Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,9,Mod(61,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.61");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.m (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(34.2198032451\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 38255 x^{8} + 1483053595 x^{6} - 139470625170 x^{5} + 5194605060018 x^{4} + \cdots + 15\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{8}\cdot 7^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 61.4 | ||
Root | \(-190.225 + 109.826i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.61 |
Dual form | 84.9.m.a.73.4 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −40.5000 | + | 23.3827i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 656.878 | + | 379.249i | 1.05101 | + | 0.606798i | 0.922931 | − | 0.384966i | \(-0.125787\pi\) |
0.128075 | + | 0.991765i | \(0.459120\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1906.96 | − | 1458.87i | 0.794236 | − | 0.607609i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1093.50 | − | 1894.00i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6909.25 | + | 11967.2i | 0.471911 | + | 0.817374i | 0.999483 | − | 0.0321363i | \(-0.0102311\pi\) |
−0.527573 | + | 0.849510i | \(0.676898\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 39984.1i | − | 1.39995i | −0.714165 | − | 0.699977i | \(-0.753194\pi\) | ||
0.714165 | − | 0.699977i | \(-0.246806\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −35471.4 | −0.700670 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 33086.2 | − | 19102.3i | 0.396142 | − | 0.228713i | −0.288676 | − | 0.957427i | \(-0.593215\pi\) |
0.684818 | + | 0.728714i | \(0.259882\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −119061. | − | 68739.9i | −0.913598 | − | 0.527466i | −0.0320110 | − | 0.999488i | \(-0.510191\pi\) |
−0.881587 | + | 0.472021i | \(0.843524\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −43119.7 | + | 103674.i | −0.221717 | + | 0.533081i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −74519.7 | + | 129072.i | −0.266293 | + | 0.461233i | −0.967902 | − | 0.251329i | \(-0.919132\pi\) |
0.701608 | + | 0.712563i | \(0.252466\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 92347.0 | + | 159950.i | 0.236408 | + | 0.409471i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 102276.i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 277619. | 0.392515 | 0.196258 | − | 0.980552i | \(-0.437121\pi\) | ||||
0.196258 | + | 0.980552i | \(0.437121\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.48847e6 | − | 859370.i | 1.61174 | − | 0.930536i | 0.622768 | − | 0.782406i | \(-0.286008\pi\) |
0.988968 | − | 0.148130i | \(-0.0473254\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −559649. | − | 323114.i | −0.471911 | − | 0.272458i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.80592e6 | − | 235086.i | 1.20344 | − | 0.156659i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 235213. | − | 407400.i | 0.125503 | − | 0.217377i | −0.796426 | − | 0.604735i | \(-0.793279\pi\) |
0.921929 | + | 0.387358i | \(0.126612\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 934936. | + | 1.61936e6i | 0.404132 | + | 0.699977i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.24961e6i | 0.796108i | 0.917362 | + | 0.398054i | \(0.130314\pi\) | ||||
−0.917362 | + | 0.398054i | \(0.869686\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.59615e6 | 1.34437 | 0.672187 | − | 0.740381i | \(-0.265355\pi\) | ||||
0.672187 | + | 0.740381i | \(0.265355\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.43659e6 | − | 829417.i | 0.350335 | − | 0.202266i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.14538e6 | + | 1.81598e6i | 0.644586 | + | 0.372152i | 0.786379 | − | 0.617744i | \(-0.211953\pi\) |
−0.141793 | + | 0.989896i | \(0.545287\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50821e6 | − | 5.56401e6i | 0.261623 | − | 0.965170i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −893327. | + | 1.54729e6i | −0.132047 | + | 0.228713i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.54165e6 | − | 4.40227e6i | −0.322116 | − | 0.557921i | 0.658809 | − | 0.752311i | \(-0.271061\pi\) |
−0.980924 | + | 0.194390i | \(0.937727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.04813e7i | 1.14542i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.42929e6 | 0.609065 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.58932e6 | − | 1.49495e6i | 0.213687 | − | 0.123372i | −0.389337 | − | 0.921095i | \(-0.627296\pi\) |
0.603024 | + | 0.797723i | \(0.293962\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.11403e7 | + | 6.43183e6i | 0.804592 | + | 0.464531i | 0.845074 | − | 0.534649i | \(-0.179556\pi\) |
−0.0404824 | + | 0.999180i | \(0.512889\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −677831. | − | 5.20705e6i | −0.0430288 | − | 0.330544i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.51639e7 | − | 2.62647e7i | 0.849490 | − | 1.47136i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −127634. | − | 221068.i | −0.00633382 | − | 0.0109705i | 0.862841 | − | 0.505475i | \(-0.168683\pi\) |
−0.869175 | + | 0.494505i | \(0.835349\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6.96989e6i | − | 0.307489i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.77334e7 | 1.87840 | 0.939201 | − | 0.343367i | \(-0.111567\pi\) | ||||
0.939201 | + | 0.343367i | \(0.111567\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.52724e7 | + | 8.81754e6i | −0.537795 | + | 0.310496i | −0.744185 | − | 0.667974i | \(-0.767162\pi\) |
0.206390 | + | 0.978470i | \(0.433829\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.48010e6 | − | 4.31864e6i | −0.236408 | − | 0.136490i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.06342e7 | + | 1.27412e7i | 0.871452 | + | 0.362451i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.56844e7 | + | 2.71662e7i | −0.402679 | + | 0.697461i | −0.994048 | − | 0.108940i | \(-0.965254\pi\) |
0.591369 | + | 0.806401i | \(0.298588\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.39148e6 | − | 4.14217e6i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.76636e7i | 1.63646i | 0.574892 | + | 0.818229i | \(0.305044\pi\) | ||||
−0.574892 | + | 0.818229i | \(0.694956\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.89781e7 | 0.555130 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.12436e7 | + | 6.49147e6i | −0.196258 | + | 0.113309i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.90230e7 | − | 4.56240e7i | −1.25949 | − | 0.727165i | −0.286512 | − | 0.958077i | \(-0.592496\pi\) |
−0.972975 | + | 0.230912i | \(0.925829\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.83315e7 | − | 7.62481e7i | −0.850624 | − | 1.11189i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.01887e7 | + | 6.96090e7i | −0.537245 | + | 0.930536i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.21391e7 | − | 9.03075e7i | −0.640131 | − | 1.10874i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.05936e7i | 0.232620i | 0.993213 | + | 0.116310i | \(0.0371065\pi\) | ||||
−0.993213 | + | 0.116310i | \(0.962893\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.02210e7 | 0.314607 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.11330e8 | − | 6.42761e7i | 1.06985 | − | 0.617681i | 0.141713 | − | 0.989908i | \(-0.454739\pi\) |
0.928142 | + | 0.372227i | \(0.121406\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.52077e7 | − | 2.03272e7i | −0.312816 | − | 0.180604i | 0.335370 | − | 0.942086i | \(-0.391139\pi\) |
−0.648186 | + | 0.761482i | \(0.724472\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.76427e7 | + | 5.17482e7i | −0.556498 | + | 0.425733i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.32367e7 | + | 9.22087e7i | −0.406140 | + | 0.703456i | −0.994453 | − | 0.105178i | \(-0.966459\pi\) |
0.588313 | + | 0.808633i | \(0.299792\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.80362e7 | − | 3.12396e7i | −0.127773 | − | 0.221309i | 0.795040 | − | 0.606556i | \(-0.207450\pi\) |
−0.922814 | + | 0.385247i | \(0.874116\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.19996e7i | 0.144918i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.06746e8 | −1.26801 | −0.634006 | − | 0.773328i | \(-0.718591\pi\) | ||||
−0.634006 | + | 0.773328i | \(0.718591\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.79008e7 | + | 5.65231e7i | −0.559751 | + | 0.323172i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.57298e7 | − | 4.37226e7i | −0.404132 | − | 0.233326i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.52263e7 | − | 8.46958e7i | 0.175663 | − | 0.422351i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.17041e7 | − | 2.02720e7i | 0.0546003 | − | 0.0945704i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.26019e7 | − | 9.11092e7i | −0.229817 | − | 0.398054i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.56198e8i | − | 0.639788i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.22341e8 | −1.62348 | −0.811742 | − | 0.584017i | \(-0.801480\pi\) | ||||
−0.811742 | + | 0.584017i | \(0.801480\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.86144e8 | + | 1.07470e8i | −0.672187 | + | 0.388088i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.55181e8 | + | 2.62799e8i | 1.54561 | + | 0.892356i | 0.998469 | + | 0.0553133i | \(0.0176158\pi\) |
0.547137 | + | 0.837043i | \(0.315718\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.27327e8 | + | 4.26100e7i | −1.04611 | + | 0.136177i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.87880e7 | + | 6.71828e7i | −0.116778 | + | 0.202266i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.33946e7 | − | 1.09803e8i | −0.179958 | − | 0.311696i | 0.761908 | − | 0.647685i | \(-0.224263\pi\) |
−0.941866 | + | 0.335989i | \(0.890929\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.98228e8i | 1.06678i | 0.845871 | + | 0.533388i | \(0.179081\pi\) | ||||
−0.845871 | + | 0.533388i | \(0.820919\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.69850e8 | −0.429724 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.78496e8 | − | 2.76260e8i | 1.14429 | − | 0.660654i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.82362e8 | + | 1.05287e8i | 0.412536 | + | 0.238178i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.90192e7 | + | 2.60608e8i | 0.147809 | + | 0.558109i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.11857e8 | − | 7.13356e8i | 0.835605 | − | 1.44731i | −0.0579324 | − | 0.998321i | \(-0.518451\pi\) |
0.893537 | − | 0.448989i | \(-0.148216\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.05855e8 | + | 1.83346e8i | 0.203612 | + | 0.352666i | 0.949690 | − | 0.313193i | \(-0.101399\pi\) |
−0.746078 | + | 0.665859i | \(0.768065\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 8.35535e7i | − | 0.152475i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.30366e9 | 2.25859 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.91092e8 | − | 2.83532e8i | 0.808284 | − | 0.466663i | −0.0380754 | − | 0.999275i | \(-0.512123\pi\) |
0.846360 | + | 0.532612i | \(0.178789\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.05874e8 | + | 1.18861e8i | 0.322116 | + | 0.185974i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.61928e7 | + | 3.54850e8i | 0.0687496 | + | 0.528130i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.07796e8 | + | 7.06324e8i | −0.577688 | + | 1.00058i | 0.418056 | + | 0.908421i | \(0.362711\pi\) |
−0.995744 | + | 0.0921631i | \(0.970622\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.45081e8 | − | 4.24493e8i | −0.330654 | − | 0.572709i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.06089e9i | − | 1.36397i | −0.731366 | − | 0.681985i | \(-0.761117\pi\) | ||
0.731366 | − | 0.681985i | \(-0.238883\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.82997e8 | −0.959872 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.60386e8 | + | 1.50334e8i | −0.304533 | + | 0.175822i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.06239e8 | + | 4.07747e8i | 0.788437 | + | 0.455204i | 0.839412 | − | 0.543496i | \(-0.182900\pi\) |
−0.0509750 | + | 0.998700i | \(0.516233\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.09448e8 | + | 1.70296e8i | 0.436562 | + | 0.181573i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.99117e7 | + | 1.21091e8i | −0.0712290 | + | 0.123372i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.06736e8 | − | 1.84873e8i | −0.103968 | − | 0.180078i | 0.809348 | − | 0.587329i | \(-0.199821\pi\) |
−0.913316 | + | 0.407251i | \(0.866487\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.38533e8i | − | 0.688107i | −0.938950 | − | 0.344053i | \(-0.888200\pi\) | ||
0.938950 | − | 0.344053i | \(-0.111800\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.01574e8 | −0.536395 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.09012e8 | − | 1.78408e8i | 0.263809 | − | 0.152310i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.57201e8 | + | 2.63965e8i | 0.373888 | + | 0.215864i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.49207e8 | + | 1.95036e8i | 0.116934 | + | 0.152851i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.52734e8 | + | 2.64542e8i | −0.114763 | + | 0.198775i | −0.917685 | − | 0.397309i | \(-0.869944\pi\) |
0.802922 | + | 0.596084i | \(0.203277\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.32710e8 | + | 4.03065e8i | 0.167720 | + | 0.290500i | 0.937618 | − | 0.347667i | \(-0.113026\pi\) |
−0.769898 | + | 0.638167i | \(0.779693\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.41829e9i | 0.980906i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.82661e9 | 1.21278 | 0.606389 | − | 0.795168i | \(-0.292617\pi\) | ||||
0.606389 | + | 0.795168i | \(0.292617\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.53528e9 | − | 1.46374e9i | 1.61664 | − | 0.933367i | 0.628857 | − | 0.777521i | \(-0.283523\pi\) |
0.987781 | − | 0.155846i | \(-0.0498104\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.03383e7 | + | 5.96883e6i | 0.00633382 | + | 0.00365683i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.29408e8 | − | 4.05009e8i | 0.311750 | − | 0.238496i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.53162e8 | + | 1.47772e9i | −0.483077 | + | 0.836714i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.62975e8 | + | 2.82280e8i | 0.0887644 | + | 0.153744i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.89976e9i | − | 0.995668i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.28912e9 | −1.15489 | −0.577443 | − | 0.816431i | \(-0.695949\pi\) | ||||
−0.577443 | + | 0.816431i | \(0.695949\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.93320e9 | + | 1.11613e9i | −0.939201 | + | 0.542248i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.01911e9 | + | 1.74308e9i | 1.41294 | + | 0.815764i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.58475e9 | − | 3.81027e9i | 0.714698 | − | 1.71837i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.12356e8 | − | 7.14221e8i | 0.179265 | − | 0.310496i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.63789e8 | − | 1.32292e9i | −0.320187 | − | 0.554581i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.31777e9i | 0.937241i | 0.883400 | + | 0.468620i | \(0.155249\pi\) | ||||
−0.883400 | + | 0.468620i | \(0.844751\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.03926e8 | 0.157605 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.32328e9 | + | 1.91869e9i | −1.25159 | + | 0.722607i | −0.971426 | − | 0.237344i | \(-0.923723\pi\) |
−0.280167 | + | 0.959951i | \(0.590390\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.30131e9 | − | 2.48336e9i | −1.56408 | − | 0.903022i | −0.996837 | − | 0.0794717i | \(-0.974677\pi\) |
−0.567243 | − | 0.823550i | \(-0.691990\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.53861e9 | + | 2.00289e8i | −0.540357 | + | 0.0703412i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.64889e7 | − | 1.15162e8i | 0.0225593 | − | 0.0390738i | −0.854525 | − | 0.519410i | \(-0.826152\pi\) |
0.877085 | + | 0.480336i | \(0.159485\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.37742e9 | + | 2.38576e9i | 0.451643 | + | 0.782268i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.46697e9i | − | 0.464974i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.69161e8 | −0.266384 | −0.133192 | − | 0.991090i | \(-0.542523\pi\) | ||||
−0.133192 | + | 0.991090i | \(0.542523\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.15545e9 | + | 2.97650e9i | −1.52826 | + | 0.882344i | −0.528829 | + | 0.848728i | \(0.677369\pi\) |
−0.999435 | + | 0.0336153i | \(0.989298\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.93710e8 | + | 1.11839e8i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.10085e9 | − | 3.08289e9i | 0.860631 | − | 0.855646i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.74850e9 | + | 4.76055e9i | −0.738428 | + | 1.27900i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.81598e9 | − | 3.14537e9i | −0.472405 | − | 0.818229i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.85148e9i | 1.47425i | 0.675757 | + | 0.737124i | \(0.263817\pi\) | ||||
−0.675757 | + | 0.737124i | \(0.736183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.05950e9 | −0.502666 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.17361e9 | + | 6.77587e8i | −0.277565 | + | 0.160252i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.62716e9 | − | 3.24884e9i | −1.28990 | − | 0.744726i | −0.311266 | − | 0.950323i | \(-0.600753\pi\) |
−0.978637 | + | 0.205597i | \(0.934086\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.45802e8 | − | 1.12004e9i | −0.0324014 | − | 0.248906i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.03576e8 | − | 5.25809e8i | 0.0654192 | − | 0.113309i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.97436e9 | − | 6.88379e9i | −0.830699 | − | 1.43881i | −0.897485 | − | 0.441046i | \(-0.854608\pi\) |
0.0667853 | − | 0.997767i | \(-0.478726\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.85567e9i | − | 0.781837i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.26724e9 | 0.839658 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.45233e9 | + | 1.99320e9i | −0.659331 | + | 0.380665i | −0.792022 | − | 0.610493i | \(-0.790972\pi\) |
0.132691 | + | 0.991157i | \(0.457638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.89106e9 | + | 2.82386e9i | 0.906831 | + | 0.523559i | 0.879410 | − | 0.476065i | \(-0.157937\pi\) |
0.0274206 | + | 0.999624i | \(0.491271\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.14531e9 | + | 1.72410e9i | 0.746289 | + | 0.310393i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.27610e9 | + | 2.21026e9i | −0.223127 | + | 0.386468i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.20612e9 | − | 3.82111e9i | −0.374723 | − | 0.649039i | 0.615563 | − | 0.788088i | \(-0.288929\pi\) |
−0.990285 | + | 0.139049i | \(0.955595\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 3.75888e9i | − | 0.620358i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.88442e9 | −1.42496 | −0.712482 | − | 0.701691i | \(-0.752429\pi\) | ||||
−0.712482 | + | 0.701691i | \(0.752429\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.15981e9 | − | 3.55637e9i | 0.960333 | − | 0.554449i | 0.0640575 | − | 0.997946i | \(-0.479596\pi\) |
0.896276 | + | 0.443498i | \(0.146263\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.22326e9 | + | 2.43830e9i | 0.640131 | + | 0.369580i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.28189e9 | + | 4.28992e9i | 0.483722 | + | 0.632298i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.75808e9 | + | 4.77714e9i | −0.395381 | + | 0.684820i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.81535e8 | − | 8.34043e8i | −0.0671515 | − | 0.116310i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 3.43041e9i | − | 0.465453i | −0.972542 | − | 0.232726i | \(-0.925235\pi\) | ||
0.972542 | − | 0.232726i | \(-0.0747647\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.26783e9 | 0.299448 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.22395e9 | + | 7.06649e8i | −0.157304 | + | 0.0908193i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.16083e9 | + | 2.97960e9i | 0.645705 | + | 0.372798i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.76468e9 | − | 6.70518e9i | 1.06775 | − | 0.816854i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.00590e9 | + | 5.20637e9i | −0.356618 | + | 0.617681i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.87853e9 | + | 8.44986e9i | 0.563754 | + | 0.976450i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.38128e9i | − | 0.718380i | −0.933264 | − | 0.359190i | \(-0.883053\pi\) | ||
0.933264 | − | 0.359190i | \(-0.116947\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.90122e9 | 0.208544 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.32242e9 | + | 3.07290e9i | −0.568941 | + | 0.328478i | −0.756726 | − | 0.653732i | \(-0.773202\pi\) |
0.187785 | + | 0.982210i | \(0.439869\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.14188e10 | + | 6.59265e9i | 1.18972 | + | 0.686883i | 0.958242 | − | 0.285958i | \(-0.0923119\pi\) |
0.231474 | + | 0.972841i | \(0.425645\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.52952e9 | − | 3.67747e9i | 0.155350 | − | 0.373514i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.40497e9 | + | 1.28258e10i | −0.733308 | + | 1.27013i | 0.222154 | + | 0.975012i | \(0.428691\pi\) |
−0.955462 | + | 0.295114i | \(0.904642\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.91814e9 | + | 3.32231e9i | 0.185232 | + | 0.320832i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 4.97927e9i | − | 0.468970i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.25237e9 | −0.482553 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.39544e9 | − | 3.69241e9i | 0.573241 | − | 0.330961i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.46093e9 | + | 8.43470e8i | 0.127773 | + | 0.0737698i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.64739e9 | − | 1.12568e9i | 0.738077 | − | 0.0960795i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.65412e9 | − | 1.15253e10i | 0.554343 | − | 0.960151i | −0.443611 | − | 0.896219i | \(-0.646303\pi\) |
0.997954 | − | 0.0639314i | \(-0.0203639\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.14410e8 | − | 8.90985e8i | −0.0418343 | − | 0.0724592i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.93620e8i | − | 0.0153734i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.05204e9 | −0.391695 | −0.195847 | − | 0.980634i | \(-0.562746\pi\) | ||||
−0.195847 | + | 0.980634i | \(0.562746\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.37321e9 | − | 4.83428e9i | 0.634006 | − | 0.366043i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.05684e10 | + | 1.18752e10i | 1.52119 | + | 0.878260i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.24107e9 | − | 1.28106e10i | −0.378655 | − | 0.925538i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.64332e9 | − | 4.57837e9i | 0.186584 | − | 0.323172i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.44081e10 | − | 2.49556e10i | −0.993777 | − | 1.72127i | −0.593351 | − | 0.804944i | \(-0.702195\pi\) |
−0.400427 | − | 0.916329i | \(-0.631138\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6.85689e9i | − | 0.462195i | −0.972931 | − | 0.231098i | \(-0.925768\pi\) | ||
0.972931 | − | 0.231098i | \(-0.0742316\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.08941e9 | 0.269421 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.77313e9 | − | 1.02372e9i | 0.114194 | − | 0.0659299i | −0.441815 | − | 0.897106i | \(-0.645665\pi\) |
0.556009 | + | 0.831176i | \(0.312332\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.13550e10 | + | 1.81028e10i | 1.97421 | + | 1.13981i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.53749e8 | + | 4.25387e9i | 0.0340910 | + | 0.261885i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.16378e10 | + | 2.01573e10i | −0.700640 | + | 1.21354i | 0.267603 | + | 0.963529i | \(0.413769\pi\) |
−0.968242 | + | 0.250014i | \(0.919565\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.58567e8 | + | 1.66029e9i | 0.0564409 | + | 0.0977585i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.09469e9i | 0.0630470i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.33762e10 | −0.753634 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.90688e9 | − | 1.67829e9i | 0.160237 | − | 0.0925128i | −0.417737 | − | 0.908568i | \(-0.637177\pi\) |
0.577974 | + | 0.816055i | \(0.303843\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.26076e9 | + | 2.45995e9i | 0.229817 | + | 0.132685i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.12692e10 | − | 4.68702e9i | −0.594834 | − | 0.247401i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.69315e9 | + | 4.66467e9i | −0.139131 | + | 0.240982i | −0.927168 | − | 0.374646i | \(-0.877764\pi\) |
0.788037 | + | 0.615628i | \(0.211098\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.65234e9 | + | 6.32603e9i | 0.184691 | + | 0.319894i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.11003e10i | − | 0.549504i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.41287e10 | −1.16944 | −0.584718 | − | 0.811237i | \(-0.698795\pi\) | ||||
−0.584718 | + | 0.811237i | \(0.698795\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.71048e10 | − | 9.87546e9i | 0.811742 | − | 0.468659i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.42280e8 | + | 1.97616e8i | 0.0159069 | + | 0.00918388i | 0.507932 | − | 0.861397i | \(-0.330410\pi\) |
−0.492025 | + | 0.870581i | \(0.663743\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.52908e10 | + | 1.99874e10i | 0.695966 | + | 0.909733i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.02589e9 | − | 8.70510e9i | 0.224062 | − | 0.388088i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.08469e9 | − | 3.61078e9i | −0.0910421 | − | 0.157690i | 0.816908 | − | 0.576768i | \(-0.195686\pi\) |
−0.907950 | + | 0.419079i | \(0.862353\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.69400e9i | 0.243619i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.45798e10 | −1.03040 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.06055e10 | + | 1.18966e10i | −0.846437 | + | 0.488690i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.84338e9 | + | 2.79632e9i | 0.194978 | + | 0.112571i | 0.594311 | − | 0.804235i | \(-0.297425\pi\) |
−0.399333 | + | 0.916806i | \(0.630758\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.22604e10 | − | 9.37950e9i | 0.483742 | − | 0.370073i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.33080e10 | + | 4.03706e10i | −0.901420 | + | 1.56130i | −0.0757670 | + | 0.997126i | \(0.524141\pi\) |
−0.825653 | + | 0.564179i | \(0.809193\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.43611e10 | − | 5.95152e10i | −1.30271 | − | 2.25636i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 3.62787e9i | − | 0.134844i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.50057e9 | 0.236905 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.88978e10 | + | 1.66841e10i | −1.03269 | + | 0.596225i | −0.917755 | − | 0.397148i | \(-0.870000\pi\) |
−0.114937 | + | 0.993373i | \(0.536667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.13497e9 | + | 2.96467e9i | 0.179958 | + | 0.103899i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.75681e9 | − | 6.62828e9i | 0.0947559 | − | 0.227825i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.94538e10 | + | 5.10155e10i | −0.993000 | + | 1.71993i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.31165e9 | − | 1.61283e10i | −0.307952 | − | 0.533388i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.29982e10i | − | 0.421724i | −0.977516 | − | 0.210862i | \(-0.932373\pi\) | ||
0.977516 | − | 0.210862i | \(-0.0676270\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.85590e10 | 0.909105 | 0.454552 | − | 0.890720i | \(-0.349799\pi\) | ||||
0.454552 | + | 0.890720i | \(0.349799\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.87894e9 | − | 3.97156e9i | 0.214862 | − | 0.124051i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.11082e9 | + | 3.52808e9i | 0.187303 | + | 0.108139i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.06272e10 | − | 3.98691e9i | 0.921290 | − | 0.119929i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.29194e10 | + | 2.23771e10i | −0.381429 | + | 0.660654i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.78709e10 | − | 3.09533e10i | −0.517890 | − | 0.897012i | −0.999784 | − | 0.0207821i | \(-0.993384\pi\) |
0.481894 | − | 0.876229i | \(-0.339949\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.07905e9i | − | 0.0875920i | −0.999040 | − | 0.0437960i | \(-0.986055\pi\) | ||
0.999040 | − | 0.0437960i | \(-0.0139452\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.84753e9 | −0.275024 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.77448e10 | − | 1.02450e10i | 0.486570 | − | 0.280921i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.67947e9 | + | 4.43374e9i | 0.206763 | + | 0.119375i | 0.599806 | − | 0.800145i | \(-0.295244\pi\) |
−0.393043 | + | 0.919520i | \(0.628578\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.88901e9 | − | 8.94079e9i | −0.235017 | − | 0.236386i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.80719e9 | − | 6.59425e9i | 0.0988529 | − | 0.171218i | −0.812357 | − | 0.583160i | \(-0.801816\pi\) |
0.911210 | + | 0.411942i | \(0.135149\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.46057e10 | − | 5.99388e10i | −0.882485 | − | 1.52851i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.85212e10i | 0.964873i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.30579e8 | −0.0155151 | −0.00775754 | − | 0.999970i | \(-0.502469\pi\) | ||||
−0.00775754 | + | 0.999970i | \(0.502469\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.69215e10 | + | 1.55431e10i | −0.650718 | + | 0.375692i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.57425e9 | − | 4.95034e9i | −0.203612 | − | 0.117555i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.39970e9 | − | 7.22079e10i | −0.219315 | − | 1.68476i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.72887e9 | + | 6.45859e9i | −0.0854894 | + | 0.148072i | −0.905600 | − | 0.424134i | \(-0.860579\pi\) |
0.820110 | + | 0.572206i | \(0.193912\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.95371e9 | + | 3.38392e9i | 0.0440158 | + | 0.0762376i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.83758e10i | 1.73532i | 0.497162 | + | 0.867658i | \(0.334375\pi\) | ||||
−0.497162 | + | 0.867658i | \(0.665625\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.00729e10 | −0.654413 | −0.327206 | − | 0.944953i | \(-0.606107\pi\) | ||||
−0.327206 | + | 0.944953i | \(0.606107\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.27982e10 | + | 3.04831e10i | −1.12930 | + | 0.651999i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.07043e10 | − | 6.18012e9i | −0.225056 | − | 0.129936i | 0.383233 | − | 0.923652i | \(-0.374811\pi\) |
−0.608289 | + | 0.793716i | \(0.708144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.65902e8 | − | 2.35367e8i | −0.0116963 | − | 0.00486469i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.32595e10 | + | 2.29661e10i | −0.269428 | + | 0.466663i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.17559e10 | + | 5.50029e10i | 0.634425 | + | 1.09886i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.53917e10i | − | 0.498789i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.11172e10 | −0.214744 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.02421e10 | − | 5.91328e9i | 0.194557 | − | 0.112328i | −0.399557 | − | 0.916708i | \(-0.630836\pi\) |
0.594114 | + | 0.804381i | \(0.297503\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.62895e10 | − | 9.40477e9i | −0.304319 | − | 0.175698i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.01681e10 | − | 1.32913e10i | −0.186833 | − | 0.244219i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.81012e9 | + | 1.35275e10i | −0.141153 | + | 0.244484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.29037e10 | − | 2.23499e10i | −0.229403 | − | 0.397337i | 0.728229 | − | 0.685334i | \(-0.240344\pi\) |
−0.957631 | + | 0.287997i | \(0.907011\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 3.81415e10i | − | 0.667056i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.27542e9 | −0.107973 | −0.0539867 | − | 0.998542i | \(-0.517193\pi\) | ||||
−0.0539867 | + | 0.998542i | \(0.517193\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.18534e9 | − | 5.30316e9i | 0.155492 | − | 0.0897733i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.98516e10 | + | 1.14613e10i | 0.330654 | + | 0.190903i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.10257e10 | − | 6.96367e10i | 1.49190 | − | 1.14133i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.03302e9 | − | 1.04495e10i | 0.0973044 | − | 0.168536i | −0.813264 | − | 0.581895i | \(-0.802311\pi\) |
0.910568 | + | 0.413359i | \(0.135645\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.48065e10 | + | 4.29661e10i | 0.393744 | + | 0.681985i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 3.03272e10i | − | 0.473763i | −0.971539 | − | 0.236881i | \(-0.923875\pi\) | ||
0.971539 | − | 0.236881i | \(-0.0761253\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.75066e10 | 1.49923 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.17114e10 | − | 1.83086e10i | 0.479936 | − | 0.277091i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.94432e10 | + | 5.74136e10i | 1.48151 | + | 0.855349i | 0.999780 | − | 0.0209721i | \(-0.00667611\pi\) |
0.481728 | + | 0.876321i | \(0.340009\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.62603e10 | + | 3.90952e10i | −0.238476 | + | 0.573376i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.03043e9 | − | 1.21771e10i | 0.101511 | − | 0.175822i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.54181e10 | − | 2.67050e10i | −0.219181 | − | 0.379632i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.01883e10i | 0.702491i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.81369e10 | −0.525625 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.01705e11 | − | 5.87193e10i | 1.38035 | − | 0.796948i | 0.388153 | − | 0.921595i | \(-0.373113\pi\) |
0.992201 | + | 0.124647i | \(0.0397797\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.14302e11 | + | 6.59924e10i | 1.52773 | + | 0.882037i | 0.999457 | + | 0.0329648i | \(0.0104949\pi\) |
0.528277 | + | 0.849072i | \(0.322838\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.05646e10 | + | 2.67701e9i | −0.270697 | + | 0.0352381i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.28319e10 | − | 5.68665e10i | 0.425651 | − | 0.737249i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.80491e10 | + | 4.85825e10i | 0.358176 | + | 0.620379i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.53889e9i | − | 0.0822481i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.99487e10 | 1.11451 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.99401e10 | + | 4.03799e10i | −0.853711 | + | 0.492890i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.64563e9 | + | 4.99156e9i | 0.103968 | + | 0.0600260i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.70060e10 | − | 2.03942e10i | 0.912367 | − | 0.241630i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.07062e10 | + | 8.78258e10i | −0.591933 | + | 1.02526i | 0.402039 | + | 0.915622i | \(0.368302\pi\) |
−0.993972 | + | 0.109635i | \(0.965032\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.72689e10 | + | 2.99106e10i | 0.198639 | + | 0.344053i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 2.73609e10i | − | 0.310130i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.33269e10 | 0.148861 | 0.0744305 | − | 0.997226i | \(-0.476286\pi\) | ||||
0.0744305 | + | 0.997226i | \(0.476286\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.43637e10 | − | 1.40664e10i | 0.268197 | − | 0.154844i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.30536e10 | − | 1.90835e10i | −0.358601 | − | 0.207039i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.72233e9 | + | 7.46863e10i | 0.103961 | + | 0.798621i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.34333e9 | + | 1.44511e10i | −0.0879362 | + | 0.152310i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.36147e10 | − | 1.10184e11i | −0.660901 | − | 1.14471i | −0.980379 | − | 0.197121i | \(-0.936841\pi\) |
0.319478 | − | 0.947594i | \(-0.396492\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.83773e11i | − | 1.88206i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.46889e10 | −0.249258 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.34889e10 | + | 7.78784e9i | −0.134259 | + | 0.0775146i | −0.565625 | − | 0.824662i | \(-0.691365\pi\) |
0.431366 | + | 0.902177i | \(0.358032\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.35807e11 | − | 7.84082e10i | −1.33269 | − | 0.769427i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.06034e10 | − | 4.41010e9i | −0.102591 | − | 0.0426694i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.62497e10 | − | 2.81452e10i | 0.155023 | − | 0.268507i | −0.778045 | − | 0.628209i | \(-0.783788\pi\) |
0.933067 | + | 0.359702i | \(0.117122\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.39206e10 | + | 9.33932e10i | 0.507236 | + | 0.878559i | 0.999965 | + | 0.00837569i | \(0.00266610\pi\) |
−0.492729 | + | 0.870183i | \(0.664001\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1.42853e10i | − | 0.132517i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.75267e10 | −0.251816 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.22142e10 | + | 4.16929e10i | −0.651507 | + | 0.376148i | −0.789033 | − | 0.614350i | \(-0.789418\pi\) |
0.137526 | + | 0.990498i | \(0.456085\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.88495e10 | − | 1.08828e10i | −0.167720 | − | 0.0968332i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.13301e11 | + | 1.48101e11i | 0.994327 | + | 1.29974i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.51218e10 | − | 6.08327e10i | 0.304020 | − | 0.526578i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.31635e10 | − | 5.74409e10i | −0.283163 | − | 0.490453i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 7.46672e9i | − | 0.0628894i | −0.999505 | − | 0.0314447i | \(-0.989989\pi\) | ||
0.999505 | − | 0.0314447i | \(-0.0100108\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.36292e11 | −1.96331 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.39778e10 | + | 4.27111e10i | −0.606389 | + | 0.350099i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.56081e10 | + | 9.01133e9i | 0.126221 | + | 0.0728736i | 0.561781 | − | 0.827286i | \(-0.310116\pi\) |
−0.435560 | + | 0.900160i | \(0.643450\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.52602e10 | − | 4.22753e10i | 0.440905 | − | 0.337302i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.84525e10 | + | 1.18563e11i | −0.538880 | + | 0.933367i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.04457e11 | + | 1.80925e11i | 0.811390 | + | 1.40537i | 0.911891 | + | 0.410432i | \(0.134622\pi\) |
−0.100502 | + | 0.994937i | \(0.532045\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.08426e10i | 0.159755i | 0.996805 | + | 0.0798775i | \(0.0254529\pi\) | ||||
−0.996805 | + | 0.0798775i | \(0.974547\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.58270e8 | −0.00422255 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.53763e10 | − | 8.87750e9i | 0.114770 | − | 0.0662627i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.34325e11 | + | 7.75528e10i | 0.989472 | + | 0.571272i | 0.905116 | − | 0.425164i | \(-0.139783\pi\) |
0.0843557 | + | 0.996436i | \(0.473117\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.19708e10 | + | 2.87819e10i | −0.0870272 | + | 0.209242i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.26105e10 | − | 1.25765e11i | 0.520996 | − | 0.902391i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.32583e10 | − | 1.44208e11i | −0.589639 | − | 1.02128i | −0.994280 | − | 0.106808i | \(-0.965937\pi\) |
0.404641 | − | 0.914476i | \(-0.367396\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 7.97969e10i | − | 0.557809i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.79412e10 | 0.606808 | 0.303404 | − | 0.952862i | \(-0.401877\pi\) | ||||
0.303404 | + | 0.952862i | \(0.401877\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.96984e10 | − | 3.44669e10i | 0.406630 | − | 0.234768i | −0.282710 | − | 0.959205i | \(-0.591234\pi\) |
0.689341 | + | 0.724437i | \(0.257900\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.32009e10 | − | 7.62157e9i | −0.0887644 | − | 0.0512481i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.17253e11 | + | 2.82811e10i | −1.44216 | + | 0.187734i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.53111e10 | − | 1.65084e11i | 0.624631 | − | 1.08189i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.44216e10 | + | 7.69404e10i | 0.287425 | + | 0.497834i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.79724e10i | − | 0.114817i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.94652e10 | −0.375099 | −0.187549 | − | 0.982255i | \(-0.560054\pi\) | ||||
−0.187549 | + | 0.982255i | \(0.560054\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.27094e10 | − | 5.35258e10i | 0.577443 | − | 0.333387i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.77426e11 | − | 1.60172e11i | −1.70629 | − | 0.985127i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.22472e11 | − | 6.03042e10i | −1.35119 | − | 0.366261i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.21964e10 | − | 9.04069e10i | 0.313067 | − | 0.542248i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.97978e10 | − | 3.42908e10i | −0.117269 | − | 0.203117i | 0.801415 | − | 0.598108i | \(-0.204081\pi\) |
−0.918685 | + | 0.394992i | \(0.870747\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.06967e10i | 0.296576i | 0.988944 | + | 0.148288i | \(0.0473763\pi\) | ||||
−0.988944 | + | 0.148288i | \(0.952624\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.63032e11 | −0.941963 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.68870e11 | + | 1.55232e11i | −1.53435 | + | 0.885860i | −0.535201 | + | 0.844725i | \(0.679764\pi\) |
−0.999154 | + | 0.0411356i | \(0.986902\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.57805e10 | + | 2.06579e10i | 0.201682 | + | 0.116441i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.49119e10 | + | 1.91372e11i | 0.138702 | + | 1.06550i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.56400e10 | + | 9.63713e10i | −0.306009 | + | 0.530023i | −0.977485 | − | 0.211003i | \(-0.932327\pi\) |
0.671476 | + | 0.741026i | \(0.265660\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.99332e11 | + | 3.45254e11i | 1.08296 | + | 1.87574i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.85679e10i | 0.206997i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.65142e10 | −0.193607 | −0.0968033 | − | 0.995304i | \(-0.530862\pi\) | ||||
−0.0968033 | + | 0.995304i | \(0.530862\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.90939e11 | − | 1.10239e11i | 1.00020 | − | 0.577468i | 0.0918951 | − | 0.995769i | \(-0.470708\pi\) |
0.908309 | + | 0.418301i | \(0.137374\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.18669e10 | + | 3.57189e10i | 0.320187 | + | 0.184860i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.31174e11 | − | 9.61489e10i | −1.18210 | − | 0.491652i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.06881e10 | + | 3.58328e10i | −0.104524 | + | 0.181041i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.41957e10 | − | 9.38698e10i | −0.270558 | − | 0.468620i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.77756e11i | 0.876870i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.08399e11 | −1.50333 | −0.751663 | − | 0.659548i | \(-0.770748\pi\) | ||||
−0.751663 | + | 0.659548i | \(0.770748\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.63590e10 | + | 9.44487e9i | −0.0788027 | + | 0.0454968i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.10257e11 | − | 6.36567e10i | −0.524868 | − | 0.303033i | 0.214056 | − | 0.976821i | \(-0.431332\pi\) |
−0.738924 | + | 0.673789i | \(0.764666\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.00434e10 | + | 3.92713e10i | 0.141342 | + | 0.184755i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.97285e10 | − | 1.55414e11i | 0.417198 | − | 0.722607i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.36226e9 | − | 1.10198e10i | −0.0292367 | − | 0.0506395i | 0.851037 | − | 0.525106i | \(-0.175974\pi\) |
−0.880274 | + | 0.474467i | \(0.842641\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 9.61694e10i | − | 0.436792i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.32271e11 | 1.04272 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.76021e11 | + | 1.01626e11i | −0.781064 | + | 0.450948i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.25426e11 | − | 1.30150e11i | −0.988764 | − | 0.570863i | −0.0838595 | − | 0.996478i | \(-0.526725\pi\) |
−0.904905 | + | 0.425614i | \(0.860058\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.76304e10 | − | 4.40885e10i | 0.249873 | − | 0.191158i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.51028e11 | + | 2.61588e11i | −0.647318 | + | 1.12119i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.29728e10 | + | 7.44311e10i | 0.182080 | + | 0.315372i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.21875e9i | 0.0260492i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.00585e11 | 1.65891 | 0.829454 | − | 0.558575i | \(-0.188652\pi\) | ||||
0.829454 | + | 0.558575i | \(0.188652\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.60093e10 | + | 3.23370e10i | −0.229319 | + | 0.132397i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.11571e11 | − | 6.44155e10i | −0.451643 | − | 0.260756i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.18531e11 | − | 2.84987e11i | 0.474409 | − | 1.14064i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.90688e11 | − | 3.30281e11i | 0.754637 | − | 1.30707i | −0.190918 | − | 0.981606i | \(-0.561146\pi\) |
0.945555 | − | 0.325463i | \(-0.105520\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.43018e10 | + | 5.94124e10i | 0.134226 | + | 0.232487i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.56160e11i | 0.991182i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.19085e11 | 1.60353 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.52010e10 | − | 2.03233e10i | 0.133192 | − | 0.0768985i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.96410e11 | − | 1.71132e11i | −1.10912 | − | 0.640349i | −0.170516 | − | 0.985355i | \(-0.554544\pi\) |
−0.938600 | + | 0.345006i | \(0.887877\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.67944e10 | + | 1.26003e10i | −0.358186 | + | 0.0466271i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.39197e11 | − | 2.41097e11i | 0.509421 | − | 0.882344i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.56372e10 | + | 4.44050e10i | 0.0927939 | + | 0.160724i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.71217e11i | 1.32889i | 0.747335 | + | 0.664447i | \(0.231333\pi\) | ||||
−0.747335 | + | 0.664447i | \(0.768667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.04604e10 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.52069e11 | − | 8.77971e10i | 0.532563 | − | 0.307476i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.92685e11 | − | 1.68982e11i | −1.01387 | − | 0.585361i | −0.101551 | − | 0.994830i | \(-0.532380\pi\) |
−0.912324 | + | 0.409470i | \(0.865714\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.34982e10 | + | 1.97364e11i | −0.183312 | + | 0.676266i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.76370e9 | − | 3.05483e9i | 0.00597800 | − | 0.0103542i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.94965e10 | − | 8.57304e10i | −0.165957 | − | 0.287447i | 0.771038 | − | 0.636790i | \(-0.219738\pi\) |
−0.936995 | + | 0.349343i | \(0.886405\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 2.57070e11i | − | 0.852664i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.43942e11 | 0.800445 | 0.400222 | − | 0.916418i | \(-0.368933\pi\) | ||||
0.400222 | + | 0.916418i | \(0.368933\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.41079e11 | − | 3.12392e11i | 1.75645 | − | 1.01409i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.47095e11 | + | 8.49251e10i | 0.472405 | + | 0.272743i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.30000e10 | + | 2.53504e11i | 0.104854 | + | 0.805484i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.90079e11 | + | 3.29227e11i | −0.597552 | + | 1.03499i | 0.395630 | + | 0.918410i | \(0.370526\pi\) |
−0.993181 | + | 0.116580i | \(0.962807\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.36823e11 | − | 2.36985e11i | −0.425579 | − | 0.737124i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.60581e11i | 0.494205i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.45316e11 | 0.747038 | 0.373519 | − | 0.927623i | \(-0.378151\pi\) | ||||
0.373519 | + | 0.927623i | \(0.378151\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.34098e10 | − | 4.81567e10i | 0.251333 | − | 0.145107i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.86360e11 | − | 1.07595e11i | −0.555666 | − | 0.320814i | 0.195738 | − | 0.980656i | \(-0.437290\pi\) |
−0.751404 | + | 0.659842i | \(0.770623\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.99689e10 | − | 3.32603e10i | −0.235952 | − | 0.0981360i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.16876e10 | − | 5.48845e10i | 0.0925217 | − | 0.160252i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.97740e10 | − | 1.03532e11i | −0.172715 | − | 0.299152i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.78234e11i | 0.509664i | 0.966985 | + | 0.254832i | \(0.0820202\pi\) | ||||
−0.966985 | + | 0.254832i | \(0.917980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.03867e11 | 0.859935 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.49619e11 | + | 8.63826e10i | −0.419053 | + | 0.241940i | −0.694672 | − | 0.719327i | \(-0.744451\pi\) |
0.275619 | + | 0.961267i | \(0.411117\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.74912e11 | + | 1.58720e11i | 0.762055 | + | 0.439973i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.20946e10 | + | 4.19524e10i | 0.0880536 | + | 0.115099i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.54638e11 | − | 2.67841e11i | 0.419920 | − | 0.727323i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.29802e11 | + | 5.71233e11i | 0.886439 | + | 1.53536i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.83937e10i | 0.0755396i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.30117e11 | 1.13268 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.97454e11 | − | 2.29470e11i | 1.03607 | − | 0.598173i | 0.117350 | − | 0.993091i | \(-0.462560\pi\) |
0.918717 | + | 0.394918i | \(0.129227\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.21923e11 | + | 1.85862e11i | 0.830699 | + | 0.479604i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.94257e11 | + | 3.01615e11i | −1.00710 | + | 0.770455i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.57171e11 | − | 4.45433e11i | 0.650323 | − | 1.12639i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.01559e10 | + | 1.56155e11i | 0.225697 | + | 0.390919i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.17227e11i | 1.77756i | 0.458337 | + | 0.888778i | \(0.348445\pi\) | ||||
−0.458337 | + | 0.888778i | \(0.651555\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.38758e11 | 0.340464 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.72823e11 | + | 9.97796e10i | −0.419829 | + | 0.242388i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.11042e11 | − | 1.21845e11i | −0.507583 | − | 0.293053i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.04233e11 | + | 2.50612e11i | −0.248212 | + | 0.596785i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.32130e10 | − | 1.61450e11i | 0.219777 | − | 0.380665i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.77589e10 | − | 3.07592e10i | −0.0414592 | − | 0.0718094i | 0.844551 | − | 0.535475i | \(-0.179867\pi\) |
−0.886010 | + | 0.463665i | \(0.846534\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3.23237e11i | − | 0.747202i | −0.927590 | − | 0.373601i | \(-0.878123\pi\) | ||
0.927590 | − | 0.373601i | \(-0.121877\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.64117e11 | −0.604554 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.35745e11 | + | 3.09313e11i | −1.21431 | + | 0.701080i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.47222e11 | − | 3.15939e11i | −1.22822 | − | 0.709112i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.08199e11 | + | 2.71025e10i | −0.462747 | + | 0.0602383i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.30060e11 | − | 5.71681e11i | 0.726475 | − | 1.25829i | −0.231889 | − | 0.972742i | \(-0.574490\pi\) |
0.958364 | − | 0.285550i | \(-0.0921762\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.85109e10 | + | 6.67029e10i | 0.0839430 | + | 0.145394i | 0.904940 | − | 0.425538i | \(-0.139915\pi\) |
−0.820997 | + | 0.570932i | \(0.806582\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.19354e11i | − | 0.257645i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.29730e11 | 0.704914 | 0.352457 | − | 0.935828i | \(-0.385346\pi\) | ||||
0.352457 | + | 0.935828i | \(0.385346\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.47097e11 | − | 2.58132e11i | 0.946637 | − | 0.546541i | 0.0546025 | − | 0.998508i | \(-0.482611\pi\) |
0.892035 | + | 0.451967i | \(0.149278\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.78696e11 | + | 1.03170e11i | 0.374723 | + | 0.216346i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.63848e10 | − | 2.12902e11i | −0.117107 | − | 0.442181i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.02342e11 | − | 6.96876e11i | 0.827654 | − | 1.43354i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.78928e10 | + | 1.52235e11i | 0.179082 | + | 0.310179i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.12614e11i | 1.43816i | 0.694928 | + | 0.719079i | \(0.255436\pi\) | ||||
−0.694928 | + | 0.719079i | \(0.744564\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.23174e11 | −0.845932 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.59819e11 | − | 2.07742e11i | 0.712482 | − | 0.411352i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.14334e11 | − | 2.96951e11i | −1.00883 | − | 0.582449i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.25502e9 | − | 5.57326e10i | −0.0140963 | − | 0.108287i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.66315e11 | + | 2.88066e11i | −0.320111 | + | 0.554449i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.50560e10 | + | 6.07187e10i | 0.0668411 | + | 0.115772i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 8.51195e11i | − | 1.60780i | −0.594762 | − | 0.803901i | \(-0.702754\pi\) | ||
0.594762 | − | 0.803901i | \(-0.297246\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.28056e11 | −0.426754 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.97102e10 | + | 5.17942e10i | −0.166310 | + | 0.0960192i | −0.580845 | − | 0.814014i | \(-0.697278\pi\) |
0.414535 | + | 0.910034i | \(0.363944\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.62089e11 | + | 1.51317e11i | 0.481366 | + | 0.277917i | 0.720986 | − | 0.692950i | \(-0.243689\pi\) |
−0.239620 | + | 0.970867i | \(0.577023\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.33226e11 | − | 9.70025e10i | −0.424390 | − | 0.176510i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.58567e10 | + | 2.74647e10i | −0.0285871 | + | 0.0495144i | −0.879965 | − | 0.475038i | \(-0.842434\pi\) |
0.851378 | + | 0.524553i | \(0.175767\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.09275e11 | + | 5.35680e11i | 0.552434 | + | 0.956844i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 2.57965e11i | − | 0.456547i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.33470e11 | −0.760115 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.83920e9 | + | 5.10332e9i | −0.0153582 | + | 0.00886706i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.90043e10 | + | 2.25191e10i | 0.0671515 | + | 0.0387699i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.27873e11 | − | 2.97864e11i | −0.388741 | − | 0.508143i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.80322e11 | + | 6.58737e11i | −0.642914 | + | 1.11356i | 0.341865 | + | 0.939749i | \(0.388941\pi\) |
−0.984779 | + | 0.173811i | \(0.944392\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.02122e10 | + | 1.38932e11i | 0.134365 | + | 0.232726i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.08310e12i | 1.79790i | 0.438047 | + | 0.898952i | \(0.355670\pi\) | ||||
−0.438047 | + | 0.898952i | \(0.644330\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.89279e11 | −1.46284 | −0.731418 | − | 0.681930i | \(-0.761141\pi\) | ||||
−0.731418 | + | 0.681930i | \(0.761141\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.18469e10 | + | 5.30279e10i | −0.149724 | + | 0.0864432i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.90203e11 | − | 3.40754e11i | −0.953469 | − | 0.550486i | −0.0593124 | − | 0.998239i | \(-0.518891\pi\) |
−0.894157 | + | 0.447754i | \(0.852224\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.05387e11 | + | 6.16139e11i | −1.28943 | + | 0.986443i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.30467e10 | − | 5.72386e10i | 0.0524345 | − | 0.0908193i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.49661e11 | − | 4.32426e11i | −0.392595 | − | 0.679995i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.61918e11i | − | 0.252350i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.78685e11 | −0.430470 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.13228e11 | − | 2.38577e11i | 0.632631 | − | 0.365250i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.68187e11 | − | 9.71028e10i | −0.255207 | − | 0.147344i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.98185e11 | + | 4.76501e11i | −0.298070 | + | 0.716660i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.80088e11 | − | 4.85127e11i | 0.417542 | − | 0.723204i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.31902e11 | − | 4.01666e11i | −0.342669 | − | 0.593520i | 0.642258 | − | 0.766488i | \(-0.277998\pi\) |
−0.984927 | + | 0.172968i | \(0.944664\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2.81144e11i | − | 0.411787i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.51575e11 | −0.220066 | −0.110033 | − | 0.993928i | \(-0.535096\pi\) | ||||
−0.110033 | + | 0.993928i | \(0.535096\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.29413e11 | + | 5.36597e11i | −1.33760 | + | 0.772263i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.95161e11 | − | 2.28146e11i | −0.563754 | − | 0.325483i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.25140e12 | − | 1.62902e11i | 1.76978 | − | 0.230382i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.58090e11 | + | 1.13985e12i | −0.922621 | + | 1.59803i | −0.127278 | + | 0.991867i | \(0.540624\pi\) |
−0.795343 | + | 0.606159i | \(0.792709\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.49211e11 | + | 2.58442e11i | 0.207378 | + | 0.359190i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.90858e12i | − | 2.62968i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.68847e10 | 0.118680 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.69992e10 | + | 4.44555e10i | −0.104272 | + | 0.0602014i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.55698e11 | + | 2.05362e11i | 0.477549 | + | 0.275713i | 0.719395 | − | 0.694602i | \(-0.244419\pi\) |
−0.241845 | + | 0.970315i | \(0.577753\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.62038e11 | + | 5.58783e11i | −0.748113 | + | 0.743780i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.43705e11 | − | 2.48905e11i | 0.189647 | − | 0.328478i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.00217e11 | + | 3.46786e11i | 0.261972 | + | 0.453749i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.44178e11i | 0.446503i | 0.974761 | + | 0.223252i | \(0.0716672\pi\) | ||||
−0.974761 | + | 0.223252i | \(0.928333\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.16615e11 | −0.793144 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.62624e10 | + | 1.51626e10i | −0.0334947 | + | 0.0193382i | −0.516654 | − | 0.856194i | \(-0.672823\pi\) |
0.483159 | + | 0.875533i | \(0.339489\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.90362e11 | − | 1.67640e11i | −0.367191 | − | 0.211998i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.40436e10 | + | 1.84702e11i | 0.0301490 | + | 0.231603i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.03677e11 | + | 3.52778e11i | −0.253245 | + | 0.438634i | −0.964417 | − | 0.264384i | \(-0.914831\pi\) |
0.711172 | + | 0.703018i | \(0.248165\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.52561e11 | + | 6.10654e11i | 0.434680 | + | 0.752888i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 6.92592e11i | − | 0.846751i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.16996e12 | 1.41841 | 0.709204 | − | 0.705003i | \(-0.249055\pi\) | ||||
0.709204 | + | 0.705003i | \(0.249055\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.00655e11 | + | 1.15848e11i | −0.241233 | + | 0.139276i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.55369e11 | − | 8.97023e10i | −0.185232 | − | 0.106944i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.81079e11 | − | 1.16905e11i | −0.332318 | − | 0.138216i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.05059e12 | − | 1.81967e12i | 1.23180 | − | 2.13353i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.16429e11 | + | 2.01660e11i | 0.135380 | + | 0.234485i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.53019e11i | 0.407089i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.11579e11 | −0.356338 | −0.178169 | − | 0.984000i | \(-0.557017\pi\) | ||||
−0.178169 | + | 0.984000i | \(0.557017\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.12721e11 | − | 1.22814e11i | 0.241276 | − | 0.139301i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.44094e11 | − | 1.40928e11i | −0.274587 | − | 0.158533i | 0.356383 | − | 0.934340i | \(-0.384010\pi\) |
−0.630970 | + | 0.775807i | \(0.717343\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.80963e11 | + | 7.59407e11i | 0.648182 | + | 0.847272i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.72677e11 | + | 2.99085e11i | −0.191080 | + | 0.330961i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.13846e11 | + | 7.16803e11i | 0.454214 | + | 0.786723i | 0.998643 | − | 0.0520849i | \(-0.0165866\pi\) |
−0.544428 | + | 0.838807i | \(0.683253\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.26091e12i | − | 1.37263i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.88904e10 | −0.0851820 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.85992e11 | − | 4.53793e11i | 0.841791 | − | 0.486008i | −0.0160817 | − | 0.999871i | \(-0.505119\pi\) |
0.857873 | + | 0.513862i | \(0.171786\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.19986e12 | + | 6.92740e11i | 1.27464 | + | 0.735912i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.23898e11 | + | 2.47789e11i | −0.341303 | + | 0.261104i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.42504e11 | + | 5.93234e11i | −0.357998 | + | 0.620070i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.53863e11 | − | 9.59320e11i | −0.574259 | − | 0.994646i | −0.996122 | − | 0.0879865i | \(-0.971957\pi\) |
0.421862 | − | 0.906660i | \(-0.361377\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.22365e11i | 0.640101i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.22049e12 | 2.26546 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.14412e11 | + | 4.70201e11i | −0.824259 | + | 0.475886i | −0.851883 | − | 0.523732i | \(-0.824539\pi\) |
0.0276241 | + | 0.999618i | \(0.491206\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.16672e10 | + | 2.40566e10i | 0.0418343 | + | 0.0241531i |
(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 | 84.9.m.a.61.4 | ✓ | 10 | |
3.2 | odd | 2 | 252.9.z.b.145.2 | 10 | |||
7.3 | odd | 6 | inner | 84.9.m.a.73.4 | yes | 10 | |
21.17 | even | 6 | 252.9.z.b.73.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.9.m.a.61.4 | ✓ | 10 | 1.1 | even | 1 | trivial | |
84.9.m.a.73.4 | yes | 10 | 7.3 | odd | 6 | inner | |
252.9.z.b.73.2 | 10 | 21.17 | even | 6 | |||
252.9.z.b.145.2 | 10 | 3.2 | odd | 2 |