Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,12,Mod(33,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.33");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.e (of order \(4\), degree \(2\), 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: | \(98.3479271116\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(21\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 33.19 | ||
Character | \(\chi\) | \(=\) | 128.33 |
Dual form | 128.12.e.b.97.19 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 475.976 | + | 475.976i | 1.13089 | + | 1.13089i | 0.990030 | + | 0.140855i | \(0.0449851\pi\) |
0.140855 | + | 0.990030i | \(0.455015\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2805.14 | + | 2805.14i | −0.401439 | + | 0.401439i | −0.878740 | − | 0.477301i | \(-0.841615\pi\) |
0.477301 | + | 0.878740i | \(0.341615\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 76033.6i | − | 1.70988i | −0.518725 | − | 0.854941i | \(-0.673593\pi\) | ||
0.518725 | − | 0.854941i | \(-0.326407\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 275960.i | 1.55780i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −409752. | + | 409752.i | −0.767116 | + | 0.767116i | −0.977598 | − | 0.210482i | \(-0.932497\pi\) |
0.210482 | + | 0.977598i | \(0.432497\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.80631e6 | + | 1.80631e6i | 1.34929 | + | 1.34929i | 0.886435 | + | 0.462853i | \(0.153174\pi\) |
0.462853 | + | 0.886435i | \(0.346826\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.67036e6 | −0.907962 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50853e6 | −0.257683 | −0.128842 | − | 0.991665i | \(-0.541126\pi\) | ||||
−0.128842 | + | 0.991665i | \(0.541126\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.45825e6 | − | 5.45825e6i | −0.505718 | − | 0.505718i | 0.407491 | − | 0.913209i | \(-0.366404\pi\) |
−0.913209 | + | 0.407491i | \(0.866404\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.61902e7 | − | 3.61902e7i | 1.93368 | − | 1.93368i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.28696e6i | − | 0.0740893i | −0.999314 | − | 0.0370446i | \(-0.988206\pi\) | ||
0.999314 | − | 0.0370446i | \(-0.0117944\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.30905e7i | 0.677694i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.70326e7 | + | 4.70326e7i | −0.630810 | + | 0.630810i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.38084e7 | − | 4.38084e7i | −0.396615 | − | 0.396615i | 0.480422 | − | 0.877037i | \(-0.340483\pi\) |
−0.877037 | + | 0.480422i | \(0.840483\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.76655e7 | 0.173560 | 0.0867798 | − | 0.996228i | \(-0.472342\pi\) | ||||
0.0867798 | + | 0.996228i | \(0.472342\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.90064e8 | −1.73504 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.13285e8 | + | 2.13285e8i | 0.686413 | + | 0.686413i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.40566e8 | + | 2.40566e8i | −0.570327 | + | 0.570327i | −0.932220 | − | 0.361893i | \(-0.882131\pi\) |
0.361893 | + | 0.932220i | \(0.382131\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.71953e9i | 3.05178i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.08336e8i | 0.146037i | 0.997331 | + | 0.0730184i | \(0.0232632\pi\) | ||||
−0.997331 | + | 0.0730184i | \(0.976737\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.91015e8 | + | 1.91015e8i | −0.198149 | + | 0.198149i | −0.799206 | − | 0.601057i | \(-0.794746\pi\) |
0.601057 | + | 0.799206i | \(0.294746\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.74106e8 | − | 7.74106e8i | −0.625362 | − | 0.625362i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.72497e9 | −1.09709 | −0.548547 | − | 0.836120i | \(-0.684819\pi\) | ||||
−0.548547 | + | 0.836120i | \(0.684819\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.80378e9 | −1.92370 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.18026e8 | − | 7.18026e8i | −0.291410 | − | 0.291410i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.00868e7 | − | 8.00868e7i | 0.0263053 | − | 0.0263053i | −0.693832 | − | 0.720137i | \(-0.744079\pi\) |
0.720137 | + | 0.693832i | \(0.244079\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.29882e9i | − | 0.615900i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.19599e9i | − | 1.14382i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.70345e9 | + | 6.70345e9i | −1.22071 | + | 1.22071i | −0.253328 | + | 0.967380i | \(0.581525\pi\) |
−0.967380 | + | 0.253328i | \(0.918475\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.82284e7 | − | 9.82284e7i | −0.0148910 | − | 0.0148910i | 0.699622 | − | 0.714513i | \(-0.253352\pi\) |
−0.714513 | + | 0.699622i | \(0.753352\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.09822e10 | 2.66366 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.01339e10 | −1.08331 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.92288e9 | − | 6.92288e9i | −0.626434 | − | 0.626434i | 0.320735 | − | 0.947169i | \(-0.396070\pi\) |
−0.947169 | + | 0.320735i | \(0.896070\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.08854e9 | − | 1.08854e9i | 0.0837865 | − | 0.0837865i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.20473e9i | − | 0.0792443i | −0.999215 | − | 0.0396221i | \(-0.987385\pi\) | ||
0.999215 | − | 0.0396221i | \(-0.0126154\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00681e10i | 1.13300i | 0.824061 | + | 0.566501i | \(0.191703\pi\) | ||||
−0.824061 | + | 0.566501i | \(0.808297\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.57503e10 | + | 1.57503e10i | −0.766394 | + | 0.766394i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.11549e10 | + | 3.11549e10i | 1.31168 | + | 1.31168i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.65053e10 | −0.603497 | −0.301748 | − | 0.953388i | \(-0.597570\pi\) | ||||
−0.301748 | + | 0.953388i | \(0.597570\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.11263e9 | 0.131054 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.19541e10 | − | 2.19541e10i | −0.611768 | − | 0.611768i | 0.331638 | − | 0.943407i | \(-0.392399\pi\) |
−0.943407 | + | 0.331638i | \(0.892399\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.23165e9 | − | 4.23165e9i | 0.103444 | − | 0.103444i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 4.17036e10i | − | 0.897051i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.11065e10i | − | 0.590482i | −0.955423 | − | 0.295241i | \(-0.904600\pi\) | ||
0.955423 | − | 0.295241i | \(-0.0953999\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.37341e11 | − | 1.37341e11i | 2.30712 | − | 2.30712i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.31681e10 | + | 1.31681e10i | 0.196276 | + | 0.196276i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.06223e10 | 0.406030 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.12128e9 | −0.0132577 | −0.00662884 | − | 0.999978i | \(-0.502110\pi\) | ||||
−0.00662884 | + | 0.999978i | \(0.502110\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.13075e11 | − | 1.13075e11i | −1.19502 | − | 1.19502i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.44136e10 | − | 6.44136e10i | 0.609831 | − | 0.609831i | −0.333071 | − | 0.942902i | \(-0.608085\pi\) |
0.942902 | + | 0.333071i | \(0.108085\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.57692e11i | − | 1.34031i | −0.742220 | − | 0.670156i | \(-0.766227\pi\) | ||
0.742220 | − | 0.670156i | \(-0.233773\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.03037e11i | 1.55251i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.50680e11 | + | 1.50680e11i | −1.03859 | + | 1.03859i | −0.0393645 | + | 0.999225i | \(0.512533\pi\) |
−0.999225 | + | 0.0393645i | \(0.987467\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00044e11 | − | 1.00044e11i | −0.622793 | − | 0.622793i | 0.323452 | − | 0.946245i | \(-0.395157\pi\) |
−0.946245 | + | 0.323452i | \(0.895157\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.29007e11 | −1.28995 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.10659e11 | −1.58618 | −0.793090 | − | 0.609105i | \(-0.791529\pi\) | ||||
−0.793090 | + | 0.609105i | \(0.791529\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.41524e9 | + | 6.41524e9i | 0.0297423 | + | 0.0297423i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.98470e11 | + | 4.98470e11i | −2.10192 | + | 2.10192i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.14699e11i | 0.440608i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 5.04814e10i | − | 0.176934i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.15655e10 | + | 5.15655e10i | −0.165151 | + | 0.165151i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.29793e11 | − | 2.29793e11i | −0.673491 | − | 0.673491i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.13068e11 | −0.303683 | −0.151842 | − | 0.988405i | \(-0.548520\pi\) | ||||
−0.151842 | + | 0.988405i | \(0.548520\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.81837e11 | −0.448167 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.98223e11 | + | 4.98223e11i | 1.12832 | + | 1.12832i | 0.990451 | + | 0.137868i | \(0.0440249\pi\) |
0.137868 | + | 0.990451i | \(0.455975\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.15010e11 | + | 4.15010e11i | −0.864718 | + | 0.864718i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 2.63866e11i | − | 0.506463i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.09163e11i | 0.193246i | 0.995321 | + | 0.0966231i | \(0.0308041\pi\) | ||||
−0.995321 | + | 0.0966231i | \(0.969196\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.81502e11 | − | 3.81502e11i | 0.623614 | − | 0.623614i | −0.322840 | − | 0.946454i | \(-0.604638\pi\) |
0.946454 | + | 0.322840i | \(0.104638\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.21045e11 | − | 8.21045e11i | −1.24069 | − | 1.24069i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.48028e12 | −2.07012 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.45777e11 | 0.318433 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.81051e12 | − | 1.81051e12i | −2.17548 | − | 2.17548i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.96155e11 | + | 9.96155e11i | −1.11123 | + | 1.11123i | −0.118241 | + | 0.992985i | \(0.537726\pi\) |
−0.992985 | + | 0.118241i | \(0.962274\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 7.33435e11i | − | 0.760306i | −0.924924 | − | 0.380153i | \(-0.875871\pi\) | ||
0.924924 | − | 0.380153i | \(-0.124129\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.16295e11i | − | 0.401419i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.76054e10 | + | 7.76054e10i | −0.0696735 | + | 0.0696735i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.44765e12 | + | 1.44765e12i | 1.21120 | + | 1.21120i | 0.970632 | + | 0.240569i | \(0.0773340\pi\) |
0.240569 | + | 0.970632i | \(0.422666\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.62388e10 | 0.0594966 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.73886e11 | −0.126684 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.22436e11 | + | 3.22436e11i | 0.219488 | + | 0.219488i | 0.808283 | − | 0.588795i | \(-0.200397\pi\) |
−0.588795 | + | 0.808283i | \(0.700397\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.09418e12 | − | 1.09418e12i | 0.696512 | − | 0.696512i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.78508e12i | − | 1.65920i | −0.558361 | − | 0.829598i | \(-0.688570\pi\) | ||
0.558361 | − | 0.829598i | \(-0.311430\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.73338e12i | 2.64116i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.50626e12 | − | 1.50626e12i | 0.787809 | − | 0.787809i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.03081e12 | − | 1.03081e12i | −0.505740 | − | 0.505740i | 0.407476 | − | 0.913216i | \(-0.366409\pi\) |
−0.913216 | + | 0.407476i | \(0.866409\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.51599e12 | 1.15878 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.38136e12 | −2.76096 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.53907e12 | − | 1.53907e12i | −0.625990 | − | 0.625990i | 0.321066 | − | 0.947057i | \(-0.395959\pi\) |
−0.947057 | + | 0.321066i | \(0.895959\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.04299e12 | − | 1.04299e12i | 0.399070 | − | 0.399070i | −0.478835 | − | 0.877905i | \(-0.658941\pi\) |
0.877905 | + | 0.478835i | \(0.158941\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 9.35088e10i | − | 0.0336799i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.34964e12i | − | 0.457903i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.18124e11 | − | 6.18124e11i | 0.197673 | − | 0.197673i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.57606e12 | + | 3.57606e12i | 1.07861 | + | 1.07861i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.44868e11 | −0.155099 | −0.0775494 | − | 0.996989i | \(-0.524710\pi\) | ||||
−0.0775494 | + | 0.996989i | \(0.524710\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.82936e12 | 1.29815 | 0.649074 | − | 0.760725i | \(-0.275157\pi\) | ||||
0.649074 | + | 0.760725i | \(0.275157\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.82350e12 | − | 4.82350e12i | −1.22510 | − | 1.22510i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.97463e12 | + | 1.97463e12i | −0.474156 | + | 0.474156i | −0.903257 | − | 0.429101i | \(-0.858831\pi\) |
0.429101 | + | 0.903257i | \(0.358831\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.29074e11i | 0.188322i | 0.995557 | + | 0.0941610i | \(0.0300169\pi\) | ||||
−0.995557 | + | 0.0941610i | \(0.969983\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 6.59026e12i | − | 1.41685i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.33091e12 | + | 3.33091e12i | −0.678165 | + | 0.678165i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.03898e11 | − | 3.03898e11i | −0.0586248 | − | 0.0586248i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.31109e11 | 0.115416 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.47305e12 | 0.775889 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.62494e12 | + | 6.62494e12i | 1.09051 | + | 1.09051i | 0.995474 | + | 0.0950325i | \(0.0302955\pi\) |
0.0950325 | + | 0.995474i | \(0.469704\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.73422e11 | − | 5.73422e11i | 0.0896162 | − | 0.0896162i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.07165e12i | − | 0.159089i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.10350e12i | − | 0.296767i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.55194e12 | + | 9.55194e12i | −1.28129 | + | 1.28129i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.72488e12 | − | 2.72488e12i | −0.347689 | − | 0.347689i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.00358e12 | 0.486152 | 0.243076 | − | 0.970007i | \(-0.421844\pi\) | ||||
0.243076 | + | 0.970007i | \(0.421844\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.13166e12 | −1.05571 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.84203e12 | + | 3.84203e12i | 0.423076 | + | 0.423076i | 0.886261 | − | 0.463185i | \(-0.153294\pi\) |
−0.463185 | + | 0.886261i | \(0.653294\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.03856e12 | + | 2.03856e12i | −0.213909 | + | 0.213909i | −0.805926 | − | 0.592017i | \(-0.798332\pi\) |
0.592017 | + | 0.805926i | \(0.298332\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.96580e13i | 2.96672i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.18553e13i | 1.13098i | 0.824754 | + | 0.565491i | \(0.191313\pi\) | ||||
−0.824754 | + | 0.565491i | \(0.808687\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.83878e12 | − | 4.83878e12i | 0.440416 | − | 0.440416i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.85614e12 | − | 7.85614e12i | −0.682485 | − | 0.682485i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.13763e11 | −0.0343213 | −0.0171606 | − | 0.999853i | \(-0.505463\pi\) | ||||
−0.0171606 | + | 0.999853i | \(0.505463\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.66336e12 | −0.527958 | −0.263979 | − | 0.964528i | \(-0.585035\pi\) | ||||
−0.263979 | + | 0.964528i | \(0.585035\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.02892e13 | + | 1.02892e13i | 0.779018 | + | 0.779018i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.06701e13 | − | 1.06701e13i | 0.772247 | − | 0.772247i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.97186e13i | − | 1.36472i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 2.08993e13i | − | 1.38368i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.35293e12 | − | 4.35293e12i | 0.275788 | − | 0.275788i | −0.555637 | − | 0.831425i | \(-0.687525\pi\) |
0.831425 | + | 0.555637i | \(0.187525\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.37086e11 | + | 9.37086e11i | 0.0568351 | + | 0.0568351i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.02833e12 | 0.233966 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.08461e12 | 0.449808 | 0.224904 | − | 0.974381i | \(-0.427793\pi\) | ||||
0.224904 | + | 0.974381i | \(0.427793\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.82911e13 | + | 1.82911e13i | 0.975193 | + | 0.975193i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.20894e13 | − | 1.20894e13i | 0.617847 | − | 0.617847i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.83271e13i | 0.898127i | 0.893500 | + | 0.449064i | \(0.148242\pi\) | ||||
−0.893500 | + | 0.449064i | \(0.851758\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.49309e11i | 0.0211199i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.48060e13 | − | 1.48060e13i | 0.667767 | − | 0.667767i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.88707e12 | + | 8.88707e12i | 0.384699 | + | 0.384699i | 0.872792 | − | 0.488093i | \(-0.162307\pi\) |
−0.488093 | + | 0.872792i | \(0.662307\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.04500e13 | −1.26548 | −0.632742 | − | 0.774363i | \(-0.718071\pi\) | ||||
−0.632742 | + | 0.774363i | \(0.718071\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.30742e14 | 5.21819 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.35589e13 | − | 1.35589e13i | −0.519870 | − | 0.519870i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.57011e13 | − | 1.57011e13i | 0.578486 | − | 0.578486i | −0.356000 | − | 0.934486i | \(-0.615860\pi\) |
0.934486 | + | 0.356000i | \(0.115860\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.63456e12i | 0.270371i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.15542e13i | 0.733919i | 0.930237 | + | 0.366959i | \(0.119601\pi\) | ||||
−0.930237 | + | 0.366959i | \(0.880399\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.93257e12 | − | 9.93257e12i | 0.325264 | − | 0.325264i | −0.525518 | − | 0.850782i | \(-0.676129\pi\) |
0.850782 | + | 0.525518i | \(0.176129\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.45755e13 | + | 1.45755e13i | 0.459173 | + | 0.459173i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.23719e12 | 0.249706 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.19962e13 | −0.933599 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.33701e11 | − | 5.33701e11i | −0.0149929 | − | 0.0149929i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.63841e13 | + | 3.63841e13i | −0.984327 | + | 0.984327i | −0.999879 | − | 0.0155521i | \(-0.995049\pi\) |
0.0155521 | + | 0.999879i | \(0.495049\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3.76082e13i | − | 0.980079i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.85434e13i | − | 0.967809i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.13097e12 | − | 4.13097e12i | 0.0999678 | − | 0.0999678i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.45236e13 | + | 1.45236e13i | 0.338811 | + | 0.338811i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.13187e13 | 1.37930 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.51088e11 | 0.0119556 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.26294e13 | + | 4.26294e13i | 0.892171 | + | 0.892171i | 0.994727 | − | 0.102556i | \(-0.0327022\pi\) |
−0.102556 | + | 0.994727i | \(0.532702\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.50578e13 | − | 7.50578e13i | 1.51574 | − | 1.51574i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.98356e13i | 1.16621i | 0.812396 | + | 0.583106i | \(0.198163\pi\) | ||||
−0.812396 | + | 0.583106i | \(0.801837\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6.26571e13i | − | 1.17890i | −0.807805 | − | 0.589449i | \(-0.799345\pi\) | ||
0.807805 | − | 0.589449i | \(-0.200655\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.88581e13 | + | 5.88581e13i | −1.06930 | + | 1.06930i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.32656e12 | − | 8.32656e12i | −0.146096 | − | 0.146096i | 0.630275 | − | 0.776372i | \(-0.282942\pi\) |
−0.776372 | + | 0.630275i | \(0.782942\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.59012e13 | 0.608499 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.43440e14 | −2.34905 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.23395e12 | + | 8.23395e12i | 0.130315 | + | 0.130315i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.97719e13 | + | 5.97719e13i | −0.914404 | + | 0.914404i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 9.52368e13i | − | 1.40862i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.31156e14i | 1.87590i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.11137e13 | + | 8.11137e13i | −1.12212 | + | 1.12212i | −0.130701 | + | 0.991422i | \(0.541723\pi\) |
−0.991422 | + | 0.130701i | \(0.958277\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.63865e13 | − | 6.63865e13i | −0.888457 | − | 0.888457i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.88393e13 | 0.502950 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.00143e13 | −0.626801 | −0.313401 | − | 0.949621i | \(-0.601468\pi\) | ||||
−0.313401 | + | 0.949621i | \(0.601468\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.47866e14 | − | 1.47866e14i | −1.79379 | − | 1.79379i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.13360e13 | + | 1.13360e13i | −0.133140 | + | 0.133140i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.38872e14i | 1.57942i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.10700e12i | 0.0672703i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.02184e13 | − | 7.02184e13i | 0.749271 | − | 0.749271i | −0.225072 | − | 0.974342i | \(-0.572262\pi\) |
0.974342 | + | 0.225072i | \(0.0722616\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.07392e13 | + | 8.07392e13i | 0.834728 | + | 0.834728i | 0.988159 | − | 0.153432i | \(-0.0490325\pi\) |
−0.153432 | + | 0.988159i | \(0.549032\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.69911e14 | −1.70229 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.65562e13 | −0.549186 | −0.274593 | − | 0.961561i | \(-0.588543\pi\) | ||||
−0.274593 | + | 0.961561i | \(0.588543\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.37943e12 | + | 3.37943e12i | 0.0318117 | + | 0.0318117i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.45941e13 | + | 5.45941e13i | −0.498277 | + | 0.498277i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.91411e13i | 0.169413i | 0.996406 | + | 0.0847065i | \(0.0269953\pi\) | ||||
−0.996406 | + | 0.0847065i | \(0.973005\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 5.69053e13i | − | 0.488499i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.40280e13 | − | 2.40280e13i | 0.200092 | − | 0.200092i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.62938e13 | − | 5.62938e13i | −0.454831 | − | 0.454831i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.09458e14 | −0.858189 | −0.429095 | − | 0.903260i | \(-0.641167\pi\) | ||||
−0.429095 | + | 0.903260i | \(0.641167\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.98965e13 | −0.227496 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.08929e12 | − | 6.08929e12i | −0.0449790 | − | 0.0449790i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.82988e13 | − | 8.82988e13i | 0.633222 | − | 0.633222i | −0.315652 | − | 0.948875i | \(-0.602223\pi\) |
0.948875 | + | 0.315652i | \(0.102223\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 2.18752e14i | − | 1.52328i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.58264e14i | − | 1.07029i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.73807e13 | − | 8.73807e13i | 0.573984 | − | 0.573984i | −0.359255 | − | 0.933239i | \(-0.616969\pi\) |
0.933239 | + | 0.359255i | \(0.116969\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.38179e13 | − | 5.38179e13i | −0.343431 | − | 0.343431i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.54041e14 | 1.57511 | 0.787555 | − | 0.616245i | \(-0.211347\pi\) | ||||
0.787555 | + | 0.616245i | \(0.211347\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.74788e14 | −1.05312 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.27126e13 | − | 5.27126e13i | −0.308677 | − | 0.308677i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.20478e14 | + | 2.20478e14i | −1.25499 | + | 1.25499i | −0.301540 | + | 0.953453i | \(0.597501\pi\) |
−0.953453 | + | 0.301540i | \(0.902499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.44996e12i | 0.0190916i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.74285e14i | 2.55200i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.62997e13 | − | 4.62997e13i | 0.242267 | − | 0.242267i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.45645e13 | − | 3.45645e13i | −0.175907 | − | 0.175907i | 0.613662 | − | 0.789569i | \(-0.289696\pi\) |
−0.789569 | + | 0.613662i | \(0.789696\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.95070e14 | −1.95579 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.54405e14 | 0.743646 | 0.371823 | − | 0.928304i | \(-0.378733\pi\) | ||||
0.371823 | + | 0.928304i | \(0.378733\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.99725e13 | + | 4.99725e13i | 0.234182 | + | 0.234182i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.15365e13 | + | 1.15365e13i | −0.0526103 | + | 0.0526103i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.97144e14i | − | 0.875014i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.08138e14i | 0.899236i | 0.893221 | + | 0.449618i | \(0.148440\pi\) | ||||
−0.893221 | + | 0.449618i | \(0.851560\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.19588e13 | + | 5.19588e13i | −0.218539 | + | 0.218539i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.09687e14 | + | 5.09687e14i | 2.08727 | + | 2.08727i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.23169e14 | 0.491175 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.63172e14 | 1.41047 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.92778e14 | − | 2.92778e14i | −1.10755 | − | 1.10755i | −0.993472 | − | 0.114073i | \(-0.963610\pi\) |
−0.114073 | − | 0.993472i | \(-0.536390\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.64588e14 | + | 1.64588e14i | −0.606521 | + | 0.606521i | −0.942035 | − | 0.335515i | \(-0.891090\pi\) |
0.335515 | + | 0.942035i | \(0.391090\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 4.76023e14i | − | 1.70905i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 4.99182e13i | − | 0.174630i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.46866e12 | + | 7.46866e12i | −0.0254618 | + | 0.0254618i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.04578e14 | − | 7.04578e14i | −2.34107 | − | 2.34107i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.93359e14 | 0.950113 | 0.475056 | − | 0.879955i | \(-0.342428\pi\) | ||||
0.475056 | + | 0.879955i | \(0.342428\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.65581e14 | 0.838519 | 0.419260 | − | 0.907866i | \(-0.362290\pi\) | ||||
0.419260 | + | 0.907866i | \(0.362290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.16984e14 | + | 1.16984e14i | 0.360111 | + | 0.360111i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.24828e13 | + | 1.24828e13i | −0.0374683 | + | 0.0374683i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.88728e14i | − | 1.43058i | −0.698828 | − | 0.715290i | \(-0.746295\pi\) | ||
0.698828 | − | 0.715290i | \(-0.253705\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 1.04969e15i | − | 2.99674i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.17621e14 | − | 2.17621e14i | 0.606010 | − | 0.606010i | −0.335891 | − | 0.941901i | \(-0.609037\pi\) |
0.941901 | + | 0.335891i | \(0.109037\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.72581e13 | + | 8.72581e13i | 0.237042 | + | 0.237042i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.48293e14 | −2.51334 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.88213e14 | −0.745346 | −0.372673 | − | 0.927963i | \(-0.621559\pi\) | ||||
−0.372673 | + | 0.927963i | \(0.621559\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.43909e13 | − | 4.43909e13i | −0.112027 | − | 0.112027i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.49098e14 | − | 3.49098e14i | 0.859818 | − | 0.859818i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.70518e14i | 1.85234i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.33246e14i | 1.72072i | 0.509685 | + | 0.860361i | \(0.329762\pi\) | ||||
−0.509685 | + | 0.860361i | \(0.670238\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.09503e13 | − | 7.09503e13i | 0.162549 | − | 0.162549i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.64165e13 | − | 1.64165e13i | −0.0367220 | − | 0.0367220i | 0.688507 | − | 0.725229i | \(-0.258266\pi\) |
−0.725229 | + | 0.688507i | \(0.758266\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.07863e14 | 1.10931 | 0.554653 | − | 0.832082i | \(-0.312851\pi\) | ||||
0.554653 | + | 0.832082i | \(0.312851\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.38767e13 | −0.157585 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.51057e14 | + | 5.51057e14i | 1.14803 | + | 1.14803i | 0.986939 | + | 0.161093i | \(0.0515018\pi\) |
0.161093 | + | 0.986939i | \(0.448498\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.26372e14 | + | 5.26372e14i | −1.07113 | + | 1.07113i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.37810e15i | 2.73946i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.56538e14i | − | 0.304006i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.80616e14 | − | 1.80616e14i | 0.342722 | − | 0.342722i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.21007e13 | + | 2.21007e13i | 0.0409785 | + | 0.0409785i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.92439e14 | −0.711094 | −0.355547 | − | 0.934658i | \(-0.615705\pi\) | ||||
−0.355547 | + | 0.934658i | \(0.615705\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.69074e14 | −1.53907 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.27655e13 | − | 8.27655e13i | −0.143265 | − | 0.143265i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.14533e12 | − | 3.14533e12i | 0.00532215 | − | 0.00532215i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.30426e14i | 0.546594i | 0.961930 | + | 0.273297i | \(0.0881141\pi\) | ||||
−0.961930 | + | 0.273297i | \(0.911886\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.06944e14i | 0.496432i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.42264e14 | + | 4.42264e14i | −0.699412 | + | 0.699412i | −0.964284 | − | 0.264871i | \(-0.914670\pi\) |
0.264871 | + | 0.964284i | \(0.414670\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.60865e13 | + | 6.60865e13i | 0.102201 | + | 0.102201i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.34383e14 | 0.959451 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.15998e13 | −0.135498 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.81971e14 | + | 5.81971e14i | 0.842071 | + | 0.842071i | 0.989128 | − | 0.147057i | \(-0.0469802\pi\) |
−0.147057 | + | 0.989128i | \(0.546980\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.32563e15 | − | 1.32563e15i | 1.87636 | − | 1.87636i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.90788e14i | 0.818102i | 0.912512 | + | 0.409051i | \(0.134140\pi\) | ||||
−0.912512 | + | 0.409051i | \(0.865860\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.61378e14i | 0.489620i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.25298e15 | + | 2.25298e15i | −2.98684 | + | 2.98684i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.70291e14 | − | 1.70291e14i | −0.220924 | − | 0.220924i | 0.587963 | − | 0.808887i | \(-0.299930\pi\) |
−0.808887 | + | 0.587963i | \(0.799930\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.52585e15 | 1.93730 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.13432e14 | 0.638024 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.42349e14 | + | 4.42349e14i | 0.538053 | + | 0.538053i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.06810e14 | − | 7.06810e14i | 0.841598 | − | 0.841598i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 9.81287e14i | − | 1.14387i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.56998e15i | − | 1.79179i | −0.444266 | − | 0.895895i | \(-0.646535\pi\) | ||
0.444266 | − | 0.895895i | \(-0.353465\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.14707e14 | − | 8.14707e14i | 0.910421 | − | 0.910421i | −0.0858840 | − | 0.996305i | \(-0.527371\pi\) |
0.996305 | + | 0.0858840i | \(0.0273715\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.19755e15 | + | 1.19755e15i | 1.31044 | + | 1.31044i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.17343e13 | −0.0447234 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.47580e14 | 0.994511 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.84988e15 | − | 1.84988e15i | −1.90162 | − | 1.90162i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.95689e14 | + | 1.95689e14i | −0.197046 | + | 0.197046i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 8.45355e14i | − | 0.833860i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1.46513e15i | − | 1.41585i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.55861e15 | − | 1.55861e15i | 1.47570 | − | 1.47570i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.62507e14 | + | 1.62507e14i | 0.150760 | + | 0.150760i | 0.778458 | − | 0.627697i | \(-0.216002\pi\) |
−0.627697 | + | 0.778458i | \(0.716002\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.92880e14 | 0.902605 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.61273e14 | 0.500026 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.52073e14 | + | 3.52073e14i | 0.307399 | + | 0.307399i | 0.843900 | − | 0.536501i | \(-0.180254\pi\) |
−0.536501 | + | 0.843900i | \(0.680254\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.71071e13 | − | 2.71071e13i | 0.0231972 | − | 0.0231972i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.78235e14i | 0.401150i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.25496e15i | 1.03191i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.42397e14 | − | 6.42397e14i | 0.517835 | − | 0.517835i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.52294e13 | + | 8.52294e13i | 0.0673575 | + | 0.0673575i | 0.739983 | − | 0.672626i | \(-0.234834\pi\) |
−0.672626 | + | 0.739983i | \(0.734834\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.90067e14 | −0.534720 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.88425e14 | 0.447091 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.50742e14 | + | 6.50742e14i | 0.484856 | + | 0.484856i | 0.906678 | − | 0.421823i | \(-0.138610\pi\) |
−0.421823 | + | 0.906678i | \(0.638610\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.71441e14 | − | 8.71441e14i | 0.636754 | − | 0.636754i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 3.12698e14i | − | 0.224088i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.48183e15i | 1.04155i | 0.853693 | + | 0.520777i | \(0.174358\pi\) | ||||
−0.853693 | + | 0.520777i | \(0.825642\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.55470e14 | + | 8.55470e14i | −0.589802 | + | 0.589802i | −0.937578 | − | 0.347776i | \(-0.886937\pi\) |
0.347776 | + | 0.937578i | \(0.386937\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.59345e14 | − | 2.59345e14i | −0.175399 | − | 0.175399i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.56767e13 | 0.0502099 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.53819e15 | 1.65218 | 0.826089 | − | 0.563539i | \(-0.190561\pi\) | ||||
0.826089 | + | 0.563539i | \(0.190561\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.29866e15 | + | 2.29866e15i | 1.46806 | + | 1.46806i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.66925e15 | + | 1.66925e15i | −1.04605 | + | 1.04605i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.56314e13i | 0.0403585i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 2.79656e15i | − | 1.68759i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.49682e14 | + | 1.49682e14i | −0.0886464 | + | 0.0886464i | −0.750039 | − | 0.661393i | \(-0.769966\pi\) |
0.661393 | + | 0.750039i | \(0.269966\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.51005e14 | − | 1.51005e14i | −0.0877722 | − | 0.0877722i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.87975e15 | −1.07243 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.51255e14 | −0.140706 | −0.0703532 | − | 0.997522i | \(-0.522413\pi\) | ||||
−0.0703532 | + | 0.997522i | \(0.522413\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.21747e14 | − | 3.21747e14i | −0.176877 | − | 0.176877i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.94619e14 | + | 3.94619e14i | −0.212971 | + | 0.212971i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.70110e15i | 0.901329i | 0.892693 | + | 0.450665i | \(0.148813\pi\) | ||||
−0.892693 | + | 0.450665i | \(0.851187\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.33302e15i | 1.21369i | 0.794819 | + | 0.606847i | \(0.207566\pi\) | ||||
−0.794819 | + | 0.606847i | \(0.792434\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.91044e15 | − | 1.91044e15i | 0.975861 | − | 0.975861i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.41607e14 | + | 1.41607e14i | 0.0710283 | + | 0.0710283i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.91749e14 | 0.0944486 | 0.0472243 | − | 0.998884i | \(-0.484962\pi\) | ||||
0.0472243 | + | 0.998884i | \(0.484962\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.17087e15 | −1.53385 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.11584e15 | − | 3.11584e15i | −1.48029 | − | 1.48029i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.21713e14 | − | 1.21713e14i | 0.0567944 | − | 0.0567944i | −0.678139 | − | 0.734934i | \(-0.737213\pi\) |
0.734934 | + | 0.678139i | \(0.237213\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 2.89296e14i | − | 0.132596i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 5.95192e14i | − | 0.267972i | −0.990983 | − | 0.133986i | \(-0.957222\pi\) | ||
0.990983 | − | 0.133986i | \(-0.0427777\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.40823e15 | + | 2.40823e15i | −1.06512 | + | 1.06512i | −0.0673975 | + | 0.997726i | \(0.521470\pi\) |
−0.997726 | + | 0.0673975i | \(0.978530\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.07562e14 | + | 1.07562e14i | 0.0467363 | + | 0.0467363i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.36514e15 | −1.00965 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.26546e14 | −0.136963 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.12907e15 | + | 2.12907e15i | 0.877441 | + | 0.877441i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.62901e14 | − | 3.62901e14i | 0.146964 | − | 0.146964i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.59339e14i | 0.182798i | 0.995814 | + | 0.0913991i | \(0.0291339\pi\) | ||||
−0.995814 | + | 0.0913991i | \(0.970866\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.30663e15i | 2.46648i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.17172e14 | − | 3.17172e14i | 0.121910 | − | 0.121910i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.87082e15 | − | 6.87082e15i | −2.59562 | − | 2.59562i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.32457e14 | 0.123447 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.14966e14 | −0.0419613 | −0.0209807 | − | 0.999780i | \(-0.506679\pi\) | ||||
−0.0209807 | + | 0.999780i | \(0.506679\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.76444e14 | − | 1.76444e14i | −0.0633061 | − | 0.0633061i | 0.674745 | − | 0.738051i | \(-0.264254\pi\) |
−0.738051 | + | 0.674745i | \(0.764254\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.10079e14 | − | 5.10079e14i | 0.179912 | − | 0.179912i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 2.12407e15i | − | 0.736540i | −0.929719 | − | 0.368270i | \(-0.879950\pi\) | ||
0.929719 | − | 0.368270i | \(-0.120050\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 5.49350e15i | − | 1.87285i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.00122e15 | − | 1.00122e15i | 0.335609 | − | 0.335609i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.15088e15 | + | 2.15088e15i | 0.708913 | + | 0.708913i | 0.966307 | − | 0.257393i | \(-0.0828636\pi\) |
−0.257393 | + | 0.966307i | \(0.582864\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.79517e15 | −0.905901 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.53799e15 | −1.76499 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.09422e14 | − | 3.09422e14i | −0.0969797 | − | 0.0969797i | 0.656952 | − | 0.753932i | \(-0.271845\pi\) |
−0.753932 | + | 0.656952i | \(0.771845\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.62461e15 | + | 3.62461e15i | −1.11726 | + | 1.11726i | −0.125115 | + | 0.992142i | \(0.539930\pi\) |
−0.992142 | + | 0.125115i | \(0.960070\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 2.59396e15i | − | 0.786392i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2.32832e15i | − | 0.694263i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00188e14 | + | 1.00188e14i | −0.0293849 | + | 0.0293849i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.90561e15 | + | 1.90561e15i | 0.549782 | + | 0.549782i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.04985e13 | 0.0228462 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.77117e14 | −0.105291 | −0.0526457 | − | 0.998613i | \(-0.516765\pi\) | ||||
−0.0526457 | + | 0.998613i | \(0.516765\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.55634e15 | − | 1.55634e15i | −0.427496 | − | 0.427496i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.32594e15 | + | 2.32594e15i | −0.628581 | + | 0.628581i | −0.947711 | − | 0.319130i | \(-0.896609\pi\) |
0.319130 | + | 0.947711i | \(0.396609\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.52546e13i | 0.0226691i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.65743e15i | 0.956901i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.34268e15 | − | 1.34268e15i | 0.345669 | − | 0.345669i | −0.512825 | − | 0.858493i | \(-0.671401\pi\) |
0.858493 | + | 0.512825i | \(0.171401\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.06216e14 | − | 3.06216e14i | −0.0775765 | − | 0.0775765i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.94061e15 | −0.483812 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.89324e14 | 0.0709869 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.81110e15 | − | 1.81110e15i | −0.437333 | − | 0.437333i | 0.453781 | − | 0.891113i | \(-0.350075\pi\) |
−0.891113 | + | 0.453781i | \(0.850075\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.59751e15 | + | 8.59751e15i | −2.04334 | + | 2.04334i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.14033e15i | 0.500685i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.63429e14i | − | 0.0376312i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.64286e15 | + | 5.64286e15i | −1.27901 | + | 1.27901i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.18446e15 | + | 3.18446e15i | 0.710537 | + | 0.710537i | 0.966648 | − | 0.256110i | \(-0.0824410\pi\) |
−0.256110 | + | 0.966648i | \(0.582441\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.62613e15 | 0.576850 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.60629e15 | 0.996119 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.89760e15 | − | 4.89760e15i | −1.04274 | − | 1.04274i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.07734e15 | − | 6.07734e15i | 1.27397 | − | 1.27397i | 0.329982 | − | 0.943987i | \(-0.392957\pi\) |
0.943987 | − | 0.329982i | \(-0.107043\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 4.55481e15i | − | 0.940128i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6.32698e13i | − | 0.0128589i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.15239e15 | − | 4.15239e15i | 0.831027 | − | 0.831027i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.96941e14 | − | 1.96941e14i | −0.0388134 | − | 0.0388134i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.62588e15 | 1.28598 | 0.642990 | − | 0.765874i | \(-0.277694\pi\) | ||||
0.642990 | + | 0.765874i | \(0.277694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.19899e16 | −2.29178 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.17160e15 | − | 3.17160e15i | −0.597060 | − | 0.597060i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.44964e15 | − | 1.44964e15i | 0.268783 | − | 0.268783i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.23539e15i | − | 1.68662i | −0.537431 | − | 0.843308i | \(-0.680605\pi\) | ||
0.537431 | − | 0.843308i | \(-0.319395\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.06630e15i | 1.63090i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.88153e14 | − | 2.88153e14i | 0.0510596 | − | 0.0510596i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.31578e15 | − | 3.31578e15i | −0.578781 | − | 0.578781i | 0.355787 | − | 0.934567i | \(-0.384213\pi\) |
−0.934567 | + | 0.355787i | \(0.884213\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.01575e16 | 1.74665 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.67333e15 | 0.961096 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.68264e14 | + | 3.68264e14i | 0.0614632 | + | 0.0614632i | 0.737170 | − | 0.675707i | \(-0.236162\pi\) |
−0.675707 | + | 0.737170i | \(0.736162\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.38559e15 | − | 9.38559e15i | 1.54334 | − | 1.54334i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.47188e15i | − | 0.238469i | −0.992866 | − | 0.119235i | \(-0.961956\pi\) | ||
0.992866 | − | 0.119235i | \(-0.0380441\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 5.58870e15i | − | 0.892178i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.05847e15 | − | 6.05847e15i | 0.953014 | − | 0.953014i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.14567e16 | + | 1.14567e16i | 1.77587 | + | 1.77587i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.16182e14 | 0.0482966 | 0.0241483 | − | 0.999708i | \(-0.492313\pi\) | ||||
0.0241483 | + | 0.999708i | \(0.492313\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.14378e15 | 0.623770 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.05739e15 | + | 2.05739e15i | 0.305216 | + | 0.305216i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.85861e15 | − | 6.85861e15i | 1.00279 | − | 1.00279i | 0.00279044 | − | 0.999996i | \(-0.499112\pi\) |
0.999996 | − | 0.00279044i | \(-0.000888226\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.92062e14i | 0.128548i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.01455e16i | − | 1.44098i | −0.693465 | − | 0.720490i | \(-0.743917\pi\) | ||
0.693465 | − | 0.720490i | \(-0.256083\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.60668e15 | + | 7.60668e15i | −1.06490 | + | 1.06490i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.16776e15 | + | 1.16776e15i | 0.161145 | + | 0.161145i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.42170e16 | −3.29418 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.34284e14 | 0.0716436 | 0.0358218 | − | 0.999358i | \(-0.488595\pi\) | ||||
0.0358218 | + | 0.999358i | \(0.488595\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.84808e15 | + | 3.84808e15i | 0.508681 | + | 0.508681i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.03391e14 | + | 5.03391e14i | −0.0656022 | + | 0.0656022i | −0.739147 | − | 0.673545i | \(-0.764771\pi\) |
0.673545 | + | 0.739147i | \(0.264771\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.15465e14i | 0.117620i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.74122e16i | 2.20566i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.91326e14 | − | 5.91326e14i | 0.0738534 | − | 0.0738534i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.93639e14 | + | 4.93639e14i | 0.0607896 | + | 0.0607896i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.12085e15 | 0.500377 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.12173e15 | −0.972446 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.82819e15 | − | 2.82819e15i | −0.333924 | − | 0.333924i | 0.520151 | − | 0.854075i | \(-0.325876\pi\) |
−0.854075 | + | 0.520151i | \(0.825876\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.72328e15 | + | 8.72328e15i | −1.01568 | + | 1.01568i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.36205e16i | 2.71218i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.54863e14i | − | 0.0401844i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.13860e14 | + | 2.13860e14i | −0.0238842 | + | 0.0238842i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.08811e16 | − | 1.08811e16i | −1.19854 | − | 1.19854i | −0.974604 | − | 0.223934i | \(-0.928110\pi\) |
−0.223934 | − | 0.974604i | \(-0.571890\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.60218e15 | 0.282702 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.58415e15 | 0.919854 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.22294e15 | − | 8.22294e15i | −0.869144 | − | 0.869144i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.87774e14 | − | 4.87774e14i | 0.0508559 | − | 0.0508559i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.46007e15i | 0.870101i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1.10309e16i | − | 1.11916i | −0.828776 | − | 0.559580i | \(-0.810962\pi\) | ||
0.828776 | − | 0.559580i | \(-0.189038\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.68941e15 | − | 3.68941e15i | 0.369269 | − | 0.369269i | −0.497942 | − | 0.867211i | \(-0.665911\pi\) |
0.867211 | + | 0.497942i | \(0.165911\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.44935e16 | − | 1.44935e16i | −1.43112 | − | 1.43112i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.80895e15 | −0.176222 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.08522e15 | 0.200415 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.79005e16 | + | 3.79005e16i | 3.59404 | + | 3.59404i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.29997e16 | + | 1.29997e16i | −1.21632 | + | 1.21632i | −0.247406 | + | 0.968912i | \(0.579578\pi\) |
−0.968912 | + | 0.247406i | \(0.920422\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.57009e15i | 0.883521i | 0.897133 | + | 0.441760i | \(0.145646\pi\) | ||||
−0.897133 | + | 0.441760i | \(0.854354\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.29074e16i | − | 1.17583i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.06170e15 | + | 2.06170e15i | −0.185330 | + | 0.185330i | −0.793674 | − | 0.608344i | \(-0.791834\pi\) |
0.608344 | + | 0.793674i | \(0.291834\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.19446e15 | + | 9.19446e15i | 0.815598 | + | 0.815598i | 0.985467 | − | 0.169869i | \(-0.0543343\pi\) |
−0.169869 | + | 0.985467i | \(0.554334\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.49467e16 | 1.30840 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.73813e15 | 0.495705 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.81254e15 | + | 7.81254e15i | 0.666065 | + | 0.666065i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.30118e15 | + | 1.30118e15i | −0.109483 | + | 0.109483i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1.17712e16i | − | 0.977528i | −0.872416 | − | 0.488764i | \(-0.837448\pi\) | ||
0.872416 | − | 0.488764i | \(-0.162552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 8.36215e15i | − | 0.685394i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.02593e16 | + | 1.02593e16i | −0.829978 | + | 0.829978i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.32778e16 | − | 1.32778e16i | −1.06026 | − | 1.06026i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.83828e15 | −0.302537 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.45533e15 | 0.735673 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.50164e14 | + | 5.50164e14i | 0.0422551 | + | 0.0422551i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.41578e15 | − | 9.41578e15i | 0.713899 | − | 0.713899i | −0.253450 | − | 0.967349i | \(-0.581565\pi\) |
0.967349 | + | 0.253450i | \(0.0815653\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.45052e15i | 0.632514i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 3.55343e14i | − | 0.0262575i | −0.999914 | − | 0.0131287i | \(-0.995821\pi\) | ||
0.999914 | − | 0.0131287i | \(-0.00417913\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.10513e16 | − | 1.10513e16i | 0.806216 | − | 0.806216i | −0.177843 | − | 0.984059i | \(-0.556912\pi\) |
0.984059 | + | 0.177843i | \(0.0569118\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.92071e15 | + | 3.92071e15i | 0.282389 | + | 0.282389i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.12704e16 | 0.801460 | 0.400730 | − | 0.916196i | \(-0.368757\pi\) | ||||
0.400730 | + | 0.916196i | \(0.368757\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.78315e15 | 0.406047 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.52294e16 | − | 1.52294e16i | −1.05579 | − | 1.05579i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.76308e15 | − | 6.76308e15i | 0.462952 | − | 0.462952i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.50098e16i | − | 1.69048i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3.09427e14i | − | 0.0206529i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.74720e16 | + | 1.74720e16i | −1.15159 | + | 1.15159i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.18211e16 | + | 1.18211e16i | 0.769414 | + | 0.769414i | 0.978003 | − | 0.208589i | \(-0.0668871\pi\) |
−0.208589 | + | 0.978003i | \(0.566887\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.46359e16 | −2.22632 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.37908e16 | 0.875430 | 0.437715 | − | 0.899114i | \(-0.355788\pi\) | ||||
0.437715 | + | 0.899114i | \(0.355788\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.35176e15 | − | 2.35176e15i | −0.147438 | − | 0.147438i | 0.629534 | − | 0.776973i | \(-0.283246\pi\) |
−0.776973 | + | 0.629534i | \(0.783246\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.79006e16 | − | 1.79006e16i | 1.10836 | − | 1.10836i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.28863e15i | 0.445724i | 0.974850 | + | 0.222862i | \(0.0715399\pi\) | ||||
−0.974850 | + | 0.222862i | \(0.928460\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.59700e15i | 0.519263i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.68516e15 | + | 1.68516e15i | −0.100534 | + | 0.100534i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.41532e15 | + | 9.41532e15i | 0.554820 | + | 0.554820i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.63463e15 | 0.502593 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.93248e15 | 0.226104 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.21198e15 | − | 1.21198e15i | −0.0688363 | − | 0.0688363i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.20814e14 | + | 1.20814e14i | −0.00677844 | + | 0.00677844i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.38258e16i | 0.766313i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.85148e15i | 0.320404i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.38649e16 | − | 1.38649e16i | 0.750026 | − | 0.750026i | −0.224457 | − | 0.974484i | \(-0.572061\pi\) |
0.974484 | + | 0.224457i | \(0.0720610\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.77756e16 | + | 1.77756e16i | 0.949997 | + | 0.949997i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.60466e15 | 0.243134 | 0.121567 | − | 0.992583i | \(-0.461208\pi\) | ||||
0.121567 | + | 0.992583i | \(0.461208\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.79915e16 | 0.938595 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.62305e14 | + | 2.62305e14i | 0.0135204 | + | 0.0135204i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.78817e16 | − | 3.78817e16i | 1.92929 | − | 1.92929i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.57692e15i | − | 0.180000i | −0.995942 | − | 0.0900002i | \(-0.971313\pi\) | ||
0.995942 | − | 0.0900002i | \(-0.0286868\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.05812e16i | 2.01789i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.17612e15 | − | 2.17612e15i | 0.106923 | − | 0.106923i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.96044e15 | − | 7.96044e15i | −0.386507 | − | 0.386507i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.35168e16 | 2.08794 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.60435e16 | −1.23484 | −0.617422 | − | 0.786632i | \(-0.711823\pi\) | ||||
−0.617422 | + | 0.786632i | \(0.711823\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.07620e16 | + | 2.07620e16i | 0.972849 | + | 0.972849i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.84804e16 | + | 2.84804e16i | −1.31885 | + | 1.31885i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.46785e15i | 0.158707i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.91020e16i | − | 1.76861i | −0.466912 | − | 0.884304i | \(-0.654633\pi\) | ||
0.466912 | − | 0.884304i | \(-0.345367\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.98233e16 | − | 2.98233e16i | 1.33320 | − | 1.33320i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.89415e15 | − | 3.89415e15i | −0.172056 | − | 0.172056i | 0.615826 | − | 0.787882i | \(-0.288822\pi\) |
−0.787882 | + | 0.615826i | \(0.788822\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.47760e14 | 0.0108198 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.00627e16 | −0.865993 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.18994e16 | − | 2.18994e16i | −0.934346 | − | 0.934346i | 0.0636279 | − | 0.997974i | \(-0.479733\pi\) |
−0.997974 | + | 0.0636279i | \(0.979733\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.62493e16 | + | 3.62493e16i | −1.52875 | + | 1.52875i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 7.92649e15i | − | 0.330436i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.83361e16i | − | 0.755607i | −0.925886 | − | 0.377803i | \(-0.876680\pi\) | ||
0.925886 | − | 0.377803i | \(-0.123320\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.52843e15 | − | 1.52843e15i | 0.0622626 | − | 0.0622626i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.70881e16 | + | 1.70881e16i | 0.688143 | + | 0.688143i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.30003e15 | 0.330428 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.46431e16 | −0.969877 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.15816e16 | − | 4.15816e16i | −1.61792 | − | 1.61792i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.35470e16 | + | 1.35470e16i | −0.521127 | + | 0.521127i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.02755e16i | − | 1.53178i | −0.642974 | − | 0.765888i | \(-0.722300\pi\) | ||
0.642974 | − | 0.765888i | \(-0.277700\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.83833e15i | 0.294743i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.03111e15 | − | 6.03111e15i | 0.224229 | − | 0.224229i | −0.586048 | − | 0.810276i | \(-0.699317\pi\) |
0.810276 | + | 0.586048i | \(0.199317\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.90070e16 | − | 2.90070e16i | −1.06631 | − | 1.06631i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.69000e16 | −2.06817 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.37405e16 | 1.57204 | 0.786020 | − | 0.618201i | \(-0.212138\pi\) | ||||
0.786020 | + | 0.618201i | \(0.212138\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.27460e16 | + | 1.27460e16i | 0.452968 | + | 0.452968i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.76080e16 | − | 2.76080e16i | 0.970189 | − | 0.970189i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.47204e16i | 1.55404i | 0.629477 | + | 0.777019i | \(0.283269\pi\) | ||||
−0.629477 | + | 0.777019i | \(0.716731\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1.10782e16i | − | 0.380689i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.24270e16 | + | 6.24270e16i | −2.12143 | + | 2.12143i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.36844e14 | + | 4.36844e14i | 0.0146807 | + | 0.0146807i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.29973e15 | 0.209371 | 0.104686 | − | 0.994505i | \(-0.466616\pi\) | ||||
0.104686 | + | 0.994505i | \(0.466616\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.72164e16 | −2.53798 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.32567e15 | − | 2.32567e15i | −0.0755997 | − | 0.0755997i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.47683e16 | − | 1.47683e16i | 0.474796 | − | 0.474796i | −0.428666 | − | 0.903463i | \(-0.641016\pi\) |
0.903463 | + | 0.428666i | \(0.141016\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 2.26289e16i | − | 0.719537i |
(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 | 128.12.e.b.33.19 | 42 | ||
4.3 | odd | 2 | 128.12.e.a.33.3 | 42 | |||
8.3 | odd | 2 | 64.12.e.a.17.19 | 42 | |||
8.5 | even | 2 | 16.12.e.a.13.4 | yes | 42 | ||
16.3 | odd | 4 | 64.12.e.a.49.19 | 42 | |||
16.5 | even | 4 | inner | 128.12.e.b.97.19 | 42 | ||
16.11 | odd | 4 | 128.12.e.a.97.3 | 42 | |||
16.13 | even | 4 | 16.12.e.a.5.4 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.12.e.a.5.4 | ✓ | 42 | 16.13 | even | 4 | ||
16.12.e.a.13.4 | yes | 42 | 8.5 | even | 2 | ||
64.12.e.a.17.19 | 42 | 8.3 | odd | 2 | |||
64.12.e.a.49.19 | 42 | 16.3 | odd | 4 | |||
128.12.e.a.33.3 | 42 | 4.3 | odd | 2 | |||
128.12.e.a.97.3 | 42 | 16.11 | odd | 4 | |||
128.12.e.b.33.19 | 42 | 1.1 | even | 1 | trivial | ||
128.12.e.b.97.19 | 42 | 16.5 | even | 4 | inner |