Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,7,Mod(13,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.13");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.f (of order \(4\), degree \(2\), 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: | \(4.60108167240\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} - 450x^{3} + 23409x^{2} - 115668x + 285768 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{7}\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(2.61494 + 2.61494i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.13 |
Dual form | 20.7.f.a.17.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −16.7249 | − | 16.7249i | −0.619442 | − | 0.619442i | 0.325946 | − | 0.945388i | \(-0.394317\pi\) |
−0.945388 | + | 0.325946i | \(0.894317\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −22.1946 | + | 123.014i | −0.177557 | + | 0.984111i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −422.022 | + | 422.022i | −1.23038 | + | 1.23038i | −0.266568 | + | 0.963816i | \(0.585890\pi\) |
−0.963816 | + | 0.266568i | \(0.914110\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 169.553i | − | 0.232583i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1359.94 | −1.02174 | −0.510872 | − | 0.859657i | \(-0.670677\pi\) | ||||
−0.510872 | + | 0.859657i | \(0.670677\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1248.94 | + | 1248.94i | 0.568477 | + | 0.568477i | 0.931702 | − | 0.363224i | \(-0.118324\pi\) |
−0.363224 | + | 0.931702i | \(0.618324\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2428.60 | − | 1686.20i | 0.719586 | − | 0.499614i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −648.372 | + | 648.372i | −0.131971 | + | 0.131971i | −0.770007 | − | 0.638036i | \(-0.779747\pi\) |
0.638036 | + | 0.770007i | \(0.279747\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 9632.63i | − | 1.40438i | −0.711990 | − | 0.702189i | \(-0.752206\pi\) | ||
0.711990 | − | 0.702189i | \(-0.247794\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14116.6 | 1.52430 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 886.911 | + | 886.911i | 0.0728948 | + | 0.0728948i | 0.742614 | − | 0.669719i | \(-0.233586\pi\) |
−0.669719 | + | 0.742614i | \(0.733586\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14639.8 | − | 5460.48i | −0.936947 | − | 0.349471i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −15028.2 | + | 15028.2i | −0.763514 | + | 0.763514i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 26789.3i | 1.09842i | 0.835685 | + | 0.549209i | \(0.185071\pi\) | ||||
−0.835685 | + | 0.549209i | \(0.814929\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6880.94 | −0.230974 | −0.115487 | − | 0.993309i | \(-0.536843\pi\) | ||||
−0.115487 | + | 0.993309i | \(0.536843\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 22744.9 | + | 22744.9i | 0.632911 | + | 0.632911i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −42547.9 | − | 61281.1i | −0.992371 | − | 1.42930i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −42367.5 | + | 42367.5i | −0.836426 | + | 0.836426i | −0.988387 | − | 0.151960i | \(-0.951441\pi\) |
0.151960 | + | 0.988387i | \(0.451441\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 41777.0i | − | 0.704278i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 132500. | 1.92250 | 0.961248 | − | 0.275684i | \(-0.0889042\pi\) | ||||
0.961248 | + | 0.275684i | \(0.0889042\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20888.6 | + | 20888.6i | 0.262727 | + | 0.262727i | 0.826161 | − | 0.563434i | \(-0.190520\pi\) |
−0.563434 | + | 0.826161i | \(0.690520\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 20857.4 | + | 3763.16i | 0.228887 | + | 0.0412966i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −31606.0 | + | 31606.0i | −0.304422 | + | 0.304422i | −0.842741 | − | 0.538319i | \(-0.819059\pi\) |
0.538319 | + | 0.842741i | \(0.319059\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 238556.i | − | 2.02769i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 21688.0 | 0.163496 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 80106.6 | + | 80106.6i | 0.538073 | + | 0.538073i | 0.922962 | − | 0.384890i | \(-0.125761\pi\) |
−0.384890 | + | 0.922962i | \(0.625761\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 30183.3 | − | 167291.i | 0.181417 | − | 1.00551i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −161105. | + | 161105.i | −0.869931 | + | 0.869931i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 290136.i | 1.41268i | 0.707871 | + | 0.706342i | \(0.249656\pi\) | ||||
−0.707871 | + | 0.706342i | \(0.750344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −253971. | −1.11891 | −0.559454 | − | 0.828862i | \(-0.688989\pi\) | ||||
−0.559454 | + | 0.828862i | \(0.688989\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 71555.1 | + | 71555.1i | 0.286166 | + | 0.286166i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −181357. | + | 125918.i | −0.660381 | + | 0.458508i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11368.7 | − | 11368.7i | 0.0377997 | − | 0.0377997i | −0.687954 | − | 0.725754i | \(-0.741491\pi\) |
0.725754 | + | 0.687954i | \(0.241491\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 29667.0i | − | 0.0903082i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 179758. | 0.502243 | 0.251122 | − | 0.967956i | \(-0.419201\pi\) | ||||
0.251122 | + | 0.967956i | \(0.419201\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −414484. | − | 414484.i | −1.06547 | − | 1.06547i | −0.997701 | − | 0.0677642i | \(-0.978413\pi\) |
−0.0677642 | − | 0.997701i | \(-0.521587\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 153524. | + | 336176.i | 0.363908 | + | 0.796861i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 573924. | − | 573924.i | 1.25714 | − | 1.25714i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 145313.i | 0.294729i | 0.989082 | + | 0.147364i | \(0.0470790\pi\) | ||||
−0.989082 | + | 0.147364i | \(0.952921\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 379089. | 0.713322 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −63129.1 | − | 63129.1i | −0.110407 | − | 0.110407i | 0.649745 | − | 0.760152i | \(-0.274876\pi\) |
−0.760152 | + | 0.649745i | \(0.774876\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −65368.3 | − | 94149.0i | −0.106441 | − | 0.153306i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 448049. | − | 448049.i | 0.680406 | − | 0.680406i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 333388.i | 0.472912i | 0.971642 | + | 0.236456i | \(0.0759859\pi\) | ||||
−0.971642 | + | 0.236456i | \(0.924014\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.05416e6 | −1.39889 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 115083. | + | 115083.i | 0.143075 | + | 0.143075i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.18495e6 | + | 213792.i | 1.38206 | + | 0.249357i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 519696. | − | 519696.i | 0.569422 | − | 0.569422i | −0.362545 | − | 0.931966i | \(-0.618092\pi\) |
0.931966 | + | 0.362545i | \(0.118092\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 230582.i | 0.237640i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.97076e6 | −1.91280 | −0.956399 | − | 0.292065i | \(-0.905658\pi\) | ||||
−0.956399 | + | 0.292065i | \(0.905658\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −862587. | − | 862587.i | −0.789389 | − | 0.789389i | 0.192005 | − | 0.981394i | \(-0.438501\pi\) |
−0.981394 | + | 0.192005i | \(0.938501\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −313311. | + | 1.73653e6i | −0.270650 | + | 1.50008i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.28226e6 | + | 1.28226e6i | −1.04671 | + | 1.04671i | −0.0478536 | + | 0.998854i | \(0.515238\pi\) |
−0.998854 | + | 0.0478536i | \(0.984762\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 186075.i | − | 0.143684i | −0.997416 | − | 0.0718419i | \(-0.977112\pi\) | ||
0.997416 | − | 0.0718419i | \(-0.0228877\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.41719e6 | 1.03624 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.01659e6 | + | 1.01659e6i | 0.704545 | + | 0.704545i | 0.965383 | − | 0.260838i | \(-0.0839987\pi\) |
−0.260838 | + | 0.965383i | \(0.583999\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −128787. | + | 89417.7i | −0.0846795 | + | 0.0587936i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 211762. | − | 211762.i | 0.132218 | − | 0.132218i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 547254.i | − | 0.324749i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 77877.5 | 0.0439598 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.21606e6 | − | 2.21606e6i | −1.19088 | − | 1.19088i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 996638. | − | 1.67971e6i | 0.510279 | − | 0.860009i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.52424e6 | − | 1.52424e6i | 0.744120 | − | 0.744120i | −0.229248 | − | 0.973368i | \(-0.573627\pi\) |
0.973368 | + | 0.229248i | \(0.0736266\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 698721.i | − | 0.325488i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.10323e6 | 0.490739 | 0.245370 | − | 0.969430i | \(-0.421091\pi\) | ||||
0.245370 | + | 0.969430i | \(0.421091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.06518e6 | + | 4.06518e6i | 1.72792 | + | 1.72792i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.51514e6 | − | 2.18223e6i | −0.615815 | − | 0.886949i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 720618. | − | 720618.i | 0.280248 | − | 0.280248i | −0.552960 | − | 0.833208i | \(-0.686502\pi\) |
0.833208 | + | 0.552960i | \(0.186502\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.89720e6i | 1.07878i | 0.842055 | + | 0.539391i | \(0.181346\pi\) | ||||
−0.842055 | + | 0.539391i | \(0.818654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.05722e6 | 0.377143 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.69849e6 | − | 1.69849e6i | −0.580838 | − | 0.580838i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.29545e6 | − | 594577.i | −1.08096 | − | 0.195031i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.98983e6 | + | 3.98983e6i | −1.25604 | + | 1.25604i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.98382e6i | − | 0.599714i | −0.953984 | − | 0.299857i | \(-0.903061\pi\) | ||
0.953984 | − | 0.299857i | \(-0.0969389\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.02159e6 | 1.16807 | 0.584033 | − | 0.811730i | \(-0.301474\pi\) | ||||
0.584033 | + | 0.811730i | \(0.301474\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 109933. | + | 109933.i | 0.0306941 | + | 0.0306941i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 152719. | − | 846450.i | 0.0410109 | − | 0.227304i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.96237e6 | + | 3.96237e6i | −1.02390 | + | 1.02390i | −0.0241894 | + | 0.999707i | \(0.507700\pi\) |
−0.999707 | + | 0.0241894i | \(0.992300\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 2.67956e6i | − | 0.666610i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −748591. | −0.179377 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.80620e6 | + | 2.80620e6i | 0.647971 | + | 0.647971i | 0.952502 | − | 0.304531i | \(-0.0984998\pi\) |
−0.304531 | + | 0.952502i | \(0.598500\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.30275e6 | + | 2.29313e6i | −0.735232 | + | 0.510477i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.05536e6 | + | 4.05536e6i | −0.870724 | + | 0.870724i | −0.992551 | − | 0.121827i | \(-0.961125\pi\) |
0.121827 | + | 0.992551i | \(0.461125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.70708e6i | − | 0.353667i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.63324e6 | −0.326635 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −593924. | − | 593924.i | −0.114708 | − | 0.114708i | 0.647423 | − | 0.762131i | \(-0.275847\pi\) |
−0.762131 | + | 0.647423i | \(0.775847\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.48275e6 | − | 3.87387e6i | 1.58279 | − | 0.722822i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.85250e6 | − | 4.85250e6i | 0.875076 | − | 0.875076i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.48674e6i | 0.607939i | 0.952682 | + | 0.303970i | \(0.0983122\pi\) | ||||
−0.952682 | + | 0.303970i | \(0.901688\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.41422e6 | −0.238496 | −0.119248 | − | 0.992864i | \(-0.538048\pi\) | ||||
−0.119248 | + | 0.992864i | \(0.538048\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.24764e6 | + | 4.24764e6i | 0.693098 | + | 0.693098i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.27146e6 | − | 6.15212e6i | −0.674623 | − | 0.971649i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 881747. | − | 881747.i | 0.134840 | − | 0.134840i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1.26845e7i | − | 1.87883i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.51204e6 | 0.647549 | 0.323775 | − | 0.946134i | \(-0.395048\pi\) | ||||
0.323775 | + | 0.946134i | \(0.395048\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.70789e6 | + | 1.70789e6i | 0.237569 | + | 0.237569i | 0.815843 | − | 0.578274i | \(-0.196274\pi\) |
−0.578274 | + | 0.815843i | \(0.696274\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.13915e6 | + | 927223.i | 0.693087 | + | 0.125049i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.88696e6 | − | 2.88696e6i | 0.377608 | − | 0.377608i | −0.492630 | − | 0.870239i | \(-0.663964\pi\) |
0.870239 | + | 0.492630i | \(0.163964\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.21379e6i | 0.534704i | 0.963599 | + | 0.267352i | \(0.0861487\pi\) | ||||
−0.963599 | + | 0.267352i | \(0.913851\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −380283. | −0.0468294 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.13057e7 | − | 1.13057e7i | −1.35148 | − | 1.35148i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.94079e6 | + | 1.62994e7i | −0.341352 | + | 1.89195i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 150378. | − | 150378.i | 0.0169541 | − | 0.0169541i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.30998e7i | 1.43491i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.89683e6 | −0.414825 | −0.207412 | − | 0.978254i | \(-0.566504\pi\) | ||||
−0.207412 | + | 0.978254i | \(0.566504\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.00645e6 | − | 3.00645e6i | −0.311111 | − | 0.311111i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.03320e6 | + | 2.10597e6i | −0.305201 | + | 0.211903i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.90391e6 | − | 2.90391e6i | 0.284186 | − | 0.284186i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.38644e7i | 1.31999i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.61956e6 | −0.150045 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.41658e6 | − | 3.41658e6i | −0.308090 | − | 0.308090i | 0.536078 | − | 0.844168i | \(-0.319905\pi\) |
−0.844168 | + | 0.536078i | \(0.819905\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −925841. | + | 2.48222e6i | −0.0812809 | + | 0.217918i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.67846e6 | − | 7.67846e6i | 0.656442 | − | 0.656442i | −0.298094 | − | 0.954537i | \(-0.596351\pi\) |
0.954537 | + | 0.298094i | \(0.0963509\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 7.64574e6i | − | 0.636668i | −0.947979 | − | 0.318334i | \(-0.896877\pi\) | ||
0.947979 | − | 0.318334i | \(-0.103123\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.91977e7 | −1.55745 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.32288e6 | + | 1.32288e6i | 0.104581 | + | 0.104581i | 0.757461 | − | 0.652880i | \(-0.226440\pi\) |
−0.652880 | + | 0.757461i | \(0.726440\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.18649e6 | − | 4.58946e6i | −0.245533 | − | 0.353637i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.43035e6 | − | 2.43035e6i | 0.182568 | − | 0.182568i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.04557e7i | 0.765875i | 0.923774 | + | 0.382937i | \(0.125087\pi\) | ||||
−0.923774 | + | 0.382937i | \(0.874913\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.42256e6 | −0.530277 | −0.265138 | − | 0.964210i | \(-0.585418\pi\) | ||||
−0.265138 | + | 0.964210i | \(0.585418\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.61536e6 | + | 4.61536e6i | 0.321652 | + | 0.321652i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.93456e7 | + | 5.29464e6i | 1.99547 | + | 0.360030i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.20306e7 | − | 1.20306e7i | 0.798357 | − | 0.798357i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.11166e6i | 0.136781i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.25795e7 | 0.795505 | 0.397752 | − | 0.917493i | \(-0.369790\pi\) | ||||
0.397752 | + | 0.917493i | \(0.369790\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.20615e6 | − | 1.20615e6i | −0.0744798 | − | 0.0744798i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −481355. | + | 2.66792e6i | −0.0290298 | + | 0.160898i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.35530e6 | + | 3.35530e6i | −0.197666 | + | 0.197666i | −0.798999 | − | 0.601333i | \(-0.794637\pi\) |
0.601333 | + | 0.798999i | \(0.294637\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.57600e7i | − | 2.05825i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.54221e6 | 0.255473 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.97354e7 | − | 1.97354e7i | −1.08487 | − | 1.08487i | −0.996047 | − | 0.0888280i | \(-0.971688\pi\) |
−0.0888280 | − | 0.996047i | \(-0.528312\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.16322e7 | + | 8.07629e6i | −0.625061 | + | 0.433985i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.57590e6 | − | 5.57590e6i | 0.292942 | − | 0.292942i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.82612e6i | − | 0.196563i | −0.995159 | − | 0.0982816i | \(-0.968665\pi\) | ||
0.995159 | − | 0.0982816i | \(-0.0313346\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 238579. | 0.0119874 | 0.00599368 | − | 0.999982i | \(-0.498092\pi\) | ||||
0.00599368 | + | 0.999982i | \(0.498092\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.76308e7 | + | 1.76308e7i | 0.866532 | + | 0.866532i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.99093e7 | + | 7.42593e6i | 0.957320 | + | 0.357069i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.83629e6 | + | 8.83629e6i | −0.415749 | + | 0.415749i | −0.883735 | − | 0.467987i | \(-0.844979\pi\) |
0.467987 | + | 0.883735i | \(0.344979\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.16668e6i | 0.0537206i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.44266e6 | 0.425574 | 0.212787 | − | 0.977099i | \(-0.431746\pi\) | ||||
0.212787 | + | 0.977099i | \(0.431746\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.88228e6 | + | 3.88228e6i | 0.171288 | + | 0.171288i | 0.787545 | − | 0.616257i | \(-0.211352\pi\) |
−0.616257 | + | 0.787545i | \(0.711352\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.62425e7 | − | 2.33938e7i | −0.701646 | − | 1.01057i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.59180e7 | + | 5.59180e7i | −2.36541 | + | 2.36541i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.32968e7i | 0.965168i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.73838e7 | −0.705448 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.41027e6 | + | 4.41027e6i | 0.175332 | + | 0.175332i | 0.789318 | − | 0.613985i | \(-0.210435\pi\) |
−0.613985 | + | 0.789318i | \(0.710435\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.56907e7 | − | 6.43944e6i | −1.39024 | − | 0.250831i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.04375e7 | − | 2.04375e7i | 0.780115 | − | 0.780115i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.21540e6i | 0.0828780i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.76309e7 | −0.646509 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.29608e7 | + | 3.29608e7i | 1.18487 | + | 1.18487i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.63677e6 | − | 3.12419e7i | 0.198669 | − | 1.10113i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.02549e7 | − | 2.02549e7i | 0.700026 | − | 0.700026i | −0.264390 | − | 0.964416i | \(-0.585170\pi\) |
0.964416 | + | 0.264390i | \(0.0851704\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.88534e7i | 0.977962i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.11216e7 | 1.36707 | 0.683533 | − | 0.729920i | \(-0.260443\pi\) | ||||
0.683533 | + | 0.729920i | \(0.260443\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.75640e7 | − | 3.75640e7i | −1.22501 | − | 1.22501i | −0.965830 | − | 0.259178i | \(-0.916548\pi\) |
−0.259178 | − | 0.965830i | \(-0.583452\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.03904e7 | + | 7.21413e6i | −0.332430 | + | 0.230809i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.01898e7 | + | 2.01898e7i | −0.633803 | + | 0.633803i | −0.949020 | − | 0.315217i | \(-0.897923\pi\) |
0.315217 | + | 0.949020i | \(0.397923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.64319e7i | − | 1.12230i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.28915e7 | 1.29675 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.24553e6 | + | 6.24553e6i | 0.185337 | + | 0.185337i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.14645e7 | − | 2.51041e7i | −0.333967 | − | 0.731299i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.11209e6 | + | 3.11209e6i | −0.0890038 | + | 0.0890038i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.66768e7i | − | 0.749112i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.35648e7 | 1.47705 | 0.738526 | − | 0.674225i | \(-0.235522\pi\) | ||||
0.738526 | + | 0.674225i | \(0.235522\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.18354e6 | + | 7.18354e6i | 0.194539 | + | 0.194539i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.14619e6 | + | 1.65084e6i | 0.0304875 | + | 0.0439107i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.35730e7 | + | 3.35730e7i | −0.877203 | + | 0.877203i | −0.993244 | − | 0.116041i | \(-0.962980\pi\) |
0.116041 | + | 0.993244i | \(0.462980\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 3.40047e7i | − | 0.872850i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.35767e6 | 0.235996 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.10252e7 | + | 5.10252e7i | 1.26445 | + | 1.26445i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.64946e6 | + | 658447.i | 0.0888732 | + | 0.0160348i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.02313e7 | − | 3.02313e7i | 0.723550 | − | 0.723550i | −0.245776 | − | 0.969327i | \(-0.579043\pi\) |
0.969327 | + | 0.245776i | \(0.0790428\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.12050e7i | − | 0.498842i | −0.968395 | − | 0.249421i | \(-0.919760\pi\) | ||
0.968395 | − | 0.249421i | \(-0.0802402\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.75389e7 | −0.868080 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.10632e7 | − | 5.10632e7i | −1.16087 | − | 1.16087i | −0.984285 | − | 0.176586i | \(-0.943495\pi\) |
−0.176586 | − | 0.984285i | \(-0.556505\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.98966e6 | + | 2.21128e7i | −0.0891766 | + | 0.494263i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.15279e6 | + | 9.15279e6i | −0.201163 | + | 0.201163i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.68160e7i | 1.44410i | 0.691841 | + | 0.722050i | \(0.256800\pi\) | ||||
−0.691841 | + | 0.722050i | \(0.743200\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.57417e7 | −0.972279 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.30250e6 | − | 1.30250e6i | −0.0272306 | − | 0.0272306i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.01866e7 | − | 4.17880e7i | 1.23772 | − | 0.859356i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.04382e6 | + | 5.04382e6i | −0.102038 | + | 0.102038i | −0.756283 | − | 0.654245i | \(-0.772987\pi\) |
0.654245 | + | 0.756283i | \(0.272987\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2.24658e7i | − | 0.447140i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.76135e7 | −1.32407 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.06926e7 | + | 5.06926e7i | 0.976828 | + | 0.976828i | 0.999738 | − | 0.0229094i | \(-0.00729292\pi\) |
−0.0229094 | + | 0.999738i | \(0.507293\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.47617e7 | + | 1.14242e7i | −0.848814 | + | 0.216638i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.34584e7 | + | 3.34584e7i | −0.624425 | + | 0.624425i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.97376e7i | 0.546245i | 0.961979 | + | 0.273123i | \(0.0880565\pi\) | ||||
−0.961979 | + | 0.273123i | \(0.911944\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.09857e7 | −0.921879 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.82121e7 | − | 2.82121e7i | −0.502157 | − | 0.502157i | 0.409951 | − | 0.912108i | \(-0.365546\pi\) |
−0.912108 | + | 0.409951i | \(0.865546\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.78626e7 | + | 8.33387e7i | 1.01395 | + | 1.46037i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.54173e6 | − | 3.54173e6i | 0.0611058 | − | 0.0611058i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.32404e7i | 1.41412i | 0.707155 | + | 0.707059i | \(0.249978\pi\) | ||||
−0.707155 | + | 0.707059i | \(0.750022\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.15010e6 | −0.0192399 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.84514e7 | − | 1.84514e7i | −0.303984 | − | 0.303984i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.78755e7 | − | 3.22516e6i | −0.290046 | − | 0.0523311i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.98898e7 | − | 4.98898e7i | 0.797333 | − | 0.797333i | −0.185341 | − | 0.982674i | \(-0.559339\pi\) |
0.982674 | + | 0.185341i | \(0.0593390\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 1.35980e8i | − | 2.14070i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.12175e8 | 1.73966 | 0.869829 | − | 0.493353i | \(-0.164229\pi\) | ||||
0.869829 | + | 0.493353i | \(0.164229\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.59391e6 | − | 8.59391e6i | −0.131303 | − | 0.131303i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.41371e6 | + | 4.66331e7i | −0.126655 | + | 0.701988i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.76173e7 | − | 5.76173e7i | 0.854613 | − | 0.854613i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.66273e7i | 0.243025i | 0.992590 | + | 0.121513i | \(0.0387745\pi\) | ||||
−0.992590 | + | 0.121513i | \(0.961226\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.41046e7 | −0.347195 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.22444e8 | − | 1.22444e8i | −1.73814 | − | 1.73814i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.16688e6 | − | 6.36463e6i | 0.128256 | − | 0.0890490i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.84555e7 | − | 4.84555e7i | 0.668244 | − | 0.668244i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.77132e7i | 1.05646i | 0.849101 | + | 0.528230i | \(0.177144\pi\) | ||||
−0.849101 | + | 0.528230i | \(0.822856\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.97347e7 | 0.666520 | 0.333260 | − | 0.942835i | \(-0.391851\pi\) | ||||
0.333260 | + | 0.942835i | \(0.391851\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.35889e6 | + | 5.35889e6i | 0.0708034 | + | 0.0708034i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.30325e7 | − | 5.95161e6i | 0.169769 | − | 0.0775297i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.07181e8 | − | 1.07181e8i | 1.37669 | − | 1.37669i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.68143e7i | 0.719591i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.70972e7 | −0.838056 | −0.419028 | − | 0.907973i | \(-0.637629\pi\) | ||||
−0.419028 | + | 0.907973i | \(0.637629\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.05301e7 | + | 9.05301e7i | 1.11514 | + | 1.11514i | 0.992444 | + | 0.122696i | \(0.0391539\pi\) |
0.122696 | + | 0.992444i | \(0.460846\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.51720e7 | + | 6.50605e7i | 0.548784 | + | 0.790405i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.54328e6 | − | 8.54328e6i | 0.102372 | − | 0.102372i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 231381.i | − | 0.00273485i | −0.999999 | − | 0.00136743i | \(-0.999565\pi\) | ||
0.999999 | − | 0.00136743i | \(-0.000435265\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.04478e7 | −0.471606 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.08251e7 | − | 2.08251e7i | −0.239538 | − | 0.239538i | 0.577121 | − | 0.816659i | \(-0.304176\pi\) |
−0.816659 | + | 0.577121i | \(0.804176\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.10114e7 | − | 7.39941e6i | −0.465398 | − | 0.0839686i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.31793e7 | + | 3.31793e7i | −0.371488 | + | 0.371488i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.49546e7i | 0.717581i | 0.933418 | + | 0.358790i | \(0.116811\pi\) | ||||
−0.933418 | + | 0.358790i | \(0.883189\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.80193e8 | −1.96430 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.72609e7 | − | 6.72609e7i | −0.723549 | − | 0.723549i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.33967e7 | − | 1.29677e8i | 0.248382 | − | 1.37666i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.96439e7 | + | 6.96439e7i | −0.729684 | + | 0.729684i | −0.970557 | − | 0.240873i | \(-0.922566\pi\) |
0.240873 | + | 0.970557i | \(0.422566\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 1.94878e7i | − | 0.201523i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.07689e7 | 0.824407 | 0.412203 | − | 0.911092i | \(-0.364759\pi\) | ||||
0.412203 | + | 0.911092i | \(0.364759\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.35152e7 | + | 8.35152e7i | 0.841439 | + | 0.841439i | 0.989046 | − | 0.147607i | \(-0.0471572\pi\) |
−0.147607 | + | 0.989046i | \(0.547157\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.67111e7 | + | 1.16026e7i | −0.166205 | + | 0.115398i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.17085e7 | + | 8.17085e7i | −0.802262 | + | 0.802262i | −0.983449 | − | 0.181186i | \(-0.942006\pi\) |
0.181186 | + | 0.983449i | \(0.442006\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.59572e6i | 0.0930163i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.32541e8 | 1.26849 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.84073e7 | − | 2.84073e7i | −0.268439 | − | 0.268439i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.25988e7 | + | 1.41020e8i | −0.490789 | + | 1.31583i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.35823e7 | − | 1.35823e7i | 0.125147 | − | 0.125147i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 1.07532e8i | − | 0.978433i | −0.872162 | − | 0.489216i | \(-0.837283\pi\) | ||
0.872162 | − | 0.489216i | \(-0.162717\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.05829e8 | −0.950979 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.25201e7 | + | 1.25201e7i | 0.111114 | + | 0.111114i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.23953e7 | + | 7.54642e7i | 0.459269 | + | 0.661478i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.33036e7 | + | 4.33036e7i | −0.374919 | + | 0.374919i | −0.869265 | − | 0.494346i | \(-0.835408\pi\) |
0.494346 | + | 0.869265i | \(0.335408\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 9.38670e7i | − | 0.802761i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.23191e7 | −0.526474 | −0.263237 | − | 0.964731i | \(-0.584790\pi\) | ||||
−0.263237 | + | 0.964731i | \(0.584790\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.73694e7 | − | 1.73694e7i | −0.144959 | − | 0.144959i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.83648e7 | − | 5.11767e6i | −0.233864 | − | 0.0421946i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.58619e7 | + | 7.58619e7i | −0.617952 | + | 0.617952i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.67847e6i | 0.0135086i | 0.999977 | + | 0.00675432i | \(0.00214998\pi\) | ||||
−0.999977 | + | 0.00675432i | \(0.997850\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.35651e8 | 1.07873 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.94281e7 | + | 5.94281e7i | 0.466969 | + | 0.466969i | 0.900931 | − | 0.433962i | \(-0.142885\pi\) |
−0.433962 | + | 0.900931i | \(0.642885\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.37401e7 | − | 2.42430e8i | 0.339630 | − | 1.88240i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.85509e7 | + | 2.85509e7i | −0.219076 | + | 0.219076i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.54356e8i | − | 1.17049i | −0.810855 | − | 0.585247i | \(-0.800997\pi\) | ||
0.810855 | − | 0.585247i | \(-0.199003\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.49843e8 | 2.62186 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.44762e8 | + | 1.44762e8i | 1.07226 | + | 1.07226i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.25255e8 | − | 8.69654e7i | 0.917008 | − | 0.636685i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.29823e7 | − | 4.29823e7i | 0.311041 | − | 0.311041i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.98667e7i | 0.142110i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.71124e8 | −1.21004 | −0.605019 | − | 0.796211i | \(-0.706834\pi\) | ||||
−0.605019 | + | 0.796211i | \(0.706834\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.28297e8 | − | 1.28297e8i | −0.896833 | − | 0.896833i | 0.0983219 | − | 0.995155i | \(-0.468653\pi\) |
−0.995155 | + | 0.0983219i | \(0.968653\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.06664e8 | − | 7.70832e7i | −1.42819 | − | 0.532699i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.46141e6 | − | 4.46141e6i | 0.0304817 | − | 0.0304817i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1.46463e8i | − | 0.989373i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.91934e7 | 0.328566 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.65486e8 | + | 1.65486e8i | 1.09290 | + | 1.09290i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.29277e8 | − | 1.86195e8i | −0.844226 | − | 1.21593i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.83155e7 | − | 5.83155e7i | 0.376583 | − | 0.376583i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.24422e8i | 2.07178i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.12555e8 | −0.710841 | −0.355420 | − | 0.934707i | \(-0.615662\pi\) | ||||
−0.355420 | + | 0.934707i | \(0.615662\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.36528e7 | + | 2.36528e7i | 0.147735 | + | 0.147735i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.28898e7 | + | 4.12985e6i | 0.141401 | + | 0.0255120i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.86772e7 | + | 3.86772e7i | −0.236316 | + | 0.236316i | −0.815323 | − | 0.579007i | \(-0.803440\pi\) |
0.579007 | + | 0.815323i | \(0.303440\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.30615e7i | 0.260239i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.58051e8 | 1.54259 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.13252e7 | − | 6.13252e7i | −0.362630 | − | 0.362630i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.14539e7 | + | 1.74334e8i | −0.183990 | + | 1.01977i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.77413e8 | + | 1.77413e8i | −1.02664 | + | 1.02664i | −0.0270085 | + | 0.999635i | \(0.508598\pi\) |
−0.999635 | + | 0.0270085i | \(0.991402\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.21774e7i | 0.298708i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.94943e7 | −0.167051 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.61909e7 | − | 2.61909e7i | −0.146766 | − | 0.146766i | 0.629906 | − | 0.776672i | \(-0.283094\pi\) |
−0.776672 | + | 0.629906i | \(0.783094\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.47617e8 | + | 1.02491e8i | −0.818447 | + | 0.568254i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.59984e8 | + | 1.59984e8i | −0.877660 | + | 0.877660i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 9.04667e7i | − | 0.491080i | −0.969387 | − | 0.245540i | \(-0.921035\pi\) | ||
0.969387 | − | 0.245540i | \(-0.0789652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.72767e7 | −0.200230 | −0.100115 | − | 0.994976i | \(-0.531921\pi\) | ||||
−0.100115 | + | 0.994976i | \(0.531921\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.54636e7 | − | 7.54636e7i | −0.401119 | − | 0.401119i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.14124e6 | − | 1.78272e7i | −0.0428240 | − | 0.0937731i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.48027e7 | − | 6.48027e7i | 0.337339 | − | 0.337339i | −0.518026 | − | 0.855365i | \(-0.673333\pi\) |
0.855365 | + | 0.518026i | \(0.173333\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 5.71288e7i | − | 0.294320i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.32837e7 | 0.271685 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.08940e8 | − | 1.08940e8i | −0.549772 | − | 0.549772i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.13497e7 | + | 3.07497e7i | 0.106641 | + | 0.153593i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.02171e8 | − | 1.02171e8i | 0.505144 | − | 0.505144i | −0.407888 | − | 0.913032i | \(-0.633735\pi\) |
0.913032 | + | 0.407888i | \(0.133735\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.62815e7i | 0.324375i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.65684e7 | −0.467813 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.09929e8 | + | 1.09929e8i | 0.527166 | + | 0.527166i | 0.919726 | − | 0.392560i | \(-0.128410\pi\) |
−0.392560 | + | 0.919726i | \(0.628410\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.73198e7 | + | 1.21461e7i | 0.319589 | + | 0.0576613i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.04754e7 | − | 7.04754e7i | 0.331218 | − | 0.331218i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 2.43420e8i | − | 1.13260i | −0.824200 | − | 0.566298i | \(-0.808375\pi\) | ||
0.824200 | − | 0.566298i | \(-0.191625\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.12016e7 | −0.0516007 | −0.0258004 | − | 0.999667i | \(-0.508213\pi\) | ||||
−0.0258004 | + | 0.999667i | \(0.508213\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.92761e6 | − | 1.92761e6i | −0.00879156 | − | 0.00879156i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.72846e6 | + | 9.58001e6i | −0.00780535 | + | 0.0432613i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.50111e8 | + | 1.50111e8i | −0.671192 | + | 0.671192i | −0.957991 | − | 0.286799i | \(-0.907409\pi\) |
0.286799 | + | 0.957991i | \(0.407409\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.78173e8i | 1.67432i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.89483e7 | −0.346114 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.74572e8 | + | 1.74572e8i | 0.757868 | + | 0.757868i | 0.975934 | − | 0.218066i | \(-0.0699749\pi\) |
−0.218066 | + | 0.975934i | \(0.569975\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.21791e8 | − | 2.23422e8i | 1.38340 | − | 0.960505i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.43703e8 | − | 2.43703e8i | 1.03754 | − | 1.03754i | 0.0382750 | − | 0.999267i | \(-0.487814\pi\) |
0.999267 | − | 0.0382750i | \(-0.0121863\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.67973e8i | − | 0.708220i | −0.935204 | − | 0.354110i | \(-0.884784\pi\) | ||
0.935204 | − | 0.354110i | \(-0.115216\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.66574e7 | −0.111312 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.40697e8 | − | 1.40697e8i | −0.581863 | − | 0.581863i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.84507e8 | + | 1.59881e8i | 0.755741 | + | 0.654871i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.19093e8 | − | 2.19093e8i | 0.888846 | − | 0.888846i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 5.49398e7i | − | 0.220767i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.57816e8 | −1.82223 | −0.911114 | − | 0.412154i | \(-0.864777\pi\) | ||||
−0.911114 | + | 0.412154i | \(0.864777\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.51743e7 | + | 6.51743e7i | 0.256960 | + | 0.256960i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.53673e8 | + | 2.21333e8i | 0.600173 | + | 0.864420i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.97943e8 | − | 2.97943e8i | 1.15270 | − | 1.15270i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 3.04786e7i | − | 0.116813i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.41603e7 | −0.167671 | −0.0838356 | − | 0.996480i | \(-0.526717\pi\) | ||||
−0.0838356 | + | 0.996480i | \(0.526717\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.97415e8 | − | 2.97415e8i | −1.11874 | − | 1.11874i | −0.991926 | − | 0.126816i | \(-0.959524\pi\) |
−0.126816 | − | 0.991926i | \(-0.540476\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.59524e7 | + | 1.55078e7i | 0.320316 | + | 0.0577925i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.69716e7 | + | 8.69716e7i | −0.321118 | + | 0.321118i | −0.849196 | − | 0.528078i | \(-0.822913\pi\) |
0.528078 | + | 0.849196i | \(0.322913\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 3.94567e8i | − | 1.44340i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.71353e7 | −0.352074 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.33636e7 | + | 2.33636e7i | 0.0839074 | + | 0.0839074i | 0.747815 | − | 0.663907i | \(-0.231103\pi\) |
−0.663907 | + | 0.747815i | \(0.731103\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.44856e7 | + | 1.35712e8i | −0.0871339 | + | 0.482942i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.02770e7 | + | 7.02770e7i | −0.247809 | + | 0.247809i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.40867e8i | 1.54046i | 0.637764 | + | 0.770232i | \(0.279859\pi\) | ||||
−0.637764 | + | 0.770232i | \(0.720141\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.14414e8 | 0.742419 | 0.371209 | − | 0.928549i | \(-0.378943\pi\) | ||||
0.371209 | + | 0.928549i | \(0.378943\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.70870e7 | + | 2.70870e7i | 0.0929439 | + | 0.0929439i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.90298e8 | + | 4.09848e8i | −2.00727 | + | 1.39366i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.37597e7 | + | 2.37597e7i | −0.0800689 | + | 0.0800689i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.14284e8i | 0.381688i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.45385e8 | 1.14324 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.41496e7 | − | 7.41496e7i | −0.243256 | − | 0.243256i | 0.574940 | − | 0.818196i | \(-0.305026\pi\) |
−0.818196 | + | 0.574940i | \(0.805026\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.02072e8 | − | 1.37949e8i | 0.982198 | − | 0.448547i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.19427e8 | + | 1.19427e8i | −0.384890 | + | 0.384890i | −0.872860 | − | 0.487970i | \(-0.837737\pi\) |
0.487970 | + | 0.872860i | \(0.337737\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.38646e8i | 1.40121i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.56844e8 | −0.813256 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.67224e8 | − | 3.67224e8i | −1.15257 | − | 1.15257i | −0.986035 | − | 0.166540i | \(-0.946741\pi\) |
−0.166540 | − | 0.986035i | \(-0.553259\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.26521e7 | + | 1.04640e8i | 0.226036 | + | 0.325555i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.27875e8 | + | 1.27875e8i | −0.394379 | + | 0.394379i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.00097e8i | 0.611764i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.40286e8 | −0.425187 | −0.212594 | − | 0.977141i | \(-0.568191\pi\) | ||||
−0.212594 | + | 0.977141i | \(0.568191\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.73106e7 | − | 9.73106e7i | −0.292389 | − | 0.292389i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.56396e8 | − | 6.43021e7i | −1.06164 | − | 0.191545i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.59095e7 | + | 8.59095e7i | −0.253713 | + | 0.253713i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 4.42502e7i | − | 0.129564i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.48014e8 | −1.59088 | −0.795440 | − | 0.606032i | \(-0.792760\pi\) | ||||
−0.795440 | + | 0.606032i | \(0.792760\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.08111e8 | + | 4.08111e8i | 1.17466 | + | 1.17466i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.34645e7 | + | 1.30052e8i | −0.0669643 | + | 0.371151i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.31702e8 | − | 8.31702e8i | 2.35348 | − | 2.35348i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.10430e6i | 0.0171276i | 0.999963 | + | 0.00856382i | \(0.00272598\pi\) | ||||
−0.999963 | + | 0.00856382i | \(0.997274\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.46382e7 | 0.0685489 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.10278e6 | − | 6.10278e6i | −0.0168368 | − | 0.0168368i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.46635e8 | − | 1.71241e8i | 0.674740 | − | 0.468477i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.74870e8 | − | 1.74870e8i | 0.474415 | − | 0.474415i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 2.94556e7i | − | 0.0792467i | −0.999215 | − | 0.0396233i | \(-0.987384\pi\) | ||
0.999215 | − | 0.0396233i | \(-0.0126158\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.28061e8 | 1.94250 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.24142e8 | + | 1.24142e8i | 0.328476 | + | 0.328476i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.46282e8 | − | 3.92190e8i | 0.383865 | − | 1.02916i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.16355e8 | + | 5.16355e8i | −1.34383 | + | 1.34383i | −0.451627 | + | 0.892207i | \(0.649156\pi\) |
−0.892207 | + | 0.451627i | \(0.850844\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 4.30739e8i | − | 1.11181i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.70872e7 | −0.0693444 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.26280e8 | − | 1.26280e8i | −0.320643 | − | 0.320643i | 0.528371 | − | 0.849014i | \(-0.322803\pi\) |
−0.849014 | + | 0.528371i | \(0.822803\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.02251e8 | − | 5.79357e8i | −1.01306 | − | 1.45910i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.54608e7 | + | 1.54608e7i | −0.0386216 | + | 0.0386216i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.71482e8i | 1.66380i | 0.554927 | + | 0.831899i | \(0.312746\pi\) | ||||
−0.554927 | + | 0.831899i | \(0.687254\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.02423e8 | −0.989072 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.38189e8 | + | 3.38189e8i | 0.824505 | + | 0.824505i | 0.986750 | − | 0.162246i | \(-0.0518737\pi\) |
−0.162246 | + | 0.986750i | \(0.551874\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.44038e8 | + | 4.40301e7i | 0.590185 | + | 0.106483i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.07037e7 | + | 1.07037e7i | −0.0256787 | + | 0.0256787i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1.08228e9i | − | 2.57571i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.72625e8 | 1.82410 | 0.912050 | − | 0.410078i | \(-0.134499\pi\) | ||||
0.912050 | + | 0.410078i | \(0.134499\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.10392e8 | − | 2.10392e8i | −0.492769 | − | 0.492769i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.92575e7 | + | 4.94711e8i | −0.207398 | + | 1.14951i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.84105e7 | + | 6.84105e7i | −0.157701 | + | 0.157701i | −0.781547 | − | 0.623846i | \(-0.785569\pi\) |
0.623846 | + | 0.781547i | \(0.285569\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.03454e7i | 0.0922718i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.07244e8 | 1.60478 | 0.802389 | − | 0.596801i | \(-0.203562\pi\) | ||||
0.802389 | + | 0.596801i | \(0.203562\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.85276e7 | + | 7.85276e7i | 0.176786 | + | 0.176786i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.59632e7 | + | 1.10834e7i | −0.0356564 | + | 0.0247565i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.62363e8 | + | 3.62363e8i | −0.803079 | + | 0.803079i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.14644e8i | − | 0.252100i | −0.992024 | − | 0.126050i | \(-0.959770\pi\) | ||
0.992024 | − | 0.126050i | \(-0.0402300\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.12234e8 | 0.244885 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.12226e8 | + | 6.12226e8i | 1.32548 | + | 1.32548i | 0.909266 | + | 0.416215i | \(0.136644\pi\) |
0.416215 | + | 0.909266i | \(0.363356\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.00736e8 | + | 3.75732e7i | 0.216410 | + | 0.0807185i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.98084e8 | + | 5.98084e8i | −1.27497 | + | 1.27497i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1.27633e9i | − | 2.69991i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.44461e8 | −0.513164 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.02596e8 | − | 4.02596e8i | −0.838657 | − | 0.838657i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.99483e8 | − | 5.75370e8i | −0.825828 | − | 1.18943i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.26664e7 | + | 7.26664e7i | −0.149077 | + | 0.149077i | −0.777705 | − | 0.628629i | \(-0.783616\pi\) |
0.628629 | + | 0.777705i | \(0.283616\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.60148e8i | 1.34403i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.58043e8 | −1.73372 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.17195e8 | − | 3.17195e8i | −0.636073 | − | 0.636073i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.29622e8 | + | 5.94716e7i | 0.656017 | + | 0.118361i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.52017e8 | + | 4.52017e8i | −0.892853 | + | 0.892853i | −0.994791 | − | 0.101938i | \(-0.967496\pi\) |
0.101938 | + | 0.994791i | \(0.467496\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4.09849e7i | − | 0.0803495i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.65270e7 | 0.109991 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.63674e8 | + | 5.63674e8i | 1.08863 | + | 1.08863i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.66147e7 | − | 9.20871e7i | 0.0318496 | − | 0.176527i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.39917e7 | + | 6.39917e7i | −0.121759 | + | 0.121759i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.32339e8i | 1.38314i | 0.722309 | + | 0.691570i | \(0.243081\pi\) | ||||
−0.722309 | + | 0.691570i | \(0.756919\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.74076e8 | 0.701290 | 0.350645 | − | 0.936509i | \(-0.385962\pi\) | ||||
0.350645 | + | 0.936509i | \(0.385962\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.99021e6 | − | 3.99021e6i | −0.00742548 | − | 0.00742548i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.07484e8 | + | 2.82919e8i | −0.752727 | + | 0.522624i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.01212e8 | − | 2.01212e8i | 0.368968 | − | 0.368968i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.78737e8i | 0.325358i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.05908e8 | −0.733496 | −0.366748 | − | 0.930320i | \(-0.619529\pi\) | ||||
−0.366748 | + | 0.930320i | \(0.619529\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.03821e8 | + | 5.03821e8i | 0.903809 | + | 0.903809i | 0.995763 | − | 0.0919544i | \(-0.0293114\pi\) |
−0.0919544 | + | 0.995763i | \(0.529311\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.08783e8 | − | 4.57179e8i | −0.371820 | − | 0.814188i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.75124e8 | + | 1.75124e8i | −0.309620 | + | 0.309620i | −0.844762 | − | 0.535142i | \(-0.820258\pi\) |
0.535142 | + | 0.844762i | \(0.320258\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.90749e8i | 0.861381i | 0.902500 | + | 0.430691i | \(0.141730\pi\) | ||||
−0.902500 | + | 0.430691i | \(0.858270\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.95573e8 | 0.515064 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.54673e8 | + | 1.54673e8i | 0.267595 | + | 0.267595i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.08859e8 | − | 5.88873e8i | −0.702286 | − | 1.01149i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.03408e8 | − | 1.03408e8i | 0.176352 | − | 0.176352i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 6.07365e8i | − | 1.02840i | −0.857669 | − | 0.514202i | \(-0.828088\pi\) | ||
0.857669 | − | 0.514202i | \(-0.171912\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.22843e8 | −0.206521 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.57928e8 | − | 1.57928e8i | −0.263618 | − | 0.263618i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.09995e8 | + | 3.78880e7i | 0.348048 | + | 0.0627959i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.28660e7 | + | 3.28660e7i | −0.0540874 | + | 0.0540874i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1.29862e8i | − | 0.212206i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.51524e7 | −0.121942 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.41127e8 | − | 3.41127e8i | −0.549628 | − | 0.549628i | 0.376705 | − | 0.926333i | \(-0.377057\pi\) |
−0.926333 | + | 0.376705i | \(0.877057\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.62491e7 | − | 2.00911e8i | 0.0579961 | − | 0.321445i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.87515e8 | − | 7.87515e8i | 1.25117 | − | 1.25117i | 0.295974 | − | 0.955196i | \(-0.404356\pi\) |
0.955196 | − | 0.295974i | \(-0.0956441\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.57007e8i | − | 0.405476i | −0.979233 | − | 0.202738i | \(-0.935016\pi\) | ||
0.979233 | − | 0.202738i | \(-0.0649840\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.87045e9 | 2.93047 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.70540e8 | − | 3.70540e8i | −0.576504 | − | 0.576504i | 0.357434 | − | 0.933938i | \(-0.383652\pi\) |
−0.933938 | + | 0.357434i | \(0.883652\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.62428e7 | − | 5.98790e7i | 0.133252 | − | 0.0925180i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.89637e8 | − | 3.89637e8i | 0.597865 | − | 0.597865i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.97617e8i | − | 0.301137i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.83979e7 | 0.0429765 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.81160e7 | − | 8.81160e7i | −0.132438 | − | 0.132438i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.88269e8 | + | 1.12948e9i | 0.430302 | + | 1.68598i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.21352e8 | + | 1.21352e8i | −0.179907 | + | 0.179907i | −0.791315 | − | 0.611408i | \(-0.790603\pi\) |
0.611408 | + | 0.791315i | \(0.290603\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 1.47523e8i | − | 0.217216i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.29574e8 | −0.628218 | −0.314109 | − | 0.949387i | \(-0.601706\pi\) | ||||
−0.314109 | + | 0.949387i | \(0.601706\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.67016e8 | − | 8.67016e8i | −1.25935 | − | 1.25935i | −0.951406 | − | 0.307939i | \(-0.900361\pi\) |
−0.307939 | − | 0.951406i | \(-0.599639\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.89226e8 | + | 7.04624e8i | 0.705796 | + | 1.01655i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.00413e8 | − | 5.00413e8i | 0.717064 | − | 0.717064i | −0.250939 | − | 0.968003i | \(-0.580739\pi\) |
0.968003 | + | 0.250939i | \(0.0807394\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.28653e9i | 1.83111i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.15538e8 | −0.728832 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.04449e8 | + | 3.04449e8i | 0.427524 | + | 0.427524i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.28917e8 | − | 7.73867e7i | −0.598280 | − | 0.107944i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.70525e7 | − | 3.70525e7i | 0.0513381 | − | 0.0513381i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1.84336e8i | − | 0.253706i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.03878e8 | −0.142020 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.94876e8 | + | 2.94876e8i | 0.400475 | + | 0.400475i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.13881e7 | − | 1.73969e8i | 0.0423466 | − | 0.234707i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.77507e8 | − | 2.77507e8i | 0.371922 | − | 0.371922i | −0.496255 | − | 0.868177i | \(-0.665292\pi\) |
0.868177 | + | 0.496255i | \(0.165292\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.34148e8i | 0.444884i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.67626e7 | 0.101530 | 0.0507650 | − | 0.998711i | \(-0.483834\pi\) | ||||
0.0507650 | + | 0.998711i | \(0.483834\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.58518e7 | + | 8.58518e7i | 0.112807 | + | 0.112807i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.16794e8 | + | 4.28244e8i | −0.805149 | + | 0.559021i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.65585e8 | + | 4.65585e8i | −0.603798 | + | 0.603798i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 7.93161e8i | − | 1.02192i | −0.859606 | − | 0.510958i | \(-0.829291\pi\) | ||
0.859606 | − | 0.510958i | \(-0.170709\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.77523e8 | −0.867252 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.24508e8 | + | 2.24508e8i | 0.285514 | + | 0.285514i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.51599e8 | − | 3.88905e8i | 1.07599 | − | 0.491381i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.46254e8 | + | 1.46254e8i | −0.183599 | + | 0.183599i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.48777e8i | 0.684461i | 0.939616 | + | 0.342231i | \(0.111182\pi\) | ||||
−0.939616 | + | 0.342231i | \(0.888818\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.29792e9 | −2.84764 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.87757e8 | − | 6.87757e8i | −0.846818 | − | 0.846818i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.88971e7 | + | 1.28037e8i | 0.108756 | + | 0.156639i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.56840e7 | + | 5.56840e7i | −0.0676880 | + | 0.0676880i | −0.740140 | − | 0.672452i | \(-0.765241\pi\) |
0.672452 | + | 0.740140i | \(0.265241\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.25651e9i | 1.51764i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.88360e8 | −1.06616 | −0.533078 | − | 0.846066i | \(-0.678965\pi\) | ||||
−0.533078 | + | 0.846066i | \(0.678965\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.17516e8 | + | 1.17516e8i | 0.140140 | + | 0.140140i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.56037e9 | + | 2.81527e8i | 1.84898 | + | 0.333599i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.61360e8 | − | 6.61360e8i | 0.778732 | − | 0.778732i | −0.200883 | − | 0.979615i | \(-0.564381\pi\) |
0.979615 | + | 0.200883i | \(0.0643811\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.03534e9i | − | 1.21139i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.75346e8 | 0.785208 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.59406e8 | + | 2.59406e8i | 0.299710 | + | 0.299710i | 0.840900 | − | 0.541190i | \(-0.182026\pi\) |
−0.541190 | + | 0.840900i | \(0.682026\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.00143e8 | + | 5.55043e8i | −0.114977 | + | 0.637260i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.09321e8 | + | 6.09321e8i | −0.695200 | + | 0.695200i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.08233e8i | 0.689626i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.40156e8 | −0.946651 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.17411e8 | + | 2.17411e8i | 0.243446 | + | 0.243446i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.48001e8 | + | 1.72189e8i | −0.275976 | + | 0.191612i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.21710e8 | − | 5.21710e8i | 0.576965 | − | 0.576965i | −0.357101 | − | 0.934066i | \(-0.616235\pi\) |
0.934066 | + | 0.357101i | \(0.116235\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 2.08912e8i | − | 0.229611i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.50595e8 | 0.492186 | 0.246093 | − | 0.969246i | \(-0.420853\pi\) | ||||
0.246093 | + | 0.969246i | \(0.420853\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.22268e9 | − | 1.22268e9i | −1.32732 | − | 1.32732i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.28123e8 | + | 6.11608e8i | −0.246124 | + | 0.659871i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.75242e8 | − | 5.75242e8i | 0.616832 | − | 0.616832i | −0.327886 | − | 0.944717i | \(-0.606336\pi\) |
0.944717 | + | 0.327886i | \(0.106336\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 4.53388e8i | − | 0.483195i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.15495e7 | −0.0334184 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.06660e8 | + | 9.06660e8i | 0.954518 | + | 0.954518i | 0.999010 | − | 0.0444920i | \(-0.0141669\pi\) |
−0.0444920 | + | 0.999010i | \(0.514167\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.91061e8 | + | 4.19210e8i | 0.304562 | + | 0.438655i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.46168e8 | + | 4.46168e8i | −0.464031 | + | 0.464031i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.70527e7i | 0.0383028i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.01456e9 | 1.04245 | 0.521227 | − | 0.853418i | \(-0.325474\pi\) | ||||
0.521227 | + | 0.853418i | \(0.325474\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.95868e8 | − | 8.95868e8i | −0.914948 | − | 0.914948i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.18354e8 | − | 9.35233e7i | −0.526208 | − | 0.0949402i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.49097e8 | − | 2.49097e8i | 0.251353 | − | 0.251353i | −0.570172 | − | 0.821525i | \(-0.693124\pi\) |
0.821525 | + | 0.570172i | \(0.193124\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 1.27342e9i | − | 1.27725i |
(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 | 20.7.f.a.13.1 | ✓ | 6 | |
3.2 | odd | 2 | 180.7.l.a.73.2 | 6 | |||
4.3 | odd | 2 | 80.7.p.d.33.3 | 6 | |||
5.2 | odd | 4 | inner | 20.7.f.a.17.1 | yes | 6 | |
5.3 | odd | 4 | 100.7.f.b.57.3 | 6 | |||
5.4 | even | 2 | 100.7.f.b.93.3 | 6 | |||
15.2 | even | 4 | 180.7.l.a.37.2 | 6 | |||
20.7 | even | 4 | 80.7.p.d.17.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.7.f.a.13.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
20.7.f.a.17.1 | yes | 6 | 5.2 | odd | 4 | inner | |
80.7.p.d.17.3 | 6 | 20.7 | even | 4 | |||
80.7.p.d.33.3 | 6 | 4.3 | odd | 2 | |||
100.7.f.b.57.3 | 6 | 5.3 | odd | 4 | |||
100.7.f.b.93.3 | 6 | 5.4 | even | 2 | |||
180.7.l.a.37.2 | 6 | 15.2 | even | 4 | |||
180.7.l.a.73.2 | 6 | 3.2 | odd | 2 |