Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,9,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.d (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: | \(3.25902888049\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 78x^{4} - 514x^{3} + 4237x^{2} - 18333x + 238980 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.6 | ||
Root | \(-4.53916 + 7.17456i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.9.d.b.3.5 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.07833 | + | 14.3491i | 0.442396 | + | 0.896820i | ||||
\(3\) | −117.615 | −1.45204 | −0.726021 | − | 0.687672i | \(-0.758633\pi\) | ||||
−0.726021 | + | 0.687672i | \(0.758633\pi\) | |||||||
\(4\) | −155.795 | + | 203.136i | −0.608572 | + | 0.793498i | ||||
\(5\) | − | 306.178i | − | 0.489884i | −0.969538 | − | 0.244942i | \(-0.921231\pi\) | ||
0.969538 | − | 0.244942i | \(-0.0787690\pi\) | |||||||
\(6\) | −832.521 | − | 1687.68i | −0.642377 | − | 1.30222i | ||||
\(7\) | 4321.70i | 1.79996i | 0.435934 | + | 0.899979i | \(0.356418\pi\) | ||||
−0.435934 | + | 0.899979i | \(0.643582\pi\) | |||||||
\(8\) | −4017.58 | − | 797.653i | −0.980855 | − | 0.194740i | ||||
\(9\) | 7272.39 | 1.10843 | ||||||||
\(10\) | 4393.38 | − | 2167.23i | 0.439338 | − | 0.216723i | ||||
\(11\) | 7172.95 | 0.489922 | 0.244961 | − | 0.969533i | \(-0.421225\pi\) | ||||
0.244961 | + | 0.969533i | \(0.421225\pi\) | |||||||
\(12\) | 18323.8 | − | 23891.9i | 0.883673 | − | 1.15219i | ||||
\(13\) | 5492.75i | 0.192317i | 0.995366 | + | 0.0961583i | \(0.0306555\pi\) | ||||
−0.995366 | + | 0.0961583i | \(0.969344\pi\) | |||||||
\(14\) | −62012.5 | + | 30590.4i | −1.61424 | + | 0.796293i | ||||
\(15\) | 36011.2i | 0.711333i | ||||||||
\(16\) | −16992.1 | − | 63294.8i | −0.259280 | − | 0.965802i | ||||
\(17\) | 6553.97 | 0.0784709 | 0.0392354 | − | 0.999230i | \(-0.487508\pi\) | ||||
0.0392354 | + | 0.999230i | \(0.487508\pi\) | |||||||
\(18\) | 51476.3 | + | 104352.i | 0.490363 | + | 0.994059i | ||||
\(19\) | −162847. | −1.24959 | −0.624793 | − | 0.780791i | \(-0.714817\pi\) | ||||
−0.624793 | + | 0.780791i | \(0.714817\pi\) | |||||||
\(20\) | 62195.6 | + | 47700.8i | 0.388722 | + | 0.298130i | ||||
\(21\) | − | 508298.i | − | 2.61361i | ||||||
\(22\) | 50772.5 | + | 102926.i | 0.216739 | + | 0.439372i | ||||
\(23\) | 310889.i | 1.11095i | 0.831534 | + | 0.555474i | \(0.187463\pi\) | ||||
−0.831534 | + | 0.555474i | \(0.812537\pi\) | |||||||
\(24\) | 472530. | + | 93816.3i | 1.42424 | + | 0.282770i | ||||
\(25\) | 296880. | 0.760013 | ||||||||
\(26\) | −78816.2 | + | 38879.5i | −0.172473 | + | 0.0850800i | ||||
\(27\) | −83670.1 | −0.157440 | ||||||||
\(28\) | −877890. | − | 673297.i | −1.42826 | − | 1.09540i | ||||
\(29\) | 586403.i | 0.829095i | 0.910028 | + | 0.414547i | \(0.136060\pi\) | ||||
−0.910028 | + | 0.414547i | \(0.863940\pi\) | |||||||
\(30\) | −516729. | + | 254899.i | −0.637937 | + | 0.314690i | ||||
\(31\) | − | 225390.i | − | 0.244055i | −0.992527 | − | 0.122027i | \(-0.961060\pi\) | ||
0.992527 | − | 0.122027i | \(-0.0389396\pi\) | |||||||
\(32\) | 787949. | − | 691844.i | 0.751447 | − | 0.659794i | ||||
\(33\) | −843649. | −0.711388 | ||||||||
\(34\) | 46391.1 | + | 94043.6i | 0.0347152 | + | 0.0703743i | ||||
\(35\) | 1.32321e6 | 0.881771 | ||||||||
\(36\) | −1.13300e6 | + | 1.47728e6i | −0.674558 | + | 0.879535i | ||||
\(37\) | 1.84804e6i | 0.986061i | 0.870012 | + | 0.493030i | \(0.164111\pi\) | ||||
−0.870012 | + | 0.493030i | \(0.835889\pi\) | |||||||
\(38\) | −1.15269e6 | − | 2.33671e6i | −0.552811 | − | 1.12065i | ||||
\(39\) | − | 646033.i | − | 0.279252i | ||||||
\(40\) | −244224. | + | 1.23009e6i | −0.0953999 | + | 0.480505i | ||||
\(41\) | 2.40081e6 | 0.849614 | 0.424807 | − | 0.905284i | \(-0.360342\pi\) | ||||
0.424807 | + | 0.905284i | \(0.360342\pi\) | |||||||
\(42\) | 7.29363e6 | − | 3.59790e6i | 2.34394 | − | 1.15625i | ||||
\(43\) | −687442. | −0.201077 | −0.100538 | − | 0.994933i | \(-0.532057\pi\) | ||||
−0.100538 | + | 0.994933i | \(0.532057\pi\) | |||||||
\(44\) | −1.11751e6 | + | 1.45708e6i | −0.298153 | + | 0.388752i | ||||
\(45\) | − | 2.22664e6i | − | 0.543001i | ||||||
\(46\) | −4.46098e6 | + | 2.20057e6i | −0.996321 | + | 0.491479i | ||||
\(47\) | − | 5.71500e6i | − | 1.17118i | −0.810606 | − | 0.585592i | \(-0.800862\pi\) | ||
0.810606 | − | 0.585592i | \(-0.199138\pi\) | |||||||
\(48\) | 1.99854e6 | + | 7.44445e6i | 0.376485 | + | 1.40239i | ||||
\(49\) | −1.29123e7 | −2.23985 | ||||||||
\(50\) | 2.10142e6 | + | 4.25997e6i | 0.336227 | + | 0.681595i | ||||
\(51\) | −770847. | −0.113943 | ||||||||
\(52\) | −1.11577e6 | − | 855741.i | −0.152603 | − | 0.117039i | ||||
\(53\) | 7.20466e6i | 0.913082i | 0.889702 | + | 0.456541i | \(0.150912\pi\) | ||||
−0.889702 | + | 0.456541i | \(0.849088\pi\) | |||||||
\(54\) | −592244. | − | 1.20059e6i | −0.0696508 | − | 0.141195i | ||||
\(55\) | − | 2.19620e6i | − | 0.240005i | ||||||
\(56\) | 3.44722e6 | − | 1.73628e7i | 0.350523 | − | 1.76550i | ||||
\(57\) | 1.91533e7 | 1.81445 | ||||||||
\(58\) | −8.41437e6 | + | 4.15075e6i | −0.743549 | + | 0.366788i | ||||
\(59\) | 4.61794e6 | 0.381101 | 0.190551 | − | 0.981677i | \(-0.438973\pi\) | ||||
0.190551 | + | 0.981677i | \(0.438973\pi\) | |||||||
\(60\) | −7.31516e6 | − | 5.61035e6i | −0.564441 | − | 0.432897i | ||||
\(61\) | − | 6.84870e6i | − | 0.494640i | −0.968934 | − | 0.247320i | \(-0.920450\pi\) | ||
0.968934 | − | 0.247320i | \(-0.0795498\pi\) | |||||||
\(62\) | 3.23415e6 | − | 1.59538e6i | 0.218873 | − | 0.107969i | ||||
\(63\) | 3.14291e7i | 1.99512i | ||||||||
\(64\) | 1.55047e7 | + | 6.40928e6i | 0.924153 | + | 0.382023i | ||||
\(65\) | 1.68176e6 | 0.0942129 | ||||||||
\(66\) | −5.97163e6 | − | 1.21056e7i | −0.314715 | − | 0.637987i | ||||
\(67\) | −6.79128e6 | −0.337018 | −0.168509 | − | 0.985700i | \(-0.553895\pi\) | ||||
−0.168509 | + | 0.985700i | \(0.553895\pi\) | |||||||
\(68\) | −1.02107e6 | + | 1.33134e6i | −0.0477552 | + | 0.0622665i | ||||
\(69\) | − | 3.65653e7i | − | 1.61314i | ||||||
\(70\) | 9.36610e6 | + | 1.89869e7i | 0.390091 | + | 0.790790i | ||||
\(71\) | 1.78351e7i | 0.701847i | 0.936404 | + | 0.350924i | \(0.114132\pi\) | ||||
−0.936404 | + | 0.350924i | \(0.885868\pi\) | |||||||
\(72\) | −2.92174e7 | − | 5.80084e6i | −1.08721 | − | 0.215855i | ||||
\(73\) | 9.60923e6 | 0.338374 | 0.169187 | − | 0.985584i | \(-0.445886\pi\) | ||||
0.169187 | + | 0.985584i | \(0.445886\pi\) | |||||||
\(74\) | −2.65177e7 | + | 1.30810e7i | −0.884319 | + | 0.436229i | ||||
\(75\) | −3.49177e7 | −1.10357 | ||||||||
\(76\) | 2.53707e7 | − | 3.30801e7i | 0.760463 | − | 0.991544i | ||||
\(77\) | 3.09993e7i | 0.881839i | ||||||||
\(78\) | 9.27000e6 | − | 4.57283e6i | 0.250439 | − | 0.123540i | ||||
\(79\) | − | 4.84326e7i | − | 1.24345i | −0.783234 | − | 0.621727i | \(-0.786431\pi\) | ||
0.783234 | − | 0.621727i | \(-0.213569\pi\) | |||||||
\(80\) | −1.93795e7 | + | 5.20262e6i | −0.473131 | + | 0.127017i | ||||
\(81\) | −3.78732e7 | −0.879817 | ||||||||
\(82\) | 1.69937e7 | + | 3.44495e7i | 0.375866 | + | 0.761951i | ||||
\(83\) | 6.07030e7 | 1.27908 | 0.639540 | − | 0.768758i | \(-0.279125\pi\) | ||||
0.639540 | + | 0.768758i | \(0.279125\pi\) | |||||||
\(84\) | 1.03253e8 | + | 7.91901e7i | 2.07390 | + | 1.59057i | ||||
\(85\) | − | 2.00668e6i | − | 0.0384417i | ||||||
\(86\) | −4.86594e6 | − | 9.86419e6i | −0.0889556 | − | 0.180330i | ||||
\(87\) | − | 6.89700e7i | − | 1.20388i | ||||||
\(88\) | −2.88179e7 | − | 5.72153e6i | −0.480543 | − | 0.0954072i | ||||
\(89\) | −2.61120e7 | −0.416179 | −0.208090 | − | 0.978110i | \(-0.566725\pi\) | ||||
−0.208090 | + | 0.978110i | \(0.566725\pi\) | |||||||
\(90\) | 3.19504e7 | − | 1.57609e7i | 0.486974 | − | 0.240221i | ||||
\(91\) | −2.37380e7 | −0.346162 | ||||||||
\(92\) | −6.31526e7 | − | 4.84348e7i | −0.881536 | − | 0.676092i | ||||
\(93\) | 2.65093e7i | 0.354378i | ||||||||
\(94\) | 8.20053e7 | − | 4.04527e7i | 1.05034 | − | 0.518127i | ||||
\(95\) | 4.98602e7i | 0.612152i | ||||||||
\(96\) | −9.26750e7 | + | 8.13715e7i | −1.09113 | + | 0.958048i | ||||
\(97\) | 9.48587e7 | 1.07150 | 0.535748 | − | 0.844378i | \(-0.320030\pi\) | ||||
0.535748 | + | 0.844378i | \(0.320030\pi\) | |||||||
\(98\) | −9.13972e7 | − | 1.85280e8i | −0.990898 | − | 2.00874i | ||||
\(99\) | 5.21645e7 | 0.543043 | ||||||||
\(100\) | −4.62523e7 | + | 6.03069e7i | −0.462523 | + | 0.603069i | ||||
\(101\) | 1.53591e8i | 1.47598i | 0.674813 | + | 0.737989i | \(0.264224\pi\) | ||||
−0.674813 | + | 0.737989i | \(0.735776\pi\) | |||||||
\(102\) | −5.45631e6 | − | 1.10610e7i | −0.0504079 | − | 0.102186i | ||||
\(103\) | 9.23743e7i | 0.820734i | 0.911920 | + | 0.410367i | \(0.134599\pi\) | ||||
−0.911920 | + | 0.410367i | \(0.865401\pi\) | |||||||
\(104\) | 4.38131e6 | − | 2.20676e7i | 0.0374517 | − | 0.188635i | ||||
\(105\) | −1.55630e8 | −1.28037 | ||||||||
\(106\) | −1.03380e8 | + | 5.09969e7i | −0.818870 | + | 0.403943i | ||||
\(107\) | −1.90283e7 | −0.145166 | −0.0725829 | − | 0.997362i | \(-0.523124\pi\) | ||||
−0.0725829 | + | 0.997362i | \(0.523124\pi\) | |||||||
\(108\) | 1.30353e7 | − | 1.69964e7i | 0.0958136 | − | 0.124928i | ||||
\(109\) | − | 1.38190e8i | − | 0.978975i | −0.872010 | − | 0.489487i | \(-0.837184\pi\) | ||
0.872010 | − | 0.489487i | \(-0.162816\pi\) | |||||||
\(110\) | 3.15135e7 | − | 1.55454e7i | 0.215241 | − | 0.106177i | ||||
\(111\) | − | 2.17358e8i | − | 1.43180i | ||||||
\(112\) | 2.73541e8 | − | 7.34349e7i | 1.73840 | − | 0.466692i | ||||
\(113\) | 1.95936e8 | 1.20171 | 0.600855 | − | 0.799358i | \(-0.294827\pi\) | ||||
0.600855 | + | 0.799358i | \(0.294827\pi\) | |||||||
\(114\) | 1.35574e8 | + | 2.74834e8i | 0.802705 | + | 1.62724i | ||||
\(115\) | 9.51873e7 | 0.544236 | ||||||||
\(116\) | −1.19119e8 | − | 9.13584e7i | −0.657885 | − | 0.504564i | ||||
\(117\) | 3.99454e7i | 0.213169i | ||||||||
\(118\) | 3.26873e7 | + | 6.62634e7i | 0.168597 | + | 0.341779i | ||||
\(119\) | 2.83243e7i | 0.141244i | ||||||||
\(120\) | 2.87245e7 | − | 1.44678e8i | 0.138525 | − | 0.697714i | ||||
\(121\) | −1.62908e8 | −0.759976 | ||||||||
\(122\) | 9.82729e7 | − | 4.84774e7i | 0.443603 | − | 0.218826i | ||||
\(123\) | −2.82372e8 | −1.23368 | ||||||||
\(124\) | 4.57847e7 | + | 3.51145e7i | 0.193657 | + | 0.148525i | ||||
\(125\) | − | 2.10499e8i | − | 0.862203i | ||||||
\(126\) | −4.50979e8 | + | 2.22465e8i | −1.78926 | + | 0.882632i | ||||
\(127\) | 4.08192e8i | 1.56910i | 0.620069 | + | 0.784548i | \(0.287105\pi\) | ||||
−0.620069 | + | 0.784548i | \(0.712895\pi\) | |||||||
\(128\) | 1.77800e7 | + | 2.67846e8i | 0.0662356 | + | 0.997804i | ||||
\(129\) | 8.08538e7 | 0.291972 | ||||||||
\(130\) | 1.19040e7 | + | 2.41318e7i | 0.0416794 | + | 0.0844920i | ||||
\(131\) | 6.22874e6 | 0.0211502 | 0.0105751 | − | 0.999944i | \(-0.496634\pi\) | ||||
0.0105751 | + | 0.999944i | \(0.496634\pi\) | |||||||
\(132\) | 1.31436e8 | − | 1.71375e8i | 0.432931 | − | 0.564485i | ||||
\(133\) | − | 7.03776e8i | − | 2.24920i | ||||||
\(134\) | −4.80709e7 | − | 9.74489e7i | −0.149095 | − | 0.302244i | ||||
\(135\) | 2.56179e7i | 0.0771274i | ||||||||
\(136\) | −2.63311e7 | − | 5.22779e6i | −0.0769685 | − | 0.0152814i | ||||
\(137\) | 1.41077e8 | 0.400475 | 0.200237 | − | 0.979747i | \(-0.435829\pi\) | ||||
0.200237 | + | 0.979747i | \(0.435829\pi\) | |||||||
\(138\) | 5.24680e8 | − | 2.58821e8i | 1.44670 | − | 0.713648i | ||||
\(139\) | −6.47844e8 | −1.73545 | −0.867723 | − | 0.497049i | \(-0.834417\pi\) | ||||
−0.867723 | + | 0.497049i | \(0.834417\pi\) | |||||||
\(140\) | −2.06148e8 | + | 2.68790e8i | −0.536621 | + | 0.699684i | ||||
\(141\) | 6.72173e8i | 1.70061i | ||||||||
\(142\) | −2.55918e8 | + | 1.26243e8i | −0.629431 | + | 0.310494i | ||||
\(143\) | 3.93992e7i | 0.0942201i | ||||||||
\(144\) | −1.23573e8 | − | 4.60304e8i | −0.287392 | − | 1.07052i | ||||
\(145\) | 1.79544e8 | 0.406161 | ||||||||
\(146\) | 6.80173e7 | + | 1.37884e8i | 0.149695 | + | 0.303461i | ||||
\(147\) | 1.51868e9 | 3.25235 | ||||||||
\(148\) | −3.75402e8 | − | 2.87914e8i | −0.782438 | − | 0.600089i | ||||
\(149\) | 5.50744e8i | 1.11739i | 0.829373 | + | 0.558695i | \(0.188698\pi\) | ||||
−0.829373 | + | 0.558695i | \(0.811302\pi\) | |||||||
\(150\) | −2.47159e8 | − | 5.01038e8i | −0.488215 | − | 0.989705i | ||||
\(151\) | − | 4.05487e7i | − | 0.0779954i | −0.999239 | − | 0.0389977i | \(-0.987584\pi\) | ||
0.999239 | − | 0.0389977i | \(-0.0124165\pi\) | |||||||
\(152\) | 6.54252e8 | + | 1.29896e8i | 1.22566 | + | 0.243344i | ||||
\(153\) | 4.76630e7 | 0.0869792 | ||||||||
\(154\) | −4.44813e8 | + | 2.19423e8i | −0.790851 | + | 0.390122i | ||||
\(155\) | −6.90094e7 | −0.119559 | ||||||||
\(156\) | 1.31232e8 | + | 1.00648e8i | 0.221586 | + | 0.169945i | ||||
\(157\) | 2.93738e8i | 0.483460i | 0.970344 | + | 0.241730i | \(0.0777149\pi\) | ||||
−0.970344 | + | 0.241730i | \(0.922285\pi\) | |||||||
\(158\) | 6.94965e8 | − | 3.42822e8i | 1.11515 | − | 0.550098i | ||||
\(159\) | − | 8.47379e8i | − | 1.32583i | ||||||
\(160\) | −2.11827e8 | − | 2.41252e8i | −0.323223 | − | 0.368122i | ||||
\(161\) | −1.34357e9 | −1.99966 | ||||||||
\(162\) | −2.68079e8 | − | 5.43448e8i | −0.389227 | − | 0.789038i | ||||
\(163\) | −4.61580e8 | −0.653878 | −0.326939 | − | 0.945045i | \(-0.606017\pi\) | ||||
−0.326939 | + | 0.945045i | \(0.606017\pi\) | |||||||
\(164\) | −3.74033e8 | + | 4.87689e8i | −0.517052 | + | 0.674168i | ||||
\(165\) | 2.58307e8i | 0.348498i | ||||||||
\(166\) | 4.29676e8 | + | 8.71034e8i | 0.565859 | + | 1.14710i | ||||
\(167\) | − | 1.08707e9i | − | 1.39762i | −0.715306 | − | 0.698811i | \(-0.753713\pi\) | ||
0.715306 | − | 0.698811i | \(-0.246287\pi\) | |||||||
\(168\) | −4.05446e8 | + | 2.04213e9i | −0.508974 | + | 2.56358i | ||||
\(169\) | 7.85560e8 | 0.963014 | ||||||||
\(170\) | 2.87941e7 | − | 1.42039e7i | 0.0344752 | − | 0.0170064i | ||||
\(171\) | −1.18429e9 | −1.38507 | ||||||||
\(172\) | 1.07100e8 | − | 1.39644e8i | 0.122370 | − | 0.159554i | ||||
\(173\) | − | 9.72883e8i | − | 1.08612i | −0.839695 | − | 0.543058i | \(-0.817266\pi\) | ||
0.839695 | − | 0.543058i | \(-0.182734\pi\) | |||||||
\(174\) | 9.89659e8 | − | 4.88193e8i | 1.07966 | − | 0.532591i | ||||
\(175\) | 1.28303e9i | 1.36799i | ||||||||
\(176\) | −1.21884e8 | − | 4.54011e8i | −0.127027 | − | 0.473168i | ||||
\(177\) | −5.43141e8 | −0.553375 | ||||||||
\(178\) | −1.84829e8 | − | 3.74684e8i | −0.184116 | − | 0.373238i | ||||
\(179\) | 1.52312e9 | 1.48362 | 0.741811 | − | 0.670610i | \(-0.233967\pi\) | ||||
0.741811 | + | 0.670610i | \(0.233967\pi\) | |||||||
\(180\) | 4.52310e8 | + | 3.46899e8i | 0.430870 | + | 0.330455i | ||||
\(181\) | − | 2.73420e8i | − | 0.254751i | −0.991855 | − | 0.127375i | \(-0.959345\pi\) | ||
0.991855 | − | 0.127375i | \(-0.0406553\pi\) | |||||||
\(182\) | −1.68026e8 | − | 3.40620e8i | −0.153140 | − | 0.310445i | ||||
\(183\) | 8.05513e8i | 0.718238i | ||||||||
\(184\) | 2.47982e8 | − | 1.24902e9i | 0.216346 | − | 1.08968i | ||||
\(185\) | 5.65828e8 | 0.483056 | ||||||||
\(186\) | −3.80386e8 | + | 1.87642e8i | −0.317813 | + | 0.156775i | ||||
\(187\) | 4.70113e7 | 0.0384446 | ||||||||
\(188\) | 1.16092e9 | + | 8.90366e8i | 0.929333 | + | 0.712750i | ||||
\(189\) | − | 3.61597e8i | − | 0.283385i | ||||||
\(190\) | −7.15450e8 | + | 3.52927e8i | −0.548990 | + | 0.270813i | ||||
\(191\) | − | 1.85158e9i | − | 1.39126i | −0.718401 | − | 0.695630i | \(-0.755125\pi\) | ||
0.718401 | − | 0.695630i | \(-0.244875\pi\) | |||||||
\(192\) | −1.82359e9 | − | 7.53830e8i | −1.34191 | − | 0.554713i | ||||
\(193\) | 5.49166e8 | 0.395799 | 0.197899 | − | 0.980222i | \(-0.436588\pi\) | ||||
0.197899 | + | 0.980222i | \(0.436588\pi\) | |||||||
\(194\) | 6.71441e8 | + | 1.36114e9i | 0.474025 | + | 0.960939i | ||||
\(195\) | −1.97801e8 | −0.136801 | ||||||||
\(196\) | 2.01166e9 | − | 2.62294e9i | 1.36311 | − | 1.77731i | ||||
\(197\) | 1.68731e9i | 1.12029i | 0.828396 | + | 0.560143i | \(0.189254\pi\) | ||||
−0.828396 | + | 0.560143i | \(0.810746\pi\) | |||||||
\(198\) | 3.69237e8 | + | 7.48514e8i | 0.240240 | + | 0.487012i | ||||
\(199\) | 1.99216e9i | 1.27032i | 0.772382 | + | 0.635158i | \(0.219065\pi\) | ||||
−0.772382 | + | 0.635158i | \(0.780935\pi\) | |||||||
\(200\) | −1.19274e9 | − | 2.36808e8i | −0.745463 | − | 0.148005i | ||||
\(201\) | 7.98759e8 | 0.489364 | ||||||||
\(202\) | −2.20389e9 | + | 1.08717e9i | −1.32369 | + | 0.652966i | ||||
\(203\) | −2.53426e9 | −1.49234 | ||||||||
\(204\) | 1.20094e8 | − | 1.56587e8i | 0.0693426 | − | 0.0904136i | ||||
\(205\) | − | 7.35074e8i | − | 0.416213i | ||||||
\(206\) | −1.32549e9 | + | 6.53856e8i | −0.736051 | + | 0.363089i | ||||
\(207\) | 2.26090e9i | 1.23140i | ||||||||
\(208\) | 3.47663e8 | − | 9.33337e7i | 0.185740 | − | 0.0498638i | ||||
\(209\) | −1.16809e9 | −0.612199 | ||||||||
\(210\) | −1.10160e9 | − | 2.23315e9i | −0.566429 | − | 1.14826i | ||||
\(211\) | 3.31179e9 | 1.67083 | 0.835415 | − | 0.549619i | \(-0.185227\pi\) | ||||
0.835415 | + | 0.549619i | \(0.185227\pi\) | |||||||
\(212\) | −1.46352e9 | − | 1.12245e9i | −0.724529 | − | 0.555676i | ||||
\(213\) | − | 2.09769e9i | − | 1.01911i | ||||||
\(214\) | −1.34688e8 | − | 2.73039e8i | −0.0642207 | − | 0.130188i | ||||
\(215\) | 2.10479e8i | 0.0985045i | ||||||||
\(216\) | 3.36151e8 | + | 6.67397e7i | 0.154426 | + | 0.0306598i | ||||
\(217\) | 9.74067e8 | 0.439288 | ||||||||
\(218\) | 1.98291e9 | − | 9.78156e8i | 0.877964 | − | 0.433094i | ||||
\(219\) | −1.13019e9 | −0.491334 | ||||||||
\(220\) | 4.46126e8 | + | 3.42155e8i | 0.190444 | + | 0.146060i | ||||
\(221\) | 3.59993e7i | 0.0150913i | ||||||||
\(222\) | 3.11889e9 | − | 1.53853e9i | 1.28407 | − | 0.633423i | ||||
\(223\) | − | 1.21904e6i | − | 0.000492943i | −1.00000 | 0.000246472i | \(-0.999922\pi\) | |||
1.00000 | 0.000246472i | \(-7.84543e-5\pi\) | ||||||||
\(224\) | 2.98994e9 | + | 3.40528e9i | 1.18760 | + | 1.35257i | ||||
\(225\) | 2.15903e9 | 0.842419 | ||||||||
\(226\) | 1.38690e9 | + | 2.81150e9i | 0.531631 | + | 1.07772i | ||||
\(227\) | −1.98748e9 | −0.748512 | −0.374256 | − | 0.927326i | \(-0.622102\pi\) | ||||
−0.374256 | + | 0.927326i | \(0.622102\pi\) | |||||||
\(228\) | −2.98399e9 | + | 3.89073e9i | −1.10422 | + | 1.43976i | ||||
\(229\) | − | 3.87381e9i | − | 1.40863i | −0.709889 | − | 0.704314i | \(-0.751255\pi\) | ||
0.709889 | − | 0.704314i | \(-0.248745\pi\) | |||||||
\(230\) | 6.73767e8 | + | 1.36585e9i | 0.240768 | + | 0.488082i | ||||
\(231\) | − | 3.64600e9i | − | 1.28047i | ||||||
\(232\) | 4.67746e8 | − | 2.35592e9i | 0.161458 | − | 0.813222i | ||||
\(233\) | −4.25730e9 | −1.44448 | −0.722238 | − | 0.691645i | \(-0.756886\pi\) | ||||
−0.722238 | + | 0.691645i | \(0.756886\pi\) | |||||||
\(234\) | −5.73182e8 | + | 2.82747e8i | −0.191174 | + | 0.0943049i | ||||
\(235\) | −1.74981e9 | −0.573745 | ||||||||
\(236\) | −7.19450e8 | + | 9.38068e8i | −0.231928 | + | 0.302403i | ||||
\(237\) | 5.69642e9i | 1.80555i | ||||||||
\(238\) | −4.06428e8 | + | 2.00488e8i | −0.126671 | + | 0.0624858i | ||||
\(239\) | − | 3.83381e9i | − | 1.17500i | −0.809223 | − | 0.587502i | \(-0.800111\pi\) | ||
0.809223 | − | 0.587502i | \(-0.199889\pi\) | |||||||
\(240\) | 2.27932e9 | − | 6.11908e8i | 0.687007 | − | 0.184434i | ||||
\(241\) | 3.13878e8 | 0.0930451 | 0.0465225 | − | 0.998917i | \(-0.485186\pi\) | ||||
0.0465225 | + | 0.998917i | \(0.485186\pi\) | |||||||
\(242\) | −1.15311e9 | − | 2.33758e9i | −0.336210 | − | 0.681562i | ||||
\(243\) | 5.00344e9 | 1.43497 | ||||||||
\(244\) | 1.39122e9 | + | 1.06699e9i | 0.392496 | + | 0.301024i | ||||
\(245\) | 3.95345e9i | 1.09727i | ||||||||
\(246\) | −1.99872e9 | − | 4.05179e9i | −0.545773 | − | 1.10639i | ||||
\(247\) | − | 8.94480e8i | − | 0.240316i | ||||||
\(248\) | −1.79783e8 | + | 9.05522e8i | −0.0475272 | + | 0.239383i | ||||
\(249\) | −7.13961e9 | −1.85728 | ||||||||
\(250\) | 3.02047e9 | − | 1.48998e9i | 0.773241 | − | 0.381435i | ||||
\(251\) | 5.87707e9 | 1.48070 | 0.740348 | − | 0.672224i | \(-0.234661\pi\) | ||||
0.740348 | + | 0.672224i | \(0.234661\pi\) | |||||||
\(252\) | −6.38436e9 | − | 4.89647e9i | −1.58312 | − | 1.21417i | ||||
\(253\) | 2.22999e9i | 0.544278i | ||||||||
\(254\) | −5.85719e9 | + | 2.88932e9i | −1.40720 | + | 0.694161i | ||||
\(255\) | 2.36016e8i | 0.0558189i | ||||||||
\(256\) | −3.71750e9 | + | 2.15103e9i | −0.865548 | + | 0.500826i | ||||
\(257\) | 6.42037e9 | 1.47173 | 0.735865 | − | 0.677129i | \(-0.236776\pi\) | ||||
0.735865 | + | 0.677129i | \(0.236776\pi\) | |||||||
\(258\) | 5.72310e8 | + | 1.16018e9i | 0.129167 | + | 0.261847i | ||||
\(259\) | −7.98665e9 | −1.77487 | ||||||||
\(260\) | −2.62009e8 | + | 3.41625e8i | −0.0573354 | + | 0.0747578i | ||||
\(261\) | 4.26455e9i | 0.918991i | ||||||||
\(262\) | 4.40891e7 | + | 8.93770e7i | 0.00935677 | + | 0.0189680i | ||||
\(263\) | 2.77731e9i | 0.580499i | 0.956951 | + | 0.290249i | \(0.0937382\pi\) | ||||
−0.956951 | + | 0.290249i | \(0.906262\pi\) | |||||||
\(264\) | 3.38943e9 | + | 6.72940e8i | 0.697768 | + | 0.138535i | ||||
\(265\) | 2.20590e9 | 0.447305 | ||||||||
\(266\) | 1.00986e10 | − | 4.98156e9i | 2.01713 | − | 0.995036i | ||||
\(267\) | 3.07117e9 | 0.604310 | ||||||||
\(268\) | 1.05804e9 | − | 1.37955e9i | 0.205100 | − | 0.267423i | ||||
\(269\) | − | 8.92780e9i | − | 1.70504i | −0.522693 | − | 0.852521i | \(-0.675072\pi\) | ||
0.522693 | − | 0.852521i | \(-0.324928\pi\) | |||||||
\(270\) | −3.67594e8 | + | 1.81332e8i | −0.0691694 | + | 0.0341208i | ||||
\(271\) | 3.90717e9i | 0.724411i | 0.932098 | + | 0.362205i | \(0.117976\pi\) | ||||
−0.932098 | + | 0.362205i | \(0.882024\pi\) | |||||||
\(272\) | −1.11366e8 | − | 4.14832e8i | −0.0203459 | − | 0.0757874i | ||||
\(273\) | 2.79196e9 | 0.502641 | ||||||||
\(274\) | 9.98592e8 | + | 2.02434e9i | 0.177168 | + | 0.359154i | ||||
\(275\) | 2.12951e9 | 0.372347 | ||||||||
\(276\) | 7.42772e9 | + | 5.69668e9i | 1.28003 | + | 0.981715i | ||||
\(277\) | − | 2.72513e9i | − | 0.462880i | −0.972849 | − | 0.231440i | \(-0.925656\pi\) | ||
0.972849 | − | 0.231440i | \(-0.0743437\pi\) | |||||||
\(278\) | −4.58565e9 | − | 9.29599e9i | −0.767753 | − | 1.55638i | ||||
\(279\) | − | 1.63912e9i | − | 0.270517i | ||||||
\(280\) | −5.31609e9 | − | 1.05546e9i | −0.864889 | − | 0.171716i | ||||
\(281\) | 2.69619e9 | 0.432440 | 0.216220 | − | 0.976345i | \(-0.430627\pi\) | ||||
0.216220 | + | 0.976345i | \(0.430627\pi\) | |||||||
\(282\) | −9.64509e9 | + | 4.75786e9i | −1.52514 | + | 0.752342i | ||||
\(283\) | −1.09816e9 | −0.171206 | −0.0856031 | − | 0.996329i | \(-0.527282\pi\) | ||||
−0.0856031 | + | 0.996329i | \(0.527282\pi\) | |||||||
\(284\) | −3.62295e9 | − | 2.77861e9i | −0.556915 | − | 0.427125i | ||||
\(285\) | − | 5.86433e9i | − | 0.888871i | ||||||
\(286\) | −5.65344e8 | + | 2.78881e8i | −0.0844985 | + | 0.0416826i | ||||
\(287\) | 1.03756e10i | 1.52927i | ||||||||
\(288\) | 5.73027e9 | − | 5.03136e9i | 0.832924 | − | 0.731333i | ||||
\(289\) | −6.93280e9 | −0.993842 | ||||||||
\(290\) | 1.27087e9 | + | 2.57629e9i | 0.179684 | + | 0.364253i | ||||
\(291\) | −1.11569e10 | −1.55586 | ||||||||
\(292\) | −1.49707e9 | + | 1.95198e9i | −0.205925 | + | 0.268499i | ||||
\(293\) | 4.39608e9i | 0.596479i | 0.954491 | + | 0.298239i | \(0.0963994\pi\) | ||||
−0.954491 | + | 0.298239i | \(0.903601\pi\) | |||||||
\(294\) | 1.07497e10 | + | 2.17917e10i | 1.43883 | + | 2.91677i | ||||
\(295\) | − | 1.41391e9i | − | 0.186695i | ||||||
\(296\) | 1.47409e9 | − | 7.42464e9i | 0.192025 | − | 0.967182i | ||||
\(297\) | −6.00161e8 | −0.0771333 | ||||||||
\(298\) | −7.90269e9 | + | 3.89835e9i | −1.00210 | + | 0.494328i | ||||
\(299\) | −1.70764e9 | −0.213654 | ||||||||
\(300\) | 5.43998e9 | − | 7.09303e9i | 0.671603 | − | 0.875682i | ||||
\(301\) | − | 2.97092e9i | − | 0.361930i | ||||||
\(302\) | 5.81838e8 | − | 2.87017e8i | 0.0699478 | − | 0.0345048i | ||||
\(303\) | − | 1.80646e10i | − | 2.14318i | ||||||
\(304\) | 2.76712e9 | + | 1.03074e10i | 0.323992 | + | 1.20685i | ||||
\(305\) | −2.09692e9 | −0.242316 | ||||||||
\(306\) | 3.37374e8 | + | 6.83922e8i | 0.0384792 | + | 0.0780047i | ||||
\(307\) | 3.80017e8 | 0.0427808 | 0.0213904 | − | 0.999771i | \(-0.493191\pi\) | ||||
0.0213904 | + | 0.999771i | \(0.493191\pi\) | |||||||
\(308\) | −6.29706e9 | − | 4.82952e9i | −0.699738 | − | 0.536663i | ||||
\(309\) | − | 1.08646e10i | − | 1.19174i | ||||||
\(310\) | −4.88471e8 | − | 9.90224e8i | −0.0528922 | − | 0.107223i | ||||
\(311\) | 6.94987e9i | 0.742908i | 0.928451 | + | 0.371454i | \(0.121141\pi\) | ||||
−0.928451 | + | 0.371454i | \(0.878859\pi\) | |||||||
\(312\) | −5.15310e8 | + | 2.59549e9i | −0.0543814 | + | 0.273906i | ||||
\(313\) | 5.51220e8 | 0.0574312 | 0.0287156 | − | 0.999588i | \(-0.490858\pi\) | ||||
0.0287156 | + | 0.999588i | \(0.490858\pi\) | |||||||
\(314\) | −4.21488e9 | + | 2.07917e9i | −0.433577 | + | 0.213881i | ||||
\(315\) | 9.62287e9 | 0.977378 | ||||||||
\(316\) | 9.83839e9 | + | 7.54554e9i | 0.986678 | + | 0.756731i | ||||
\(317\) | 9.38012e9i | 0.928905i | 0.885598 | + | 0.464452i | \(0.153749\pi\) | ||||
−0.885598 | + | 0.464452i | \(0.846251\pi\) | |||||||
\(318\) | 1.21591e10 | − | 5.99802e9i | 1.18903 | − | 0.586543i | ||||
\(319\) | 4.20624e9i | 0.406192i | ||||||||
\(320\) | 1.96238e9 | − | 4.74720e9i | 0.187147 | − | 0.452728i | ||||
\(321\) | 2.23802e9 | 0.210787 | ||||||||
\(322\) | −9.51021e9 | − | 1.92790e10i | −0.884640 | − | 1.79333i | ||||
\(323\) | −1.06730e9 | −0.0980561 | ||||||||
\(324\) | 5.90044e9 | − | 7.69340e9i | 0.535432 | − | 0.698133i | ||||
\(325\) | 1.63069e9i | 0.146163i | ||||||||
\(326\) | −3.26722e9 | − | 6.62327e9i | −0.289273 | − | 0.586411i | ||||
\(327\) | 1.62533e10i | 1.42151i | ||||||||
\(328\) | −9.64544e9 | − | 1.91501e9i | −0.833349 | − | 0.165454i | ||||
\(329\) | 2.46985e10 | 2.10808 | ||||||||
\(330\) | −3.70647e9 | + | 1.82838e9i | −0.312540 | + | 0.154174i | ||||
\(331\) | 1.45676e10 | 1.21360 | 0.606801 | − | 0.794854i | \(-0.292452\pi\) | ||||
0.606801 | + | 0.794854i | \(0.292452\pi\) | |||||||
\(332\) | −9.45719e9 | + | 1.23309e10i | −0.778412 | + | 1.01495i | ||||
\(333\) | 1.34396e10i | 1.09298i | ||||||||
\(334\) | 1.55984e10 | − | 7.69460e9i | 1.25342 | − | 0.618302i | ||||
\(335\) | 2.07934e9i | 0.165100i | ||||||||
\(336\) | −3.21726e10 | + | 8.63708e9i | −2.52423 | + | 0.677656i | ||||
\(337\) | −1.43980e10 | −1.11630 | −0.558152 | − | 0.829739i | \(-0.688489\pi\) | ||||
−0.558152 | + | 0.829739i | \(0.688489\pi\) | |||||||
\(338\) | 5.56046e9 | + | 1.12721e10i | 0.426033 | + | 0.863651i | ||||
\(339\) | −2.30451e10 | −1.74493 | ||||||||
\(340\) | 4.07628e8 | + | 3.12629e8i | 0.0305034 | + | 0.0233945i | ||||
\(341\) | − | 1.61671e9i | − | 0.119568i | ||||||
\(342\) | −8.38278e9 | − | 1.69935e10i | −0.612750 | − | 1.24216i | ||||
\(343\) | − | 3.08892e10i | − | 2.23167i | ||||||
\(344\) | 2.76186e9 | + | 5.48341e8i | 0.197227 | + | 0.0391577i | ||||
\(345\) | −1.11955e10 | −0.790254 | ||||||||
\(346\) | 1.39600e10 | − | 6.88639e9i | 0.974051 | − | 0.480493i | ||||
\(347\) | 1.26794e10 | 0.874539 | 0.437270 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437270 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(348\) | 1.40103e10 | + | 1.07452e10i | 0.955277 | + | 0.732648i | ||||
\(349\) | 1.29547e10i | 0.873222i | 0.899650 | + | 0.436611i | \(0.143821\pi\) | ||||
−0.899650 | + | 0.436611i | \(0.856179\pi\) | |||||||
\(350\) | −1.84103e10 | + | 9.08168e9i | −1.22684 | + | 0.605193i | ||||
\(351\) | − | 4.59579e8i | − | 0.0302783i | ||||||
\(352\) | 5.65192e9 | − | 4.96256e9i | 0.368150 | − | 0.323248i | ||||
\(353\) | −2.77667e10 | −1.78824 | −0.894120 | − | 0.447828i | \(-0.852198\pi\) | ||||
−0.894120 | + | 0.447828i | \(0.852198\pi\) | |||||||
\(354\) | −3.84453e9 | − | 7.79359e9i | −0.244811 | − | 0.496278i | ||||
\(355\) | 5.46072e9 | 0.343824 | ||||||||
\(356\) | 4.06811e9 | − | 5.30428e9i | 0.253275 | − | 0.330237i | ||||
\(357\) | − | 3.33137e9i | − | 0.205093i | ||||||
\(358\) | 1.07812e10 | + | 2.18555e10i | 0.656347 | + | 1.33054i | ||||
\(359\) | − | 1.05991e10i | − | 0.638103i | −0.947737 | − | 0.319052i | \(-0.896636\pi\) | ||
0.947737 | − | 0.319052i | \(-0.103364\pi\) | |||||||
\(360\) | −1.77609e9 | + | 8.94572e9i | −0.105744 | + | 0.532605i | ||||
\(361\) | 9.53565e9 | 0.561464 | ||||||||
\(362\) | 3.92333e9 | − | 1.93536e9i | 0.228466 | − | 0.112701i | ||||
\(363\) | 1.91605e10 | 1.10352 | ||||||||
\(364\) | 3.69825e9 | − | 4.82204e9i | 0.210664 | − | 0.274679i | ||||
\(365\) | − | 2.94213e9i | − | 0.165764i | ||||||
\(366\) | −1.15584e10 | + | 5.70169e9i | −0.644130 | + | 0.317745i | ||||
\(367\) | − | 1.91289e10i | − | 1.05445i | −0.849726 | − | 0.527224i | \(-0.823233\pi\) | ||
0.849726 | − | 0.527224i | \(-0.176767\pi\) | |||||||
\(368\) | 1.96777e10 | − | 5.28267e9i | 1.07296 | − | 0.288046i | ||||
\(369\) | 1.74596e10 | 0.941735 | ||||||||
\(370\) | 4.00511e9 | + | 8.11913e9i | 0.213702 | + | 0.433214i | ||||
\(371\) | −3.11363e10 | −1.64351 | ||||||||
\(372\) | −5.38499e9 | − | 4.13001e9i | −0.281198 | − | 0.215665i | ||||
\(373\) | 3.40704e10i | 1.76012i | 0.474865 | + | 0.880059i | \(0.342497\pi\) | ||||
−0.474865 | + | 0.880059i | \(0.657503\pi\) | |||||||
\(374\) | 3.32761e8 | + | 6.74570e8i | 0.0170077 | + | 0.0344779i | ||||
\(375\) | 2.47579e10i | 1.25196i | ||||||||
\(376\) | −4.55859e9 | + | 2.29605e10i | −0.228076 | + | 1.14876i | ||||
\(377\) | −3.22097e9 | −0.159449 | ||||||||
\(378\) | 5.18859e9 | − | 2.55950e9i | 0.254146 | − | 0.125368i | ||||
\(379\) | 4.16311e9 | 0.201772 | 0.100886 | − | 0.994898i | \(-0.467832\pi\) | ||||
0.100886 | + | 0.994898i | \(0.467832\pi\) | |||||||
\(380\) | −1.01284e10 | − | 7.76794e9i | −0.485742 | − | 0.372539i | ||||
\(381\) | − | 4.80096e10i | − | 2.27839i | ||||||
\(382\) | 2.65685e10 | − | 1.31061e10i | 1.24771 | − | 0.615487i | ||||
\(383\) | − | 7.32538e9i | − | 0.340436i | −0.985406 | − | 0.170218i | \(-0.945553\pi\) | ||
0.985406 | − | 0.170218i | \(-0.0544472\pi\) | |||||||
\(384\) | −2.09120e9 | − | 3.15028e10i | −0.0961769 | − | 1.44885i | ||||
\(385\) | 9.49130e9 | 0.431999 | ||||||||
\(386\) | 3.88718e9 | + | 7.88004e9i | 0.175100 | + | 0.354960i | ||||
\(387\) | −4.99935e9 | −0.222879 | ||||||||
\(388\) | −1.47785e10 | + | 1.92692e10i | −0.652083 | + | 0.850230i | ||||
\(389\) | − | 4.02169e10i | − | 1.75635i | −0.478341 | − | 0.878174i | \(-0.658762\pi\) | ||
0.478341 | − | 0.878174i | \(-0.341238\pi\) | |||||||
\(390\) | −1.40010e9 | − | 2.83827e9i | −0.0605202 | − | 0.122686i | ||||
\(391\) | 2.03756e9i | 0.0871771i | ||||||||
\(392\) | 5.18761e10 | + | 1.02995e10i | 2.19696 | + | 0.436187i | ||||
\(393\) | −7.32596e8 | −0.0307110 | ||||||||
\(394\) | −2.42114e10 | + | 1.19433e10i | −1.00469 | + | 0.495610i | ||||
\(395\) | −1.48290e10 | −0.609148 | ||||||||
\(396\) | −8.12694e9 | + | 1.05965e10i | −0.330481 | + | 0.430903i | ||||
\(397\) | − | 6.79229e9i | − | 0.273435i | −0.990610 | − | 0.136717i | \(-0.956345\pi\) | ||
0.990610 | − | 0.136717i | \(-0.0436552\pi\) | |||||||
\(398\) | −2.85857e10 | + | 1.41012e10i | −1.13924 | + | 0.561982i | ||||
\(399\) | 8.27749e10i | 3.26593i | ||||||||
\(400\) | −5.04463e9 | − | 1.87910e10i | −0.197056 | − | 0.734023i | ||||
\(401\) | −5.36689e9 | −0.207561 | −0.103780 | − | 0.994600i | \(-0.533094\pi\) | ||||
−0.103780 | + | 0.994600i | \(0.533094\pi\) | |||||||
\(402\) | 5.65388e9 | + | 1.14615e10i | 0.216492 | + | 0.438871i | ||||
\(403\) | 1.23801e9 | 0.0469358 | ||||||||
\(404\) | −3.11998e10 | − | 2.39286e10i | −1.17119 | − | 0.898239i | ||||
\(405\) | 1.15959e10i | 0.431009i | ||||||||
\(406\) | −1.79383e10 | − | 3.63643e10i | −0.660202 | − | 1.33836i | ||||
\(407\) | 1.32559e10i | 0.483093i | ||||||||
\(408\) | 3.09694e9 | + | 6.14869e8i | 0.111762 | + | 0.0221892i | ||||
\(409\) | −1.14532e10 | −0.409293 | −0.204647 | − | 0.978836i | \(-0.565605\pi\) | ||||
−0.204647 | + | 0.978836i | \(0.565605\pi\) | |||||||
\(410\) | 1.05477e10 | − | 5.20309e9i | 0.373268 | − | 0.184131i | ||||
\(411\) | −1.65929e10 | −0.581506 | ||||||||
\(412\) | −1.87645e10 | − | 1.43914e10i | −0.651251 | − | 0.499476i | ||||
\(413\) | 1.99573e10i | 0.685966i | ||||||||
\(414\) | −3.24420e10 | + | 1.60034e10i | −1.10435 | + | 0.544768i | ||||
\(415\) | − | 1.85859e10i | − | 0.626601i | ||||||
\(416\) | 3.80013e9 | + | 4.32801e9i | 0.126889 | + | 0.144516i | ||||
\(417\) | 7.61964e10 | 2.51994 | ||||||||
\(418\) | −8.26816e9 | − | 1.67611e10i | −0.270834 | − | 0.549033i | ||||
\(419\) | 3.53809e10 | 1.14792 | 0.573961 | − | 0.818883i | \(-0.305406\pi\) | ||||
0.573961 | + | 0.818883i | \(0.305406\pi\) | |||||||
\(420\) | 2.42462e10 | − | 3.16139e10i | 0.779197 | − | 1.01597i | ||||
\(421\) | 4.32861e10i | 1.37791i | 0.724806 | + | 0.688953i | \(0.241929\pi\) | ||||
−0.724806 | + | 0.688953i | \(0.758071\pi\) | |||||||
\(422\) | 2.34419e10 | + | 4.75212e10i | 0.739168 | + | 1.49843i | ||||
\(423\) | − | 4.15617e10i | − | 1.29817i | ||||||
\(424\) | 5.74682e9 | − | 2.89453e10i | 0.177813 | − | 0.895601i | ||||
\(425\) | 1.94574e9 | 0.0596389 | ||||||||
\(426\) | 3.00999e10 | − | 1.48481e10i | 0.913960 | − | 0.450851i | ||||
\(427\) | 2.95980e10 | 0.890330 | ||||||||
\(428\) | 2.96450e9 | − | 3.86532e9i | 0.0883439 | − | 0.115189i | ||||
\(429\) | − | 4.63396e9i | − | 0.136812i | ||||||
\(430\) | −3.02020e9 | + | 1.48984e9i | −0.0883408 | + | 0.0435779i | ||||
\(431\) | − | 2.06603e10i | − | 0.598724i | −0.954140 | − | 0.299362i | \(-0.903226\pi\) | ||
0.954140 | − | 0.299362i | \(-0.0967739\pi\) | |||||||
\(432\) | 1.42173e9 | + | 5.29588e9i | 0.0408210 | + | 0.152056i | ||||
\(433\) | −3.26720e10 | −0.929447 | −0.464723 | − | 0.885456i | \(-0.653846\pi\) | ||||
−0.464723 | + | 0.885456i | \(0.653846\pi\) | |||||||
\(434\) | 6.89477e9 | + | 1.39770e10i | 0.194339 | + | 0.393963i | ||||
\(435\) | −2.11171e10 | −0.589762 | ||||||||
\(436\) | 2.80714e10 | + | 2.15293e10i | 0.776815 | + | 0.595777i | ||||
\(437\) | − | 5.06274e10i | − | 1.38822i | ||||||
\(438\) | −7.99988e9 | − | 1.62173e10i | −0.217364 | − | 0.440638i | ||||
\(439\) | 2.83909e10i | 0.764401i | 0.924079 | + | 0.382201i | \(0.124834\pi\) | ||||
−0.924079 | + | 0.382201i | \(0.875166\pi\) | |||||||
\(440\) | −1.75180e9 | + | 8.82340e9i | −0.0467385 | + | 0.235410i | ||||
\(441\) | −9.39030e10 | −2.48270 | ||||||||
\(442\) | −5.16559e8 | + | 2.54815e8i | −0.0135341 | + | 0.00667630i | ||||
\(443\) | −1.69063e10 | −0.438968 | −0.219484 | − | 0.975616i | \(-0.570437\pi\) | ||||
−0.219484 | + | 0.975616i | \(0.570437\pi\) | |||||||
\(444\) | 4.41531e10 | + | 3.38631e10i | 1.13613 | + | 0.871355i | ||||
\(445\) | 7.99491e9i | 0.203880i | ||||||||
\(446\) | 1.74921e7 | − | 8.62873e6i | 0.000442081 | − | 0.000218076i | ||||
\(447\) | − | 6.47760e10i | − | 1.62250i | ||||||
\(448\) | −2.76990e10 | + | 6.70067e10i | −0.687624 | + | 1.66344i | ||||
\(449\) | 2.99952e10 | 0.738016 | 0.369008 | − | 0.929426i | \(-0.379697\pi\) | ||||
0.369008 | + | 0.929426i | \(0.379697\pi\) | |||||||
\(450\) | 1.52823e10 | + | 3.09801e10i | 0.372682 | + | 0.755498i | ||||
\(451\) | 1.72209e10 | 0.416245 | ||||||||
\(452\) | −3.05257e10 | + | 3.98015e10i | −0.731327 | + | 0.953555i | ||||
\(453\) | 4.76915e9i | 0.113253i | ||||||||
\(454\) | −1.40680e10 | − | 2.85185e10i | −0.331138 | − | 0.671280i | ||||
\(455\) | 7.26805e9i | 0.169579i | ||||||||
\(456\) | −7.69501e10 | − | 1.52777e10i | −1.77971 | − | 0.353345i | ||||
\(457\) | 6.23791e9 | 0.143013 | 0.0715063 | − | 0.997440i | \(-0.477219\pi\) | ||||
0.0715063 | + | 0.997440i | \(0.477219\pi\) | |||||||
\(458\) | 5.55857e10 | − | 2.74201e10i | 1.26329 | − | 0.623171i | ||||
\(459\) | −5.48371e8 | −0.0123545 | ||||||||
\(460\) | −1.48297e10 | + | 1.93359e10i | −0.331207 | + | 0.431851i | ||||
\(461\) | 4.50780e10i | 0.998070i | 0.866582 | + | 0.499035i | \(0.166312\pi\) | ||||
−0.866582 | + | 0.499035i | \(0.833688\pi\) | |||||||
\(462\) | 5.23168e10 | − | 2.58076e10i | 1.14835 | − | 0.566473i | ||||
\(463\) | 1.05219e10i | 0.228965i | 0.993425 | + | 0.114482i | \(0.0365210\pi\) | ||||
−0.993425 | + | 0.114482i | \(0.963479\pi\) | |||||||
\(464\) | 3.71163e10 | − | 9.96424e9i | 0.800742 | − | 0.214967i | ||||
\(465\) | 8.11656e9 | 0.173604 | ||||||||
\(466\) | −3.01346e10 | − | 6.10885e10i | −0.639030 | − | 1.29544i | ||||
\(467\) | −5.51764e10 | −1.16008 | −0.580038 | − | 0.814590i | \(-0.696962\pi\) | ||||
−0.580038 | + | 0.814590i | \(0.696962\pi\) | |||||||
\(468\) | −8.11434e9 | − | 6.22328e9i | −0.169149 | − | 0.129729i | ||||
\(469\) | − | 2.93499e10i | − | 0.606617i | ||||||
\(470\) | −1.23857e10 | − | 2.51082e10i | −0.253822 | − | 0.514546i | ||||
\(471\) | − | 3.45481e10i | − | 0.702005i | ||||||
\(472\) | −1.85530e10 | − | 3.68352e9i | −0.373805 | − | 0.0742155i | ||||
\(473\) | −4.93099e9 | −0.0985121 | ||||||||
\(474\) | −8.17386e10 | + | 4.03212e10i | −1.61925 | + | 0.798766i | ||||
\(475\) | −4.83461e10 | −0.949702 | ||||||||
\(476\) | −5.75366e9 | − | 4.41276e9i | −0.112077 | − | 0.0859573i | ||||
\(477\) | 5.23950e10i | 1.01208i | ||||||||
\(478\) | 5.50118e10 | − | 2.71370e10i | 1.05377 | − | 0.519816i | ||||
\(479\) | 2.46128e10i | 0.467540i | 0.972292 | + | 0.233770i | \(0.0751063\pi\) | ||||
−0.972292 | + | 0.233770i | \(0.924894\pi\) | |||||||
\(480\) | 2.49141e10 | + | 2.83750e10i | 0.469333 | + | 0.534529i | ||||
\(481\) | −1.01508e10 | −0.189636 | ||||||||
\(482\) | 2.22173e9 | + | 4.50388e9i | 0.0411627 | + | 0.0834447i | ||||
\(483\) | 1.58024e11 | 2.90359 | ||||||||
\(484\) | 2.53801e10 | − | 3.30923e10i | 0.462501 | − | 0.603040i | ||||
\(485\) | − | 2.90436e10i | − | 0.524909i | ||||||
\(486\) | 3.54160e10 | + | 7.17949e10i | 0.634825 | + | 1.28691i | ||||
\(487\) | − | 1.03802e10i | − | 0.184539i | −0.995734 | − | 0.0922695i | \(-0.970588\pi\) | ||
0.995734 | − | 0.0922695i | \(-0.0294121\pi\) | |||||||
\(488\) | −5.46289e9 | + | 2.75152e10i | −0.0963260 | + | 0.485170i | ||||
\(489\) | 5.42890e10 | 0.949459 | ||||||||
\(490\) | −5.67285e10 | + | 2.79838e10i | −0.984049 | + | 0.485425i | ||||
\(491\) | 5.19024e10 | 0.893020 | 0.446510 | − | 0.894779i | \(-0.352667\pi\) | ||||
0.446510 | + | 0.894779i | \(0.352667\pi\) | |||||||
\(492\) | 4.39920e10 | − | 5.73598e10i | 0.750781 | − | 0.978920i | ||||
\(493\) | 3.84327e9i | 0.0650598i | ||||||||
\(494\) | 1.28350e10 | − | 6.33142e9i | 0.215520 | − | 0.106315i | ||||
\(495\) | − | 1.59716e10i | − | 0.266028i | ||||||
\(496\) | −1.42660e10 | + | 3.82986e9i | −0.235709 | + | 0.0632785i | ||||
\(497\) | −7.70780e10 | −1.26330 | ||||||||
\(498\) | −5.05365e10 | − | 1.02447e11i | −0.821651 | − | 1.66564i | ||||
\(499\) | −8.02548e9 | −0.129440 | −0.0647200 | − | 0.997903i | \(-0.520615\pi\) | ||||
−0.0647200 | + | 0.997903i | \(0.520615\pi\) | |||||||
\(500\) | 4.27598e10 | + | 3.27946e10i | 0.684157 | + | 0.524713i | ||||
\(501\) | 1.27856e11i | 2.02941i | ||||||||
\(502\) | 4.15998e10 | + | 8.43308e10i | 0.655053 | + | 1.32792i | ||||
\(503\) | 1.37392e10i | 0.214629i | 0.994225 | + | 0.107314i | \(0.0342252\pi\) | ||||
−0.994225 | + | 0.107314i | \(0.965775\pi\) | |||||||
\(504\) | 2.50695e10 | − | 1.26269e11i | 0.388529 | − | 1.95692i | ||||
\(505\) | 4.70261e10 | 0.723058 | ||||||||
\(506\) | −3.19984e10 | + | 1.57846e10i | −0.488120 | + | 0.240786i | ||||
\(507\) | −9.23940e10 | −1.39834 | ||||||||
\(508\) | −8.29183e10 | − | 6.35940e10i | −1.24507 | − | 0.954908i | ||||
\(509\) | − | 6.98889e10i | − | 1.04121i | −0.853798 | − | 0.520604i | \(-0.825707\pi\) | ||
0.853798 | − | 0.520604i | \(-0.174293\pi\) | |||||||
\(510\) | −3.38663e9 | + | 1.67060e9i | −0.0500595 | + | 0.0246940i | ||||
\(511\) | 4.15282e10i | 0.609059i | ||||||||
\(512\) | −5.71791e10 | − | 3.81172e10i | −0.832065 | − | 0.554678i | ||||
\(513\) | 1.36254e10 | 0.196735 | ||||||||
\(514\) | 4.54455e10 | + | 9.21267e10i | 0.651086 | + | 1.31988i | ||||
\(515\) | 2.82830e10 | 0.402065 | ||||||||
\(516\) | −1.25966e10 | + | 1.64243e10i | −0.177686 | + | 0.231680i | ||||
\(517\) | − | 4.09934e10i | − | 0.573789i | ||||||
\(518\) | −5.65322e10 | − | 1.14601e11i | −0.785193 | − | 1.59174i | ||||
\(519\) | 1.14426e11i | 1.57709i | ||||||||
\(520\) | −6.75660e9 | − | 1.34146e9i | −0.0924092 | − | 0.0183470i | ||||
\(521\) | 1.24271e11 | 1.68662 | 0.843312 | − | 0.537425i | \(-0.180603\pi\) | ||||
0.843312 | + | 0.537425i | \(0.180603\pi\) | |||||||
\(522\) | −6.11925e10 | + | 3.01859e10i | −0.824169 | + | 0.406557i | ||||
\(523\) | −1.30062e11 | −1.73838 | −0.869189 | − | 0.494480i | \(-0.835359\pi\) | ||||
−0.869189 | + | 0.494480i | \(0.835359\pi\) | |||||||
\(524\) | −9.70404e8 | + | 1.26528e9i | −0.0128714 | + | 0.0167827i | ||||
\(525\) | − | 1.50904e11i | − | 1.98638i | ||||||
\(526\) | −3.98519e10 | + | 1.96587e10i | −0.520603 | + | 0.256810i | ||||
\(527\) | − | 1.47720e9i | − | 0.0191512i | ||||||
\(528\) | 1.43354e10 | + | 5.33986e10i | 0.184448 | + | 0.687060i | ||||
\(529\) | −1.83409e10 | −0.234206 | ||||||||
\(530\) | 1.56141e10 | + | 3.16528e10i | 0.197886 | + | 0.401152i | ||||
\(531\) | 3.35834e10 | 0.422423 | ||||||||
\(532\) | 1.42962e11 | + | 1.09644e11i | 1.78474 | + | 1.36880i | ||||
\(533\) | 1.31870e10i | 0.163395i | ||||||||
\(534\) | 2.17388e10 | + | 4.40687e10i | 0.267344 | + | 0.541957i | ||||
\(535\) | 5.82603e9i | 0.0711144i | ||||||||
\(536\) | 2.72845e10 | + | 5.41709e9i | 0.330565 | + | 0.0656307i | ||||
\(537\) | −1.79143e11 | −2.15428 | ||||||||
\(538\) | 1.28106e11 | − | 6.31939e10i | 1.52912 | − | 0.754303i | ||||
\(539\) | −9.26190e10 | −1.09735 | ||||||||
\(540\) | −5.20391e9 | − | 3.99113e9i | −0.0612005 | − | 0.0469376i | ||||
\(541\) | − | 1.23457e11i | − | 1.44121i | −0.693347 | − | 0.720604i | \(-0.743865\pi\) | ||
0.693347 | − | 0.720604i | \(-0.256135\pi\) | |||||||
\(542\) | −5.60644e10 | + | 2.76562e10i | −0.649666 | + | 0.320476i | ||||
\(543\) | 3.21584e10i | 0.369909i | ||||||||
\(544\) | 5.16419e9 | − | 4.53432e9i | 0.0589667 | − | 0.0517746i | ||||
\(545\) | −4.23108e10 | −0.479584 | ||||||||
\(546\) | 1.97624e10 | + | 4.00621e10i | 0.222366 | + | 0.450779i | ||||
\(547\) | 6.29196e10 | 0.702808 | 0.351404 | − | 0.936224i | \(-0.385704\pi\) | ||||
0.351404 | + | 0.936224i | \(0.385704\pi\) | |||||||
\(548\) | −2.19791e10 | + | 2.86578e10i | −0.243718 | + | 0.317776i | ||||
\(549\) | − | 4.98064e10i | − | 0.548272i | ||||||
\(550\) | 1.50733e10 | + | 3.05565e10i | 0.164725 | + | 0.333929i | ||||
\(551\) | − | 9.54941e10i | − | 1.03602i | ||||||
\(552\) | −2.91665e10 | + | 1.46904e11i | −0.314143 | + | 1.58226i | ||||
\(553\) | 2.09311e11 | 2.23816 | ||||||||
\(554\) | 3.91033e10 | − | 1.92894e10i | 0.415120 | − | 0.204776i | ||||
\(555\) | −6.65500e10 | −0.701417 | ||||||||
\(556\) | 1.00930e11 | − | 1.31600e11i | 1.05614 | − | 1.37707i | ||||
\(557\) | 1.43749e11i | 1.49343i | 0.665146 | + | 0.746713i | \(0.268369\pi\) | ||||
−0.665146 | + | 0.746713i | \(0.731631\pi\) | |||||||
\(558\) | 2.35200e10 | − | 1.16022e10i | 0.242605 | − | 0.119676i | ||||
\(559\) | − | 3.77595e9i | − | 0.0386704i | ||||||
\(560\) | −2.24841e10 | − | 8.37522e10i | −0.228625 | − | 0.851616i | ||||
\(561\) | −5.52925e9 | −0.0558232 | ||||||||
\(562\) | 1.90845e10 | + | 3.86880e10i | 0.191310 | + | 0.387821i | ||||
\(563\) | 1.24137e11 | 1.23557 | 0.617786 | − | 0.786346i | \(-0.288030\pi\) | ||||
0.617786 | + | 0.786346i | \(0.288030\pi\) | |||||||
\(564\) | −1.36542e11 | − | 1.04721e11i | −1.34943 | − | 1.03494i | ||||
\(565\) | − | 5.99911e10i | − | 0.588699i | ||||||
\(566\) | −7.77313e9 | − | 1.57576e10i | −0.0757409 | − | 0.153541i | ||||
\(567\) | − | 1.63677e11i | − | 1.58363i | ||||||
\(568\) | 1.42262e10 | − | 7.16541e10i | 0.136678 | − | 0.688411i | ||||
\(569\) | −6.03923e9 | −0.0576146 | −0.0288073 | − | 0.999585i | \(-0.509171\pi\) | ||||
−0.0288073 | + | 0.999585i | \(0.509171\pi\) | |||||||
\(570\) | 8.41479e10 | − | 4.15096e10i | 0.797157 | − | 0.393233i | ||||
\(571\) | 1.39234e11 | 1.30979 | 0.654895 | − | 0.755720i | \(-0.272713\pi\) | ||||
0.654895 | + | 0.755720i | \(0.272713\pi\) | |||||||
\(572\) | −8.00339e9 | − | 6.13819e9i | −0.0747635 | − | 0.0573398i | ||||
\(573\) | 2.17774e11i | 2.02017i | ||||||||
\(574\) | −1.48880e11 | + | 7.34416e10i | −1.37148 | + | 0.676542i | ||||
\(575\) | 9.22968e10i | 0.844336i | ||||||||
\(576\) | 1.12756e11 | + | 4.66107e10i | 1.02436 | + | 0.423444i | ||||
\(577\) | −1.45928e11 | −1.31654 | −0.658272 | − | 0.752780i | \(-0.728713\pi\) | ||||
−0.658272 | + | 0.752780i | \(0.728713\pi\) | |||||||
\(578\) | −4.90727e10 | − | 9.94796e10i | −0.439671 | − | 0.891298i | ||||
\(579\) | −6.45904e10 | −0.574716 | ||||||||
\(580\) | −2.79719e10 | + | 3.64717e10i | −0.247178 | + | 0.322288i | ||||
\(581\) | 2.62340e11i | 2.30229i | ||||||||
\(582\) | −7.89719e10 | − | 1.60091e11i | −0.688304 | − | 1.39532i | ||||
\(583\) | 5.16786e10i | 0.447339i | ||||||||
\(584\) | −3.86059e10 | − | 7.66484e9i | −0.331896 | − | 0.0658949i | ||||
\(585\) | 1.22304e10 | 0.104428 | ||||||||
\(586\) | −6.30799e10 | + | 3.11169e10i | −0.534934 | + | 0.263880i | ||||
\(587\) | 3.80703e10 | 0.320652 | 0.160326 | − | 0.987064i | \(-0.448745\pi\) | ||||
0.160326 | + | 0.987064i | \(0.448745\pi\) | |||||||
\(588\) | −2.36602e11 | + | 3.08498e11i | −1.97929 | + | 2.58073i | ||||
\(589\) | 3.67041e10i | 0.304968i | ||||||||
\(590\) | 2.02884e10 | − | 1.00081e10i | 0.167432 | − | 0.0825933i | ||||
\(591\) | − | 1.98453e11i | − | 1.62670i | ||||||
\(592\) | 1.16971e11 | − | 3.14021e10i | 0.952340 | − | 0.255665i | ||||
\(593\) | −7.93163e10 | −0.641421 | −0.320711 | − | 0.947177i | \(-0.603922\pi\) | ||||
−0.320711 | + | 0.947177i | \(0.603922\pi\) | |||||||
\(594\) | −4.24814e9 | − | 8.61178e9i | −0.0341234 | − | 0.0691747i | ||||
\(595\) | 8.67225e9 | 0.0691933 | ||||||||
\(596\) | −1.11876e11 | − | 8.58029e10i | −0.886647 | − | 0.680012i | ||||
\(597\) | − | 2.34309e11i | − | 1.84455i | ||||||
\(598\) | −1.20872e10 | − | 2.45031e10i | −0.0945195 | − | 0.191609i | ||||
\(599\) | 7.53655e10i | 0.585417i | 0.956202 | + | 0.292709i | \(0.0945566\pi\) | ||||
−0.956202 | + | 0.292709i | \(0.905443\pi\) | |||||||
\(600\) | 1.40285e11 | + | 2.78522e10i | 1.08244 | + | 0.214909i | ||||
\(601\) | −1.21175e11 | −0.928785 | −0.464392 | − | 0.885630i | \(-0.653727\pi\) | ||||
−0.464392 | + | 0.885630i | \(0.653727\pi\) | |||||||
\(602\) | 4.26300e10 | − | 2.10291e10i | 0.324586 | − | 0.160116i | ||||
\(603\) | −4.93888e10 | −0.373559 | ||||||||
\(604\) | 8.23688e9 | + | 6.31726e9i | 0.0618892 | + | 0.0474658i | ||||
\(605\) | 4.98787e10i | 0.372301i | ||||||||
\(606\) | 2.59212e11 | − | 1.27868e11i | 1.92205 | − | 0.948134i | ||||
\(607\) | 2.19334e10i | 0.161566i | 0.996732 | + | 0.0807832i | \(0.0257422\pi\) | ||||
−0.996732 | + | 0.0807832i | \(0.974258\pi\) | |||||||
\(608\) | −1.28315e11 | + | 1.12665e11i | −0.938997 | + | 0.824469i | ||||
\(609\) | 2.98068e11 | 2.16693 | ||||||||
\(610\) | −1.48427e10 | − | 3.00890e10i | −0.107200 | − | 0.217314i | ||||
\(611\) | 3.13911e10 | 0.225238 | ||||||||
\(612\) | −7.42563e9 | + | 9.68205e9i | −0.0529331 | + | 0.0690179i | ||||
\(613\) | − | 4.23372e10i | − | 0.299833i | −0.988699 | − | 0.149917i | \(-0.952099\pi\) | ||
0.988699 | − | 0.149917i | \(-0.0479005\pi\) | |||||||
\(614\) | 2.68988e9 | + | 5.45291e9i | 0.0189261 | + | 0.0383667i | ||||
\(615\) | 8.64560e10i | 0.604359i | ||||||||
\(616\) | 2.47267e10 | − | 1.24542e11i | 0.171729 | − | 0.864956i | ||||
\(617\) | 1.11249e11 | 0.767635 | 0.383817 | − | 0.923409i | \(-0.374609\pi\) | ||||
0.383817 | + | 0.923409i | \(0.374609\pi\) | |||||||
\(618\) | 1.55898e11 | − | 7.69035e10i | 1.06878 | − | 0.527221i | ||||
\(619\) | −1.10105e11 | −0.749972 | −0.374986 | − | 0.927030i | \(-0.622353\pi\) | ||||
−0.374986 | + | 0.927030i | \(0.622353\pi\) | |||||||
\(620\) | 1.07513e10 | − | 1.40183e10i | 0.0727601 | − | 0.0948696i | ||||
\(621\) | − | 2.60121e10i | − | 0.174908i | ||||||
\(622\) | −9.97245e10 | + | 4.91934e10i | −0.666255 | + | 0.328659i | ||||
\(623\) | − | 1.12848e11i | − | 0.749104i | ||||||
\(624\) | −4.08905e10 | + | 1.09775e10i | −0.269702 | + | 0.0724043i | ||||
\(625\) | 5.15188e10 | 0.337634 | ||||||||
\(626\) | 3.90172e9 | + | 7.90952e9i | 0.0254073 | + | 0.0515054i | ||||
\(627\) | 1.37386e11 | 0.888939 | ||||||||
\(628\) | −5.96685e10 | − | 4.57627e10i | −0.383625 | − | 0.294221i | ||||
\(629\) | 1.21120e10i | 0.0773770i | ||||||||
\(630\) | 6.81139e10 | + | 1.38080e11i | 0.432388 | + | 0.876532i | ||||
\(631\) | 4.27197e10i | 0.269470i | 0.990882 | + | 0.134735i | \(0.0430184\pi\) | ||||
−0.990882 | + | 0.134735i | \(0.956982\pi\) | |||||||
\(632\) | −3.86324e10 | + | 1.94582e11i | −0.242150 | + | 1.21965i | ||||
\(633\) | −3.89517e11 | −2.42612 | ||||||||
\(634\) | −1.34596e11 | + | 6.63956e10i | −0.833060 | + | 0.410943i | ||||
\(635\) | 1.24979e11 | 0.768675 | ||||||||
\(636\) | 1.72133e11 | + | 1.32017e11i | 1.05205 | + | 0.806866i | ||||
\(637\) | − | 7.09239e10i | − | 0.430759i | ||||||
\(638\) | −6.03558e10 | + | 2.97731e10i | −0.364281 | + | 0.179697i | ||||
\(639\) | 1.29704e11i | 0.777946i | ||||||||
\(640\) | 8.20085e10 | − | 5.44384e9i | 0.488809 | − | 0.0324478i | ||||
\(641\) | 3.95082e10 | 0.234021 | 0.117011 | − | 0.993131i | \(-0.462669\pi\) | ||||
0.117011 | + | 0.993131i | \(0.462669\pi\) | |||||||
\(642\) | 1.58414e10 | + | 3.21136e10i | 0.0932511 | + | 0.189038i | ||||
\(643\) | −2.31888e11 | −1.35655 | −0.678273 | − | 0.734810i | \(-0.737271\pi\) | ||||
−0.678273 | + | 0.734810i | \(0.737271\pi\) | |||||||
\(644\) | 2.09320e11 | − | 2.72926e11i | 1.21694 | − | 1.58673i | ||||
\(645\) | − | 2.47556e10i | − | 0.143033i | ||||||
\(646\) | −7.55467e9 | − | 1.53147e10i | −0.0433796 | − | 0.0879386i | ||||
\(647\) | − | 2.28008e11i | − | 1.30117i | −0.759434 | − | 0.650584i | \(-0.774524\pi\) | ||
0.759434 | − | 0.650584i | \(-0.225476\pi\) | |||||||
\(648\) | 1.52159e11 | + | 3.02097e10i | 0.862973 | + | 0.171335i | ||||
\(649\) | 3.31242e10 | 0.186710 | ||||||||
\(650\) | −2.33990e10 | + | 1.15426e10i | −0.131082 | + | 0.0646619i | ||||
\(651\) | −1.14565e11 | −0.637865 | ||||||||
\(652\) | 7.19117e10 | − | 9.37634e10i | 0.397932 | − | 0.518851i | ||||
\(653\) | − | 2.39319e11i | − | 1.31621i | −0.752927 | − | 0.658104i | \(-0.771359\pi\) | ||
0.752927 | − | 0.658104i | \(-0.228641\pi\) | |||||||
\(654\) | −2.33221e11 | + | 1.15046e11i | −1.27484 | + | 0.628871i | ||||
\(655\) | − | 1.90710e9i | − | 0.0103612i | ||||||
\(656\) | −4.07949e10 | − | 1.51959e11i | −0.220288 | − | 0.820560i | ||||
\(657\) | 6.98820e10 | 0.375063 | ||||||||
\(658\) | 1.74824e11 | + | 3.54402e11i | 0.932606 | + | 1.89057i | ||||
\(659\) | −1.93384e10 | −0.102537 | −0.0512684 | − | 0.998685i | \(-0.516326\pi\) | ||||
−0.0512684 | + | 0.998685i | \(0.516326\pi\) | |||||||
\(660\) | −5.24713e10 | − | 4.02428e10i | −0.276532 | − | 0.212086i | ||||
\(661\) | 6.26405e10i | 0.328133i | 0.986449 | + | 0.164066i | \(0.0524611\pi\) | ||||
−0.986449 | + | 0.164066i | \(0.947539\pi\) | |||||||
\(662\) | 1.03114e11 | + | 2.09032e11i | 0.536892 | + | 1.08838i | ||||
\(663\) | − | 4.23408e9i | − | 0.0219131i | ||||||
\(664\) | −2.43879e11 | − | 4.84199e10i | −1.25459 | − | 0.249087i | ||||
\(665\) | −2.15481e11 | −1.10185 | ||||||||
\(666\) | −1.92847e11 | + | 9.51302e10i | −0.980203 | + | 0.483528i | ||||
\(667\) | −1.82306e11 | −0.921082 | ||||||||
\(668\) | 2.20822e11 | + | 1.69359e11i | 1.10901 | + | 0.850554i | ||||
\(669\) | 1.43377e8i | 0.000715774i | ||||||||
\(670\) | −2.98367e10 | + | 1.47182e10i | −0.148065 | + | 0.0730393i | ||||
\(671\) | − | 4.91254e10i | − | 0.242335i | ||||||
\(672\) | −3.51663e11 | − | 4.00513e11i | −1.72445 | − | 1.96399i | ||||
\(673\) | 2.62188e11 | 1.27806 | 0.639031 | − | 0.769181i | \(-0.279335\pi\) | ||||
0.639031 | + | 0.769181i | \(0.279335\pi\) | |||||||
\(674\) | −1.01914e11 | − | 2.06598e11i | −0.493848 | − | 1.00112i | ||||
\(675\) | −2.48400e10 | −0.119656 | ||||||||
\(676\) | −1.22386e11 | + | 1.59575e11i | −0.586064 | + | 0.764150i | ||||
\(677\) | 7.51591e10i | 0.357789i | 0.983868 | + | 0.178894i | \(0.0572520\pi\) | ||||
−0.983868 | + | 0.178894i | \(0.942748\pi\) | |||||||
\(678\) | −1.63120e11 | − | 3.30676e11i | −0.771951 | − | 1.56489i | ||||
\(679\) | 4.09951e11i | 1.92865i | ||||||||
\(680\) | −1.60063e9 | + | 8.06199e9i | −0.00748611 | + | 0.0377057i | ||||
\(681\) | 2.33758e11 | 1.08687 | ||||||||
\(682\) | 2.31984e10 | − | 1.14436e10i | 0.107231 | − | 0.0528963i | ||||
\(683\) | 2.26925e11 | 1.04280 | 0.521399 | − | 0.853313i | \(-0.325410\pi\) | ||||
0.521399 | + | 0.853313i | \(0.325410\pi\) | |||||||
\(684\) | 1.84506e11 | − | 2.40571e11i | 0.842917 | − | 1.09905i | ||||
\(685\) | − | 4.31947e10i | − | 0.196186i | ||||||
\(686\) | 4.43232e11 | − | 2.18644e11i | 2.00140 | − | 0.987280i | ||||
\(687\) | 4.55620e11i | 2.04539i | ||||||||
\(688\) | 1.16811e10 | + | 4.35115e10i | 0.0521351 | + | 0.194201i | ||||
\(689\) | −3.95734e10 | −0.175601 | ||||||||
\(690\) | −7.92454e10 | − | 1.60645e11i | −0.349605 | − | 0.708716i | ||||
\(691\) | 1.78978e11 | 0.785034 | 0.392517 | − | 0.919745i | \(-0.371604\pi\) | ||||
0.392517 | + | 0.919745i | \(0.371604\pi\) | |||||||
\(692\) | 1.97627e11 | + | 1.51570e11i | 0.861832 | + | 0.660980i | ||||
\(693\) | 2.25439e11i | 0.977453i | ||||||||
\(694\) | 8.97486e10 | + | 1.81938e11i | 0.386892 | + | 0.784304i | ||||
\(695\) | 1.98355e11i | 0.850168i | ||||||||
\(696\) | −5.50142e10 | + | 2.77093e11i | −0.234443 | + | 1.18083i | ||||
\(697\) | 1.57348e10 | 0.0666700 | ||||||||
\(698\) | −1.85888e11 | + | 9.16974e10i | −0.783123 | + | 0.386309i | ||||
\(699\) | 5.00724e11 | 2.09744 | ||||||||
\(700\) | −2.60628e11 | − | 1.99888e11i | −1.08550 | − | 0.832522i | ||||
\(701\) | − | 3.94384e11i | − | 1.63323i | −0.577182 | − | 0.816615i | \(-0.695848\pi\) | ||
0.577182 | − | 0.816615i | \(-0.304152\pi\) | |||||||
\(702\) | 6.59456e9 | − | 3.25305e9i | 0.0271542 | − | 0.0133950i | ||||
\(703\) | − | 3.00948e11i | − | 1.23217i | ||||||
\(704\) | 1.11215e11 | + | 4.59734e10i | 0.452763 | + | 0.187161i | ||||
\(705\) | 2.05804e11 | 0.833101 | ||||||||
\(706\) | −1.96542e11 | − | 3.98428e11i | −0.791109 | − | 1.60373i | ||||
\(707\) | −6.63773e11 | −2.65670 | ||||||||
\(708\) | 8.46184e10 | − | 1.10331e11i | 0.336769 | − | 0.439102i | ||||
\(709\) | − | 2.95896e11i | − | 1.17099i | −0.810675 | − | 0.585496i | \(-0.800900\pi\) | ||
0.810675 | − | 0.585496i | \(-0.199100\pi\) | |||||||
\(710\) | 3.86528e10 | + | 7.83565e10i | 0.152106 | + | 0.308348i | ||||
\(711\) | − | 3.52221e11i | − | 1.37828i | ||||||
\(712\) | 1.04907e11 | + | 2.08283e10i | 0.408211 | + | 0.0810466i | ||||
\(713\) | 7.00712e10 | 0.271132 | ||||||||
\(714\) | 4.78022e10 | − | 2.35805e10i | 0.183931 | − | 0.0907320i | ||||
\(715\) | 1.20632e10 | 0.0461570 | ||||||||
\(716\) | −2.37294e11 | + | 3.09401e11i | −0.902891 | + | 1.17725i | ||||
\(717\) | 4.50915e11i | 1.70615i | ||||||||
\(718\) | 1.52088e11 | − | 7.50239e10i | 0.572264 | − | 0.282294i | ||||
\(719\) | − | 5.83303e10i | − | 0.218262i | −0.994027 | − | 0.109131i | \(-0.965193\pi\) | ||
0.994027 | − | 0.109131i | \(-0.0348068\pi\) | |||||||
\(720\) | −1.40935e11 | + | 3.78354e10i | −0.524431 | + | 0.140789i | ||||
\(721\) | −3.99214e11 | −1.47729 | ||||||||
\(722\) | 6.74965e10 | + | 1.36828e11i | 0.248389 | + | 0.503532i | ||||
\(723\) | −3.69169e10 | −0.135105 | ||||||||
\(724\) | 5.55413e10 | + | 4.25973e10i | 0.202144 | + | 0.155034i | ||||
\(725\) | 1.74091e11i | 0.630123i | ||||||||
\(726\) | 1.35624e11 | + | 2.74936e11i | 0.488191 | + | 0.989657i | ||||
\(727\) | − | 1.79422e11i | − | 0.642302i | −0.947028 | − | 0.321151i | \(-0.895930\pi\) | ||
0.947028 | − | 0.321151i | \(-0.104070\pi\) | |||||||
\(728\) | 9.53694e10 | + | 1.89347e10i | 0.339534 | + | 0.0674114i | ||||
\(729\) | −3.39995e11 | −1.20382 | ||||||||
\(730\) | 4.22170e10 | − | 2.08254e10i | 0.148661 | − | 0.0733333i | ||||
\(731\) | −4.50547e9 | −0.0157787 | ||||||||
\(732\) | −1.63628e11 | − | 1.25495e11i | −0.569921 | − | 0.437100i | ||||
\(733\) | 4.89146e11i | 1.69443i | 0.531252 | + | 0.847214i | \(0.321722\pi\) | ||||
−0.531252 | + | 0.847214i | \(0.678278\pi\) | |||||||
\(734\) | 2.74483e11 | − | 1.35401e11i | 0.945651 | − | 0.466483i | ||||
\(735\) | − | 4.64986e11i | − | 1.59328i | ||||||
\(736\) | 2.15087e11 | + | 2.44965e11i | 0.732997 | + | 0.834819i | ||||
\(737\) | −4.87135e10 | −0.165112 | ||||||||
\(738\) | 1.23585e11 | + | 2.50530e11i | 0.416620 | + | 0.844567i | ||||
\(739\) | −7.93815e10 | −0.266159 | −0.133080 | − | 0.991105i | \(-0.542487\pi\) | ||||
−0.133080 | + | 0.991105i | \(0.542487\pi\) | |||||||
\(740\) | −8.81528e10 | + | 1.14940e11i | −0.293974 | + | 0.383304i | ||||
\(741\) | 1.05205e11i | 0.348949i | ||||||||
\(742\) | −2.20393e11 | − | 4.46779e11i | −0.727081 | − | 1.47393i | ||||
\(743\) | − | 3.46525e11i | − | 1.13705i | −0.822666 | − | 0.568525i | \(-0.807514\pi\) | ||
0.822666 | − | 0.568525i | \(-0.192486\pi\) | |||||||
\(744\) | 2.11453e10 | − | 1.06503e11i | 0.0690115 | − | 0.347594i | ||||
\(745\) | 1.68625e11 | 0.547392 | ||||||||
\(746\) | −4.88880e11 | + | 2.41161e11i | −1.57851 | + | 0.778668i | ||||
\(747\) | 4.41455e11 | 1.41777 | ||||||||
\(748\) | −7.32410e9 | + | 9.54966e9i | −0.0233963 | + | 0.0305057i | ||||
\(749\) | − | 8.22344e10i | − | 0.261292i | ||||||
\(750\) | −3.55254e11 | + | 1.75245e11i | −1.12278 | + | 0.553859i | ||||
\(751\) | 4.95183e11i | 1.55670i | 0.627828 | + | 0.778352i | \(0.283944\pi\) | ||||
−0.627828 | + | 0.778352i | \(0.716056\pi\) | |||||||
\(752\) | −3.61730e11 | + | 9.71102e10i | −1.13113 | + | 0.303664i | ||||
\(753\) | −6.91234e11 | −2.15003 | ||||||||
\(754\) | −2.27991e10 | − | 4.62180e10i | −0.0705394 | − | 0.142997i | ||||
\(755\) | −1.24151e10 | −0.0382087 | ||||||||
\(756\) | 7.34532e10 | + | 5.63348e10i | 0.224866 | + | 0.172460i | ||||
\(757\) | − | 2.26936e11i | − | 0.691066i | −0.938407 | − | 0.345533i | \(-0.887698\pi\) | ||
0.938407 | − | 0.345533i | \(-0.112302\pi\) | |||||||
\(758\) | 2.94678e10 | + | 5.97369e10i | 0.0892630 | + | 0.180953i | ||||
\(759\) | − | 2.62281e11i | − | 0.790315i | ||||||
\(760\) | 3.97712e10 | − | 2.00317e11i | 0.119210 | − | 0.600433i | ||||
\(761\) | 2.72409e10 | 0.0812236 | 0.0406118 | − | 0.999175i | \(-0.487069\pi\) | ||||
0.0406118 | + | 0.999175i | \(0.487069\pi\) | |||||||
\(762\) | 6.88896e11 | − | 3.39828e11i | 2.04331 | − | 1.00795i | ||||
\(763\) | 5.97217e11 | 1.76211 | ||||||||
\(764\) | 3.76121e11 | + | 2.88465e11i | 1.10396 | + | 0.846682i | ||||
\(765\) | − | 1.45933e10i | − | 0.0426097i | ||||||
\(766\) | 1.05113e11 | − | 5.18515e10i | 0.305310 | − | 0.150607i | ||||
\(767\) | 2.53652e10i | 0.0732921i | ||||||||
\(768\) | 4.37235e11 | − | 2.52994e11i | 1.25681 | − | 0.727220i | ||||
\(769\) | 1.27241e11 | 0.363849 | 0.181925 | − | 0.983312i | \(-0.441767\pi\) | ||||
0.181925 | + | 0.983312i | \(0.441767\pi\) | |||||||
\(770\) | 6.71825e10 | + | 1.36192e11i | 0.191114 | + | 0.387425i | ||||
\(771\) | −7.55135e11 | −2.13701 | ||||||||
\(772\) | −8.55570e10 | + | 1.11555e11i | −0.240872 | + | 0.314065i | ||||
\(773\) | − | 2.59208e11i | − | 0.725991i | −0.931791 | − | 0.362995i | \(-0.881754\pi\) | ||
0.931791 | − | 0.362995i | \(-0.118246\pi\) | |||||||
\(774\) | −3.53870e10 | − | 7.17362e10i | −0.0986007 | − | 0.199882i | ||||
\(775\) | − | 6.69138e10i | − | 0.185485i | ||||||
\(776\) | −3.81103e11 | − | 7.56644e10i | −1.05098 | − | 0.208663i | ||||
\(777\) | 9.39354e11 | 2.57718 | ||||||||
\(778\) | 5.77078e11 | − | 2.84669e11i | 1.57513 | − | 0.777001i | ||||
\(779\) | −3.90965e11 | −1.06167 | ||||||||
\(780\) | 3.08163e10 | − | 4.01804e10i | 0.0832533 | − | 0.108551i | ||||
\(781\) | 1.27930e11i | 0.343851i | ||||||||
\(782\) | −2.92371e10 | + | 1.44225e10i | −0.0781822 | + | 0.0385668i | ||||
\(783\) | − | 4.90644e10i | − | 0.130533i | ||||||
\(784\) | 2.19407e11 | + | 8.17279e11i | 0.580746 | + | 2.16325i | ||||
\(785\) | 8.99359e10 | 0.236840 | ||||||||
\(786\) | −5.18556e9 | − | 1.05121e10i | −0.0135864 | − | 0.0275423i | ||||
\(787\) | 4.49274e11 | 1.17115 | 0.585575 | − | 0.810618i | \(-0.300869\pi\) | ||||
0.585575 | + | 0.810618i | \(0.300869\pi\) | |||||||
\(788\) | −3.42752e11 | − | 2.62873e11i | −0.888945 | − | 0.681775i | ||||
\(789\) | − | 3.26654e11i | − | 0.842908i | ||||||
\(790\) | −1.04964e11 | − | 2.12783e11i | −0.269485 | − | 0.546296i | ||||
\(791\) | 8.46775e11i | 2.16303i | ||||||||
\(792\) | −2.09575e11 | − | 4.16092e10i | −0.532646 | − | 0.105752i | ||||
\(793\) | 3.76182e10 | 0.0951274 | ||||||||
\(794\) | 9.74633e10 | − | 4.80780e10i | 0.245222 | − | 0.120966i | ||||
\(795\) | −2.59448e11 | −0.649505 | ||||||||
\(796\) | −4.04678e11 | − | 3.10367e11i | −1.00799 | − | 0.773079i | ||||
\(797\) | 6.66061e10i | 0.165075i | 0.996588 | + | 0.0825374i | \(0.0263024\pi\) | ||||
−0.996588 | + | 0.0825374i | \(0.973698\pi\) | |||||||
\(798\) | −1.18775e12 | + | 5.85908e11i | −2.92895 | + | 1.44483i | ||||
\(799\) | − | 3.74559e10i | − | 0.0919038i | ||||||
\(800\) | 2.33926e11 | − | 2.05395e11i | 0.571110 | − | 0.501452i | ||||
\(801\) | −1.89897e11 | −0.461304 | ||||||||
\(802\) | −3.79886e10 | − | 7.70102e10i | −0.0918240 | − | 0.186145i | ||||
\(803\) | 6.89265e10 | 0.165777 | ||||||||
\(804\) | −1.24442e11 | + | 1.62256e11i | −0.297813 | + | 0.388309i | ||||
\(805\) | 4.11370e11i | 0.979602i | ||||||||
\(806\) | 8.76305e9 | + | 1.77644e10i | 0.0207642 | + | 0.0420930i | ||||
\(807\) | 1.05005e12i | 2.47579i | ||||||||
\(808\) | 1.22512e11 | − | 6.17064e11i | 0.287431 | − | 1.44772i | ||||
\(809\) | −1.25912e9 | −0.00293949 | −0.00146974 | − | 0.999999i | \(-0.500468\pi\) | ||||
−0.00146974 | + | 0.999999i | \(0.500468\pi\) | |||||||
\(810\) | −1.66392e11 | + | 8.20799e10i | −0.386537 | + | 0.190676i | ||||
\(811\) | 6.64956e10 | 0.153713 | 0.0768563 | − | 0.997042i | \(-0.475512\pi\) | ||||
0.0768563 | + | 0.997042i | \(0.475512\pi\) | |||||||
\(812\) | 3.94823e11 | − | 5.14798e11i | 0.908194 | − | 1.18417i | ||||
\(813\) | − | 4.59543e11i | − | 1.05188i | ||||||
\(814\) | −1.90210e11 | + | 9.38294e10i | −0.433247 | + | 0.213718i | ||||
\(815\) | 1.41326e11i | 0.320325i | ||||||||
\(816\) | 1.30983e10 | + | 4.87907e10i | 0.0295431 | + | 0.110046i | ||||
\(817\) | 1.11948e11 | 0.251263 | ||||||||
\(818\) | −8.10697e10 | − | 1.64344e11i | −0.181070 | − | 0.367063i | ||||
\(819\) | −1.72632e11 | −0.383695 | ||||||||
\(820\) | 1.49320e11 | + | 1.14520e11i | 0.330264 | + | 0.253296i | ||||
\(821\) | − | 3.44376e10i | − | 0.0757984i | −0.999282 | − | 0.0378992i | \(-0.987933\pi\) | ||
0.999282 | − | 0.0378992i | \(-0.0120666\pi\) | |||||||
\(822\) | −1.17450e11 | − | 2.38093e11i | −0.257256 | − | 0.521506i | ||||
\(823\) | − | 6.67198e11i | − | 1.45430i | −0.686476 | − | 0.727152i | \(-0.740843\pi\) | ||
0.686476 | − | 0.727152i | \(-0.259157\pi\) | |||||||
\(824\) | 7.36827e10 | − | 3.71121e11i | 0.159829 | − | 0.805021i | ||||
\(825\) | −2.50463e11 | −0.540664 | ||||||||
\(826\) | −2.86370e11 | + | 1.41265e11i | −0.615188 | + | 0.303468i | ||||
\(827\) | 6.65965e11 | 1.42374 | 0.711868 | − | 0.702313i | \(-0.247849\pi\) | ||||
0.711868 | + | 0.702313i | \(0.247849\pi\) | |||||||
\(828\) | −4.59270e11 | − | 3.52236e11i | −0.977118 | − | 0.749399i | ||||
\(829\) | − | 4.92924e10i | − | 0.104367i | −0.998638 | − | 0.0521834i | \(-0.983382\pi\) | ||
0.998638 | − | 0.0521834i | \(-0.0166180\pi\) | |||||||
\(830\) | 2.66691e11 | − | 1.31557e11i | 0.561948 | − | 0.277206i | ||||
\(831\) | 3.20518e11i | 0.672121i | ||||||||
\(832\) | −3.52046e10 | + | 8.51636e10i | −0.0734693 | + | 0.177730i | ||||
\(833\) | −8.46265e10 | −0.175763 | ||||||||
\(834\) | 5.39343e11 | + | 1.09335e12i | 1.11481 | + | 2.25993i | ||||
\(835\) | −3.32835e11 | −0.684673 | ||||||||
\(836\) | 1.81983e11 | − | 2.37282e11i | 0.372568 | − | 0.485779i | ||||
\(837\) | 1.88584e10i | 0.0384240i | ||||||||
\(838\) | 2.50437e11 | + | 5.07684e11i | 0.507836 | + | 1.02948i | ||||
\(839\) | − | 8.54314e11i | − | 1.72413i | −0.506799 | − | 0.862064i | \(-0.669172\pi\) | ||
0.506799 | − | 0.862064i | \(-0.330828\pi\) | |||||||
\(840\) | 6.25255e11 | + | 1.24138e11i | 1.25586 | + | 0.249338i | ||||
\(841\) | 1.56378e11 | 0.312602 | ||||||||
\(842\) | −6.21117e11 | + | 3.06393e11i | −1.23573 | + | 0.609580i | ||||
\(843\) | −3.17114e11 | −0.627921 | ||||||||
\(844\) | −5.15958e11 | + | 6.72742e11i | −1.01682 | + | 1.32580i | ||||
\(845\) | − | 2.40521e11i | − | 0.471766i | ||||||
\(846\) | 5.96374e11 | − | 2.94188e11i | 1.16423 | − | 0.574305i | ||||
\(847\) | − | 7.04038e11i | − | 1.36792i | ||||||
\(848\) | 4.56017e11 | − | 1.22423e11i | 0.881857 | − | 0.236743i | ||||
\(849\) | 1.29160e11 | 0.248599 | ||||||||
\(850\) | 1.37726e10 | + | 2.79197e10i | 0.0263840 | + | 0.0534854i | ||||
\(851\) | −5.74534e11 | −1.09546 | ||||||||
\(852\) | 4.26115e11 | + | 3.26808e11i | 0.808664 | + | 0.620203i | ||||
\(853\) | 7.82406e11i | 1.47787i | 0.673778 | + | 0.738934i | \(0.264671\pi\) | ||||
−0.673778 | + | 0.738934i | \(0.735329\pi\) | |||||||
\(854\) | 2.09505e11 | + | 4.24706e11i | 0.393878 | + | 0.798466i | ||||
\(855\) | 3.62603e11i | 0.678526i | ||||||||
\(856\) | 7.64476e10 | + | 1.51780e10i | 0.142387 | + | 0.0282695i | ||||
\(857\) | −1.52126e11 | −0.282020 | −0.141010 | − | 0.990008i | \(-0.545035\pi\) | ||||
−0.141010 | + | 0.990008i | \(0.545035\pi\) | |||||||
\(858\) | 6.64932e10 | − | 3.28007e10i | 0.122695 | − | 0.0605249i | ||||
\(859\) | −4.22089e11 | −0.775231 | −0.387616 | − | 0.921821i | \(-0.626701\pi\) | ||||
−0.387616 | + | 0.921821i | \(0.626701\pi\) | |||||||
\(860\) | −4.27559e10 | − | 3.27915e10i | −0.0781631 | − | 0.0599471i | ||||
\(861\) | − | 1.22033e12i | − | 2.22056i | ||||||
\(862\) | 2.96457e11 | − | 1.46240e11i | 0.536948 | − | 0.264873i | ||||
\(863\) | 6.63648e11i | 1.19645i | 0.801328 | + | 0.598225i | \(0.204127\pi\) | ||||
−0.801328 | + | 0.598225i | \(0.795873\pi\) | |||||||
\(864\) | −6.59277e10 | + | 5.78866e10i | −0.118308 | + | 0.103878i | ||||
\(865\) | −2.97875e11 | −0.532071 | ||||||||
\(866\) | −2.31263e11 | − | 4.68815e11i | −0.411183 | − | 0.833546i | ||||
\(867\) | 8.15405e11 | 1.44310 | ||||||||
\(868\) | −1.51754e11 | + | 1.97868e11i | −0.267339 | + | 0.348575i | ||||
\(869\) | − | 3.47405e11i | − | 0.609195i | ||||||
\(870\) | −1.49474e11 | − | 3.03012e11i | −0.260908 | − | 0.528911i | ||||
\(871\) | − | 3.73028e10i | − | 0.0648141i | ||||||
\(872\) | −1.10228e11 | + | 5.55191e11i | −0.190645 | + | 0.960232i | ||||
\(873\) | 6.89849e11 | 1.18767 | ||||||||
\(874\) | 7.26459e11 | − | 3.58357e11i | 1.24499 | − | 0.614145i | ||||
\(875\) | 9.09712e11 | 1.55193 | ||||||||
\(876\) | 1.76078e11 | − | 2.29583e11i | 0.299012 | − | 0.389872i | ||||
\(877\) | 1.83107e11i | 0.309533i | 0.987951 | + | 0.154767i | \(0.0494626\pi\) | ||||
−0.987951 | + | 0.154767i | \(0.950537\pi\) | |||||||
\(878\) | −4.07385e11 | + | 2.00960e11i | −0.685531 | + | 0.338168i | ||||
\(879\) | − | 5.17047e11i | − | 0.866112i | ||||||
\(880\) | −1.39008e11 | + | 3.73181e10i | −0.231798 | + | 0.0622284i | ||||
\(881\) | 3.83245e11 | 0.636170 | 0.318085 | − | 0.948062i | \(-0.396960\pi\) | ||||
0.318085 | + | 0.948062i | \(0.396960\pi\) | |||||||
\(882\) | −6.64676e11 | − | 1.34742e12i | −1.09834 | − | 2.22654i | ||||
\(883\) | −5.57963e11 | −0.917831 | −0.458916 | − | 0.888480i | \(-0.651762\pi\) | ||||
−0.458916 | + | 0.888480i | \(0.651762\pi\) | |||||||
\(884\) | −7.31274e9 | − | 5.60850e9i | −0.0119749 | − | 0.00918412i | ||||
\(885\) | 1.66298e11i | 0.271090i | ||||||||
\(886\) | −1.19668e11 | − | 2.42590e11i | −0.194197 | − | 0.393675i | ||||
\(887\) | 5.00815e11i | 0.809064i | 0.914524 | + | 0.404532i | \(0.132566\pi\) | ||||
−0.914524 | + | 0.404532i | \(0.867434\pi\) | |||||||
\(888\) | −1.73376e11 | + | 8.73252e11i | −0.278829 | + | 1.40439i | ||||
\(889\) | −1.76408e12 | −2.82430 | ||||||||
\(890\) | −1.14720e11 | + | 5.65906e10i | −0.182843 | + | 0.0901954i | ||||
\(891\) | −2.71663e11 | −0.431042 | ||||||||
\(892\) | 2.47629e8 | + | 1.89919e8i | 0.000391150 | + | 0.000299992i | ||||
\(893\) | 9.30673e11i | 1.46349i | ||||||||
\(894\) | 9.29478e11 | − | 4.58506e11i | 1.45509 | − | 0.717785i | ||||
\(895\) | − | 4.66346e11i | − | 0.726803i | ||||||
\(896\) | −1.15755e12 | + | 7.68397e10i | −1.79600 | + | 0.119221i | ||||
\(897\) | 2.00844e11 | 0.310234 | ||||||||
\(898\) | 2.12316e11 | + | 4.30404e11i | 0.326495 | + | 0.661868i | ||||
\(899\) | 1.32169e11 | 0.202345 | ||||||||
\(900\) | −3.36365e11 | + | 4.38575e11i | −0.512673 | + | 0.668458i | ||||
\(901\) | 4.72191e10i | 0.0716503i | ||||||||
\(902\) | 1.21895e11 | + | 2.47104e11i | 0.184145 | + | 0.373297i | ||||
\(903\) | 3.49426e11i | 0.525538i | ||||||||
\(904\) | −7.87188e11 | − | 1.56289e11i | −1.17870 | − | 0.234021i | ||||
\(905\) | −8.37150e10 | −0.124798 | ||||||||
\(906\) | −6.84331e10 | + | 3.37576e10i | −0.101567 | + | 0.0501024i | ||||
\(907\) | −2.38926e11 | −0.353048 | −0.176524 | − | 0.984296i | \(-0.556485\pi\) | ||||
−0.176524 | + | 0.984296i | \(0.556485\pi\) | |||||||
\(908\) | 3.09638e11 | − | 4.03727e11i | 0.455523 | − | 0.593943i | ||||
\(909\) | 1.11697e12i | 1.63601i | ||||||||
\(910\) | −1.04290e11 | + | 5.14457e10i | −0.152082 | + | 0.0750211i | ||||
\(911\) | − | 5.49254e11i | − | 0.797443i | −0.917072 | − | 0.398721i | \(-0.869454\pi\) | ||
0.917072 | − | 0.398721i | \(-0.130546\pi\) | |||||||
\(912\) | −3.25456e11 | − | 1.21231e12i | −0.470450 | − | 1.75240i | ||||
\(913\) | 4.35419e11 | 0.626649 | ||||||||
\(914\) | 4.41540e10 | + | 8.95085e10i | 0.0632681 | + | 0.128256i | ||||
\(915\) | 2.46630e11 | 0.351853 | ||||||||
\(916\) | 7.86908e11 | + | 6.03518e11i | 1.11774 | + | 0.857252i | ||||
\(917\) | 2.69187e10i | 0.0380695i | ||||||||
\(918\) | −3.88155e9 | − | 7.86864e9i | −0.00546556 | − | 0.0110797i | ||||
\(919\) | − | 1.35358e12i | − | 1.89768i | −0.315756 | − | 0.948840i | \(-0.602258\pi\) | ||
0.315756 | − | 0.948840i | \(-0.397742\pi\) | |||||||
\(920\) | −3.82423e11 | − | 7.59264e10i | −0.533817 | − | 0.105984i | ||||
\(921\) | −4.46958e10 | −0.0621196 | ||||||||
\(922\) | −6.46829e11 | + | 3.19077e11i | −0.895089 | + | 0.441542i | ||||
\(923\) | −9.79639e10 | −0.134977 | ||||||||
\(924\) | 7.40632e11 | + | 5.68026e11i | 1.01605 | + | 0.779257i | ||||
\(925\) | 5.48645e11i | 0.749419i | ||||||||
\(926\) | −1.50980e11 | + | 7.44773e10i | −0.205340 | + | 0.101293i | ||||
\(927\) | 6.71782e11i | 0.909723i | ||||||||
\(928\) | 4.05699e11 | + | 4.62056e11i | 0.547032 | + | 0.623021i | ||||
\(929\) | 1.05298e12 | 1.41370 | 0.706850 | − | 0.707363i | \(-0.250116\pi\) | ||||
0.706850 | + | 0.707363i | \(0.250116\pi\) | |||||||
\(930\) | 5.74517e10 | + | 1.16466e11i | 0.0768018 | + | 0.155692i | ||||
\(931\) | 2.10273e12 | 2.79888 | ||||||||
\(932\) | 6.63264e11 | − | 8.64809e11i | 0.879068 | − | 1.14619i | ||||
\(933\) | − | 8.17412e11i | − | 1.07873i | ||||||
\(934\) | −3.90557e11 | − | 7.91733e11i | −0.513212 | − | 1.04038i | ||||
\(935\) | − | 1.43938e10i | − | 0.0188334i | ||||||
\(936\) | 3.18626e10 | − | 1.60484e11i | 0.0415124 | − | 0.209088i | ||||
\(937\) | −1.25357e12 | −1.62626 | −0.813131 | − | 0.582080i | \(-0.802239\pi\) | ||||
−0.813131 | + | 0.582080i | \(0.802239\pi\) | |||||||
\(938\) | 4.21145e11 | − | 2.07748e11i | 0.544026 | − | 0.268365i | ||||
\(939\) | −6.48320e10 | −0.0833925 | ||||||||
\(940\) | 2.72610e11 | − | 3.55448e11i | 0.349165 | − | 0.455265i | ||||
\(941\) | 1.06766e12i | 1.36168i | 0.732431 | + | 0.680841i | \(0.238386\pi\) | ||||
−0.732431 | + | 0.680841i | \(0.761614\pi\) | |||||||
\(942\) | 4.95734e11 | − | 2.44543e11i | 0.629572 | − | 0.310564i | ||||
\(943\) | 7.46384e11i | 0.943878i | ||||||||
\(944\) | −7.84687e10 | − | 2.92292e11i | −0.0988117 | − | 0.368068i | ||||
\(945\) | −1.10713e11 | −0.138826 | ||||||||
\(946\) | −3.49032e10 | − | 7.07553e10i | −0.0435813 | − | 0.0883476i | ||||
\(947\) | −1.86163e11 | −0.231470 | −0.115735 | − | 0.993280i | \(-0.536922\pi\) | ||||
−0.115735 | + | 0.993280i | \(0.536922\pi\) | |||||||
\(948\) | −1.15715e12 | − | 8.87471e11i | −1.43270 | − | 1.09881i | ||||
\(949\) | 5.27811e10i | 0.0650750i | ||||||||
\(950\) | −3.42210e11 | − | 6.93724e11i | −0.420144 | − | 0.851711i | ||||
\(951\) | − | 1.10325e12i | − | 1.34881i | ||||||
\(952\) | 2.25929e10 | − | 1.13795e11i | 0.0275058 | − | 0.138540i | ||||
\(953\) | 3.12215e11 | 0.378514 | 0.189257 | − | 0.981928i | \(-0.439392\pi\) | ||||
0.189257 | + | 0.981928i | \(0.439392\pi\) | |||||||
\(954\) | −7.51823e11 | + | 3.70869e11i | −0.907657 | + | 0.447742i | ||||
\(955\) | −5.66911e11 | −0.681556 | ||||||||
\(956\) | 7.78784e11 | + | 5.97287e11i | 0.932364 | + | 0.715075i | ||||
\(957\) | − | 4.94719e11i | − | 0.589808i | ||||||
\(958\) | −3.53172e11 | + | 1.74217e11i | −0.419299 | + | 0.206838i | ||||
\(959\) | 6.09694e11i | 0.720837i | ||||||||
\(960\) | −2.30806e11 | + | 5.58344e11i | −0.271745 | + | 0.657380i | ||||
\(961\) | 8.02090e11 | 0.940437 | ||||||||
\(962\) | −7.18508e10 | − | 1.45655e11i | −0.0838940 | − | 0.170069i | ||||
\(963\) | −1.38381e11 | −0.160906 | ||||||||
\(964\) | −4.89005e10 | + | 6.37599e10i | −0.0566246 | + | 0.0738311i | ||||
\(965\) | − | 1.68142e11i | − | 0.193895i | ||||||
\(966\) | 1.11855e12 | + | 2.26751e12i | 1.28454 | + | 2.60400i | ||||
\(967\) | 8.68168e11i | 0.992883i | 0.868070 | + | 0.496441i | \(0.165360\pi\) | ||||
−0.868070 | + | 0.496441i | \(0.834640\pi\) | |||||||
\(968\) | 6.54495e11 | + | 1.29944e11i | 0.745427 | + | 0.147998i | ||||
\(969\) | 1.25530e11 | 0.142382 | ||||||||
\(970\) | 4.16751e11 | − | 2.05580e11i | 0.470749 | − | 0.232217i | ||||
\(971\) | −1.09375e12 | −1.23039 | −0.615194 | − | 0.788376i | \(-0.710922\pi\) | ||||
−0.615194 | + | 0.788376i | \(0.710922\pi\) | |||||||
\(972\) | −7.79508e11 | + | 1.01638e12i | −0.873284 | + | 1.13865i | ||||
\(973\) | − | 2.79978e12i | − | 3.12373i | ||||||
\(974\) | 1.48946e11 | − | 7.34742e10i | 0.165498 | − | 0.0816393i | ||||
\(975\) | − | 1.91794e11i | − | 0.212235i | ||||||
\(976\) | −4.33487e11 | + | 1.16374e11i | −0.477724 | + | 0.128250i | ||||
\(977\) | −3.26541e11 | −0.358392 | −0.179196 | − | 0.983813i | \(-0.557350\pi\) | ||||
−0.179196 | + | 0.983813i | \(0.557350\pi\) | |||||||
\(978\) | 3.84275e11 | + | 7.78999e11i | 0.420036 | + | 0.851494i | ||||
\(979\) | −1.87300e11 | −0.203895 | ||||||||
\(980\) | −8.03086e11 | − | 6.15925e11i | −0.870678 | − | 0.667765i | ||||
\(981\) | − | 1.00497e12i | − | 1.08512i | ||||||
\(982\) | 3.67382e11 | + | 7.44753e11i | 0.395068 | + | 0.800878i | ||||
\(983\) | 1.39780e12i | 1.49704i | 0.663115 | + | 0.748518i | \(0.269234\pi\) | ||||
−0.663115 | + | 0.748518i | \(0.730766\pi\) | |||||||
\(984\) | 1.13445e12 | + | 2.25235e11i | 1.21006 | + | 0.240246i | ||||
\(985\) | 5.16615e11 | 0.548811 | ||||||||
\(986\) | −5.51475e10 | + | 2.72039e10i | −0.0583469 | + | 0.0287822i | ||||
\(987\) | −2.90493e12 | −3.06102 | ||||||||
\(988\) | 1.81701e11 | + | 1.39355e11i | 0.190690 | + | 0.146250i | ||||
\(989\) | − | 2.13718e11i | − | 0.223386i | ||||||
\(990\) | 2.29178e11 | − | 1.13052e11i | 0.238579 | − | 0.117690i | ||||
\(991\) | 1.15200e11i | 0.119442i | 0.998215 | + | 0.0597211i | \(0.0190211\pi\) | ||||
−0.998215 | + | 0.0597211i | \(0.980979\pi\) | |||||||
\(992\) | −1.55935e11 | − | 1.77596e11i | −0.161026 | − | 0.183394i | ||||
\(993\) | −1.71338e12 | −1.76220 | ||||||||
\(994\) | −5.45583e11 | − | 1.10600e12i | −0.558876 | − | 1.13295i | ||||
\(995\) | 6.09955e11 | 0.622308 | ||||||||
\(996\) | 1.11231e12 | − | 1.45031e12i | 1.13029 | − | 1.47375i | ||||
\(997\) | 6.83531e11i | 0.691796i | 0.938272 | + | 0.345898i | \(0.112426\pi\) | ||||
−0.938272 | + | 0.345898i | \(0.887574\pi\) | |||||||
\(998\) | −5.68070e10 | − | 1.15159e11i | −0.0572637 | − | 0.116084i | ||||
\(999\) | − | 1.54625e11i | − | 0.155245i |
(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 | 8.9.d.b.3.6 | yes | 6 | |
3.2 | odd | 2 | 72.9.b.b.19.1 | 6 | |||
4.3 | odd | 2 | 32.9.d.b.15.5 | 6 | |||
8.3 | odd | 2 | inner | 8.9.d.b.3.5 | ✓ | 6 | |
8.5 | even | 2 | 32.9.d.b.15.6 | 6 | |||
12.11 | even | 2 | 288.9.b.b.271.4 | 6 | |||
16.3 | odd | 4 | 256.9.c.n.255.11 | 12 | |||
16.5 | even | 4 | 256.9.c.n.255.12 | 12 | |||
16.11 | odd | 4 | 256.9.c.n.255.2 | 12 | |||
16.13 | even | 4 | 256.9.c.n.255.1 | 12 | |||
24.5 | odd | 2 | 288.9.b.b.271.3 | 6 | |||
24.11 | even | 2 | 72.9.b.b.19.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.9.d.b.3.5 | ✓ | 6 | 8.3 | odd | 2 | inner | |
8.9.d.b.3.6 | yes | 6 | 1.1 | even | 1 | trivial | |
32.9.d.b.15.5 | 6 | 4.3 | odd | 2 | |||
32.9.d.b.15.6 | 6 | 8.5 | even | 2 | |||
72.9.b.b.19.1 | 6 | 3.2 | odd | 2 | |||
72.9.b.b.19.2 | 6 | 24.11 | even | 2 | |||
256.9.c.n.255.1 | 12 | 16.13 | even | 4 | |||
256.9.c.n.255.2 | 12 | 16.11 | odd | 4 | |||
256.9.c.n.255.11 | 12 | 16.3 | odd | 4 | |||
256.9.c.n.255.12 | 12 | 16.5 | even | 4 | |||
288.9.b.b.271.3 | 6 | 24.5 | odd | 2 | |||
288.9.b.b.271.4 | 6 | 12.11 | even | 2 |