246 | − | 1.94150i | 0.487384 | − | 0.0625639i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.0689 | −1.41716 | −0.708580 | − | 0.705631i | \(-0.750664\pi\) | ||||
−0.708580 | + | 0.705631i | \(0.750664\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.40962 | + | 10.6947i | −0.302281 | + | 0.343564i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.0481 | 1.50985 | 0.754923 | − | 0.655813i | \(-0.227674\pi\) | ||||
0.754923 | + | 0.655813i | \(0.227674\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.05573 | − | 1.66925i | −0.0338451 | − | 0.0535138i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 7.62436i | − | 0.243925i | −0.992535 | − | 0.121962i | \(-0.961081\pi\) | ||
0.992535 | − | 0.121962i | \(-0.0389187\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.3044i | 0.553051i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.85410 | + | 22.2340i | 0.0911245 | + | 0.709876i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.58756 | 0.146320 | 0.0731602 | − | 0.997320i | \(-0.476692\pi\) | ||||
0.0731602 | + | 0.997320i | \(0.476692\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 33.5940 | + | 5.33942i | 1.06931 | + | 0.169955i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.34154i | 0.0426585i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.7214 | −1.00766 | −0.503831 | − | 0.863802i | \(-0.668077\pi\) | ||||
−0.503831 | + | 0.863802i | \(0.668077\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 37.9455 | + | 33.3859i | 1.20416 | + | 1.05947i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 60.1134i | 1.90381i | 0.306394 | + | 0.951905i | \(0.400878\pi\) | ||||
−0.306394 | + | 0.951905i | \(0.599122\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.50189 | − | 9.62940i | 0.205711 | − | 0.304661i |
(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 | 2100.2.d.k.1301.6 | yes | 8 | |
3.2 | odd | 2 | inner | 2100.2.d.k.1301.4 | yes | 8 | |
5.2 | odd | 4 | 2100.2.f.i.1049.13 | 16 | |||
5.3 | odd | 4 | 2100.2.f.i.1049.4 | 16 | |||
5.4 | even | 2 | 2100.2.d.l.1301.3 | yes | 8 | ||
7.6 | odd | 2 | inner | 2100.2.d.k.1301.3 | ✓ | 8 | |
15.2 | even | 4 | 2100.2.f.i.1049.15 | 16 | |||
15.8 | even | 4 | 2100.2.f.i.1049.2 | 16 | |||
15.14 | odd | 2 | 2100.2.d.l.1301.5 | yes | 8 | ||
21.20 | even | 2 | inner | 2100.2.d.k.1301.5 | yes | 8 | |
35.13 | even | 4 | 2100.2.f.i.1049.14 | 16 | |||
35.27 | even | 4 | 2100.2.f.i.1049.3 | 16 | |||
35.34 | odd | 2 | 2100.2.d.l.1301.6 | yes | 8 | ||
105.62 | odd | 4 | 2100.2.f.i.1049.1 | 16 | |||
105.83 | odd | 4 | 2100.2.f.i.1049.16 | 16 | |||
105.104 | even | 2 | 2100.2.d.l.1301.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.d.k.1301.3 | ✓ | 8 | 7.6 | odd | 2 | inner | |
2100.2.d.k.1301.4 | yes | 8 | 3.2 | odd | 2 | inner | |
2100.2.d.k.1301.5 | yes | 8 | 21.20 | even | 2 | inner | |
2100.2.d.k.1301.6 | yes | 8 | 1.1 | even | 1 | trivial | |
2100.2.d.l.1301.3 | yes | 8 | 5.4 | even | 2 | ||
2100.2.d.l.1301.4 | yes | 8 | 105.104 | even | 2 | ||
2100.2.d.l.1301.5 | yes | 8 | 15.14 | odd | 2 | ||
2100.2.d.l.1301.6 | yes | 8 | 35.34 | odd | 2 | ||
2100.2.f.i.1049.1 | 16 | 105.62 | odd | 4 | |||
2100.2.f.i.1049.2 | 16 | 15.8 | even | 4 | |||
2100.2.f.i.1049.3 | 16 | 35.27 | even | 4 | |||
2100.2.f.i.1049.4 | 16 | 5.3 | odd | 4 | |||
2100.2.f.i.1049.13 | 16 | 5.2 | odd | 4 | |||
2100.2.f.i.1049.14 | 16 | 35.13 | even | 4 | |||
2100.2.f.i.1049.15 | 16 | 15.2 | even | 4 | |||
2100.2.f.i.1049.16 | 16 | 105.83 | odd | 4 |