Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,16,Mod(1,23)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(23, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("23.1");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.a (trivial) |
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: | yes |
Analytic conductor: | \(32.8195061730\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 68942 x^{10} - 977032 x^{9} + 1644150380 x^{8} + 50352376602 x^{7} - 15614385123802 x^{6} - 702635376772966 x^{5} + \cdots + 34\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{22}\cdot 3^{6}\cdot 5^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-61.7354\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 23.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −145.471 | −0.803621 | −0.401810 | − | 0.915723i | \(-0.631619\pi\) | ||||
−0.401810 | + | 0.915723i | \(0.631619\pi\) | |||||||
\(3\) | 254.987 | 0.0673144 | 0.0336572 | − | 0.999433i | \(-0.489285\pi\) | ||||
0.0336572 | + | 0.999433i | \(0.489285\pi\) | |||||||
\(4\) | −11606.2 | −0.354194 | ||||||||
\(5\) | −233086. | −1.33426 | −0.667130 | − | 0.744942i | \(-0.732477\pi\) | ||||
−0.667130 | + | 0.744942i | \(0.732477\pi\) | |||||||
\(6\) | −37093.1 | −0.0540953 | ||||||||
\(7\) | 2.20456e6 | 1.01178 | 0.505891 | − | 0.862597i | \(-0.331164\pi\) | ||||
0.505891 | + | 0.862597i | \(0.331164\pi\) | |||||||
\(8\) | 6.45516e6 | 1.08826 | ||||||||
\(9\) | −1.42839e7 | −0.995469 | ||||||||
\(10\) | 3.39071e7 | 1.07224 | ||||||||
\(11\) | 9.38765e7 | 1.45249 | 0.726243 | − | 0.687438i | \(-0.241265\pi\) | ||||
0.726243 | + | 0.687438i | \(0.241265\pi\) | |||||||
\(12\) | −2.95944e6 | −0.0238424 | ||||||||
\(13\) | −1.18996e8 | −0.525967 | −0.262983 | − | 0.964800i | \(-0.584706\pi\) | ||||
−0.262983 | + | 0.964800i | \(0.584706\pi\) | |||||||
\(14\) | −3.20700e8 | −0.813089 | ||||||||
\(15\) | −5.94337e7 | −0.0898149 | ||||||||
\(16\) | −5.58724e8 | −0.520352 | ||||||||
\(17\) | −1.65607e8 | −0.0978842 | −0.0489421 | − | 0.998802i | \(-0.515585\pi\) | ||||
−0.0489421 | + | 0.998802i | \(0.515585\pi\) | |||||||
\(18\) | 2.07789e9 | 0.799979 | ||||||||
\(19\) | 7.03866e9 | 1.80650 | 0.903251 | − | 0.429113i | \(-0.141174\pi\) | ||||
0.903251 | + | 0.429113i | \(0.141174\pi\) | |||||||
\(20\) | 2.70524e9 | 0.472587 | ||||||||
\(21\) | 5.62134e8 | 0.0681076 | ||||||||
\(22\) | −1.36563e10 | −1.16725 | ||||||||
\(23\) | 3.40483e9 | 0.208514 | ||||||||
\(24\) | 1.64598e9 | 0.0732555 | ||||||||
\(25\) | 2.38113e10 | 0.780248 | ||||||||
\(26\) | 1.73105e10 | 0.422678 | ||||||||
\(27\) | −7.30098e9 | −0.134324 | ||||||||
\(28\) | −2.55867e10 | −0.358367 | ||||||||
\(29\) | −2.60002e10 | −0.279892 | −0.139946 | − | 0.990159i | \(-0.544693\pi\) | ||||
−0.139946 | + | 0.990159i | \(0.544693\pi\) | |||||||
\(30\) | 8.64587e9 | 0.0721771 | ||||||||
\(31\) | −1.38242e11 | −0.902457 | −0.451229 | − | 0.892408i | \(-0.649014\pi\) | ||||
−0.451229 | + | 0.892408i | \(0.649014\pi\) | |||||||
\(32\) | −1.30245e11 | −0.670092 | ||||||||
\(33\) | 2.39373e10 | 0.0977732 | ||||||||
\(34\) | 2.40910e10 | 0.0786618 | ||||||||
\(35\) | −5.13852e11 | −1.34998 | ||||||||
\(36\) | 1.65782e11 | 0.352589 | ||||||||
\(37\) | 1.31561e11 | 0.227832 | 0.113916 | − | 0.993490i | \(-0.463661\pi\) | ||||
0.113916 | + | 0.993490i | \(0.463661\pi\) | |||||||
\(38\) | −1.02392e12 | −1.45174 | ||||||||
\(39\) | −3.03425e10 | −0.0354052 | ||||||||
\(40\) | −1.50460e12 | −1.45202 | ||||||||
\(41\) | −4.64703e11 | −0.372646 | −0.186323 | − | 0.982489i | \(-0.559657\pi\) | ||||
−0.186323 | + | 0.982489i | \(0.559657\pi\) | |||||||
\(42\) | −8.17741e10 | −0.0547326 | ||||||||
\(43\) | −2.76285e12 | −1.55004 | −0.775021 | − | 0.631936i | \(-0.782261\pi\) | ||||
−0.775021 | + | 0.631936i | \(0.782261\pi\) | |||||||
\(44\) | −1.08955e12 | −0.514462 | ||||||||
\(45\) | 3.32937e12 | 1.32821 | ||||||||
\(46\) | −4.95303e11 | −0.167566 | ||||||||
\(47\) | 8.88872e11 | 0.255921 | 0.127960 | − | 0.991779i | \(-0.459157\pi\) | ||||
0.127960 | + | 0.991779i | \(0.459157\pi\) | |||||||
\(48\) | −1.42467e11 | −0.0350272 | ||||||||
\(49\) | 1.12534e11 | 0.0237036 | ||||||||
\(50\) | −3.46385e12 | −0.627023 | ||||||||
\(51\) | −4.22277e10 | −0.00658902 | ||||||||
\(52\) | 1.38110e12 | 0.186294 | ||||||||
\(53\) | −3.03201e12 | −0.354537 | −0.177269 | − | 0.984163i | \(-0.556726\pi\) | ||||
−0.177269 | + | 0.984163i | \(0.556726\pi\) | |||||||
\(54\) | 1.06208e12 | 0.107945 | ||||||||
\(55\) | −2.18813e13 | −1.93799 | ||||||||
\(56\) | 1.42308e13 | 1.10108 | ||||||||
\(57\) | 1.79477e12 | 0.121604 | ||||||||
\(58\) | 3.78227e12 | 0.224927 | ||||||||
\(59\) | 3.46464e11 | 0.0181246 | 0.00906230 | − | 0.999959i | \(-0.497115\pi\) | ||||
0.00906230 | + | 0.999959i | \(0.497115\pi\) | |||||||
\(60\) | 6.89801e11 | 0.0318119 | ||||||||
\(61\) | −1.69272e13 | −0.689624 | −0.344812 | − | 0.938672i | \(-0.612057\pi\) | ||||
−0.344812 | + | 0.938672i | \(0.612057\pi\) | |||||||
\(62\) | 2.01102e13 | 0.725233 | ||||||||
\(63\) | −3.14897e13 | −1.00720 | ||||||||
\(64\) | 3.72551e13 | 1.05885 | ||||||||
\(65\) | 2.77363e13 | 0.701776 | ||||||||
\(66\) | −3.48217e12 | −0.0785726 | ||||||||
\(67\) | −3.26635e13 | −0.658417 | −0.329209 | − | 0.944257i | \(-0.606782\pi\) | ||||
−0.329209 | + | 0.944257i | \(0.606782\pi\) | |||||||
\(68\) | 1.92208e12 | 0.0346700 | ||||||||
\(69\) | 8.68185e11 | 0.0140360 | ||||||||
\(70\) | 7.47504e13 | 1.08487 | ||||||||
\(71\) | 4.12553e13 | 0.538323 | 0.269161 | − | 0.963095i | \(-0.413254\pi\) | ||||
0.269161 | + | 0.963095i | \(0.413254\pi\) | |||||||
\(72\) | −9.22047e13 | −1.08333 | ||||||||
\(73\) | 1.12820e14 | 1.19527 | 0.597635 | − | 0.801768i | \(-0.296107\pi\) | ||||
0.597635 | + | 0.801768i | \(0.296107\pi\) | |||||||
\(74\) | −1.91383e13 | −0.183091 | ||||||||
\(75\) | 6.07156e12 | 0.0525220 | ||||||||
\(76\) | −8.16924e13 | −0.639852 | ||||||||
\(77\) | 2.06957e14 | 1.46960 | ||||||||
\(78\) | 4.41395e12 | 0.0284523 | ||||||||
\(79\) | −2.27725e14 | −1.33416 | −0.667080 | − | 0.744986i | \(-0.732456\pi\) | ||||
−0.667080 | + | 0.744986i | \(0.732456\pi\) | |||||||
\(80\) | 1.30231e14 | 0.694285 | ||||||||
\(81\) | 2.03097e14 | 0.986427 | ||||||||
\(82\) | 6.76007e13 | 0.299466 | ||||||||
\(83\) | 8.49695e13 | 0.343698 | 0.171849 | − | 0.985123i | \(-0.445026\pi\) | ||||
0.171849 | + | 0.985123i | \(0.445026\pi\) | |||||||
\(84\) | −6.52426e12 | −0.0241233 | ||||||||
\(85\) | 3.86007e13 | 0.130603 | ||||||||
\(86\) | 4.01914e14 | 1.24565 | ||||||||
\(87\) | −6.62970e12 | −0.0188408 | ||||||||
\(88\) | 6.05988e14 | 1.58068 | ||||||||
\(89\) | 2.27743e13 | 0.0545783 | 0.0272892 | − | 0.999628i | \(-0.491313\pi\) | ||||
0.0272892 | + | 0.999628i | \(0.491313\pi\) | |||||||
\(90\) | −4.84326e14 | −1.06738 | ||||||||
\(91\) | −2.62335e14 | −0.532164 | ||||||||
\(92\) | −3.95172e13 | −0.0738546 | ||||||||
\(93\) | −3.52498e13 | −0.0607484 | ||||||||
\(94\) | −1.29305e14 | −0.205663 | ||||||||
\(95\) | −1.64061e15 | −2.41034 | ||||||||
\(96\) | −3.32106e13 | −0.0451069 | ||||||||
\(97\) | −1.34059e15 | −1.68464 | −0.842319 | − | 0.538979i | \(-0.818810\pi\) | ||||
−0.842319 | + | 0.538979i | \(0.818810\pi\) | |||||||
\(98\) | −1.63704e13 | −0.0190487 | ||||||||
\(99\) | −1.34092e15 | −1.44590 | ||||||||
\(100\) | −2.76359e14 | −0.276359 | ||||||||
\(101\) | 1.33589e15 | 1.23982 | 0.619912 | − | 0.784671i | \(-0.287168\pi\) | ||||
0.619912 | + | 0.784671i | \(0.287168\pi\) | |||||||
\(102\) | 6.14290e12 | 0.00529507 | ||||||||
\(103\) | 2.10271e15 | 1.68461 | 0.842306 | − | 0.538999i | \(-0.181197\pi\) | ||||
0.842306 | + | 0.538999i | \(0.181197\pi\) | |||||||
\(104\) | −7.68140e14 | −0.572388 | ||||||||
\(105\) | −1.31025e14 | −0.0908731 | ||||||||
\(106\) | 4.41069e14 | 0.284913 | ||||||||
\(107\) | −1.80074e15 | −1.08411 | −0.542054 | − | 0.840344i | \(-0.682353\pi\) | ||||
−0.542054 | + | 0.840344i | \(0.682353\pi\) | |||||||
\(108\) | 8.47369e13 | 0.0475767 | ||||||||
\(109\) | −2.37799e15 | −1.24598 | −0.622991 | − | 0.782229i | \(-0.714083\pi\) | ||||
−0.622991 | + | 0.782229i | \(0.714083\pi\) | |||||||
\(110\) | 3.18308e15 | 1.55741 | ||||||||
\(111\) | 3.35464e13 | 0.0153364 | ||||||||
\(112\) | −1.23174e15 | −0.526483 | ||||||||
\(113\) | −3.29653e15 | −1.31816 | −0.659080 | − | 0.752073i | \(-0.729054\pi\) | ||||
−0.659080 | + | 0.752073i | \(0.729054\pi\) | |||||||
\(114\) | −2.61086e14 | −0.0977232 | ||||||||
\(115\) | −7.93615e14 | −0.278212 | ||||||||
\(116\) | 3.01764e14 | 0.0991362 | ||||||||
\(117\) | 1.69973e15 | 0.523583 | ||||||||
\(118\) | −5.04004e13 | −0.0145653 | ||||||||
\(119\) | −3.65092e14 | −0.0990375 | ||||||||
\(120\) | −3.83654e14 | −0.0977418 | ||||||||
\(121\) | 4.63555e15 | 1.10971 | ||||||||
\(122\) | 2.46242e15 | 0.554196 | ||||||||
\(123\) | −1.18493e14 | −0.0250845 | ||||||||
\(124\) | 1.60447e15 | 0.319645 | ||||||||
\(125\) | 1.56314e15 | 0.293206 | ||||||||
\(126\) | 4.58084e15 | 0.809405 | ||||||||
\(127\) | 1.03840e16 | 1.72917 | 0.864586 | − | 0.502485i | \(-0.167581\pi\) | ||||
0.864586 | + | 0.502485i | \(0.167581\pi\) | |||||||
\(128\) | −1.15167e15 | −0.180823 | ||||||||
\(129\) | −7.04489e14 | −0.104340 | ||||||||
\(130\) | −4.03482e15 | −0.563962 | ||||||||
\(131\) | −1.22834e16 | −1.62100 | −0.810502 | − | 0.585735i | \(-0.800806\pi\) | ||||
−0.810502 | + | 0.585735i | \(0.800806\pi\) | |||||||
\(132\) | −2.77821e14 | −0.0346307 | ||||||||
\(133\) | 1.55172e16 | 1.82779 | ||||||||
\(134\) | 4.75158e15 | 0.529118 | ||||||||
\(135\) | 1.70175e15 | 0.179223 | ||||||||
\(136\) | −1.06902e15 | −0.106523 | ||||||||
\(137\) | 1.00516e16 | 0.948047 | 0.474024 | − | 0.880512i | \(-0.342801\pi\) | ||||
0.474024 | + | 0.880512i | \(0.342801\pi\) | |||||||
\(138\) | −1.26296e14 | −0.0112796 | ||||||||
\(139\) | −1.28795e16 | −1.08965 | −0.544825 | − | 0.838550i | \(-0.683404\pi\) | ||||
−0.544825 | + | 0.838550i | \(0.683404\pi\) | |||||||
\(140\) | 5.96388e15 | 0.478155 | ||||||||
\(141\) | 2.26651e14 | 0.0172272 | ||||||||
\(142\) | −6.00145e15 | −0.432607 | ||||||||
\(143\) | −1.11710e16 | −0.763959 | ||||||||
\(144\) | 7.98075e15 | 0.517995 | ||||||||
\(145\) | 6.06026e15 | 0.373449 | ||||||||
\(146\) | −1.64121e16 | −0.960544 | ||||||||
\(147\) | 2.86947e13 | 0.00159559 | ||||||||
\(148\) | −1.52693e15 | −0.0806968 | ||||||||
\(149\) | −1.30886e16 | −0.657651 | −0.328826 | − | 0.944391i | \(-0.606653\pi\) | ||||
−0.328826 | + | 0.944391i | \(0.606653\pi\) | |||||||
\(150\) | −8.83235e14 | −0.0422077 | ||||||||
\(151\) | −3.07794e16 | −1.39937 | −0.699686 | − | 0.714450i | \(-0.746677\pi\) | ||||
−0.699686 | + | 0.714450i | \(0.746677\pi\) | |||||||
\(152\) | 4.54357e16 | 1.96594 | ||||||||
\(153\) | 2.36552e15 | 0.0974407 | ||||||||
\(154\) | −3.01062e16 | −1.18100 | ||||||||
\(155\) | 3.22222e16 | 1.20411 | ||||||||
\(156\) | 3.52162e14 | 0.0125403 | ||||||||
\(157\) | −3.69229e16 | −1.25328 | −0.626641 | − | 0.779308i | \(-0.715571\pi\) | ||||
−0.626641 | + | 0.779308i | \(0.715571\pi\) | |||||||
\(158\) | 3.31274e16 | 1.07216 | ||||||||
\(159\) | −7.73123e14 | −0.0238655 | ||||||||
\(160\) | 3.03581e16 | 0.894077 | ||||||||
\(161\) | 7.50615e15 | 0.210971 | ||||||||
\(162\) | −2.95446e16 | −0.792713 | ||||||||
\(163\) | −5.23541e15 | −0.134135 | −0.0670677 | − | 0.997748i | \(-0.521364\pi\) | ||||
−0.0670677 | + | 0.997748i | \(0.521364\pi\) | |||||||
\(164\) | 5.39345e15 | 0.131989 | ||||||||
\(165\) | −5.57943e15 | −0.130455 | ||||||||
\(166\) | −1.23606e16 | −0.276203 | ||||||||
\(167\) | −8.53288e14 | −0.0182273 | −0.00911364 | − | 0.999958i | \(-0.502901\pi\) | ||||
−0.00911364 | + | 0.999958i | \(0.502901\pi\) | |||||||
\(168\) | 3.62866e15 | 0.0741186 | ||||||||
\(169\) | −3.70258e16 | −0.723359 | ||||||||
\(170\) | −5.61527e15 | −0.104955 | ||||||||
\(171\) | −1.00540e17 | −1.79832 | ||||||||
\(172\) | 3.20662e16 | 0.549016 | ||||||||
\(173\) | 4.95062e16 | 0.811546 | 0.405773 | − | 0.913974i | \(-0.367002\pi\) | ||||
0.405773 | + | 0.913974i | \(0.367002\pi\) | |||||||
\(174\) | 9.64428e14 | 0.0151409 | ||||||||
\(175\) | 5.24935e16 | 0.789441 | ||||||||
\(176\) | −5.24511e16 | −0.755804 | ||||||||
\(177\) | 8.83438e13 | 0.00122005 | ||||||||
\(178\) | −3.31300e15 | −0.0438603 | ||||||||
\(179\) | −1.22568e17 | −1.55589 | −0.777946 | − | 0.628331i | \(-0.783738\pi\) | ||||
−0.777946 | + | 0.628331i | \(0.783738\pi\) | |||||||
\(180\) | −3.86414e16 | −0.470445 | ||||||||
\(181\) | −6.08764e16 | −0.710984 | −0.355492 | − | 0.934679i | \(-0.615687\pi\) | ||||
−0.355492 | + | 0.934679i | \(0.615687\pi\) | |||||||
\(182\) | 3.81621e16 | 0.427658 | ||||||||
\(183\) | −4.31622e15 | −0.0464216 | ||||||||
\(184\) | 2.19787e16 | 0.226918 | ||||||||
\(185\) | −3.06650e16 | −0.303987 | ||||||||
\(186\) | 5.12782e15 | 0.0488187 | ||||||||
\(187\) | −1.55466e16 | −0.142175 | ||||||||
\(188\) | −1.03165e16 | −0.0906456 | ||||||||
\(189\) | −1.60955e16 | −0.135907 | ||||||||
\(190\) | 2.38661e17 | 1.93700 | ||||||||
\(191\) | 2.28398e17 | 1.78214 | 0.891072 | − | 0.453861i | \(-0.149954\pi\) | ||||
0.891072 | + | 0.453861i | \(0.149954\pi\) | |||||||
\(192\) | 9.49955e15 | 0.0712760 | ||||||||
\(193\) | −2.06335e17 | −1.48899 | −0.744497 | − | 0.667626i | \(-0.767311\pi\) | ||||
−0.744497 | + | 0.667626i | \(0.767311\pi\) | |||||||
\(194\) | 1.95016e17 | 1.35381 | ||||||||
\(195\) | 7.07239e15 | 0.0472397 | ||||||||
\(196\) | −1.30610e15 | −0.00839567 | ||||||||
\(197\) | −8.71433e16 | −0.539185 | −0.269592 | − | 0.962975i | \(-0.586889\pi\) | ||||
−0.269592 | + | 0.962975i | \(0.586889\pi\) | |||||||
\(198\) | 1.95065e17 | 1.16196 | ||||||||
\(199\) | −2.12118e17 | −1.21669 | −0.608345 | − | 0.793673i | \(-0.708166\pi\) | ||||
−0.608345 | + | 0.793673i | \(0.708166\pi\) | |||||||
\(200\) | 1.53706e17 | 0.849111 | ||||||||
\(201\) | −8.32875e15 | −0.0443210 | ||||||||
\(202\) | −1.94333e17 | −0.996348 | ||||||||
\(203\) | −5.73190e16 | −0.283190 | ||||||||
\(204\) | 4.90104e14 | 0.00233379 | ||||||||
\(205\) | 1.08316e17 | 0.497206 | ||||||||
\(206\) | −3.05883e17 | −1.35379 | ||||||||
\(207\) | −4.86341e16 | −0.207570 | ||||||||
\(208\) | 6.64861e16 | 0.273688 | ||||||||
\(209\) | 6.60765e17 | 2.62392 | ||||||||
\(210\) | 1.90604e16 | 0.0730275 | ||||||||
\(211\) | 4.65805e16 | 0.172221 | 0.0861105 | − | 0.996286i | \(-0.472556\pi\) | ||||
0.0861105 | + | 0.996286i | \(0.472556\pi\) | |||||||
\(212\) | 3.51902e16 | 0.125575 | ||||||||
\(213\) | 1.05196e16 | 0.0362369 | ||||||||
\(214\) | 2.61955e17 | 0.871212 | ||||||||
\(215\) | 6.43980e17 | 2.06816 | ||||||||
\(216\) | −4.71290e16 | −0.146179 | ||||||||
\(217\) | −3.04763e17 | −0.913091 | ||||||||
\(218\) | 3.45928e17 | 1.00130 | ||||||||
\(219\) | 2.87677e16 | 0.0804589 | ||||||||
\(220\) | 2.53959e17 | 0.686425 | ||||||||
\(221\) | 1.97067e16 | 0.0514838 | ||||||||
\(222\) | −4.88002e15 | −0.0123246 | ||||||||
\(223\) | −6.90479e17 | −1.68603 | −0.843013 | − | 0.537894i | \(-0.819220\pi\) | ||||
−0.843013 | + | 0.537894i | \(0.819220\pi\) | |||||||
\(224\) | −2.87132e17 | −0.677987 | ||||||||
\(225\) | −3.40118e17 | −0.776712 | ||||||||
\(226\) | 4.79548e17 | 1.05930 | ||||||||
\(227\) | −3.86349e17 | −0.825631 | −0.412816 | − | 0.910815i | \(-0.635455\pi\) | ||||
−0.412816 | + | 0.910815i | \(0.635455\pi\) | |||||||
\(228\) | −2.08305e16 | −0.0430713 | ||||||||
\(229\) | −6.43885e17 | −1.28837 | −0.644187 | − | 0.764868i | \(-0.722804\pi\) | ||||
−0.644187 | + | 0.764868i | \(0.722804\pi\) | |||||||
\(230\) | 1.15448e17 | 0.223577 | ||||||||
\(231\) | 5.27712e16 | 0.0989252 | ||||||||
\(232\) | −1.67835e17 | −0.304595 | ||||||||
\(233\) | −7.96458e17 | −1.39957 | −0.699783 | − | 0.714355i | \(-0.746720\pi\) | ||||
−0.699783 | + | 0.714355i | \(0.746720\pi\) | |||||||
\(234\) | −2.47261e17 | −0.420762 | ||||||||
\(235\) | −2.07183e17 | −0.341464 | ||||||||
\(236\) | −4.02114e15 | −0.00641962 | ||||||||
\(237\) | −5.80669e16 | −0.0898083 | ||||||||
\(238\) | 5.31102e16 | 0.0795886 | ||||||||
\(239\) | 4.05410e17 | 0.588722 | 0.294361 | − | 0.955694i | \(-0.404893\pi\) | ||||
0.294361 | + | 0.955694i | \(0.404893\pi\) | |||||||
\(240\) | 3.32071e16 | 0.0467354 | ||||||||
\(241\) | −3.42909e16 | −0.0467791 | −0.0233895 | − | 0.999726i | \(-0.507446\pi\) | ||||
−0.0233895 | + | 0.999726i | \(0.507446\pi\) | |||||||
\(242\) | −6.74337e17 | −0.891789 | ||||||||
\(243\) | 1.56548e17 | 0.200725 | ||||||||
\(244\) | 1.96461e17 | 0.244261 | ||||||||
\(245\) | −2.62301e16 | −0.0316267 | ||||||||
\(246\) | 1.72373e16 | 0.0201584 | ||||||||
\(247\) | −8.37575e17 | −0.950160 | ||||||||
\(248\) | −8.92373e17 | −0.982107 | ||||||||
\(249\) | 2.16661e16 | 0.0231359 | ||||||||
\(250\) | −2.27391e17 | −0.235626 | ||||||||
\(251\) | 1.21742e18 | 1.22430 | 0.612150 | − | 0.790742i | \(-0.290305\pi\) | ||||
0.612150 | + | 0.790742i | \(0.290305\pi\) | |||||||
\(252\) | 3.65477e17 | 0.356743 | ||||||||
\(253\) | 3.19633e17 | 0.302864 | ||||||||
\(254\) | −1.51057e18 | −1.38960 | ||||||||
\(255\) | 9.84266e15 | 0.00879146 | ||||||||
\(256\) | −1.05324e18 | −0.913539 | ||||||||
\(257\) | 9.87898e17 | 0.832174 | 0.416087 | − | 0.909325i | \(-0.363401\pi\) | ||||
0.416087 | + | 0.909325i | \(0.363401\pi\) | |||||||
\(258\) | 1.02483e17 | 0.0838499 | ||||||||
\(259\) | 2.90035e17 | 0.230516 | ||||||||
\(260\) | −3.21914e17 | −0.248565 | ||||||||
\(261\) | 3.71383e17 | 0.278624 | ||||||||
\(262\) | 1.78688e18 | 1.30267 | ||||||||
\(263\) | 3.94844e16 | 0.0279742 | 0.0139871 | − | 0.999902i | \(-0.495548\pi\) | ||||
0.0139871 | + | 0.999902i | \(0.495548\pi\) | |||||||
\(264\) | 1.54519e17 | 0.106403 | ||||||||
\(265\) | 7.06718e17 | 0.473044 | ||||||||
\(266\) | −2.25730e18 | −1.46885 | ||||||||
\(267\) | 5.80715e15 | 0.00367391 | ||||||||
\(268\) | 3.79100e17 | 0.233207 | ||||||||
\(269\) | −7.87854e17 | −0.471306 | −0.235653 | − | 0.971837i | \(-0.575723\pi\) | ||||
−0.235653 | + | 0.971837i | \(0.575723\pi\) | |||||||
\(270\) | −2.47556e17 | −0.144027 | ||||||||
\(271\) | 2.78972e18 | 1.57867 | 0.789334 | − | 0.613964i | \(-0.210426\pi\) | ||||
0.789334 | + | 0.613964i | \(0.210426\pi\) | |||||||
\(272\) | 9.25289e16 | 0.0509343 | ||||||||
\(273\) | −6.68919e16 | −0.0358223 | ||||||||
\(274\) | −1.46221e18 | −0.761870 | ||||||||
\(275\) | 2.23532e18 | 1.13330 | ||||||||
\(276\) | −1.00764e16 | −0.00497148 | ||||||||
\(277\) | 3.07769e18 | 1.47784 | 0.738918 | − | 0.673795i | \(-0.235337\pi\) | ||||
0.738918 | + | 0.673795i | \(0.235337\pi\) | |||||||
\(278\) | 1.87359e18 | 0.875665 | ||||||||
\(279\) | 1.97463e18 | 0.898368 | ||||||||
\(280\) | −3.31699e18 | −1.46913 | ||||||||
\(281\) | 4.14344e18 | 1.78675 | 0.893375 | − | 0.449313i | \(-0.148331\pi\) | ||||
0.893375 | + | 0.449313i | \(0.148331\pi\) | |||||||
\(282\) | −3.29710e16 | −0.0138441 | ||||||||
\(283\) | −1.46638e18 | −0.599581 | −0.299790 | − | 0.954005i | \(-0.596917\pi\) | ||||
−0.299790 | + | 0.954005i | \(0.596917\pi\) | |||||||
\(284\) | −4.78819e17 | −0.190671 | ||||||||
\(285\) | −4.18334e17 | −0.162251 | ||||||||
\(286\) | 1.62505e18 | 0.613933 | ||||||||
\(287\) | −1.02447e18 | −0.377037 | ||||||||
\(288\) | 1.86040e18 | 0.667056 | ||||||||
\(289\) | −2.83500e18 | −0.990419 | ||||||||
\(290\) | −8.81591e17 | −0.300111 | ||||||||
\(291\) | −3.41832e17 | −0.113400 | ||||||||
\(292\) | −1.30942e18 | −0.423358 | ||||||||
\(293\) | 1.19799e18 | 0.377526 | 0.188763 | − | 0.982023i | \(-0.439552\pi\) | ||||
0.188763 | + | 0.982023i | \(0.439552\pi\) | |||||||
\(294\) | −4.17425e15 | −0.00128225 | ||||||||
\(295\) | −8.07558e16 | −0.0241829 | ||||||||
\(296\) | 8.49248e17 | 0.247940 | ||||||||
\(297\) | −6.85391e17 | −0.195103 | ||||||||
\(298\) | 1.90401e18 | 0.528502 | ||||||||
\(299\) | −4.05162e17 | −0.109672 | ||||||||
\(300\) | −7.04679e16 | −0.0186030 | ||||||||
\(301\) | −6.09087e18 | −1.56831 | ||||||||
\(302\) | 4.47751e18 | 1.12456 | ||||||||
\(303\) | 3.40634e17 | 0.0834581 | ||||||||
\(304\) | −3.93267e18 | −0.940017 | ||||||||
\(305\) | 3.94549e18 | 0.920137 | ||||||||
\(306\) | −3.44114e17 | −0.0783053 | ||||||||
\(307\) | −3.53107e18 | −0.784094 | −0.392047 | − | 0.919945i | \(-0.628233\pi\) | ||||
−0.392047 | + | 0.919945i | \(0.628233\pi\) | |||||||
\(308\) | −2.40199e18 | −0.520523 | ||||||||
\(309\) | 5.36163e17 | 0.113399 | ||||||||
\(310\) | −4.68739e18 | −0.967649 | ||||||||
\(311\) | −2.60736e18 | −0.525410 | −0.262705 | − | 0.964876i | \(-0.584615\pi\) | ||||
−0.262705 | + | 0.964876i | \(0.584615\pi\) | |||||||
\(312\) | −1.95865e17 | −0.0385299 | ||||||||
\(313\) | −2.42498e18 | −0.465722 | −0.232861 | − | 0.972510i | \(-0.574809\pi\) | ||||
−0.232861 | + | 0.972510i | \(0.574809\pi\) | |||||||
\(314\) | 5.37121e18 | 1.00716 | ||||||||
\(315\) | 7.33980e18 | 1.34386 | ||||||||
\(316\) | 2.64303e18 | 0.472552 | ||||||||
\(317\) | 5.66141e18 | 0.988508 | 0.494254 | − | 0.869318i | \(-0.335441\pi\) | ||||
0.494254 | + | 0.869318i | \(0.335441\pi\) | |||||||
\(318\) | 1.12467e17 | 0.0191788 | ||||||||
\(319\) | −2.44080e18 | −0.406540 | ||||||||
\(320\) | −8.68361e18 | −1.41278 | ||||||||
\(321\) | −4.59165e17 | −0.0729761 | ||||||||
\(322\) | −1.09193e18 | −0.169541 | ||||||||
\(323\) | −1.16565e18 | −0.176828 | ||||||||
\(324\) | −2.35719e18 | −0.349387 | ||||||||
\(325\) | −2.83345e18 | −0.410384 | ||||||||
\(326\) | 7.61599e17 | 0.107794 | ||||||||
\(327\) | −6.06356e17 | −0.0838725 | ||||||||
\(328\) | −2.99973e18 | −0.405535 | ||||||||
\(329\) | 1.95957e18 | 0.258936 | ||||||||
\(330\) | 8.11644e17 | 0.104836 | ||||||||
\(331\) | −7.23418e16 | −0.00913438 | −0.00456719 | − | 0.999990i | \(-0.501454\pi\) | ||||
−0.00456719 | + | 0.999990i | \(0.501454\pi\) | |||||||
\(332\) | −9.86175e17 | −0.121736 | ||||||||
\(333\) | −1.87921e18 | −0.226800 | ||||||||
\(334\) | 1.24128e17 | 0.0146478 | ||||||||
\(335\) | 7.61338e18 | 0.878499 | ||||||||
\(336\) | −3.14078e17 | −0.0354399 | ||||||||
\(337\) | 9.42326e18 | 1.03987 | 0.519933 | − | 0.854207i | \(-0.325957\pi\) | ||||
0.519933 | + | 0.854207i | \(0.325957\pi\) | |||||||
\(338\) | 5.38617e18 | 0.581306 | ||||||||
\(339\) | −8.40570e17 | −0.0887312 | ||||||||
\(340\) | −4.48008e17 | −0.0462588 | ||||||||
\(341\) | −1.29777e19 | −1.31081 | ||||||||
\(342\) | 1.46256e19 | 1.44516 | ||||||||
\(343\) | −1.02182e19 | −0.987800 | ||||||||
\(344\) | −1.78346e19 | −1.68685 | ||||||||
\(345\) | −2.02361e17 | −0.0187277 | ||||||||
\(346\) | −7.20170e18 | −0.652175 | ||||||||
\(347\) | −9.59185e18 | −0.850024 | −0.425012 | − | 0.905188i | \(-0.639730\pi\) | ||||
−0.425012 | + | 0.905188i | \(0.639730\pi\) | |||||||
\(348\) | 7.69458e16 | 0.00667330 | ||||||||
\(349\) | 6.56731e18 | 0.557438 | 0.278719 | − | 0.960373i | \(-0.410090\pi\) | ||||
0.278719 | + | 0.960373i | \(0.410090\pi\) | |||||||
\(350\) | −7.63627e18 | −0.634411 | ||||||||
\(351\) | 8.68790e17 | 0.0706499 | ||||||||
\(352\) | −1.22269e19 | −0.973299 | ||||||||
\(353\) | −8.79452e18 | −0.685334 | −0.342667 | − | 0.939457i | \(-0.611330\pi\) | ||||
−0.342667 | + | 0.939457i | \(0.611330\pi\) | |||||||
\(354\) | −1.28514e16 | −0.000980455 0 | ||||||||
\(355\) | −9.61602e18 | −0.718262 | ||||||||
\(356\) | −2.64324e17 | −0.0193313 | ||||||||
\(357\) | −9.30936e16 | −0.00666666 | ||||||||
\(358\) | 1.78301e19 | 1.25035 | ||||||||
\(359\) | 1.67070e19 | 1.14733 | 0.573667 | − | 0.819089i | \(-0.305520\pi\) | ||||
0.573667 | + | 0.819089i | \(0.305520\pi\) | |||||||
\(360\) | 2.14916e19 | 1.44544 | ||||||||
\(361\) | 3.43617e19 | 2.26345 | ||||||||
\(362\) | 8.85575e18 | 0.571361 | ||||||||
\(363\) | 1.18200e18 | 0.0746998 | ||||||||
\(364\) | 3.04472e18 | 0.188489 | ||||||||
\(365\) | −2.62968e19 | −1.59480 | ||||||||
\(366\) | 6.27884e17 | 0.0373054 | ||||||||
\(367\) | −5.31239e18 | −0.309239 | −0.154620 | − | 0.987974i | \(-0.549415\pi\) | ||||
−0.154620 | + | 0.987974i | \(0.549415\pi\) | |||||||
\(368\) | −1.90236e18 | −0.108501 | ||||||||
\(369\) | 6.63777e18 | 0.370958 | ||||||||
\(370\) | 4.46087e18 | 0.244290 | ||||||||
\(371\) | −6.68426e18 | −0.358714 | ||||||||
\(372\) | 4.09118e17 | 0.0215167 | ||||||||
\(373\) | 2.34477e19 | 1.20860 | 0.604302 | − | 0.796756i | \(-0.293452\pi\) | ||||
0.604302 | + | 0.796756i | \(0.293452\pi\) | |||||||
\(374\) | 2.26158e18 | 0.114255 | ||||||||
\(375\) | 3.98580e17 | 0.0197370 | ||||||||
\(376\) | 5.73781e18 | 0.278508 | ||||||||
\(377\) | 3.09392e18 | 0.147214 | ||||||||
\(378\) | 2.34142e18 | 0.109217 | ||||||||
\(379\) | −1.60533e19 | −0.734125 | −0.367063 | − | 0.930196i | \(-0.619637\pi\) | ||||
−0.367063 | + | 0.930196i | \(0.619637\pi\) | |||||||
\(380\) | 1.90413e19 | 0.853729 | ||||||||
\(381\) | 2.64779e18 | 0.116398 | ||||||||
\(382\) | −3.32253e19 | −1.43217 | ||||||||
\(383\) | −4.40510e19 | −1.86194 | −0.930969 | − | 0.365099i | \(-0.881035\pi\) | ||||
−0.930969 | + | 0.365099i | \(0.881035\pi\) | |||||||
\(384\) | −2.93661e17 | −0.0121720 | ||||||||
\(385\) | −4.82386e19 | −1.96083 | ||||||||
\(386\) | 3.00157e19 | 1.19659 | ||||||||
\(387\) | 3.94642e19 | 1.54302 | ||||||||
\(388\) | 1.55591e19 | 0.596689 | ||||||||
\(389\) | 3.79555e19 | 1.42775 | 0.713876 | − | 0.700273i | \(-0.246938\pi\) | ||||
0.713876 | + | 0.700273i | \(0.246938\pi\) | |||||||
\(390\) | −1.02883e18 | −0.0379628 | ||||||||
\(391\) | −5.63864e17 | −0.0204103 | ||||||||
\(392\) | 7.26426e17 | 0.0257956 | ||||||||
\(393\) | −3.13211e18 | −0.109117 | ||||||||
\(394\) | 1.26768e19 | 0.433300 | ||||||||
\(395\) | 5.30795e19 | 1.78012 | ||||||||
\(396\) | 1.55630e19 | 0.512131 | ||||||||
\(397\) | −1.75731e19 | −0.567439 | −0.283719 | − | 0.958907i | \(-0.591568\pi\) | ||||
−0.283719 | + | 0.958907i | \(0.591568\pi\) | |||||||
\(398\) | 3.08570e19 | 0.977757 | ||||||||
\(399\) | 3.95667e18 | 0.123036 | ||||||||
\(400\) | −1.33039e19 | −0.406004 | ||||||||
\(401\) | −1.14532e19 | −0.343040 | −0.171520 | − | 0.985181i | \(-0.554868\pi\) | ||||
−0.171520 | + | 0.985181i | \(0.554868\pi\) | |||||||
\(402\) | 1.21159e18 | 0.0356172 | ||||||||
\(403\) | 1.64503e19 | 0.474663 | ||||||||
\(404\) | −1.55046e19 | −0.439138 | ||||||||
\(405\) | −4.73389e19 | −1.31615 | ||||||||
\(406\) | 8.33824e18 | 0.227577 | ||||||||
\(407\) | 1.23505e19 | 0.330923 | ||||||||
\(408\) | −2.72586e17 | −0.00717056 | ||||||||
\(409\) | −3.70597e19 | −0.957143 | −0.478572 | − | 0.878049i | \(-0.658845\pi\) | ||||
−0.478572 | + | 0.878049i | \(0.658845\pi\) | |||||||
\(410\) | −1.57568e19 | −0.399565 | ||||||||
\(411\) | 2.56302e18 | 0.0638173 | ||||||||
\(412\) | −2.44045e19 | −0.596680 | ||||||||
\(413\) | 7.63802e17 | 0.0183381 | ||||||||
\(414\) | 7.07485e18 | 0.166807 | ||||||||
\(415\) | −1.98052e19 | −0.458583 | ||||||||
\(416\) | 1.54986e19 | 0.352446 | ||||||||
\(417\) | −3.28410e18 | −0.0733492 | ||||||||
\(418\) | −9.61221e19 | −2.10863 | ||||||||
\(419\) | 8.68391e19 | 1.87116 | 0.935578 | − | 0.353120i | \(-0.114879\pi\) | ||||
0.935578 | + | 0.353120i | \(0.114879\pi\) | |||||||
\(420\) | 1.52071e18 | 0.0321867 | ||||||||
\(421\) | −3.76050e18 | −0.0781861 | −0.0390931 | − | 0.999236i | \(-0.512447\pi\) | ||||
−0.0390931 | + | 0.999236i | \(0.512447\pi\) | |||||||
\(422\) | −6.77611e18 | −0.138400 | ||||||||
\(423\) | −1.26965e19 | −0.254761 | ||||||||
\(424\) | −1.95721e19 | −0.385828 | ||||||||
\(425\) | −3.94332e18 | −0.0763740 | ||||||||
\(426\) | −1.53029e18 | −0.0291207 | ||||||||
\(427\) | −3.73171e19 | −0.697749 | ||||||||
\(428\) | 2.08998e19 | 0.383985 | ||||||||
\(429\) | −2.84845e18 | −0.0514255 | ||||||||
\(430\) | −9.36803e19 | −1.66201 | ||||||||
\(431\) | −1.04399e20 | −1.82019 | −0.910095 | − | 0.414400i | \(-0.863992\pi\) | ||||
−0.910095 | + | 0.414400i | \(0.863992\pi\) | |||||||
\(432\) | 4.07924e18 | 0.0698958 | ||||||||
\(433\) | −1.06713e20 | −1.79705 | −0.898525 | − | 0.438923i | \(-0.855360\pi\) | ||||
−0.898525 | + | 0.438923i | \(0.855360\pi\) | |||||||
\(434\) | 4.43341e19 | 0.733778 | ||||||||
\(435\) | 1.54529e18 | 0.0251385 | ||||||||
\(436\) | 2.75995e19 | 0.441319 | ||||||||
\(437\) | 2.39654e19 | 0.376682 | ||||||||
\(438\) | −4.18486e18 | −0.0646584 | ||||||||
\(439\) | −2.63377e19 | −0.400031 | −0.200016 | − | 0.979793i | \(-0.564099\pi\) | ||||
−0.200016 | + | 0.979793i | \(0.564099\pi\) | |||||||
\(440\) | −1.41247e20 | −2.10904 | ||||||||
\(441\) | −1.60743e18 | −0.0235962 | ||||||||
\(442\) | −2.86674e18 | −0.0413735 | ||||||||
\(443\) | 1.05962e20 | 1.50357 | 0.751785 | − | 0.659408i | \(-0.229193\pi\) | ||||
0.751785 | + | 0.659408i | \(0.229193\pi\) | |||||||
\(444\) | −3.89347e17 | −0.00543206 | ||||||||
\(445\) | −5.30836e18 | −0.0728217 | ||||||||
\(446\) | 1.00445e20 | 1.35492 | ||||||||
\(447\) | −3.33742e18 | −0.0442694 | ||||||||
\(448\) | 8.21311e19 | 1.07133 | ||||||||
\(449\) | −4.12026e18 | −0.0528539 | −0.0264269 | − | 0.999651i | \(-0.508413\pi\) | ||||
−0.0264269 | + | 0.999651i | \(0.508413\pi\) | |||||||
\(450\) | 4.94772e19 | 0.624182 | ||||||||
\(451\) | −4.36247e19 | −0.541263 | ||||||||
\(452\) | 3.82602e19 | 0.466884 | ||||||||
\(453\) | −7.84835e18 | −0.0941980 | ||||||||
\(454\) | 5.62026e19 | 0.663494 | ||||||||
\(455\) | 6.11464e19 | 0.710045 | ||||||||
\(456\) | 1.15855e19 | 0.132336 | ||||||||
\(457\) | 1.76790e19 | 0.198649 | 0.0993246 | − | 0.995055i | \(-0.468332\pi\) | ||||
0.0993246 | + | 0.995055i | \(0.468332\pi\) | |||||||
\(458\) | 9.36664e19 | 1.03536 | ||||||||
\(459\) | 1.20910e18 | 0.0131482 | ||||||||
\(460\) | 9.21088e18 | 0.0985411 | ||||||||
\(461\) | 3.96193e19 | 0.417013 | 0.208507 | − | 0.978021i | \(-0.433140\pi\) | ||||
0.208507 | + | 0.978021i | \(0.433140\pi\) | |||||||
\(462\) | −7.67667e18 | −0.0794983 | ||||||||
\(463\) | −1.46144e20 | −1.48910 | −0.744551 | − | 0.667566i | \(-0.767336\pi\) | ||||
−0.744551 | + | 0.667566i | \(0.767336\pi\) | |||||||
\(464\) | 1.45269e19 | 0.145643 | ||||||||
\(465\) | 8.21623e18 | 0.0810541 | ||||||||
\(466\) | 1.15861e20 | 1.12472 | ||||||||
\(467\) | 1.89194e20 | 1.80730 | 0.903651 | − | 0.428269i | \(-0.140877\pi\) | ||||
0.903651 | + | 0.428269i | \(0.140877\pi\) | |||||||
\(468\) | −1.97275e19 | −0.185450 | ||||||||
\(469\) | −7.20086e19 | −0.666175 | ||||||||
\(470\) | 3.01391e19 | 0.274408 | ||||||||
\(471\) | −9.41486e18 | −0.0843640 | ||||||||
\(472\) | 2.23648e18 | 0.0197242 | ||||||||
\(473\) | −2.59366e20 | −2.25141 | ||||||||
\(474\) | 8.44705e18 | 0.0721718 | ||||||||
\(475\) | 1.67600e20 | 1.40952 | ||||||||
\(476\) | 4.23734e18 | 0.0350785 | ||||||||
\(477\) | 4.33089e19 | 0.352931 | ||||||||
\(478\) | −5.89754e19 | −0.473109 | ||||||||
\(479\) | −1.42619e20 | −1.12632 | −0.563158 | − | 0.826349i | \(-0.690414\pi\) | ||||
−0.563158 | + | 0.826349i | \(0.690414\pi\) | |||||||
\(480\) | 7.74092e18 | 0.0601843 | ||||||||
\(481\) | −1.56553e19 | −0.119832 | ||||||||
\(482\) | 4.98833e18 | 0.0375926 | ||||||||
\(483\) | 1.91397e18 | 0.0142014 | ||||||||
\(484\) | −5.38013e19 | −0.393054 | ||||||||
\(485\) | 3.12471e20 | 2.24774 | ||||||||
\(486\) | −2.27732e19 | −0.161306 | ||||||||
\(487\) | −4.00797e19 | −0.279548 | −0.139774 | − | 0.990183i | \(-0.544638\pi\) | ||||
−0.139774 | + | 0.990183i | \(0.544638\pi\) | |||||||
\(488\) | −1.09268e20 | −0.750489 | ||||||||
\(489\) | −1.33496e18 | −0.00902925 | ||||||||
\(490\) | 3.81571e18 | 0.0254159 | ||||||||
\(491\) | 9.80799e19 | 0.643382 | 0.321691 | − | 0.946845i | \(-0.395749\pi\) | ||||
0.321691 | + | 0.946845i | \(0.395749\pi\) | |||||||
\(492\) | 1.37526e18 | 0.00888477 | ||||||||
\(493\) | 4.30582e18 | 0.0273971 | ||||||||
\(494\) | 1.21843e20 | 0.763568 | ||||||||
\(495\) | 3.12549e20 | 1.92921 | ||||||||
\(496\) | 7.72391e19 | 0.469596 | ||||||||
\(497\) | 9.09500e19 | 0.544665 | ||||||||
\(498\) | −3.15178e18 | −0.0185924 | ||||||||
\(499\) | 1.53727e20 | 0.893297 | 0.446648 | − | 0.894710i | \(-0.352618\pi\) | ||||
0.446648 | + | 0.894710i | \(0.352618\pi\) | |||||||
\(500\) | −1.81422e19 | −0.103852 | ||||||||
\(501\) | −2.17577e17 | −0.00122696 | ||||||||
\(502\) | −1.77099e20 | −0.983873 | ||||||||
\(503\) | −8.89831e19 | −0.487021 | −0.243510 | − | 0.969898i | \(-0.578299\pi\) | ||||
−0.243510 | + | 0.969898i | \(0.578299\pi\) | |||||||
\(504\) | −2.03271e20 | −1.09609 | ||||||||
\(505\) | −3.11376e20 | −1.65425 | ||||||||
\(506\) | −4.64973e19 | −0.243388 | ||||||||
\(507\) | −9.44108e18 | −0.0486925 | ||||||||
\(508\) | −1.20519e20 | −0.612462 | ||||||||
\(509\) | −8.52937e19 | −0.427104 | −0.213552 | − | 0.976932i | \(-0.568503\pi\) | ||||
−0.213552 | + | 0.976932i | \(0.568503\pi\) | |||||||
\(510\) | −1.43182e18 | −0.00706500 | ||||||||
\(511\) | 2.48720e20 | 1.20935 | ||||||||
\(512\) | 1.90954e20 | 0.914962 | ||||||||
\(513\) | −5.13892e19 | −0.242656 | ||||||||
\(514\) | −1.43710e20 | −0.668752 | ||||||||
\(515\) | −4.90111e20 | −2.24771 | ||||||||
\(516\) | 8.17647e18 | 0.0369567 | ||||||||
\(517\) | 8.34442e19 | 0.371721 | ||||||||
\(518\) | −4.21916e19 | −0.185248 | ||||||||
\(519\) | 1.26234e19 | 0.0546288 | ||||||||
\(520\) | 1.79042e20 | 0.763713 | ||||||||
\(521\) | −1.91291e20 | −0.804287 | −0.402143 | − | 0.915577i | \(-0.631735\pi\) | ||||
−0.402143 | + | 0.915577i | \(0.631735\pi\) | |||||||
\(522\) | −5.40255e19 | −0.223908 | ||||||||
\(523\) | −3.26310e20 | −1.33312 | −0.666558 | − | 0.745453i | \(-0.732233\pi\) | ||||
−0.666558 | + | 0.745453i | \(0.732233\pi\) | |||||||
\(524\) | 1.42564e20 | 0.574150 | ||||||||
\(525\) | 1.33851e19 | 0.0531408 | ||||||||
\(526\) | −5.74383e18 | −0.0224806 | ||||||||
\(527\) | 2.28939e19 | 0.0883364 | ||||||||
\(528\) | −1.33743e19 | −0.0508765 | ||||||||
\(529\) | 1.15928e19 | 0.0434783 | ||||||||
\(530\) | −1.02807e20 | −0.380148 | ||||||||
\(531\) | −4.94886e18 | −0.0180425 | ||||||||
\(532\) | −1.80096e20 | −0.647391 | ||||||||
\(533\) | 5.52979e19 | 0.195999 | ||||||||
\(534\) | −8.44771e17 | −0.00295243 | ||||||||
\(535\) | 4.19726e20 | 1.44648 | ||||||||
\(536\) | −2.10848e20 | −0.716528 | ||||||||
\(537\) | −3.12532e19 | −0.104734 | ||||||||
\(538\) | 1.14610e20 | 0.378752 | ||||||||
\(539\) | 1.05643e19 | 0.0344291 | ||||||||
\(540\) | −1.97509e19 | −0.0634797 | ||||||||
\(541\) | 3.49946e20 | 1.10923 | 0.554615 | − | 0.832107i | \(-0.312866\pi\) | ||||
0.554615 | + | 0.832107i | \(0.312866\pi\) | |||||||
\(542\) | −4.05823e20 | −1.26865 | ||||||||
\(543\) | −1.55227e19 | −0.0478595 | ||||||||
\(544\) | 2.15695e19 | 0.0655915 | ||||||||
\(545\) | 5.54275e20 | 1.66246 | ||||||||
\(546\) | 9.73082e18 | 0.0287875 | ||||||||
\(547\) | 7.11736e19 | 0.207689 | 0.103845 | − | 0.994594i | \(-0.466886\pi\) | ||||
0.103845 | + | 0.994594i | \(0.466886\pi\) | |||||||
\(548\) | −1.16661e20 | −0.335793 | ||||||||
\(549\) | 2.41787e20 | 0.686499 | ||||||||
\(550\) | −3.25174e20 | −0.910742 | ||||||||
\(551\) | −1.83006e20 | −0.505626 | ||||||||
\(552\) | 5.60427e18 | 0.0152748 | ||||||||
\(553\) | −5.02035e20 | −1.34988 | ||||||||
\(554\) | −4.47714e20 | −1.18762 | ||||||||
\(555\) | −7.81917e18 | −0.0204627 | ||||||||
\(556\) | 1.49482e20 | 0.385948 | ||||||||
\(557\) | 4.00940e20 | 1.02133 | 0.510664 | − | 0.859780i | \(-0.329400\pi\) | ||||
0.510664 | + | 0.859780i | \(0.329400\pi\) | |||||||
\(558\) | −2.87251e20 | −0.721947 | ||||||||
\(559\) | 3.28769e20 | 0.815270 | ||||||||
\(560\) | 2.87101e20 | 0.702465 | ||||||||
\(561\) | −3.96419e18 | −0.00957046 | ||||||||
\(562\) | −6.02750e20 | −1.43587 | ||||||||
\(563\) | −5.48584e20 | −1.28953 | −0.644763 | − | 0.764383i | \(-0.723044\pi\) | ||||
−0.644763 | + | 0.764383i | \(0.723044\pi\) | |||||||
\(564\) | −2.63056e18 | −0.00610175 | ||||||||
\(565\) | 7.68372e20 | 1.75877 | ||||||||
\(566\) | 2.13315e20 | 0.481836 | ||||||||
\(567\) | 4.47739e20 | 0.998049 | ||||||||
\(568\) | 2.66310e20 | 0.585834 | ||||||||
\(569\) | −6.89130e20 | −1.49609 | −0.748047 | − | 0.663645i | \(-0.769008\pi\) | ||||
−0.748047 | + | 0.663645i | \(0.769008\pi\) | |||||||
\(570\) | 6.08554e19 | 0.130388 | ||||||||
\(571\) | 6.10610e20 | 1.29120 | 0.645599 | − | 0.763676i | \(-0.276608\pi\) | ||||
0.645599 | + | 0.763676i | \(0.276608\pi\) | |||||||
\(572\) | 1.29653e20 | 0.270590 | ||||||||
\(573\) | 5.82386e19 | 0.119964 | ||||||||
\(574\) | 1.49030e20 | 0.302994 | ||||||||
\(575\) | 8.10732e19 | 0.162693 | ||||||||
\(576\) | −5.32147e20 | −1.05405 | ||||||||
\(577\) | −4.96230e20 | −0.970206 | −0.485103 | − | 0.874457i | \(-0.661218\pi\) | ||||
−0.485103 | + | 0.874457i | \(0.661218\pi\) | |||||||
\(578\) | 4.12409e20 | 0.795921 | ||||||||
\(579\) | −5.26127e19 | −0.100231 | ||||||||
\(580\) | −7.03368e19 | −0.132273 | ||||||||
\(581\) | 1.87321e20 | 0.347748 | ||||||||
\(582\) | 4.97265e19 | 0.0911309 | ||||||||
\(583\) | −2.84635e20 | −0.514960 | ||||||||
\(584\) | 7.28273e20 | 1.30076 | ||||||||
\(585\) | −3.96182e20 | −0.698596 | ||||||||
\(586\) | −1.74273e20 | −0.303388 | ||||||||
\(587\) | −1.19460e20 | −0.205322 | −0.102661 | − | 0.994716i | \(-0.532736\pi\) | ||||
−0.102661 | + | 0.994716i | \(0.532736\pi\) | |||||||
\(588\) | −3.33038e17 | −0.000565150 0 | ||||||||
\(589\) | −9.73038e20 | −1.63029 | ||||||||
\(590\) | 1.17476e19 | 0.0194339 | ||||||||
\(591\) | −2.22204e19 | −0.0362949 | ||||||||
\(592\) | −7.35064e19 | −0.118553 | ||||||||
\(593\) | 3.03034e20 | 0.482593 | 0.241297 | − | 0.970451i | \(-0.422427\pi\) | ||||
0.241297 | + | 0.970451i | \(0.422427\pi\) | |||||||
\(594\) | 9.97044e19 | 0.156789 | ||||||||
\(595\) | 8.50976e19 | 0.132142 | ||||||||
\(596\) | 1.51909e20 | 0.232936 | ||||||||
\(597\) | −5.40873e19 | −0.0819008 | ||||||||
\(598\) | 5.89392e19 | 0.0881344 | ||||||||
\(599\) | 4.74013e20 | 0.699986 | 0.349993 | − | 0.936752i | \(-0.386184\pi\) | ||||
0.349993 | + | 0.936752i | \(0.386184\pi\) | |||||||
\(600\) | 3.91929e19 | 0.0571574 | ||||||||
\(601\) | 9.70281e20 | 1.39746 | 0.698729 | − | 0.715386i | \(-0.253749\pi\) | ||||
0.698729 | + | 0.715386i | \(0.253749\pi\) | |||||||
\(602\) | 8.86044e20 | 1.26032 | ||||||||
\(603\) | 4.66561e20 | 0.655434 | ||||||||
\(604\) | 3.57233e20 | 0.495650 | ||||||||
\(605\) | −1.08048e21 | −1.48065 | ||||||||
\(606\) | −4.95523e19 | −0.0670686 | ||||||||
\(607\) | 7.84690e20 | 1.04902 | 0.524509 | − | 0.851405i | \(-0.324249\pi\) | ||||
0.524509 | + | 0.851405i | \(0.324249\pi\) | |||||||
\(608\) | −9.16747e20 | −1.21052 | ||||||||
\(609\) | −1.46156e19 | −0.0190628 | ||||||||
\(610\) | −5.73954e20 | −0.739441 | ||||||||
\(611\) | −1.05772e20 | −0.134606 | ||||||||
\(612\) | −2.74547e19 | −0.0345129 | ||||||||
\(613\) | 1.18575e21 | 1.47244 | 0.736222 | − | 0.676740i | \(-0.236608\pi\) | ||||
0.736222 | + | 0.676740i | \(0.236608\pi\) | |||||||
\(614\) | 5.13667e20 | 0.630114 | ||||||||
\(615\) | 2.76190e19 | 0.0334692 | ||||||||
\(616\) | 1.33594e21 | 1.59930 | ||||||||
\(617\) | −7.47579e20 | −0.884134 | −0.442067 | − | 0.896982i | \(-0.645755\pi\) | ||||
−0.442067 | + | 0.896982i | \(0.645755\pi\) | |||||||
\(618\) | −7.79961e19 | −0.0911296 | ||||||||
\(619\) | 6.53384e20 | 0.754204 | 0.377102 | − | 0.926172i | \(-0.376921\pi\) | ||||
0.377102 | + | 0.926172i | \(0.376921\pi\) | |||||||
\(620\) | −3.73978e20 | −0.426489 | ||||||||
\(621\) | −2.48586e19 | −0.0280085 | ||||||||
\(622\) | 3.79295e20 | 0.422230 | ||||||||
\(623\) | 5.02074e19 | 0.0552214 | ||||||||
\(624\) | 1.69531e19 | 0.0184232 | ||||||||
\(625\) | −1.09101e21 | −1.17146 | ||||||||
\(626\) | 3.52765e20 | 0.374263 | ||||||||
\(627\) | 1.68486e20 | 0.176627 | ||||||||
\(628\) | 4.28536e20 | 0.443905 | ||||||||
\(629\) | −2.17875e19 | −0.0223012 | ||||||||
\(630\) | −1.06773e21 | −1.07996 | ||||||||
\(631\) | 1.54960e21 | 1.54882 | 0.774408 | − | 0.632686i | \(-0.218048\pi\) | ||||
0.774408 | + | 0.632686i | \(0.218048\pi\) | |||||||
\(632\) | −1.47000e21 | −1.45191 | ||||||||
\(633\) | 1.18774e19 | 0.0115930 | ||||||||
\(634\) | −8.23570e20 | −0.794385 | ||||||||
\(635\) | −2.42037e21 | −2.30716 | ||||||||
\(636\) | 8.97304e18 | 0.00845301 | ||||||||
\(637\) | −1.33912e19 | −0.0124673 | ||||||||
\(638\) | 3.55066e20 | 0.326704 | ||||||||
\(639\) | −5.89287e20 | −0.535883 | ||||||||
\(640\) | 2.68438e20 | 0.241265 | ||||||||
\(641\) | −1.46173e21 | −1.29847 | −0.649235 | − | 0.760588i | \(-0.724911\pi\) | ||||
−0.649235 | + | 0.760588i | \(0.724911\pi\) | |||||||
\(642\) | 6.67951e19 | 0.0586451 | ||||||||
\(643\) | 2.22399e20 | 0.192997 | 0.0964986 | − | 0.995333i | \(-0.469236\pi\) | ||||
0.0964986 | + | 0.995333i | \(0.469236\pi\) | |||||||
\(644\) | −8.71181e19 | −0.0747248 | ||||||||
\(645\) | 1.64206e20 | 0.139217 | ||||||||
\(646\) | 1.69569e20 | 0.142103 | ||||||||
\(647\) | 3.95771e20 | 0.327840 | 0.163920 | − | 0.986474i | \(-0.447586\pi\) | ||||
0.163920 | + | 0.986474i | \(0.447586\pi\) | |||||||
\(648\) | 1.31102e21 | 1.07349 | ||||||||
\(649\) | 3.25248e19 | 0.0263257 | ||||||||
\(650\) | 4.12185e20 | 0.329793 | ||||||||
\(651\) | −7.77105e19 | −0.0614642 | ||||||||
\(652\) | 6.07633e19 | 0.0475100 | ||||||||
\(653\) | −1.35609e21 | −1.04819 | −0.524096 | − | 0.851659i | \(-0.675597\pi\) | ||||
−0.524096 | + | 0.851659i | \(0.675597\pi\) | |||||||
\(654\) | 8.82072e19 | 0.0674017 | ||||||||
\(655\) | 2.86309e21 | 2.16284 | ||||||||
\(656\) | 2.59641e20 | 0.193907 | ||||||||
\(657\) | −1.61151e21 | −1.18985 | ||||||||
\(658\) | −2.85061e20 | −0.208086 | ||||||||
\(659\) | 1.52648e21 | 1.10167 | 0.550834 | − | 0.834615i | \(-0.314310\pi\) | ||||
0.550834 | + | 0.834615i | \(0.314310\pi\) | |||||||
\(660\) | 6.47562e19 | 0.0462063 | ||||||||
\(661\) | −2.55018e21 | −1.79912 | −0.899558 | − | 0.436802i | \(-0.856111\pi\) | ||||
−0.899558 | + | 0.436802i | \(0.856111\pi\) | |||||||
\(662\) | 1.05236e19 | 0.00734058 | ||||||||
\(663\) | 5.02494e18 | 0.00346561 | ||||||||
\(664\) | 5.48491e20 | 0.374032 | ||||||||
\(665\) | −3.61683e21 | −2.43874 | ||||||||
\(666\) | 2.73370e20 | 0.182261 | ||||||||
\(667\) | −8.85260e19 | −0.0583616 | ||||||||
\(668\) | 9.90345e18 | 0.00645599 | ||||||||
\(669\) | −1.76063e20 | −0.113494 | ||||||||
\(670\) | −1.10752e21 | −0.705980 | ||||||||
\(671\) | −1.58907e21 | −1.00167 | ||||||||
\(672\) | −7.32149e19 | −0.0456383 | ||||||||
\(673\) | −1.57816e20 | −0.0972832 | −0.0486416 | − | 0.998816i | \(-0.515489\pi\) | ||||
−0.0486416 | + | 0.998816i | \(0.515489\pi\) | |||||||
\(674\) | −1.37081e21 | −0.835657 | ||||||||
\(675\) | −1.73846e20 | −0.104806 | ||||||||
\(676\) | 4.29730e20 | 0.256209 | ||||||||
\(677\) | 6.80625e20 | 0.401322 | 0.200661 | − | 0.979661i | \(-0.435691\pi\) | ||||
0.200661 | + | 0.979661i | \(0.435691\pi\) | |||||||
\(678\) | 1.22278e20 | 0.0713062 | ||||||||
\(679\) | −2.95541e21 | −1.70449 | ||||||||
\(680\) | 2.49173e20 | 0.142130 | ||||||||
\(681\) | −9.85140e19 | −0.0555769 | ||||||||
\(682\) | 1.88787e21 | 1.05339 | ||||||||
\(683\) | −1.57669e20 | −0.0870145 | −0.0435073 | − | 0.999053i | \(-0.513853\pi\) | ||||
−0.0435073 | + | 0.999053i | \(0.513853\pi\) | |||||||
\(684\) | 1.16688e21 | 0.636953 | ||||||||
\(685\) | −2.34288e21 | −1.26494 | ||||||||
\(686\) | 1.48645e21 | 0.793816 | ||||||||
\(687\) | −1.64182e20 | −0.0867262 | ||||||||
\(688\) | 1.54367e21 | 0.806568 | ||||||||
\(689\) | 3.60798e20 | 0.186475 | ||||||||
\(690\) | 2.94377e19 | 0.0150500 | ||||||||
\(691\) | 5.50128e20 | 0.278214 | 0.139107 | − | 0.990277i | \(-0.455577\pi\) | ||||
0.139107 | + | 0.990277i | \(0.455577\pi\) | |||||||
\(692\) | −5.74580e20 | −0.287445 | ||||||||
\(693\) | −2.95615e21 | −1.46294 | ||||||||
\(694\) | 1.39533e21 | 0.683097 | ||||||||
\(695\) | 3.00202e21 | 1.45388 | ||||||||
\(696\) | −4.27957e19 | −0.0205037 | ||||||||
\(697\) | 7.69582e19 | 0.0364762 | ||||||||
\(698\) | −9.55351e20 | −0.447969 | ||||||||
\(699\) | −2.03086e20 | −0.0942110 | ||||||||
\(700\) | −6.09251e20 | −0.279615 | ||||||||
\(701\) | 2.68019e21 | 1.21697 | 0.608487 | − | 0.793564i | \(-0.291777\pi\) | ||||
0.608487 | + | 0.793564i | \(0.291777\pi\) | |||||||
\(702\) | −1.26384e20 | −0.0567757 | ||||||||
\(703\) | 9.26015e20 | 0.411579 | ||||||||
\(704\) | 3.49737e21 | 1.53797 | ||||||||
\(705\) | −5.28290e19 | −0.0229855 | ||||||||
\(706\) | 1.27935e21 | 0.550748 | ||||||||
\(707\) | 2.94505e21 | 1.25443 | ||||||||
\(708\) | −1.02534e18 | −0.000432133 0 | ||||||||
\(709\) | −2.48670e21 | −1.03700 | −0.518498 | − | 0.855079i | \(-0.673509\pi\) | ||||
−0.518498 | + | 0.855079i | \(0.673509\pi\) | |||||||
\(710\) | 1.39885e21 | 0.577210 | ||||||||
\(711\) | 3.25280e21 | 1.32811 | ||||||||
\(712\) | 1.47012e20 | 0.0593953 | ||||||||
\(713\) | −4.70689e20 | −0.188175 | ||||||||
\(714\) | 1.35424e19 | 0.00535746 | ||||||||
\(715\) | 2.60379e21 | 1.01932 | ||||||||
\(716\) | 1.42255e21 | 0.551088 | ||||||||
\(717\) | 1.03374e20 | 0.0396295 | ||||||||
\(718\) | −2.43038e21 | −0.922021 | ||||||||
\(719\) | 2.06378e21 | 0.774811 | 0.387406 | − | 0.921909i | \(-0.373371\pi\) | ||||
0.387406 | + | 0.921909i | \(0.373371\pi\) | |||||||
\(720\) | −1.86020e21 | −0.691139 | ||||||||
\(721\) | 4.63555e21 | 1.70446 | ||||||||
\(722\) | −4.99862e21 | −1.81895 | ||||||||
\(723\) | −8.74374e18 | −0.00314891 | ||||||||
\(724\) | 7.06546e20 | 0.251826 | ||||||||
\(725\) | −6.19097e20 | −0.218385 | ||||||||
\(726\) | −1.71947e20 | −0.0600303 | ||||||||
\(727\) | 2.34336e21 | 0.809714 | 0.404857 | − | 0.914380i | \(-0.367321\pi\) | ||||
0.404857 | + | 0.914380i | \(0.367321\pi\) | |||||||
\(728\) | −1.69341e21 | −0.579132 | ||||||||
\(729\) | −2.87430e21 | −0.972915 | ||||||||
\(730\) | 3.82542e21 | 1.28161 | ||||||||
\(731\) | 4.57548e20 | 0.151725 | ||||||||
\(732\) | 5.00950e19 | 0.0164423 | ||||||||
\(733\) | 3.54047e21 | 1.15022 | 0.575111 | − | 0.818076i | \(-0.304959\pi\) | ||||
0.575111 | + | 0.818076i | \(0.304959\pi\) | |||||||
\(734\) | 7.72798e20 | 0.248511 | ||||||||
\(735\) | −6.68833e18 | −0.00212894 | ||||||||
\(736\) | −4.43460e20 | −0.139724 | ||||||||
\(737\) | −3.06633e21 | −0.956341 | ||||||||
\(738\) | −9.65601e20 | −0.298109 | ||||||||
\(739\) | −2.35180e21 | −0.718733 | −0.359366 | − | 0.933197i | \(-0.617007\pi\) | ||||
−0.359366 | + | 0.933197i | \(0.617007\pi\) | |||||||
\(740\) | 3.55905e20 | 0.107670 | ||||||||
\(741\) | −2.13571e20 | −0.0639595 | ||||||||
\(742\) | 9.72365e20 | 0.288270 | ||||||||
\(743\) | −4.10274e21 | −1.20409 | −0.602044 | − | 0.798463i | \(-0.705647\pi\) | ||||
−0.602044 | + | 0.798463i | \(0.705647\pi\) | |||||||
\(744\) | −2.27543e20 | −0.0661100 | ||||||||
\(745\) | 3.05076e21 | 0.877477 | ||||||||
\(746\) | −3.41096e21 | −0.971258 | ||||||||
\(747\) | −1.21369e21 | −0.342141 | ||||||||
\(748\) | 1.80438e20 | 0.0503577 | ||||||||
\(749\) | −3.96984e21 | −1.09688 | ||||||||
\(750\) | −5.79818e19 | −0.0158611 | ||||||||
\(751\) | −1.93322e21 | −0.523579 | −0.261790 | − | 0.965125i | \(-0.584313\pi\) | ||||
−0.261790 | + | 0.965125i | \(0.584313\pi\) | |||||||
\(752\) | −4.96634e20 | −0.133169 | ||||||||
\(753\) | 3.10426e20 | 0.0824131 | ||||||||
\(754\) | −4.50076e20 | −0.118304 | ||||||||
\(755\) | 7.17424e21 | 1.86713 | ||||||||
\(756\) | 1.86808e20 | 0.0481373 | ||||||||
\(757\) | 6.12942e21 | 1.56387 | 0.781935 | − | 0.623360i | \(-0.214233\pi\) | ||||
0.781935 | + | 0.623360i | \(0.214233\pi\) | |||||||
\(758\) | 2.33529e21 | 0.589958 | ||||||||
\(759\) | 8.15022e19 | 0.0203871 | ||||||||
\(760\) | −1.05904e22 | −2.62307 | ||||||||
\(761\) | 8.03720e21 | 1.97115 | 0.985575 | − | 0.169238i | \(-0.0541306\pi\) | ||||
0.985575 | + | 0.169238i | \(0.0541306\pi\) | |||||||
\(762\) | −3.85176e20 | −0.0935400 | ||||||||
\(763\) | −5.24243e21 | −1.26066 | ||||||||
\(764\) | −2.65085e21 | −0.631225 | ||||||||
\(765\) | −5.51368e20 | −0.130011 | ||||||||
\(766\) | 6.40814e21 | 1.49629 | ||||||||
\(767\) | −4.12279e19 | −0.00953293 | ||||||||
\(768\) | −2.68562e20 | −0.0614944 | ||||||||
\(769\) | −3.38739e21 | −0.768100 | −0.384050 | − | 0.923312i | \(-0.625471\pi\) | ||||
−0.384050 | + | 0.923312i | \(0.625471\pi\) | |||||||
\(770\) | 7.01731e21 | 1.57576 | ||||||||
\(771\) | 2.51901e20 | 0.0560173 | ||||||||
\(772\) | 2.39477e21 | 0.527393 | ||||||||
\(773\) | −4.69410e21 | −1.02378 | −0.511889 | − | 0.859051i | \(-0.671054\pi\) | ||||
−0.511889 | + | 0.859051i | \(0.671054\pi\) | |||||||
\(774\) | −5.74089e21 | −1.24000 | ||||||||
\(775\) | −3.29171e21 | −0.704141 | ||||||||
\(776\) | −8.65369e21 | −1.83332 | ||||||||
\(777\) | 7.39551e19 | 0.0155171 | ||||||||
\(778\) | −5.52142e21 | −1.14737 | ||||||||
\(779\) | −3.27089e21 | −0.673186 | ||||||||
\(780\) | −8.20838e19 | −0.0167320 | ||||||||
\(781\) | 3.87291e21 | 0.781906 | ||||||||
\(782\) | 8.20258e19 | 0.0164021 | ||||||||
\(783\) | 1.89827e20 | 0.0375962 | ||||||||
\(784\) | −6.28756e19 | −0.0123342 | ||||||||
\(785\) | 8.60620e21 | 1.67220 | ||||||||
\(786\) | 4.55630e20 | 0.0876887 | ||||||||
\(787\) | −5.09190e21 | −0.970665 | −0.485332 | − | 0.874330i | \(-0.661301\pi\) | ||||
−0.485332 | + | 0.874330i | \(0.661301\pi\) | |||||||
\(788\) | 1.01141e21 | 0.190976 | ||||||||
\(789\) | 1.00680e19 | 0.00188307 | ||||||||
\(790\) | −7.72151e21 | −1.43054 | ||||||||
\(791\) | −7.26740e21 | −1.33369 | ||||||||
\(792\) | −8.65586e21 | −1.57352 | ||||||||
\(793\) | 2.01428e21 | 0.362719 | ||||||||
\(794\) | 2.55637e21 | 0.456005 | ||||||||
\(795\) | 1.80204e20 | 0.0318427 | ||||||||
\(796\) | 2.46189e21 | 0.430944 | ||||||||
\(797\) | −1.04193e21 | −0.180676 | −0.0903380 | − | 0.995911i | \(-0.528795\pi\) | ||||
−0.0903380 | + | 0.995911i | \(0.528795\pi\) | |||||||
\(798\) | −5.75581e20 | −0.0988746 | ||||||||
\(799\) | −1.47204e20 | −0.0250506 | ||||||||
\(800\) | −3.10129e21 | −0.522838 | ||||||||
\(801\) | −3.25306e20 | −0.0543310 | ||||||||
\(802\) | 1.66611e21 | 0.275674 | ||||||||
\(803\) | 1.05912e22 | 1.73611 | ||||||||
\(804\) | 9.66654e19 | 0.0156982 | ||||||||
\(805\) | −1.74957e21 | −0.281490 | ||||||||
\(806\) | −2.39303e21 | −0.381449 | ||||||||
\(807\) | −2.00892e20 | −0.0317257 | ||||||||
\(808\) | 8.62337e21 | 1.34925 | ||||||||
\(809\) | 4.47787e21 | 0.694157 | 0.347079 | − | 0.937836i | \(-0.387174\pi\) | ||||
0.347079 | + | 0.937836i | \(0.387174\pi\) | |||||||
\(810\) | 6.88642e21 | 1.05768 | ||||||||
\(811\) | 7.25868e21 | 1.10459 | 0.552295 | − | 0.833649i | \(-0.313752\pi\) | ||||
0.552295 | + | 0.833649i | \(0.313752\pi\) | |||||||
\(812\) | 6.65257e20 | 0.100304 | ||||||||
\(813\) | 7.11341e20 | 0.106267 | ||||||||
\(814\) | −1.79664e21 | −0.265936 | ||||||||
\(815\) | 1.22030e21 | 0.178971 | ||||||||
\(816\) | 2.35936e19 | 0.00342861 | ||||||||
\(817\) | −1.94468e22 | −2.80015 | ||||||||
\(818\) | 5.39110e21 | 0.769180 | ||||||||
\(819\) | 3.74716e21 | 0.529752 | ||||||||
\(820\) | −1.25714e21 | −0.176108 | ||||||||
\(821\) | −7.54628e21 | −1.04751 | −0.523756 | − | 0.851868i | \(-0.675470\pi\) | ||||
−0.523756 | + | 0.851868i | \(0.675470\pi\) | |||||||
\(822\) | −3.72844e20 | −0.0512849 | ||||||||
\(823\) | 3.66981e21 | 0.500201 | 0.250101 | − | 0.968220i | \(-0.419536\pi\) | ||||
0.250101 | + | 0.968220i | \(0.419536\pi\) | |||||||
\(824\) | 1.35733e22 | 1.83329 | ||||||||
\(825\) | 5.69977e20 | 0.0762874 | ||||||||
\(826\) | −1.11111e20 | −0.0147369 | ||||||||
\(827\) | 8.69685e20 | 0.114306 | 0.0571532 | − | 0.998365i | \(-0.481798\pi\) | ||||
0.0571532 | + | 0.998365i | \(0.481798\pi\) | |||||||
\(828\) | 5.64459e20 | 0.0735199 | ||||||||
\(829\) | 3.01196e20 | 0.0388768 | 0.0194384 | − | 0.999811i | \(-0.493812\pi\) | ||||
0.0194384 | + | 0.999811i | \(0.493812\pi\) | |||||||
\(830\) | 2.88107e21 | 0.368526 | ||||||||
\(831\) | 7.84770e20 | 0.0994797 | ||||||||
\(832\) | −4.43321e21 | −0.556921 | ||||||||
\(833\) | −1.86365e19 | −0.00232021 | ||||||||
\(834\) | 4.77740e20 | 0.0589449 | ||||||||
\(835\) | 1.98889e20 | 0.0243199 | ||||||||
\(836\) | −7.66899e21 | −0.929376 | ||||||||
\(837\) | 1.00930e21 | 0.121222 | ||||||||
\(838\) | −1.26326e22 | −1.50370 | ||||||||
\(839\) | 1.09299e22 | 1.28945 | 0.644723 | − | 0.764416i | \(-0.276973\pi\) | ||||
0.644723 | + | 0.764416i | \(0.276973\pi\) | |||||||
\(840\) | −8.45789e20 | −0.0988934 | ||||||||
\(841\) | −7.95318e21 | −0.921660 | ||||||||
\(842\) | 5.47043e20 | 0.0628320 | ||||||||
\(843\) | 1.05652e21 | 0.120274 | ||||||||
\(844\) | −5.40624e20 | −0.0609996 | ||||||||
\(845\) | 8.63017e21 | 0.965149 | ||||||||
\(846\) | 1.84698e21 | 0.204731 | ||||||||
\(847\) | 1.02194e22 | 1.12279 | ||||||||
\(848\) | 1.69406e21 | 0.184484 | ||||||||
\(849\) | −3.73907e20 | −0.0403605 | ||||||||
\(850\) | 5.73639e20 | 0.0613757 | ||||||||
\(851\) | 4.47943e20 | 0.0475063 | ||||||||
\(852\) | −1.22093e20 | −0.0128349 | ||||||||
\(853\) | −3.43543e21 | −0.357984 | −0.178992 | − | 0.983851i | \(-0.557284\pi\) | ||||
−0.178992 | + | 0.983851i | \(0.557284\pi\) | |||||||
\(854\) | 5.42856e21 | 0.560725 | ||||||||
\(855\) | 2.34343e22 | 2.39942 | ||||||||
\(856\) | −1.16241e22 | −1.17979 | ||||||||
\(857\) | −1.39531e22 | −1.40383 | −0.701913 | − | 0.712263i | \(-0.747670\pi\) | ||||
−0.701913 | + | 0.712263i | \(0.747670\pi\) | |||||||
\(858\) | 4.14366e20 | 0.0413266 | ||||||||
\(859\) | 4.49229e21 | 0.444139 | 0.222069 | − | 0.975031i | \(-0.428719\pi\) | ||||
0.222069 | + | 0.975031i | \(0.428719\pi\) | |||||||
\(860\) | −7.47418e21 | −0.732529 | ||||||||
\(861\) | −2.61225e20 | −0.0253800 | ||||||||
\(862\) | 1.51870e22 | 1.46274 | ||||||||
\(863\) | −1.06612e22 | −1.01795 | −0.508975 | − | 0.860781i | \(-0.669976\pi\) | ||||
−0.508975 | + | 0.860781i | \(0.669976\pi\) | |||||||
\(864\) | 9.50913e20 | 0.0900094 | ||||||||
\(865\) | −1.15392e22 | −1.08281 | ||||||||
\(866\) | 1.55237e22 | 1.44415 | ||||||||
\(867\) | −7.22887e20 | −0.0666695 | ||||||||
\(868\) | 3.53715e21 | 0.323411 | ||||||||
\(869\) | −2.13781e22 | −1.93785 | ||||||||
\(870\) | −2.24794e20 | −0.0202018 | ||||||||
\(871\) | 3.88683e21 | 0.346305 | ||||||||
\(872\) | −1.53503e22 | −1.35595 | ||||||||
\(873\) | 1.91488e22 | 1.67700 | ||||||||
\(874\) | −3.48627e21 | −0.302709 | ||||||||
\(875\) | 3.44604e21 | 0.296661 | ||||||||
\(876\) | −3.33885e20 | −0.0284981 | ||||||||
\(877\) | −2.71530e21 | −0.229785 | −0.114892 | − | 0.993378i | \(-0.536652\pi\) | ||||
−0.114892 | + | 0.993378i | \(0.536652\pi\) | |||||||
\(878\) | 3.83137e21 | 0.321473 | ||||||||
\(879\) | 3.05473e20 | 0.0254130 | ||||||||
\(880\) | 1.22256e22 | 1.00844 | ||||||||
\(881\) | −1.49011e22 | −1.21871 | −0.609355 | − | 0.792898i | \(-0.708572\pi\) | ||||
−0.609355 | + | 0.792898i | \(0.708572\pi\) | |||||||
\(882\) | 2.33834e20 | 0.0189624 | ||||||||
\(883\) | −5.10279e21 | −0.410301 | −0.205150 | − | 0.978730i | \(-0.565768\pi\) | ||||
−0.205150 | + | 0.978730i | \(0.565768\pi\) | |||||||
\(884\) | −2.28720e20 | −0.0182353 | ||||||||
\(885\) | −2.05917e19 | −0.00162786 | ||||||||
\(886\) | −1.54144e22 | −1.20830 | ||||||||
\(887\) | −1.22436e22 | −0.951658 | −0.475829 | − | 0.879538i | \(-0.657852\pi\) | ||||
−0.475829 | + | 0.879538i | \(0.657852\pi\) | |||||||
\(888\) | 2.16547e20 | 0.0166900 | ||||||||
\(889\) | 2.28922e22 | 1.74955 | ||||||||
\(890\) | 7.72212e20 | 0.0585210 | ||||||||
\(891\) | 1.90660e22 | 1.43277 | ||||||||
\(892\) | 8.01386e21 | 0.597180 | ||||||||
\(893\) | 6.25647e21 | 0.462321 | ||||||||
\(894\) | 4.85497e20 | 0.0355758 | ||||||||
\(895\) | 2.85688e22 | 2.07596 | ||||||||
\(896\) | −2.53893e21 | −0.182954 | ||||||||
\(897\) | −1.03311e20 | −0.00738248 | ||||||||
\(898\) | 5.99377e20 | 0.0424744 | ||||||||
\(899\) | 3.59431e21 | 0.252591 | ||||||||
\(900\) | 3.94748e21 | 0.275107 | ||||||||
\(901\) | 5.02123e20 | 0.0347036 | ||||||||
\(902\) | 6.34612e21 | 0.434970 | ||||||||
\(903\) | −1.55309e21 | −0.105570 | ||||||||
\(904\) | −2.12796e22 | −1.43450 | ||||||||
\(905\) | 1.41894e22 | 0.948637 | ||||||||
\(906\) | 1.14171e21 | 0.0756994 | ||||||||
\(907\) | −8.29904e21 | −0.545724 | −0.272862 | − | 0.962053i | \(-0.587970\pi\) | ||||
−0.272862 | + | 0.962053i | \(0.587970\pi\) | |||||||
\(908\) | 4.48406e21 | 0.292434 | ||||||||
\(909\) | −1.90817e22 | −1.23421 | ||||||||
\(910\) | −8.89502e21 | −0.570606 | ||||||||
\(911\) | −4.57221e21 | −0.290896 | −0.145448 | − | 0.989366i | \(-0.546462\pi\) | ||||
−0.145448 | + | 0.989366i | \(0.546462\pi\) | |||||||
\(912\) | −1.00278e21 | −0.0632767 | ||||||||
\(913\) | 7.97664e21 | 0.499217 | ||||||||
\(914\) | −2.57178e21 | −0.159639 | ||||||||
\(915\) | 1.00605e21 | 0.0619385 | ||||||||
\(916\) | 7.47307e21 | 0.456334 | ||||||||
\(917\) | −2.70796e22 | −1.64010 | ||||||||
\(918\) | −1.75888e20 | −0.0105662 | ||||||||
\(919\) | −1.91276e22 | −1.13971 | −0.569856 | − | 0.821745i | \(-0.693001\pi\) | ||||
−0.569856 | + | 0.821745i | \(0.693001\pi\) | |||||||
\(920\) | −5.12291e21 | −0.302767 | ||||||||
\(921\) | −9.00375e20 | −0.0527809 | ||||||||
\(922\) | −5.76345e21 | −0.335120 | ||||||||
\(923\) | −4.90923e21 | −0.283140 | ||||||||
\(924\) | −6.12475e20 | −0.0350387 | ||||||||
\(925\) | 3.13264e21 | 0.177766 | ||||||||
\(926\) | 2.12597e22 | 1.19667 | ||||||||
\(927\) | −3.00349e22 | −1.67698 | ||||||||
\(928\) | 3.38638e21 | 0.187554 | ||||||||
\(929\) | −2.52638e22 | −1.38797 | −0.693987 | − | 0.719987i | \(-0.744148\pi\) | ||||
−0.693987 | + | 0.719987i | \(0.744148\pi\) | |||||||
\(930\) | −1.19522e21 | −0.0651368 | ||||||||
\(931\) | 7.92091e20 | 0.0428206 | ||||||||
\(932\) | 9.24388e21 | 0.495718 | ||||||||
\(933\) | −6.64842e20 | −0.0353677 | ||||||||
\(934\) | −2.75222e22 | −1.45239 | ||||||||
\(935\) | 3.62370e21 | 0.189699 | ||||||||
\(936\) | 1.09720e22 | 0.569794 | ||||||||
\(937\) | −7.57750e21 | −0.390372 | −0.195186 | − | 0.980766i | \(-0.562531\pi\) | ||||
−0.195186 | + | 0.980766i | \(0.562531\pi\) | |||||||
\(938\) | 1.04752e22 | 0.535352 | ||||||||
\(939\) | −6.18339e20 | −0.0313498 | ||||||||
\(940\) | 2.40462e21 | 0.120945 | ||||||||
\(941\) | 2.62206e21 | 0.130834 | 0.0654169 | − | 0.997858i | \(-0.479162\pi\) | ||||
0.0654169 | + | 0.997858i | \(0.479162\pi\) | |||||||
\(942\) | 1.36959e21 | 0.0677966 | ||||||||
\(943\) | −1.58223e21 | −0.0777021 | ||||||||
\(944\) | −1.93578e20 | −0.00943118 | ||||||||
\(945\) | 3.75162e21 | 0.181335 | ||||||||
\(946\) | 3.77303e22 | 1.80928 | ||||||||
\(947\) | −1.96405e22 | −0.934387 | −0.467193 | − | 0.884155i | \(-0.654735\pi\) | ||||
−0.467193 | + | 0.884155i | \(0.654735\pi\) | |||||||
\(948\) | 6.73938e20 | 0.0318095 | ||||||||
\(949\) | −1.34252e22 | −0.628672 | ||||||||
\(950\) | −2.43809e22 | −1.13272 | ||||||||
\(951\) | 1.44358e21 | 0.0665409 | ||||||||
\(952\) | −2.35673e21 | −0.107778 | ||||||||
\(953\) | 1.28475e22 | 0.582935 | 0.291468 | − | 0.956581i | \(-0.405856\pi\) | ||||
0.291468 | + | 0.956581i | \(0.405856\pi\) | |||||||
\(954\) | −6.30018e21 | −0.283622 | ||||||||
\(955\) | −5.32364e22 | −2.37784 | ||||||||
\(956\) | −4.70529e21 | −0.208522 | ||||||||
\(957\) | −6.22373e20 | −0.0273660 | ||||||||
\(958\) | 2.07469e22 | 0.905130 | ||||||||
\(959\) | 2.21593e22 | 0.959217 | ||||||||
\(960\) | −2.21421e21 | −0.0951007 | ||||||||
\(961\) | −4.35446e21 | −0.185571 | ||||||||
\(962\) | 2.27739e21 | 0.0962995 | ||||||||
\(963\) | 2.57216e22 | 1.07920 | ||||||||
\(964\) | 3.97989e20 | 0.0165689 | ||||||||
\(965\) | 4.80937e22 | 1.98670 | ||||||||
\(966\) | −2.78427e20 | −0.0114125 | ||||||||
\(967\) | −4.78106e22 | −1.94458 | −0.972289 | − | 0.233780i | \(-0.924890\pi\) | ||||
−0.972289 | + | 0.233780i | \(0.924890\pi\) | |||||||
\(968\) | 2.99232e22 | 1.20766 | ||||||||
\(969\) | −2.97227e20 | −0.0119031 | ||||||||
\(970\) | −4.54554e22 | −1.80633 | ||||||||
\(971\) | 2.76633e22 | 1.09084 | 0.545418 | − | 0.838164i | \(-0.316371\pi\) | ||||
0.545418 | + | 0.838164i | \(0.316371\pi\) | |||||||
\(972\) | −1.81693e21 | −0.0710955 | ||||||||
\(973\) | −2.83936e22 | −1.10249 | ||||||||
\(974\) | 5.83042e21 | 0.224651 | ||||||||
\(975\) | −7.22493e20 | −0.0276248 | ||||||||
\(976\) | 9.45765e21 | 0.358847 | ||||||||
\(977\) | 2.80871e22 | 1.05754 | 0.528771 | − | 0.848764i | \(-0.322653\pi\) | ||||
0.528771 | + | 0.848764i | \(0.322653\pi\) | |||||||
\(978\) | 1.94198e20 | 0.00725609 | ||||||||
\(979\) | 2.13797e21 | 0.0792742 | ||||||||
\(980\) | 3.04433e20 | 0.0112020 | ||||||||
\(981\) | 3.39670e22 | 1.24034 | ||||||||
\(982\) | −1.42678e22 | −0.517035 | ||||||||
\(983\) | −2.12935e22 | −0.765767 | −0.382883 | − | 0.923797i | \(-0.625069\pi\) | ||||
−0.382883 | + | 0.923797i | \(0.625069\pi\) | |||||||
\(984\) | −7.64892e20 | −0.0272984 | ||||||||
\(985\) | 2.03119e22 | 0.719412 | ||||||||
\(986\) | −6.26371e20 | −0.0220168 | ||||||||
\(987\) | 4.99665e20 | 0.0174301 | ||||||||
\(988\) | 9.72109e21 | 0.336541 | ||||||||
\(989\) | −9.40701e21 | −0.323206 | ||||||||
\(990\) | −4.54668e22 | −1.55035 | ||||||||
\(991\) | −2.88007e22 | −0.974655 | −0.487327 | − | 0.873219i | \(-0.662028\pi\) | ||||
−0.487327 | + | 0.873219i | \(0.662028\pi\) | |||||||
\(992\) | 1.80052e22 | 0.604730 | ||||||||
\(993\) | −1.84462e19 | −0.000614876 0 | ||||||||
\(994\) | −1.32306e22 | −0.437704 | ||||||||
\(995\) | 4.94417e22 | 1.62338 | ||||||||
\(996\) | −2.51462e20 | −0.00819458 | ||||||||
\(997\) | 2.14781e22 | 0.694676 | 0.347338 | − | 0.937740i | \(-0.387086\pi\) | ||||
0.347338 | + | 0.937740i | \(0.387086\pi\) | |||||||
\(998\) | −2.23628e22 | −0.717871 | ||||||||
\(999\) | −9.60526e20 | −0.0306033 |
(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 | 23.16.a.a.1.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
23.16.a.a.1.5 | ✓ | 12 | 1.1 | even | 1 | trivial |