Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,11,Mod(11,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.11");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.b (of order \(2\), degree \(1\), 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: | \(12.7071450535\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + 84 x^{18} - 86 x^{17} - 51565 x^{16} + 188134 x^{15} - 12946328 x^{14} + \cdots + 11\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{94}\cdot 3^{4}\cdot 5^{29} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.17 | ||
Root | \(13.6469 - 4.79406i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.11 |
Dual form | 20.11.b.a.11.18 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 30.5298 | − | 9.58811i | 0.954056 | − | 0.299629i | ||||
\(3\) | − | 321.971i | − | 1.32498i | −0.749069 | − | 0.662492i | \(-0.769499\pi\) | ||
0.749069 | − | 0.662492i | \(-0.230501\pi\) | |||||||
\(4\) | 840.136 | − | 585.446i | 0.820445 | − | 0.571725i | ||||
\(5\) | −1397.54 | −0.447214 | ||||||||
\(6\) | −3087.10 | − | 9829.71i | −0.397003 | − | 1.26411i | ||||
\(7\) | − | 9880.78i | − | 0.587897i | −0.955821 | − | 0.293948i | \(-0.905031\pi\) | ||
0.955821 | − | 0.293948i | \(-0.0949694\pi\) | |||||||
\(8\) | 20035.9 | − | 25928.9i | 0.611446 | − | 0.791286i | ||||
\(9\) | −44616.5 | −0.755584 | ||||||||
\(10\) | −42666.7 | + | 13399.8i | −0.426667 | + | 0.133998i | ||||
\(11\) | 116297.i | 0.722113i | 0.932544 | + | 0.361056i | \(0.117584\pi\) | ||||
−0.932544 | + | 0.361056i | \(0.882416\pi\) | |||||||
\(12\) | −188497. | − | 270500.i | −0.757526 | − | 1.08708i | ||||
\(13\) | −522308. | −1.40673 | −0.703364 | − | 0.710830i | \(-0.748320\pi\) | ||||
−0.703364 | + | 0.710830i | \(0.748320\pi\) | |||||||
\(14\) | −94738.1 | − | 301658.i | −0.176151 | − | 0.560886i | ||||
\(15\) | 449968.i | 0.592551i | ||||||||
\(16\) | 363082. | − | 983709.i | 0.346262 | − | 0.938138i | ||||
\(17\) | 1.21816e6 | 0.857948 | 0.428974 | − | 0.903317i | \(-0.358875\pi\) | ||||
0.428974 | + | 0.903317i | \(0.358875\pi\) | |||||||
\(18\) | −1.36213e6 | + | 427788.i | −0.720869 | + | 0.226394i | ||||
\(19\) | − | 1.43420e6i | − | 0.579217i | −0.957145 | − | 0.289609i | \(-0.906475\pi\) | ||
0.957145 | − | 0.289609i | \(-0.0935252\pi\) | |||||||
\(20\) | −1.17413e6 | + | 818186.i | −0.366914 | + | 0.255683i | ||||
\(21\) | −3.18133e6 | −0.778954 | ||||||||
\(22\) | 1.11507e6 | + | 3.55052e6i | 0.216366 | + | 0.688936i | ||||
\(23\) | − | 6.87353e6i | − | 1.06792i | −0.845508 | − | 0.533962i | \(-0.820702\pi\) | ||
0.845508 | − | 0.533962i | \(-0.179298\pi\) | |||||||
\(24\) | −8.34835e6 | − | 6.45097e6i | −1.04844 | − | 0.810156i | ||||
\(25\) | 1.95312e6 | 0.200000 | ||||||||
\(26\) | −1.59460e7 | + | 5.00795e6i | −1.34210 | + | 0.421496i | ||||
\(27\) | − | 4.64686e6i | − | 0.323848i | ||||||
\(28\) | −5.78467e6 | − | 8.30120e6i | −0.336115 | − | 0.482337i | ||||
\(29\) | 2.86090e7 | 1.39480 | 0.697400 | − | 0.716682i | \(-0.254340\pi\) | ||||
0.697400 | + | 0.716682i | \(0.254340\pi\) | |||||||
\(30\) | 4.31435e6 | + | 1.37374e7i | 0.177545 | + | 0.565327i | ||||
\(31\) | 3.98357e7i | 1.39144i | 0.718313 | + | 0.695720i | \(0.244914\pi\) | ||||
−0.718313 | + | 0.695720i | \(0.755086\pi\) | |||||||
\(32\) | 1.65289e6 | − | 3.35137e7i | 0.0492601 | − | 0.998786i | ||||
\(33\) | 3.74443e7 | 0.956788 | ||||||||
\(34\) | 3.71903e7 | − | 1.16799e7i | 0.818530 | − | 0.257066i | ||||
\(35\) | 1.38088e7i | 0.262915i | ||||||||
\(36\) | −3.74839e7 | + | 2.61205e7i | −0.619915 | + | 0.431986i | ||||
\(37\) | 1.09043e8 | 1.57250 | 0.786250 | − | 0.617909i | \(-0.212020\pi\) | ||||
0.786250 | + | 0.617909i | \(0.212020\pi\) | |||||||
\(38\) | −1.37513e7 | − | 4.37858e7i | −0.173550 | − | 0.552606i | ||||
\(39\) | 1.68168e8i | 1.86389i | ||||||||
\(40\) | −2.80010e7 | + | 3.62367e7i | −0.273447 | + | 0.353874i | ||||
\(41\) | 3.34019e7 | 0.288305 | 0.144152 | − | 0.989555i | \(-0.453954\pi\) | ||||
0.144152 | + | 0.989555i | \(0.453954\pi\) | |||||||
\(42\) | −9.71253e7 | + | 3.05029e7i | −0.743166 | + | 0.233397i | ||||
\(43\) | 7.92659e7i | 0.539193i | 0.962973 | + | 0.269597i | \(0.0868903\pi\) | ||||
−0.962973 | + | 0.269597i | \(0.913110\pi\) | |||||||
\(44\) | 6.80856e7 | + | 9.77053e7i | 0.412850 | + | 0.592454i | ||||
\(45\) | 6.23534e7 | 0.337907 | ||||||||
\(46\) | −6.59042e7 | − | 2.09847e8i | −0.319981 | − | 1.01886i | ||||
\(47\) | − | 4.50036e8i | − | 1.96227i | −0.193331 | − | 0.981134i | \(-0.561929\pi\) | ||
0.193331 | − | 0.981134i | \(-0.438071\pi\) | |||||||
\(48\) | −3.16726e8 | − | 1.16902e8i | −1.24302 | − | 0.458791i | ||||
\(49\) | 1.84845e8 | 0.654377 | ||||||||
\(50\) | 5.96285e7 | − | 1.87268e7i | 0.190811 | − | 0.0599257i | ||||
\(51\) | − | 3.92213e8i | − | 1.13677i | ||||||
\(52\) | −4.38810e8 | + | 3.05783e8i | −1.15414 | + | 0.804262i | ||||
\(53\) | −2.29617e8 | −0.549065 | −0.274533 | − | 0.961578i | \(-0.588523\pi\) | ||||
−0.274533 | + | 0.961578i | \(0.588523\pi\) | |||||||
\(54\) | −4.45546e7 | − | 1.41868e8i | −0.0970340 | − | 0.308969i | ||||
\(55\) | − | 1.62530e8i | − | 0.322939i | ||||||
\(56\) | −2.56198e8 | − | 1.97970e8i | −0.465195 | − | 0.359467i | ||||
\(57\) | −4.61771e8 | −0.767454 | ||||||||
\(58\) | 8.73425e8 | − | 2.74306e8i | 1.33072 | − | 0.417922i | ||||
\(59\) | 1.31191e9i | 1.83503i | 0.397698 | + | 0.917516i | \(0.369809\pi\) | ||||
−0.397698 | + | 0.917516i | \(0.630191\pi\) | |||||||
\(60\) | 2.63432e8 | + | 3.78035e8i | 0.338776 | + | 0.486156i | ||||
\(61\) | −8.17592e8 | −0.968027 | −0.484014 | − | 0.875060i | \(-0.660822\pi\) | ||||
−0.484014 | + | 0.875060i | \(0.660822\pi\) | |||||||
\(62\) | 3.81949e8 | + | 1.21618e9i | 0.416915 | + | 1.32751i | ||||
\(63\) | 4.40846e8i | 0.444205i | ||||||||
\(64\) | −2.70871e8 | − | 1.03901e9i | −0.252268 | − | 0.967657i | ||||
\(65\) | 7.29948e8 | 0.629108 | ||||||||
\(66\) | 1.14317e9 | − | 3.59020e8i | 0.912830 | − | 0.286681i | ||||
\(67\) | − | 5.25343e8i | − | 0.389107i | −0.980892 | − | 0.194554i | \(-0.937674\pi\) | ||
0.980892 | − | 0.194554i | \(-0.0623258\pi\) | |||||||
\(68\) | 1.02342e9 | − | 7.13169e8i | 0.703899 | − | 0.490510i | ||||
\(69\) | −2.21308e9 | −1.41498 | ||||||||
\(70\) | 1.32400e8 | + | 4.21580e8i | 0.0787770 | + | 0.250836i | ||||
\(71\) | − | 1.13070e9i | − | 0.626694i | −0.949639 | − | 0.313347i | \(-0.898550\pi\) | ||
0.949639 | − | 0.313347i | \(-0.101450\pi\) | |||||||
\(72\) | −8.93929e8 | + | 1.15685e9i | −0.461999 | + | 0.597883i | ||||
\(73\) | 1.23872e9 | 0.597528 | 0.298764 | − | 0.954327i | \(-0.403426\pi\) | ||||
0.298764 | + | 0.954327i | \(0.403426\pi\) | |||||||
\(74\) | 3.32907e9 | − | 1.04552e9i | 1.50025 | − | 0.471166i | ||||
\(75\) | − | 6.28850e8i | − | 0.264997i | ||||||
\(76\) | −8.39647e8 | − | 1.20492e9i | −0.331153 | − | 0.475216i | ||||
\(77\) | 1.14911e9 | 0.424528 | ||||||||
\(78\) | 1.61242e9 | + | 5.13414e9i | 0.558476 | + | 1.77826i | ||||
\(79\) | − | 1.72330e9i | − | 0.560049i | −0.959993 | − | 0.280025i | \(-0.909657\pi\) | ||
0.959993 | − | 0.280025i | \(-0.0903426\pi\) | |||||||
\(80\) | −5.07422e8 | + | 1.37478e9i | −0.154853 | + | 0.419548i | ||||
\(81\) | −4.13071e9 | −1.18468 | ||||||||
\(82\) | 1.01975e9 | − | 3.20261e8i | 0.275059 | − | 0.0863844i | ||||
\(83\) | 5.52854e9i | 1.40352i | 0.712411 | + | 0.701762i | \(0.247603\pi\) | ||||
−0.712411 | + | 0.701762i | \(0.752397\pi\) | |||||||
\(84\) | −2.67275e9 | + | 1.86250e9i | −0.639089 | + | 0.445347i | ||||
\(85\) | −1.70243e9 | −0.383686 | ||||||||
\(86\) | 7.60011e8 | + | 2.41997e9i | 0.161558 | + | 0.514420i | ||||
\(87\) | − | 9.21126e9i | − | 1.84809i | ||||||
\(88\) | 3.01545e9 | + | 2.33011e9i | 0.571398 | + | 0.441533i | ||||
\(89\) | −3.77598e8 | −0.0676207 | −0.0338104 | − | 0.999428i | \(-0.510764\pi\) | ||||
−0.0338104 | + | 0.999428i | \(0.510764\pi\) | |||||||
\(90\) | 1.90364e9 | − | 5.97852e8i | 0.322383 | − | 0.101247i | ||||
\(91\) | 5.16082e9i | 0.827011i | ||||||||
\(92\) | −4.02408e9 | − | 5.77470e9i | −0.610559 | − | 0.876174i | ||||
\(93\) | 1.28260e10 | 1.84364 | ||||||||
\(94\) | −4.31500e9 | − | 1.37395e10i | −0.587951 | − | 1.87211i | ||||
\(95\) | 2.00435e9i | 0.259034i | ||||||||
\(96\) | −1.07904e10 | − | 5.32184e8i | −1.32338 | − | 0.0652688i | ||||
\(97\) | −3.29891e9 | −0.384160 | −0.192080 | − | 0.981379i | \(-0.561523\pi\) | ||||
−0.192080 | + | 0.981379i | \(0.561523\pi\) | |||||||
\(98\) | 5.64329e9 | − | 1.77232e9i | 0.624313 | − | 0.196070i | ||||
\(99\) | − | 5.18876e9i | − | 0.545617i | ||||||
\(100\) | 1.64089e9 | − | 1.14345e9i | 0.164089 | − | 0.114345i | ||||
\(101\) | −1.36534e10 | −1.29907 | −0.649537 | − | 0.760330i | \(-0.725037\pi\) | ||||
−0.649537 | + | 0.760330i | \(0.725037\pi\) | |||||||
\(102\) | −3.76059e9 | − | 1.19742e10i | −0.340608 | − | 1.08454i | ||||
\(103\) | 7.59746e9i | 0.655364i | 0.944788 | + | 0.327682i | \(0.106267\pi\) | ||||
−0.944788 | + | 0.327682i | \(0.893733\pi\) | |||||||
\(104\) | −1.04649e10 | + | 1.35429e10i | −0.860138 | + | 1.11313i | ||||
\(105\) | 4.44604e9 | 0.348359 | ||||||||
\(106\) | −7.01015e9 | + | 2.20159e9i | −0.523839 | + | 0.164516i | ||||
\(107\) | 2.71478e10i | 1.93560i | 0.251717 | + | 0.967801i | \(0.419005\pi\) | ||||
−0.251717 | + | 0.967801i | \(0.580995\pi\) | |||||||
\(108\) | −2.72049e9 | − | 3.90399e9i | −0.185152 | − | 0.265699i | ||||
\(109\) | 1.34821e10 | 0.876245 | 0.438122 | − | 0.898915i | \(-0.355644\pi\) | ||||
0.438122 | + | 0.898915i | \(0.355644\pi\) | |||||||
\(110\) | −1.55836e9 | − | 4.96201e9i | −0.0967617 | − | 0.308102i | ||||
\(111\) | − | 3.51088e10i | − | 2.08354i | ||||||
\(112\) | −9.71981e9 | − | 3.58753e9i | −0.551528 | − | 0.203566i | ||||
\(113\) | 1.51614e10 | 0.822899 | 0.411449 | − | 0.911433i | \(-0.365023\pi\) | ||||
0.411449 | + | 0.911433i | \(0.365023\pi\) | |||||||
\(114\) | −1.40978e10 | + | 4.42751e9i | −0.732194 | + | 0.229951i | ||||
\(115\) | 9.60605e9i | 0.477590i | ||||||||
\(116\) | 2.40354e10 | − | 1.67490e10i | 1.14436 | − | 0.797442i | ||||
\(117\) | 2.33036e10 | 1.06290 | ||||||||
\(118\) | 1.25787e10 | + | 4.00523e10i | 0.549828 | + | 1.75072i | ||||
\(119\) | − | 1.20364e10i | − | 0.504385i | ||||||
\(120\) | 1.16672e10 | + | 9.01550e9i | 0.468878 | + | 0.362313i | ||||
\(121\) | 1.24124e10 | 0.478553 | ||||||||
\(122\) | −2.49609e10 | + | 7.83917e9i | −0.923552 | + | 0.290049i | ||||
\(123\) | − | 1.07545e10i | − | 0.382000i | ||||||
\(124\) | 2.33217e10 | + | 3.34674e10i | 0.795520 | + | 1.14160i | ||||
\(125\) | −2.72958e9 | −0.0894427 | ||||||||
\(126\) | 4.22688e9 | + | 1.34589e10i | 0.133097 | + | 0.423797i | ||||
\(127\) | 4.87268e10i | 1.47485i | 0.675427 | + | 0.737427i | \(0.263959\pi\) | ||||
−0.675427 | + | 0.737427i | \(0.736041\pi\) | |||||||
\(128\) | −1.82318e10 | − | 2.91237e10i | −0.530615 | − | 0.847613i | ||||
\(129\) | 2.55214e10 | 0.714423 | ||||||||
\(130\) | 2.22852e10 | − | 6.99883e9i | 0.600204 | − | 0.188499i | ||||
\(131\) | − | 9.99247e8i | − | 0.0259010i | −0.999916 | − | 0.0129505i | \(-0.995878\pi\) | ||
0.999916 | − | 0.0129505i | \(-0.00412238\pi\) | |||||||
\(132\) | 3.14583e10 | − | 2.19216e10i | 0.784993 | − | 0.547020i | ||||
\(133\) | −1.41710e10 | −0.340520 | ||||||||
\(134\) | −5.03705e9 | − | 1.60386e10i | −0.116588 | − | 0.371230i | ||||
\(135\) | 6.49418e9i | 0.144829i | ||||||||
\(136\) | 2.44069e10 | − | 3.15856e10i | 0.524589 | − | 0.678882i | ||||
\(137\) | −4.30128e10 | −0.891240 | −0.445620 | − | 0.895222i | \(-0.647017\pi\) | ||||
−0.445620 | + | 0.895222i | \(0.647017\pi\) | |||||||
\(138\) | −6.75648e10 | + | 2.12192e10i | −1.34997 | + | 0.423969i | ||||
\(139\) | 1.98596e10i | 0.382734i | 0.981519 | + | 0.191367i | \(0.0612921\pi\) | ||||
−0.981519 | + | 0.191367i | \(0.938708\pi\) | |||||||
\(140\) | 8.08432e9 | + | 1.16013e10i | 0.150315 | + | 0.215708i | ||||
\(141\) | −1.44899e11 | −2.59997 | ||||||||
\(142\) | −1.08413e10 | − | 3.45200e10i | −0.187776 | − | 0.597901i | ||||
\(143\) | − | 6.07429e10i | − | 1.01582i | ||||||
\(144\) | −1.61994e10 | + | 4.38896e10i | −0.261630 | + | 0.708842i | ||||
\(145\) | −3.99822e10 | −0.623774 | ||||||||
\(146\) | 3.78178e10 | − | 1.18770e10i | 0.570075 | − | 0.179037i | ||||
\(147\) | − | 5.95149e10i | − | 0.867040i | ||||||
\(148\) | 9.16112e10 | − | 6.38390e10i | 1.29015 | − | 0.899037i | ||||
\(149\) | −2.30686e10 | −0.314116 | −0.157058 | − | 0.987589i | \(-0.550201\pi\) | ||||
−0.157058 | + | 0.987589i | \(0.550201\pi\) | |||||||
\(150\) | −6.02949e9 | − | 1.91987e10i | −0.0794006 | − | 0.252822i | ||||
\(151\) | − | 8.15340e9i | − | 0.103861i | −0.998651 | − | 0.0519307i | \(-0.983463\pi\) | ||
0.998651 | − | 0.0519307i | \(-0.0165375\pi\) | |||||||
\(152\) | −3.71872e10 | − | 2.87354e10i | −0.458327 | − | 0.354160i | ||||
\(153\) | −5.43501e10 | −0.648251 | ||||||||
\(154\) | 3.50819e10 | − | 1.10178e10i | 0.405023 | − | 0.127201i | ||||
\(155\) | − | 5.56721e10i | − | 0.622271i | ||||||
\(156\) | 9.84535e10 | + | 1.41284e11i | 1.06563 | + | 1.52922i | ||||
\(157\) | 1.66306e11 | 1.74345 | 0.871724 | − | 0.489997i | \(-0.163002\pi\) | ||||
0.871724 | + | 0.489997i | \(0.163002\pi\) | |||||||
\(158\) | −1.65232e10 | − | 5.26121e10i | −0.167807 | − | 0.534318i | ||||
\(159\) | 7.39299e10i | 0.727503i | ||||||||
\(160\) | −2.30999e9 | + | 4.68368e10i | −0.0220298 | + | 0.446671i | ||||
\(161\) | −6.79159e10 | −0.627830 | ||||||||
\(162\) | −1.26110e11 | + | 3.96057e10i | −1.13025 | + | 0.354963i | ||||
\(163\) | 7.41987e9i | 0.0644849i | 0.999480 | + | 0.0322425i | \(0.0102649\pi\) | ||||
−0.999480 | + | 0.0322425i | \(0.989735\pi\) | |||||||
\(164\) | 2.80622e10 | − | 1.95550e10i | 0.236538 | − | 0.164831i | ||||
\(165\) | −5.23300e10 | −0.427889 | ||||||||
\(166\) | 5.30083e10 | + | 1.68785e11i | 0.420536 | + | 1.33904i | ||||
\(167\) | − | 8.08722e10i | − | 0.622611i | −0.950310 | − | 0.311306i | \(-0.899234\pi\) | ||
0.950310 | − | 0.311306i | \(-0.100766\pi\) | |||||||
\(168\) | −6.37406e10 | + | 8.24882e10i | −0.476288 | + | 0.616376i | ||||
\(169\) | 1.34948e11 | 0.978885 | ||||||||
\(170\) | −5.19750e10 | + | 1.63231e10i | −0.366058 | + | 0.114963i | ||||
\(171\) | 6.39889e10i | 0.437647i | ||||||||
\(172\) | 4.64059e10 | + | 6.65942e10i | 0.308270 | + | 0.442379i | ||||
\(173\) | −1.70411e11 | −1.09968 | −0.549841 | − | 0.835270i | \(-0.685312\pi\) | ||||
−0.549841 | + | 0.835270i | \(0.685312\pi\) | |||||||
\(174\) | −8.83186e10 | − | 2.81218e11i | −0.553740 | − | 1.76318i | ||||
\(175\) | − | 1.92984e10i | − | 0.117579i | ||||||
\(176\) | 1.14402e11 | + | 4.22253e10i | 0.677442 | + | 0.250040i | ||||
\(177\) | 4.22397e11 | 2.43139 | ||||||||
\(178\) | −1.15280e10 | + | 3.62045e9i | −0.0645140 | + | 0.0202611i | ||||
\(179\) | − | 4.09183e10i | − | 0.222665i | −0.993783 | − | 0.111333i | \(-0.964488\pi\) | ||
0.993783 | − | 0.111333i | \(-0.0355119\pi\) | |||||||
\(180\) | 5.23854e10 | − | 3.65046e10i | 0.277235 | − | 0.193190i | ||||
\(181\) | 7.20812e10 | 0.371047 | 0.185524 | − | 0.982640i | \(-0.440602\pi\) | ||||
0.185524 | + | 0.982640i | \(0.440602\pi\) | |||||||
\(182\) | 4.94825e10 | + | 1.57559e11i | 0.247796 | + | 0.789015i | ||||
\(183\) | 2.63241e11i | 1.28262i | ||||||||
\(184\) | −1.78223e11 | − | 1.37717e11i | −0.845034 | − | 0.652978i | ||||
\(185\) | −1.52393e11 | −0.703243 | ||||||||
\(186\) | 3.91574e11 | − | 1.22977e11i | 1.75893 | − | 0.552406i | ||||
\(187\) | 1.41669e11i | 0.619535i | ||||||||
\(188\) | −2.63472e11 | − | 3.78092e11i | −1.12188 | − | 1.60993i | ||||
\(189\) | −4.59146e10 | −0.190389 | ||||||||
\(190\) | 1.92180e10 | + | 6.11925e10i | 0.0776139 | + | 0.247133i | ||||
\(191\) | 8.10586e10i | 0.318884i | 0.987207 | + | 0.159442i | \(0.0509694\pi\) | ||||
−0.987207 | + | 0.159442i | \(0.949031\pi\) | |||||||
\(192\) | −3.34533e11 | + | 8.72125e10i | −1.28213 | + | 0.334251i | ||||
\(193\) | 4.12567e11 | 1.54066 | 0.770331 | − | 0.637644i | \(-0.220091\pi\) | ||||
0.770331 | + | 0.637644i | \(0.220091\pi\) | |||||||
\(194\) | −1.00715e11 | + | 3.16303e10i | −0.366510 | + | 0.115105i | ||||
\(195\) | − | 2.35022e11i | − | 0.833559i | ||||||
\(196\) | 1.55295e11 | − | 1.08217e11i | 0.536881 | − | 0.374124i | ||||
\(197\) | 1.51409e11 | 0.510295 | 0.255148 | − | 0.966902i | \(-0.417876\pi\) | ||||
0.255148 | + | 0.966902i | \(0.417876\pi\) | |||||||
\(198\) | −4.97504e10 | − | 1.58412e11i | −0.163482 | − | 0.520549i | ||||
\(199\) | 3.84001e11i | 1.23046i | 0.788348 | + | 0.615229i | \(0.210936\pi\) | ||||
−0.788348 | + | 0.615229i | \(0.789064\pi\) | |||||||
\(200\) | 3.91325e10 | − | 5.06423e10i | 0.122289 | − | 0.158257i | ||||
\(201\) | −1.69145e11 | −0.515561 | ||||||||
\(202\) | −4.16835e11 | + | 1.30910e11i | −1.23939 | + | 0.389240i | ||||
\(203\) | − | 2.82679e11i | − | 0.819999i | ||||||
\(204\) | −2.29620e11 | − | 3.29513e11i | −0.649918 | − | 0.932656i | ||||
\(205\) | −4.66806e10 | −0.128934 | ||||||||
\(206\) | 7.28453e10 | + | 2.31949e11i | 0.196366 | + | 0.625254i | ||||
\(207\) | 3.06673e11i | 0.806907i | ||||||||
\(208\) | −1.89641e11 | + | 5.13800e11i | −0.487096 | + | 1.31971i | ||||
\(209\) | 1.66793e11 | 0.418260 | ||||||||
\(210\) | 1.35737e11 | − | 4.26291e10i | 0.332354 | − | 0.104378i | ||||
\(211\) | − | 3.93275e11i | − | 0.940339i | −0.882576 | − | 0.470169i | \(-0.844193\pi\) | ||
0.882576 | − | 0.470169i | \(-0.155807\pi\) | |||||||
\(212\) | −1.92909e11 | + | 1.34428e11i | −0.450478 | + | 0.313914i | ||||
\(213\) | −3.64053e11 | −0.830360 | ||||||||
\(214\) | 2.60296e11 | + | 8.28817e11i | 0.579961 | + | 1.84667i | ||||
\(215\) | − | 1.10778e11i | − | 0.241135i | ||||||
\(216\) | −1.20488e11 | − | 9.31038e10i | −0.256256 | − | 0.198015i | ||||
\(217\) | 3.93608e11 | 0.818023 | ||||||||
\(218\) | 4.11606e11 | − | 1.29268e11i | 0.835987 | − | 0.262548i | ||||
\(219\) | − | 3.98832e11i | − | 0.791716i | ||||||
\(220\) | −9.51526e10 | − | 1.36547e11i | −0.184632 | − | 0.264954i | ||||
\(221\) | −6.36257e11 | −1.20690 | ||||||||
\(222\) | −3.36627e11 | − | 1.07186e12i | −0.624287 | − | 1.98781i | ||||
\(223\) | − | 4.92177e11i | − | 0.892476i | −0.894914 | − | 0.446238i | \(-0.852763\pi\) | ||
0.894914 | − | 0.446238i | \(-0.147237\pi\) | |||||||
\(224\) | −3.31142e11 | − | 1.63319e10i | −0.587183 | − | 0.0289598i | ||||
\(225\) | −8.71415e10 | −0.151117 | ||||||||
\(226\) | 4.62874e11 | − | 1.45369e11i | 0.785091 | − | 0.246564i | ||||
\(227\) | − | 1.43066e11i | − | 0.237359i | −0.992933 | − | 0.118680i | \(-0.962134\pi\) | ||
0.992933 | − | 0.118680i | \(-0.0378662\pi\) | |||||||
\(228\) | −3.87950e11 | + | 2.70342e11i | −0.629654 | + | 0.438772i | ||||
\(229\) | 1.63175e11 | 0.259105 | 0.129553 | − | 0.991573i | \(-0.458646\pi\) | ||||
0.129553 | + | 0.991573i | \(0.458646\pi\) | |||||||
\(230\) | 9.21039e10 | + | 2.93271e11i | 0.143100 | + | 0.455648i | ||||
\(231\) | − | 3.69979e11i | − | 0.562493i | ||||||
\(232\) | 5.73205e11 | − | 7.41798e11i | 0.852845 | − | 1.10369i | ||||
\(233\) | −2.54521e11 | −0.370633 | −0.185316 | − | 0.982679i | \(-0.559331\pi\) | ||||
−0.185316 | + | 0.982679i | \(0.559331\pi\) | |||||||
\(234\) | 7.11453e11 | − | 2.23437e11i | 1.01407 | − | 0.318476i | ||||
\(235\) | 6.28945e11i | 0.877553i | ||||||||
\(236\) | 7.68052e11 | + | 1.10218e12i | 1.04913 | + | 1.50554i | ||||
\(237\) | −5.54854e11 | −0.742056 | ||||||||
\(238\) | −1.15406e11 | − | 3.67469e11i | −0.151128 | − | 0.481211i | ||||
\(239\) | 3.35494e11i | 0.430224i | 0.976589 | + | 0.215112i | \(0.0690117\pi\) | ||||
−0.976589 | + | 0.215112i | \(0.930988\pi\) | |||||||
\(240\) | 4.42638e11 | + | 1.63375e11i | 0.555895 | + | 0.205178i | ||||
\(241\) | −1.29161e12 | −1.58872 | −0.794359 | − | 0.607449i | \(-0.792193\pi\) | ||||
−0.794359 | + | 0.607449i | \(0.792193\pi\) | |||||||
\(242\) | 3.78949e11 | − | 1.19012e11i | 0.456566 | − | 0.143388i | ||||
\(243\) | 1.05558e12i | 1.24583i | ||||||||
\(244\) | −6.86889e11 | + | 4.78656e11i | −0.794214 | + | 0.553445i | ||||
\(245\) | −2.58329e11 | −0.292646 | ||||||||
\(246\) | −1.03115e11 | − | 3.28331e11i | −0.114458 | − | 0.364449i | ||||
\(247\) | 7.49095e11i | 0.814802i | ||||||||
\(248\) | 1.03290e12 | + | 7.98143e11i | 1.10103 | + | 0.850790i | ||||
\(249\) | 1.78003e12 | 1.85965 | ||||||||
\(250\) | −8.33334e10 | + | 2.61715e10i | −0.0853334 | + | 0.0267996i | ||||
\(251\) | 3.91363e11i | 0.392836i | 0.980520 | + | 0.196418i | \(0.0629309\pi\) | ||||
−0.980520 | + | 0.196418i | \(0.937069\pi\) | |||||||
\(252\) | 2.58091e11 | + | 3.70370e11i | 0.253963 | + | 0.364446i | ||||
\(253\) | 7.99371e11 | 0.771162 | ||||||||
\(254\) | 4.67198e11 | + | 1.48762e12i | 0.441908 | + | 1.40709i | ||||
\(255\) | 5.48135e11i | 0.508378i | ||||||||
\(256\) | −8.35855e11 | − | 7.14333e11i | −0.760206 | − | 0.649682i | ||||
\(257\) | 3.42869e11 | 0.305818 | 0.152909 | − | 0.988240i | \(-0.451136\pi\) | ||||
0.152909 | + | 0.988240i | \(0.451136\pi\) | |||||||
\(258\) | 7.79162e11 | − | 2.44702e11i | 0.681599 | − | 0.214061i | ||||
\(259\) | − | 1.07743e12i | − | 0.924467i | ||||||
\(260\) | 6.13256e11 | − | 4.27345e11i | 0.516149 | − | 0.359677i | ||||
\(261\) | −1.27643e12 | −1.05389 | ||||||||
\(262\) | −9.58089e9 | − | 3.05068e10i | −0.00776067 | − | 0.0247110i | ||||
\(263\) | − | 1.67441e12i | − | 1.33071i | −0.746526 | − | 0.665356i | \(-0.768280\pi\) | ||
0.746526 | − | 0.665356i | \(-0.231720\pi\) | |||||||
\(264\) | 7.50228e11 | − | 9.70888e11i | 0.585024 | − | 0.757094i | ||||
\(265\) | 3.20899e11 | 0.245549 | ||||||||
\(266\) | −4.32638e11 | + | 1.35873e11i | −0.324875 | + | 0.102030i | ||||
\(267\) | 1.21576e11i | 0.0895964i | ||||||||
\(268\) | −3.07560e11 | − | 4.41360e11i | −0.222462 | − | 0.319241i | ||||
\(269\) | −2.68766e12 | −1.90815 | −0.954077 | − | 0.299561i | \(-0.903160\pi\) | ||||
−0.954077 | + | 0.299561i | \(0.903160\pi\) | |||||||
\(270\) | 6.22670e10 | + | 1.98266e11i | 0.0433949 | + | 0.138175i | ||||
\(271\) | − | 1.92161e12i | − | 1.31468i | −0.753595 | − | 0.657339i | \(-0.771682\pi\) | ||
0.753595 | − | 0.657339i | \(-0.228318\pi\) | |||||||
\(272\) | 4.42293e11 | − | 1.19832e12i | 0.297074 | − | 0.804873i | ||||
\(273\) | 1.66163e12 | 1.09578 | ||||||||
\(274\) | −1.31317e12 | + | 4.12411e11i | −0.850293 | + | 0.267041i | ||||
\(275\) | 2.27143e11i | 0.144423i | ||||||||
\(276\) | −1.85929e12 | + | 1.29564e12i | −1.16092 | + | 0.808981i | ||||
\(277\) | −8.69557e11 | −0.533211 | −0.266605 | − | 0.963806i | \(-0.585902\pi\) | ||||
−0.266605 | + | 0.963806i | \(0.585902\pi\) | |||||||
\(278\) | 1.90416e11 | + | 6.06311e11i | 0.114678 | + | 0.365150i | ||||
\(279\) | − | 1.77733e12i | − | 1.05135i | ||||||
\(280\) | 3.58047e11 | + | 2.76671e11i | 0.208041 | + | 0.160759i | ||||
\(281\) | 1.80190e12 | 1.02849 | 0.514244 | − | 0.857644i | \(-0.328072\pi\) | ||||
0.514244 | + | 0.857644i | \(0.328072\pi\) | |||||||
\(282\) | −4.42373e12 | + | 1.38931e12i | −2.48052 | + | 0.779026i | ||||
\(283\) | 1.85966e12i | 1.02448i | 0.858843 | + | 0.512238i | \(0.171184\pi\) | ||||
−0.858843 | + | 0.512238i | \(0.828816\pi\) | |||||||
\(284\) | −6.61964e11 | − | 9.49942e11i | −0.358297 | − | 0.514169i | ||||
\(285\) | 6.45345e11 | 0.343216 | ||||||||
\(286\) | −5.82410e11 | − | 1.85447e12i | −0.304368 | − | 0.969146i | ||||
\(287\) | − | 3.30037e11i | − | 0.169494i | ||||||
\(288\) | −7.37463e10 | + | 1.49526e12i | −0.0372201 | + | 0.754667i | ||||
\(289\) | −5.32073e11 | −0.263926 | ||||||||
\(290\) | −1.22065e12 | + | 3.83354e11i | −0.595115 | + | 0.186900i | ||||
\(291\) | 1.06215e12i | 0.509006i | ||||||||
\(292\) | 1.04069e12 | − | 7.25203e11i | 0.490239 | − | 0.341622i | ||||
\(293\) | 8.47213e10 | 0.0392333 | 0.0196166 | − | 0.999808i | \(-0.493755\pi\) | ||||
0.0196166 | + | 0.999808i | \(0.493755\pi\) | |||||||
\(294\) | −5.70636e11 | − | 1.81698e12i | −0.259790 | − | 0.827204i | ||||
\(295\) | − | 1.83345e12i | − | 0.820652i | ||||||
\(296\) | 2.18478e12 | − | 2.82737e12i | 0.961498 | − | 1.24430i | ||||
\(297\) | 5.40416e11 | 0.233855 | ||||||||
\(298\) | −7.04280e11 | + | 2.21184e11i | −0.299684 | + | 0.0941181i | ||||
\(299\) | 3.59010e12i | 1.50228i | ||||||||
\(300\) | −3.68158e11 | − | 5.28320e11i | −0.151505 | − | 0.217416i | ||||
\(301\) | 7.83210e11 | 0.316990 | ||||||||
\(302\) | −7.81758e10 | − | 2.48922e11i | −0.0311198 | − | 0.0990896i | ||||
\(303\) | 4.39600e12i | 1.72125i | ||||||||
\(304\) | −1.41083e12 | − | 5.20731e11i | −0.543386 | − | 0.200561i | ||||
\(305\) | 1.14262e12 | 0.432915 | ||||||||
\(306\) | −1.65930e12 | + | 5.21115e11i | −0.618468 | + | 0.194235i | ||||
\(307\) | − | 1.21008e12i | − | 0.443734i | −0.975077 | − | 0.221867i | \(-0.928785\pi\) | ||
0.975077 | − | 0.221867i | \(-0.0712150\pi\) | |||||||
\(308\) | 9.65405e11 | − | 6.72739e11i | 0.348302 | − | 0.242713i | ||||
\(309\) | 2.44616e12 | 0.868347 | ||||||||
\(310\) | −5.33791e11 | − | 1.69966e12i | −0.186450 | − | 0.593681i | ||||
\(311\) | 2.96100e10i | 0.0101774i | 0.999987 | + | 0.00508869i | \(0.00161979\pi\) | ||||
−0.999987 | + | 0.00508869i | \(0.998380\pi\) | |||||||
\(312\) | 4.36041e12 | + | 3.36940e12i | 1.47487 | + | 1.13967i | ||||
\(313\) | 2.37961e12 | 0.792106 | 0.396053 | − | 0.918228i | \(-0.370380\pi\) | ||||
0.396053 | + | 0.918228i | \(0.370380\pi\) | |||||||
\(314\) | 5.07728e12 | − | 1.59456e12i | 1.66335 | − | 0.522387i | ||||
\(315\) | − | 6.16101e11i | − | 0.198655i | ||||||
\(316\) | −1.00890e12 | − | 1.44781e12i | −0.320194 | − | 0.459490i | ||||
\(317\) | −4.50103e12 | −1.40610 | −0.703049 | − | 0.711141i | \(-0.748179\pi\) | ||||
−0.703049 | + | 0.711141i | \(0.748179\pi\) | |||||||
\(318\) | 7.08849e11 | + | 2.25707e12i | 0.217981 | + | 0.694078i | ||||
\(319\) | 3.32714e12i | 1.00720i | ||||||||
\(320\) | 3.78553e11 | + | 1.45207e12i | 0.112818 | + | 0.432750i | ||||
\(321\) | 8.74081e12 | 2.56464 | ||||||||
\(322\) | −2.07346e12 | + | 6.51185e11i | −0.598985 | + | 0.188116i | ||||
\(323\) | − | 1.74709e12i | − | 0.496938i | ||||||
\(324\) | −3.47036e12 | + | 2.41831e12i | −0.971963 | + | 0.677309i | ||||
\(325\) | −1.02013e12 | −0.281346 | ||||||||
\(326\) | 7.11425e10 | + | 2.26527e11i | 0.0193215 | + | 0.0615222i | ||||
\(327\) | − | 4.34085e12i | − | 1.16101i | ||||||
\(328\) | 6.69236e11 | − | 8.66074e11i | 0.176283 | − | 0.228132i | ||||
\(329\) | −4.44671e12 | −1.15361 | ||||||||
\(330\) | −1.59762e12 | + | 5.01746e11i | −0.408230 | + | 0.128208i | ||||
\(331\) | 4.96316e12i | 1.24916i | 0.780960 | + | 0.624581i | \(0.214730\pi\) | ||||
−0.780960 | + | 0.624581i | \(0.785270\pi\) | |||||||
\(332\) | 3.23666e12 | + | 4.64473e12i | 0.802430 | + | 1.15152i | ||||
\(333\) | −4.86513e12 | −1.18815 | ||||||||
\(334\) | −7.75412e11 | − | 2.46901e12i | −0.186552 | − | 0.594006i | ||||
\(335\) | 7.34190e11i | 0.174014i | ||||||||
\(336\) | −1.15508e12 | + | 3.12950e12i | −0.269722 | + | 0.730767i | ||||
\(337\) | 4.05843e12 | 0.933702 | 0.466851 | − | 0.884336i | \(-0.345389\pi\) | ||||
0.466851 | + | 0.884336i | \(0.345389\pi\) | |||||||
\(338\) | 4.11992e12 | − | 1.29389e12i | 0.933911 | − | 0.293302i | ||||
\(339\) | − | 4.88153e12i | − | 1.09033i | ||||||
\(340\) | −1.43028e12 | + | 9.96684e11i | −0.314793 | + | 0.219363i | ||||
\(341\) | −4.63278e12 | −1.00478 | ||||||||
\(342\) | 6.13533e11 | + | 1.95357e12i | 0.131132 | + | 0.417540i | ||||
\(343\) | − | 4.61749e12i | − | 0.972603i | ||||||
\(344\) | 2.05528e12 | + | 1.58816e12i | 0.426656 | + | 0.329687i | ||||
\(345\) | 3.09287e12 | 0.632800 | ||||||||
\(346\) | −5.20261e12 | + | 1.63392e12i | −1.04916 | + | 0.329496i | ||||
\(347\) | − | 7.15107e12i | − | 1.42142i | −0.703483 | − | 0.710712i | \(-0.748373\pi\) | ||
0.703483 | − | 0.710712i | \(-0.251627\pi\) | |||||||
\(348\) | −5.39270e12 | − | 7.73871e12i | −1.05660 | − | 1.51626i | ||||
\(349\) | −3.81727e12 | −0.737268 | −0.368634 | − | 0.929575i | \(-0.620174\pi\) | ||||
−0.368634 | + | 0.929575i | \(0.620174\pi\) | |||||||
\(350\) | −1.85035e11 | − | 5.89176e11i | −0.0352301 | − | 0.112177i | ||||
\(351\) | 2.42709e12i | 0.455566i | ||||||||
\(352\) | 3.89754e12 | + | 1.92227e11i | 0.721236 | + | 0.0355713i | ||||
\(353\) | −5.12751e12 | −0.935477 | −0.467739 | − | 0.883867i | \(-0.654931\pi\) | ||||
−0.467739 | + | 0.883867i | \(0.654931\pi\) | |||||||
\(354\) | 1.28957e13 | − | 4.04999e12i | 2.31968 | − | 0.728514i | ||||
\(355\) | 1.58020e12i | 0.280266i | ||||||||
\(356\) | −3.17234e11 | + | 2.21063e11i | −0.0554791 | + | 0.0386604i | ||||
\(357\) | −3.87538e12 | −0.668302 | ||||||||
\(358\) | −3.92329e11 | − | 1.24923e12i | −0.0667169 | − | 0.212435i | ||||
\(359\) | − | 2.06638e12i | − | 0.346528i | −0.984875 | − | 0.173264i | \(-0.944569\pi\) | ||
0.984875 | − | 0.173264i | \(-0.0554315\pi\) | |||||||
\(360\) | 1.24930e12 | − | 1.61675e12i | 0.206612 | − | 0.267381i | ||||
\(361\) | 4.07414e12 | 0.664507 | ||||||||
\(362\) | 2.20062e12 | − | 6.91123e11i | 0.354000 | − | 0.111176i | ||||
\(363\) | − | 3.99645e12i | − | 0.634075i | ||||||
\(364\) | 3.02138e12 | + | 4.33579e12i | 0.472823 | + | 0.678518i | ||||
\(365\) | −1.73116e12 | −0.267223 | ||||||||
\(366\) | 2.52399e12 | + | 8.03670e12i | 0.384310 | + | 1.22369i | ||||
\(367\) | 1.18436e13i | 1.77891i | 0.457024 | + | 0.889454i | \(0.348915\pi\) | ||||
−0.457024 | + | 0.889454i | \(0.651085\pi\) | |||||||
\(368\) | −6.76155e12 | − | 2.49565e12i | −1.00186 | − | 0.369781i | ||||
\(369\) | −1.49028e12 | −0.217839 | ||||||||
\(370\) | −4.65252e12 | + | 1.46116e12i | −0.670933 | + | 0.210712i | ||||
\(371\) | 2.26879e12i | 0.322794i | ||||||||
\(372\) | 1.07756e13 | − | 7.50891e12i | 1.51260 | − | 1.05405i | ||||
\(373\) | −1.15627e13 | −1.60145 | −0.800726 | − | 0.599031i | \(-0.795553\pi\) | ||||
−0.800726 | + | 0.599031i | \(0.795553\pi\) | |||||||
\(374\) | 1.35834e12 | + | 4.32512e12i | 0.185630 | + | 0.591071i | ||||
\(375\) | 8.78845e11i | 0.118510i | ||||||||
\(376\) | −1.16689e13 | − | 9.01686e12i | −1.55271 | − | 1.19982i | ||||
\(377\) | −1.49427e13 | −1.96211 | ||||||||
\(378\) | −1.40176e12 | + | 4.40234e11i | −0.181642 | + | 0.0570460i | ||||
\(379\) | 3.30334e12i | 0.422432i | 0.977439 | + | 0.211216i | \(0.0677423\pi\) | ||||
−0.977439 | + | 0.211216i | \(0.932258\pi\) | |||||||
\(380\) | 1.17344e12 | + | 1.68393e12i | 0.148096 | + | 0.212523i | ||||
\(381\) | 1.56886e13 | 1.95416 | ||||||||
\(382\) | 7.77199e11 | + | 2.47470e12i | 0.0955467 | + | 0.304233i | ||||
\(383\) | 5.18660e11i | 0.0629345i | 0.999505 | + | 0.0314672i | \(0.0100180\pi\) | ||||
−0.999505 | + | 0.0314672i | \(0.989982\pi\) | |||||||
\(384\) | −9.37701e12 | + | 5.87012e12i | −1.12307 | + | 0.703057i | ||||
\(385\) | −1.60592e12 | −0.189855 | ||||||||
\(386\) | 1.25956e13 | − | 3.95574e12i | 1.46988 | − | 0.461626i | ||||
\(387\) | − | 3.53657e12i | − | 0.407406i | ||||||
\(388\) | −2.77153e12 | + | 1.93133e12i | −0.315182 | + | 0.219634i | ||||
\(389\) | 3.58538e12 | 0.402520 | 0.201260 | − | 0.979538i | \(-0.435496\pi\) | ||||
0.201260 | + | 0.979538i | \(0.435496\pi\) | |||||||
\(390\) | −2.25342e12 | − | 7.17518e12i | −0.249758 | − | 0.795261i | ||||
\(391\) | − | 8.37308e12i | − | 0.916224i | ||||||
\(392\) | 3.70354e12 | − | 4.79283e12i | 0.400116 | − | 0.517800i | ||||
\(393\) | −3.21729e11 | −0.0343184 | ||||||||
\(394\) | 4.62249e12 | − | 1.45173e12i | 0.486850 | − | 0.152899i | ||||
\(395\) | 2.40839e12i | 0.250462i | ||||||||
\(396\) | −3.03774e12 | − | 4.35927e12i | −0.311943 | − | 0.447649i | ||||
\(397\) | 5.16380e11 | 0.0523621 | 0.0261811 | − | 0.999657i | \(-0.491665\pi\) | ||||
0.0261811 | + | 0.999657i | \(0.491665\pi\) | |||||||
\(398\) | 3.68184e12 | + | 1.17235e13i | 0.368680 | + | 1.17393i | ||||
\(399\) | 4.56266e12i | 0.451184i | ||||||||
\(400\) | 7.09144e11 | − | 1.92131e12i | 0.0692523 | − | 0.187628i | ||||
\(401\) | 8.69234e12 | 0.838330 | 0.419165 | − | 0.907910i | \(-0.362323\pi\) | ||||
0.419165 | + | 0.907910i | \(0.362323\pi\) | |||||||
\(402\) | −5.16397e12 | + | 1.62179e12i | −0.491874 | + | 0.154477i | ||||
\(403\) | − | 2.08065e13i | − | 1.95738i | ||||||
\(404\) | −1.14707e13 | + | 7.99333e12i | −1.06582 | + | 0.742713i | ||||
\(405\) | 5.77285e12 | 0.529804 | ||||||||
\(406\) | −2.71036e12 | − | 8.63012e12i | −0.245695 | − | 0.782324i | ||||
\(407\) | 1.26814e13i | 1.13552i | ||||||||
\(408\) | −1.01697e13 | − | 7.85833e12i | −0.899508 | − | 0.695072i | ||||
\(409\) | 1.87261e13 | 1.63618 | 0.818088 | − | 0.575093i | \(-0.195034\pi\) | ||||
0.818088 | + | 0.575093i | \(0.195034\pi\) | |||||||
\(410\) | −1.42515e12 | + | 4.47579e11i | −0.123010 | + | 0.0386323i | ||||
\(411\) | 1.38489e13i | 1.18088i | ||||||||
\(412\) | 4.44791e12 | + | 6.38290e12i | 0.374688 | + | 0.537690i | ||||
\(413\) | 1.29627e13 | 1.07881 | ||||||||
\(414\) | 2.94041e12 | + | 9.36265e12i | 0.241772 | + | 0.769834i | ||||
\(415\) | − | 7.72637e12i | − | 0.627675i | ||||||
\(416\) | −8.63320e11 | + | 1.75045e13i | −0.0692955 | + | 1.40502i | ||||
\(417\) | 6.39423e12 | 0.507117 | ||||||||
\(418\) | 5.09216e12 | − | 1.59923e12i | 0.399044 | − | 0.125323i | ||||
\(419\) | − | 1.83208e13i | − | 1.41865i | −0.704883 | − | 0.709324i | \(-0.749000\pi\) | ||
0.704883 | − | 0.709324i | \(-0.251000\pi\) | |||||||
\(420\) | 3.73528e12 | − | 2.60292e12i | 0.285809 | − | 0.199165i | ||||
\(421\) | 6.36675e12 | 0.481402 | 0.240701 | − | 0.970599i | \(-0.422623\pi\) | ||||
0.240701 | + | 0.970599i | \(0.422623\pi\) | |||||||
\(422\) | −3.77077e12 | − | 1.20066e13i | −0.281752 | − | 0.897136i | ||||
\(423\) | 2.00790e13i | 1.48266i | ||||||||
\(424\) | −4.60057e12 | + | 5.95370e12i | −0.335724 | + | 0.434468i | ||||
\(425\) | 2.37922e12 | 0.171590 | ||||||||
\(426\) | −1.11145e13 | + | 3.49058e12i | −0.792210 | + | 0.248800i | ||||
\(427\) | 8.07845e12i | 0.569100i | ||||||||
\(428\) | 1.58936e13 | + | 2.28079e13i | 1.10663 | + | 1.58806i | ||||
\(429\) | −1.95575e13 | −1.34594 | ||||||||
\(430\) | −1.06215e12 | − | 3.38201e12i | −0.0722508 | − | 0.230056i | ||||
\(431\) | − | 2.18784e12i | − | 0.147106i | −0.997291 | − | 0.0735528i | \(-0.976566\pi\) | ||
0.997291 | − | 0.0735528i | \(-0.0234337\pi\) | |||||||
\(432\) | −4.57116e12 | − | 1.68719e12i | −0.303814 | − | 0.112136i | ||||
\(433\) | 1.68547e13 | 1.10734 | 0.553672 | − | 0.832735i | \(-0.313226\pi\) | ||||
0.553672 | + | 0.832735i | \(0.313226\pi\) | |||||||
\(434\) | 1.20168e13 | − | 3.77396e12i | 0.780440 | − | 0.245103i | ||||
\(435\) | 1.28731e13i | 0.826490i | ||||||||
\(436\) | 1.13268e13 | − | 7.89305e12i | 0.718911 | − | 0.500971i | ||||
\(437\) | −9.85801e12 | −0.618561 | ||||||||
\(438\) | −3.82404e12 | − | 1.21763e13i | −0.237221 | − | 0.755341i | ||||
\(439\) | − | 1.97691e12i | − | 0.121245i | −0.998161 | − | 0.0606225i | \(-0.980691\pi\) | ||
0.998161 | − | 0.0606225i | \(-0.0193086\pi\) | |||||||
\(440\) | −4.21422e12 | − | 3.25643e12i | −0.255537 | − | 0.197460i | ||||
\(441\) | −8.24715e12 | −0.494437 | ||||||||
\(442\) | −1.94248e13 | + | 6.10050e12i | −1.15145 | + | 0.361622i | ||||
\(443\) | 8.05360e12i | 0.472032i | 0.971749 | + | 0.236016i | \(0.0758418\pi\) | ||||
−0.971749 | + | 0.236016i | \(0.924158\pi\) | |||||||
\(444\) | −2.05543e13 | − | 2.94962e13i | −1.19121 | − | 1.70943i | ||||
\(445\) | 5.27710e11 | 0.0302409 | ||||||||
\(446\) | −4.71905e12 | − | 1.50261e13i | −0.267411 | − | 0.851473i | ||||
\(447\) | 7.42743e12i | 0.416199i | ||||||||
\(448\) | −1.02663e13 | + | 2.67641e12i | −0.568883 | + | 0.148308i | ||||
\(449\) | −8.91317e12 | −0.488428 | −0.244214 | − | 0.969721i | \(-0.578530\pi\) | ||||
−0.244214 | + | 0.969721i | \(0.578530\pi\) | |||||||
\(450\) | −2.66041e12 | + | 8.35523e11i | −0.144174 | + | 0.0452789i | ||||
\(451\) | 3.88454e12i | 0.208189i | ||||||||
\(452\) | 1.27376e13 | − | 8.87617e12i | 0.675144 | − | 0.470472i | ||||
\(453\) | −2.62516e12 | −0.137615 | ||||||||
\(454\) | −1.37173e12 | − | 4.36777e12i | −0.0711196 | − | 0.226454i | ||||
\(455\) | − | 7.21246e12i | − | 0.369851i | ||||||
\(456\) | −9.25198e12 | + | 1.19732e13i | −0.469257 | + | 0.607276i | ||||
\(457\) | 1.48751e13 | 0.746239 | 0.373119 | − | 0.927783i | \(-0.378288\pi\) | ||||
0.373119 | + | 0.927783i | \(0.378288\pi\) | |||||||
\(458\) | 4.98170e12 | − | 1.56454e12i | 0.247201 | − | 0.0776354i | ||||
\(459\) | − | 5.66063e12i | − | 0.277844i | ||||||
\(460\) | 5.62382e12 | + | 8.07039e12i | 0.273050 | + | 0.391837i | ||||
\(461\) | −1.35057e13 | −0.648655 | −0.324328 | − | 0.945945i | \(-0.605138\pi\) | ||||
−0.324328 | + | 0.945945i | \(0.605138\pi\) | |||||||
\(462\) | −3.54740e12 | − | 1.12954e13i | −0.168539 | − | 0.536650i | ||||
\(463\) | 1.57917e13i | 0.742207i | 0.928591 | + | 0.371104i | \(0.121021\pi\) | ||||
−0.928591 | + | 0.371104i | \(0.878979\pi\) | |||||||
\(464\) | 1.03874e13 | − | 2.81429e13i | 0.482966 | − | 1.30851i | ||||
\(465\) | −1.79248e13 | −0.824499 | ||||||||
\(466\) | −7.77047e12 | + | 2.44038e12i | −0.353604 | + | 0.111052i | ||||
\(467\) | − | 4.34882e13i | − | 1.95789i | −0.204133 | − | 0.978943i | \(-0.565438\pi\) | ||
0.204133 | − | 0.978943i | \(-0.434562\pi\) | |||||||
\(468\) | 1.95782e13 | − | 1.36430e13i | 0.872053 | − | 0.607687i | ||||
\(469\) | −5.19080e12 | −0.228755 | ||||||||
\(470\) | 6.03039e12 | + | 1.92015e13i | 0.262940 | + | 0.837234i | ||||
\(471\) | − | 5.35457e13i | − | 2.31004i | ||||||
\(472\) | 3.40163e13 | + | 2.62852e13i | 1.45204 | + | 1.12202i | ||||
\(473\) | −9.21839e12 | −0.389358 | ||||||||
\(474\) | −1.69396e13 | + | 5.32000e12i | −0.707963 | + | 0.222341i | ||||
\(475\) | − | 2.80117e12i | − | 0.115843i | ||||||
\(476\) | −7.04667e12 | − | 1.01122e13i | −0.288369 | − | 0.413820i | ||||
\(477\) | 1.02447e13 | 0.414865 | ||||||||
\(478\) | 3.21675e12 | + | 1.02425e13i | 0.128907 | + | 0.410458i | ||||
\(479\) | − | 4.52122e12i | − | 0.179299i | −0.995973 | − | 0.0896496i | \(-0.971425\pi\) | ||
0.995973 | − | 0.0896496i | \(-0.0285747\pi\) | |||||||
\(480\) | 1.50801e13 | + | 7.43750e11i | 0.591832 | + | 0.0291891i | ||||
\(481\) | −5.69543e13 | −2.21208 | ||||||||
\(482\) | −3.94326e13 | + | 1.23841e13i | −1.51573 | + | 0.476025i | ||||
\(483\) | 2.18669e13i | 0.831864i | ||||||||
\(484\) | 1.04281e13 | − | 7.26681e12i | 0.392627 | − | 0.273601i | ||||
\(485\) | 4.61037e12 | 0.171801 | ||||||||
\(486\) | 1.01210e13 | + | 3.22266e13i | 0.373286 | + | 1.18859i | ||||
\(487\) | − | 1.43856e13i | − | 0.525150i | −0.964912 | − | 0.262575i | \(-0.915428\pi\) | ||
0.964912 | − | 0.262575i | \(-0.0845717\pi\) | |||||||
\(488\) | −1.63812e13 | + | 2.11992e13i | −0.591896 | + | 0.765987i | ||||
\(489\) | 2.38898e12 | 0.0854415 | ||||||||
\(490\) | −7.88674e12 | + | 2.47689e12i | −0.279201 | + | 0.0876852i | ||||
\(491\) | 5.09640e13i | 1.78589i | 0.450161 | + | 0.892947i | \(0.351367\pi\) | ||||
−0.450161 | + | 0.892947i | \(0.648633\pi\) | |||||||
\(492\) | −6.29615e12 | − | 9.03521e12i | −0.218399 | − | 0.313410i | ||||
\(493\) | 3.48504e13 | 1.19667 | ||||||||
\(494\) | 7.18240e12 | + | 2.28697e13i | 0.244138 | + | 0.777366i | ||||
\(495\) | 7.25152e12i | 0.244007i | ||||||||
\(496\) | 3.91868e13 | + | 1.44636e13i | 1.30536 | + | 0.481802i | ||||
\(497\) | −1.11722e13 | −0.368432 | ||||||||
\(498\) | 5.43440e13 | − | 1.70671e13i | 1.77421 | − | 0.557204i | ||||
\(499\) | 4.39550e13i | 1.42071i | 0.703843 | + | 0.710356i | \(0.251466\pi\) | ||||
−0.703843 | + | 0.710356i | \(0.748534\pi\) | |||||||
\(500\) | −2.29321e12 | + | 1.59802e12i | −0.0733829 | + | 0.0511366i | ||||
\(501\) | −2.60385e13 | −0.824950 | ||||||||
\(502\) | 3.75243e12 | + | 1.19482e13i | 0.117705 | + | 0.374787i | ||||
\(503\) | − | 3.50091e13i | − | 1.08728i | −0.839319 | − | 0.543639i | \(-0.817046\pi\) | ||
0.839319 | − | 0.543639i | \(-0.182954\pi\) | |||||||
\(504\) | 1.14306e13 | + | 8.83272e12i | 0.351494 | + | 0.271608i | ||||
\(505\) | 1.90812e13 | 0.580964 | ||||||||
\(506\) | 2.44046e13 | − | 7.66446e12i | 0.735732 | − | 0.231062i | ||||
\(507\) | − | 4.34493e13i | − | 1.29701i | ||||||
\(508\) | 2.85269e13 | + | 4.09371e13i | 0.843210 | + | 1.21004i | ||||
\(509\) | 3.35614e13 | 0.982315 | 0.491158 | − | 0.871071i | \(-0.336574\pi\) | ||||
0.491158 | + | 0.871071i | \(0.336574\pi\) | |||||||
\(510\) | 5.25558e12 | + | 1.67344e13i | 0.152324 | + | 0.485021i | ||||
\(511\) | − | 1.22395e13i | − | 0.351285i | ||||||
\(512\) | −3.23676e13 | − | 1.37942e13i | −0.919942 | − | 0.392054i | ||||
\(513\) | −6.66452e12 | −0.187578 | ||||||||
\(514\) | 1.04677e13 | − | 3.28747e12i | 0.291767 | − | 0.0916317i | ||||
\(515\) | − | 1.06178e13i | − | 0.293088i | ||||||
\(516\) | 2.14414e13 | − | 1.49414e13i | 0.586145 | − | 0.408453i | ||||
\(517\) | 5.23379e13 | 1.41698 | ||||||||
\(518\) | −1.03306e13 | − | 3.28938e13i | −0.276997 | − | 0.881994i | ||||
\(519\) | 5.48674e13i | 1.45706i | ||||||||
\(520\) | 1.46251e13 | − | 1.89267e13i | 0.384666 | − | 0.497805i | ||||
\(521\) | −4.27804e13 | −1.11444 | −0.557219 | − | 0.830365i | \(-0.688132\pi\) | ||||
−0.557219 | + | 0.830365i | \(0.688132\pi\) | |||||||
\(522\) | −3.89692e13 | + | 1.22386e13i | −1.00547 | + | 0.315775i | ||||
\(523\) | 3.45386e13i | 0.882665i | 0.897344 | + | 0.441332i | \(0.145494\pi\) | ||||
−0.897344 | + | 0.441332i | \(0.854506\pi\) | |||||||
\(524\) | −5.85005e11 | − | 8.39503e11i | −0.0148082 | − | 0.0212503i | ||||
\(525\) | −6.21353e12 | −0.155791 | ||||||||
\(526\) | −1.60545e13 | − | 5.11195e13i | −0.398719 | − | 1.26957i | ||||
\(527\) | 4.85264e13i | 1.19378i | ||||||||
\(528\) | 1.35953e13 | − | 3.68343e13i | 0.331299 | − | 0.897600i | ||||
\(529\) | −5.81890e12 | −0.140463 | ||||||||
\(530\) | 9.79698e12 | − | 3.07682e12i | 0.234268 | − | 0.0735736i | ||||
\(531\) | − | 5.85328e13i | − | 1.38652i | ||||||
\(532\) | −1.19056e13 | + | 8.29637e12i | −0.279378 | + | 0.194684i | ||||
\(533\) | −1.74461e13 | −0.405567 | ||||||||
\(534\) | 1.16568e12 | + | 3.71168e12i | 0.0268456 | + | 0.0854800i | ||||
\(535\) | − | 3.79402e13i | − | 0.865627i | ||||||
\(536\) | −1.36216e13 | − | 1.05257e13i | −0.307895 | − | 0.237918i | ||||
\(537\) | −1.31745e13 | −0.295028 | ||||||||
\(538\) | −8.20538e13 | + | 2.57696e13i | −1.82049 | + | 0.571738i | ||||
\(539\) | 2.14970e13i | 0.472534i | ||||||||
\(540\) | 3.80199e12 | + | 5.45600e12i | 0.0828024 | + | 0.118824i | ||||
\(541\) | −1.36577e13 | −0.294707 | −0.147353 | − | 0.989084i | \(-0.547075\pi\) | ||||
−0.147353 | + | 0.989084i | \(0.547075\pi\) | |||||||
\(542\) | −1.84246e13 | − | 5.86664e13i | −0.393915 | − | 1.25428i | ||||
\(543\) | − | 2.32081e13i | − | 0.491632i | ||||||
\(544\) | 2.01349e12 | − | 4.08251e13i | 0.0422625 | − | 0.856906i | ||||
\(545\) | −1.88418e13 | −0.391869 | ||||||||
\(546\) | 5.07294e13 | − | 1.59319e13i | 1.04543 | − | 0.328326i | ||||
\(547\) | 6.18712e13i | 1.26343i | 0.775200 | + | 0.631716i | \(0.217649\pi\) | ||||
−0.775200 | + | 0.631716i | \(0.782351\pi\) | |||||||
\(548\) | −3.61366e13 | + | 2.51817e13i | −0.731214 | + | 0.509544i | ||||
\(549\) | 3.64781e13 | 0.731426 | ||||||||
\(550\) | 2.17787e12 | + | 6.93462e12i | 0.0432731 | + | 0.137787i | ||||
\(551\) | − | 4.10309e13i | − | 0.807892i | ||||||
\(552\) | −4.43409e13 | + | 5.73826e13i | −0.865186 | + | 1.11966i | ||||
\(553\) | −1.70276e13 | −0.329251 | ||||||||
\(554\) | −2.65474e13 | + | 8.33741e12i | −0.508713 | + | 0.159765i | ||||
\(555\) | 4.90661e13i | 0.931786i | ||||||||
\(556\) | 1.16268e13 | + | 1.66848e13i | 0.218819 | + | 0.314013i | ||||
\(557\) | 5.87222e13 | 1.09528 | 0.547642 | − | 0.836713i | \(-0.315526\pi\) | ||||
0.547642 | + | 0.836713i | \(0.315526\pi\) | |||||||
\(558\) | −1.70412e13 | − | 5.42615e13i | −0.315014 | − | 1.00305i | ||||
\(559\) | − | 4.14013e13i | − | 0.758498i | ||||||
\(560\) | 1.35839e13 | + | 5.01373e12i | 0.246651 | + | 0.0910375i | ||||
\(561\) | 4.56133e13 | 0.820874 | ||||||||
\(562\) | 5.50117e13 | − | 1.72768e13i | 0.981236 | − | 0.308165i | ||||
\(563\) | − | 2.89544e13i | − | 0.511885i | −0.966692 | − | 0.255942i | \(-0.917614\pi\) | ||
0.966692 | − | 0.255942i | \(-0.0823858\pi\) | |||||||
\(564\) | −1.21735e14 | + | 8.48304e13i | −2.13314 | + | 1.48647i | ||||
\(565\) | −2.11887e13 | −0.368012 | ||||||||
\(566\) | 1.78307e13 | + | 5.67751e13i | 0.306962 | + | 0.977408i | ||||
\(567\) | 4.08147e13i | 0.696468i | ||||||||
\(568\) | −2.93178e13 | − | 2.26546e13i | −0.495895 | − | 0.383190i | ||||
\(569\) | 1.61498e13 | 0.270774 | 0.135387 | − | 0.990793i | \(-0.456772\pi\) | ||||
0.135387 | + | 0.990793i | \(0.456772\pi\) | |||||||
\(570\) | 1.97022e13 | − | 6.18764e12i | 0.327447 | − | 0.102837i | ||||
\(571\) | 4.58480e13i | 0.755335i | 0.925941 | + | 0.377667i | \(0.123274\pi\) | ||||
−0.925941 | + | 0.377667i | \(0.876726\pi\) | |||||||
\(572\) | −3.55617e13 | − | 5.10323e13i | −0.580768 | − | 0.833422i | ||||
\(573\) | 2.60985e13 | 0.422516 | ||||||||
\(574\) | −3.16443e12 | − | 1.00760e13i | −0.0507851 | − | 0.161706i | ||||
\(575\) | − | 1.34249e13i | − | 0.213585i | ||||||
\(576\) | 1.20853e13 | + | 4.63571e13i | 0.190610 | + | 0.731146i | ||||
\(577\) | −4.20889e12 | −0.0658095 | −0.0329048 | − | 0.999458i | \(-0.510476\pi\) | ||||
−0.0329048 | + | 0.999458i | \(0.510476\pi\) | |||||||
\(578\) | −1.62441e13 | + | 5.10157e12i | −0.251800 | + | 0.0790797i | ||||
\(579\) | − | 1.32835e14i | − | 2.04135i | ||||||
\(580\) | −3.35905e13 | + | 2.34074e13i | −0.511772 | + | 0.356627i | ||||
\(581\) | 5.46263e13 | 0.825128 | ||||||||
\(582\) | 1.01841e13 | + | 3.24273e13i | 0.152513 | + | 0.485620i | ||||
\(583\) | − | 2.67037e13i | − | 0.396487i | ||||||
\(584\) | 2.48188e13 | − | 3.21186e13i | 0.365356 | − | 0.472816i | ||||
\(585\) | −3.25677e13 | −0.475344 | ||||||||
\(586\) | 2.58652e12 | − | 8.12317e11i | 0.0374307 | − | 0.0117554i | ||||
\(587\) | − | 1.56343e13i | − | 0.224331i | −0.993690 | − | 0.112165i | \(-0.964221\pi\) | ||
0.993690 | − | 0.112165i | \(-0.0357787\pi\) | |||||||
\(588\) | −3.48428e13 | − | 5.00006e13i | −0.495708 | − | 0.711359i | ||||
\(589\) | 5.71324e13 | 0.805946 | ||||||||
\(590\) | −1.75793e13 | − | 5.59748e13i | −0.245891 | − | 0.782948i | ||||
\(591\) | − | 4.87494e13i | − | 0.676133i | ||||||
\(592\) | 3.95916e13 | − | 1.07267e14i | 0.544496 | − | 1.47522i | ||||
\(593\) | 5.47586e13 | 0.746757 | 0.373378 | − | 0.927679i | \(-0.378199\pi\) | ||||
0.373378 | + | 0.927679i | \(0.378199\pi\) | |||||||
\(594\) | 1.64988e13 | − | 5.18157e12i | 0.223110 | − | 0.0700695i | ||||
\(595\) | 1.68214e13i | 0.225568i | ||||||||
\(596\) | −1.93808e13 | + | 1.35054e13i | −0.257715 | + | 0.179588i | ||||
\(597\) | 1.23637e14 | 1.63034 | ||||||||
\(598\) | 3.44223e13 | + | 1.09605e14i | 0.450126 | + | 1.43326i | ||||
\(599\) | 7.28349e13i | 0.944507i | 0.881463 | + | 0.472254i | \(0.156559\pi\) | ||||
−0.881463 | + | 0.472254i | \(0.843441\pi\) | |||||||
\(600\) | −1.63054e13 | − | 1.25996e13i | −0.209688 | − | 0.162031i | ||||
\(601\) | −1.08097e14 | −1.37861 | −0.689303 | − | 0.724474i | \(-0.742083\pi\) | ||||
−0.689303 | + | 0.724474i | \(0.742083\pi\) | |||||||
\(602\) | 2.39112e13 | − | 7.50950e12i | 0.302426 | − | 0.0949792i | ||||
\(603\) | 2.34390e13i | 0.294003i | ||||||||
\(604\) | −4.77338e12 | − | 6.84997e12i | −0.0593801 | − | 0.0852126i | ||||
\(605\) | −1.73469e13 | −0.214015 | ||||||||
\(606\) | 4.21494e13 | + | 1.34209e14i | 0.515737 | + | 1.64217i | ||||
\(607\) | 1.24452e14i | 1.51028i | 0.655561 | + | 0.755142i | \(0.272432\pi\) | ||||
−0.655561 | + | 0.755142i | \(0.727568\pi\) | |||||||
\(608\) | −4.80653e13 | − | 2.37058e12i | −0.578514 | − | 0.0285323i | ||||
\(609\) | −9.10144e13 | −1.08649 | ||||||||
\(610\) | 3.48840e13 | − | 1.09556e13i | 0.413025 | − | 0.129714i | ||||
\(611\) | 2.35058e14i | 2.76038i | ||||||||
\(612\) | −4.56615e13 | + | 3.18191e13i | −0.531855 | + | 0.370621i | ||||
\(613\) | −1.02467e14 | −1.18381 | −0.591903 | − | 0.806009i | \(-0.701623\pi\) | ||||
−0.591903 | + | 0.806009i | \(0.701623\pi\) | |||||||
\(614\) | −1.16024e13 | − | 3.69435e13i | −0.132955 | − | 0.423347i | ||||
\(615\) | 1.50298e13i | 0.170835i | ||||||||
\(616\) | 2.30233e13 | − | 2.97950e13i | 0.259576 | − | 0.335923i | ||||
\(617\) | −1.44047e13 | −0.161094 | −0.0805470 | − | 0.996751i | \(-0.525667\pi\) | ||||
−0.0805470 | + | 0.996751i | \(0.525667\pi\) | |||||||
\(618\) | 7.46809e13 | − | 2.34541e13i | 0.828452 | − | 0.260182i | ||||
\(619\) | − | 1.46669e14i | − | 1.61393i | −0.590596 | − | 0.806967i | \(-0.701107\pi\) | ||
0.590596 | − | 0.806967i | \(-0.298893\pi\) | |||||||
\(620\) | −3.25930e13 | − | 4.67722e13i | −0.355768 | − | 0.510539i | ||||
\(621\) | −3.19403e13 | −0.345845 | ||||||||
\(622\) | 2.83904e11 | + | 9.03986e11i | 0.00304943 | + | 0.00970979i | ||||
\(623\) | 3.73097e12i | 0.0397540i | ||||||||
\(624\) | 1.65429e14 | + | 6.10588e13i | 1.74859 | + | 0.645395i | ||||
\(625\) | 3.81470e12 | 0.0400000 | ||||||||
\(626\) | 7.26489e13 | − | 2.28159e13i | 0.755713 | − | 0.237338i | ||||
\(627\) | − | 5.37026e13i | − | 0.554188i | ||||||
\(628\) | 1.39720e14 | − | 9.73631e13i | 1.43040 | − | 0.996773i | ||||
\(629\) | 1.32833e14 | 1.34912 | ||||||||
\(630\) | −5.90724e12 | − | 1.88094e13i | −0.0595226 | − | 0.189528i | ||||
\(631\) | 1.47209e13i | 0.147159i | 0.997289 | + | 0.0735797i | \(0.0234423\pi\) | ||||
−0.997289 | + | 0.0735797i | \(0.976558\pi\) | |||||||
\(632\) | −4.46833e13 | − | 3.45278e13i | −0.443159 | − | 0.342440i | ||||
\(633\) | −1.26623e14 | −1.24593 | ||||||||
\(634\) | −1.37416e14 | + | 4.31564e13i | −1.34150 | + | 0.421307i | ||||
\(635\) | − | 6.80977e13i | − | 0.659575i | ||||||
\(636\) | 4.32820e13 | + | 6.21112e13i | 0.415931 | + | 0.596877i | ||||
\(637\) | −9.65463e13 | −0.920531 | ||||||||
\(638\) | 3.19009e13 | + | 1.01577e14i | 0.301787 | + | 0.960928i | ||||
\(639\) | 5.04479e13i | 0.473520i | ||||||||
\(640\) | 2.54797e13 | + | 4.07017e13i | 0.237298 | + | 0.379064i | ||||
\(641\) | 1.33596e14 | 1.23454 | 0.617269 | − | 0.786752i | \(-0.288239\pi\) | ||||
0.617269 | + | 0.786752i | \(0.288239\pi\) | |||||||
\(642\) | 2.66855e14 | − | 8.38079e13i | 2.44681 | − | 0.768440i | ||||
\(643\) | − | 1.78623e14i | − | 1.62511i | −0.582885 | − | 0.812555i | \(-0.698076\pi\) | ||
0.582885 | − | 0.812555i | \(-0.301924\pi\) | |||||||
\(644\) | −5.70586e13 | + | 3.97611e13i | −0.515100 | + | 0.358946i | ||||
\(645\) | −3.56672e13 | −0.319499 | ||||||||
\(646\) | −1.67513e13 | − | 5.33383e13i | −0.148897 | − | 0.474107i | ||||
\(647\) | 7.75013e11i | 0.00683578i | 0.999994 | + | 0.00341789i | \(0.00108795\pi\) | ||||
−0.999994 | + | 0.00341789i | \(0.998912\pi\) | |||||||
\(648\) | −8.27624e13 | + | 1.07105e14i | −0.724366 | + | 0.937419i | ||||
\(649\) | −1.52571e14 | −1.32510 | ||||||||
\(650\) | −3.11445e13 | + | 9.78116e12i | −0.268420 | + | 0.0842992i | ||||
\(651\) | − | 1.26731e14i | − | 1.08387i | ||||||
\(652\) | 4.34393e12 | + | 6.23370e12i | 0.0368676 | + | 0.0529064i | ||||
\(653\) | 1.63485e14 | 1.37693 | 0.688463 | − | 0.725271i | \(-0.258286\pi\) | ||||
0.688463 | + | 0.725271i | \(0.258286\pi\) | |||||||
\(654\) | −4.16206e13 | − | 1.32525e14i | −0.347872 | − | 1.10767i | ||||
\(655\) | 1.39649e12i | 0.0115833i | ||||||||
\(656\) | 1.21276e13 | − | 3.28578e13i | 0.0998289 | − | 0.270470i | ||||
\(657\) | −5.52673e13 | −0.451483 | ||||||||
\(658\) | −1.35757e14 | + | 4.26356e13i | −1.10061 | + | 0.345655i | ||||
\(659\) | 8.74538e13i | 0.703642i | 0.936067 | + | 0.351821i | \(0.114437\pi\) | ||||
−0.936067 | + | 0.351821i | \(0.885563\pi\) | |||||||
\(660\) | −4.39643e13 | + | 3.06364e13i | −0.351059 | + | 0.244635i | ||||
\(661\) | 8.72541e13 | 0.691478 | 0.345739 | − | 0.938331i | \(-0.387628\pi\) | ||||
0.345739 | + | 0.938331i | \(0.387628\pi\) | |||||||
\(662\) | 4.75874e13 | + | 1.51524e14i | 0.374284 | + | 1.19177i | ||||
\(663\) | 2.04856e14i | 1.59912i | ||||||||
\(664\) | 1.43349e14 | + | 1.10769e14i | 1.11059 | + | 0.858179i | ||||
\(665\) | 1.98046e13 | 0.152285 | ||||||||
\(666\) | −1.48531e14 | + | 4.66474e13i | −1.13357 | + | 0.356005i | ||||
\(667\) | − | 1.96644e14i | − | 1.48954i | ||||||
\(668\) | −4.73463e13 | − | 6.79437e13i | −0.355962 | − | 0.510819i | ||||
\(669\) | −1.58467e14 | −1.18252 | ||||||||
\(670\) | 7.03949e12 | + | 2.24147e13i | 0.0521396 | + | 0.166019i | ||||
\(671\) | − | 9.50836e13i | − | 0.699025i | ||||||
\(672\) | −5.25839e12 | + | 1.06618e14i | −0.0383713 | + | 0.778009i | ||||
\(673\) | −1.83493e14 | −1.32906 | −0.664531 | − | 0.747261i | \(-0.731369\pi\) | ||||
−0.664531 | + | 0.747261i | \(0.731369\pi\) | |||||||
\(674\) | 1.23903e14 | − | 3.89126e13i | 0.890803 | − | 0.279764i | ||||
\(675\) | − | 9.07590e12i | − | 0.0647695i | ||||||
\(676\) | 1.13374e14 | − | 7.90046e13i | 0.803122 | − | 0.559653i | ||||
\(677\) | −2.25381e14 | −1.58480 | −0.792400 | − | 0.610002i | \(-0.791169\pi\) | ||||
−0.792400 | + | 0.610002i | \(0.791169\pi\) | |||||||
\(678\) | −4.68046e13 | − | 1.49032e14i | −0.326693 | − | 1.04023i | ||||
\(679\) | 3.25958e13i | 0.225846i | ||||||||
\(680\) | −3.41097e13 | + | 4.41422e13i | −0.234603 | + | 0.303605i | ||||
\(681\) | −4.60630e13 | −0.314497 | ||||||||
\(682\) | −1.41438e14 | + | 4.44196e13i | −0.958613 | + | 0.301060i | ||||
\(683\) | − | 6.01818e13i | − | 0.404913i | −0.979291 | − | 0.202456i | \(-0.935108\pi\) | ||
0.979291 | − | 0.202456i | \(-0.0648924\pi\) | |||||||
\(684\) | 3.74621e13 | + | 5.37594e13i | 0.250214 | + | 0.359066i | ||||
\(685\) | 6.01122e13 | 0.398575 | ||||||||
\(686\) | −4.42730e13 | − | 1.40971e14i | −0.291420 | − | 0.927918i | ||||
\(687\) | − | 5.25377e13i | − | 0.343311i | ||||||
\(688\) | 7.79746e13 | + | 2.87800e13i | 0.505838 | + | 0.186702i | ||||
\(689\) | 1.19931e14 | 0.772386 | ||||||||
\(690\) | 9.44247e13 | − | 2.96548e13i | 0.603727 | − | 0.189605i | ||||
\(691\) | − | 2.08918e13i | − | 0.132613i | −0.997799 | − | 0.0663063i | \(-0.978879\pi\) | ||
0.997799 | − | 0.0663063i | \(-0.0211214\pi\) | |||||||
\(692\) | −1.43168e14 | + | 9.97664e13i | −0.902228 | + | 0.628715i | ||||
\(693\) | −5.12690e13 | −0.320766 | ||||||||
\(694\) | −6.85653e13 | − | 2.18321e14i | −0.425899 | − | 1.35612i | ||||
\(695\) | − | 2.77547e13i | − | 0.171164i | ||||||
\(696\) | −2.38838e14 | − | 1.84555e14i | −1.46237 | − | 1.13001i | ||||
\(697\) | 4.06890e13 | 0.247351 | ||||||||
\(698\) | −1.16540e14 | + | 3.66004e13i | −0.703395 | + | 0.220906i | ||||
\(699\) | 8.19484e13i | 0.491083i | ||||||||
\(700\) | −1.12982e13 | − | 1.62133e13i | −0.0672230 | − | 0.0964675i | ||||
\(701\) | 1.20064e14 | 0.709291 | 0.354645 | − | 0.935001i | \(-0.384602\pi\) | ||||
0.354645 | + | 0.935001i | \(0.384602\pi\) | |||||||
\(702\) | 2.32713e13 | + | 7.40987e13i | 0.136500 | + | 0.434635i | ||||
\(703\) | − | 1.56390e14i | − | 0.910819i | ||||||
\(704\) | 1.20834e14 | − | 3.15014e13i | 0.698758 | − | 0.182166i | ||||
\(705\) | 2.02502e14 | 1.16274 | ||||||||
\(706\) | −1.56542e14 | + | 4.91632e13i | −0.892498 | + | 0.280296i | ||||
\(707\) | 1.34906e14i | 0.763722i | ||||||||
\(708\) | 3.54871e14 | − | 2.47291e14i | 1.99482 | − | 1.39009i | ||||
\(709\) | −1.88963e14 | −1.05474 | −0.527371 | − | 0.849635i | \(-0.676822\pi\) | ||||
−0.527371 | + | 0.849635i | \(0.676822\pi\) | |||||||
\(710\) | 1.51512e13 | + | 4.82432e13i | 0.0839758 | + | 0.267390i | ||||
\(711\) | 7.68877e13i | 0.423164i | ||||||||
\(712\) | −7.56550e12 | + | 9.79069e12i | −0.0413464 | + | 0.0535074i | ||||
\(713\) | 2.73812e14 | 1.48595 | ||||||||
\(714\) | −1.18314e14 | + | 3.71575e13i | −0.637597 | + | 0.200242i | ||||
\(715\) | 8.48908e13i | 0.454287i | ||||||||
\(716\) | −2.39555e13 | − | 3.43770e13i | −0.127303 | − | 0.182685i | ||||
\(717\) | 1.08019e14 | 0.570040 | ||||||||
\(718\) | −1.98127e13 | − | 6.30863e13i | −0.103830 | − | 0.330608i | ||||
\(719\) | 1.51449e14i | 0.788174i | 0.919073 | + | 0.394087i | \(0.128939\pi\) | ||||
−0.919073 | + | 0.394087i | \(0.871061\pi\) | |||||||
\(720\) | 2.26394e13 | − | 6.13376e13i | 0.117004 | − | 0.317004i | ||||
\(721\) | 7.50689e13 | 0.385286 | ||||||||
\(722\) | 1.24383e14 | − | 3.90633e13i | 0.633977 | − | 0.199105i | ||||
\(723\) | 4.15862e14i | 2.10503i | ||||||||
\(724\) | 6.05580e13 | − | 4.21997e13i | 0.304424 | − | 0.212137i | ||||
\(725\) | 5.58769e13 | 0.278960 | ||||||||
\(726\) | −3.83184e13 | − | 1.22011e14i | −0.189987 | − | 0.604943i | ||||
\(727\) | − | 1.11161e14i | − | 0.547371i | −0.961819 | − | 0.273686i | \(-0.911757\pi\) | ||
0.961819 | − | 0.273686i | \(-0.0882428\pi\) | |||||||
\(728\) | 1.33814e14 | + | 1.03401e14i | 0.654403 | + | 0.505673i | ||||
\(729\) | 9.59514e13 | 0.466030 | ||||||||
\(730\) | −5.28520e13 | + | 1.65986e13i | −0.254945 | + | 0.0800676i | ||||
\(731\) | 9.65588e13i | 0.462600i | ||||||||
\(732\) | 1.54114e14 | + | 2.21158e14i | 0.733306 | + | 1.05232i | ||||
\(733\) | 5.92775e13 | 0.280137 | 0.140068 | − | 0.990142i | \(-0.455268\pi\) | ||||
0.140068 | + | 0.990142i | \(0.455268\pi\) | |||||||
\(734\) | 1.13558e14 | + | 3.61583e14i | 0.533012 | + | 1.69718i | ||||
\(735\) | 8.31746e13i | 0.387752i | ||||||||
\(736\) | −2.30357e14 | − | 1.13612e13i | −1.06663 | − | 0.0526060i | ||||
\(737\) | 6.10959e13 | 0.280979 | ||||||||
\(738\) | −4.54978e13 | + | 1.42889e13i | −0.207830 | + | 0.0652706i | ||||
\(739\) | 1.37698e14i | 0.624748i | 0.949959 | + | 0.312374i | \(0.101124\pi\) | ||||
−0.949959 | + | 0.312374i | \(0.898876\pi\) | |||||||
\(740\) | −1.28031e14 | + | 8.92177e13i | −0.576973 | + | 0.402061i | ||||
\(741\) | 2.41187e14 | 1.07960 | ||||||||
\(742\) | 2.17534e13 | + | 6.92657e13i | 0.0967182 | + | 0.307963i | ||||
\(743\) | 1.17414e14i | 0.518533i | 0.965806 | + | 0.259266i | \(0.0834808\pi\) | ||||
−0.965806 | + | 0.259266i | \(0.916519\pi\) | |||||||
\(744\) | 2.56979e14 | − | 3.32563e14i | 1.12728 | − | 1.45884i | ||||
\(745\) | 3.22394e13 | 0.140477 | ||||||||
\(746\) | −3.53006e14 | + | 1.10864e14i | −1.52787 | + | 0.479841i | ||||
\(747\) | − | 2.46664e14i | − | 1.06048i | ||||||
\(748\) | 8.29394e13 | + | 1.19021e14i | 0.354204 | + | 0.508295i | ||||
\(749\) | 2.68242e14 | 1.13793 | ||||||||
\(750\) | 8.42646e12 | + | 2.68309e13i | 0.0355090 | + | 0.113065i | ||||
\(751\) | 1.17502e14i | 0.491864i | 0.969287 | + | 0.245932i | \(0.0790940\pi\) | ||||
−0.969287 | + | 0.245932i | \(0.920906\pi\) | |||||||
\(752\) | −4.42705e14 | − | 1.63400e14i | −1.84088 | − | 0.679458i | ||||
\(753\) | 1.26008e14 | 0.520501 | ||||||||
\(754\) | −4.56197e14 | + | 1.43272e14i | −1.87196 | + | 0.587903i | ||||
\(755\) | 1.13947e13i | 0.0464482i | ||||||||
\(756\) | −3.85745e13 | + | 2.68805e13i | −0.156204 | + | 0.108850i | ||||
\(757\) | −3.51706e14 | −1.41482 | −0.707409 | − | 0.706805i | \(-0.750136\pi\) | ||||
−0.707409 | + | 0.706805i | \(0.750136\pi\) | |||||||
\(758\) | 3.16728e13 | + | 1.00850e14i | 0.126573 | + | 0.403024i | ||||
\(759\) | − | 2.57374e14i | − | 1.02178i | ||||||
\(760\) | 5.19706e13 | + | 4.01590e13i | 0.204970 | + | 0.158385i | ||||
\(761\) | −1.95381e14 | −0.765525 | −0.382763 | − | 0.923847i | \(-0.625027\pi\) | ||||
−0.382763 | + | 0.923847i | \(0.625027\pi\) | |||||||
\(762\) | 4.78970e14 | − | 1.50424e14i | 1.86438 | − | 0.585521i | ||||
\(763\) | − | 1.33214e14i | − | 0.515142i | ||||||
\(764\) | 4.74555e13 | + | 6.81003e13i | 0.182314 | + | 0.261627i | ||||
\(765\) | 7.59566e13 | 0.289907 | ||||||||
\(766\) | 4.97297e12 | + | 1.58346e13i | 0.0188570 | + | 0.0600430i | ||||
\(767\) | − | 6.85221e14i | − | 2.58139i | ||||||
\(768\) | −2.29995e14 | + | 2.69121e14i | −0.860819 | + | 1.00726i | ||||
\(769\) | 8.91848e13 | 0.331634 | 0.165817 | − | 0.986157i | \(-0.446974\pi\) | ||||
0.165817 | + | 0.986157i | \(0.446974\pi\) | |||||||
\(770\) | −4.90285e13 | + | 1.53978e13i | −0.181132 | + | 0.0568859i | ||||
\(771\) | − | 1.10394e14i | − | 0.405204i | ||||||
\(772\) | 3.46612e14 | − | 2.41536e14i | 1.26403 | − | 0.880835i | ||||
\(773\) | −9.96400e13 | −0.361024 | −0.180512 | − | 0.983573i | \(-0.557775\pi\) | ||||
−0.180512 | + | 0.983573i | \(0.557775\pi\) | |||||||
\(774\) | −3.39090e13 | − | 1.07971e14i | −0.122070 | − | 0.388688i | ||||
\(775\) | 7.78042e13i | 0.278288i | ||||||||
\(776\) | −6.60965e13 | + | 8.55370e13i | −0.234893 | + | 0.303980i | ||||
\(777\) | −3.46903e14 | −1.22490 | ||||||||
\(778\) | 1.09461e14 | − | 3.43770e13i | 0.384026 | − | 0.120606i | ||||
\(779\) | − | 4.79050e13i | − | 0.166991i | ||||||
\(780\) | −1.37593e14 | − | 1.97451e14i | −0.476566 | − | 0.683889i | ||||
\(781\) | 1.31497e14 | 0.452544 | ||||||||
\(782\) | −8.02820e13 | − | 2.55628e14i | −0.274527 | − | 0.874129i | ||||
\(783\) | − | 1.32942e14i | − | 0.451703i | ||||||
\(784\) | 6.71140e13 | − | 1.81834e14i | 0.226586 | − | 0.613896i | ||||
\(785\) | −2.32419e14 | −0.779694 | ||||||||
\(786\) | −9.82231e12 | + | 3.08477e12i | −0.0327417 | + | 0.0102828i | ||||
\(787\) | 4.33579e14i | 1.43613i | 0.695975 | + | 0.718066i | \(0.254973\pi\) | ||||
−0.695975 | + | 0.718066i | \(0.745027\pi\) | |||||||
\(788\) | 1.27204e14 | − | 8.86420e13i | 0.418669 | − | 0.291748i | ||||
\(789\) | −5.39113e14 | −1.76317 | ||||||||
\(790\) | 2.30919e13 | + | 7.35276e13i | 0.0750454 | + | 0.238954i | ||||
\(791\) | − | 1.49806e14i | − | 0.483780i | ||||||
\(792\) | −1.34539e14 | − | 1.03961e14i | −0.431739 | − | 0.333615i | ||||
\(793\) | 4.27035e14 | 1.36175 | ||||||||
\(794\) | 1.57650e13 | − | 4.95111e12i | 0.0499564 | − | 0.0156892i | ||||
\(795\) | − | 1.03320e14i | − | 0.325349i | ||||||
\(796\) | 2.24812e14 | + | 3.22613e14i | 0.703483 | + | 1.00952i | ||||
\(797\) | −2.10616e14 | −0.654939 | −0.327469 | − | 0.944862i | \(-0.606196\pi\) | ||||
−0.327469 | + | 0.944862i | \(0.606196\pi\) | |||||||
\(798\) | 4.37473e13 | + | 1.39297e14i | 0.135188 | + | 0.430455i | ||||
\(799\) | − | 5.48217e14i | − | 1.68352i | ||||||
\(800\) | 3.22831e12 | − | 6.54564e13i | 0.00985201 | − | 0.199757i | ||||
\(801\) | 1.68471e13 | 0.0510931 | ||||||||
\(802\) | 2.65375e14 | − | 8.33431e13i | 0.799813 | − | 0.251187i | ||||
\(803\) | 1.44059e14i | 0.431483i | ||||||||
\(804\) | −1.42105e14 | + | 9.90255e13i | −0.422990 | + | 0.294759i | ||||
\(805\) | 9.49153e13 | 0.280774 | ||||||||
\(806\) | −1.99495e14 | − | 6.35219e14i | −0.586486 | − | 1.86745i | ||||
\(807\) | 8.65350e14i | 2.52828i | ||||||||
\(808\) | −2.73558e14 | + | 3.54017e14i | −0.794313 | + | 1.02794i | ||||
\(809\) | −5.03919e14 | −1.45418 | −0.727090 | − | 0.686542i | \(-0.759128\pi\) | ||||
−0.727090 | + | 0.686542i | \(0.759128\pi\) | |||||||
\(810\) | 1.76244e14 | − | 5.53507e13i | 0.505462 | − | 0.158744i | ||||
\(811\) | 2.98074e14i | 0.849610i | 0.905285 | + | 0.424805i | \(0.139657\pi\) | ||||
−0.905285 | + | 0.424805i | \(0.860343\pi\) | |||||||
\(812\) | −1.65493e14 | − | 2.37489e14i | −0.468813 | − | 0.672764i | ||||
\(813\) | −6.18704e14 | −1.74193 | ||||||||
\(814\) | 1.21591e14 | + | 3.87161e14i | 0.340235 | + | 1.08335i | ||||
\(815\) | − | 1.03696e13i | − | 0.0288385i | ||||||
\(816\) | −3.85824e14 | − | 1.42405e14i | −1.06644 | − | 0.393619i | ||||
\(817\) | 1.13683e14 | 0.312310 | ||||||||
\(818\) | 5.71703e14 | − | 1.79548e14i | 1.56100 | − | 0.490245i | ||||
\(819\) | − | 2.30257e14i | − | 0.624876i | ||||||
\(820\) | −3.92181e13 | + | 2.73290e13i | −0.105783 | + | 0.0737147i | ||||
\(821\) | −1.54116e14 | −0.413174 | −0.206587 | − | 0.978428i | \(-0.566236\pi\) | ||||
−0.206587 | + | 0.978428i | \(0.566236\pi\) | |||||||
\(822\) | 1.32785e14 | + | 4.22803e14i | 0.353825 | + | 1.12662i | ||||
\(823\) | 5.40009e13i | 0.143022i | 0.997440 | + | 0.0715108i | \(0.0227820\pi\) | ||||
−0.997440 | + | 0.0715108i | \(0.977218\pi\) | |||||||
\(824\) | 1.96994e14 | + | 1.52222e14i | 0.518580 | + | 0.400720i | ||||
\(825\) | 7.31334e13 | 0.191358 | ||||||||
\(826\) | 3.95748e14 | − | 1.24288e14i | 1.02925 | − | 0.323242i | ||||
\(827\) | 3.42473e14i | 0.885316i | 0.896691 | + | 0.442658i | \(0.145964\pi\) | ||||
−0.896691 | + | 0.442658i | \(0.854036\pi\) | |||||||
\(828\) | 1.79540e14 | + | 2.57647e14i | 0.461328 | + | 0.662023i | ||||
\(829\) | −1.54734e14 | −0.395195 | −0.197598 | − | 0.980283i | \(-0.563314\pi\) | ||||
−0.197598 | + | 0.980283i | \(0.563314\pi\) | |||||||
\(830\) | −7.40813e13 | − | 2.35884e14i | −0.188069 | − | 0.598837i | ||||
\(831\) | 2.79972e14i | 0.706496i | ||||||||
\(832\) | 1.41478e14 | + | 5.42686e14i | 0.354873 | + | 1.36123i | ||||
\(833\) | 2.25172e14 | 0.561421 | ||||||||
\(834\) | 1.95215e14 | − | 6.13086e13i | 0.483818 | − | 0.151947i | ||||
\(835\) | 1.13022e14i | 0.278440i | ||||||||
\(836\) | 1.40129e14 | − | 9.76484e13i | 0.343160 | − | 0.239130i | ||||
\(837\) | 1.85111e14 | 0.450614 | ||||||||
\(838\) | −1.75662e14 | − | 5.59331e14i | −0.425067 | − | 1.35347i | ||||
\(839\) | − | 2.50962e14i | − | 0.603668i | −0.953360 | − | 0.301834i | \(-0.902401\pi\) | ||
0.953360 | − | 0.301834i | \(-0.0975989\pi\) | |||||||
\(840\) | 8.90802e13 | − | 1.15281e14i | 0.213003 | − | 0.275652i | ||||
\(841\) | 3.97765e14 | 0.945467 | ||||||||
\(842\) | 1.94376e14 | − | 6.10452e13i | 0.459284 | − | 0.144242i | ||||
\(843\) | − | 5.80161e14i | − | 1.36273i | ||||||
\(844\) | −2.30242e14 | − | 3.30405e14i | −0.537615 | − | 0.771497i | ||||
\(845\) | −1.88595e14 | −0.437771 | ||||||||
\(846\) | 1.92520e14 | + | 6.13008e14i | 0.444246 | + | 1.41454i | ||||
\(847\) | − | 1.22645e14i | − | 0.281340i | ||||||
\(848\) | −8.33696e13 | + | 2.25876e14i | −0.190120 | + | 0.515099i | ||||
\(849\) | 5.98758e14 | 1.35742 | ||||||||
\(850\) | 7.26372e13 | − | 2.28123e13i | 0.163706 | − | 0.0514131i | ||||
\(851\) | − | 7.49512e14i | − | 1.67931i | ||||||
\(852\) | −3.05854e14 | + | 2.13133e14i | −0.681265 | + | 0.474738i | ||||
\(853\) | −2.39173e14 | −0.529623 | −0.264812 | − | 0.964300i | \(-0.585310\pi\) | ||||
−0.264812 | + | 0.964300i | \(0.585310\pi\) | |||||||
\(854\) | 7.74571e13 | + | 2.46633e14i | 0.170519 | + | 0.542954i | ||||
\(855\) | − | 8.94272e13i | − | 0.195722i | ||||||
\(856\) | 7.03912e14 | + | 5.43930e14i | 1.53161 | + | 1.18352i | ||||
\(857\) | −6.21909e14 | −1.34531 | −0.672656 | − | 0.739956i | \(-0.734846\pi\) | ||||
−0.672656 | + | 0.739956i | \(0.734846\pi\) | |||||||
\(858\) | −5.97085e14 | + | 1.87519e14i | −1.28410 | + | 0.403283i | ||||
\(859\) | 3.04870e14i | 0.651853i | 0.945395 | + | 0.325926i | \(0.105676\pi\) | ||||
−0.945395 | + | 0.325926i | \(0.894324\pi\) | |||||||
\(860\) | −6.48543e13 | − | 9.30682e13i | −0.137863 | − | 0.197838i | ||||
\(861\) | −1.06262e14 | −0.224576 | ||||||||
\(862\) | −2.09773e13 | − | 6.67943e13i | −0.0440770 | − | 0.140347i | ||||
\(863\) | − | 6.53448e13i | − | 0.136508i | −0.997668 | − | 0.0682538i | \(-0.978257\pi\) | ||
0.997668 | − | 0.0682538i | \(-0.0217428\pi\) | |||||||
\(864\) | −1.55733e14 | − | 7.68076e12i | −0.323454 | − | 0.0159528i | ||||
\(865\) | 2.38156e14 | 0.491792 | ||||||||
\(866\) | 5.14572e14 | − | 1.61605e14i | 1.05647 | − | 0.331792i | ||||
\(867\) | 1.71312e14i | 0.349698i | ||||||||
\(868\) | 3.30684e14 | − | 2.30436e14i | 0.671143 | − | 0.467684i | ||||
\(869\) | 2.00415e14 | 0.404419 | ||||||||
\(870\) | 1.23429e14 | + | 3.93014e14i | 0.247640 | + | 0.788518i | ||||
\(871\) | 2.74391e14i | 0.547368i | ||||||||
\(872\) | 2.70126e14 | − | 3.49576e14i | 0.535776 | − | 0.693361i | ||||
\(873\) | 1.47186e14 | 0.290265 | ||||||||
\(874\) | −3.00963e14 | + | 9.45197e13i | −0.590141 | + | 0.185338i | ||||
\(875\) | 2.69703e13i | 0.0525831i | ||||||||
\(876\) | −2.33495e14 | − | 3.35073e14i | −0.452643 | − | 0.649560i | ||||
\(877\) | 6.16479e14 | 1.18829 | 0.594143 | − | 0.804360i | \(-0.297492\pi\) | ||||
0.594143 | + | 0.804360i | \(0.297492\pi\) | |||||||
\(878\) | −1.89548e13 | − | 6.03545e13i | −0.0363284 | − | 0.115674i | ||||
\(879\) | − | 2.72778e13i | − | 0.0519835i | ||||||
\(880\) | −1.59882e14 | − | 5.90117e13i | −0.302961 | − | 0.111821i | ||||
\(881\) | 4.73843e14 | 0.892801 | 0.446401 | − | 0.894833i | \(-0.352706\pi\) | ||||
0.446401 | + | 0.894833i | \(0.352706\pi\) | |||||||
\(882\) | −2.51784e14 | + | 7.90746e13i | −0.471720 | + | 0.148147i | ||||
\(883\) | 1.26271e14i | 0.235234i | 0.993059 | + | 0.117617i | \(0.0375255\pi\) | ||||
−0.993059 | + | 0.117617i | \(0.962475\pi\) | |||||||
\(884\) | −5.34542e14 | + | 3.72494e14i | −0.990195 | + | 0.690014i | ||||
\(885\) | −5.90318e14 | −1.08735 | ||||||||
\(886\) | 7.72189e13 | + | 2.45875e14i | 0.141434 | + | 0.450345i | ||||
\(887\) | − | 4.38556e14i | − | 0.798743i | −0.916789 | − | 0.399372i | \(-0.869228\pi\) | ||
0.916789 | − | 0.399372i | \(-0.130772\pi\) | |||||||
\(888\) | −9.10332e14 | − | 7.03435e14i | −1.64867 | − | 1.27397i | ||||
\(889\) | 4.81458e14 | 0.867062 | ||||||||
\(890\) | 1.61109e13 | − | 5.05974e12i | 0.0288515 | − | 0.00906104i | ||||
\(891\) | − | 4.80390e14i | − | 0.855470i | ||||||
\(892\) | −2.88143e14 | − | 4.13496e14i | −0.510251 | − | 0.732228i | ||||
\(893\) | −6.45442e14 | −1.13658 | ||||||||
\(894\) | 7.12150e13 | + | 2.26758e14i | 0.124705 | + | 0.397077i | ||||
\(895\) | 5.71851e13i | 0.0995789i | ||||||||
\(896\) | −2.87765e14 | + | 1.80145e14i | −0.498309 | + | 0.311947i | ||||
\(897\) | 1.15591e15 | 1.99050 | ||||||||
\(898\) | −2.72117e14 | + | 8.54605e13i | −0.465988 | + | 0.146347i | ||||
\(899\) | 1.13966e15i | 1.94078i | ||||||||
\(900\) | −7.32108e13 | + | 5.10167e13i | −0.123983 | + | 0.0863972i | ||||
\(901\) | −2.79710e14 | −0.471069 | ||||||||
\(902\) | 3.72454e13 | + | 1.18594e14i | 0.0623793 | + | 0.198624i | ||||
\(903\) | − | 2.52171e14i | − | 0.420007i | ||||||
\(904\) | 3.03771e14 | − | 3.93117e14i | 0.503158 | − | 0.651148i | ||||
\(905\) | −1.00737e14 | −0.165937 | ||||||||
\(906\) | −8.01456e13 | + | 2.51703e13i | −0.131292 | + | 0.0412333i | ||||
\(907\) | 3.95261e13i | 0.0643943i | 0.999482 | + | 0.0321972i | \(0.0102504\pi\) | ||||
−0.999482 | + | 0.0321972i | \(0.989750\pi\) | |||||||
\(908\) | −8.37573e13 | − | 1.20195e14i | −0.135704 | − | 0.194740i | ||||
\(909\) | 6.09166e14 | 0.981559 | ||||||||
\(910\) | −6.91539e13 | − | 2.20195e14i | −0.110818 | − | 0.352858i | ||||
\(911\) | 7.25957e14i | 1.15696i | 0.815696 | + | 0.578481i | \(0.196354\pi\) | ||||
−0.815696 | + | 0.578481i | \(0.803646\pi\) | |||||||
\(912\) | −1.67661e14 | + | 4.54248e14i | −0.265740 | + | 0.719978i | ||||
\(913\) | −6.42953e14 | −1.01350 | ||||||||
\(914\) | 4.54133e14 | − | 1.42624e14i | 0.711954 | − | 0.223594i | ||||
\(915\) | − | 3.67891e14i | − | 0.573606i | ||||||
\(916\) | 1.37089e14 | − | 9.55302e13i | 0.212582 | − | 0.148137i | ||||
\(917\) | −9.87334e12 | −0.0152271 | ||||||||
\(918\) | −5.42748e13 | − | 1.72818e14i | −0.0832501 | − | 0.265079i | ||||
\(919\) | 1.05122e15i | 1.60367i | 0.597545 | + | 0.801836i | \(0.296143\pi\) | ||||
−0.597545 | + | 0.801836i | \(0.703857\pi\) | |||||||
\(920\) | 2.49074e14 | + | 1.92465e14i | 0.377911 | + | 0.292021i | ||||
\(921\) | −3.89611e14 | −0.587940 | ||||||||
\(922\) | −4.12327e14 | + | 1.29495e14i | −0.618853 | + | 0.194356i | ||||
\(923\) | 5.90574e14i | 0.881589i | ||||||||
\(924\) | −2.16603e14 | − | 3.10833e14i | −0.321591 | − | 0.461495i | ||||
\(925\) | 2.12975e14 | 0.314500 | ||||||||
\(926\) | 1.51413e14 | + | 4.82119e14i | 0.222386 | + | 0.708107i | ||||
\(927\) | − | 3.38972e14i | − | 0.495182i | ||||||
\(928\) | 4.72875e13 | − | 9.58792e14i | 0.0687079 | − | 1.39311i | ||||
\(929\) | 2.69891e14 | 0.390040 | 0.195020 | − | 0.980799i | \(-0.437523\pi\) | ||||
0.195020 | + | 0.980799i | \(0.437523\pi\) | |||||||
\(930\) | −5.47241e14 | + | 1.71865e14i | −0.786618 | + | 0.247043i | ||||
\(931\) | − | 2.65105e14i | − | 0.379027i | ||||||
\(932\) | −2.13832e14 | + | 1.49008e14i | −0.304084 | + | 0.211900i | ||||
\(933\) | 9.53356e12 | 0.0134849 | ||||||||
\(934\) | −4.16970e14 | − | 1.32769e15i | −0.586639 | − | 1.86793i | ||||
\(935\) | − | 1.97988e14i | − | 0.277065i | ||||||
\(936\) | 4.66907e14 | − | 6.04235e14i | 0.649907 | − | 0.841059i | ||||
\(937\) | 9.48225e14 | 1.31284 | 0.656422 | − | 0.754394i | \(-0.272069\pi\) | ||||
0.656422 | + | 0.754394i | \(0.272069\pi\) | |||||||
\(938\) | −1.58474e14 | + | 4.97700e13i | −0.218245 | + | 0.0685415i | ||||
\(939\) | − | 7.66164e14i | − | 1.04953i | ||||||
\(940\) | 3.68213e14 | + | 5.28399e14i | 0.501718 | + | 0.719984i | ||||
\(941\) | −9.63938e14 | −1.30648 | −0.653238 | − | 0.757153i | \(-0.726590\pi\) | ||||
−0.653238 | + | 0.757153i | \(0.726590\pi\) | |||||||
\(942\) | −5.13402e14 | − | 1.63474e15i | −0.692155 | − | 2.20391i | ||||
\(943\) | − | 2.29589e14i | − | 0.307888i | ||||||
\(944\) | 1.29054e15 | + | 4.76330e14i | 1.72151 | + | 0.635401i | ||||
\(945\) | 6.41676e13 | 0.0851446 | ||||||||
\(946\) | −2.81436e14 | + | 8.83870e13i | −0.371470 | + | 0.116663i | ||||
\(947\) | − | 5.67490e14i | − | 0.745089i | −0.928014 | − | 0.372545i | \(-0.878485\pi\) | ||
0.928014 | − | 0.372545i | \(-0.121515\pi\) | |||||||
\(948\) | −4.66153e14 | + | 3.24837e14i | −0.608817 | + | 0.424252i | ||||
\(949\) | −6.46993e14 | −0.840560 | ||||||||
\(950\) | −2.68579e13 | − | 8.55192e13i | −0.0347100 | − | 0.110521i | ||||
\(951\) | 1.44920e15i | 1.86306i | ||||||||
\(952\) | −3.12090e14 | − | 2.41160e14i | −0.399113 | − | 0.308404i | ||||
\(953\) | 8.56825e14 | 1.09000 | 0.545002 | − | 0.838435i | \(-0.316529\pi\) | ||||
0.545002 | + | 0.838435i | \(0.316529\pi\) | |||||||
\(954\) | 3.12768e14 | − | 9.82272e13i | 0.395804 | − | 0.124305i | ||||
\(955\) | − | 1.13283e14i | − | 0.142609i | ||||||
\(956\) | 1.96413e14 | + | 2.81860e14i | 0.245970 | + | 0.352975i | ||||
\(957\) | 1.07124e15 | 1.33453 | ||||||||
\(958\) | −4.33500e13 | − | 1.38032e14i | −0.0537232 | − | 0.171061i | ||||
\(959\) | 4.25000e14i | 0.523957i | ||||||||
\(960\) | 4.67524e14 | − | 1.21883e14i | 0.573386 | − | 0.149482i | ||||
\(961\) | −7.67257e14 | −0.936103 | ||||||||
\(962\) | −1.73880e15 | + | 5.46084e14i | −2.11045 | + | 0.662802i | ||||
\(963\) | − | 1.21124e15i | − | 1.46251i | ||||||
\(964\) | −1.08513e15 | + | 7.56169e14i | −1.30346 | + | 0.908309i | ||||
\(965\) | −5.76579e14 | −0.689005 | ||||||||
\(966\) | 2.09663e14 | + | 6.67593e14i | 0.249250 | + | 0.793645i | ||||
\(967\) | − | 1.02528e15i | − | 1.21258i | −0.795243 | − | 0.606290i | \(-0.792657\pi\) | ||
0.795243 | − | 0.606290i | \(-0.207343\pi\) | |||||||
\(968\) | 2.48694e14 | − | 3.21840e14i | 0.292609 | − | 0.378672i | ||||
\(969\) | −5.62512e14 | −0.658435 | ||||||||
\(970\) | 1.40754e14 | − | 4.42047e13i | 0.163908 | − | 0.0514766i | ||||
\(971\) | − | 9.33882e14i | − | 1.08192i | −0.841048 | − | 0.540961i | \(-0.818061\pi\) | ||
0.841048 | − | 0.540961i | \(-0.181939\pi\) | |||||||
\(972\) | 6.17984e14 | + | 8.86830e14i | 0.712272 | + | 1.02214i | ||||
\(973\) | 1.96229e14 | 0.225008 | ||||||||
\(974\) | −1.37931e14 | − | 4.39189e14i | −0.157350 | − | 0.501022i | ||||
\(975\) | 3.28454e14i | 0.372779i | ||||||||
\(976\) | −2.96853e14 | + | 8.04273e14i | −0.335191 | + | 0.908143i | ||||
\(977\) | −7.61153e14 | −0.855065 | −0.427532 | − | 0.904000i | \(-0.640617\pi\) | ||||
−0.427532 | + | 0.904000i | \(0.640617\pi\) | |||||||
\(978\) | 7.29352e13 | − | 2.29058e13i | 0.0815160 | − | 0.0256007i | ||||
\(979\) | − | 4.39135e13i | − | 0.0488298i | ||||||
\(980\) | −2.17032e14 | + | 1.51238e14i | −0.240100 | + | 0.167313i | ||||
\(981\) | −6.01524e14 | −0.662077 | ||||||||
\(982\) | 4.88648e14 | + | 1.55592e15i | 0.535105 | + | 1.70384i | ||||
\(983\) | 1.84790e14i | 0.201331i | 0.994920 | + | 0.100665i | \(0.0320971\pi\) | ||||
−0.994920 | + | 0.100665i | \(0.967903\pi\) | |||||||
\(984\) | −2.78851e14 | − | 2.15475e14i | −0.302271 | − | 0.233572i | ||||
\(985\) | −2.11601e14 | −0.228211 | ||||||||
\(986\) | 1.06397e15 | − | 3.34149e14i | 1.14169 | − | 0.358555i | ||||
\(987\) | 1.43171e15i | 1.52852i | ||||||||
\(988\) | 4.38555e14 | + | 6.29341e14i | 0.465842 | + | 0.668500i | ||||
\(989\) | 5.44837e14 | 0.575818 | ||||||||
\(990\) | 6.95283e13 | + | 2.21387e14i | 0.0731115 | + | 0.232797i | ||||
\(991\) | − | 2.82161e14i | − | 0.295208i | −0.989047 | − | 0.147604i | \(-0.952844\pi\) | ||
0.989047 | − | 0.147604i | \(-0.0471562\pi\) | |||||||
\(992\) | 1.33504e15 | + | 6.58442e13i | 1.38975 | + | 0.0685424i | ||||
\(993\) | 1.59800e15 | 1.65512 | ||||||||
\(994\) | −3.41085e14 | + | 1.07120e14i | −0.351504 | + | 0.110393i | ||||
\(995\) | − | 5.36657e14i | − | 0.550277i | ||||||
\(996\) | 1.49547e15 | − | 1.04211e15i | 1.52574 | − | 1.06321i | ||||
\(997\) | 6.39034e14 | 0.648707 | 0.324353 | − | 0.945936i | \(-0.394853\pi\) | ||||
0.324353 | + | 0.945936i | \(0.394853\pi\) | |||||||
\(998\) | 4.21446e14 | + | 1.34194e15i | 0.425686 | + | 1.35544i | ||||
\(999\) | − | 5.06709e14i | − | 0.509250i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 20.11.b.a.11.17 | ✓ | 20 | |
3.2 | odd | 2 | 180.11.c.a.91.4 | 20 | |||
4.3 | odd | 2 | inner | 20.11.b.a.11.18 | yes | 20 | |
5.2 | odd | 4 | 100.11.d.c.99.26 | 40 | |||
5.3 | odd | 4 | 100.11.d.c.99.15 | 40 | |||
5.4 | even | 2 | 100.11.b.e.51.4 | 20 | |||
8.3 | odd | 2 | 320.11.b.d.191.4 | 20 | |||
8.5 | even | 2 | 320.11.b.d.191.17 | 20 | |||
12.11 | even | 2 | 180.11.c.a.91.3 | 20 | |||
20.3 | even | 4 | 100.11.d.c.99.25 | 40 | |||
20.7 | even | 4 | 100.11.d.c.99.16 | 40 | |||
20.19 | odd | 2 | 100.11.b.e.51.3 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.11.b.a.11.17 | ✓ | 20 | 1.1 | even | 1 | trivial | |
20.11.b.a.11.18 | yes | 20 | 4.3 | odd | 2 | inner | |
100.11.b.e.51.3 | 20 | 20.19 | odd | 2 | |||
100.11.b.e.51.4 | 20 | 5.4 | even | 2 | |||
100.11.d.c.99.15 | 40 | 5.3 | odd | 4 | |||
100.11.d.c.99.16 | 40 | 20.7 | even | 4 | |||
100.11.d.c.99.25 | 40 | 20.3 | even | 4 | |||
100.11.d.c.99.26 | 40 | 5.2 | odd | 4 | |||
180.11.c.a.91.3 | 20 | 12.11 | even | 2 | |||
180.11.c.a.91.4 | 20 | 3.2 | odd | 2 | |||
320.11.b.d.191.4 | 20 | 8.3 | odd | 2 | |||
320.11.b.d.191.17 | 20 | 8.5 | even | 2 |