Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,21,Mod(5,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 21, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.5");
S:= CuspForms(chi, 21);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 21 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.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: | \(15.2108259062\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 3396x^{4} + 2813589x^{2} + 548136050 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{31}\cdot 3^{17} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(-29.2393i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.5 |
Dual form | 6.21.b.a.5.4 |
$q$-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 \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 724.077i | − | 0.707107i | ||||||
\(3\) | −57693.2 | + | 12580.8i | −0.977040 | + | 0.213056i | ||||
\(4\) | −524288. | −0.500000 | ||||||||
\(5\) | 8.94833e6i | 0.916309i | 0.888873 | + | 0.458154i | \(0.151489\pi\) | ||||
−0.888873 | + | 0.458154i | \(0.848511\pi\) | |||||||
\(6\) | 9.10944e6 | + | 4.17744e7i | 0.150654 | + | 0.690872i | ||||
\(7\) | −3.40159e7 | −0.120421 | −0.0602103 | − | 0.998186i | \(-0.519177\pi\) | ||||
−0.0602103 | + | 0.998186i | \(0.519177\pi\) | |||||||
\(8\) | 3.79625e8i | 0.353553i | ||||||||
\(9\) | 3.17023e9 | − | 1.45165e9i | 0.909214 | − | 0.416329i | ||||
\(10\) | 6.47928e9 | 0.647928 | ||||||||
\(11\) | − | 6.27231e9i | − | 0.241825i | −0.992663 | − | 0.120912i | \(-0.961418\pi\) | ||
0.992663 | − | 0.120912i | \(-0.0385820\pi\) | |||||||
\(12\) | 3.02479e10 | − | 6.59594e9i | 0.488520 | − | 0.106528i | ||||
\(13\) | −1.12795e11 | −0.818191 | −0.409095 | − | 0.912492i | \(-0.634156\pi\) | ||||
−0.409095 | + | 0.912492i | \(0.634156\pi\) | |||||||
\(14\) | 2.46301e10i | 0.0851503i | ||||||||
\(15\) | −1.12577e11 | − | 5.16258e11i | −0.195225 | − | 0.895270i | ||||
\(16\) | 2.74878e11 | 0.250000 | ||||||||
\(17\) | − | 3.26898e12i | − | 1.62152i | −0.585378 | − | 0.810761i | \(-0.699054\pi\) | ||
0.585378 | − | 0.810761i | \(-0.300946\pi\) | |||||||
\(18\) | −1.05111e12 | − | 2.29549e12i | −0.294389 | − | 0.642911i | ||||
\(19\) | 8.13493e12 | 1.32684 | 0.663419 | − | 0.748248i | \(-0.269105\pi\) | ||||
0.663419 | + | 0.748248i | \(0.269105\pi\) | |||||||
\(20\) | − | 4.69150e12i | − | 0.458154i | ||||||
\(21\) | 1.96249e12 | − | 4.27946e11i | 0.117656 | − | 0.0256564i | ||||
\(22\) | −4.54164e12 | −0.170996 | ||||||||
\(23\) | − | 5.77587e13i | − | 1.39425i | −0.716952 | − | 0.697123i | \(-0.754463\pi\) | ||
0.716952 | − | 0.697123i | \(-0.245537\pi\) | |||||||
\(24\) | −4.77597e12 | − | 2.19018e13i | −0.0753268 | − | 0.345436i | ||||
\(25\) | 1.52949e13 | 0.160379 | ||||||||
\(26\) | 8.16720e13i | 0.578548i | ||||||||
\(27\) | −1.64638e14 | + | 1.23634e14i | −0.799637 | + | 0.600484i | ||||
\(28\) | 1.78341e13 | 0.0602103 | ||||||||
\(29\) | 6.61014e14i | 1.57120i | 0.618736 | + | 0.785599i | \(0.287645\pi\) | ||||
−0.618736 | + | 0.785599i | \(0.712355\pi\) | |||||||
\(30\) | −3.73811e14 | + | 8.15143e13i | −0.633052 | + | 0.138045i | ||||
\(31\) | 1.33200e15 | 1.62513 | 0.812564 | − | 0.582873i | \(-0.198071\pi\) | ||||
0.812564 | + | 0.582873i | \(0.198071\pi\) | |||||||
\(32\) | − | 1.99033e14i | − | 0.176777i | ||||||
\(33\) | 7.89104e13 | + | 3.61870e14i | 0.0515223 | + | 0.236272i | ||||
\(34\) | −2.36699e15 | −1.14659 | ||||||||
\(35\) | − | 3.04385e14i | − | 0.110343i | ||||||
\(36\) | −1.66212e15 | + | 7.61082e14i | −0.454607 | + | 0.208165i | ||||
\(37\) | 1.65175e15 | 0.343499 | 0.171750 | − | 0.985141i | \(-0.445058\pi\) | ||||
0.171750 | + | 0.985141i | \(0.445058\pi\) | |||||||
\(38\) | − | 5.89032e15i | − | 0.938216i | ||||||
\(39\) | 6.50748e15 | − | 1.41904e15i | 0.799405 | − | 0.174321i | ||||
\(40\) | −3.39701e15 | −0.323964 | ||||||||
\(41\) | − | 1.90964e16i | − | 1.42270i | −0.702840 | − | 0.711348i | \(-0.748085\pi\) | ||
0.702840 | − | 0.711348i | \(-0.251915\pi\) | |||||||
\(42\) | −3.09866e14 | − | 1.42099e15i | −0.0181418 | − | 0.0831952i | ||||
\(43\) | 1.96411e16 | 0.908826 | 0.454413 | − | 0.890791i | \(-0.349849\pi\) | ||||
0.454413 | + | 0.890791i | \(0.349849\pi\) | |||||||
\(44\) | 3.28850e15i | 0.120912i | ||||||||
\(45\) | 1.29898e16 | + | 2.83683e16i | 0.381486 | + | 0.833121i | ||||
\(46\) | −4.18218e16 | −0.985880 | ||||||||
\(47\) | 2.59733e16i | 0.493796i | 0.969041 | + | 0.246898i | \(0.0794113\pi\) | ||||
−0.969041 | + | 0.246898i | \(0.920589\pi\) | |||||||
\(48\) | −1.58586e16 | + | 3.45817e15i | −0.244260 | + | 0.0532641i | ||||
\(49\) | −7.86352e16 | −0.985499 | ||||||||
\(50\) | − | 1.10747e16i | − | 0.113405i | ||||||
\(51\) | 4.11262e16 | + | 1.88598e17i | 0.345475 | + | 1.58429i | ||||
\(52\) | 5.91368e16 | 0.409095 | ||||||||
\(53\) | − | 1.97975e17i | − | 1.13201i | −0.824400 | − | 0.566007i | \(-0.808488\pi\) | ||
0.824400 | − | 0.566007i | \(-0.191512\pi\) | |||||||
\(54\) | 8.95208e16 | + | 1.19211e17i | 0.424606 | + | 0.565429i | ||||
\(55\) | 5.61267e16 | 0.221586 | ||||||||
\(56\) | − | 1.29133e16i | − | 0.0425751i | ||||||
\(57\) | −4.69330e17 | + | 1.02344e17i | −1.29637 | + | 0.282691i | ||||
\(58\) | 4.78626e17 | 1.11100 | ||||||||
\(59\) | − | 7.73122e17i | − | 1.51261i | −0.654217 | − | 0.756307i | \(-0.727002\pi\) | ||
0.654217 | − | 0.756307i | \(-0.272998\pi\) | |||||||
\(60\) | 5.90226e16 | + | 2.70668e17i | 0.0976127 | + | 0.447635i | ||||
\(61\) | −1.23592e17 | −0.173258 | −0.0866288 | − | 0.996241i | \(-0.527609\pi\) | ||||
−0.0866288 | + | 0.996241i | \(0.527609\pi\) | |||||||
\(62\) | − | 9.64471e17i | − | 1.14914i | ||||||
\(63\) | −1.07838e17 | + | 4.93791e16i | −0.109488 | + | 0.0501346i | ||||
\(64\) | −1.44115e17 | −0.125000 | ||||||||
\(65\) | − | 1.00932e18i | − | 0.749715i | ||||||
\(66\) | 2.62022e17 | − | 5.71373e16i | 0.167070 | − | 0.0364318i | ||||
\(67\) | −3.35174e17 | −0.183875 | −0.0919373 | − | 0.995765i | \(-0.529306\pi\) | ||||
−0.0919373 | + | 0.995765i | \(0.529306\pi\) | |||||||
\(68\) | 1.71389e18i | 0.810761i | ||||||||
\(69\) | 7.26649e17 | + | 3.33229e18i | 0.297053 | + | 1.36223i | ||||
\(70\) | −2.20398e17 | −0.0780239 | ||||||||
\(71\) | 1.61150e18i | 0.495047i | 0.968882 | + | 0.247524i | \(0.0796167\pi\) | ||||
−0.968882 | + | 0.247524i | \(0.920383\pi\) | |||||||
\(72\) | 5.51083e17 | + | 1.20350e18i | 0.147195 | + | 0.321456i | ||||
\(73\) | 3.68460e17 | 0.0857357 | 0.0428679 | − | 0.999081i | \(-0.486351\pi\) | ||||
0.0428679 | + | 0.999081i | \(0.486351\pi\) | |||||||
\(74\) | − | 1.19599e18i | − | 0.242891i | ||||||
\(75\) | −8.82412e17 | + | 1.92421e17i | −0.156696 | + | 0.0341697i | ||||
\(76\) | −4.26505e18 | −0.663419 | ||||||||
\(77\) | 2.13358e17i | 0.0291207i | ||||||||
\(78\) | −1.02750e18 | − | 4.71192e18i | −0.123263 | − | 0.565265i | ||||
\(79\) | 2.03414e18 | 0.214838 | 0.107419 | − | 0.994214i | \(-0.465741\pi\) | ||||
0.107419 | + | 0.994214i | \(0.465741\pi\) | |||||||
\(80\) | 2.45970e18i | 0.229077i | ||||||||
\(81\) | 7.94309e18 | − | 9.20414e18i | 0.653340 | − | 0.757064i | ||||
\(82\) | −1.38272e19 | −1.00600 | ||||||||
\(83\) | 8.34509e18i | 0.537836i | 0.963163 | + | 0.268918i | \(0.0866661\pi\) | ||||
−0.963163 | + | 0.268918i | \(0.913334\pi\) | |||||||
\(84\) | −1.02891e18 | + | 2.24367e17i | −0.0588279 | + | 0.0128282i | ||||
\(85\) | 2.92519e19 | 1.48581 | ||||||||
\(86\) | − | 1.42217e19i | − | 0.642637i | ||||||
\(87\) | −8.31607e18 | − | 3.81361e19i | −0.334754 | − | 1.53512i | ||||
\(88\) | 2.38113e18 | 0.0854979 | ||||||||
\(89\) | 1.06627e19i | 0.341955i | 0.985275 | + | 0.170977i | \(0.0546925\pi\) | ||||
−0.985275 | + | 0.170977i | \(0.945307\pi\) | |||||||
\(90\) | 2.05408e19 | − | 9.40564e18i | 0.589105 | − | 0.269751i | ||||
\(91\) | 3.83680e18 | 0.0985271 | ||||||||
\(92\) | 3.02822e19i | 0.697123i | ||||||||
\(93\) | −7.68474e19 | + | 1.67576e19i | −1.58781 | + | 0.346244i | ||||
\(94\) | 1.88066e19 | 0.349167 | ||||||||
\(95\) | 7.27940e19i | 1.21579i | ||||||||
\(96\) | 2.50399e18 | + | 1.14828e19i | 0.0376634 | + | 0.172718i | ||||
\(97\) | −6.98216e19 | −0.946831 | −0.473416 | − | 0.880839i | \(-0.656979\pi\) | ||||
−0.473416 | + | 0.880839i | \(0.656979\pi\) | |||||||
\(98\) | 5.69380e19i | 0.696853i | ||||||||
\(99\) | −9.10520e18 | − | 1.98847e19i | −0.100679 | − | 0.219870i | ||||
\(100\) | −8.01893e18 | −0.0801893 | ||||||||
\(101\) | − | 2.06224e19i | − | 0.186692i | −0.995634 | − | 0.0933458i | \(-0.970244\pi\) | ||
0.995634 | − | 0.0933458i | \(-0.0297562\pi\) | |||||||
\(102\) | 1.36559e20 | − | 2.97786e19i | 1.12026 | − | 0.244288i | ||||
\(103\) | 1.43042e20 | 1.06436 | 0.532182 | − | 0.846630i | \(-0.321372\pi\) | ||||
0.532182 | + | 0.846630i | \(0.321372\pi\) | |||||||
\(104\) | − | 4.28196e19i | − | 0.289274i | ||||||
\(105\) | 3.82940e18 | + | 1.75610e19i | 0.0235092 | + | 0.107809i | ||||
\(106\) | −1.43349e20 | −0.800455 | ||||||||
\(107\) | − | 5.16777e19i | − | 0.262703i | −0.991336 | − | 0.131352i | \(-0.958068\pi\) | ||
0.991336 | − | 0.131352i | \(-0.0419317\pi\) | |||||||
\(108\) | 8.63178e19 | − | 6.48200e19i | 0.399818 | − | 0.300242i | ||||
\(109\) | −1.71463e20 | −0.724280 | −0.362140 | − | 0.932124i | \(-0.617954\pi\) | ||||
−0.362140 | + | 0.932124i | \(0.617954\pi\) | |||||||
\(110\) | − | 4.06401e19i | − | 0.156685i | ||||||
\(111\) | −9.52945e19 | + | 2.07802e19i | −0.335613 | + | 0.0731847i | ||||
\(112\) | −9.35021e18 | −0.0301052 | ||||||||
\(113\) | − | 5.90152e20i | − | 1.73852i | −0.494356 | − | 0.869260i | \(-0.664596\pi\) | ||
0.494356 | − | 0.869260i | \(-0.335404\pi\) | |||||||
\(114\) | 7.41047e19 | + | 3.39831e20i | 0.199893 | + | 0.916674i | ||||
\(115\) | 5.16844e20 | 1.27756 | ||||||||
\(116\) | − | 3.46562e20i | − | 0.785599i | ||||||
\(117\) | −3.57585e20 | + | 1.63738e20i | −0.743911 | + | 0.340637i | ||||
\(118\) | −5.59800e20 | −1.06958 | ||||||||
\(119\) | 1.11197e20i | 0.195265i | ||||||||
\(120\) | 1.95984e20 | − | 4.27370e19i | 0.316526 | − | 0.0690226i | ||||
\(121\) | 6.33408e20 | 0.941521 | ||||||||
\(122\) | 8.94902e19i | 0.122512i | ||||||||
\(123\) | 2.40247e20 | + | 1.10173e21i | 0.303114 | + | 1.39003i | ||||
\(124\) | −6.98352e20 | −0.812564 | ||||||||
\(125\) | 9.90243e20i | 1.06326i | ||||||||
\(126\) | 3.57543e19 | + | 7.80832e19i | 0.0354505 | + | 0.0774198i | ||||
\(127\) | 1.01666e21 | 0.931403 | 0.465701 | − | 0.884942i | \(-0.345802\pi\) | ||||
0.465701 | + | 0.884942i | \(0.345802\pi\) | |||||||
\(128\) | 1.04351e20i | 0.0883883i | ||||||||
\(129\) | −1.13316e21 | + | 2.47100e20i | −0.887959 | + | 0.193631i | ||||
\(130\) | −7.30828e20 | −0.530129 | ||||||||
\(131\) | − | 1.29442e21i | − | 0.869688i | −0.900506 | − | 0.434844i | \(-0.856804\pi\) | ||
0.900506 | − | 0.434844i | \(-0.143196\pi\) | |||||||
\(132\) | −4.13718e19 | − | 1.89724e20i | −0.0257611 | − | 0.118136i | ||||
\(133\) | −2.76717e20 | −0.159779 | ||||||||
\(134\) | 2.42692e20i | 0.130019i | ||||||||
\(135\) | −1.10632e21 | − | 1.47324e21i | −0.550229 | − | 0.732714i | ||||
\(136\) | 1.24099e21 | 0.573294 | ||||||||
\(137\) | − | 1.30008e21i | − | 0.558166i | −0.960267 | − | 0.279083i | \(-0.909970\pi\) | ||
0.960267 | − | 0.279083i | \(-0.0900304\pi\) | |||||||
\(138\) | 2.41283e21 | − | 5.26150e20i | 0.963245 | − | 0.210048i | ||||
\(139\) | 4.71307e20 | 0.175048 | 0.0875238 | − | 0.996162i | \(-0.472105\pi\) | ||||
0.0875238 | + | 0.996162i | \(0.472105\pi\) | |||||||
\(140\) | 1.59585e20i | 0.0551713i | ||||||||
\(141\) | −3.26763e20 | − | 1.49848e21i | −0.105206 | − | 0.482459i | ||||
\(142\) | 1.16685e21 | 0.350051 | ||||||||
\(143\) | 7.07483e20i | 0.197859i | ||||||||
\(144\) | 8.71427e20 | − | 3.99026e20i | 0.227304 | − | 0.104082i | ||||
\(145\) | −5.91497e21 | −1.43970 | ||||||||
\(146\) | − | 2.66794e20i | − | 0.0606243i | ||||||
\(147\) | 4.53672e21 | − | 9.89291e20i | 0.962872 | − | 0.209967i | ||||
\(148\) | −8.65990e20 | −0.171750 | ||||||||
\(149\) | 5.11768e21i | 0.948878i | 0.880288 | + | 0.474439i | \(0.157349\pi\) | ||||
−0.880288 | + | 0.474439i | \(0.842651\pi\) | |||||||
\(150\) | 1.39328e20 | + | 6.38934e20i | 0.0241616 | + | 0.110801i | ||||
\(151\) | 4.26746e21 | 0.692469 | 0.346234 | − | 0.938148i | \(-0.387460\pi\) | ||||
0.346234 | + | 0.938148i | \(0.387460\pi\) | |||||||
\(152\) | 3.08822e21i | 0.469108i | ||||||||
\(153\) | −4.74541e21 | − | 1.03634e22i | −0.675086 | − | 1.47431i | ||||
\(154\) | 1.54488e20 | 0.0205914 | ||||||||
\(155\) | 1.19192e22i | 1.48912i | ||||||||
\(156\) | −3.41180e21 | + | 7.43987e20i | −0.399703 | + | 0.0871604i | ||||
\(157\) | −1.25544e22 | −1.37975 | −0.689874 | − | 0.723930i | \(-0.742334\pi\) | ||||
−0.689874 | + | 0.723930i | \(0.742334\pi\) | |||||||
\(158\) | − | 1.47288e21i | − | 0.151913i | ||||||
\(159\) | 2.49068e21 | + | 1.14218e22i | 0.241183 | + | 1.10602i | ||||
\(160\) | 1.78101e21 | 0.161982 | ||||||||
\(161\) | 1.96471e21i | 0.167896i | ||||||||
\(162\) | −6.66451e21 | − | 5.75141e21i | −0.535325 | − | 0.461981i | ||||
\(163\) | 2.46622e22 | 1.86275 | 0.931376 | − | 0.364058i | \(-0.118609\pi\) | ||||
0.931376 | + | 0.364058i | \(0.118609\pi\) | |||||||
\(164\) | 1.00120e22i | 0.711348i | ||||||||
\(165\) | −3.23813e21 | + | 7.06116e20i | −0.216498 | + | 0.0472103i | ||||
\(166\) | 6.04249e21 | 0.380307 | ||||||||
\(167\) | − | 1.78096e22i | − | 1.05558i | −0.849376 | − | 0.527789i | \(-0.823021\pi\) | ||
0.849376 | − | 0.527789i | \(-0.176979\pi\) | |||||||
\(168\) | 1.62459e20 | + | 7.45009e20i | 0.00907090 | + | 0.0415976i | ||||
\(169\) | −6.28235e21 | −0.330564 | ||||||||
\(170\) | − | 2.11806e22i | − | 1.05063i | ||||||
\(171\) | 2.57896e22 | − | 1.18091e22i | 1.20638 | − | 0.552401i | ||||
\(172\) | −1.02976e22 | −0.454413 | ||||||||
\(173\) | − | 4.02033e22i | − | 1.67417i | −0.547069 | − | 0.837087i | \(-0.684257\pi\) | ||
0.547069 | − | 0.837087i | \(-0.315743\pi\) | |||||||
\(174\) | −2.76135e22 | + | 6.02147e21i | −1.08550 | + | 0.236707i | ||||
\(175\) | −5.20269e20 | −0.0193129 | ||||||||
\(176\) | − | 1.72412e21i | − | 0.0604562i | ||||||
\(177\) | 9.72646e21 | + | 4.46039e22i | 0.322272 | + | 1.47788i | ||||
\(178\) | 7.72065e21 | 0.241799 | ||||||||
\(179\) | 1.83768e22i | 0.544176i | 0.962272 | + | 0.272088i | \(0.0877141\pi\) | ||||
−0.962272 | + | 0.272088i | \(0.912286\pi\) | |||||||
\(180\) | −6.81041e21 | − | 1.48731e22i | −0.190743 | − | 0.416560i | ||||
\(181\) | −3.72326e22 | −0.986592 | −0.493296 | − | 0.869862i | \(-0.664208\pi\) | ||||
−0.493296 | + | 0.869862i | \(0.664208\pi\) | |||||||
\(182\) | − | 2.77814e21i | − | 0.0696692i | ||||||
\(183\) | 7.13043e21 | − | 1.55488e21i | 0.169280 | − | 0.0369136i | ||||
\(184\) | 2.19267e22 | 0.492940 | ||||||||
\(185\) | 1.47804e22i | 0.314751i | ||||||||
\(186\) | 1.21338e22 | + | 5.56435e22i | 0.244831 | + | 1.12275i | ||||
\(187\) | −2.05040e22 | −0.392124 | ||||||||
\(188\) | − | 1.36175e22i | − | 0.246898i | ||||||
\(189\) | 5.60031e21 | − | 4.20553e21i | 0.0962928 | − | 0.0723107i | ||||
\(190\) | 5.27085e22 | 0.859695 | ||||||||
\(191\) | − | 9.66181e21i | − | 0.149529i | −0.997201 | − | 0.0747644i | \(-0.976180\pi\) | ||
0.997201 | − | 0.0747644i | \(-0.0238205\pi\) | |||||||
\(192\) | 8.31447e21 | − | 1.81308e21i | 0.122130 | − | 0.0266320i | ||||
\(193\) | −4.32416e22 | −0.603016 | −0.301508 | − | 0.953464i | \(-0.597490\pi\) | ||||
−0.301508 | + | 0.953464i | \(0.597490\pi\) | |||||||
\(194\) | 5.05563e22i | 0.669511i | ||||||||
\(195\) | 1.26980e22 | + | 5.82311e22i | 0.159732 | + | 0.732502i | ||||
\(196\) | 4.12275e22 | 0.492749 | ||||||||
\(197\) | − | 2.07513e22i | − | 0.235713i | −0.993031 | − | 0.117856i | \(-0.962398\pi\) | ||
0.993031 | − | 0.117856i | \(-0.0376022\pi\) | |||||||
\(198\) | −1.43981e22 | + | 6.59287e21i | −0.155472 | + | 0.0711906i | ||||
\(199\) | −1.69741e23 | −1.74283 | −0.871415 | − | 0.490547i | \(-0.836797\pi\) | ||||
−0.871415 | + | 0.490547i | \(0.836797\pi\) | |||||||
\(200\) | 5.80632e21i | 0.0567024i | ||||||||
\(201\) | 1.93373e22 | − | 4.21674e21i | 0.179653 | − | 0.0391757i | ||||
\(202\) | −1.49322e22 | −0.132011 | ||||||||
\(203\) | − | 2.24850e22i | − | 0.189205i | ||||||
\(204\) | −2.15620e22 | − | 9.88796e22i | −0.172738 | − | 0.792146i | ||||
\(205\) | 1.70880e23 | 1.30363 | ||||||||
\(206\) | − | 1.03573e23i | − | 0.752618i | ||||||
\(207\) | −8.38454e22 | − | 1.83109e23i | −0.580465 | − | 1.26767i | ||||
\(208\) | −3.10047e22 | −0.204548 | ||||||||
\(209\) | − | 5.10248e22i | − | 0.320862i | ||||||
\(210\) | 1.27155e22 | − | 2.77278e21i | 0.0762325 | − | 0.0166235i | ||||
\(211\) | 3.30449e23 | 1.88921 | 0.944605 | − | 0.328210i | \(-0.106445\pi\) | ||||
0.944605 | + | 0.328210i | \(0.106445\pi\) | |||||||
\(212\) | 1.03796e23i | 0.566007i | ||||||||
\(213\) | −2.02739e22 | − | 9.29726e22i | −0.105473 | − | 0.483681i | ||||
\(214\) | −3.74186e22 | −0.185759 | ||||||||
\(215\) | 1.75755e23i | 0.832765i | ||||||||
\(216\) | −4.69347e22 | − | 6.25008e22i | −0.212303 | − | 0.282714i | ||||
\(217\) | −4.53091e22 | −0.195699 | ||||||||
\(218\) | 1.24153e23i | 0.512143i | ||||||||
\(219\) | −2.12577e22 | + | 4.63551e21i | −0.0837672 | + | 0.0182665i | ||||
\(220\) | −2.94265e22 | −0.110793 | ||||||||
\(221\) | 3.68723e23i | 1.32671i | ||||||||
\(222\) | 1.50465e22 | + | 6.90006e22i | 0.0517494 | + | 0.237314i | ||||
\(223\) | −2.13081e23 | −0.700640 | −0.350320 | − | 0.936630i | \(-0.613927\pi\) | ||||
−0.350320 | + | 0.936630i | \(0.613927\pi\) | |||||||
\(224\) | 6.77028e21i | 0.0212876i | ||||||||
\(225\) | 4.84884e22 | − | 2.22028e22i | 0.145818 | − | 0.0667703i | ||||
\(226\) | −4.27316e23 | −1.22932 | ||||||||
\(227\) | 1.26750e23i | 0.348889i | 0.984667 | + | 0.174445i | \(0.0558130\pi\) | ||||
−0.984667 | + | 0.174445i | \(0.944187\pi\) | |||||||
\(228\) | 2.46064e23 | − | 5.36575e22i | 0.648187 | − | 0.141346i | ||||
\(229\) | 3.25585e23 | 0.820936 | 0.410468 | − | 0.911875i | \(-0.365365\pi\) | ||||
0.410468 | + | 0.911875i | \(0.365365\pi\) | |||||||
\(230\) | − | 3.74235e23i | − | 0.903371i | ||||||
\(231\) | −2.68421e21 | − | 1.23093e22i | −0.00620435 | − | 0.0284521i | ||||
\(232\) | −2.50938e23 | −0.555502 | ||||||||
\(233\) | 2.33845e23i | 0.495872i | 0.968776 | + | 0.247936i | \(0.0797523\pi\) | ||||
−0.968776 | + | 0.247936i | \(0.920248\pi\) | |||||||
\(234\) | 1.18559e23 | + | 2.58919e23i | 0.240866 | + | 0.526024i | ||||
\(235\) | −2.32417e23 | −0.452470 | ||||||||
\(236\) | 4.05339e23i | 0.756307i | ||||||||
\(237\) | −1.17356e23 | + | 2.55911e22i | −0.209905 | + | 0.0457725i | ||||
\(238\) | 8.05153e22 | 0.138073 | ||||||||
\(239\) | − | 8.68378e23i | − | 1.42801i | −0.700143 | − | 0.714003i | \(-0.746880\pi\) | ||
0.700143 | − | 0.714003i | \(-0.253120\pi\) | |||||||
\(240\) | −3.09449e22 | − | 1.41908e23i | −0.0488063 | − | 0.223818i | ||||
\(241\) | 1.05378e24 | 1.59433 | 0.797167 | − | 0.603759i | \(-0.206331\pi\) | ||||
0.797167 | + | 0.603759i | \(0.206331\pi\) | |||||||
\(242\) | − | 4.58636e23i | − | 0.665756i | ||||||
\(243\) | −3.42468e23 | + | 6.30946e23i | −0.477042 | + | 0.878880i | ||||
\(244\) | 6.47978e22 | 0.0866288 | ||||||||
\(245\) | − | 7.03653e23i | − | 0.903021i | ||||||
\(246\) | 7.97738e23 | − | 1.73957e23i | 0.982900 | − | 0.214334i | ||||
\(247\) | −9.17576e23 | −1.08561 | ||||||||
\(248\) | 5.05661e23i | 0.574569i | ||||||||
\(249\) | −1.04988e23 | − | 4.81455e23i | −0.114589 | − | 0.525487i | ||||
\(250\) | 7.17012e23 | 0.751842 | ||||||||
\(251\) | − | 9.08149e23i | − | 0.914998i | −0.889210 | − | 0.457499i | \(-0.848745\pi\) | ||
0.889210 | − | 0.457499i | \(-0.151255\pi\) | |||||||
\(252\) | 5.65383e22 | − | 2.58889e22i | 0.0547441 | − | 0.0250673i | ||||
\(253\) | −3.62281e23 | −0.337163 | ||||||||
\(254\) | − | 7.36139e23i | − | 0.658601i | ||||||
\(255\) | −1.68764e24 | + | 3.68011e23i | −1.45170 | + | 0.316562i | ||||
\(256\) | 7.55579e22 | 0.0625000 | ||||||||
\(257\) | − | 3.56336e23i | − | 0.283484i | −0.989904 | − | 0.141742i | \(-0.954730\pi\) | ||
0.989904 | − | 0.141742i | \(-0.0452703\pi\) | |||||||
\(258\) | 1.78919e23 | + | 8.20494e23i | 0.136918 | + | 0.627882i | ||||
\(259\) | −5.61856e22 | −0.0413644 | ||||||||
\(260\) | 5.29176e23i | 0.374858i | ||||||||
\(261\) | 9.59561e23 | + | 2.09557e24i | 0.654135 | + | 1.42856i | ||||
\(262\) | −9.37262e23 | −0.614962 | ||||||||
\(263\) | 1.05160e24i | 0.664188i | 0.943246 | + | 0.332094i | \(0.107755\pi\) | ||||
−0.943246 | + | 0.332094i | \(0.892245\pi\) | |||||||
\(264\) | −1.37375e23 | + | 2.99564e22i | −0.0835349 | + | 0.0182159i | ||||
\(265\) | 1.77155e24 | 1.03727 | ||||||||
\(266\) | 2.00364e23i | 0.112981i | ||||||||
\(267\) | −1.34145e23 | − | 6.15168e23i | −0.0728556 | − | 0.334104i | ||||
\(268\) | 1.75728e23 | 0.0919373 | ||||||||
\(269\) | 1.96187e24i | 0.988888i | 0.869209 | + | 0.494444i | \(0.164628\pi\) | ||||
−0.869209 | + | 0.494444i | \(0.835372\pi\) | |||||||
\(270\) | −1.06674e24 | + | 8.01061e23i | −0.518107 | + | 0.389070i | ||||
\(271\) | 2.44812e22 | 0.0114588 | 0.00572940 | − | 0.999984i | \(-0.498176\pi\) | ||||
0.00572940 | + | 0.999984i | \(0.498176\pi\) | |||||||
\(272\) | − | 8.98570e23i | − | 0.405380i | ||||||
\(273\) | −2.21358e23 | + | 4.82699e22i | −0.0962649 | + | 0.0209918i | ||||
\(274\) | −9.41356e23 | −0.394683 | ||||||||
\(275\) | − | 9.59343e22i | − | 0.0387835i | ||||||
\(276\) | −3.80973e23 | − | 1.74708e24i | −0.148526 | − | 0.681117i | ||||
\(277\) | 1.05647e24 | 0.397247 | 0.198623 | − | 0.980076i | \(-0.436353\pi\) | ||||
0.198623 | + | 0.980076i | \(0.436353\pi\) | |||||||
\(278\) | − | 3.41263e23i | − | 0.123777i | ||||||
\(279\) | 4.22275e24 | − | 1.93360e24i | 1.47759 | − | 0.676588i | ||||
\(280\) | 1.15552e23 | 0.0390120 | ||||||||
\(281\) | − | 2.00543e23i | − | 0.0653347i | −0.999466 | − | 0.0326674i | \(-0.989600\pi\) | ||
0.999466 | − | 0.0326674i | \(-0.0104002\pi\) | |||||||
\(282\) | −1.08502e24 | + | 2.36602e23i | −0.341150 | + | 0.0743922i | ||||
\(283\) | −2.42419e24 | −0.735702 | −0.367851 | − | 0.929885i | \(-0.619906\pi\) | ||||
−0.367851 | + | 0.929885i | \(0.619906\pi\) | |||||||
\(284\) | − | 8.44889e23i | − | 0.247524i | ||||||
\(285\) | −9.15804e23 | − | 4.19972e24i | −0.259032 | − | 1.18788i | ||||
\(286\) | 5.12272e23 | 0.139907 | ||||||||
\(287\) | 6.49579e23i | 0.171322i | ||||||||
\(288\) | −2.88926e23 | − | 6.30981e23i | −0.0735973 | − | 0.160728i | ||||
\(289\) | −6.62198e24 | −1.62933 | ||||||||
\(290\) | 4.28290e24i | 1.01802i | ||||||||
\(291\) | 4.02823e24 | − | 8.78409e23i | 0.925092 | − | 0.201728i | ||||
\(292\) | −1.93179e23 | −0.0428679 | ||||||||
\(293\) | − | 2.70956e24i | − | 0.581061i | −0.956866 | − | 0.290531i | \(-0.906168\pi\) | ||
0.956866 | − | 0.290531i | \(-0.0938319\pi\) | |||||||
\(294\) | −7.16323e23 | − | 3.28493e24i | −0.148469 | − | 0.680853i | ||||
\(295\) | 6.91815e24 | 1.38602 | ||||||||
\(296\) | 6.27044e23i | 0.121445i | ||||||||
\(297\) | 7.75473e23 | + | 1.03266e24i | 0.145212 | + | 0.193372i | ||||
\(298\) | 3.70559e24 | 0.670958 | ||||||||
\(299\) | 6.51487e24i | 1.14076i | ||||||||
\(300\) | 4.62638e23 | − | 1.00884e23i | 0.0783481 | − | 0.0170848i | ||||
\(301\) | −6.68108e23 | −0.109441 | ||||||||
\(302\) | − | 3.08997e24i | − | 0.489649i | ||||||
\(303\) | 2.59445e23 | + | 1.18977e24i | 0.0397758 | + | 0.182405i | ||||
\(304\) | 2.23611e24 | 0.331709 | ||||||||
\(305\) | − | 1.10594e24i | − | 0.158757i | ||||||
\(306\) | −7.50392e24 | + | 3.43604e24i | −1.04249 | + | 0.477358i | ||||
\(307\) | −4.68021e24 | −0.629334 | −0.314667 | − | 0.949202i | \(-0.601893\pi\) | ||||
−0.314667 | + | 0.949202i | \(0.601893\pi\) | |||||||
\(308\) | − | 1.11861e23i | − | 0.0145603i | ||||||
\(309\) | −8.25253e24 | + | 1.79957e24i | −1.03993 | + | 0.226769i | ||||
\(310\) | 8.63040e24 | 1.05297 | ||||||||
\(311\) | 1.01483e25i | 1.19892i | 0.800406 | + | 0.599458i | \(0.204617\pi\) | ||||
−0.800406 | + | 0.599458i | \(0.795383\pi\) | |||||||
\(312\) | 5.38704e23 | + | 2.47040e24i | 0.0616317 | + | 0.282632i | ||||
\(313\) | −1.15960e25 | −1.28489 | −0.642443 | − | 0.766334i | \(-0.722079\pi\) | ||||
−0.642443 | + | 0.766334i | \(0.722079\pi\) | |||||||
\(314\) | 9.09036e24i | 0.975629i | ||||||||
\(315\) | −4.41860e23 | − | 9.64972e23i | −0.0459388 | − | 0.100325i | ||||
\(316\) | −1.06648e24 | −0.107419 | ||||||||
\(317\) | − | 1.95397e24i | − | 0.190688i | −0.995444 | − | 0.0953442i | \(-0.969605\pi\) | ||
0.995444 | − | 0.0953442i | \(-0.0303952\pi\) | |||||||
\(318\) | 8.27028e24 | − | 1.80344e24i | 0.782076 | − | 0.170542i | ||||
\(319\) | 4.14609e24 | 0.379955 | ||||||||
\(320\) | − | 1.28959e24i | − | 0.114539i | ||||||
\(321\) | 6.50145e23 | + | 2.98145e24i | 0.0559706 | + | 0.256671i | ||||
\(322\) | 1.42260e24 | 0.118720 | ||||||||
\(323\) | − | 2.65929e25i | − | 2.15150i | ||||||
\(324\) | −4.16447e24 | + | 4.82562e24i | −0.326670 | + | 0.378532i | ||||
\(325\) | −1.72518e24 | −0.131220 | ||||||||
\(326\) | − | 1.78573e25i | − | 1.31717i | ||||||
\(327\) | 9.89227e24 | − | 2.15714e24i | 0.707650 | − | 0.154312i | ||||
\(328\) | 7.24946e24 | 0.502999 | ||||||||
\(329\) | − | 8.83503e23i | − | 0.0594633i | ||||||
\(330\) | 5.11283e23 | + | 2.34466e24i | 0.0333827 | + | 0.153088i | ||||
\(331\) | 3.47626e23 | 0.0220207 | 0.0110104 | − | 0.999939i | \(-0.496495\pi\) | ||||
0.0110104 | + | 0.999939i | \(0.496495\pi\) | |||||||
\(332\) | − | 4.37523e24i | − | 0.268918i | ||||||
\(333\) | 5.23642e24 | − | 2.39776e24i | 0.312314 | − | 0.143009i | ||||
\(334\) | −1.28955e25 | −0.746406 | ||||||||
\(335\) | − | 2.99924e24i | − | 0.168486i | ||||||
\(336\) | 5.39444e23 | − | 1.17633e23i | 0.0294140 | − | 0.00641410i | ||||
\(337\) | 2.00958e25 | 1.06367 | 0.531835 | − | 0.846848i | \(-0.321503\pi\) | ||||
0.531835 | + | 0.846848i | \(0.321503\pi\) | |||||||
\(338\) | 4.54891e24i | 0.233744i | ||||||||
\(339\) | 7.42456e24 | + | 3.40478e25i | 0.370403 | + | 1.69860i | ||||
\(340\) | −1.53364e25 | −0.742907 | ||||||||
\(341\) | − | 8.35472e24i | − | 0.392996i | ||||||
\(342\) | −8.55068e24 | − | 1.86737e25i | −0.390607 | − | 0.853039i | ||||
\(343\) | 5.38905e24 | 0.239095 | ||||||||
\(344\) | 7.45625e24i | 0.321319i | ||||||||
\(345\) | −2.98184e25 | + | 6.50229e24i | −1.24823 | + | 0.272192i | ||||
\(346\) | −2.91103e25 | −1.18382 | ||||||||
\(347\) | − | 1.98604e25i | − | 0.784682i | −0.919820 | − | 0.392341i | \(-0.871665\pi\) | ||
0.919820 | − | 0.392341i | \(-0.128335\pi\) | |||||||
\(348\) | 4.36001e24 | + | 1.99943e25i | 0.167377 | + | 0.767562i | ||||
\(349\) | 6.39167e24 | 0.238430 | 0.119215 | − | 0.992868i | \(-0.461962\pi\) | ||||
0.119215 | + | 0.992868i | \(0.461962\pi\) | |||||||
\(350\) | 3.76715e23i | 0.0136563i | ||||||||
\(351\) | 1.85703e25 | − | 1.39453e25i | 0.654256 | − | 0.491310i | ||||
\(352\) | −1.24840e24 | −0.0427490 | ||||||||
\(353\) | 3.71258e25i | 1.23574i | 0.786279 | + | 0.617872i | \(0.212005\pi\) | ||||
−0.786279 | + | 0.617872i | \(0.787995\pi\) | |||||||
\(354\) | 3.22967e25 | − | 7.04271e24i | 1.04502 | − | 0.227881i | ||||
\(355\) | −1.44202e25 | −0.453616 | ||||||||
\(356\) | − | 5.59035e24i | − | 0.170977i | ||||||
\(357\) | −1.39894e24 | − | 6.41532e24i | −0.0416024 | − | 0.190781i | ||||
\(358\) | 1.33062e25 | 0.384790 | ||||||||
\(359\) | 5.59063e25i | 1.57223i | 0.618080 | + | 0.786115i | \(0.287911\pi\) | ||||
−0.618080 | + | 0.786115i | \(0.712089\pi\) | |||||||
\(360\) | −1.07693e25 | + | 4.93127e24i | −0.294553 | + | 0.134876i | ||||
\(361\) | 2.85871e25 | 0.760498 | ||||||||
\(362\) | 2.69593e25i | 0.697626i | ||||||||
\(363\) | −3.65434e25 | + | 7.96876e24i | −0.919903 | + | 0.200597i | ||||
\(364\) | −2.01159e24 | −0.0492636 | ||||||||
\(365\) | 3.29710e24i | 0.0785604i | ||||||||
\(366\) | −1.12586e24 | − | 5.16298e24i | −0.0261019 | − | 0.119699i | ||||
\(367\) | 1.51052e24 | 0.0340774 | 0.0170387 | − | 0.999855i | \(-0.494576\pi\) | ||||
0.0170387 | + | 0.999855i | \(0.494576\pi\) | |||||||
\(368\) | − | 1.58766e25i | − | 0.348561i | ||||||
\(369\) | −2.77212e25 | − | 6.05399e25i | −0.592309 | − | 1.29353i | ||||
\(370\) | 1.07021e25 | 0.222563 | ||||||||
\(371\) | 6.73429e24i | 0.136318i | ||||||||
\(372\) | 4.02902e25 | − | 8.78580e24i | 0.793907 | − | 0.173122i | ||||
\(373\) | 1.98247e25 | 0.380293 | 0.190146 | − | 0.981756i | \(-0.439104\pi\) | ||||
0.190146 | + | 0.981756i | \(0.439104\pi\) | |||||||
\(374\) | 1.48465e25i | 0.277273i | ||||||||
\(375\) | −1.24580e25 | − | 5.71303e25i | −0.226535 | − | 1.03885i | ||||
\(376\) | −9.86010e24 | −0.174583 | ||||||||
\(377\) | − | 7.45588e25i | − | 1.28554i | ||||||
\(378\) | −3.04513e24 | − | 4.05506e24i | −0.0511314 | − | 0.0680893i | ||||
\(379\) | 2.76776e25 | 0.452622 | 0.226311 | − | 0.974055i | \(-0.427333\pi\) | ||||
0.226311 | + | 0.974055i | \(0.427333\pi\) | |||||||
\(380\) | − | 3.81650e25i | − | 0.607896i | ||||||
\(381\) | −5.86543e25 | + | 1.27903e25i | −0.910018 | + | 0.198441i | ||||
\(382\) | −6.99590e24 | −0.105733 | ||||||||
\(383\) | − | 2.45606e25i | − | 0.361620i | −0.983518 | − | 0.180810i | \(-0.942128\pi\) | ||
0.983518 | − | 0.180810i | \(-0.0578718\pi\) | |||||||
\(384\) | −1.31281e24 | − | 6.02032e24i | −0.0188317 | − | 0.0863589i | ||||
\(385\) | −1.90920e24 | −0.0266835 | ||||||||
\(386\) | 3.13103e25i | 0.426397i | ||||||||
\(387\) | 6.22668e25 | − | 2.85120e25i | 0.826317 | − | 0.378371i | ||||
\(388\) | 3.66066e25 | 0.473416 | ||||||||
\(389\) | 1.14023e26i | 1.43713i | 0.695461 | + | 0.718564i | \(0.255200\pi\) | ||||
−0.695461 | + | 0.718564i | \(0.744800\pi\) | |||||||
\(390\) | 4.21638e25 | − | 9.19437e24i | 0.517957 | − | 0.112947i | ||||
\(391\) | −1.88812e26 | −2.26080 | ||||||||
\(392\) | − | 2.98519e25i | − | 0.348426i | ||||||
\(393\) | 1.62848e25 | + | 7.46794e25i | 0.185292 | + | 0.849719i | ||||
\(394\) | −1.50255e25 | −0.166674 | ||||||||
\(395\) | 1.82022e25i | 0.196858i | ||||||||
\(396\) | 4.77375e24 | + | 1.04253e25i | 0.0503393 | + | 0.109935i | ||||
\(397\) | 1.65157e26 | 1.69822 | 0.849108 | − | 0.528219i | \(-0.177140\pi\) | ||||
0.849108 | + | 0.528219i | \(0.177140\pi\) | |||||||
\(398\) | 1.22905e26i | 1.23237i | ||||||||
\(399\) | 1.59647e25 | − | 3.48131e24i | 0.156110 | − | 0.0340419i | ||||
\(400\) | 4.20423e24 | 0.0400946 | ||||||||
\(401\) | − | 4.85521e25i | − | 0.451611i | −0.974172 | − | 0.225805i | \(-0.927499\pi\) | ||
0.974172 | − | 0.225805i | \(-0.0725014\pi\) | |||||||
\(402\) | −3.05325e24 | − | 1.40017e25i | −0.0277014 | − | 0.127034i | ||||
\(403\) | −1.50242e26 | −1.32966 | ||||||||
\(404\) | 1.08121e25i | 0.0933458i | ||||||||
\(405\) | 8.23616e25 | + | 7.10774e25i | 0.693705 | + | 0.598661i | ||||
\(406\) | −1.62809e25 | −0.133788 | ||||||||
\(407\) | − | 1.03603e25i | − | 0.0830666i | ||||||
\(408\) | −7.15965e25 | + | 1.56125e25i | −0.560131 | + | 0.122144i | ||||
\(409\) | 1.02044e26 | 0.779032 | 0.389516 | − | 0.921020i | \(-0.372642\pi\) | ||||
0.389516 | + | 0.921020i | \(0.372642\pi\) | |||||||
\(410\) | − | 1.23731e26i | − | 0.921804i | ||||||
\(411\) | 1.63560e25 | + | 7.50056e25i | 0.118921 | + | 0.545350i | ||||
\(412\) | −7.49949e25 | −0.532182 | ||||||||
\(413\) | 2.62984e25i | 0.182150i | ||||||||
\(414\) | −1.32585e26 | + | 6.07106e25i | −0.896376 | + | 0.410451i | ||||
\(415\) | −7.46745e25 | −0.492824 | ||||||||
\(416\) | 2.24498e25i | 0.144637i | ||||||||
\(417\) | −2.71912e25 | + | 5.92941e24i | −0.171029 | + | 0.0372950i | ||||
\(418\) | −3.69459e25 | −0.226884 | ||||||||
\(419\) | − | 1.36478e26i | − | 0.818320i | −0.912463 | − | 0.409160i | \(-0.865822\pi\) | ||
0.912463 | − | 0.409160i | \(-0.134178\pi\) | |||||||
\(420\) | −2.00771e24 | − | 9.20700e24i | −0.0117546 | − | 0.0539045i | ||||
\(421\) | 2.27236e26 | 1.29914 | 0.649572 | − | 0.760300i | \(-0.274948\pi\) | ||||
0.649572 | + | 0.760300i | \(0.274948\pi\) | |||||||
\(422\) | − | 2.39271e26i | − | 1.33587i | ||||||
\(423\) | 3.77041e25 | + | 8.23413e25i | 0.205582 | + | 0.448966i | ||||
\(424\) | 7.51563e25 | 0.400227 | ||||||||
\(425\) | − | 4.99987e25i | − | 0.260057i | ||||||
\(426\) | −6.73193e25 | + | 1.46799e25i | −0.342014 | + | 0.0745806i | ||||
\(427\) | 4.20409e24 | 0.0208638 | ||||||||
\(428\) | 2.70940e25i | 0.131352i | ||||||||
\(429\) | −8.90067e24 | − | 4.08170e25i | −0.0421551 | − | 0.193316i | ||||
\(430\) | 1.27260e26 | 0.588854 | ||||||||
\(431\) | − | 1.13707e26i | − | 0.514062i | −0.966403 | − | 0.257031i | \(-0.917256\pi\) | ||
0.966403 | − | 0.257031i | \(-0.0827443\pi\) | |||||||
\(432\) | −4.52554e25 | + | 3.39843e25i | −0.199909 | + | 0.150121i | ||||
\(433\) | 8.08804e24 | 0.0349112 | 0.0174556 | − | 0.999848i | \(-0.494443\pi\) | ||||
0.0174556 | + | 0.999848i | \(0.494443\pi\) | |||||||
\(434\) | 3.28073e25i | 0.138380i | ||||||||
\(435\) | 3.41254e26 | − | 7.44149e25i | 1.40665 | − | 0.306738i | ||||
\(436\) | 8.98962e25 | 0.362140 | ||||||||
\(437\) | − | 4.69863e26i | − | 1.84994i | ||||||
\(438\) | 3.35647e24 | + | 1.53922e25i | 0.0129164 | + | 0.0592324i | ||||
\(439\) | −4.09891e26 | −1.54178 | −0.770892 | − | 0.636966i | \(-0.780189\pi\) | ||||
−0.770892 | + | 0.636966i | \(0.780189\pi\) | |||||||
\(440\) | 2.13071e25i | 0.0783425i | ||||||||
\(441\) | −2.49292e26 | + | 1.14151e26i | −0.896029 | + | 0.410292i | ||||
\(442\) | 2.66984e26 | 0.938129 | ||||||||
\(443\) | 4.13953e26i | 1.42205i | 0.703168 | + | 0.711024i | \(0.251768\pi\) | ||||
−0.703168 | + | 0.711024i | \(0.748232\pi\) | |||||||
\(444\) | 4.99618e25 | − | 1.08948e25i | 0.167806 | − | 0.0365924i | ||||
\(445\) | −9.54137e25 | −0.313336 | ||||||||
\(446\) | 1.54287e26i | 0.495427i | ||||||||
\(447\) | −6.43843e25 | − | 2.95255e26i | −0.202164 | − | 0.927091i | ||||
\(448\) | 4.90220e24 | 0.0150526 | ||||||||
\(449\) | 4.87243e26i | 1.46313i | 0.681774 | + | 0.731563i | \(0.261209\pi\) | ||||
−0.681774 | + | 0.731563i | \(0.738791\pi\) | |||||||
\(450\) | −1.60766e25 | − | 3.51093e25i | −0.0472137 | − | 0.103109i | ||||
\(451\) | −1.19778e26 | −0.344043 | ||||||||
\(452\) | 3.09410e26i | 0.869260i | ||||||||
\(453\) | −2.46204e26 | + | 5.36879e25i | −0.676570 | + | 0.147535i | ||||
\(454\) | 9.17765e25 | 0.246702 | ||||||||
\(455\) | 3.43330e25i | 0.0902812i | ||||||||
\(456\) | −3.88522e25 | − | 1.78170e26i | −0.0999464 | − | 0.458337i | ||||
\(457\) | −3.83152e26 | −0.964293 | −0.482146 | − | 0.876091i | \(-0.660143\pi\) | ||||
−0.482146 | + | 0.876091i | \(0.660143\pi\) | |||||||
\(458\) | − | 2.35749e26i | − | 0.580490i | ||||||
\(459\) | 4.04158e26 | + | 5.38198e26i | 0.973697 | + | 1.29663i | ||||
\(460\) | −2.70975e26 | −0.638780 | ||||||||
\(461\) | 6.01682e26i | 1.38790i | 0.720024 | + | 0.693949i | \(0.244131\pi\) | ||||
−0.720024 | + | 0.693949i | \(0.755869\pi\) | |||||||
\(462\) | −8.91290e24 | + | 1.94357e24i | −0.0201187 | + | 0.00438714i | ||||
\(463\) | 3.27432e26 | 0.723287 | 0.361644 | − | 0.932316i | \(-0.382216\pi\) | ||||
0.361644 | + | 0.932316i | \(0.382216\pi\) | |||||||
\(464\) | 1.81698e26i | 0.392800i | ||||||||
\(465\) | −1.49952e26 | − | 6.87656e26i | −0.317266 | − | 1.45493i | ||||
\(466\) | 1.69322e26 | 0.350635 | ||||||||
\(467\) | − | 7.17003e26i | − | 1.45329i | −0.687013 | − | 0.726645i | \(-0.741078\pi\) | ||
0.687013 | − | 0.726645i | \(-0.258922\pi\) | |||||||
\(468\) | 1.87478e26 | − | 8.58460e25i | 0.371955 | − | 0.170318i | ||||
\(469\) | 1.14012e25 | 0.0221423 | ||||||||
\(470\) | 1.68288e26i | 0.319944i | ||||||||
\(471\) | 7.24304e26 | − | 1.57944e26i | 1.34807 | − | 0.293964i | ||||
\(472\) | 2.93497e26 | 0.534790 | ||||||||
\(473\) | − | 1.23195e26i | − | 0.219777i | ||||||
\(474\) | 1.85299e25 | + | 8.49750e25i | 0.0323661 | + | 0.148425i | ||||
\(475\) | 1.24423e26 | 0.212796 | ||||||||
\(476\) | − | 5.82993e25i | − | 0.0976324i | ||||||
\(477\) | −2.87390e26 | − | 6.27627e26i | −0.471290 | − | 1.02924i | ||||
\(478\) | −6.28773e26 | −1.00975 | ||||||||
\(479\) | 9.67519e26i | 1.52161i | 0.648978 | + | 0.760807i | \(0.275197\pi\) | ||||
−0.648978 | + | 0.760807i | \(0.724803\pi\) | |||||||
\(480\) | −1.02752e26 | + | 2.24065e25i | −0.158263 | + | 0.0345113i | ||||
\(481\) | −1.86308e26 | −0.281048 | ||||||||
\(482\) | − | 7.63018e26i | − | 1.12736i | ||||||
\(483\) | −2.47176e25 | − | 1.13351e26i | −0.0357713 | − | 0.164041i | ||||
\(484\) | −3.32088e26 | −0.470760 | ||||||||
\(485\) | − | 6.24787e26i | − | 0.867590i | ||||||
\(486\) | 4.56854e26 | + | 2.47973e26i | 0.621462 | + | 0.337320i | ||||
\(487\) | 1.81474e26 | 0.241838 | 0.120919 | − | 0.992662i | \(-0.461416\pi\) | ||||
0.120919 | + | 0.992662i | \(0.461416\pi\) | |||||||
\(488\) | − | 4.69186e25i | − | 0.0612558i | ||||||
\(489\) | −1.42284e27 | + | 3.10269e26i | −1.81998 | + | 0.396871i | ||||
\(490\) | −5.09499e26 | −0.638532 | ||||||||
\(491\) | − | 2.54099e26i | − | 0.312024i | −0.987755 | − | 0.156012i | \(-0.950136\pi\) | ||
0.987755 | − | 0.156012i | \(-0.0498639\pi\) | |||||||
\(492\) | −1.25958e26 | − | 5.77624e26i | −0.151557 | − | 0.695015i | ||||
\(493\) | 2.16084e27 | 2.54773 | ||||||||
\(494\) | 6.64396e26i | 0.767640i | ||||||||
\(495\) | 1.77935e26 | − | 8.14763e25i | 0.201469 | − | 0.0922527i | ||||
\(496\) | 3.66137e26 | 0.406282 | ||||||||
\(497\) | − | 5.48165e25i | − | 0.0596139i | ||||||
\(498\) | −3.48611e26 | + | 7.60191e25i | −0.371576 | + | 0.0810269i | ||||
\(499\) | 1.56657e25 | 0.0163661 | 0.00818306 | − | 0.999967i | \(-0.497395\pi\) | ||||
0.00818306 | + | 0.999967i | \(0.497395\pi\) | |||||||
\(500\) | − | 5.19172e26i | − | 0.531632i | ||||||
\(501\) | 2.24059e26 | + | 1.02749e27i | 0.224897 | + | 1.03134i | ||||
\(502\) | −6.57570e26 | −0.647001 | ||||||||
\(503\) | 1.98270e25i | 0.0191240i | 0.999954 | + | 0.00956198i | \(0.00304372\pi\) | ||||
−0.999954 | + | 0.00956198i | \(0.996956\pi\) | |||||||
\(504\) | −1.87456e25 | − | 4.09381e25i | −0.0177253 | − | 0.0387099i | ||||
\(505\) | 1.84536e26 | 0.171067 | ||||||||
\(506\) | 2.62319e26i | 0.238410i | ||||||||
\(507\) | 3.62449e26 | − | 7.90367e25i | 0.322974 | − | 0.0704287i | ||||
\(508\) | −5.33021e26 | −0.465701 | ||||||||
\(509\) | 5.01291e26i | 0.429450i | 0.976675 | + | 0.214725i | \(0.0688855\pi\) | ||||
−0.976675 | + | 0.214725i | \(0.931115\pi\) | |||||||
\(510\) | 2.66468e26 | + | 1.22198e27i | 0.223843 | + | 1.02651i | ||||
\(511\) | −1.25335e25 | −0.0103244 | ||||||||
\(512\) | − | 5.47097e25i | − | 0.0441942i | ||||||
\(513\) | −1.33932e27 | + | 1.00576e27i | −1.06099 | + | 0.796745i | ||||
\(514\) | −2.58014e26 | −0.200453 | ||||||||
\(515\) | 1.27998e27i | 0.975285i | ||||||||
\(516\) | 5.94101e26 | − | 1.29551e26i | 0.443980 | − | 0.0968156i | ||||
\(517\) | 1.62912e26 | 0.119412 | ||||||||
\(518\) | 4.06827e25i | 0.0292491i | ||||||||
\(519\) | 5.05788e26 | + | 2.31946e27i | 0.356693 | + | 1.63574i | ||||
\(520\) | 3.83164e26 | 0.265064 | ||||||||
\(521\) | − | 2.48658e27i | − | 1.68743i | −0.536792 | − | 0.843714i | \(-0.680364\pi\) | ||
0.536792 | − | 0.843714i | \(-0.319636\pi\) | |||||||
\(522\) | 1.51735e27 | − | 6.94797e26i | 1.01014 | − | 0.462544i | ||||
\(523\) | −2.14559e27 | −1.40130 | −0.700649 | − | 0.713506i | \(-0.747106\pi\) | ||||
−0.700649 | + | 0.713506i | \(0.747106\pi\) | |||||||
\(524\) | 6.78650e26i | 0.434844i | ||||||||
\(525\) | 3.00160e25 | − | 6.54538e24i | 0.0188695 | − | 0.00411474i | ||||
\(526\) | 7.61437e26 | 0.469652 | ||||||||
\(527\) | − | 4.35428e27i | − | 2.63518i | ||||||
\(528\) | 2.16907e25 | + | 9.94700e25i | 0.0128806 | + | 0.0590681i | ||||
\(529\) | −1.61991e27 | −0.943921 | ||||||||
\(530\) | − | 1.28274e27i | − | 0.733464i | ||||||
\(531\) | −1.12230e27 | − | 2.45098e27i | −0.629745 | − | 1.37529i | ||||
\(532\) | 1.45079e26 | 0.0798894 | ||||||||
\(533\) | 2.15397e27i | 1.16404i | ||||||||
\(534\) | −4.45429e26 | + | 9.71316e25i | −0.236247 | + | 0.0515167i | ||||
\(535\) | 4.62429e26 | 0.240717 | ||||||||
\(536\) | − | 1.27240e26i | − | 0.0650095i | ||||||
\(537\) | −2.31194e26 | − | 1.06022e27i | −0.115940 | − | 0.531681i | ||||
\(538\) | 1.42055e27 | 0.699250 | ||||||||
\(539\) | 4.93224e26i | 0.238318i | ||||||||
\(540\) | 5.80030e26 | + | 7.72400e26i | 0.275114 | + | 0.366357i | ||||
\(541\) | 1.38669e27 | 0.645666 | 0.322833 | − | 0.946456i | \(-0.395365\pi\) | ||||
0.322833 | + | 0.946456i | \(0.395365\pi\) | |||||||
\(542\) | − | 1.77263e25i | − | 0.00810259i | ||||||
\(543\) | 2.14807e27 | − | 4.68414e26i | 0.963940 | − | 0.210200i | ||||
\(544\) | −6.50634e26 | −0.286647 | ||||||||
\(545\) | − | 1.53431e27i | − | 0.663664i | ||||||
\(546\) | 3.49512e25 | + | 1.60280e26i | 0.0148435 | + | 0.0680696i | ||||
\(547\) | 4.53095e26 | 0.188936 | 0.0944682 | − | 0.995528i | \(-0.469885\pi\) | ||||
0.0944682 | + | 0.995528i | \(0.469885\pi\) | |||||||
\(548\) | 6.81615e26i | 0.279083i | ||||||||
\(549\) | −3.91816e26 | + | 1.79412e26i | −0.157528 | + | 0.0721322i | ||||
\(550\) | −6.94639e25 | −0.0274241 | ||||||||
\(551\) | 5.37731e27i | 2.08472i | ||||||||
\(552\) | −1.26502e27 | + | 2.75854e26i | −0.481622 | + | 0.105024i | ||||
\(553\) | −6.91931e25 | −0.0258709 | ||||||||
\(554\) | − | 7.64967e26i | − | 0.280896i | ||||||
\(555\) | −1.85948e26 | − | 8.52727e26i | −0.0670598 | − | 0.307525i | ||||
\(556\) | −2.47101e26 | −0.0875238 | ||||||||
\(557\) | − | 6.94941e26i | − | 0.241767i | −0.992667 | − | 0.120883i | \(-0.961427\pi\) | ||
0.992667 | − | 0.120883i | \(-0.0385727\pi\) | |||||||
\(558\) | −1.40007e27 | − | 3.05760e27i | −0.478420 | − | 1.04481i | ||||
\(559\) | −2.21541e27 | −0.743593 | ||||||||
\(560\) | − | 8.36687e25i | − | 0.0275856i | ||||||
\(561\) | 1.18294e27 | − | 2.57956e26i | 0.383121 | − | 0.0835445i | ||||
\(562\) | −1.45209e26 | −0.0461986 | ||||||||
\(563\) | 1.02406e27i | 0.320067i | 0.987112 | + | 0.160033i | \(0.0511602\pi\) | ||||
−0.987112 | + | 0.160033i | \(0.948840\pi\) | |||||||
\(564\) | 1.71318e26 | + | 7.85636e26i | 0.0526032 | + | 0.241229i | ||||
\(565\) | 5.28087e27 | 1.59302 | ||||||||
\(566\) | 1.75530e27i | 0.520220i | ||||||||
\(567\) | −2.70191e26 | + | 3.13087e26i | −0.0786757 | + | 0.0911662i | ||||
\(568\) | −6.11765e26 | −0.175026 | ||||||||
\(569\) | 5.02276e27i | 1.41195i | 0.708236 | + | 0.705975i | \(0.249491\pi\) | ||||
−0.708236 | + | 0.705975i | \(0.750509\pi\) | |||||||
\(570\) | −3.04092e27 | + | 6.63113e26i | −0.839957 | + | 0.183163i | ||||
\(571\) | −4.72620e27 | −1.28278 | −0.641388 | − | 0.767217i | \(-0.721641\pi\) | ||||
−0.641388 | + | 0.767217i | \(0.721641\pi\) | |||||||
\(572\) | − | 3.70925e26i | − | 0.0989294i | ||||||
\(573\) | 1.21553e26 | + | 5.57421e26i | 0.0318580 | + | 0.146096i | ||||
\(574\) | 4.70345e26 | 0.121143 | ||||||||
\(575\) | − | 8.83414e26i | − | 0.223607i | ||||||
\(576\) | −4.56879e26 | + | 2.09205e26i | −0.113652 | + | 0.0520411i | ||||
\(577\) | −1.59165e27 | −0.389125 | −0.194562 | − | 0.980890i | \(-0.562329\pi\) | ||||
−0.194562 | + | 0.980890i | \(0.562329\pi\) | |||||||
\(578\) | 4.79483e27i | 1.15211i | ||||||||
\(579\) | 2.49475e27 | − | 5.44013e26i | 0.589171 | − | 0.128476i | ||||
\(580\) | 3.10115e27 | 0.719851 | ||||||||
\(581\) | − | 2.83865e26i | − | 0.0647666i | ||||||
\(582\) | −6.36036e26 | − | 2.91675e27i | −0.142643 | − | 0.654139i | ||||
\(583\) | −1.24176e27 | −0.273749 | ||||||||
\(584\) | 1.39877e26i | 0.0303122i | ||||||||
\(585\) | −1.46518e27 | − | 3.19979e27i | −0.312128 | − | 0.681652i | ||||
\(586\) | −1.96193e27 | −0.410873 | ||||||||
\(587\) | − | 5.36082e26i | − | 0.110370i | −0.998476 | − | 0.0551849i | \(-0.982425\pi\) | ||
0.998476 | − | 0.0551849i | \(-0.0175748\pi\) | |||||||
\(588\) | −2.37855e27 | + | 5.18673e26i | −0.481436 | + | 0.104983i | ||||
\(589\) | 1.08357e28 | 2.15628 | ||||||||
\(590\) | − | 5.00927e27i | − | 0.980065i | ||||||
\(591\) | 2.61067e26 | + | 1.19721e27i | 0.0502201 | + | 0.230301i | ||||
\(592\) | 4.54028e26 | 0.0858748 | ||||||||
\(593\) | − | 1.93679e26i | − | 0.0360194i | −0.999838 | − | 0.0180097i | \(-0.994267\pi\) | ||
0.999838 | − | 0.0180097i | \(-0.00573298\pi\) | |||||||
\(594\) | 7.47727e26 | − | 5.61502e26i | 0.136735 | − | 0.102680i | ||||
\(595\) | −9.95028e26 | −0.178923 | ||||||||
\(596\) | − | 2.68314e27i | − | 0.474439i | ||||||
\(597\) | 9.79288e27 | − | 2.13547e27i | 1.70281 | − | 0.371321i | ||||
\(598\) | 4.71727e27 | 0.806638 | ||||||||
\(599\) | − | 1.09596e28i | − | 1.84300i | −0.388377 | − | 0.921501i | \(-0.626964\pi\) | ||
0.388377 | − | 0.921501i | \(-0.373036\pi\) | |||||||
\(600\) | −7.30480e25 | − | 3.34986e26i | −0.0120808 | − | 0.0554005i | ||||
\(601\) | −1.07060e28 | −1.74134 | −0.870668 | − | 0.491871i | \(-0.836313\pi\) | ||||
−0.870668 | + | 0.491871i | \(0.836313\pi\) | |||||||
\(602\) | 4.83762e26i | 0.0773868i | ||||||||
\(603\) | −1.06258e27 | + | 4.86555e26i | −0.167181 | + | 0.0765524i | ||||
\(604\) | −2.23738e27 | −0.346234 | ||||||||
\(605\) | 5.66794e27i | 0.862724i | ||||||||
\(606\) | 8.61486e26 | − | 1.87858e26i | 0.128980 | − | 0.0281258i | ||||
\(607\) | −7.53237e27 | −1.10929 | −0.554644 | − | 0.832088i | \(-0.687146\pi\) | ||||
−0.554644 | + | 0.832088i | \(0.687146\pi\) | |||||||
\(608\) | − | 1.61912e27i | − | 0.234554i | ||||||
\(609\) | 2.82878e26 | + | 1.29723e27i | 0.0403113 | + | 0.184861i | ||||
\(610\) | −8.00788e26 | −0.112258 | ||||||||
\(611\) | − | 2.92964e27i | − | 0.404020i | ||||||
\(612\) | 2.48796e27 | + | 5.43342e27i | 0.337543 | + | 0.737155i | ||||
\(613\) | −9.64517e26 | −0.128738 | −0.0643688 | − | 0.997926i | \(-0.520503\pi\) | ||||
−0.0643688 | + | 0.997926i | \(0.520503\pi\) | |||||||
\(614\) | 3.38883e27i | 0.445007i | ||||||||
\(615\) | −9.85864e27 | + | 2.14981e27i | −1.27370 | + | 0.277746i | ||||
\(616\) | −8.09961e25 | −0.0102957 | ||||||||
\(617\) | − | 1.68600e27i | − | 0.210865i | −0.994426 | − | 0.105433i | \(-0.966377\pi\) | ||
0.994426 | − | 0.105433i | \(-0.0336228\pi\) | |||||||
\(618\) | 1.30303e27 | + | 5.97547e27i | 0.160350 | + | 0.735338i | ||||
\(619\) | −5.30171e26 | −0.0641962 | −0.0320981 | − | 0.999485i | \(-0.510219\pi\) | ||||
−0.0320981 | + | 0.999485i | \(0.510219\pi\) | |||||||
\(620\) | − | 6.24908e27i | − | 0.744559i | ||||||
\(621\) | 7.14096e27 | + | 9.50929e27i | 0.837222 | + | 1.11489i | ||||
\(622\) | 7.34815e27 | 0.847762 | ||||||||
\(623\) | − | 3.62702e26i | − | 0.0411784i | ||||||
\(624\) | 1.78876e27 | − | 3.90063e26i | 0.199851 | − | 0.0435802i | ||||
\(625\) | −7.40238e27 | −0.813900 | ||||||||
\(626\) | 8.39639e27i | 0.908551i | ||||||||
\(627\) | 6.41931e26 | + | 2.94379e27i | 0.0683617 | + | 0.313495i | ||||
\(628\) | 6.58212e27 | 0.689874 | ||||||||
\(629\) | − | 5.39952e27i | − | 0.556992i | ||||||
\(630\) | −6.98714e26 | + | 3.19941e26i | −0.0709405 | + | 0.0324836i | ||||
\(631\) | 9.11781e27 | 0.911165 | 0.455582 | − | 0.890194i | \(-0.349431\pi\) | ||||
0.455582 | + | 0.890194i | \(0.349431\pi\) | |||||||
\(632\) | 7.72212e26i | 0.0759566i | ||||||||
\(633\) | −1.90647e28 | + | 4.15730e27i | −1.84583 | + | 0.402508i | ||||
\(634\) | −1.41482e27 | −0.134837 | ||||||||
\(635\) | 9.09738e27i | 0.853452i | ||||||||
\(636\) | −1.30583e27 | − | 5.98832e27i | −0.120591 | − | 0.553011i | ||||
\(637\) | 8.86962e27 | 0.806326 | ||||||||
\(638\) | − | 3.00209e27i | − | 0.268668i | ||||||
\(639\) | 2.33933e27 | + | 5.10883e27i | 0.206102 | + | 0.450104i | ||||
\(640\) | −9.33763e26 | −0.0809910 | ||||||||
\(641\) | − | 7.97553e27i | − | 0.681051i | −0.940235 | − | 0.340525i | \(-0.889395\pi\) | ||
0.940235 | − | 0.340525i | \(-0.110605\pi\) | |||||||
\(642\) | 2.15880e27 | − | 4.70755e26i | 0.181494 | − | 0.0395772i | ||||
\(643\) | 1.57198e28 | 1.30118 | 0.650590 | − | 0.759430i | \(-0.274522\pi\) | ||||
0.650590 | + | 0.759430i | \(0.274522\pi\) | |||||||
\(644\) | − | 1.03008e27i | − | 0.0839480i | ||||||
\(645\) | −2.21113e27 | − | 1.01399e28i | −0.177426 | − | 0.813645i | ||||
\(646\) | −1.92553e28 | −1.52134 | ||||||||
\(647\) | 9.57693e27i | 0.745047i | 0.928023 | + | 0.372523i | \(0.121507\pi\) | ||||
−0.928023 | + | 0.372523i | \(0.878493\pi\) | |||||||
\(648\) | 3.49412e27 | + | 3.01540e27i | 0.267663 | + | 0.230991i | ||||
\(649\) | −4.84926e27 | −0.365787 | ||||||||
\(650\) | 1.24916e27i | 0.0927868i | ||||||||
\(651\) | 2.61403e27 | − | 5.70024e26i | 0.191206 | − | 0.0416949i | ||||
\(652\) | −1.29301e28 | −0.931376 | ||||||||
\(653\) | − | 1.11408e28i | − | 0.790287i | −0.918619 | − | 0.395144i | \(-0.870695\pi\) | ||
0.918619 | − | 0.395144i | \(-0.129305\pi\) | |||||||
\(654\) | −1.56194e27 | − | 7.16277e27i | −0.109115 | − | 0.500384i | ||||
\(655\) | 1.15829e28 | 0.796902 | ||||||||
\(656\) | − | 5.24917e27i | − | 0.355674i | ||||||
\(657\) | 1.16810e27 | − | 5.34875e26i | 0.0779521 | − | 0.0356943i | ||||
\(658\) | −6.39724e26 | −0.0420469 | ||||||||
\(659\) | − | 1.35425e27i | − | 0.0876687i | −0.999039 | − | 0.0438343i | \(-0.986043\pi\) | ||
0.999039 | − | 0.0438343i | \(-0.0139574\pi\) | |||||||
\(660\) | 1.69771e27 | − | 3.70208e26i | 0.108249 | − | 0.0236052i | ||||
\(661\) | −1.35330e28 | −0.849923 | −0.424962 | − | 0.905211i | \(-0.639712\pi\) | ||||
−0.424962 | + | 0.905211i | \(0.639712\pi\) | |||||||
\(662\) | − | 2.51708e26i | − | 0.0155710i | ||||||
\(663\) | −4.63881e27 | − | 2.12728e28i | −0.282665 | − | 1.29625i | ||||
\(664\) | −3.16800e27 | −0.190154 | ||||||||
\(665\) | − | 2.47615e27i | − | 0.146407i | ||||||
\(666\) | −1.73616e27 | − | 3.79157e27i | −0.101122 | − | 0.220840i | ||||
\(667\) | 3.81794e28 | 2.19064 | ||||||||
\(668\) | 9.33737e27i | 0.527789i | ||||||||
\(669\) | 1.22933e28 | − | 2.68072e27i | 0.684554 | − | 0.149276i | ||||
\(670\) | −2.17168e27 | −0.119138 | ||||||||
\(671\) | 7.75208e26i | 0.0418980i | ||||||||
\(672\) | −8.51752e25 | − | 3.90599e26i | −0.00453545 | − | 0.0207988i | ||||
\(673\) | −2.20466e28 | −1.15662 | −0.578310 | − | 0.815817i | \(-0.696288\pi\) | ||||
−0.578310 | + | 0.815817i | \(0.696288\pi\) | |||||||
\(674\) | − | 1.45509e28i | − | 0.752128i | ||||||
\(675\) | −2.51812e27 | + | 1.89097e27i | −0.128245 | + | 0.0963048i | ||||
\(676\) | 3.29376e27 | 0.165282 | ||||||||
\(677\) | 2.69058e28i | 1.33033i | 0.746697 | + | 0.665165i | \(0.231639\pi\) | ||||
−0.746697 | + | 0.665165i | \(0.768361\pi\) | |||||||
\(678\) | 2.46532e28 | − | 5.37596e27i | 1.20109 | − | 0.261914i | ||||
\(679\) | 2.37504e27 | 0.114018 | ||||||||
\(680\) | 1.11047e28i | 0.525315i | ||||||||
\(681\) | −1.59461e27 | − | 7.31259e27i | −0.0743331 | − | 0.340879i | ||||
\(682\) | −6.04946e27 | −0.277890 | ||||||||
\(683\) | 1.64443e28i | 0.744405i | 0.928152 | + | 0.372203i | \(0.121397\pi\) | ||||
−0.928152 | + | 0.372203i | \(0.878603\pi\) | |||||||
\(684\) | −1.35212e28 | + | 6.19135e27i | −0.603190 | + | 0.276201i | ||||
\(685\) | 1.16335e28 | 0.511452 | ||||||||
\(686\) | − | 3.90209e27i | − | 0.169066i | ||||||
\(687\) | −1.87840e28 | + | 4.09611e27i | −0.802088 | + | 0.174906i | ||||
\(688\) | 5.39890e27 | 0.227207 | ||||||||
\(689\) | 2.23305e28i | 0.926204i | ||||||||
\(690\) | 4.70816e27 | + | 2.15908e28i | 0.192469 | + | 0.882629i | ||||
\(691\) | −2.42166e27 | −0.0975736 | −0.0487868 | − | 0.998809i | \(-0.515535\pi\) | ||||
−0.0487868 | + | 0.998809i | \(0.515535\pi\) | |||||||
\(692\) | 2.10781e28i | 0.837087i | ||||||||
\(693\) | 3.09721e26 | + | 6.76395e26i | 0.0121238 | + | 0.0264769i | ||||
\(694\) | −1.43805e28 | −0.554854 | ||||||||
\(695\) | 4.21741e27i | 0.160398i | ||||||||
\(696\) | 1.44774e28 | − | 3.15699e27i | 0.542748 | − | 0.118353i | ||||
\(697\) | −6.24255e28 | −2.30693 | ||||||||
\(698\) | − | 4.62807e27i | − | 0.168595i | ||||||
\(699\) | −2.94195e27 | − | 1.34913e28i | −0.105649 | − | 0.484487i | ||||
\(700\) | 2.72771e26 | 0.00965645 | ||||||||
\(701\) | 2.52344e27i | 0.0880670i | 0.999030 | + | 0.0440335i | \(0.0140208\pi\) | ||||
−0.999030 | + | 0.0440335i | \(0.985979\pi\) | |||||||
\(702\) | −1.00975e28 | − | 1.34463e28i | −0.347409 | − | 0.462629i | ||||
\(703\) | 1.34368e28 | 0.455768 | ||||||||
\(704\) | 9.03935e26i | 0.0302281i | ||||||||
\(705\) | 1.34089e28 | − | 2.92398e27i | 0.442081 | − | 0.0964015i | ||||
\(706\) | 2.68819e28 | 0.873803 | ||||||||
\(707\) | 7.01488e26i | 0.0224815i | ||||||||
\(708\) | −5.09947e27 | − | 2.33853e28i | −0.161136 | − | 0.738942i | ||||
\(709\) | 1.94408e28 | 0.605692 | 0.302846 | − | 0.953039i | \(-0.402063\pi\) | ||||
0.302846 | + | 0.953039i | \(0.402063\pi\) | |||||||
\(710\) | 1.04414e28i | 0.320755i | ||||||||
\(711\) | 6.44871e27 | − | 2.95286e27i | 0.195333 | − | 0.0894432i | ||||
\(712\) | −4.04784e27 | −0.120899 | ||||||||
\(713\) | − | 7.69346e28i | − | 2.26583i | ||||||
\(714\) | −4.64519e27 | + | 1.01294e27i | −0.134903 | + | 0.0294173i | ||||
\(715\) | −6.33078e27 | −0.181300 | ||||||||
\(716\) | − | 9.63473e27i | − | 0.272088i | ||||||
\(717\) | 1.09249e28 | + | 5.00996e28i | 0.304246 | + | 1.39522i | ||||
\(718\) | 4.04805e28 | 1.11174 | ||||||||
\(719\) | − | 1.12460e28i | − | 0.304585i | −0.988335 | − | 0.152292i | \(-0.951334\pi\) | ||
0.988335 | − | 0.152292i | \(-0.0486655\pi\) | |||||||
\(720\) | 3.57062e27 | + | 7.79781e27i | 0.0953715 | + | 0.208280i | ||||
\(721\) | −4.86568e27 | −0.128171 | ||||||||
\(722\) | − | 2.06993e28i | − | 0.537753i | ||||||
\(723\) | −6.07959e28 | + | 1.32573e28i | −1.55773 | + | 0.339683i | ||||
\(724\) | 1.95206e28 | 0.493296 | ||||||||
\(725\) | 1.01101e28i | 0.251987i | ||||||||
\(726\) | 5.77000e27 | + | 2.64602e28i | 0.141843 | + | 0.650470i | ||||
\(727\) | −9.91377e27 | −0.240378 | −0.120189 | − | 0.992751i | \(-0.538350\pi\) | ||||
−0.120189 | + | 0.992751i | \(0.538350\pi\) | |||||||
\(728\) | 1.45655e27i | 0.0348346i | ||||||||
\(729\) | 1.18203e28 | − | 4.07098e28i | 0.278838 | − | 0.960338i | ||||
\(730\) | 2.38736e27 | 0.0555506 | ||||||||
\(731\) | − | 6.42062e28i | − | 1.47368i | ||||||
\(732\) | −3.73840e27 | + | 8.15206e26i | −0.0846398 | + | 0.0184568i | ||||
\(733\) | 3.83319e28 | 0.856092 | 0.428046 | − | 0.903757i | \(-0.359202\pi\) | ||||
0.428046 | + | 0.903757i | \(0.359202\pi\) | |||||||
\(734\) | − | 1.09373e27i | − | 0.0240963i | ||||||
\(735\) | 8.85249e27 | + | 4.05960e28i | 0.192394 | + | 0.882288i | ||||
\(736\) | −1.14959e28 | −0.246470 | ||||||||
\(737\) | 2.10231e27i | 0.0444654i | ||||||||
\(738\) | −4.38356e28 | + | 2.00723e28i | −0.914667 | + | 0.418826i | ||||
\(739\) | −7.41025e27 | −0.152542 | −0.0762708 | − | 0.997087i | \(-0.524301\pi\) | ||||
−0.0762708 | + | 0.997087i | \(0.524301\pi\) | |||||||
\(740\) | − | 7.74916e27i | − | 0.157376i | ||||||
\(741\) | 5.29379e28 | − | 1.15438e28i | 1.06068 | − | 0.231295i | ||||
\(742\) | 4.87615e27 | 0.0963913 | ||||||||
\(743\) | − | 1.78527e28i | − | 0.348189i | −0.984729 | − | 0.174094i | \(-0.944300\pi\) | ||
0.984729 | − | 0.174094i | \(-0.0556998\pi\) | |||||||
\(744\) | −6.36160e27 | − | 2.91732e28i | −0.122416 | − | 0.561377i | ||||
\(745\) | −4.57946e28 | −0.869465 | ||||||||
\(746\) | − | 1.43546e28i | − | 0.268908i | ||||||
\(747\) | 1.21141e28 | + | 2.64559e28i | 0.223917 | + | 0.489008i | ||||
\(748\) | 1.07500e28 | 0.196062 | ||||||||
\(749\) | 1.75786e27i | 0.0316349i | ||||||||
\(750\) | −4.13668e28 | + | 9.02056e27i | −0.734579 | + | 0.160185i | ||||
\(751\) | 2.22914e28 | 0.390605 | 0.195302 | − | 0.980743i | \(-0.437431\pi\) | ||||
0.195302 | + | 0.980743i | \(0.437431\pi\) | |||||||
\(752\) | 7.13947e27i | 0.123449i | ||||||||
\(753\) | 1.14252e28 | + | 5.23941e28i | 0.194946 | + | 0.893989i | ||||
\(754\) | −5.39864e28 | −0.909014 | ||||||||
\(755\) | 3.81866e28i | 0.634515i | ||||||||
\(756\) | −2.93617e27 | + | 2.20491e27i | −0.0481464 | + | 0.0361553i | ||||
\(757\) | −6.75656e28 | −1.09337 | −0.546685 | − | 0.837339i | \(-0.684110\pi\) | ||||
−0.546685 | + | 0.837339i | \(0.684110\pi\) | |||||||
\(758\) | − | 2.00407e28i | − | 0.320052i | ||||||
\(759\) | 2.09011e28 | − | 4.55777e27i | 0.329422 | − | 0.0718347i | ||||
\(760\) | −2.76344e28 | −0.429848 | ||||||||
\(761\) | 1.26732e29i | 1.94554i | 0.231771 | + | 0.972770i | \(0.425548\pi\) | ||||
−0.231771 | + | 0.972770i | \(0.574452\pi\) | |||||||
\(762\) | 9.26119e27 | + | 4.24702e28i | 0.140319 | + | 0.643480i | ||||
\(763\) | 5.83247e27 | 0.0872182 | ||||||||
\(764\) | 5.06557e27i | 0.0747644i | ||||||||
\(765\) | 9.27353e28 | − | 4.24635e28i | 1.35092 | − | 0.618587i | ||||
\(766\) | −1.77838e28 | −0.255704 | ||||||||
\(767\) | 8.72040e28i | 1.23761i | ||||||||
\(768\) | −4.35918e27 | + | 9.50575e26i | −0.0610650 | + | 0.0133160i | ||||
\(769\) | 4.01610e28 | 0.555317 | 0.277658 | − | 0.960680i | \(-0.410442\pi\) | ||||
0.277658 | + | 0.960680i | \(0.410442\pi\) | |||||||
\(770\) | 1.38241e27i | 0.0188681i | ||||||||
\(771\) | 4.48297e27 | + | 2.05581e28i | 0.0603980 | + | 0.276975i | ||||
\(772\) | 2.26711e28 | 0.301508 | ||||||||
\(773\) | − | 2.41271e28i | − | 0.316746i | −0.987379 | − | 0.158373i | \(-0.949375\pi\) | ||
0.987379 | − | 0.158373i | \(-0.0506248\pi\) | |||||||
\(774\) | −2.06449e28 | − | 4.50860e28i | −0.267548 | − | 0.584295i | ||||
\(775\) | 2.03728e28 | 0.260636 | ||||||||
\(776\) | − | 2.65060e28i | − | 0.334755i | ||||||
\(777\) | 3.24153e27 | − | 7.06857e26i | 0.0404147 | − | 0.00881295i | ||||
\(778\) | 8.25613e28 | 1.01620 | ||||||||
\(779\) | − | 1.55347e29i | − | 1.88769i | ||||||
\(780\) | −6.65743e27 | − | 3.05299e28i | −0.0798658 | − | 0.366251i | ||||
\(781\) | 1.01078e28 | 0.119715 | ||||||||
\(782\) | 1.36714e29i | 1.59863i | ||||||||
\(783\) | −8.17241e28 | − | 1.08828e29i | −0.943479 | − | 1.25639i | ||||
\(784\) | −2.16151e28 | −0.246375 | ||||||||
\(785\) | − | 1.12341e29i | − | 1.26427i | ||||||
\(786\) | 5.40737e28 | − | 1.17915e28i | 0.600842 | − | 0.131022i | ||||
\(787\) | −1.14847e29 | −1.26000 | −0.630002 | − | 0.776594i | \(-0.716946\pi\) | ||||
−0.630002 | + | 0.776594i | \(0.716946\pi\) | |||||||
\(788\) | 1.08797e28i | 0.117856i | ||||||||
\(789\) | −1.32299e28 | − | 6.06700e28i | −0.141510 | − | 0.648939i | ||||
\(790\) | 1.31798e28 | 0.139199 | ||||||||
\(791\) | 2.00745e28i | 0.209354i | ||||||||
\(792\) | 7.54873e27 | − | 3.45656e27i | 0.0777359 | − | 0.0355953i | ||||
\(793\) | 1.39405e28 | 0.141758 | ||||||||
\(794\) | − | 1.19587e29i | − | 1.20082i | ||||||
\(795\) | −1.02206e29 | + | 2.22874e28i | −1.01346 | + | 0.220998i | ||||
\(796\) | 8.89930e28 | 0.871415 | ||||||||
\(797\) | 1.24679e29i | 1.20562i | 0.797884 | + | 0.602810i | \(0.205952\pi\) | ||||
−0.797884 | + | 0.602810i | \(0.794048\pi\) | |||||||
\(798\) | −2.52074e27 | − | 1.15597e28i | −0.0240712 | − | 0.110387i | ||||
\(799\) | 8.49060e28 | 0.800701 | ||||||||
\(800\) | − | 3.04419e27i | − | 0.0283512i | ||||||
\(801\) | 1.54786e28 | + | 3.38034e28i | 0.142366 | + | 0.310910i | ||||
\(802\) | −3.51555e28 | −0.319337 | ||||||||
\(803\) | − | 2.31110e27i | − | 0.0207330i | ||||||
\(804\) | −1.01383e28 | + | 2.21079e27i | −0.0898264 | + | 0.0195878i | ||||
\(805\) | −1.75809e28 | −0.153845 | ||||||||
\(806\) | 1.08787e29i | 0.940215i | ||||||||
\(807\) | −2.46818e28 | − | 1.13187e29i | −0.210689 | − | 0.966183i | ||||
\(808\) | 7.82877e27 | 0.0660055 | ||||||||
\(809\) | 2.58748e28i | 0.215473i | 0.994179 | + | 0.107736i | \(0.0343603\pi\) | ||||
−0.994179 | + | 0.107736i | \(0.965640\pi\) | |||||||
\(810\) | 5.14655e28 | − | 5.96362e28i | 0.423317 | − | 0.490523i | ||||
\(811\) | −1.27235e29 | −1.03371 | −0.516856 | − | 0.856072i | \(-0.672898\pi\) | ||||
−0.516856 | + | 0.856072i | \(0.672898\pi\) | |||||||
\(812\) | 1.17886e28i | 0.0946024i | ||||||||
\(813\) | −1.41240e27 | + | 3.07992e26i | −0.0111957 | + | 0.00244137i | ||||
\(814\) | −7.50163e27 | −0.0587370 | ||||||||
\(815\) | 2.20685e29i | 1.70686i | ||||||||
\(816\) | 1.13047e28 | + | 5.18414e28i | 0.0863688 | + | 0.396073i | ||||
\(817\) | 1.59779e29 | 1.20586 | ||||||||
\(818\) | − | 7.38879e28i | − | 0.550859i | ||||||
\(819\) | 1.21636e28 | − | 5.56970e27i | 0.0895822 | − | 0.0410197i | ||||
\(820\) | −8.95906e28 | −0.651814 | ||||||||
\(821\) | − | 2.27509e29i | − | 1.63518i | −0.575799 | − | 0.817591i | \(-0.695309\pi\) | ||
0.575799 | − | 0.817591i | \(-0.304691\pi\) | |||||||
\(822\) | 5.43099e28 | − | 1.18430e28i | 0.385621 | − | 0.0840897i | ||||
\(823\) | −3.57076e28 | −0.250474 | −0.125237 | − | 0.992127i | \(-0.539969\pi\) | ||||
−0.125237 | + | 0.992127i | \(0.539969\pi\) | |||||||
\(824\) | 5.43021e28i | 0.376309i | ||||||||
\(825\) | 1.20693e27 | + | 5.53476e27i | 0.00826307 | + | 0.0378930i | ||||
\(826\) | 1.90421e28 | 0.128799 | ||||||||
\(827\) | 1.32016e29i | 0.882210i | 0.897455 | + | 0.441105i | \(0.145413\pi\) | ||||
−0.897455 | + | 0.441105i | \(0.854587\pi\) | |||||||
\(828\) | 4.39592e28 | + | 9.60017e28i | 0.290232 | + | 0.633834i | ||||
\(829\) | 1.43965e29 | 0.939097 | 0.469549 | − | 0.882907i | \(-0.344417\pi\) | ||||
0.469549 | + | 0.882907i | \(0.344417\pi\) | |||||||
\(830\) | 5.40701e28i | 0.348479i | ||||||||
\(831\) | −6.09513e28 | + | 1.32912e28i | −0.388126 | + | 0.0846359i | ||||
\(832\) | 1.62554e28 | 0.102274 | ||||||||
\(833\) | 2.57057e29i | 1.59801i | ||||||||
\(834\) | 4.29335e27 | + | 1.96886e28i | 0.0263715 | + | 0.120935i | ||||
\(835\) | 1.59366e29 | 0.967234 | ||||||||
\(836\) | 2.67517e28i | 0.160431i | ||||||||
\(837\) | −2.19298e29 | + | 1.64681e29i | −1.29951 | + | 0.975863i | ||||
\(838\) | −9.88209e28 | −0.578640 | ||||||||
\(839\) | − | 2.06955e29i | − | 1.19745i | −0.800955 | − | 0.598724i | \(-0.795675\pi\) | ||
0.800955 | − | 0.598724i | \(-0.204325\pi\) | |||||||
\(840\) | −6.66658e27 | + | 1.45373e27i | −0.0381163 | + | 0.00831175i | ||||
\(841\) | −2.59946e29 | −1.46866 | ||||||||
\(842\) | − | 1.64537e29i | − | 0.918633i | ||||||
\(843\) | 2.52298e27 | + | 1.15700e28i | 0.0139200 | + | 0.0638346i | ||||
\(844\) | −1.73251e29 | −0.944605 | ||||||||
\(845\) | − | 5.62165e28i | − | 0.302898i | ||||||
\(846\) | 5.96215e28 | − | 2.73007e28i | 0.317467 | − | 0.145368i | ||||
\(847\) | −2.15459e28 | −0.113379 | ||||||||
\(848\) | − | 5.44190e28i | − | 0.283003i | ||||||
\(849\) | 1.39859e29 | − | 3.04981e28i | 0.718810 | − | 0.156746i | ||||
\(850\) | −3.62029e28 | −0.183888 | ||||||||
\(851\) | − | 9.54027e28i | − | 0.478922i | ||||||
\(852\) | 1.06294e28 | + | 4.87444e28i | 0.0527364 | + | 0.241840i | ||||
\(853\) | −7.04114e28 | −0.345265 | −0.172632 | − | 0.984986i | \(-0.555227\pi\) | ||||
−0.172632 | + | 0.984986i | \(0.555227\pi\) | |||||||
\(854\) | − | 3.04409e27i | − | 0.0147529i | ||||||
\(855\) | 1.05671e29 | + | 2.30774e29i | 0.506170 | + | 1.10542i | ||||
\(856\) | 1.96181e28 | 0.0928796 | ||||||||
\(857\) | − | 2.94528e29i | − | 1.37822i | −0.724658 | − | 0.689109i | \(-0.758002\pi\) | ||
0.724658 | − | 0.689109i | \(-0.241998\pi\) | |||||||
\(858\) | −2.95546e28 | + | 6.44477e27i | −0.136695 | + | 0.0298081i | ||||
\(859\) | 2.41150e29 | 1.10244 | 0.551222 | − | 0.834359i | \(-0.314162\pi\) | ||||
0.551222 | + | 0.834359i | \(0.314162\pi\) | |||||||
\(860\) | − | 9.21461e28i | − | 0.416383i | ||||||
\(861\) | −8.17220e27 | − | 3.74763e28i | −0.0365012 | − | 0.167388i | ||||
\(862\) | −8.23329e28 | −0.363497 | ||||||||
\(863\) | − | 2.67410e29i | − | 1.16700i | −0.812115 | − | 0.583498i | \(-0.801684\pi\) | ||
0.812115 | − | 0.583498i | \(-0.198316\pi\) | |||||||
\(864\) | 2.46073e28 | + | 3.27684e28i | 0.106152 | + | 0.141357i | ||||
\(865\) | 3.59752e29 | 1.53406 | ||||||||
\(866\) | − | 5.85637e27i | − | 0.0246859i | ||||||
\(867\) | 3.82043e29 | − | 8.33096e28i | 1.59192 | − | 0.347139i | ||||
\(868\) | 2.37550e28 | 0.0978495 | ||||||||
\(869\) | − | 1.27588e28i | − | 0.0519531i | ||||||
\(870\) | −5.38821e28 | − | 2.47094e29i | −0.216896 | − | 0.994649i | ||||
\(871\) | 3.78058e28 | 0.150445 | ||||||||
\(872\) | − | 6.50918e28i | − | 0.256071i | ||||||
\(873\) | −2.21351e29 | + | 1.01357e29i | −0.860872 | + | 0.394193i | ||||
\(874\) | −3.40217e29 | −1.30810 | ||||||||
\(875\) | − | 3.36840e28i | − | 0.128039i | ||||||
\(876\) | 1.11451e28 | − | 2.43034e27i | 0.0418836 | − | 0.00913327i | ||||
\(877\) | −2.36384e29 | −0.878258 | −0.439129 | − | 0.898424i | \(-0.644713\pi\) | ||||
−0.439129 | + | 0.898424i | \(0.644713\pi\) | |||||||
\(878\) | 2.96793e29i | 1.09021i | ||||||||
\(879\) | 3.40883e28 | + | 1.56323e29i | 0.123799 | + | 0.567720i | ||||
\(880\) | 1.54280e28 | 0.0553965 | ||||||||
\(881\) | 1.19713e28i | 0.0424994i | 0.999774 | + | 0.0212497i | \(0.00676450\pi\) | ||||
−0.999774 | + | 0.0212497i | \(0.993236\pi\) | |||||||
\(882\) | 8.26540e28 | + | 1.80507e29i | 0.290120 | + | 0.633588i | ||||
\(883\) | 1.99349e29 | 0.691841 | 0.345921 | − | 0.938264i | \(-0.387567\pi\) | ||||
0.345921 | + | 0.938264i | \(0.387567\pi\) | |||||||
\(884\) | − | 1.93317e29i | − | 0.663357i | ||||||
\(885\) | −3.99130e29 | + | 8.70356e28i | −1.35420 | + | 0.295300i | ||||
\(886\) | 2.99734e29 | 1.00554 | ||||||||
\(887\) | 1.42732e29i | 0.473461i | 0.971575 | + | 0.236730i | \(0.0760758\pi\) | ||||
−0.971575 | + | 0.236730i | \(0.923924\pi\) | |||||||
\(888\) | −7.88869e27 | − | 3.61762e28i | −0.0258747 | − | 0.118657i | ||||
\(889\) | −3.45825e28 | −0.112160 | ||||||||
\(890\) | 6.90869e28i | 0.221562i | ||||||||
\(891\) | −5.77312e28 | − | 4.98215e28i | −0.183077 | − | 0.157994i | ||||
\(892\) | 1.11716e29 | 0.350320 | ||||||||
\(893\) | 2.11291e29i | 0.655187i | ||||||||
\(894\) | −2.13788e29 | + | 4.66192e28i | −0.655553 | + | 0.142952i | ||||
\(895\) | −1.64441e29 | −0.498633 | ||||||||
\(896\) | − | 3.54957e27i | − | 0.0106438i | ||||||
\(897\) | −8.19620e28 | − | 3.75864e29i | −0.243046 | − | 1.11457i | ||||
\(898\) | 3.52801e29 | 1.03459 | ||||||||
\(899\) | 8.80471e29i | 2.55340i | ||||||||
\(900\) | −2.54219e28 | + | 1.16407e28i | −0.0729092 | + | 0.0333851i | ||||
\(901\) | −6.47176e29 | −1.83558 | ||||||||
\(902\) | 8.67287e28i | 0.243275i | ||||||||
\(903\) | 3.85453e28 | − | 8.40531e27i | 0.106929 | − | 0.0233172i | ||||
\(904\) | 2.24037e29 | 0.614659 | ||||||||
\(905\) | − | 3.33169e29i | − | 0.904023i | ||||||
\(906\) | 3.88742e28 | + | 1.78270e29i | 0.104323 | + | 0.478407i | ||||
\(907\) | 2.67162e28 | 0.0709090 | 0.0354545 | − | 0.999371i | \(-0.488712\pi\) | ||||
0.0354545 | + | 0.999371i | \(0.488712\pi\) | |||||||
\(908\) | − | 6.64533e28i | − | 0.174445i | ||||||
\(909\) | −2.99365e28 | − | 6.53777e28i | −0.0777251 | − | 0.169743i | ||||
\(910\) | 2.48597e28 | 0.0638385 | ||||||||
\(911\) | − | 3.11664e29i | − | 0.791594i | −0.918338 | − | 0.395797i | \(-0.870468\pi\) | ||
0.918338 | − | 0.395797i | \(-0.129532\pi\) | |||||||
\(912\) | −1.29009e29 | + | 2.81320e28i | −0.324093 | + | 0.0706728i | ||||
\(913\) | 5.23430e28 | 0.130062 | ||||||||
\(914\) | 2.77432e29i | 0.681858i | ||||||||
\(915\) | 1.39136e28 | + | 6.38054e28i | 0.0338243 | + | 0.155112i | ||||
\(916\) | −1.70700e29 | −0.410468 | ||||||||
\(917\) | 4.40309e28i | 0.104728i | ||||||||
\(918\) | 3.89697e29 | − | 2.92641e29i | 0.916855 | − | 0.688508i | ||||
\(919\) | −2.53137e28 | −0.0589116 | −0.0294558 | − | 0.999566i | \(-0.509377\pi\) | ||||
−0.0294558 | + | 0.999566i | \(0.509377\pi\) | |||||||
\(920\) | 1.96207e29i | 0.451685i | ||||||||
\(921\) | 2.70016e29 | − | 5.88806e28i | 0.614885 | − | 0.134084i | ||||
\(922\) | 4.35664e29 | 0.981392 | ||||||||
\(923\) | − | 1.81768e29i | − | 0.405043i | ||||||
\(924\) | 1.40730e27 | + | 6.45363e27i | 0.00310217 | + | 0.0142260i | ||||
\(925\) | 2.52633e28 | 0.0550899 | ||||||||
\(926\) | − | 2.37086e29i | − | 0.511441i | ||||||
\(927\) | 4.53475e29 | − | 2.07646e29i | 0.967734 | − | 0.443125i | ||||
\(928\) | 1.31564e29 | 0.277751 | ||||||||
\(929\) | 8.29659e29i | 1.73278i | 0.499370 | + | 0.866389i | \(0.333565\pi\) | ||||
−0.499370 | + | 0.866389i | \(0.666435\pi\) | |||||||
\(930\) | −4.97916e29 | + | 1.08577e29i | −1.02879 | + | 0.224341i | ||||
\(931\) | −6.39692e29 | −1.30760 | ||||||||
\(932\) | − | 1.22602e29i | − | 0.247936i | ||||||
\(933\) | −1.27673e29 | − | 5.85488e29i | −0.255437 | − | 1.17139i | ||||
\(934\) | −5.19166e29 | −1.02763 | ||||||||
\(935\) | − | 1.83477e29i | − | 0.359307i | ||||||
\(936\) | −6.21591e28 | − | 1.35748e29i | −0.120433 | − | 0.263012i | ||||
\(937\) | 9.65495e29 | 1.85078 | 0.925388 | − | 0.379020i | \(-0.123739\pi\) | ||||
0.925388 | + | 0.379020i | \(0.123739\pi\) | |||||||
\(938\) | − | 8.25537e27i | − | 0.0156570i | ||||||
\(939\) | 6.69010e29 | − | 1.45886e29i | 1.25538 | − | 0.273753i | ||||
\(940\) | 1.21854e29 | 0.226235 | ||||||||
\(941\) | 2.29411e29i | 0.421423i | 0.977548 | + | 0.210711i | \(0.0675780\pi\) | ||||
−0.977548 | + | 0.210711i | \(0.932422\pi\) | |||||||
\(942\) | −1.14364e29 | − | 5.24452e29i | −0.207864 | − | 0.953228i | ||||
\(943\) | −1.10298e30 | −1.98359 | ||||||||
\(944\) | − | 2.12514e29i | − | 0.378153i | ||||||
\(945\) | 3.76324e28 | + | 5.01134e28i | 0.0662589 | + | 0.0882339i | ||||
\(946\) | −8.92027e28 | −0.155406 | ||||||||
\(947\) | − | 7.09753e29i | − | 1.22351i | −0.791047 | − | 0.611755i | \(-0.790464\pi\) | ||
0.791047 | − | 0.611755i | \(-0.209536\pi\) | |||||||
\(948\) | 6.15285e28 | − | 1.34171e28i | 0.104953 | − | 0.0228863i | ||||
\(949\) | −4.15603e28 | −0.0701482 | ||||||||
\(950\) | − | 9.00918e28i | − | 0.150470i | ||||||
\(951\) | 2.45824e28 | + | 1.12731e29i | 0.0406274 | + | 0.186310i | ||||
\(952\) | −4.22132e28 | −0.0690365 | ||||||||
\(953\) | − | 1.87844e29i | − | 0.303997i | −0.988381 | − | 0.151998i | \(-0.951429\pi\) | ||
0.988381 | − | 0.151998i | \(-0.0485708\pi\) | |||||||
\(954\) | −4.54451e29 | + | 2.08093e29i | −0.727785 | + | 0.333253i | ||||
\(955\) | 8.64570e28 | 0.137014 | ||||||||
\(956\) | 4.55280e29i | 0.714003i | ||||||||
\(957\) | −2.39201e29 | + | 5.21609e28i | −0.371231 | + | 0.0809517i | ||||
\(958\) | 7.00559e29 | 1.07594 | ||||||||
\(959\) | 4.42232e28i | 0.0672147i | ||||||||
\(960\) | 1.62240e28 | + | 7.44006e28i | 0.0244032 | + | 0.111909i | ||||
\(961\) | 1.10243e30 | 1.64104 | ||||||||
\(962\) | 1.34901e29i | 0.198731i | ||||||||
\(963\) | −7.50179e28 | − | 1.63830e29i | −0.109371 | − | 0.238853i | ||||
\(964\) | −5.52484e29 | −0.797167 | ||||||||
\(965\) | − | 3.86940e29i | − | 0.552549i | ||||||
\(966\) | −8.20746e28 | + | 1.78974e28i | −0.115995 | + | 0.0252941i | ||||
\(967\) | −4.74584e29 | −0.663817 | −0.331909 | − | 0.943312i | \(-0.607693\pi\) | ||||
−0.331909 | + | 0.943312i | \(0.607693\pi\) | |||||||
\(968\) | 2.40458e29i | 0.332878i | ||||||||
\(969\) | 3.34559e29 | + | 1.53423e30i | 0.458390 | + | 2.10210i | ||||
\(970\) | −4.52394e29 | −0.613478 | ||||||||
\(971\) | 8.35211e29i | 1.12100i | 0.828156 | + | 0.560498i | \(0.189390\pi\) | ||||
−0.828156 | + | 0.560498i | \(0.810610\pi\) | |||||||
\(972\) | 1.79552e29 | − | 3.30798e29i | 0.238521 | − | 0.439440i | ||||
\(973\) | −1.60319e28 | −0.0210794 | ||||||||
\(974\) | − | 1.31401e29i | − | 0.171005i | ||||||
\(975\) | 9.95313e28 | − | 2.17041e28i | 0.128207 | − | 0.0279573i | ||||
\(976\) | −3.39727e28 | −0.0433144 | ||||||||
\(977\) | 1.73023e29i | 0.218352i | 0.994022 | + | 0.109176i | \(0.0348213\pi\) | ||||
−0.994022 | + | 0.109176i | \(0.965179\pi\) | |||||||
\(978\) | 2.24659e29 | + | 1.03025e30i | 0.280630 | + | 1.28692i | ||||
\(979\) | 6.68800e28 | 0.0826931 | ||||||||
\(980\) | 3.68917e29i | 0.451511i | ||||||||
\(981\) | −5.43579e29 | + | 2.48905e29i | −0.658525 | + | 0.301539i | ||||
\(982\) | −1.83987e29 | −0.220634 | ||||||||
\(983\) | 1.37945e30i | 1.63746i | 0.574181 | + | 0.818728i | \(0.305320\pi\) | ||||
−0.574181 | + | 0.818728i | \(0.694680\pi\) | |||||||
\(984\) | −4.18244e29 | + | 9.12037e28i | −0.491450 | + | 0.107167i | ||||
\(985\) | 1.85689e29 | 0.215986 | ||||||||
\(986\) | − | 1.56462e30i | − | 1.80152i | ||||||
\(987\) | 1.11151e28 | + | 5.09721e28i | 0.0126690 | + | 0.0580980i | ||||
\(988\) | 4.81074e29 | 0.542803 | ||||||||
\(989\) | − | 1.13444e30i | − | 1.26713i | ||||||
\(990\) | −5.89951e28 | − | 1.28838e29i | −0.0652325 | − | 0.142460i | ||||
\(991\) | 1.31180e30 | 1.43592 | 0.717959 | − | 0.696085i | \(-0.245077\pi\) | ||||
0.717959 | + | 0.696085i | \(0.245077\pi\) | |||||||
\(992\) | − | 2.65112e29i | − | 0.287285i | ||||||
\(993\) | −2.00557e28 | + | 4.37340e27i | −0.0215151 | + | 0.00469166i | ||||
\(994\) | −3.96914e28 | −0.0421534 | ||||||||
\(995\) | − | 1.51889e30i | − | 1.59697i | ||||||
\(996\) | 5.50437e28 | + | 2.52421e29i | 0.0572947 | + | 0.262744i | ||||
\(997\) | −1.40329e29 | −0.144609 | −0.0723045 | − | 0.997383i | \(-0.523035\pi\) | ||||
−0.0723045 | + | 0.997383i | \(0.523035\pi\) | |||||||
\(998\) | − | 1.13432e28i | − | 0.0115726i | ||||||
\(999\) | −2.71940e29 | + | 2.04212e29i | −0.274675 | + | 0.206266i |
(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 | 6.21.b.a.5.1 | ✓ | 6 | |
3.2 | odd | 2 | inner | 6.21.b.a.5.4 | yes | 6 | |
4.3 | odd | 2 | 48.21.e.b.17.5 | 6 | |||
12.11 | even | 2 | 48.21.e.b.17.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.21.b.a.5.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
6.21.b.a.5.4 | yes | 6 | 3.2 | odd | 2 | inner | |
48.21.e.b.17.5 | 6 | 4.3 | odd | 2 | |||
48.21.e.b.17.6 | 6 | 12.11 | even | 2 |