Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,22,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (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: | \(58.6902423003\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.13 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.22.c.b.20.14 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2426.55i | − | 1.67562i | −0.545964 | − | 0.837808i | \(-0.683837\pi\) | ||
0.545964 | − | 0.837808i | \(-0.316163\pi\) | |||||||
\(3\) | 100608. | + | 18395.7i | 0.983692 | + | 0.179863i | ||||
\(4\) | −3.79100e6 | −1.80769 | ||||||||
\(5\) | −2.12980e7 | −0.975337 | −0.487668 | − | 0.873029i | \(-0.662153\pi\) | ||||
−0.487668 | + | 0.873029i | \(0.662153\pi\) | |||||||
\(6\) | 4.46381e7 | − | 2.44130e8i | 0.301382 | − | 1.64829i | ||||
\(7\) | 5.03992e8 | + | 5.51850e8i | 0.674363 | + | 0.738400i | ||||
\(8\) | 4.11022e9i | 1.35338i | ||||||||
\(9\) | 9.78355e9 | + | 3.70150e9i | 0.935298 | + | 0.353860i | ||||
\(10\) | 5.16808e10i | 1.63429i | ||||||||
\(11\) | − | 1.35194e11i | − | 1.57157i | −0.618498 | − | 0.785787i | \(-0.712258\pi\) | ||
0.618498 | − | 0.785787i | \(-0.287742\pi\) | |||||||
\(12\) | −3.81405e11 | − | 6.97380e10i | −1.77821 | − | 0.325137i | ||||
\(13\) | − | 6.90926e11i | − | 1.39004i | −0.718992 | − | 0.695019i | \(-0.755396\pi\) | ||
0.718992 | − | 0.695019i | \(-0.244604\pi\) | |||||||
\(14\) | 1.33909e12 | − | 1.22296e12i | 1.23727 | − | 1.12997i | ||||
\(15\) | −2.14275e12 | − | 3.91792e11i | −0.959431 | − | 0.175427i | ||||
\(16\) | 2.02335e12 | 0.460056 | ||||||||
\(17\) | 7.37208e12 | 0.886903 | 0.443452 | − | 0.896298i | \(-0.353754\pi\) | ||||
0.443452 | + | 0.896298i | \(0.353754\pi\) | |||||||
\(18\) | 8.98188e12 | − | 2.37403e13i | 0.592934 | − | 1.56720i | ||||
\(19\) | − | 6.66819e11i | − | 0.0249514i | −0.999922 | − | 0.0124757i | \(-0.996029\pi\) | ||
0.999922 | − | 0.0124757i | \(-0.00397124\pi\) | |||||||
\(20\) | 8.07410e13 | 1.76311 | ||||||||
\(21\) | 4.05539e13 | + | 6.47917e13i | 0.530555 | + | 0.847651i | ||||
\(22\) | −3.28056e14 | −2.63335 | ||||||||
\(23\) | − | 1.94024e13i | − | 0.0976593i | −0.998807 | − | 0.0488296i | \(-0.984451\pi\) | ||
0.998807 | − | 0.0488296i | \(-0.0155491\pi\) | |||||||
\(24\) | −7.56102e13 | + | 4.13520e14i | −0.243423 | + | 1.33131i | ||||
\(25\) | −2.32304e13 | −0.0487178 | ||||||||
\(26\) | −1.67657e15 | −2.32917 | ||||||||
\(27\) | 9.16211e14 | + | 5.52375e14i | 0.856399 | + | 0.516315i | ||||
\(28\) | −1.91063e15 | − | 2.09206e15i | −1.21904 | − | 1.33480i | ||||
\(29\) | 8.36096e14i | 0.369043i | 0.982828 | + | 0.184522i | \(0.0590736\pi\) | ||||
−0.982828 | + | 0.184522i | \(0.940926\pi\) | |||||||
\(30\) | −9.50703e14 | + | 5.19950e15i | −0.293949 | + | 1.60764i | ||||
\(31\) | 6.31855e14i | 0.138459i | 0.997601 | + | 0.0692293i | \(0.0220540\pi\) | ||||
−0.997601 | + | 0.0692293i | \(0.977946\pi\) | |||||||
\(32\) | 3.70999e15i | 0.582503i | ||||||||
\(33\) | 2.48699e15 | − | 1.36016e16i | 0.282668 | − | 1.54594i | ||||
\(34\) | − | 1.78887e16i | − | 1.48611i | ||||||
\(35\) | −1.07340e16 | − | 1.17533e16i | −0.657732 | − | 0.720188i | ||||
\(36\) | −3.70895e16 | − | 1.40324e16i | −1.69073 | − | 0.639670i | ||||
\(37\) | −4.54005e16 | −1.55218 | −0.776092 | − | 0.630620i | \(-0.782801\pi\) | ||||
−0.776092 | + | 0.630620i | \(0.782801\pi\) | |||||||
\(38\) | −1.61807e15 | −0.0418090 | ||||||||
\(39\) | 1.27101e16 | − | 6.95126e16i | 0.250017 | − | 1.36737i | ||||
\(40\) | − | 8.75396e16i | − | 1.32000i | ||||||
\(41\) | 1.81592e16 | 0.211284 | 0.105642 | − | 0.994404i | \(-0.466310\pi\) | ||||
0.105642 | + | 0.994404i | \(0.466310\pi\) | |||||||
\(42\) | 1.57220e17 | − | 9.84062e16i | 1.42034 | − | 0.889006i | ||||
\(43\) | −2.33482e17 | −1.64754 | −0.823768 | − | 0.566927i | \(-0.808132\pi\) | ||||
−0.823768 | + | 0.566927i | \(0.808132\pi\) | |||||||
\(44\) | 5.12521e17i | 2.84092i | ||||||||
\(45\) | −2.08371e17 | − | 7.88347e16i | −0.912231 | − | 0.345133i | ||||
\(46\) | −4.70810e16 | −0.163640 | ||||||||
\(47\) | −4.03473e17 | −1.11889 | −0.559444 | − | 0.828868i | \(-0.688985\pi\) | ||||
−0.559444 | + | 0.828868i | \(0.688985\pi\) | |||||||
\(48\) | 2.03565e17 | + | 3.72209e16i | 0.452553 | + | 0.0827472i | ||||
\(49\) | −5.05306e16 | + | 5.56255e17i | −0.0904681 | + | 0.995899i | ||||
\(50\) | 5.63699e16i | 0.0816323i | ||||||||
\(51\) | 7.41689e17 | + | 1.35614e17i | 0.872439 | + | 0.159521i | ||||
\(52\) | 2.61930e18i | 2.51276i | ||||||||
\(53\) | − | 1.74197e18i | − | 1.36818i | −0.729397 | − | 0.684091i | \(-0.760199\pi\) | ||
0.729397 | − | 0.684091i | \(-0.239801\pi\) | |||||||
\(54\) | 1.34037e18 | − | 2.22323e18i | 0.865146 | − | 1.43500i | ||||
\(55\) | 2.87937e18i | 1.53281i | ||||||||
\(56\) | −2.26822e18 | + | 2.07152e18i | −0.999336 | + | 0.912670i | ||||
\(57\) | 1.22666e16 | − | 6.70873e16i | 0.00448784 | − | 0.0245445i | ||||
\(58\) | 2.02883e18 | 0.618375 | ||||||||
\(59\) | 2.02108e18 | 0.514798 | 0.257399 | − | 0.966305i | \(-0.417134\pi\) | ||||
0.257399 | + | 0.966305i | \(0.417134\pi\) | |||||||
\(60\) | 8.12318e18 | + | 1.48528e18i | 1.73435 | + | 0.317118i | ||||
\(61\) | − | 3.65717e18i | − | 0.656420i | −0.944605 | − | 0.328210i | \(-0.893555\pi\) | ||
0.944605 | − | 0.328210i | \(-0.106445\pi\) | |||||||
\(62\) | 1.53323e18 | 0.232003 | ||||||||
\(63\) | 2.88816e18 | + | 7.26458e18i | 0.369441 | + | 0.929254i | ||||
\(64\) | 1.32458e19 | 1.43611 | ||||||||
\(65\) | 1.47154e19i | 1.35575i | ||||||||
\(66\) | −3.30050e19 | − | 6.03480e18i | −2.59041 | − | 0.473644i | ||||
\(67\) | −2.52039e19 | −1.68920 | −0.844602 | − | 0.535395i | \(-0.820163\pi\) | ||||
−0.844602 | + | 0.535395i | \(0.820163\pi\) | |||||||
\(68\) | −2.79476e19 | −1.60325 | ||||||||
\(69\) | 3.56920e17 | − | 1.95204e18i | 0.0175653 | − | 0.0960666i | ||||
\(70\) | −2.85200e19 | + | 2.60467e19i | −1.20676 | + | 1.10211i | ||||
\(71\) | 5.48009e18i | 0.199791i | 0.994998 | + | 0.0998953i | \(0.0318508\pi\) | ||||
−0.994998 | + | 0.0998953i | \(0.968149\pi\) | |||||||
\(72\) | −1.52140e19 | + | 4.02125e19i | −0.478907 | + | 1.26581i | ||||
\(73\) | − | 5.62964e19i | − | 1.53317i | −0.642143 | − | 0.766585i | \(-0.721954\pi\) | ||
0.642143 | − | 0.766585i | \(-0.278046\pi\) | |||||||
\(74\) | 1.10167e20i | 2.60086i | ||||||||
\(75\) | −2.33717e18 | − | 4.27340e17i | −0.0479233 | − | 0.00876254i | ||||
\(76\) | 2.52791e18i | 0.0451044i | ||||||||
\(77\) | 7.46068e19 | − | 6.81367e19i | 1.16045 | − | 1.05981i | ||||
\(78\) | −1.68676e20 | − | 3.08416e19i | −2.29118 | − | 0.418932i | ||||
\(79\) | 8.73500e19 | 1.03796 | 0.518978 | − | 0.854788i | \(-0.326313\pi\) | ||||
0.518978 | + | 0.854788i | \(0.326313\pi\) | |||||||
\(80\) | −4.30934e19 | −0.448710 | ||||||||
\(81\) | 8.20168e19 | + | 7.24276e19i | 0.749566 | + | 0.661929i | ||||
\(82\) | − | 4.40642e19i | − | 0.354030i | ||||||
\(83\) | −2.61893e20 | −1.85270 | −0.926348 | − | 0.376669i | \(-0.877070\pi\) | ||||
−0.926348 | + | 0.376669i | \(0.877070\pi\) | |||||||
\(84\) | −1.53740e20 | − | 2.45626e20i | −0.959079 | − | 1.53229i | ||||
\(85\) | −1.57011e20 | −0.865029 | ||||||||
\(86\) | 5.66557e20i | 2.76064i | ||||||||
\(87\) | −1.53805e19 | + | 8.41179e19i | −0.0663773 | + | 0.363025i | ||||
\(88\) | 5.55677e20 | 2.12694 | ||||||||
\(89\) | 2.02022e20 | 0.686756 | 0.343378 | − | 0.939197i | \(-0.388429\pi\) | ||||
0.343378 | + | 0.939197i | \(0.388429\pi\) | |||||||
\(90\) | −1.91297e20 | + | 5.05622e20i | −0.578310 | + | 1.52855i | ||||
\(91\) | 3.81288e20 | − | 3.48221e20i | 1.02640 | − | 0.937390i | ||||
\(92\) | 7.35546e19i | 0.176538i | ||||||||
\(93\) | −1.16234e19 | + | 6.35696e19i | −0.0249036 | + | 0.136200i | ||||
\(94\) | 9.79048e20i | 1.87483i | ||||||||
\(95\) | 1.42019e19i | 0.0243360i | ||||||||
\(96\) | −6.82478e19 | + | 3.73254e20i | −0.104771 | + | 0.573003i | ||||
\(97\) | − | 9.52519e20i | − | 1.31151i | −0.754975 | − | 0.655753i | \(-0.772351\pi\) | ||
0.754975 | − | 0.655753i | \(-0.227649\pi\) | |||||||
\(98\) | 1.34978e21 | + | 1.22615e20i | 1.66875 | + | 0.151590i | ||||
\(99\) | 5.00421e20 | − | 1.32268e21i | 0.556117 | − | 1.46989i | ||||
\(100\) | 8.80667e19 | 0.0880667 | ||||||||
\(101\) | −6.73540e20 | −0.606721 | −0.303361 | − | 0.952876i | \(-0.598109\pi\) | ||||
−0.303361 | + | 0.952876i | \(0.598109\pi\) | |||||||
\(102\) | 3.29075e20 | − | 1.79975e21i | 0.267297 | − | 1.46187i | ||||
\(103\) | 1.08886e21i | 0.798325i | 0.916880 | + | 0.399162i | \(0.130699\pi\) | ||||
−0.916880 | + | 0.399162i | \(0.869301\pi\) | |||||||
\(104\) | 2.83986e21 | 1.88125 | ||||||||
\(105\) | −8.63719e20 | − | 1.37994e21i | −0.517470 | − | 0.826745i | ||||
\(106\) | −4.22698e21 | −2.29255 | ||||||||
\(107\) | 8.35706e19i | 0.0410699i | 0.999789 | + | 0.0205349i | \(0.00653694\pi\) | ||||
−0.999789 | + | 0.0205349i | \(0.993463\pi\) | |||||||
\(108\) | −3.47336e21 | − | 2.09406e21i | −1.54810 | − | 0.933338i | ||||
\(109\) | −1.04792e21 | −0.423983 | −0.211992 | − | 0.977271i | \(-0.567995\pi\) | ||||
−0.211992 | + | 0.977271i | \(0.567995\pi\) | |||||||
\(110\) | 6.98694e21 | 2.56841 | ||||||||
\(111\) | −4.56765e21 | − | 8.35173e20i | −1.52687 | − | 0.279181i | ||||
\(112\) | 1.01975e21 | + | 1.11658e21i | 0.310245 | + | 0.339705i | ||||
\(113\) | 2.30241e21i | 0.638055i | 0.947745 | + | 0.319027i | \(0.103356\pi\) | ||||
−0.947745 | + | 0.319027i | \(0.896644\pi\) | |||||||
\(114\) | −1.62791e20 | − | 2.97655e19i | −0.0411272 | − | 0.00751990i | ||||
\(115\) | 4.13234e20i | 0.0952507i | ||||||||
\(116\) | − | 3.16964e21i | − | 0.667116i | ||||||
\(117\) | 2.55746e21 | − | 6.75971e21i | 0.491879 | − | 1.30010i | ||||
\(118\) | − | 4.90425e21i | − | 0.862604i | ||||||
\(119\) | 3.71547e21 | + | 4.06828e21i | 0.598095 | + | 0.654889i | ||||
\(120\) | 1.61035e21 | − | 8.80718e21i | 0.237420 | − | 1.29848i | ||||
\(121\) | −1.08772e22 | −1.46984 | ||||||||
\(122\) | −8.87431e21 | −1.09991 | ||||||||
\(123\) | 1.82696e21 | + | 3.34050e20i | 0.207838 | + | 0.0380022i | ||||
\(124\) | − | 2.39536e21i | − | 0.250290i | ||||||
\(125\) | 1.06505e22 | 1.02285 | ||||||||
\(126\) | 1.76279e22 | − | 7.00826e21i | 1.55707 | − | 0.619041i | ||||
\(127\) | 4.04865e21 | 0.329133 | 0.164566 | − | 0.986366i | \(-0.447378\pi\) | ||||
0.164566 | + | 0.986366i | \(0.447378\pi\) | |||||||
\(128\) | − | 2.43611e22i | − | 1.82386i | ||||||
\(129\) | −2.34902e22 | − | 4.29506e21i | −1.62067 | − | 0.296331i | ||||
\(130\) | 3.57076e22 | 2.27173 | ||||||||
\(131\) | 3.00868e22 | 1.76615 | 0.883074 | − | 0.469233i | \(-0.155470\pi\) | ||||
0.883074 | + | 0.469233i | \(0.155470\pi\) | |||||||
\(132\) | −9.42817e21 | + | 5.15637e22i | −0.510977 | + | 2.79459i | ||||
\(133\) | 3.67984e20 | − | 3.36071e20i | 0.0184241 | − | 0.0168263i | ||||
\(134\) | 6.11585e22i | 2.83046i | ||||||||
\(135\) | −1.95135e22 | − | 1.17645e22i | −0.835277 | − | 0.503581i | ||||
\(136\) | 3.03008e22i | 1.20032i | ||||||||
\(137\) | 4.47790e21i | 0.164251i | 0.996622 | + | 0.0821256i | \(0.0261709\pi\) | ||||
−0.996622 | + | 0.0821256i | \(0.973829\pi\) | |||||||
\(138\) | −4.73672e21 | − | 8.66086e20i | −0.160971 | − | 0.0294327i | ||||
\(139\) | − | 1.92513e22i | − | 0.606464i | −0.952917 | − | 0.303232i | \(-0.901934\pi\) | ||
0.952917 | − | 0.303232i | \(-0.0980658\pi\) | |||||||
\(140\) | 4.06928e22 | + | 4.45569e22i | 1.18898 | + | 1.30188i | ||||
\(141\) | −4.05926e22 | − | 7.42216e21i | −1.10064 | − | 0.201247i | ||||
\(142\) | 1.32977e22 | 0.334772 | ||||||||
\(143\) | −9.34092e22 | −2.18455 | ||||||||
\(144\) | 1.97955e22 | + | 7.48943e21i | 0.430290 | + | 0.162795i | ||||
\(145\) | − | 1.78072e22i | − | 0.359941i | ||||||
\(146\) | −1.36606e23 | −2.56901 | ||||||||
\(147\) | −1.53165e22 | + | 5.50342e22i | −0.268118 | + | 0.963386i | ||||
\(148\) | 1.72114e23 | 2.80587 | ||||||||
\(149\) | − | 3.14380e22i | − | 0.477528i | −0.971078 | − | 0.238764i | \(-0.923258\pi\) | ||
0.971078 | − | 0.238764i | \(-0.0767422\pi\) | |||||||
\(150\) | −1.03696e21 | + | 5.67126e21i | −0.0146827 | + | 0.0803010i | ||||
\(151\) | −9.72543e22 | −1.28425 | −0.642127 | − | 0.766598i | \(-0.721948\pi\) | ||||
−0.642127 | + | 0.766598i | \(0.721948\pi\) | |||||||
\(152\) | 2.74077e21 | 0.0337688 | ||||||||
\(153\) | 7.21251e22 | + | 2.72877e22i | 0.829519 | + | 0.313840i | ||||
\(154\) | −1.65337e23 | − | 1.81037e23i | −1.77584 | − | 1.94447i | ||||
\(155\) | − | 1.34573e22i | − | 0.135044i | ||||||
\(156\) | −4.81838e22 | + | 2.63523e23i | −0.451953 | + | 2.47178i | ||||
\(157\) | − | 6.32705e22i | − | 0.554952i | −0.960733 | − | 0.277476i | \(-0.910502\pi\) | ||
0.960733 | − | 0.277476i | \(-0.0894979\pi\) | |||||||
\(158\) | − | 2.11959e23i | − | 1.73922i | ||||||
\(159\) | 3.20447e22 | − | 1.75256e23i | 0.246086 | − | 1.34587i | ||||
\(160\) | − | 7.90156e22i | − | 0.568137i | ||||||
\(161\) | 1.07072e22 | − | 9.77866e21i | 0.0721116 | − | 0.0658578i | ||||
\(162\) | 1.75749e23 | − | 1.99018e23i | 1.10914 | − | 1.25599i | ||||
\(163\) | −1.30386e23 | −0.771367 | −0.385684 | − | 0.922631i | \(-0.626034\pi\) | ||||
−0.385684 | + | 0.922631i | \(0.626034\pi\) | |||||||
\(164\) | −6.88415e22 | −0.381936 | ||||||||
\(165\) | −5.29679e22 | + | 2.89687e23i | −0.275697 | + | 1.50782i | ||||
\(166\) | 6.35497e23i | 3.10441i | ||||||||
\(167\) | −1.36451e22 | −0.0625827 | −0.0312914 | − | 0.999510i | \(-0.509962\pi\) | ||||
−0.0312914 | + | 0.999510i | \(0.509962\pi\) | |||||||
\(168\) | −2.66308e23 | + | 1.66685e23i | −1.14719 | + | 0.718042i | ||||
\(169\) | −2.30315e23 | −0.932204 | ||||||||
\(170\) | 3.80995e23i | 1.44946i | ||||||||
\(171\) | 2.46823e21 | − | 6.52386e21i | 0.00882930 | − | 0.0233370i | ||||
\(172\) | 8.85132e23 | 2.97824 | ||||||||
\(173\) | −1.99065e23 | −0.630248 | −0.315124 | − | 0.949050i | \(-0.602046\pi\) | ||||
−0.315124 | + | 0.949050i | \(0.602046\pi\) | |||||||
\(174\) | 2.04116e23 | + | 3.73217e22i | 0.608290 | + | 0.111223i | ||||
\(175\) | −1.17080e22 | − | 1.28197e22i | −0.0328535 | − | 0.0359732i | ||||
\(176\) | − | 2.73545e23i | − | 0.723012i | ||||||
\(177\) | 2.03336e23 | + | 3.71791e22i | 0.506403 | + | 0.0925933i | ||||
\(178\) | − | 4.90216e23i | − | 1.15074i | ||||||
\(179\) | − | 5.24603e23i | − | 1.16111i | −0.814220 | − | 0.580556i | \(-0.802835\pi\) | ||
0.814220 | − | 0.580556i | \(-0.197165\pi\) | |||||||
\(180\) | 7.89933e23 | + | 2.98863e23i | 1.64903 | + | 0.623893i | ||||
\(181\) | 4.30309e23i | 0.847531i | 0.905772 | + | 0.423766i | \(0.139292\pi\) | ||||
−0.905772 | + | 0.423766i | \(0.860708\pi\) | |||||||
\(182\) | −8.44977e23 | − | 9.25214e23i | −1.57071 | − | 1.71986i | ||||
\(183\) | 6.72760e22 | − | 3.67940e23i | 0.118066 | − | 0.645714i | ||||
\(184\) | 7.97482e22 | 0.132170 | ||||||||
\(185\) | 9.66943e23 | 1.51390 | ||||||||
\(186\) | 1.54255e23 | + | 2.82048e22i | 0.228220 | + | 0.0417289i | ||||
\(187\) | − | 9.96661e23i | − | 1.39383i | ||||||
\(188\) | 1.52957e24 | 2.02261 | ||||||||
\(189\) | 1.56935e23 | + | 7.84003e23i | 0.196277 | + | 0.980548i | ||||
\(190\) | 3.44617e22 | 0.0407779 | ||||||||
\(191\) | − | 1.08992e24i | − | 1.22052i | −0.792200 | − | 0.610261i | \(-0.791064\pi\) | ||
0.792200 | − | 0.610261i | \(-0.208936\pi\) | |||||||
\(192\) | 1.33263e24 | + | 2.43665e23i | 1.41269 | + | 0.258303i | ||||
\(193\) | 8.70767e23 | 0.874078 | 0.437039 | − | 0.899443i | \(-0.356027\pi\) | ||||
0.437039 | + | 0.899443i | \(0.356027\pi\) | |||||||
\(194\) | −2.31134e24 | −2.19758 | ||||||||
\(195\) | −2.70699e23 | + | 1.48048e24i | −0.243850 | + | 1.33364i | ||||
\(196\) | 1.91562e23 | − | 2.10877e24i | 0.163538 | − | 1.80028i | ||||
\(197\) | 1.30581e24i | 1.05678i | 0.849002 | + | 0.528389i | \(0.177204\pi\) | ||||
−0.849002 | + | 0.528389i | \(0.822796\pi\) | |||||||
\(198\) | −3.20955e24 | − | 1.21430e24i | −2.46297 | − | 0.931839i | ||||
\(199\) | − | 2.13981e24i | − | 1.55746i | −0.627357 | − | 0.778732i | \(-0.715863\pi\) | ||
0.627357 | − | 0.778732i | \(-0.284137\pi\) | |||||||
\(200\) | − | 9.54822e22i | − | 0.0659337i | ||||||
\(201\) | −2.53571e24 | − | 4.63642e23i | −1.66166 | − | 0.303826i | ||||
\(202\) | 1.63438e24i | 1.01663i | ||||||||
\(203\) | −4.61399e23 | + | 4.21385e23i | −0.272501 | + | 0.248869i | ||||
\(204\) | −2.81175e24 | − | 5.14114e23i | −1.57710 | − | 0.288365i | ||||
\(205\) | −3.86755e23 | −0.206073 | ||||||||
\(206\) | 2.64217e24 | 1.33769 | ||||||||
\(207\) | 7.18180e22 | − | 1.89825e23i | 0.0345577 | − | 0.0913406i | ||||
\(208\) | − | 1.39798e24i | − | 0.639495i | ||||||
\(209\) | −9.01500e22 | −0.0392130 | ||||||||
\(210\) | −3.34849e24 | + | 2.09586e24i | −1.38531 | + | 0.867081i | ||||
\(211\) | 3.50234e24 | 1.37845 | 0.689227 | − | 0.724546i | \(-0.257950\pi\) | ||||
0.689227 | + | 0.724546i | \(0.257950\pi\) | |||||||
\(212\) | 6.60381e24i | 2.47325i | ||||||||
\(213\) | −1.00810e23 | + | 5.51340e23i | −0.0359350 | + | 0.196532i | ||||
\(214\) | 2.02788e23 | 0.0688174 | ||||||||
\(215\) | 4.97272e24 | 1.60690 | ||||||||
\(216\) | −2.27038e24 | + | 3.76583e24i | −0.698771 | + | 1.15903i | ||||
\(217\) | −3.48689e23 | + | 3.18450e23i | −0.102238 | + | 0.0933713i | ||||
\(218\) | 2.54283e24i | 0.710433i | ||||||||
\(219\) | 1.03561e24 | − | 5.66386e24i | 0.275761 | − | 1.50817i | ||||
\(220\) | − | 1.09157e25i | − | 2.77085i | ||||||
\(221\) | − | 5.09356e24i | − | 1.23283i | ||||||
\(222\) | −2.02659e24 | + | 1.10837e25i | −0.467800 | + | 2.55845i | ||||
\(223\) | 6.84362e24i | 1.50690i | 0.657505 | + | 0.753450i | \(0.271612\pi\) | ||||
−0.657505 | + | 0.753450i | \(0.728388\pi\) | |||||||
\(224\) | −2.04736e24 | + | 1.86980e24i | −0.430120 | + | 0.392819i | ||||
\(225\) | −2.27276e23 | − | 8.59875e22i | −0.0455657 | − | 0.0172393i | ||||
\(226\) | 5.58691e24 | 1.06914 | ||||||||
\(227\) | −8.94973e23 | −0.163508 | −0.0817539 | − | 0.996653i | \(-0.526052\pi\) | ||||
−0.0817539 | + | 0.996653i | \(0.526052\pi\) | |||||||
\(228\) | −4.65026e22 | + | 2.54328e23i | −0.00811263 | + | 0.0443689i | ||||
\(229\) | 6.05322e24i | 1.00859i | 0.863532 | + | 0.504294i | \(0.168247\pi\) | ||||
−0.863532 | + | 0.504294i | \(0.831753\pi\) | |||||||
\(230\) | 1.00273e24 | 0.159604 | ||||||||
\(231\) | 8.75946e24 | − | 5.48265e24i | 1.33215 | − | 0.833805i | ||||
\(232\) | −3.43654e24 | −0.499456 | ||||||||
\(233\) | − | 1.60887e24i | − | 0.223504i | −0.993736 | − | 0.111752i | \(-0.964354\pi\) | ||
0.993736 | − | 0.111752i | \(-0.0356462\pi\) | |||||||
\(234\) | −1.64028e25 | − | 6.20582e24i | −2.17847 | − | 0.824200i | ||||
\(235\) | 8.59319e24 | 1.09129 | ||||||||
\(236\) | −7.66191e24 | −0.930596 | ||||||||
\(237\) | 8.78811e24 | + | 1.60686e24i | 1.02103 | + | 0.186690i | ||||
\(238\) | 9.87189e24 | − | 9.01577e24i | 1.09734 | − | 1.00218i | ||||
\(239\) | 1.54728e25i | 1.64585i | 0.568151 | + | 0.822924i | \(0.307659\pi\) | ||||
−0.568151 | + | 0.822924i | \(0.692341\pi\) | |||||||
\(240\) | −4.33553e24 | − | 7.92731e23i | −0.441392 | − | 0.0807064i | ||||
\(241\) | 7.68657e24i | 0.749124i | 0.927202 | + | 0.374562i | \(0.122207\pi\) | ||||
−0.927202 | + | 0.374562i | \(0.877793\pi\) | |||||||
\(242\) | 2.63941e25i | 2.46289i | ||||||||
\(243\) | 6.91918e24 | + | 8.79555e24i | 0.618285 | + | 0.785954i | ||||
\(244\) | 1.38643e25i | 1.18660i | ||||||||
\(245\) | 1.07620e24 | − | 1.18472e25i | 0.0882369 | − | 0.971337i | ||||
\(246\) | 8.10591e23 | − | 4.43321e24i | 0.0636771 | − | 0.348257i | ||||
\(247\) | −4.60723e23 | −0.0346834 | ||||||||
\(248\) | −2.59706e24 | −0.187387 | ||||||||
\(249\) | −2.63485e25 | − | 4.81770e24i | −1.82248 | − | 0.333232i | ||||
\(250\) | − | 2.58439e25i | − | 1.71391i | ||||||
\(251\) | 3.13427e24 | 0.199325 | 0.0996626 | − | 0.995021i | \(-0.468224\pi\) | ||||
0.0996626 | + | 0.995021i | \(0.468224\pi\) | |||||||
\(252\) | −1.09490e25 | − | 2.75400e25i | −0.667835 | − | 1.67980i | ||||
\(253\) | −2.62309e24 | −0.153479 | ||||||||
\(254\) | − | 9.82425e24i | − | 0.551500i | ||||||
\(255\) | −1.57965e25 | − | 2.88832e24i | −0.850922 | − | 0.155587i | ||||
\(256\) | −3.13351e25 | −1.61999 | ||||||||
\(257\) | 3.53632e25 | 1.75491 | 0.877454 | − | 0.479662i | \(-0.159241\pi\) | ||||
0.877454 | + | 0.479662i | \(0.159241\pi\) | |||||||
\(258\) | −1.04222e25 | + | 5.70001e25i | −0.496538 | + | 2.71562i | ||||
\(259\) | −2.28815e25 | − | 2.50543e25i | −1.04674 | − | 1.14613i | ||||
\(260\) | − | 5.57860e25i | − | 2.45079i | ||||||
\(261\) | −3.09481e24 | + | 8.17999e24i | −0.130590 | + | 0.345166i | ||||
\(262\) | − | 7.30072e25i | − | 2.95939i | ||||||
\(263\) | − | 2.37157e25i | − | 0.923635i | −0.886975 | − | 0.461817i | \(-0.847198\pi\) | ||
0.886975 | − | 0.461817i | \(-0.152802\pi\) | |||||||
\(264\) | 5.59055e25 | + | 1.02221e25i | 2.09225 | + | 0.382558i | ||||
\(265\) | 3.71005e25i | 1.33444i | ||||||||
\(266\) | −8.15494e23 | − | 8.92932e23i | −0.0281945 | − | 0.0308717i | ||||
\(267\) | 2.03250e25 | + | 3.71632e24i | 0.675556 | + | 0.123522i | ||||
\(268\) | 9.55480e25 | 3.05356 | ||||||||
\(269\) | −3.86632e25 | −1.18823 | −0.594113 | − | 0.804382i | \(-0.702497\pi\) | ||||
−0.594113 | + | 0.804382i | \(0.702497\pi\) | |||||||
\(270\) | −2.85472e25 | + | 4.73505e25i | −0.843809 | + | 1.39960i | ||||
\(271\) | − | 2.93748e25i | − | 0.835213i | −0.908628 | − | 0.417606i | \(-0.862869\pi\) | ||
0.908628 | − | 0.417606i | \(-0.137131\pi\) | |||||||
\(272\) | 1.49163e25 | 0.408025 | ||||||||
\(273\) | 4.47663e25 | − | 2.80198e25i | 1.17827 | − | 0.737491i | ||||
\(274\) | 1.08659e25 | 0.275222 | ||||||||
\(275\) | 3.14062e24i | 0.0765635i | ||||||||
\(276\) | −1.35309e24 | + | 7.40018e24i | −0.0317527 | + | 0.173659i | ||||
\(277\) | 8.10073e24 | 0.183015 | 0.0915075 | − | 0.995804i | \(-0.470831\pi\) | ||||
0.0915075 | + | 0.995804i | \(0.470831\pi\) | |||||||
\(278\) | −4.67144e25 | −1.01620 | ||||||||
\(279\) | −2.33881e24 | + | 6.18179e24i | −0.0489949 | + | 0.129500i | ||||
\(280\) | 4.83087e25 | − | 4.41192e25i | 0.974689 | − | 0.890161i | ||||
\(281\) | − | 6.08086e25i | − | 1.18181i | −0.806740 | − | 0.590906i | \(-0.798770\pi\) | ||
0.806740 | − | 0.590906i | \(-0.201230\pi\) | |||||||
\(282\) | −1.80102e25 | + | 9.85000e25i | −0.337213 | + | 1.84425i | ||||
\(283\) | − | 5.91160e25i | − | 1.06647i | −0.845968 | − | 0.533234i | \(-0.820977\pi\) | ||
0.845968 | − | 0.533234i | \(-0.179023\pi\) | |||||||
\(284\) | − | 2.07750e25i | − | 0.361160i | ||||||
\(285\) | −2.61254e23 | + | 1.42883e24i | −0.00437716 | + | 0.0239391i | ||||
\(286\) | 2.26662e26i | 3.66046i | ||||||||
\(287\) | 9.15208e24 | + | 1.00211e25i | 0.142482 | + | 0.156012i | ||||
\(288\) | −1.37325e25 | + | 3.62969e25i | −0.206124 | + | 0.544814i | ||||
\(289\) | −1.47444e25 | −0.213403 | ||||||||
\(290\) | −4.32101e25 | −0.603124 | ||||||||
\(291\) | 1.75222e25 | − | 9.58309e25i | 0.235892 | − | 1.29012i | ||||
\(292\) | 2.13420e26i | 2.77150i | ||||||||
\(293\) | 2.98281e25 | 0.373693 | 0.186847 | − | 0.982389i | \(-0.440173\pi\) | ||||
0.186847 | + | 0.982389i | \(0.440173\pi\) | |||||||
\(294\) | 1.33543e26 | + | 3.71662e25i | 1.61427 | + | 0.449264i | ||||
\(295\) | −4.30450e25 | −0.502102 | ||||||||
\(296\) | − | 1.86606e26i | − | 2.10069i | ||||||
\(297\) | 7.46779e25 | − | 1.23866e26i | 0.811427 | − | 1.34589i | ||||
\(298\) | −7.62859e25 | −0.800153 | ||||||||
\(299\) | −1.34056e25 | −0.135750 | ||||||||
\(300\) | 8.86021e24 | + | 1.62005e24i | 0.0866305 | + | 0.0158400i | ||||
\(301\) | −1.17673e26 | − | 1.28847e26i | −1.11104 | − | 1.21654i | ||||
\(302\) | 2.35993e26i | 2.15192i | ||||||||
\(303\) | −6.77635e25 | − | 1.23902e25i | −0.596826 | − | 0.109127i | ||||
\(304\) | − | 1.34921e24i | − | 0.0114791i | ||||||
\(305\) | 7.78905e25i | 0.640230i | ||||||||
\(306\) | 6.62151e25 | − | 1.75015e26i | 0.525875 | − | 1.38996i | ||||
\(307\) | − | 1.36868e26i | − | 1.05039i | −0.850982 | − | 0.525195i | \(-0.823993\pi\) | ||
0.850982 | − | 0.525195i | \(-0.176007\pi\) | |||||||
\(308\) | −2.82835e26 | + | 2.58306e26i | −2.09773 | + | 1.91581i | ||||
\(309\) | −2.00302e25 | + | 1.09548e26i | −0.143589 | + | 0.785305i | ||||
\(310\) | −3.26548e25 | −0.226281 | ||||||||
\(311\) | 2.42912e26 | 1.62729 | 0.813646 | − | 0.581360i | \(-0.197479\pi\) | ||||
0.813646 | + | 0.581360i | \(0.197479\pi\) | |||||||
\(312\) | 2.85712e26 | + | 5.22411e25i | 1.85057 | + | 0.338368i | ||||
\(313\) | 1.44764e26i | 0.906664i | 0.891342 | + | 0.453332i | \(0.149765\pi\) | ||||
−0.891342 | + | 0.453332i | \(0.850235\pi\) | |||||||
\(314\) | −1.53529e26 | −0.929886 | ||||||||
\(315\) | −6.15121e25 | − | 1.54721e26i | −0.360329 | − | 0.906336i | ||||
\(316\) | −3.31144e26 | −1.87630 | ||||||||
\(317\) | 9.95556e24i | 0.0545687i | 0.999628 | + | 0.0272843i | \(0.00868595\pi\) | ||||
−0.999628 | + | 0.0272843i | \(0.991314\pi\) | |||||||
\(318\) | −4.25268e26 | − | 7.77581e25i | −2.25516 | − | 0.412345i | ||||
\(319\) | 1.13035e26 | 0.579978 | ||||||||
\(320\) | −2.82109e26 | −1.40069 | ||||||||
\(321\) | −1.53734e24 | + | 8.40786e24i | −0.00738697 | + | 0.0404001i | ||||
\(322\) | −2.37284e25 | − | 2.59816e25i | −0.110353 | − | 0.120831i | ||||
\(323\) | − | 4.91584e24i | − | 0.0221295i | ||||||
\(324\) | −3.10926e26 | − | 2.74573e26i | −1.35498 | − | 1.19656i | ||||
\(325\) | 1.60505e25i | 0.0677195i | ||||||||
\(326\) | 3.16388e26i | 1.29252i | ||||||||
\(327\) | −1.05429e26 | − | 1.92771e25i | −0.417069 | − | 0.0762590i | ||||
\(328\) | 7.46382e25i | 0.285947i | ||||||||
\(329\) | −2.03347e26 | − | 2.22656e26i | −0.754538 | − | 0.826187i | ||||
\(330\) | 7.02942e26 | + | 1.28529e26i | 2.52652 | + | 0.461962i | ||||
\(331\) | 6.39974e25 | 0.222827 | 0.111414 | − | 0.993774i | \(-0.464462\pi\) | ||||
0.111414 | + | 0.993774i | \(0.464462\pi\) | |||||||
\(332\) | 9.92838e26 | 3.34910 | ||||||||
\(333\) | −4.44179e26 | − | 1.68050e26i | −1.45175 | − | 0.549255i | ||||
\(334\) | 3.31106e25i | 0.104865i | ||||||||
\(335\) | 5.36794e26 | 1.64754 | ||||||||
\(336\) | 8.20547e25 | + | 1.31096e26i | 0.244085 | + | 0.389967i | ||||
\(337\) | 1.73484e25 | 0.0500201 | 0.0250101 | − | 0.999687i | \(-0.492038\pi\) | ||||
0.0250101 | + | 0.999687i | \(0.492038\pi\) | |||||||
\(338\) | 5.58870e26i | 1.56202i | ||||||||
\(339\) | −4.23543e25 | + | 2.31640e26i | −0.114763 | + | 0.627649i | ||||
\(340\) | 5.95229e26 | 1.56371 | ||||||||
\(341\) | 8.54231e25 | 0.217598 | ||||||||
\(342\) | −1.58305e25 | − | 5.98929e24i | −0.0391039 | − | 0.0147945i | ||||
\(343\) | −3.32436e26 | + | 2.52463e26i | −0.796380 | + | 0.604796i | ||||
\(344\) | − | 9.59663e26i | − | 2.22974i | ||||||
\(345\) | −7.60171e24 | + | 4.15746e25i | −0.0171321 | + | 0.0936973i | ||||
\(346\) | 4.83043e26i | 1.05605i | ||||||||
\(347\) | − | 7.07497e26i | − | 1.50060i | −0.661097 | − | 0.750300i | \(-0.729909\pi\) | ||
0.661097 | − | 0.750300i | \(-0.270091\pi\) | |||||||
\(348\) | 5.83077e25 | − | 3.18891e26i | 0.119990 | − | 0.656237i | ||||
\(349\) | 2.67758e26i | 0.534657i | 0.963605 | + | 0.267329i | \(0.0861410\pi\) | ||||
−0.963605 | + | 0.267329i | \(0.913859\pi\) | |||||||
\(350\) | −3.11077e25 | + | 2.84100e25i | −0.0602773 | + | 0.0550498i | ||||
\(351\) | 3.81651e26 | − | 6.33034e26i | 0.717697 | − | 1.19043i | ||||
\(352\) | 5.01569e26 | 0.915446 | ||||||||
\(353\) | 6.23142e26 | 1.10396 | 0.551979 | − | 0.833858i | \(-0.313873\pi\) | ||||
0.551979 | + | 0.833858i | \(0.313873\pi\) | |||||||
\(354\) | 9.02170e25 | − | 4.93407e26i | 0.155151 | − | 0.848537i | ||||
\(355\) | − | 1.16715e26i | − | 0.194863i | ||||||
\(356\) | −7.65864e26 | −1.24144 | ||||||||
\(357\) | 2.98967e26 | + | 4.77650e26i | 0.470551 | + | 0.751784i | ||||
\(358\) | −1.27298e27 | −1.94558 | ||||||||
\(359\) | 8.91157e26i | 1.32270i | 0.750076 | + | 0.661352i | \(0.230017\pi\) | ||||
−0.750076 | + | 0.661352i | \(0.769983\pi\) | |||||||
\(360\) | 3.24028e26 | − | 8.56448e26i | 0.467096 | − | 1.23460i | ||||
\(361\) | 7.13765e26 | 0.999377 | ||||||||
\(362\) | 1.04417e27 | 1.42014 | ||||||||
\(363\) | −1.09433e27 | − | 2.00093e26i | −1.44587 | − | 0.264371i | ||||
\(364\) | −1.44546e27 | + | 1.32011e27i | −1.85542 | + | 1.69451i | ||||
\(365\) | 1.19900e27i | 1.49536i | ||||||||
\(366\) | −8.92825e26 | − | 1.63249e26i | −1.08197 | − | 0.197833i | ||||
\(367\) | − | 1.06658e25i | − | 0.0125603i | −0.999980 | − | 0.00628017i | \(-0.998001\pi\) | ||
0.999980 | − | 0.00628017i | \(-0.00199905\pi\) | |||||||
\(368\) | − | 3.92579e25i | − | 0.0449288i | ||||||
\(369\) | 1.77661e26 | + | 6.72162e25i | 0.197613 | + | 0.0747648i | ||||
\(370\) | − | 2.34634e27i | − | 2.53672i | ||||||
\(371\) | 9.61305e26 | − | 8.77938e26i | 1.01027 | − | 0.922652i | ||||
\(372\) | 4.40643e25 | − | 2.40993e26i | 0.0450180 | − | 0.246208i | ||||
\(373\) | 1.71703e26 | 0.170543 | 0.0852717 | − | 0.996358i | \(-0.472824\pi\) | ||||
0.0852717 | + | 0.996358i | \(0.472824\pi\) | |||||||
\(374\) | −2.41845e27 | −2.33553 | ||||||||
\(375\) | 1.07152e27 | + | 1.95922e26i | 1.00617 | + | 0.183974i | ||||
\(376\) | − | 1.65836e27i | − | 1.51428i | ||||||
\(377\) | 5.77681e26 | 0.512984 | ||||||||
\(378\) | 1.90243e27 | − | 3.80810e26i | 1.64302 | − | 0.328885i | ||||
\(379\) | 5.46489e26 | 0.459061 | 0.229530 | − | 0.973302i | \(-0.426281\pi\) | ||||
0.229530 | + | 0.973302i | \(0.426281\pi\) | |||||||
\(380\) | − | 5.38396e25i | − | 0.0439920i | ||||||
\(381\) | 4.07326e26 | + | 7.44776e25i | 0.323765 | + | 0.0591988i | ||||
\(382\) | −2.64476e27 | −2.04513 | ||||||||
\(383\) | 1.50047e26 | 0.112886 | 0.0564432 | − | 0.998406i | \(-0.482024\pi\) | ||||
0.0564432 | + | 0.998406i | \(0.482024\pi\) | |||||||
\(384\) | 4.48139e26 | − | 2.45092e27i | 0.328046 | − | 1.79412i | ||||
\(385\) | −1.58898e27 | + | 1.45118e27i | −1.13183 | + | 1.03367i | ||||
\(386\) | − | 2.11296e27i | − | 1.46462i | ||||||
\(387\) | −2.28429e27 | − | 8.64235e26i | −1.54094 | − | 0.582997i | ||||
\(388\) | 3.61100e27i | 2.37080i | ||||||||
\(389\) | − | 8.44448e26i | − | 0.539638i | −0.962911 | − | 0.269819i | \(-0.913036\pi\) | ||
0.962911 | − | 0.269819i | \(-0.0869638\pi\) | |||||||
\(390\) | 3.59247e27 | + | 6.56866e26i | 2.23468 | + | 0.408600i | ||||
\(391\) | − | 1.43036e26i | − | 0.0866143i | ||||||
\(392\) | −2.28633e27 | − | 2.07692e26i | −1.34783 | − | 0.122438i | ||||
\(393\) | 3.02697e27 | + | 5.53467e26i | 1.73735 | + | 0.317665i | ||||
\(394\) | 3.16861e27 | 1.77076 | ||||||||
\(395\) | −1.86039e27 | −1.01236 | ||||||||
\(396\) | −1.89710e27 | + | 5.01428e27i | −1.00529 | + | 2.65711i | ||||
\(397\) | − | 1.33880e27i | − | 0.690899i | −0.938437 | − | 0.345450i | \(-0.887726\pi\) | ||
0.938437 | − | 0.345450i | \(-0.112274\pi\) | |||||||
\(398\) | −5.19236e27 | −2.60971 | ||||||||
\(399\) | 4.32043e25 | − | 2.70421e25i | 0.0211501 | − | 0.0132381i | ||||
\(400\) | −4.70033e25 | −0.0224129 | ||||||||
\(401\) | − | 9.39132e26i | − | 0.436225i | −0.975924 | − | 0.218113i | \(-0.930010\pi\) | ||
0.975924 | − | 0.218113i | \(-0.0699900\pi\) | |||||||
\(402\) | −1.12505e27 | + | 6.15303e27i | −0.509095 | + | 2.78430i | ||||
\(403\) | 4.36565e26 | 0.192462 | ||||||||
\(404\) | 2.55339e27 | 1.09676 | ||||||||
\(405\) | −1.74680e27 | − | 1.54257e27i | −0.731080 | − | 0.645604i | ||||
\(406\) | 1.02251e27 | + | 1.11961e27i | 0.417009 | + | 0.456608i | ||||
\(407\) | 6.13789e27i | 2.43937i | ||||||||
\(408\) | −5.57404e26 | + | 3.04850e27i | −0.215893 | + | 1.18074i | ||||
\(409\) | 4.42423e27i | 1.67010i | 0.550174 | + | 0.835050i | \(0.314561\pi\) | ||||
−0.550174 | + | 0.835050i | \(0.685439\pi\) | |||||||
\(410\) | 9.38482e26i | 0.345299i | ||||||||
\(411\) | −8.23740e25 | + | 4.50512e26i | −0.0295428 | + | 0.161573i | ||||
\(412\) | − | 4.12786e27i | − | 1.44312i | ||||||
\(413\) | 1.01861e27 | + | 1.11533e27i | 0.347161 | + | 0.380127i | ||||
\(414\) | −4.60619e26 | − | 1.74270e26i | −0.153052 | − | 0.0579055i | ||||
\(415\) | 5.57781e27 | 1.80700 | ||||||||
\(416\) | 2.56333e27 | 0.809701 | ||||||||
\(417\) | 3.54141e26 | − | 1.93684e27i | 0.109081 | − | 0.596574i | ||||
\(418\) | 2.18754e26i | 0.0657059i | ||||||||
\(419\) | −1.04379e27 | −0.305751 | −0.152875 | − | 0.988245i | \(-0.548853\pi\) | ||||
−0.152875 | + | 0.988245i | \(0.548853\pi\) | |||||||
\(420\) | 3.27436e27 | + | 5.23135e27i | 0.935425 | + | 1.49450i | ||||
\(421\) | −3.05496e27 | −0.851222 | −0.425611 | − | 0.904906i | \(-0.639941\pi\) | ||||
−0.425611 | + | 0.904906i | \(0.639941\pi\) | |||||||
\(422\) | − | 8.49861e27i | − | 2.30976i | ||||||
\(423\) | −3.94740e27 | − | 1.49346e27i | −1.04649 | − | 0.395930i | ||||
\(424\) | 7.15987e27 | 1.85167 | ||||||||
\(425\) | −1.71257e26 | −0.0432080 | ||||||||
\(426\) | 1.33786e27 | + | 2.44621e26i | 0.329313 | + | 0.0602132i | ||||
\(427\) | 2.01821e27 | − | 1.84318e27i | 0.484700 | − | 0.442665i | ||||
\(428\) | − | 3.16816e26i | − | 0.0742417i | ||||||
\(429\) | −9.39770e27 | − | 1.71832e27i | −2.14892 | − | 0.392919i | ||||
\(430\) | − | 1.20666e28i | − | 2.69255i | ||||||
\(431\) | − | 2.99105e27i | − | 0.651347i | −0.945482 | − | 0.325673i | \(-0.894409\pi\) | ||
0.945482 | − | 0.325673i | \(-0.105591\pi\) | |||||||
\(432\) | 1.85381e27 | + | 1.11765e27i | 0.393992 | + | 0.237534i | ||||
\(433\) | − | 1.68899e27i | − | 0.350351i | −0.984537 | − | 0.175175i | \(-0.943951\pi\) | ||
0.984537 | − | 0.175175i | \(-0.0560492\pi\) | |||||||
\(434\) | 7.72735e26 | + | 8.46112e26i | 0.156455 | + | 0.171311i | ||||
\(435\) | 3.27576e26 | − | 1.79155e27i | 0.0647402 | − | 0.354071i | ||||
\(436\) | 3.97266e27 | 0.766431 | ||||||||
\(437\) | −1.29379e25 | −0.00243674 | ||||||||
\(438\) | −1.37437e28 | − | 2.51296e27i | −2.52711 | − | 0.462070i | ||||
\(439\) | − | 8.32144e27i | − | 1.49390i | −0.664882 | − | 0.746949i | \(-0.731518\pi\) | ||
0.664882 | − | 0.746949i | \(-0.268482\pi\) | |||||||
\(440\) | −1.18348e28 | −2.07448 | ||||||||
\(441\) | −2.55335e27 | + | 5.25512e27i | −0.437024 | + | 0.899450i | ||||
\(442\) | −1.23598e28 | −2.06575 | ||||||||
\(443\) | 6.80601e27i | 1.11085i | 0.831568 | + | 0.555423i | \(0.187443\pi\) | ||||
−0.831568 | + | 0.555423i | \(0.812557\pi\) | |||||||
\(444\) | 1.73160e28 | + | 3.16615e27i | 2.76011 | + | 0.504673i | ||||
\(445\) | −4.30266e27 | −0.669819 | ||||||||
\(446\) | 1.66064e28 | 2.52499 | ||||||||
\(447\) | 5.78322e26 | − | 3.16291e27i | 0.0858897 | − | 0.469740i | ||||
\(448\) | 6.67575e27 | + | 7.30967e27i | 0.968458 | + | 1.06042i | ||||
\(449\) | 5.68492e27i | 0.805634i | 0.915280 | + | 0.402817i | \(0.131969\pi\) | ||||
−0.915280 | + | 0.402817i | \(0.868031\pi\) | |||||||
\(450\) | −2.08653e26 | + | 5.51498e26i | −0.0288864 | + | 0.0763506i | ||||
\(451\) | − | 2.45501e27i | − | 0.332048i | ||||||
\(452\) | − | 8.72843e27i | − | 1.15341i | ||||||
\(453\) | −9.78456e27 | − | 1.78906e27i | −1.26331 | − | 0.230990i | ||||
\(454\) | 2.17170e27i | 0.273976i | ||||||||
\(455\) | −8.12068e27 | + | 7.41643e27i | −1.00109 | + | 0.914271i | ||||
\(456\) | 2.75743e26 | + | 5.04183e25i | 0.0332180 | + | 0.00607376i | ||||
\(457\) | −8.96403e26 | −0.105532 | −0.0527659 | − | 0.998607i | \(-0.516804\pi\) | ||||
−0.0527659 | + | 0.998607i | \(0.516804\pi\) | |||||||
\(458\) | 1.46885e28 | 1.69001 | ||||||||
\(459\) | 6.75438e27 | + | 4.07215e27i | 0.759543 | + | 0.457921i | ||||
\(460\) | − | 1.56657e27i | − | 0.172184i | ||||||
\(461\) | 6.42135e27 | 0.689869 | 0.344934 | − | 0.938627i | \(-0.387901\pi\) | ||||
0.344934 | + | 0.938627i | \(0.387901\pi\) | |||||||
\(462\) | −1.33039e28 | − | 2.12553e28i | −1.39714 | − | 2.23216i | ||||
\(463\) | −5.84379e27 | −0.599921 | −0.299960 | − | 0.953952i | \(-0.596973\pi\) | ||||
−0.299960 | + | 0.953952i | \(0.596973\pi\) | |||||||
\(464\) | 1.69171e27i | 0.169781i | ||||||||
\(465\) | 2.47556e26 | − | 1.35391e27i | 0.0242894 | − | 0.132841i | ||||
\(466\) | −3.90402e27 | −0.374507 | ||||||||
\(467\) | 1.13932e28 | 1.06860 | 0.534302 | − | 0.845294i | \(-0.320574\pi\) | ||||
0.534302 | + | 0.845294i | \(0.320574\pi\) | |||||||
\(468\) | −9.69535e27 | + | 2.56261e28i | −0.889165 | + | 2.35018i | ||||
\(469\) | −1.27025e28 | − | 1.39088e28i | −1.13914 | − | 1.24731i | ||||
\(470\) | − | 2.08518e28i | − | 1.82859i | ||||||
\(471\) | 1.16390e27 | − | 6.36552e27i | 0.0998154 | − | 0.545901i | ||||
\(472\) | 8.30707e27i | 0.696718i | ||||||||
\(473\) | 3.15654e28i | 2.58922i | ||||||||
\(474\) | 3.89914e27 | − | 2.13248e28i | 0.312821 | − | 1.71085i | ||||
\(475\) | 1.54905e25i | 0.00121558i | ||||||||
\(476\) | −1.40853e28 | − | 1.54229e28i | −1.08117 | − | 1.18384i | ||||
\(477\) | 6.44790e27 | − | 1.70426e28i | 0.484145 | − | 1.27966i | ||||
\(478\) | 3.75454e28 | 2.75781 | ||||||||
\(479\) | 1.11198e28 | 0.799047 | 0.399523 | − | 0.916723i | \(-0.369176\pi\) | ||||
0.399523 | + | 0.916723i | \(0.369176\pi\) | |||||||
\(480\) | 1.45354e27 | − | 7.94959e27i | 0.102187 | − | 0.558871i | ||||
\(481\) | 3.13684e28i | 2.15759i | ||||||||
\(482\) | 1.86519e28 | 1.25524 | ||||||||
\(483\) | 1.25712e27 | − | 7.86844e26i | 0.0827810 | − | 0.0518136i | ||||
\(484\) | 4.12355e28 | 2.65702 | ||||||||
\(485\) | 2.02868e28i | 1.27916i | ||||||||
\(486\) | 2.13429e28 | − | 1.67898e28i | 1.31696 | − | 1.03601i | ||||
\(487\) | 1.17717e28 | 0.710859 | 0.355429 | − | 0.934703i | \(-0.384335\pi\) | ||||
0.355429 | + | 0.934703i | \(0.384335\pi\) | |||||||
\(488\) | 1.50318e28 | 0.888386 | ||||||||
\(489\) | −1.31179e28 | − | 2.39854e27i | −0.758788 | − | 0.138741i | ||||
\(490\) | −2.87477e28 | − | 2.61146e27i | −1.62759 | − | 0.147851i | ||||
\(491\) | − | 2.57361e28i | − | 1.42622i | −0.701052 | − | 0.713110i | \(-0.747286\pi\) | ||
0.701052 | − | 0.713110i | \(-0.252714\pi\) | |||||||
\(492\) | −6.92600e27 | − | 1.26639e27i | −0.375707 | − | 0.0686962i | ||||
\(493\) | 6.16376e27i | 0.327306i | ||||||||
\(494\) | 1.11797e27i | 0.0581161i | ||||||||
\(495\) | −1.06580e28 | + | 2.81705e28i | −0.542401 | + | 1.43364i | ||||
\(496\) | 1.27846e27i | 0.0636987i | ||||||||
\(497\) | −3.02419e27 | + | 2.76192e27i | −0.147525 | + | 0.134731i | ||||
\(498\) | −1.16904e28 | + | 6.39361e28i | −0.558369 | + | 3.05378i | ||||
\(499\) | −3.59436e28 | −1.68099 | −0.840496 | − | 0.541818i | \(-0.817736\pi\) | ||||
−0.840496 | + | 0.541818i | \(0.817736\pi\) | |||||||
\(500\) | −4.03759e28 | −1.84900 | ||||||||
\(501\) | −1.37281e27 | − | 2.51011e26i | −0.0615621 | − | 0.0112563i | ||||
\(502\) | − | 7.60547e27i | − | 0.333993i | ||||||
\(503\) | −3.28278e28 | −1.41181 | −0.705907 | − | 0.708304i | \(-0.749461\pi\) | ||||
−0.705907 | + | 0.708304i | \(0.749461\pi\) | |||||||
\(504\) | −2.98590e28 | + | 1.18710e28i | −1.25763 | + | 0.499994i | ||||
\(505\) | 1.43451e28 | 0.591758 | ||||||||
\(506\) | 6.36507e27i | 0.257171i | ||||||||
\(507\) | −2.31715e28 | − | 4.23679e27i | −0.917001 | − | 0.167669i | ||||
\(508\) | −1.53484e28 | −0.594970 | ||||||||
\(509\) | 1.78603e28 | 0.678192 | 0.339096 | − | 0.940752i | \(-0.389879\pi\) | ||||
0.339096 | + | 0.940752i | \(0.389879\pi\) | |||||||
\(510\) | −7.00866e27 | + | 3.83311e28i | −0.260704 | + | 1.42582i | ||||
\(511\) | 3.10671e28 | − | 2.83729e28i | 1.13209 | − | 1.03391i | ||||
\(512\) | 2.49474e28i | 0.890615i | ||||||||
\(513\) | 3.68334e26 | − | 6.10947e26i | 0.0128828 | − | 0.0213684i | ||||
\(514\) | − | 8.58107e28i | − | 2.94055i | ||||||
\(515\) | − | 2.31905e28i | − | 0.778636i | ||||||
\(516\) | 8.90513e28 | + | 1.62826e28i | 2.92967 | + | 0.535676i | ||||
\(517\) | 5.45472e28i | 1.75842i | ||||||||
\(518\) | −6.07955e28 | + | 5.55231e28i | −1.92048 | + | 1.75393i | ||||
\(519\) | −2.00276e28 | − | 3.66194e27i | −0.619970 | − | 0.113359i | ||||
\(520\) | −6.04834e28 | −1.83485 | ||||||||
\(521\) | 1.00903e28 | 0.299991 | 0.149995 | − | 0.988687i | \(-0.452074\pi\) | ||||
0.149995 | + | 0.988687i | \(0.452074\pi\) | |||||||
\(522\) | 1.98492e28 | + | 7.50972e27i | 0.578365 | + | 0.218818i | ||||
\(523\) | − | 3.31551e28i | − | 0.946854i | −0.880833 | − | 0.473427i | \(-0.843017\pi\) | ||
0.880833 | − | 0.473427i | \(-0.156983\pi\) | |||||||
\(524\) | −1.14059e29 | −3.19265 | ||||||||
\(525\) | −9.42085e26 | − | 1.50514e27i | −0.0258474 | − | 0.0412957i | ||||
\(526\) | −5.75474e28 | −1.54766 | ||||||||
\(527\) | 4.65808e27i | 0.122799i | ||||||||
\(528\) | 5.03204e27 | − | 2.75208e28i | 0.130043 | − | 0.711221i | ||||
\(529\) | 3.90951e28 | 0.990463 | ||||||||
\(530\) | 9.00264e28 | 2.23601 | ||||||||
\(531\) | 1.97733e28 | + | 7.48102e27i | 0.481490 | + | 0.182166i | ||||
\(532\) | −1.39503e27 | + | 1.27405e27i | −0.0333051 | + | 0.0304168i | ||||
\(533\) | − | 1.25467e28i | − | 0.293692i | ||||||
\(534\) | 9.01785e27 | − | 4.93196e28i | 0.206976 | − | 1.13197i | ||||
\(535\) | − | 1.77989e27i | − | 0.0400570i | ||||||
\(536\) | − | 1.03593e29i | − | 2.28614i | ||||||
\(537\) | 9.65043e27 | − | 5.27793e28i | 0.208841 | − | 1.14218i | ||||
\(538\) | 9.38183e28i | 1.99101i | ||||||||
\(539\) | 7.52025e28 | + | 6.83144e27i | 1.56513 | + | 0.142177i | ||||
\(540\) | 7.39758e28 | + | 4.45993e28i | 1.50992 | + | 0.910319i | ||||
\(541\) | 1.63947e28 | 0.328196 | 0.164098 | − | 0.986444i | \(-0.447529\pi\) | ||||
0.164098 | + | 0.986444i | \(0.447529\pi\) | |||||||
\(542\) | −7.12794e28 | −1.39950 | ||||||||
\(543\) | −7.91583e27 | + | 4.32925e28i | −0.152440 | + | 0.833709i | ||||
\(544\) | 2.73503e28i | 0.516624i | ||||||||
\(545\) | 2.23186e28 | 0.413527 | ||||||||
\(546\) | −6.79914e28 | − | 1.08628e29i | −1.23575 | − | 1.97432i | ||||
\(547\) | 4.86913e28 | 0.868130 | 0.434065 | − | 0.900882i | \(-0.357079\pi\) | ||||
0.434065 | + | 0.900882i | \(0.357079\pi\) | |||||||
\(548\) | − | 1.69757e28i | − | 0.296916i | ||||||
\(549\) | 1.35370e28 | − | 3.57801e28i | 0.232281 | − | 0.613948i | ||||
\(550\) | 7.62088e27 | 0.128291 | ||||||||
\(551\) | 5.57525e26 | 0.00920815 | ||||||||
\(552\) | 8.02330e27 | + | 1.46702e27i | 0.130015 | + | 0.0237726i | ||||
\(553\) | 4.40237e28 | + | 4.82041e28i | 0.699959 | + | 0.766426i | ||||
\(554\) | − | 1.96569e28i | − | 0.306663i | ||||||
\(555\) | 9.72821e28 | + | 1.77876e28i | 1.48921 | + | 0.272295i | ||||
\(556\) | 7.29819e28i | 1.09630i | ||||||||
\(557\) | − | 1.60545e28i | − | 0.236656i | −0.992975 | − | 0.118328i | \(-0.962247\pi\) | ||
0.992975 | − | 0.118328i | \(-0.0377534\pi\) | |||||||
\(558\) | 1.50004e28 | + | 5.67525e27i | 0.216992 | + | 0.0820967i | ||||
\(559\) | 1.61319e29i | 2.29014i | ||||||||
\(560\) | −2.17187e28 | − | 2.37811e28i | −0.302593 | − | 0.331327i | ||||
\(561\) | 1.83343e28 | − | 1.00272e29i | 0.250699 | − | 1.37110i | ||||
\(562\) | −1.47555e29 | −1.98027 | ||||||||
\(563\) | −6.06869e28 | −0.799386 | −0.399693 | − | 0.916649i | \(-0.630883\pi\) | ||||
−0.399693 | + | 0.916649i | \(0.630883\pi\) | |||||||
\(564\) | 1.53887e29 | + | 2.81374e28i | 1.98962 | + | 0.363792i | ||||
\(565\) | − | 4.90367e28i | − | 0.622319i | ||||||
\(566\) | −1.43448e29 | −1.78699 | ||||||||
\(567\) | 1.36660e27 | + | 8.17639e28i | 0.0167117 | + | 0.999860i | ||||
\(568\) | −2.25244e28 | −0.270393 | ||||||||
\(569\) | − | 4.05731e28i | − | 0.478144i | −0.971002 | − | 0.239072i | \(-0.923157\pi\) | ||
0.971002 | − | 0.239072i | \(-0.0768433\pi\) | |||||||
\(570\) | 3.46712e27 | + | 6.33947e26i | 0.0401128 | + | 0.00733444i | ||||
\(571\) | −6.86431e28 | −0.779682 | −0.389841 | − | 0.920882i | \(-0.627470\pi\) | ||||
−0.389841 | + | 0.920882i | \(0.627470\pi\) | |||||||
\(572\) | 3.54114e29 | 3.94898 | ||||||||
\(573\) | 2.00499e28 | − | 1.09655e29i | 0.219527 | − | 1.20062i | ||||
\(574\) | 2.43168e28 | − | 2.22080e28i | 0.261416 | − | 0.238745i | ||||
\(575\) | 4.50727e26i | 0.00475774i | ||||||||
\(576\) | 1.29591e29 | + | 4.90292e28i | 1.34319 | + | 0.508181i | ||||
\(577\) | − | 7.50036e28i | − | 0.763371i | −0.924292 | − | 0.381686i | \(-0.875344\pi\) | ||
0.924292 | − | 0.381686i | \(-0.124656\pi\) | |||||||
\(578\) | 3.57781e28i | 0.357581i | ||||||||
\(579\) | 8.76060e28 | + | 1.60183e28i | 0.859823 | + | 0.157214i | ||||
\(580\) | 6.75072e28i | 0.650663i | ||||||||
\(581\) | −1.31992e29 | − | 1.44526e29i | −1.24939 | − | 1.36803i | ||||
\(582\) | −2.32539e29 | − | 4.25186e28i | −2.16174 | − | 0.395264i | ||||
\(583\) | −2.35504e29 | −2.15020 | ||||||||
\(584\) | 2.31390e29 | 2.07496 | ||||||||
\(585\) | −5.44690e28 | + | 1.43969e29i | −0.479747 | + | 1.26804i | ||||
\(586\) | − | 7.23794e28i | − | 0.626167i | ||||||
\(587\) | 2.17091e29 | 1.84477 | 0.922384 | − | 0.386274i | \(-0.126238\pi\) | ||||
0.922384 | + | 0.386274i | \(0.126238\pi\) | |||||||
\(588\) | 5.80648e28 | − | 2.08635e29i | 0.484675 | − | 1.74150i | ||||
\(589\) | 4.21333e26 | 0.00345473 | ||||||||
\(590\) | 1.04451e29i | 0.841330i | ||||||||
\(591\) | −2.40212e28 | + | 1.31375e29i | −0.190076 | + | 1.03954i | ||||
\(592\) | −9.18611e28 | −0.714092 | ||||||||
\(593\) | −8.31854e28 | −0.635291 | −0.317646 | − | 0.948209i | \(-0.602892\pi\) | ||||
−0.317646 | + | 0.948209i | \(0.602892\pi\) | |||||||
\(594\) | −3.00568e29 | − | 1.81210e29i | −2.25520 | − | 1.35964i | ||||
\(595\) | −7.91322e28 | − | 8.66464e28i | −0.583344 | − | 0.638737i | ||||
\(596\) | 1.19181e29i | 0.863223i | ||||||||
\(597\) | 3.93632e28 | − | 2.15282e29i | 0.280130 | − | 1.53206i | ||||
\(598\) | 3.25295e28i | 0.227465i | ||||||||
\(599\) | − | 2.59144e29i | − | 1.78057i | −0.455404 | − | 0.890285i | \(-0.650505\pi\) | ||
0.455404 | − | 0.890285i | \(-0.349495\pi\) | |||||||
\(600\) | 1.75646e27 | − | 9.60627e27i | 0.0118591 | − | 0.0648584i | ||||
\(601\) | − | 2.24164e29i | − | 1.48725i | −0.668597 | − | 0.743625i | \(-0.733105\pi\) | ||
0.668597 | − | 0.743625i | \(-0.266895\pi\) | |||||||
\(602\) | −3.12654e29 | + | 2.85540e29i | −2.03846 | + | 1.86167i | ||||
\(603\) | −2.46584e29 | − | 9.32922e28i | −1.57991 | − | 0.597742i | ||||
\(604\) | 3.68691e29 | 2.32154 | ||||||||
\(605\) | 2.31663e29 | 1.43359 | ||||||||
\(606\) | −3.00655e28 | + | 1.64432e29i | −0.182855 | + | 1.00005i | ||||
\(607\) | 1.14847e29i | 0.686495i | 0.939245 | + | 0.343247i | \(0.111527\pi\) | ||||
−0.939245 | + | 0.343247i | \(0.888473\pi\) | |||||||
\(608\) | 2.47389e27 | 0.0145343 | ||||||||
\(609\) | −5.41721e28 | + | 3.39070e28i | −0.312820 | + | 0.195798i | ||||
\(610\) | 1.89005e29 | 1.07278 | ||||||||
\(611\) | 2.78770e29i | 1.55530i | ||||||||
\(612\) | −2.73426e29 | − | 1.03448e29i | −1.49951 | − | 0.567325i | ||||
\(613\) | −1.14554e29 | −0.617555 | −0.308777 | − | 0.951134i | \(-0.599920\pi\) | ||||
−0.308777 | + | 0.951134i | \(0.599920\pi\) | |||||||
\(614\) | −3.32118e29 | −1.76005 | ||||||||
\(615\) | −3.89106e28 | − | 7.11462e27i | −0.202712 | − | 0.0370649i | ||||
\(616\) | 2.80057e29 | + | 3.06650e29i | 1.43433 | + | 1.57053i | ||||
\(617\) | 2.67043e29i | 1.34458i | 0.740286 | + | 0.672292i | \(0.234690\pi\) | ||||
−0.740286 | + | 0.672292i | \(0.765310\pi\) | |||||||
\(618\) | 2.65823e29 | + | 4.86044e28i | 1.31587 | + | 0.240601i | ||||
\(619\) | − | 8.76085e28i | − | 0.426378i | −0.977011 | − | 0.213189i | \(-0.931615\pi\) | ||
0.977011 | − | 0.213189i | \(-0.0683849\pi\) | |||||||
\(620\) | 5.10166e28i | 0.244117i | ||||||||
\(621\) | 1.07174e28 | − | 1.77767e28i | 0.0504229 | − | 0.0836353i | ||||
\(622\) | − | 5.89440e29i | − | 2.72672i | ||||||
\(623\) | 1.01817e29 | + | 1.11486e29i | 0.463123 | + | 0.507101i | ||||
\(624\) | 2.57169e28 | − | 1.40648e29i | 0.115022 | − | 0.629066i | ||||
\(625\) | −2.15757e29 | −0.948909 | ||||||||
\(626\) | 3.51278e29 | 1.51922 | ||||||||
\(627\) | −9.06980e27 | − | 1.65837e27i | −0.0385735 | − | 0.00705297i | ||||
\(628\) | 2.39859e29i | 1.00318i | ||||||||
\(629\) | −3.34696e29 | −1.37664 | ||||||||
\(630\) | −3.75439e29 | + | 1.49262e29i | −1.51867 | + | 0.603774i | ||||
\(631\) | 1.30590e29 | 0.519521 | 0.259761 | − | 0.965673i | \(-0.416356\pi\) | ||||
0.259761 | + | 0.965673i | \(0.416356\pi\) | |||||||
\(632\) | 3.59028e29i | 1.40475i | ||||||||
\(633\) | 3.52363e29 | + | 6.44279e28i | 1.35597 | + | 0.247933i | ||||
\(634\) | 2.41577e28 | 0.0914362 | ||||||||
\(635\) | −8.62283e28 | −0.321015 | ||||||||
\(636\) | −1.21482e29 | + | 6.64396e29i | −0.444847 | + | 2.43292i | ||||
\(637\) | 3.84332e29 | + | 3.49129e28i | 1.38434 | + | 0.125754i | ||||
\(638\) | − | 2.74286e29i | − | 0.971821i | ||||||
\(639\) | −2.02845e28 | + | 5.36147e28i | −0.0706979 | + | 0.186864i | ||||
\(640\) | 5.18844e29i | 1.77888i | ||||||||
\(641\) | − | 1.42504e29i | − | 0.480637i | −0.970694 | − | 0.240318i | \(-0.922748\pi\) | ||
0.970694 | − | 0.240318i | \(-0.0772519\pi\) | |||||||
\(642\) | 2.04021e28 | + | 3.73043e27i | 0.0676951 | + | 0.0123777i | ||||
\(643\) | 6.97978e28i | 0.227838i | 0.993490 | + | 0.113919i | \(0.0363404\pi\) | ||||
−0.993490 | + | 0.113919i | \(0.963660\pi\) | |||||||
\(644\) | −4.05911e28 | + | 3.70709e28i | −0.130355 | + | 0.119051i | ||||
\(645\) | 5.00295e29 | + | 9.14764e28i | 1.58070 | + | 0.289023i | ||||
\(646\) | −1.19285e28 | −0.0370805 | ||||||||
\(647\) | 2.02043e29 | 0.617942 | 0.308971 | − | 0.951071i | \(-0.400015\pi\) | ||||
0.308971 | + | 0.951071i | \(0.400015\pi\) | |||||||
\(648\) | −2.97693e29 | + | 3.37107e29i | −0.895842 | + | 1.01445i | ||||
\(649\) | − | 2.73238e29i | − | 0.809043i | ||||||
\(650\) | 3.89474e28 | 0.113472 | ||||||||
\(651\) | −4.09390e28 | + | 2.56242e28i | −0.117364 | + | 0.0734598i | ||||
\(652\) | 4.94294e29 | 1.39439 | ||||||||
\(653\) | − | 5.42702e29i | − | 1.50651i | −0.657727 | − | 0.753256i | \(-0.728482\pi\) | ||
0.657727 | − | 0.753256i | \(-0.271518\pi\) | |||||||
\(654\) | −4.67770e28 | + | 2.55828e29i | −0.127781 | + | 0.698847i | ||||
\(655\) | −6.40790e29 | −1.72259 | ||||||||
\(656\) | 3.67424e28 | 0.0972024 | ||||||||
\(657\) | 2.08381e29 | − | 5.50778e29i | 0.542527 | − | 1.43397i | ||||
\(658\) | −5.40288e29 | + | 4.93432e29i | −1.38437 | + | 1.26432i | ||||
\(659\) | − | 1.77217e29i | − | 0.446897i | −0.974716 | − | 0.223449i | \(-0.928268\pi\) | ||
0.974716 | − | 0.223449i | \(-0.0717315\pi\) | |||||||
\(660\) | 2.00802e29 | − | 1.09821e30i | 0.498375 | − | 2.72567i | ||||
\(661\) | 6.03714e29i | 1.47474i | 0.675489 | + | 0.737370i | \(0.263933\pi\) | ||||
−0.675489 | + | 0.737370i | \(0.736067\pi\) | |||||||
\(662\) | − | 1.55293e29i | − | 0.373373i | ||||||
\(663\) | 9.36995e28 | − | 5.12453e29i | 0.221741 | − | 1.21272i | ||||
\(664\) | − | 1.07644e30i | − | 2.50740i | ||||||
\(665\) | −7.83734e27 | + | 7.15766e27i | −0.0179697 | + | 0.0164113i | ||||
\(666\) | −4.07782e29 | + | 1.07782e30i | −0.920342 | + | 2.43258i | ||||
\(667\) | 1.62223e28 | 0.0360405 | ||||||||
\(668\) | 5.17287e28 | 0.113130 | ||||||||
\(669\) | −1.25893e29 | + | 6.88522e29i | −0.271036 | + | 1.48233i | ||||
\(670\) | − | 1.30256e30i | − | 2.76065i | ||||||
\(671\) | −4.94427e29 | −1.03161 | ||||||||
\(672\) | −2.40377e29 | + | 1.50455e29i | −0.493759 | + | 0.309050i | ||||
\(673\) | −7.43604e28 | −0.150378 | −0.0751889 | − | 0.997169i | \(-0.523956\pi\) | ||||
−0.0751889 | + | 0.997169i | \(0.523956\pi\) | |||||||
\(674\) | − | 4.20967e28i | − | 0.0838145i | ||||||
\(675\) | −2.12840e28 | − | 1.28319e28i | −0.0417218 | − | 0.0251537i | ||||
\(676\) | 8.73123e29 | 1.68514 | ||||||||
\(677\) | −3.51683e29 | −0.668299 | −0.334149 | − | 0.942520i | \(-0.608449\pi\) | ||||
−0.334149 | + | 0.942520i | \(0.608449\pi\) | |||||||
\(678\) | 5.62087e29 | + | 1.02775e29i | 1.05170 | + | 0.192298i | ||||
\(679\) | 5.25647e29 | − | 4.80062e29i | 0.968416 | − | 0.884432i | ||||
\(680\) | − | 6.45349e29i | − | 1.17071i | ||||||
\(681\) | −9.00414e28 | − | 1.64636e28i | −0.160841 | − | 0.0294091i | ||||
\(682\) | − | 2.07284e29i | − | 0.364610i | ||||||
\(683\) | − | 7.68223e29i | − | 1.33067i | −0.746546 | − | 0.665334i | \(-0.768289\pi\) | ||
0.746546 | − | 0.665334i | \(-0.231711\pi\) | |||||||
\(684\) | −9.35707e27 | + | 2.47320e28i | −0.0159607 | + | 0.0421861i | ||||
\(685\) | − | 9.53706e28i | − | 0.160200i | ||||||
\(686\) | 6.12614e29 | + | 8.06674e29i | 1.01341 | + | 1.33443i | ||||
\(687\) | −1.11353e29 | + | 6.09002e29i | −0.181408 | + | 0.992140i | ||||
\(688\) | −4.72416e29 | −0.757960 | ||||||||
\(689\) | −1.20357e30 | −1.90182 | ||||||||
\(690\) | 1.00883e29 | + | 1.84459e28i | 0.157001 | + | 0.0287068i | ||||
\(691\) | 1.13347e30i | 1.73736i | 0.495375 | + | 0.868679i | \(0.335031\pi\) | ||||
−0.495375 | + | 0.868679i | \(0.664969\pi\) | |||||||
\(692\) | 7.54658e29 | 1.13929 | ||||||||
\(693\) | 9.82128e29 | − | 3.90462e29i | 1.46039 | − | 0.580603i | ||||
\(694\) | −1.71678e30 | −2.51443 | ||||||||
\(695\) | 4.10016e29i | 0.591507i | ||||||||
\(696\) | −3.45743e29 | − | 6.32174e28i | −0.491311 | − | 0.0898338i | ||||
\(697\) | 1.33871e29 | 0.187388 | ||||||||
\(698\) | 6.49729e29 | 0.895881 | ||||||||
\(699\) | 2.95963e28 | − | 1.61865e29i | 0.0402001 | − | 0.219859i | ||||
\(700\) | 4.43849e28 | + | 4.85996e28i | 0.0593890 | + | 0.0650284i | ||||
\(701\) | − | 5.77205e29i | − | 0.760836i | −0.924815 | − | 0.380418i | \(-0.875780\pi\) | ||
0.924815 | − | 0.380418i | \(-0.124220\pi\) | |||||||
\(702\) | −1.53609e30 | − | 9.26095e29i | −1.99470 | − | 1.20259i | ||||
\(703\) | 3.02739e28i | 0.0387292i | ||||||||
\(704\) | − | 1.79075e30i | − | 2.25695i | ||||||
\(705\) | 8.64542e29 | + | 1.58077e29i | 1.07350 | + | 0.196284i | ||||
\(706\) | − | 1.51209e30i | − | 1.84981i | ||||||
\(707\) | −3.39459e29 | − | 3.71693e29i | −0.409150 | − | 0.448003i | ||||
\(708\) | −7.70849e29 | − | 1.40946e29i | −0.915420 | − | 0.167380i | ||||
\(709\) | −1.84024e29 | −0.215322 | −0.107661 | − | 0.994188i | \(-0.534336\pi\) | ||||
−0.107661 | + | 0.994188i | \(0.534336\pi\) | |||||||
\(710\) | −2.83215e29 | −0.326516 | ||||||||
\(711\) | 8.54594e29 | + | 3.23326e29i | 0.970798 | + | 0.367291i | ||||
\(712\) | 8.30353e29i | 0.929443i | ||||||||
\(713\) | 1.22595e28 | 0.0135218 | ||||||||
\(714\) | 1.15904e30 | − | 7.25458e29i | 1.25970 | − | 0.788462i | ||||
\(715\) | 1.98943e30 | 2.13067 | ||||||||
\(716\) | 1.98877e30i | 2.09893i | ||||||||
\(717\) | −2.84632e29 | + | 1.55668e30i | −0.296028 | + | 1.61901i | ||||
\(718\) | 2.16244e30 | 2.21634 | ||||||||
\(719\) | 8.18084e29 | 0.826313 | 0.413157 | − | 0.910660i | \(-0.364426\pi\) | ||||
0.413157 | + | 0.910660i | \(0.364426\pi\) | |||||||
\(720\) | −4.21606e29 | − | 1.59510e29i | −0.419678 | − | 0.158780i | ||||
\(721\) | −6.00885e29 | + | 5.48774e29i | −0.589483 | + | 0.538361i | ||||
\(722\) | − | 1.73199e30i | − | 1.67457i | ||||||
\(723\) | −1.41400e29 | + | 7.73330e29i | −0.134740 | + | 0.736907i | ||||
\(724\) | − | 1.63130e30i | − | 1.53207i | ||||||
\(725\) | − | 1.94229e28i | − | 0.0179790i | ||||||
\(726\) | −4.85537e29 | + | 2.65545e30i | −0.442984 | + | 2.42273i | ||||
\(727\) | 1.90847e30i | 1.71622i | 0.513462 | + | 0.858112i | \(0.328363\pi\) | ||||
−0.513462 | + | 0.858112i | \(0.671637\pi\) | |||||||
\(728\) | 1.43126e30 | + | 1.56717e30i | 1.26865 | + | 1.38911i | ||||
\(729\) | 5.34325e29 | + | 1.01218e30i | 0.466838 | + | 0.884343i | ||||
\(730\) | 2.90944e30 | 2.50565 | ||||||||
\(731\) | −1.72125e30 | −1.46121 | ||||||||
\(732\) | −2.55044e29 | + | 1.39486e30i | −0.213426 | + | 1.16725i | ||||
\(733\) | − | 9.30043e29i | − | 0.767205i | −0.923498 | − | 0.383602i | \(-0.874683\pi\) | ||
0.923498 | − | 0.383602i | \(-0.125317\pi\) | |||||||
\(734\) | −2.58812e28 | −0.0210463 | ||||||||
\(735\) | 3.26211e29 | − | 1.17212e30i | 0.261506 | − | 0.939626i | ||||
\(736\) | 7.19828e28 | 0.0568868 | ||||||||
\(737\) | 3.40742e30i | 2.65471i | ||||||||
\(738\) | 1.63104e29 | − | 4.31104e29i | 0.125277 | − | 0.331124i | ||||
\(739\) | −7.79190e29 | −0.590034 | −0.295017 | − | 0.955492i | \(-0.595325\pi\) | ||||
−0.295017 | + | 0.955492i | \(0.595325\pi\) | |||||||
\(740\) | −3.66568e30 | −2.73667 | ||||||||
\(741\) | −4.63523e28 | − | 8.47530e27i | −0.0341178 | − | 0.00623827i | ||||
\(742\) | −2.13036e30 | − | 2.33266e30i | −1.54601 | − | 1.69282i | ||||
\(743\) | − | 3.05717e29i | − | 0.218745i | −0.994001 | − | 0.109372i | \(-0.965116\pi\) | ||
0.994001 | − | 0.109372i | \(-0.0348841\pi\) | |||||||
\(744\) | −2.61285e29 | − | 4.77747e28i | −0.184331 | − | 0.0337040i | ||||
\(745\) | 6.69567e29i | 0.465750i | ||||||||
\(746\) | − | 4.16646e29i | − | 0.285765i | ||||||
\(747\) | −2.56225e30 | − | 9.69398e29i | −1.73282 | − | 0.655595i | ||||
\(748\) | 3.77835e30i | 2.51962i | ||||||||
\(749\) | −4.61184e28 | + | 4.21189e28i | −0.0303260 | + | 0.0276960i | ||||
\(750\) | 4.75416e29 | − | 2.60010e30i | 0.308269 | − | 1.68596i | ||||
\(751\) | 8.50345e29 | 0.543721 | 0.271860 | − | 0.962337i | \(-0.412361\pi\) | ||||
0.271860 | + | 0.962337i | \(0.412361\pi\) | |||||||
\(752\) | −8.16367e29 | −0.514752 | ||||||||
\(753\) | 3.15332e29 | + | 5.76570e28i | 0.196075 | + | 0.0358513i | ||||
\(754\) | − | 1.40177e30i | − | 0.859564i | ||||||
\(755\) | 2.07133e30 | 1.25258 | ||||||||
\(756\) | −5.94940e29 | − | 2.97216e30i | −0.354809 | − | 1.77253i | ||||
\(757\) | −3.03706e30 | −1.78627 | −0.893134 | − | 0.449791i | \(-0.851498\pi\) | ||||
−0.893134 | + | 0.449791i | \(0.851498\pi\) | |||||||
\(758\) | − | 1.32609e30i | − | 0.769210i | ||||||
\(759\) | −2.63904e29 | − | 4.82535e28i | −0.150976 | − | 0.0276052i | ||||
\(760\) | −5.83731e28 | −0.0329359 | ||||||||
\(761\) | 6.28773e29 | 0.349909 | 0.174954 | − | 0.984577i | \(-0.444022\pi\) | ||||
0.174954 | + | 0.984577i | \(0.444022\pi\) | |||||||
\(762\) | 1.80724e29 | − | 9.88398e29i | 0.0991946 | − | 0.542506i | ||||
\(763\) | −5.28142e29 | − | 5.78293e29i | −0.285919 | − | 0.313069i | ||||
\(764\) | 4.13191e30i | 2.20633i | ||||||||
\(765\) | −1.53612e30 | − | 5.81176e29i | −0.809061 | − | 0.306099i | ||||
\(766\) | − | 3.64098e29i | − | 0.189154i | ||||||
\(767\) | − | 1.39642e30i | − | 0.715589i | ||||||
\(768\) | −3.15256e30 | − | 5.76431e29i | −1.59357 | − | 0.291376i | ||||
\(769\) | 1.58491e30i | 0.790275i | 0.918622 | + | 0.395138i | \(0.129303\pi\) | ||||
−0.918622 | + | 0.395138i | \(0.870697\pi\) | |||||||
\(770\) | 3.52136e30 | + | 3.85574e30i | 1.73204 | + | 1.89651i | ||||
\(771\) | 3.55782e30 | + | 6.50530e29i | 1.72629 | + | 0.315643i | ||||
\(772\) | −3.30108e30 | −1.58006 | ||||||||
\(773\) | 3.16378e30 | 1.49390 | 0.746951 | − | 0.664879i | \(-0.231517\pi\) | ||||
0.746951 | + | 0.664879i | \(0.231517\pi\) | |||||||
\(774\) | −2.09711e30 | + | 5.54294e30i | −0.976880 | + | 2.58202i | ||||
\(775\) | − | 1.46783e28i | − | 0.00674539i | ||||||
\(776\) | 3.91506e30 | 1.77497 | ||||||||
\(777\) | −1.84117e30 | − | 2.94158e30i | −0.823518 | − | 1.31571i | ||||
\(778\) | −2.04910e30 | −0.904226 | ||||||||
\(779\) | − | 1.21089e28i | − | 0.00527182i | ||||||
\(780\) | 1.02622e30 | − | 5.61252e30i | 0.440806 | − | 2.41082i | ||||
\(781\) | 7.40876e29 | 0.313985 | ||||||||
\(782\) | −3.47085e29 | −0.145132 | ||||||||
\(783\) | −4.61839e29 | + | 7.66041e29i | −0.190542 | + | 0.316048i | ||||
\(784\) | −1.02241e29 | + | 1.12550e30i | −0.0416204 | + | 0.458170i | ||||
\(785\) | 1.34754e30i | 0.541265i | ||||||||
\(786\) | 1.34302e30 | − | 7.34510e30i | 0.532285 | − | 2.91113i | ||||
\(787\) | − | 3.14723e30i | − | 1.23082i | −0.788207 | − | 0.615410i | \(-0.788991\pi\) | ||
0.788207 | − | 0.615410i | \(-0.211009\pi\) | |||||||
\(788\) | − | 4.95032e30i | − | 1.91033i | ||||||
\(789\) | 4.36266e29 | − | 2.38599e30i | 0.166128 | − | 0.908572i | ||||
\(790\) | 4.51432e30i | 1.69632i | ||||||||
\(791\) | −1.27058e30 | + | 1.16039e30i | −0.471140 | + | 0.430281i | ||||
\(792\) | 5.43650e30 | + | 2.05684e30i | 1.98932 | + | 0.752638i | ||||
\(793\) | −2.52683e30 | −0.912448 | ||||||||
\(794\) | −3.24866e30 | −1.15768 | ||||||||
\(795\) | −6.82489e29 | + | 3.73261e30i | −0.240016 | + | 1.31268i | ||||
\(796\) | 8.11202e30i | 2.81541i | ||||||||
\(797\) | −3.44359e30 | −1.17950 | −0.589752 | − | 0.807584i | \(-0.700775\pi\) | ||||
−0.589752 | + | 0.807584i | \(0.700775\pi\) | |||||||
\(798\) | −6.56191e28 | − | 1.04838e29i | −0.0221820 | − | 0.0354394i | ||||
\(799\) | −2.97443e30 | −0.992346 | ||||||||
\(800\) | − | 8.61848e28i | − | 0.0283782i | ||||||
\(801\) | 1.97649e30 | + | 7.47783e29i | 0.642322 | + | 0.243016i | ||||
\(802\) | −2.27885e30 | −0.730947 | ||||||||
\(803\) | −7.61094e30 | −2.40949 | ||||||||
\(804\) | 9.61289e30 | + | 1.75767e30i | 3.00376 | + | 0.549223i | ||||
\(805\) | −2.28043e29 | + | 2.08266e29i | −0.0703331 | + | 0.0642336i | ||||
\(806\) | − | 1.05935e30i | − | 0.322493i | ||||||
\(807\) | −3.88983e30 | − | 7.11236e29i | −1.16885 | − | 0.213718i | ||||
\(808\) | − | 2.76840e30i | − | 0.821125i | ||||||
\(809\) | − | 9.62295e29i | − | 0.281740i | −0.990028 | − | 0.140870i | \(-0.955010\pi\) | ||
0.990028 | − | 0.140870i | \(-0.0449900\pi\) | |||||||
\(810\) | −3.74312e30 | + | 4.23869e30i | −1.08179 | + | 1.22501i | ||||
\(811\) | 1.71177e30i | 0.488346i | 0.969732 | + | 0.244173i | \(0.0785164\pi\) | ||||
−0.969732 | + | 0.244173i | \(0.921484\pi\) | |||||||
\(812\) | 1.74917e30 | − | 1.59747e30i | 0.492598 | − | 0.449879i | ||||
\(813\) | 5.40369e29 | − | 2.95534e30i | 0.150224 | − | 0.821592i | ||||
\(814\) | 1.48939e31 | 4.08745 | ||||||||
\(815\) | 2.77697e30 | 0.752343 | ||||||||
\(816\) | 1.50070e30 | + | 2.74395e29i | 0.401371 | + | 0.0733888i | ||||
\(817\) | 1.55690e29i | 0.0411084i | ||||||||
\(818\) | 1.07356e31 | 2.79845 | ||||||||
\(819\) | 5.01929e30 | − | 1.99550e30i | 1.29170 | − | 0.513537i | ||||
\(820\) | 1.46619e30 | 0.372516 | ||||||||
\(821\) | − | 1.17086e30i | − | 0.293699i | −0.989159 | − | 0.146850i | \(-0.953087\pi\) | ||
0.989159 | − | 0.146850i | \(-0.0469133\pi\) | |||||||
\(822\) | 1.09319e30 | + | 1.99885e29i | 0.270734 | + | 0.0495024i | ||||
\(823\) | −7.35520e29 | −0.179844 | −0.0899221 | − | 0.995949i | \(-0.528662\pi\) | ||||
−0.0899221 | + | 0.995949i | \(0.528662\pi\) | |||||||
\(824\) | −4.47544e30 | −1.08044 | ||||||||
\(825\) | −5.77738e28 | + | 3.15971e29i | −0.0137710 | + | 0.0753149i | ||||
\(826\) | 2.70641e30 | − | 2.47170e30i | 0.636947 | − | 0.581709i | ||||
\(827\) | − | 1.24276e30i | − | 0.288787i | −0.989520 | − | 0.144394i | \(-0.953877\pi\) | ||
0.989520 | − | 0.144394i | \(-0.0461232\pi\) | |||||||
\(828\) | −2.72262e29 | + | 7.19625e29i | −0.0624697 | + | 0.165116i | ||||
\(829\) | 3.26641e30i | 0.740028i | 0.929026 | + | 0.370014i | \(0.120647\pi\) | ||||
−0.929026 | + | 0.370014i | \(0.879353\pi\) | |||||||
\(830\) | − | 1.35349e31i | − | 3.02784i | ||||||
\(831\) | 8.14998e29 | + | 1.49018e29i | 0.180030 | + | 0.0329177i | ||||
\(832\) | − | 9.15184e30i | − | 1.99624i | ||||||
\(833\) | −3.72515e29 | + | 4.10076e30i | −0.0802365 | + | 0.883266i | ||||
\(834\) | −4.69983e30 | − | 8.59342e29i | −0.999629 | − | 0.182777i | ||||
\(835\) | 2.90614e29 | 0.0610392 | ||||||||
\(836\) | 3.41759e29 | 0.0708849 | ||||||||
\(837\) | −3.49021e29 | + | 5.78913e29i | −0.0714882 | + | 0.118576i | ||||
\(838\) | 2.53282e30i | 0.512321i | ||||||||
\(839\) | 4.31511e30 | 0.861968 | 0.430984 | − | 0.902360i | \(-0.358167\pi\) | ||||
0.430984 | + | 0.902360i | \(0.358167\pi\) | |||||||
\(840\) | 5.67184e30 | − | 3.55007e30i | 1.11890 | − | 0.700333i | ||||
\(841\) | 4.43379e30 | 0.863807 | ||||||||
\(842\) | 7.41301e30i | 1.42632i | ||||||||
\(843\) | 1.11862e30 | − | 6.11783e30i | 0.212565 | − | 1.16254i | ||||
\(844\) | −1.32774e31 | −2.49182 | ||||||||
\(845\) | 4.90525e30 | 0.909213 | ||||||||
\(846\) | −3.62395e30 | + | 9.57857e30i | −0.663427 | + | 1.75352i | ||||
\(847\) | −5.48202e30 | − | 6.00258e30i | −0.991208 | − | 1.08533i | ||||
\(848\) | − | 3.52461e30i | − | 0.629441i | ||||||
\(849\) | 1.08748e30 | − | 5.94754e30i | 0.191818 | − | 1.04907i | ||||
\(850\) | 4.15563e29i | 0.0724000i | ||||||||
\(851\) | 8.80880e29i | 0.151585i | ||||||||
\(852\) | 3.82171e29 | − | 2.09013e30i | 0.0649593 | − | 0.355270i | ||||
\(853\) | − | 4.54969e30i | − | 0.763866i | −0.924190 | − | 0.381933i | \(-0.875259\pi\) | ||
0.924190 | − | 0.381933i | \(-0.124741\pi\) | |||||||
\(854\) | −4.47258e30 | − | 4.89728e30i | −0.741737 | − | 0.812171i | ||||
\(855\) | −5.25685e28 | + | 1.38945e29i | −0.00861155 | + | 0.0227615i | ||||
\(856\) | −3.43493e29 | −0.0555832 | ||||||||
\(857\) | −2.06974e30 | −0.330840 | −0.165420 | − | 0.986223i | \(-0.552898\pi\) | ||||
−0.165420 | + | 0.986223i | \(0.552898\pi\) | |||||||
\(858\) | −4.16960e30 | + | 2.28040e31i | −0.658382 | + | 3.60076i | ||||
\(859\) | − | 6.62806e29i | − | 0.103385i | −0.998663 | − | 0.0516926i | \(-0.983538\pi\) | ||
0.998663 | − | 0.0516926i | \(-0.0164616\pi\) | |||||||
\(860\) | −1.88516e31 | −2.90479 | ||||||||
\(861\) | 7.36426e29 | + | 1.17656e30i | 0.112098 | + | 0.179095i | ||||
\(862\) | −7.25794e30 | −1.09141 | ||||||||
\(863\) | 6.69570e30i | 0.994678i | 0.867556 | + | 0.497339i | \(0.165690\pi\) | ||||
−0.867556 | + | 0.497339i | \(0.834310\pi\) | |||||||
\(864\) | −2.04931e30 | + | 3.39914e30i | −0.300755 | + | 0.498855i | ||||
\(865\) | 4.23970e30 | 0.614705 | ||||||||
\(866\) | −4.09841e30 | −0.587054 | ||||||||
\(867\) | −1.48340e30 | − | 2.71233e29i | −0.209923 | − | 0.0383833i | ||||
\(868\) | 1.32188e30 | − | 1.20724e30i | 0.184814 | − | 0.168787i | ||||
\(869\) | − | 1.18092e31i | − | 1.63122i | ||||||
\(870\) | −4.34728e30 | − | 7.94879e29i | −0.593288 | − | 0.108480i | ||||
\(871\) | 1.74140e31i | 2.34806i | ||||||||
\(872\) | − | 4.30717e30i | − | 0.573811i | ||||||
\(873\) | 3.52575e30 | − | 9.31902e30i | 0.464090 | − | 1.22665i | ||||
\(874\) | 3.13945e28i | 0.00408304i | ||||||||
\(875\) | 5.36774e30 | + | 5.87746e30i | 0.689775 | + | 0.755274i | ||||
\(876\) | −3.92600e30 | + | 2.14717e31i | −0.498491 | + | 2.72630i | ||||
\(877\) | −1.24118e31 | −1.55718 | −0.778591 | − | 0.627532i | \(-0.784065\pi\) | ||||
−0.778591 | + | 0.627532i | \(0.784065\pi\) | |||||||
\(878\) | −2.01924e31 | −2.50320 | ||||||||
\(879\) | 3.00094e30 | + | 5.48708e29i | 0.367599 | + | 0.0672137i | ||||
\(880\) | 5.82597e30i | 0.705180i | ||||||||
\(881\) | 9.60245e30 | 1.14851 | 0.574256 | − | 0.818676i | \(-0.305292\pi\) | ||||
0.574256 | + | 0.818676i | \(0.305292\pi\) | |||||||
\(882\) | 1.27518e31 | + | 6.19583e30i | 1.50713 | + | 0.732284i | ||||
\(883\) | −4.97632e30 | −0.581194 | −0.290597 | − | 0.956846i | \(-0.593854\pi\) | ||||
−0.290597 | + | 0.956846i | \(0.593854\pi\) | |||||||
\(884\) | 1.93097e31i | 2.22857i | ||||||||
\(885\) | −4.33067e30 | − | 7.91842e29i | −0.493913 | − | 0.0903097i | ||||
\(886\) | 1.65151e31 | 1.86135 | ||||||||
\(887\) | −4.02920e30 | −0.448767 | −0.224383 | − | 0.974501i | \(-0.572037\pi\) | ||||
−0.224383 | + | 0.974501i | \(0.572037\pi\) | |||||||
\(888\) | 3.43275e30 | − | 1.87741e31i | 0.377838 | − | 2.06644i | ||||
\(889\) | 2.04048e30 | + | 2.23425e30i | 0.221955 | + | 0.243031i | ||||
\(890\) | 1.04406e31i | 1.12236i | ||||||||
\(891\) | 9.79179e30 | − | 1.10882e31i | 1.04027 | − | 1.17800i | ||||
\(892\) | − | 2.59442e31i | − | 2.72401i | ||||||
\(893\) | 2.69043e29i | 0.0279179i | ||||||||
\(894\) | −7.67496e30 | − | 1.40333e30i | −0.787104 | − | 0.143918i | ||||
\(895\) | 1.11730e31i | 1.13248i | ||||||||
\(896\) | 1.34437e31 | − | 1.22778e31i | 1.34674 | − | 1.22995i | ||||
\(897\) | −1.34871e30 | − | 2.46606e29i | −0.133536 | − | 0.0244164i | ||||
\(898\) | 1.37948e31 | 1.34993 | ||||||||
\(899\) | −5.28291e29 | −0.0510972 | ||||||||
\(900\) | 8.61605e29 | + | 3.25979e29i | 0.0823686 | + | 0.0311633i | ||||
\(901\) | − | 1.28419e31i | − | 1.21344i | ||||||
\(902\) | −5.95722e30 | −0.556385 | ||||||||
\(903\) | −9.46862e30 | − | 1.51277e31i | −0.874108 | − | 1.39654i | ||||
\(904\) | −9.46339e30 | −0.863531 | ||||||||
\(905\) | − | 9.16475e30i | − | 0.826629i | ||||||
\(906\) | −4.34124e30 | + | 2.37427e31i | −0.387051 | + | 2.11682i | ||||
\(907\) | 2.11316e31 | 1.86233 | 0.931165 | − | 0.364598i | \(-0.118793\pi\) | ||||
0.931165 | + | 0.364598i | \(0.118793\pi\) | |||||||
\(908\) | 3.39285e30 | 0.295572 | ||||||||
\(909\) | −6.58962e30 | − | 2.49311e30i | −0.567465 | − | 0.214694i | ||||
\(910\) | 1.79964e31 | + | 1.97053e31i | 1.53197 | + | 1.67744i | ||||
\(911\) | − | 1.39457e31i | − | 1.17354i | −0.809753 | − | 0.586770i | \(-0.800399\pi\) | ||
0.809753 | − | 0.586770i | \(-0.199601\pi\) | |||||||
\(912\) | 2.48196e28 | − | 1.35741e29i | 0.00206466 | − | 0.0112918i | ||||
\(913\) | 3.54064e31i | 2.91165i | ||||||||
\(914\) | 2.17517e30i | 0.176831i | ||||||||
\(915\) | −1.43285e30 | + | 7.83640e30i | −0.115154 | + | 0.629789i | ||||
\(916\) | − | 2.29478e31i | − | 1.82322i | ||||||
\(917\) | 1.51635e31 | + | 1.66034e31i | 1.19103 | + | 1.30412i | ||||
\(918\) | 9.88129e30 | − | 1.63899e31i | 0.767301 | − | 1.27270i | ||||
\(919\) | −1.30738e31 | −1.00366 | −0.501832 | − | 0.864965i | \(-0.667340\pi\) | ||||
−0.501832 | + | 0.864965i | \(0.667340\pi\) | |||||||
\(920\) | −1.69848e30 | −0.128910 | ||||||||
\(921\) | 2.51779e30 | − | 1.37700e31i | 0.188926 | − | 1.03326i | ||||
\(922\) | − | 1.55817e31i | − | 1.15596i | ||||||
\(923\) | 3.78634e30 | 0.277716 | ||||||||
\(924\) | −3.32071e31 | + | 2.07847e31i | −2.40811 | + | 1.50726i | ||||
\(925\) | 1.05467e30 | 0.0756189 | ||||||||
\(926\) | 1.41803e31i | 1.00524i | ||||||||
\(927\) | −4.03040e30 | + | 1.06529e31i | −0.282495 | + | 0.746672i | ||||
\(928\) | −3.10191e30 | −0.214969 | ||||||||
\(929\) | 1.45756e31 | 0.998757 | 0.499379 | − | 0.866384i | \(-0.333562\pi\) | ||||
0.499379 | + | 0.866384i | \(0.333562\pi\) | |||||||
\(930\) | −3.28533e30 | − | 6.00707e29i | −0.222591 | − | 0.0406997i | ||||
\(931\) | 3.70922e29 | + | 3.36947e28i | 0.0248491 | + | 0.00225731i | ||||
\(932\) | 6.09925e30i | 0.404026i | ||||||||
\(933\) | 2.44389e31 | + | 4.46854e30i | 1.60075 | + | 0.292690i | ||||
\(934\) | − | 2.76461e31i | − | 1.79057i | ||||||
\(935\) | 2.12269e31i | 1.35946i | ||||||||
\(936\) | 2.77839e31 | + | 1.05117e31i | 1.75953 | + | 0.665699i | ||||
\(937\) | − | 1.56185e31i | − | 0.978081i | −0.872261 | − | 0.489040i | \(-0.837347\pi\) | ||
0.872261 | − | 0.489040i | \(-0.162653\pi\) | |||||||
\(938\) | −3.37503e31 | + | 3.08234e31i | −2.09001 | + | 1.90876i | ||||
\(939\) | −2.66304e30 | + | 1.45644e31i | −0.163075 | + | 0.891878i | ||||
\(940\) | −3.25768e31 | −1.97272 | ||||||||
\(941\) | 2.46100e31 | 1.47374 | 0.736870 | − | 0.676034i | \(-0.236303\pi\) | ||||
0.736870 | + | 0.676034i | \(0.236303\pi\) | |||||||
\(942\) | −1.54463e31 | − | 2.82427e30i | −0.914721 | − | 0.167252i | ||||
\(943\) | − | 3.52332e29i | − | 0.0206338i | ||||||
\(944\) | 4.08935e30 | 0.236836 | ||||||||
\(945\) | −3.34240e30 | − | 1.66977e31i | −0.191436 | − | 0.956365i | ||||
\(946\) | 7.65952e31 | 4.33855 | ||||||||
\(947\) | − | 2.24985e30i | − | 0.126032i | −0.998013 | − | 0.0630158i | \(-0.979928\pi\) | ||
0.998013 | − | 0.0630158i | \(-0.0200719\pi\) | |||||||
\(948\) | −3.33157e31 | − | 6.09162e30i | −1.84570 | − | 0.337478i | ||||
\(949\) | −3.88966e31 | −2.13116 | ||||||||
\(950\) | 3.75885e28 | 0.00203684 | ||||||||
\(951\) | −1.83139e29 | + | 1.00161e30i | −0.00981490 | + | 0.0536787i | ||||
\(952\) | −1.67215e31 | + | 1.52714e31i | −0.886314 | + | 0.809450i | ||||
\(953\) | 3.17530e30i | 0.166460i | 0.996530 | + | 0.0832299i | \(0.0265236\pi\) | ||||
−0.996530 | + | 0.0832299i | \(0.973476\pi\) | |||||||
\(954\) | −4.13549e31 | − | 1.56462e31i | −2.14422 | − | 0.811241i | ||||
\(955\) | 2.32132e31i | 1.19042i | ||||||||
\(956\) | − | 5.86573e31i | − | 2.97518i | ||||||
\(957\) | 1.13722e31 | + | 2.07936e30i | 0.570520 | + | 0.104317i | ||||
\(958\) | − | 2.69827e31i | − | 1.33890i | ||||||
\(959\) | −2.47113e30 | + | 2.25683e30i | −0.121283 | + | 0.110765i | ||||
\(960\) | −2.83824e31 | − | 5.18958e30i | −1.37785 | − | 0.251932i | ||||
\(961\) | 2.04263e31 | 0.980829 | ||||||||
\(962\) | 7.61171e31 | 3.61530 | ||||||||
\(963\) | −3.09336e29 | + | 8.17617e29i | −0.0145330 | + | 0.0384126i | ||||
\(964\) | − | 2.91398e31i | − | 1.35419i | ||||||
\(965\) | −1.85456e31 | −0.852520 | ||||||||
\(966\) | −1.90932e30 | − | 3.05046e30i | −0.0868197 | − | 0.138709i | ||||
\(967\) | −5.65467e30 | −0.254348 | −0.127174 | − | 0.991880i | \(-0.540591\pi\) | ||||
−0.127174 | + | 0.991880i | \(0.540591\pi\) | |||||||
\(968\) | − | 4.47077e31i | − | 1.98926i | ||||||
\(969\) | 9.04302e28 | − | 4.94572e29i | 0.00398028 | − | 0.0217686i | ||||
\(970\) | 4.92269e31 | 2.14338 | ||||||||
\(971\) | −6.16171e30 | −0.265399 | −0.132700 | − | 0.991156i | \(-0.542365\pi\) | ||||
−0.132700 | + | 0.991156i | \(0.542365\pi\) | |||||||
\(972\) | −2.62306e31 | − | 3.33439e31i | −1.11767 | − | 1.42076i | ||||
\(973\) | 1.06238e31 | − | 9.70251e30i | 0.447813 | − | 0.408977i | ||||
\(974\) | − | 2.85645e31i | − | 1.19113i | ||||||
\(975\) | −2.95260e29 | + | 1.61481e30i | −0.0121803 | + | 0.0666151i | ||||
\(976\) | − | 7.39972e30i | − | 0.301990i | ||||||
\(977\) | − | 4.41902e31i | − | 1.78416i | −0.451882 | − | 0.892078i | \(-0.649247\pi\) | ||
0.451882 | − | 0.892078i | \(-0.350753\pi\) | |||||||
\(978\) | −5.82018e30 | + | 3.18312e31i | −0.232476 | + | 1.27144i | ||||
\(979\) | − | 2.73121e31i | − | 1.07929i | ||||||
\(980\) | −4.07989e30 | + | 4.49126e31i | −0.159505 | + | 1.75588i | ||||
\(981\) | −1.02524e31 | − | 3.87887e30i | −0.396551 | − | 0.150031i | ||||
\(982\) | −6.24499e31 | −2.38980 | ||||||||
\(983\) | 1.21606e31 | 0.460410 | 0.230205 | − | 0.973142i | \(-0.426060\pi\) | ||||
0.230205 | + | 0.973142i | \(0.426060\pi\) | |||||||
\(984\) | −1.37302e30 | + | 7.50920e30i | −0.0514314 | + | 0.281284i | ||||
\(985\) | − | 2.78112e31i | − | 1.03071i | ||||||
\(986\) | 1.49567e31 | 0.548439 | ||||||||
\(987\) | −1.63624e31 | − | 2.61417e31i | −0.593632 | − | 0.948427i | ||||
\(988\) | 1.74660e30 | 0.0626969 | ||||||||
\(989\) | 4.53012e30i | 0.160897i | ||||||||
\(990\) | 6.83571e31 | + | 2.58622e31i | 2.40223 | + | 0.908857i | ||||
\(991\) | −2.86108e31 | −0.994846 | −0.497423 | − | 0.867508i | \(-0.665720\pi\) | ||||
−0.497423 | + | 0.867508i | \(0.665720\pi\) | |||||||
\(992\) | −2.34418e30 | −0.0806525 | ||||||||
\(993\) | 6.43864e30 | + | 1.17727e30i | 0.219193 | + | 0.0400784i | ||||
\(994\) | 6.70194e30 | + | 7.33835e30i | 0.225758 | + | 0.247196i | ||||
\(995\) | 4.55738e31i | 1.51905i | ||||||||
\(996\) | 9.98873e31 | + | 1.82639e31i | 3.29448 | + | 0.602380i | ||||
\(997\) | 2.23701e31i | 0.730077i | 0.930992 | + | 0.365039i | \(0.118944\pi\) | ||||
−0.930992 | + | 0.365039i | \(0.881056\pi\) | |||||||
\(998\) | 8.72189e31i | 2.81670i | ||||||||
\(999\) | −4.15965e31 | − | 2.50781e31i | −1.32929 | − | 0.801415i |
(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 | 21.22.c.b.20.13 | ✓ | 52 | |
3.2 | odd | 2 | inner | 21.22.c.b.20.40 | yes | 52 | |
7.6 | odd | 2 | inner | 21.22.c.b.20.39 | yes | 52 | |
21.20 | even | 2 | inner | 21.22.c.b.20.14 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.22.c.b.20.13 | ✓ | 52 | 1.1 | even | 1 | trivial | |
21.22.c.b.20.14 | yes | 52 | 21.20 | even | 2 | inner | |
21.22.c.b.20.39 | yes | 52 | 7.6 | odd | 2 | inner | |
21.22.c.b.20.40 | yes | 52 | 3.2 | odd | 2 | inner |