Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,8,Mod(49,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.49");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(46.8577538226\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 6) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.49 |
Dual form | 150.8.c.k.49.2 |
$q$-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 \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 8.00000i | − 0.707107i | ||||||||
\(3\) | 27.0000i | 0.577350i | ||||||||
\(4\) | −64.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 216.000 | 0.408248 | ||||||||
\(7\) | 1576.00i | 1.73665i | 0.495993 | + | 0.868327i | \(0.334804\pi\) | ||||
−0.495993 | + | 0.868327i | \(0.665196\pi\) | |||||||
\(8\) | 512.000i | 0.353553i | ||||||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7332.00 | 1.66092 | 0.830459 | − | 0.557080i | \(-0.188078\pi\) | ||||
0.830459 | + | 0.557080i | \(0.188078\pi\) | |||||||
\(12\) | − 1728.00i | − 0.288675i | ||||||||
\(13\) | − 3802.00i | − 0.479966i | −0.970777 | − | 0.239983i | \(-0.922858\pi\) | ||||
0.970777 | − | 0.239983i | \(-0.0771419\pi\) | |||||||
\(14\) | 12608.0 | 1.22800 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 6606.00i | 0.326112i | 0.986617 | + | 0.163056i | \(0.0521352\pi\) | ||||
−0.986617 | + | 0.163056i | \(0.947865\pi\) | |||||||
\(18\) | 5832.00i | 0.235702i | ||||||||
\(19\) | −24860.0 | −0.831502 | −0.415751 | − | 0.909478i | \(-0.636481\pi\) | ||||
−0.415751 | + | 0.909478i | \(0.636481\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −42552.0 | −1.00266 | ||||||||
\(22\) | − 58656.0i | − 1.17445i | ||||||||
\(23\) | 41448.0i | 0.710323i | 0.934805 | + | 0.355162i | \(0.115574\pi\) | ||||
−0.934805 | + | 0.355162i | \(0.884426\pi\) | |||||||
\(24\) | −13824.0 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −30416.0 | −0.339387 | ||||||||
\(27\) | − 19683.0i | − 0.192450i | ||||||||
\(28\) | − 100864.i | − 0.868327i | ||||||||
\(29\) | 41610.0 | 0.316814 | 0.158407 | − | 0.987374i | \(-0.449364\pi\) | ||||
0.158407 | + | 0.987374i | \(0.449364\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 33152.0 | 0.199868 | 0.0999341 | − | 0.994994i | \(-0.468137\pi\) | ||||
0.0999341 | + | 0.994994i | \(0.468137\pi\) | |||||||
\(32\) | − 32768.0i | − 0.176777i | ||||||||
\(33\) | 197964.i | 0.958931i | ||||||||
\(34\) | 52848.0 | 0.230596 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | 36466.0i | 0.118354i | 0.998248 | + | 0.0591769i | \(0.0188476\pi\) | ||||
−0.998248 | + | 0.0591769i | \(0.981152\pi\) | |||||||
\(38\) | 198880.i | 0.587961i | ||||||||
\(39\) | 102654. | 0.277108 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −639078. | −1.44814 | −0.724070 | − | 0.689727i | \(-0.757731\pi\) | ||||
−0.724070 | + | 0.689727i | \(0.757731\pi\) | |||||||
\(42\) | 340416.i | 0.708986i | ||||||||
\(43\) | − 156412.i | − 0.300006i | −0.988686 | − | 0.150003i | \(-0.952072\pi\) | ||||
0.988686 | − | 0.150003i | \(-0.0479284\pi\) | |||||||
\(44\) | −469248. | −0.830459 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 331584. | 0.502275 | ||||||||
\(47\) | 433776.i | 0.609429i | 0.952444 | + | 0.304714i | \(0.0985610\pi\) | ||||
−0.952444 | + | 0.304714i | \(0.901439\pi\) | |||||||
\(48\) | 110592.i | 0.144338i | ||||||||
\(49\) | −1.66023e6 | −2.01596 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −178362. | −0.188281 | ||||||||
\(52\) | 243328.i | 0.239983i | ||||||||
\(53\) | 786078.i | 0.725271i | 0.931931 | + | 0.362635i | \(0.118123\pi\) | ||||
−0.931931 | + | 0.362635i | \(0.881877\pi\) | |||||||
\(54\) | −157464. | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −806912. | −0.614000 | ||||||||
\(57\) | − 671220.i | − 0.480068i | ||||||||
\(58\) | − 332880.i | − 0.224022i | ||||||||
\(59\) | −745140. | −0.472341 | −0.236171 | − | 0.971712i | \(-0.575892\pi\) | ||||
−0.236171 | + | 0.971712i | \(0.575892\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.66062e6 | −0.936732 | −0.468366 | − | 0.883535i | \(-0.655157\pi\) | ||||
−0.468366 | + | 0.883535i | \(0.655157\pi\) | |||||||
\(62\) | − 265216.i | − 0.141328i | ||||||||
\(63\) | − 1.14890e6i | − 0.578884i | ||||||||
\(64\) | −262144. | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.58371e6 | 0.678067 | ||||||||
\(67\) | 3.29084e6i | 1.33673i | 0.743832 | + | 0.668366i | \(0.233006\pi\) | ||||
−0.743832 | + | 0.668366i | \(0.766994\pi\) | |||||||
\(68\) | − 422784.i | − 0.163056i | ||||||||
\(69\) | −1.11910e6 | −0.410105 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.71615e6 | 1.89539 | 0.947697 | − | 0.319171i | \(-0.103404\pi\) | ||||
0.947697 | + | 0.319171i | \(0.103404\pi\) | |||||||
\(72\) | − 373248.i | − 0.117851i | ||||||||
\(73\) | 2.65990e6i | 0.800267i | 0.916457 | + | 0.400134i | \(0.131036\pi\) | ||||
−0.916457 | + | 0.400134i | \(0.868964\pi\) | |||||||
\(74\) | 291728. | 0.0836888 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.59104e6 | 0.415751 | ||||||||
\(77\) | 1.15552e7i | 2.88444i | ||||||||
\(78\) | − 821232.i | − 0.195945i | ||||||||
\(79\) | −3.80744e6 | −0.868837 | −0.434418 | − | 0.900711i | \(-0.643046\pi\) | ||||
−0.434418 | + | 0.900711i | \(0.643046\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 5.11262e6i | 1.02399i | ||||||||
\(83\) | 2.22947e6i | 0.427984i | 0.976835 | + | 0.213992i | \(0.0686467\pi\) | ||||
−0.976835 | + | 0.213992i | \(0.931353\pi\) | |||||||
\(84\) | 2.72333e6 | 0.501329 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.25130e6 | −0.212137 | ||||||||
\(87\) | 1.12347e6i | 0.182913i | ||||||||
\(88\) | 3.75398e6i | 0.587223i | ||||||||
\(89\) | −5.99121e6 | −0.900844 | −0.450422 | − | 0.892816i | \(-0.648726\pi\) | ||||
−0.450422 | + | 0.892816i | \(0.648726\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.99195e6 | 0.833534 | ||||||||
\(92\) | − 2.65267e6i | − 0.355162i | ||||||||
\(93\) | 895104.i | 0.115394i | ||||||||
\(94\) | 3.47021e6 | 0.430931 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 884736. | 0.102062 | ||||||||
\(97\) | 4.06013e6i | 0.451688i | 0.974163 | + | 0.225844i | \(0.0725139\pi\) | ||||
−0.974163 | + | 0.225844i | \(0.927486\pi\) | |||||||
\(98\) | 1.32819e7i | 1.42550i | ||||||||
\(99\) | −5.34503e6 | −0.553639 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.72819e7 | −1.66904 | −0.834522 | − | 0.550975i | \(-0.814256\pi\) | ||||
−0.834522 | + | 0.550975i | \(0.814256\pi\) | |||||||
\(102\) | 1.42690e6i | 0.133135i | ||||||||
\(103\) | − 1.43623e7i | − 1.29507i | −0.762035 | − | 0.647536i | \(-0.775799\pi\) | ||||
0.762035 | − | 0.647536i | \(-0.224201\pi\) | |||||||
\(104\) | 1.94662e6 | 0.169694 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.28862e6 | 0.512844 | ||||||||
\(107\) | − 6.45440e6i | − 0.509346i | −0.967027 | − | 0.254673i | \(-0.918032\pi\) | ||||
0.967027 | − | 0.254673i | \(-0.0819678\pi\) | |||||||
\(108\) | 1.25971e6i | 0.0962250i | ||||||||
\(109\) | 884410. | 0.0654125 | 0.0327063 | − | 0.999465i | \(-0.489587\pi\) | ||||
0.0327063 | + | 0.999465i | \(0.489587\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −984582. | −0.0683316 | ||||||||
\(112\) | 6.45530e6i | 0.434163i | ||||||||
\(113\) | 1.21325e7i | 0.790999i | 0.918466 | + | 0.395499i | \(0.129428\pi\) | ||||
−0.918466 | + | 0.395499i | \(0.870572\pi\) | |||||||
\(114\) | −5.36976e6 | −0.339459 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.66304e6 | −0.158407 | ||||||||
\(117\) | 2.77166e6i | 0.159989i | ||||||||
\(118\) | 5.96112e6i | 0.333996i | ||||||||
\(119\) | −1.04111e7 | −0.566344 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.42711e7 | 1.75865 | ||||||||
\(122\) | 1.32849e7i | 0.662369i | ||||||||
\(123\) | − 1.72551e7i | − 0.836084i | ||||||||
\(124\) | −2.12173e6 | −0.0999341 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9.19123e6 | −0.409333 | ||||||||
\(127\) | − 6.86806e6i | − 0.297524i | −0.988873 | − | 0.148762i | \(-0.952471\pi\) | ||||
0.988873 | − | 0.148762i | \(-0.0475288\pi\) | |||||||
\(128\) | 2.09715e6i | 0.0883883i | ||||||||
\(129\) | 4.22312e6 | 0.173209 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.95208e7 | −1.53595 | −0.767973 | − | 0.640482i | \(-0.778735\pi\) | ||||
−0.767973 | + | 0.640482i | \(0.778735\pi\) | |||||||
\(132\) | − 1.26697e7i | − 0.479466i | ||||||||
\(133\) | − 3.91794e7i | − 1.44403i | ||||||||
\(134\) | 2.63267e7 | 0.945212 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.38227e6 | −0.115298 | ||||||||
\(137\) | − 1.91741e7i | − 0.637078i | −0.947910 | − | 0.318539i | \(-0.896808\pi\) | ||||
0.947910 | − | 0.318539i | \(-0.103192\pi\) | |||||||
\(138\) | 8.95277e6i | 0.289988i | ||||||||
\(139\) | −1.32449e7 | −0.418309 | −0.209154 | − | 0.977883i | \(-0.567071\pi\) | ||||
−0.209154 | + | 0.977883i | \(0.567071\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.17120e7 | −0.351854 | ||||||||
\(142\) | − 4.57292e7i | − 1.34025i | ||||||||
\(143\) | − 2.78763e7i | − 0.797184i | ||||||||
\(144\) | −2.98598e6 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.12792e7 | 0.565874 | ||||||||
\(147\) | − 4.48263e7i | − 1.16392i | ||||||||
\(148\) | − 2.33382e6i | − 0.0591769i | ||||||||
\(149\) | −5.73624e7 | −1.42061 | −0.710306 | − | 0.703893i | \(-0.751444\pi\) | ||||
−0.710306 | + | 0.703893i | \(0.751444\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.10873e7 | −0.734790 | −0.367395 | − | 0.930065i | \(-0.619750\pi\) | ||||
−0.367395 | + | 0.930065i | \(0.619750\pi\) | |||||||
\(152\) | − 1.27283e7i | − 0.293981i | ||||||||
\(153\) | − 4.81577e6i | − 0.108704i | ||||||||
\(154\) | 9.24419e7 | 2.03961 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.56986e6 | −0.138554 | ||||||||
\(157\) | 3.37835e7i | 0.696715i | 0.937362 | + | 0.348358i | \(0.113261\pi\) | ||||
−0.937362 | + | 0.348358i | \(0.886739\pi\) | |||||||
\(158\) | 3.04595e7i | 0.614360i | ||||||||
\(159\) | −2.12241e7 | −0.418735 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.53220e7 | −1.23359 | ||||||||
\(162\) | − 4.25153e6i | − 0.0785674i | ||||||||
\(163\) | 6.26659e7i | 1.13338i | 0.823932 | + | 0.566689i | \(0.191776\pi\) | ||||
−0.823932 | + | 0.566689i | \(0.808224\pi\) | |||||||
\(164\) | 4.09010e7 | 0.724070 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.78357e7 | 0.302631 | ||||||||
\(167\) | − 6.27072e7i | − 1.04186i | −0.853599 | − | 0.520931i | \(-0.825585\pi\) | ||||
0.853599 | − | 0.520931i | \(-0.174415\pi\) | |||||||
\(168\) | − 2.17866e7i | − 0.354493i | ||||||||
\(169\) | 4.82933e7 | 0.769633 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.81229e7 | 0.277167 | ||||||||
\(172\) | 1.00104e7i | 0.150003i | ||||||||
\(173\) | − 2.70521e7i | − 0.397228i | −0.980078 | − | 0.198614i | \(-0.936356\pi\) | ||||
0.980078 | − | 0.198614i | \(-0.0636440\pi\) | |||||||
\(174\) | 8.98776e6 | 0.129339 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00319e7 | 0.415229 | ||||||||
\(177\) | − 2.01188e7i | − 0.272706i | ||||||||
\(178\) | 4.79297e7i | 0.636993i | ||||||||
\(179\) | 1.34281e8 | 1.74996 | 0.874981 | − | 0.484157i | \(-0.160874\pi\) | ||||
0.874981 | + | 0.484157i | \(0.160874\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.14661e8 | 1.43727 | 0.718636 | − | 0.695386i | \(-0.244767\pi\) | ||||
0.718636 | + | 0.695386i | \(0.244767\pi\) | |||||||
\(182\) | − 4.79356e7i | − 0.589398i | ||||||||
\(183\) | − 4.48367e7i | − 0.540822i | ||||||||
\(184\) | −2.12214e7 | −0.251137 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.16083e6 | 0.0815959 | ||||||||
\(187\) | 4.84352e7i | 0.541646i | ||||||||
\(188\) | − 2.77617e7i | − 0.304714i | ||||||||
\(189\) | 3.10204e7 | 0.334219 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.63605e7 | 0.169895 | 0.0849474 | − | 0.996385i | \(-0.472928\pi\) | ||||
0.0849474 | + | 0.996385i | \(0.472928\pi\) | |||||||
\(192\) | − 7.07789e6i | − 0.0721688i | ||||||||
\(193\) | − 1.54198e8i | − 1.54394i | −0.635661 | − | 0.771968i | \(-0.719272\pi\) | ||||
0.635661 | − | 0.771968i | \(-0.280728\pi\) | |||||||
\(194\) | 3.24810e7 | 0.319392 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.06255e8 | 1.00798 | ||||||||
\(197\) | − 8.32288e7i | − 0.775607i | −0.921742 | − | 0.387804i | \(-0.873234\pi\) | ||||
0.921742 | − | 0.387804i | \(-0.126766\pi\) | |||||||
\(198\) | 4.27602e7i | 0.391482i | ||||||||
\(199\) | 7.61722e7 | 0.685190 | 0.342595 | − | 0.939483i | \(-0.388694\pi\) | ||||
0.342595 | + | 0.939483i | \(0.388694\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.88526e7 | −0.771763 | ||||||||
\(202\) | 1.38256e8i | 1.18019i | ||||||||
\(203\) | 6.55774e7i | 0.550196i | ||||||||
\(204\) | 1.14152e7 | 0.0941405 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.14898e8 | −0.915755 | ||||||||
\(207\) | − 3.02156e7i | − 0.236774i | ||||||||
\(208\) | − 1.55730e7i | − 0.119991i | ||||||||
\(209\) | −1.82274e8 | −1.38106 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.52446e7 | 0.258288 | 0.129144 | − | 0.991626i | \(-0.458777\pi\) | ||||
0.129144 | + | 0.991626i | \(0.458777\pi\) | |||||||
\(212\) | − 5.03090e7i | − 0.362635i | ||||||||
\(213\) | 1.54336e8i | 1.09431i | ||||||||
\(214\) | −5.16352e7 | −0.360162 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00777e7 | 0.0680414 | ||||||||
\(217\) | 5.22476e7i | 0.347102i | ||||||||
\(218\) | − 7.07528e6i | − 0.0462536i | ||||||||
\(219\) | −7.18172e7 | −0.462034 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.51160e7 | 0.156523 | ||||||||
\(222\) | 7.87666e6i | 0.0483177i | ||||||||
\(223\) | − 1.89131e8i | − 1.14208i | −0.820922 | − | 0.571040i | \(-0.806540\pi\) | ||||
0.820922 | − | 0.571040i | \(-0.193460\pi\) | |||||||
\(224\) | 5.16424e7 | 0.307000 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.70600e7 | 0.559320 | ||||||||
\(227\) | 1.76100e8i | 0.999239i | 0.866245 | + | 0.499620i | \(0.166527\pi\) | ||||
−0.866245 | + | 0.499620i | \(0.833473\pi\) | |||||||
\(228\) | 4.29581e7i | 0.240034i | ||||||||
\(229\) | −6.50396e7 | −0.357894 | −0.178947 | − | 0.983859i | \(-0.557269\pi\) | ||||
−0.178947 | + | 0.983859i | \(0.557269\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.11991e8 | −1.66533 | ||||||||
\(232\) | 2.13043e7i | 0.112011i | ||||||||
\(233\) | − 2.51319e8i | − 1.30160i | −0.759248 | − | 0.650802i | \(-0.774433\pi\) | ||||
0.759248 | − | 0.650802i | \(-0.225567\pi\) | |||||||
\(234\) | 2.21733e7 | 0.113129 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.76890e7 | 0.236171 | ||||||||
\(237\) | − 1.02801e8i | − 0.501623i | ||||||||
\(238\) | 8.32884e7i | 0.400466i | ||||||||
\(239\) | −2.13079e8 | −1.00960 | −0.504799 | − | 0.863237i | \(-0.668434\pi\) | ||||
−0.504799 | + | 0.863237i | \(0.668434\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.57284e8 | 1.18400 | 0.592001 | − | 0.805937i | \(-0.298338\pi\) | ||||
0.592001 | + | 0.805937i | \(0.298338\pi\) | |||||||
\(242\) | − 2.74168e8i | − 1.24355i | ||||||||
\(243\) | 1.43489e7i | 0.0641500i | ||||||||
\(244\) | 1.06280e8 | 0.468366 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.38041e8 | −0.591200 | ||||||||
\(247\) | 9.45177e7i | 0.399093i | ||||||||
\(248\) | 1.69738e7i | 0.0706641i | ||||||||
\(249\) | −6.01956e7 | −0.247097 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.23058e8 | 0.491193 | 0.245596 | − | 0.969372i | \(-0.421016\pi\) | ||||
0.245596 | + | 0.969372i | \(0.421016\pi\) | |||||||
\(252\) | 7.35299e7i | 0.289442i | ||||||||
\(253\) | 3.03897e8i | 1.17979i | ||||||||
\(254\) | −5.49445e7 | −0.210381 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | 4.43334e8i | 1.62916i | 0.580048 | + | 0.814582i | \(0.303034\pi\) | ||||
−0.580048 | + | 0.814582i | \(0.696966\pi\) | |||||||
\(258\) | − 3.37850e7i | − 0.122477i | ||||||||
\(259\) | −5.74704e7 | −0.205539 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.03337e7 | −0.105605 | ||||||||
\(262\) | 3.16166e8i | 1.08608i | ||||||||
\(263\) | 2.98925e8i | 1.01325i | 0.862166 | + | 0.506625i | \(0.169107\pi\) | ||||
−0.862166 | + | 0.506625i | \(0.830893\pi\) | |||||||
\(264\) | −1.01358e8 | −0.339033 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.13435e8 | −1.02108 | ||||||||
\(267\) | − 1.61763e8i | − 0.520102i | ||||||||
\(268\) | − 2.10614e8i | − 0.668366i | ||||||||
\(269\) | −2.08908e8 | −0.654368 | −0.327184 | − | 0.944961i | \(-0.606100\pi\) | ||||
−0.327184 | + | 0.944961i | \(0.606100\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.12749e7 | −0.0344129 | −0.0172064 | − | 0.999852i | \(-0.505477\pi\) | ||||
−0.0172064 | + | 0.999852i | \(0.505477\pi\) | |||||||
\(272\) | 2.70582e7i | 0.0815281i | ||||||||
\(273\) | 1.61783e8i | 0.481241i | ||||||||
\(274\) | −1.53393e8 | −0.450482 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.16221e7 | 0.205053 | ||||||||
\(277\) | 6.58964e8i | 1.86287i | 0.363907 | + | 0.931435i | \(0.381443\pi\) | ||||
−0.363907 | + | 0.931435i | \(0.618557\pi\) | |||||||
\(278\) | 1.05959e8i | 0.295789i | ||||||||
\(279\) | −2.41678e7 | −0.0666227 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.05123e8 | −0.282634 | −0.141317 | − | 0.989964i | \(-0.545134\pi\) | ||||
−0.141317 | + | 0.989964i | \(0.545134\pi\) | |||||||
\(282\) | 9.36956e7i | 0.248798i | ||||||||
\(283\) | 3.30161e8i | 0.865911i | 0.901415 | + | 0.432956i | \(0.142529\pi\) | ||||
−0.901415 | + | 0.432956i | \(0.857471\pi\) | |||||||
\(284\) | −3.65834e8 | −0.947697 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.23010e8 | −0.563694 | ||||||||
\(287\) | − 1.00719e9i | − 2.51492i | ||||||||
\(288\) | 2.38879e7i | 0.0589256i | ||||||||
\(289\) | 3.66699e8 | 0.893651 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.09623e8 | −0.260782 | ||||||||
\(292\) | − 1.70233e8i | − 0.400134i | ||||||||
\(293\) | − 8.71002e7i | − 0.202294i | −0.994871 | − | 0.101147i | \(-0.967749\pi\) | ||||
0.994871 | − | 0.101147i | \(-0.0322512\pi\) | |||||||
\(294\) | −3.58610e8 | −0.823014 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.86706e7 | −0.0418444 | ||||||||
\(297\) | − 1.44316e8i | − 0.319644i | ||||||||
\(298\) | 4.58899e8i | 1.00452i | ||||||||
\(299\) | 1.57585e8 | 0.340931 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.46505e8 | 0.521007 | ||||||||
\(302\) | 2.48698e8i | 0.519575i | ||||||||
\(303\) | − 4.66612e8i | − 0.963623i | ||||||||
\(304\) | −1.01827e8 | −0.207876 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.85262e7 | −0.0768654 | ||||||||
\(307\) | 3.91709e8i | 0.772644i | 0.922364 | + | 0.386322i | \(0.126255\pi\) | ||||
−0.922364 | + | 0.386322i | \(0.873745\pi\) | |||||||
\(308\) | − 7.39535e8i | − 1.44222i | ||||||||
\(309\) | 3.87782e8 | 0.747710 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.04936e8 | −0.386328 | −0.193164 | − | 0.981166i | \(-0.561875\pi\) | ||||
−0.193164 | + | 0.981166i | \(0.561875\pi\) | |||||||
\(312\) | 5.25588e7i | 0.0979726i | ||||||||
\(313\) | 8.77202e8i | 1.61694i | 0.588536 | + | 0.808471i | \(0.299705\pi\) | ||||
−0.588536 | + | 0.808471i | \(0.700295\pi\) | |||||||
\(314\) | 2.70268e8 | 0.492652 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.43676e8 | 0.434418 | ||||||||
\(317\) | 4.40831e8i | 0.777256i | 0.921395 | + | 0.388628i | \(0.127051\pi\) | ||||
−0.921395 | + | 0.388628i | \(0.872949\pi\) | |||||||
\(318\) | 1.69793e8i | 0.296090i | ||||||||
\(319\) | 3.05085e8 | 0.526202 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.74269e8 | 0.294071 | ||||||||
\(322\) | 5.22576e8i | 0.872277i | ||||||||
\(323\) | − 1.64225e8i | − 0.271163i | ||||||||
\(324\) | −3.40122e7 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.01327e8 | 0.801419 | ||||||||
\(327\) | 2.38791e7i | 0.0377659i | ||||||||
\(328\) | − 3.27208e8i | − 0.511995i | ||||||||
\(329\) | −6.83631e8 | −1.05837 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.11223e9 | 1.68576 | 0.842882 | − | 0.538099i | \(-0.180857\pi\) | ||||
0.842882 | + | 0.538099i | \(0.180857\pi\) | |||||||
\(332\) | − 1.42686e8i | − 0.213992i | ||||||||
\(333\) | − 2.65837e7i | − 0.0394513i | ||||||||
\(334\) | −5.01658e8 | −0.736707 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.74293e8 | −0.250664 | ||||||||
\(337\) | − 2.88198e8i | − 0.410191i | −0.978742 | − | 0.205096i | \(-0.934249\pi\) | ||||
0.978742 | − | 0.205096i | \(-0.0657506\pi\) | |||||||
\(338\) | − 3.86347e8i | − 0.544213i | ||||||||
\(339\) | −3.27577e8 | −0.456683 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.43070e8 | 0.331965 | ||||||||
\(342\) | − 1.44984e8i | − 0.195987i | ||||||||
\(343\) | − 1.31862e9i | − 1.76438i | ||||||||
\(344\) | 8.00829e7 | 0.106068 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.16417e8 | −0.280883 | ||||||||
\(347\) | 1.10601e9i | 1.42103i | 0.703680 | + | 0.710517i | \(0.251539\pi\) | ||||
−0.703680 | + | 0.710517i | \(0.748461\pi\) | |||||||
\(348\) | − 7.19021e7i | − 0.0914564i | ||||||||
\(349\) | 1.32184e9 | 1.66453 | 0.832264 | − | 0.554379i | \(-0.187044\pi\) | ||||
0.832264 | + | 0.554379i | \(0.187044\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.48348e7 | −0.0923695 | ||||||||
\(352\) | − 2.40255e8i | − 0.293612i | ||||||||
\(353\) | 1.20395e9i | 1.45679i | 0.685157 | + | 0.728396i | \(0.259734\pi\) | ||||
−0.685157 | + | 0.728396i | \(0.740266\pi\) | |||||||
\(354\) | −1.60950e8 | −0.192832 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.83437e8 | 0.450422 | ||||||||
\(357\) | − 2.81099e8i | − 0.326979i | ||||||||
\(358\) | − 1.07425e9i | − 1.23741i | ||||||||
\(359\) | 1.32057e9 | 1.50637 | 0.753185 | − | 0.657809i | \(-0.228516\pi\) | ||||
0.753185 | + | 0.657809i | \(0.228516\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.75852e8 | −0.308604 | ||||||||
\(362\) | − 9.17284e8i | − 1.01630i | ||||||||
\(363\) | 9.25318e8i | 1.01536i | ||||||||
\(364\) | −3.83485e8 | −0.416767 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.58693e8 | −0.382419 | ||||||||
\(367\) | − 1.75107e9i | − 1.84915i | −0.381000 | − | 0.924575i | \(-0.624420\pi\) | ||||
0.381000 | − | 0.924575i | \(-0.375580\pi\) | |||||||
\(368\) | 1.69771e8i | 0.177581i | ||||||||
\(369\) | 4.65888e8 | 0.482713 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.23886e9 | −1.25954 | ||||||||
\(372\) | − 5.72867e7i | − 0.0576970i | ||||||||
\(373\) | − 4.87945e8i | − 0.486844i | −0.969920 | − | 0.243422i | \(-0.921730\pi\) | ||||
0.969920 | − | 0.243422i | \(-0.0782701\pi\) | |||||||
\(374\) | 3.87482e8 | 0.383001 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.22093e8 | −0.215466 | ||||||||
\(377\) | − 1.58201e8i | − 0.152060i | ||||||||
\(378\) | − 2.48163e8i | − 0.236329i | ||||||||
\(379\) | −1.11007e9 | −1.04740 | −0.523700 | − | 0.851903i | \(-0.675449\pi\) | ||||
−0.523700 | + | 0.851903i | \(0.675449\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.85438e8 | 0.171775 | ||||||||
\(382\) | − 1.30884e8i | − 0.120134i | ||||||||
\(383\) | 1.86912e9i | 1.69997i | 0.526810 | + | 0.849983i | \(0.323388\pi\) | ||||
−0.526810 | + | 0.849983i | \(0.676612\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.23359e9 | −1.09173 | ||||||||
\(387\) | 1.14024e8i | 0.100002i | ||||||||
\(388\) | − 2.59848e8i | − 0.225844i | ||||||||
\(389\) | 2.73895e8 | 0.235918 | 0.117959 | − | 0.993018i | \(-0.462365\pi\) | ||||
0.117959 | + | 0.993018i | \(0.462365\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.73805e8 | −0.231645 | ||||||||
\(392\) | − 8.50039e8i | − 0.712751i | ||||||||
\(393\) | − 1.06706e9i | − 0.886779i | ||||||||
\(394\) | −6.65831e8 | −0.548437 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.42082e8 | 0.276820 | ||||||||
\(397\) | − 6.24552e8i | − 0.500958i | −0.968122 | − | 0.250479i | \(-0.919412\pi\) | ||||
0.968122 | − | 0.250479i | \(-0.0805882\pi\) | |||||||
\(398\) | − 6.09378e8i | − 0.484502i | ||||||||
\(399\) | 1.05784e9 | 0.833712 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.55500e8 | 0.430208 | 0.215104 | − | 0.976591i | \(-0.430991\pi\) | ||||
0.215104 | + | 0.976591i | \(0.430991\pi\) | |||||||
\(402\) | 7.10821e8i | 0.545719i | ||||||||
\(403\) | − 1.26044e8i | − 0.0959299i | ||||||||
\(404\) | 1.10604e9 | 0.834522 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.24619e8 | 0.389048 | ||||||||
\(407\) | 2.67369e8i | 0.196576i | ||||||||
\(408\) | − 9.13213e7i | − 0.0665674i | ||||||||
\(409\) | 2.15770e9 | 1.55941 | 0.779704 | − | 0.626149i | \(-0.215370\pi\) | ||||
0.779704 | + | 0.626149i | \(0.215370\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.17700e8 | 0.367817 | ||||||||
\(412\) | 9.19188e8i | 0.647536i | ||||||||
\(413\) | − 1.17434e9i | − 0.820293i | ||||||||
\(414\) | −2.41725e8 | −0.167425 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.24584e8 | −0.0848468 | ||||||||
\(417\) | − 3.57612e8i | − 0.241511i | ||||||||
\(418\) | 1.45819e9i | 0.976555i | ||||||||
\(419\) | −1.67797e9 | −1.11438 | −0.557191 | − | 0.830384i | \(-0.688121\pi\) | ||||
−0.557191 | + | 0.830384i | \(0.688121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.25233e8 | −0.343056 | −0.171528 | − | 0.985179i | \(-0.554870\pi\) | ||||
−0.171528 | + | 0.985179i | \(0.554870\pi\) | |||||||
\(422\) | − 2.81957e8i | − 0.182637i | ||||||||
\(423\) | − 3.16223e8i | − 0.203143i | ||||||||
\(424\) | −4.02472e8 | −0.256422 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.23469e9 | 0.773791 | ||||||||
\(427\) | − 2.61713e9i | − 1.62678i | ||||||||
\(428\) | 4.13082e8i | 0.254673i | ||||||||
\(429\) | 7.52659e8 | 0.460254 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.70593e8 | 0.102634 | 0.0513169 | − | 0.998682i | \(-0.483658\pi\) | ||||
0.0513169 | + | 0.998682i | \(0.483658\pi\) | |||||||
\(432\) | − 8.06216e7i | − 0.0481125i | ||||||||
\(433\) | − 1.68797e9i | − 0.999210i | −0.866253 | − | 0.499605i | \(-0.833478\pi\) | ||||
0.866253 | − | 0.499605i | \(-0.166522\pi\) | |||||||
\(434\) | 4.17980e8 | 0.245438 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.66022e7 | −0.0327063 | ||||||||
\(437\) | − 1.03040e9i | − 0.590636i | ||||||||
\(438\) | 5.74538e8i | 0.326708i | ||||||||
\(439\) | 1.17850e9 | 0.664817 | 0.332409 | − | 0.943135i | \(-0.392139\pi\) | ||||
0.332409 | + | 0.943135i | \(0.392139\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.21031e9 | 0.671988 | ||||||||
\(442\) | − 2.00928e8i | − 0.110678i | ||||||||
\(443\) | 7.15755e8i | 0.391157i | 0.980688 | + | 0.195579i | \(0.0626585\pi\) | ||||
−0.980688 | + | 0.195579i | \(0.937342\pi\) | |||||||
\(444\) | 6.30132e7 | 0.0341658 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.51305e9 | −0.807573 | ||||||||
\(447\) | − 1.54879e9i | − 0.820191i | ||||||||
\(448\) | − 4.13139e8i | − 0.217082i | ||||||||
\(449\) | 1.37358e9 | 0.716132 | 0.358066 | − | 0.933696i | \(-0.383436\pi\) | ||||
0.358066 | + | 0.933696i | \(0.383436\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.68572e9 | −2.40524 | ||||||||
\(452\) | − 7.76480e8i | − 0.395499i | ||||||||
\(453\) | − 8.39357e8i | − 0.424231i | ||||||||
\(454\) | 1.40880e9 | 0.706569 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.43665e8 | 0.169730 | ||||||||
\(457\) | − 1.84752e9i | − 0.905488i | −0.891641 | − | 0.452744i | \(-0.850445\pi\) | ||||
0.891641 | − | 0.452744i | \(-0.149555\pi\) | |||||||
\(458\) | 5.20317e8i | 0.253069i | ||||||||
\(459\) | 1.30026e8 | 0.0627604 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.09414e9 | 1.47091 | 0.735455 | − | 0.677573i | \(-0.236968\pi\) | ||||
0.735455 | + | 0.677573i | \(0.236968\pi\) | |||||||
\(462\) | 2.49593e9i | 1.17757i | ||||||||
\(463\) | 3.00451e9i | 1.40682i | 0.710782 | + | 0.703412i | \(0.248341\pi\) | ||||
−0.710782 | + | 0.703412i | \(0.751659\pi\) | |||||||
\(464\) | 1.70435e8 | 0.0792036 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.01055e9 | −0.920373 | ||||||||
\(467\) | 2.99252e9i | 1.35965i | 0.733374 | + | 0.679825i | \(0.237944\pi\) | ||||
−0.733374 | + | 0.679825i | \(0.762056\pi\) | |||||||
\(468\) | − 1.77386e8i | − 0.0799943i | ||||||||
\(469\) | −5.18636e9 | −2.32144 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.12154e8 | −0.402249 | ||||||||
\(472\) | − 3.81512e8i | − 0.166998i | ||||||||
\(473\) | − 1.14681e9i | − 0.498286i | ||||||||
\(474\) | −8.22407e8 | −0.354701 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.66308e8 | 0.283172 | ||||||||
\(477\) | − 5.73051e8i | − 0.241757i | ||||||||
\(478\) | 1.70464e9i | 0.713894i | ||||||||
\(479\) | −1.84041e9 | −0.765141 | −0.382570 | − | 0.923926i | \(-0.624961\pi\) | ||||
−0.382570 | + | 0.923926i | \(0.624961\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.38644e8 | 0.0568058 | ||||||||
\(482\) | − 2.05827e9i | − 0.837216i | ||||||||
\(483\) | − 1.76370e9i | − 0.712211i | ||||||||
\(484\) | −2.19335e9 | −0.879323 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.14791e8 | 0.0453609 | ||||||||
\(487\) | 4.26676e8i | 0.167397i | 0.996491 | + | 0.0836983i | \(0.0266732\pi\) | ||||
−0.996491 | + | 0.0836983i | \(0.973327\pi\) | |||||||
\(488\) | − 8.50236e8i | − 0.331185i | ||||||||
\(489\) | −1.69198e9 | −0.654356 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.07547e7 | 0.0231630 | 0.0115815 | − | 0.999933i | \(-0.496313\pi\) | ||||
0.0115815 | + | 0.999933i | \(0.496313\pi\) | |||||||
\(492\) | 1.10433e9i | 0.418042i | ||||||||
\(493\) | 2.74876e8i | 0.103317i | ||||||||
\(494\) | 7.56142e8 | 0.282201 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.35791e8 | 0.0499671 | ||||||||
\(497\) | 9.00866e9i | 3.29164i | ||||||||
\(498\) | 4.81565e8i | 0.174724i | ||||||||
\(499\) | −3.24588e9 | −1.16945 | −0.584723 | − | 0.811233i | \(-0.698797\pi\) | ||||
−0.584723 | + | 0.811233i | \(0.698797\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.69310e9 | 0.601519 | ||||||||
\(502\) | − 9.84464e8i | − 0.347326i | ||||||||
\(503\) | − 7.44381e8i | − 0.260800i | −0.991461 | − | 0.130400i | \(-0.958374\pi\) | ||||
0.991461 | − | 0.130400i | \(-0.0416262\pi\) | |||||||
\(504\) | 5.88239e8 | 0.204667 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.43117e9 | 0.834237 | ||||||||
\(507\) | 1.30392e9i | 0.444348i | ||||||||
\(508\) | 4.39556e8i | 0.148762i | ||||||||
\(509\) | 4.44155e8 | 0.149287 | 0.0746436 | − | 0.997210i | \(-0.476218\pi\) | ||||
0.0746436 | + | 0.997210i | \(0.476218\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.19200e9 | −1.38979 | ||||||||
\(512\) | − 1.34218e8i | − 0.0441942i | ||||||||
\(513\) | 4.89319e8i | 0.160023i | ||||||||
\(514\) | 3.54667e9 | 1.15199 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.70280e8 | −0.0866044 | ||||||||
\(517\) | 3.18045e9i | 1.01221i | ||||||||
\(518\) | 4.59763e8i | 0.145338i | ||||||||
\(519\) | 7.30407e8 | 0.229340 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.04963e9 | 0.944745 | 0.472372 | − | 0.881399i | \(-0.343398\pi\) | ||||
0.472372 | + | 0.881399i | \(0.343398\pi\) | |||||||
\(522\) | 2.42670e8i | 0.0746738i | ||||||||
\(523\) | − 1.40306e9i | − 0.428866i | −0.976739 | − | 0.214433i | \(-0.931210\pi\) | ||||
0.976739 | − | 0.214433i | \(-0.0687904\pi\) | |||||||
\(524\) | 2.52933e9 | 0.767973 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.39140e9 | 0.716476 | ||||||||
\(527\) | 2.19002e8i | 0.0651795i | ||||||||
\(528\) | 8.10861e8i | 0.239733i | ||||||||
\(529\) | 1.68689e9 | 0.495441 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.43207e8 | 0.157447 | ||||||||
\(532\) | 2.50748e9i | 0.722016i | ||||||||
\(533\) | 2.42977e9i | 0.695058i | ||||||||
\(534\) | −1.29410e9 | −0.367768 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.68491e9 | −0.472606 | ||||||||
\(537\) | 3.62558e9i | 1.01034i | ||||||||
\(538\) | 1.67126e9i | 0.462708i | ||||||||
\(539\) | −1.21728e10 | −3.34835 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.21106e9 | 1.14341 | 0.571704 | − | 0.820460i | \(-0.306283\pi\) | ||||
0.571704 | + | 0.820460i | \(0.306283\pi\) | |||||||
\(542\) | 9.01994e7i | 0.0243336i | ||||||||
\(543\) | 3.09583e9i | 0.829809i | ||||||||
\(544\) | 2.16465e8 | 0.0576491 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.29426e9 | 0.340289 | ||||||||
\(547\) | − 1.99956e9i | − 0.522371i | −0.965289 | − | 0.261185i | \(-0.915887\pi\) | ||||
0.965289 | − | 0.261185i | \(-0.0841134\pi\) | |||||||
\(548\) | 1.22714e9i | 0.318539i | ||||||||
\(549\) | 1.21059e9 | 0.312244 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.03442e9 | −0.263432 | ||||||||
\(552\) | − 5.72977e8i | − 0.144994i | ||||||||
\(553\) | − 6.00053e9i | − 1.50887i | ||||||||
\(554\) | 5.27172e9 | 1.31725 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.47674e8 | 0.209154 | ||||||||
\(557\) | 3.37403e9i | 0.827287i | 0.910439 | + | 0.413643i | \(0.135744\pi\) | ||||
−0.910439 | + | 0.413643i | \(0.864256\pi\) | |||||||
\(558\) | 1.93342e8i | 0.0471094i | ||||||||
\(559\) | −5.94678e8 | −0.143993 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.30775e9 | −0.312719 | ||||||||
\(562\) | 8.40983e8i | 0.199853i | ||||||||
\(563\) | − 5.58021e9i | − 1.31787i | −0.752201 | − | 0.658933i | \(-0.771008\pi\) | ||||
0.752201 | − | 0.658933i | \(-0.228992\pi\) | |||||||
\(564\) | 7.49565e8 | 0.175927 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.64129e9 | 0.612292 | ||||||||
\(567\) | 8.37551e8i | 0.192961i | ||||||||
\(568\) | 2.92667e9i | 0.670123i | ||||||||
\(569\) | 8.88310e8 | 0.202149 | 0.101074 | − | 0.994879i | \(-0.467772\pi\) | ||||
0.101074 | + | 0.994879i | \(0.467772\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.79171e9 | −0.402755 | −0.201377 | − | 0.979514i | \(-0.564542\pi\) | ||||
−0.201377 | + | 0.979514i | \(0.564542\pi\) | |||||||
\(572\) | 1.78408e9i | 0.398592i | ||||||||
\(573\) | 4.41734e8i | 0.0980888i | ||||||||
\(574\) | −8.05750e9 | −1.77831 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | − 3.82103e9i | − 0.828066i | −0.910262 | − | 0.414033i | \(-0.864120\pi\) | ||||
0.910262 | − | 0.414033i | \(-0.135880\pi\) | |||||||
\(578\) | − 2.93360e9i | − 0.631906i | ||||||||
\(579\) | 4.16336e9 | 0.891392 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.51364e9 | −0.743260 | ||||||||
\(582\) | 8.76987e8i | 0.184401i | ||||||||
\(583\) | 5.76352e9i | 1.20461i | ||||||||
\(584\) | −1.36187e9 | −0.282937 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.96802e8 | −0.143043 | ||||||||
\(587\) | − 4.36219e9i | − 0.890166i | −0.895489 | − | 0.445083i | \(-0.853174\pi\) | ||||
0.895489 | − | 0.445083i | \(-0.146826\pi\) | |||||||
\(588\) | 2.86888e9i | 0.581959i | ||||||||
\(589\) | −8.24159e8 | −0.166191 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.24718e9 | 0.447797 | ||||||||
\(592\) | 1.49365e8i | 0.0295884i | ||||||||
\(593\) | 6.38531e9i | 1.25745i | 0.777628 | + | 0.628724i | \(0.216423\pi\) | ||||
−0.777628 | + | 0.628724i | \(0.783577\pi\) | |||||||
\(594\) | −1.15453e9 | −0.226022 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.67120e9 | 0.710306 | ||||||||
\(597\) | 2.05665e9i | 0.395594i | ||||||||
\(598\) | − 1.26068e9i | − 0.241075i | ||||||||
\(599\) | −8.04297e8 | −0.152905 | −0.0764527 | − | 0.997073i | \(-0.524359\pi\) | ||||
−0.0764527 | + | 0.997073i | \(0.524359\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.87162e9 | −0.915403 | −0.457702 | − | 0.889106i | \(-0.651327\pi\) | ||||
−0.457702 | + | 0.889106i | \(0.651327\pi\) | |||||||
\(602\) | − 1.97204e9i | − 0.368408i | ||||||||
\(603\) | − 2.39902e9i | − 0.445577i | ||||||||
\(604\) | 1.98959e9 | 0.367395 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.73290e9 | −0.681384 | ||||||||
\(607\) | − 7.17517e9i | − 1.30218i | −0.759000 | − | 0.651091i | \(-0.774312\pi\) | ||||
0.759000 | − | 0.651091i | \(-0.225688\pi\) | |||||||
\(608\) | 8.14612e8i | 0.146990i | ||||||||
\(609\) | −1.77059e9 | −0.317656 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.64922e9 | 0.292505 | ||||||||
\(612\) | 3.08210e8i | 0.0543521i | ||||||||
\(613\) | 3.47891e9i | 0.610002i | 0.952352 | + | 0.305001i | \(0.0986567\pi\) | ||||
−0.952352 | + | 0.305001i | \(0.901343\pi\) | |||||||
\(614\) | 3.13367e9 | 0.546342 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.91628e9 | −1.01980 | ||||||||
\(617\) | 2.39378e8i | 0.0410286i | 0.999790 | + | 0.0205143i | \(0.00653037\pi\) | ||||
−0.999790 | + | 0.0205143i | \(0.993470\pi\) | |||||||
\(618\) | − 3.10226e9i | − 0.528711i | ||||||||
\(619\) | 5.52959e9 | 0.937078 | 0.468539 | − | 0.883443i | \(-0.344781\pi\) | ||||
0.468539 | + | 0.883443i | \(0.344781\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.15821e8 | 0.136702 | ||||||||
\(622\) | 1.63949e9i | 0.273175i | ||||||||
\(623\) | − 9.44215e9i | − 1.56445i | ||||||||
\(624\) | 4.20471e8 | 0.0692771 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.01762e9 | 1.14335 | ||||||||
\(627\) | − 4.92139e9i | − 0.797354i | ||||||||
\(628\) | − 2.16214e9i | − 0.348358i | ||||||||
\(629\) | −2.40894e8 | −0.0385966 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.13683e9 | −0.972392 | −0.486196 | − | 0.873850i | \(-0.661616\pi\) | ||||
−0.486196 | + | 0.873850i | \(0.661616\pi\) | |||||||
\(632\) | − 1.94941e9i | − 0.307180i | ||||||||
\(633\) | 9.51603e8i | 0.149122i | ||||||||
\(634\) | 3.52664e9 | 0.549603 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.35834e9 | 0.209368 | ||||||||
\(637\) | 6.31221e9i | 0.967594i | ||||||||
\(638\) | − 2.44068e9i | − 0.372081i | ||||||||
\(639\) | −4.16707e9 | −0.631798 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.07038e10 | 1.60522 | 0.802611 | − | 0.596503i | \(-0.203444\pi\) | ||||
0.802611 | + | 0.596503i | \(0.203444\pi\) | |||||||
\(642\) | − 1.39415e9i | − 0.207940i | ||||||||
\(643\) | − 1.39803e9i | − 0.207385i | −0.994609 | − | 0.103692i | \(-0.966934\pi\) | ||||
0.994609 | − | 0.103692i | \(-0.0330658\pi\) | |||||||
\(644\) | 4.18061e9 | 0.616793 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.31380e9 | −0.191741 | ||||||||
\(647\) | 5.31605e9i | 0.771656i | 0.922571 | + | 0.385828i | \(0.126084\pi\) | ||||
−0.922571 | + | 0.385828i | \(0.873916\pi\) | |||||||
\(648\) | 2.72098e8i | 0.0392837i | ||||||||
\(649\) | −5.46337e9 | −0.784520 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.41068e9 | −0.200399 | ||||||||
\(652\) | − 4.01062e9i | − 0.566689i | ||||||||
\(653\) | 3.24403e9i | 0.455921i | 0.973670 | + | 0.227960i | \(0.0732057\pi\) | ||||
−0.973670 | + | 0.227960i | \(0.926794\pi\) | |||||||
\(654\) | 1.91033e8 | 0.0267046 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.61766e9 | −0.362035 | ||||||||
\(657\) | − 1.93907e9i | − 0.266756i | ||||||||
\(658\) | 5.46905e9i | 0.748378i | ||||||||
\(659\) | 5.16506e9 | 0.703034 | 0.351517 | − | 0.936181i | \(-0.385666\pi\) | ||||
0.351517 | + | 0.936181i | \(0.385666\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.22515e9 | −0.434356 | −0.217178 | − | 0.976132i | \(-0.569685\pi\) | ||||
−0.217178 | + | 0.976132i | \(0.569685\pi\) | |||||||
\(662\) | − 8.89784e9i | − 1.19201i | ||||||||
\(663\) | 6.78132e8i | 0.0903685i | ||||||||
\(664\) | −1.14149e9 | −0.151315 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.12670e8 | −0.0278963 | ||||||||
\(667\) | 1.72465e9i | 0.225041i | ||||||||
\(668\) | 4.01326e9i | 0.520931i | ||||||||
\(669\) | 5.10655e9 | 0.659380 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.21757e10 | −1.55583 | ||||||||
\(672\) | 1.39434e9i | 0.177246i | ||||||||
\(673\) | − 2.00633e9i | − 0.253718i | −0.991921 | − | 0.126859i | \(-0.959510\pi\) | ||||
0.991921 | − | 0.126859i | \(-0.0404895\pi\) | |||||||
\(674\) | −2.30559e9 | −0.290049 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.09077e9 | −0.384816 | ||||||||
\(677\) | − 1.00211e10i | − 1.24124i | −0.784112 | − | 0.620619i | \(-0.786881\pi\) | ||||
0.784112 | − | 0.620619i | \(-0.213119\pi\) | |||||||
\(678\) | 2.62062e9i | 0.322924i | ||||||||
\(679\) | −6.39876e9 | −0.784425 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.75471e9 | −0.576911 | ||||||||
\(682\) | − 1.94456e9i | − 0.234734i | ||||||||
\(683\) | − 5.84861e9i | − 0.702393i | −0.936302 | − | 0.351196i | \(-0.885775\pi\) | ||||
0.936302 | − | 0.351196i | \(-0.114225\pi\) | |||||||
\(684\) | −1.15987e9 | −0.138584 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.05490e10 | −1.24760 | ||||||||
\(687\) | − 1.75607e9i | − 0.206630i | ||||||||
\(688\) | − 6.40664e8i | − 0.0750016i | ||||||||
\(689\) | 2.98867e9 | 0.348105 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.58686e9 | 0.298263 | 0.149131 | − | 0.988817i | \(-0.452352\pi\) | ||||
0.149131 | + | 0.988817i | \(0.452352\pi\) | |||||||
\(692\) | 1.73134e9i | 0.198614i | ||||||||
\(693\) | − 8.42376e9i | − 0.961479i | ||||||||
\(694\) | 8.84805e9 | 1.00482 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.75217e8 | −0.0646694 | ||||||||
\(697\) | − 4.22175e9i | − 0.472256i | ||||||||
\(698\) | − 1.05747e10i | − 1.17700i | ||||||||
\(699\) | 6.78560e9 | 0.751481 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.74460e9 | −0.191286 | −0.0956429 | − | 0.995416i | \(-0.530491\pi\) | ||||
−0.0956429 | + | 0.995416i | \(0.530491\pi\) | |||||||
\(702\) | 5.98678e8i | 0.0653151i | ||||||||
\(703\) | − 9.06545e8i | − 0.0984114i | ||||||||
\(704\) | −1.92204e9 | −0.207615 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.63161e9 | 1.03011 | ||||||||
\(707\) | − 2.72363e10i | − 2.89855i | ||||||||
\(708\) | 1.28760e9i | 0.136353i | ||||||||
\(709\) | 1.12051e10 | 1.18074 | 0.590368 | − | 0.807134i | \(-0.298983\pi\) | ||||
0.590368 | + | 0.807134i | \(0.298983\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.77562e9 | 0.289612 | ||||||||
\(712\) | − 3.06750e9i | − 0.318496i | ||||||||
\(713\) | 1.37408e9i | 0.141971i | ||||||||
\(714\) | −2.24879e9 | −0.231209 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.59398e9 | −0.874981 | ||||||||
\(717\) | − 5.75314e9i | − 0.582892i | ||||||||
\(718\) | − 1.05646e10i | − 1.06516i | ||||||||
\(719\) | 9.36568e8 | 0.0939698 | 0.0469849 | − | 0.998896i | \(-0.485039\pi\) | ||||
0.0469849 | + | 0.998896i | \(0.485039\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.26350e10 | 2.24909 | ||||||||
\(722\) | 2.20682e9i | 0.218216i | ||||||||
\(723\) | 6.94666e9i | 0.683584i | ||||||||
\(724\) | −7.33827e9 | −0.718636 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.40255e9 | 0.717965 | ||||||||
\(727\) | − 4.20445e9i | − 0.405825i | −0.979197 | − | 0.202913i | \(-0.934959\pi\) | ||||
0.979197 | − | 0.202913i | \(-0.0650407\pi\) | |||||||
\(728\) | 3.06788e9i | 0.294699i | ||||||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.03326e9 | 0.0978358 | ||||||||
\(732\) | 2.86955e9i | 0.270411i | ||||||||
\(733\) | − 1.15491e10i | − 1.08314i | −0.840655 | − | 0.541571i | \(-0.817830\pi\) | ||||
0.840655 | − | 0.541571i | \(-0.182170\pi\) | |||||||
\(734\) | −1.40086e10 | −1.30755 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.35817e9 | 0.125569 | ||||||||
\(737\) | 2.41284e10i | 2.22020i | ||||||||
\(738\) | − 3.72710e9i | − 0.341330i | ||||||||
\(739\) | 1.39655e10 | 1.27292 | 0.636460 | − | 0.771310i | \(-0.280398\pi\) | ||||
0.636460 | + | 0.771310i | \(0.280398\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.55198e9 | −0.230416 | ||||||||
\(742\) | 9.91087e9i | 0.890632i | ||||||||
\(743\) | 1.43832e10i | 1.28646i | 0.765673 | + | 0.643230i | \(0.222406\pi\) | ||||
−0.765673 | + | 0.643230i | \(0.777594\pi\) | |||||||
\(744\) | −4.58293e8 | −0.0407979 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.90356e9 | −0.344251 | ||||||||
\(747\) | − 1.62528e9i | − 0.142661i | ||||||||
\(748\) | − 3.09985e9i | − 0.270823i | ||||||||
\(749\) | 1.01721e10 | 0.884557 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.70841e8 | −0.0577936 | −0.0288968 | − | 0.999582i | \(-0.509199\pi\) | ||||
−0.0288968 | + | 0.999582i | \(0.509199\pi\) | |||||||
\(752\) | 1.77675e9i | 0.152357i | ||||||||
\(753\) | 3.32257e9i | 0.283590i | ||||||||
\(754\) | −1.26561e9 | −0.107523 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.98531e9 | −0.167110 | ||||||||
\(757\) | 1.91569e10i | 1.60506i | 0.596613 | + | 0.802529i | \(0.296513\pi\) | ||||
−0.596613 | + | 0.802529i | \(0.703487\pi\) | |||||||
\(758\) | 8.88055e9i | 0.740624i | ||||||||
\(759\) | −8.20521e9 | −0.681151 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.79120e10 | 1.47332 | 0.736660 | − | 0.676263i | \(-0.236402\pi\) | ||||
0.736660 | + | 0.676263i | \(0.236402\pi\) | |||||||
\(762\) | − 1.48350e9i | − 0.121463i | ||||||||
\(763\) | 1.39383e9i | 0.113599i | ||||||||
\(764\) | −1.04707e9 | −0.0849474 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.49529e10 | 1.20206 | ||||||||
\(767\) | 2.83302e9i | 0.226708i | ||||||||
\(768\) | 4.52985e8i | 0.0360844i | ||||||||
\(769\) | 2.14072e10 | 1.69753 | 0.848765 | − | 0.528771i | \(-0.177347\pi\) | ||||
0.848765 | + | 0.528771i | \(0.177347\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.19700e10 | −0.940599 | ||||||||
\(772\) | 9.86870e9i | 0.771968i | ||||||||
\(773\) | − 7.55163e8i | − 0.0588047i | −0.999568 | − | 0.0294024i | \(-0.990640\pi\) | ||||
0.999568 | − | 0.0294024i | \(-0.00936041\pi\) | |||||||
\(774\) | 9.12195e8 | 0.0707122 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.07878e9 | −0.159696 | ||||||||
\(777\) | − 1.55170e9i | − 0.118668i | ||||||||
\(778\) | − 2.19116e9i | − 0.166819i | ||||||||
\(779\) | 1.58875e10 | 1.20413 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.19108e10 | 3.14809 | ||||||||
\(782\) | 2.19044e9i | 0.163798i | ||||||||
\(783\) | − 8.19010e8i | − 0.0609709i | ||||||||
\(784\) | −6.80031e9 | −0.503991 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.53649e9 | −0.627047 | ||||||||
\(787\) | − 2.04665e10i | − 1.49669i | −0.663308 | − | 0.748347i | \(-0.730848\pi\) | ||||
0.663308 | − | 0.748347i | \(-0.269152\pi\) | |||||||
\(788\) | 5.32664e9i | 0.387804i | ||||||||
\(789\) | −8.07097e9 | −0.585000 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.91208e10 | −1.37369 | ||||||||
\(792\) | − 2.73665e9i | − 0.195741i | ||||||||
\(793\) | 6.31367e9i | 0.449599i | ||||||||
\(794\) | −4.99641e9 | −0.354231 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.87502e9 | −0.342595 | ||||||||
\(797\) | 1.03098e10i | 0.721348i | 0.932692 | + | 0.360674i | \(0.117453\pi\) | ||||
−0.932692 | + | 0.360674i | \(0.882547\pi\) | |||||||
\(798\) | − 8.46274e9i | − 0.589523i | ||||||||
\(799\) | −2.86552e9 | −0.198742 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.36759e9 | 0.300281 | ||||||||
\(802\) | − 4.44400e9i | − 0.304203i | ||||||||
\(803\) | 1.95024e10i | 1.32918i | ||||||||
\(804\) | 5.68656e9 | 0.385881 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.00835e9 | −0.0678327 | ||||||||
\(807\) | − 5.64051e9i | − 0.377799i | ||||||||
\(808\) | − 8.84835e9i | − 0.590096i | ||||||||
\(809\) | 4.16428e8 | 0.0276516 | 0.0138258 | − | 0.999904i | \(-0.495599\pi\) | ||||
0.0138258 | + | 0.999904i | \(0.495599\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.82687e9 | −0.383586 | −0.191793 | − | 0.981435i | \(-0.561430\pi\) | ||||
−0.191793 | + | 0.981435i | \(0.561430\pi\) | |||||||
\(812\) | − 4.19695e9i | − 0.275098i | ||||||||
\(813\) | − 3.04423e8i | − 0.0198683i | ||||||||
\(814\) | 2.13895e9 | 0.139000 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −7.30571e8 | −0.0470703 | ||||||||
\(817\) | 3.88840e9i | 0.249456i | ||||||||
\(818\) | − 1.72616e10i | − 1.10267i | ||||||||
\(819\) | −4.36813e9 | −0.277845 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.08333e10 | −1.31388 | −0.656941 | − | 0.753942i | \(-0.728150\pi\) | ||||
−0.656941 | + | 0.753942i | \(0.728150\pi\) | |||||||
\(822\) | − 4.14160e9i | − 0.260086i | ||||||||
\(823\) | 4.23403e9i | 0.264761i | 0.991199 | + | 0.132381i | \(0.0422621\pi\) | ||||
−0.991199 | + | 0.132381i | \(0.957738\pi\) | |||||||
\(824\) | 7.35350e9 | 0.457877 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.39473e9 | −0.580035 | ||||||||
\(827\) | − 5.70597e9i | − 0.350800i | −0.984497 | − | 0.175400i | \(-0.943878\pi\) | ||||
0.984497 | − | 0.175400i | \(-0.0561219\pi\) | |||||||
\(828\) | 1.93380e9i | 0.118387i | ||||||||
\(829\) | −2.51612e10 | −1.53388 | −0.766940 | − | 0.641719i | \(-0.778221\pi\) | ||||
−0.766940 | + | 0.641719i | \(0.778221\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.77920e10 | −1.07553 | ||||||||
\(832\) | 9.96671e8i | 0.0599957i | ||||||||
\(833\) | − 1.09675e10i | − 0.657431i | ||||||||
\(834\) | −2.86090e9 | −0.170774 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.16655e10 | 0.690528 | ||||||||
\(837\) | − 6.52531e8i | − 0.0384647i | ||||||||
\(838\) | 1.34237e10i | 0.787988i | ||||||||
\(839\) | −2.27048e10 | −1.32724 | −0.663622 | − | 0.748068i | \(-0.730982\pi\) | ||||
−0.663622 | + | 0.748068i | \(0.730982\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.55185e10 | −0.899629 | ||||||||
\(842\) | 4.20187e9i | 0.242577i | ||||||||
\(843\) | − 2.83832e9i | − 0.163179i | ||||||||
\(844\) | −2.25565e9 | −0.129144 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.52978e9 | −0.143644 | ||||||||
\(847\) | 5.40112e10i | 3.05416i | ||||||||
\(848\) | 3.21978e9i | 0.181318i | ||||||||
\(849\) | −8.91435e9 | −0.499934 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.51144e9 | −0.0840695 | ||||||||
\(852\) | − 9.87751e9i | − 0.547153i | ||||||||
\(853\) | 2.86872e10i | 1.58258i | 0.611439 | + | 0.791292i | \(0.290591\pi\) | ||||
−0.611439 | + | 0.791292i | \(0.709409\pi\) | |||||||
\(854\) | −2.09371e10 | −1.15031 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.30465e9 | 0.180081 | ||||||||
\(857\) | − 5.34950e9i | − 0.290322i | −0.989408 | − | 0.145161i | \(-0.953630\pi\) | ||||
0.989408 | − | 0.145161i | \(-0.0463701\pi\) | |||||||
\(858\) | − 6.02127e9i | − 0.325449i | ||||||||
\(859\) | 1.40330e10 | 0.755394 | 0.377697 | − | 0.925929i | \(-0.376716\pi\) | ||||
0.377697 | + | 0.925929i | \(0.376716\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.71940e10 | 1.45199 | ||||||||
\(862\) | − 1.36474e9i | − 0.0725731i | ||||||||
\(863\) | 3.24994e10i | 1.72122i | 0.509261 | + | 0.860612i | \(0.329919\pi\) | ||||
−0.509261 | + | 0.860612i | \(0.670081\pi\) | |||||||
\(864\) | −6.44973e8 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.35038e10 | −0.706549 | ||||||||
\(867\) | 9.90088e9i | 0.515949i | ||||||||
\(868\) | − 3.34384e9i | − 0.173551i | ||||||||
\(869\) | −2.79162e10 | −1.44307 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.25118e10 | 0.641586 | ||||||||
\(872\) | 4.52818e8i | 0.0231268i | ||||||||
\(873\) | − 2.95983e9i | − 0.150563i | ||||||||
\(874\) | −8.24318e9 | −0.417642 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.59630e9 | 0.231017 | ||||||||
\(877\) | 3.38694e10i | 1.69554i | 0.530361 | + | 0.847772i | \(0.322056\pi\) | ||||
−0.530361 | + | 0.847772i | \(0.677944\pi\) | |||||||
\(878\) | − 9.42797e9i | − 0.470097i | ||||||||
\(879\) | 2.35171e9 | 0.116794 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.52708e10 | −0.752397 | −0.376198 | − | 0.926539i | \(-0.622769\pi\) | ||||
−0.376198 | + | 0.926539i | \(0.622769\pi\) | |||||||
\(882\) | − 9.68248e9i | − 0.475167i | ||||||||
\(883\) | − 1.12045e10i | − 0.547685i | −0.961775 | − | 0.273842i | \(-0.911705\pi\) | ||||
0.961775 | − | 0.273842i | \(-0.0882946\pi\) | |||||||
\(884\) | −1.60742e9 | −0.0782614 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.72604e9 | 0.276590 | ||||||||
\(887\) | − 6.97232e9i | − 0.335463i | −0.985833 | − | 0.167732i | \(-0.946356\pi\) | ||||
0.985833 | − | 0.167732i | \(-0.0536442\pi\) | |||||||
\(888\) | − 5.04106e8i | − 0.0241589i | ||||||||
\(889\) | 1.08241e10 | 0.516695 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.89653e9 | 0.184546 | ||||||||
\(892\) | 1.21044e10i | 0.571040i | ||||||||
\(893\) | − 1.07837e10i | − 0.506742i | ||||||||
\(894\) | −1.23903e10 | −0.579963 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.30511e9 | −0.153500 | ||||||||
\(897\) | 4.25480e9i | 0.196837i | ||||||||
\(898\) | − 1.09887e10i | − 0.506382i | ||||||||
\(899\) | 1.37945e9 | 0.0633211 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.19283e9 | −0.236520 | ||||||||
\(902\) | 3.74858e10i | 1.70076i | ||||||||
\(903\) | 6.65564e9i | 0.300804i | ||||||||
\(904\) | −6.21184e9 | −0.279660 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.71485e9 | −0.299977 | ||||||||
\(907\) | − 1.18095e9i | − 0.0525539i | −0.999655 | − | 0.0262770i | \(-0.991635\pi\) | ||||
0.999655 | − | 0.0262770i | \(-0.00836518\pi\) | |||||||
\(908\) | − 1.12704e10i | − 0.499620i | ||||||||
\(909\) | 1.25985e10 | 0.556348 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.27915e10 | 0.560541 | 0.280271 | − | 0.959921i | \(-0.409576\pi\) | ||||
0.280271 | + | 0.959921i | \(0.409576\pi\) | |||||||
\(912\) | − 2.74932e9i | − 0.120017i | ||||||||
\(913\) | 1.63465e10i | 0.710847i | ||||||||
\(914\) | −1.47802e10 | −0.640276 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.16254e9 | 0.178947 | ||||||||
\(917\) | − 6.22848e10i | − 2.66741i | ||||||||
\(918\) | − 1.04021e9i | − 0.0443783i | ||||||||
\(919\) | −3.52353e10 | −1.49752 | −0.748761 | − | 0.662840i | \(-0.769351\pi\) | ||||
−0.748761 | + | 0.662840i | \(0.769351\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.05761e10 | −0.446086 | ||||||||
\(922\) | − 2.47531e10i | − 1.04009i | ||||||||
\(923\) | − 2.17328e10i | − 0.909725i | ||||||||
\(924\) | 1.99674e10 | 0.832665 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.40361e10 | 0.994775 | ||||||||
\(927\) | 1.04701e10i | 0.431691i | ||||||||
\(928\) | − 1.36348e9i | − 0.0560054i | ||||||||
\(929\) | 2.17764e10 | 0.891111 | 0.445556 | − | 0.895254i | \(-0.353006\pi\) | ||||
0.445556 | + | 0.895254i | \(0.353006\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.12734e10 | 1.67628 | ||||||||
\(932\) | 1.60844e10i | 0.650802i | ||||||||
\(933\) | − 5.53327e9i | − 0.223047i | ||||||||
\(934\) | 2.39401e10 | 0.961418 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.41909e9 | −0.0565645 | ||||||||
\(937\) | − 1.15795e10i | − 0.459833i | −0.973210 | − | 0.229916i | \(-0.926155\pi\) | ||||
0.973210 | − | 0.229916i | \(-0.0738453\pi\) | |||||||
\(938\) | 4.14909e10i | 1.64151i | ||||||||
\(939\) | −2.36845e10 | −0.933542 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.83930e10 | −1.50207 | −0.751033 | − | 0.660265i | \(-0.770444\pi\) | ||||
−0.751033 | + | 0.660265i | \(0.770444\pi\) | |||||||
\(942\) | 7.29723e9i | 0.284433i | ||||||||
\(943\) | − 2.64885e10i | − 1.02865i | ||||||||
\(944\) | −3.05209e9 | −0.118085 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.17450e9 | −0.352341 | ||||||||
\(947\) | − 1.11841e10i | − 0.427933i | −0.976841 | − | 0.213966i | \(-0.931362\pi\) | ||||
0.976841 | − | 0.213966i | \(-0.0686383\pi\) | |||||||
\(948\) | 6.57926e9i | 0.250812i | ||||||||
\(949\) | 1.01129e10 | 0.384101 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.19024e10 | −0.448749 | ||||||||
\(952\) | − 5.33046e9i | − 0.200233i | ||||||||
\(953\) | − 5.19835e9i | − 0.194554i | −0.995257 | − | 0.0972770i | \(-0.968987\pi\) | ||||
0.995257 | − | 0.0972770i | \(-0.0310133\pi\) | |||||||
\(954\) | −4.58441e9 | −0.170948 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.36371e10 | 0.504799 | ||||||||
\(957\) | 8.23728e9i | 0.303803i | ||||||||
\(958\) | 1.47233e10i | 0.541036i | ||||||||
\(959\) | 3.02183e10 | 1.10638 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.64136e10 | −0.960053 | ||||||||
\(962\) | − 1.10915e9i | − 0.0401677i | ||||||||
\(963\) | 4.70526e9i | 0.169782i | ||||||||
\(964\) | −1.64662e10 | −0.592001 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.41096e10 | −0.503609 | ||||||||
\(967\) | 2.69243e8i | 0.00957529i | 0.999989 | + | 0.00478765i | \(0.00152396\pi\) | ||||
−0.999989 | + | 0.00478765i | \(0.998476\pi\) | |||||||
\(968\) | 1.75468e10i | 0.621776i | ||||||||
\(969\) | 4.43408e9 | 0.156556 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.37283e9 | 0.153284 | 0.0766418 | − | 0.997059i | \(-0.475580\pi\) | ||||
0.0766418 | + | 0.997059i | \(0.475580\pi\) | |||||||
\(972\) | − 9.18330e8i | − 0.0320750i | ||||||||
\(973\) | − 2.08740e10i | − 0.726457i | ||||||||
\(974\) | 3.41341e9 | 0.118367 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.80189e9 | −0.234183 | ||||||||
\(977\) | 3.74991e10i | 1.28644i | 0.765681 | + | 0.643220i | \(0.222402\pi\) | ||||
−0.765681 | + | 0.643220i | \(0.777598\pi\) | |||||||
\(978\) | 1.35358e10i | 0.462699i | ||||||||
\(979\) | −4.39276e10 | −1.49623 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.44735e8 | −0.0218042 | ||||||||
\(982\) | − 4.86038e8i | − 0.0163787i | ||||||||
\(983\) | − 3.06190e10i | − 1.02814i | −0.857748 | − | 0.514071i | \(-0.828137\pi\) | ||||
0.857748 | − | 0.514071i | \(-0.171863\pi\) | |||||||
\(984\) | 8.83461e9 | 0.295600 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.19901e9 | 0.0730562 | ||||||||
\(987\) | − 1.84580e10i | − 0.611048i | ||||||||
\(988\) | − 6.04913e9i | − 0.199546i | ||||||||
\(989\) | 6.48296e9 | 0.213102 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.72703e10 | −0.563693 | −0.281847 | − | 0.959459i | \(-0.590947\pi\) | ||||
−0.281847 | + | 0.959459i | \(0.590947\pi\) | |||||||
\(992\) | − 1.08632e9i | − 0.0353320i | ||||||||
\(993\) | 3.00302e10i | 0.973276i | ||||||||
\(994\) | 7.20692e10 | 2.32754 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.85252e9 | 0.123548 | ||||||||
\(997\) | 3.75077e9i | 0.119864i | 0.998202 | + | 0.0599319i | \(0.0190883\pi\) | ||||
−0.998202 | + | 0.0599319i | \(0.980912\pi\) | |||||||
\(998\) | 2.59670e10i | 0.826923i | ||||||||
\(999\) | 7.17760e8 | 0.0227772 |
(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 | 150.8.c.k.49.1 | 2 | ||
3.2 | odd | 2 | 450.8.c.a.199.2 | 2 | |||
5.2 | odd | 4 | 6.8.a.a.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 150.8.a.e.1.1 | 1 | |||
5.4 | even | 2 | inner | 150.8.c.k.49.2 | 2 | ||
15.2 | even | 4 | 18.8.a.a.1.1 | 1 | |||
15.8 | even | 4 | 450.8.a.ba.1.1 | 1 | |||
15.14 | odd | 2 | 450.8.c.a.199.1 | 2 | |||
20.7 | even | 4 | 48.8.a.b.1.1 | 1 | |||
35.2 | odd | 12 | 294.8.e.c.67.1 | 2 | |||
35.12 | even | 12 | 294.8.e.d.67.1 | 2 | |||
35.17 | even | 12 | 294.8.e.d.79.1 | 2 | |||
35.27 | even | 4 | 294.8.a.l.1.1 | 1 | |||
35.32 | odd | 12 | 294.8.e.c.79.1 | 2 | |||
40.27 | even | 4 | 192.8.a.n.1.1 | 1 | |||
40.37 | odd | 4 | 192.8.a.f.1.1 | 1 | |||
45.2 | even | 12 | 162.8.c.i.109.1 | 2 | |||
45.7 | odd | 12 | 162.8.c.d.109.1 | 2 | |||
45.22 | odd | 12 | 162.8.c.d.55.1 | 2 | |||
45.32 | even | 12 | 162.8.c.i.55.1 | 2 | |||
60.47 | odd | 4 | 144.8.a.h.1.1 | 1 | |||
120.77 | even | 4 | 576.8.a.h.1.1 | 1 | |||
120.107 | odd | 4 | 576.8.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.8.a.a.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
18.8.a.a.1.1 | 1 | 15.2 | even | 4 | |||
48.8.a.b.1.1 | 1 | 20.7 | even | 4 | |||
144.8.a.h.1.1 | 1 | 60.47 | odd | 4 | |||
150.8.a.e.1.1 | 1 | 5.3 | odd | 4 | |||
150.8.c.k.49.1 | 2 | 1.1 | even | 1 | trivial | ||
150.8.c.k.49.2 | 2 | 5.4 | even | 2 | inner | ||
162.8.c.d.55.1 | 2 | 45.22 | odd | 12 | |||
162.8.c.d.109.1 | 2 | 45.7 | odd | 12 | |||
162.8.c.i.55.1 | 2 | 45.32 | even | 12 | |||
162.8.c.i.109.1 | 2 | 45.2 | even | 12 | |||
192.8.a.f.1.1 | 1 | 40.37 | odd | 4 | |||
192.8.a.n.1.1 | 1 | 40.27 | even | 4 | |||
294.8.a.l.1.1 | 1 | 35.27 | even | 4 | |||
294.8.e.c.67.1 | 2 | 35.2 | odd | 12 | |||
294.8.e.c.79.1 | 2 | 35.32 | odd | 12 | |||
294.8.e.d.67.1 | 2 | 35.12 | even | 12 | |||
294.8.e.d.79.1 | 2 | 35.17 | even | 12 | |||
450.8.a.ba.1.1 | 1 | 15.8 | even | 4 | |||
450.8.c.a.199.1 | 2 | 15.14 | odd | 2 | |||
450.8.c.a.199.2 | 2 | 3.2 | odd | 2 | |||
576.8.a.h.1.1 | 1 | 120.77 | even | 4 | |||
576.8.a.i.1.1 | 1 | 120.107 | odd | 4 |