Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,17,Mod(7,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 17, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.7");
S:= CuspForms(chi, 17);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 17 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.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: | \(19.4789452628\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 37115 x^{14} + 433616 x^{13} + 965822723 x^{12} + 11579264195 x^{11} + 12661863519850 x^{10} + 162120109773543 x^{9} + \cdots + 43\!\cdots\!49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{106}\cdot 3^{51} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 7.7 | ||
Root | \(72.8587 + 126.195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.7 |
Dual form | 12.17.d.a.7.8 |
$q$-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 \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −119.478 | − | 226.409i | −0.466710 | − | 0.884411i | ||||
\(3\) | − | 3788.00i | − | 0.577350i | ||||||
\(4\) | −36986.2 | + | 54101.7i | −0.564364 | + | 0.825526i | ||||
\(5\) | −481576. | −1.23283 | −0.616417 | − | 0.787420i | \(-0.711416\pi\) | ||||
−0.616417 | + | 0.787420i | \(0.711416\pi\) | |||||||
\(6\) | −857637. | + | 452581.i | −0.510615 | + | 0.269455i | ||||
\(7\) | 515341.i | 0.0893943i | 0.999001 | + | 0.0446972i | \(0.0142323\pi\) | ||||
−0.999001 | + | 0.0446972i | \(0.985768\pi\) | |||||||
\(8\) | 1.66681e7 | + | 1.91007e6i | 0.993498 | + | 0.113849i | ||||
\(9\) | −1.43489e7 | −0.333333 | ||||||||
\(10\) | 5.75375e7 | + | 1.09033e8i | 0.575375 | + | 1.09033i | ||||
\(11\) | 1.66130e8i | 0.775010i | 0.921868 | + | 0.387505i | \(0.126663\pi\) | ||||
−0.921868 | + | 0.387505i | \(0.873337\pi\) | |||||||
\(12\) | 2.04937e8 | + | 1.40103e8i | 0.476618 | + | 0.325836i | ||||
\(13\) | −4.92842e8 | −0.604173 | −0.302086 | − | 0.953281i | \(-0.597683\pi\) | ||||
−0.302086 | + | 0.953281i | \(0.597683\pi\) | |||||||
\(14\) | 1.16678e8 | − | 6.15717e7i | 0.0790613 | − | 0.0417212i | ||||
\(15\) | 1.82421e9i | 0.711777i | ||||||||
\(16\) | −1.55901e9 | − | 4.00203e9i | −0.362986 | − | 0.931795i | ||||
\(17\) | 7.46224e9 | 1.06974 | 0.534869 | − | 0.844935i | \(-0.320361\pi\) | ||||
0.534869 | + | 0.844935i | \(0.320361\pi\) | |||||||
\(18\) | 1.71437e9 | + | 3.24872e9i | 0.155570 | + | 0.294804i | ||||
\(19\) | 3.55999e9i | 0.209614i | 0.994493 | + | 0.104807i | \(0.0334225\pi\) | ||||
−0.994493 | + | 0.104807i | \(0.966577\pi\) | |||||||
\(20\) | 1.78116e10 | − | 2.60540e10i | 0.695767 | − | 1.01774i | ||||
\(21\) | 1.95211e9 | 0.0516118 | ||||||||
\(22\) | 3.76134e10 | − | 1.98489e10i | 0.685427 | − | 0.361705i | ||||
\(23\) | − | 1.41839e11i | − | 1.81123i | −0.424105 | − | 0.905613i | \(-0.639411\pi\) | ||
0.424105 | − | 0.905613i | \(-0.360589\pi\) | |||||||
\(24\) | 7.23532e9 | − | 6.31388e10i | 0.0657306 | − | 0.573596i | ||||
\(25\) | 7.93271e10 | 0.519878 | ||||||||
\(26\) | 5.88837e10 | + | 1.11584e11i | 0.281973 | + | 0.534337i | ||||
\(27\) | 5.43536e10i | 0.192450i | ||||||||
\(28\) | −2.78808e10 | − | 1.90605e10i | −0.0737973 | − | 0.0504510i | ||||
\(29\) | 9.07879e11 | 1.81486 | 0.907432 | − | 0.420200i | \(-0.138040\pi\) | ||||
0.907432 | + | 0.420200i | \(0.138040\pi\) | |||||||
\(30\) | 4.13017e11 | − | 2.17952e11i | 0.629503 | − | 0.332193i | ||||
\(31\) | 1.71098e11i | 0.200609i | 0.994957 | + | 0.100305i | \(0.0319818\pi\) | ||||
−0.994957 | + | 0.100305i | \(0.968018\pi\) | |||||||
\(32\) | −7.19828e11 | + | 8.31128e11i | −0.654680 | + | 0.755906i | ||||
\(33\) | 6.29301e11 | 0.447452 | ||||||||
\(34\) | −8.91571e11 | − | 1.68952e12i | −0.499257 | − | 0.946088i | ||||
\(35\) | − | 2.48175e11i | − | 0.110208i | ||||||
\(36\) | 5.30711e11 | − | 7.76300e11i | 0.188121 | − | 0.275175i | ||||
\(37\) | −3.92591e12 | −1.11770 | −0.558852 | − | 0.829267i | \(-0.688758\pi\) | ||||
−0.558852 | + | 0.829267i | \(0.688758\pi\) | |||||||
\(38\) | 8.06015e11 | − | 4.25340e11i | 0.185385 | − | 0.0978289i | ||||
\(39\) | 1.86688e12i | 0.348819i | ||||||||
\(40\) | −8.02696e12 | − | 9.19841e11i | −1.22482 | − | 0.140357i | ||||
\(41\) | 6.33127e12 | 0.792902 | 0.396451 | − | 0.918056i | \(-0.370242\pi\) | ||||
0.396451 | + | 0.918056i | \(0.370242\pi\) | |||||||
\(42\) | −2.33233e11 | − | 4.41975e11i | −0.0240877 | − | 0.0456461i | ||||
\(43\) | 1.38507e13i | 1.18502i | 0.805564 | + | 0.592508i | \(0.201862\pi\) | ||||
−0.805564 | + | 0.592508i | \(0.798138\pi\) | |||||||
\(44\) | −8.98793e12 | − | 6.14452e12i | −0.639791 | − | 0.437388i | ||||
\(45\) | 6.91008e12 | 0.410944 | ||||||||
\(46\) | −3.21136e13 | + | 1.69466e13i | −1.60187 | + | 0.845317i | ||||
\(47\) | 3.46437e13i | 1.45493i | 0.686146 | + | 0.727464i | \(0.259301\pi\) | ||||
−0.686146 | + | 0.727464i | \(0.740699\pi\) | |||||||
\(48\) | −1.51597e13 | + | 5.90553e12i | −0.537972 | + | 0.209570i | ||||
\(49\) | 3.29674e13 | 0.992009 | ||||||||
\(50\) | −9.47781e12 | − | 1.79604e13i | −0.242632 | − | 0.459786i | ||||
\(51\) | − | 2.82669e13i | − | 0.617614i | ||||||
\(52\) | 1.82284e13 | − | 2.66636e13i | 0.340974 | − | 0.498760i | ||||
\(53\) | 8.06522e13 | 1.29542 | 0.647708 | − | 0.761889i | \(-0.275728\pi\) | ||||
0.647708 | + | 0.761889i | \(0.275728\pi\) | |||||||
\(54\) | 1.23061e13 | − | 6.49404e12i | 0.170205 | − | 0.0898183i | ||||
\(55\) | − | 8.00043e13i | − | 0.955458i | ||||||
\(56\) | −9.84334e11 | + | 8.58976e12i | −0.0101774 | + | 0.0888131i | ||||
\(57\) | 1.34852e13 | 0.121021 | ||||||||
\(58\) | −1.08471e14 | − | 2.05552e14i | −0.847014 | − | 1.60508i | ||||
\(59\) | 1.70599e14i | 1.16188i | 0.813946 | + | 0.580940i | \(0.197315\pi\) | ||||
−0.813946 | + | 0.580940i | \(0.802685\pi\) | |||||||
\(60\) | −9.86926e13 | − | 6.74704e13i | −0.587590 | − | 0.401701i | ||||
\(61\) | 3.04136e14 | 1.58646 | 0.793231 | − | 0.608921i | \(-0.208397\pi\) | ||||
0.793231 | + | 0.608921i | \(0.208397\pi\) | |||||||
\(62\) | 3.87381e13 | − | 2.04424e13i | 0.177421 | − | 0.0936263i | ||||
\(63\) | − | 7.39457e12i | − | 0.0297981i | ||||||
\(64\) | 2.74178e14 | + | 6.36745e13i | 0.974077 | + | 0.226217i | ||||
\(65\) | 2.37341e14 | 0.744845 | ||||||||
\(66\) | −7.51874e13 | − | 1.42479e14i | −0.208830 | − | 0.395732i | ||||
\(67\) | 3.16979e14i | 0.780606i | 0.920686 | + | 0.390303i | \(0.127630\pi\) | ||||
−0.920686 | + | 0.390303i | \(0.872370\pi\) | |||||||
\(68\) | −2.76000e14 | + | 4.03719e14i | −0.603722 | + | 0.883097i | ||||
\(69\) | −5.37285e14 | −1.04571 | ||||||||
\(70\) | −5.61892e13 | + | 2.96514e13i | −0.0974694 | + | 0.0514353i | ||||
\(71\) | − | 1.80534e14i | − | 0.279572i | −0.990182 | − | 0.139786i | \(-0.955359\pi\) | ||
0.990182 | − | 0.139786i | \(-0.0446414\pi\) | |||||||
\(72\) | −2.39169e14 | − | 2.74074e13i | −0.331166 | − | 0.0379496i | ||||
\(73\) | −1.28620e15 | −1.59487 | −0.797435 | − | 0.603405i | \(-0.793810\pi\) | ||||
−0.797435 | + | 0.603405i | \(0.793810\pi\) | |||||||
\(74\) | 4.69059e14 | + | 8.88863e14i | 0.521644 | + | 0.988510i | ||||
\(75\) | − | 3.00491e14i | − | 0.300152i | ||||||
\(76\) | −1.92602e14 | − | 1.31671e14i | −0.173042 | − | 0.118299i | ||||
\(77\) | −8.56137e13 | −0.0692815 | ||||||||
\(78\) | 4.22680e14 | − | 2.23051e14i | 0.308500 | − | 0.162797i | ||||
\(79\) | − | 1.91899e15i | − | 1.26490i | −0.774602 | − | 0.632450i | \(-0.782050\pi\) | ||
0.774602 | − | 0.632450i | \(-0.217950\pi\) | |||||||
\(80\) | 7.50783e14 | + | 1.92728e15i | 0.447501 | + | 1.14875i | ||||
\(81\) | 2.05891e14 | 0.111111 | ||||||||
\(82\) | −7.56445e14 | − | 1.43346e15i | −0.370055 | − | 0.701251i | ||||
\(83\) | 2.98068e15i | 1.32340i | 0.749769 | + | 0.661700i | \(0.230165\pi\) | ||||
−0.749769 | + | 0.661700i | \(0.769835\pi\) | |||||||
\(84\) | −7.22010e13 | + | 1.05612e14i | −0.0291279 | + | 0.0426069i | ||||
\(85\) | −3.59363e15 | −1.31881 | ||||||||
\(86\) | 3.13593e15 | − | 1.65485e15i | 1.04804 | − | 0.553059i | ||||
\(87\) | − | 3.43904e15i | − | 1.04781i | ||||||
\(88\) | −3.17320e14 | + | 2.76908e15i | −0.0882340 | + | 0.769971i | ||||
\(89\) | −8.50551e14 | −0.216063 | −0.108031 | − | 0.994147i | \(-0.534455\pi\) | ||||
−0.108031 | + | 0.994147i | \(0.534455\pi\) | |||||||
\(90\) | −8.25601e14 | − | 1.56451e15i | −0.191792 | − | 0.363444i | ||||
\(91\) | − | 2.53982e14i | − | 0.0540096i | ||||||
\(92\) | 7.67372e15 | + | 5.24608e15i | 1.49521 | + | 1.02219i | ||||
\(93\) | 6.48118e14 | 0.115822 | ||||||||
\(94\) | 7.84365e15 | − | 4.13915e15i | 1.28675 | − | 0.679029i | ||||
\(95\) | − | 1.71441e15i | − | 0.258419i | ||||||
\(96\) | 3.14831e15 | + | 2.72671e15i | 0.436423 | + | 0.377980i | ||||
\(97\) | −1.30607e15 | −0.166645 | −0.0833224 | − | 0.996523i | \(-0.526553\pi\) | ||||
−0.0833224 | + | 0.996523i | \(0.526553\pi\) | |||||||
\(98\) | −3.93886e15 | − | 7.46411e15i | −0.462980 | − | 0.877343i | ||||
\(99\) | − | 2.38379e15i | − | 0.258337i | ||||||
\(100\) | −2.93400e15 | + | 4.29173e15i | −0.293400 | + | 0.429173i | ||||
\(101\) | 1.08578e16 | 1.00270 | 0.501350 | − | 0.865245i | \(-0.332837\pi\) | ||||
0.501350 | + | 0.865245i | \(0.332837\pi\) | |||||||
\(102\) | −6.39989e15 | + | 3.37727e15i | −0.546224 | + | 0.288246i | ||||
\(103\) | 1.78830e15i | 0.141170i | 0.997506 | + | 0.0705851i | \(0.0224866\pi\) | ||||
−0.997506 | + | 0.0705851i | \(0.977513\pi\) | |||||||
\(104\) | −8.21476e15 | − | 9.41361e14i | −0.600245 | − | 0.0687844i | ||||
\(105\) | −9.40087e14 | −0.0636288 | ||||||||
\(106\) | −9.63613e15 | − | 1.82604e16i | −0.604583 | − | 1.14568i | ||||
\(107\) | − | 1.27220e16i | − | 0.740433i | −0.928945 | − | 0.370217i | \(-0.879283\pi\) | ||
0.928945 | − | 0.370217i | \(-0.120717\pi\) | |||||||
\(108\) | −2.94062e15 | − | 2.01033e15i | −0.158873 | − | 0.108612i | ||||
\(109\) | 1.17768e16 | 0.591037 | 0.295519 | − | 0.955337i | \(-0.404508\pi\) | ||||
0.295519 | + | 0.955337i | \(0.404508\pi\) | |||||||
\(110\) | −1.81137e16 | + | 9.55873e15i | −0.845017 | + | 0.445922i | ||||
\(111\) | 1.48713e16i | 0.645307i | ||||||||
\(112\) | 2.06241e15 | − | 8.03423e14i | 0.0832972 | − | 0.0324489i | ||||
\(113\) | −1.61155e16 | −0.606201 | −0.303100 | − | 0.952959i | \(-0.598022\pi\) | ||||
−0.303100 | + | 0.952959i | \(0.598022\pi\) | |||||||
\(114\) | −1.61119e15 | − | 3.05318e15i | −0.0564816 | − | 0.107032i | ||||
\(115\) | 6.83061e16i | 2.23294i | ||||||||
\(116\) | −3.35790e16 | + | 4.91178e16i | −1.02424 | + | 1.49822i | ||||
\(117\) | 7.07175e15 | 0.201391 | ||||||||
\(118\) | 3.86253e16 | − | 2.03828e16i | 1.02758 | − | 0.542261i | ||||
\(119\) | 3.84559e15i | 0.0956286i | ||||||||
\(120\) | −3.48435e15 | + | 3.04061e16i | −0.0810349 | + | 0.707149i | ||||
\(121\) | 1.83505e16 | 0.399359 | ||||||||
\(122\) | −3.63375e16 | − | 6.88592e16i | −0.740417 | − | 1.40308i | ||||
\(123\) | − | 2.39828e16i | − | 0.457782i | ||||||
\(124\) | −9.25668e15 | − | 6.32826e15i | −0.165608 | − | 0.113217i | ||||
\(125\) | 3.52806e16 | 0.591910 | ||||||||
\(126\) | −1.67420e15 | + | 8.83486e14i | −0.0263538 | + | 0.0139071i | ||||
\(127\) | 5.34191e16i | 0.789345i | 0.918822 | + | 0.394673i | \(0.129142\pi\) | ||||
−0.918822 | + | 0.394673i | \(0.870858\pi\) | |||||||
\(128\) | −1.83417e16 | − | 6.96841e16i | −0.254542 | − | 0.967062i | ||||
\(129\) | 5.24664e16 | 0.684170 | ||||||||
\(130\) | −2.83569e16 | − | 5.37361e16i | −0.347626 | − | 0.658748i | ||||
\(131\) | − | 1.48466e17i | − | 1.71181i | −0.517132 | − | 0.855905i | \(-0.673000\pi\) | ||
0.517132 | − | 0.855905i | \(-0.327000\pi\) | |||||||
\(132\) | −2.32754e16 | + | 3.40462e16i | −0.252526 | + | 0.369383i | ||||
\(133\) | −1.83461e15 | −0.0187383 | ||||||||
\(134\) | 7.17669e16 | − | 3.78719e16i | 0.690376 | − | 0.364316i | ||||
\(135\) | − | 2.61754e16i | − | 0.237259i | ||||||
\(136\) | 1.24382e17 | + | 1.42534e16i | 1.06278 | + | 0.121788i | ||||
\(137\) | 1.59937e14 | 0.00128880 | 0.000644398 | − | 1.00000i | \(-0.499795\pi\) | ||||
0.000644398 | 1.00000i | \(0.499795\pi\) | ||||||||
\(138\) | 6.41936e16 | + | 1.21646e17i | 0.488044 | + | 0.924838i | ||||
\(139\) | 1.28935e16i | 0.0925234i | 0.998929 | + | 0.0462617i | \(0.0147308\pi\) | ||||
−0.998929 | + | 0.0462617i | \(0.985269\pi\) | |||||||
\(140\) | 1.34267e16 | + | 9.17906e15i | 0.0909798 | + | 0.0621976i | ||||
\(141\) | 1.31230e17 | 0.840003 | ||||||||
\(142\) | −4.08746e16 | + | 2.15698e16i | −0.247256 | + | 0.130479i | ||||
\(143\) | − | 8.18761e16i | − | 0.468240i | ||||||
\(144\) | 2.23701e16 | + | 5.74247e16i | 0.120995 | + | 0.310598i | ||||
\(145\) | −4.37212e17 | −2.23742 | ||||||||
\(146\) | 1.53672e17 | + | 2.91207e17i | 0.744341 | + | 1.41052i | ||||
\(147\) | − | 1.24880e17i | − | 0.572736i | ||||||
\(148\) | 1.45205e17 | − | 2.12399e17i | 0.630793 | − | 0.922694i | ||||
\(149\) | −1.67950e17 | −0.691338 | −0.345669 | − | 0.938357i | \(-0.612348\pi\) | ||||
−0.345669 | + | 0.938357i | \(0.612348\pi\) | |||||||
\(150\) | −6.80338e16 | + | 3.59019e16i | −0.265457 | + | 0.140084i | ||||
\(151\) | 4.43174e17i | 1.63968i | 0.572595 | + | 0.819838i | \(0.305937\pi\) | ||||
−0.572595 | + | 0.819838i | \(0.694063\pi\) | |||||||
\(152\) | −6.79982e15 | + | 5.93385e16i | −0.0238643 | + | 0.208251i | ||||
\(153\) | −1.07075e17 | −0.356580 | ||||||||
\(154\) | 1.02289e16 | + | 1.93837e16i | 0.0323344 | + | 0.0612733i | ||||
\(155\) | − | 8.23966e16i | − | 0.247318i | ||||||
\(156\) | −1.01002e17 | − | 6.90489e16i | −0.287959 | − | 0.196861i | ||||
\(157\) | −1.71679e17 | −0.465071 | −0.232536 | − | 0.972588i | \(-0.574702\pi\) | ||||
−0.232536 | + | 0.972588i | \(0.574702\pi\) | |||||||
\(158\) | −4.34477e17 | + | 2.29276e17i | −1.11869 | + | 0.590341i | ||||
\(159\) | − | 3.05510e17i | − | 0.747909i | ||||||
\(160\) | 3.46652e17 | − | 4.00251e17i | 0.807111 | − | 0.931906i | ||||
\(161\) | 7.30953e16 | 0.161913 | ||||||||
\(162\) | −2.45994e16 | − | 4.66156e16i | −0.0518566 | − | 0.0982678i | ||||
\(163\) | 2.62267e17i | 0.526311i | 0.964753 | + | 0.263156i | \(0.0847633\pi\) | ||||
−0.964753 | + | 0.263156i | \(0.915237\pi\) | |||||||
\(164\) | −2.34169e17 | + | 3.42532e17i | −0.447486 | + | 0.654561i | ||||
\(165\) | −3.03056e17 | −0.551634 | ||||||||
\(166\) | 6.74854e17 | − | 3.56125e17i | 1.17043 | − | 0.617644i | ||||
\(167\) | − | 4.22305e17i | − | 0.698063i | −0.937111 | − | 0.349032i | \(-0.886511\pi\) | ||
0.937111 | − | 0.349032i | \(-0.113489\pi\) | |||||||
\(168\) | 3.25380e16 | + | 3.72865e15i | 0.0512763 | + | 0.00587595i | ||||
\(169\) | −4.22523e17 | −0.634975 | ||||||||
\(170\) | 4.29359e17 | + | 8.13631e17i | 0.615501 | + | 1.16637i | ||||
\(171\) | − | 5.10820e16i | − | 0.0698714i | ||||||
\(172\) | −7.49347e17 | − | 5.12285e17i | −0.978262 | − | 0.668781i | ||||
\(173\) | 8.67929e17 | 1.08172 | 0.540861 | − | 0.841112i | \(-0.318099\pi\) | ||||
0.540861 | + | 0.841112i | \(0.318099\pi\) | |||||||
\(174\) | −7.78630e17 | + | 4.10889e17i | −0.926696 | + | 0.489024i | ||||
\(175\) | 4.08805e16i | 0.0464741i | ||||||||
\(176\) | 6.64858e17 | − | 2.58999e17i | 0.722150 | − | 0.281318i | ||||
\(177\) | 6.46230e17 | 0.670812 | ||||||||
\(178\) | 1.01622e17 | + | 1.92573e17i | 0.100839 | + | 0.191088i | ||||
\(179\) | 9.21178e17i | 0.874016i | 0.899458 | + | 0.437008i | \(0.143962\pi\) | ||||
−0.899458 | + | 0.437008i | \(0.856038\pi\) | |||||||
\(180\) | −2.55577e17 | + | 3.73847e17i | −0.231922 | + | 0.339245i | ||||
\(181\) | 1.58908e18 | 1.37948 | 0.689741 | − | 0.724056i | \(-0.257724\pi\) | ||||
0.689741 | + | 0.724056i | \(0.257724\pi\) | |||||||
\(182\) | −5.75038e16 | + | 3.03451e16i | −0.0477667 | + | 0.0252068i | ||||
\(183\) | − | 1.15207e18i | − | 0.915944i | ||||||
\(184\) | 2.70922e17 | − | 2.36419e18i | 0.206206 | − | 1.79945i | ||||
\(185\) | 1.89062e18 | 1.37794 | ||||||||
\(186\) | −7.74356e16 | − | 1.46740e17i | −0.0540552 | − | 0.102434i | ||||
\(187\) | 1.23970e18i | 0.829058i | ||||||||
\(188\) | −1.87428e18 | − | 1.28134e18i | −1.20108 | − | 0.821109i | ||||
\(189\) | −2.80106e16 | −0.0172039 | ||||||||
\(190\) | −3.88157e17 | + | 2.04833e17i | −0.228549 | + | 0.120607i | ||||
\(191\) | 1.10519e18i | 0.623978i | 0.950086 | + | 0.311989i | \(0.100995\pi\) | ||||
−0.950086 | + | 0.311989i | \(0.899005\pi\) | |||||||
\(192\) | 2.41199e17 | − | 1.03859e18i | 0.130607 | − | 0.562384i | ||||
\(193\) | −9.46462e17 | −0.491637 | −0.245819 | − | 0.969316i | \(-0.579057\pi\) | ||||
−0.245819 | + | 0.969316i | \(0.579057\pi\) | |||||||
\(194\) | 1.56046e17 | + | 2.95706e17i | 0.0777748 | + | 0.147383i | ||||
\(195\) | − | 8.99046e17i | − | 0.430036i | ||||||
\(196\) | −1.21934e18 | + | 1.78359e18i | −0.559854 | + | 0.818929i | ||||
\(197\) | −1.18890e18 | −0.524103 | −0.262051 | − | 0.965054i | \(-0.584399\pi\) | ||||
−0.262051 | + | 0.965054i | \(0.584399\pi\) | |||||||
\(198\) | −5.39711e17 | + | 2.84809e17i | −0.228476 | + | 0.120568i | ||||
\(199\) | − | 1.82188e17i | − | 0.0740788i | −0.999314 | − | 0.0370394i | \(-0.988207\pi\) | ||
0.999314 | − | 0.0370394i | \(-0.0117927\pi\) | |||||||
\(200\) | 1.32223e18 | + | 1.51520e17i | 0.516498 | + | 0.0591875i | ||||
\(201\) | 1.20071e18 | 0.450683 | ||||||||
\(202\) | −1.29727e18 | − | 2.45831e18i | −0.467970 | − | 0.886799i | ||||
\(203\) | 4.67867e17i | 0.162239i | ||||||||
\(204\) | 1.52929e18 | + | 1.04549e18i | 0.509856 | + | 0.348559i | ||||
\(205\) | −3.04898e18 | −0.977516 | ||||||||
\(206\) | 4.04888e17 | − | 2.13662e17i | 0.124852 | − | 0.0658855i | ||||
\(207\) | 2.03523e18i | 0.603742i | ||||||||
\(208\) | 7.68348e17 | + | 1.97237e18i | 0.219306 | + | 0.562965i | ||||
\(209\) | −5.91423e17 | −0.162453 | ||||||||
\(210\) | 1.12319e17 | + | 2.12844e17i | 0.0296962 | + | 0.0562740i | ||||
\(211\) | 2.01089e18i | 0.511833i | 0.966699 | + | 0.255916i | \(0.0823772\pi\) | ||||
−0.966699 | + | 0.255916i | \(0.917623\pi\) | |||||||
\(212\) | −2.98302e18 | + | 4.36342e18i | −0.731086 | + | 1.06940i | ||||
\(213\) | −6.83863e17 | −0.161411 | ||||||||
\(214\) | −2.88038e18 | + | 1.52000e18i | −0.654847 | + | 0.345567i | ||||
\(215\) | − | 6.67017e18i | − | 1.46093i | ||||||
\(216\) | −1.03819e17 | + | 9.05973e17i | −0.0219102 | + | 0.191199i | ||||
\(217\) | −8.81737e16 | −0.0179333 | ||||||||
\(218\) | −1.40706e18 | − | 2.66637e18i | −0.275843 | − | 0.522720i | ||||
\(219\) | 4.87211e18i | 0.920798i | ||||||||
\(220\) | 4.32837e18 | + | 2.95905e18i | 0.788756 | + | 0.539226i | ||||
\(221\) | −3.67771e18 | −0.646307 | ||||||||
\(222\) | 3.36701e18 | − | 1.77679e18i | 0.570716 | − | 0.301171i | ||||
\(223\) | − | 2.03402e18i | − | 0.332595i | −0.986076 | − | 0.166298i | \(-0.946819\pi\) | ||
0.986076 | − | 0.166298i | \(-0.0531812\pi\) | |||||||
\(224\) | −4.28314e17 | − | 3.70957e17i | −0.0675737 | − | 0.0585247i | ||||
\(225\) | −1.13826e18 | −0.173293 | ||||||||
\(226\) | 1.92544e18 | + | 3.64870e18i | 0.282920 | + | 0.536130i | ||||
\(227\) | − | 8.31593e18i | − | 1.17952i | −0.807580 | − | 0.589758i | \(-0.799223\pi\) | ||
0.807580 | − | 0.589758i | \(-0.200777\pi\) | |||||||
\(228\) | −4.98767e17 | + | 7.29574e17i | −0.0682998 | + | 0.0999058i | ||||
\(229\) | 7.19478e18 | 0.951335 | 0.475667 | − | 0.879625i | \(-0.342207\pi\) | ||||
0.475667 | + | 0.879625i | \(0.342207\pi\) | |||||||
\(230\) | 1.54651e19 | − | 8.16106e18i | 1.97484 | − | 1.04213i | ||||
\(231\) | 3.24304e17i | 0.0399997i | ||||||||
\(232\) | 1.51326e19 | + | 1.73411e18i | 1.80306 | + | 0.206620i | ||||
\(233\) | −7.76947e18 | −0.894425 | −0.447212 | − | 0.894428i | \(-0.647583\pi\) | ||||
−0.447212 | + | 0.894428i | \(0.647583\pi\) | |||||||
\(234\) | −8.44916e17 | − | 1.60111e18i | −0.0939911 | − | 0.178112i | ||||
\(235\) | − | 1.66836e19i | − | 1.79368i | ||||||
\(236\) | −9.22971e18 | − | 6.30982e18i | −0.959162 | − | 0.655724i | ||||
\(237\) | −7.26912e18 | −0.730290 | ||||||||
\(238\) | 8.70677e17 | − | 4.59463e17i | 0.0845749 | − | 0.0446308i | ||||
\(239\) | 1.13707e19i | 1.06808i | 0.845460 | + | 0.534038i | \(0.179326\pi\) | ||||
−0.845460 | + | 0.534038i | \(0.820674\pi\) | |||||||
\(240\) | 7.30052e18 | − | 2.84396e18i | 0.663230 | − | 0.258365i | ||||
\(241\) | 5.22286e18 | 0.458957 | 0.229479 | − | 0.973314i | \(-0.426298\pi\) | ||||
0.229479 | + | 0.973314i | \(0.426298\pi\) | |||||||
\(242\) | −2.19247e18 | − | 4.15471e18i | −0.186385 | − | 0.353198i | ||||
\(243\) | − | 7.79915e17i | − | 0.0641500i | ||||||
\(244\) | −1.12488e19 | + | 1.64543e19i | −0.895342 | + | 1.30967i | ||||
\(245\) | −1.58763e19 | −1.22298 | ||||||||
\(246\) | −5.42993e18 | + | 2.86541e18i | −0.404868 | + | 0.213651i | ||||
\(247\) | − | 1.75452e18i | − | 0.126643i | ||||||
\(248\) | −3.26808e17 | + | 2.85188e18i | −0.0228391 | + | 0.199305i | ||||
\(249\) | 1.12908e19 | 0.764065 | ||||||||
\(250\) | −4.21525e18 | − | 7.98785e18i | −0.276250 | − | 0.523492i | ||||
\(251\) | 1.98339e19i | 1.25898i | 0.777008 | + | 0.629491i | \(0.216736\pi\) | ||||
−0.777008 | + | 0.629491i | \(0.783264\pi\) | |||||||
\(252\) | 4.00059e17 | + | 2.73497e17i | 0.0245991 | + | 0.0168170i | ||||
\(253\) | 2.35637e19 | 1.40372 | ||||||||
\(254\) | 1.20946e19 | − | 6.38239e18i | 0.698105 | − | 0.368395i | ||||
\(255\) | 1.36127e19i | 0.761415i | ||||||||
\(256\) | −1.35857e19 | + | 1.24784e19i | −0.736482 | + | 0.676457i | ||||
\(257\) | 2.61741e19 | 1.37533 | 0.687665 | − | 0.726028i | \(-0.258636\pi\) | ||||
0.687665 | + | 0.726028i | \(0.258636\pi\) | |||||||
\(258\) | −6.26857e18 | − | 1.18789e19i | −0.319309 | − | 0.605087i | ||||
\(259\) | − | 2.02318e18i | − | 0.0999165i | ||||||
\(260\) | −8.77833e18 | + | 1.28405e19i | −0.420364 | + | 0.614888i | ||||
\(261\) | −1.30271e19 | −0.604954 | ||||||||
\(262\) | −3.36140e19 | + | 1.77383e19i | −1.51394 | + | 0.798919i | ||||
\(263\) | 8.72728e18i | 0.381270i | 0.981661 | + | 0.190635i | \(0.0610547\pi\) | ||||
−0.981661 | + | 0.190635i | \(0.938945\pi\) | |||||||
\(264\) | 1.04893e19 | + | 1.20201e18i | 0.444543 | + | 0.0509419i | ||||
\(265\) | −3.88401e19 | −1.59703 | ||||||||
\(266\) | 2.19195e17 | + | 4.15372e17i | 0.00874535 | + | 0.0165724i | ||||
\(267\) | 3.22188e18i | 0.124744i | ||||||||
\(268\) | −1.71491e19 | − | 1.17238e19i | −0.644411 | − | 0.440546i | ||||
\(269\) | 1.34355e18 | 0.0490046 | 0.0245023 | − | 0.999700i | \(-0.492200\pi\) | ||||
0.0245023 | + | 0.999700i | \(0.492200\pi\) | |||||||
\(270\) | −5.92634e18 | + | 3.12737e18i | −0.209834 | + | 0.110731i | ||||
\(271\) | − | 4.73624e19i | − | 1.62809i | −0.580799 | − | 0.814047i | \(-0.697260\pi\) | ||
0.580799 | − | 0.814047i | \(-0.302740\pi\) | |||||||
\(272\) | −1.16337e19 | − | 2.98641e19i | −0.388300 | − | 0.996777i | ||||
\(273\) | −9.62081e17 | −0.0311825 | ||||||||
\(274\) | −1.91089e16 | − | 3.62112e16i | −0.000601494 | − | 0.00113983i | ||||
\(275\) | 1.31786e19i | 0.402911i | ||||||||
\(276\) | 1.98721e19 | − | 2.90680e19i | 0.590162 | − | 0.863262i | ||||
\(277\) | 3.65464e19 | 1.05440 | 0.527202 | − | 0.849740i | \(-0.323241\pi\) | ||||
0.527202 | + | 0.849740i | \(0.323241\pi\) | |||||||
\(278\) | 2.91920e18 | − | 1.54048e18i | 0.0818287 | − | 0.0431816i | ||||
\(279\) | − | 2.45507e18i | − | 0.0668698i | ||||||
\(280\) | 4.74031e17 | − | 4.13662e18i | 0.0125471 | − | 0.109492i | ||||
\(281\) | 5.34347e19 | 1.37459 | 0.687295 | − | 0.726379i | \(-0.258798\pi\) | ||||
0.687295 | + | 0.726379i | \(0.258798\pi\) | |||||||
\(282\) | −1.56791e19 | − | 2.97117e19i | −0.392038 | − | 0.742908i | ||||
\(283\) | 6.88848e19i | 1.67430i | 0.546977 | + | 0.837148i | \(0.315779\pi\) | ||||
−0.546977 | + | 0.837148i | \(0.684221\pi\) | |||||||
\(284\) | 9.76721e18 | + | 6.67728e18i | 0.230794 | + | 0.157780i | ||||
\(285\) | −6.49416e18 | −0.149198 | ||||||||
\(286\) | −1.85375e19 | + | 9.78236e18i | −0.414117 | + | 0.218532i | ||||
\(287\) | 3.26276e18i | 0.0708810i | ||||||||
\(288\) | 1.03287e19 | − | 1.19258e19i | 0.218227 | − | 0.251969i | ||||
\(289\) | 7.02379e18 | 0.144341 | ||||||||
\(290\) | 5.22371e19 | + | 9.89888e19i | 1.04423 | + | 1.97880i | ||||
\(291\) | 4.94738e18i | 0.0962125i | ||||||||
\(292\) | 4.75716e19 | − | 6.95855e19i | 0.900087 | − | 1.31661i | ||||
\(293\) | 2.18046e19 | 0.401428 | 0.200714 | − | 0.979650i | \(-0.435674\pi\) | ||||
0.200714 | + | 0.979650i | \(0.435674\pi\) | |||||||
\(294\) | −2.82740e19 | + | 1.49204e19i | −0.506534 | + | 0.267302i | ||||
\(295\) | − | 8.21565e19i | − | 1.43240i | ||||||
\(296\) | −6.54377e19 | − | 7.49875e18i | −1.11044 | − | 0.127249i | ||||
\(297\) | −9.02978e18 | −0.149151 | ||||||||
\(298\) | 2.00663e19 | + | 3.80255e19i | 0.322654 | + | 0.611427i | ||||
\(299\) | 6.99042e19i | 1.09429i | ||||||||
\(300\) | 1.62570e19 | + | 1.11140e19i | 0.247783 | + | 0.169395i | ||||
\(301\) | −7.13784e18 | −0.105934 | ||||||||
\(302\) | 1.00339e20 | − | 5.29493e19i | 1.45015 | − | 0.765253i | ||||
\(303\) | − | 4.11293e19i | − | 0.578909i | ||||||
\(304\) | 1.42472e19 | − | 5.55008e18i | 0.195317 | − | 0.0760870i | ||||
\(305\) | −1.46465e20 | −1.95584 | ||||||||
\(306\) | 1.27931e19 | + | 2.42427e19i | 0.166419 | + | 0.315363i | ||||
\(307\) | − | 9.64113e19i | − | 1.22186i | −0.791685 | − | 0.610929i | \(-0.790796\pi\) | ||
0.791685 | − | 0.610929i | \(-0.209204\pi\) | |||||||
\(308\) | 3.16652e18 | − | 4.63184e18i | 0.0391000 | − | 0.0571937i | ||||
\(309\) | 6.77408e18 | 0.0815046 | ||||||||
\(310\) | −1.86553e19 | + | 9.84455e18i | −0.218731 | + | 0.115426i | ||||
\(311\) | − | 1.43879e20i | − | 1.64404i | −0.569457 | − | 0.822021i | \(-0.692846\pi\) | ||
0.569457 | − | 0.822021i | \(-0.307154\pi\) | |||||||
\(312\) | −3.56587e18 | + | 3.11175e19i | −0.0397127 | + | 0.346551i | ||||
\(313\) | −4.88496e19 | −0.530282 | −0.265141 | − | 0.964210i | \(-0.585418\pi\) | ||||
−0.265141 | + | 0.964210i | \(0.585418\pi\) | |||||||
\(314\) | 2.05118e19 | + | 3.88696e19i | 0.217053 | + | 0.411314i | ||||
\(315\) | 3.56105e18i | 0.0367361i | ||||||||
\(316\) | 1.03821e20 | + | 7.09761e19i | 1.04421 | + | 0.713864i | ||||
\(317\) | −3.53189e19 | −0.346365 | −0.173182 | − | 0.984890i | \(-0.555405\pi\) | ||||
−0.173182 | + | 0.984890i | \(0.555405\pi\) | |||||||
\(318\) | −6.91703e19 | + | 3.65016e19i | −0.661458 | + | 0.349056i | ||||
\(319\) | 1.50826e20i | 1.40654i | ||||||||
\(320\) | −1.32038e20 | − | 3.06641e19i | −1.20087 | − | 0.278888i | ||||
\(321\) | −4.81909e19 | −0.427489 | ||||||||
\(322\) | −8.73326e18 | − | 1.65494e19i | −0.0755665 | − | 0.143198i | ||||
\(323\) | 2.65655e19i | 0.224232i | ||||||||
\(324\) | −7.61513e18 | + | 1.11391e19i | −0.0627071 | + | 0.0917251i | ||||
\(325\) | −3.90957e19 | −0.314096 | ||||||||
\(326\) | 5.93796e19 | − | 3.13350e19i | 0.465475 | − | 0.245635i | ||||
\(327\) | − | 4.46104e19i | − | 0.341236i | ||||||
\(328\) | 1.05530e20 | + | 1.20931e19i | 0.787747 | + | 0.0902710i | ||||
\(329\) | −1.78533e19 | −0.130062 | ||||||||
\(330\) | 3.62084e19 | + | 6.86146e19i | 0.257453 | + | 0.487871i | ||||
\(331\) | 2.76309e20i | 1.91766i | 0.283984 | + | 0.958829i | \(0.408344\pi\) | ||||
−0.283984 | + | 0.958829i | \(0.591656\pi\) | |||||||
\(332\) | −1.61260e20 | − | 1.10244e20i | −1.09250 | − | 0.746880i | ||||
\(333\) | 5.63326e19 | 0.372568 | ||||||||
\(334\) | −9.56138e19 | + | 5.04561e19i | −0.617375 | + | 0.325793i | ||||
\(335\) | − | 1.52649e20i | − | 0.962357i | ||||||
\(336\) | −3.04336e18 | − | 7.81239e18i | −0.0187344 | − | 0.0480916i | ||||
\(337\) | −8.73126e19 | −0.524853 | −0.262426 | − | 0.964952i | \(-0.584523\pi\) | ||||
−0.262426 | + | 0.964952i | \(0.584523\pi\) | |||||||
\(338\) | 5.04821e19 | + | 9.56630e19i | 0.296349 | + | 0.561579i | ||||
\(339\) | 6.10455e19i | 0.349990i | ||||||||
\(340\) | 1.32915e20 | − | 1.94421e20i | 0.744289 | − | 1.08871i | ||||
\(341\) | −2.84246e19 | −0.155474 | ||||||||
\(342\) | −1.15654e19 | + | 6.10316e18i | −0.0617950 | + | 0.0326096i | ||||
\(343\) | 3.41157e19i | 0.178074i | ||||||||
\(344\) | −2.64558e19 | + | 2.30866e20i | −0.134913 | + | 1.17731i | ||||
\(345\) | 2.58743e20 | 1.28919 | ||||||||
\(346\) | −1.03698e20 | − | 1.96507e20i | −0.504850 | − | 0.956686i | ||||
\(347\) | − | 1.16347e20i | − | 0.553505i | −0.960941 | − | 0.276752i | \(-0.910742\pi\) | ||
0.960941 | − | 0.276752i | \(-0.0892581\pi\) | |||||||
\(348\) | 1.86058e20 | + | 1.27197e20i | 0.864996 | + | 0.591348i | ||||
\(349\) | −9.54017e19 | −0.433464 | −0.216732 | − | 0.976231i | \(-0.569540\pi\) | ||||
−0.216732 | + | 0.976231i | \(0.569540\pi\) | |||||||
\(350\) | 9.25571e18 | − | 4.88430e18i | 0.0411022 | − | 0.0216899i | ||||
\(351\) | − | 2.67878e19i | − | 0.116273i | ||||||
\(352\) | −1.38076e20 | − | 1.19585e20i | −0.585835 | − | 0.507384i | ||||
\(353\) | 2.98288e20 | 1.23719 | 0.618597 | − | 0.785709i | \(-0.287701\pi\) | ||||
0.618597 | + | 0.785709i | \(0.287701\pi\) | |||||||
\(354\) | −7.72100e19 | − | 1.46312e20i | −0.313074 | − | 0.593273i | ||||
\(355\) | 8.69409e19i | 0.344665i | ||||||||
\(356\) | 3.14586e19 | − | 4.60162e19i | 0.121938 | − | 0.178366i | ||||
\(357\) | 1.45671e19 | 0.0552112 | ||||||||
\(358\) | 2.08563e20 | − | 1.10060e20i | 0.772989 | − | 0.407912i | ||||
\(359\) | − | 2.93045e20i | − | 1.06213i | −0.847330 | − | 0.531067i | \(-0.821791\pi\) | ||
0.847330 | − | 0.531067i | \(-0.178209\pi\) | |||||||
\(360\) | 1.15178e20 | + | 1.31987e19i | 0.408273 | + | 0.0467855i | ||||
\(361\) | 2.75768e20 | 0.956062 | ||||||||
\(362\) | −1.89859e20 | − | 3.59781e20i | −0.643817 | − | 1.22003i | ||||
\(363\) | − | 6.95114e19i | − | 0.230570i | ||||||
\(364\) | 1.37408e19 | + | 9.39381e18i | 0.0445864 | + | 0.0304811i | ||||
\(365\) | 6.19402e20 | 1.96621 | ||||||||
\(366\) | −2.60838e20 | + | 1.37646e20i | −0.810071 | + | 0.427480i | ||||
\(367\) | 1.76985e20i | 0.537784i | 0.963170 | + | 0.268892i | \(0.0866575\pi\) | ||||
−0.963170 | + | 0.268892i | \(0.913343\pi\) | |||||||
\(368\) | −5.67643e20 | + | 2.21129e20i | −1.68769 | + | 0.657450i | ||||
\(369\) | −9.08467e19 | −0.264301 | ||||||||
\(370\) | −2.25887e20 | − | 4.28055e20i | −0.643100 | − | 1.21867i | ||||
\(371\) | 4.15633e19i | 0.115803i | ||||||||
\(372\) | −2.39714e19 | + | 3.50643e19i | −0.0653657 | + | 0.0956140i | ||||
\(373\) | −1.79144e19 | −0.0478114 | −0.0239057 | − | 0.999714i | \(-0.507610\pi\) | ||||
−0.0239057 | + | 0.999714i | \(0.507610\pi\) | |||||||
\(374\) | 2.80680e20 | − | 1.48117e20i | 0.733228 | − | 0.386929i | ||||
\(375\) | − | 1.33643e20i | − | 0.341740i | ||||||
\(376\) | −6.61718e19 | + | 5.77446e20i | −0.165642 | + | 1.44547i | ||||
\(377\) | −4.47441e20 | −1.09649 | ||||||||
\(378\) | 3.34664e18 | + | 6.34186e18i | 0.00802925 | + | 0.0152154i | ||||
\(379\) | 7.62685e20i | 1.79156i | 0.444496 | + | 0.895781i | \(0.353383\pi\) | ||||
−0.444496 | + | 0.895781i | \(0.646617\pi\) | |||||||
\(380\) | 9.27522e19 | + | 6.34093e19i | 0.213332 | + | 0.145843i | ||||
\(381\) | 2.02351e20 | 0.455729 | ||||||||
\(382\) | 2.50225e20 | − | 1.32045e20i | 0.551853 | − | 0.291217i | ||||
\(383\) | 4.79376e20i | 1.03535i | 0.855578 | + | 0.517673i | \(0.173202\pi\) | ||||
−0.855578 | + | 0.517673i | \(0.826798\pi\) | |||||||
\(384\) | −2.63963e20 | + | 6.94783e19i | −0.558333 | + | 0.146960i | ||||
\(385\) | 4.12295e19 | 0.0854126 | ||||||||
\(386\) | 1.13081e20 | + | 2.14288e20i | 0.229452 | + | 0.434809i | ||||
\(387\) | − | 1.98743e20i | − | 0.395006i | ||||||
\(388\) | 4.83065e19 | − | 7.06605e19i | 0.0940484 | − | 0.137570i | ||||
\(389\) | −6.78359e20 | −1.29379 | −0.646893 | − | 0.762581i | \(-0.723932\pi\) | ||||
−0.646893 | + | 0.762581i | \(0.723932\pi\) | |||||||
\(390\) | −2.03552e20 | + | 1.07416e20i | −0.380329 | + | 0.200702i | ||||
\(391\) | − | 1.05844e21i | − | 1.93754i | ||||||
\(392\) | 5.49504e20 | + | 6.29698e19i | 0.985559 | + | 0.112939i | ||||
\(393\) | −5.62387e20 | −0.988315 | ||||||||
\(394\) | 1.42047e20 | + | 2.69178e20i | 0.244604 | + | 0.463522i | ||||
\(395\) | 9.24138e20i | 1.55941i | ||||||||
\(396\) | 1.28967e20 | + | 8.81672e19i | 0.213264 | + | 0.145796i | ||||
\(397\) | −7.98038e20 | −1.29330 | −0.646651 | − | 0.762786i | \(-0.723831\pi\) | ||||
−0.646651 | + | 0.762786i | \(0.723831\pi\) | |||||||
\(398\) | −4.12489e19 | + | 2.17673e19i | −0.0655161 | + | 0.0345733i | ||||
\(399\) | 6.94949e18i | 0.0108186i | ||||||||
\(400\) | −1.23672e20 | − | 3.17469e20i | −0.188708 | − | 0.484419i | ||||
\(401\) | 2.57175e20 | 0.384657 | 0.192328 | − | 0.981331i | \(-0.438396\pi\) | ||||
0.192328 | + | 0.981331i | \(0.438396\pi\) | |||||||
\(402\) | −1.43459e20 | − | 2.71853e20i | −0.210338 | − | 0.398589i | ||||
\(403\) | − | 8.43243e19i | − | 0.121203i | ||||||
\(404\) | −4.01589e20 | + | 5.87425e20i | −0.565888 | + | 0.827755i | ||||
\(405\) | −9.91521e19 | −0.136981 | ||||||||
\(406\) | 1.05929e20 | − | 5.58996e19i | 0.143485 | − | 0.0757183i | ||||
\(407\) | − | 6.52213e20i | − | 0.866232i | ||||||
\(408\) | 5.39917e19 | − | 4.71157e20i | 0.0703146 | − | 0.613598i | ||||
\(409\) | 6.00294e20 | 0.766616 | 0.383308 | − | 0.923621i | \(-0.374785\pi\) | ||||
0.383308 | + | 0.923621i | \(0.374785\pi\) | |||||||
\(410\) | 3.64285e20 | + | 6.90317e20i | 0.456216 | + | 0.864526i | ||||
\(411\) | − | 6.05840e17i | − | 0.000744087i | ||||||
\(412\) | −9.67501e19 | − | 6.61424e19i | −0.116540 | − | 0.0796714i | ||||
\(413\) | −8.79168e19 | −0.103866 | ||||||||
\(414\) | 4.60795e20 | − | 2.43165e20i | 0.533956 | − | 0.281772i | ||||
\(415\) | − | 1.43542e21i | − | 1.63153i | ||||||
\(416\) | 3.54762e20 | − | 4.09615e20i | 0.395540 | − | 0.456698i | ||||
\(417\) | 4.88404e19 | 0.0534184 | ||||||||
\(418\) | 7.06618e19 | + | 1.33904e20i | 0.0758184 | + | 0.143675i | ||||
\(419\) | 4.24662e20i | 0.447025i | 0.974701 | + | 0.223512i | \(0.0717523\pi\) | ||||
−0.974701 | + | 0.223512i | \(0.928248\pi\) | |||||||
\(420\) | 3.47702e19 | − | 5.08603e19i | 0.0359098 | − | 0.0525272i | ||||
\(421\) | −4.73419e20 | −0.479721 | −0.239861 | − | 0.970807i | \(-0.577102\pi\) | ||||
−0.239861 | + | 0.970807i | \(0.577102\pi\) | |||||||
\(422\) | 4.55283e20 | − | 2.40256e20i | 0.452670 | − | 0.238877i | ||||
\(423\) | − | 4.97099e20i | − | 0.484976i | ||||||
\(424\) | 1.34432e21 | + | 1.54051e20i | 1.28699 | + | 0.147481i | ||||
\(425\) | 5.91957e20 | 0.556133 | ||||||||
\(426\) | 8.17064e19 | + | 1.54833e20i | 0.0753320 | + | 0.142753i | ||||
\(427\) | 1.56734e20i | 0.141821i | ||||||||
\(428\) | 6.88282e20 | + | 4.70539e20i | 0.611247 | + | 0.417874i | ||||
\(429\) | −3.10146e20 | −0.270339 | ||||||||
\(430\) | −1.51019e21 | + | 7.96936e20i | −1.29206 | + | 0.681829i | ||||
\(431\) | − | 1.74966e21i | − | 1.46938i | −0.678401 | − | 0.734692i | \(-0.737327\pi\) | ||
0.678401 | − | 0.734692i | \(-0.262673\pi\) | |||||||
\(432\) | 2.17525e20 | − | 8.47380e19i | 0.179324 | − | 0.0698567i | ||||
\(433\) | −2.61610e20 | −0.211715 | −0.105857 | − | 0.994381i | \(-0.533759\pi\) | ||||
−0.105857 | + | 0.994381i | \(0.533759\pi\) | |||||||
\(434\) | 1.05348e19 | + | 1.99633e19i | 0.00836966 | + | 0.0158604i | ||||
\(435\) | 1.65616e21i | 1.29178i | ||||||||
\(436\) | −4.35578e20 | + | 6.37144e20i | −0.333560 | + | 0.487917i | ||||
\(437\) | 5.04946e20 | 0.379658 | ||||||||
\(438\) | 1.10309e21 | − | 5.82109e20i | 0.814364 | − | 0.429745i | ||||
\(439\) | − | 1.05652e20i | − | 0.0765882i | −0.999267 | − | 0.0382941i | \(-0.987808\pi\) | ||
0.999267 | − | 0.0382941i | \(-0.0121924\pi\) | |||||||
\(440\) | 1.52813e20 | − | 1.33352e21i | 0.108778 | − | 0.949246i | ||||
\(441\) | −4.73046e20 | −0.330670 | ||||||||
\(442\) | 4.39404e20 | + | 8.32666e20i | 0.301638 | + | 0.571601i | ||||
\(443\) | 1.41940e21i | 0.956915i | 0.878111 | + | 0.478458i | \(0.158804\pi\) | ||||
−0.878111 | + | 0.478458i | \(0.841196\pi\) | |||||||
\(444\) | −8.04565e20 | − | 5.50034e20i | −0.532718 | − | 0.364188i | ||||
\(445\) | 4.09605e20 | 0.266370 | ||||||||
\(446\) | −4.60520e20 | + | 2.43020e20i | −0.294151 | + | 0.155225i | ||||
\(447\) | 6.36194e20i | 0.399144i | ||||||||
\(448\) | −3.28140e19 | + | 1.41295e20i | −0.0202225 | + | 0.0870770i | ||||
\(449\) | −1.56836e21 | −0.949459 | −0.474729 | − | 0.880132i | \(-0.657454\pi\) | ||||
−0.474729 | + | 0.880132i | \(0.657454\pi\) | |||||||
\(450\) | 1.35996e20 | + | 2.57712e20i | 0.0808773 | + | 0.153262i | ||||
\(451\) | 1.05182e21i | 0.614507i | ||||||||
\(452\) | 5.96051e20 | − | 8.71876e20i | 0.342118 | − | 0.500435i | ||||
\(453\) | 1.67874e21 | 0.946668 | ||||||||
\(454\) | −1.88280e21 | + | 9.93568e20i | −1.04318 | + | 0.550492i | ||||
\(455\) | 1.22311e20i | 0.0665849i | ||||||||
\(456\) | 2.24774e20 | + | 2.57577e19i | 0.120234 | + | 0.0137781i | ||||
\(457\) | 2.87857e21 | 1.51303 | 0.756514 | − | 0.653977i | \(-0.226901\pi\) | ||||
0.756514 | + | 0.653977i | \(0.226901\pi\) | |||||||
\(458\) | −8.59615e20 | − | 1.62896e21i | −0.443997 | − | 0.841371i | ||||
\(459\) | 4.05599e20i | 0.205871i | ||||||||
\(460\) | −3.69548e21 | − | 2.52638e21i | −1.84335 | − | 1.26019i | ||||
\(461\) | 3.00691e20 | 0.147405 | 0.0737027 | − | 0.997280i | \(-0.476518\pi\) | ||||
0.0737027 | + | 0.997280i | \(0.476518\pi\) | |||||||
\(462\) | 7.34254e19 | − | 3.87471e19i | 0.0353762 | − | 0.0186682i | ||||
\(463\) | − | 3.71205e21i | − | 1.75779i | −0.477019 | − | 0.878893i | \(-0.658283\pi\) | ||
0.477019 | − | 0.878893i | \(-0.341717\pi\) | |||||||
\(464\) | −1.41540e21 | − | 3.63336e21i | −0.658770 | − | 1.69108i | ||||
\(465\) | −3.12118e20 | −0.142789 | ||||||||
\(466\) | 9.28278e20 | + | 1.75908e21i | 0.417437 | + | 0.791039i | ||||
\(467\) | 3.36056e21i | 1.48551i | 0.669562 | + | 0.742756i | \(0.266482\pi\) | ||||
−0.669562 | + | 0.742756i | \(0.733518\pi\) | |||||||
\(468\) | −2.61557e20 | + | 3.82593e20i | −0.113658 | + | 0.166253i | ||||
\(469\) | −1.63352e20 | −0.0697818 | ||||||||
\(470\) | −3.77731e21 | + | 1.99331e21i | −1.58635 | + | 0.837130i | ||||
\(471\) | 6.50319e20i | 0.268509i | ||||||||
\(472\) | −3.25856e20 | + | 2.84357e21i | −0.132279 | + | 1.15433i | ||||
\(473\) | −2.30102e21 | −0.918400 | ||||||||
\(474\) | 8.68498e20 | + | 1.64580e21i | 0.340833 | + | 0.645876i | ||||
\(475\) | 2.82404e20i | 0.108974i | ||||||||
\(476\) | −2.08053e20 | − | 1.42234e20i | −0.0789439 | − | 0.0539693i | ||||
\(477\) | −1.15727e21 | −0.431805 | ||||||||
\(478\) | 2.57442e21 | − | 1.35854e21i | 0.944618 | − | 0.498481i | ||||
\(479\) | 3.81556e20i | 0.137681i | 0.997628 | + | 0.0688405i | \(0.0219300\pi\) | ||||
−0.997628 | + | 0.0688405i | \(0.978070\pi\) | |||||||
\(480\) | −1.51615e21 | − | 1.31311e21i | −0.538036 | − | 0.465986i | ||||
\(481\) | 1.93486e21 | 0.675287 | ||||||||
\(482\) | −6.24015e20 | − | 1.18250e21i | −0.214200 | − | 0.405907i | ||||
\(483\) | − | 2.76885e20i | − | 0.0934807i | ||||||
\(484\) | −6.78713e20 | + | 9.92790e20i | −0.225384 | + | 0.329681i | ||||
\(485\) | 6.28970e20 | 0.205445 | ||||||||
\(486\) | −1.76580e20 | + | 9.31824e19i | −0.0567350 | + | 0.0299394i | ||||
\(487\) | 2.20764e21i | 0.697746i | 0.937170 | + | 0.348873i | \(0.113435\pi\) | ||||
−0.937170 | + | 0.348873i | \(0.886565\pi\) | |||||||
\(488\) | 5.06938e21 | + | 5.80920e20i | 1.57615 | + | 0.180617i | ||||
\(489\) | 9.93466e20 | 0.303866 | ||||||||
\(490\) | 1.89686e21 | + | 3.59453e21i | 0.570777 | + | 1.08162i | ||||
\(491\) | − | 4.03031e21i | − | 1.19313i | −0.802567 | − | 0.596563i | \(-0.796533\pi\) | ||
0.802567 | − | 0.596563i | \(-0.203467\pi\) | |||||||
\(492\) | 1.29751e21 | + | 8.87032e20i | 0.377911 | + | 0.258356i | ||||
\(493\) | 6.77481e21 | 1.94143 | ||||||||
\(494\) | −3.97238e20 | + | 2.09626e20i | −0.112005 | + | 0.0591056i | ||||
\(495\) | 1.14797e21i | 0.318486i | ||||||||
\(496\) | 6.84739e20 | − | 2.66744e20i | 0.186927 | − | 0.0728184i | ||||
\(497\) | 9.30367e19 | 0.0249921 | ||||||||
\(498\) | −1.34900e21 | − | 2.55634e21i | −0.356597 | − | 0.675747i | ||||
\(499\) | 1.41774e20i | 0.0368801i | 0.999830 | + | 0.0184400i | \(0.00586998\pi\) | ||||
−0.999830 | + | 0.0184400i | \(0.994130\pi\) | |||||||
\(500\) | −1.30489e21 | + | 1.90874e21i | −0.334053 | + | 0.488637i | ||||
\(501\) | −1.59969e21 | −0.403027 | ||||||||
\(502\) | 4.49059e21 | − | 2.36971e21i | 1.11346 | − | 0.587579i | ||||
\(503\) | − | 3.80963e21i | − | 0.929692i | −0.885392 | − | 0.464846i | \(-0.846110\pi\) | ||
0.885392 | − | 0.464846i | \(-0.153890\pi\) | |||||||
\(504\) | 1.41241e19 | − | 1.23254e20i | 0.00339248 | − | 0.0296044i | ||||
\(505\) | −5.22885e21 | −1.23616 | ||||||||
\(506\) | −2.81534e21 | − | 5.33504e21i | −0.655129 | − | 1.24146i | ||||
\(507\) | 1.60051e21i | 0.366603i | ||||||||
\(508\) | −2.89006e21 | − | 1.97577e21i | −0.651625 | − | 0.445478i | ||||
\(509\) | −1.24890e21 | −0.277196 | −0.138598 | − | 0.990349i | \(-0.544260\pi\) | ||||
−0.138598 | + | 0.990349i | \(0.544260\pi\) | |||||||
\(510\) | 3.08203e21 | − | 1.62641e21i | 0.673403 | − | 0.355360i | ||||
\(511\) | − | 6.62830e20i | − | 0.142572i | ||||||
\(512\) | 4.44842e21 | + | 1.58503e21i | 0.941989 | + | 0.335644i | ||||
\(513\) | −1.93498e20 | −0.0403403 | ||||||||
\(514\) | −3.12722e21 | − | 5.92606e21i | −0.641880 | − | 1.21636i | ||||
\(515\) | − | 8.61202e20i | − | 0.174039i | ||||||
\(516\) | −1.94053e21 | + | 2.83852e21i | −0.386121 | + | 0.564800i | ||||
\(517\) | −5.75537e21 | −1.12758 | ||||||||
\(518\) | −4.58067e20 | + | 2.41725e20i | −0.0883672 | + | 0.0466320i | ||||
\(519\) | − | 3.28771e21i | − | 0.624532i | ||||||
\(520\) | 3.95603e21 | + | 4.53337e20i | 0.740002 | + | 0.0847996i | ||||
\(521\) | 6.64621e21 | 1.22426 | 0.612128 | − | 0.790759i | \(-0.290314\pi\) | ||||
0.612128 | + | 0.790759i | \(0.290314\pi\) | |||||||
\(522\) | 1.55644e21 | + | 2.94945e21i | 0.282338 | + | 0.535028i | ||||
\(523\) | − | 4.92052e21i | − | 0.879017i | −0.898238 | − | 0.439509i | \(-0.855153\pi\) | ||
0.898238 | − | 0.439509i | \(-0.144847\pi\) | |||||||
\(524\) | 8.03224e21 | + | 5.49118e21i | 1.41314 | + | 0.966085i | ||||
\(525\) | 1.54855e20 | 0.0268319 | ||||||||
\(526\) | 1.97593e21 | − | 1.04271e21i | 0.337199 | − | 0.177942i | ||||
\(527\) | 1.27677e21i | 0.214600i | ||||||||
\(528\) | −9.81088e20 | − | 2.51848e21i | −0.162419 | − | 0.416934i | ||||
\(529\) | −1.39857e22 | −2.28054 | ||||||||
\(530\) | 4.64053e21 | + | 8.79376e21i | 0.745350 | + | 1.41243i | ||||
\(531\) | − | 2.44791e21i | − | 0.387293i | ||||||
\(532\) | 6.78552e19 | − | 9.92554e19i | 0.0105752 | − | 0.0154690i | ||||
\(533\) | −3.12032e21 | −0.479050 | ||||||||
\(534\) | 7.29464e20 | − | 3.84943e20i | 0.110325 | − | 0.0582192i | ||||
\(535\) | 6.12661e21i | 0.912830i | ||||||||
\(536\) | −6.05451e20 | + | 5.28345e21i | −0.0888711 | + | 0.775531i | ||||
\(537\) | 3.48942e21 | 0.504614 | ||||||||
\(538\) | −1.60525e20 | − | 3.04193e20i | −0.0228709 | − | 0.0433402i | ||||
\(539\) | 5.47688e21i | 0.768817i | ||||||||
\(540\) | 1.41613e21 | + | 9.68126e20i | 0.195863 | + | 0.133900i | ||||
\(541\) | −6.02561e20 | −0.0821150 | −0.0410575 | − | 0.999157i | \(-0.513073\pi\) | ||||
−0.0410575 | + | 0.999157i | \(0.513073\pi\) | |||||||
\(542\) | −1.07233e22 | + | 5.65875e21i | −1.43990 | + | 0.759847i | ||||
\(543\) | − | 6.01941e21i | − | 0.796444i | ||||||
\(544\) | −5.37153e21 | + | 6.20207e21i | −0.700336 | + | 0.808622i | ||||
\(545\) | −5.67141e21 | −0.728651 | ||||||||
\(546\) | 1.14947e20 | + | 2.17824e20i | 0.0145532 | + | 0.0275781i | ||||
\(547\) | 9.62662e21i | 1.20109i | 0.799591 | + | 0.600545i | \(0.205049\pi\) | ||||
−0.799591 | + | 0.600545i | \(0.794951\pi\) | |||||||
\(548\) | −5.91546e18 | + | 8.65285e18i | −0.000727350 | + | 0.00106393i | ||||
\(549\) | −4.36402e21 | −0.528821 | ||||||||
\(550\) | 2.98376e21 | − | 1.57455e21i | 0.356338 | − | 0.188042i | ||||
\(551\) | 3.23204e21i | 0.380421i | ||||||||
\(552\) | −8.95554e21 | − | 1.02625e21i | −1.03891 | − | 0.119053i | ||||
\(553\) | 9.88933e20 | 0.113075 | ||||||||
\(554\) | −4.36648e21 | − | 8.27444e21i | −0.492100 | − | 0.932525i | ||||
\(555\) | − | 7.16168e21i | − | 0.795556i | ||||||
\(556\) | −6.97559e20 | − | 4.76881e20i | −0.0763805 | − | 0.0522169i | ||||
\(557\) | 8.71078e21 | 0.940190 | 0.470095 | − | 0.882616i | \(-0.344220\pi\) | ||||
0.470095 | + | 0.882616i | \(0.344220\pi\) | |||||||
\(558\) | −5.55850e20 | + | 2.93326e20i | −0.0591403 | + | 0.0312088i | ||||
\(559\) | − | 6.82622e21i | − | 0.715955i | ||||||
\(560\) | −9.93205e20 | + | 3.86909e20i | −0.102692 | + | 0.0400041i | ||||
\(561\) | 4.69599e21 | 0.478657 | ||||||||
\(562\) | −6.38425e21 | − | 1.20981e22i | −0.641534 | − | 1.21570i | ||||
\(563\) | 5.56357e21i | 0.551171i | 0.961277 | + | 0.275585i | \(0.0888717\pi\) | ||||
−0.961277 | + | 0.275585i | \(0.911128\pi\) | |||||||
\(564\) | −4.85370e21 | + | 7.09977e21i | −0.474068 | + | 0.693444i | ||||
\(565\) | 7.76084e21 | 0.747345 | ||||||||
\(566\) | 1.55962e22 | − | 8.23020e21i | 1.48076 | − | 0.781410i | ||||
\(567\) | 1.06104e20i | 0.00993270i | ||||||||
\(568\) | 3.44833e20 | − | 3.00917e21i | 0.0318289 | − | 0.277754i | ||||
\(569\) | 7.52487e21 | 0.684859 | 0.342429 | − | 0.939544i | \(-0.388750\pi\) | ||||
0.342429 | + | 0.939544i | \(0.388750\pi\) | |||||||
\(570\) | 7.75907e20 | + | 1.47034e21i | 0.0696323 | + | 0.131953i | ||||
\(571\) | 8.32216e21i | 0.736456i | 0.929735 | + | 0.368228i | \(0.120035\pi\) | ||||
−0.929735 | + | 0.368228i | \(0.879965\pi\) | |||||||
\(572\) | 4.42963e21 | + | 3.02828e21i | 0.386544 | + | 0.264258i | ||||
\(573\) | 4.18645e21 | 0.360254 | ||||||||
\(574\) | 7.38718e20 | − | 3.89827e20i | 0.0626879 | − | 0.0330808i | ||||
\(575\) | − | 1.12517e22i | − | 0.941616i | ||||||
\(576\) | −3.93416e21 | − | 9.13659e20i | −0.324692 | − | 0.0754057i | ||||
\(577\) | 2.34802e21 | 0.191115 | 0.0955577 | − | 0.995424i | \(-0.469537\pi\) | ||||
0.0955577 | + | 0.995424i | \(0.469537\pi\) | |||||||
\(578\) | −8.39186e20 | − | 1.59025e21i | −0.0673652 | − | 0.127656i | ||||
\(579\) | 3.58519e21i | 0.283847i | ||||||||
\(580\) | 1.61708e22 | − | 2.36539e22i | 1.26272 | − | 1.84705i | ||||
\(581\) | −1.53607e21 | −0.118304 | ||||||||
\(582\) | 1.12013e21 | − | 5.91101e20i | 0.0850913 | − | 0.0449033i | ||||
\(583\) | 1.33988e22i | 1.00396i | ||||||||
\(584\) | −2.14385e22 | − | 2.45672e21i | −1.58450 | − | 0.181574i | ||||
\(585\) | −3.40558e21 | −0.248282 | ||||||||
\(586\) | −2.60516e21 | − | 4.93676e21i | −0.187350 | − | 0.355027i | ||||
\(587\) | − | 1.45286e22i | − | 1.03067i | −0.856989 | − | 0.515335i | \(-0.827667\pi\) | ||
0.856989 | − | 0.515335i | \(-0.172333\pi\) | |||||||
\(588\) | 6.75623e21 | + | 4.61884e21i | 0.472809 | + | 0.323232i | ||||
\(589\) | −6.09108e20 | −0.0420506 | ||||||||
\(590\) | −1.86010e22 | + | 9.81587e21i | −1.26683 | + | 0.668517i | ||||
\(591\) | 4.50356e21i | 0.302591i | ||||||||
\(592\) | 6.12055e21 | + | 1.57116e22i | 0.405711 | + | 1.04147i | ||||
\(593\) | 1.96426e22 | 1.28458 | 0.642289 | − | 0.766462i | \(-0.277985\pi\) | ||||
0.642289 | + | 0.766462i | \(0.277985\pi\) | |||||||
\(594\) | 1.07886e21 | + | 2.04442e21i | 0.0696101 | + | 0.131911i | ||||
\(595\) | − | 1.85194e21i | − | 0.117894i | ||||||
\(596\) | 6.21183e21 | − | 9.08638e21i | 0.390166 | − | 0.570717i | ||||
\(597\) | −6.90126e20 | −0.0427694 | ||||||||
\(598\) | 1.58270e22 | − | 8.35199e21i | 0.967805 | − | 0.510717i | ||||
\(599\) | 9.81500e21i | 0.592210i | 0.955155 | + | 0.296105i | \(0.0956878\pi\) | ||||
−0.955155 | + | 0.296105i | \(0.904312\pi\) | |||||||
\(600\) | 5.73957e20 | − | 5.00862e21i | 0.0341719 | − | 0.298200i | ||||
\(601\) | 2.43315e22 | 1.42947 | 0.714733 | − | 0.699397i | \(-0.246548\pi\) | ||||
0.714733 | + | 0.699397i | \(0.246548\pi\) | |||||||
\(602\) | 8.52812e20 | + | 1.61607e21i | 0.0494403 | + | 0.0936890i | ||||
\(603\) | − | 4.54830e21i | − | 0.260202i | ||||||
\(604\) | −2.39764e22 | − | 1.63913e22i | −1.35360 | − | 0.925375i | ||||
\(605\) | −8.83713e21 | −0.492343 | ||||||||
\(606\) | −9.31205e21 | + | 4.91404e21i | −0.511993 | + | 0.270183i | ||||
\(607\) | 8.50789e21i | 0.461650i | 0.972995 | + | 0.230825i | \(0.0741424\pi\) | ||||
−0.972995 | + | 0.230825i | \(0.925858\pi\) | |||||||
\(608\) | −2.95881e21 | − | 2.56258e21i | −0.158449 | − | 0.137230i | ||||
\(609\) | 1.77228e21 | 0.0936685 | ||||||||
\(610\) | 1.74992e22 | + | 3.31609e22i | 0.912811 | + | 1.72977i | ||||
\(611\) | − | 1.70739e22i | − | 0.879028i | ||||||
\(612\) | 3.96029e21 | − | 5.79293e21i | 0.201241 | − | 0.294366i | ||||
\(613\) | −1.83326e21 | −0.0919476 | −0.0459738 | − | 0.998943i | \(-0.514639\pi\) | ||||
−0.0459738 | + | 0.998943i | \(0.514639\pi\) | |||||||
\(614\) | −2.18284e22 | + | 1.15190e22i | −1.08063 | + | 0.570253i | ||||
\(615\) | 1.15495e22i | 0.564369i | ||||||||
\(616\) | −1.42702e21 | − | 1.63528e20i | −0.0688311 | − | 0.00788762i | ||||
\(617\) | −1.27024e22 | −0.604789 | −0.302394 | − | 0.953183i | \(-0.597786\pi\) | ||||
−0.302394 | + | 0.953183i | \(0.597786\pi\) | |||||||
\(618\) | −8.09351e20 | − | 1.53371e21i | −0.0380390 | − | 0.0720836i | ||||
\(619\) | 2.22936e22i | 1.03432i | 0.855889 | + | 0.517160i | \(0.173011\pi\) | ||||
−0.855889 | + | 0.517160i | \(0.826989\pi\) | |||||||
\(620\) | 4.45779e21 | + | 3.04753e21i | 0.204167 | + | 0.139577i | ||||
\(621\) | 7.70945e21 | 0.348571 | ||||||||
\(622\) | −3.25754e22 | + | 1.71903e22i | −1.45401 | + | 0.767291i | ||||
\(623\) | − | 4.38324e20i | − | 0.0193148i | ||||||
\(624\) | 7.47132e21 | − | 2.91050e21i | 0.325028 | − | 0.126617i | ||||
\(625\) | −2.90946e22 | −1.24960 | ||||||||
\(626\) | 5.83644e21 | + | 1.10600e22i | 0.247488 | + | 0.468987i | ||||
\(627\) | 2.24031e21i | 0.0937923i | ||||||||
\(628\) | 6.34974e21 | − | 9.28811e21i | 0.262470 | − | 0.383928i | ||||
\(629\) | −2.92961e22 | −1.19565 | ||||||||
\(630\) | 8.06253e20 | − | 4.25465e20i | 0.0324898 | − | 0.0171451i | ||||
\(631\) | − | 3.06104e22i | − | 1.21796i | −0.793185 | − | 0.608981i | \(-0.791578\pi\) | ||
0.793185 | − | 0.608981i | \(-0.208422\pi\) | |||||||
\(632\) | 3.66540e21 | − | 3.19860e22i | 0.144007 | − | 1.25667i | ||||
\(633\) | 7.61723e21 | 0.295507 | ||||||||
\(634\) | 4.21983e21 | + | 7.99653e21i | 0.161652 | + | 0.306329i | ||||
\(635\) | − | 2.57253e22i | − | 0.973131i | ||||||
\(636\) | 1.65286e22 | + | 1.12996e22i | 0.617418 | + | 0.422093i | ||||
\(637\) | −1.62477e22 | −0.599345 | ||||||||
\(638\) | 3.41484e22 | − | 1.80204e22i | 1.24396 | − | 0.656445i | ||||
\(639\) | 2.59047e21i | 0.0931906i | ||||||||
\(640\) | 8.83292e21 | + | 3.35582e22i | 0.313808 | + | 1.19223i | ||||
\(641\) | −2.86248e22 | −1.00433 | −0.502167 | − | 0.864771i | \(-0.667464\pi\) | ||||
−0.502167 | + | 0.864771i | \(0.667464\pi\) | |||||||
\(642\) | 5.75774e21 | + | 1.09109e22i | 0.199513 | + | 0.378076i | ||||
\(643\) | − | 5.10567e22i | − | 1.74729i | −0.486563 | − | 0.873646i | \(-0.661749\pi\) | ||
0.486563 | − | 0.873646i | \(-0.338251\pi\) | |||||||
\(644\) | −2.70352e21 | + | 3.95458e21i | −0.0913781 | + | 0.133664i | ||||
\(645\) | −2.52666e22 | −0.843467 | ||||||||
\(646\) | 6.01468e21 | − | 3.17399e21i | 0.198313 | − | 0.104651i | ||||
\(647\) | 3.44255e22i | 1.12111i | 0.828119 | + | 0.560553i | \(0.189411\pi\) | ||||
−0.828119 | + | 0.560553i | \(0.810589\pi\) | |||||||
\(648\) | 3.43182e21 | + | 3.93266e20i | 0.110389 | + | 0.0126499i | ||||
\(649\) | −2.83417e22 | −0.900469 | ||||||||
\(650\) | 4.67107e21 | + | 8.85163e21i | 0.146592 | + | 0.277790i | ||||
\(651\) | 3.34002e20i | 0.0103538i | ||||||||
\(652\) | −1.41891e22 | − | 9.70025e21i | −0.434484 | − | 0.297031i | ||||
\(653\) | 1.62027e22 | 0.490097 | 0.245049 | − | 0.969511i | \(-0.421196\pi\) | ||||
0.245049 | + | 0.969511i | \(0.421196\pi\) | |||||||
\(654\) | −1.01002e22 | + | 5.32995e21i | −0.301792 | + | 0.159258i | ||||
\(655\) | 7.14975e22i | 2.11038i | ||||||||
\(656\) | −9.87053e21 | − | 2.53379e22i | −0.287812 | − | 0.738822i | ||||
\(657\) | 1.84555e22 | 0.531623 | ||||||||
\(658\) | 2.13307e21 | + | 4.04215e21i | 0.0607014 | + | 0.115029i | ||||
\(659\) | 4.22721e21i | 0.118842i | 0.998233 | + | 0.0594210i | \(0.0189254\pi\) | ||||
−0.998233 | + | 0.0594210i | \(0.981075\pi\) | |||||||
\(660\) | 1.12089e22 | − | 1.63958e22i | 0.311323 | − | 0.455388i | ||||
\(661\) | 2.30284e22 | 0.631906 | 0.315953 | − | 0.948775i | \(-0.397676\pi\) | ||||
0.315953 | + | 0.948775i | \(0.397676\pi\) | |||||||
\(662\) | 6.25589e22 | − | 3.30128e22i | 1.69600 | − | 0.894990i | ||||
\(663\) | 1.39311e22i | 0.373146i | ||||||||
\(664\) | −5.69330e21 | + | 4.96824e22i | −0.150667 | + | 1.31480i | ||||
\(665\) | 8.83503e20 | 0.0231012 | ||||||||
\(666\) | −6.73049e21 | − | 1.27542e22i | −0.173881 | − | 0.329503i | ||||
\(667\) | − | 1.28773e23i | − | 3.28713i | ||||||
\(668\) | 2.28474e22 | + | 1.56195e22i | 0.576269 | + | 0.393962i | ||||
\(669\) | −7.70485e21 | −0.192024 | ||||||||
\(670\) | −3.45612e22 | + | 1.82382e22i | −0.851119 | + | 0.449141i | ||||
\(671\) | 5.05263e22i | 1.22952i | ||||||||
\(672\) | −1.40518e21 | + | 1.62245e21i | −0.0337892 | + | 0.0390137i | ||||
\(673\) | 7.63006e22 | 1.81304 | 0.906520 | − | 0.422163i | \(-0.138729\pi\) | ||||
0.906520 | + | 0.422163i | \(0.138729\pi\) | |||||||
\(674\) | 1.04319e22 | + | 1.97684e22i | 0.244954 | + | 0.464186i | ||||
\(675\) | 4.31171e21i | 0.100051i | ||||||||
\(676\) | 1.56275e22 | − | 2.28592e22i | 0.358357 | − | 0.524188i | ||||
\(677\) | 3.76411e22 | 0.853008 | 0.426504 | − | 0.904486i | \(-0.359745\pi\) | ||||
0.426504 | + | 0.904486i | \(0.359745\pi\) | |||||||
\(678\) | 1.38213e22 | − | 7.29357e21i | 0.309535 | − | 0.163344i | ||||
\(679\) | − | 6.73070e20i | − | 0.0148971i | ||||||
\(680\) | −5.98991e22 | − | 6.86407e21i | −1.31023 | − | 0.150145i | ||||
\(681\) | −3.15007e22 | −0.680994 | ||||||||
\(682\) | 3.39610e21 | + | 6.43558e21i | 0.0725614 | + | 0.137503i | ||||
\(683\) | − | 6.54593e21i | − | 0.138231i | −0.997609 | − | 0.0691155i | \(-0.977982\pi\) | ||
0.997609 | − | 0.0691155i | \(-0.0220177\pi\) | |||||||
\(684\) | 2.76362e21 | + | 1.88933e21i | 0.0576806 | + | 0.0394329i | ||||
\(685\) | −7.70217e19 | −0.00158887 | ||||||||
\(686\) | 7.72410e21 | − | 4.07606e21i | 0.157491 | − | 0.0831090i | ||||
\(687\) | − | 2.72538e22i | − | 0.549253i | ||||||
\(688\) | 5.54309e22 | − | 2.15934e22i | 1.10419 | − | 0.430145i | ||||
\(689\) | −3.97488e22 | −0.782655 | ||||||||
\(690\) | −3.09140e22 | − | 5.85818e22i | −0.601677 | − | 1.14017i | ||||
\(691\) | − | 1.66502e22i | − | 0.320328i | −0.987090 | − | 0.160164i | \(-0.948798\pi\) | ||
0.987090 | − | 0.160164i | \(-0.0512024\pi\) | |||||||
\(692\) | −3.21014e22 | + | 4.69564e22i | −0.610485 | + | 0.892989i | ||||
\(693\) | 1.22846e21 | 0.0230938 | ||||||||
\(694\) | −2.63421e22 | + | 1.39009e22i | −0.489525 | + | 0.258326i | ||||
\(695\) | − | 6.20918e21i | − | 0.114066i | ||||||
\(696\) | 6.56879e21 | − | 5.73224e22i | 0.119292 | − | 1.04100i | ||||
\(697\) | 4.72454e22 | 0.848198 | ||||||||
\(698\) | 1.13984e22 | + | 2.15998e22i | 0.202302 | + | 0.383360i | ||||
\(699\) | 2.94307e22i | 0.516396i | ||||||||
\(700\) | −2.21170e21 | − | 1.51201e21i | −0.0383656 | − | 0.0262283i | ||||
\(701\) | 4.07553e22 | 0.698939 | 0.349470 | − | 0.936948i | \(-0.386362\pi\) | ||||
0.349470 | + | 0.936948i | \(0.386362\pi\) | |||||||
\(702\) | −6.06499e21 | + | 3.20054e21i | −0.102833 | + | 0.0542658i | ||||
\(703\) | − | 1.39762e22i | − | 0.234287i | ||||||
\(704\) | −1.05783e22 | + | 4.55493e22i | −0.175321 | + | 0.754919i | ||||
\(705\) | −6.31973e22 | −1.03558 | ||||||||
\(706\) | −3.56387e22 | − | 6.75350e22i | −0.577410 | − | 1.09419i | ||||
\(707\) | 5.59547e21i | 0.0896357i | ||||||||
\(708\) | −2.39016e22 | + | 3.49621e22i | −0.378582 | + | 0.553773i | ||||
\(709\) | 2.58315e21 | 0.0404558 | 0.0202279 | − | 0.999795i | \(-0.493561\pi\) | ||||
0.0202279 | + | 0.999795i | \(0.493561\pi\) | |||||||
\(710\) | 1.96842e22 | − | 1.03875e22i | 0.304826 | − | 0.160859i | ||||
\(711\) | 2.75354e22i | 0.421633i | ||||||||
\(712\) | −1.41771e22 | − | 1.62461e21i | −0.214658 | − | 0.0245985i | ||||
\(713\) | 2.42683e22 | 0.363349 | ||||||||
\(714\) | −1.74044e21 | − | 3.29812e21i | −0.0257676 | − | 0.0488294i | ||||
\(715\) | 3.94295e22i | 0.577262i | ||||||||
\(716\) | −4.98373e22 | − | 3.40709e22i | −0.721523 | − | 0.493263i | ||||
\(717\) | 4.30720e22 | 0.616654 | ||||||||
\(718\) | −6.63481e22 | + | 3.50124e22i | −0.939362 | + | 0.495708i | ||||
\(719\) | 1.13920e23i | 1.59503i | 0.603299 | + | 0.797515i | \(0.293853\pi\) | ||||
−0.603299 | + | 0.797515i | \(0.706147\pi\) | |||||||
\(720\) | −1.07729e22 | − | 2.76543e22i | −0.149167 | − | 0.382916i | ||||
\(721\) | −9.21584e20 | −0.0126198 | ||||||||
\(722\) | −3.29481e22 | − | 6.24364e22i | −0.446203 | − | 0.845551i | ||||
\(723\) | − | 1.97842e22i | − | 0.264979i | ||||||
\(724\) | −5.87738e22 | + | 8.59716e22i | −0.778530 | + | 1.13880i | ||||
\(725\) | 7.20194e22 | 0.943507 | ||||||||
\(726\) | −1.57380e22 | + | 8.30506e21i | −0.203919 | + | 0.107609i | ||||
\(727\) | 1.06494e22i | 0.136474i | 0.997669 | + | 0.0682370i | \(0.0217374\pi\) | ||||
−0.997669 | + | 0.0682370i | \(0.978263\pi\) | |||||||
\(728\) | 4.85122e20 | − | 4.23340e21i | 0.00614893 | − | 0.0536585i | ||||
\(729\) | −2.95431e21 | −0.0370370 | ||||||||
\(730\) | −7.40047e22 | − | 1.40238e23i | −0.917648 | − | 1.73894i | ||||
\(731\) | 1.03357e23i | 1.26766i | ||||||||
\(732\) | 6.23287e22 | + | 4.26105e22i | 0.756136 | + | 0.516926i | ||||
\(733\) | −9.85179e22 | −1.18218 | −0.591089 | − | 0.806606i | \(-0.701302\pi\) | ||||
−0.591089 | + | 0.806606i | \(0.701302\pi\) | |||||||
\(734\) | 4.00710e22 | − | 2.11458e22i | 0.475622 | − | 0.250989i | ||||
\(735\) | 6.01392e22i | 0.706089i | ||||||||
\(736\) | 1.17886e23 | + | 1.02100e23i | 1.36912 | + | 1.18577i | ||||
\(737\) | −5.26598e22 | −0.604978 | ||||||||
\(738\) | 1.08542e22 | + | 2.05685e22i | 0.123352 | + | 0.233750i | ||||
\(739\) | 2.62544e22i | 0.295152i | 0.989051 | + | 0.147576i | \(0.0471472\pi\) | ||||
−0.989051 | + | 0.147576i | \(0.952853\pi\) | |||||||
\(740\) | −6.99270e22 | + | 1.02286e23i | −0.777662 | + | 1.13753i | ||||
\(741\) | −6.64610e21 | −0.0731175 | ||||||||
\(742\) | 9.41032e21 | − | 4.96589e21i | 0.102417 | − | 0.0540463i | ||||
\(743\) | − | 6.77760e22i | − | 0.729736i | −0.931059 | − | 0.364868i | \(-0.881114\pi\) | ||
0.931059 | − | 0.364868i | \(-0.118886\pi\) | |||||||
\(744\) | 1.08029e22 | + | 1.23795e21i | 0.115069 | + | 0.0131862i | ||||
\(745\) | 8.08807e22 | 0.852304 | ||||||||
\(746\) | 2.14037e21 | + | 4.05598e21i | 0.0223140 | + | 0.0422849i | ||||
\(747\) | − | 4.27696e22i | − | 0.441133i | ||||||
\(748\) | −6.70700e22 | − | 4.58519e22i | −0.684409 | − | 0.467891i | ||||
\(749\) | 6.55617e21 | 0.0661905 | ||||||||
\(750\) | −3.02579e22 | + | 1.59673e22i | −0.302238 | + | 0.159493i | ||||
\(751\) | − | 3.55558e22i | − | 0.351391i | −0.984445 | − | 0.175696i | \(-0.943783\pi\) | ||
0.984445 | − | 0.175696i | \(-0.0562175\pi\) | |||||||
\(752\) | 1.38645e23 | − | 5.40100e22i | 1.35569 | − | 0.528119i | ||||
\(753\) | 7.51309e22 | 0.726873 | ||||||||
\(754\) | 5.34592e22 | + | 1.01305e23i | 0.511743 | + | 0.969749i | ||||
\(755\) | − | 2.13422e23i | − | 2.02145i | ||||||
\(756\) | 1.03601e21 | − | 1.51542e21i | 0.00970929 | − | 0.0142023i | ||||
\(757\) | −6.10956e22 | −0.566556 | −0.283278 | − | 0.959038i | \(-0.591422\pi\) | ||||
−0.283278 | + | 0.959038i | \(0.591422\pi\) | |||||||
\(758\) | 1.72679e23 | − | 9.11239e22i | 1.58448 | − | 0.836139i | ||||
\(759\) | − | 8.92593e22i | − | 0.810437i | ||||||
\(760\) | 3.27463e21 | − | 2.85759e22i | 0.0294207 | − | 0.256739i | ||||
\(761\) | −7.31694e22 | −0.650508 | −0.325254 | − | 0.945627i | \(-0.605450\pi\) | ||||
−0.325254 | + | 0.945627i | \(0.605450\pi\) | |||||||
\(762\) | −2.41765e22 | − | 4.58142e22i | −0.212693 | − | 0.403051i | ||||
\(763\) | 6.06906e21i | 0.0528354i | ||||||||
\(764\) | −5.97925e22 | − | 4.08767e22i | −0.515110 | − | 0.352151i | ||||
\(765\) | 5.15647e22 | 0.439603 | ||||||||
\(766\) | 1.08535e23 | − | 5.72747e22i | 0.915672 | − | 0.483206i | ||||
\(767\) | − | 8.40786e22i | − | 0.701977i | ||||||
\(768\) | 4.72682e22 | + | 5.14626e22i | 0.390553 | + | 0.425208i | ||||
\(769\) | −5.63191e22 | −0.460516 | −0.230258 | − | 0.973130i | \(-0.573957\pi\) | ||||
−0.230258 | + | 0.973130i | \(0.573957\pi\) | |||||||
\(770\) | −4.92600e21 | − | 9.33472e21i | −0.0398629 | − | 0.0755398i | ||||
\(771\) | − | 9.91474e22i | − | 0.794047i | ||||||
\(772\) | 3.50060e22 | − | 5.12052e22i | 0.277463 | − | 0.405859i | ||||
\(773\) | −1.23390e23 | −0.967934 | −0.483967 | − | 0.875086i | \(-0.660804\pi\) | ||||
−0.483967 | + | 0.875086i | \(0.660804\pi\) | |||||||
\(774\) | −4.49971e22 | + | 2.37453e22i | −0.349347 | + | 0.184353i | ||||
\(775\) | 1.35727e22i | 0.104292i | ||||||||
\(776\) | −2.17697e22 | − | 2.49468e21i | −0.165561 | − | 0.0189723i | ||||
\(777\) | −7.66381e21 | −0.0576868 | ||||||||
\(778\) | 8.10487e22 | + | 1.53587e23i | 0.603823 | + | 1.14424i | ||||
\(779\) | 2.25393e22i | 0.166204i | ||||||||
\(780\) | 4.86399e22 | + | 3.32523e22i | 0.355006 | + | 0.242697i | ||||
\(781\) | 2.99922e22 | 0.216671 | ||||||||
\(782\) | −2.39639e23 | + | 1.26459e23i | −1.71358 | + | 0.904268i | ||||
\(783\) | 4.93465e22i | 0.349271i | ||||||||
\(784\) | −5.13965e22 | − | 1.31936e23i | −0.360085 | − | 0.924348i | ||||
\(785\) | 8.26763e22 | 0.573355 | ||||||||
\(786\) | 6.71927e22 | + | 1.27330e23i | 0.461256 | + | 0.874076i | ||||
\(787\) | 4.32717e22i | 0.294039i | 0.989134 | + | 0.147020i | \(0.0469681\pi\) | ||||
−0.989134 | + | 0.147020i | \(0.953032\pi\) | |||||||
\(788\) | 4.39730e22 | − | 6.43216e22i | 0.295785 | − | 0.432660i | ||||
\(789\) | 3.30589e22 | 0.220126 | ||||||||
\(790\) | 2.09233e23 | − | 1.10414e23i | 1.37916 | − | 0.727792i | ||||
\(791\) | − | 8.30498e21i | − | 0.0541909i | ||||||
\(792\) | 4.55319e21 | − | 3.97333e22i | 0.0294113 | − | 0.256657i | ||||
\(793\) | −1.49891e23 | −0.958497 | ||||||||
\(794\) | 9.53478e22 | + | 1.80683e23i | 0.603596 | + | 1.14381i | ||||
\(795\) | 1.47126e23i | 0.922047i | ||||||||
\(796\) | 9.85665e21 | + | 6.73842e21i | 0.0611540 | + | 0.0418074i | ||||
\(797\) | 1.00831e23 | 0.619336 | 0.309668 | − | 0.950845i | \(-0.399782\pi\) | ||||
0.309668 | + | 0.950845i | \(0.399782\pi\) | |||||||
\(798\) | 1.57343e21 | − | 8.30309e20i | 0.00956806 | − | 0.00504913i | ||||
\(799\) | 2.58520e23i | 1.55639i | ||||||||
\(800\) | −5.71019e22 | + | 6.59309e22i | −0.340354 | + | 0.392979i | ||||
\(801\) | 1.22045e22 | 0.0720210 | ||||||||
\(802\) | −3.07266e22 | − | 5.82267e22i | −0.179523 | − | 0.340194i | ||||
\(803\) | − | 2.13677e23i | − | 1.23604i | ||||||
\(804\) | −4.44098e22 | + | 6.49607e22i | −0.254349 | + | 0.372051i | ||||
\(805\) | −3.52009e22 | −0.199612 | ||||||||
\(806\) | −1.90918e22 | + | 1.00749e22i | −0.107193 | + | 0.0565665i | ||||
\(807\) | − | 5.08937e21i | − | 0.0282928i | ||||||
\(808\) | 1.80979e23 | + | 2.07391e22i | 0.996181 | + | 0.114156i | ||||
\(809\) | −2.78402e23 | −1.51735 | −0.758673 | − | 0.651472i | \(-0.774152\pi\) | ||||
−0.758673 | + | 0.651472i | \(0.774152\pi\) | |||||||
\(810\) | 1.18465e22 | + | 2.24489e22i | 0.0639306 | + | 0.121148i | ||||
\(811\) | 1.53217e23i | 0.818731i | 0.912371 | + | 0.409365i | \(0.134250\pi\) | ||||
−0.912371 | + | 0.409365i | \(0.865750\pi\) | |||||||
\(812\) | −2.53124e22 | − | 1.73046e22i | −0.133932 | − | 0.0915616i | ||||
\(813\) | −1.79409e23 | −0.939980 | ||||||||
\(814\) | −1.47667e23 | + | 7.79249e22i | −0.766105 | + | 0.404279i | ||||
\(815\) | − | 1.26301e23i | − | 0.648854i | ||||||
\(816\) | −1.13125e23 | + | 4.40685e22i | −0.575489 | + | 0.224185i | ||||
\(817\) | −4.93085e22 | −0.248396 | ||||||||
\(818\) | −7.17218e22 | − | 1.35912e23i | −0.357787 | − | 0.678003i | ||||
\(819\) | 3.64436e21i | 0.0180032i | ||||||||
\(820\) | 1.12770e23 | − | 1.64955e23i | 0.551675 | − | 0.806965i | ||||
\(821\) | −6.35989e22 | −0.308109 | −0.154054 | − | 0.988062i | \(-0.549233\pi\) | ||||
−0.154054 | + | 0.988062i | \(0.549233\pi\) | |||||||
\(822\) | −1.37168e20 | + | 7.23844e19i | −0.000658078 | + | 0.000347273i | ||||
\(823\) | 1.19757e22i | 0.0568985i | 0.999595 | + | 0.0284492i | \(0.00905689\pi\) | ||||
−0.999595 | + | 0.0284492i | \(0.990943\pi\) | |||||||
\(824\) | −3.41577e21 | + | 2.98076e22i | −0.0160721 | + | 0.140252i | ||||
\(825\) | 4.99206e22 | 0.232621 | ||||||||
\(826\) | 1.05041e22 | + | 1.99052e22i | 0.0484750 | + | 0.0918598i | ||||
\(827\) | − | 4.37654e22i | − | 0.200026i | −0.994986 | − | 0.100013i | \(-0.968112\pi\) | ||
0.994986 | − | 0.100013i | \(-0.0318885\pi\) | |||||||
\(828\) | −1.10109e23 | − | 7.52755e22i | −0.498405 | − | 0.340730i | ||||
\(829\) | −1.65734e23 | −0.742976 | −0.371488 | − | 0.928438i | \(-0.621152\pi\) | ||||
−0.371488 | + | 0.928438i | \(0.621152\pi\) | |||||||
\(830\) | −3.24993e23 | + | 1.71501e23i | −1.44294 | + | 0.761452i | ||||
\(831\) | − | 1.38438e23i | − | 0.608760i | ||||||
\(832\) | −1.35127e23 | − | 3.13815e22i | −0.588511 | − | 0.136674i | ||||
\(833\) | 2.46010e23 | 1.06119 | ||||||||
\(834\) | −5.83534e21 | − | 1.10579e22i | −0.0249309 | − | 0.0472438i | ||||
\(835\) | 2.03372e23i | 0.860596i | ||||||||
\(836\) | 2.18745e22 | − | 3.19970e22i | 0.0916827 | − | 0.134109i | ||||
\(837\) | −9.29979e21 | −0.0386073 | ||||||||
\(838\) | 9.61474e22 | − | 5.07377e22i | 0.395353 | − | 0.208631i | ||||
\(839\) | − | 4.56435e22i | − | 0.185902i | −0.995671 | − | 0.0929509i | \(-0.970370\pi\) | ||
0.995671 | − | 0.0929509i | \(-0.0296300\pi\) | |||||||
\(840\) | −1.56695e22 | − | 1.79563e21i | −0.0632151 | − | 0.00724406i | ||||
\(841\) | 5.73998e23 | 2.29373 | ||||||||
\(842\) | 5.65630e22 | + | 1.07186e23i | 0.223890 | + | 0.424270i | ||||
\(843\) | − | 2.02410e23i | − | 0.793619i | ||||||
\(844\) | −1.08792e23 | − | 7.43750e22i | −0.422531 | − | 0.288860i | ||||
\(845\) | 2.03477e23 | 0.782818 | ||||||||
\(846\) | −1.12548e23 | + | 5.93923e22i | −0.428918 | + | 0.226343i | ||||
\(847\) | 9.45673e21i | 0.0357005i | ||||||||
\(848\) | −1.25738e23 | − | 3.22772e23i | −0.470218 | − | 1.20706i | ||||
\(849\) | 2.60935e23 | 0.966655 | ||||||||
\(850\) | −7.07257e22 | − | 1.34025e23i | −0.259553 | − | 0.491850i | ||||
\(851\) | 5.56847e23i | 2.02442i | ||||||||
\(852\) | 2.52935e22 | − | 3.69981e22i | 0.0910945 | − | 0.133249i | ||||
\(853\) | 2.70000e23 | 0.963322 | 0.481661 | − | 0.876358i | \(-0.340034\pi\) | ||||
0.481661 | + | 0.876358i | \(0.340034\pi\) | |||||||
\(854\) | 3.54860e22 | − | 1.87262e22i | 0.125428 | − | 0.0661891i | ||||
\(855\) | 2.45999e22i | 0.0861397i | ||||||||
\(856\) | 2.42999e22 | − | 2.12052e23i | 0.0842974 | − | 0.735619i | ||||
\(857\) | 1.22894e23 | 0.422361 | 0.211180 | − | 0.977447i | \(-0.432269\pi\) | ||||
0.211180 | + | 0.977447i | \(0.432269\pi\) | |||||||
\(858\) | 3.70555e22 | + | 7.02199e22i | 0.126170 | + | 0.239090i | ||||
\(859\) | − | 3.65955e23i | − | 1.23448i | −0.786776 | − | 0.617238i | \(-0.788252\pi\) | ||
0.786776 | − | 0.617238i | \(-0.211748\pi\) | |||||||
\(860\) | 3.60867e23 | + | 2.46704e23i | 1.20603 | + | 0.824496i | ||||
\(861\) | 1.23593e22 | 0.0409232 | ||||||||
\(862\) | −3.96139e23 | + | 2.09045e23i | −1.29954 | + | 0.685776i | ||||
\(863\) | 3.30833e23i | 1.07528i | 0.843174 | + | 0.537641i | \(0.180684\pi\) | ||||
−0.843174 | + | 0.537641i | \(0.819316\pi\) | |||||||
\(864\) | −4.51748e22 | − | 3.91252e22i | −0.145474 | − | 0.125993i | ||||
\(865\) | −4.17973e23 | −1.33358 | ||||||||
\(866\) | 3.12566e22 | + | 5.92309e22i | 0.0988094 | + | 0.187243i | ||||
\(867\) | − | 2.66061e22i | − | 0.0833351i | ||||||
\(868\) | 3.26121e21 | − | 4.77034e21i | 0.0101209 | − | 0.0148044i | ||||
\(869\) | 3.18802e23 | 0.980310 | ||||||||
\(870\) | 3.74969e23 | − | 1.97874e23i | 1.14246 | − | 0.602885i | ||||
\(871\) | − | 1.56221e23i | − | 0.471621i | ||||||
\(872\) | 1.96297e23 | + | 2.24944e22i | 0.587194 | + | 0.0672889i | ||||
\(873\) | 1.87407e22 | 0.0555483 | ||||||||
\(874\) | −6.03297e22 | − | 1.14324e23i | −0.177190 | − | 0.335774i | ||||
\(875\) | 1.81815e22i | 0.0529134i | ||||||||
\(876\) | −2.63589e23 | − | 1.80201e23i | −0.760143 | − | 0.519666i | ||||
\(877\) | −3.85703e23 | −1.10219 | −0.551094 | − | 0.834443i | \(-0.685790\pi\) | ||||
−0.551094 | + | 0.834443i | \(0.685790\pi\) | |||||||
\(878\) | −2.39206e22 | + | 1.26231e22i | −0.0677354 | + | 0.0357445i | ||||
\(879\) | − | 8.25958e22i | − | 0.231764i | ||||||
\(880\) | −3.20179e23 | + | 1.24728e23i | −0.890291 | + | 0.346818i | ||||
\(881\) | 2.31132e23 | 0.636873 | 0.318437 | − | 0.947944i | \(-0.396842\pi\) | ||||
0.318437 | + | 0.947944i | \(0.396842\pi\) | |||||||
\(882\) | 5.65184e22 | + | 1.07102e23i | 0.154327 | + | 0.292448i | ||||
\(883\) | 6.69705e21i | 0.0181217i | 0.999959 | + | 0.00906083i | \(0.00288419\pi\) | ||||
−0.999959 | + | 0.00906083i | \(0.997116\pi\) | |||||||
\(884\) | 1.36024e23 | − | 1.98970e23i | 0.364753 | − | 0.533543i | ||||
\(885\) | −3.11208e23 | −0.826999 | ||||||||
\(886\) | 3.21364e23 | − | 1.69586e23i | 0.846306 | − | 0.446602i | ||||
\(887\) | 1.24237e23i | 0.324237i | 0.986771 | + | 0.162119i | \(0.0518327\pi\) | ||||
−0.986771 | + | 0.162119i | \(0.948167\pi\) | |||||||
\(888\) | −2.84052e22 | + | 2.47878e23i | −0.0734674 | + | 0.641111i | ||||
\(889\) | −2.75290e22 | −0.0705630 | ||||||||
\(890\) | −4.89386e22 | − | 9.27382e22i | −0.124317 | − | 0.235580i | ||||
\(891\) | 3.42048e22i | 0.0861122i | ||||||||
\(892\) | 1.10044e23 | + | 7.52305e22i | 0.274566 | + | 0.187705i | ||||
\(893\) | −1.23331e23 | −0.304973 | ||||||||
\(894\) | 1.44040e23 | − | 7.60110e22i | 0.353007 | − | 0.186284i | ||||
\(895\) | − | 4.43617e23i | − | 1.07752i | ||||||
\(896\) | 3.59111e22 | − | 9.45222e21i | 0.0864498 | − | 0.0227546i | ||||
\(897\) | 2.64797e23 | 0.631791 | ||||||||
\(898\) | 1.87384e23 | + | 3.55092e23i | 0.443121 | + | 0.839711i | ||||
\(899\) | 1.55336e23i | 0.364079i | ||||||||
\(900\) | 4.20998e22 | − | 6.15816e22i | 0.0978002 | − | 0.143058i | ||||
\(901\) | 6.01846e23 | 1.38576 | ||||||||
\(902\) | 2.38141e23 | − | 1.25668e23i | 0.543477 | − | 0.286797i | ||||
\(903\) | 2.70381e22i | 0.0611609i | ||||||||
\(904\) | −2.68615e23 | − | 3.07817e22i | −0.602259 | − | 0.0690152i | ||||
\(905\) | −7.65260e23 | −1.70067 | ||||||||
\(906\) | −2.00572e23 | − | 3.80082e23i | −0.441819 | − | 0.837243i | ||||
\(907\) | 5.42263e23i | 1.18400i | 0.805938 | + | 0.592000i | \(0.201662\pi\) | ||||
−0.805938 | + | 0.592000i | \(0.798338\pi\) | |||||||
\(908\) | 4.49906e23 | + | 3.07574e23i | 0.973721 | + | 0.665677i | ||||
\(909\) | −1.55798e23 | −0.334233 | ||||||||
\(910\) | 2.76924e22 | − | 1.46135e22i | 0.0588884 | − | 0.0310758i | ||||
\(911\) | − | 7.67160e23i | − | 1.61711i | −0.588422 | − | 0.808554i | \(-0.700251\pi\) | ||
0.588422 | − | 0.808554i | \(-0.299749\pi\) | |||||||
\(912\) | −2.10237e22 | − | 5.39683e22i | −0.0439288 | − | 0.112766i | ||||
\(913\) | −4.95182e23 | −1.02565 | ||||||||
\(914\) | −3.43925e23 | − | 6.51734e23i | −0.706145 | − | 1.33814i | ||||
\(915\) | 5.54807e23i | 1.12921i | ||||||||
\(916\) | −2.66107e23 | + | 3.89249e23i | −0.536899 | + | 0.785352i | ||||
\(917\) | 7.65104e22 | 0.153026 | ||||||||
\(918\) | 9.18314e22 | − | 4.84601e22i | 0.182075 | − | 0.0960821i | ||||
\(919\) | − | 5.38528e23i | − | 1.05848i | −0.848471 | − | 0.529242i | \(-0.822476\pi\) | ||
0.848471 | − | 0.529242i | \(-0.177524\pi\) | |||||||
\(920\) | −1.30469e23 | + | 1.13854e24i | −0.254217 | + | 2.21842i | ||||
\(921\) | −3.65206e23 | −0.705441 | ||||||||
\(922\) | −3.59259e22 | − | 6.80793e22i | −0.0687955 | − | 0.130367i | ||||
\(923\) | 8.89750e22i | 0.168910i | ||||||||
\(924\) | −1.75454e22 | − | 1.19948e22i | −0.0330208 | − | 0.0225744i | ||||
\(925\) | −3.11431e23 | −0.581070 | ||||||||
\(926\) | −8.40442e23 | + | 4.43507e23i | −1.55461 | + | 0.820376i | ||||
\(927\) | − | 2.56602e22i | − | 0.0470567i | ||||||
\(928\) | −6.53517e23 | + | 7.54563e23i | −1.18815 | + | 1.37187i | ||||
\(929\) | −8.87061e22 | −0.159892 | −0.0799461 | − | 0.996799i | \(-0.525475\pi\) | ||||
−0.0799461 | + | 0.996799i | \(0.525475\pi\) | |||||||
\(930\) | 3.72911e22 | + | 7.06663e22i | 0.0666410 | + | 0.126284i | ||||
\(931\) | 1.17364e23i | 0.207939i | ||||||||
\(932\) | 2.87363e23 | − | 4.20341e23i | 0.504781 | − | 0.738371i | ||||
\(933\) | −5.45012e23 | −0.949189 | ||||||||
\(934\) | 7.60861e23 | − | 4.01512e23i | 1.31380 | − | 0.693303i | ||||
\(935\) | − | 5.97011e23i | − | 1.02209i | ||||||
\(936\) | 1.17873e23 | + | 1.35075e22i | 0.200082 | + | 0.0229281i | ||||
\(937\) | 2.88142e23 | 0.484943 | 0.242471 | − | 0.970159i | \(-0.422042\pi\) | ||||
0.242471 | + | 0.970159i | \(0.422042\pi\) | |||||||
\(938\) | 1.95169e22 | + | 3.69844e22i | 0.0325678 | + | 0.0617157i | ||||
\(939\) | 1.85042e23i | 0.306158i | ||||||||
\(940\) | 9.02609e23 | + | 6.17061e23i | 1.48073 | + | 1.01229i | ||||
\(941\) | −6.32626e23 | −1.02904 | −0.514518 | − | 0.857480i | \(-0.672029\pi\) | ||||
−0.514518 | + | 0.857480i | \(0.672029\pi\) | |||||||
\(942\) | 1.47238e23 | − | 7.76985e22i | 0.237472 | − | 0.125316i | ||||
\(943\) | − | 8.98020e23i | − | 1.43613i | ||||||
\(944\) | 6.82743e23 | − | 2.65967e23i | 1.08263 | − | 0.421746i | ||||
\(945\) | 1.34892e22 | 0.0212096 | ||||||||
\(946\) | 2.74921e23 | + | 5.20973e23i | 0.428626 | + | 0.812243i | ||||
\(947\) | 1.24941e24i | 1.93155i | 0.259378 | + | 0.965776i | \(0.416483\pi\) | ||||
−0.259378 | + | 0.965776i | \(0.583517\pi\) | |||||||
\(948\) | 2.68857e23 | − | 3.93272e23i | 0.412149 | − | 0.602873i | ||||
\(949\) | 6.33893e23 | 0.963577 | ||||||||
\(950\) | 6.39388e22 | − | 3.37410e22i | 0.0963775 | − | 0.0508591i | ||||
\(951\) | 1.33788e23i | 0.199974i | ||||||||
\(952\) | −7.34534e21 | + | 6.40989e22i | −0.0108872 | + | 0.0950068i | ||||
\(953\) | −8.68851e23 | −1.27703 | −0.638517 | − | 0.769608i | \(-0.720452\pi\) | ||||
−0.638517 | + | 0.769608i | \(0.720452\pi\) | |||||||
\(954\) | 1.38268e23 | + | 2.62017e23i | 0.201528 | + | 0.381893i | ||||
\(955\) | − | 5.32232e23i | − | 0.769261i | ||||||
\(956\) | −6.15171e23 | − | 4.20557e23i | −0.881724 | − | 0.602784i | ||||
\(957\) | 5.71329e23 | 0.812065 | ||||||||
\(958\) | 8.63877e22 | − | 4.55874e22i | 0.121767 | − | 0.0642571i | ||||
\(959\) | 8.24220e19i | 0.000115211i | ||||||||
\(960\) | −1.16155e23 | + | 5.00158e23i | −0.161016 | + | 0.693325i | ||||
\(961\) | 6.98149e23 | 0.959756 | ||||||||
\(962\) | −2.31172e23 | − | 4.38069e23i | −0.315163 | − | 0.597231i | ||||
\(963\) | 1.82547e23i | 0.246811i | ||||||||
\(964\) | −1.93174e23 | + | 2.82565e23i | −0.259019 | + | 0.378881i | ||||
\(965\) | 4.55793e23 | 0.606107 | ||||||||
\(966\) | −6.26892e22 | + | 3.30815e22i | −0.0826753 | + | 0.0436283i | ||||
\(967\) | 2.59154e23i | 0.338959i | 0.985534 | + | 0.169479i | \(0.0542086\pi\) | ||||
−0.985534 | + | 0.169479i | \(0.945791\pi\) | |||||||
\(968\) | 3.05868e23 | + | 3.50506e22i | 0.396763 | + | 0.0454666i | ||||
\(969\) | 1.00630e23 | 0.129461 | ||||||||
\(970\) | −7.51479e22 | − | 1.42405e23i | −0.0958833 | − | 0.181698i | ||||
\(971\) | − | 2.71728e23i | − | 0.343859i | −0.985109 | − | 0.171930i | \(-0.945000\pi\) | ||
0.985109 | − | 0.171930i | \(-0.0550002\pi\) | |||||||
\(972\) | 4.21947e22 | + | 2.88461e22i | 0.0529575 | + | 0.0362040i | ||||
\(973\) | −6.64453e21 | −0.00827107 | ||||||||
\(974\) | 4.99830e23 | − | 2.63764e23i | 0.617094 | − | 0.325645i | ||||
\(975\) | 1.48095e23i | 0.181344i | ||||||||
\(976\) | −4.74153e23 | − | 1.21716e24i | −0.575863 | − | 1.47826i | ||||
\(977\) | −5.31693e23 | −0.640478 | −0.320239 | − | 0.947337i | \(-0.603763\pi\) | ||||
−0.320239 | + | 0.947337i | \(0.603763\pi\) | |||||||
\(978\) | −1.18697e23 | − | 2.24930e23i | −0.141817 | − | 0.268742i | ||||
\(979\) | − | 1.41302e23i | − | 0.167451i | ||||||
\(980\) | 5.87202e23 | − | 8.58933e23i | 0.690207 | − | 1.00960i | ||||
\(981\) | −1.68984e23 | −0.197012 | ||||||||
\(982\) | −9.12498e23 | + | 4.81532e23i | −1.05521 | + | 0.556843i | ||||
\(983\) | − | 5.65847e23i | − | 0.649039i | −0.945879 | − | 0.324520i | \(-0.894797\pi\) | ||
0.945879 | − | 0.324520i | \(-0.105203\pi\) | |||||||
\(984\) | 4.58087e22 | − | 3.99749e23i | 0.0521180 | − | 0.454806i | ||||
\(985\) | 5.72546e23 | 0.646131 | ||||||||
\(986\) | −8.09438e23 | − | 1.53388e24i | −0.906084 | − | 1.71702i | ||||
\(987\) | 6.76283e22i | 0.0750915i | ||||||||
\(988\) | 9.49223e22 | + | 6.48928e22i | 0.104547 | + | 0.0714729i | ||||
\(989\) | 1.96457e24 | 2.14633 | ||||||||
\(990\) | 2.59912e23 | − | 1.37157e23i | 0.281672 | − | 0.148641i | ||||
\(991\) | 3.28127e22i | 0.0352738i | 0.999844 | + | 0.0176369i | \(0.00561429\pi\) | ||||
−0.999844 | + | 0.0176369i | \(0.994386\pi\) | |||||||
\(992\) | −1.42204e23 | − | 1.23161e23i | −0.151642 | − | 0.131335i | ||||
\(993\) | 1.04666e24 | 1.10716 | ||||||||
\(994\) | −1.11158e22 | − | 2.10644e22i | −0.0116641 | − | 0.0221033i | ||||
\(995\) | 8.77371e22i | 0.0913268i | ||||||||
\(996\) | −4.17604e23 | + | 6.10852e23i | −0.431211 | + | 0.630756i | ||||
\(997\) | −4.03691e22 | −0.0413511 | −0.0206756 | − | 0.999786i | \(-0.506582\pi\) | ||||
−0.0206756 | + | 0.999786i | \(0.506582\pi\) | |||||||
\(998\) | 3.20989e22 | − | 1.69388e22i | 0.0326171 | − | 0.0172123i | ||||
\(999\) | − | 2.13388e23i | − | 0.215102i |
(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 | 12.17.d.a.7.7 | ✓ | 16 | |
3.2 | odd | 2 | 36.17.d.d.19.10 | 16 | |||
4.3 | odd | 2 | inner | 12.17.d.a.7.8 | yes | 16 | |
12.11 | even | 2 | 36.17.d.d.19.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.17.d.a.7.7 | ✓ | 16 | 1.1 | even | 1 | trivial | |
12.17.d.a.7.8 | yes | 16 | 4.3 | odd | 2 | inner | |
36.17.d.d.19.9 | 16 | 12.11 | even | 2 | |||
36.17.d.d.19.10 | 16 | 3.2 | odd | 2 |