Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,22,Mod(49,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.49");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.b (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: | \(209.608008215\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{649})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 325x^{2} + 26244 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 3) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-12.2377i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.49 |
Dual form | 75.22.b.d.49.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1937.96i | − 1.33822i | −0.743162 | − | 0.669112i | \(-0.766675\pi\) | ||||
0.743162 | − | 0.669112i | \(-0.233325\pi\) | |||||||
\(3\) | 59049.0i | 0.577350i | ||||||||
\(4\) | −1.65852e6 | −0.790843 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.14434e8 | 0.772624 | ||||||||
\(7\) | − 4.78205e7i | − 0.0639860i | −0.999488 | − | 0.0319930i | \(-0.989815\pi\) | ||||
0.999488 | − | 0.0319930i | \(-0.0101854\pi\) | |||||||
\(8\) | − 8.50053e8i | − 0.279899i | ||||||||
\(9\) | −3.48678e9 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.60111e11 | 1.86122 | 0.930609 | − | 0.366016i | \(-0.119278\pi\) | ||||
0.930609 | + | 0.366016i | \(0.119278\pi\) | |||||||
\(12\) | − 9.79338e10i | − 0.456593i | ||||||||
\(13\) | − 7.86968e11i | − 1.58326i | −0.611001 | − | 0.791630i | \(-0.709233\pi\) | ||||
0.611001 | − | 0.791630i | \(-0.290767\pi\) | |||||||
\(14\) | −9.26741e10 | −0.0856276 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.12553e12 | −1.16541 | ||||||||
\(17\) | 2.97477e12i | 0.357881i | 0.983860 | + | 0.178941i | \(0.0572670\pi\) | ||||
−0.983860 | + | 0.178941i | \(0.942733\pi\) | |||||||
\(18\) | 6.75723e12i | 0.446075i | ||||||||
\(19\) | 2.99456e13 | 1.12052 | 0.560260 | − | 0.828317i | \(-0.310701\pi\) | ||||
0.560260 | + | 0.828317i | \(0.310701\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82376e12 | 0.0369423 | ||||||||
\(22\) | − 3.10287e14i | − 2.49073i | ||||||||
\(23\) | − 1.91401e14i | − 0.963390i | −0.876339 | − | 0.481695i | \(-0.840021\pi\) | ||||
0.876339 | − | 0.481695i | \(-0.159979\pi\) | |||||||
\(24\) | 5.01948e13 | 0.161600 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.52511e15 | −2.11876 | ||||||||
\(27\) | − 2.05891e14i | − 0.192450i | ||||||||
\(28\) | 7.93112e13i | 0.0506029i | ||||||||
\(29\) | −9.68170e14 | −0.427339 | −0.213670 | − | 0.976906i | \(-0.568542\pi\) | ||||
−0.213670 | + | 0.976906i | \(0.568542\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.80459e15 | 0.614570 | 0.307285 | − | 0.951618i | \(-0.400580\pi\) | ||||
0.307285 | + | 0.951618i | \(0.400580\pi\) | |||||||
\(32\) | 8.15035e15i | 1.27968i | ||||||||
\(33\) | 9.45437e15i | 1.07457i | ||||||||
\(34\) | 5.76496e15 | 0.478925 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.78290e15 | 0.263614 | ||||||||
\(37\) | − 3.05038e16i | − 1.04288i | −0.853287 | − | 0.521441i | \(-0.825395\pi\) | ||||
0.853287 | − | 0.521441i | \(-0.174605\pi\) | |||||||
\(38\) | − 5.80331e16i | − 1.49951i | ||||||||
\(39\) | 4.64697e16 | 0.914095 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.22806e16 | −0.259237 | −0.129618 | − | 0.991564i | \(-0.541375\pi\) | ||||
−0.129618 | + | 0.991564i | \(0.541375\pi\) | |||||||
\(42\) | − 5.47231e15i | − 0.0494371i | ||||||||
\(43\) | 1.63711e17i | 1.15521i | 0.816317 | + | 0.577604i | \(0.196012\pi\) | ||||
−0.816317 | + | 0.577604i | \(0.803988\pi\) | |||||||
\(44\) | −2.65546e17 | −1.47193 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.70927e17 | −1.28923 | ||||||||
\(47\) | − 4.08678e17i | − 1.13332i | −0.823951 | − | 0.566662i | \(-0.808235\pi\) | ||||
0.823951 | − | 0.566662i | \(-0.191765\pi\) | |||||||
\(48\) | − 3.02657e17i | − 0.672850i | ||||||||
\(49\) | 5.56259e17 | 0.995906 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.75657e17 | −0.206623 | ||||||||
\(52\) | 1.30520e18i | 1.25211i | ||||||||
\(53\) | 4.34009e17i | 0.340881i | 0.985368 | + | 0.170440i | \(0.0545190\pi\) | ||||
−0.985368 | + | 0.170440i | \(0.945481\pi\) | |||||||
\(54\) | −3.99008e17 | −0.257541 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.06500e16 | −0.0179096 | ||||||||
\(57\) | 1.76826e18i | 0.646932i | ||||||||
\(58\) | 1.87627e18i | 0.571875i | ||||||||
\(59\) | 5.14341e18 | 1.31010 | 0.655051 | − | 0.755584i | \(-0.272647\pi\) | ||||
0.655051 | + | 0.755584i | \(0.272647\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.98980e18 | 0.357147 | 0.178573 | − | 0.983927i | \(-0.442852\pi\) | ||||
0.178573 | + | 0.983927i | \(0.442852\pi\) | |||||||
\(62\) | − 5.43517e18i | − 0.822432i | ||||||||
\(63\) | 1.66740e17i | 0.0213287i | ||||||||
\(64\) | 5.04601e18 | 0.547089 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.83222e19 | 1.43802 | ||||||||
\(67\) | 1.36361e19i | 0.913913i | 0.889489 | + | 0.456956i | \(0.151060\pi\) | ||||
−0.889489 | + | 0.456956i | \(0.848940\pi\) | |||||||
\(68\) | − 4.93370e18i | − 0.283028i | ||||||||
\(69\) | 1.13020e19 | 0.556213 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.35641e18 | 0.268196 | 0.134098 | − | 0.990968i | \(-0.457186\pi\) | ||||
0.134098 | + | 0.990968i | \(0.457186\pi\) | |||||||
\(72\) | 2.96395e18i | 0.0932996i | ||||||||
\(73\) | 6.81650e19i | 1.85640i | 0.372081 | + | 0.928200i | \(0.378644\pi\) | ||||
−0.372081 | + | 0.928200i | \(0.621356\pi\) | |||||||
\(74\) | −5.91149e19 | −1.39561 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.96652e19 | −0.886155 | ||||||||
\(77\) | − 7.65658e18i | − 0.119092i | ||||||||
\(78\) | − 9.00562e19i | − 1.22326i | ||||||||
\(79\) | 2.12282e19 | 0.252249 | 0.126124 | − | 0.992014i | \(-0.459746\pi\) | ||||
0.126124 | + | 0.992014i | \(0.459746\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 4.31789e19i | 0.346917i | ||||||||
\(83\) | 1.10803e20i | 0.783849i | 0.919997 | + | 0.391924i | \(0.128191\pi\) | ||||
−0.919997 | + | 0.391924i | \(0.871809\pi\) | |||||||
\(84\) | −4.68325e18 | −0.0292156 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.17266e20 | 1.54593 | ||||||||
\(87\) | − 5.71695e19i | − 0.246724i | ||||||||
\(88\) | − 1.36102e20i | − 0.520952i | ||||||||
\(89\) | 7.67205e18 | 0.0260805 | 0.0130403 | − | 0.999915i | \(-0.495849\pi\) | ||||
0.0130403 | + | 0.999915i | \(0.495849\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.76333e19 | −0.101306 | ||||||||
\(92\) | 3.17442e20i | 0.761890i | ||||||||
\(93\) | 1.65608e20i | 0.354822i | ||||||||
\(94\) | −7.92000e20 | −1.51664 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.81270e20 | −0.738824 | ||||||||
\(97\) | − 4.63755e20i | − 0.638535i | −0.947665 | − | 0.319268i | \(-0.896563\pi\) | ||||
0.947665 | − | 0.319268i | \(-0.103437\pi\) | |||||||
\(98\) | − 1.07801e21i | − 1.33274i | ||||||||
\(99\) | −5.58271e20 | −0.620406 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.75642e20 | 0.158217 | 0.0791086 | − | 0.996866i | \(-0.474793\pi\) | ||||
0.0791086 | + | 0.996866i | \(0.474793\pi\) | |||||||
\(102\) | 3.40415e20i | 0.276508i | ||||||||
\(103\) | − 1.29018e21i | − 0.945933i | −0.881080 | − | 0.472967i | \(-0.843183\pi\) | ||||
0.881080 | − | 0.472967i | \(-0.156817\pi\) | |||||||
\(104\) | −6.68965e20 | −0.443152 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.41091e20 | 0.456175 | ||||||||
\(107\) | − 5.76913e19i | − 0.0283518i | −0.999900 | − | 0.0141759i | \(-0.995488\pi\) | ||||
0.999900 | − | 0.0141759i | \(-0.00451248\pi\) | |||||||
\(108\) | 3.41474e20i | 0.152198i | ||||||||
\(109\) | 5.74941e20 | 0.232619 | 0.116309 | − | 0.993213i | \(-0.462894\pi\) | ||||
0.116309 | + | 0.993213i | \(0.462894\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.80122e21 | 0.602109 | ||||||||
\(112\) | 2.45106e20i | 0.0745700i | ||||||||
\(113\) | − 4.56755e21i | − 1.26578i | −0.774240 | − | 0.632892i | \(-0.781868\pi\) | ||||
0.774240 | − | 0.632892i | \(-0.218132\pi\) | |||||||
\(114\) | 3.42680e21 | 0.865740 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.60573e21 | 0.337958 | ||||||||
\(117\) | 2.74399e21i | 0.527753i | ||||||||
\(118\) | − 9.96770e21i | − 1.75321i | ||||||||
\(119\) | 1.42255e20 | 0.0228994 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.82352e22 | 2.46413 | ||||||||
\(122\) | − 3.85615e21i | − 0.477942i | ||||||||
\(123\) | − 1.31565e21i | − 0.149671i | ||||||||
\(124\) | −4.65146e21 | −0.486028 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.23134e20 | 0.0285425 | ||||||||
\(127\) | − 1.84938e22i | − 1.50344i | −0.659480 | − | 0.751722i | \(-0.729224\pi\) | ||||
0.659480 | − | 0.751722i | \(-0.270776\pi\) | |||||||
\(128\) | 7.31359e21i | 0.547553i | ||||||||
\(129\) | −9.66700e21 | −0.666960 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.25296e22 | −0.735509 | −0.367754 | − | 0.929923i | \(-0.619873\pi\) | ||||
−0.367754 | + | 0.929923i | \(0.619873\pi\) | |||||||
\(132\) | − 1.56802e22i | − 0.849820i | ||||||||
\(133\) | − 1.43201e21i | − 0.0716976i | ||||||||
\(134\) | 2.64261e22 | 1.22302 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.52871e21 | 0.100171 | ||||||||
\(137\) | − 3.84075e22i | − 1.40880i | −0.709801 | − | 0.704402i | \(-0.751215\pi\) | ||||
0.709801 | − | 0.704402i | \(-0.248785\pi\) | |||||||
\(138\) | − 2.19028e22i | − 0.744338i | ||||||||
\(139\) | 9.58856e21 | 0.302063 | 0.151032 | − | 0.988529i | \(-0.451740\pi\) | ||||
0.151032 | + | 0.988529i | \(0.451740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.41320e22 | 0.654324 | ||||||||
\(142\) | − 1.42564e22i | − 0.358907i | ||||||||
\(143\) | − 1.26002e23i | − 2.94679i | ||||||||
\(144\) | 1.78716e22 | 0.388470 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.32101e23 | 2.48428 | ||||||||
\(147\) | 3.28465e22i | 0.574986i | ||||||||
\(148\) | 5.05911e22i | 0.824757i | ||||||||
\(149\) | −3.44428e22 | −0.523170 | −0.261585 | − | 0.965180i | \(-0.584245\pi\) | ||||
−0.261585 | + | 0.965180i | \(0.584245\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.63152e22 | −0.479546 | −0.239773 | − | 0.970829i | \(-0.577073\pi\) | ||||
−0.239773 | + | 0.970829i | \(0.577073\pi\) | |||||||
\(152\) | − 2.54553e22i | − 0.313632i | ||||||||
\(153\) | − 1.03724e22i | − 0.119294i | ||||||||
\(154\) | −1.48381e22 | −0.159372 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.70708e22 | −0.722906 | ||||||||
\(157\) | 9.41986e22i | 0.826225i | 0.910680 | + | 0.413112i | \(0.135558\pi\) | ||||
−0.910680 | + | 0.413112i | \(0.864442\pi\) | |||||||
\(158\) | − 4.11393e22i | − 0.337565i | ||||||||
\(159\) | −2.56278e22 | −0.196808 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.15290e21 | −0.0616435 | ||||||||
\(162\) | − 2.35610e22i | − 0.148692i | ||||||||
\(163\) | − 1.80771e23i | − 1.06945i | −0.845027 | − | 0.534723i | \(-0.820416\pi\) | ||||
0.845027 | − | 0.534723i | \(-0.179584\pi\) | |||||||
\(164\) | 3.69528e22 | 0.205016 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.14732e23 | 1.04897 | ||||||||
\(167\) | − 3.71934e22i | − 0.170586i | −0.996356 | − | 0.0852929i | \(-0.972817\pi\) | ||||
0.996356 | − | 0.0852929i | \(-0.0271826\pi\) | |||||||
\(168\) | − 2.40034e21i | − 0.0103401i | ||||||||
\(169\) | −3.72255e23 | −1.50671 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.04414e23 | −0.373507 | ||||||||
\(172\) | − 2.71518e23i | − 0.913589i | ||||||||
\(173\) | 2.58398e23i | 0.818096i | 0.912513 | + | 0.409048i | \(0.134139\pi\) | ||||
−0.912513 | + | 0.409048i | \(0.865861\pi\) | |||||||
\(174\) | −1.10792e23 | −0.330172 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.20652e23 | −2.16908 | ||||||||
\(177\) | 3.03713e23i | 0.756388i | ||||||||
\(178\) | − 1.48681e22i | − 0.0349016i | ||||||||
\(179\) | 3.35184e23 | 0.741868 | 0.370934 | − | 0.928659i | \(-0.379038\pi\) | ||||
0.370934 | + | 0.928659i | \(0.379038\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.92267e23 | −0.378687 | −0.189343 | − | 0.981911i | \(-0.560636\pi\) | ||||
−0.189343 | + | 0.981911i | \(0.560636\pi\) | |||||||
\(182\) | 7.29316e22i | 0.135571i | ||||||||
\(183\) | 1.17496e23i | 0.206199i | ||||||||
\(184\) | −1.62701e23 | −0.269652 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.20941e23 | 0.474831 | ||||||||
\(187\) | 4.76292e23i | 0.666095i | ||||||||
\(188\) | 6.77800e23i | 0.896281i | ||||||||
\(189\) | −9.84583e21 | −0.0123141 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.60821e23 | −0.516038 | −0.258019 | − | 0.966140i | \(-0.583070\pi\) | ||||
−0.258019 | + | 0.966140i | \(0.583070\pi\) | |||||||
\(192\) | 2.97962e23i | 0.315862i | ||||||||
\(193\) | 1.29600e24i | 1.30093i | 0.759536 | + | 0.650465i | \(0.225426\pi\) | ||||
−0.759536 | + | 0.650465i | \(0.774574\pi\) | |||||||
\(194\) | −8.98736e23 | −0.854503 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.22566e23 | −0.787605 | ||||||||
\(197\) | − 2.05711e24i | − 1.66480i | −0.554172 | − | 0.832402i | \(-0.686965\pi\) | ||||
0.554172 | − | 0.832402i | \(-0.313035\pi\) | |||||||
\(198\) | 1.08190e24i | 0.830242i | ||||||||
\(199\) | −5.34557e22 | −0.0389078 | −0.0194539 | − | 0.999811i | \(-0.506193\pi\) | ||||
−0.0194539 | + | 0.999811i | \(0.506193\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.05198e23 | −0.527648 | ||||||||
\(202\) | − 3.40386e23i | − 0.211730i | ||||||||
\(203\) | 4.62984e22i | 0.0273437i | ||||||||
\(204\) | 2.91330e23 | 0.163406 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.50032e24 | −1.26587 | ||||||||
\(207\) | 6.67374e23i | 0.321130i | ||||||||
\(208\) | 4.03363e24i | 1.84515i | ||||||||
\(209\) | 4.79460e24 | 2.08553 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.16142e24 | −1.24427 | −0.622137 | − | 0.782908i | \(-0.713735\pi\) | ||||
−0.622137 | + | 0.782908i | \(0.713735\pi\) | |||||||
\(212\) | − 7.19813e23i | − 0.269583i | ||||||||
\(213\) | 4.34388e23i | 0.154843i | ||||||||
\(214\) | −1.11803e23 | −0.0379410 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.75018e23 | −0.0538665 | ||||||||
\(217\) | − 1.34117e23i | − 0.0393239i | ||||||||
\(218\) | − 1.11421e24i | − 0.311296i | ||||||||
\(219\) | −4.02508e24 | −1.07179 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.34105e24 | 0.566619 | ||||||||
\(222\) | − 3.49068e24i | − 0.805756i | ||||||||
\(223\) | − 3.10623e24i | − 0.683963i | −0.939707 | − | 0.341981i | \(-0.888902\pi\) | ||||
0.939707 | − | 0.341981i | \(-0.111098\pi\) | |||||||
\(224\) | 3.89754e23 | 0.0818817 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.85171e24 | −1.69390 | ||||||||
\(227\) | 2.04882e24i | 0.374310i | 0.982330 | + | 0.187155i | \(0.0599267\pi\) | ||||
−0.982330 | + | 0.187155i | \(0.940073\pi\) | |||||||
\(228\) | − 2.93268e24i | − 0.511622i | ||||||||
\(229\) | −4.12622e24 | −0.687512 | −0.343756 | − | 0.939059i | \(-0.611699\pi\) | ||||
−0.343756 | + | 0.939059i | \(0.611699\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.52113e23 | 0.0687577 | ||||||||
\(232\) | 8.22995e23i | 0.119612i | ||||||||
\(233\) | 3.43270e24i | 0.476869i | 0.971159 | + | 0.238434i | \(0.0766342\pi\) | ||||
−0.971159 | + | 0.238434i | \(0.923366\pi\) | |||||||
\(234\) | 5.31773e24 | 0.706252 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.53044e24 | −1.03609 | ||||||||
\(237\) | 1.25351e24i | 0.145636i | ||||||||
\(238\) | − 2.75684e23i | − 0.0306445i | ||||||||
\(239\) | −8.29149e24 | −0.881972 | −0.440986 | − | 0.897514i | \(-0.645371\pi\) | ||||
−0.440986 | + | 0.897514i | \(0.645371\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.30526e25 | −1.27209 | −0.636045 | − | 0.771652i | \(-0.719431\pi\) | ||||
−0.636045 | + | 0.771652i | \(0.719431\pi\) | |||||||
\(242\) | − 3.53389e25i | − 3.29756i | ||||||||
\(243\) | 7.17898e23i | 0.0641500i | ||||||||
\(244\) | −3.30012e24 | −0.282447 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.54967e24 | −0.200293 | ||||||||
\(247\) | − 2.35662e25i | − 1.77407i | ||||||||
\(248\) | − 2.38405e24i | − 0.172017i | ||||||||
\(249\) | −6.54282e24 | −0.452555 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.77630e25 | −1.12965 | −0.564823 | − | 0.825212i | \(-0.691056\pi\) | ||||
−0.564823 | + | 0.825212i | \(0.691056\pi\) | |||||||
\(252\) | − 2.76541e23i | − 0.0168676i | ||||||||
\(253\) | − 3.06453e25i | − 1.79308i | ||||||||
\(254\) | −3.58402e25 | −2.01194 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.47557e25 | 1.27984 | ||||||||
\(257\) | 5.70058e24i | 0.282893i | 0.989946 | + | 0.141446i | \(0.0451752\pi\) | ||||
−0.989946 | + | 0.141446i | \(0.954825\pi\) | |||||||
\(258\) | 1.87342e25i | 0.892542i | ||||||||
\(259\) | −1.45871e24 | −0.0667299 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.37580e24 | 0.142446 | ||||||||
\(262\) | 2.42818e25i | 0.984275i | ||||||||
\(263\) | 9.73572e23i | 0.0379169i | 0.999820 | + | 0.0189584i | \(0.00603502\pi\) | ||||
−0.999820 | + | 0.0189584i | \(0.993965\pi\) | |||||||
\(264\) | 8.03672e24 | 0.300772 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.77518e24 | −0.0959474 | ||||||||
\(267\) | 4.53027e23i | 0.0150576i | ||||||||
\(268\) | − 2.26157e25i | − 0.722761i | ||||||||
\(269\) | 5.78587e25 | 1.77816 | 0.889078 | − | 0.457756i | \(-0.151347\pi\) | ||||
0.889078 | + | 0.457756i | \(0.151347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.29033e25 | 1.21987 | 0.609934 | − | 0.792452i | \(-0.291196\pi\) | ||||
0.609934 | + | 0.792452i | \(0.291196\pi\) | |||||||
\(272\) | − 1.52473e25i | − 0.417079i | ||||||||
\(273\) | − 2.22221e24i | − 0.0584893i | ||||||||
\(274\) | −7.44321e25 | −1.88530 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.87446e25 | −0.439877 | ||||||||
\(277\) | − 6.39000e25i | − 1.44366i | −0.692073 | − | 0.721828i | \(-0.743302\pi\) | ||||
0.692073 | − | 0.721828i | \(-0.256698\pi\) | |||||||
\(278\) | − 1.85822e25i | − 0.404228i | ||||||||
\(279\) | −9.77899e24 | −0.204857 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.23104e25 | 0.627951 | 0.313976 | − | 0.949431i | \(-0.398339\pi\) | ||||
0.313976 | + | 0.949431i | \(0.398339\pi\) | |||||||
\(282\) | − 4.67668e25i | − 0.875632i | ||||||||
\(283\) | − 1.00627e25i | − 0.181534i | −0.995872 | − | 0.0907668i | \(-0.971068\pi\) | ||||
0.995872 | − | 0.0907668i | \(-0.0289318\pi\) | |||||||
\(284\) | −1.22007e25 | −0.212101 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.44186e26 | −3.94346 | ||||||||
\(287\) | 1.06547e24i | 0.0165875i | ||||||||
\(288\) | − 2.84185e25i | − 0.426560i | ||||||||
\(289\) | 6.02427e25 | 0.871921 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.73842e25 | 0.368659 | ||||||||
\(292\) | − 1.13053e26i | − 1.46812i | ||||||||
\(293\) | 4.93011e25i | 0.617656i | 0.951118 | + | 0.308828i | \(0.0999367\pi\) | ||||
−0.951118 | + | 0.308828i | \(0.900063\pi\) | |||||||
\(294\) | 6.36551e25 | 0.769461 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.59298e25 | −0.291902 | ||||||||
\(297\) | − 3.29654e25i | − 0.358191i | ||||||||
\(298\) | 6.67487e25i | 0.700119i | ||||||||
\(299\) | −1.50627e26 | −1.52530 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.82877e24 | 0.0739172 | ||||||||
\(302\) | 7.03772e25i | 0.641740i | ||||||||
\(303\) | 1.03715e25i | 0.0913467i | ||||||||
\(304\) | −1.53487e26 | −1.30587 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.01012e25 | −0.159642 | ||||||||
\(307\) | 1.49828e25i | 0.114985i | 0.998346 | + | 0.0574925i | \(0.0183105\pi\) | ||||
−0.998346 | + | 0.0574925i | \(0.981689\pi\) | |||||||
\(308\) | 1.26986e25i | 0.0941830i | ||||||||
\(309\) | 7.61840e25 | 0.546135 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.48794e26 | −0.996786 | −0.498393 | − | 0.866951i | \(-0.666076\pi\) | ||||
−0.498393 | + | 0.866951i | \(0.666076\pi\) | |||||||
\(312\) | − 3.95017e25i | − 0.255854i | ||||||||
\(313\) | − 1.10961e26i | − 0.694951i | −0.937689 | − | 0.347476i | \(-0.887039\pi\) | ||||
0.937689 | − | 0.347476i | \(-0.112961\pi\) | |||||||
\(314\) | 1.82553e26 | 1.10567 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.52074e25 | −0.199489 | ||||||||
\(317\) | − 7.14805e25i | − 0.391801i | −0.980624 | − | 0.195900i | \(-0.937237\pi\) | ||||
0.980624 | − | 0.195900i | \(-0.0627629\pi\) | |||||||
\(318\) | 4.96656e25i | 0.263373i | ||||||||
\(319\) | −1.55014e26 | −0.795371 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.40661e24 | 0.0163689 | ||||||||
\(322\) | 1.77379e25i | 0.0824928i | ||||||||
\(323\) | 8.90810e25i | 0.401013i | ||||||||
\(324\) | −2.01637e25 | −0.0878715 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.50326e26 | −1.43116 | ||||||||
\(327\) | 3.39497e25i | 0.134302i | ||||||||
\(328\) | 1.89397e25i | 0.0725601i | ||||||||
\(329\) | −1.95432e25 | −0.0725168 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.05668e26 | −1.76065 | −0.880323 | − | 0.474375i | \(-0.842674\pi\) | ||||
−0.880323 | + | 0.474375i | \(0.842674\pi\) | |||||||
\(332\) | − 1.83769e26i | − 0.619901i | ||||||||
\(333\) | 1.06360e26i | 0.347628i | ||||||||
\(334\) | −7.20791e25 | −0.228282 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.44732e25 | −0.0430530 | ||||||||
\(337\) | − 3.50546e26i | − 1.01072i | −0.862909 | − | 0.505360i | \(-0.831360\pi\) | ||||
0.862909 | − | 0.505360i | \(-0.168640\pi\) | |||||||
\(338\) | 7.21413e26i | 2.01632i | ||||||||
\(339\) | 2.69709e26 | 0.730801 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.49044e26 | 1.14385 | ||||||||
\(342\) | 2.02349e26i | 0.499835i | ||||||||
\(343\) | − 5.33106e25i | − 0.127710i | ||||||||
\(344\) | 1.39163e26 | 0.323341 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.00763e26 | 1.09480 | ||||||||
\(347\) | 3.51664e26i | 0.745879i | 0.927856 | + | 0.372940i | \(0.121650\pi\) | ||||
−0.927856 | + | 0.372940i | \(0.878350\pi\) | |||||||
\(348\) | 9.48166e25i | 0.195120i | ||||||||
\(349\) | −5.74285e26 | −1.14673 | −0.573364 | − | 0.819300i | \(-0.694362\pi\) | ||||
−0.573364 | + | 0.819300i | \(0.694362\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.62030e26 | −0.304698 | ||||||||
\(352\) | 1.30496e27i | 2.38176i | ||||||||
\(353\) | 1.85373e25i | 0.0328406i | 0.999865 | + | 0.0164203i | \(0.00522698\pi\) | ||||
−0.999865 | + | 0.0164203i | \(0.994773\pi\) | |||||||
\(354\) | 5.88583e26 | 1.01222 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.27242e25 | −0.0206256 | ||||||||
\(357\) | 8.40001e24i | 0.0132210i | ||||||||
\(358\) | − 6.49572e26i | − 0.992785i | ||||||||
\(359\) | 3.41606e26 | 0.507030 | 0.253515 | − | 0.967331i | \(-0.418413\pi\) | ||||
0.253515 | + | 0.967331i | \(0.418413\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.82527e26 | 0.255565 | ||||||||
\(362\) | 3.72605e26i | 0.506768i | ||||||||
\(363\) | 1.07677e27i | 1.42267i | ||||||||
\(364\) | 6.24154e25 | 0.0801175 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.27702e26 | 0.275940 | ||||||||
\(367\) | − 5.79162e26i | − 0.682034i | −0.940057 | − | 0.341017i | \(-0.889229\pi\) | ||||
0.940057 | − | 0.341017i | \(-0.110771\pi\) | |||||||
\(368\) | 9.81031e26i | 1.12274i | ||||||||
\(369\) | 7.76878e25 | 0.0864123 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.07546e25 | 0.0218116 | ||||||||
\(372\) | − 2.74664e26i | − 0.280609i | ||||||||
\(373\) | − 1.74513e27i | − 1.73335i | −0.498877 | − | 0.866673i | \(-0.666254\pi\) | ||||
0.498877 | − | 0.866673i | \(-0.333746\pi\) | |||||||
\(374\) | 9.23032e26 | 0.891384 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.47398e26 | −0.317216 | ||||||||
\(377\) | 7.61919e26i | 0.676588i | ||||||||
\(378\) | 1.90808e25i | 0.0164790i | ||||||||
\(379\) | −1.08818e27 | −0.914093 | −0.457046 | − | 0.889443i | \(-0.651093\pi\) | ||||
−0.457046 | + | 0.889443i | \(0.651093\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.09204e27 | 0.868014 | ||||||||
\(382\) | 8.93050e26i | 0.690575i | ||||||||
\(383\) | − 2.35974e27i | − 1.77532i | −0.460498 | − | 0.887661i | \(-0.652329\pi\) | ||||
0.460498 | − | 0.887661i | \(-0.347671\pi\) | |||||||
\(384\) | −4.31860e26 | −0.316130 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.51159e27 | 1.74094 | ||||||||
\(387\) | − 5.70827e26i | − 0.385070i | ||||||||
\(388\) | 7.69145e26i | 0.504981i | ||||||||
\(389\) | 2.72162e27 | 1.73923 | 0.869616 | − | 0.493729i | \(-0.164367\pi\) | ||||
0.869616 | + | 0.493729i | \(0.164367\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.69373e26 | 0.344779 | ||||||||
\(392\) | − 4.72850e26i | − 0.278753i | ||||||||
\(393\) | − 7.39859e26i | − 0.424646i | ||||||||
\(394\) | −3.98660e27 | −2.22788 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.25903e26 | 0.490644 | ||||||||
\(397\) | 2.20086e27i | 1.13577i | 0.823106 | + | 0.567887i | \(0.192239\pi\) | ||||
−0.823106 | + | 0.567887i | \(0.807761\pi\) | |||||||
\(398\) | 1.03595e26i | 0.0520673i | ||||||||
\(399\) | 8.45589e25 | 0.0413946 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.61699e27 | 1.21559 | 0.607793 | − | 0.794096i | \(-0.292055\pi\) | ||||
0.607793 | + | 0.794096i | \(0.292055\pi\) | |||||||
\(402\) | 1.56044e27i | 0.706111i | ||||||||
\(403\) | − 2.20712e27i | − 0.973023i | ||||||||
\(404\) | −2.91305e26 | −0.125125 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.97242e25 | 0.0365920 | ||||||||
\(407\) | − 4.88398e27i | − 1.94103i | ||||||||
\(408\) | 1.49318e26i | 0.0578335i | ||||||||
\(409\) | 8.92474e26 | 0.336900 | 0.168450 | − | 0.985710i | \(-0.446124\pi\) | ||||
0.168450 | + | 0.985710i | \(0.446124\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.26793e27 | 0.813373 | ||||||||
\(412\) | 2.13979e27i | 0.748085i | ||||||||
\(413\) | − 2.45961e26i | − 0.0838282i | ||||||||
\(414\) | 1.29334e27 | 0.429744 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.41407e27 | 2.02607 | ||||||||
\(417\) | 5.66195e26i | 0.174396i | ||||||||
\(418\) | − 9.29172e27i | − 2.79091i | ||||||||
\(419\) | 2.48238e27 | 0.727144 | 0.363572 | − | 0.931566i | \(-0.381557\pi\) | ||||
0.363572 | + | 0.931566i | \(0.381557\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.09797e27 | 1.14184 | 0.570922 | − | 0.821004i | \(-0.306586\pi\) | ||||
0.570922 | + | 0.821004i | \(0.306586\pi\) | |||||||
\(422\) | 6.12669e27i | 1.66512i | ||||||||
\(423\) | 1.42497e27i | 0.377774i | ||||||||
\(424\) | 3.68931e26 | 0.0954121 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.41825e26 | 0.207215 | ||||||||
\(427\) | − 9.51534e25i | − 0.0228524i | ||||||||
\(428\) | 9.56820e25i | 0.0224218i | ||||||||
\(429\) | 7.44029e27 | 1.70133 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.89793e27 | −1.06660 | −0.533299 | − | 0.845927i | \(-0.679048\pi\) | ||||
−0.533299 | + | 0.845927i | \(0.679048\pi\) | |||||||
\(432\) | 1.05530e27i | 0.224283i | ||||||||
\(433\) | − 2.06118e27i | − 0.427557i | −0.976882 | − | 0.213778i | \(-0.931423\pi\) | ||||
0.976882 | − | 0.213778i | \(-0.0685770\pi\) | |||||||
\(434\) | −2.59913e26 | −0.0526242 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.53549e26 | −0.183965 | ||||||||
\(437\) | − 5.73161e27i | − 1.07950i | ||||||||
\(438\) | 7.80042e27i | 1.43430i | ||||||||
\(439\) | −1.00358e28 | −1.80167 | −0.900835 | − | 0.434161i | \(-0.857045\pi\) | ||||
−0.900835 | + | 0.434161i | \(0.857045\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.93956e27 | −0.331969 | ||||||||
\(442\) | − 4.53684e27i | − 0.758263i | ||||||||
\(443\) | 4.23345e27i | 0.690964i | 0.938425 | + | 0.345482i | \(0.112285\pi\) | ||||
−0.938425 | + | 0.345482i | \(0.887715\pi\) | |||||||
\(444\) | −2.98735e27 | −0.476173 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.01973e27 | −0.915295 | ||||||||
\(447\) | − 2.03382e27i | − 0.302053i | ||||||||
\(448\) | − 2.41303e26i | − 0.0350061i | ||||||||
\(449\) | 6.74432e27 | 0.955766 | 0.477883 | − | 0.878424i | \(-0.341404\pi\) | ||||
0.477883 | + | 0.878424i | \(0.341404\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.56737e27 | −0.482496 | ||||||||
\(452\) | 7.57537e27i | 1.00104i | ||||||||
\(453\) | − 2.14438e27i | − 0.276866i | ||||||||
\(454\) | 3.97052e27 | 0.500911 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.50311e27 | 0.181076 | ||||||||
\(457\) | 1.13821e28i | 1.34000i | 0.742362 | + | 0.669998i | \(0.233705\pi\) | ||||
−0.742362 | + | 0.669998i | \(0.766295\pi\) | |||||||
\(458\) | 7.99644e27i | 0.920045i | ||||||||
\(459\) | 6.12478e26 | 0.0688743 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.24175e27 | 0.670574 | 0.335287 | − | 0.942116i | \(-0.391167\pi\) | ||||
0.335287 | + | 0.942116i | \(0.391167\pi\) | |||||||
\(462\) | − 8.76175e26i | − 0.0920132i | ||||||||
\(463\) | − 2.31855e27i | − 0.238021i | −0.992893 | − | 0.119011i | \(-0.962028\pi\) | ||||
0.992893 | − | 0.119011i | \(-0.0379723\pi\) | |||||||
\(464\) | 4.96238e27 | 0.498025 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.65242e27 | 0.638157 | ||||||||
\(467\) | 9.47846e26i | 0.0889018i | 0.999012 | + | 0.0444509i | \(0.0141538\pi\) | ||||
−0.999012 | + | 0.0444509i | \(0.985846\pi\) | |||||||
\(468\) | − 4.55096e27i | − 0.417370i | ||||||||
\(469\) | 6.52086e26 | 0.0584776 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.56234e27 | −0.477021 | ||||||||
\(472\) | − 4.37217e27i | − 0.366696i | ||||||||
\(473\) | 2.62120e28i | 2.15009i | ||||||||
\(474\) | 2.42924e27 | 0.194893 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.35932e26 | −0.0181098 | ||||||||
\(477\) | − 1.51330e27i | − 0.113627i | ||||||||
\(478\) | 1.60685e28i | 1.18028i | ||||||||
\(479\) | 1.76996e28 | 1.27186 | 0.635932 | − | 0.771745i | \(-0.280616\pi\) | ||||
0.635932 | + | 0.771745i | \(0.280616\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.40055e28 | −1.65115 | ||||||||
\(482\) | 2.52954e28i | 1.70234i | ||||||||
\(483\) | − 5.40470e26i | − 0.0355899i | ||||||||
\(484\) | −3.02434e28 | −1.94874 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.39125e27 | 0.0858471 | ||||||||
\(487\) | − 1.99209e28i | − 1.20297i | −0.798885 | − | 0.601484i | \(-0.794576\pi\) | ||||
0.798885 | − | 0.601484i | \(-0.205424\pi\) | |||||||
\(488\) | − 1.69144e27i | − 0.0999649i | ||||||||
\(489\) | 1.06743e28 | 0.617445 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.71237e27 | −0.316563 | −0.158282 | − | 0.987394i | \(-0.550595\pi\) | ||||
−0.158282 | + | 0.987394i | \(0.550595\pi\) | |||||||
\(492\) | 2.18203e27i | 0.118366i | ||||||||
\(493\) | − 2.88008e27i | − 0.152937i | ||||||||
\(494\) | −4.56702e28 | −2.37411 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.43750e28 | −0.716226 | ||||||||
\(497\) | − 3.51787e26i | − 0.0171608i | ||||||||
\(498\) | 1.26797e28i | 0.605620i | ||||||||
\(499\) | 1.17032e28 | 0.547332 | 0.273666 | − | 0.961825i | \(-0.411764\pi\) | ||||
0.273666 | + | 0.961825i | \(0.411764\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.19623e27 | 0.0984878 | ||||||||
\(502\) | 3.44239e28i | 1.51172i | ||||||||
\(503\) | − 3.15184e28i | − 1.35550i | −0.735292 | − | 0.677750i | \(-0.762955\pi\) | ||||
0.735292 | − | 0.677750i | \(-0.237045\pi\) | |||||||
\(504\) | 1.41738e26 | 0.00596987 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.93893e28 | −2.39954 | ||||||||
\(507\) | − 2.19813e28i | − 0.869899i | ||||||||
\(508\) | 3.06723e28i | 1.18899i | ||||||||
\(509\) | −4.58029e28 | −1.73923 | −0.869613 | − | 0.493733i | \(-0.835632\pi\) | ||||
−0.869613 | + | 0.493733i | \(0.835632\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.25969e27 | 0.118784 | ||||||||
\(512\) | − 3.26377e28i | − 1.16516i | ||||||||
\(513\) | − 6.16552e27i | − 0.215644i | ||||||||
\(514\) | 1.10475e28 | 0.378574 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.60329e28 | 0.527461 | ||||||||
\(517\) | − 6.54337e28i | − 2.10936i | ||||||||
\(518\) | 2.82691e27i | 0.0892996i | ||||||||
\(519\) | −1.52581e28 | −0.472328 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.19044e27 | −0.154315 | −0.0771575 | − | 0.997019i | \(-0.524584\pi\) | ||||
−0.0771575 | + | 0.997019i | \(0.524584\pi\) | |||||||
\(522\) | − 6.54215e27i | − 0.190625i | ||||||||
\(523\) | − 2.08282e27i | − 0.0594817i | −0.999558 | − | 0.0297408i | \(-0.990532\pi\) | ||||
0.999558 | − | 0.0297408i | \(-0.00946820\pi\) | |||||||
\(524\) | 2.07805e28 | 0.581672 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.88674e27 | 0.0507413 | ||||||||
\(527\) | 8.34299e27i | 0.219943i | ||||||||
\(528\) | − 4.84587e28i | − 1.25232i | ||||||||
\(529\) | 2.83724e27 | 0.0718805 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.79340e28 | −0.436701 | ||||||||
\(532\) | 2.37502e27i | 0.0567016i | ||||||||
\(533\) | 1.75342e28i | 0.410439i | ||||||||
\(534\) | 8.77946e26 | 0.0201504 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.15914e28 | 0.255803 | ||||||||
\(537\) | 1.97923e28i | 0.428318i | ||||||||
\(538\) | − 1.12128e29i | − 2.37957i | ||||||||
\(539\) | 8.90630e28 | 1.85360 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.25240e28 | −0.250710 | −0.125355 | − | 0.992112i | \(-0.540007\pi\) | ||||
−0.125355 | + | 0.992112i | \(0.540007\pi\) | |||||||
\(542\) | − 8.31446e28i | − 1.63246i | ||||||||
\(543\) | − 1.13532e28i | − 0.218635i | ||||||||
\(544\) | −2.42454e28 | −0.457974 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.30654e27 | −0.0782718 | ||||||||
\(547\) | − 5.63104e28i | − 1.00397i | −0.864875 | − | 0.501987i | \(-0.832603\pi\) | ||||
0.864875 | − | 0.501987i | \(-0.167397\pi\) | |||||||
\(548\) | 6.36996e28i | 1.11414i | ||||||||
\(549\) | −6.93801e27 | −0.119049 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.89924e28 | −0.478842 | ||||||||
\(552\) | − 9.60733e27i | − 0.155683i | ||||||||
\(553\) | − 1.01514e27i | − 0.0161404i | ||||||||
\(554\) | −1.23835e29 | −1.93193 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.59028e28 | −0.238885 | ||||||||
\(557\) | − 4.80914e28i | − 0.708904i | −0.935074 | − | 0.354452i | \(-0.884667\pi\) | ||||
0.935074 | − | 0.354452i | \(-0.115333\pi\) | |||||||
\(558\) | 1.89513e28i | 0.274144i | ||||||||
\(559\) | 1.28836e29 | 1.82899 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.81246e28 | −0.384570 | ||||||||
\(562\) | − 6.26161e28i | − 0.840339i | ||||||||
\(563\) | − 1.81812e28i | − 0.239488i | −0.992805 | − | 0.119744i | \(-0.961793\pi\) | ||||
0.992805 | − | 0.119744i | \(-0.0382074\pi\) | |||||||
\(564\) | −4.00234e28 | −0.517468 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.95011e28 | −0.242933 | ||||||||
\(567\) | − 5.81386e26i | − 0.00710956i | ||||||||
\(568\) | − 6.25333e27i | − 0.0750679i | ||||||||
\(569\) | −1.75144e28 | −0.206403 | −0.103201 | − | 0.994660i | \(-0.532909\pi\) | ||||
−0.103201 | + | 0.994660i | \(0.532909\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.67794e29 | 1.90589 | 0.952946 | − | 0.303140i | \(-0.0980350\pi\) | ||||
0.952946 | + | 0.303140i | \(0.0980350\pi\) | |||||||
\(572\) | 2.08977e29i | 2.33045i | ||||||||
\(573\) | − 2.72110e28i | − 0.297935i | ||||||||
\(574\) | 2.06484e27 | 0.0221978 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.75943e28 | −0.182363 | ||||||||
\(577\) | − 7.49346e28i | − 0.762669i | −0.924437 | − | 0.381335i | \(-0.875465\pi\) | ||||
0.924437 | − | 0.381335i | \(-0.124535\pi\) | |||||||
\(578\) | − 1.16748e29i | − 1.16683i | ||||||||
\(579\) | −7.65276e28 | −0.751092 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.29867e27 | 0.0501554 | ||||||||
\(582\) | − 5.30694e28i | − 0.493348i | ||||||||
\(583\) | 6.94895e28i | 0.634453i | ||||||||
\(584\) | 5.79439e28 | 0.519604 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.55433e28 | 0.826562 | ||||||||
\(587\) | − 1.69908e29i | − 1.44382i | −0.691985 | − | 0.721912i | \(-0.743264\pi\) | ||||
0.691985 | − | 0.721912i | \(-0.256736\pi\) | |||||||
\(588\) | − 5.44766e28i | − 0.454724i | ||||||||
\(589\) | 8.39849e28 | 0.688638 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.21471e29 | 0.961175 | ||||||||
\(592\) | 1.56348e29i | 1.21539i | ||||||||
\(593\) | − 1.26592e29i | − 0.966787i | −0.875403 | − | 0.483394i | \(-0.839404\pi\) | ||||
0.875403 | − | 0.483394i | \(-0.160596\pi\) | |||||||
\(594\) | −6.38854e28 | −0.479340 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.71241e28 | 0.413746 | ||||||||
\(597\) | − 3.15650e27i | − 0.0224634i | ||||||||
\(598\) | 2.91907e29i | 2.04119i | ||||||||
\(599\) | −1.73983e29 | −1.19544 | −0.597718 | − | 0.801706i | \(-0.703926\pi\) | ||||
−0.597718 | + | 0.801706i | \(0.703926\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.58691e29 | −1.71633 | −0.858164 | − | 0.513376i | \(-0.828395\pi\) | ||||
−0.858164 | + | 0.513376i | \(0.828395\pi\) | |||||||
\(602\) | − 1.51718e28i | − 0.0989178i | ||||||||
\(603\) | − 4.75461e28i | − 0.304638i | ||||||||
\(604\) | 6.02294e28 | 0.379246 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.00994e28 | 0.122242 | ||||||||
\(607\) | 1.61646e29i | 0.966238i | 0.875555 | + | 0.483119i | \(0.160496\pi\) | ||||
−0.875555 | + | 0.483119i | \(0.839504\pi\) | |||||||
\(608\) | 2.44067e29i | 1.43391i | ||||||||
\(609\) | −2.73387e27 | −0.0157869 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.21617e29 | −1.79434 | ||||||||
\(612\) | 1.72028e28i | 0.0943427i | ||||||||
\(613\) | 8.86426e28i | 0.477868i | 0.971036 | + | 0.238934i | \(0.0767979\pi\) | ||||
−0.971036 | + | 0.238934i | \(0.923202\pi\) | |||||||
\(614\) | 2.90361e28 | 0.153876 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.50850e27 | −0.0333337 | ||||||||
\(617\) | 7.14976e28i | 0.359996i | 0.983667 | + | 0.179998i | \(0.0576091\pi\) | ||||
−0.983667 | + | 0.179998i | \(0.942391\pi\) | |||||||
\(618\) | − 1.47641e29i | − 0.730851i | ||||||||
\(619\) | 3.79378e28 | 0.184638 | 0.0923188 | − | 0.995730i | \(-0.470572\pi\) | ||||
0.0923188 | + | 0.995730i | \(0.470572\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.94078e28 | −0.185404 | ||||||||
\(622\) | 2.88356e29i | 1.33392i | ||||||||
\(623\) | − 3.66882e26i | − 0.00166879i | ||||||||
\(624\) | −2.38182e29 | −1.06530 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.15037e29 | −0.930000 | ||||||||
\(627\) | 2.83116e29i | 1.20408i | ||||||||
\(628\) | − 1.56230e29i | − 0.653414i | ||||||||
\(629\) | 9.07416e28 | 0.373228 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.22002e29 | 1.67883 | 0.839415 | − | 0.543491i | \(-0.182898\pi\) | ||||
0.839415 | + | 0.543491i | \(0.182898\pi\) | |||||||
\(632\) | − 1.80451e28i | − 0.0706041i | ||||||||
\(633\) | − 1.86679e29i | − 0.718382i | ||||||||
\(634\) | −1.38526e29 | −0.524317 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.25042e28 | 0.155644 | ||||||||
\(637\) | − 4.37758e29i | − 1.57678i | ||||||||
\(638\) | 3.00411e29i | 1.06438i | ||||||||
\(639\) | −2.56502e28 | −0.0893988 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.45898e29 | −0.829364 | −0.414682 | − | 0.909966i | \(-0.636107\pi\) | ||||
−0.414682 | + | 0.909966i | \(0.636107\pi\) | |||||||
\(642\) | − 6.60186e27i | − 0.0219053i | ||||||||
\(643\) | 3.81795e29i | 1.24628i | 0.782111 | + | 0.623139i | \(0.214143\pi\) | ||||
−0.782111 | + | 0.623139i | \(0.785857\pi\) | |||||||
\(644\) | 1.51803e28 | 0.0487503 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.72635e29 | 0.536646 | ||||||||
\(647\) | 3.01566e29i | 0.922332i | 0.887314 | + | 0.461166i | \(0.152569\pi\) | ||||
−0.887314 | + | 0.461166i | \(0.847431\pi\) | |||||||
\(648\) | − 1.03347e28i | − 0.0310999i | ||||||||
\(649\) | 8.23515e29 | 2.43839 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.91947e27 | 0.0227037 | ||||||||
\(652\) | 2.99812e29i | 0.845764i | ||||||||
\(653\) | 2.27685e29i | 0.632042i | 0.948752 | + | 0.316021i | \(0.102347\pi\) | ||||
−0.948752 | + | 0.316021i | \(0.897653\pi\) | |||||||
\(654\) | 6.57929e28 | 0.179727 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.14200e29 | 0.302117 | ||||||||
\(657\) | − 2.37677e29i | − 0.618800i | ||||||||
\(658\) | 3.78738e28i | 0.0970437i | ||||||||
\(659\) | 4.45804e29 | 1.12421 | 0.562104 | − | 0.827066i | \(-0.309992\pi\) | ||||
0.562104 | + | 0.827066i | \(0.309992\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.54039e29 | 1.10912 | 0.554559 | − | 0.832144i | \(-0.312887\pi\) | ||||
0.554559 | + | 0.832144i | \(0.312887\pi\) | |||||||
\(662\) | 9.79963e29i | 2.35614i | ||||||||
\(663\) | 1.38236e29i | 0.327138i | ||||||||
\(664\) | 9.41886e28 | 0.219398 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.06121e29 | 0.465204 | ||||||||
\(667\) | 1.85309e29i | 0.411694i | ||||||||
\(668\) | 6.16859e28i | 0.134907i | ||||||||
\(669\) | 1.83420e29 | 0.394886 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.18588e29 | 0.664727 | ||||||||
\(672\) | 2.30146e28i | 0.0472744i | ||||||||
\(673\) | 5.05512e28i | 0.102229i | 0.998693 | + | 0.0511144i | \(0.0162773\pi\) | ||||
−0.998693 | + | 0.0511144i | \(0.983723\pi\) | |||||||
\(674\) | −6.79342e29 | −1.35257 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.17391e29 | 1.19157 | ||||||||
\(677\) | 3.44673e29i | 0.654977i | 0.944855 | + | 0.327489i | \(0.106202\pi\) | ||||
−0.944855 | + | 0.327489i | \(0.893798\pi\) | |||||||
\(678\) | − 5.22685e29i | − 0.977975i | ||||||||
\(679\) | −2.21770e28 | −0.0408573 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.20981e29 | −0.216108 | ||||||||
\(682\) | − 8.70228e29i | − 1.53072i | ||||||||
\(683\) | 3.07293e29i | 0.532273i | 0.963935 | + | 0.266137i | \(0.0857472\pi\) | ||||
−0.963935 | + | 0.266137i | \(0.914253\pi\) | |||||||
\(684\) | 1.73172e29 | 0.295385 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.03314e29 | −0.170905 | ||||||||
\(687\) | − 2.43649e29i | − 0.396935i | ||||||||
\(688\) | − 8.39108e29i | − 1.34629i | ||||||||
\(689\) | 3.41552e29 | 0.539703 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.85532e28 | 0.120405 | 0.0602025 | − | 0.998186i | \(-0.480825\pi\) | ||||
0.0602025 | + | 0.998186i | \(0.480825\pi\) | |||||||
\(692\) | − 4.28557e29i | − 0.646986i | ||||||||
\(693\) | 2.66968e28i | 0.0396973i | ||||||||
\(694\) | 6.81509e29 | 0.998153 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.85971e28 | −0.0690578 | ||||||||
\(697\) | − 6.62797e28i | − 0.0927761i | ||||||||
\(698\) | 1.11294e30i | 1.53458i | ||||||||
\(699\) | −2.02698e29 | −0.275320 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.75849e29 | 1.02268 | 0.511338 | − | 0.859380i | \(-0.329150\pi\) | ||||
0.511338 | + | 0.859380i | \(0.329150\pi\) | |||||||
\(702\) | 3.14006e29i | 0.407755i | ||||||||
\(703\) | − 9.13453e29i | − 1.16857i | ||||||||
\(704\) | 8.07920e29 | 1.01825 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.59244e28 | 0.0439481 | ||||||||
\(707\) | − 8.39929e27i | − 0.0101237i | ||||||||
\(708\) | − 5.03714e29i | − 0.598184i | ||||||||
\(709\) | −1.53428e30 | −1.79523 | −0.897613 | − | 0.440785i | \(-0.854700\pi\) | ||||
−0.897613 | + | 0.440785i | \(0.854700\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.40182e28 | −0.0840829 | ||||||||
\(712\) | − 6.52165e27i | − 0.00729991i | ||||||||
\(713\) | − 5.36801e29i | − 0.592070i | ||||||||
\(714\) | 1.62788e28 | 0.0176926 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.55909e29 | −0.586701 | ||||||||
\(717\) | − 4.89604e29i | − 0.509206i | ||||||||
\(718\) | − 6.62017e29i | − 0.678520i | ||||||||
\(719\) | −5.56901e29 | −0.562503 | −0.281252 | − | 0.959634i | \(-0.590750\pi\) | ||||
−0.281252 | + | 0.959634i | \(0.590750\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.16973e28 | −0.0605265 | ||||||||
\(722\) | − 3.53729e29i | − 0.342003i | ||||||||
\(723\) | − 7.70743e29i | − 0.734442i | ||||||||
\(724\) | 3.18879e29 | 0.299482 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.08673e30 | 1.90384 | ||||||||
\(727\) | 1.43096e29i | 0.128681i | 0.997928 | + | 0.0643407i | \(0.0204945\pi\) | ||||
−0.997928 | + | 0.0643407i | \(0.979506\pi\) | |||||||
\(728\) | 3.19902e28i | 0.0283556i | ||||||||
\(729\) | −4.23912e28 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.87003e29 | −0.413428 | ||||||||
\(732\) | − 1.94869e29i | − 0.163071i | ||||||||
\(733\) | − 6.81141e29i | − 0.561882i | −0.959725 | − | 0.280941i | \(-0.909353\pi\) | ||||
0.959725 | − | 0.280941i | \(-0.0906465\pi\) | |||||||
\(734\) | −1.12239e30 | −0.912714 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.55999e30 | 1.23283 | ||||||||
\(737\) | 2.18328e30i | 1.70099i | ||||||||
\(738\) | − 1.50555e29i | − 0.115639i | ||||||||
\(739\) | −2.16993e30 | −1.64315 | −0.821577 | − | 0.570097i | \(-0.806906\pi\) | ||||
−0.821577 | + | 0.570097i | \(0.806906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.39156e30 | 1.02426 | ||||||||
\(742\) | − 4.02214e28i | − 0.0291888i | ||||||||
\(743\) | − 1.40097e29i | − 0.100241i | −0.998743 | − | 0.0501206i | \(-0.984039\pi\) | ||||
0.998743 | − | 0.0501206i | \(-0.0159606\pi\) | |||||||
\(744\) | 1.40776e29 | 0.0993143 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.38199e30 | −2.31960 | ||||||||
\(747\) | − 3.86347e29i | − 0.261283i | ||||||||
\(748\) | − 7.89939e29i | − 0.526777i | ||||||||
\(749\) | −2.75883e27 | −0.00181412 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.06099e29 | 0.515429 | 0.257715 | − | 0.966221i | \(-0.417031\pi\) | ||||
0.257715 | + | 0.966221i | \(0.417031\pi\) | |||||||
\(752\) | 2.09469e30i | 1.32079i | ||||||||
\(753\) | − 1.04889e30i | − 0.652202i | ||||||||
\(754\) | 1.47656e30 | 0.905427 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.63295e28 | 0.00973853 | ||||||||
\(757\) | 1.54959e30i | 0.911401i | 0.890133 | + | 0.455700i | \(0.150611\pi\) | ||||
−0.890133 | + | 0.455700i | \(0.849389\pi\) | |||||||
\(758\) | 2.10885e30i | 1.22326i | ||||||||
\(759\) | 1.80958e30 | 1.03523 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.04061e29 | 0.113559 | 0.0567793 | − | 0.998387i | \(-0.481917\pi\) | ||||
0.0567793 | + | 0.998387i | \(0.481917\pi\) | |||||||
\(762\) | − 2.11633e30i | − 1.16160i | ||||||||
\(763\) | − 2.74940e28i | − 0.0148843i | ||||||||
\(764\) | 7.64280e29 | 0.408105 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.57307e30 | −2.37578 | ||||||||
\(767\) | − 4.04770e30i | − 2.07423i | ||||||||
\(768\) | 1.46180e30i | 0.738915i | ||||||||
\(769\) | −1.27880e30 | −0.637641 | −0.318821 | − | 0.947815i | \(-0.603287\pi\) | ||||
−0.318821 | + | 0.947815i | \(0.603287\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.36614e29 | −0.163328 | ||||||||
\(772\) | − 2.14944e30i | − 1.02883i | ||||||||
\(773\) | 3.43774e30i | 1.62326i | 0.584172 | + | 0.811630i | \(0.301419\pi\) | ||||
−0.584172 | + | 0.811630i | \(0.698581\pi\) | |||||||
\(774\) | −1.10624e30 | −0.515309 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.94216e29 | −0.178725 | ||||||||
\(777\) | − 8.61352e28i | − 0.0385265i | ||||||||
\(778\) | − 5.27439e30i | − 2.32748i | ||||||||
\(779\) | −6.67206e29 | −0.290480 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.17784e30 | 0.499172 | ||||||||
\(782\) | − 1.10342e30i | − 0.461392i | ||||||||
\(783\) | 1.99338e29i | 0.0822414i | ||||||||
\(784\) | −2.85112e30 | −1.16064 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.43381e30 | −0.568271 | ||||||||
\(787\) | − 1.06317e30i | − 0.415784i | −0.978152 | − | 0.207892i | \(-0.933340\pi\) | ||||
0.978152 | − | 0.207892i | \(-0.0666602\pi\) | |||||||
\(788\) | 3.41176e30i | 1.31660i | ||||||||
\(789\) | −5.74885e28 | −0.0218913 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.18423e29 | −0.0809925 | ||||||||
\(792\) | 4.74560e29i | 0.173651i | ||||||||
\(793\) | − 1.56591e30i | − 0.565456i | ||||||||
\(794\) | 4.26517e30 | 1.51992 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.86572e28 | 0.0307699 | ||||||||
\(797\) | 2.59470e30i | 0.888742i | 0.895843 | + | 0.444371i | \(0.146573\pi\) | ||||
−0.895843 | + | 0.444371i | \(0.853427\pi\) | |||||||
\(798\) | − 1.63871e29i | − 0.0553953i | ||||||||
\(799\) | 1.21572e30 | 0.405595 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.67508e28 | −0.00869351 | ||||||||
\(802\) | − 5.07160e30i | − 1.62672i | ||||||||
\(803\) | 1.09139e31i | 3.45516i | ||||||||
\(804\) | 1.33544e30 | 0.417286 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.27730e30 | −1.30212 | ||||||||
\(807\) | 3.41650e30i | 1.02662i | ||||||||
\(808\) | − 1.49305e29i | − 0.0442848i | ||||||||
\(809\) | 4.54632e30 | 1.33107 | 0.665534 | − | 0.746367i | \(-0.268204\pi\) | ||||
0.665534 | + | 0.746367i | \(0.268204\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.33885e30 | −1.52310 | −0.761550 | − | 0.648106i | \(-0.775561\pi\) | ||||
−0.761550 | + | 0.648106i | \(0.775561\pi\) | |||||||
\(812\) | − 7.67867e28i | − 0.0216246i | ||||||||
\(813\) | 2.53339e30i | 0.704291i | ||||||||
\(814\) | −9.46493e30 | −2.59753 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9.00335e29 | 0.240801 | ||||||||
\(817\) | 4.90243e30i | 1.29443i | ||||||||
\(818\) | − 1.72957e30i | − 0.450847i | ||||||||
\(819\) | 1.31219e29 | 0.0337688 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.77652e30 | −1.69982 | −0.849911 | − | 0.526926i | \(-0.823344\pi\) | ||||
−0.849911 | + | 0.526926i | \(0.823344\pi\) | |||||||
\(822\) | − 4.39514e30i | − 1.08848i | ||||||||
\(823\) | 2.32096e30i | 0.567506i | 0.958897 | + | 0.283753i | \(0.0915795\pi\) | ||||
−0.958897 | + | 0.283753i | \(0.908420\pi\) | |||||||
\(824\) | −1.09672e30 | −0.264766 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.76661e29 | −0.112181 | ||||||||
\(827\) | − 3.93890e30i | − 0.915307i | −0.889131 | − | 0.457654i | \(-0.848690\pi\) | ||||
0.889131 | − | 0.457654i | \(-0.151310\pi\) | |||||||
\(828\) | − 1.10685e30i | − 0.253963i | ||||||||
\(829\) | −3.15777e30 | −0.715415 | −0.357708 | − | 0.933834i | \(-0.616442\pi\) | ||||
−0.357708 | + | 0.933834i | \(0.616442\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.77323e30 | 0.833495 | ||||||||
\(832\) | − 3.97105e30i | − 0.866184i | ||||||||
\(833\) | 1.65474e30i | 0.356416i | ||||||||
\(834\) | 1.09726e30 | 0.233381 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.95194e30 | −1.64933 | ||||||||
\(837\) | − 5.77440e29i | − 0.118274i | ||||||||
\(838\) | − 4.81074e30i | − 0.973082i | ||||||||
\(839\) | 1.71221e28 | 0.00342024 | 0.00171012 | − | 0.999999i | \(-0.499456\pi\) | ||||
0.00171012 | + | 0.999999i | \(0.499456\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.19549e30 | −0.817381 | ||||||||
\(842\) | − 7.94168e30i | − 1.52804i | ||||||||
\(843\) | 1.90790e30i | 0.362548i | ||||||||
\(844\) | 5.24327e30 | 0.984026 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.76153e30 | 0.505547 | ||||||||
\(847\) | − 8.72016e29i | − 0.157670i | ||||||||
\(848\) | − 2.22453e30i | − 0.397266i | ||||||||
\(849\) | 5.94193e29 | 0.104809 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.83845e30 | −1.00470 | ||||||||
\(852\) | − 7.20441e29i | − 0.122457i | ||||||||
\(853\) | 2.27930e30i | 0.382680i | 0.981524 | + | 0.191340i | \(0.0612833\pi\) | ||||
−0.981524 | + | 0.191340i | \(0.938717\pi\) | |||||||
\(854\) | −1.84403e29 | −0.0305816 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.90406e28 | −0.00793563 | ||||||||
\(857\) | 1.06629e31i | 1.70441i | 0.523204 | + | 0.852207i | \(0.324737\pi\) | ||||
−0.523204 | + | 0.852207i | \(0.675263\pi\) | |||||||
\(858\) | − 1.44190e31i | − 2.27676i | ||||||||
\(859\) | 8.93547e29 | 0.139376 | 0.0696882 | − | 0.997569i | \(-0.477800\pi\) | ||||
0.0696882 | + | 0.997569i | \(0.477800\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.29150e28 | −0.00957682 | ||||||||
\(862\) | 9.49196e30i | 1.42735i | ||||||||
\(863\) | 2.82417e30i | 0.419543i | 0.977750 | + | 0.209772i | \(0.0672721\pi\) | ||||
−0.977750 | + | 0.209772i | \(0.932728\pi\) | |||||||
\(864\) | 1.67809e30 | 0.246275 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.99448e30 | −0.572167 | ||||||||
\(867\) | 3.55727e30i | 0.503404i | ||||||||
\(868\) | 2.22435e29i | 0.0310990i | ||||||||
\(869\) | 3.39886e30 | 0.469490 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.07312e31 | 1.44696 | ||||||||
\(872\) | − 4.88730e29i | − 0.0651097i | ||||||||
\(873\) | 1.61701e30i | 0.212845i | ||||||||
\(874\) | −1.11076e31 | −1.44461 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.67566e30 | 0.847620 | ||||||||
\(877\) | − 9.06575e30i | − 1.13739i | −0.822550 | − | 0.568693i | \(-0.807449\pi\) | ||||
0.822550 | − | 0.568693i | \(-0.192551\pi\) | |||||||
\(878\) | 1.94490e31i | 2.41104i | ||||||||
\(879\) | −2.91118e30 | −0.356604 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.51630e31 | 1.81359 | 0.906794 | − | 0.421574i | \(-0.138522\pi\) | ||||
0.906794 | + | 0.421574i | \(0.138522\pi\) | |||||||
\(882\) | 3.75877e30i | 0.444248i | ||||||||
\(883\) | − 1.16543e31i | − 1.36113i | −0.732688 | − | 0.680565i | \(-0.761735\pi\) | ||||
0.732688 | − | 0.680565i | \(-0.238265\pi\) | |||||||
\(884\) | −3.88267e30 | −0.448107 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.20424e30 | 0.924664 | ||||||||
\(887\) | 7.76908e30i | 0.865309i | 0.901560 | + | 0.432655i | \(0.142423\pi\) | ||||
−0.901560 | + | 0.432655i | \(0.857577\pi\) | |||||||
\(888\) | − 1.53113e30i | − 0.168529i | ||||||||
\(889\) | −8.84384e29 | −0.0961994 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.94657e30 | 0.206802 | ||||||||
\(892\) | 5.15174e30i | 0.540907i | ||||||||
\(893\) | − 1.22381e31i | − 1.26991i | ||||||||
\(894\) | −3.94144e30 | −0.404214 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.49740e29 | 0.0350357 | ||||||||
\(897\) | − 8.89435e30i | − 0.880630i | ||||||||
\(898\) | − 1.30702e31i | − 1.27903i | ||||||||
\(899\) | −2.71532e30 | −0.262630 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.29108e30 | −0.121995 | ||||||||
\(902\) | 6.91340e30i | 0.645688i | ||||||||
\(903\) | 4.62281e29i | 0.0426761i | ||||||||
\(904\) | −3.88266e30 | −0.354292 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.15570e30 | −0.370509 | ||||||||
\(907\) | − 5.71533e30i | − 0.503692i | −0.967767 | − | 0.251846i | \(-0.918962\pi\) | ||||
0.967767 | − | 0.251846i | \(-0.0810376\pi\) | |||||||
\(908\) | − 3.39800e30i | − 0.296021i | ||||||||
\(909\) | −6.12425e29 | −0.0527390 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.22259e30 | 0.187032 | 0.0935160 | − | 0.995618i | \(-0.470189\pi\) | ||||
0.0935160 | + | 0.995618i | \(0.470189\pi\) | |||||||
\(912\) | − 9.06324e30i | − 0.753942i | ||||||||
\(913\) | 1.77408e31i | 1.45891i | ||||||||
\(914\) | 2.20581e31 | 1.79322 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.84342e30 | 0.543714 | ||||||||
\(917\) | 5.99171e29i | 0.0470623i | ||||||||
\(918\) | − 1.18695e30i | − 0.0921693i | ||||||||
\(919\) | 9.94638e30 | 0.763576 | 0.381788 | − | 0.924250i | \(-0.375308\pi\) | ||||
0.381788 | + | 0.924250i | \(0.375308\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.84722e29 | −0.0663866 | ||||||||
\(922\) | − 1.20962e31i | − 0.897378i | ||||||||
\(923\) | − 5.78926e30i | − 0.424624i | ||||||||
\(924\) | −7.49838e29 | −0.0543766 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.49324e30 | −0.318526 | ||||||||
\(927\) | 4.49859e30i | 0.315311i | ||||||||
\(928\) | − 7.89093e30i | − 0.546858i | ||||||||
\(929\) | −6.57341e30 | −0.450429 | −0.225214 | − | 0.974309i | \(-0.572308\pi\) | ||||
−0.225214 | + | 0.974309i | \(0.572308\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.66575e31 | 1.11593 | ||||||||
\(932\) | − 5.69320e30i | − 0.377128i | ||||||||
\(933\) | − 8.78615e30i | − 0.575495i | ||||||||
\(934\) | 1.83688e30 | 0.118970 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.33254e30 | 0.147717 | ||||||||
\(937\) | 9.88672e30i | 0.619137i | 0.950877 | + | 0.309568i | \(0.100185\pi\) | ||||
−0.950877 | + | 0.309568i | \(0.899815\pi\) | |||||||
\(938\) | − 1.26371e30i | − 0.0782561i | ||||||||
\(939\) | 6.55213e30 | 0.401230 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.35253e31 | 0.809947 | 0.404973 | − | 0.914328i | \(-0.367281\pi\) | ||||
0.404973 | + | 0.914328i | \(0.367281\pi\) | |||||||
\(942\) | 1.07796e31i | 0.638361i | ||||||||
\(943\) | 4.26454e30i | 0.249746i | ||||||||
\(944\) | −2.63627e31 | −1.52681 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.07976e31 | 2.87731 | ||||||||
\(947\) | 2.26830e31i | 1.27065i | 0.772245 | + | 0.635325i | \(0.219134\pi\) | ||||
−0.772245 | + | 0.635325i | \(0.780866\pi\) | |||||||
\(948\) | − 2.07896e30i | − 0.115175i | ||||||||
\(949\) | 5.36437e31 | 2.93916 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.22085e30 | 0.226206 | ||||||||
\(952\) | − 1.20924e29i | − 0.00640952i | ||||||||
\(953\) | 3.45875e31i | 1.81319i | 0.422002 | + | 0.906595i | \(0.361327\pi\) | ||||
−0.422002 | + | 0.906595i | \(0.638673\pi\) | |||||||
\(954\) | −2.93270e30 | −0.152058 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.37516e31 | 0.697501 | ||||||||
\(957\) | − 9.15344e30i | − 0.459207i | ||||||||
\(958\) | − 3.43011e31i | − 1.70204i | ||||||||
\(959\) | −1.83667e30 | −0.0901438 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.29598e31 | −0.622304 | ||||||||
\(962\) | 4.65216e31i | 2.20961i | ||||||||
\(963\) | 2.01157e29i | 0.00945059i | ||||||||
\(964\) | 2.16480e31 | 1.00602 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.04741e30 | −0.0476272 | ||||||||
\(967\) | 1.92820e31i | 0.867311i | 0.901079 | + | 0.433655i | \(0.142776\pi\) | ||||
−0.901079 | + | 0.433655i | \(0.857224\pi\) | |||||||
\(968\) | − 1.55009e31i | − 0.689707i | ||||||||
\(969\) | −5.26015e30 | −0.231525 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.95793e31 | −1.27405 | −0.637024 | − | 0.770844i | \(-0.719835\pi\) | ||||
−0.637024 | + | 0.770844i | \(0.719835\pi\) | |||||||
\(972\) | − 1.19065e30i | − 0.0507326i | ||||||||
\(973\) | − 4.58530e29i | − 0.0193278i | ||||||||
\(974\) | −3.86058e31 | −1.60984 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.01988e31 | −0.416222 | ||||||||
\(977\) | − 4.86581e31i | − 1.96455i | −0.187453 | − | 0.982274i | \(-0.560023\pi\) | ||||
0.187453 | − | 0.982274i | \(-0.439977\pi\) | |||||||
\(978\) | − 2.06864e31i | − 0.826280i | ||||||||
\(979\) | 1.22838e30 | 0.0485415 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00469e30 | −0.0775396 | ||||||||
\(982\) | 1.10703e31i | 0.423633i | ||||||||
\(983\) | 4.31738e31i | 1.63459i | 0.576220 | + | 0.817294i | \(0.304527\pi\) | ||||
−0.576220 | + | 0.817294i | \(0.695473\pi\) | |||||||
\(984\) | −1.11837e30 | −0.0418926 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.58146e30 | −0.204664 | ||||||||
\(987\) | − 1.15401e30i | − 0.0418676i | ||||||||
\(988\) | 3.90850e31i | 1.40301i | ||||||||
\(989\) | 3.13345e31 | 1.11292 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.44591e31 | 1.19820 | 0.599101 | − | 0.800673i | \(-0.295525\pi\) | ||||
0.599101 | + | 0.800673i | \(0.295525\pi\) | |||||||
\(992\) | 2.28584e31i | 0.786453i | ||||||||
\(993\) | − 2.98592e31i | − 1.01651i | ||||||||
\(994\) | −6.81748e29 | −0.0229650 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.08514e31 | 0.357900 | ||||||||
\(997\) | − 3.62353e31i | − 1.18259i | −0.806457 | − | 0.591293i | \(-0.798618\pi\) | ||||
0.806457 | − | 0.591293i | \(-0.201382\pi\) | |||||||
\(998\) | − 2.26804e31i | − 0.732452i | ||||||||
\(999\) | −6.28046e30 | −0.200703 |
(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 | 75.22.b.d.49.1 | 4 | ||
5.2 | odd | 4 | 3.22.a.c.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 75.22.a.d.1.1 | 2 | |||
5.4 | even | 2 | inner | 75.22.b.d.49.4 | 4 | ||
15.2 | even | 4 | 9.22.a.e.1.1 | 2 | |||
20.7 | even | 4 | 48.22.a.g.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.22.a.c.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
9.22.a.e.1.1 | 2 | 15.2 | even | 4 | |||
48.22.a.g.1.2 | 2 | 20.7 | even | 4 | |||
75.22.a.d.1.1 | 2 | 5.3 | odd | 4 | |||
75.22.b.d.49.1 | 4 | 1.1 | even | 1 | trivial | ||
75.22.b.d.49.4 | 4 | 5.4 | even | 2 | inner |