Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,22,Mod(5,8)]
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([0, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(22.3581875430\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 10 x^{19} + 8499037025 x^{18} - 76491332940 x^{17} + \cdots + 35\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{190}\cdot 3^{14}\cdot 5^{4}\cdot 7^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.16 | ||
Root | \(0.500000 + 44665.4i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.22.b.a.5.15 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1174.53 | + | 847.130i | 0.811054 | + | 0.584972i | ||||
\(3\) | − | 178662.i | − | 1.74686i | −0.486949 | − | 0.873430i | \(-0.661890\pi\) | ||
0.486949 | − | 0.873430i | \(-0.338110\pi\) | |||||||
\(4\) | 661894. | + | 1.98996e6i | 0.315616 | + | 0.948887i | ||||
\(5\) | 3.12530e7i | 1.43122i | 0.698501 | + | 0.715609i | \(0.253851\pi\) | ||||
−0.698501 | + | 0.715609i | \(0.746149\pi\) | |||||||
\(6\) | 1.51350e8 | − | 2.09844e8i | 1.02186 | − | 1.41680i | ||||
\(7\) | 2.98846e8 | 0.399869 | 0.199934 | − | 0.979809i | \(-0.435927\pi\) | ||||
0.199934 | + | 0.979809i | \(0.435927\pi\) | |||||||
\(8\) | −9.08340e8 | + | 2.89798e9i | −0.299091 | + | 0.954225i | ||||
\(9\) | −2.14596e10 | −2.05152 | ||||||||
\(10\) | −2.64753e10 | + | 3.67076e10i | −0.837223 | + | 1.16079i | ||||
\(11\) | − | 1.69327e10i | − | 0.196835i | −0.995145 | − | 0.0984177i | \(-0.968622\pi\) | ||
0.995145 | − | 0.0984177i | \(-0.0313781\pi\) | |||||||
\(12\) | 3.55530e11 | − | 1.18255e11i | 1.65757 | − | 0.551337i | ||||
\(13\) | 5.06807e11i | 1.01962i | 0.860288 | + | 0.509809i | \(0.170284\pi\) | ||||
−0.860288 | + | 0.509809i | \(0.829716\pi\) | |||||||
\(14\) | 3.51004e11 | + | 2.53161e11i | 0.324315 | + | 0.233912i | ||||
\(15\) | 5.58370e12 | 2.50014 | ||||||||
\(16\) | −3.52184e12 | + | 2.63429e12i | −0.800773 | + | 0.598967i | ||||
\(17\) | 9.27906e12 | 1.11632 | 0.558162 | − | 0.829732i | \(-0.311507\pi\) | ||||
0.558162 | + | 0.829732i | \(0.311507\pi\) | |||||||
\(18\) | −2.52050e13 | − | 1.81791e13i | −1.66389 | − | 1.20008i | ||||
\(19\) | 5.18928e13i | 1.94175i | 0.239577 | + | 0.970877i | \(0.422991\pi\) | ||||
−0.239577 | + | 0.970877i | \(0.577009\pi\) | |||||||
\(20\) | −6.21921e13 | + | 2.06861e13i | −1.35806 | + | 0.451715i | ||||
\(21\) | − | 5.33923e13i | − | 0.698515i | ||||||
\(22\) | 1.43442e13 | − | 1.98880e13i | 0.115143 | − | 0.159644i | ||||
\(23\) | 2.52326e14 | 1.27004 | 0.635022 | − | 0.772494i | \(-0.280991\pi\) | ||||
0.635022 | + | 0.772494i | \(0.280991\pi\) | |||||||
\(24\) | 5.17758e14 | + | 1.62285e14i | 1.66690 | + | 0.522470i | ||||
\(25\) | −4.99910e14 | −1.04839 | ||||||||
\(26\) | −4.29332e14 | + | 5.95261e14i | −0.596448 | + | 0.826965i | ||||
\(27\) | 1.96515e15i | 1.83686i | ||||||||
\(28\) | 1.97804e14 | + | 5.94691e14i | 0.126205 | + | 0.379431i | ||||
\(29\) | − | 3.59359e14i | − | 0.158617i | −0.996850 | − | 0.0793086i | \(-0.974729\pi\) | ||
0.996850 | − | 0.0793086i | \(-0.0252712\pi\) | |||||||
\(30\) | 6.55823e15 | + | 4.73012e15i | 2.02775 | + | 1.46251i | ||||
\(31\) | 7.41345e14 | 0.162451 | 0.0812256 | − | 0.996696i | \(-0.474117\pi\) | ||||
0.0812256 | + | 0.996696i | \(0.474117\pi\) | |||||||
\(32\) | −6.36809e15 | + | 1.10596e14i | −0.999849 | + | 0.0173646i | ||||
\(33\) | −3.02522e15 | −0.343844 | ||||||||
\(34\) | 1.08985e16 | + | 7.86057e15i | 0.905399 | + | 0.653019i | ||||
\(35\) | 9.33981e15i | 0.572300i | ||||||||
\(36\) | −1.42040e16 | − | 4.27038e16i | −0.647492 | − | 1.94666i | ||||
\(37\) | − | 3.56134e16i | − | 1.21757i | −0.793334 | − | 0.608787i | \(-0.791656\pi\) | ||
0.793334 | − | 0.608787i | \(-0.208344\pi\) | |||||||
\(38\) | −4.39599e16 | + | 6.09497e16i | −1.13587 | + | 1.57487i | ||||
\(39\) | 9.05470e16 | 1.78113 | ||||||||
\(40\) | −9.05704e16 | − | 2.83883e16i | −1.36570 | − | 0.428065i | ||||
\(41\) | −4.38833e16 | −0.510586 | −0.255293 | − | 0.966864i | \(-0.582172\pi\) | ||||
−0.255293 | + | 0.966864i | \(0.582172\pi\) | |||||||
\(42\) | 4.52302e16 | − | 6.27109e16i | 0.408612 | − | 0.566533i | ||||
\(43\) | 6.67420e16i | 0.470956i | 0.971880 | + | 0.235478i | \(0.0756655\pi\) | ||||
−0.971880 | + | 0.235478i | \(0.924334\pi\) | |||||||
\(44\) | 3.36954e16 | − | 1.12077e16i | 0.186774 | − | 0.0621243i | ||||
\(45\) | − | 6.70677e17i | − | 2.93618i | ||||||
\(46\) | 2.96364e17 | + | 2.13752e17i | 1.03007 | + | 0.742940i | ||||
\(47\) | −1.54355e17 | −0.428048 | −0.214024 | − | 0.976828i | \(-0.568657\pi\) | ||||
−0.214024 | + | 0.976828i | \(0.568657\pi\) | |||||||
\(48\) | 4.70646e17 | + | 6.29218e17i | 1.04631 | + | 1.39884i | ||||
\(49\) | −4.69237e17 | −0.840105 | ||||||||
\(50\) | −5.87160e17 | − | 4.23489e17i | −0.850298 | − | 0.613277i | ||||
\(51\) | − | 1.65781e18i | − | 1.95006i | ||||||
\(52\) | −1.00853e18 | + | 3.35453e17i | −0.967503 | + | 0.321808i | ||||
\(53\) | 1.64102e18i | 1.28890i | 0.764648 | + | 0.644448i | \(0.222913\pi\) | ||||
−0.764648 | + | 0.644448i | \(0.777087\pi\) | |||||||
\(54\) | −1.66474e18 | + | 2.30813e18i | −1.07451 | + | 1.48979i | ||||
\(55\) | 5.29197e17 | 0.281714 | ||||||||
\(56\) | −2.71454e17 | + | 8.66049e17i | −0.119597 | + | 0.381565i | ||||
\(57\) | 9.27125e18 | 3.39197 | ||||||||
\(58\) | 3.04424e17 | − | 4.22079e17i | 0.0927866 | − | 0.128647i | ||||
\(59\) | − | 4.37549e18i | − | 1.11450i | −0.830344 | − | 0.557251i | \(-0.811856\pi\) | ||
0.830344 | − | 0.557251i | \(-0.188144\pi\) | |||||||
\(60\) | 3.69582e18 | + | 1.11114e19i | 0.789083 | + | 2.37235i | ||||
\(61\) | 3.59042e17i | 0.0644439i | 0.999481 | + | 0.0322219i | \(0.0102583\pi\) | ||||
−0.999481 | + | 0.0322219i | \(0.989742\pi\) | |||||||
\(62\) | 8.70733e17 | + | 6.28016e17i | 0.131757 | + | 0.0950294i | ||||
\(63\) | −6.41312e18 | −0.820340 | ||||||||
\(64\) | −7.57321e18 | − | 5.26470e18i | −0.821089 | − | 0.570800i | ||||
\(65\) | −1.58392e19 | −1.45930 | ||||||||
\(66\) | −3.55322e18 | − | 2.56276e18i | −0.278876 | − | 0.201139i | ||||
\(67\) | − | 1.04612e19i | − | 0.701127i | −0.936539 | − | 0.350564i | \(-0.885990\pi\) | ||
0.936539 | − | 0.350564i | \(-0.114010\pi\) | |||||||
\(68\) | 6.14176e18 | + | 1.84650e19i | 0.352330 | + | 1.05927i | ||||
\(69\) | − | 4.50809e19i | − | 2.21859i | ||||||
\(70\) | −7.91203e18 | + | 1.09699e19i | −0.334779 | + | 0.464166i | ||||
\(71\) | 2.52620e19 | 0.920989 | 0.460494 | − | 0.887663i | \(-0.347672\pi\) | ||||
0.460494 | + | 0.887663i | \(0.347672\pi\) | |||||||
\(72\) | 1.94926e19 | − | 6.21896e19i | 0.613592 | − | 1.95761i | ||||
\(73\) | −9.66939e18 | −0.263335 | −0.131668 | − | 0.991294i | \(-0.542033\pi\) | ||||
−0.131668 | + | 0.991294i | \(0.542033\pi\) | |||||||
\(74\) | 3.01692e19 | − | 4.18291e19i | 0.712247 | − | 0.987518i | ||||
\(75\) | 8.93147e19i | 1.83139i | ||||||||
\(76\) | −1.03265e20 | + | 3.43475e19i | −1.84251 | + | 0.612848i | ||||
\(77\) | − | 5.06027e18i | − | 0.0787083i | ||||||
\(78\) | 1.06350e20 | + | 7.67051e19i | 1.44459 | + | 1.04191i | ||||
\(79\) | −5.47438e19 | −0.650505 | −0.325253 | − | 0.945627i | \(-0.605449\pi\) | ||||
−0.325253 | + | 0.945627i | \(0.605449\pi\) | |||||||
\(80\) | −8.23292e19 | − | 1.10068e20i | −0.857253 | − | 1.14608i | ||||
\(81\) | 1.26622e20 | 1.15722 | ||||||||
\(82\) | −5.15423e19 | − | 3.71749e19i | −0.414113 | − | 0.298679i | ||||
\(83\) | 1.31783e20i | 0.932264i | 0.884715 | + | 0.466132i | \(0.154353\pi\) | ||||
−0.884715 | + | 0.466132i | \(0.845647\pi\) | |||||||
\(84\) | 1.06249e20 | − | 3.53400e19i | 0.662812 | − | 0.220462i | ||||
\(85\) | 2.89998e20i | 1.59770i | ||||||||
\(86\) | −5.65391e19 | + | 7.83905e19i | −0.275496 | + | 0.381970i | ||||
\(87\) | −6.42038e19 | −0.277082 | ||||||||
\(88\) | 4.90706e19 | + | 1.53806e19i | 0.187825 | + | 0.0588717i | ||||
\(89\) | −2.00107e20 | −0.680247 | −0.340123 | − | 0.940381i | \(-0.610469\pi\) | ||||
−0.340123 | + | 0.940381i | \(0.610469\pi\) | |||||||
\(90\) | 5.68150e20 | − | 7.87731e20i | 1.71758 | − | 2.38140i | ||||
\(91\) | 1.51457e20i | 0.407714i | ||||||||
\(92\) | 1.67013e20 | + | 5.02118e20i | 0.400846 | + | 1.20513i | ||||
\(93\) | − | 1.32450e20i | − | 0.283779i | ||||||
\(94\) | −1.81295e20 | − | 1.30759e20i | −0.347170 | − | 0.250396i | ||||
\(95\) | −1.62180e21 | −2.77908 | ||||||||
\(96\) | 1.97593e19 | + | 1.13773e21i | 0.0303335 | + | 1.74660i | ||||
\(97\) | 1.40141e21 | 1.92957 | 0.964786 | − | 0.263036i | \(-0.0847238\pi\) | ||||
0.964786 | + | 0.263036i | \(0.0847238\pi\) | |||||||
\(98\) | −5.51133e20 | − | 3.97505e20i | −0.681370 | − | 0.491438i | ||||
\(99\) | 3.63370e20i | 0.403812i | ||||||||
\(100\) | −3.30887e20 | − | 9.94801e20i | −0.330887 | − | 0.994801i | ||||
\(101\) | − | 7.48916e20i | − | 0.674619i | −0.941394 | − | 0.337310i | \(-0.890483\pi\) | ||
0.941394 | − | 0.337310i | \(-0.109517\pi\) | |||||||
\(102\) | 1.40438e21 | − | 1.94715e21i | 1.14073 | − | 1.58161i | ||||
\(103\) | 1.85952e21 | 1.36336 | 0.681679 | − | 0.731651i | \(-0.261250\pi\) | ||||
0.681679 | + | 0.731651i | \(0.261250\pi\) | |||||||
\(104\) | −1.46872e21 | − | 4.60353e20i | −0.972945 | − | 0.304959i | ||||
\(105\) | 1.66867e21 | 0.999728 | ||||||||
\(106\) | −1.39016e21 | + | 1.92743e21i | −0.753968 | + | 1.04536i | ||||
\(107\) | − | 1.84717e21i | − | 0.907773i | −0.891060 | − | 0.453886i | \(-0.850037\pi\) | ||
0.891060 | − | 0.453886i | \(-0.149963\pi\) | |||||||
\(108\) | −3.91057e21 | + | 1.30072e21i | −1.74297 | + | 0.579742i | ||||
\(109\) | − | 3.16859e21i | − | 1.28200i | −0.767540 | − | 0.641000i | \(-0.778520\pi\) | ||
0.767540 | − | 0.641000i | \(-0.221480\pi\) | |||||||
\(110\) | 6.21558e20 | + | 4.48298e20i | 0.228485 | + | 0.164795i | ||||
\(111\) | −6.36275e21 | −2.12693 | ||||||||
\(112\) | −1.05249e21 | + | 7.87245e20i | −0.320204 | + | 0.239508i | ||||
\(113\) | −1.05802e20 | −0.0293203 | −0.0146602 | − | 0.999893i | \(-0.504667\pi\) | ||||
−0.0146602 | + | 0.999893i | \(0.504667\pi\) | |||||||
\(114\) | 1.08894e22 | + | 7.85396e21i | 2.75107 | + | 1.98421i | ||||
\(115\) | 7.88592e21i | 1.81771i | ||||||||
\(116\) | 7.15111e20 | − | 2.37858e20i | 0.150510 | − | 0.0500621i | ||||
\(117\) | − | 1.08759e22i | − | 2.09177i | ||||||
\(118\) | 3.70661e21 | − | 5.13915e21i | 0.651952 | − | 0.903920i | ||||
\(119\) | 2.77301e21 | 0.446384 | ||||||||
\(120\) | −5.07190e21 | + | 1.61815e22i | −0.747769 | + | 2.38569i | ||||
\(121\) | 7.11353e21 | 0.961256 | ||||||||
\(122\) | −3.04155e20 | + | 4.21706e20i | −0.0376979 | + | 0.0522674i | ||||
\(123\) | 7.84027e21i | 0.891923i | ||||||||
\(124\) | 4.90692e20 | + | 1.47525e21i | 0.0512721 | + | 0.154148i | ||||
\(125\) | − | 7.21089e20i | − | 0.0692522i | ||||||
\(126\) | −7.53241e21 | − | 5.43275e21i | −0.665339 | − | 0.479876i | ||||
\(127\) | 2.41309e21 | 0.196171 | 0.0980855 | − | 0.995178i | \(-0.468728\pi\) | ||||
0.0980855 | + | 0.995178i | \(0.468728\pi\) | |||||||
\(128\) | −4.43508e21 | − | 1.25990e22i | −0.332045 | − | 0.943263i | ||||
\(129\) | 1.19242e22 | 0.822694 | ||||||||
\(130\) | −1.86037e22 | − | 1.34179e22i | −1.18357 | − | 0.853648i | ||||
\(131\) | − | 1.00194e22i | − | 0.588154i | −0.955782 | − | 0.294077i | \(-0.904988\pi\) | ||
0.955782 | − | 0.294077i | \(-0.0950123\pi\) | |||||||
\(132\) | −2.00238e21 | − | 6.02008e21i | −0.108523 | − | 0.326269i | ||||
\(133\) | 1.55079e22i | 0.776447i | ||||||||
\(134\) | 8.86201e21 | − | 1.22870e22i | 0.410140 | − | 0.568652i | ||||
\(135\) | −6.14167e22 | −2.62895 | ||||||||
\(136\) | −8.42854e21 | + | 2.68905e22i | −0.333883 | + | 1.06522i | ||||
\(137\) | 1.16848e22 | 0.428604 | 0.214302 | − | 0.976767i | \(-0.431252\pi\) | ||||
0.214302 | + | 0.976767i | \(0.431252\pi\) | |||||||
\(138\) | 3.81894e22 | − | 5.29489e22i | 1.29781 | − | 1.79940i | ||||
\(139\) | − | 2.54754e22i | − | 0.802538i | −0.915960 | − | 0.401269i | \(-0.868569\pi\) | ||
0.915960 | − | 0.401269i | \(-0.131431\pi\) | |||||||
\(140\) | −1.85859e22 | + | 6.18197e21i | −0.543048 | + | 0.180627i | ||||
\(141\) | 2.75773e22i | 0.747741i | ||||||||
\(142\) | 2.96710e22 | + | 2.14002e22i | 0.746971 | + | 0.538753i | ||||
\(143\) | 8.58161e21 | 0.200697 | ||||||||
\(144\) | 7.55774e22 | − | 5.65308e22i | 1.64280 | − | 1.22879i | ||||
\(145\) | 1.12310e22 | 0.227016 | ||||||||
\(146\) | −1.13570e22 | − | 8.19122e21i | −0.213579 | − | 0.154044i | ||||
\(147\) | 8.38347e22i | 1.46755i | ||||||||
\(148\) | 7.08693e22 | − | 2.35723e22i | 1.15534 | − | 0.384286i | ||||
\(149\) | 3.66823e22i | 0.557187i | 0.960409 | + | 0.278594i | \(0.0898683\pi\) | ||||
−0.960409 | + | 0.278594i | \(0.910132\pi\) | |||||||
\(150\) | −7.56612e22 | + | 1.04903e23i | −1.07131 | + | 1.48535i | ||||
\(151\) | 3.98226e22 | 0.525862 | 0.262931 | − | 0.964815i | \(-0.415311\pi\) | ||||
0.262931 | + | 0.964815i | \(0.415311\pi\) | |||||||
\(152\) | −1.50384e23 | − | 4.71363e22i | −1.85287 | − | 0.580761i | ||||
\(153\) | −1.99125e23 | −2.29016 | ||||||||
\(154\) | 4.28670e21 | − | 5.94344e21i | 0.0460422 | − | 0.0638367i | ||||
\(155\) | 2.31692e22i | 0.232503i | ||||||||
\(156\) | 5.99325e22 | + | 1.80185e23i | 0.562153 | + | 1.69009i | ||||
\(157\) | − | 1.00324e23i | − | 0.879953i | −0.898009 | − | 0.439977i | \(-0.854987\pi\) | ||
0.898009 | − | 0.439977i | \(-0.145013\pi\) | |||||||
\(158\) | −6.42983e22 | − | 4.63751e22i | −0.527595 | − | 0.380527i | ||||
\(159\) | 2.93188e23 | 2.25152 | ||||||||
\(160\) | −3.45645e21 | − | 1.99022e23i | −0.0248525 | − | 1.43100i | ||||
\(161\) | 7.54064e22 | 0.507851 | ||||||||
\(162\) | 1.48721e23 | + | 1.07265e23i | 0.938565 | + | 0.676940i | ||||
\(163\) | 1.66045e23i | 0.982326i | 0.871068 | + | 0.491163i | \(0.163428\pi\) | ||||
−0.871068 | + | 0.491163i | \(0.836572\pi\) | |||||||
\(164\) | −2.90461e22 | − | 8.73261e22i | −0.161149 | − | 0.484489i | ||||
\(165\) | − | 9.45472e22i | − | 0.492116i | ||||||
\(166\) | −1.11637e23 | + | 1.54783e23i | −0.545348 | + | 0.756116i | ||||
\(167\) | 3.63488e22 | 0.166712 | 0.0833561 | − | 0.996520i | \(-0.473436\pi\) | ||||
0.0833561 | + | 0.996520i | \(0.473436\pi\) | |||||||
\(168\) | 1.54730e23 | + | 4.84983e22i | 0.666540 | + | 0.208920i | ||||
\(169\) | −9.78904e21 | −0.0396214 | ||||||||
\(170\) | −2.45666e23 | + | 3.40612e23i | −0.934612 | + | 1.29582i | ||||
\(171\) | − | 1.11360e24i | − | 3.98355i | ||||||
\(172\) | −1.32814e23 | + | 4.41761e22i | −0.446884 | + | 0.148641i | ||||
\(173\) | 4.44315e23i | 1.40672i | 0.710835 | + | 0.703358i | \(0.248317\pi\) | ||||
−0.710835 | + | 0.703358i | \(0.751683\pi\) | |||||||
\(174\) | −7.54093e22 | − | 5.43889e22i | −0.224728 | − | 0.162085i | ||||
\(175\) | −1.49396e23 | −0.419217 | ||||||||
\(176\) | 4.46056e22 | + | 5.96342e22i | 0.117898 | + | 0.157620i | ||||
\(177\) | −7.81732e23 | −1.94688 | ||||||||
\(178\) | −2.35032e23 | − | 1.69516e23i | −0.551717 | − | 0.397925i | ||||
\(179\) | − | 3.32159e23i | − | 0.735173i | −0.929989 | − | 0.367587i | \(-0.880184\pi\) | ||
0.929989 | − | 0.367587i | \(-0.119816\pi\) | |||||||
\(180\) | 1.33462e24 | − | 4.43917e23i | 2.78610 | − | 0.926703i | ||||
\(181\) | − | 2.07408e23i | − | 0.408507i | −0.978918 | − | 0.204254i | \(-0.934523\pi\) | ||
0.978918 | − | 0.204254i | \(-0.0654768\pi\) | |||||||
\(182\) | −1.28304e23 | + | 1.77891e23i | −0.238501 | + | 0.330678i | ||||
\(183\) | 6.41470e22 | 0.112574 | ||||||||
\(184\) | −2.29197e23 | + | 7.31234e23i | −0.379859 | + | 1.21191i | ||||
\(185\) | 1.11302e24 | 1.74262 | ||||||||
\(186\) | 1.12202e23 | − | 1.55567e23i | 0.166003 | − | 0.230160i | ||||
\(187\) | − | 1.57120e23i | − | 0.219732i | ||||||
\(188\) | −1.02167e23 | − | 3.07160e23i | −0.135099 | − | 0.406170i | ||||
\(189\) | 5.87277e23i | 0.734504i | ||||||||
\(190\) | −1.90486e24 | − | 1.37388e24i | −2.25398 | − | 1.62568i | ||||
\(191\) | 5.53919e23 | 0.620292 | 0.310146 | − | 0.950689i | \(-0.399622\pi\) | ||||
0.310146 | + | 0.950689i | \(0.399622\pi\) | |||||||
\(192\) | −9.40600e23 | + | 1.35304e24i | −0.997108 | + | 1.43433i | ||||
\(193\) | −4.76903e23 | −0.478716 | −0.239358 | − | 0.970931i | \(-0.576937\pi\) | ||||
−0.239358 | + | 0.970931i | \(0.576937\pi\) | |||||||
\(194\) | 1.64600e24 | + | 1.18717e24i | 1.56499 | + | 1.12875i | ||||
\(195\) | 2.82986e24i | 2.54919i | ||||||||
\(196\) | −3.10585e23 | − | 9.33763e23i | −0.265150 | − | 0.797165i | ||||
\(197\) | 1.38831e24i | 1.12355i | 0.827290 | + | 0.561775i | \(0.189881\pi\) | ||||
−0.827290 | + | 0.561775i | \(0.810119\pi\) | |||||||
\(198\) | −3.07821e23 | + | 4.26789e23i | −0.236219 | + | 0.327513i | ||||
\(199\) | 2.31118e24 | 1.68220 | 0.841099 | − | 0.540881i | \(-0.181909\pi\) | ||||
0.841099 | + | 0.540881i | \(0.181909\pi\) | |||||||
\(200\) | 4.54088e23 | − | 1.44873e24i | 0.313563 | − | 1.00040i | ||||
\(201\) | −1.86902e24 | −1.22477 | ||||||||
\(202\) | 6.34429e23 | − | 8.79625e23i | 0.394633 | − | 0.547152i | ||||
\(203\) | − | 1.07393e23i | − | 0.0634261i | ||||||
\(204\) | 3.29898e24 | − | 1.09730e24i | 1.85039 | − | 0.615471i | ||||
\(205\) | − | 1.37148e24i | − | 0.730760i | ||||||
\(206\) | 2.18406e24 | + | 1.57526e24i | 1.10576 | + | 0.797526i | ||||
\(207\) | −5.41481e24 | −2.60552 | ||||||||
\(208\) | −1.33508e24 | − | 1.78489e24i | −0.610718 | − | 0.816483i | ||||
\(209\) | 8.78685e23 | 0.382206 | ||||||||
\(210\) | 1.95990e24 | + | 1.41358e24i | 0.810833 | + | 0.584813i | ||||
\(211\) | 5.53529e23i | 0.217858i | 0.994050 | + | 0.108929i | \(0.0347422\pi\) | ||||
−0.994050 | + | 0.108929i | \(0.965258\pi\) | |||||||
\(212\) | −3.26557e24 | + | 1.08618e24i | −1.22302 | + | 0.406796i | ||||
\(213\) | − | 4.51334e24i | − | 1.60884i | ||||||
\(214\) | 1.56479e24 | − | 2.16956e24i | 0.531021 | − | 0.736252i | ||||
\(215\) | −2.08588e24 | −0.674041 | ||||||||
\(216\) | −5.69497e24 | − | 1.78502e24i | −1.75278 | − | 0.549389i | ||||
\(217\) | 2.21548e23 | 0.0649592 | ||||||||
\(218\) | 2.68421e24 | − | 3.72161e24i | 0.749935 | − | 1.03977i | ||||
\(219\) | 1.72755e24i | 0.460010i | ||||||||
\(220\) | 3.50272e23 | + | 1.05308e24i | 0.0889135 | + | 0.267315i | ||||
\(221\) | 4.70270e24i | 1.13822i | ||||||||
\(222\) | −7.47325e24 | − | 5.39008e24i | −1.72506 | − | 1.24420i | ||||
\(223\) | 3.17162e24 | 0.698361 | 0.349180 | − | 0.937056i | \(-0.386460\pi\) | ||||
0.349180 | + | 0.937056i | \(0.386460\pi\) | |||||||
\(224\) | −1.90308e24 | + | 3.30512e22i | −0.399809 | + | 0.00694356i | ||||
\(225\) | 1.07279e25 | 2.15079 | ||||||||
\(226\) | −1.24267e23 | − | 8.96277e22i | −0.0237803 | − | 0.0171516i | ||||
\(227\) | − | 9.35215e23i | − | 0.170860i | −0.996344 | − | 0.0854299i | \(-0.972774\pi\) | ||
0.996344 | − | 0.0854299i | \(-0.0272264\pi\) | |||||||
\(228\) | 6.13659e24 | + | 1.84494e25i | 1.07056 | + | 3.21860i | ||||
\(229\) | − | 1.00652e25i | − | 1.67707i | −0.544850 | − | 0.838533i | \(-0.683413\pi\) | ||
0.544850 | − | 0.838533i | \(-0.316587\pi\) | |||||||
\(230\) | −6.68040e24 | + | 9.26225e24i | −1.06331 | + | 1.47426i | ||||
\(231\) | −9.04075e23 | −0.137492 | ||||||||
\(232\) | 1.04142e24 | + | 3.26420e23i | 0.151356 | + | 0.0474410i | ||||
\(233\) | 4.28113e24 | 0.594732 | 0.297366 | − | 0.954764i | \(-0.403892\pi\) | ||||
0.297366 | + | 0.954764i | \(0.403892\pi\) | |||||||
\(234\) | 9.21330e24 | − | 1.27741e25i | 1.22363 | − | 1.69654i | ||||
\(235\) | − | 4.82405e24i | − | 0.612631i | ||||||
\(236\) | 8.70705e24 | − | 2.89611e24i | 1.05754 | − | 0.351754i | ||||
\(237\) | 9.78063e24i | 1.13634i | ||||||||
\(238\) | 3.25699e24 | + | 2.34910e24i | 0.362041 | + | 0.261122i | ||||
\(239\) | −1.01975e25 | −1.08471 | −0.542356 | − | 0.840149i | \(-0.682468\pi\) | ||||
−0.542356 | + | 0.840149i | \(0.682468\pi\) | |||||||
\(240\) | −1.96649e25 | + | 1.47091e25i | −2.00205 | + | 1.49750i | ||||
\(241\) | −7.47572e24 | −0.728575 | −0.364287 | − | 0.931287i | \(-0.618687\pi\) | ||||
−0.364287 | + | 0.931287i | \(0.618687\pi\) | |||||||
\(242\) | 8.35507e24 | + | 6.02609e24i | 0.779630 | + | 0.562308i | ||||
\(243\) | − | 2.06626e24i | − | 0.184637i | ||||||
\(244\) | −7.14479e23 | + | 2.37648e23i | −0.0611500 | + | 0.0203395i | ||||
\(245\) | − | 1.46650e25i | − | 1.20237i | ||||||
\(246\) | −6.64172e24 | + | 9.20864e24i | −0.521750 | + | 0.723397i | ||||
\(247\) | −2.62996e25 | −1.97985 | ||||||||
\(248\) | −6.73393e23 | + | 2.14840e24i | −0.0485877 | + | 0.155015i | ||||
\(249\) | 2.35445e25 | 1.62854 | ||||||||
\(250\) | 6.10856e23 | − | 8.46942e23i | 0.0405106 | − | 0.0561673i | ||||
\(251\) | 1.08621e25i | 0.690783i | 0.938459 | + | 0.345391i | \(0.112254\pi\) | ||||
−0.938459 | + | 0.345391i | \(0.887746\pi\) | |||||||
\(252\) | −4.24481e24 | − | 1.27619e25i | −0.258912 | − | 0.778410i | ||||
\(253\) | − | 4.27255e24i | − | 0.249990i | ||||||
\(254\) | 2.83425e24 | + | 2.04420e24i | 0.159105 | + | 0.114755i | ||||
\(255\) | 5.18116e25 | 2.79097 | ||||||||
\(256\) | 5.46389e24 | − | 1.85551e25i | 0.282476 | − | 0.959274i | ||||
\(257\) | −2.46308e25 | −1.22231 | −0.611153 | − | 0.791512i | \(-0.709294\pi\) | ||||
−0.611153 | + | 0.791512i | \(0.709294\pi\) | |||||||
\(258\) | 1.40054e25 | + | 1.01014e25i | 0.667249 | + | 0.481253i | ||||
\(259\) | − | 1.06429e25i | − | 0.486870i | ||||||
\(260\) | −1.04839e25 | − | 3.15194e25i | −0.460577 | − | 1.38471i | ||||
\(261\) | 7.71172e24i | 0.325406i | ||||||||
\(262\) | 8.48770e24 | − | 1.17680e25i | 0.344054 | − | 0.477025i | ||||
\(263\) | 1.97728e25 | 0.770074 | 0.385037 | − | 0.922901i | \(-0.374189\pi\) | ||||
0.385037 | + | 0.922901i | \(0.374189\pi\) | |||||||
\(264\) | 2.74793e24 | − | 8.76704e24i | 0.102841 | − | 0.328104i | ||||
\(265\) | −5.12868e25 | −1.84469 | ||||||||
\(266\) | −1.31372e25 | + | 1.82146e25i | −0.454200 | + | 0.629740i | ||||
\(267\) | 3.57514e25i | 1.18830i | ||||||||
\(268\) | 2.08174e25 | − | 6.92422e24i | 0.665290 | − | 0.221287i | ||||
\(269\) | 2.42083e25i | 0.743987i | 0.928235 | + | 0.371993i | \(0.121326\pi\) | ||||
−0.928235 | + | 0.371993i | \(0.878674\pi\) | |||||||
\(270\) | −7.21359e25 | − | 5.20279e25i | −2.13222 | − | 1.53786i | ||||
\(271\) | −1.14270e25 | −0.324904 | −0.162452 | − | 0.986716i | \(-0.551940\pi\) | ||||
−0.162452 | + | 0.986716i | \(0.551940\pi\) | |||||||
\(272\) | −3.26794e25 | + | 2.44437e25i | −0.893923 | + | 0.668642i | ||||
\(273\) | 2.70596e25 | 0.712219 | ||||||||
\(274\) | 1.37242e25 | + | 9.89856e24i | 0.347621 | + | 0.250721i | ||||
\(275\) | 8.46482e24i | 0.206360i | ||||||||
\(276\) | 8.97092e25 | − | 2.98388e25i | 2.10519 | − | 0.700222i | ||||
\(277\) | − | 7.54507e25i | − | 1.70461i | −0.523043 | − | 0.852307i | \(-0.675203\pi\) | ||
0.523043 | − | 0.852307i | \(-0.324797\pi\) | |||||||
\(278\) | 2.15810e25 | − | 2.99217e25i | 0.469462 | − | 0.650902i | ||||
\(279\) | −1.59090e25 | −0.333272 | ||||||||
\(280\) | −2.70666e25 | − | 8.48372e24i | −0.546103 | − | 0.171170i | ||||
\(281\) | −5.69982e25 | −1.10776 | −0.553879 | − | 0.832597i | \(-0.686853\pi\) | ||||
−0.553879 | + | 0.832597i | \(0.686853\pi\) | |||||||
\(282\) | −2.33616e25 | + | 3.23904e25i | −0.437407 | + | 0.606458i | ||||
\(283\) | − | 9.95326e24i | − | 0.179559i | −0.995962 | − | 0.0897797i | \(-0.971384\pi\) | ||
0.995962 | − | 0.0897797i | \(-0.0286163\pi\) | |||||||
\(284\) | 1.67207e25 | + | 5.02703e25i | 0.290679 | + | 0.873914i | ||||
\(285\) | 2.89754e26i | 4.85466i | ||||||||
\(286\) | 1.00794e25 | + | 7.26974e24i | 0.162776 | + | 0.117402i | ||||
\(287\) | −1.31143e25 | −0.204168 | ||||||||
\(288\) | 1.36657e26 | − | 2.37335e24i | 2.05121 | − | 0.0356238i | ||||
\(289\) | 1.70091e25 | 0.246181 | ||||||||
\(290\) | 1.31912e25 | + | 9.51415e24i | 0.184122 | + | 0.132798i | ||||
\(291\) | − | 2.50378e26i | − | 3.37069i | ||||||
\(292\) | −6.40011e24 | − | 1.92417e25i | −0.0831127 | − | 0.249875i | ||||
\(293\) | − | 5.05103e25i | − | 0.632805i | −0.948625 | − | 0.316402i | \(-0.897525\pi\) | ||
0.948625 | − | 0.316402i | \(-0.102475\pi\) | |||||||
\(294\) | −7.10189e25 | + | 9.84664e25i | −0.858473 | + | 1.19026i | ||||
\(295\) | 1.36747e26 | 1.59510 | ||||||||
\(296\) | 1.03207e26 | + | 3.23491e25i | 1.16184 | + | 0.364166i | ||||
\(297\) | 3.32753e25 | 0.361559 | ||||||||
\(298\) | −3.10747e25 | + | 4.30846e25i | −0.325939 | + | 0.451909i | ||||
\(299\) | 1.27880e26i | 1.29496i | ||||||||
\(300\) | −1.77733e26 | + | 5.91169e25i | −1.73778 | + | 0.578014i | ||||
\(301\) | 1.99456e25i | 0.188321i | ||||||||
\(302\) | 4.67729e25 | + | 3.37349e25i | 0.426502 | + | 0.307614i | ||||
\(303\) | −1.33803e26 | −1.17847 | ||||||||
\(304\) | −1.36700e26 | − | 1.82758e26i | −1.16305 | − | 1.55491i | ||||
\(305\) | −1.12211e25 | −0.0922333 | ||||||||
\(306\) | −2.33879e26 | − | 1.68685e26i | −1.85745 | − | 1.33968i | ||||
\(307\) | 3.58137e24i | 0.0274850i | 0.999906 | + | 0.0137425i | \(0.00437452\pi\) | ||||
−0.999906 | + | 0.0137425i | \(0.995625\pi\) | |||||||
\(308\) | 1.00697e25 | − | 3.34936e24i | 0.0746853 | − | 0.0248416i | ||||
\(309\) | − | 3.32225e26i | − | 2.38160i | ||||||
\(310\) | −1.96273e25 | + | 2.72130e25i | −0.136008 | + | 0.188572i | ||||
\(311\) | 2.92172e26 | 1.95728 | 0.978642 | − | 0.205571i | \(-0.0659051\pi\) | ||||
0.978642 | + | 0.205571i | \(0.0659051\pi\) | |||||||
\(312\) | −8.22475e25 | + | 2.62403e26i | −0.532720 | + | 1.69960i | ||||
\(313\) | 6.40749e25 | 0.401303 | 0.200652 | − | 0.979663i | \(-0.435694\pi\) | ||||
0.200652 | + | 0.979663i | \(0.435694\pi\) | |||||||
\(314\) | 8.49877e25 | − | 1.17834e26i | 0.514748 | − | 0.713689i | ||||
\(315\) | − | 2.00429e26i | − | 1.17409i | ||||||
\(316\) | −3.62346e25 | − | 1.08938e26i | −0.205310 | − | 0.617256i | ||||
\(317\) | − | 2.40904e26i | − | 1.32045i | −0.751069 | − | 0.660224i | \(-0.770461\pi\) | ||
0.751069 | − | 0.660224i | \(-0.229539\pi\) | |||||||
\(318\) | 3.44358e26 | + | 2.48368e26i | 1.82611 | + | 1.31708i | ||||
\(319\) | −6.08493e24 | −0.0312215 | ||||||||
\(320\) | 1.64537e26 | − | 2.36685e26i | 0.816940 | − | 1.17516i | ||||
\(321\) | −3.30018e26 | −1.58575 | ||||||||
\(322\) | 8.85672e25 | + | 6.38790e25i | 0.411895 | + | 0.297079i | ||||
\(323\) | 4.81517e26i | 2.16763i | ||||||||
\(324\) | 8.38101e25 | + | 2.51972e26i | 0.365236 | + | 1.09807i | ||||
\(325\) | − | 2.53358e26i | − | 1.06895i | ||||||
\(326\) | −1.40662e26 | + | 1.95025e26i | −0.574633 | + | 0.796719i | ||||
\(327\) | −5.66106e26 | −2.23948 | ||||||||
\(328\) | 3.98610e25 | − | 1.27173e26i | 0.152712 | − | 0.487214i | ||||
\(329\) | −4.61283e25 | −0.171163 | ||||||||
\(330\) | 8.00937e25 | − | 1.11049e26i | 0.287874 | − | 0.399132i | ||||
\(331\) | − | 1.09753e25i | − | 0.0382140i | −0.999817 | − | 0.0191070i | \(-0.993918\pi\) | ||
0.999817 | − | 0.0191070i | \(-0.00608232\pi\) | |||||||
\(332\) | −2.62243e26 | + | 8.72263e25i | −0.884614 | + | 0.294237i | ||||
\(333\) | 7.64251e26i | 2.49788i | ||||||||
\(334\) | 4.26928e25 | + | 3.07922e25i | 0.135213 | + | 0.0975220i | ||||
\(335\) | 3.26944e26 | 1.00347 | ||||||||
\(336\) | 1.40651e26 | + | 1.88039e26i | 0.418388 | + | 0.559352i | ||||
\(337\) | 5.36457e26 | 1.54675 | 0.773377 | − | 0.633947i | \(-0.218566\pi\) | ||||
0.773377 | + | 0.633947i | \(0.218566\pi\) | |||||||
\(338\) | −1.14975e25 | − | 8.29258e24i | −0.0321351 | − | 0.0231774i | ||||
\(339\) | 1.89027e25i | 0.0512185i | ||||||||
\(340\) | −5.77085e26 | + | 1.91948e26i | −1.51604 | + | 0.504261i | ||||
\(341\) | − | 1.25530e25i | − | 0.0319761i | ||||||
\(342\) | 9.43364e26 | − | 1.30796e27i | 2.33027 | − | 3.23087i | ||||
\(343\) | −3.07149e26 | −0.735801 | ||||||||
\(344\) | −1.93417e26 | − | 6.06244e25i | −0.449398 | − | 0.140859i | ||||
\(345\) | 1.40891e27 | 3.17529 | ||||||||
\(346\) | −3.76392e26 | + | 5.21861e26i | −0.822890 | + | 1.14092i | ||||
\(347\) | 1.78294e26i | 0.378161i | 0.981962 | + | 0.189080i | \(0.0605507\pi\) | ||||
−0.981962 | + | 0.189080i | \(0.939449\pi\) | |||||||
\(348\) | −4.24961e25 | − | 1.27763e26i | −0.0874514 | − | 0.262920i | ||||
\(349\) | 5.73446e26i | 1.14505i | 0.819886 | + | 0.572527i | \(0.194037\pi\) | ||||
−0.819886 | + | 0.572527i | \(0.805963\pi\) | |||||||
\(350\) | −1.75470e26 | − | 1.26558e26i | −0.340008 | − | 0.245230i | ||||
\(351\) | −9.95952e26 | −1.87290 | ||||||||
\(352\) | 1.87269e24 | + | 1.07829e26i | 0.00341797 | + | 0.196806i | ||||
\(353\) | −2.84034e26 | −0.503195 | −0.251597 | − | 0.967832i | \(-0.580956\pi\) | ||||
−0.251597 | + | 0.967832i | \(0.580956\pi\) | |||||||
\(354\) | −9.18169e26 | − | 6.62229e26i | −1.57902 | − | 1.13887i | ||||
\(355\) | 7.89511e26i | 1.31814i | ||||||||
\(356\) | −1.32449e26 | − | 3.98204e26i | −0.214697 | − | 0.645478i | ||||
\(357\) | − | 4.95430e26i | − | 0.779770i | ||||||
\(358\) | 2.81382e26 | − | 3.90132e26i | 0.430056 | − | 0.596265i | ||||
\(359\) | −4.61851e26 | −0.685504 | −0.342752 | − | 0.939426i | \(-0.611359\pi\) | ||||
−0.342752 | + | 0.939426i | \(0.611359\pi\) | |||||||
\(360\) | 1.94361e27 | + | 6.09203e26i | 2.80177 | + | 0.878184i | ||||
\(361\) | −1.97865e27 | −2.77041 | ||||||||
\(362\) | 1.75701e26 | − | 2.43607e26i | 0.238965 | − | 0.331321i | ||||
\(363\) | − | 1.27092e27i | − | 1.67918i | ||||||
\(364\) | −3.01394e26 | + | 1.00249e26i | −0.386874 | + | 0.128681i | ||||
\(365\) | − | 3.02197e26i | − | 0.376890i | ||||||
\(366\) | 7.53426e25 | + | 5.43408e25i | 0.0913039 | + | 0.0658529i | ||||
\(367\) | 1.47117e27 | 1.73249 | 0.866243 | − | 0.499623i | \(-0.166528\pi\) | ||||
0.866243 | + | 0.499623i | \(0.166528\pi\) | |||||||
\(368\) | −8.88650e26 | + | 6.64698e26i | −1.01702 | + | 0.760715i | ||||
\(369\) | 9.41720e26 | 1.04748 | ||||||||
\(370\) | 1.30728e27 | + | 9.42876e26i | 1.41335 | + | 1.01938i | ||||
\(371\) | 4.90413e26i | 0.515390i | ||||||||
\(372\) | 2.63570e26 | − | 8.76679e25i | 0.269275 | − | 0.0895653i | ||||
\(373\) | − | 1.34633e27i | − | 1.33724i | −0.743603 | − | 0.668621i | \(-0.766885\pi\) | ||
0.743603 | − | 0.668621i | \(-0.233115\pi\) | |||||||
\(374\) | 1.33101e26 | − | 1.84542e26i | 0.128537 | − | 0.178215i | ||||
\(375\) | −1.28831e26 | −0.120974 | ||||||||
\(376\) | 1.40207e26 | − | 4.47317e26i | 0.128025 | − | 0.408454i | ||||
\(377\) | 1.82126e26 | 0.161729 | ||||||||
\(378\) | −4.97500e26 | + | 6.89775e26i | −0.429664 | + | 0.595722i | ||||
\(379\) | 1.00783e27i | 0.846597i | 0.905990 | + | 0.423299i | \(0.139128\pi\) | ||||
−0.905990 | + | 0.423299i | \(0.860872\pi\) | |||||||
\(380\) | −1.07346e27 | − | 3.22732e27i | −0.877120 | − | 2.63703i | ||||
\(381\) | − | 4.31127e26i | − | 0.342683i | ||||||
\(382\) | 6.50595e26 | + | 4.69242e26i | 0.503090 | + | 0.362853i | ||||
\(383\) | −2.67432e26 | −0.201199 | −0.100600 | − | 0.994927i | \(-0.532076\pi\) | ||||
−0.100600 | + | 0.994927i | \(0.532076\pi\) | |||||||
\(384\) | −2.25097e27 | + | 7.92379e26i | −1.64775 | + | 0.580037i | ||||
\(385\) | 1.58148e26 | 0.112649 | ||||||||
\(386\) | −5.60137e26 | − | 4.03998e26i | −0.388264 | − | 0.280035i | ||||
\(387\) | − | 1.43226e27i | − | 0.966176i | ||||||
\(388\) | 9.27583e26 | + | 2.78874e27i | 0.609003 | + | 1.83095i | ||||
\(389\) | 1.00027e27i | 0.639212i | 0.947551 | + | 0.319606i | \(0.103550\pi\) | ||||
−0.947551 | + | 0.319606i | \(0.896450\pi\) | |||||||
\(390\) | −2.39726e27 | + | 3.32376e27i | −1.49120 | + | 2.06753i | ||||
\(391\) | 2.34134e27 | 1.41778 | ||||||||
\(392\) | 4.26227e26 | − | 1.35984e27i | 0.251268 | − | 0.801649i | ||||
\(393\) | −1.79008e27 | −1.02742 | ||||||||
\(394\) | −1.17608e27 | + | 1.63062e27i | −0.657245 | + | 0.911259i | ||||
\(395\) | − | 1.71091e27i | − | 0.931015i | ||||||
\(396\) | −7.23091e26 | + | 2.40512e26i | −0.383172 | + | 0.127449i | ||||
\(397\) | 4.09541e25i | 0.0211347i | 0.999944 | + | 0.0105674i | \(0.00336376\pi\) | ||||
−0.999944 | + | 0.0105674i | \(0.996636\pi\) | |||||||
\(398\) | 2.71456e27 | + | 1.95787e27i | 1.36435 | + | 0.984039i | ||||
\(399\) | 2.77068e27 | 1.35635 | ||||||||
\(400\) | 1.76060e27 | − | 1.31691e27i | 0.839520 | − | 0.627950i | ||||
\(401\) | −9.84276e26 | −0.457195 | −0.228597 | − | 0.973521i | \(-0.573414\pi\) | ||||
−0.228597 | + | 0.973521i | \(0.573414\pi\) | |||||||
\(402\) | −2.19522e27 | − | 1.58330e27i | −0.993355 | − | 0.716457i | ||||
\(403\) | 3.75719e26i | 0.165638i | ||||||||
\(404\) | 1.49031e27 | − | 4.95703e26i | 0.640137 | − | 0.212920i | ||||
\(405\) | 3.95730e27i | 1.65623i | ||||||||
\(406\) | 9.09759e25 | − | 1.26136e26i | 0.0371025 | − | 0.0514419i | ||||
\(407\) | −6.03031e26 | −0.239662 | ||||||||
\(408\) | 4.80431e27 | + | 1.50586e27i | 1.86080 | + | 0.583247i | ||||
\(409\) | 3.41873e27 | 1.29054 | 0.645268 | − | 0.763956i | \(-0.276746\pi\) | ||||
0.645268 | + | 0.763956i | \(0.276746\pi\) | |||||||
\(410\) | 1.16182e27 | − | 1.61085e27i | 0.427474 | − | 0.592686i | ||||
\(411\) | − | 2.08763e27i | − | 0.748711i | ||||||
\(412\) | 1.23081e27 | + | 3.70037e27i | 0.430297 | + | 1.29367i | ||||
\(413\) | − | 1.30760e27i | − | 0.445655i | ||||||
\(414\) | −6.35987e27 | − | 4.58705e27i | −2.11322 | − | 1.52416i | ||||
\(415\) | −4.11860e27 | −1.33427 | ||||||||
\(416\) | −5.60509e25 | − | 3.22739e27i | −0.0177053 | − | 1.01946i | ||||
\(417\) | −4.55148e27 | −1.40192 | ||||||||
\(418\) | 1.03204e27 | + | 7.44360e26i | 0.309989 | + | 0.223580i | ||||
\(419\) | − | 1.46751e27i | − | 0.429865i | −0.976629 | − | 0.214933i | \(-0.931047\pi\) | ||
0.976629 | − | 0.214933i | \(-0.0689532\pi\) | |||||||
\(420\) | 1.10448e27 | + | 3.32058e27i | 0.315530 | + | 0.948629i | ||||
\(421\) | 1.09266e27i | 0.304455i | 0.988345 | + | 0.152228i | \(0.0486447\pi\) | ||||
−0.988345 | + | 0.152228i | \(0.951355\pi\) | |||||||
\(422\) | −4.68911e26 | + | 6.50137e26i | −0.127441 | + | 0.176695i | ||||
\(423\) | 3.31240e27 | 0.878150 | ||||||||
\(424\) | −4.75565e27 | − | 1.49061e27i | −1.22990 | − | 0.385498i | ||||
\(425\) | −4.63870e27 | −1.17034 | ||||||||
\(426\) | 3.82339e27 | − | 5.30106e27i | 0.941126 | − | 1.30485i | ||||
\(427\) | 1.07298e26i | 0.0257691i | ||||||||
\(428\) | 3.67579e27 | − | 1.22263e27i | 0.861374 | − | 0.286507i | ||||
\(429\) | − | 1.53321e27i | − | 0.350589i | ||||||
\(430\) | −2.44993e27 | − | 1.76701e27i | −0.546683 | − | 0.394295i | ||||
\(431\) | −6.19140e27 | −1.34827 | −0.674136 | − | 0.738608i | \(-0.735484\pi\) | ||||
−0.674136 | + | 0.738608i | \(0.735484\pi\) | |||||||
\(432\) | −5.17677e27 | − | 6.92094e27i | −1.10022 | − | 1.47091i | ||||
\(433\) | −2.24766e26 | −0.0466237 | −0.0233119 | − | 0.999728i | \(-0.507421\pi\) | ||||
−0.0233119 | + | 0.999728i | \(0.507421\pi\) | |||||||
\(434\) | 2.60215e26 | + | 1.87680e26i | 0.0526854 | + | 0.0379993i | ||||
\(435\) | − | 2.00656e27i | − | 0.396565i | ||||||
\(436\) | 6.30538e27 | − | 2.09727e27i | 1.21647 | − | 0.404620i | ||||
\(437\) | 1.30939e28i | 2.46611i | ||||||||
\(438\) | −1.46346e27 | + | 2.02906e27i | −0.269093 | + | 0.373093i | ||||
\(439\) | 6.04486e27 | 1.08520 | 0.542599 | − | 0.839992i | \(-0.317440\pi\) | ||||
0.542599 | + | 0.839992i | \(0.317440\pi\) | |||||||
\(440\) | −4.80691e26 | + | 1.53360e27i | −0.0842583 | + | 0.268819i | ||||
\(441\) | 1.00697e28 | 1.72349 | ||||||||
\(442\) | −3.98379e27 | + | 5.52346e27i | −0.665830 | + | 0.923161i | ||||
\(443\) | 1.14428e28i | 1.86764i | 0.357742 | + | 0.933820i | \(0.383547\pi\) | ||||
−0.357742 | + | 0.933820i | \(0.616453\pi\) | |||||||
\(444\) | −4.21147e27 | − | 1.26616e28i | −0.671293 | − | 2.01822i | ||||
\(445\) | − | 6.25393e27i | − | 0.973582i | ||||||
\(446\) | 3.72516e27 | + | 2.68677e27i | 0.566408 | + | 0.408521i | ||||
\(447\) | 6.55373e27 | 0.973329 | ||||||||
\(448\) | −2.26322e27 | − | 1.57333e27i | −0.328328 | − | 0.228245i | ||||
\(449\) | 5.23182e27 | 0.741423 | 0.370712 | − | 0.928748i | \(-0.379114\pi\) | ||||
0.370712 | + | 0.928748i | \(0.379114\pi\) | |||||||
\(450\) | 1.26002e28 | + | 9.08791e27i | 1.74440 | + | 1.25815i | ||||
\(451\) | 7.43063e26i | 0.100501i | ||||||||
\(452\) | −7.00294e25 | − | 2.10541e26i | −0.00925395 | − | 0.0278217i | ||||
\(453\) | − | 7.11477e27i | − | 0.918607i | ||||||
\(454\) | 7.92249e26 | − | 1.09844e27i | 0.0999482 | − | 0.138577i | ||||
\(455\) | −4.73348e27 | −0.583527 | ||||||||
\(456\) | −8.42145e27 | + | 2.68679e28i | −1.01451 | + | 3.23670i | ||||
\(457\) | −1.46186e28 | −1.72102 | −0.860508 | − | 0.509438i | \(-0.829853\pi\) | ||||
−0.860508 | + | 0.509438i | \(0.829853\pi\) | |||||||
\(458\) | 8.52654e27 | − | 1.18219e28i | 0.981037 | − | 1.36019i | ||||
\(459\) | 1.82348e28i | 2.05053i | ||||||||
\(460\) | −1.56927e28 | + | 5.21964e27i | −1.72480 | + | 0.573698i | ||||
\(461\) | − | 9.86587e27i | − | 1.05993i | −0.848021 | − | 0.529963i | \(-0.822206\pi\) | ||
0.848021 | − | 0.529963i | \(-0.177794\pi\) | |||||||
\(462\) | −1.06186e27 | − | 7.65869e26i | −0.111514 | − | 0.0804292i | ||||
\(463\) | −1.03281e28 | −1.06028 | −0.530138 | − | 0.847911i | \(-0.677860\pi\) | ||||
−0.530138 | + | 0.847911i | \(0.677860\pi\) | |||||||
\(464\) | 9.46656e26 | + | 1.26561e27i | 0.0950065 | + | 0.127016i | ||||
\(465\) | 4.13945e27 | 0.406150 | ||||||||
\(466\) | 5.02832e27 | + | 3.62667e27i | 0.482360 | + | 0.347902i | ||||
\(467\) | − | 3.56189e27i | − | 0.334082i | −0.985950 | − | 0.167041i | \(-0.946579\pi\) | ||
0.985950 | − | 0.167041i | \(-0.0534213\pi\) | |||||||
\(468\) | 2.16426e28 | − | 7.19869e27i | 1.98485 | − | 0.660195i | ||||
\(469\) | − | 3.12629e27i | − | 0.280359i | ||||||
\(470\) | 4.08659e27 | − | 5.66599e27i | 0.358372 | − | 0.496876i | ||||
\(471\) | −1.79241e28 | −1.53716 | ||||||||
\(472\) | 1.26801e28 | + | 3.97443e27i | 1.06348 | + | 0.333337i | ||||
\(473\) | 1.13012e27 | 0.0927007 | ||||||||
\(474\) | −8.28546e27 | + | 1.14876e28i | −0.664728 | + | 0.921634i | ||||
\(475\) | − | 2.59417e28i | − | 2.03571i | ||||||
\(476\) | 1.83544e27 | + | 5.51818e27i | 0.140886 | + | 0.423568i | ||||
\(477\) | − | 3.52158e28i | − | 2.64420i | ||||||
\(478\) | −1.19772e28 | − | 8.63858e27i | −0.879759 | − | 0.634526i | ||||
\(479\) | 2.46990e28 | 1.77483 | 0.887415 | − | 0.460971i | \(-0.152499\pi\) | ||||
0.887415 | + | 0.460971i | \(0.152499\pi\) | |||||||
\(480\) | −3.55575e28 | + | 6.17535e26i | −2.49976 | + | 0.0434139i | ||||
\(481\) | 1.80491e28 | 1.24146 | ||||||||
\(482\) | −8.78046e27 | − | 6.33291e27i | −0.590913 | − | 0.426196i | ||||
\(483\) | − | 1.34722e28i | − | 0.887145i | ||||||
\(484\) | 4.70841e27 | + | 1.41557e28i | 0.303387 | + | 0.912123i | ||||
\(485\) | 4.37981e28i | 2.76164i | ||||||||
\(486\) | 1.75039e27 | − | 2.42689e27i | 0.108008 | − | 0.149751i | ||||
\(487\) | −9.98326e27 | −0.602862 | −0.301431 | − | 0.953488i | \(-0.597464\pi\) | ||||
−0.301431 | + | 0.953488i | \(0.597464\pi\) | |||||||
\(488\) | −1.04050e27 | − | 3.26132e26i | −0.0614939 | − | 0.0192746i | ||||
\(489\) | 2.96659e28 | 1.71599 | ||||||||
\(490\) | 1.24232e28 | − | 1.72245e28i | 0.703355 | − | 0.975189i | ||||
\(491\) | 2.04646e28i | 1.13409i | 0.823687 | + | 0.567045i | \(0.191914\pi\) | ||||
−0.823687 | + | 0.567045i | \(0.808086\pi\) | |||||||
\(492\) | −1.56018e28 | + | 5.18943e27i | −0.846334 | + | 0.281505i | ||||
\(493\) | − | 3.33452e27i | − | 0.177068i | ||||||
\(494\) | −3.08898e28 | − | 2.22792e28i | −1.60576 | − | 1.15816i | ||||
\(495\) | −1.13564e28 | −0.577943 | ||||||||
\(496\) | −2.61090e27 | + | 1.95292e27i | −0.130087 | + | 0.0973029i | ||||
\(497\) | 7.54943e27 | 0.368275 | ||||||||
\(498\) | 2.76538e28 | + | 1.99453e28i | 1.32083 | + | 0.952648i | ||||
\(499\) | − | 2.44867e28i | − | 1.14518i | −0.819841 | − | 0.572591i | \(-0.805938\pi\) | ||
0.819841 | − | 0.572591i | \(-0.194062\pi\) | |||||||
\(500\) | 1.43494e27 | − | 4.77285e26i | 0.0657126 | − | 0.0218571i | ||||
\(501\) | − | 6.49414e27i | − | 0.291223i | ||||||
\(502\) | −9.20164e27 | + | 1.27579e28i | −0.404088 | + | 0.560262i | ||||
\(503\) | −3.35320e28 | −1.44210 | −0.721051 | − | 0.692882i | \(-0.756341\pi\) | ||||
−0.721051 | + | 0.692882i | \(0.756341\pi\) | |||||||
\(504\) | 5.82529e27 | − | 1.85851e28i | 0.245356 | − | 0.782788i | ||||
\(505\) | 2.34058e28 | 0.965528 | ||||||||
\(506\) | 3.61941e27 | − | 5.01825e27i | 0.146237 | − | 0.202755i | ||||
\(507\) | 1.74893e27i | 0.0692130i | ||||||||
\(508\) | 1.59721e27 | + | 4.80196e27i | 0.0619146 | + | 0.186144i | ||||
\(509\) | 1.11713e28i | 0.424195i | 0.977249 | + | 0.212097i | \(0.0680294\pi\) | ||||
−0.977249 | + | 0.212097i | \(0.931971\pi\) | |||||||
\(510\) | 6.08543e28 | + | 4.38911e28i | 2.26362 | + | 1.63264i | ||||
\(511\) | −2.88966e27 | −0.105300 | ||||||||
\(512\) | 2.21361e28 | − | 1.71649e28i | 0.790252 | − | 0.612782i | ||||
\(513\) | −1.01977e29 | −3.56673 | ||||||||
\(514\) | −2.89296e28 | − | 2.08655e28i | −0.991356 | − | 0.715015i | ||||
\(515\) | 5.81155e28i | 1.95126i | ||||||||
\(516\) | 7.89258e27 | + | 2.37287e28i | 0.259655 | + | 0.780644i | ||||
\(517\) | 2.61364e27i | 0.0842550i | ||||||||
\(518\) | 9.01593e27 | − | 1.25004e28i | 0.284805 | − | 0.394878i | ||||
\(519\) | 7.93820e28 | 2.45734 | ||||||||
\(520\) | 1.43874e28 | − | 4.59018e28i | 0.436463 | − | 1.39250i | ||||
\(521\) | −4.03710e28 | −1.20025 | −0.600127 | − | 0.799905i | \(-0.704883\pi\) | ||||
−0.600127 | + | 0.799905i | \(0.704883\pi\) | |||||||
\(522\) | −6.53283e27 | + | 9.05766e27i | −0.190354 | + | 0.263922i | ||||
\(523\) | − | 2.77341e28i | − | 0.792038i | −0.918242 | − | 0.396019i | \(-0.870391\pi\) | ||
0.918242 | − | 0.396019i | \(-0.129609\pi\) | |||||||
\(524\) | 1.99381e28 | − | 6.63176e27i | 0.558092 | − | 0.185631i | ||||
\(525\) | 2.66913e28i | 0.732314i | ||||||||
\(526\) | 2.32237e28 | + | 1.67501e28i | 0.624571 | + | 0.450471i | ||||
\(527\) | 6.87899e27 | 0.181348 | ||||||||
\(528\) | 1.06544e28 | − | 7.96931e27i | 0.275341 | − | 0.205951i | ||||
\(529\) | 2.41966e28 | 0.613013 | ||||||||
\(530\) | −6.02380e28 | − | 4.34466e28i | −1.49615 | − | 1.07909i | ||||
\(531\) | 9.38964e28i | 2.28642i | ||||||||
\(532\) | −3.08602e28 | + | 1.02646e28i | −0.736761 | + | 0.245059i | ||||
\(533\) | − | 2.22404e28i | − | 0.520603i | ||||||
\(534\) | −3.02861e28 | + | 4.19911e28i | −0.695120 | + | 0.963772i | ||||
\(535\) | 5.77295e28 | 1.29922 | ||||||||
\(536\) | 3.03164e28 | + | 9.50234e27i | 0.669033 | + | 0.209701i | ||||
\(537\) | −5.93442e28 | −1.28425 | ||||||||
\(538\) | −2.05076e28 | + | 2.84334e28i | −0.435211 | + | 0.603413i | ||||
\(539\) | 7.94545e27i | 0.165362i | ||||||||
\(540\) | −4.06514e28 | − | 1.22217e29i | −0.829738 | − | 2.49458i | ||||
\(541\) | 1.63598e28i | 0.327496i | 0.986502 | + | 0.163748i | \(0.0523584\pi\) | ||||
−0.986502 | + | 0.163748i | \(0.947642\pi\) | |||||||
\(542\) | −1.34214e28 | − | 9.68017e27i | −0.263515 | − | 0.190060i | ||||
\(543\) | −3.70558e28 | −0.713605 | ||||||||
\(544\) | −5.90899e28 | + | 1.02623e27i | −1.11616 | + | 0.0193845i | ||||
\(545\) | 9.90279e28 | 1.83482 | ||||||||
\(546\) | 3.17823e28 | + | 2.29230e28i | 0.577648 | + | 0.416628i | ||||
\(547\) | − | 6.66163e28i | − | 1.18772i | −0.804569 | − | 0.593859i | \(-0.797604\pi\) | ||
0.804569 | − | 0.593859i | \(-0.202396\pi\) | |||||||
\(548\) | 7.73412e27 | + | 2.32523e28i | 0.135274 | + | 0.406697i | ||||
\(549\) | − | 7.70491e27i | − | 0.132208i | ||||||
\(550\) | −7.17080e27 | + | 9.94220e27i | −0.120715 | + | 0.167369i | ||||
\(551\) | 1.86482e28 | 0.307996 | ||||||||
\(552\) | 1.30644e29 | + | 4.09488e28i | 2.11703 | + | 0.663561i | ||||
\(553\) | −1.63600e28 | −0.260117 | ||||||||
\(554\) | 6.39166e28 | − | 8.86192e28i | 0.997151 | − | 1.38253i | ||||
\(555\) | − | 1.98855e29i | − | 3.04411i | ||||||
\(556\) | 5.06951e28 | − | 1.68620e28i | 0.761518 | − | 0.253294i | ||||
\(557\) | 1.08955e29i | 1.60608i | 0.595925 | + | 0.803040i | \(0.296786\pi\) | ||||
−0.595925 | + | 0.803040i | \(0.703214\pi\) | |||||||
\(558\) | −1.86856e28 | − | 1.34770e28i | −0.270301 | − | 0.194955i | ||||
\(559\) | −3.38253e28 | −0.480195 | ||||||||
\(560\) | −2.46037e28 | − | 3.28933e28i | −0.342789 | − | 0.458283i | ||||
\(561\) | −2.80712e28 | −0.383841 | ||||||||
\(562\) | −6.69462e28 | − | 4.82849e28i | −0.898452 | − | 0.648008i | ||||
\(563\) | − | 8.28756e28i | − | 1.09166i | −0.837895 | − | 0.545832i | \(-0.816214\pi\) | ||
0.837895 | − | 0.545832i | \(-0.183786\pi\) | |||||||
\(564\) | −5.48777e28 | + | 1.82532e28i | −0.709521 | + | 0.235999i | ||||
\(565\) | − | 3.30661e27i | − | 0.0419638i | ||||||
\(566\) | 8.43171e27 | − | 1.16904e28i | 0.105037 | − | 0.145632i | ||||
\(567\) | 3.78403e28 | 0.462735 | ||||||||
\(568\) | −2.29464e28 | + | 7.32087e28i | −0.275460 | + | 0.878830i | ||||
\(569\) | −1.33952e29 | −1.57860 | −0.789298 | − | 0.614010i | \(-0.789556\pi\) | ||||
−0.789298 | + | 0.614010i | \(0.789556\pi\) | |||||||
\(570\) | −2.45459e29 | + | 3.40325e29i | −2.83984 | + | 3.93739i | ||||
\(571\) | − | 2.81406e28i | − | 0.319635i | −0.987147 | − | 0.159817i | \(-0.948909\pi\) | ||
0.987147 | − | 0.159817i | \(-0.0510905\pi\) | |||||||
\(572\) | 5.68012e27 | + | 1.70771e28i | 0.0633431 | + | 0.190439i | ||||
\(573\) | − | 9.89642e28i | − | 1.08356i | ||||||
\(574\) | −1.54032e28 | − | 1.11096e28i | −0.165591 | − | 0.119432i | ||||
\(575\) | −1.26140e29 | −1.33150 | ||||||||
\(576\) | 1.62518e29 | + | 1.12979e29i | 1.68448 | + | 1.17101i | ||||
\(577\) | 4.95811e28 | 0.504627 | 0.252313 | − | 0.967646i | \(-0.418809\pi\) | ||||
0.252313 | + | 0.967646i | \(0.418809\pi\) | |||||||
\(578\) | 1.99777e28 | + | 1.44089e28i | 0.199666 | + | 0.144009i | ||||
\(579\) | 8.52042e28i | 0.836250i | ||||||||
\(580\) | 7.43376e27 | + | 2.23493e28i | 0.0716498 | + | 0.215412i | ||||
\(581\) | 3.93828e28i | 0.372784i | ||||||||
\(582\) | 2.12102e29 | − | 2.94076e29i | 1.97176 | − | 2.73381i | ||||
\(583\) | 2.77870e28 | 0.253700 | ||||||||
\(584\) | 8.78309e27 | − | 2.80217e28i | 0.0787612 | − | 0.251281i | ||||
\(585\) | 3.39904e29 | 2.99378 | ||||||||
\(586\) | 4.27888e28 | − | 5.93259e28i | 0.370173 | − | 0.513239i | ||||
\(587\) | 1.42608e29i | 1.21184i | 0.795526 | + | 0.605919i | \(0.207194\pi\) | ||||
−0.795526 | + | 0.605919i | \(0.792806\pi\) | |||||||
\(588\) | −1.66828e29 | + | 5.54897e28i | −1.39254 | + | 0.463180i | ||||
\(589\) | 3.84705e28i | 0.315440i | ||||||||
\(590\) | 1.60614e29 | + | 1.15842e29i | 1.29371 | + | 0.933086i | ||||
\(591\) | 2.48039e29 | 1.96269 | ||||||||
\(592\) | 9.38159e28 | + | 1.25425e29i | 0.729287 | + | 0.975001i | ||||
\(593\) | −1.13065e29 | −0.863483 | −0.431742 | − | 0.901997i | \(-0.642101\pi\) | ||||
−0.431742 | + | 0.901997i | \(0.642101\pi\) | |||||||
\(594\) | 3.90829e28 | + | 2.81885e28i | 0.293244 | + | 0.211502i | ||||
\(595\) | 8.66647e28i | 0.638873i | ||||||||
\(596\) | −7.29964e28 | + | 2.42798e28i | −0.528708 | + | 0.175857i | ||||
\(597\) | − | 4.12920e29i | − | 2.93857i | ||||||
\(598\) | −1.08331e29 | + | 1.50199e29i | −0.757516 | + | 1.05028i | ||||
\(599\) | −8.35529e28 | −0.574090 | −0.287045 | − | 0.957917i | \(-0.592673\pi\) | ||||
−0.287045 | + | 0.957917i | \(0.592673\pi\) | |||||||
\(600\) | −2.58832e29 | − | 8.11281e28i | −1.74755 | − | 0.547751i | ||||
\(601\) | −1.31030e29 | −0.869336 | −0.434668 | − | 0.900591i | \(-0.643134\pi\) | ||||
−0.434668 | + | 0.900591i | \(0.643134\pi\) | |||||||
\(602\) | −1.68965e28 | + | 2.34267e28i | −0.110162 | + | 0.152738i | ||||
\(603\) | 2.24494e29i | 1.43838i | ||||||||
\(604\) | 2.63583e28 | + | 7.92454e28i | 0.165970 | + | 0.498984i | ||||
\(605\) | 2.22319e29i | 1.37577i | ||||||||
\(606\) | −1.57155e29 | − | 1.13348e29i | −0.955799 | − | 0.689369i | ||||
\(607\) | −5.68586e28 | −0.339872 | −0.169936 | − | 0.985455i | \(-0.554356\pi\) | ||||
−0.169936 | + | 0.985455i | \(0.554356\pi\) | |||||||
\(608\) | −5.73914e27 | − | 3.30458e29i | −0.0337178 | − | 1.94146i | ||||
\(609\) | −1.91870e28 | −0.110796 | ||||||||
\(610\) | −1.31795e28 | − | 9.50574e27i | −0.0748061 | − | 0.0539539i | ||||
\(611\) | − | 7.82282e28i | − | 0.436446i | ||||||
\(612\) | −1.31800e29 | − | 3.96252e29i | −0.722812 | − | 2.17311i | ||||
\(613\) | − | 2.41527e29i | − | 1.30206i | −0.759052 | − | 0.651030i | \(-0.774337\pi\) | ||
0.759052 | − | 0.651030i | \(-0.225663\pi\) | |||||||
\(614\) | −3.03389e27 | + | 4.20643e27i | −0.0160780 | + | 0.0222918i | ||||
\(615\) | −2.45031e29 | −1.27654 | ||||||||
\(616\) | 1.46646e28 | + | 4.59644e27i | 0.0751054 | + | 0.0235410i | ||||
\(617\) | 2.33971e29 | 1.17806 | 0.589032 | − | 0.808110i | \(-0.299509\pi\) | ||||
0.589032 | + | 0.808110i | \(0.299509\pi\) | |||||||
\(618\) | 2.81438e29 | − | 3.90209e29i | 1.39317 | − | 1.93160i | ||||
\(619\) | 6.73316e28i | 0.327693i | 0.986486 | + | 0.163847i | \(0.0523902\pi\) | ||||
−0.986486 | + | 0.163847i | \(0.947610\pi\) | |||||||
\(620\) | −4.61059e28 | + | 1.53356e28i | −0.220619 | + | 0.0733816i | ||||
\(621\) | 4.95857e29i | 2.33289i | ||||||||
\(622\) | 3.43165e29 | + | 2.47507e29i | 1.58746 | + | 1.14496i | ||||
\(623\) | −5.98010e28 | −0.272010 | ||||||||
\(624\) | −3.18892e29 | + | 2.38527e29i | −1.42628 | + | 1.06684i | ||||
\(625\) | −2.15839e29 | −0.949272 | ||||||||
\(626\) | 7.52580e28 | + | 5.42798e28i | 0.325478 | + | 0.234751i | ||||
\(627\) | − | 1.56987e29i | − | 0.667660i | ||||||
\(628\) | 1.99641e29 | − | 6.64040e28i | 0.834976 | − | 0.277727i | ||||
\(629\) | − | 3.30459e29i | − | 1.35921i | ||||||
\(630\) | 1.69789e29 | − | 2.35410e29i | 0.686807 | − | 0.952246i | ||||
\(631\) | −1.15456e29 | −0.459312 | −0.229656 | − | 0.973272i | \(-0.573760\pi\) | ||||
−0.229656 | + | 0.973272i | \(0.573760\pi\) | |||||||
\(632\) | 4.97260e28 | − | 1.58647e29i | 0.194560 | − | 0.620728i | ||||
\(633\) | 9.88943e28 | 0.380568 | ||||||||
\(634\) | 2.04077e29 | − | 2.82949e29i | 0.772425 | − | 1.07095i | ||||
\(635\) | 7.54162e28i | 0.280764i | ||||||||
\(636\) | 1.94059e29 | + | 5.83432e29i | 0.710616 | + | 2.13644i | ||||
\(637\) | − | 2.37813e29i | − | 0.856586i | ||||||
\(638\) | −7.14693e27 | − | 5.15472e27i | −0.0253223 | − | 0.0182637i | ||||
\(639\) | −5.42112e29 | −1.88943 | ||||||||
\(640\) | 3.93757e29 | − | 1.38609e29i | 1.35002 | − | 0.475229i | ||||
\(641\) | 4.45875e29 | 1.50385 | 0.751924 | − | 0.659249i | \(-0.229126\pi\) | ||||
0.751924 | + | 0.659249i | \(0.229126\pi\) | |||||||
\(642\) | −3.87617e29 | − | 2.79568e29i | −1.28613 | − | 0.927620i | ||||
\(643\) | 3.74184e29i | 1.22143i | 0.791849 | + | 0.610717i | \(0.209119\pi\) | ||||
−0.791849 | + | 0.610717i | \(0.790881\pi\) | |||||||
\(644\) | 4.99111e28 | + | 1.50056e29i | 0.160286 | + | 0.481894i | ||||
\(645\) | 3.72667e29i | 1.17745i | ||||||||
\(646\) | −4.07907e29 | + | 5.65556e29i | −1.26800 | + | 1.75806i | ||||
\(647\) | 1.27928e29 | 0.391264 | 0.195632 | − | 0.980677i | \(-0.437324\pi\) | ||||
0.195632 | + | 0.980677i | \(0.437324\pi\) | |||||||
\(648\) | −1.15015e29 | + | 3.66947e29i | −0.346113 | + | 1.10425i | ||||
\(649\) | −7.40889e28 | −0.219373 | ||||||||
\(650\) | 2.14627e29 | − | 2.97577e29i | 0.625308 | − | 0.866979i | ||||
\(651\) | − | 3.95821e28i | − | 0.113475i | ||||||
\(652\) | −3.30423e29 | + | 1.09904e29i | −0.932116 | + | 0.310037i | ||||
\(653\) | 2.46770e29i | 0.685021i | 0.939514 | + | 0.342510i | \(0.111277\pi\) | ||||
−0.939514 | + | 0.342510i | \(0.888723\pi\) | |||||||
\(654\) | −6.64909e29 | − | 4.79565e29i | −1.81634 | − | 1.31003i | ||||
\(655\) | 3.13135e29 | 0.841778 | ||||||||
\(656\) | 1.54550e29 | − | 1.15601e29i | 0.408864 | − | 0.305824i | ||||
\(657\) | 2.07501e29 | 0.540238 | ||||||||
\(658\) | −5.41791e28 | − | 3.90767e28i | −0.138823 | − | 0.100126i | ||||
\(659\) | − | 3.76657e29i | − | 0.949838i | −0.880029 | − | 0.474919i | \(-0.842477\pi\) | ||
0.880029 | − | 0.474919i | \(-0.157523\pi\) | |||||||
\(660\) | 1.88145e29 | − | 6.25802e28i | 0.466962 | − | 0.155319i | ||||
\(661\) | 5.90601e29i | 1.44271i | 0.692566 | + | 0.721355i | \(0.256480\pi\) | ||||
−0.692566 | + | 0.721355i | \(0.743520\pi\) | |||||||
\(662\) | 9.29750e27 | − | 1.28908e28i | 0.0223541 | − | 0.0309936i | ||||
\(663\) | 8.40192e29 | 1.98832 | ||||||||
\(664\) | −3.81904e29 | − | 1.19704e29i | −0.889589 | − | 0.278832i | ||||
\(665\) | −4.84669e29 | −1.11127 | ||||||||
\(666\) | −6.47420e29 | + | 8.97636e29i | −1.46119 | + | 2.02591i | ||||
\(667\) | − | 9.06756e28i | − | 0.201451i | ||||||
\(668\) | 2.40591e28 | + | 7.23327e28i | 0.0526170 | + | 0.158191i | ||||
\(669\) | − | 5.66646e29i | − | 1.21994i | ||||||
\(670\) | 3.84006e29 | + | 2.76964e29i | 0.813865 | + | 0.586999i | ||||
\(671\) | 6.07955e27 | 0.0126848 | ||||||||
\(672\) | 5.90497e27 | + | 3.40007e29i | 0.0121294 | + | 0.698410i | ||||
\(673\) | 2.15360e29 | 0.435519 | 0.217760 | − | 0.976002i | \(-0.430125\pi\) | ||||
0.217760 | + | 0.976002i | \(0.430125\pi\) | |||||||
\(674\) | 6.30086e29 | + | 4.54449e29i | 1.25450 | + | 0.904807i | ||||
\(675\) | − | 9.82398e29i | − | 1.92574i | ||||||
\(676\) | −6.47930e27 | − | 1.94798e28i | −0.0125051 | − | 0.0375962i | ||||
\(677\) | − | 8.99548e29i | − | 1.70940i | −0.519124 | − | 0.854699i | \(-0.673742\pi\) | ||
0.519124 | − | 0.854699i | \(-0.326258\pi\) | |||||||
\(678\) | −1.60130e28 | + | 2.22018e28i | −0.0299614 | + | 0.0415409i | ||||
\(679\) | 4.18804e29 | 0.771576 | ||||||||
\(680\) | −8.40409e29 | − | 2.63417e29i | −1.52457 | − | 0.477859i | ||||
\(681\) | −1.67087e29 | −0.298468 | ||||||||
\(682\) | 1.06340e28 | − | 1.47439e28i | 0.0187051 | − | 0.0259343i | ||||
\(683\) | 5.90620e29i | 1.02304i | 0.859272 | + | 0.511518i | \(0.170917\pi\) | ||||
−0.859272 | + | 0.511518i | \(0.829083\pi\) | |||||||
\(684\) | 2.21602e30 | − | 7.37086e29i | 3.77994 | − | 1.25727i | ||||
\(685\) | 3.65185e29i | 0.613426i | ||||||||
\(686\) | −3.60756e29 | − | 2.60195e29i | −0.596774 | − | 0.430423i | ||||
\(687\) | −1.79827e30 | −2.92960 | ||||||||
\(688\) | −1.75817e29 | − | 2.35054e29i | −0.282087 | − | 0.377129i | ||||
\(689\) | −8.31683e29 | −1.31418 | ||||||||
\(690\) | 1.65481e30 | + | 1.19353e30i | 2.57533 | + | 1.85745i | ||||
\(691\) | 4.03124e28i | 0.0617901i | 0.999523 | + | 0.0308951i | \(0.00983577\pi\) | ||||
−0.999523 | + | 0.0308951i | \(0.990164\pi\) | |||||||
\(692\) | −8.84169e29 | + | 2.94089e29i | −1.33482 | + | 0.443982i | ||||
\(693\) | 1.08591e29i | 0.161472i | ||||||||
\(694\) | −1.51038e29 | + | 2.09412e29i | −0.221214 | + | 0.306709i | ||||
\(695\) | 7.96182e29 | 1.14861 | ||||||||
\(696\) | 5.83188e28 | − | 1.86061e29i | 0.0828727 | − | 0.264398i | ||||
\(697\) | −4.07196e29 | −0.569980 | ||||||||
\(698\) | −4.85784e29 | + | 6.73531e29i | −0.669824 | + | 0.928700i | ||||
\(699\) | − | 7.64874e29i | − | 1.03891i | ||||||
\(700\) | −9.88843e28 | − | 2.97292e29i | −0.132312 | − | 0.397790i | ||||
\(701\) | − | 1.27766e30i | − | 1.68413i | −0.539373 | − | 0.842067i | \(-0.681339\pi\) | ||
0.539373 | − | 0.842067i | \(-0.318661\pi\) | |||||||
\(702\) | −1.16978e30 | − | 8.43701e29i | −1.51902 | − | 1.09559i | ||||
\(703\) | 1.84808e30 | 2.36423 | ||||||||
\(704\) | −8.91456e28 | + | 1.28235e29i | −0.112354 | + | 0.161619i | ||||
\(705\) | −8.61872e29 | −1.07018 | ||||||||
\(706\) | −3.33607e29 | − | 2.40614e29i | −0.408118 | − | 0.294355i | ||||
\(707\) | − | 2.23810e29i | − | 0.269759i | ||||||
\(708\) | −5.17424e29 | − | 1.55562e30i | −0.614465 | − | 1.84737i | ||||
\(709\) | 8.61111e29i | 1.00757i | 0.863830 | + | 0.503783i | \(0.168059\pi\) | ||||
−0.863830 | + | 0.503783i | \(0.831941\pi\) | |||||||
\(710\) | −6.68818e29 | + | 9.27305e29i | −0.771073 | + | 1.06908i | ||||
\(711\) | 1.17478e30 | 1.33453 | ||||||||
\(712\) | 1.81765e29 | − | 5.79905e29i | 0.203456 | − | 0.649108i | ||||
\(713\) | 1.87060e29 | 0.206320 | ||||||||
\(714\) | 4.19694e29 | − | 5.81898e29i | 0.456143 | − | 0.632435i | ||||
\(715\) | 2.68201e29i | 0.287241i | ||||||||
\(716\) | 6.60984e29 | − | 2.19854e29i | 0.697597 | − | 0.232032i | ||||
\(717\) | 1.82190e30i | 1.89484i | ||||||||
\(718\) | −5.42458e29 | − | 3.91247e29i | −0.555980 | − | 0.401000i | ||||
\(719\) | −7.17709e29 | −0.724928 | −0.362464 | − | 0.931998i | \(-0.618064\pi\) | ||||
−0.362464 | + | 0.931998i | \(0.618064\pi\) | |||||||
\(720\) | 1.76676e30 | + | 2.36202e30i | 1.75867 | + | 2.35121i | ||||
\(721\) | 5.55710e29 | 0.545165 | ||||||||
\(722\) | −2.32399e30 | − | 1.67618e30i | −2.24695 | − | 1.62061i | ||||
\(723\) | 1.33562e30i | 1.27272i | ||||||||
\(724\) | 4.12733e29 | − | 1.37282e29i | 0.387627 | − | 0.128931i | ||||
\(725\) | 1.79647e29i | 0.166292i | ||||||||
\(726\) | 1.07663e30 | − | 1.49273e30i | 0.982273 | − | 1.36190i | ||||
\(727\) | −2.93731e29 | −0.264143 | −0.132071 | − | 0.991240i | \(-0.542163\pi\) | ||||
−0.132071 | + | 0.991240i | \(0.542163\pi\) | |||||||
\(728\) | −4.38920e29 | − | 1.37575e29i | −0.389050 | − | 0.121944i | ||||
\(729\) | 9.55345e29 | 0.834682 | ||||||||
\(730\) | 2.56000e29 | − | 3.54940e29i | 0.220470 | − | 0.305678i | ||||
\(731\) | 6.19303e29i | 0.525740i | ||||||||
\(732\) | 4.24585e28 | + | 1.27650e29i | 0.0355303 | + | 0.106820i | ||||
\(733\) | − | 1.28152e30i | − | 1.05714i | −0.848890 | − | 0.528569i | \(-0.822729\pi\) | ||
0.848890 | − | 0.528569i | \(-0.177271\pi\) | |||||||
\(734\) | 1.72794e30 | + | 1.24627e30i | 1.40514 | + | 1.01346i | ||||
\(735\) | −2.62008e30 | −2.10038 | ||||||||
\(736\) | −1.60683e30 | + | 2.79062e28i | −1.26985 | + | 0.0220538i | ||||
\(737\) | −1.77137e29 | −0.138007 | ||||||||
\(738\) | 1.10608e30 | + | 7.97759e29i | 0.849561 | + | 0.612745i | ||||
\(739\) | 1.95302e29i | 0.147891i | 0.997262 | + | 0.0739453i | \(0.0235590\pi\) | ||||
−0.997262 | + | 0.0739453i | \(0.976441\pi\) | |||||||
\(740\) | 7.36704e29 | + | 2.21487e30i | 0.549997 | + | 1.65355i | ||||
\(741\) | 4.69874e30i | 3.45852i | ||||||||
\(742\) | −4.15443e29 | + | 5.76005e29i | −0.301489 | + | 0.418009i | ||||
\(743\) | 7.65776e29 | 0.547923 | 0.273961 | − | 0.961741i | \(-0.411666\pi\) | ||||
0.273961 | + | 0.961741i | \(0.411666\pi\) | |||||||
\(744\) | 3.83838e29 | + | 1.20310e29i | 0.270789 | + | 0.0848759i | ||||
\(745\) | −1.14643e30 | −0.797457 | ||||||||
\(746\) | 1.14052e30 | − | 1.58131e30i | 0.782250 | − | 1.08458i | ||||
\(747\) | − | 2.82801e30i | − | 1.91256i | ||||||
\(748\) | 3.12662e29 | − | 1.03997e29i | 0.208501 | − | 0.0693509i | ||||
\(749\) | − | 5.52019e29i | − | 0.362990i | ||||||
\(750\) | −1.51316e29 | − | 1.09137e29i | −0.0981164 | − | 0.0707664i | ||||
\(751\) | −2.22552e30 | −1.42302 | −0.711512 | − | 0.702674i | \(-0.751989\pi\) | ||||
−0.711512 | + | 0.702674i | \(0.751989\pi\) | |||||||
\(752\) | 5.43613e29 | − | 4.06615e29i | 0.342770 | − | 0.256387i | ||||
\(753\) | 1.94065e30 | 1.20670 | ||||||||
\(754\) | 2.13913e29 | + | 1.54284e29i | 0.131171 | + | 0.0946069i | ||||
\(755\) | 1.24457e30i | 0.752623i | ||||||||
\(756\) | −1.16866e30 | + | 3.88715e29i | −0.696961 | + | 0.231821i | ||||
\(757\) | 5.24409e29i | 0.308435i | 0.988037 | + | 0.154217i | \(0.0492856\pi\) | ||||
−0.988037 | + | 0.154217i | \(0.950714\pi\) | |||||||
\(758\) | −8.53765e29 | + | 1.18373e30i | −0.495236 | + | 0.686636i | ||||
\(759\) | −7.63341e29 | −0.436697 | ||||||||
\(760\) | 1.47315e30 | − | 4.69995e30i | 0.831197 | − | 2.65186i | ||||
\(761\) | 2.82547e30 | 1.57236 | 0.786179 | − | 0.617999i | \(-0.212057\pi\) | ||||
0.786179 | + | 0.617999i | \(0.212057\pi\) | |||||||
\(762\) | 3.65221e29 | − | 5.06372e29i | 0.200460 | − | 0.277934i | ||||
\(763\) | − | 9.46921e29i | − | 0.512632i | ||||||
\(764\) | 3.66636e29 | + | 1.10228e30i | 0.195774 | + | 0.588587i | ||||
\(765\) | − | 6.22325e30i | − | 3.27772i | ||||||
\(766\) | −3.14107e29 | − | 2.26550e29i | −0.163183 | − | 0.117696i | ||||
\(767\) | 2.21753e30 | 1.13637 | ||||||||
\(768\) | −3.31508e30 | − | 9.76187e29i | −1.67572 | − | 0.493447i | ||||
\(769\) | −2.60437e30 | −1.29860 | −0.649300 | − | 0.760532i | \(-0.724938\pi\) | ||||
−0.649300 | + | 0.760532i | \(0.724938\pi\) | |||||||
\(770\) | 1.85750e29 | + | 1.33972e29i | 0.0913642 | + | 0.0658964i | ||||
\(771\) | 4.40057e30i | 2.13520i | ||||||||
\(772\) | −3.15659e29 | − | 9.49017e29i | −0.151090 | − | 0.454247i | ||||
\(773\) | − | 2.19908e30i | − | 1.03838i | −0.854659 | − | 0.519189i | \(-0.826234\pi\) | ||
0.854659 | − | 0.519189i | \(-0.173766\pi\) | |||||||
\(774\) | 1.21331e30 | − | 1.68223e30i | 0.565186 | − | 0.783620i | ||||
\(775\) | −3.70606e29 | −0.170312 | ||||||||
\(776\) | −1.27295e30 | + | 4.06125e30i | −0.577118 | + | 1.84125i | ||||
\(777\) | −1.90148e30 | −0.850494 | ||||||||
\(778\) | −8.47355e29 | + | 1.17484e30i | −0.373921 | + | 0.518435i | ||||
\(779\) | − | 2.27723e30i | − | 0.991433i | ||||||
\(780\) | −5.63131e30 | + | 1.87307e30i | −2.41889 | + | 0.804564i | ||||
\(781\) | − | 4.27753e29i | − | 0.181283i | ||||||
\(782\) | 2.74998e30 | + | 1.98342e30i | 1.14990 | + | 0.829363i | ||||
\(783\) | 7.06195e29 | 0.291358 | ||||||||
\(784\) | 1.65258e30 | − | 1.23610e30i | 0.672734 | − | 0.503195i | ||||
\(785\) | 3.13543e30 | 1.25941 | ||||||||
\(786\) | −2.10250e30 | − | 1.51643e30i | −0.833296 | − | 0.601014i | ||||
\(787\) | − | 2.48348e30i | − | 0.971239i | −0.874170 | − | 0.485620i | \(-0.838594\pi\) | ||
0.874170 | − | 0.485620i | \(-0.161406\pi\) | |||||||
\(788\) | −2.76269e30 | + | 9.18917e29i | −1.06612 | + | 0.354610i | ||||
\(789\) | − | 3.53264e30i | − | 1.34521i | ||||||
\(790\) | 1.44936e30 | − | 2.00951e30i | 0.544618 | − | 0.755103i | ||||
\(791\) | −3.16184e28 | −0.0117243 | ||||||||
\(792\) | −1.05304e30 | − | 3.30063e29i | −0.385327 | − | 0.120776i | ||||
\(793\) | −1.81965e29 | −0.0657082 | ||||||||
\(794\) | −3.46934e28 | + | 4.81018e28i | −0.0123632 | + | 0.0171414i | ||||
\(795\) | 9.16299e30i | 3.22242i | ||||||||
\(796\) | 1.52976e30 | + | 4.59917e30i | 0.530928 | + | 1.59622i | ||||
\(797\) | − | 2.70053e30i | − | 0.924988i | −0.886622 | − | 0.462494i | \(-0.846955\pi\) | ||
0.886622 | − | 0.462494i | \(-0.153045\pi\) | |||||||
\(798\) | 3.25424e30 | + | 2.34712e30i | 1.10007 | + | 0.793424i | ||||
\(799\) | −1.43227e30 | −0.477841 | ||||||||
\(800\) | 3.18347e30 | − | 5.52880e28i | 1.04823 | − | 0.0182048i | ||||
\(801\) | 4.29422e30 | 1.39554 | ||||||||
\(802\) | −1.15606e30 | − | 8.33810e29i | −0.370809 | − | 0.267446i | ||||
\(803\) | 1.63729e29i | 0.0518337i | ||||||||
\(804\) | −1.23709e30 | − | 3.71927e30i | −0.386557 | − | 1.16217i | ||||
\(805\) | 2.35667e30i | 0.726846i | ||||||||
\(806\) | −3.18283e29 | + | 4.41294e29i | −0.0968937 | + | 0.134341i | ||||
\(807\) | 4.32509e30 | 1.29964 | ||||||||
\(808\) | 2.17034e30 | + | 6.80270e29i | 0.643738 | + | 0.201773i | ||||
\(809\) | −3.79900e29 | −0.111227 | −0.0556134 | − | 0.998452i | \(-0.517711\pi\) | ||||
−0.0556134 | + | 0.998452i | \(0.517711\pi\) | |||||||
\(810\) | −3.35235e30 | + | 4.64797e30i | −0.968849 | + | 1.34329i | ||||
\(811\) | − | 5.66301e30i | − | 1.61558i | −0.589471 | − | 0.807790i | \(-0.700664\pi\) | ||
0.589471 | − | 0.807790i | \(-0.299336\pi\) | |||||||
\(812\) | 2.13708e29 | − | 7.10828e28i | 0.0601842 | − | 0.0200183i | ||||
\(813\) | 2.04157e30i | 0.567563i | ||||||||
\(814\) | −7.08279e29 | − | 5.10846e29i | −0.194378 | − | 0.140195i | ||||
\(815\) | −5.18939e30 | −1.40592 | ||||||||
\(816\) | 4.36715e30 | + | 5.83855e30i | 1.16802 | + | 1.56156i | ||||
\(817\) | −3.46343e30 | −0.914480 | ||||||||
\(818\) | 4.01541e30 | + | 2.89611e30i | 1.04669 | + | 0.754928i | ||||
\(819\) | − | 3.25022e30i | − | 0.836433i | ||||||
\(820\) | 2.72920e30 | − | 9.07777e29i | 0.693409 | − | 0.230639i | ||||
\(821\) | 6.44047e30i | 1.61553i | 0.589507 | + | 0.807763i | \(0.299322\pi\) | ||||
−0.589507 | + | 0.807763i | \(0.700678\pi\) | |||||||
\(822\) | 1.76849e30 | − | 2.45199e30i | 0.437975 | − | 0.607245i | ||||
\(823\) | 3.58633e30 | 0.876905 | 0.438452 | − | 0.898754i | \(-0.355527\pi\) | ||||
0.438452 | + | 0.898754i | \(0.355527\pi\) | |||||||
\(824\) | −1.68908e30 | + | 5.38885e30i | −0.407768 | + | 1.30095i | ||||
\(825\) | 1.51234e30 | 0.360481 | ||||||||
\(826\) | 1.10770e30 | − | 1.53581e30i | 0.260695 | − | 0.361450i | ||||
\(827\) | − | 5.93139e30i | − | 1.37831i | −0.724612 | − | 0.689157i | \(-0.757981\pi\) | ||
0.724612 | − | 0.689157i | \(-0.242019\pi\) | |||||||
\(828\) | −3.58403e30 | − | 1.07753e31i | −0.822344 | − | 2.47235i | ||||
\(829\) | 6.70193e30i | 1.51837i | 0.650876 | + | 0.759184i | \(0.274402\pi\) | ||||
−0.650876 | + | 0.759184i | \(0.725598\pi\) | |||||||
\(830\) | −4.83743e30 | − | 3.48899e30i | −1.08217 | − | 0.780513i | ||||
\(831\) | −1.34802e31 | −2.97772 | ||||||||
\(832\) | 2.66819e30 | − | 3.83816e30i | 0.581998 | − | 0.837197i | ||||
\(833\) | −4.35408e30 | −0.937830 | ||||||||
\(834\) | −5.34585e30 | − | 3.85569e30i | −1.13703 | − | 0.820085i | ||||
\(835\) | 1.13601e30i | 0.238602i | ||||||||
\(836\) | 5.81597e29 | + | 1.74855e30i | 0.120630 | + | 0.362670i | ||||
\(837\) | 1.45685e30i | 0.298400i | ||||||||
\(838\) | 1.24317e30 | − | 1.72363e30i | 0.251459 | − | 0.348644i | ||||
\(839\) | −2.22879e30 | −0.445214 | −0.222607 | − | 0.974908i | \(-0.571457\pi\) | ||||
−0.222607 | + | 0.974908i | \(0.571457\pi\) | |||||||
\(840\) | −1.51572e30 | + | 4.83576e30i | −0.299010 | + | 0.953965i | ||||
\(841\) | 5.00370e30 | 0.974841 | ||||||||
\(842\) | −9.25626e29 | + | 1.28336e30i | −0.178098 | + | 0.246930i | ||||
\(843\) | 1.01834e31i | 1.93510i | ||||||||
\(844\) | −1.10150e30 | + | 3.66377e29i | −0.206723 | + | 0.0687595i | ||||
\(845\) | − | 3.05936e29i | − | 0.0567068i | ||||||
\(846\) | 3.89052e30 | + | 2.80603e30i | 0.712227 | + | 0.513693i | ||||
\(847\) | 2.12585e30 | 0.384376 | ||||||||
\(848\) | −4.32293e30 | − | 5.77942e30i | −0.772007 | − | 1.03211i | ||||
\(849\) | −1.77827e30 | −0.313665 | ||||||||
\(850\) | −5.44829e30 | − | 3.92958e30i | −0.949209 | − | 0.684616i | ||||
\(851\) | − | 8.98617e30i | − | 1.54637i | ||||||
\(852\) | 8.98137e30 | − | 2.98736e30i | 1.52661 | − | 0.507775i | ||||
\(853\) | − | 5.01110e30i | − | 0.841334i | −0.907215 | − | 0.420667i | \(-0.861796\pi\) | ||
0.907215 | − | 0.420667i | \(-0.138204\pi\) | |||||||
\(854\) | −9.08954e28 | + | 1.26025e29i | −0.0150742 | + | 0.0209001i | ||||
\(855\) | 3.48033e31 | 5.70133 | ||||||||
\(856\) | 5.35306e30 | + | 1.67786e30i | 0.866219 | + | 0.271507i | ||||
\(857\) | 7.58197e30 | 1.21195 | 0.605973 | − | 0.795485i | \(-0.292784\pi\) | ||||
0.605973 | + | 0.795485i | \(0.292784\pi\) | |||||||
\(858\) | 1.29882e30 | − | 1.80080e30i | 0.205085 | − | 0.284347i | ||||
\(859\) | 9.10584e30i | 1.42034i | 0.704031 | + | 0.710169i | \(0.251381\pi\) | ||||
−0.704031 | + | 0.710169i | \(0.748619\pi\) | |||||||
\(860\) | −1.38063e30 | − | 4.15082e30i | −0.212738 | − | 0.639589i | ||||
\(861\) | 2.34303e30i | 0.356652i | ||||||||
\(862\) | −7.27199e30 | − | 5.24492e30i | −1.09352 | − | 0.788701i | ||||
\(863\) | −8.75139e30 | −1.30006 | −0.650030 | − | 0.759908i | \(-0.725244\pi\) | ||||
−0.650030 | + | 0.759908i | \(0.725244\pi\) | |||||||
\(864\) | −2.17338e29 | − | 1.25143e31i | −0.0318963 | − | 1.83658i | ||||
\(865\) | −1.38861e31 | −2.01332 | ||||||||
\(866\) | −2.63994e29 | − | 1.90406e29i | −0.0378143 | − | 0.0272736i | ||||
\(867\) | − | 3.03887e30i | − | 0.430043i | ||||||
\(868\) | 1.46641e29 | + | 4.40872e29i | 0.0205021 | + | 0.0616389i | ||||
\(869\) | 9.26961e29i | 0.128042i | ||||||||
\(870\) | 1.69981e30 | − | 2.35676e30i | 0.231979 | − | 0.321635i | ||||
\(871\) | 5.30182e30 | 0.714882 | ||||||||
\(872\) | 9.18252e30 | + | 2.87816e30i | 1.22332 | + | 0.383435i | ||||
\(873\) | −3.00737e31 | −3.95856 | ||||||||
\(874\) | −1.10922e31 | + | 1.53792e31i | −1.44261 | + | 2.00015i | ||||
\(875\) | − | 2.15494e29i | − | 0.0276918i | ||||||
\(876\) | −3.43775e30 | + | 1.14345e30i | −0.436497 | + | 0.145186i | ||||
\(877\) | 1.02617e31i | 1.28743i | 0.765266 | + | 0.643715i | \(0.222608\pi\) | ||||
−0.765266 | + | 0.643715i | \(0.777392\pi\) | |||||||
\(878\) | 7.09988e30 | + | 5.12078e30i | 0.880154 | + | 0.634811i | ||||
\(879\) | −9.02425e30 | −1.10542 | ||||||||
\(880\) | −1.86375e30 | + | 1.39406e30i | −0.225589 | + | 0.168738i | ||||
\(881\) | 4.73054e30 | 0.565801 | 0.282901 | − | 0.959149i | \(-0.408703\pi\) | ||||
0.282901 | + | 0.959149i | \(0.408703\pi\) | |||||||
\(882\) | 1.18271e31 | + | 8.53031e30i | 1.39784 | + | 1.00819i | ||||
\(883\) | 1.26828e30i | 0.148125i | 0.997254 | + | 0.0740626i | \(0.0235965\pi\) | ||||
−0.997254 | + | 0.0740626i | \(0.976404\pi\) | |||||||
\(884\) | −9.35818e30 | + | 3.11269e30i | −1.08005 | + | 0.359242i | ||||
\(885\) | − | 2.44314e31i | − | 2.78641i | ||||||
\(886\) | −9.69354e30 | + | 1.34399e31i | −1.09252 | + | 1.51476i | ||||
\(887\) | −1.34347e31 | −1.49634 | −0.748170 | − | 0.663507i | \(-0.769067\pi\) | ||||
−0.748170 | + | 0.663507i | \(0.769067\pi\) | |||||||
\(888\) | 5.77954e30 | − | 1.84391e31i | 0.636146 | − | 2.02957i | ||||
\(889\) | 7.21142e29 | 0.0784427 | ||||||||
\(890\) | 5.29789e30 | − | 7.34543e30i | 0.569518 | − | 0.789627i | ||||
\(891\) | − | 2.14405e30i | − | 0.227781i | ||||||
\(892\) | 2.09928e30 | + | 6.31139e30i | 0.220414 | + | 0.662665i | ||||
\(893\) | − | 8.00991e30i | − | 0.831165i | ||||||
\(894\) | 7.69756e30 | + | 5.55186e30i | 0.789422 | + | 0.569370i | ||||
\(895\) | 1.03810e31 | 1.05219 | ||||||||
\(896\) | −1.32541e30 | − | 3.76517e30i | −0.132775 | − | 0.377182i | ||||
\(897\) | 2.28473e31 | 2.26212 | ||||||||
\(898\) | 6.14493e30 | + | 4.43203e30i | 0.601334 | + | 0.433712i | ||||
\(899\) | − | 2.66409e29i | − | 0.0257675i | ||||||
\(900\) | 7.10072e30 | + | 2.13481e31i | 0.678822 | + | 2.04085i | ||||
\(901\) | 1.52272e31i | 1.43883i | ||||||||
\(902\) | −6.29471e29 | + | 8.72751e29i | −0.0587905 | + | 0.0815120i | ||||
\(903\) | 3.56351e30 | 0.328970 | ||||||||
\(904\) | 9.61038e28 | − | 3.06611e29i | 0.00876944 | − | 0.0279782i | ||||
\(905\) | 6.48210e30 | 0.584663 | ||||||||
\(906\) | 6.02714e30 | − | 8.35652e30i | 0.537359 | − | 0.745040i | ||||
\(907\) | − | 1.68871e31i | − | 1.48826i | −0.668033 | − | 0.744132i | \(-0.732863\pi\) | ||
0.668033 | − | 0.744132i | \(-0.267137\pi\) | |||||||
\(908\) | 1.86104e30 | − | 6.19014e29i | 0.162127 | − | 0.0539261i | ||||
\(909\) | 1.60715e31i | 1.38400i | ||||||||
\(910\) | −5.55962e30 | − | 4.00988e30i | −0.473272 | − | 0.341347i | ||||
\(911\) | 1.11512e31 | 0.938379 | 0.469190 | − | 0.883097i | \(-0.344546\pi\) | ||||
0.469190 | + | 0.883097i | \(0.344546\pi\) | |||||||
\(912\) | −3.26519e31 | + | 2.44231e31i | −2.71620 | + | 2.03168i | ||||
\(913\) | 2.23144e30 | 0.183503 | ||||||||
\(914\) | −1.71700e31 | − | 1.23838e31i | −1.39584 | − | 1.00675i | ||||
\(915\) | 2.00478e30i | 0.161119i | ||||||||
\(916\) | 2.00294e31 | − | 6.66210e30i | 1.59135 | − | 0.529309i | ||||
\(917\) | − | 2.99424e30i | − | 0.235185i | ||||||
\(918\) | −1.54472e31 | + | 2.14173e31i | −1.19950 | + | 1.66309i | ||||
\(919\) | 1.42554e31 | 1.09438 | 0.547189 | − | 0.837009i | \(-0.315698\pi\) | ||||
0.547189 | + | 0.837009i | \(0.315698\pi\) | |||||||
\(920\) | −2.28532e31 | − | 7.16309e30i | −1.73450 | − | 0.543661i | ||||
\(921\) | 6.39854e29 | 0.0480125 | ||||||||
\(922\) | 8.35767e30 | − | 1.15878e31i | 0.620027 | − | 0.859657i | ||||
\(923\) | 1.28029e31i | 0.939057i | ||||||||
\(924\) | −5.98402e29 | − | 1.79907e30i | −0.0433948 | − | 0.130465i | ||||
\(925\) | 1.78035e31i | 1.27649i | ||||||||
\(926\) | −1.21306e31 | − | 8.74922e30i | −0.859941 | − | 0.620232i | ||||
\(927\) | −3.99046e31 | −2.79696 | ||||||||
\(928\) | 3.97437e28 | + | 2.28843e30i | 0.00275432 | + | 0.158593i | ||||
\(929\) | 1.65266e31 | 1.13245 | 0.566226 | − | 0.824250i | \(-0.308403\pi\) | ||||
0.566226 | + | 0.824250i | \(0.308403\pi\) | |||||||
\(930\) | 4.86192e30 | + | 3.50665e30i | 0.329410 | + | 0.237587i | ||||
\(931\) | − | 2.43500e31i | − | 1.63128i | ||||||
\(932\) | 2.83366e30 | + | 8.51928e30i | 0.187707 | + | 0.564334i | ||||
\(933\) | − | 5.21999e31i | − | 3.41910i | ||||||
\(934\) | 3.01739e30 | − | 4.18355e30i | 0.195429 | − | 0.270959i | ||||
\(935\) | 4.91045e30 | 0.314485 | ||||||||
\(936\) | 3.15181e31 | + | 9.87901e30i | 1.99602 | + | 0.625629i | ||||
\(937\) | 8.77702e30 | 0.549644 | 0.274822 | − | 0.961495i | \(-0.411381\pi\) | ||||
0.274822 | + | 0.961495i | \(0.411381\pi\) | |||||||
\(938\) | 2.64837e30 | − | 3.67192e30i | 0.164002 | − | 0.227386i | ||||
\(939\) | − | 1.14477e31i | − | 0.701021i | ||||||
\(940\) | 9.59966e30 | − | 3.19301e30i | 0.581317 | − | 0.193356i | ||||
\(941\) | 4.85137e30i | 0.290518i | 0.989394 | + | 0.145259i | \(0.0464015\pi\) | ||||
−0.989394 | + | 0.145259i | \(0.953598\pi\) | |||||||
\(942\) | −2.10524e31 | − | 1.51840e31i | −1.24672 | − | 0.899193i | ||||
\(943\) | −1.10729e31 | −0.648467 | ||||||||
\(944\) | 1.15263e31 | + | 1.54098e31i | 0.667550 | + | 0.892463i | ||||
\(945\) | −1.83541e31 | −1.05124 | ||||||||
\(946\) | 1.32736e30 | + | 9.57360e29i | 0.0751852 | + | 0.0542273i | ||||
\(947\) | 2.34170e31i | 1.31177i | 0.754863 | + | 0.655883i | \(0.227704\pi\) | ||||
−0.754863 | + | 0.655883i | \(0.772296\pi\) | |||||||
\(948\) | −1.94631e31 | + | 6.47374e30i | −1.07826 | + | 0.358647i | ||||
\(949\) | − | 4.90051e30i | − | 0.268501i | ||||||
\(950\) | 2.19760e31 | − | 3.04694e31i | 1.19083 | − | 1.65107i | ||||
\(951\) | −4.30402e31 | −2.30664 | ||||||||
\(952\) | −2.51883e30 | + | 8.03613e30i | −0.133509 | + | 0.425950i | ||||
\(953\) | −1.62933e31 | −0.854151 | −0.427076 | − | 0.904216i | \(-0.640456\pi\) | ||||
−0.427076 | + | 0.904216i | \(0.640456\pi\) | |||||||
\(954\) | 2.98323e31 | − | 4.13620e31i | 1.54678 | − | 2.14459i | ||||
\(955\) | 1.73116e31i | 0.887774i | ||||||||
\(956\) | −6.74964e30 | − | 2.02926e31i | −0.342352 | − | 1.02927i | ||||
\(957\) | 1.08714e30i | 0.0545395i | ||||||||
\(958\) | 2.90098e31 | + | 2.09233e31i | 1.43948 | + | 1.03823i | ||||
\(959\) | 3.49196e30 | 0.171385 | ||||||||
\(960\) | −4.22866e31 | − | 2.93965e31i | −2.05284 | − | 1.42708i | ||||
\(961\) | −2.02759e31 | −0.973610 | ||||||||
\(962\) | 2.11993e31 | + | 1.52900e31i | 1.00689 | + | 0.726220i | ||||
\(963\) | 3.96396e31i | 1.86231i | ||||||||
\(964\) | −4.94813e30 | − | 1.48764e31i | −0.229950 | − | 0.691335i | ||||
\(965\) | − | 1.49046e31i | − | 0.685147i | ||||||
\(966\) | 1.14127e31 | − | 1.58236e31i | 0.518955 | − | 0.719522i | ||||
\(967\) | 3.73495e31 | 1.67999 | 0.839996 | − | 0.542593i | \(-0.182557\pi\) | ||||
0.839996 | + | 0.542593i | \(0.182557\pi\) | |||||||
\(968\) | −6.46151e30 | + | 2.06149e31i | −0.287503 | + | 0.917254i | ||||
\(969\) | 8.60286e31 | 3.78654 | ||||||||
\(970\) | −3.71027e31 | + | 5.14422e31i | −1.61548 | + | 2.23984i | ||||
\(971\) | − | 2.84559e30i | − | 0.122566i | −0.998120 | − | 0.0612830i | \(-0.980481\pi\) | ||
0.998120 | − | 0.0612830i | \(-0.0195192\pi\) | |||||||
\(972\) | 4.11178e30 | − | 1.36765e30i | 0.175200 | − | 0.0582744i | ||||
\(973\) | − | 7.61322e30i | − | 0.320910i | ||||||
\(974\) | −1.17256e31 | − | 8.45712e30i | −0.488954 | − | 0.352658i | ||||
\(975\) | −4.52653e31 | −1.86731 | ||||||||
\(976\) | −9.45819e29 | − | 1.26449e30i | −0.0385998 | − | 0.0516050i | ||||
\(977\) | −9.12612e30 | −0.368463 | −0.184231 | − | 0.982883i | \(-0.558980\pi\) | ||||
−0.184231 | + | 0.982883i | \(0.558980\pi\) | |||||||
\(978\) | 3.48435e31 | + | 2.51308e31i | 1.39176 | + | 1.00380i | ||||
\(979\) | 3.38835e30i | 0.133897i | ||||||||
\(980\) | 2.91829e31 | − | 9.70671e30i | 1.14092 | − | 0.379488i | ||||
\(981\) | 6.79969e31i | 2.63005i | ||||||||
\(982\) | −1.73362e31 | + | 2.40363e31i | −0.663411 | + | 0.919808i | ||||
\(983\) | 4.18979e31 | 1.58628 | 0.793141 | − | 0.609037i | \(-0.208444\pi\) | ||||
0.793141 | + | 0.609037i | \(0.208444\pi\) | |||||||
\(984\) | −2.27209e31 | − | 7.12163e30i | −0.851094 | − | 0.266766i | ||||
\(985\) | −4.33889e31 | −1.60805 | ||||||||
\(986\) | 2.82477e30 | − | 3.91650e30i | 0.103580 | − | 0.143612i | ||||
\(987\) | 8.24136e30i | 0.298998i | ||||||||
\(988\) | −1.74076e31 | − | 5.23353e31i | −0.624871 | − | 1.87865i | ||||
\(989\) | 1.68407e31i | 0.598135i | ||||||||
\(990\) | −1.33384e31 | − | 9.62032e30i | −0.468743 | − | 0.338080i | ||||
\(991\) | 4.03029e30 | 0.140140 | 0.0700701 | − | 0.997542i | \(-0.477678\pi\) | ||||
0.0700701 | + | 0.997542i | \(0.477678\pi\) | |||||||
\(992\) | −4.72096e30 | + | 8.19898e28i | −0.162427 | + | 0.00282090i | ||||
\(993\) | −1.96087e30 | −0.0667545 | ||||||||
\(994\) | 8.86704e30 | + | 6.39535e30i | 0.298691 | + | 0.215430i | ||||
\(995\) | 7.22313e31i | 2.40759i | ||||||||
\(996\) | 1.55840e31 | + | 4.68527e31i | 0.513991 | + | 1.54530i | ||||
\(997\) | − | 6.29686e30i | − | 0.205506i | −0.994707 | − | 0.102753i | \(-0.967235\pi\) | ||
0.994707 | − | 0.102753i | \(-0.0327651\pi\) | |||||||
\(998\) | 2.07434e31 | − | 2.87604e31i | 0.669900 | − | 0.928804i | ||||
\(999\) | 6.99857e31 | 2.23651 |
(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 | 8.22.b.a.5.16 | yes | 20 | |
4.3 | odd | 2 | 32.22.b.a.17.19 | 20 | |||
8.3 | odd | 2 | 32.22.b.a.17.2 | 20 | |||
8.5 | even | 2 | inner | 8.22.b.a.5.15 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.22.b.a.5.15 | ✓ | 20 | 8.5 | even | 2 | inner | |
8.22.b.a.5.16 | yes | 20 | 1.1 | even | 1 | trivial | |
32.22.b.a.17.2 | 20 | 8.3 | odd | 2 | |||
32.22.b.a.17.19 | 20 | 4.3 | odd | 2 |