Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,3,Mod(161,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, 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("864.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.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: | \(23.5422948407\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.3 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 864.161 |
Dual form | 864.3.e.f.161.5 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.78194i | − 0.756388i | −0.925726 | − | 0.378194i | \(-0.876545\pi\) | ||||
0.925726 | − | 0.378194i | \(-0.123455\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.953512 | −0.136216 | −0.0681080 | − | 0.997678i | \(-0.521696\pi\) | ||||
−0.0681080 | + | 0.997678i | \(0.521696\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.6969i | 1.06336i | 0.846946 | + | 0.531679i | \(0.178439\pi\) | ||||
−0.846946 | + | 0.531679i | \(0.821561\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.69694 | −0.668995 | −0.334498 | − | 0.942397i | \(-0.608567\pi\) | ||||
−0.334498 | + | 0.942397i | \(0.608567\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.73545i | 0.278556i | 0.990253 | + | 0.139278i | \(0.0444781\pi\) | ||||
−0.990253 | + | 0.139278i | \(0.955522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.2699 | 1.54052 | 0.770260 | − | 0.637730i | \(-0.220126\pi\) | ||||
0.770260 | + | 0.637730i | \(0.220126\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.69694i | 0.117258i | 0.998280 | + | 0.0586291i | \(0.0186729\pi\) | ||||
−0.998280 | + | 0.0586291i | \(0.981327\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.6969 | 0.427878 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 21.7060i | 0.748483i | 0.927331 | + | 0.374242i | \(0.122097\pi\) | ||||
−0.927331 | + | 0.374242i | \(0.877903\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.5953 | 0.728881 | 0.364440 | − | 0.931227i | \(-0.381260\pi\) | ||||
0.364440 | + | 0.931227i | \(0.381260\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.60612i | 0.103032i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 24.0908 | 0.651103 | 0.325552 | − | 0.945524i | \(-0.394450\pi\) | ||||
0.325552 | + | 0.945524i | \(0.394450\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 19.7990i | − 0.482902i | −0.970413 | − | 0.241451i | \(-0.922377\pi\) | ||||
0.970413 | − | 0.241451i | \(-0.0776233\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 49.0047 | 1.13964 | 0.569822 | − | 0.821768i | \(-0.307012\pi\) | ||||
0.569822 | + | 0.821768i | \(0.307012\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 59.3939i | − 1.26370i | −0.775091 | − | 0.631850i | \(-0.782296\pi\) | ||||
0.775091 | − | 0.631850i | \(-0.217704\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.0908 | −0.981445 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 48.1796i | − 0.909049i | −0.890734 | − | 0.454524i | \(-0.849809\pi\) | ||||
0.890734 | − | 0.454524i | \(-0.150191\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 44.2371 | 0.804311 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.6061i | 0.213663i | 0.994277 | + | 0.106832i | \(0.0340706\pi\) | ||||
−0.994277 | + | 0.106832i | \(0.965929\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | −0.0655738 | −0.0327869 | − | 0.999462i | \(-0.510438\pi\) | ||||
−0.0327869 | + | 0.999462i | \(0.510438\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 32.8913i | 0.506020i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 111.358 | 1.66207 | 0.831034 | − | 0.556222i | \(-0.187750\pi\) | ||||
0.831034 | + | 0.556222i | \(0.187750\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 56.6969i | − 0.798548i | −0.916832 | − | 0.399274i | \(-0.869262\pi\) | ||||
0.916832 | − | 0.399274i | \(-0.130738\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 35.6969 | 0.488999 | 0.244500 | − | 0.969649i | \(-0.421376\pi\) | ||||
0.244500 | + | 0.969649i | \(0.421376\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 11.1532i | − 0.144846i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 144.442 | 1.82839 | 0.914193 | − | 0.405280i | \(-0.132826\pi\) | ||||
0.914193 | + | 0.405280i | \(0.132826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 101.697i | 1.22526i | 0.790368 | + | 0.612632i | \(0.209889\pi\) | ||||
−0.790368 | + | 0.612632i | \(0.790111\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.9092 | 0.210696 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 19.0060i | 0.213551i | 0.994283 | + | 0.106775i | \(0.0340526\pi\) | ||||
−0.994283 | + | 0.106775i | \(0.965947\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.29263 | 0.0911278 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 110.697i | − 1.16523i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 27.0000 | 0.278351 | 0.139175 | − | 0.990268i | \(-0.455555\pi\) | ||||
0.139175 | + | 0.990268i | \(0.455555\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 189.665i | 1.87787i | 0.344091 | + | 0.938936i | \(0.388187\pi\) | ||||
−0.344091 | + | 0.938936i | \(0.611813\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 74.4605 | 0.722918 | 0.361459 | − | 0.932388i | \(-0.382279\pi\) | ||||
0.361459 | + | 0.932388i | \(0.382279\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 138.576i | 1.29510i | 0.762024 | + | 0.647549i | \(0.224206\pi\) | ||||
−0.762024 | + | 0.647549i | \(0.775794\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −114.879 | −1.05393 | −0.526966 | − | 0.849886i | \(-0.676670\pi\) | ||||
−0.526966 | + | 0.849886i | \(0.676670\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 157.663i | − 1.39525i | −0.716463 | − | 0.697625i | \(-0.754240\pi\) | ||||
0.716463 | − | 0.697625i | \(-0.245760\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.1997 | 0.0886927 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 4.51531i | − 0.0379438i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.8184 | −0.130730 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 135.004i | − 1.08003i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 125.661 | 0.989458 | 0.494729 | − | 0.869047i | \(-0.335267\pi\) | ||||
0.494729 | + | 0.869047i | \(0.335267\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 223.182i | 1.70368i | 0.523805 | + | 0.851838i | \(0.324512\pi\) | ||||
−0.523805 | + | 0.851838i | \(0.675488\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −27.9092 | −0.209843 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 162.142i | 1.18352i | 0.806116 | + | 0.591758i | \(0.201566\pi\) | ||||
−0.806116 | + | 0.591758i | \(0.798434\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −69.9819 | −0.503467 | −0.251734 | − | 0.967797i | \(-0.581001\pi\) | ||||
−0.251734 | + | 0.967797i | \(0.581001\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 101.728i | − 0.711381i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 82.0908 | 0.566144 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 216.171i | − 1.45081i | −0.688322 | − | 0.725405i | \(-0.741652\pi\) | ||||
0.688322 | − | 0.725405i | \(-0.258348\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −92.5772 | −0.613094 | −0.306547 | − | 0.951855i | \(-0.599174\pi\) | ||||
−0.306547 | + | 0.951855i | \(0.599174\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 85.4541i | − 0.551317i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 292.545 | 1.86334 | 0.931672 | − | 0.363301i | \(-0.118351\pi\) | ||||
0.931672 | + | 0.363301i | \(0.118351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 2.57156i | − 0.0159724i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 112.601 | 0.690804 | 0.345402 | − | 0.938455i | \(-0.387743\pi\) | ||||
0.345402 | + | 0.938455i | \(0.387743\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 106.182i | − 0.635818i | −0.948121 | − | 0.317909i | \(-0.897019\pi\) | ||||
0.948121 | − | 0.317909i | \(-0.102981\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −93.3633 | −0.552445 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 224.271i | 1.29636i | 0.761486 | + | 0.648182i | \(0.224470\pi\) | ||||
−0.761486 | + | 0.648182i | \(0.775530\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.1997 | −0.0582838 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 113.424i | 0.633656i | 0.948483 | + | 0.316828i | \(0.102618\pi\) | ||||
−0.948483 | + | 0.316828i | \(0.897382\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −160.182 | −0.884981 | −0.442491 | − | 0.896773i | \(-0.645905\pi\) | ||||
−0.442491 | + | 0.896773i | \(0.645905\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 91.1100i | − 0.492486i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −55.3903 | −0.296205 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 200.697i | − 1.05077i | −0.850865 | − | 0.525385i | \(-0.823921\pi\) | ||||
0.850865 | − | 0.525385i | \(-0.176079\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −152.909 | −0.792276 | −0.396138 | − | 0.918191i | \(-0.629650\pi\) | ||||
−0.396138 | + | 0.918191i | \(0.629650\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.2883i | 0.0776056i | 0.999247 | + | 0.0388028i | \(0.0123544\pi\) | ||||
−0.999247 | + | 0.0388028i | \(0.987646\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −231.299 | −1.16230 | −0.581152 | − | 0.813795i | \(-0.697398\pi\) | ||||
−0.581152 | + | 0.813795i | \(0.697398\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 20.6969i | − 0.101955i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −74.8786 | −0.365261 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 342.368i | 1.63812i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −185.819 | −0.880659 | −0.440329 | − | 0.897836i | \(-0.645138\pi\) | ||||
−0.440329 | + | 0.897836i | \(0.645138\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 185.333i | − 0.862012i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.5449 | −0.0992852 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 41.1839i | − 0.186353i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −272.964 | −1.22405 | −0.612027 | − | 0.790837i | \(-0.709646\pi\) | ||||
−0.612027 | + | 0.790837i | \(0.709646\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 307.757i | 1.35576i | 0.735173 | + | 0.677879i | \(0.237101\pi\) | ||||
−0.735173 | + | 0.677879i | \(0.762899\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 200.424 | 0.875216 | 0.437608 | − | 0.899166i | \(-0.355826\pi\) | ||||
0.437608 | + | 0.899166i | \(0.355826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 381.687i | − 1.63814i | −0.573693 | − | 0.819070i | \(-0.694490\pi\) | ||||
0.573693 | − | 0.819070i | \(-0.305510\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −224.624 | −0.955847 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 254.697i | − 1.06568i | −0.846217 | − | 0.532839i | \(-0.821125\pi\) | ||||
0.846217 | − | 0.532839i | \(-0.178875\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 283.757 | 1.17742 | 0.588708 | − | 0.808346i | \(-0.299637\pi\) | ||||
0.588708 | + | 0.808346i | \(0.299637\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 181.877i | 0.742353i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −254.558 | −1.03060 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 54.0000i | − 0.215139i | −0.994198 | − | 0.107570i | \(-0.965693\pi\) | ||||
0.994198 | − | 0.107570i | \(-0.0343069\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −31.5459 | −0.124687 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 202.725i | − 0.788815i | −0.918936 | − | 0.394407i | \(-0.870950\pi\) | ||||
0.918936 | − | 0.394407i | \(-0.129050\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.9709 | −0.0886906 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 162.879i | 0.619310i | 0.950849 | + | 0.309655i | \(0.100214\pi\) | ||||
−0.950849 | + | 0.309655i | \(0.899786\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −182.212 | −0.687593 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 119.715i | − 0.445038i | −0.974928 | − | 0.222519i | \(-0.928572\pi\) | ||||
0.974928 | − | 0.222519i | \(-0.0714280\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −337.601 | −1.24576 | −0.622879 | − | 0.782318i | \(-0.714037\pi\) | ||||
−0.622879 | + | 0.782318i | \(0.714037\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 125.121i | 0.454987i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −268.182 | −0.968165 | −0.484082 | − | 0.875022i | \(-0.660846\pi\) | ||||
−0.484082 | + | 0.875022i | \(0.660846\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 272.322i | 0.969117i | 0.874759 | + | 0.484559i | \(0.161020\pi\) | ||||
−0.874759 | + | 0.484559i | \(0.838980\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 67.4104 | 0.238199 | 0.119100 | − | 0.992882i | \(-0.461999\pi\) | ||||
0.119100 | + | 0.992882i | \(0.461999\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.8786i | 0.0657790i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 266.576 | 0.922407 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 378.345i | − 1.29128i | −0.763642 | − | 0.645639i | \(-0.776591\pi\) | ||||
0.763642 | − | 0.645639i | \(-0.223409\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 47.6756 | 0.161612 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 23.4551i | − 0.0784452i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −46.7265 | −0.155238 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.1278i | 0.0495992i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −425.699 | −1.38664 | −0.693321 | − | 0.720629i | \(-0.743853\pi\) | ||||
−0.693321 | + | 0.720629i | \(0.743853\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 556.999i | 1.79099i | 0.445068 | + | 0.895497i | \(0.353179\pi\) | ||||
−0.445068 | + | 0.895497i | \(0.646821\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 169.636 | 0.541967 | 0.270984 | − | 0.962584i | \(-0.412651\pi\) | ||||
0.270984 | + | 0.962584i | \(0.412651\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 225.128i | 0.710183i | 0.934832 | + | 0.355091i | \(0.115550\pi\) | ||||
−0.934832 | + | 0.355091i | \(0.884450\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −253.894 | −0.795906 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 138.606i | 0.429121i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −93.0306 | −0.286248 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 56.6328i | 0.172136i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −315.005 | −0.951677 | −0.475839 | − | 0.879533i | \(-0.657855\pi\) | ||||
−0.475839 | + | 0.879533i | \(0.657855\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 421.151i | − 1.25717i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −642.545 | −1.90666 | −0.953331 | − | 0.301928i | \(-0.902370\pi\) | ||||
−0.953331 | + | 0.301928i | \(0.902370\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 264.296i | 0.775061i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 92.5772 | 0.269904 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 301.515i | − 0.868920i | −0.900691 | − | 0.434460i | \(-0.856939\pi\) | ||||
0.900691 | − | 0.434460i | \(-0.143061\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 180.454 | 0.517060 | 0.258530 | − | 0.966003i | \(-0.416762\pi\) | ||||
0.258530 | + | 0.966003i | \(0.416762\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 331.825i | 0.940014i | 0.882663 | + | 0.470007i | \(0.155749\pi\) | ||||
−0.882663 | + | 0.470007i | \(0.844251\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −214.424 | −0.604012 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 566.908i | 1.57913i | 0.613666 | + | 0.789566i | \(0.289694\pi\) | ||||
−0.613666 | + | 0.789566i | \(0.710306\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 495.727 | 1.37320 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 135.004i | − 0.369873i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −219.192 | −0.597253 | −0.298627 | − | 0.954370i | \(-0.596529\pi\) | ||||
−0.298627 | + | 0.954370i | \(0.596529\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 45.9398i | 0.123827i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 606.454 | 1.62588 | 0.812941 | − | 0.582346i | \(-0.197865\pi\) | ||||
0.812941 | + | 0.582346i | \(0.197865\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 188.776i | − 0.500732i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 124.708 | 0.329044 | 0.164522 | − | 0.986373i | \(-0.447392\pi\) | ||||
0.164522 | + | 0.986373i | \(0.447392\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 58.4541i | − 0.152622i | −0.997084 | − | 0.0763108i | \(-0.975686\pi\) | ||||
0.997084 | − | 0.0763108i | \(-0.0243141\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −42.1806 | −0.109560 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 121.526i | 0.312406i | 0.987725 | + | 0.156203i | \(0.0499255\pi\) | ||||
−0.987725 | + | 0.156203i | \(0.950075\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.7712 | −0.0326630 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 546.272i | − 1.38297i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −330.091 | −0.831463 | −0.415732 | − | 0.909487i | \(-0.636474\pi\) | ||||
−0.415732 | + | 0.909487i | \(0.636474\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 506.202i | − 1.26235i | −0.775641 | − | 0.631174i | \(-0.782573\pi\) | ||||
0.775641 | − | 0.631174i | \(-0.217427\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −196.510 | −0.487618 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 281.789i | 0.692356i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −521.302 | −1.27458 | −0.637289 | − | 0.770625i | \(-0.719944\pi\) | ||||
−0.637289 | + | 0.770625i | \(0.719944\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 12.0201i | − 0.0291043i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 384.612 | 0.926775 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 133.151i | − 0.317783i | −0.987296 | − | 0.158891i | \(-0.949208\pi\) | ||||
0.987296 | − | 0.158891i | \(-0.0507920\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −129.031 | −0.306486 | −0.153243 | − | 0.988189i | \(-0.548972\pi\) | ||||
−0.153243 | + | 0.988189i | \(0.548972\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 50.6548i | 0.119188i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.81405 | 0.00893219 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 509.333i | − 1.18175i | −0.806764 | − | 0.590873i | \(-0.798783\pi\) | ||||
0.806764 | − | 0.590873i | \(-0.201217\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.54489 | −0.0128058 | −0.00640288 | − | 0.999980i | \(-0.502038\pi\) | ||||
−0.00640288 | + | 0.999980i | \(0.502038\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 78.9391i | 0.180639i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 337.514 | 0.768825 | 0.384412 | − | 0.923162i | \(-0.374404\pi\) | ||||
0.384412 | + | 0.923162i | \(0.374404\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 475.212i | − 1.07271i | −0.843991 | − | 0.536357i | \(-0.819800\pi\) | ||||
0.843991 | − | 0.536357i | \(-0.180200\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 71.8796 | 0.161527 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 251.858i | − 0.560932i | −0.959864 | − | 0.280466i | \(-0.909511\pi\) | ||||
0.959864 | − | 0.280466i | \(-0.0904890\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 231.588 | 0.513498 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 31.3622i | − 0.0689280i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 42.5755 | 0.0931630 | 0.0465815 | − | 0.998914i | \(-0.485167\pi\) | ||||
0.0465815 | + | 0.998914i | \(0.485167\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 552.346i | − 1.19815i | −0.800694 | − | 0.599074i | \(-0.795536\pi\) | ||||
0.800694 | − | 0.599074i | \(-0.204464\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 524.084 | 1.13193 | 0.565966 | − | 0.824429i | \(-0.308504\pi\) | ||||
0.565966 | + | 0.824429i | \(0.308504\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 130.423i | 0.279279i | 0.990202 | + | 0.139640i | \(0.0445944\pi\) | ||||
−0.990202 | + | 0.139640i | \(0.955406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −106.182 | −0.226400 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 573.205i | 1.21185i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 313.098 | 0.659154 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 572.302i | 1.19479i | 0.801949 | + | 0.597393i | \(0.203797\pi\) | ||||
−0.801949 | + | 0.597393i | \(0.796203\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −209.516 | −0.435585 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 102.112i | − 0.210541i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 141.957 | 0.291494 | 0.145747 | − | 0.989322i | \(-0.453441\pi\) | ||||
0.145747 | + | 0.989322i | \(0.453441\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 464.394i | − 0.945812i | −0.881113 | − | 0.472906i | \(-0.843205\pi\) | ||||
0.881113 | − | 0.472906i | \(-0.156795\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −102.788 | −0.208494 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 54.0612i | 0.108775i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −144.356 | −0.289290 | −0.144645 | − | 0.989484i | \(-0.546204\pi\) | ||||
−0.144645 | + | 0.989484i | \(0.546204\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 733.485i | 1.45822i | 0.684396 | + | 0.729110i | \(0.260066\pi\) | ||||
−0.684396 | + | 0.729110i | \(0.739934\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 717.302 | 1.42040 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 300.680i | 0.590727i | 0.955385 | + | 0.295364i | \(0.0954408\pi\) | ||||
−0.955385 | + | 0.295364i | \(0.904559\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.0374 | −0.0666095 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 281.605i | − 0.546806i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 694.727 | 1.34377 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 375.988i | 0.721666i | 0.932630 | + | 0.360833i | \(0.117508\pi\) | ||||
−0.932630 | + | 0.360833i | \(0.882492\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 665.001 | 1.27151 | 0.635757 | − | 0.771890i | \(-0.280688\pi\) | ||||
0.635757 | + | 0.771890i | \(0.280688\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 106.999i | 0.203034i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 521.727 | 0.986251 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 172.191i | 0.323059i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 524.084 | 0.979596 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 562.515i | − 1.04363i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −818.302 | −1.51257 | −0.756287 | − | 0.654241i | \(-0.772988\pi\) | ||||
−0.756287 | + | 0.654241i | \(0.772988\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 434.464i | 0.797181i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 625.532 | 1.14357 | 0.571784 | − | 0.820404i | \(-0.306251\pi\) | ||||
0.571784 | + | 0.820404i | \(0.306251\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 635.333i | 1.15305i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −137.728 | −0.249055 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.9087i | 0.0501054i | 0.999686 | + | 0.0250527i | \(0.00797536\pi\) | ||||
−0.999686 | + | 0.0250527i | \(0.992025\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −426.191 | −0.762416 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 461.574i | 0.819848i | 0.912120 | + | 0.409924i | \(0.134445\pi\) | ||||
−0.912120 | + | 0.409924i | \(0.865555\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −596.272 | −1.05535 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 983.092i | − 1.72775i | −0.503703 | − | 0.863877i | \(-0.668029\pi\) | ||||
0.503703 | − | 0.863877i | \(-0.331971\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 692.856 | 1.21341 | 0.606704 | − | 0.794928i | \(-0.292491\pi\) | ||||
0.606704 | + | 0.794928i | \(0.292491\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.8490i | 0.0501721i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −154.545 | −0.267842 | −0.133921 | − | 0.990992i | \(-0.542757\pi\) | ||||
−0.133921 | + | 0.990992i | \(0.542757\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 96.9692i | − 0.166901i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 563.554 | 0.966644 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 867.545i | − 1.47793i | −0.673744 | − | 0.738965i | \(-0.735315\pi\) | ||||
0.673744 | − | 0.738965i | \(-0.264685\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 661.362 | 1.12286 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 343.675i | 0.579553i | 0.957094 | + | 0.289776i | \(0.0935809\pi\) | ||||
−0.957094 | + | 0.289776i | \(0.906419\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.0766 | −0.0287002 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 908.969i | 1.51748i | 0.651395 | + | 0.758739i | \(0.274184\pi\) | ||||
−0.651395 | + | 0.758739i | \(0.725816\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −419.817 | −0.698531 | −0.349266 | − | 0.937024i | \(-0.613569\pi\) | ||||
−0.349266 | + | 0.937024i | \(0.613569\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 59.8241i | 0.0988828i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −131.671 | −0.216921 | −0.108461 | − | 0.994101i | \(-0.534592\pi\) | ||||
−0.108461 | + | 0.994101i | \(0.534592\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 516.545i | 0.845409i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −494.727 | −0.807058 | −0.403529 | − | 0.914967i | \(-0.632217\pi\) | ||||
−0.403529 | + | 0.914967i | \(0.632217\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 500.330i | − 0.810908i | −0.914116 | − | 0.405454i | \(-0.867114\pi\) | ||||
0.914116 | − | 0.405454i | \(-0.132886\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 636.974 | 1.02904 | 0.514519 | − | 0.857479i | \(-0.327971\pi\) | ||||
0.514519 | + | 0.857479i | \(0.327971\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 18.1225i | − 0.0290890i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −243.152 | −0.389043 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 114.081i | 0.181369i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 365.541 | 0.579305 | 0.289652 | − | 0.957132i | \(-0.406460\pi\) | ||||
0.289652 | + | 0.957132i | \(0.406460\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 475.243i | − 0.748414i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 418.243 | 0.656582 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 843.812i | − 1.31640i | −0.752843 | − | 0.658200i | \(-0.771318\pi\) | ||||
0.752843 | − | 0.658200i | \(-0.228682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1252.22 | 1.94746 | 0.973732 | − | 0.227696i | \(-0.0731192\pi\) | ||||
0.973732 | + | 0.227696i | \(0.0731192\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 799.151i | 1.23516i | 0.786507 | + | 0.617582i | \(0.211888\pi\) | ||||
−0.786507 | + | 0.617582i | \(0.788112\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −147.453 | −0.227200 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 798.227i | 1.22240i | 0.791477 | + | 0.611199i | \(0.209313\pi\) | ||||
−0.791477 | + | 0.611199i | \(0.790687\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 844.059 | 1.28864 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 106.151i | 0.161079i | 0.996751 | + | 0.0805395i | \(0.0256643\pi\) | ||||
−0.996751 | + | 0.0805395i | \(0.974336\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 772.272 | 1.16834 | 0.584170 | − | 0.811631i | \(-0.301420\pi\) | ||||
0.584170 | + | 0.811631i | \(0.301420\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 105.551i | 0.158723i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −58.5398 | −0.0877658 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 46.7878i | − 0.0697284i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 494.637 | 0.734973 | 0.367486 | − | 0.930029i | \(-0.380218\pi\) | ||||
0.367486 | + | 0.930029i | \(0.380218\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1089.14i | − 1.60877i | −0.594109 | − | 0.804385i | \(-0.702495\pi\) | ||||
0.594109 | − | 0.804385i | \(-0.297505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.7448 | −0.0379158 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1126.60i | − 1.64949i | −0.565502 | − | 0.824747i | \(-0.691318\pi\) | ||||
0.565502 | − | 0.824747i | \(-0.308682\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 613.210 | 0.895197 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 419.015i | 0.608149i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −462.019 | −0.668624 | −0.334312 | − | 0.942462i | \(-0.608504\pi\) | ||||
−0.334312 | + | 0.942462i | \(0.608504\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 264.667i | 0.380816i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 93.7571 | 0.134515 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 189.193i | − 0.269891i | −0.990853 | − | 0.134945i | \(-0.956914\pi\) | ||||
0.990853 | − | 0.134945i | \(-0.0430859\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 705.136 | 1.00304 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 180.848i | − 0.255796i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −926.302 | −1.30649 | −0.653245 | − | 0.757146i | \(-0.726593\pi\) | ||||
−0.653245 | + | 0.757146i | \(0.726593\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 60.9382i | 0.0854673i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −384.727 | −0.538080 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 957.453i | − 1.33165i | −0.746110 | − | 0.665823i | \(-0.768081\pi\) | ||||
0.746110 | − | 0.665823i | \(-0.231919\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −70.9990 | −0.0984729 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 232.188i | 0.320259i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −979.545 | −1.34738 | −0.673690 | − | 0.739015i | \(-0.735291\pi\) | ||||
−0.673690 | + | 0.739015i | \(0.735291\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 232.059i | 0.317454i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −452.636 | −0.617511 | −0.308756 | − | 0.951141i | \(-0.599913\pi\) | ||||
−0.308756 | + | 0.951141i | \(0.599913\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1302.55i | 1.76737i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 460.026 | 0.622497 | 0.311249 | − | 0.950328i | \(-0.399253\pi\) | ||||
0.311249 | + | 0.950328i | \(0.399253\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 393.119i | − 0.529097i | −0.964372 | − | 0.264549i | \(-0.914777\pi\) | ||||
0.964372 | − | 0.264549i | \(-0.0852230\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −817.545 | −1.09738 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 132.133i | − 0.176413i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −611.229 | −0.813887 | −0.406944 | − | 0.913453i | \(-0.633405\pi\) | ||||
−0.406944 | + | 0.913453i | \(0.633405\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 350.121i | 0.463737i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 106.182 | 0.140266 | 0.0701332 | − | 0.997538i | \(-0.477658\pi\) | ||||
0.0701332 | + | 0.997538i | \(0.477658\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 844.843i | 1.11017i | 0.831792 | + | 0.555087i | \(0.187315\pi\) | ||||
−0.831792 | + | 0.555087i | \(0.812685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 109.538 | 0.143562 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 109.635i | − 0.142940i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −588.728 | −0.765575 | −0.382788 | − | 0.923836i | \(-0.625036\pi\) | ||||
−0.382788 | + | 0.923836i | \(0.625036\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.87858i | 0.0127795i | 0.999980 | + | 0.00638976i | \(0.00203394\pi\) | ||||
−0.999980 | + | 0.00638976i | \(0.997966\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 241.701 | 0.311872 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 579.514i | − 0.743921i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 663.181 | 0.849143 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 1106.39i | − 1.40941i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −118.409 | −0.150456 | −0.0752279 | − | 0.997166i | \(-0.523968\pi\) | ||||
−0.0752279 | + | 0.997166i | \(0.523968\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 150.334i | 0.190055i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.7878 | 0.0438685 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 371.477i | 0.466095i | 0.972465 | + | 0.233047i | \(0.0748697\pi\) | ||||
−0.972465 | + | 0.233047i | \(0.925130\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 281.257 | 0.352011 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 417.545i | 0.519981i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.72549 | −0.0120814 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 64.7746i | 0.0800675i | 0.999198 | + | 0.0400337i | \(0.0127465\pi\) | ||||
−0.999198 | + | 0.0400337i | \(0.987253\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −782.832 | −0.965268 | −0.482634 | − | 0.875822i | \(-0.660320\pi\) | ||||
−0.482634 | + | 0.875822i | \(0.660320\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 425.850i | − 0.522515i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1434.36 | 1.75564 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 589.748i | − 0.718329i | −0.933274 | − | 0.359164i | \(-0.883062\pi\) | ||||
0.933274 | − | 0.359164i | \(-0.116938\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 492.821 | 0.598810 | 0.299405 | − | 0.954126i | \(-0.403212\pi\) | ||||
0.299405 | + | 0.954126i | \(0.403212\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 475.212i | − 0.574622i | −0.957837 | − | 0.287311i | \(-0.907239\pi\) | ||||
0.957837 | − | 0.287311i | \(-0.0927613\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −597.637 | −0.720913 | −0.360456 | − | 0.932776i | \(-0.617379\pi\) | ||||
−0.360456 | + | 0.932776i | \(0.617379\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 227.732i | − 0.273387i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −401.572 | −0.480925 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 290.636i | − 0.346407i | −0.984886 | − | 0.173204i | \(-0.944588\pi\) | ||||
0.984886 | − | 0.173204i | \(-0.0554119\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 369.849 | 0.439773 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 353.094i | 0.417863i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.0830 | 0.0178076 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 64.9714i | 0.0763472i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −201.273 | −0.235960 | −0.117980 | − | 0.993016i | \(-0.537642\pi\) | ||||
−0.117980 | + | 0.993016i | \(0.537642\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1009.64i | − 1.17811i | −0.808093 | − | 0.589055i | \(-0.799500\pi\) | ||||
0.808093 | − | 0.589055i | \(-0.200500\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1172.12 | −1.36452 | −0.682261 | − | 0.731109i | \(-0.739003\pi\) | ||||
−0.682261 | + | 0.731109i | \(0.739003\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 755.755i | 0.875730i | 0.899041 | + | 0.437865i | \(0.144265\pi\) | ||||
−0.899041 | + | 0.437865i | \(0.855735\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 848.179 | 0.980553 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1689.53i | 1.94423i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −968.478 | −1.11192 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 128.728i | 0.147117i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −317.818 | −0.362393 | −0.181196 | − | 0.983447i | \(-0.557997\pi\) | ||||
−0.181196 | + | 0.983447i | \(0.557997\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 705.755i | − 0.801084i | −0.916278 | − | 0.400542i | \(-0.868822\pi\) | ||||
0.916278 | − | 0.400542i | \(-0.131178\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 505.389 | 0.572355 | 0.286177 | − | 0.958177i | \(-0.407615\pi\) | ||||
0.286177 | + | 0.958177i | \(0.407615\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1581.00i | 1.78241i | 0.453602 | + | 0.891205i | \(0.350139\pi\) | ||||
−0.453602 | + | 0.891205i | \(0.649861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −119.819 | −0.134780 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1738.45i | − 1.94676i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 428.964 | 0.479290 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 490.454i | 0.545555i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 228.152 | 0.253221 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 605.797i | 0.669389i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −773.875 | −0.853225 | −0.426612 | − | 0.904435i | \(-0.640293\pi\) | ||||
−0.426612 | + | 0.904435i | \(0.640293\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1785.51i | − 1.95995i | −0.199121 | − | 0.979975i | \(-0.563809\pi\) | ||||
0.199121 | − | 0.979975i | \(-0.436191\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1189.54 | −1.30289 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 212.806i | − 0.232068i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −992.402 | −1.07987 | −0.539936 | − | 0.841706i | \(-0.681552\pi\) | ||||
−0.539936 | + | 0.841706i | \(0.681552\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 493.090i | 0.534225i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 257.698 | 0.278592 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 887.568i | − 0.955401i | −0.878523 | − | 0.477701i | \(-0.841470\pi\) | ||||
0.878523 | − | 0.477701i | \(-0.158530\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1407.61 | −1.51194 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 209.483i | 0.224046i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 493.000 | 0.526147 | 0.263074 | − | 0.964776i | \(-0.415264\pi\) | ||||
0.263074 | + | 0.964776i | \(0.415264\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 379.770i | − 0.403581i | −0.979429 | − | 0.201791i | \(-0.935324\pi\) | ||||
0.979429 | − | 0.201791i | \(-0.0646761\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 53.3967 | 0.0566242 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 414.092i | 0.437267i | 0.975807 | + | 0.218633i | \(0.0701599\pi\) | ||||
−0.975807 | + | 0.218633i | \(0.929840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −310.454 | −0.327138 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1254.36i | 1.31623i | 0.752919 | + | 0.658113i | \(0.228645\pi\) | ||||
−0.752919 | + | 0.658113i | \(0.771355\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −759.024 | −0.794789 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 154.604i | − 0.161214i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −450.452 | −0.468733 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 578.293i | 0.599268i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −522.755 | −0.540595 | −0.270297 | − | 0.962777i | \(-0.587122\pi\) | ||||
−0.270297 | + | 0.962777i | \(0.587122\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1044.66i | 1.07586i | 0.842988 | + | 0.537932i | \(0.180794\pi\) | ||||
−0.842988 | + | 0.537932i | \(0.819206\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 66.7286 | 0.0685803 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1375.71i | 1.40809i | 0.710154 | + | 0.704047i | \(0.248625\pi\) | ||||
−0.710154 | + | 0.704047i | \(0.751375\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −222.312 | −0.227081 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 451.757i | 0.459570i | 0.973241 | + | 0.229785i | \(0.0738023\pi\) | ||||
−0.973241 | + | 0.229785i | \(0.926198\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 57.8194 | 0.0586999 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 132.163i | 0.133633i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1811.29 | −1.82774 | −0.913872 | − | 0.406002i | \(-0.866923\pi\) | ||||
−0.913872 | + | 0.406002i | \(0.866923\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 874.757i | 0.879153i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −377.546 | −0.378682 | −0.189341 | − | 0.981911i | \(-0.560635\pi\) | ||||
−0.189341 | + | 0.981911i | \(0.560635\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 864.3.e.f.161.3 | ✓ | 8 | |
3.2 | odd | 2 | inner | 864.3.e.f.161.5 | yes | 8 | |
4.3 | odd | 2 | inner | 864.3.e.f.161.4 | yes | 8 | |
8.3 | odd | 2 | 1728.3.e.u.1025.6 | 8 | |||
8.5 | even | 2 | 1728.3.e.u.1025.5 | 8 | |||
12.11 | even | 2 | inner | 864.3.e.f.161.6 | yes | 8 | |
24.5 | odd | 2 | 1728.3.e.u.1025.3 | 8 | |||
24.11 | even | 2 | 1728.3.e.u.1025.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.3.e.f.161.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
864.3.e.f.161.4 | yes | 8 | 4.3 | odd | 2 | inner | |
864.3.e.f.161.5 | yes | 8 | 3.2 | odd | 2 | inner | |
864.3.e.f.161.6 | yes | 8 | 12.11 | even | 2 | inner | |
1728.3.e.u.1025.3 | 8 | 24.5 | odd | 2 | |||
1728.3.e.u.1025.4 | 8 | 24.11 | even | 2 | |||
1728.3.e.u.1025.5 | 8 | 8.5 | even | 2 | |||
1728.3.e.u.1025.6 | 8 | 8.3 | odd | 2 |