Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,35,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 35, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 35);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 35 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(21.9676962128\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 789518143 x^{8} + \cdots + 50\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{54}\cdot 3^{65}\cdot 5^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.6 | ||
Root | \(3839.21i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.35.b.a.2.5 |
$q$-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 \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 46070.5i | 0.351490i | 0.984436 | + | 0.175745i | \(0.0562335\pi\) | ||||
−0.984436 | + | 0.175745i | \(0.943767\pi\) | |||||||
\(3\) | 1.11570e8 | + | 6.50325e7i | 0.863948 | + | 0.503580i | ||||
\(4\) | 1.50574e10 | 0.876455 | ||||||||
\(5\) | 1.37507e12i | 1.80234i | 0.433468 | + | 0.901169i | \(0.357290\pi\) | ||||
−0.433468 | + | 0.901169i | \(0.642710\pi\) | |||||||
\(6\) | −2.99608e12 | + | 5.14011e12i | −0.177004 | + | 0.303669i | ||||
\(7\) | −2.89657e14 | −1.24514 | −0.622569 | − | 0.782565i | \(-0.713911\pi\) | ||||
−0.622569 | + | 0.782565i | \(0.713911\pi\) | |||||||
\(8\) | 1.48519e15i | 0.659556i | ||||||||
\(9\) | 8.21874e15 | + | 1.45114e16i | 0.492813 | + | 0.870135i | ||||
\(10\) | −6.33504e16 | −0.633504 | ||||||||
\(11\) | − | 2.11971e17i | − | 0.419373i | −0.977769 | − | 0.209687i | \(-0.932756\pi\) | ||
0.977769 | − | 0.209687i | \(-0.0672444\pi\) | |||||||
\(12\) | 1.67996e18 | + | 9.79218e17i | 0.757211 | + | 0.441365i | ||||
\(13\) | 1.85219e18 | 0.214115 | 0.107058 | − | 0.994253i | \(-0.465857\pi\) | ||||
0.107058 | + | 0.994253i | \(0.465857\pi\) | |||||||
\(14\) | − | 1.33446e19i | − | 0.437654i | ||||||
\(15\) | −8.94245e19 | + | 1.53418e20i | −0.907622 | + | 1.55713i | ||||
\(16\) | 1.90260e20 | 0.644627 | ||||||||
\(17\) | − | 1.25054e21i | − | 1.51170i | −0.654747 | − | 0.755848i | \(-0.727225\pi\) | ||
0.654747 | − | 0.755848i | \(-0.272775\pi\) | |||||||
\(18\) | −6.68548e20 | + | 3.78642e20i | −0.305844 | + | 0.173219i | ||||
\(19\) | −1.89372e21 | −0.345545 | −0.172772 | − | 0.984962i | \(-0.555273\pi\) | ||||
−0.172772 | + | 0.984962i | \(0.555273\pi\) | |||||||
\(20\) | 2.07050e22i | 1.57967i | ||||||||
\(21\) | −3.23171e22 | − | 1.88371e22i | −1.07573 | − | 0.627027i | ||||
\(22\) | 9.76562e21 | 0.147406 | ||||||||
\(23\) | 9.09177e22i | 0.644578i | 0.946641 | + | 0.322289i | \(0.104452\pi\) | ||||
−0.946641 | + | 0.322289i | \(0.895548\pi\) | |||||||
\(24\) | −9.65854e22 | + | 1.65703e23i | −0.332139 | + | 0.569822i | ||||
\(25\) | −1.30875e24 | −2.24842 | ||||||||
\(26\) | 8.53312e22i | 0.0752594i | ||||||||
\(27\) | −2.67439e22 | + | 2.15353e24i | −0.0124177 | + | 0.999923i | ||||
\(28\) | −4.36147e24 | −1.09131 | ||||||||
\(29\) | 1.52476e24i | 0.210105i | 0.994467 | + | 0.105052i | \(0.0335010\pi\) | ||||
−0.994467 | + | 0.105052i | \(0.966499\pi\) | |||||||
\(30\) | −7.06803e24 | − | 4.11983e24i | −0.547315 | − | 0.319020i | ||||
\(31\) | 1.41016e25 | 0.625346 | 0.312673 | − | 0.949861i | \(-0.398776\pi\) | ||||
0.312673 | + | 0.949861i | \(0.398776\pi\) | |||||||
\(32\) | 3.42807e25i | 0.886136i | ||||||||
\(33\) | 1.37850e25 | − | 2.36497e25i | 0.211188 | − | 0.362317i | ||||
\(34\) | 5.76129e25 | 0.531347 | ||||||||
\(35\) | − | 3.98300e26i | − | 2.24416i | ||||||
\(36\) | 1.23753e26 | + | 2.18504e26i | 0.431929 | + | 0.762634i | ||||
\(37\) | 5.80826e26 | 1.27238 | 0.636190 | − | 0.771533i | \(-0.280510\pi\) | ||||
0.636190 | + | 0.771533i | \(0.280510\pi\) | |||||||
\(38\) | − | 8.72447e25i | − | 0.121456i | ||||||
\(39\) | 2.06649e26 | + | 1.20452e26i | 0.184984 | + | 0.107824i | ||||
\(40\) | −2.04224e27 | −1.18874 | ||||||||
\(41\) | 2.01941e27i | 0.772500i | 0.922394 | + | 0.386250i | \(0.126230\pi\) | ||||
−0.922394 | + | 0.386250i | \(0.873770\pi\) | |||||||
\(42\) | 8.67835e26 | − | 1.48887e27i | 0.220394 | − | 0.378110i | ||||
\(43\) | −1.60735e27 | −0.273619 | −0.136810 | − | 0.990597i | \(-0.543685\pi\) | ||||
−0.136810 | + | 0.990597i | \(0.543685\pi\) | |||||||
\(44\) | − | 3.19173e27i | − | 0.367562i | ||||||
\(45\) | −1.99543e28 | + | 1.13014e28i | −1.56828 | + | 0.888216i | ||||
\(46\) | −4.18863e27 | −0.226563 | ||||||||
\(47\) | 1.09494e28i | 0.410891i | 0.978669 | + | 0.205446i | \(0.0658644\pi\) | ||||
−0.978669 | + | 0.205446i | \(0.934136\pi\) | |||||||
\(48\) | 2.12274e28 | + | 1.23731e28i | 0.556925 | + | 0.324622i | ||||
\(49\) | 2.97842e28 | 0.550367 | ||||||||
\(50\) | − | 6.02950e28i | − | 0.790298i | ||||||
\(51\) | 8.13254e28 | − | 1.39523e29i | 0.761261 | − | 1.30603i | ||||
\(52\) | 2.78890e28 | 0.187662 | ||||||||
\(53\) | 2.12189e29i | 1.03284i | 0.856336 | + | 0.516419i | \(0.172735\pi\) | ||||
−0.856336 | + | 0.516419i | \(0.827265\pi\) | |||||||
\(54\) | −9.92142e28 | − | 1.23211e27i | −0.351463 | − | 0.00436470i | ||||
\(55\) | 2.91476e29 | 0.755852 | ||||||||
\(56\) | − | 4.30195e29i | − | 0.821237i | ||||||
\(57\) | −2.11283e29 | − | 1.23153e29i | −0.298533 | − | 0.174010i | ||||
\(58\) | −7.02465e28 | −0.0738498 | ||||||||
\(59\) | 6.32771e29i | 0.497465i | 0.968572 | + | 0.248732i | \(0.0800140\pi\) | ||||
−0.968572 | + | 0.248732i | \(0.919986\pi\) | |||||||
\(60\) | −1.34650e30 | + | 2.31007e30i | −0.795490 | + | 1.36475i | ||||
\(61\) | −1.22298e30 | −0.545520 | −0.272760 | − | 0.962082i | \(-0.587937\pi\) | ||||
−0.272760 | + | 0.962082i | \(0.587937\pi\) | |||||||
\(62\) | 6.49669e29i | 0.219803i | ||||||||
\(63\) | −2.38061e30 | − | 4.20333e30i | −0.613620 | − | 1.08344i | ||||
\(64\) | 1.68932e30 | 0.333159 | ||||||||
\(65\) | 2.54689e30i | 0.385908i | ||||||||
\(66\) | 1.08955e30 | + | 6.35082e29i | 0.127351 | + | 0.0742306i | ||||
\(67\) | 1.32113e31 | 1.19584 | 0.597922 | − | 0.801555i | \(-0.295993\pi\) | ||||
0.597922 | + | 0.801555i | \(0.295993\pi\) | |||||||
\(68\) | − | 1.88298e31i | − | 1.32493i | ||||||
\(69\) | −5.91261e30 | + | 1.01437e31i | −0.324597 | + | 0.556882i | ||||
\(70\) | 1.83499e31 | 0.788800 | ||||||||
\(71\) | − | 6.14008e30i | − | 0.207387i | −0.994609 | − | 0.103694i | \(-0.966934\pi\) | ||
0.994609 | − | 0.103694i | \(-0.0330662\pi\) | |||||||
\(72\) | −2.15521e31 | + | 1.22064e31i | −0.573902 | + | 0.325038i | ||||
\(73\) | 7.66818e31 | 1.61512 | 0.807558 | − | 0.589789i | \(-0.200789\pi\) | ||||
0.807558 | + | 0.589789i | \(0.200789\pi\) | |||||||
\(74\) | 2.67590e31i | 0.447229i | ||||||||
\(75\) | −1.46018e32 | − | 8.51115e31i | −1.94252 | − | 1.13226i | ||||
\(76\) | −2.85144e31 | −0.302854 | ||||||||
\(77\) | 6.13989e31i | 0.522177i | ||||||||
\(78\) | −5.54930e30 | + | 9.52043e30i | −0.0378992 | + | 0.0650202i | ||||
\(79\) | 2.85419e31 | 0.156972 | 0.0784860 | − | 0.996915i | \(-0.474991\pi\) | ||||
0.0784860 | + | 0.996915i | \(0.474991\pi\) | |||||||
\(80\) | 2.61622e32i | 1.16184i | ||||||||
\(81\) | −1.43033e32 | + | 2.38531e32i | −0.514270 | + | 0.857628i | ||||
\(82\) | −9.30352e31 | −0.271526 | ||||||||
\(83\) | − | 6.49866e32i | − | 1.54346i | −0.635948 | − | 0.771732i | \(-0.719391\pi\) | ||
0.635948 | − | 0.771732i | \(-0.280609\pi\) | |||||||
\(84\) | −4.86611e32 | − | 2.83637e32i | −0.942832 | − | 0.549561i | ||||
\(85\) | 1.71958e33 | 2.72459 | ||||||||
\(86\) | − | 7.40515e31i | − | 0.0961746i | ||||||
\(87\) | −9.91589e31 | + | 1.70118e32i | −0.105805 | + | 0.181520i | ||||
\(88\) | 3.14817e32 | 0.276600 | ||||||||
\(89\) | − | 2.50617e31i | − | 0.0181711i | −0.999959 | − | 0.00908555i | \(-0.997108\pi\) | ||
0.999959 | − | 0.00908555i | \(-0.00289206\pi\) | |||||||
\(90\) | −5.20661e32 | − | 9.19303e32i | −0.312199 | − | 0.551234i | ||||
\(91\) | −5.36498e32 | −0.266603 | ||||||||
\(92\) | 1.36898e33i | 0.564943i | ||||||||
\(93\) | 1.57332e33 | + | 9.17063e32i | 0.540266 | + | 0.314912i | ||||
\(94\) | −5.04445e32 | −0.144424 | ||||||||
\(95\) | − | 2.60401e33i | − | 0.622789i | ||||||
\(96\) | −2.22936e33 | + | 3.82471e33i | −0.446241 | + | 0.765576i | ||||
\(97\) | −4.22129e33 | −0.708477 | −0.354238 | − | 0.935155i | \(-0.615260\pi\) | ||||
−0.354238 | + | 0.935155i | \(0.615260\pi\) | |||||||
\(98\) | 1.37217e33i | 0.193449i | ||||||||
\(99\) | 3.07600e33 | − | 1.74213e33i | 0.364911 | − | 0.206673i | ||||
\(100\) | −1.97064e34 | −1.97064 | ||||||||
\(101\) | 5.19823e33i | 0.438926i | 0.975621 | + | 0.219463i | \(0.0704306\pi\) | ||||
−0.975621 | + | 0.219463i | \(0.929569\pi\) | |||||||
\(102\) | 6.42789e33 | + | 3.74671e33i | 0.459056 | + | 0.267576i | ||||
\(103\) | 2.48020e34 | 1.50056 | 0.750282 | − | 0.661118i | \(-0.229918\pi\) | ||||
0.750282 | + | 0.661118i | \(0.229918\pi\) | |||||||
\(104\) | 2.75084e33i | 0.141221i | ||||||||
\(105\) | 2.59024e34 | − | 4.44385e34i | 1.13011 | − | 1.93884i | ||||
\(106\) | −9.77565e33 | −0.363033 | ||||||||
\(107\) | − | 1.10751e34i | − | 0.350610i | −0.984514 | − | 0.175305i | \(-0.943909\pi\) | ||
0.984514 | − | 0.175305i | \(-0.0560911\pi\) | |||||||
\(108\) | −4.02693e32 | + | 3.24265e34i | −0.0108835 | + | 0.876387i | ||||
\(109\) | −1.06092e34 | −0.245150 | −0.122575 | − | 0.992459i | \(-0.539115\pi\) | ||||
−0.122575 | + | 0.992459i | \(0.539115\pi\) | |||||||
\(110\) | 1.34285e34i | 0.265675i | ||||||||
\(111\) | 6.48030e34 | + | 3.77725e34i | 1.09927 | + | 0.640745i | ||||
\(112\) | −5.51102e34 | −0.802649 | ||||||||
\(113\) | − | 9.42920e34i | − | 1.18070i | −0.807146 | − | 0.590352i | \(-0.798989\pi\) | ||
0.807146 | − | 0.590352i | \(-0.201011\pi\) | |||||||
\(114\) | 5.67374e33 | − | 9.73392e33i | 0.0611627 | − | 0.104931i | ||||
\(115\) | −1.25019e35 | −1.16175 | ||||||||
\(116\) | 2.29589e34i | 0.184147i | ||||||||
\(117\) | 1.52226e34 | + | 2.68778e34i | 0.105519 | + | 0.186309i | ||||
\(118\) | −2.91521e34 | −0.174854 | ||||||||
\(119\) | 3.62226e35i | 1.88227i | ||||||||
\(120\) | −2.27854e35 | − | 1.32812e35i | −1.02701 | − | 0.598627i | ||||
\(121\) | 2.10545e35 | 0.824126 | ||||||||
\(122\) | − | 5.63432e34i | − | 0.191745i | ||||||
\(123\) | −1.31327e35 | + | 2.25306e35i | −0.389016 | + | 0.667400i | ||||
\(124\) | 2.12333e35 | 0.548087 | ||||||||
\(125\) | − | 9.99235e35i | − | 2.25008i | ||||||
\(126\) | 1.93650e35 | − | 1.09676e35i | 0.380818 | − | 0.215682i | ||||
\(127\) | 6.46878e35 | 1.11214 | 0.556069 | − | 0.831136i | \(-0.312309\pi\) | ||||
0.556069 | + | 0.831136i | \(0.312309\pi\) | |||||||
\(128\) | 6.66766e35i | 1.00324i | ||||||||
\(129\) | −1.79333e35 | − | 1.04530e35i | −0.236393 | − | 0.137789i | ||||
\(130\) | −1.17337e35 | −0.135643 | ||||||||
\(131\) | − | 3.35779e35i | − | 0.340754i | −0.985379 | − | 0.170377i | \(-0.945501\pi\) | ||
0.985379 | − | 0.170377i | \(-0.0544986\pi\) | |||||||
\(132\) | 2.07566e35 | − | 3.56102e35i | 0.185097 | − | 0.317554i | ||||
\(133\) | 5.48529e35 | 0.430251 | ||||||||
\(134\) | 6.08652e35i | 0.420327i | ||||||||
\(135\) | −2.96126e36 | − | 3.67749e34i | −1.80220 | − | 0.0223809i | ||||
\(136\) | 1.85728e36 | 0.997048 | ||||||||
\(137\) | 4.09884e36i | 1.94273i | 0.237600 | + | 0.971363i | \(0.423639\pi\) | ||||
−0.237600 | + | 0.971363i | \(0.576361\pi\) | |||||||
\(138\) | −4.67327e35 | − | 2.72397e35i | −0.195739 | − | 0.114093i | ||||
\(139\) | −2.84153e36 | −1.05269 | −0.526345 | − | 0.850271i | \(-0.676438\pi\) | ||||
−0.526345 | + | 0.850271i | \(0.676438\pi\) | |||||||
\(140\) | − | 5.99735e36i | − | 1.96690i | ||||||
\(141\) | −7.12067e35 | + | 1.22163e36i | −0.206917 | + | 0.354989i | ||||
\(142\) | 2.82877e35 | 0.0728946 | ||||||||
\(143\) | − | 3.92610e35i | − | 0.0897942i | ||||||
\(144\) | 1.56370e36 | + | 2.76094e36i | 0.317681 | + | 0.560913i | ||||
\(145\) | −2.09666e36 | −0.378680 | ||||||||
\(146\) | 3.53277e36i | 0.567697i | ||||||||
\(147\) | 3.32303e36 | + | 1.93694e36i | 0.475488 | + | 0.277154i | ||||
\(148\) | 8.74571e36 | 1.11518 | ||||||||
\(149\) | − | 7.58984e36i | − | 0.863110i | −0.902087 | − | 0.431555i | \(-0.857965\pi\) | ||
0.902087 | − | 0.431555i | \(-0.142035\pi\) | |||||||
\(150\) | 3.92113e36 | − | 6.72714e36i | 0.397979 | − | 0.682777i | ||||
\(151\) | −9.23227e36 | −0.836952 | −0.418476 | − | 0.908228i | \(-0.637436\pi\) | ||||
−0.418476 | + | 0.908228i | \(0.637436\pi\) | |||||||
\(152\) | − | 2.81253e36i | − | 0.227906i | ||||||
\(153\) | 1.81470e37 | − | 1.02778e37i | 1.31538 | − | 0.744984i | ||||
\(154\) | −2.82868e36 | −0.183540 | ||||||||
\(155\) | 1.93908e37i | 1.12708i | ||||||||
\(156\) | 3.11159e36 | + | 1.81369e36i | 0.162130 | + | 0.0945030i | ||||
\(157\) | −1.09003e37 | −0.509498 | −0.254749 | − | 0.967007i | \(-0.581993\pi\) | ||||
−0.254749 | + | 0.967007i | \(0.581993\pi\) | |||||||
\(158\) | 1.31494e36i | 0.0551742i | ||||||||
\(159\) | −1.37992e37 | + | 2.36740e37i | −0.520117 | + | 0.892319i | ||||
\(160\) | −4.71385e37 | −1.59712 | ||||||||
\(161\) | − | 2.63350e37i | − | 0.802588i | ||||||
\(162\) | −1.09892e37 | − | 6.58961e36i | −0.301448 | − | 0.180761i | ||||
\(163\) | 1.44159e37 | 0.356167 | 0.178083 | − | 0.984015i | \(-0.443010\pi\) | ||||
0.178083 | + | 0.984015i | \(0.443010\pi\) | |||||||
\(164\) | 3.04070e37i | 0.677061i | ||||||||
\(165\) | 3.25201e37 | + | 1.89554e37i | 0.653017 | + | 0.380633i | ||||
\(166\) | 2.99397e37 | 0.542512 | ||||||||
\(167\) | − | 5.15715e36i | − | 0.0843781i | −0.999110 | − | 0.0421890i | \(-0.986567\pi\) | ||
0.999110 | − | 0.0421890i | \(-0.0134332\pi\) | |||||||
\(168\) | 2.79766e37 | − | 4.79970e37i | 0.413559 | − | 0.709507i | ||||
\(169\) | −7.13991e37 | −0.954155 | ||||||||
\(170\) | 7.92220e37i | 0.957666i | ||||||||
\(171\) | −1.55640e37 | − | 2.74805e37i | −0.170289 | − | 0.300671i | ||||
\(172\) | −2.42025e37 | −0.239815 | ||||||||
\(173\) | − | 1.31796e38i | − | 1.18336i | −0.806171 | − | 0.591682i | \(-0.798464\pi\) | ||
0.806171 | − | 0.591682i | \(-0.201536\pi\) | |||||||
\(174\) | −7.83744e36 | − | 4.56831e36i | −0.0638024 | − | 0.0371893i | ||||
\(175\) | 3.79090e38 | 2.79959 | ||||||||
\(176\) | − | 4.03297e37i | − | 0.270339i | ||||||
\(177\) | −4.11507e37 | + | 7.05986e37i | −0.250514 | + | 0.429784i | ||||
\(178\) | 1.15461e36 | 0.00638697 | ||||||||
\(179\) | − | 1.83650e38i | − | 0.923614i | −0.886980 | − | 0.461807i | \(-0.847201\pi\) | ||
0.886980 | − | 0.461807i | \(-0.152799\pi\) | |||||||
\(180\) | −3.00459e38 | + | 1.70169e38i | −1.37452 | + | 0.778481i | ||||
\(181\) | 9.72091e37 | 0.404735 | 0.202368 | − | 0.979310i | \(-0.435136\pi\) | ||||
0.202368 | + | 0.979310i | \(0.435136\pi\) | |||||||
\(182\) | − | 2.47168e37i | − | 0.0937083i | ||||||
\(183\) | −1.36448e38 | − | 7.95331e37i | −0.471301 | − | 0.274713i | ||||
\(184\) | −1.35030e38 | −0.425135 | ||||||||
\(185\) | 7.98679e38i | 2.29326i | ||||||||
\(186\) | −4.22496e37 | + | 7.24839e37i | −0.110688 | + | 0.189898i | ||||
\(187\) | −2.65077e38 | −0.633965 | ||||||||
\(188\) | 1.64869e38i | 0.360128i | ||||||||
\(189\) | 7.74656e36 | − | 6.23784e38i | 0.0154617 | − | 1.24504i | ||||
\(190\) | 1.19968e38 | 0.218904 | ||||||||
\(191\) | − | 7.95406e38i | − | 1.32746i | −0.747972 | − | 0.663730i | \(-0.768972\pi\) | ||
0.747972 | − | 0.663730i | \(-0.231028\pi\) | |||||||
\(192\) | 1.88478e38 | + | 1.09860e38i | 0.287832 | + | 0.167772i | ||||
\(193\) | −3.61070e37 | −0.0504798 | −0.0252399 | − | 0.999681i | \(-0.508035\pi\) | ||||
−0.0252399 | + | 0.999681i | \(0.508035\pi\) | |||||||
\(194\) | − | 1.94477e38i | − | 0.249023i | ||||||
\(195\) | −1.65631e38 | + | 2.84158e38i | −0.194336 | + | 0.333404i | ||||
\(196\) | 4.48471e38 | 0.482371 | ||||||||
\(197\) | 1.21476e39i | 1.19830i | 0.800639 | + | 0.599148i | \(0.204494\pi\) | ||||
−0.800639 | + | 0.599148i | \(0.795506\pi\) | |||||||
\(198\) | 8.02611e37 | + | 1.41713e38i | 0.0726435 | + | 0.128263i | ||||
\(199\) | 8.05000e38 | 0.668796 | 0.334398 | − | 0.942432i | \(-0.391467\pi\) | ||||
0.334398 | + | 0.942432i | \(0.391467\pi\) | |||||||
\(200\) | − | 1.94374e39i | − | 1.48296i | ||||||
\(201\) | 1.47399e39 | + | 8.59164e38i | 1.03315 | + | 0.602203i | ||||
\(202\) | −2.39485e38 | −0.154278 | ||||||||
\(203\) | − | 4.41657e38i | − | 0.261609i | ||||||
\(204\) | 1.22455e39 | − | 2.10085e39i | 0.667210 | − | 1.14467i | ||||
\(205\) | −2.77684e39 | −1.39231 | ||||||||
\(206\) | 1.14264e39i | 0.527433i | ||||||||
\(207\) | −1.31934e39 | + | 7.47229e38i | −0.560870 | + | 0.317657i | ||||
\(208\) | 3.52397e38 | 0.138024 | ||||||||
\(209\) | 4.01414e38i | 0.144912i | ||||||||
\(210\) | 2.04731e39 | + | 1.19334e39i | 0.681482 | + | 0.397224i | ||||
\(211\) | −5.53346e39 | −1.69901 | −0.849503 | − | 0.527583i | \(-0.823098\pi\) | ||||
−0.849503 | + | 0.527583i | \(0.823098\pi\) | |||||||
\(212\) | 3.19500e39i | 0.905236i | ||||||||
\(213\) | 3.99305e38 | − | 6.85052e38i | 0.104436 | − | 0.179172i | ||||
\(214\) | 5.10237e38 | 0.123236 | ||||||||
\(215\) | − | 2.21023e39i | − | 0.493155i | ||||||
\(216\) | −3.19839e39 | − | 3.97197e37i | −0.659505 | − | 0.00819016i | ||||
\(217\) | −4.08463e39 | −0.778641 | ||||||||
\(218\) | − | 4.88772e38i | − | 0.0861680i | ||||||
\(219\) | 8.55542e39 | + | 4.98680e39i | 1.39538 | + | 0.813340i | ||||
\(220\) | 4.38886e39 | 0.662470 | ||||||||
\(221\) | − | 2.31622e39i | − | 0.323677i | ||||||
\(222\) | −1.74020e39 | + | 2.98551e39i | −0.225216 | + | 0.386383i | ||||
\(223\) | 9.88371e39 | 1.18505 | 0.592526 | − | 0.805552i | \(-0.298131\pi\) | ||||
0.592526 | + | 0.805552i | \(0.298131\pi\) | |||||||
\(224\) | − | 9.92965e39i | − | 1.10336i | ||||||
\(225\) | −1.07563e40 | − | 1.89918e40i | −1.10805 | − | 1.95643i | ||||
\(226\) | 4.34408e39 | 0.415006 | ||||||||
\(227\) | 1.96927e40i | 1.74528i | 0.488364 | + | 0.872640i | \(0.337594\pi\) | ||||
−0.488364 | + | 0.872640i | \(0.662406\pi\) | |||||||
\(228\) | −3.18137e39 | − | 1.85436e39i | −0.261650 | − | 0.152512i | ||||
\(229\) | 1.66216e40 | 1.26902 | 0.634511 | − | 0.772913i | \(-0.281201\pi\) | ||||
0.634511 | + | 0.772913i | \(0.281201\pi\) | |||||||
\(230\) | − | 5.75968e39i | − | 0.408343i | ||||||
\(231\) | −3.99292e39 | + | 6.85030e39i | −0.262958 | + | 0.451134i | ||||
\(232\) | −2.26455e39 | −0.138576 | ||||||||
\(233\) | 4.22978e39i | 0.240584i | 0.992739 | + | 0.120292i | \(0.0383831\pi\) | ||||
−0.992739 | + | 0.120292i | \(0.961617\pi\) | |||||||
\(234\) | −1.23827e39 | + | 7.01315e38i | −0.0654858 | + | 0.0370888i | ||||
\(235\) | −1.50562e40 | −0.740565 | ||||||||
\(236\) | 9.52787e39i | 0.436005i | ||||||||
\(237\) | 3.18443e39 | + | 1.85615e39i | 0.135616 | + | 0.0790481i | ||||
\(238\) | −1.66880e40 | −0.661599 | ||||||||
\(239\) | − | 4.32007e40i | − | 1.59487i | −0.603402 | − | 0.797437i | \(-0.706189\pi\) | ||
0.603402 | − | 0.797437i | \(-0.293811\pi\) | |||||||
\(240\) | −1.70139e40 | + | 2.91893e40i | −0.585078 | + | 1.00377i | ||||
\(241\) | 3.68186e40 | 1.17972 | 0.589859 | − | 0.807506i | \(-0.299183\pi\) | ||||
0.589859 | + | 0.807506i | \(0.299183\pi\) | |||||||
\(242\) | 9.69992e39i | 0.289672i | ||||||||
\(243\) | −3.14705e40 | + | 1.73112e40i | −0.876188 | + | 0.481970i | ||||
\(244\) | −1.84148e40 | −0.478124 | ||||||||
\(245\) | 4.09555e40i | 0.991947i | ||||||||
\(246\) | −1.03800e40 | − | 6.05031e39i | −0.234585 | − | 0.136735i | ||||
\(247\) | −3.50752e39 | −0.0739864 | ||||||||
\(248\) | 2.09435e40i | 0.412450i | ||||||||
\(249\) | 4.22624e40 | − | 7.25058e40i | 0.777258 | − | 1.33347i | ||||
\(250\) | 4.60353e40 | 0.790881 | ||||||||
\(251\) | − | 1.00568e41i | − | 1.61438i | −0.590295 | − | 0.807188i | \(-0.700989\pi\) | ||
0.590295 | − | 0.807188i | \(-0.299011\pi\) | |||||||
\(252\) | −3.58458e40 | − | 6.32911e40i | −0.537810 | − | 0.949584i | ||||
\(253\) | 1.92719e40 | 0.270319 | ||||||||
\(254\) | 2.98020e40i | 0.390906i | ||||||||
\(255\) | 1.91854e41 | + | 1.11829e41i | 2.35390 | + | 1.37205i | ||||
\(256\) | −1.69602e39 | −0.0194694 | ||||||||
\(257\) | 3.25250e40i | 0.349425i | 0.984619 | + | 0.174713i | \(0.0558996\pi\) | ||||
−0.984619 | + | 0.174713i | \(0.944100\pi\) | |||||||
\(258\) | 4.81575e39 | − | 8.26196e39i | 0.0484316 | − | 0.0830898i | ||||
\(259\) | −1.68240e41 | −1.58429 | ||||||||
\(260\) | 3.83495e40i | 0.338231i | ||||||||
\(261\) | −2.21264e40 | + | 1.25316e40i | −0.182819 | + | 0.103542i | ||||
\(262\) | 1.54695e40 | 0.119772 | ||||||||
\(263\) | − | 1.55707e41i | − | 1.12995i | −0.825107 | − | 0.564977i | \(-0.808885\pi\) | ||
0.825107 | − | 0.564977i | \(-0.191115\pi\) | |||||||
\(264\) | 3.51242e40 | + | 2.04733e40i | 0.238968 | + | 0.139290i | ||||
\(265\) | −2.91775e41 | −1.86152 | ||||||||
\(266\) | 2.52710e40i | 0.151229i | ||||||||
\(267\) | 1.62983e39 | − | 2.79615e39i | 0.00915061 | − | 0.0156989i | ||||
\(268\) | 1.98928e41 | 1.04810 | ||||||||
\(269\) | 3.56146e41i | 1.76133i | 0.473743 | + | 0.880663i | \(0.342903\pi\) | ||||
−0.473743 | + | 0.880663i | \(0.657097\pi\) | |||||||
\(270\) | 1.69424e39 | − | 1.36427e41i | 0.00786666 | − | 0.633455i | ||||
\(271\) | −4.37392e40 | −0.190719 | −0.0953593 | − | 0.995443i | \(-0.530400\pi\) | ||||
−0.0953593 | + | 0.995443i | \(0.530400\pi\) | |||||||
\(272\) | − | 2.37927e41i | − | 0.974481i | ||||||
\(273\) | −5.98573e40 | − | 3.48898e40i | −0.230331 | − | 0.134256i | ||||
\(274\) | −1.88836e41 | −0.682849 | ||||||||
\(275\) | 2.77418e41i | 0.942928i | ||||||||
\(276\) | −8.90283e40 | + | 1.52738e41i | −0.284494 | + | 0.488082i | ||||
\(277\) | −1.17525e41 | −0.353161 | −0.176581 | − | 0.984286i | \(-0.556504\pi\) | ||||
−0.176581 | + | 0.984286i | \(0.556504\pi\) | |||||||
\(278\) | − | 1.30911e41i | − | 0.370010i | ||||||
\(279\) | 1.15898e41 | + | 2.04634e41i | 0.308179 | + | 0.544135i | ||||
\(280\) | 5.91550e41 | 1.48015 | ||||||||
\(281\) | − | 4.55949e41i | − | 1.07376i | −0.843657 | − | 0.536882i | \(-0.819602\pi\) | ||
0.843657 | − | 0.536882i | \(-0.180398\pi\) | |||||||
\(282\) | −5.62811e40 | − | 3.28053e40i | −0.124775 | − | 0.0727293i | ||||
\(283\) | 8.37173e41 | 1.74761 | 0.873807 | − | 0.486273i | \(-0.161644\pi\) | ||||
0.873807 | + | 0.486273i | \(0.161644\pi\) | |||||||
\(284\) | − | 9.24535e40i | − | 0.181766i | ||||||
\(285\) | 1.69345e41 | − | 2.90530e41i | 0.313624 | − | 0.538057i | ||||
\(286\) | 1.80877e40 | 0.0315618 | ||||||||
\(287\) | − | 5.84936e41i | − | 0.961869i | ||||||
\(288\) | −4.97461e41 | + | 2.81744e41i | −0.771058 | + | 0.436700i | ||||
\(289\) | −8.79514e41 | −1.28523 | ||||||||
\(290\) | − | 9.65942e40i | − | 0.133102i | ||||||
\(291\) | −4.70971e41 | − | 2.74521e41i | −0.612088 | − | 0.356775i | ||||
\(292\) | 1.15463e42 | 1.41557 | ||||||||
\(293\) | 1.58031e42i | 1.82807i | 0.405634 | + | 0.914036i | \(0.367051\pi\) | ||||
−0.405634 | + | 0.914036i | \(0.632949\pi\) | |||||||
\(294\) | −8.92358e40 | + | 1.53094e41i | −0.0974169 | + | 0.167130i | ||||
\(295\) | −8.70108e41 | −0.896600 | ||||||||
\(296\) | 8.62635e41i | 0.839205i | ||||||||
\(297\) | 4.56485e41 | + | 5.66893e39i | 0.419341 | + | 0.00520765i | ||||
\(298\) | 3.49668e41 | 0.303375 | ||||||||
\(299\) | 1.68397e41i | 0.138014i | ||||||||
\(300\) | −2.19865e42 | − | 1.28156e42i | −1.70253 | − | 0.992376i | ||||
\(301\) | 4.65580e41 | 0.340694 | ||||||||
\(302\) | − | 4.25336e41i | − | 0.294180i | ||||||
\(303\) | −3.38053e41 | + | 5.79968e41i | −0.221035 | + | 0.379210i | ||||
\(304\) | −3.60300e41 | −0.222748 | ||||||||
\(305\) | − | 1.68168e42i | − | 0.983212i | ||||||
\(306\) | 4.73505e41 | + | 8.36043e41i | 0.261855 | + | 0.462343i | ||||
\(307\) | 2.55730e41 | 0.133792 | 0.0668959 | − | 0.997760i | \(-0.478690\pi\) | ||||
0.0668959 | + | 0.997760i | \(0.478690\pi\) | |||||||
\(308\) | 9.24506e41i | 0.457665i | ||||||||
\(309\) | 2.76717e42 | + | 1.61294e42i | 1.29641 | + | 0.755654i | ||||
\(310\) | −8.93344e41 | −0.396159 | ||||||||
\(311\) | − | 1.84247e42i | − | 0.773523i | −0.922180 | − | 0.386762i | \(-0.873594\pi\) | ||
0.922180 | − | 0.386762i | \(-0.126406\pi\) | |||||||
\(312\) | −1.78894e41 | + | 3.06913e41i | −0.0711161 | + | 0.122008i | ||||
\(313\) | −1.93846e42 | −0.729799 | −0.364900 | − | 0.931047i | \(-0.618897\pi\) | ||||
−0.364900 | + | 0.931047i | \(0.618897\pi\) | |||||||
\(314\) | − | 5.02180e41i | − | 0.179084i | ||||||
\(315\) | 5.77989e42 | − | 3.27352e42i | 1.95272 | − | 1.10595i | ||||
\(316\) | 4.29766e41 | 0.137579 | ||||||||
\(317\) | − | 5.77707e41i | − | 0.175267i | −0.996153 | − | 0.0876335i | \(-0.972070\pi\) | ||
0.996153 | − | 0.0876335i | \(-0.0279304\pi\) | |||||||
\(318\) | −1.09067e42 | − | 6.35734e41i | −0.313642 | − | 0.182816i | ||||
\(319\) | 3.23205e41 | 0.0881123 | ||||||||
\(320\) | 2.32294e42i | 0.600465i | ||||||||
\(321\) | 7.20242e41 | − | 1.23566e42i | 0.176560 | − | 0.302909i | ||||
\(322\) | 1.21327e42 | 0.282102 | ||||||||
\(323\) | 2.36816e42i | 0.522359i | ||||||||
\(324\) | −2.15370e42 | + | 3.59165e42i | −0.450734 | + | 0.751672i | ||||
\(325\) | −2.42405e42 | −0.481421 | ||||||||
\(326\) | 6.64150e41i | 0.125189i | ||||||||
\(327\) | −1.18367e42 | − | 6.89943e41i | −0.211797 | − | 0.123453i | ||||
\(328\) | −2.99920e42 | −0.509507 | ||||||||
\(329\) | − | 3.17157e42i | − | 0.511616i | ||||||
\(330\) | −8.73286e41 | + | 1.49822e42i | −0.133789 | + | 0.229529i | ||||
\(331\) | −6.86360e42 | −0.998794 | −0.499397 | − | 0.866373i | \(-0.666445\pi\) | ||||
−0.499397 | + | 0.866373i | \(0.666445\pi\) | |||||||
\(332\) | − | 9.78528e42i | − | 1.35278i | ||||||
\(333\) | 4.77366e42 | + | 8.42859e42i | 0.627046 | + | 1.10714i | ||||
\(334\) | 2.37593e41 | 0.0296581 | ||||||||
\(335\) | 1.81665e43i | 2.15531i | ||||||||
\(336\) | −6.14867e42 | − | 3.58395e42i | −0.693448 | − | 0.404199i | ||||
\(337\) | −1.24578e43 | −1.33578 | −0.667889 | − | 0.744261i | \(-0.732802\pi\) | ||||
−0.667889 | + | 0.744261i | \(0.732802\pi\) | |||||||
\(338\) | − | 3.28940e42i | − | 0.335376i | ||||||
\(339\) | 6.13204e42 | − | 1.05202e43i | 0.594580 | − | 1.02007i | ||||
\(340\) | 2.58924e43 | 2.38798 | ||||||||
\(341\) | − | 2.98913e42i | − | 0.262253i | ||||||
\(342\) | 1.26604e42 | − | 7.17041e41i | 0.105683 | − | 0.0598550i | ||||
\(343\) | 7.04816e42 | 0.559855 | ||||||||
\(344\) | − | 2.38722e42i | − | 0.180467i | ||||||
\(345\) | −1.39484e43 | − | 8.13027e42i | −1.00369 | − | 0.585033i | ||||
\(346\) | 6.07191e42 | 0.415941 | ||||||||
\(347\) | 4.95559e42i | 0.323217i | 0.986855 | + | 0.161609i | \(0.0516682\pi\) | ||||
−0.986855 | + | 0.161609i | \(0.948332\pi\) | |||||||
\(348\) | −1.49307e42 | + | 2.56153e42i | −0.0927329 | + | 0.159094i | ||||
\(349\) | 7.20849e42 | 0.426395 | 0.213197 | − | 0.977009i | \(-0.431612\pi\) | ||||
0.213197 | + | 0.977009i | \(0.431612\pi\) | |||||||
\(350\) | 1.74649e43i | 0.984030i | ||||||||
\(351\) | −4.95347e40 | + | 3.98873e42i | −0.00265882 | + | 0.214099i | ||||
\(352\) | 7.26652e42 | 0.371622 | ||||||||
\(353\) | − | 3.47119e43i | − | 1.69164i | −0.533468 | − | 0.845820i | \(-0.679112\pi\) | ||
0.533468 | − | 0.845820i | \(-0.320888\pi\) | |||||||
\(354\) | −3.25251e42 | − | 1.89583e42i | −0.151065 | − | 0.0880531i | ||||
\(355\) | 8.44307e42 | 0.373782 | ||||||||
\(356\) | − | 3.77364e41i | − | 0.0159261i | ||||||
\(357\) | −2.35565e43 | + | 4.04138e43i | −0.947874 | + | 1.62618i | ||||
\(358\) | 8.46087e42 | 0.324641 | ||||||||
\(359\) | − | 3.85182e43i | − | 1.40948i | −0.709463 | − | 0.704742i | \(-0.751063\pi\) | ||
0.709463 | − | 0.704742i | \(-0.248937\pi\) | |||||||
\(360\) | −1.67847e43 | − | 2.96358e43i | −0.585828 | − | 1.03437i | ||||
\(361\) | −2.64485e43 | −0.880599 | ||||||||
\(362\) | 4.47847e42i | 0.142261i | ||||||||
\(363\) | 2.34906e43 | + | 1.36923e43i | 0.712002 | + | 0.415014i | ||||
\(364\) | −8.07826e42 | −0.233665 | ||||||||
\(365\) | 1.05443e44i | 2.91098i | ||||||||
\(366\) | 3.66413e42 | − | 6.28623e42i | 0.0965591 | − | 0.165658i | ||||
\(367\) | −5.67891e42 | −0.142870 | −0.0714351 | − | 0.997445i | \(-0.522758\pi\) | ||||
−0.0714351 | + | 0.997445i | \(0.522758\pi\) | |||||||
\(368\) | 1.72980e43i | 0.415512i | ||||||||
\(369\) | −2.93044e43 | + | 1.65970e43i | −0.672179 | + | 0.380698i | ||||
\(370\) | −3.67956e43 | −0.806058 | ||||||||
\(371\) | − | 6.14619e43i | − | 1.28603i | ||||||
\(372\) | 2.36901e43 | + | 1.38086e43i | 0.473519 | + | 0.276006i | ||||
\(373\) | −1.19236e43 | −0.227696 | −0.113848 | − | 0.993498i | \(-0.536318\pi\) | ||||
−0.113848 | + | 0.993498i | \(0.536318\pi\) | |||||||
\(374\) | − | 1.22123e43i | − | 0.222833i | ||||||
\(375\) | 6.49827e43 | − | 1.11485e44i | 1.13310 | − | 1.94395i | ||||
\(376\) | −1.62619e43 | −0.271006 | ||||||||
\(377\) | 2.82414e42i | 0.0449866i | ||||||||
\(378\) | 2.87381e43 | + | 3.56888e41i | 0.437620 | + | 0.00543465i | ||||
\(379\) | 6.56483e43 | 0.955777 | 0.477889 | − | 0.878420i | \(-0.341402\pi\) | ||||
0.477889 | + | 0.878420i | \(0.341402\pi\) | |||||||
\(380\) | − | 3.92095e43i | − | 0.545846i | ||||||
\(381\) | 7.21724e43 | + | 4.20680e43i | 0.960830 | + | 0.560051i | ||||
\(382\) | 3.66448e43 | 0.466590 | ||||||||
\(383\) | − | 9.44163e42i | − | 0.114992i | −0.998346 | − | 0.0574960i | \(-0.981688\pi\) | ||
0.998346 | − | 0.0574960i | \(-0.0183117\pi\) | |||||||
\(384\) | −4.33614e43 | + | 7.43914e43i | −0.505211 | + | 0.866746i | ||||
\(385\) | −8.44280e43 | −0.941140 | ||||||||
\(386\) | − | 1.66347e42i | − | 0.0177432i | ||||||
\(387\) | −1.32104e43 | − | 2.33249e43i | −0.134843 | − | 0.238086i | ||||
\(388\) | −6.35616e43 | −0.620948 | ||||||||
\(389\) | 7.11826e42i | 0.0665627i | 0.999446 | + | 0.0332813i | \(0.0105957\pi\) | ||||
−0.999446 | + | 0.0332813i | \(0.989404\pi\) | |||||||
\(390\) | −1.30913e43 | − | 7.63070e42i | −0.117188 | − | 0.0683071i | ||||
\(391\) | 1.13696e44 | 0.974406 | ||||||||
\(392\) | 4.42351e43i | 0.362997i | ||||||||
\(393\) | 2.18365e43 | − | 3.74630e43i | 0.171597 | − | 0.294394i | ||||
\(394\) | −5.59646e43 | −0.421189 | ||||||||
\(395\) | 3.92472e43i | 0.282917i | ||||||||
\(396\) | 4.63164e43 | − | 2.62320e43i | 0.319828 | − | 0.181139i | ||||
\(397\) | −7.99956e43 | −0.529209 | −0.264605 | − | 0.964357i | \(-0.585241\pi\) | ||||
−0.264605 | + | 0.964357i | \(0.585241\pi\) | |||||||
\(398\) | 3.70868e43i | 0.235075i | ||||||||
\(399\) | 6.11996e43 | + | 3.56722e43i | 0.371714 | + | 0.216666i | ||||
\(400\) | −2.49004e44 | −1.44939 | ||||||||
\(401\) | 6.80463e42i | 0.0379621i | 0.999820 | + | 0.0189811i | \(0.00604222\pi\) | ||||
−0.999820 | + | 0.0189811i | \(0.993958\pi\) | |||||||
\(402\) | −3.95822e43 | + | 6.79076e43i | −0.211669 | + | 0.363141i | ||||
\(403\) | 2.61188e43 | 0.133896 | ||||||||
\(404\) | 7.82716e43i | 0.384699i | ||||||||
\(405\) | −3.27998e44 | − | 1.96681e44i | −1.54574 | − | 0.926888i | ||||
\(406\) | 2.03474e43 | 0.0919531 | ||||||||
\(407\) | − | 1.23118e44i | − | 0.533602i | ||||||
\(408\) | 2.07218e44 | + | 1.20783e44i | 0.861398 | + | 0.502094i | ||||
\(409\) | 1.69922e44 | 0.677568 | 0.338784 | − | 0.940864i | \(-0.389984\pi\) | ||||
0.338784 | + | 0.940864i | \(0.389984\pi\) | |||||||
\(410\) | − | 1.27930e44i | − | 0.489382i | ||||||
\(411\) | −2.66558e44 | + | 4.57310e44i | −0.978319 | + | 1.67842i | ||||
\(412\) | 3.73453e44 | 1.31518 | ||||||||
\(413\) | − | 1.83287e44i | − | 0.619412i | ||||||
\(414\) | −3.44253e43 | − | 6.07829e43i | −0.111653 | − | 0.197140i | ||||
\(415\) | 8.93614e44 | 2.78184 | ||||||||
\(416\) | 6.34942e43i | 0.189735i | ||||||||
\(417\) | −3.17031e44 | − | 1.84792e44i | −0.909470 | − | 0.530114i | ||||
\(418\) | −1.84933e43 | −0.0509353 | ||||||||
\(419\) | − | 2.16731e44i | − | 0.573169i | −0.958055 | − | 0.286584i | \(-0.907480\pi\) | ||
0.958055 | − | 0.286584i | \(-0.0925199\pi\) | |||||||
\(420\) | 3.90023e44 | − | 6.69127e44i | 0.990494 | − | 1.69930i | ||||
\(421\) | −5.04802e44 | −1.23119 | −0.615596 | − | 0.788062i | \(-0.711085\pi\) | ||||
−0.615596 | + | 0.788062i | \(0.711085\pi\) | |||||||
\(422\) | − | 2.54929e44i | − | 0.597184i | ||||||
\(423\) | −1.58891e44 | + | 8.99903e43i | −0.357531 | + | 0.202493i | ||||
\(424\) | −3.15140e44 | −0.681215 | ||||||||
\(425\) | 1.63664e45i | 3.39893i | ||||||||
\(426\) | 3.15607e43 | + | 1.83962e43i | 0.0629772 | + | 0.0367083i | ||||
\(427\) | 3.54243e44 | 0.679247 | ||||||||
\(428\) | − | 1.66762e44i | − | 0.307294i | ||||||
\(429\) | 2.55324e43 | − | 4.38036e43i | 0.0452186 | − | 0.0775775i | ||||
\(430\) | 1.01826e44 | 0.173339 | ||||||||
\(431\) | − | 6.17185e44i | − | 1.00995i | −0.863133 | − | 0.504977i | \(-0.831501\pi\) | ||
0.863133 | − | 0.504977i | \(-0.168499\pi\) | |||||||
\(432\) | −5.08831e42 | + | 4.09731e44i | −0.00800478 | + | 0.644577i | ||||
\(433\) | −9.20555e44 | −1.39237 | −0.696186 | − | 0.717861i | \(-0.745121\pi\) | ||||
−0.696186 | + | 0.717861i | \(0.745121\pi\) | |||||||
\(434\) | − | 1.88181e44i | − | 0.273685i | ||||||
\(435\) | −2.33925e44 | − | 1.36351e44i | −0.327160 | − | 0.190696i | ||||
\(436\) | −1.59747e44 | −0.214863 | ||||||||
\(437\) | − | 1.72173e44i | − | 0.222731i | ||||||
\(438\) | −2.29745e44 | + | 3.94153e44i | −0.285881 | + | 0.490461i | ||||
\(439\) | −3.60164e44 | −0.431125 | −0.215563 | − | 0.976490i | \(-0.569159\pi\) | ||||
−0.215563 | + | 0.976490i | \(0.569159\pi\) | |||||||
\(440\) | 4.32896e44i | 0.498527i | ||||||||
\(441\) | 2.44788e44 | + | 4.32210e44i | 0.271228 | + | 0.478893i | ||||
\(442\) | 1.06710e44 | 0.113769 | ||||||||
\(443\) | − | 6.41952e44i | − | 0.658627i | −0.944221 | − | 0.329313i | \(-0.893183\pi\) | ||
0.944221 | − | 0.329313i | \(-0.106817\pi\) | |||||||
\(444\) | 9.75763e44 | + | 5.68755e44i | 0.963460 | + | 0.561584i | ||||
\(445\) | 3.44618e43 | 0.0327505 | ||||||||
\(446\) | 4.55348e44i | 0.416534i | ||||||||
\(447\) | 4.93586e44 | − | 8.46802e44i | 0.434645 | − | 0.745683i | ||||
\(448\) | −4.89322e44 | −0.414829 | ||||||||
\(449\) | 8.45159e44i | 0.689844i | 0.938631 | + | 0.344922i | \(0.112095\pi\) | ||||
−0.938631 | + | 0.344922i | \(0.887905\pi\) | |||||||
\(450\) | 8.74965e44 | − | 4.95549e44i | 0.687666 | − | 0.389470i | ||||
\(451\) | 4.28056e44 | 0.323966 | ||||||||
\(452\) | − | 1.41979e45i | − | 1.03483i | ||||||
\(453\) | −1.03005e45 | − | 6.00397e44i | −0.723083 | − | 0.421472i | ||||
\(454\) | −9.07252e44 | −0.613449 | ||||||||
\(455\) | − | 7.37725e44i | − | 0.480508i | ||||||
\(456\) | 1.82906e44 | − | 3.13795e44i | 0.114769 | − | 0.196899i | ||||
\(457\) | 2.16960e45 | 1.31161 | 0.655804 | − | 0.754931i | \(-0.272330\pi\) | ||||
0.655804 | + | 0.754931i | \(0.272330\pi\) | |||||||
\(458\) | 7.65766e44i | 0.446049i | ||||||||
\(459\) | 2.69306e45 | + | 3.34442e43i | 1.51158 | + | 0.0187718i | ||||
\(460\) | −1.88245e45 | −1.01822 | ||||||||
\(461\) | − | 3.98780e44i | − | 0.207883i | −0.994583 | − | 0.103941i | \(-0.966855\pi\) | ||
0.994583 | − | 0.103941i | \(-0.0331454\pi\) | |||||||
\(462\) | −3.15597e44 | − | 1.83956e44i | −0.158569 | − | 0.0924273i | ||||
\(463\) | 1.17118e45 | 0.567215 | 0.283608 | − | 0.958940i | \(-0.408469\pi\) | ||||
0.283608 | + | 0.958940i | \(0.408469\pi\) | |||||||
\(464\) | 2.90102e44i | 0.135439i | ||||||||
\(465\) | −1.26103e45 | + | 2.16344e45i | −0.567578 | + | 0.973743i | ||||
\(466\) | −1.94868e44 | −0.0845630 | ||||||||
\(467\) | 4.94974e44i | 0.207107i | 0.994624 | + | 0.103554i | \(0.0330214\pi\) | ||||
−0.994624 | + | 0.103554i | \(0.966979\pi\) | |||||||
\(468\) | 2.29213e44 | + | 4.04709e44i | 0.0924825 | + | 0.163291i | ||||
\(469\) | −3.82675e45 | −1.48899 | ||||||||
\(470\) | − | 6.93649e44i | − | 0.260301i | ||||||
\(471\) | −1.21615e45 | − | 7.08870e44i | −0.440180 | − | 0.256573i | ||||
\(472\) | −9.39784e44 | −0.328106 | ||||||||
\(473\) | 3.40712e44i | 0.114749i | ||||||||
\(474\) | −8.55138e43 | + | 1.46708e44i | −0.0277846 | + | 0.0476676i | ||||
\(475\) | 2.47841e45 | 0.776931 | ||||||||
\(476\) | 5.45418e45i | 1.64972i | ||||||||
\(477\) | −3.07916e45 | + | 1.74392e45i | −0.898709 | + | 0.508997i | ||||
\(478\) | 1.99028e45 | 0.560583 | ||||||||
\(479\) | − | 2.32078e45i | − | 0.630856i | −0.948950 | − | 0.315428i | \(-0.897852\pi\) | ||
0.948950 | − | 0.315428i | \(-0.102148\pi\) | |||||||
\(480\) | −5.25927e45 | − | 3.06554e45i | −1.37983 | − | 0.804276i | ||||
\(481\) | 1.07580e45 | 0.272436 | ||||||||
\(482\) | 1.69625e45i | 0.414659i | ||||||||
\(483\) | 1.71263e45 | − | 2.93820e45i | 0.404168 | − | 0.693395i | ||||
\(484\) | 3.17025e45 | 0.722309 | ||||||||
\(485\) | − | 5.80459e45i | − | 1.27691i | ||||||
\(486\) | −7.97536e44 | − | 1.44986e45i | −0.169408 | − | 0.307971i | ||||
\(487\) | 6.50178e45 | 1.33364 | 0.666822 | − | 0.745217i | \(-0.267654\pi\) | ||||
0.666822 | + | 0.745217i | \(0.267654\pi\) | |||||||
\(488\) | − | 1.81635e45i | − | 0.359801i | ||||||
\(489\) | 1.60839e45 | + | 9.37503e44i | 0.307710 | + | 0.179359i | ||||
\(490\) | −1.88684e45 | −0.348660 | ||||||||
\(491\) | 4.73253e45i | 0.844710i | 0.906430 | + | 0.422355i | \(0.138796\pi\) | ||||
−0.906430 | + | 0.422355i | \(0.861204\pi\) | |||||||
\(492\) | −1.97744e45 | + | 3.39252e45i | −0.340955 | + | 0.584946i | ||||
\(493\) | 1.90677e45 | 0.317614 | ||||||||
\(494\) | − | 1.61593e44i | − | 0.0260055i | ||||||
\(495\) | 2.39556e45 | + | 4.22972e45i | 0.372494 | + | 0.657694i | ||||
\(496\) | 2.68298e45 | 0.403115 | ||||||||
\(497\) | 1.77852e45i | 0.258226i | ||||||||
\(498\) | 3.34038e45 | + | 1.94705e45i | 0.468703 | + | 0.273199i | ||||
\(499\) | −8.44527e45 | −1.14526 | −0.572630 | − | 0.819814i | \(-0.694077\pi\) | ||||
−0.572630 | + | 0.819814i | \(0.694077\pi\) | |||||||
\(500\) | − | 1.50459e46i | − | 1.97209i | ||||||
\(501\) | 3.35382e44 | − | 5.75385e44i | 0.0424912 | − | 0.0728983i | ||||
\(502\) | 4.63320e45 | 0.567437 | ||||||||
\(503\) | − | 4.59418e44i | − | 0.0543941i | −0.999630 | − | 0.0271971i | \(-0.991342\pi\) | ||
0.999630 | − | 0.0271971i | \(-0.00865816\pi\) | |||||||
\(504\) | 6.24273e45 | − | 3.53566e45i | 0.714587 | − | 0.404717i | ||||
\(505\) | −7.14795e45 | −0.791094 | ||||||||
\(506\) | 8.87868e44i | 0.0950144i | ||||||||
\(507\) | −7.96603e45 | − | 4.64326e45i | −0.824340 | − | 0.480494i | ||||
\(508\) | 9.74028e45 | 0.974739 | ||||||||
\(509\) | 1.73226e45i | 0.167652i | 0.996480 | + | 0.0838262i | \(0.0267140\pi\) | ||||
−0.996480 | + | 0.0838262i | \(0.973286\pi\) | |||||||
\(510\) | −5.15200e45 | + | 8.83883e45i | −0.482262 | + | 0.827374i | ||||
\(511\) | −2.22114e46 | −2.01104 | ||||||||
\(512\) | 1.13768e46i | 0.996395i | ||||||||
\(513\) | 5.06455e43 | − | 4.07818e45i | 0.00429087 | − | 0.345518i | ||||
\(514\) | −1.49844e45 | −0.122820 | ||||||||
\(515\) | 3.41046e46i | 2.70452i | ||||||||
\(516\) | −2.70028e45 | − | 1.57395e45i | −0.207188 | − | 0.120766i | ||||
\(517\) | 2.32096e45 | 0.172317 | ||||||||
\(518\) | − | 7.75092e45i | − | 0.556861i | ||||||
\(519\) | 8.57102e45 | − | 1.47045e46i | 0.595919 | − | 1.02237i | ||||
\(520\) | −3.78261e45 | −0.254528 | ||||||||
\(521\) | − | 1.68417e46i | − | 1.09685i | −0.836201 | − | 0.548423i | \(-0.815228\pi\) | ||
0.836201 | − | 0.548423i | \(-0.184772\pi\) | |||||||
\(522\) | −5.77338e44 | − | 1.01938e45i | −0.0363941 | − | 0.0642593i | ||||
\(523\) | −2.29640e46 | −1.40126 | −0.700631 | − | 0.713524i | \(-0.747098\pi\) | ||||
−0.700631 | + | 0.713524i | \(0.747098\pi\) | |||||||
\(524\) | − | 5.05595e45i | − | 0.298656i | ||||||
\(525\) | 4.22952e46 | + | 2.46531e46i | 2.41870 | + | 1.40982i | ||||
\(526\) | 7.17351e45 | 0.397168 | ||||||||
\(527\) | − | 1.76346e46i | − | 0.945333i | ||||||
\(528\) | 2.62274e45 | − | 4.49960e45i | 0.136138 | − | 0.233559i | ||||
\(529\) | 1.16291e46 | 0.584519 | ||||||||
\(530\) | − | 1.34422e46i | − | 0.654308i | ||||||
\(531\) | −9.18240e45 | + | 5.20058e45i | −0.432862 | + | 0.245157i | ||||
\(532\) | 8.25941e45 | 0.377095 | ||||||||
\(533\) | 3.74032e45i | 0.165404i | ||||||||
\(534\) | 1.28820e44 | + | 7.50870e43i | 0.00551801 | + | 0.00321635i | ||||
\(535\) | 1.52291e46 | 0.631917 | ||||||||
\(536\) | 1.96213e46i | 0.788725i | ||||||||
\(537\) | 1.19432e46 | − | 2.04900e46i | 0.465114 | − | 0.797955i | ||||
\(538\) | −1.64079e46 | −0.619089 | ||||||||
\(539\) | − | 6.31338e45i | − | 0.230809i | ||||||
\(540\) | −4.45888e46 | − | 5.53733e44i | −1.57955 | − | 0.0196158i | ||||
\(541\) | −3.02027e46 | −1.03679 | −0.518397 | − | 0.855140i | \(-0.673471\pi\) | ||||
−0.518397 | + | 0.855140i | \(0.673471\pi\) | |||||||
\(542\) | − | 2.01509e45i | − | 0.0670357i | ||||||
\(543\) | 1.08457e46 | + | 6.32175e45i | 0.349670 | + | 0.203817i | ||||
\(544\) | 4.28693e46 | 1.33957 | ||||||||
\(545\) | − | 1.45885e46i | − | 0.441844i | ||||||
\(546\) | 1.60739e45 | − | 2.75766e45i | 0.0471897 | − | 0.0809591i | ||||
\(547\) | 3.59015e46 | 1.02171 | 0.510855 | − | 0.859667i | \(-0.329329\pi\) | ||||
0.510855 | + | 0.859667i | \(0.329329\pi\) | |||||||
\(548\) | 6.17178e46i | 1.70271i | ||||||||
\(549\) | −1.00513e46 | − | 1.77471e46i | −0.268840 | − | 0.474676i | ||||
\(550\) | −1.27808e46 | −0.331430 | ||||||||
\(551\) | − | 2.88747e45i | − | 0.0726006i | ||||||
\(552\) | −1.50653e46 | − | 8.78133e45i | −0.367295 | − | 0.214090i | ||||
\(553\) | −8.26736e45 | −0.195452 | ||||||||
\(554\) | − | 5.41443e45i | − | 0.124133i | ||||||
\(555\) | −5.19401e46 | + | 8.91089e46i | −1.15484 | + | 1.98126i | ||||
\(556\) | −4.27860e46 | −0.922635 | ||||||||
\(557\) | − | 2.86942e46i | − | 0.600145i | −0.953916 | − | 0.300073i | \(-0.902989\pi\) | ||
0.953916 | − | 0.300073i | \(-0.0970109\pi\) | |||||||
\(558\) | −9.42761e45 | + | 5.33946e45i | −0.191258 | + | 0.108322i | ||||
\(559\) | −2.97711e45 | −0.0585861 | ||||||||
\(560\) | − | 7.57807e46i | − | 1.44665i | ||||||
\(561\) | −2.95748e46 | − | 1.72386e46i | −0.547713 | − | 0.319252i | ||||
\(562\) | 2.10058e46 | 0.377418 | ||||||||
\(563\) | 7.09664e46i | 1.23711i | 0.785740 | + | 0.618557i | \(0.212282\pi\) | ||||
−0.785740 | + | 0.618557i | \(0.787718\pi\) | |||||||
\(564\) | −1.07219e46 | + | 1.83945e46i | −0.181353 | + | 0.311132i | ||||
\(565\) | 1.29659e47 | 2.12803 | ||||||||
\(566\) | 3.85690e46i | 0.614269i | ||||||||
\(567\) | 4.14305e46 | − | 6.90921e46i | 0.640337 | − | 1.06787i | ||||
\(568\) | 9.11917e45 | 0.136783 | ||||||||
\(569\) | 1.46145e45i | 0.0212753i | 0.999943 | + | 0.0106376i | \(0.00338613\pi\) | ||||
−0.999943 | + | 0.0106376i | \(0.996614\pi\) | |||||||
\(570\) | 1.33849e46 | + | 7.80181e45i | 0.189122 | + | 0.110236i | ||||
\(571\) | −9.93026e46 | −1.36190 | −0.680952 | − | 0.732328i | \(-0.738434\pi\) | ||||
−0.680952 | + | 0.732328i | \(0.738434\pi\) | |||||||
\(572\) | − | 5.91167e45i | − | 0.0787005i | ||||||
\(573\) | 5.17272e46 | − | 8.87438e46i | 0.668483 | − | 1.14686i | ||||
\(574\) | 2.69483e46 | 0.338088 | ||||||||
\(575\) | − | 1.18989e47i | − | 1.44928i | ||||||
\(576\) | 1.38841e46 | + | 2.45144e46i | 0.164185 | + | 0.289893i | ||||
\(577\) | 6.65273e46 | 0.763856 | 0.381928 | − | 0.924192i | \(-0.375260\pi\) | ||||
0.381928 | + | 0.924192i | \(0.375260\pi\) | |||||||
\(578\) | − | 4.05197e46i | − | 0.451744i | ||||||
\(579\) | −4.02848e45 | − | 2.34813e45i | −0.0436119 | − | 0.0254206i | ||||
\(580\) | −3.15702e46 | −0.331895 | ||||||||
\(581\) | 1.88238e47i | 1.92182i | ||||||||
\(582\) | 1.26473e46 | − | 2.16979e46i | 0.125403 | − | 0.215143i | ||||
\(583\) | 4.49779e46 | 0.433145 | ||||||||
\(584\) | 1.13887e47i | 1.06526i | ||||||||
\(585\) | −3.69590e46 | + | 2.09322e46i | −0.335792 | + | 0.190181i | ||||
\(586\) | −7.28058e46 | −0.642549 | ||||||||
\(587\) | − | 8.11276e46i | − | 0.695538i | −0.937580 | − | 0.347769i | \(-0.886939\pi\) | ||
0.937580 | − | 0.347769i | \(-0.113061\pi\) | |||||||
\(588\) | 5.00362e46 | + | 2.91652e46i | 0.416744 | + | 0.242913i | ||||
\(589\) | −2.67045e46 | −0.216085 | ||||||||
\(590\) | − | 4.00863e46i | − | 0.315146i | ||||||
\(591\) | −7.89987e46 | + | 1.35531e47i | −0.603438 | + | 1.03527i | ||||
\(592\) | 1.10508e47 | 0.820210 | ||||||||
\(593\) | − | 1.36306e47i | − | 0.983068i | −0.870858 | − | 0.491534i | \(-0.836436\pi\) | ||
0.870858 | − | 0.491534i | \(-0.163564\pi\) | |||||||
\(594\) | −2.61171e44 | + | 2.10305e46i | −0.00183044 | + | 0.147394i | ||||
\(595\) | −4.98088e47 | −3.39249 | ||||||||
\(596\) | − | 1.14283e47i | − | 0.756477i | ||||||
\(597\) | 8.98142e46 | + | 5.23511e46i | 0.577805 | + | 0.336792i | ||||
\(598\) | −7.75812e45 | −0.0485106 | ||||||||
\(599\) | 7.94216e46i | 0.482706i | 0.970437 | + | 0.241353i | \(0.0775911\pi\) | ||||
−0.970437 | + | 0.241353i | \(0.922409\pi\) | |||||||
\(600\) | 1.26406e47 | − | 2.16864e47i | 0.746789 | − | 1.28120i | ||||
\(601\) | −1.19385e46 | −0.0685621 | −0.0342811 | − | 0.999412i | \(-0.510914\pi\) | ||||
−0.0342811 | + | 0.999412i | \(0.510914\pi\) | |||||||
\(602\) | 2.14495e46i | 0.119751i | ||||||||
\(603\) | 1.08580e47 | + | 1.91715e47i | 0.589328 | + | 1.04055i | ||||
\(604\) | −1.39014e47 | −0.733550 | ||||||||
\(605\) | 2.89515e47i | 1.48535i | ||||||||
\(606\) | −2.67194e46 | − | 1.55743e46i | −0.133289 | − | 0.0776916i | ||||
\(607\) | 1.55661e47 | 0.755046 | 0.377523 | − | 0.926000i | \(-0.376776\pi\) | ||||
0.377523 | + | 0.926000i | \(0.376776\pi\) | |||||||
\(608\) | − | 6.49181e46i | − | 0.306200i | ||||||
\(609\) | 2.87221e46 | − | 4.92759e46i | 0.131741 | − | 0.226017i | ||||
\(610\) | 7.74761e46 | 0.345589 | ||||||||
\(611\) | 2.02803e46i | 0.0879780i | ||||||||
\(612\) | 2.73247e47 | − | 1.54757e47i | 1.15287 | − | 0.652945i | ||||
\(613\) | 4.35404e46 | 0.178675 | 0.0893376 | − | 0.996001i | \(-0.471525\pi\) | ||||
0.0893376 | + | 0.996001i | \(0.471525\pi\) | |||||||
\(614\) | 1.17816e46i | 0.0470265i | ||||||||
\(615\) | −3.09813e47 | − | 1.80585e47i | −1.20288 | − | 0.701138i | ||||
\(616\) | −9.11888e46 | −0.344405 | ||||||||
\(617\) | − | 3.98888e47i | − | 1.46556i | −0.680467 | − | 0.732779i | \(-0.738223\pi\) | ||
0.680467 | − | 0.732779i | \(-0.261777\pi\) | |||||||
\(618\) | −7.43089e46 | + | 1.27485e47i | −0.265605 | + | 0.455675i | ||||
\(619\) | 4.65103e47 | 1.61736 | 0.808682 | − | 0.588246i | \(-0.200181\pi\) | ||||
0.808682 | + | 0.588246i | \(0.200181\pi\) | |||||||
\(620\) | 2.91974e47i | 0.987838i | ||||||||
\(621\) | −1.95794e47 | − | 2.43150e45i | −0.644528 | − | 0.00800417i | ||||
\(622\) | 8.48835e46 | 0.271886 | ||||||||
\(623\) | 7.25931e45i | 0.0226255i | ||||||||
\(624\) | 3.93171e46 | + | 2.29173e46i | 0.119246 | + | 0.0695064i | ||||
\(625\) | 6.12228e47 | 1.80698 | ||||||||
\(626\) | − | 8.93059e46i | − | 0.256517i | ||||||
\(627\) | −2.61049e46 | + | 4.47859e46i | −0.0729750 | + | 0.125197i | ||||
\(628\) | −1.64129e47 | −0.446552 | ||||||||
\(629\) | − | 7.26344e47i | − | 1.92345i | ||||||
\(630\) | 1.50813e47 | + | 2.66283e47i | 0.388731 | + | 0.686362i | ||||
\(631\) | −5.29430e47 | −1.32834 | −0.664170 | − | 0.747582i | \(-0.731215\pi\) | ||||
−0.664170 | + | 0.747582i | \(0.731215\pi\) | |||||||
\(632\) | 4.23901e46i | 0.103532i | ||||||||
\(633\) | −6.17370e47 | − | 3.59855e47i | −1.46785 | − | 0.855586i | ||||
\(634\) | 2.66153e46 | 0.0616046 | ||||||||
\(635\) | 8.89505e47i | 2.00445i | ||||||||
\(636\) | −2.07779e47 | + | 3.56468e47i | −0.455859 | + | 0.782077i | ||||
\(637\) | 5.51658e46 | 0.117842 | ||||||||
\(638\) | 1.48902e46i | 0.0309706i | ||||||||
\(639\) | 8.91012e46 | − | 5.04637e46i | 0.180455 | − | 0.102203i | ||||
\(640\) | −9.16853e47 | −1.80817 | ||||||||
\(641\) | 9.73157e47i | 1.86895i | 0.356035 | + | 0.934473i | \(0.384128\pi\) | ||||
−0.356035 | + | 0.934473i | \(0.615872\pi\) | |||||||
\(642\) | 5.69273e46 | + | 3.31819e46i | 0.106469 | + | 0.0620592i | ||||
\(643\) | 1.00525e48 | 1.83100 | 0.915499 | − | 0.402321i | \(-0.131796\pi\) | ||||
0.915499 | + | 0.402321i | \(0.131796\pi\) | |||||||
\(644\) | − | 3.96535e47i | − | 0.703432i | ||||||
\(645\) | 1.43737e47 | − | 2.46596e47i | 0.248343 | − | 0.426060i | ||||
\(646\) | −1.09103e47 | −0.183604 | ||||||||
\(647\) | − | 6.56618e46i | − | 0.107632i | −0.998551 | − | 0.0538158i | \(-0.982862\pi\) | ||
0.998551 | − | 0.0538158i | \(-0.0171384\pi\) | |||||||
\(648\) | −3.54263e47 | − | 2.12431e47i | −0.565654 | − | 0.339190i | ||||
\(649\) | 1.34129e47 | 0.208624 | ||||||||
\(650\) | − | 1.11677e47i | − | 0.169215i | ||||||
\(651\) | −4.55724e47 | − | 2.65634e47i | −0.672706 | − | 0.392109i | ||||
\(652\) | 2.17066e47 | 0.312164 | ||||||||
\(653\) | − | 1.14073e48i | − | 1.59831i | −0.601127 | − | 0.799153i | \(-0.705281\pi\) | ||
0.601127 | − | 0.799153i | \(-0.294719\pi\) | |||||||
\(654\) | 3.17861e46 | − | 5.45325e46i | 0.0433925 | − | 0.0744447i | ||||
\(655\) | 4.61721e47 | 0.614154 | ||||||||
\(656\) | 3.84213e47i | 0.497975i | ||||||||
\(657\) | 6.30227e47 | + | 1.11276e48i | 0.795950 | + | 1.40537i | ||||
\(658\) | 1.46116e47 | 0.179828 | ||||||||
\(659\) | − | 8.65814e47i | − | 1.03842i | −0.854647 | − | 0.519209i | \(-0.826226\pi\) | ||
0.854647 | − | 0.519209i | \(-0.173774\pi\) | |||||||
\(660\) | 4.89667e47 | + | 2.85419e47i | 0.572340 | + | 0.333607i | ||||
\(661\) | −1.10241e48 | −1.25579 | −0.627895 | − | 0.778298i | \(-0.716083\pi\) | ||||
−0.627895 | + | 0.778298i | \(0.716083\pi\) | |||||||
\(662\) | − | 3.16210e47i | − | 0.351066i | ||||||
\(663\) | 1.50630e47 | − | 2.58422e47i | 0.162997 | − | 0.279640i | ||||
\(664\) | 9.65173e47 | 1.01800 | ||||||||
\(665\) | 7.54268e47i | 0.775457i | ||||||||
\(666\) | −3.88310e47 | + | 2.19925e47i | −0.389150 | + | 0.220400i | ||||
\(667\) | −1.38628e47 | −0.135429 | ||||||||
\(668\) | − | 7.76531e46i | − | 0.0739536i | ||||||
\(669\) | 1.10273e48 | + | 6.42762e47i | 1.02382 | + | 0.596769i | ||||
\(670\) | −8.36942e47 | −0.757572 | ||||||||
\(671\) | 2.59235e47i | 0.228777i | ||||||||
\(672\) | 6.45749e47 | − | 1.10785e48i | 0.555631 | − | 0.953247i | ||||
\(673\) | −1.36930e46 | −0.0114879 | −0.00574397 | − | 0.999984i | \(-0.501828\pi\) | ||||
−0.00574397 | + | 0.999984i | \(0.501828\pi\) | |||||||
\(674\) | − | 5.73939e47i | − | 0.469513i | ||||||
\(675\) | 3.50012e46 | − | 2.81844e48i | 0.0279202 | − | 2.24825i | ||||
\(676\) | −1.07508e48 | −0.836273 | ||||||||
\(677\) | 7.44194e46i | 0.0564519i | 0.999602 | + | 0.0282260i | \(0.00898580\pi\) | ||||
−0.999602 | + | 0.0282260i | \(0.991014\pi\) | |||||||
\(678\) | 4.84671e47 | + | 2.82506e47i | 0.358544 | + | 0.208989i | ||||
\(679\) | 1.22273e48 | 0.882151 | ||||||||
\(680\) | 2.55390e48i | 1.79702i | ||||||||
\(681\) | −1.28066e48 | + | 2.19712e48i | −0.878889 | + | 1.50783i | ||||
\(682\) | 1.37711e47 | 0.0921795 | ||||||||
\(683\) | 7.99538e47i | 0.522020i | 0.965336 | + | 0.261010i | \(0.0840556\pi\) | ||||
−0.965336 | + | 0.261010i | \(0.915944\pi\) | |||||||
\(684\) | −2.34353e47 | − | 4.13784e47i | −0.149251 | − | 0.263524i | ||||
\(685\) | −5.63621e48 | −3.50145 | ||||||||
\(686\) | 3.24712e47i | 0.196784i | ||||||||
\(687\) | 1.85448e48 | + | 1.08094e48i | 1.09637 | + | 0.639055i | ||||
\(688\) | −3.05815e47 | −0.176382 | ||||||||
\(689\) | 3.93013e47i | 0.221146i | ||||||||
\(690\) | 3.74566e47 | − | 6.42610e47i | 0.205634 | − | 0.352787i | ||||
\(691\) | −1.79689e47 | −0.0962484 | −0.0481242 | − | 0.998841i | \(-0.515324\pi\) | ||||
−0.0481242 | + | 0.998841i | \(0.515324\pi\) | |||||||
\(692\) | − | 1.98450e48i | − | 1.03717i | ||||||
\(693\) | −8.90984e47 | + | 5.04621e47i | −0.454365 | + | 0.257336i | ||||
\(694\) | −2.28307e47 | −0.113608 | ||||||||
\(695\) | − | 3.90731e48i | − | 1.89730i | ||||||
\(696\) | −2.52657e47 | − | 1.47270e47i | −0.119722 | − | 0.0697840i | ||||
\(697\) | 2.52534e48 | 1.16779 | ||||||||
\(698\) | 3.32099e47i | 0.149874i | ||||||||
\(699\) | −2.75073e47 | + | 4.71918e47i | −0.121153 | + | 0.207852i | ||||
\(700\) | 5.70809e48 | 2.45372 | ||||||||
\(701\) | 2.52645e48i | 1.06000i | 0.847999 | + | 0.529998i | \(0.177807\pi\) | ||||
−0.847999 | + | 0.529998i | \(0.822193\pi\) | |||||||
\(702\) | −1.83763e47 | − | 2.28209e45i | −0.0752536 | − | 0.000934548i | ||||
\(703\) | −1.09992e48 | −0.439664 | ||||||||
\(704\) | − | 3.58086e47i | − | 0.139718i | ||||||
\(705\) | −1.67983e48 | − | 9.79145e47i | −0.639810 | − | 0.372934i | ||||
\(706\) | 1.59919e48 | 0.594595 | ||||||||
\(707\) | − | 1.50570e48i | − | 0.546524i | ||||||
\(708\) | −6.19621e47 | + | 1.06303e48i | −0.219564 | + | 0.376686i | ||||
\(709\) | 1.93768e48 | 0.670340 | 0.335170 | − | 0.942158i | \(-0.391206\pi\) | ||||
0.335170 | + | 0.942158i | \(0.391206\pi\) | |||||||
\(710\) | 3.88977e47i | 0.131381i | ||||||||
\(711\) | 2.34578e47 | + | 4.14183e47i | 0.0773579 | + | 0.136587i | ||||
\(712\) | 3.72214e46 | 0.0119849 | ||||||||
\(713\) | 1.28209e48i | 0.403084i | ||||||||
\(714\) | −1.86188e48 | − | 1.08526e48i | −0.571588 | − | 0.333169i | ||||
\(715\) | 5.39867e47 | 0.161839 | ||||||||
\(716\) | − | 2.76529e48i | − | 0.809506i | ||||||
\(717\) | 2.80945e48 | − | 4.81992e48i | 0.803147 | − | 1.37789i | ||||
\(718\) | 1.77455e48 | 0.495420 | ||||||||
\(719\) | 4.77661e48i | 1.30235i | 0.758926 | + | 0.651177i | \(0.225724\pi\) | ||||
−0.758926 | + | 0.651177i | \(0.774276\pi\) | |||||||
\(720\) | −3.79650e48 | + | 2.15020e48i | −1.01095 | + | 0.572568i | ||||
\(721\) | −7.18408e48 | −1.86841 | ||||||||
\(722\) | − | 1.21850e48i | − | 0.309522i | ||||||
\(723\) | 4.10787e48 | + | 2.39441e48i | 1.01921 | + | 0.594083i | ||||
\(724\) | 1.46371e48 | 0.354732 | ||||||||
\(725\) | − | 1.99554e48i | − | 0.472404i | ||||||
\(726\) | −6.30810e47 | + | 1.08222e48i | −0.145873 | + | 0.250262i | ||||
\(727\) | 5.41424e48 | 1.22307 | 0.611537 | − | 0.791216i | \(-0.290552\pi\) | ||||
0.611537 | + | 0.791216i | \(0.290552\pi\) | |||||||
\(728\) | − | 7.96800e47i | − | 0.175839i | ||||||
\(729\) | −4.63697e48 | − | 1.15188e47i | −0.999692 | − | 0.0248335i | ||||
\(730\) | −4.85782e48 | −1.02318 | ||||||||
\(731\) | 2.01005e48i | 0.413629i | ||||||||
\(732\) | −2.05455e48 | − | 1.19756e48i | −0.413074 | − | 0.240774i | ||||
\(733\) | 9.14560e47 | 0.179657 | 0.0898286 | − | 0.995957i | \(-0.471368\pi\) | ||||
0.0898286 | + | 0.995957i | \(0.471368\pi\) | |||||||
\(734\) | − | 2.61630e47i | − | 0.0502175i | ||||||
\(735\) | −2.66343e48 | + | 4.56942e48i | −0.499525 | + | 0.856991i | ||||
\(736\) | −3.11673e48 | −0.571184 | ||||||||
\(737\) | − | 2.80041e48i | − | 0.501505i | ||||||
\(738\) | −7.64632e47 | − | 1.35007e48i | −0.133812 | − | 0.236265i | ||||
\(739\) | −1.90775e48 | −0.326262 | −0.163131 | − | 0.986604i | \(-0.552159\pi\) | ||||
−0.163131 | + | 0.986604i | \(0.552159\pi\) | |||||||
\(740\) | 1.20260e49i | 2.00994i | ||||||||
\(741\) | −3.91335e47 | − | 2.28103e47i | −0.0639204 | − | 0.0372581i | ||||
\(742\) | 2.83158e48 | 0.452026 | ||||||||
\(743\) | − | 5.70257e48i | − | 0.889736i | −0.895596 | − | 0.444868i | \(-0.853251\pi\) | ||
0.895596 | − | 0.444868i | \(-0.146749\pi\) | |||||||
\(744\) | −1.36201e48 | + | 2.33668e48i | −0.207702 | + | 0.356336i | ||||
\(745\) | 1.04366e49 | 1.55562 | ||||||||
\(746\) | − | 5.49325e47i | − | 0.0800331i | ||||||
\(747\) | 9.43047e48 | − | 5.34108e48i | 1.34302 | − | 0.760639i | ||||
\(748\) | −3.99137e48 | −0.555642 | ||||||||
\(749\) | 3.20798e48i | 0.436557i | ||||||||
\(750\) | 5.13618e48 | + | 2.99379e48i | 0.683280 | + | 0.398272i | ||||
\(751\) | −6.57375e48 | −0.854937 | −0.427469 | − | 0.904030i | \(-0.640595\pi\) | ||||
−0.427469 | + | 0.904030i | \(0.640595\pi\) | |||||||
\(752\) | 2.08324e48i | 0.264872i | ||||||||
\(753\) | 6.54015e48 | − | 1.12204e49i | 0.812968 | − | 1.39474i | ||||
\(754\) | −1.30110e47 | −0.0158124 | ||||||||
\(755\) | − | 1.26951e49i | − | 1.50847i | ||||||
\(756\) | 1.16643e47 | − | 9.39255e48i | 0.0135515 | − | 1.09122i | ||||
\(757\) | −1.02690e49 | −1.16654 | −0.583269 | − | 0.812279i | \(-0.698227\pi\) | ||||
−0.583269 | + | 0.812279i | \(0.698227\pi\) | |||||||
\(758\) | 3.02445e48i | 0.335946i | ||||||||
\(759\) | 2.15018e48 | + | 1.25330e48i | 0.233541 | + | 0.136127i | ||||
\(760\) | 3.86744e48 | 0.410764 | ||||||||
\(761\) | 2.25359e48i | 0.234064i | 0.993128 | + | 0.117032i | \(0.0373380\pi\) | ||||
−0.993128 | + | 0.117032i | \(0.962662\pi\) | |||||||
\(762\) | −1.93810e48 | + | 3.32502e48i | −0.196853 | + | 0.337722i | ||||
\(763\) | 3.07303e48 | 0.305246 | ||||||||
\(764\) | − | 1.19767e49i | − | 1.16346i | ||||||
\(765\) | 1.41328e49 | + | 2.49535e49i | 1.34271 | + | 2.37076i | ||||
\(766\) | 4.34981e47 | 0.0404186 | ||||||||
\(767\) | 1.17201e48i | 0.106515i | ||||||||
\(768\) | −1.89226e47 | − | 1.10296e47i | −0.0168205 | − | 0.00980440i | ||||
\(769\) | −4.31209e48 | −0.374921 | −0.187460 | − | 0.982272i | \(-0.560026\pi\) | ||||
−0.187460 | + | 0.982272i | \(0.560026\pi\) | |||||||
\(770\) | − | 3.88964e48i | − | 0.330802i | ||||||
\(771\) | −2.11518e48 | + | 3.62883e48i | −0.175964 | + | 0.301885i | ||||
\(772\) | −5.43677e47 | −0.0442432 | ||||||||
\(773\) | 1.97513e49i | 1.57233i | 0.618015 | + | 0.786166i | \(0.287937\pi\) | ||||
−0.618015 | + | 0.786166i | \(0.712063\pi\) | |||||||
\(774\) | 1.07459e48 | − | 6.08610e47i | 0.0836849 | − | 0.0473961i | ||||
\(775\) | −1.84555e49 | −1.40604 | ||||||||
\(776\) | − | 6.26941e48i | − | 0.467280i | ||||||
\(777\) | −1.87706e49 | − | 1.09411e49i | −1.36874 | − | 0.797816i | ||||
\(778\) | −3.27942e47 | −0.0233961 | ||||||||
\(779\) | − | 3.82419e48i | − | 0.266933i | ||||||
\(780\) | −2.49396e48 | + | 4.27867e48i | −0.170326 | + | 0.292214i | ||||
\(781\) | −1.30152e48 | −0.0869727 | ||||||||
\(782\) | 5.23803e48i | 0.342494i | ||||||||
\(783\) | −3.28361e48 | − | 4.07781e46i | −0.210088 | − | 0.00260902i | ||||
\(784\) | 5.66675e48 | 0.354781 | ||||||||
\(785\) | − | 1.49887e49i | − | 0.918288i | ||||||
\(786\) | 1.72594e48 | + | 1.00602e48i | 0.103477 | + | 0.0603147i | ||||
\(787\) | 1.17946e49 | 0.692009 | 0.346005 | − | 0.938233i | \(-0.387538\pi\) | ||||
0.346005 | + | 0.938233i | \(0.387538\pi\) | |||||||
\(788\) | 1.82911e49i | 1.05025i | ||||||||
\(789\) | 1.01260e49 | − | 1.73723e49i | 0.569022 | − | 0.976221i | ||||
\(790\) | −1.80814e48 | −0.0994425 | ||||||||
\(791\) | 2.73123e49i | 1.47014i | ||||||||
\(792\) | 2.58740e48 | + | 4.56843e48i | 0.136312 | + | 0.240679i | ||||
\(793\) | −2.26518e48 | −0.116804 | ||||||||
\(794\) | − | 3.68544e48i | − | 0.186012i | ||||||
\(795\) | −3.25535e49 | − | 1.89749e49i | −1.60826 | − | 0.937427i | ||||
\(796\) | 1.21212e49 | 0.586169 | ||||||||
\(797\) | 1.32082e49i | 0.625248i | 0.949877 | + | 0.312624i | \(0.101208\pi\) | ||||
−0.949877 | + | 0.312624i | \(0.898792\pi\) | |||||||
\(798\) | −1.64344e48 | + | 2.81950e48i | −0.0761560 | + | 0.130654i | ||||
\(799\) | 1.36926e49 | 0.621143 | ||||||||
\(800\) | − | 4.48650e49i | − | 1.99241i | ||||||
\(801\) | 3.63681e47 | − | 2.05976e47i | 0.0158113 | − | 0.00895496i | ||||
\(802\) | −3.13493e47 | −0.0133433 | ||||||||
\(803\) | − | 1.62543e49i | − | 0.677336i | ||||||
\(804\) | 2.21944e49 | + | 1.29368e49i | 0.905506 | + | 0.527804i | ||||
\(805\) | 3.62125e49 | 1.44653 | ||||||||
\(806\) | 1.20331e48i | 0.0470631i | ||||||||
\(807\) | −2.31611e49 | + | 3.97354e49i | −0.886970 | + | 1.52170i | ||||
\(808\) | −7.72034e48 | −0.289496 | ||||||||
\(809\) | − | 2.42411e48i | − | 0.0890077i | −0.999009 | − | 0.0445039i | \(-0.985829\pi\) | ||
0.999009 | − | 0.0445039i | \(-0.0141707\pi\) | |||||||
\(810\) | 9.06121e48 | − | 1.51110e49i | 0.325792 | − | 0.543311i | ||||
\(811\) | 2.85977e49 | 1.00688 | 0.503439 | − | 0.864031i | \(-0.332068\pi\) | ||||
0.503439 | + | 0.864031i | \(0.332068\pi\) | |||||||
\(812\) | − | 6.65020e48i | − | 0.229289i | ||||||
\(813\) | −4.88000e48 | − | 2.84447e48i | −0.164771 | − | 0.0960422i | ||||
\(814\) | 5.67212e48 | 0.187556 | ||||||||
\(815\) | 1.98230e49i | 0.641933i | ||||||||
\(816\) | 1.54730e49 | − | 2.65457e49i | 0.490729 | − | 0.841901i | ||||
\(817\) | 3.04387e48 | 0.0945478 | ||||||||
\(818\) | 7.82839e48i | 0.238159i | ||||||||
\(819\) | −4.40934e48 | − | 7.78534e48i | −0.131385 | − | 0.231980i | ||||
\(820\) | −4.18119e49 | −1.22029 | ||||||||
\(821\) | − | 5.12068e49i | − | 1.46384i | −0.681391 | − | 0.731920i | \(-0.738624\pi\) | ||
0.681391 | − | 0.731920i | \(-0.261376\pi\) | |||||||
\(822\) | −2.10685e49 | − | 1.22805e49i | −0.589947 | − | 0.343870i | ||||
\(823\) | −2.01348e49 | −0.552269 | −0.276135 | − | 0.961119i | \(-0.589054\pi\) | ||||
−0.276135 | + | 0.961119i | \(0.589054\pi\) | |||||||
\(824\) | 3.68356e49i | 0.989705i | ||||||||
\(825\) | −1.80412e49 | + | 3.09516e49i | −0.474840 | + | 0.814641i | ||||
\(826\) | 8.44411e48 | 0.217717 | ||||||||
\(827\) | 5.62062e49i | 1.41968i | 0.704363 | + | 0.709840i | \(0.251233\pi\) | ||||
−0.704363 | + | 0.709840i | \(0.748767\pi\) | |||||||
\(828\) | −1.98659e49 | + | 1.12513e49i | −0.491577 | + | 0.278412i | ||||
\(829\) | −4.27281e49 | −1.03583 | −0.517913 | − | 0.855433i | \(-0.673291\pi\) | ||||
−0.517913 | + | 0.855433i | \(0.673291\pi\) | |||||||
\(830\) | 4.11693e49i | 0.977791i | ||||||||
\(831\) | −1.31123e49 | − | 7.64292e48i | −0.305113 | − | 0.177845i | ||||
\(832\) | 3.12893e48 | 0.0713344 | ||||||||
\(833\) | − | 3.72462e49i | − | 0.831987i | ||||||
\(834\) | 8.51345e48 | − | 1.46058e49i | 0.186330 | − | 0.319670i | ||||
\(835\) | 7.09146e48 | 0.152078 | ||||||||
\(836\) | 6.04424e48i | 0.127009i | ||||||||
\(837\) | −3.77132e47 | + | 3.03682e49i | −0.00776535 | + | 0.625298i | ||||
\(838\) | 9.98491e48 | 0.201463 | ||||||||
\(839\) | − | 4.10848e49i | − | 0.812321i | −0.913802 | − | 0.406161i | \(-0.866867\pi\) | ||
0.913802 | − | 0.406161i | \(-0.133133\pi\) | |||||||
\(840\) | 6.59995e49 | + | 3.84699e49i | 1.27877 | + | 0.745373i | ||||
\(841\) | 5.03413e49 | 0.955856 | ||||||||
\(842\) | − | 2.32565e49i | − | 0.432752i | ||||||
\(843\) | 2.96515e49 | − | 5.08705e49i | 0.540727 | − | 0.927677i | ||||
\(844\) | −8.33194e49 | −1.48910 | ||||||||
\(845\) | − | 9.81791e49i | − | 1.71971i | ||||||
\(846\) | −4.14590e48 | − | 7.32020e48i | −0.0711742 | − | 0.125669i | ||||
\(847\) | −6.09858e49 | −1.02615 | ||||||||
\(848\) | 4.03711e49i | 0.665796i | ||||||||
\(849\) | 9.34037e49 | + | 5.44434e49i | 1.50985 | + | 0.880064i | ||||
\(850\) | −7.54011e49 | −1.19469 | ||||||||
\(851\) | 5.28074e49i | 0.820148i | ||||||||
\(852\) | 6.01248e48 | − | 1.03151e49i | 0.0915336 | − | 0.157036i | ||||
\(853\) | 1.11189e50 | 1.65931 | 0.829654 | − | 0.558278i | \(-0.188538\pi\) | ||||
0.829654 | + | 0.558278i | \(0.188538\pi\) | |||||||
\(854\) | 1.63202e49i | 0.238749i | ||||||||
\(855\) | 3.77878e49 | − | 2.14016e49i | 0.541910 | − | 0.306919i | ||||
\(856\) | 1.64486e49 | 0.231247 | ||||||||
\(857\) | 6.36191e49i | 0.876826i | 0.898774 | + | 0.438413i | \(0.144459\pi\) | ||||
−0.898774 | + | 0.438413i | \(0.855541\pi\) | |||||||
\(858\) | 2.01806e48 | + | 1.17629e48i | 0.0272678 | + | 0.0158939i | ||||
\(859\) | −9.69012e49 | −1.28365 | −0.641823 | − | 0.766853i | \(-0.721822\pi\) | ||||
−0.641823 | + | 0.766853i | \(0.721822\pi\) | |||||||
\(860\) | − | 3.32802e49i | − | 0.432228i | ||||||
\(861\) | 3.80398e49 | − | 6.52615e49i | 0.484378 | − | 0.831005i | ||||
\(862\) | 2.84340e49 | 0.354989 | ||||||||
\(863\) | − | 6.57393e49i | − | 0.804714i | −0.915483 | − | 0.402357i | \(-0.868191\pi\) | ||
0.915483 | − | 0.402357i | \(-0.131809\pi\) | |||||||
\(864\) | −7.38245e49 | − | 9.16800e47i | −0.886067 | − | 0.0110038i | ||||
\(865\) | 1.81229e50 | 2.13282 | ||||||||
\(866\) | − | 4.24105e49i | − | 0.489406i | ||||||
\(867\) | −9.81277e49 | − | 5.71970e49i | −1.11037 | − | 0.647215i | ||||
\(868\) | −6.15038e49 | −0.682444 | ||||||||
\(869\) | − | 6.05006e48i | − | 0.0658299i | ||||||
\(870\) | 6.28176e48 | − | 1.07771e49i | 0.0670277 | − | 0.114993i | ||||
\(871\) | 2.44698e49 | 0.256048 | ||||||||
\(872\) | − | 1.57567e49i | − | 0.161690i | ||||||
\(873\) | −3.46937e49 | − | 6.12568e49i | −0.349147 | − | 0.616471i | ||||
\(874\) | 7.93209e48 | 0.0782876 | ||||||||
\(875\) | 2.89435e50i | 2.80166i | ||||||||
\(876\) | 1.28822e50 | + | 7.50882e49i | 1.22298 | + | 0.712856i | ||||
\(877\) | −1.50282e50 | −1.39931 | −0.699653 | − | 0.714483i | \(-0.746662\pi\) | ||||
−0.699653 | + | 0.714483i | \(0.746662\pi\) | |||||||
\(878\) | − | 1.65929e49i | − | 0.151536i | ||||||
\(879\) | −1.02772e50 | + | 1.76316e50i | −0.920581 | + | 1.57936i | ||||
\(880\) | 5.54563e49 | 0.487243 | ||||||||
\(881\) | − | 7.88501e48i | − | 0.0679535i | −0.999423 | − | 0.0339768i | \(-0.989183\pi\) | ||
0.999423 | − | 0.0339768i | \(-0.0108172\pi\) | |||||||
\(882\) | −1.99121e49 | + | 1.12775e49i | −0.168326 | + | 0.0953341i | ||||
\(883\) | −8.22028e49 | −0.681640 | −0.340820 | − | 0.940129i | \(-0.610705\pi\) | ||||
−0.340820 | + | 0.940129i | \(0.610705\pi\) | |||||||
\(884\) | − | 3.48763e49i | − | 0.283688i | ||||||
\(885\) | −9.70783e49 | − | 5.65852e49i | −0.774616 | − | 0.451510i | ||||
\(886\) | 2.95751e49 | 0.231501 | ||||||||
\(887\) | − | 1.37822e50i | − | 1.05832i | −0.848522 | − | 0.529159i | \(-0.822507\pi\) | ||
0.848522 | − | 0.529159i | \(-0.177493\pi\) | |||||||
\(888\) | −5.60993e49 | + | 9.62445e49i | −0.422607 | + | 0.725030i | ||||
\(889\) | −1.87373e50 | −1.38476 | ||||||||
\(890\) | 1.58767e48i | 0.0115115i | ||||||||
\(891\) | 5.05616e49 | + | 3.03189e49i | 0.359666 | + | 0.215671i | ||||
\(892\) | 1.48823e50 | 1.03864 | ||||||||
\(893\) | − | 2.07351e49i | − | 0.141981i | ||||||
\(894\) | 3.90126e49 | + | 2.27398e49i | 0.262100 | + | 0.152774i | ||||
\(895\) | 2.52533e50 | 1.66466 | ||||||||
\(896\) | − | 1.93133e50i | − | 1.24917i | ||||||
\(897\) | −1.09512e49 | + | 1.87881e49i | −0.0695011 | + | 0.119237i | ||||
\(898\) | −3.89369e49 | −0.242473 | ||||||||
\(899\) | 2.15016e49i | 0.131388i | ||||||||
\(900\) | −1.61962e50 | − | 2.85967e50i | −0.971158 | − | 1.71472i | ||||
\(901\) | 2.65350e50 | 1.56134 | ||||||||
\(902\) | 1.97208e49i | 0.113871i | ||||||||
\(903\) | 5.19450e49 | + | 3.02778e49i | 0.294342 | + | 0.171567i | ||||
\(904\) | 1.40041e50 | 0.778740 | ||||||||
\(905\) | 1.33670e50i | 0.729470i | ||||||||
\(906\) | 2.76606e49 | − | 4.74549e49i | 0.148143 | − | 0.254157i | ||||
\(907\) | −1.82011e50 | −0.956694 | −0.478347 | − | 0.878171i | \(-0.658764\pi\) | ||||
−0.478347 | + | 0.878171i | \(0.658764\pi\) | |||||||
\(908\) | 2.96520e50i | 1.52966i | ||||||||
\(909\) | −7.54335e49 | + | 4.27229e49i | −0.381925 | + | 0.216309i | ||||
\(910\) | 3.39874e49 | 0.168894 | ||||||||
\(911\) | − | 3.27498e50i | − | 1.59734i | −0.601772 | − | 0.798668i | \(-0.705538\pi\) | ||
0.601772 | − | 0.798668i | \(-0.294462\pi\) | |||||||
\(912\) | −4.01988e49 | − | 2.34312e49i | −0.192442 | − | 0.112171i | ||||
\(913\) | −1.37753e50 | −0.647287 | ||||||||
\(914\) | 9.99546e49i | 0.461018i | ||||||||
\(915\) | 1.09364e50 | − | 1.87626e50i | 0.495126 | − | 0.849444i | ||||
\(916\) | 2.50278e50 | 1.11224 | ||||||||
\(917\) | 9.72607e49i | 0.424286i | ||||||||
\(918\) | −1.54079e48 | + | 1.24071e50i | −0.00659810 | + | 0.531306i | ||||
\(919\) | 2.90746e50 | 1.22222 | 0.611111 | − | 0.791545i | \(-0.290723\pi\) | ||||
0.611111 | + | 0.791545i | \(0.290723\pi\) | |||||||
\(920\) | − | 1.85676e50i | − | 0.766237i | ||||||
\(921\) | 2.85319e49 | + | 1.66308e49i | 0.115589 | + | 0.0673750i | ||||
\(922\) | 1.83720e49 | 0.0730687 | ||||||||
\(923\) | − | 1.13726e49i | − | 0.0444048i | ||||||
\(924\) | −6.01229e49 | + | 1.03148e50i | −0.230471 | + | 0.395399i | ||||
\(925\) | −7.60158e50 | −2.86085 | ||||||||
\(926\) | 5.39570e49i | 0.199371i | ||||||||
\(927\) | 2.03841e50 | + | 3.59912e50i | 0.739498 | + | 1.30569i | ||||
\(928\) | −5.22699e49 | −0.186181 | ||||||||
\(929\) | 5.81572e49i | 0.203393i | 0.994815 | + | 0.101697i | \(0.0324271\pi\) | ||||
−0.994815 | + | 0.101697i | \(0.967573\pi\) | |||||||
\(930\) | −9.96707e49 | − | 5.80963e49i | −0.342261 | − | 0.199498i | ||||
\(931\) | −5.64029e49 | −0.190176 | ||||||||
\(932\) | 6.36894e49i | 0.210861i | ||||||||
\(933\) | 1.19820e50 | − | 2.05565e50i | 0.389531 | − | 0.668284i | ||||
\(934\) | −2.28037e49 | −0.0727962 | ||||||||
\(935\) | − | 3.64501e50i | − | 1.14262i | ||||||
\(936\) | −3.99186e49 | + | 2.26084e49i | −0.122881 | + | 0.0695955i | ||||
\(937\) | −3.18119e50 | −0.961648 | −0.480824 | − | 0.876817i | \(-0.659662\pi\) | ||||
−0.480824 | + | 0.876817i | \(0.659662\pi\) | |||||||
\(938\) | − | 1.76300e50i | − | 0.523365i | ||||||
\(939\) | −2.16275e50 | − | 1.26063e50i | −0.630509 | − | 0.367513i | ||||
\(940\) | −2.26708e50 | −0.649071 | ||||||||
\(941\) | 5.90386e50i | 1.66002i | 0.557751 | + | 0.830008i | \(0.311664\pi\) | ||||
−0.557751 | + | 0.830008i | \(0.688336\pi\) | |||||||
\(942\) | 3.26580e49 | − | 5.60285e49i | 0.0901830 | − | 0.154719i | ||||
\(943\) | −1.83600e50 | −0.497937 | ||||||||
\(944\) | 1.20391e50i | 0.320679i | ||||||||
\(945\) | 8.57750e50 | + | 1.06521e49i | 2.24398 | + | 0.0278673i | ||||
\(946\) | −1.56968e49 | −0.0403330 | ||||||||
\(947\) | 4.83635e50i | 1.22059i | 0.792176 | + | 0.610293i | \(0.208948\pi\) | ||||
−0.792176 | + | 0.610293i | \(0.791052\pi\) | |||||||
\(948\) | 4.79492e49 | + | 2.79487e49i | 0.118861 | + | 0.0692820i | ||||
\(949\) | 1.42029e50 | 0.345821 | ||||||||
\(950\) | 1.14182e50i | 0.273084i | ||||||||
\(951\) | 3.75697e49 | − | 6.44550e49i | 0.0882610 | − | 0.151422i | ||||
\(952\) | −5.37974e50 | −1.24146 | ||||||||
\(953\) | 1.06655e50i | 0.241770i | 0.992667 | + | 0.120885i | \(0.0385732\pi\) | ||||
−0.992667 | + | 0.120885i | \(0.961427\pi\) | |||||||
\(954\) | −8.03435e49 | − | 1.41858e50i | −0.178907 | − | 0.315888i | ||||
\(955\) | 1.09374e51 | 2.39253 | ||||||||
\(956\) | − | 6.50489e50i | − | 1.39783i | ||||||
\(957\) | 3.60601e49 | + | 2.10188e49i | 0.0761245 | + | 0.0443716i | ||||
\(958\) | 1.06919e50 | 0.221740 | ||||||||
\(959\) | − | 1.18726e51i | − | 2.41896i | ||||||
\(960\) | −1.51066e50 | + | 2.59171e50i | −0.302383 | + | 0.518771i | ||||
\(961\) | −3.09652e50 | −0.608943 | ||||||||
\(962\) | 4.95625e49i | 0.0957585i | ||||||||
\(963\) | 1.60715e50 | − | 9.10235e49i | 0.305078 | − | 0.172785i | ||||
\(964\) | 5.54392e50 | 1.03397 | ||||||||
\(965\) | − | 4.96499e49i | − | 0.0909816i | ||||||
\(966\) | 1.35365e50 | + | 7.89016e49i | 0.243721 | + | 0.142061i | ||||
\(967\) | −3.36710e50 | −0.595670 | −0.297835 | − | 0.954617i | \(-0.596265\pi\) | ||||
−0.297835 | + | 0.954617i | \(0.596265\pi\) | |||||||
\(968\) | 3.12699e50i | 0.543557i | ||||||||
\(969\) | −1.54008e50 | + | 2.64217e50i | −0.263050 | + | 0.451291i | ||||
\(970\) | 2.67421e50 | 0.448823 | ||||||||
\(971\) | − | 2.84226e50i | − | 0.468745i | −0.972147 | − | 0.234372i | \(-0.924697\pi\) | ||
0.972147 | − | 0.234372i | \(-0.0753035\pi\) | |||||||
\(972\) | −4.73863e50 | + | 2.60661e50i | −0.767939 | + | 0.422425i | ||||
\(973\) | 8.23068e50 | 1.31074 | ||||||||
\(974\) | 2.99541e50i | 0.468763i | ||||||||
\(975\) | −2.70453e50 | − | 1.57642e50i | −0.415923 | − | 0.242434i | ||||
\(976\) | −2.32684e50 | −0.351657 | ||||||||
\(977\) | − | 3.22972e50i | − | 0.479686i | −0.970812 | − | 0.239843i | \(-0.922904\pi\) | ||
0.970812 | − | 0.239843i | \(-0.0770959\pi\) | |||||||
\(978\) | −4.31913e49 | + | 7.40995e49i | −0.0630428 | + | 0.108157i | ||||
\(979\) | −5.31236e48 | −0.00762048 | ||||||||
\(980\) | 6.16682e50i | 0.869396i | ||||||||
\(981\) | −8.71943e49 | − | 1.53955e50i | −0.120813 | − | 0.213314i | ||||
\(982\) | −2.18030e50 | −0.296907 | ||||||||
\(983\) | 6.30288e50i | 0.843586i | 0.906692 | + | 0.421793i | \(0.138599\pi\) | ||||
−0.906692 | + | 0.421793i | \(0.861401\pi\) | |||||||
\(984\) | −3.34622e50 | − | 1.95045e50i | −0.440188 | − | 0.256578i | ||||
\(985\) | −1.67038e51 | −2.15973 | ||||||||
\(986\) | 8.78458e49i | 0.111638i | ||||||||
\(987\) | 2.06255e50 | − | 3.53853e50i | 0.257640 | − | 0.442010i | ||||
\(988\) | −5.28140e49 | −0.0648457 | ||||||||
\(989\) | − | 1.46137e50i | − | 0.176369i | ||||||
\(990\) | −1.94866e50 | + | 1.10365e50i | −0.231173 | + | 0.130928i | ||||
\(991\) | 9.39428e50 | 1.09550 | 0.547749 | − | 0.836643i | \(-0.315485\pi\) | ||||
0.547749 | + | 0.836643i | \(0.315485\pi\) | |||||||
\(992\) | 4.83414e50i | 0.554141i | ||||||||
\(993\) | −7.65774e50 | − | 4.46357e50i | −0.862906 | − | 0.502973i | ||||
\(994\) | −8.19373e49 | −0.0907638 | ||||||||
\(995\) | 1.10693e51i | 1.20540i | ||||||||
\(996\) | 6.36361e50 | − | 1.09175e51i | 0.681231 | − | 1.16873i | ||||
\(997\) | 1.61786e49 | 0.0170264 | 0.00851318 | − | 0.999964i | \(-0.497290\pi\) | ||||
0.00851318 | + | 0.999964i | \(0.497290\pi\) | |||||||
\(998\) | − | 3.89078e50i | − | 0.402548i | ||||||
\(999\) | −1.55336e49 | + | 1.25082e51i | −0.0158000 | + | 1.27228i |
(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 | 3.35.b.a.2.6 | yes | 10 | |
3.2 | odd | 2 | inner | 3.35.b.a.2.5 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.35.b.a.2.5 | ✓ | 10 | 3.2 | odd | 2 | inner | |
3.35.b.a.2.6 | yes | 10 | 1.1 | even | 1 | trivial |