Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(15,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, 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("224.15");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.g (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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.292213762624.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 15.3 | ||
Root | \(1.85837 + 0.739226i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.15 |
Dual form | 224.3.g.b.15.4 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.0974366 | −0.0324789 | −0.0162394 | − | 0.999868i | \(-0.505169\pi\) | ||||
−0.0162394 | + | 0.999868i | \(0.505169\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.46547i | − 0.693094i | −0.938033 | − | 0.346547i | \(-0.887354\pi\) | ||||
0.938033 | − | 0.346547i | \(-0.112646\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.64575i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.99051 | −0.998945 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.92866 | 0.266242 | 0.133121 | − | 0.991100i | \(-0.457500\pi\) | ||||
0.133121 | + | 0.991100i | \(0.457500\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 19.1586i | − 1.47374i | −0.676036 | − | 0.736869i | \(-0.736304\pi\) | ||||
0.676036 | − | 0.736869i | \(-0.263696\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.337664i | 0.0225109i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.3897 | −0.846456 | −0.423228 | − | 0.906023i | \(-0.639103\pi\) | ||||
−0.423228 | + | 0.906023i | \(0.639103\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.09744 | −0.426181 | −0.213090 | − | 0.977032i | \(-0.568353\pi\) | ||||
−0.213090 | + | 0.977032i | \(0.568353\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.257793i | 0.0122759i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 16.7598i | − 0.728687i | −0.931265 | − | 0.364344i | \(-0.881293\pi\) | ||||
0.931265 | − | 0.364344i | \(-0.118707\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.9905 | 0.519620 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.75293 | 0.0649234 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 27.1649i | − 0.936720i | −0.883538 | − | 0.468360i | \(-0.844845\pi\) | ||||
0.883538 | − | 0.468360i | \(-0.155155\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 44.8923i | − 1.44814i | −0.689728 | − | 0.724069i | \(-0.742270\pi\) | ||||
0.689728 | − | 0.724069i | \(-0.257730\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.285359 | −0.00864723 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.16878 | −0.261965 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 39.5687i | 1.06943i | 0.845034 | + | 0.534713i | \(0.179580\pi\) | ||||
−0.845034 | + | 0.534713i | \(0.820420\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.86675i | 0.0478653i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 45.8766 | 1.11894 | 0.559471 | − | 0.828850i | \(-0.311004\pi\) | ||||
0.559471 | + | 0.828850i | \(0.311004\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −61.0334 | −1.41938 | −0.709690 | − | 0.704514i | \(-0.751165\pi\) | ||||
−0.709690 | + | 0.704514i | \(0.751165\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 31.1563i | 0.692363i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 46.2793i | 0.984666i | 0.870407 | + | 0.492333i | \(0.163856\pi\) | ||||
−0.870407 | + | 0.492333i | \(0.836144\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.40209 | 0.0274919 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.69424i | 0.182910i | 0.995809 | + | 0.0914551i | \(0.0291518\pi\) | ||||
−0.995809 | + | 0.0914551i | \(0.970848\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 10.1492i | − 0.184531i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.788986 | 0.0138419 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 114.554 | 1.94159 | 0.970796 | − | 0.239907i | \(-0.0771170\pi\) | ||||
0.970796 | + | 0.239907i | \(0.0771170\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 7.48032i | − 0.122628i | −0.998119 | − | 0.0613141i | \(-0.980471\pi\) | ||||
0.998119 | − | 0.0613141i | \(-0.0195291\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 23.7866i | 0.377566i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −66.3935 | −1.02144 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0590 | 0.179985 | 0.0899925 | − | 0.995942i | \(-0.471316\pi\) | ||||
0.0899925 | + | 0.995942i | \(0.471316\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.63302i | 0.0236669i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 129.187i | 1.81953i | 0.415124 | + | 0.909765i | \(0.363738\pi\) | ||||
−0.415124 | + | 0.909765i | \(0.636262\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −18.2854 | −0.250484 | −0.125242 | − | 0.992126i | \(-0.539971\pi\) | ||||
−0.125242 | + | 0.992126i | \(0.539971\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.26575 | −0.0168767 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 7.74851i | − 0.100630i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 42.6168i | 0.539454i | 0.962937 | + | 0.269727i | \(0.0869334\pi\) | ||||
−0.962937 | + | 0.269727i | \(0.913067\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 80.7438 | 0.996836 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 109.670 | 1.32133 | 0.660663 | − | 0.750683i | \(-0.270275\pi\) | ||||
0.660663 | + | 0.750683i | \(0.270275\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 49.8673i | 0.586674i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.64685i | 0.0304236i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −80.9162 | −0.909170 | −0.454585 | − | 0.890703i | \(-0.650212\pi\) | ||||
−0.454585 | + | 0.890703i | \(0.650212\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −50.6889 | −0.557020 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.37415i | 0.0470339i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 28.0614i | 0.295384i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 162.086 | 1.67099 | 0.835495 | − | 0.549498i | \(-0.185181\pi\) | ||||
0.835495 | + | 0.549498i | \(0.185181\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −26.3301 | −0.265961 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 106.827i | 1.05769i | 0.848717 | + | 0.528847i | \(0.177375\pi\) | ||||
−0.848717 | + | 0.528847i | \(0.822625\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 126.626i | − 1.22938i | −0.788768 | − | 0.614691i | \(-0.789281\pi\) | ||||
0.788768 | − | 0.614691i | \(-0.210719\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.893374 | 0.00850832 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −87.0191 | −0.813263 | −0.406632 | − | 0.913592i | \(-0.633297\pi\) | ||||
−0.406632 | + | 0.913592i | \(0.633297\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 189.921i | − 1.74240i | −0.490930 | − | 0.871199i | \(-0.663343\pi\) | ||||
0.490930 | − | 0.871199i | \(-0.336657\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 3.85544i | − 0.0347337i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −40.1848 | −0.355617 | −0.177809 | − | 0.984065i | \(-0.556901\pi\) | ||||
−0.177809 | + | 0.984065i | \(0.556901\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −58.0806 | −0.505049 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 172.245i | 1.47218i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 38.0717i | 0.319930i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −112.423 | −0.929115 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.47006 | −0.0363420 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 131.655i | − 1.05324i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 153.657i | − 1.20989i | −0.796266 | − | 0.604947i | \(-0.793194\pi\) | ||||
0.796266 | − | 0.604947i | \(-0.206806\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.94688 | 0.0460999 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −61.8649 | −0.472251 | −0.236126 | − | 0.971723i | \(-0.575878\pi\) | ||||
−0.236126 | + | 0.971723i | \(0.575878\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.4238i | 0.161081i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 6.07474i | − 0.0449981i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 105.943 | 0.773307 | 0.386653 | − | 0.922225i | \(-0.373631\pi\) | ||||
0.386653 | + | 0.922225i | \(0.373631\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 185.384 | 1.33370 | 0.666848 | − | 0.745194i | \(-0.267643\pi\) | ||||
0.666848 | + | 0.745194i | \(0.267643\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 4.50930i | − 0.0319808i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 56.1090i | − 0.392371i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −94.1392 | −0.649236 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.682056 | 0.00463984 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 47.4096i | 0.318185i | 0.987264 | + | 0.159093i | \(0.0508568\pi\) | ||||
−0.987264 | + | 0.159093i | \(0.949143\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 114.576i | − 0.758780i | −0.925237 | − | 0.379390i | \(-0.876134\pi\) | ||||
0.925237 | − | 0.379390i | \(-0.123866\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 129.371 | 0.845563 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −155.573 | −1.00370 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 294.095i | − 1.87322i | −0.350378 | − | 0.936608i | \(-0.613947\pi\) | ||||
0.350378 | − | 0.936608i | \(-0.386053\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 0.944573i | − 0.00594071i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −44.3423 | −0.275418 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −171.021 | −1.04921 | −0.524603 | − | 0.851347i | \(-0.675786\pi\) | ||||
−0.524603 | + | 0.851347i | \(0.675786\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.988902i | 0.00599335i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 120.657i | − 0.722499i | −0.932469 | − | 0.361249i | \(-0.882350\pi\) | ||||
0.932469 | − | 0.361249i | \(-0.117650\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −198.052 | −1.17190 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 72.8001 | 0.425731 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 108.339i | − 0.626236i | −0.949714 | − | 0.313118i | \(-0.898626\pi\) | ||||
0.949714 | − | 0.313118i | \(-0.101374\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 34.3696i | − 0.196398i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.1617 | −0.0630607 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 161.438 | 0.901886 | 0.450943 | − | 0.892553i | \(-0.351088\pi\) | ||||
0.450943 | + | 0.892553i | \(0.351088\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 7.14696i | − 0.0394860i | −0.999805 | − | 0.0197430i | \(-0.993715\pi\) | ||||
0.999805 | − | 0.0197430i | \(-0.00628479\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.728856i | 0.00398282i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 137.124 | 0.741212 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −42.1427 | −0.225362 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 4.63782i | − 0.0245388i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 73.2983i | 0.383761i | 0.981418 | + | 0.191880i | \(0.0614586\pi\) | ||||
−0.981418 | + | 0.191880i | \(0.938541\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −85.0705 | −0.440780 | −0.220390 | − | 0.975412i | \(-0.570733\pi\) | ||||
−0.220390 | + | 0.975412i | \(0.570733\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.46916 | 0.0331752 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 140.460i | 0.712996i | 0.934296 | + | 0.356498i | \(0.116029\pi\) | ||||
−0.934296 | + | 0.356498i | \(0.883971\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 143.082i | 0.719006i | 0.933144 | + | 0.359503i | \(0.117054\pi\) | ||||
−0.933144 | + | 0.359503i | \(0.882946\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.17499 | −0.00584571 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −71.8715 | −0.354047 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 158.984i | − 0.775532i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 150.679i | 0.727919i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.7146 | −0.113467 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 111.955 | 0.530591 | 0.265295 | − | 0.964167i | \(-0.414531\pi\) | ||||
0.265295 | + | 0.964167i | \(0.414531\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 12.5875i | − 0.0590962i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 211.509i | 0.983765i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −118.774 | −0.547345 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.78166 | 0.00813545 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 275.687i | 1.24745i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 311.438i | − 1.39658i | −0.715814 | − | 0.698291i | \(-0.753944\pi\) | ||||
0.715814 | − | 0.698291i | \(-0.246056\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −116.791 | −0.519072 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −74.3581 | −0.327569 | −0.163784 | − | 0.986496i | \(-0.552370\pi\) | ||||
−0.163784 | + | 0.986496i | \(0.552370\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 78.2710i | − 0.341795i | −0.985289 | − | 0.170897i | \(-0.945333\pi\) | ||||
0.985289 | − | 0.170897i | \(-0.0546667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.754988i | 0.00326835i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 93.0573 | 0.399388 | 0.199694 | − | 0.979858i | \(-0.436005\pi\) | ||||
0.199694 | + | 0.979858i | \(0.436005\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 160.380 | 0.682466 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 4.15244i | − 0.0175208i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 291.605i | 1.22011i | 0.792361 | + | 0.610053i | \(0.208852\pi\) | ||||
−0.792361 | + | 0.610053i | \(0.791148\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 223.748 | 0.928413 | 0.464207 | − | 0.885727i | \(-0.346340\pi\) | ||||
0.464207 | + | 0.885727i | \(0.346340\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −23.6438 | −0.0972996 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 24.2583i | 0.0990135i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 155.135i | 0.628079i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.6859 | −0.0429151 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 310.605 | 1.23747 | 0.618734 | − | 0.785600i | \(-0.287646\pi\) | ||||
0.618734 | + | 0.785600i | \(0.287646\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 49.0838i | − 0.194007i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 4.85889i | − 0.0190545i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 175.472 | 0.682769 | 0.341385 | − | 0.939924i | \(-0.389104\pi\) | ||||
0.341385 | + | 0.939924i | \(0.389104\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 104.689 | 0.404205 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 244.226i | 0.935732i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 312.127i | − 1.18680i | −0.804910 | − | 0.593398i | \(-0.797786\pi\) | ||||
0.804910 | − | 0.593398i | \(-0.202214\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.5951 | 0.126774 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.88419 | 0.0295288 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 142.817i | 0.530918i | 0.964122 | + | 0.265459i | \(0.0855234\pi\) | ||||
−0.964122 | + | 0.265459i | \(0.914477\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 266.117i | 0.981982i | 0.871165 | + | 0.490991i | \(0.163365\pi\) | ||||
−0.871165 | + | 0.490991i | \(0.836635\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.93895 | 0.0180914 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 38.0448 | 0.138345 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 366.740i | 1.32397i | 0.749516 | + | 0.661986i | \(0.230286\pi\) | ||||
−0.749516 | + | 0.661986i | \(0.769714\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 403.604i | 1.44661i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 147.977 | 0.526607 | 0.263303 | − | 0.964713i | \(-0.415188\pi\) | ||||
0.263303 | + | 0.964713i | \(0.415188\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −327.739 | −1.15809 | −0.579043 | − | 0.815297i | \(-0.696574\pi\) | ||||
−0.579043 | + | 0.815297i | \(0.696574\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 2.73421i | − 0.00959372i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 121.378i | − 0.422920i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −81.9352 | −0.283513 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.7931 | −0.0542718 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 259.881i | 0.886966i | 0.896283 | + | 0.443483i | \(0.146257\pi\) | ||||
−0.896283 | + | 0.443483i | \(0.853743\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 396.983i | − 1.34571i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.13375 | 0.0172853 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −321.094 | −1.07389 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 161.479i | 0.536475i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 10.4089i | − 0.0343527i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −25.9228 | −0.0849929 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −290.462 | −0.946131 | −0.473065 | − | 0.881027i | \(-0.656853\pi\) | ||||
−0.473065 | + | 0.881027i | \(0.656853\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.3380i | 0.0399289i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 74.9081i | 0.240862i | 0.992722 | + | 0.120431i | \(0.0384276\pi\) | ||||
−0.992722 | + | 0.120431i | \(0.961572\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 284.507 | 0.908969 | 0.454485 | − | 0.890755i | \(-0.349823\pi\) | ||||
0.454485 | + | 0.890755i | \(0.349823\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 82.4319 | 0.261689 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.2631i | 0.0386850i | 0.999813 | + | 0.0193425i | \(0.00615729\pi\) | ||||
−0.999813 | + | 0.0193425i | \(0.993843\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 79.5567i | − 0.249394i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.47885 | 0.0264139 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 116.520 | 0.360743 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 248.880i | − 0.765784i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.5053i | 0.0565911i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 122.443 | 0.372169 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −194.466 | −0.587510 | −0.293755 | − | 0.955881i | \(-0.594905\pi\) | ||||
−0.293755 | + | 0.955881i | \(0.594905\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 355.743i | − 1.06830i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 41.7901i | − 0.124747i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.596077 | 0.00176877 | 0.000884387 | − | 1.00000i | \(-0.499718\pi\) | ||||
0.000884387 | 1.00000i | \(0.499718\pi\) | ||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.91547 | 0.0115500 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 131.474i | − 0.385555i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.65918 | 0.0164034 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 204.867 | 0.590394 | 0.295197 | − | 0.955436i | \(-0.404615\pi\) | ||||
0.295197 | + | 0.955436i | \(0.404615\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 128.396i | − 0.367898i | −0.982936 | − | 0.183949i | \(-0.941112\pi\) | ||||
0.982936 | − | 0.183949i | \(-0.0588882\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 33.5837i | − 0.0956801i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −190.841 | −0.540627 | −0.270314 | − | 0.962772i | \(-0.587127\pi\) | ||||
−0.270314 | + | 0.962772i | \(0.587127\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 447.692 | 1.26111 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 3.70957i | − 0.0103910i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 215.704i | − 0.600847i | −0.953806 | − | 0.300424i | \(-0.902872\pi\) | ||||
0.953806 | − | 0.300424i | \(-0.0971281\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −295.432 | −0.818370 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.9541 | 0.0301766 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 63.3674i | 0.173609i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 454.789i | 1.23921i | 0.784915 | + | 0.619604i | \(0.212707\pi\) | ||||
−0.784915 | + | 0.619604i | \(0.787293\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −412.454 | −1.11776 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.6485 | 0.0691335 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 360.748i | − 0.967153i | −0.875302 | − | 0.483576i | \(-0.839338\pi\) | ||||
0.875302 | − | 0.483576i | \(-0.160662\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.8280i | 0.0342080i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −520.441 | −1.38048 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 268.427 | 0.708250 | 0.354125 | − | 0.935198i | \(-0.384779\pi\) | ||||
0.354125 | + | 0.935198i | \(0.384779\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.9718i | 0.0392960i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 581.532i | − 1.51836i | −0.650881 | − | 0.759180i | \(-0.725600\pi\) | ||||
0.650881 | − | 0.759180i | \(-0.274400\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.8522 | −0.0697461 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 548.721 | 1.41788 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 512.278i | − 1.31691i | −0.752620 | − | 0.658455i | \(-0.771210\pi\) | ||||
0.752620 | − | 0.658455i | \(-0.228790\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 241.169i | 0.616801i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.02790 | 0.0153382 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 147.687 | 0.373892 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 81.3250i | − 0.204849i | −0.994741 | − | 0.102424i | \(-0.967340\pi\) | ||||
0.994741 | − | 0.102424i | \(-0.0326600\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 2.08746i | − 0.00523173i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 527.441 | 1.31531 | 0.657657 | − | 0.753318i | \(-0.271548\pi\) | ||||
0.657657 | + | 0.753318i | \(0.271548\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −860.073 | −2.13418 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 279.815i | − 0.690902i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 115.883i | 0.284726i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −58.6727 | −0.143454 | −0.0717270 | − | 0.997424i | \(-0.522851\pi\) | ||||
−0.0717270 | + | 0.997424i | \(0.522851\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.3227 | −0.0251161 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 303.081i | − 0.733853i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 380.058i | − 0.915803i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.0632 | −0.0433169 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −760.704 | −1.81552 | −0.907761 | − | 0.419487i | \(-0.862210\pi\) | ||||
−0.907761 | + | 0.419487i | \(0.862210\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 46.2918i | − 0.109957i | −0.998488 | − | 0.0549784i | \(-0.982491\pi\) | ||||
0.998488 | − | 0.0549784i | \(-0.0175090\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 416.074i | − 0.983627i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −186.930 | −0.439835 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.7911 | −0.0463491 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.46707i | 0.0127437i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 336.176i | 0.779991i | 0.920817 | + | 0.389996i | \(0.127523\pi\) | ||||
−0.920817 | + | 0.389996i | \(0.872477\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −372.694 | −0.860725 | −0.430363 | − | 0.902656i | \(-0.641614\pi\) | ||||
−0.430363 | + | 0.902656i | \(0.641614\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.17260 | 0.0210864 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 135.711i | 0.310553i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 397.478i | − 0.905418i | −0.891658 | − | 0.452709i | \(-0.850458\pi\) | ||||
0.891658 | − | 0.452709i | \(-0.149542\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 62.9335 | 0.142706 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −273.530 | −0.617450 | −0.308725 | − | 0.951151i | \(-0.599902\pi\) | ||||
−0.308725 | + | 0.951151i | \(0.599902\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 280.413i | 0.630141i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 4.61943i | − 0.0103343i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 428.702 | 0.954792 | 0.477396 | − | 0.878688i | \(-0.341581\pi\) | ||||
0.477396 | + | 0.878688i | \(0.341581\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 134.357 | 0.297909 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.1639i | 0.0246443i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 175.661i | 0.386068i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.0500 | 0.0219913 | 0.0109956 | − | 0.999940i | \(-0.496500\pi\) | ||||
0.0109956 | + | 0.999940i | \(0.496500\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.2243 | −0.0549548 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 825.802i | 1.79133i | 0.444732 | + | 0.895664i | \(0.353299\pi\) | ||||
−0.444732 | + | 0.895664i | \(0.646701\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 114.707i | − 0.247748i | −0.992298 | − | 0.123874i | \(-0.960468\pi\) | ||||
0.992298 | − | 0.123874i | \(-0.0395318\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.1585 | 0.0325989 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 201.727 | 0.431964 | 0.215982 | − | 0.976397i | \(-0.430705\pi\) | ||||
0.215982 | + | 0.976397i | \(0.430705\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 31.9051i | − 0.0680280i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28.6556i | 0.0608399i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −178.746 | −0.377899 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −105.190 | −0.221452 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 87.1561i | − 0.182717i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 597.538i | − 1.24747i | −0.781636 | − | 0.623735i | \(-0.785615\pi\) | ||||
0.781636 | − | 0.623735i | \(-0.214385\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 758.081 | 1.57605 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.32056 | 0.00894526 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 561.705i | − 1.15815i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 345.125i | 0.708675i | 0.935118 | + | 0.354337i | \(0.115294\pi\) | ||||
−0.935118 | + | 0.354337i | \(0.884706\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.6637 | 0.0340770 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −373.498 | −0.760689 | −0.380344 | − | 0.924845i | \(-0.624195\pi\) | ||||
−0.380344 | + | 0.924845i | \(0.624195\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 390.896i | 0.792892i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 91.2464i | 0.184336i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 341.796 | 0.687718 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 850.317 | 1.70404 | 0.852021 | − | 0.523508i | \(-0.175377\pi\) | ||||
0.852021 | + | 0.523508i | \(0.175377\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.7564i | 0.0234659i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 459.256i | − 0.913033i | −0.889715 | − | 0.456517i | \(-0.849097\pi\) | ||||
0.889715 | − | 0.456517i | \(-0.150903\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 370.206 | 0.733082 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.2975 | 0.0380620 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 673.910i | 1.32399i | 0.749509 | + | 0.661994i | \(0.230290\pi\) | ||||
−0.749509 | + | 0.661994i | \(0.769710\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 48.3785i | 0.0946742i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.1943 | −0.0276691 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −438.820 | −0.852078 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 135.536i | 0.262159i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.5562i | 0.0203394i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −486.473 | −0.933729 | −0.466864 | − | 0.884329i | \(-0.654616\pi\) | ||||
−0.466864 | + | 0.884329i | \(0.654616\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 680.087 | 1.30036 | 0.650179 | − | 0.759781i | \(-0.274694\pi\) | ||||
0.650179 | + | 0.759781i | \(0.274694\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.34886i | 0.00637878i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 645.988i | 1.22578i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 248.109 | 0.469015 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1029.90 | −1.93954 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 878.931i | − 1.64903i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 301.562i | 0.563668i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.7299 | −0.0292922 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.5006 | −0.0380346 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 794.999i | 1.46950i | 0.678339 | + | 0.734749i | \(0.262700\pi\) | ||||
−0.678339 | + | 0.734749i | \(0.737300\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.696375i | 0.00128246i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −658.167 | −1.20765 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 736.752 | 1.34690 | 0.673448 | − | 0.739235i | \(-0.264813\pi\) | ||||
0.673448 | + | 0.739235i | \(0.264813\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 67.2518i | 0.122499i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 219.966i | 0.399212i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 112.754 | 0.203894 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.3609 | −0.0240737 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 415.758i | 0.746423i | 0.927746 | + | 0.373212i | \(0.121743\pi\) | ||||
−0.927746 | + | 0.373212i | \(0.878257\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1169.31i | 2.09179i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.10624 | 0.00731950 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 96.4996 | 0.171402 | 0.0857012 | − | 0.996321i | \(-0.472687\pi\) | ||||
0.0857012 | + | 0.996321i | \(0.472687\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 139.259i | 0.246476i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 213.628i | − 0.376769i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 347.953 | 0.611517 | 0.305759 | − | 0.952109i | \(-0.401090\pi\) | ||||
0.305759 | + | 0.952109i | \(0.401090\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.7251 | 0.0240370 | 0.0120185 | − | 0.999928i | \(-0.496174\pi\) | ||||
0.0120185 | + | 0.999928i | \(0.496174\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 7.14193i | − 0.0124641i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 217.718i | − 0.378641i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −827.320 | −1.43383 | −0.716915 | − | 0.697161i | \(-0.754446\pi\) | ||||
−0.716915 | + | 0.697161i | \(0.754446\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.28898 | 0.0143160 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 290.160i | − 0.499414i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.3911i | 0.0486983i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 596.912 | 1.02036 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 675.987 | 1.15160 | 0.575798 | − | 0.817592i | \(-0.304692\pi\) | ||||
0.575798 | + | 0.817592i | \(0.304692\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 363.512i | 0.617169i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 13.6860i | − 0.0231573i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −414.116 | −0.698341 | −0.349171 | − | 0.937059i | \(-0.613537\pi\) | ||||
−0.349171 | + | 0.937059i | \(0.613537\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 131.936 | 0.221742 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 13.9414i | − 0.0233525i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 723.303i | 1.20752i | 0.797167 | + | 0.603759i | \(0.206331\pi\) | ||||
−0.797167 | + | 0.603759i | \(0.793669\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 68.7503 | 0.114393 | 0.0571966 | − | 0.998363i | \(-0.481784\pi\) | ||||
0.0571966 | + | 0.998363i | \(0.481784\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −108.416 | −0.179795 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 389.599i | 0.643965i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 141.263i | 0.232724i | 0.993207 | + | 0.116362i | \(0.0371232\pi\) | ||||
−0.993207 | + | 0.116362i | \(0.962877\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.00292 | 0.0114990 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 886.646 | 1.45114 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 96.7370i | − 0.157809i | −0.996882 | − | 0.0789046i | \(-0.974858\pi\) | ||||
0.996882 | − | 0.0789046i | \(-0.0251422\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.4909i | 0.0251884i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 580.418 | 0.940709 | 0.470355 | − | 0.882478i | \(-0.344126\pi\) | ||||
0.470355 | + | 0.882478i | \(0.344126\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −157.945 | −0.255161 | −0.127581 | − | 0.991828i | \(-0.540721\pi\) | ||||
−0.127581 | + | 0.991828i | \(0.540721\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 29.3788i | − 0.0473089i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 214.084i | 0.343634i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −131.484 | −0.210375 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.31067 | 0.00368528 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 569.384i | − 0.905221i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 771.793i | 1.22313i | 0.791195 | + | 0.611564i | \(0.209459\pi\) | ||||
−0.791195 | + | 0.611564i | \(0.790541\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.9085 | −0.0172330 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −532.493 | −0.838571 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 134.110i | 0.210534i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 1161.45i | − 1.81761i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −586.903 | −0.915605 | −0.457802 | − | 0.889054i | \(-0.651363\pi\) | ||||
−0.457802 | + | 0.889054i | \(0.651363\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −865.328 | −1.34577 | −0.672883 | − | 0.739749i | \(-0.734944\pi\) | ||||
−0.672883 | + | 0.739749i | \(0.734944\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 20.6087i | − 0.0319515i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 132.883i | − 0.205383i | −0.994713 | − | 0.102691i | \(-0.967255\pi\) | ||||
0.994713 | − | 0.102691i | \(-0.0327454\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 335.489 | 0.516933 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.5729 | 0.0177771 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 364.309i | − 0.557900i | −0.960306 | − | 0.278950i | \(-0.910014\pi\) | ||||
0.960306 | − | 0.278950i | \(-0.0899865\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 214.391i | 0.327315i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 164.395 | 0.250220 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.8972 | 0.0286756 | 0.0143378 | − | 0.999897i | \(-0.495436\pi\) | ||||
0.0143378 | + | 0.999897i | \(0.495436\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 339.106i | 0.513019i | 0.966542 | + | 0.256510i | \(0.0825725\pi\) | ||||
−0.966542 | + | 0.256510i | \(0.917427\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 26.8620i | − 0.0405159i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 74.2436 | 0.111644 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −455.278 | −0.682576 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 30.3454i | 0.0453594i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 21.9073i | − 0.0326487i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 674.869 | 1.00278 | 0.501389 | − | 0.865222i | \(-0.332823\pi\) | ||||
0.501389 | + | 0.865222i | \(0.332823\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 22.7715 | 0.0337355 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 988.747i | − 1.46048i | −0.683189 | − | 0.730242i | \(-0.739407\pi\) | ||||
0.683189 | − | 0.730242i | \(-0.260593\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 428.839i | − 0.631575i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.24520 | 0.0106391 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 518.125 | 0.758602 | 0.379301 | − | 0.925273i | \(-0.376165\pi\) | ||||
0.379301 | + | 0.925273i | \(0.376165\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 367.143i | − 0.535975i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.62646i | 0.0111011i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 185.728 | 0.269562 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 617.021 | 0.892940 | 0.446470 | − | 0.894799i | \(-0.352681\pi\) | ||||
0.446470 | + | 0.894799i | \(0.352681\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 69.6630i | 0.100524i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 642.442i | − 0.924377i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −660.153 | −0.947135 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.06718 | −0.0129717 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 97.6954i | − 0.139366i | −0.997569 | − | 0.0696829i | \(-0.977801\pi\) | ||||
0.997569 | − | 0.0696829i | \(-0.0221987\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 320.405i | − 0.455768i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.6268 | −0.0221657 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 282.638 | 0.399771 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1249.74i | 1.76269i | 0.472476 | + | 0.881343i | \(0.343360\pi\) | ||||
−0.472476 | + | 0.881343i | \(0.656640\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 383.147i | − 0.538885i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −752.386 | −1.05524 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −194.444 | −0.271950 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 28.4130i | − 0.0396277i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 424.744i | 0.590743i | 0.955382 | + | 0.295372i | \(0.0954435\pi\) | ||||
−0.955382 | + | 0.295372i | \(0.904557\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −335.022 | −0.464663 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.8012 | −0.0301538 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 352.886i | − 0.486739i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 79.1445i | 0.108865i | 0.998517 | + | 0.0544323i | \(0.0173349\pi\) | ||||
−0.998517 | + | 0.0544323i | \(0.982665\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −724.390 | −0.993676 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 878.255 | 1.20144 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 663.766i | − 0.905548i | −0.891625 | − | 0.452774i | \(-0.850434\pi\) | ||||
0.891625 | − | 0.452774i | \(-0.149566\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 2.36365i | − 0.00321584i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.3167 | 0.0479196 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −832.112 | −1.12600 | −0.562998 | − | 0.826458i | \(-0.690352\pi\) | ||||
−0.562998 | + | 0.826458i | \(0.690352\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 15.1159i | − 0.0203993i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 283.217i | − 0.381180i | −0.981670 | − | 0.190590i | \(-0.938960\pi\) | ||||
0.981670 | − | 0.190590i | \(-0.0610401\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 164.297 | 0.220532 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −985.989 | −1.31993 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 230.231i | 0.307385i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 374.981i | 0.499309i | 0.968335 | + | 0.249654i | \(0.0803170\pi\) | ||||
−0.968335 | + | 0.249654i | \(0.919683\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −30.2642 | −0.0401916 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −397.059 | −0.525906 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 63.0951i | − 0.0833488i | −0.999131 | − | 0.0416744i | \(-0.986731\pi\) | ||||
0.999131 | − | 0.0416744i | \(-0.0132692\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.78255i | 0.00630113i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 467.505 | 0.614330 | 0.307165 | − | 0.951656i | \(-0.400620\pi\) | ||||
0.307165 | + | 0.951656i | \(0.400620\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −502.485 | −0.658564 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 448.332i | − 0.586055i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 2194.69i | − 2.86140i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 900.573 | 1.17110 | 0.585548 | − | 0.810638i | \(-0.300879\pi\) | ||||
0.585548 | + | 0.810638i | \(0.300879\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.0974 | −0.0221756 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1222.76i | − 1.58184i | −0.611920 | − | 0.790919i | \(-0.709603\pi\) | ||||
0.611920 | − | 0.790919i | \(-0.290397\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 583.173i | − 0.752482i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.2005 | −0.0131281 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −371.483 | −0.476872 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 378.344i | 0.484435i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 47.6182i | − 0.0608151i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1019.18 | −1.29832 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −862.942 | −1.09650 | −0.548248 | − | 0.836316i | \(-0.684705\pi\) | ||||
−0.548248 | + | 0.836316i | \(0.684705\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 30.4126i | 0.0385457i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 106.319i | 0.134411i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −143.312 | −0.180722 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.27339 | −0.00411747 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1078.34i | 1.35300i | 0.736442 | + | 0.676500i | \(0.236504\pi\) | ||||
−0.736442 | + | 0.676500i | \(0.763496\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 665.947i | − 0.833476i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 727.477 | 0.908211 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −53.5516 | −0.0666894 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 153.667i | 0.190891i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 13.9156i | − 0.0172436i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 333.388 | 0.412099 | 0.206050 | − | 0.978542i | \(-0.433939\pi\) | ||||
0.206050 | + | 0.978542i | \(0.433939\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1246.04 | 1.53642 | 0.768211 | − | 0.640197i | \(-0.221147\pi\) | ||||
0.768211 | + | 0.640197i | \(0.221147\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 25.9295i | − 0.0318936i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 592.667i | 0.727199i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 494.214 | 0.604913 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 455.719 | 0.556433 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1458.68i | − 1.77671i | −0.459162 | − | 0.888353i | \(-0.651850\pi\) | ||||
0.459162 | − | 0.888353i | \(-0.348150\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 464.047i | 0.563848i | 0.959437 | + | 0.281924i | \(0.0909725\pi\) | ||||
−0.959437 | + | 0.281924i | \(0.909027\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.70695 | −0.00449328 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1077.41 | −1.30279 | −0.651394 | − | 0.758739i | \(-0.725816\pi\) | ||||
−0.651394 | + | 0.758739i | \(0.725816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.9354i | 0.0433479i | 0.999765 | + | 0.0216740i | \(0.00689958\pi\) | ||||
−0.999765 | + | 0.0216740i | \(0.993100\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 35.7339i | − 0.0430011i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 100.728 | 0.120922 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −418.134 | −0.500760 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 78.6932i | − 0.0940181i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 734.676i | − 0.875656i | −0.899059 | − | 0.437828i | \(-0.855748\pi\) | ||||
0.899059 | − | 0.437828i | \(-0.144252\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 103.069 | 0.122555 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.4183 | −0.0171036 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 686.342i | 0.812239i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 297.443i | 0.351173i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.9337 | 0.0376133 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 663.164 | 0.779276 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 402.566i | 0.471942i | 0.971760 | + | 0.235971i | \(0.0758270\pi\) | ||||
−0.971760 | + | 0.235971i | \(0.924173\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 252.287i | − 0.295072i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 552.003 | 0.644110 | 0.322055 | − | 0.946721i | \(-0.395626\pi\) | ||||
0.322055 | + | 0.946721i | \(0.395626\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 330.117 | 0.384303 | 0.192152 | − | 0.981365i | \(-0.438453\pi\) | ||||
0.192152 | + | 0.981365i | \(0.438453\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.8267i | 0.0137360i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1116.67i | 1.29394i | 0.762516 | + | 0.646969i | \(0.223964\pi\) | ||||
−0.762516 | + | 0.646969i | \(0.776036\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −375.445 | −0.434041 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.98348 | 0.00920817 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 124.810i | 0.143625i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 231.033i | − 0.265251i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1457.24 | −1.66923 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −348.326 | −0.398087 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.747441i | 0 0.000852270i | 1.00000 | 0.000426135i | \(0.000135643\pi\) | |||||
−1.00000 | 0.000426135i | \(0.999864\pi\) | ||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 25.3219i | − 0.0288076i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −247.826 | −0.281301 | −0.140650 | − | 0.990059i | \(-0.544919\pi\) | ||||
−0.140650 | + | 0.990059i | \(0.544919\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1613.74 | 1.82757 | 0.913784 | − | 0.406200i | \(-0.133146\pi\) | ||||
0.913784 | + | 0.406200i | \(0.133146\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 38.6807i | 0.0437070i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1110.59i | 1.25207i | 0.779795 | + | 0.626034i | \(0.215323\pi\) | ||||
−0.779795 | + | 0.626034i | \(0.784677\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −406.537 | −0.457297 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 236.471 | 0.265400 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 374.744i | − 0.419646i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 559.458i | − 0.625092i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31.2863 | 0.0348788 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1219.49 | −1.35650 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 139.498i | − 0.154825i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 15.7340i | − 0.0174241i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.7676 | −0.0273675 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 518.009 | 0.571123 | 0.285562 | − | 0.958360i | \(-0.407820\pi\) | ||||
0.285562 | + | 0.958360i | \(0.407820\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 960.430i | − 1.05658i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1065.61i | 1.16972i | 0.811135 | + | 0.584860i | \(0.198850\pi\) | ||||
−0.811135 | + | 0.584860i | \(0.801150\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 321.186 | 0.351792 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.52583 | 0.00276047 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 163.679i | 0.178494i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1183.66i | 1.28799i | 0.765030 | + | 0.643994i | \(0.222724\pi\) | ||||
−0.765030 | + | 0.643994i | \(0.777276\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.3016 | 0.0307292 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2475.03 | 2.68151 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 514.018i | 0.555695i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1138.43i | 1.22809i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −379.019 | −0.407986 | −0.203993 | − | 0.978972i | \(-0.565392\pi\) | ||||
−0.203993 | + | 0.978972i | \(0.565392\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 56.6821 | 0.0608830 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 7.29878i | − 0.00782292i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 146.044i | 0.156197i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1316.09 | 1.40458 | 0.702289 | − | 0.711892i | \(-0.252161\pi\) | ||||
0.702289 | + | 0.711892i | \(0.252161\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.7214 | −0.0295223 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 497.031i | − 0.528194i | −0.964496 | − | 0.264097i | \(-0.914926\pi\) | ||||
0.964496 | − | 0.264097i | \(-0.0850739\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 768.883i | − 0.815359i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.0723 | −0.0170077 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −808.487 | −0.853735 | −0.426867 | − | 0.904314i | \(-0.640383\pi\) | ||||
−0.426867 | + | 0.904314i | \(0.640383\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 350.322i | 0.369148i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 1.19488i | − 0.00125644i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1345.58 | −1.41194 | −0.705969 | − | 0.708243i | \(-0.749488\pi\) | ||||
−0.705969 | + | 0.708243i | \(0.749488\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 254.013 | 0.265982 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.75173i | 0.00810004i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 280.299i | − 0.292283i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1054.32 | −1.09710 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 782.346 | 0.812405 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 294.809i | 0.305502i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 140.279i | 0.145066i | 0.997366 | + | 0.0725330i | \(0.0231083\pi\) | ||||
−0.997366 | + | 0.0725330i | \(0.976892\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.3533 | −0.0117165 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1438.67 | −1.48164 | −0.740820 | − | 0.671704i | \(-0.765563\pi\) | ||||
−0.740820 | + | 0.671704i | \(0.765563\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 490.479i | − 0.504090i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 24.2500i | 0.0248718i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 902.190 | 0.923428 | 0.461714 | − | 0.887029i | \(-0.347235\pi\) | ||||
0.461714 | + | 0.887029i | \(0.347235\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −236.976 | −0.242059 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1707.49i | 1.74056i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 503.193i | 0.511896i | 0.966691 | + | 0.255948i | \(0.0823875\pi\) | ||||
−0.966691 | + | 0.255948i | \(0.917612\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 486.761 | 0.494173 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.9305 | −0.0120876 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1022.91i | 1.03428i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 906.322i | 0.914553i | 0.889325 | + | 0.457277i | \(0.151175\pi\) | ||||
−0.889325 | + | 0.457277i | \(0.848825\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.9481 | 0.0190816 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 495.847 | 0.498339 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 608.625i | 0.610457i | 0.952279 | + | 0.305228i | \(0.0987328\pi\) | ||||
−0.952279 | + | 0.305228i | \(0.901267\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 69.3613i | 0.0694308i |
(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 | 224.3.g.b.15.3 | 8 | ||
3.2 | odd | 2 | 2016.3.g.b.1135.5 | 8 | |||
4.3 | odd | 2 | 56.3.g.b.43.8 | yes | 8 | ||
7.6 | odd | 2 | 1568.3.g.m.687.6 | 8 | |||
8.3 | odd | 2 | inner | 224.3.g.b.15.4 | 8 | ||
8.5 | even | 2 | 56.3.g.b.43.7 | ✓ | 8 | ||
12.11 | even | 2 | 504.3.g.b.379.1 | 8 | |||
16.3 | odd | 4 | 1792.3.d.j.1023.9 | 16 | |||
16.5 | even | 4 | 1792.3.d.j.1023.10 | 16 | |||
16.11 | odd | 4 | 1792.3.d.j.1023.8 | 16 | |||
16.13 | even | 4 | 1792.3.d.j.1023.7 | 16 | |||
24.5 | odd | 2 | 504.3.g.b.379.2 | 8 | |||
24.11 | even | 2 | 2016.3.g.b.1135.4 | 8 | |||
28.3 | even | 6 | 392.3.k.n.275.2 | 16 | |||
28.11 | odd | 6 | 392.3.k.o.275.2 | 16 | |||
28.19 | even | 6 | 392.3.k.n.67.4 | 16 | |||
28.23 | odd | 6 | 392.3.k.o.67.4 | 16 | |||
28.27 | even | 2 | 392.3.g.m.99.8 | 8 | |||
56.5 | odd | 6 | 392.3.k.n.67.2 | 16 | |||
56.13 | odd | 2 | 392.3.g.m.99.7 | 8 | |||
56.27 | even | 2 | 1568.3.g.m.687.5 | 8 | |||
56.37 | even | 6 | 392.3.k.o.67.2 | 16 | |||
56.45 | odd | 6 | 392.3.k.n.275.4 | 16 | |||
56.53 | even | 6 | 392.3.k.o.275.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.b.43.7 | ✓ | 8 | 8.5 | even | 2 | ||
56.3.g.b.43.8 | yes | 8 | 4.3 | odd | 2 | ||
224.3.g.b.15.3 | 8 | 1.1 | even | 1 | trivial | ||
224.3.g.b.15.4 | 8 | 8.3 | odd | 2 | inner | ||
392.3.g.m.99.7 | 8 | 56.13 | odd | 2 | |||
392.3.g.m.99.8 | 8 | 28.27 | even | 2 | |||
392.3.k.n.67.2 | 16 | 56.5 | odd | 6 | |||
392.3.k.n.67.4 | 16 | 28.19 | even | 6 | |||
392.3.k.n.275.2 | 16 | 28.3 | even | 6 | |||
392.3.k.n.275.4 | 16 | 56.45 | odd | 6 | |||
392.3.k.o.67.2 | 16 | 56.37 | even | 6 | |||
392.3.k.o.67.4 | 16 | 28.23 | odd | 6 | |||
392.3.k.o.275.2 | 16 | 28.11 | odd | 6 | |||
392.3.k.o.275.4 | 16 | 56.53 | even | 6 | |||
504.3.g.b.379.1 | 8 | 12.11 | even | 2 | |||
504.3.g.b.379.2 | 8 | 24.5 | odd | 2 | |||
1568.3.g.m.687.5 | 8 | 56.27 | even | 2 | |||
1568.3.g.m.687.6 | 8 | 7.6 | odd | 2 | |||
1792.3.d.j.1023.7 | 16 | 16.13 | even | 4 | |||
1792.3.d.j.1023.8 | 16 | 16.11 | odd | 4 | |||
1792.3.d.j.1023.9 | 16 | 16.3 | odd | 4 | |||
1792.3.d.j.1023.10 | 16 | 16.5 | even | 4 | |||
2016.3.g.b.1135.4 | 8 | 24.11 | even | 2 | |||
2016.3.g.b.1135.5 | 8 | 3.2 | odd | 2 |