Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,3,Mod(1101,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.1101");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.e (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: | \(51.7712502285\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 89x^{12} + 3026x^{10} + 49092x^{8} + 390297x^{6} + 1440495x^{4} + 1994425x^{2} + 151875 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1101.10 | ||
Root | \(2.16913i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1101 |
Dual form | 1900.3.e.g.1101.5 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 2.16913i | 0.723042i | 0.932364 | + | 0.361521i | \(0.117742\pi\) | ||||
−0.932364 | + | 0.361521i | \(0.882258\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.18099 | 1.16871 | 0.584356 | − | 0.811497i | \(-0.301347\pi\) | ||||
0.584356 | + | 0.811497i | \(0.301347\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.29489 | 0.477211 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.30255 | 0.300232 | 0.150116 | − | 0.988668i | \(-0.452035\pi\) | ||||
0.150116 | + | 0.988668i | \(0.452035\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 8.86162i | − | 0.681663i | −0.940124 | − | 0.340832i | \(-0.889291\pi\) | ||
0.940124 | − | 0.340832i | \(-0.110709\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 10.2495 | 0.602910 | 0.301455 | − | 0.953480i | \(-0.402528\pi\) | ||||
0.301455 | + | 0.953480i | \(0.402528\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 18.5676 | − | 4.03031i | 0.977243 | − | 0.212122i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 17.7456i | 0.845028i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.896508 | 0.0389786 | 0.0194893 | − | 0.999810i | \(-0.493796\pi\) | ||||
0.0194893 | + | 0.999810i | \(0.493796\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 28.8383i | 1.06808i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 17.9058i | 0.617442i | 0.951153 | + | 0.308721i | \(0.0999010\pi\) | ||||
−0.951153 | + | 0.308721i | \(0.900099\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 40.8943i | − | 1.31917i | −0.751629 | − | 0.659586i | \(-0.770732\pi\) | ||
0.751629 | − | 0.659586i | \(-0.229268\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.16364i | 0.217080i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.68123i | − | 0.207601i | −0.994598 | − | 0.103800i | \(-0.966900\pi\) | ||
0.994598 | − | 0.103800i | \(-0.0331003\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 19.2220 | 0.492871 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 69.9101i | − | 1.70512i | −0.522626 | − | 0.852562i | \(-0.675048\pi\) | ||
0.522626 | − | 0.852562i | \(-0.324952\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 25.9969 | 0.604579 | 0.302290 | − | 0.953216i | \(-0.402249\pi\) | ||||
0.302290 | + | 0.953216i | \(0.402249\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.4912 | −0.265770 | −0.132885 | − | 0.991131i | \(-0.542424\pi\) | ||||
−0.132885 | + | 0.991131i | \(0.542424\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.9286 | 0.365889 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 22.2324i | 0.435929i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 55.9407i | − | 1.05549i | −0.849404 | − | 0.527743i | \(-0.823038\pi\) | ||
0.849404 | − | 0.527743i | \(-0.176962\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.74226 | + | 40.2755i | 0.153373 | + | 0.706588i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 105.529i | − | 1.78862i | −0.447444 | − | 0.894312i | \(-0.647666\pi\) | ||
0.447444 | − | 0.894312i | \(-0.352334\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −48.2803 | −0.791480 | −0.395740 | − | 0.918363i | \(-0.629512\pi\) | ||||
−0.395740 | + | 0.918363i | \(0.629512\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 35.1365 | 0.557722 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 14.6303i | − | 0.218363i | −0.994022 | − | 0.109181i | \(-0.965177\pi\) | ||
0.994022 | − | 0.109181i | \(-0.0348229\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.94464i | 0.0281832i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.89388i | − | 0.0407588i | −0.999792 | − | 0.0203794i | \(-0.993513\pi\) | ||
0.999792 | − | 0.0203794i | \(-0.00648742\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 75.9531 | 1.04045 | 0.520227 | − | 0.854028i | \(-0.325847\pi\) | ||||
0.520227 | + | 0.854028i | \(0.325847\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 27.0181 | 0.350885 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 86.1594i | 1.09063i | 0.838233 | + | 0.545313i | \(0.183589\pi\) | ||||
−0.838233 | + | 0.545313i | \(0.816411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −23.8998 | −0.295060 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 52.0562 | 0.627183 | 0.313591 | − | 0.949558i | \(-0.398468\pi\) | ||||
0.313591 | + | 0.949558i | \(0.398468\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −38.8400 | −0.446437 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 39.5469i | 0.444347i | 0.975007 | + | 0.222174i | \(0.0713151\pi\) | ||||
−0.975007 | + | 0.222174i | \(0.928685\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 72.4968i | − | 0.796668i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 88.7050 | 0.953817 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 172.660i | 1.78000i | 0.455962 | + | 0.889999i | \(0.349295\pi\) | ||||
−0.455962 | + | 0.889999i | \(0.650705\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.1841 | 0.143274 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −143.421 | −1.42001 | −0.710007 | − | 0.704194i | \(-0.751308\pi\) | ||||
−0.710007 | + | 0.704194i | \(0.751308\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 101.659i | 0.986979i | 0.869752 | + | 0.493490i | \(0.164279\pi\) | ||||
−0.869752 | + | 0.493490i | \(0.835721\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 155.201i | − | 1.45048i | −0.688497 | − | 0.725239i | \(-0.741729\pi\) | ||
0.688497 | − | 0.725239i | \(-0.258271\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 52.7937i | − | 0.484345i | −0.970233 | − | 0.242173i | \(-0.922140\pi\) | ||
0.970233 | − | 0.242173i | \(-0.0778601\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.6616 | 0.150104 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 90.0032i | 0.796488i | 0.917279 | + | 0.398244i | \(0.130380\pi\) | ||||
−0.917279 | + | 0.398244i | \(0.869620\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 38.0597i | − | 0.325297i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 83.8508 | 0.704629 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −110.093 | −0.909861 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 151.644 | 1.23288 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 74.1001i | − | 0.583466i | −0.956500 | − | 0.291733i | \(-0.905768\pi\) | ||
0.956500 | − | 0.291733i | \(-0.0942318\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 56.3906i | 0.437136i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −59.3187 | −0.452814 | −0.226407 | − | 0.974033i | \(-0.572698\pi\) | ||||
−0.226407 | + | 0.974033i | \(0.572698\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 151.902 | − | 32.9720i | 1.14212 | − | 0.247909i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 153.881 | 1.12322 | 0.561610 | − | 0.827402i | \(-0.310182\pi\) | ||||
0.561610 | + | 0.827402i | \(0.310182\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 42.6118 | 0.306560 | 0.153280 | − | 0.988183i | \(-0.451016\pi\) | ||||
0.153280 | + | 0.988183i | \(0.451016\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 27.0950i | − | 0.192163i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 29.2659i | − | 0.204657i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 38.8893i | 0.264553i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 43.1276 | 0.289447 | 0.144723 | − | 0.989472i | \(-0.453771\pi\) | ||||
0.144723 | + | 0.989472i | \(0.453771\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 88.7161i | 0.587524i | 0.955879 | + | 0.293762i | \(0.0949073\pi\) | ||||
−0.955879 | + | 0.293762i | \(0.905093\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 44.0204 | 0.287715 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 86.8111 | 0.552937 | 0.276469 | − | 0.961023i | \(-0.410836\pi\) | ||||
0.276469 | + | 0.961023i | \(0.410836\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 121.342 | 0.763160 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.33432 | 0.0455548 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 116.020 | 0.711781 | 0.355890 | − | 0.934528i | \(-0.384178\pi\) | ||||
0.355890 | + | 0.934528i | \(0.384178\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 184.203i | 1.10301i | 0.834172 | + | 0.551505i | \(0.185946\pi\) | ||||
−0.834172 | + | 0.551505i | \(0.814054\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 90.4717 | 0.535335 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 79.7460 | − | 17.3098i | 0.466351 | − | 0.101227i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 180.352i | 1.04250i | 0.853404 | + | 0.521249i | \(0.174534\pi\) | ||||
−0.853404 | + | 0.521249i | \(0.825466\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 228.905 | 1.29325 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 62.4477i | − | 0.348870i | −0.984669 | − | 0.174435i | \(-0.944190\pi\) | ||
0.984669 | − | 0.174435i | \(-0.0558099\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 229.533i | 1.26814i | 0.773277 | + | 0.634069i | \(0.218616\pi\) | ||||
−0.773277 | + | 0.634069i | \(0.781384\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 104.726i | − | 0.572273i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 33.8494 | 0.181013 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 235.926i | 1.24828i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −250.559 | −1.31182 | −0.655912 | − | 0.754837i | \(-0.727716\pi\) | ||||
−0.655912 | + | 0.754837i | \(0.727716\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 144.603i | − | 0.749239i | −0.927179 | − | 0.374619i | \(-0.877773\pi\) | ||
0.927179 | − | 0.374619i | \(-0.122227\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 172.063 | 0.873414 | 0.436707 | − | 0.899604i | \(-0.356145\pi\) | ||||
0.436707 | + | 0.899604i | \(0.356145\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 334.796 | 1.68239 | 0.841196 | − | 0.540731i | \(-0.181852\pi\) | ||||
0.841196 | + | 0.540731i | \(0.181852\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 31.7350 | 0.157885 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 146.487i | 0.721613i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.85041 | 0.0186010 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 61.3205 | − | 13.3103i | 0.293399 | − | 0.0636857i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 47.6699i | − | 0.225924i | −0.993599 | − | 0.112962i | \(-0.963966\pi\) | ||
0.993599 | − | 0.112962i | \(-0.0360338\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.27718 | 0.0294703 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 334.556i | − | 1.54173i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 164.752i | 0.752292i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 90.8270i | − | 0.410982i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 289.875i | 1.29989i | 0.759981 | + | 0.649945i | \(0.225208\pi\) | ||||
−0.759981 | + | 0.649945i | \(0.774792\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 39.5372i | 0.174172i | 0.996201 | + | 0.0870862i | \(0.0277556\pi\) | ||||
−0.996201 | + | 0.0870862i | \(0.972244\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.51216 | 0.0109701 | 0.00548507 | − | 0.999985i | \(-0.498254\pi\) | ||||
0.00548507 | + | 0.999985i | \(0.498254\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 58.6057i | 0.253704i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 161.184 | 0.691775 | 0.345887 | − | 0.938276i | \(-0.387578\pi\) | ||||
0.345887 | + | 0.938276i | \(0.387578\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −186.891 | −0.788568 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 140.111 | 0.586240 | 0.293120 | − | 0.956076i | \(-0.405306\pi\) | ||||
0.293120 | + | 0.956076i | \(0.405306\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 12.3672i | − | 0.0513163i | −0.999671 | − | 0.0256582i | \(-0.991832\pi\) | ||
0.999671 | − | 0.0256582i | \(-0.00816814\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 207.703i | 0.854745i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −35.7151 | − | 164.539i | −0.144596 | − | 0.666151i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 112.916i | 0.453479i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −463.827 | −1.84792 | −0.923958 | − | 0.382494i | \(-0.875065\pi\) | ||||
−0.923958 | + | 0.382494i | \(0.875065\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.96076 | 0.0117026 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 244.454i | 0.951185i | 0.879666 | + | 0.475592i | \(0.157766\pi\) | ||||
−0.879666 | + | 0.475592i | \(0.842234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 62.8401i | − | 0.242626i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 76.9037i | 0.294650i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −67.3381 | −0.256038 | −0.128019 | − | 0.991772i | \(-0.540862\pi\) | ||||
−0.128019 | + | 0.991772i | \(0.540862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −85.7822 | −0.321281 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.2184i | 0.0417040i | 0.999783 | + | 0.0208520i | \(0.00663788\pi\) | ||||
−0.999783 | + | 0.0208520i | \(0.993362\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 96.9961 | 0.357919 | 0.178960 | − | 0.983856i | \(-0.442727\pi\) | ||||
0.178960 | + | 0.983856i | \(0.442727\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 157.255 | 0.576025 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −34.6288 | −0.125014 | −0.0625069 | − | 0.998045i | \(-0.519910\pi\) | ||||
−0.0625069 | + | 0.998045i | \(0.519910\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 175.637i | − | 0.629523i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 334.616i | 1.19080i | 0.803428 | + | 0.595402i | \(0.203007\pi\) | ||||
−0.803428 | + | 0.595402i | \(0.796993\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 219.370 | 0.775158 | 0.387579 | − | 0.921836i | \(-0.373311\pi\) | ||||
0.387579 | + | 0.921836i | \(0.373311\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 571.934i | − | 1.99280i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −183.948 | −0.636499 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −374.521 | −1.28701 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 7.91053i | − | 0.0269984i | −0.999909 | − | 0.0134992i | \(-0.995703\pi\) | ||
0.999909 | − | 0.0134992i | \(-0.00429706\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 95.2399i | 0.320673i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 7.94451i | − | 0.0265703i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 212.680 | 0.706580 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 311.099i | − | 1.02673i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 245.743i | 0.800466i | 0.916413 | + | 0.400233i | \(0.131071\pi\) | ||||
−0.916413 | + | 0.400233i | \(0.868929\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −220.511 | −0.713627 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −512.022 | −1.64637 | −0.823187 | − | 0.567771i | \(-0.807806\pi\) | ||||
−0.823187 | + | 0.567771i | \(0.807806\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 502.653 | 1.60592 | 0.802960 | − | 0.596033i | \(-0.203257\pi\) | ||||
0.802960 | + | 0.596033i | \(0.203257\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 173.029i | 0.545834i | 0.962038 | + | 0.272917i | \(0.0879885\pi\) | ||||
−0.962038 | + | 0.272917i | \(0.912012\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 59.1349i | 0.185376i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 336.651 | 1.04876 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 190.308 | − | 41.3086i | 0.589190 | − | 0.127890i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 114.516 | 0.350202 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −102.190 | −0.310609 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 287.986i | − | 0.870049i | −0.900419 | − | 0.435025i | \(-0.856740\pi\) | ||
0.900419 | − | 0.435025i | \(-0.143260\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 32.9901i | − | 0.0990694i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 135.116i | 0.400939i | 0.979700 | + | 0.200469i | \(0.0642467\pi\) | ||||
−0.979700 | + | 0.200469i | \(0.935753\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −195.228 | −0.575894 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 135.056i | − | 0.396057i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −254.195 | −0.741093 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −302.548 | −0.871896 | −0.435948 | − | 0.899972i | \(-0.643587\pi\) | ||||
−0.435948 | + | 0.899972i | \(0.643587\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −241.844 | −0.692964 | −0.346482 | − | 0.938057i | \(-0.612624\pi\) | ||||
−0.346482 | + | 0.938057i | \(0.612624\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 255.554 | 0.728074 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −182.840 | −0.517960 | −0.258980 | − | 0.965883i | \(-0.583386\pi\) | ||||
−0.258980 | + | 0.965883i | \(0.583386\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 181.883i | 0.509476i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 187.980 | 0.523622 | 0.261811 | − | 0.965119i | \(-0.415680\pi\) | ||||
0.261811 | + | 0.965119i | \(0.415680\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 328.513 | − | 149.667i | 0.910009 | − | 0.414589i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 238.806i | − | 0.657867i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 168.184 | 0.458268 | 0.229134 | − | 0.973395i | \(-0.426411\pi\) | ||||
0.229134 | + | 0.973395i | \(0.426411\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 300.256i | − | 0.813703i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 457.651i | − | 1.23356i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 677.168i | 1.81546i | 0.419550 | + | 0.907732i | \(0.362188\pi\) | ||||
−0.419550 | + | 0.907732i | \(0.637812\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 158.675 | 0.420888 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 410.871i | − | 1.08409i | −0.840349 | − | 0.542046i | \(-0.817650\pi\) | ||
0.840349 | − | 0.542046i | \(-0.182350\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 160.732 | 0.421870 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 253.500i | 0.661880i | 0.943652 | + | 0.330940i | \(0.107366\pi\) | ||||
−0.943652 | + | 0.330940i | \(0.892634\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 111.654 | 0.288512 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 105.069 | 0.270101 | 0.135051 | − | 0.990839i | \(-0.456880\pi\) | ||||
0.135051 | + | 0.990839i | \(0.456880\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.18873 | 0.0235006 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 128.670i | − | 0.327404i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −38.8390 | −0.0978313 | −0.0489156 | − | 0.998803i | \(-0.515577\pi\) | ||||
−0.0489156 | + | 0.998803i | \(0.515577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 71.5203 | + | 329.493i | 0.179249 | + | 0.825798i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 386.689i | − | 0.964311i | −0.876086 | − | 0.482155i | \(-0.839854\pi\) | ||
0.876086 | − | 0.482155i | \(-0.160146\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −362.390 | −0.899231 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 25.3677i | − | 0.0623284i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 299.046i | 0.731165i | 0.930779 | + | 0.365582i | \(0.119130\pi\) | ||||
−0.930779 | + | 0.365582i | \(0.880870\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 333.787i | 0.812134i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 863.330i | − | 2.09039i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 92.4304i | 0.221656i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −228.600 | −0.545585 | −0.272793 | − | 0.962073i | \(-0.587947\pi\) | ||||
−0.272793 | + | 0.962073i | \(0.587947\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 373.332i | 0.886775i | 0.896330 | + | 0.443387i | \(0.146223\pi\) | ||||
−0.896330 | + | 0.443387i | \(0.853777\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −53.6484 | −0.126828 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −394.980 | −0.925012 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 63.4815 | 0.147976 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 216.245i | − | 0.501729i | −0.968022 | − | 0.250865i | \(-0.919285\pi\) | ||
0.968022 | − | 0.250865i | \(-0.0807149\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 652.519i | − | 1.50697i | −0.657464 | − | 0.753486i | \(-0.728371\pi\) | ||
0.657464 | − | 0.753486i | \(-0.271629\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.6460 | − | 3.61321i | 0.0380916 | − | 0.00826821i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 607.514i | − | 1.38386i | −0.721965 | − | 0.691929i | \(-0.756761\pi\) | ||
0.721965 | − | 0.691929i | \(-0.243239\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 77.0014 | 0.174606 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −513.684 | −1.15956 | −0.579779 | − | 0.814774i | \(-0.696861\pi\) | ||||
−0.579779 | + | 0.814774i | \(0.696861\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 93.5491i | 0.209282i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 223.870i | − | 0.498596i | −0.968427 | − | 0.249298i | \(-0.919800\pi\) | ||
0.968427 | − | 0.249298i | \(-0.0801998\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 230.881i | − | 0.511932i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −192.436 | −0.424804 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 438.522 | 0.959567 | 0.479784 | − | 0.877387i | \(-0.340715\pi\) | ||||
0.479784 | + | 0.877387i | \(0.340715\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 295.577i | 0.643959i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 703.015 | 1.52498 | 0.762489 | − | 0.647001i | \(-0.223977\pi\) | ||||
0.762489 | + | 0.647001i | \(0.223977\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −642.827 | −1.38839 | −0.694197 | − | 0.719785i | \(-0.744240\pi\) | ||||
−0.694197 | + | 0.719785i | \(0.744240\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −927.468 | −1.98601 | −0.993006 | − | 0.118061i | \(-0.962332\pi\) | ||||
−0.993006 | + | 0.118061i | \(0.962332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 119.690i | − | 0.255203i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 188.304i | 0.399797i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 85.8561 | 0.181514 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 240.260i | − | 0.503689i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 257.644 | 0.537880 | 0.268940 | − | 0.963157i | \(-0.413327\pi\) | ||||
0.268940 | + | 0.963157i | \(0.413327\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −68.0682 | −0.141514 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.9091i | 0.0329380i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 609.090i | 1.25070i | 0.780345 | + | 0.625349i | \(0.215043\pi\) | ||||
−0.780345 | + | 0.625349i | \(0.784957\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 251.663i | 0.514647i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 138.936 | 0.282966 | 0.141483 | − | 0.989941i | \(-0.454813\pi\) | ||||
0.141483 | + | 0.989941i | \(0.454813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 183.525i | 0.372262i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 23.6748i | − | 0.0476354i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 228.666 | 0.458248 | 0.229124 | − | 0.973397i | \(-0.426414\pi\) | ||||
0.229124 | + | 0.973397i | \(0.426414\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −399.558 | −0.797522 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −465.208 | −0.924868 | −0.462434 | − | 0.886654i | \(-0.653024\pi\) | ||||
−0.462434 | + | 0.886654i | \(0.653024\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 196.244i | 0.387070i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 395.633i | 0.777276i | 0.921391 | + | 0.388638i | \(0.127054\pi\) | ||||
−0.921391 | + | 0.388638i | \(0.872946\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 621.372 | 1.21599 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 116.227 | + | 535.459i | 0.226564 | + | 1.04378i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −41.2528 | −0.0797926 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −391.207 | −0.753770 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 204.842i | 0.393172i | 0.980487 | + | 0.196586i | \(0.0629854\pi\) | ||||
−0.980487 | + | 0.196586i | \(0.937015\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 755.700i | − | 1.44493i | −0.691406 | − | 0.722466i | \(-0.743008\pi\) | ||
0.691406 | − | 0.722466i | \(-0.256992\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 419.146i | − | 0.795343i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −528.196 | −0.998481 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 453.235i | − | 0.853550i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −619.517 | −1.16232 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 135.457 | 0.252248 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 59.2100 | 0.109852 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 458.741 | 0.847951 | 0.423975 | − | 0.905674i | \(-0.360634\pi\) | ||||
0.423975 | + | 0.905674i | \(0.360634\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −497.886 | −0.916916 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 731.948i | − | 1.33811i | −0.743211 | − | 0.669057i | \(-0.766698\pi\) | ||
0.743211 | − | 0.669057i | \(-0.233302\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −207.359 | −0.377702 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 72.1661 | + | 332.469i | 0.130973 | + | 0.603391i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 704.869i | 1.27463i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 534.752 | 0.960057 | 0.480028 | − | 0.877253i | \(-0.340626\pi\) | ||||
0.480028 | + | 0.877253i | \(0.340626\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 230.375i | − | 0.412120i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 73.4236i | 0.130880i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 408.400i | − | 0.725401i | −0.931906 | − | 0.362700i | \(-0.881855\pi\) | ||
0.931906 | − | 0.362700i | \(-0.118145\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −195.524 | −0.344840 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 465.410i | − | 0.817944i | −0.912547 | − | 0.408972i | \(-0.865887\pi\) | ||
0.912547 | − | 0.408972i | \(-0.134113\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −60.8428 | −0.106555 | −0.0532774 | − | 0.998580i | \(-0.516967\pi\) | ||||
−0.0532774 | + | 0.998580i | \(0.516967\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 543.493i | − | 0.948504i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 657.921 | 1.14024 | 0.570122 | − | 0.821560i | \(-0.306896\pi\) | ||||
0.570122 | + | 0.821560i | \(0.306896\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 313.662 | 0.541731 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 425.871 | 0.732996 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 184.747i | − | 0.316890i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1050.70 | −1.78996 | −0.894978 | − | 0.446110i | \(-0.852809\pi\) | ||||
−0.894978 | + | 0.446110i | \(0.852809\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −164.817 | − | 759.311i | −0.279825 | − | 1.28915i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 373.225i | 0.631515i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −520.953 | −0.878505 | −0.439252 | − | 0.898364i | \(-0.644757\pi\) | ||||
−0.439252 | + | 0.898364i | \(0.644757\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 726.214i | 1.21644i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 518.236i | 0.865169i | 0.901593 | + | 0.432584i | \(0.142398\pi\) | ||||
−0.901593 | + | 0.432584i | \(0.857602\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 312.656i | − | 0.520226i | −0.965578 | − | 0.260113i | \(-0.916240\pi\) | ||
0.965578 | − | 0.260113i | \(-0.0837598\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 62.8356i | − | 0.104205i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 40.6637i | − | 0.0669913i | −0.999439 | − | 0.0334956i | \(-0.989336\pi\) | ||
0.999439 | − | 0.0334956i | \(-0.0106640\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −317.750 | −0.521756 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 110.692i | 0.181166i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.2110 | −0.0378646 | −0.0189323 | − | 0.999821i | \(-0.506027\pi\) | ||||
−0.0189323 | + | 0.999821i | \(0.506027\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −782.983 | −1.26902 | −0.634508 | − | 0.772916i | \(-0.718797\pi\) | ||||
−0.634508 | + | 0.772916i | \(0.718797\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −669.801 | −1.08207 | −0.541034 | − | 0.841000i | \(-0.681967\pi\) | ||||
−0.541034 | + | 0.841000i | \(0.681967\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.8538i | 0.0416325i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 323.533i | 0.519314i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 28.8717 | + | 133.012i | 0.0460474 | + | 0.212140i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 78.7286i | − | 0.125165i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −190.219 | −0.301457 | −0.150728 | − | 0.988575i | \(-0.548162\pi\) | ||||
−0.150728 | + | 0.988575i | \(0.548162\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 103.402 | 0.163352 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 158.876i | − | 0.249413i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 12.4289i | − | 0.0194505i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 519.869i | 0.811029i | 0.914089 | + | 0.405514i | \(0.132908\pi\) | ||||
−0.914089 | + | 0.405514i | \(0.867092\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −594.211 | −0.924123 | −0.462062 | − | 0.886848i | \(-0.652890\pi\) | ||||
−0.462062 | + | 0.886848i | \(0.652890\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −830.788 | −1.28406 | −0.642031 | − | 0.766679i | \(-0.721908\pi\) | ||||
−0.642031 | + | 0.766679i | \(0.721908\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 348.514i | − | 0.537002i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 725.694 | 1.11474 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −726.157 | −1.11203 | −0.556016 | − | 0.831172i | \(-0.687671\pi\) | ||||
−0.556016 | + | 0.831172i | \(0.687671\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 326.211 | 0.496516 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.7289i | 0.0466295i | 0.999728 | + | 0.0233148i | \(0.00742199\pi\) | ||||
−0.999728 | + | 0.0233148i | \(0.992578\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 721.605i | − | 1.09169i | −0.837887 | − | 0.545844i | \(-0.816209\pi\) | ||
0.837887 | − | 0.545844i | \(-0.183791\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 197.015 | 0.297157 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0527i | 0.0240670i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −628.776 | −0.939875 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −159.448 | −0.237627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 435.074i | 0.646469i | 0.946319 | + | 0.323235i | \(0.104770\pi\) | ||||
−0.946319 | + | 0.323235i | \(0.895230\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 607.496i | − | 0.897335i | −0.893699 | − | 0.448667i | \(-0.851899\pi\) | ||
0.893699 | − | 0.448667i | \(-0.148101\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1412.53i | 2.08031i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −85.7611 | −0.125934 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 291.254i | 0.426434i | 0.977005 | + | 0.213217i | \(0.0683941\pi\) | ||||
−0.977005 | + | 0.213217i | \(0.931606\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.44920i | 0.00793188i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −495.726 | −0.719486 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −444.232 | −0.642883 | −0.321441 | − | 0.946929i | \(-0.604167\pi\) | ||||
−0.321441 | + | 0.946929i | \(0.604167\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 116.040 | 0.167446 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 716.542i | − | 1.02804i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 349.627i | 0.500182i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 481.762 | 0.687250 | 0.343625 | − | 0.939107i | \(-0.388345\pi\) | ||||
0.343625 | + | 0.939107i | \(0.388345\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.9578 | − | 142.622i | −0.0440367 | − | 0.202877i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1173.33 | −1.65959 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1135.31 | −1.60128 | −0.800642 | − | 0.599143i | \(-0.795508\pi\) | ||||
−0.800642 | + | 0.599143i | \(0.795508\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 370.046i | 0.520458i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 36.6621i | − | 0.0514195i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 303.919i | 0.423876i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.5461 | 0.0174493 | 0.00872467 | − | 0.999962i | \(-0.497223\pi\) | ||||
0.00872467 | + | 0.999962i | \(0.497223\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 831.670i | 1.15350i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.8261 | 0.0371038 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 387.455 | 0.532951 | 0.266475 | − | 0.963842i | \(-0.414141\pi\) | ||||
0.266475 | + | 0.963842i | \(0.414141\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −665.632 | −0.913076 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 266.455 | 0.364507 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −550.259 | −0.750694 | −0.375347 | − | 0.926884i | \(-0.622477\pi\) | ||||
−0.375347 | + | 0.926884i | \(0.622477\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 48.3173i | − | 0.0655595i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −72.2829 | −0.0978118 | −0.0489059 | − | 0.998803i | \(-0.515573\pi\) | ||||
−0.0489059 | + | 0.998803i | \(0.515573\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 356.906 | − | 77.4706i | 0.481655 | − | 0.104549i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 330.742i | 0.445144i | 0.974916 | + | 0.222572i | \(0.0714453\pi\) | ||||
−0.974916 | + | 0.222572i | \(0.928555\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 223.576 | 0.299298 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1269.70i | − | 1.69519i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 964.716i | 1.28458i | 0.766464 | + | 0.642288i | \(0.222015\pi\) | ||||
−0.766464 | + | 0.642288i | \(0.777985\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1006.10i | − | 1.33612i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 865.952 | 1.14393 | 0.571963 | − | 0.820279i | \(-0.306182\pi\) | ||||
0.571963 | + | 0.820279i | \(0.306182\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.42226i | 0.00846148i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 280.071 | 0.368030 | 0.184015 | − | 0.982923i | \(-0.441091\pi\) | ||||
0.184015 | + | 0.982923i | \(0.441091\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 431.904i | − | 0.566061i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −935.156 | −1.21924 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −627.438 | −0.815915 | −0.407957 | − | 0.913001i | \(-0.633759\pi\) | ||||
−0.407957 | + | 0.913001i | \(0.633759\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −530.252 | −0.687746 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 684.186i | 0.885105i | 0.896743 | + | 0.442552i | \(0.145927\pi\) | ||||
−0.896743 | + | 0.442552i | \(0.854073\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 136.308 | 0.175429 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −281.760 | − | 1298.06i | −0.361694 | − | 1.66632i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 9.55717i | − | 0.0122371i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −516.374 | −0.659481 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 918.570i | − | 1.16718i | −0.812049 | − | 0.583589i | \(-0.801648\pi\) | ||
0.812049 | − | 0.583589i | \(-0.198352\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 146.065i | − | 0.185126i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 736.315i | 0.930866i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 427.841i | 0.539522i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1245.67i | − | 1.56295i | −0.623938 | − | 0.781474i | \(-0.714468\pi\) | ||
0.623938 | − | 0.781474i | \(-0.285532\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −128.028 | −0.160236 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 169.850i | 0.212047i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 250.839 | 0.312377 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.3341 | −0.0301537 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1198.51 | 1.48148 | 0.740738 | − | 0.671794i | \(-0.234476\pi\) | ||||
0.740738 | + | 0.671794i | \(0.234476\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 295.291i | 0.364107i | 0.983289 | + | 0.182054i | \(0.0582744\pi\) | ||||
−0.983289 | + | 0.182054i | \(0.941726\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 210.397i | 0.258791i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 482.701 | − | 104.776i | 0.590821 | − | 0.128244i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 311.366i | − | 0.380179i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −271.018 | −0.330107 | −0.165054 | − | 0.986285i | \(-0.552780\pi\) | ||||
−0.165054 | + | 0.986285i | \(0.552780\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 146.642 | 0.178180 | 0.0890900 | − | 0.996024i | \(-0.471604\pi\) | ||||
0.0890900 | + | 0.996024i | \(0.471604\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1037.94i | 1.25506i | 0.778591 | + | 0.627532i | \(0.215935\pi\) | ||||
−0.778591 | + | 0.627532i | \(0.784065\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1008.15i | 1.21610i | 0.793898 | + | 0.608050i | \(0.208048\pi\) | ||||
−0.793898 | + | 0.608050i | \(0.791952\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 75.1143i | − | 0.0903903i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 183.759 | 0.220599 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1179.32 | 1.40899 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1596.51i | 1.90287i | 0.307850 | + | 0.951435i | \(0.400390\pi\) | ||||
−0.307850 | + | 0.951435i | \(0.599610\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 520.381 | 0.618765 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −725.824 | −0.861002 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −900.671 | −1.06337 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 475.841i | 0.560472i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 6.88629i | − | 0.00809199i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −733.131 | −0.859474 | −0.429737 | − | 0.902954i | \(-0.641394\pi\) | ||||
−0.429737 | + | 0.902954i | \(0.641394\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 473.032i | 0.551963i | 0.961163 | + | 0.275981i | \(0.0890028\pi\) | ||||
−0.961163 | + | 0.275981i | \(0.910997\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 694.138 | 0.808077 | 0.404038 | − | 0.914742i | \(-0.367606\pi\) | ||||
0.404038 | + | 0.914742i | \(0.367606\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1240.60 | 1.44088 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 301.961i | 0.349897i | 0.984578 | + | 0.174948i | \(0.0559759\pi\) | ||||
−0.984578 | + | 0.174948i | \(0.944024\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 399.007i | − | 0.460216i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 284.546i | 0.327440i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −129.648 | −0.148850 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 741.556i | 0.849434i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 954.932i | 1.08886i | 0.838806 | + | 0.544431i | \(0.183254\pi\) | ||||
−0.838806 | + | 0.544431i | \(0.816746\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.1589 | 0.0195210 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −355.458 | −0.403471 | −0.201736 | − | 0.979440i | \(-0.564658\pi\) | ||||
−0.201736 | + | 0.979440i | \(0.564658\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −378.377 | −0.428514 | −0.214257 | − | 0.976777i | \(-0.568733\pi\) | ||||
−0.214257 | + | 0.976777i | \(0.568733\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1001.77i | − | 1.12939i | −0.825301 | − | 0.564693i | \(-0.808994\pi\) | ||
0.825301 | − | 0.564693i | \(-0.191006\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 606.212i | − | 0.681904i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −78.9303 | −0.0885863 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −231.932 | + | 50.3434i | −0.259722 | + | 0.0563756i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.2326 | 0.0192114 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 732.247 | 0.814513 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 573.363i | − | 0.636363i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 461.331i | 0.510887i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1687.59i | 1.86063i | 0.366765 | + | 0.930314i | \(0.380465\pi\) | ||||
−0.366765 | + | 0.930314i | \(0.619535\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −615.980 | −0.677646 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 932.015i | − | 1.02307i | −0.859263 | − | 0.511534i | \(-0.829077\pi\) | ||
0.859263 | − | 0.511534i | \(-0.170923\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 171.918 | 0.188300 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −485.286 | −0.529210 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 702.329 | 0.764232 | 0.382116 | − | 0.924114i | \(-0.375195\pi\) | ||||
0.382116 | + | 0.924114i | \(0.375195\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −533.047 | −0.578770 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.6444 | −0.0277838 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 436.614i | 0.470997i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1337.11 | 1.43930 | 0.719650 | − | 0.694337i | \(-0.244302\pi\) | ||||
0.719650 | + | 0.694337i | \(0.244302\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 332.891 | − | 72.2578i | 0.357563 | − | 0.0776131i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1110.64i | − | 1.19040i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1370.84 | 1.46301 | 0.731507 | − | 0.681834i | \(-0.238817\pi\) | ||||
0.731507 | + | 0.681834i | \(0.238817\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1090.32i | 1.16115i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 879.481i | 0.934624i | 0.884093 | + | 0.467312i | \(0.154777\pi\) | ||||
−0.884093 | + | 0.467312i | \(0.845223\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 62.6749i | − | 0.0664633i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −235.757 | −0.248951 | −0.124476 | − | 0.992223i | \(-0.539725\pi\) | ||||
−0.124476 | + | 0.992223i | \(0.539725\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 673.068i | − | 0.709239i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −375.322 | −0.394661 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 518.106i | 0.543657i | 0.962346 | + | 0.271829i | \(0.0876284\pi\) | ||||
−0.962346 | + | 0.271829i | \(0.912372\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −128.271 | −0.134034 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1258.90 | 1.31272 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −711.348 | −0.740216 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 666.573i | − | 0.692184i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.2136 | 0.0560637 | 0.0280319 | − | 0.999607i | \(-0.491076\pi\) | ||||
0.0280319 | + | 0.999607i | \(0.491076\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 89.6035 | + | 412.803i | 0.0924701 | + | 0.426009i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1229.47i | − | 1.26619i | −0.774075 | − | 0.633093i | \(-0.781785\pi\) | ||
0.774075 | − | 0.633093i | \(-0.218215\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 348.607 | 0.358280 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 957.658i | − | 0.980202i | −0.871666 | − | 0.490101i | \(-0.836960\pi\) | ||
0.871666 | − | 0.490101i | \(-0.163040\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 130.606i | 0.133407i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 226.743i | − | 0.231135i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1624.35i | − | 1.65244i | −0.563348 | − | 0.826220i | \(-0.690487\pi\) | ||
0.563348 | − | 0.826220i | \(-0.309513\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 221.664i | − | 0.224583i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.3064 | 0.0235657 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 496.019i | − | 0.500524i | −0.968178 | − | 0.250262i | \(-0.919483\pi\) | ||
0.968178 | − | 0.250262i | \(-0.0805167\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 624.678 | 0.629082 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −231.271 | −0.231967 | −0.115983 | − | 0.993251i | \(-0.537002\pi\) | ||||
−0.115983 | + | 0.993251i | \(0.537002\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 221.514 | 0.221735 |
(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 | 1900.3.e.g.1101.10 | yes | 14 | |
5.2 | odd | 4 | 1900.3.g.d.949.19 | 28 | |||
5.3 | odd | 4 | 1900.3.g.d.949.10 | 28 | |||
5.4 | even | 2 | 1900.3.e.h.1101.5 | yes | 14 | ||
19.18 | odd | 2 | inner | 1900.3.e.g.1101.5 | ✓ | 14 | |
95.18 | even | 4 | 1900.3.g.d.949.20 | 28 | |||
95.37 | even | 4 | 1900.3.g.d.949.9 | 28 | |||
95.94 | odd | 2 | 1900.3.e.h.1101.10 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.3.e.g.1101.5 | ✓ | 14 | 19.18 | odd | 2 | inner | |
1900.3.e.g.1101.10 | yes | 14 | 1.1 | even | 1 | trivial | |
1900.3.e.h.1101.5 | yes | 14 | 5.4 | even | 2 | ||
1900.3.e.h.1101.10 | yes | 14 | 95.94 | odd | 2 | ||
1900.3.g.d.949.9 | 28 | 95.37 | even | 4 | |||
1900.3.g.d.949.10 | 28 | 5.3 | odd | 4 | |||
1900.3.g.d.949.19 | 28 | 5.2 | odd | 4 | |||
1900.3.g.d.949.20 | 28 | 95.18 | even | 4 |