Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,3,Mod(127,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.b (of order \(2\), degree \(1\), 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: | \(20.9264843029\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.127 |
Dual form | 768.3.b.d.127.1 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.92820i | 0.985641i | 0.870131 | + | 0.492820i | \(0.164034\pi\) | ||||
−0.870131 | + | 0.492820i | \(0.835966\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.92820i | 0.418315i | 0.977882 | + | 0.209157i | \(0.0670721\pi\) | ||||
−0.977882 | + | 0.209157i | \(0.932928\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.9282 | 1.35711 | 0.678555 | − | 0.734550i | \(-0.262607\pi\) | ||||
0.678555 | + | 0.734550i | \(0.262607\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 23.8564i | − 1.83511i | −0.397611 | − | 0.917554i | \(-0.630161\pi\) | ||||
0.397611 | − | 0.917554i | \(-0.369839\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 8.53590i | − 0.569060i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −19.8564 | −1.16802 | −0.584012 | − | 0.811745i | \(-0.698518\pi\) | ||||
−0.584012 | + | 0.811745i | \(0.698518\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 30.9282 | 1.62780 | 0.813900 | − | 0.581005i | \(-0.197340\pi\) | ||||
0.813900 | + | 0.581005i | \(0.197340\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 5.07180i | − 0.241514i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 8.00000i | − 0.347826i | −0.984761 | − | 0.173913i | \(-0.944359\pi\) | ||||
0.984761 | − | 0.173913i | \(-0.0556412\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.712813 | 0.0285125 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 16.9282i | 0.583731i | 0.956459 | + | 0.291866i | \(0.0942760\pi\) | ||||
−0.956459 | + | 0.291866i | \(0.905724\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.6410i | 1.24648i | 0.782029 | + | 0.623242i | \(0.214185\pi\) | ||||
−0.782029 | + | 0.623242i | \(0.785815\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −25.8564 | −0.783527 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −14.4308 | −0.412308 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 9.71281i | − 0.262508i | −0.991349 | − | 0.131254i | \(-0.958100\pi\) | ||||
0.991349 | − | 0.131254i | \(-0.0419004\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 41.3205i | 1.05950i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.14359 | 0.198624 | 0.0993121 | − | 0.995056i | \(-0.468336\pi\) | ||||
0.0993121 | + | 0.995056i | \(0.468336\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.35898 | −0.124628 | −0.0623138 | − | 0.998057i | \(-0.519848\pi\) | ||||
−0.0623138 | + | 0.998057i | \(0.519848\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 14.7846i | 0.328547i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 69.8564i | 1.48631i | 0.669121 | + | 0.743153i | \(0.266671\pi\) | ||||
−0.669121 | + | 0.743153i | \(0.733329\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 40.4256 | 0.825013 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 34.3923 | 0.674359 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 0.928203i | − 0.0175133i | −0.999962 | − | 0.00875663i | \(-0.997213\pi\) | ||||
0.999962 | − | 0.00875663i | \(-0.00278736\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 73.5692i | 1.33762i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −53.5692 | −0.939811 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 108.210 | 1.83407 | 0.917036 | − | 0.398805i | \(-0.130575\pi\) | ||||
0.917036 | + | 0.398805i | \(0.130575\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.0000i | 0.229508i | 0.993394 | + | 0.114754i | \(0.0366080\pi\) | ||||
−0.993394 | + | 0.114754i | \(0.963392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.78461i | 0.139438i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 117.569 | 1.80876 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16.4974 | 0.246230 | 0.123115 | − | 0.992392i | \(-0.460712\pi\) | ||||
0.123115 | + | 0.992392i | \(0.460712\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.8564i | 0.200817i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 43.1384i | 0.607584i | 0.952738 | + | 0.303792i | \(0.0982527\pi\) | ||||
−0.952738 | + | 0.303792i | \(0.901747\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −25.4256 | −0.348296 | −0.174148 | − | 0.984719i | \(-0.555717\pi\) | ||||
−0.174148 | + | 0.984719i | \(0.555717\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.23463 | −0.0164617 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 43.7128i | 0.567699i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 96.7846i | − 1.22512i | −0.790423 | − | 0.612561i | \(-0.790139\pi\) | ||||
0.790423 | − | 0.612561i | \(-0.209861\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 62.9282 | 0.758171 | 0.379086 | − | 0.925362i | \(-0.376239\pi\) | ||||
0.379086 | + | 0.925362i | \(0.376239\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 97.8564i | − 1.15125i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 29.3205i | − 0.337017i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 50.2872 | 0.565025 | 0.282512 | − | 0.959264i | \(-0.408832\pi\) | ||||
0.282512 | + | 0.959264i | \(0.408832\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 69.8564 | 0.767653 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 66.9282i | − 0.719658i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 152.420i | 1.60443i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −145.138 | −1.49627 | −0.748136 | − | 0.663545i | \(-0.769051\pi\) | ||||
−0.748136 | + | 0.663545i | \(0.769051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 44.7846 | 0.452370 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 159.072i | 1.57497i | 0.616335 | + | 0.787484i | \(0.288617\pi\) | ||||
−0.616335 | + | 0.787484i | \(0.711383\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 24.7846i | 0.240627i | 0.992736 | + | 0.120314i | \(0.0383900\pi\) | ||||
−0.992736 | + | 0.120314i | \(0.961610\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 24.9948 | 0.238046 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −42.0666 | −0.393146 | −0.196573 | − | 0.980489i | \(-0.562981\pi\) | ||||
−0.196573 | + | 0.980489i | \(0.562981\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.8564i | 0.182169i | 0.995843 | + | 0.0910844i | \(0.0290333\pi\) | ||||
−0.995843 | + | 0.0910844i | \(0.970967\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.8231i | 0.151559i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.13844 | −0.0100747 | −0.00503734 | − | 0.999987i | \(-0.501603\pi\) | ||||
−0.00503734 | + | 0.999987i | \(0.501603\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 39.4256 | 0.342832 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 71.5692i | − 0.611703i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 58.1436i | − 0.488602i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 101.851 | 0.841746 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.1051 | −0.114676 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 126.718i | 1.01374i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 171.349i | 1.34920i | 0.738182 | + | 0.674601i | \(0.235684\pi\) | ||||
−0.738182 | + | 0.674601i | \(0.764316\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.28203 | 0.0719537 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 57.0718 | 0.435663 | 0.217831 | − | 0.975986i | \(-0.430102\pi\) | ||||
0.217831 | + | 0.975986i | \(0.430102\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 90.5641i | 0.680933i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 25.6077i | − 0.189687i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 154.133 | 1.12506 | 0.562530 | − | 0.826777i | \(-0.309828\pi\) | ||||
0.562530 | + | 0.826777i | \(0.309828\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 167.923 | 1.20808 | 0.604040 | − | 0.796954i | \(-0.293557\pi\) | ||||
0.604040 | + | 0.796954i | \(0.293557\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 120.995i | − 0.858119i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 356.133i | − 2.49044i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −83.4256 | −0.575349 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −70.0192 | −0.476321 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 124.354i | 0.834589i | 0.908771 | + | 0.417295i | \(0.137022\pi\) | ||||
−0.908771 | + | 0.417295i | \(0.862978\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 48.2102i | − 0.319273i | −0.987176 | − | 0.159637i | \(-0.948968\pi\) | ||||
0.987176 | − | 0.159637i | \(-0.0510322\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −59.5692 | −0.389341 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −190.431 | −1.22859 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 166.287i | − 1.05915i | −0.848262 | − | 0.529577i | \(-0.822351\pi\) | ||||
0.848262 | − | 0.529577i | \(-0.177649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.60770i | 0.0101113i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 23.4256 | 0.145501 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −31.9230 | −0.195847 | −0.0979235 | − | 0.995194i | \(-0.531220\pi\) | ||||
−0.0979235 | + | 0.995194i | \(0.531220\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 127.426i | − 0.772277i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 210.144i | 1.25834i | 0.777266 | + | 0.629172i | \(0.216606\pi\) | ||||
−0.777266 | + | 0.629172i | \(0.783394\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −400.128 | −2.36762 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 92.7846 | 0.542600 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 163.779i | − 0.946702i | −0.880874 | − | 0.473351i | \(-0.843044\pi\) | ||||
0.880874 | − | 0.473351i | \(-0.156956\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.08726i | 0.0119272i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −187.426 | −1.05890 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −186.067 | −1.03948 | −0.519739 | − | 0.854325i | \(-0.673971\pi\) | ||||
−0.519739 | + | 0.854325i | \(0.673971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 42.9948i | 0.237541i | 0.992922 | + | 0.118770i | \(0.0378952\pi\) | ||||
−0.992922 | + | 0.118770i | \(0.962105\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 24.2487i | − 0.132507i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 47.8667 | 0.258739 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −296.420 | −1.58514 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 15.2154i | − 0.0805047i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 87.4256i | 0.457726i | 0.973459 | + | 0.228863i | \(0.0735007\pi\) | ||||
−0.973459 | + | 0.228863i | \(0.926499\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.5744 | 0.137691 | 0.0688455 | − | 0.997627i | \(-0.478068\pi\) | ||||
0.0688455 | + | 0.997627i | \(0.478068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −203.636 | −1.04429 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 251.492i | − 1.27661i | −0.769783 | − | 0.638305i | \(-0.779636\pi\) | ||||
0.769783 | − | 0.638305i | \(-0.220364\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 68.0770i | − 0.342095i | −0.985263 | − | 0.171048i | \(-0.945285\pi\) | ||||
0.985263 | − | 0.171048i | \(-0.0547152\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −28.5744 | −0.142161 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −49.5692 | −0.244183 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 40.1333i | 0.195772i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 24.0000i | − 0.115942i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 461.703 | 2.20910 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −258.641 | −1.22579 | −0.612893 | − | 0.790166i | \(-0.709995\pi\) | ||||
−0.612893 | + | 0.790166i | \(0.709995\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 74.7180i | − 0.350789i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 26.4102i | − 0.122838i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −113.149 | −0.521423 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 44.0385 | 0.201089 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 473.703i | 2.14345i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.21024i | 0.0368172i | 0.999831 | + | 0.0184086i | \(0.00585997\pi\) | ||||
−0.999831 | + | 0.0184086i | \(0.994140\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.13844 | 0.00950417 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 238.928 | 1.05255 | 0.526274 | − | 0.850315i | \(-0.323589\pi\) | ||||
0.526274 | + | 0.850315i | \(0.323589\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 181.846i | − 0.794088i | −0.917800 | − | 0.397044i | \(-0.870036\pi\) | ||||
0.917800 | − | 0.397044i | \(-0.129964\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 75.7128i | − 0.327761i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 385.138 | 1.65295 | 0.826477 | − | 0.562970i | \(-0.190341\pi\) | ||||
0.826477 | + | 0.562970i | \(0.190341\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −344.267 | −1.46496 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 167.636i | 0.707324i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 403.979i | − 1.69029i | −0.534537 | − | 0.845145i | \(-0.679514\pi\) | ||||
0.534537 | − | 0.845145i | \(-0.320486\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −51.4359 | −0.213427 | −0.106714 | − | 0.994290i | \(-0.534033\pi\) | ||||
−0.106714 | + | 0.994290i | \(0.534033\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 199.226i | 0.813166i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 737.836i | − 2.98719i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −108.995 | −0.437730 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.21024 | −0.0167738 | −0.00838692 | − | 0.999965i | \(-0.502670\pi\) | ||||
−0.00838692 | + | 0.999965i | \(0.502670\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 119.426i | − 0.472038i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 169.492i | 0.664676i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −91.7025 | −0.356819 | −0.178410 | − | 0.983956i | \(-0.557095\pi\) | ||||
−0.178410 | + | 0.983956i | \(0.557095\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.4411 | 0.109811 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 50.7846i | 0.194577i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 269.856i | − 1.02607i | −0.858368 | − | 0.513035i | \(-0.828521\pi\) | ||||
0.858368 | − | 0.513035i | \(-0.171479\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.57437 | 0.0172618 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −87.1000 | −0.326217 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 200.354i | 0.744810i | 0.928070 | + | 0.372405i | \(0.121467\pi\) | ||||
−0.928070 | + | 0.372405i | \(0.878533\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 497.205i | − 1.83471i | −0.398076 | − | 0.917353i | \(-0.630322\pi\) | ||||
0.398076 | − | 0.917353i | \(-0.369678\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −120.995 | −0.443205 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.6410 | 0.0386946 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 257.559i | − 0.929816i | −0.885359 | − | 0.464908i | \(-0.846087\pi\) | ||||
0.885359 | − | 0.464908i | \(-0.153913\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 115.923i | 0.415495i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −194.000 | −0.690391 | −0.345196 | − | 0.938531i | \(-0.612187\pi\) | ||||
−0.345196 | + | 0.938531i | \(0.612187\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 332.210 | 1.17389 | 0.586944 | − | 0.809628i | \(-0.300331\pi\) | ||||
0.586944 | + | 0.809628i | \(0.300331\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 264.000i | − 0.926316i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.8461i | 0.0830874i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 105.277 | 0.364280 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 251.387 | 0.863873 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 465.902i | 1.59011i | 0.606537 | + | 0.795055i | \(0.292558\pi\) | ||||
−0.606537 | + | 0.795055i | \(0.707442\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 533.282i | 1.80774i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −77.5692 | −0.261176 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −190.851 | −0.638299 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 15.6922i | − 0.0521335i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 275.520i | − 0.909308i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −68.9948 | −0.226213 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −215.769 | −0.702831 | −0.351416 | − | 0.936220i | \(-0.614300\pi\) | ||||
−0.351416 | + | 0.936220i | \(0.614300\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 42.9282i | − 0.138926i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 175.005i | − 0.562718i | −0.959603 | − | 0.281359i | \(-0.909215\pi\) | ||||
0.959603 | − | 0.281359i | \(-0.0907851\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 433.979 | 1.38652 | 0.693258 | − | 0.720690i | \(-0.256175\pi\) | ||||
0.693258 | + | 0.720690i | \(0.256175\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −43.2923 | −0.137436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 88.4871i | − 0.279139i | −0.990212 | − | 0.139570i | \(-0.955428\pi\) | ||||
0.990212 | − | 0.139570i | \(-0.0445719\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 252.708i | 0.792187i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 72.8616 | 0.226983 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −614.123 | −1.90131 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 17.0052i | − 0.0523236i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 34.3923i | − 0.105175i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −204.554 | −0.621744 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 107.061 | 0.323449 | 0.161724 | − | 0.986836i | \(-0.448294\pi\) | ||||
0.161724 | + | 0.986836i | \(0.448294\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 29.1384i | − 0.0875028i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 81.3027i | 0.242694i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −38.5744 | −0.114464 | −0.0572320 | − | 0.998361i | \(-0.518227\pi\) | ||||
−0.0572320 | + | 0.998361i | \(0.518227\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.97183 | 0.00581662 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 576.841i | 1.69162i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 261.856i | 0.763430i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −68.2872 | −0.197934 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −65.9127 | −0.189950 | −0.0949751 | − | 0.995480i | \(-0.530277\pi\) | ||||
−0.0949751 | + | 0.995480i | \(0.530277\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 367.703i | − 1.05359i | −0.849993 | − | 0.526794i | \(-0.823394\pi\) | ||||
0.849993 | − | 0.526794i | \(-0.176606\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 123.962i | 0.353167i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 158.862 | 0.450033 | 0.225016 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225016 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −212.595 | −0.598859 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 100.708i | 0.282094i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 140.287i | − 0.390772i | −0.980726 | − | 0.195386i | \(-0.937404\pi\) | ||||
0.980726 | − | 0.195386i | \(-0.0625960\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 595.554 | 1.64973 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −176.412 | −0.485982 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 125.303i | − 0.343295i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 505.051i | − 1.37616i | −0.725634 | − | 0.688081i | \(-0.758454\pi\) | ||||
0.725634 | − | 0.688081i | \(-0.241546\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 24.4308 | 0.0662081 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.71797 | 0.00732606 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 215.128i | 0.576751i | 0.957517 | + | 0.288376i | \(0.0931151\pi\) | ||||
−0.957517 | + | 0.288376i | \(0.906885\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 219.482i | − 0.585285i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 403.846 | 1.07121 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −204.785 | −0.540329 | −0.270164 | − | 0.962814i | \(-0.587078\pi\) | ||||
−0.270164 | + | 0.962814i | \(0.587078\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 296.785i | − 0.778962i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 588.554i | 1.53669i | 0.640034 | + | 0.768347i | \(0.278920\pi\) | ||||
−0.640034 | + | 0.768347i | \(0.721080\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −215.426 | −0.559547 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −16.0770 | −0.0415425 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 534.477i | − 1.37398i | −0.726669 | − | 0.686988i | \(-0.758932\pi\) | ||||
0.726669 | − | 0.686988i | \(-0.241068\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 158.851i | 0.406269i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −98.8513 | −0.251530 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 476.974 | 1.20753 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 340.277i | 0.857121i | 0.903513 | + | 0.428560i | \(0.140979\pi\) | ||||
−0.903513 | + | 0.428560i | \(0.859021\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 156.862i | − 0.393137i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −300.123 | −0.748436 | −0.374218 | − | 0.927341i | \(-0.622089\pi\) | ||||
−0.374218 | + | 0.927341i | \(0.622089\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 921.836 | 2.28743 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 44.3538i | 0.109516i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 144.995i | − 0.356253i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −513.692 | −1.25597 | −0.627986 | − | 0.778225i | \(-0.716120\pi\) | ||||
−0.627986 | + | 0.778225i | \(0.716120\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −266.967 | −0.649554 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 316.862i | 0.767219i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 310.123i | 0.747284i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −290.851 | −0.697485 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −91.9437 | −0.219436 | −0.109718 | − | 0.993963i | \(-0.534995\pi\) | ||||
−0.109718 | + | 0.993963i | \(0.534995\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 513.559i | − 1.21985i | −0.792457 | − | 0.609927i | \(-0.791199\pi\) | ||||
0.792457 | − | 0.609927i | \(-0.208801\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 209.569i | 0.495436i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.1539 | −0.0333033 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −40.9948 | −0.0960067 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 616.841i | 1.43786i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 446.123i | 1.03509i | 0.855657 | + | 0.517544i | \(0.173154\pi\) | ||||
−0.855657 | + | 0.517544i | \(0.826846\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 43.7231 | 0.100977 | 0.0504886 | − | 0.998725i | \(-0.483922\pi\) | ||||
0.0504886 | + | 0.998725i | \(0.483922\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 144.497 | 0.332178 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 247.426i | − 0.566191i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 381.072i | 0.868045i | 0.900902 | + | 0.434023i | \(0.142906\pi\) | ||||
−0.900902 | + | 0.434023i | \(0.857094\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 121.277 | 0.275004 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 181.513 | 0.409736 | 0.204868 | − | 0.978790i | \(-0.434324\pi\) | ||||
0.204868 | + | 0.978790i | \(0.434324\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 247.825i | 0.556911i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 215.387i | − 0.481850i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 397.825 | 0.886026 | 0.443013 | − | 0.896515i | \(-0.353910\pi\) | ||||
0.443013 | + | 0.896515i | \(0.353910\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 121.569 | 0.269555 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 83.5026i | 0.184332i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 344.267i | 0.756630i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −526.862 | −1.15287 | −0.576435 | − | 0.817143i | \(-0.695557\pi\) | ||||
−0.576435 | + | 0.817143i | \(0.695557\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 103.177 | 0.224786 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 888.908i | − 1.92822i | −0.265510 | − | 0.964108i | \(-0.585540\pi\) | ||||
0.265510 | − | 0.964108i | \(-0.414460\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 515.923i | 1.11430i | 0.830410 | + | 0.557152i | \(0.188106\pi\) | ||||
−0.830410 | + | 0.557152i | \(0.811894\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 329.836 | 0.709324 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 439.195 | 0.940460 | 0.470230 | − | 0.882544i | \(-0.344171\pi\) | ||||
0.470230 | + | 0.882544i | \(0.344171\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 48.3078i | 0.103002i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 288.018i | 0.611503i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −80.0000 | −0.169133 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.0460 | 0.0464127 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 2.78461i | − 0.00583776i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 179.559i | 0.374862i | 0.982278 | + | 0.187431i | \(0.0600161\pi\) | ||||
−0.982278 | + | 0.187431i | \(0.939984\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −231.713 | −0.481731 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −40.5744 | −0.0840049 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 715.272i | − 1.47479i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 494.221i | − 1.01483i | −0.861703 | − | 0.507413i | \(-0.830602\pi\) | ||||
0.861703 | − | 0.507413i | \(-0.169398\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 55.2923 | 0.113072 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 226.487 | 0.461277 | 0.230639 | − | 0.973039i | \(-0.425918\pi\) | ||||
0.230639 | + | 0.973039i | \(0.425918\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 336.133i | − 0.681812i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 220.708i | 0.445874i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −126.318 | −0.254161 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −239.195 | −0.479348 | −0.239674 | − | 0.970853i | \(-0.577041\pi\) | ||||
−0.239674 | + | 0.970853i | \(0.577041\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 363.979i | − 0.726506i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 298.831i | 0.594097i | 0.954862 | + | 0.297048i | \(0.0960023\pi\) | ||||
−0.954862 | + | 0.297048i | \(0.903998\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −783.938 | −1.55235 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 693.042 | 1.36695 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 713.195i | 1.40117i | 0.713570 | + | 0.700584i | \(0.247077\pi\) | ||||
−0.713570 | + | 0.700584i | \(0.752923\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 74.4514i | − 0.145697i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −160.708 | −0.313270 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −122.144 | −0.237172 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1042.83i | 2.01708i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 283.674i | 0.546579i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −748.985 | −1.43759 | −0.718795 | − | 0.695222i | \(-0.755306\pi\) | ||||
−0.718795 | + | 0.695222i | \(0.755306\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 338.908 | 0.648007 | 0.324003 | − | 0.946056i | \(-0.394971\pi\) | ||||
0.324003 | + | 0.946056i | \(0.394971\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 3.61524i | − 0.00688618i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 767.272i | − 1.45592i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 465.000 | 0.879017 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 324.631 | 0.611357 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 194.277i | − 0.364497i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 207.313i | − 0.387501i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 322.277 | 0.600143 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 603.482 | 1.11963 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 3.56922i | − 0.00659745i | −0.999995 | − | 0.00329872i | \(-0.998950\pi\) | ||||
0.999995 | − | 0.00329872i | \(-0.00105002\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 74.4693i | − 0.137144i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −97.8564 | −0.179553 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 530.067 | 0.969043 | 0.484522 | − | 0.874779i | \(-0.338994\pi\) | ||||
0.484522 | + | 0.874779i | \(0.338994\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 42.0000i | 0.0765027i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 523.559i | 0.950198i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 283.405 | 0.512486 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −82.9076 | −0.149383 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 721.790i | − 1.29585i | −0.761703 | − | 0.647926i | \(-0.775637\pi\) | ||||
0.761703 | − | 0.647926i | \(-0.224363\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 127.846i | 0.228705i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 513.415 | 0.915179 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.50258 | 0.0133261 | 0.00666303 | − | 0.999978i | \(-0.497879\pi\) | ||||
0.00666303 | + | 0.999978i | \(0.497879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 5.61046i | − 0.00993001i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.3538i | 0.0464794i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 500.697 | 0.879960 | 0.439980 | − | 0.898008i | \(-0.354985\pi\) | ||||
0.439980 | + | 0.898008i | \(0.354985\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 553.072 | 0.968602 | 0.484301 | − | 0.874901i | \(-0.339074\pi\) | ||||
0.484301 | + | 0.874901i | \(0.339074\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 151.426i | − 0.264268i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 5.70250i | − 0.00991740i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 889.426 | 1.54147 | 0.770733 | − | 0.637159i | \(-0.219890\pi\) | ||||
0.770733 | + | 0.637159i | \(0.219890\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −46.0282 | −0.0794960 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 184.267i | 0.317154i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 13.8564i | − 0.0237674i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 352.708 | 0.602919 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 317.892 | 0.541554 | 0.270777 | − | 0.962642i | \(-0.412719\pi\) | ||||
0.270777 | + | 0.962642i | \(0.412719\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1195.10i | 2.02903i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 435.597i | 0.737051i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −508.543 | −0.857577 | −0.428789 | − | 0.903405i | \(-0.641060\pi\) | ||||
−0.428789 | + | 0.903405i | \(0.641060\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 286.543 | 0.481586 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 117.913i | 0.197509i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 548.246i | − 0.915269i | −0.889140 | − | 0.457634i | \(-0.848697\pi\) | ||||
0.889140 | − | 0.457634i | \(-0.151303\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 542.000 | 0.901830 | 0.450915 | − | 0.892567i | \(-0.351098\pi\) | ||||
0.450915 | + | 0.892567i | \(0.351098\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 49.4923 | 0.0820767 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 501.944i | 0.829659i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 527.944i | 0.869759i | 0.900489 | + | 0.434879i | \(0.143209\pi\) | ||||
−0.900489 | + | 0.434879i | \(0.856791\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 85.8564 | 0.140979 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1666.52 | 2.72753 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 738.000i | 1.20392i | 0.798528 | + | 0.601958i | \(0.205612\pi\) | ||||
−0.798528 | + | 0.601958i | \(0.794388\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 69.5129i | − 0.113029i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −389.979 | −0.632057 | −0.316029 | − | 0.948750i | \(-0.602350\pi\) | ||||
−0.316029 | + | 0.948750i | \(0.602350\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1006.89 | −1.62663 | −0.813317 | − | 0.581820i | \(-0.802341\pi\) | ||||
−0.813317 | + | 0.581820i | \(0.802341\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 41.5692i | 0.0669392i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 147.251i | 0.236358i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −606.672 | −0.970675 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −799.692 | −1.27543 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 192.862i | 0.306616i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1043.77i | 1.65415i | 0.562091 | + | 0.827075i | \(0.309997\pi\) | ||||
−0.562091 | + | 0.827075i | \(0.690003\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 447.979 | 0.707708 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −844.441 | −1.32983 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 964.410i | − 1.51399i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 129.415i | 0.202528i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1100.96 | −1.71757 | −0.858786 | − | 0.512334i | \(-0.828781\pi\) | ||||
−0.858786 | + | 0.512334i | \(0.828781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −508.785 | −0.791267 | −0.395633 | − | 0.918409i | \(-0.629475\pi\) | ||||
−0.395633 | + | 0.918409i | \(0.629475\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 45.7437i | 0.0709205i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 804.862i | 1.24399i | 0.783021 | + | 0.621995i | \(0.213678\pi\) | ||||
−0.783021 | + | 0.621995i | \(0.786322\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1615.38 | 2.48904 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 195.979 | 0.301044 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1284.62i | − 1.96726i | −0.180202 | − | 0.983630i | \(-0.557675\pi\) | ||||
0.180202 | − | 0.983630i | \(-0.442325\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 281.261i | 0.429407i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −76.2769 | −0.116099 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −219.523 | −0.333116 | −0.166558 | − | 0.986032i | \(-0.553265\pi\) | ||||
−0.166558 | + | 0.986032i | \(0.553265\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 598.267i | − 0.905093i | −0.891741 | − | 0.452547i | \(-0.850516\pi\) | ||||
0.891741 | − | 0.452547i | \(-0.149484\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 820.477i | − 1.23752i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −446.318 | −0.671155 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 135.426 | 0.203037 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 14.2205i | − 0.0212564i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 208.995i | 0.311468i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −575.149 | −0.854604 | −0.427302 | − | 0.904109i | \(-0.640536\pi\) | ||||
−0.427302 | + | 0.904109i | \(0.640536\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.70388 | −0.00548724 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 450.805i | − 0.665887i | −0.942947 | − | 0.332943i | \(-0.891958\pi\) | ||||
0.942947 | − | 0.332943i | \(-0.108042\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 424.995i | − 0.625913i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −413.836 | −0.607688 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1186.45 | −1.73711 | −0.868555 | − | 0.495593i | \(-0.834951\pi\) | ||||
−0.868555 | + | 0.495593i | \(0.834951\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 759.600i | 1.10891i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 314.967i | 0.458467i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.1436 | −0.0321387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −870.508 | −1.25978 | −0.629890 | − | 0.776685i | \(-0.716900\pi\) | ||||
−0.629890 | + | 0.776685i | \(0.716900\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 131.138i | 0.189233i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 827.559i | 1.19073i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −161.703 | −0.231998 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −667.079 | −0.954334 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 218.785i | − 0.312104i | −0.987749 | − | 0.156052i | \(-0.950123\pi\) | ||||
0.987749 | − | 0.156052i | \(-0.0498767\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 300.400i | − 0.427311i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 596.287 | 0.845797 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −465.795 | −0.658832 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 85.8461i | − 0.121081i | −0.998166 | − | 0.0605403i | \(-0.980718\pi\) | ||||
0.998166 | − | 0.0605403i | \(-0.0192824\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 290.354i | − 0.408374i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 309.128 | 0.433560 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1755.10 | 2.45468 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 699.713i | 0.975890i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 816.728i | 1.13592i | 0.823055 | + | 0.567961i | \(0.192268\pi\) | ||||
−0.823055 | + | 0.567961i | \(0.807732\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −72.5744 | −0.100658 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 89.0897 | 0.123222 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.0666i | 0.0166436i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 62.6410i | 0.0861637i | 0.999072 | + | 0.0430819i | \(0.0137176\pi\) | ||||
−0.999072 | + | 0.0430819i | \(0.986282\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 106.410 | 0.145568 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 72.3895i | − 0.0987579i | −0.998780 | − | 0.0493790i | \(-0.984276\pi\) | ||||
0.998780 | − | 0.0493790i | \(-0.0157242\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 345.069i | − 0.469482i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 246.277 | 0.334161 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 651.061 | 0.881003 | 0.440502 | − | 0.897752i | \(-0.354801\pi\) | ||||
0.440502 | + | 0.897752i | \(0.354801\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1277.97i | 1.72465i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 951.272i | − 1.28031i | −0.768245 | − | 0.640156i | \(-0.778870\pi\) | ||||
0.768245 | − | 0.640156i | \(-0.221130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −612.841 | −0.822605 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 188.785 | 0.252724 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 123.180i | − 0.164459i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 280.323i | 0.373266i | 0.982430 | + | 0.186633i | \(0.0597576\pi\) | ||||
−0.982430 | + | 0.186633i | \(0.940242\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.29234 | 0.00968438 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 237.590 | 0.314689 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 246.708i | 0.325902i | 0.986634 | + | 0.162951i | \(0.0521012\pi\) | ||||
−0.986634 | + | 0.162951i | \(0.947899\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 206.851i | 0.272531i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −739.569 | −0.971839 | −0.485919 | − | 0.874004i | \(-0.661515\pi\) | ||||
−0.485919 | + | 0.874004i | \(0.661515\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −58.1436 | −0.0762039 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 293.569i | − 0.383751i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 2581.51i | − 3.36572i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1017.96 | 1.32374 | 0.661872 | − | 0.749617i | \(-0.269762\pi\) | ||||
0.661872 | + | 0.749617i | \(0.269762\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 158.833 | 0.206010 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 50.9179i | − 0.0658705i | −0.999457 | − | 0.0329352i | \(-0.989514\pi\) | ||||
0.999457 | − | 0.0329352i | \(-0.0104855\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.5438i | 0.0355404i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −49.2614 | −0.0633995 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 251.867 | 0.323321 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 643.979i | 0.824557i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 87.9615i | − 0.112339i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 819.497 | 1.04395 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −759.041 | −0.964474 | −0.482237 | − | 0.876041i | \(-0.660176\pi\) | ||||
−0.482237 | + | 0.876041i | \(0.660176\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 467.405i | 0.592402i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 3.33358i | − 0.00421439i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 333.990 | 0.421172 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.92305 | −0.00996610 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.2102i | 0.0178297i | 0.999960 | + | 0.00891483i | \(0.00283772\pi\) | ||||
−0.999960 | + | 0.00891483i | \(0.997162\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1387.10i | − 1.73604i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 150.862 | 0.188342 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −379.559 | −0.472676 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 115.446i | 0.143411i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 347.023i | − 0.430016i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −715.528 | −0.884460 | −0.442230 | − | 0.896902i | \(-0.645812\pi\) | ||||
−0.442230 | + | 0.896902i | \(0.645812\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 250.641 | 0.309052 | 0.154526 | − | 0.987989i | \(-0.450615\pi\) | ||||
0.154526 | + | 0.987989i | \(0.450615\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 861.184i | 1.05927i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 157.323i | − 0.193035i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −165.744 | −0.202869 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 209.569 | 0.255884 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 908.641i | − 1.10675i | −0.832933 | − | 0.553375i | \(-0.813340\pi\) | ||||
0.832933 | − | 0.553375i | \(-0.186660\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 514.200i | − 0.624787i | −0.949953 | − | 0.312394i | \(-0.898869\pi\) | ||||
0.949953 | − | 0.312394i | \(-0.101131\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18.4308 | −0.0223403 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1240.61 | −1.50013 | −0.750067 | − | 0.661362i | \(-0.769979\pi\) | ||||
−0.750067 | + | 0.661362i | \(0.769979\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 352.410i | 0.425103i | 0.977150 | + | 0.212551i | \(0.0681773\pi\) | ||||
−0.977150 | + | 0.212551i | \(0.931823\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 446.105i | 0.536829i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −802.708 | −0.963635 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1035.63 | −1.24028 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 200.785i | − 0.239886i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1038.81i | − 1.23815i | −0.785331 | − | 0.619076i | \(-0.787507\pi\) | ||||
0.785331 | − | 0.619076i | \(-0.212493\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 554.436 | 0.659258 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 336.018 | 0.398598 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1971.91i | − 2.33362i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 298.241i | 0.352115i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −575.405 | −0.677744 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −77.7025 | −0.0913073 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1382.80i | − 1.62110i | −0.585668 | − | 0.810551i | \(-0.699168\pi\) | ||||
0.585668 | − | 0.810551i | \(-0.300832\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 457.261i | 0.534809i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −893.518 | −1.04261 | −0.521306 | − | 0.853370i | \(-0.674555\pi\) | ||||
−0.521306 | + | 0.853370i | \(0.674555\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1549.85 | −1.80425 | −0.902125 | − | 0.431475i | \(-0.857993\pi\) | ||||
−0.902125 | + | 0.431475i | \(0.857993\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 41.3027i | − 0.0479706i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 347.405i | − 0.402555i | −0.979534 | − | 0.201278i | \(-0.935491\pi\) | ||||
0.979534 | − | 0.201278i | \(-0.0645093\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 807.138 | 0.933108 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −182.345 | −0.210317 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1444.82i | − 1.66262i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 393.569i | − 0.451859i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −435.415 | −0.498758 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −371.056 | −0.424064 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1216.24i | − 1.38681i | −0.720546 | − | 0.693407i | \(-0.756109\pi\) | ||||
0.720546 | − | 0.693407i | \(-0.243891\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 806.967i | − 0.918051i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −270.533 | −0.307075 | −0.153538 | − | 0.988143i | \(-0.549067\pi\) | ||||
−0.153538 | + | 0.988143i | \(0.549067\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 368.918 | 0.417801 | 0.208900 | − | 0.977937i | \(-0.433012\pi\) | ||||
0.208900 | + | 0.977937i | \(0.433012\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 923.672i | − 1.04370i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 240.154i | 0.270748i | 0.990795 | + | 0.135374i | \(0.0432237\pi\) | ||||
−0.990795 | + | 0.135374i | \(0.956776\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −501.744 | −0.564391 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 134.354 | 0.150790 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2160.53i | 2.41941i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 916.974i | − 1.02455i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 330.564 | 0.368522 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −654.123 | −0.727612 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.4308i | 0.0204559i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.1797i | 0.0300993i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −211.887 | −0.234130 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1141.05 | −1.25805 | −0.629025 | − | 0.777385i | \(-0.716546\pi\) | ||||
−0.629025 | + | 0.777385i | \(0.716546\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 477.215i | 0.524989i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1755.94i | 1.92748i | 0.266835 | + | 0.963742i | \(0.414022\pi\) | ||||
−0.266835 | + | 0.963742i | \(0.585978\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 939.405 | 1.02892 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 119.503 | 0.130604 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 167.118i | 0.182244i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1414.18i | − 1.53882i | −0.638753 | − | 0.769412i | \(-0.720549\pi\) | ||||
0.638753 | − | 0.769412i | \(-0.279451\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 373.723 | 0.405780 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1029.13 | 1.11498 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 6.92342i | − 0.00748478i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 74.3538i | 0.0802091i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1848.06 | −1.98930 | −0.994651 | − | 0.103295i | \(-0.967061\pi\) | ||||
−0.994651 | + | 0.103295i | \(0.967061\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1250.29 | 1.34296 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 303.118i | 0.324885i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 1460.82i | − 1.56237i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 170.554 | 0.182021 | 0.0910105 | − | 0.995850i | \(-0.470990\pi\) | ||||
0.0910105 | + | 0.995850i | \(0.470990\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −751.674 | −0.800505 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 281.523i | − 0.299174i | −0.988749 | − | 0.149587i | \(-0.952206\pi\) | ||||
0.988749 | − | 0.149587i | \(-0.0477945\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 65.1487i | − 0.0690867i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 74.9845 | 0.0793487 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1533.43 | −1.61925 | −0.809625 | − | 0.586947i | \(-0.800330\pi\) | ||||
−0.809625 | + | 0.586947i | \(0.800330\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 606.564i | 0.639161i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 153.264i | 0.161161i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −414.133 | −0.434557 | −0.217279 | − | 0.976110i | \(-0.569718\pi\) | ||||
−0.217279 | + | 0.976110i | \(0.569718\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −430.851 | −0.451153 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 437.703i | − 0.457369i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 451.334i | 0.470629i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −532.128 | −0.553723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −126.200 | −0.131049 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 130.964i | 0.135714i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 228.918i | − 0.236730i | −0.992970 | − | 0.118365i | \(-0.962235\pi\) | ||||
0.992970 | − | 0.118365i | \(-0.0377653\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1063.69 | 1.09772 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 968.877 | 0.997813 | 0.498907 | − | 0.866656i | \(-0.333735\pi\) | ||||
0.498907 | + | 0.866656i | \(0.333735\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 491.713i | 0.505357i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 29.4538i | 0.0302090i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −648.144 | −0.663402 | −0.331701 | − | 0.943385i | \(-0.607622\pi\) | ||||
−0.331701 | + | 0.943385i | \(0.607622\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 750.697 | 0.766800 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 59.5692i | 0.0607230i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1035.56i | 1.05347i | 0.850030 | + | 0.526734i | \(0.176584\pi\) | ||||
−0.850030 | + | 0.526734i | \(0.823416\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1239.41 | 1.25828 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 354.297 | 0.358964 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.8719i | 0.0433487i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1032.44i | − 1.04181i | −0.853614 | − | 0.520906i | \(-0.825594\pi\) | ||||
0.853614 | − | 0.520906i | \(-0.174406\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −185.436 | −0.186743 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 335.497 | 0.337183 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 456.277i | 0.457650i | 0.973468 | + | 0.228825i | \(0.0734883\pi\) | ||||
−0.973468 | + | 0.228825i | \(0.926512\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 50.4693i | 0.0505198i |
(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 | 768.3.b.d.127.2 | 4 | ||
3.2 | odd | 2 | 2304.3.b.k.127.2 | 4 | |||
4.3 | odd | 2 | 768.3.b.a.127.4 | 4 | |||
8.3 | odd | 2 | inner | 768.3.b.d.127.1 | 4 | ||
8.5 | even | 2 | 768.3.b.a.127.3 | 4 | |||
12.11 | even | 2 | 2304.3.b.o.127.2 | 4 | |||
16.3 | odd | 4 | 96.3.g.a.31.4 | yes | 4 | ||
16.5 | even | 4 | 192.3.g.c.127.3 | 4 | |||
16.11 | odd | 4 | 192.3.g.c.127.1 | 4 | |||
16.13 | even | 4 | 96.3.g.a.31.2 | ✓ | 4 | ||
24.5 | odd | 2 | 2304.3.b.o.127.3 | 4 | |||
24.11 | even | 2 | 2304.3.b.k.127.3 | 4 | |||
48.5 | odd | 4 | 576.3.g.j.127.3 | 4 | |||
48.11 | even | 4 | 576.3.g.j.127.4 | 4 | |||
48.29 | odd | 4 | 288.3.g.d.127.1 | 4 | |||
48.35 | even | 4 | 288.3.g.d.127.2 | 4 | |||
80.3 | even | 4 | 2400.3.j.a.799.2 | 4 | |||
80.13 | odd | 4 | 2400.3.j.b.799.3 | 4 | |||
80.19 | odd | 4 | 2400.3.e.a.1951.2 | 4 | |||
80.29 | even | 4 | 2400.3.e.a.1951.3 | 4 | |||
80.67 | even | 4 | 2400.3.j.b.799.4 | 4 | |||
80.77 | odd | 4 | 2400.3.j.a.799.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.3.g.a.31.2 | ✓ | 4 | 16.13 | even | 4 | ||
96.3.g.a.31.4 | yes | 4 | 16.3 | odd | 4 | ||
192.3.g.c.127.1 | 4 | 16.11 | odd | 4 | |||
192.3.g.c.127.3 | 4 | 16.5 | even | 4 | |||
288.3.g.d.127.1 | 4 | 48.29 | odd | 4 | |||
288.3.g.d.127.2 | 4 | 48.35 | even | 4 | |||
576.3.g.j.127.3 | 4 | 48.5 | odd | 4 | |||
576.3.g.j.127.4 | 4 | 48.11 | even | 4 | |||
768.3.b.a.127.3 | 4 | 8.5 | even | 2 | |||
768.3.b.a.127.4 | 4 | 4.3 | odd | 2 | |||
768.3.b.d.127.1 | 4 | 8.3 | odd | 2 | inner | ||
768.3.b.d.127.2 | 4 | 1.1 | even | 1 | trivial | ||
2304.3.b.k.127.2 | 4 | 3.2 | odd | 2 | |||
2304.3.b.k.127.3 | 4 | 24.11 | even | 2 | |||
2304.3.b.o.127.2 | 4 | 12.11 | even | 2 | |||
2304.3.b.o.127.3 | 4 | 24.5 | odd | 2 | |||
2400.3.e.a.1951.2 | 4 | 80.19 | odd | 4 | |||
2400.3.e.a.1951.3 | 4 | 80.29 | even | 4 | |||
2400.3.j.a.799.1 | 4 | 80.77 | odd | 4 | |||
2400.3.j.a.799.2 | 4 | 80.3 | even | 4 | |||
2400.3.j.b.799.3 | 4 | 80.13 | odd | 4 | |||
2400.3.j.b.799.4 | 4 | 80.67 | even | 4 |