Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,21,Mod(7,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 21, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.7");
S:= CuspForms(chi, 21);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 21 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.4216518123\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} - 1800529 x^{18} + 10471600 x^{17} + 1401323871170 x^{16} - 8255926364216 x^{15} + \cdots + 17\!\cdots\!88 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{174}\cdot 3^{82}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 7.2 | ||
Root | \(470.592 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.7 |
Dual form | 12.21.d.a.7.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1009.00 | + | 174.621i | −0.985353 | + | 0.170528i | ||||
\(3\) | − | 34092.0i | − | 0.577350i | ||||||
\(4\) | 987591. | − | 352385.i | 0.941840 | − | 0.336061i | ||||
\(5\) | 5.90557e6 | 0.604730 | 0.302365 | − | 0.953192i | \(-0.402224\pi\) | ||||
0.302365 | + | 0.953192i | \(0.402224\pi\) | |||||||
\(6\) | 5.95317e6 | + | 3.43988e7i | 0.0984545 | + | 0.568894i | ||||
\(7\) | 2.05952e8i | 0.729096i | 0.931185 | + | 0.364548i | \(0.118777\pi\) | ||||
−0.931185 | + | 0.364548i | \(0.881223\pi\) | |||||||
\(8\) | −9.34947e8 | + | 5.28011e8i | −0.870737 | + | 0.491749i | ||||
\(9\) | −1.16226e9 | −0.333333 | ||||||||
\(10\) | −5.95872e9 | + | 1.03123e9i | −0.595872 | + | 0.103123i | ||||
\(11\) | 6.76899e9i | 0.260974i | 0.991450 | + | 0.130487i | \(0.0416541\pi\) | ||||
−0.991450 | + | 0.130487i | \(0.958346\pi\) | |||||||
\(12\) | −1.20135e10 | − | 3.36689e10i | −0.194025 | − | 0.543772i | ||||
\(13\) | 1.26265e10 | 0.0915900 | 0.0457950 | − | 0.998951i | \(-0.485418\pi\) | ||||
0.0457950 | + | 0.998951i | \(0.485418\pi\) | |||||||
\(14\) | −3.59635e10 | − | 2.07805e11i | −0.124331 | − | 0.718417i | ||||
\(15\) | − | 2.01332e11i | − | 0.349141i | ||||||
\(16\) | 8.51161e11 | − | 6.96025e11i | 0.774126 | − | 0.633031i | ||||
\(17\) | −4.23901e11 | −0.210269 | −0.105134 | − | 0.994458i | \(-0.533527\pi\) | ||||
−0.105134 | + | 0.994458i | \(0.533527\pi\) | |||||||
\(18\) | 1.17272e12 | − | 2.02955e11i | 0.328451 | − | 0.0568427i | ||||
\(19\) | − | 2.41340e12i | − | 0.393634i | −0.980440 | − | 0.196817i | \(-0.936939\pi\) | ||
0.980440 | − | 0.196817i | \(-0.0630606\pi\) | |||||||
\(20\) | 5.83228e12 | − | 2.08103e12i | 0.569559 | − | 0.203226i | ||||
\(21\) | 7.02130e12 | 0.420944 | ||||||||
\(22\) | −1.18201e12 | − | 6.82992e12i | −0.0445034 | − | 0.257151i | ||||
\(23\) | − | 2.16590e13i | − | 0.522829i | −0.965227 | − | 0.261415i | \(-0.915811\pi\) | ||
0.965227 | − | 0.261415i | \(-0.0841890\pi\) | |||||||
\(24\) | 1.80009e13 | + | 3.18742e13i | 0.283911 | + | 0.502720i | ||||
\(25\) | −6.04917e13 | −0.634302 | ||||||||
\(26\) | −1.27401e13 | + | 2.20484e12i | −0.0902485 | + | 0.0156187i | ||||
\(27\) | 3.96238e13i | 0.192450i | ||||||||
\(28\) | 7.25743e13 | + | 2.03396e14i | 0.245021 | + | 0.686692i | ||||
\(29\) | −5.86863e14 | −1.39494 | −0.697472 | − | 0.716612i | \(-0.745692\pi\) | ||||
−0.697472 | + | 0.716612i | \(0.745692\pi\) | |||||||
\(30\) | 3.51568e13 | + | 2.03145e14i | 0.0595384 | + | 0.344027i | ||||
\(31\) | 1.62128e15i | 1.97807i | 0.147678 | + | 0.989035i | \(0.452820\pi\) | ||||
−0.147678 | + | 0.989035i | \(0.547180\pi\) | |||||||
\(32\) | −7.37282e14 | + | 8.50921e14i | −0.654838 | + | 0.755769i | ||||
\(33\) | 2.30768e14 | 0.150673 | ||||||||
\(34\) | 4.27716e14 | − | 7.40219e13i | 0.207189 | − | 0.0358568i | ||||
\(35\) | 1.21626e15i | 0.440906i | ||||||||
\(36\) | −1.14784e15 | + | 4.09564e14i | −0.313947 | + | 0.112020i | ||||
\(37\) | 2.36165e15 | 0.491131 | 0.245566 | − | 0.969380i | \(-0.421026\pi\) | ||||
0.245566 | + | 0.969380i | \(0.421026\pi\) | |||||||
\(38\) | 4.21430e14 | + | 2.43512e15i | 0.0671258 | + | 0.387869i | ||||
\(39\) | − | 4.30461e14i | − | 0.0528795i | ||||||
\(40\) | −5.52139e15 | + | 3.11821e15i | −0.526561 | + | 0.297375i | ||||
\(41\) | −5.51421e15 | −0.410813 | −0.205407 | − | 0.978677i | \(-0.565852\pi\) | ||||
−0.205407 | + | 0.978677i | \(0.565852\pi\) | |||||||
\(42\) | −7.08450e15 | + | 1.22606e15i | −0.414778 | + | 0.0717828i | ||||
\(43\) | 2.09388e16i | 0.968872i | 0.874827 | + | 0.484436i | \(0.160975\pi\) | ||||
−0.874827 | + | 0.484436i | \(0.839025\pi\) | |||||||
\(44\) | 2.38529e15 | + | 6.68499e15i | 0.0877031 | + | 0.245796i | ||||
\(45\) | −6.86381e15 | −0.201577 | ||||||||
\(46\) | 3.78211e15 | + | 2.18540e16i | 0.0891571 | + | 0.515171i | ||||
\(47\) | 4.99979e16i | 0.950547i | 0.879838 | + | 0.475273i | \(0.157651\pi\) | ||||
−0.879838 | + | 0.475273i | \(0.842349\pi\) | |||||||
\(48\) | −2.37289e16 | − | 2.90177e16i | −0.365481 | − | 0.446942i | ||||
\(49\) | 3.73762e16 | 0.468419 | ||||||||
\(50\) | 6.10362e16 | − | 1.05631e16i | 0.625011 | − | 0.108166i | ||||
\(51\) | 1.44516e16i | 0.121399i | ||||||||
\(52\) | 1.24698e16 | − | 4.44938e15i | 0.0862632 | − | 0.0307798i | ||||
\(53\) | −2.14062e17 | −1.22400 | −0.612001 | − | 0.790857i | \(-0.709635\pi\) | ||||
−0.612001 | + | 0.790857i | \(0.709635\pi\) | |||||||
\(54\) | −6.91914e15 | − | 3.99804e16i | −0.0328182 | − | 0.189631i | ||||
\(55\) | 3.99747e16i | 0.157819i | ||||||||
\(56\) | −1.08745e17 | − | 1.92554e17i | −0.358532 | − | 0.634851i | ||||
\(57\) | −8.22775e16 | −0.227265 | ||||||||
\(58\) | 5.92145e17 | − | 1.02478e17i | 1.37451 | − | 0.237877i | ||||
\(59\) | − | 5.17989e17i | − | 1.01344i | −0.862109 | − | 0.506722i | \(-0.830857\pi\) | ||
0.862109 | − | 0.506722i | \(-0.169143\pi\) | |||||||
\(60\) | −7.09465e16 | − | 1.98834e17i | −0.117333 | − | 0.328835i | ||||
\(61\) | 1.08120e18 | 1.51568 | 0.757838 | − | 0.652443i | \(-0.226256\pi\) | ||||
0.757838 | + | 0.652443i | \(0.226256\pi\) | |||||||
\(62\) | −2.83110e17 | − | 1.63588e18i | −0.337317 | − | 1.94910i | ||||
\(63\) | − | 2.39370e17i | − | 0.243032i | ||||||
\(64\) | 5.95330e17 | − | 9.87325e17i | 0.516366 | − | 0.856368i | ||||
\(65\) | 7.45664e16 | 0.0553872 | ||||||||
\(66\) | −2.32845e17 | + | 4.02969e16i | −0.148466 | + | 0.0256940i | ||||
\(67\) | 2.98959e18i | 1.64007i | 0.572311 | + | 0.820036i | \(0.306047\pi\) | ||||
−0.572311 | + | 0.820036i | \(0.693953\pi\) | |||||||
\(68\) | −4.18641e17 | + | 1.49376e17i | −0.198040 | + | 0.0706631i | ||||
\(69\) | −7.38397e17 | −0.301856 | ||||||||
\(70\) | −2.12385e17 | − | 1.22721e18i | −0.0751870 | − | 0.434448i | ||||
\(71\) | 6.13386e18i | 1.88430i | 0.335191 | + | 0.942150i | \(0.391199\pi\) | ||||
−0.335191 | + | 0.942150i | \(0.608801\pi\) | |||||||
\(72\) | 1.08665e18 | − | 6.13687e17i | 0.290246 | − | 0.163916i | ||||
\(73\) | −4.46233e18 | −1.03832 | −0.519162 | − | 0.854676i | \(-0.673756\pi\) | ||||
−0.519162 | + | 0.854676i | \(0.673756\pi\) | |||||||
\(74\) | −2.38290e18 | + | 4.12393e17i | −0.483938 | + | 0.0837517i | ||||
\(75\) | 2.06228e18i | 0.366214i | ||||||||
\(76\) | −8.50446e17 | − | 2.38345e18i | −0.132285 | − | 0.370741i | ||||
\(77\) | −1.39408e18 | −0.190275 | ||||||||
\(78\) | 7.51674e16 | + | 4.34335e17i | 0.00901745 | + | 0.0521050i | ||||
\(79\) | 1.16938e19i | 1.23505i | 0.786549 | + | 0.617527i | \(0.211866\pi\) | ||||
−0.786549 | + | 0.617527i | \(0.788134\pi\) | |||||||
\(80\) | 5.02659e18 | − | 4.11042e18i | 0.468137 | − | 0.382813i | ||||
\(81\) | 1.35085e18 | 0.111111 | ||||||||
\(82\) | 5.56384e18 | − | 9.62895e17i | 0.404796 | − | 0.0700552i | ||||
\(83\) | 1.74622e19i | 1.12543i | 0.826651 | + | 0.562714i | \(0.190243\pi\) | ||||
−0.826651 | + | 0.562714i | \(0.809757\pi\) | |||||||
\(84\) | 6.93417e18 | − | 2.47420e18i | 0.396462 | − | 0.141463i | ||||
\(85\) | −2.50337e18 | −0.127156 | ||||||||
\(86\) | −3.65634e18 | − | 2.11272e19i | −0.165220 | − | 0.954680i | ||||
\(87\) | 2.00073e19i | 0.805371i | ||||||||
\(88\) | −3.57410e18 | − | 6.32865e18i | −0.128334 | − | 0.227240i | ||||
\(89\) | −3.64001e19 | −1.16735 | −0.583677 | − | 0.811986i | \(-0.698387\pi\) | ||||
−0.583677 | + | 0.811986i | \(0.698387\pi\) | |||||||
\(90\) | 6.92559e18 | − | 1.19856e18i | 0.198624 | − | 0.0343745i | ||||
\(91\) | 2.60044e18i | 0.0667779i | ||||||||
\(92\) | −7.63231e18 | − | 2.13902e19i | −0.175702 | − | 0.492422i | ||||
\(93\) | 5.52727e19 | 1.14204 | ||||||||
\(94\) | −8.73068e18 | − | 5.04480e19i | −0.162095 | − | 0.936624i | ||||
\(95\) | − | 1.42525e19i | − | 0.238043i | ||||||
\(96\) | 2.90096e19 | + | 2.51354e19i | 0.436344 | + | 0.378071i | ||||
\(97\) | 2.48785e19 | 0.337371 | 0.168685 | − | 0.985670i | \(-0.446048\pi\) | ||||
0.168685 | + | 0.985670i | \(0.446048\pi\) | |||||||
\(98\) | −3.77126e19 | + | 6.52666e18i | −0.461558 | + | 0.0798786i | ||||
\(99\) | − | 7.86734e18i | − | 0.0869913i | ||||||
\(100\) | −5.97411e19 | + | 2.13164e19i | −0.597411 | + | 0.213164i | ||||
\(101\) | −2.64097e19 | −0.239083 | −0.119542 | − | 0.992829i | \(-0.538142\pi\) | ||||
−0.119542 | + | 0.992829i | \(0.538142\pi\) | |||||||
\(102\) | −2.52355e18 | − | 1.45817e19i | −0.0207019 | − | 0.119621i | ||||
\(103\) | − | 3.98038e19i | − | 0.296178i | −0.988974 | − | 0.148089i | \(-0.952688\pi\) | ||
0.988974 | − | 0.148089i | \(-0.0473122\pi\) | |||||||
\(104\) | −1.18051e19 | + | 6.66691e18i | −0.0797508 | + | 0.0450393i | ||||
\(105\) | 4.14647e19 | 0.254557 | ||||||||
\(106\) | 2.15989e20 | − | 3.73798e19i | 1.20607 | − | 0.208727i | ||||
\(107\) | − | 3.02934e20i | − | 1.53996i | −0.638065 | − | 0.769982i | \(-0.720265\pi\) | ||
0.638065 | − | 0.769982i | \(-0.279735\pi\) | |||||||
\(108\) | 1.39628e19 | + | 3.91321e19i | 0.0646749 | + | 0.181257i | ||||
\(109\) | 1.35701e20 | 0.573218 | 0.286609 | − | 0.958048i | \(-0.407472\pi\) | ||||
0.286609 | + | 0.958048i | \(0.407472\pi\) | |||||||
\(110\) | −6.98042e18 | − | 4.03345e19i | −0.0269125 | − | 0.155507i | ||||
\(111\) | − | 8.05132e19i | − | 0.283555i | ||||||
\(112\) | 1.43348e20 | + | 1.75298e20i | 0.461541 | + | 0.564413i | ||||
\(113\) | −3.70898e20 | −1.09262 | −0.546311 | − | 0.837582i | \(-0.683968\pi\) | ||||
−0.546311 | + | 0.837582i | \(0.683968\pi\) | |||||||
\(114\) | 8.30181e19 | − | 1.43674e19i | 0.223936 | − | 0.0387551i | ||||
\(115\) | − | 1.27909e20i | − | 0.316171i | ||||||
\(116\) | −5.79580e20 | + | 2.06802e20i | −1.31381 | + | 0.468786i | ||||
\(117\) | −1.46752e19 | −0.0305300 | ||||||||
\(118\) | 9.04516e19 | + | 5.22651e20i | 0.172821 | + | 0.998601i | ||||
\(119\) | − | 8.73031e19i | − | 0.153306i | ||||||
\(120\) | 1.06306e20 | + | 1.88235e20i | 0.171690 | + | 0.304010i | ||||
\(121\) | 6.26931e20 | 0.931893 | ||||||||
\(122\) | −1.09093e21 | + | 1.88799e20i | −1.49347 | + | 0.258465i | ||||
\(123\) | 1.87990e20i | 0.237183i | ||||||||
\(124\) | 5.71316e20 | + | 1.60116e21i | 0.664752 | + | 1.86303i | ||||
\(125\) | −9.20437e20 | −0.988311 | ||||||||
\(126\) | 4.17989e19 | + | 2.41524e20i | 0.0414438 | + | 0.239472i | ||||
\(127\) | 2.10185e20i | 0.192559i | 0.995354 | + | 0.0962795i | \(0.0306942\pi\) | ||||
−0.995354 | + | 0.0962795i | \(0.969306\pi\) | |||||||
\(128\) | −4.28281e20 | + | 1.10017e21i | −0.362768 | + | 0.931879i | ||||
\(129\) | 7.13843e20 | 0.559378 | ||||||||
\(130\) | −7.52376e19 | + | 1.30208e19i | −0.0545760 | + | 0.00944508i | ||||
\(131\) | − | 1.58116e21i | − | 1.06234i | −0.847265 | − | 0.531171i | \(-0.821752\pi\) | ||
0.847265 | − | 0.531171i | \(-0.178248\pi\) | |||||||
\(132\) | 2.27905e20 | − | 8.13193e19i | 0.141910 | − | 0.0506354i | ||||
\(133\) | 4.97043e20 | 0.286997 | ||||||||
\(134\) | −5.22044e20 | − | 3.01650e21i | −0.279679 | − | 1.61605i | ||||
\(135\) | 2.34001e20i | 0.116380i | ||||||||
\(136\) | 3.96325e20 | − | 2.23824e20i | 0.183089 | − | 0.103399i | ||||
\(137\) | 2.24984e20 | 0.0965930 | 0.0482965 | − | 0.998833i | \(-0.484621\pi\) | ||||
0.0482965 | + | 0.998833i | \(0.484621\pi\) | |||||||
\(138\) | 7.45044e20 | − | 1.28940e20i | 0.297434 | − | 0.0514749i | ||||
\(139\) | − | 1.83608e21i | − | 0.681934i | −0.940075 | − | 0.340967i | \(-0.889246\pi\) | ||
0.940075 | − | 0.340967i | \(-0.110754\pi\) | |||||||
\(140\) | 4.28593e20 | + | 1.20117e21i | 0.148171 | + | 0.415263i | ||||
\(141\) | 1.70453e21 | 0.548798 | ||||||||
\(142\) | −1.07110e21 | − | 6.18907e21i | −0.321326 | − | 1.85670i | ||||
\(143\) | 8.54684e19i | 0.0239026i | ||||||||
\(144\) | −9.89271e20 | + | 8.08963e20i | −0.258042 | + | 0.211010i | ||||
\(145\) | −3.46576e21 | −0.843564 | ||||||||
\(146\) | 4.50250e21 | − | 7.79216e20i | 1.02312 | − | 0.177064i | ||||
\(147\) | − | 1.27423e21i | − | 0.270442i | ||||||
\(148\) | 2.33234e21 | − | 8.32210e20i | 0.462567 | − | 0.165050i | ||||
\(149\) | 4.24159e20 | 0.0786441 | 0.0393221 | − | 0.999227i | \(-0.487480\pi\) | ||||
0.0393221 | + | 0.999227i | \(0.487480\pi\) | |||||||
\(150\) | −3.60117e20 | − | 2.08084e21i | −0.0624498 | − | 0.360850i | ||||
\(151\) | 2.20341e21i | 0.357541i | 0.983891 | + | 0.178771i | \(0.0572120\pi\) | ||||
−0.983891 | + | 0.178771i | \(0.942788\pi\) | |||||||
\(152\) | 1.27430e21 | + | 2.25640e21i | 0.193569 | + | 0.342752i | ||||
\(153\) | 4.92683e20 | 0.0700896 | ||||||||
\(154\) | 1.40663e21 | − | 2.43436e20i | 0.187488 | − | 0.0324473i | ||||
\(155\) | 9.57459e21i | 1.19620i | ||||||||
\(156\) | −1.51688e20 | − | 4.25119e20i | −0.0177707 | − | 0.0498041i | ||||
\(157\) | −7.03267e21 | −0.772901 | −0.386450 | − | 0.922310i | \(-0.626299\pi\) | ||||
−0.386450 | + | 0.922310i | \(0.626299\pi\) | |||||||
\(158\) | −2.04199e21 | − | 1.17991e22i | −0.210612 | − | 1.21696i | ||||
\(159\) | 7.29781e21i | 0.706677i | ||||||||
\(160\) | −4.35407e21 | + | 5.02517e21i | −0.396000 | + | 0.457036i | ||||
\(161\) | 4.46071e21 | 0.381193 | ||||||||
\(162\) | −1.36301e21 | + | 2.35887e20i | −0.109484 | + | 0.0189476i | ||||
\(163\) | 1.38896e22i | 1.04909i | 0.851382 | + | 0.524546i | \(0.175765\pi\) | ||||
−0.851382 | + | 0.524546i | \(0.824235\pi\) | |||||||
\(164\) | −5.44578e21 | + | 1.94313e21i | −0.386920 | + | 0.138058i | ||||
\(165\) | 1.36282e21 | 0.0911167 | ||||||||
\(166\) | −3.04926e21 | − | 1.76194e22i | −0.191917 | − | 1.10894i | ||||
\(167\) | 1.87374e22i | 1.11057i | 0.831661 | + | 0.555284i | \(0.187390\pi\) | ||||
−0.831661 | + | 0.555284i | \(0.812610\pi\) | |||||||
\(168\) | −6.56454e21 | + | 3.70732e21i | −0.366532 | + | 0.206999i | ||||
\(169\) | −1.88455e22 | −0.991611 | ||||||||
\(170\) | 2.52591e21 | − | 4.37141e20i | 0.125293 | − | 0.0216837i | ||||
\(171\) | 2.80500e21i | 0.131211i | ||||||||
\(172\) | 7.37851e21 | + | 2.06789e22i | 0.325600 | + | 0.912522i | ||||
\(173\) | 3.56106e22 | 1.48292 | 0.741460 | − | 0.670997i | \(-0.234134\pi\) | ||||
0.741460 | + | 0.670997i | \(0.234134\pi\) | |||||||
\(174\) | −3.49369e21 | − | 2.01874e22i | −0.137338 | − | 0.793574i | ||||
\(175\) | − | 1.24584e22i | − | 0.462467i | ||||||
\(176\) | 4.71139e21 | + | 5.76150e21i | 0.165205 | + | 0.202027i | ||||
\(177\) | −1.76592e22 | −0.585113 | ||||||||
\(178\) | 3.67278e22 | − | 6.35622e21i | 1.15026 | − | 0.199067i | ||||
\(179\) | − | 2.77215e21i | − | 0.0820891i | −0.999157 | − | 0.0410446i | \(-0.986931\pi\) | ||
0.999157 | − | 0.0410446i | \(-0.0130686\pi\) | |||||||
\(180\) | −6.77864e21 | + | 2.41871e21i | −0.189853 | + | 0.0677420i | ||||
\(181\) | −9.24582e21 | −0.244996 | −0.122498 | − | 0.992469i | \(-0.539091\pi\) | ||||
−0.122498 | + | 0.992469i | \(0.539091\pi\) | |||||||
\(182\) | −4.54091e20 | − | 2.62385e21i | −0.0113875 | − | 0.0657998i | ||||
\(183\) | − | 3.68601e22i | − | 0.875076i | ||||||
\(184\) | 1.14362e22 | + | 2.02500e22i | 0.257101 | + | 0.455247i | ||||
\(185\) | 1.39469e22 | 0.297002 | ||||||||
\(186\) | −5.57702e22 | + | 9.65177e21i | −1.12531 | + | 0.194750i | ||||
\(187\) | − | 2.86938e21i | − | 0.0548747i | ||||||
\(188\) | 1.76185e22 | + | 4.93775e22i | 0.319441 | + | 0.895263i | ||||
\(189\) | −8.16058e21 | −0.140315 | ||||||||
\(190\) | 2.48878e21 | + | 1.43808e22i | 0.0405930 | + | 0.234556i | ||||
\(191\) | − | 4.29885e22i | − | 0.665301i | −0.943050 | − | 0.332651i | \(-0.892057\pi\) | ||
0.943050 | − | 0.332651i | \(-0.107943\pi\) | |||||||
\(192\) | −3.36598e22 | − | 2.02960e22i | −0.494424 | − | 0.298124i | ||||
\(193\) | −9.00989e22 | −1.25645 | −0.628227 | − | 0.778030i | \(-0.716219\pi\) | ||||
−0.628227 | + | 0.778030i | \(0.716219\pi\) | |||||||
\(194\) | −2.51025e22 | + | 4.34431e21i | −0.332429 | + | 0.0575312i | ||||
\(195\) | − | 2.54211e21i | − | 0.0319778i | ||||||
\(196\) | 3.69124e22 | − | 1.31708e22i | 0.441175 | − | 0.157417i | ||||
\(197\) | 1.15963e23 | 1.31721 | 0.658606 | − | 0.752488i | \(-0.271146\pi\) | ||||
0.658606 | + | 0.752488i | \(0.271146\pi\) | |||||||
\(198\) | 1.37380e21 | + | 7.93815e21i | 0.0148345 | + | 0.0857171i | ||||
\(199\) | − | 1.56229e23i | − | 1.60410i | −0.597259 | − | 0.802048i | \(-0.703744\pi\) | ||
0.597259 | − | 0.802048i | \(-0.296256\pi\) | |||||||
\(200\) | 5.65565e22 | − | 3.19403e22i | 0.552310 | − | 0.311917i | ||||
\(201\) | 1.01921e23 | 0.946897 | ||||||||
\(202\) | 2.66474e22 | − | 4.61168e21i | 0.235581 | − | 0.0407704i | ||||
\(203\) | − | 1.20865e23i | − | 1.01705i | ||||||
\(204\) | 5.09253e21 | + | 1.42723e22i | 0.0407974 | + | 0.114338i | ||||
\(205\) | −3.25645e22 | −0.248431 | ||||||||
\(206\) | 6.95057e21 | + | 4.01621e22i | 0.0505066 | + | 0.291840i | ||||
\(207\) | 2.51734e22i | 0.174276i | ||||||||
\(208\) | 1.07471e22 | − | 8.78834e21i | 0.0709022 | − | 0.0579793i | ||||
\(209\) | 1.63363e22 | 0.102728 | ||||||||
\(210\) | −4.18380e22 | + | 7.24060e21i | −0.250829 | + | 0.0434092i | ||||
\(211\) | − | 1.17155e23i | − | 0.669787i | −0.942256 | − | 0.334893i | \(-0.891300\pi\) | ||
0.942256 | − | 0.334893i | \(-0.108700\pi\) | |||||||
\(212\) | −2.11406e23 | + | 7.54325e22i | −1.15281 | + | 0.411339i | ||||
\(213\) | 2.09115e23 | 1.08790 | ||||||||
\(214\) | 5.28987e22 | + | 3.05661e23i | 0.262607 | + | 1.51741i | ||||
\(215\) | 1.23655e23i | 0.585906i | ||||||||
\(216\) | −2.09218e22 | − | 3.70461e22i | −0.0946371 | − | 0.167573i | ||||
\(217\) | −3.33906e23 | −1.44220 | ||||||||
\(218\) | −1.36923e23 | + | 2.36963e22i | −0.564822 | + | 0.0977498i | ||||
\(219\) | 1.52130e23i | 0.599477i | ||||||||
\(220\) | 1.40865e22 | + | 3.94787e22i | 0.0530367 | + | 0.148640i | ||||
\(221\) | −5.35237e21 | −0.0192585 | ||||||||
\(222\) | 1.40593e22 | + | 8.12379e22i | 0.0483541 | + | 0.279402i | ||||
\(223\) | 2.42049e23i | 0.795894i | 0.917408 | + | 0.397947i | \(0.130277\pi\) | ||||
−0.917408 | + | 0.397947i | \(0.869723\pi\) | |||||||
\(224\) | −1.75249e23 | − | 1.51844e23i | −0.551029 | − | 0.477440i | ||||
\(225\) | 7.03072e22 | 0.211434 | ||||||||
\(226\) | 3.74236e23 | − | 6.47665e22i | 1.07662 | − | 0.186323i | ||||
\(227\) | 3.47473e23i | 0.956451i | 0.878237 | + | 0.478226i | \(0.158720\pi\) | ||||
−0.878237 | + | 0.478226i | \(0.841280\pi\) | |||||||
\(228\) | −8.12565e22 | + | 2.89934e22i | −0.214047 | + | 0.0763748i | ||||
\(229\) | −6.89301e23 | −1.73802 | −0.869009 | − | 0.494796i | \(-0.835243\pi\) | ||||
−0.869009 | + | 0.494796i | \(0.835243\pi\) | |||||||
\(230\) | 2.23355e22 | + | 1.29060e23i | 0.0539160 | + | 0.311540i | ||||
\(231\) | 4.75271e22i | 0.109855i | ||||||||
\(232\) | 5.48685e23 | − | 3.09870e23i | 1.21463 | − | 0.685962i | ||||
\(233\) | 3.89392e22 | 0.0825710 | 0.0412855 | − | 0.999147i | \(-0.486855\pi\) | ||||
0.0412855 | + | 0.999147i | \(0.486855\pi\) | |||||||
\(234\) | 1.48073e22 | − | 2.56260e21i | 0.0300828 | − | 0.00520623i | ||||
\(235\) | 2.95266e23i | 0.574824i | ||||||||
\(236\) | −1.82532e23 | − | 5.11561e23i | −0.340579 | − | 0.954503i | ||||
\(237\) | 3.98666e23 | 0.713059 | ||||||||
\(238\) | 1.52449e22 | + | 8.80889e22i | 0.0261430 | + | 0.151061i | ||||
\(239\) | 1.44771e23i | 0.238069i | 0.992890 | + | 0.119034i | \(0.0379799\pi\) | ||||
−0.992890 | + | 0.119034i | \(0.962020\pi\) | |||||||
\(240\) | −1.40132e23 | − | 1.71366e23i | −0.221017 | − | 0.270279i | ||||
\(241\) | 5.15881e22 | 0.0780511 | 0.0390255 | − | 0.999238i | \(-0.487575\pi\) | ||||
0.0390255 | + | 0.999238i | \(0.487575\pi\) | |||||||
\(242\) | −6.32574e23 | + | 1.09475e23i | −0.918243 | + | 0.158914i | ||||
\(243\) | − | 4.60532e22i | − | 0.0641500i | ||||||
\(244\) | 1.06778e24 | − | 3.80998e23i | 1.42752 | − | 0.509359i | ||||
\(245\) | 2.20727e23 | 0.283267 | ||||||||
\(246\) | −3.28270e22 | − | 1.89682e23i | −0.0404464 | − | 0.233709i | ||||
\(247\) | − | 3.04727e22i | − | 0.0360530i | ||||||
\(248\) | −8.56056e23 | − | 1.51581e24i | −0.972714 | − | 1.72238i | ||||
\(249\) | 5.95321e23 | 0.649767 | ||||||||
\(250\) | 9.28722e23 | − | 1.60727e23i | 0.973835 | − | 0.168535i | ||||
\(251\) | − | 1.23652e24i | − | 1.24584i | −0.782284 | − | 0.622922i | \(-0.785945\pi\) | ||
0.782284 | − | 0.622922i | \(-0.214055\pi\) | |||||||
\(252\) | −8.43504e22 | − | 2.36399e23i | −0.0816736 | − | 0.228897i | ||||
\(253\) | 1.46610e23 | 0.136445 | ||||||||
\(254\) | −3.67026e22 | − | 2.12077e23i | −0.0328367 | − | 0.189738i | ||||
\(255\) | 8.53449e22i | 0.0734135i | ||||||||
\(256\) | 2.40024e23 | − | 1.18486e24i | 0.198543 | − | 0.980092i | ||||
\(257\) | −8.60196e23 | −0.684331 | −0.342166 | − | 0.939640i | \(-0.611160\pi\) | ||||
−0.342166 | + | 0.939640i | \(0.611160\pi\) | |||||||
\(258\) | −7.20268e23 | + | 1.24652e23i | −0.551185 | + | 0.0953898i | ||||
\(259\) | 4.86385e23i | 0.358082i | ||||||||
\(260\) | 7.36411e22 | − | 2.62761e22i | 0.0521659 | − | 0.0186135i | ||||
\(261\) | 6.82088e23 | 0.464981 | ||||||||
\(262\) | 2.76104e23 | + | 1.59540e24i | 0.181159 | + | 1.04678i | ||||
\(263\) | 1.72793e24i | 1.09136i | 0.837993 | + | 0.545681i | \(0.183729\pi\) | ||||
−0.837993 | + | 0.545681i | \(0.816271\pi\) | |||||||
\(264\) | −2.15756e23 | + | 1.21848e23i | −0.131197 | + | 0.0740934i | ||||
\(265\) | −1.26416e24 | −0.740190 | ||||||||
\(266\) | −5.01518e23 | + | 8.67942e22i | −0.282794 | + | 0.0489411i | ||||
\(267\) | 1.24095e24i | 0.673972i | ||||||||
\(268\) | 1.05349e24 | + | 2.95249e24i | 0.551164 | + | 1.54469i | ||||
\(269\) | 2.20117e23 | 0.110951 | 0.0554754 | − | 0.998460i | \(-0.482333\pi\) | ||||
0.0554754 | + | 0.998460i | \(0.482333\pi\) | |||||||
\(270\) | −4.08614e22 | − | 2.36107e23i | −0.0198461 | − | 0.114676i | ||||
\(271\) | − | 6.79773e23i | − | 0.318179i | −0.987264 | − | 0.159089i | \(-0.949144\pi\) | ||
0.987264 | − | 0.159089i | \(-0.0508558\pi\) | |||||||
\(272\) | −3.60808e23 | + | 2.95046e23i | −0.162775 | + | 0.133107i | ||||
\(273\) | 8.86541e22 | 0.0385543 | ||||||||
\(274\) | −2.27009e23 | + | 3.92869e22i | −0.0951782 | + | 0.0164718i | ||||
\(275\) | − | 4.09468e23i | − | 0.165536i | ||||||
\(276\) | −7.29235e23 | + | 2.60200e23i | −0.284300 | + | 0.101442i | ||||
\(277\) | −2.13863e24 | −0.804153 | −0.402076 | − | 0.915606i | \(-0.631711\pi\) | ||||
−0.402076 | + | 0.915606i | \(0.631711\pi\) | |||||||
\(278\) | 3.20617e23 | + | 1.85260e24i | 0.116289 | + | 0.671946i | ||||
\(279\) | − | 1.88435e24i | − | 0.659357i | ||||||
\(280\) | −6.42200e23 | − | 1.13714e24i | −0.216815 | − | 0.383914i | ||||
\(281\) | 2.80680e24 | 0.914425 | 0.457212 | − | 0.889358i | \(-0.348848\pi\) | ||||
0.457212 | + | 0.889358i | \(0.348848\pi\) | |||||||
\(282\) | −1.71987e24 | + | 2.97646e23i | −0.540760 | + | 0.0935856i | ||||
\(283\) | − | 3.40662e24i | − | 1.03386i | −0.856029 | − | 0.516928i | \(-0.827076\pi\) | ||
0.856029 | − | 0.516928i | \(-0.172924\pi\) | |||||||
\(284\) | 2.16148e24 | + | 6.05774e24i | 0.633239 | + | 1.77471i | ||||
\(285\) | −4.85895e23 | −0.137434 | ||||||||
\(286\) | −1.49246e22 | − | 8.62377e22i | −0.00407607 | − | 0.0235525i | ||||
\(287\) | − | 1.13566e24i | − | 0.299522i | ||||||
\(288\) | 8.56914e23 | − | 9.88992e23i | 0.218279 | − | 0.251923i | ||||
\(289\) | −3.88454e24 | −0.955787 | ||||||||
\(290\) | 3.49695e24 | − | 6.05193e23i | 0.831208 | − | 0.143851i | ||||
\(291\) | − | 8.48158e23i | − | 0.194781i | ||||||
\(292\) | −4.40696e24 | + | 1.57246e24i | −0.977936 | + | 0.348940i | ||||
\(293\) | 7.02659e24 | 1.50684 | 0.753422 | − | 0.657537i | \(-0.228402\pi\) | ||||
0.753422 | + | 0.657537i | \(0.228402\pi\) | |||||||
\(294\) | 2.22507e23 | + | 1.28570e24i | 0.0461179 | + | 0.266480i | ||||
\(295\) | − | 3.05902e24i | − | 0.612861i | ||||||
\(296\) | −2.20801e24 | + | 1.24698e24i | −0.427646 | + | 0.241513i | ||||
\(297\) | −2.68213e23 | −0.0502244 | ||||||||
\(298\) | −4.27977e23 | + | 7.40671e22i | −0.0774922 | + | 0.0134110i | ||||
\(299\) | − | 2.73476e23i | − | 0.0478859i | ||||||
\(300\) | 7.26718e23 | + | 2.03669e24i | 0.123070 | + | 0.344915i | ||||
\(301\) | −4.31237e24 | −0.706401 | ||||||||
\(302\) | −3.84762e23 | − | 2.22325e24i | −0.0609709 | − | 0.352304i | ||||
\(303\) | 9.00357e23i | 0.138035i | ||||||||
\(304\) | −1.67979e24 | − | 2.05419e24i | −0.249183 | − | 0.304723i | ||||
\(305\) | 6.38508e24 | 0.916574 | ||||||||
\(306\) | −4.97118e23 | + | 8.60328e22i | −0.0690630 | + | 0.0119523i | ||||
\(307\) | 1.66365e24i | 0.223707i | 0.993725 | + | 0.111853i | \(0.0356787\pi\) | ||||
−0.993725 | + | 0.111853i | \(0.964321\pi\) | |||||||
\(308\) | −1.37679e24 | + | 4.91255e23i | −0.179209 | + | 0.0639440i | ||||
\(309\) | −1.35699e24 | −0.170998 | ||||||||
\(310\) | −1.67192e24 | − | 9.66078e24i | −0.203986 | − | 1.17868i | ||||
\(311\) | − | 2.45007e24i | − | 0.289451i | −0.989472 | − | 0.144726i | \(-0.953770\pi\) | ||
0.989472 | − | 0.144726i | \(-0.0462299\pi\) | |||||||
\(312\) | 2.27288e23 | + | 4.02458e23i | 0.0260034 | + | 0.0460442i | ||||
\(313\) | 1.50967e25 | 1.67278 | 0.836390 | − | 0.548134i | \(-0.184662\pi\) | ||||
0.836390 | + | 0.548134i | \(0.184662\pi\) | |||||||
\(314\) | 7.09597e24 | − | 1.22805e24i | 0.761580 | − | 0.131801i | ||||
\(315\) | − | 1.41361e24i | − | 0.146969i | ||||||
\(316\) | 4.12074e24 | + | 1.15487e25i | 0.415053 | + | 1.16322i | ||||
\(317\) | −1.24603e25 | −1.21600 | −0.608002 | − | 0.793935i | \(-0.708029\pi\) | ||||
−0.608002 | + | 0.793935i | \(0.708029\pi\) | |||||||
\(318\) | −1.27435e24 | − | 7.36350e24i | −0.120508 | − | 0.696327i | ||||
\(319\) | − | 3.97247e24i | − | 0.364044i | ||||||
\(320\) | 3.51576e24 | − | 5.83071e24i | 0.312262 | − | 0.517871i | ||||
\(321\) | −1.03276e25 | −0.889099 | ||||||||
\(322\) | −4.50086e24 | + | 7.78932e23i | −0.375610 | + | 0.0650041i | ||||
\(323\) | 1.02304e24i | 0.0827691i | ||||||||
\(324\) | 1.33409e24 | − | 4.76020e23i | 0.104649 | − | 0.0373401i | ||||
\(325\) | −7.63796e23 | −0.0580957 | ||||||||
\(326\) | −2.42541e24 | − | 1.40146e25i | −0.178900 | − | 1.03373i | ||||
\(327\) | − | 4.62633e24i | − | 0.330947i | ||||||
\(328\) | 5.15549e24 | − | 2.91156e24i | 0.357710 | − | 0.202017i | ||||
\(329\) | −1.02972e25 | −0.693040 | ||||||||
\(330\) | −1.37508e24 | + | 2.37976e23i | −0.0897821 | + | 0.0155380i | ||||
\(331\) | 1.80663e25i | 1.14443i | 0.820104 | + | 0.572215i | \(0.193916\pi\) | ||||
−0.820104 | + | 0.572215i | \(0.806084\pi\) | |||||||
\(332\) | 6.15342e24 | + | 1.72455e25i | 0.378213 | + | 1.05997i | ||||
\(333\) | −2.74485e24 | −0.163710 | ||||||||
\(334\) | −3.27195e24 | − | 1.89061e25i | −0.189383 | − | 1.09430i | ||||
\(335\) | 1.76552e25i | 0.991801i | ||||||||
\(336\) | 5.97625e24 | − | 4.88700e24i | 0.325864 | − | 0.266471i | ||||
\(337\) | 2.99368e25 | 1.58455 | 0.792276 | − | 0.610163i | \(-0.208896\pi\) | ||||
0.792276 | + | 0.610163i | \(0.208896\pi\) | |||||||
\(338\) | 1.90152e25 | − | 3.29082e24i | 0.977087 | − | 0.169098i | ||||
\(339\) | 1.26446e25i | 0.630826i | ||||||||
\(340\) | −2.47231e24 | + | 8.82152e23i | −0.119761 | + | 0.0427321i | ||||
\(341\) | −1.09744e25 | −0.516225 | ||||||||
\(342\) | −4.89812e23 | − | 2.83025e24i | −0.0223753 | − | 0.129290i | ||||
\(343\) | 2.41310e25i | 1.07062i | ||||||||
\(344\) | −1.10559e25 | − | 1.95766e25i | −0.476441 | − | 0.843632i | ||||
\(345\) | −4.36065e24 | −0.182541 | ||||||||
\(346\) | −3.59311e25 | + | 6.21835e24i | −1.46120 | + | 0.252880i | ||||
\(347\) | 1.43147e25i | 0.565573i | 0.959183 | + | 0.282787i | \(0.0912588\pi\) | ||||
−0.959183 | + | 0.282787i | \(0.908741\pi\) | |||||||
\(348\) | 7.05028e24 | + | 1.97590e25i | 0.270654 | + | 0.758531i | ||||
\(349\) | 6.25217e24 | 0.233226 | 0.116613 | − | 0.993177i | \(-0.462796\pi\) | ||||
0.116613 | + | 0.993177i | \(0.462796\pi\) | |||||||
\(350\) | 2.17549e24 | + | 1.25705e25i | 0.0788637 | + | 0.455693i | ||||
\(351\) | 5.00308e23i | 0.0176265i | ||||||||
\(352\) | −5.75987e24 | − | 4.99065e24i | −0.197236 | − | 0.170896i | ||||
\(353\) | −3.54447e25 | −1.17979 | −0.589894 | − | 0.807480i | \(-0.700831\pi\) | ||||
−0.589894 | + | 0.807480i | \(0.700831\pi\) | |||||||
\(354\) | 1.78182e25 | − | 3.08367e24i | 0.576542 | − | 0.0997782i | ||||
\(355\) | 3.62239e25i | 1.13949i | ||||||||
\(356\) | −3.59484e25 | + | 1.28269e25i | −1.09946 | + | 0.392302i | ||||
\(357\) | −2.97633e24 | −0.0885114 | ||||||||
\(358\) | 4.84074e23 | + | 2.79710e24i | 0.0139985 | + | 0.0808868i | ||||
\(359\) | − | 2.11289e25i | − | 0.594199i | −0.954847 | − | 0.297099i | \(-0.903981\pi\) | ||
0.954847 | − | 0.297099i | \(-0.0960192\pi\) | |||||||
\(360\) | 6.41730e24 | − | 3.62417e24i | 0.175520 | − | 0.0991251i | ||||
\(361\) | 3.17655e25 | 0.845052 | ||||||||
\(362\) | 9.32904e24 | − | 1.61451e24i | 0.241408 | − | 0.0417788i | ||||
\(363\) | − | 2.13733e25i | − | 0.538028i | ||||||
\(364\) | 9.16357e23 | + | 2.56817e24i | 0.0224415 | + | 0.0628942i | ||||
\(365\) | −2.63526e25 | −0.627906 | ||||||||
\(366\) | 6.43654e24 | + | 3.71919e25i | 0.149225 | + | 0.862258i | ||||
\(367\) | − | 3.58317e25i | − | 0.808365i | −0.914678 | − | 0.404182i | \(-0.867556\pi\) | ||
0.914678 | − | 0.404182i | \(-0.132444\pi\) | |||||||
\(368\) | −1.50752e25 | − | 1.84353e25i | −0.330967 | − | 0.404736i | ||||
\(369\) | 6.40895e24 | 0.136938 | ||||||||
\(370\) | −1.40724e25 | + | 2.43541e24i | −0.292652 | + | 0.0506472i | ||||
\(371\) | − | 4.40865e25i | − | 0.892415i | ||||||
\(372\) | 5.45868e25 | − | 1.94773e25i | 1.07562 | − | 0.383795i | ||||
\(373\) | 7.05709e25 | 1.35375 | 0.676873 | − | 0.736100i | \(-0.263335\pi\) | ||||
0.676873 | + | 0.736100i | \(0.263335\pi\) | |||||||
\(374\) | 5.01054e23 | + | 2.89521e24i | 0.00935768 | + | 0.0540709i | ||||
\(375\) | 3.13795e25i | 0.570602i | ||||||||
\(376\) | −2.63995e25 | − | 4.67454e25i | −0.467430 | − | 0.827676i | ||||
\(377\) | −7.41000e24 | −0.127763 | ||||||||
\(378\) | 8.23404e24 | − | 1.42501e24i | 0.138259 | − | 0.0239276i | ||||
\(379\) | − | 1.20689e26i | − | 1.97368i | −0.161710 | − | 0.986838i | \(-0.551701\pi\) | ||
0.161710 | − | 0.986838i | \(-0.448299\pi\) | |||||||
\(380\) | −5.02237e24 | − | 1.40756e25i | −0.0799968 | − | 0.224198i | ||||
\(381\) | 7.16560e24 | 0.111174 | ||||||||
\(382\) | 7.50668e24 | + | 4.33754e25i | 0.113453 | + | 0.655556i | ||||
\(383\) | − | 9.86961e25i | − | 1.45316i | −0.687084 | − | 0.726578i | \(-0.741110\pi\) | ||
0.687084 | − | 0.726578i | \(-0.258890\pi\) | |||||||
\(384\) | 3.75069e25 | + | 1.46009e25i | 0.538021 | + | 0.209444i | ||||
\(385\) | −8.23286e24 | −0.115065 | ||||||||
\(386\) | 9.09099e25 | − | 1.57331e25i | 1.23805 | − | 0.214261i | ||||
\(387\) | − | 2.43363e25i | − | 0.322957i | ||||||
\(388\) | 2.45698e25 | − | 8.76683e24i | 0.317749 | − | 0.113377i | ||||
\(389\) | 4.70979e25 | 0.593615 | 0.296808 | − | 0.954937i | \(-0.404078\pi\) | ||||
0.296808 | + | 0.954937i | \(0.404078\pi\) | |||||||
\(390\) | 4.43906e23 | + | 2.56500e24i | 0.00545312 | + | 0.0315094i | ||||
\(391\) | 9.18126e24i | 0.109935i | ||||||||
\(392\) | −3.49447e25 | + | 1.97350e25i | −0.407869 | + | 0.230344i | ||||
\(393\) | −5.39050e25 | −0.613343 | ||||||||
\(394\) | −1.17006e26 | + | 2.02495e25i | −1.29792 | + | 0.224622i | ||||
\(395\) | 6.90587e25i | 0.746875i | ||||||||
\(396\) | −2.77233e24 | − | 7.76971e24i | −0.0292344 | − | 0.0819319i | ||||
\(397\) | −5.03199e25 | −0.517410 | −0.258705 | − | 0.965956i | \(-0.583296\pi\) | ||||
−0.258705 | + | 0.965956i | \(0.583296\pi\) | |||||||
\(398\) | 2.72808e25 | + | 1.57635e26i | 0.273544 | + | 1.58060i | ||||
\(399\) | − | 1.69452e25i | − | 0.165698i | ||||||
\(400\) | −5.14882e25 | + | 4.21038e25i | −0.491030 | + | 0.401533i | ||||
\(401\) | −1.03621e26 | −0.963842 | −0.481921 | − | 0.876215i | \(-0.660061\pi\) | ||||
−0.481921 | + | 0.876215i | \(0.660061\pi\) | |||||||
\(402\) | −1.02838e26 | + | 1.77975e25i | −0.933027 | + | 0.161473i | ||||
\(403\) | 2.04711e25i | 0.181172i | ||||||||
\(404\) | −2.60819e25 | + | 9.30637e24i | −0.225178 | + | 0.0803465i | ||||
\(405\) | 7.97754e24 | 0.0671922 | ||||||||
\(406\) | 2.11056e25 | + | 1.21953e26i | 0.173435 | + | 1.00215i | ||||
\(407\) | 1.59860e25i | 0.128172i | ||||||||
\(408\) | −7.63061e24 | − | 1.35115e25i | −0.0596977 | − | 0.105706i | ||||
\(409\) | 1.69384e26 | 1.29312 | 0.646560 | − | 0.762863i | \(-0.276207\pi\) | ||||
0.646560 | + | 0.762863i | \(0.276207\pi\) | |||||||
\(410\) | 3.28576e25 | − | 5.68644e24i | 0.244792 | − | 0.0423645i | ||||
\(411\) | − | 7.67014e24i | − | 0.0557680i | ||||||
\(412\) | −1.40263e25 | − | 3.93099e25i | −0.0995337 | − | 0.278952i | ||||
\(413\) | 1.06681e26 | 0.738899 | ||||||||
\(414\) | −4.39580e24 | − | 2.54000e25i | −0.0297190 | − | 0.171724i | ||||
\(415\) | 1.03124e26i | 0.680581i | ||||||||
\(416\) | −9.30926e24 | + | 1.07441e25i | −0.0599766 | + | 0.0692209i | ||||
\(417\) | −6.25954e25 | −0.393715 | ||||||||
\(418\) | −1.64833e25 | + | 2.85265e24i | −0.101224 | + | 0.0175181i | ||||
\(419\) | 7.62924e25i | 0.457448i | 0.973491 | + | 0.228724i | \(0.0734553\pi\) | ||||
−0.973491 | + | 0.228724i | \(0.926545\pi\) | |||||||
\(420\) | 4.09502e25 | − | 1.46116e25i | 0.239752 | − | 0.0855468i | ||||
\(421\) | −1.31909e25 | −0.0754143 | −0.0377072 | − | 0.999289i | \(-0.512005\pi\) | ||||
−0.0377072 | + | 0.999289i | \(0.512005\pi\) | |||||||
\(422\) | 2.04577e25 | + | 1.18210e26i | 0.114218 | + | 0.659976i | ||||
\(423\) | − | 5.81107e25i | − | 0.316849i | ||||||
\(424\) | 2.00137e26 | − | 1.13027e26i | 1.06578 | − | 0.601901i | ||||
\(425\) | 2.56425e25 | 0.133374 | ||||||||
\(426\) | −2.10997e26 | + | 3.65159e25i | −1.07197 | + | 0.185518i | ||||
\(427\) | 2.22674e26i | 1.10507i | ||||||||
\(428\) | −1.06750e26 | − | 2.99175e26i | −0.517522 | − | 1.45040i | ||||
\(429\) | 2.91378e24 | 0.0138002 | ||||||||
\(430\) | −2.15928e25 | − | 1.24768e26i | −0.0999134 | − | 0.577324i | ||||
\(431\) | 3.31943e25i | 0.150069i | 0.997181 | + | 0.0750344i | \(0.0239067\pi\) | ||||
−0.997181 | + | 0.0750344i | \(0.976093\pi\) | |||||||
\(432\) | 2.75791e25 | + | 3.37262e25i | 0.121827 | + | 0.148981i | ||||
\(433\) | −2.91084e26 | −1.25643 | −0.628217 | − | 0.778038i | \(-0.716215\pi\) | ||||
−0.628217 | + | 0.778038i | \(0.716215\pi\) | |||||||
\(434\) | 3.36911e26 | − | 5.83069e25i | 1.42108 | − | 0.245936i | ||||
\(435\) | 1.18154e26i | 0.487032i | ||||||||
\(436\) | 1.34018e26 | − | 4.78192e25i | 0.539879 | − | 0.192636i | ||||
\(437\) | −5.22718e25 | −0.205804 | ||||||||
\(438\) | −2.65650e25 | − | 1.53499e26i | −0.102228 | − | 0.590696i | ||||
\(439\) | − | 1.21156e26i | − | 0.455721i | −0.973694 | − | 0.227861i | \(-0.926827\pi\) | ||
0.973694 | − | 0.227861i | \(-0.0731731\pi\) | |||||||
\(440\) | −2.11071e25 | − | 3.73742e25i | −0.0776072 | − | 0.137419i | ||||
\(441\) | −4.34409e25 | −0.156140 | ||||||||
\(442\) | 5.40054e24 | − | 9.34635e23i | 0.0189764 | − | 0.00328412i | ||||
\(443\) | 1.34686e26i | 0.462683i | 0.972873 | + | 0.231342i | \(0.0743115\pi\) | ||||
−0.972873 | + | 0.231342i | \(0.925689\pi\) | |||||||
\(444\) | −2.83717e25 | − | 7.95141e25i | −0.0952917 | − | 0.267063i | ||||
\(445\) | −2.14963e26 | −0.705934 | ||||||||
\(446\) | −4.22669e25 | − | 2.44228e26i | −0.135722 | − | 0.784237i | ||||
\(447\) | − | 1.44604e25i | − | 0.0454052i | ||||||
\(448\) | 2.03341e26 | + | 1.22609e26i | 0.624375 | + | 0.376481i | ||||
\(449\) | 5.47469e26 | 1.64398 | 0.821990 | − | 0.569502i | \(-0.192864\pi\) | ||||
0.821990 | + | 0.569502i | \(0.192864\pi\) | |||||||
\(450\) | −7.09401e25 | + | 1.22771e25i | −0.208337 | + | 0.0360554i | ||||
\(451\) | − | 3.73256e25i | − | 0.107212i | ||||||
\(452\) | −3.66295e26 | + | 1.30699e26i | −1.02908 | + | 0.367187i | ||||
\(453\) | 7.51186e25 | 0.206427 | ||||||||
\(454\) | −6.06761e25 | − | 3.50601e26i | −0.163102 | − | 0.942442i | ||||
\(455\) | 1.53571e25i | 0.0403826i | ||||||||
\(456\) | 7.69251e25 | − | 4.34434e25i | 0.197888 | − | 0.111757i | ||||
\(457\) | −4.62101e26 | −1.16299 | −0.581494 | − | 0.813551i | \(-0.697532\pi\) | ||||
−0.581494 | + | 0.813551i | \(0.697532\pi\) | |||||||
\(458\) | 6.95506e26 | − | 1.20366e26i | 1.71256 | − | 0.296381i | ||||
\(459\) | − | 1.67965e25i | − | 0.0404663i | ||||||
\(460\) | −4.50731e25 | − | 1.26321e26i | −0.106253 | − | 0.297782i | ||||
\(461\) | 4.88785e26 | 1.12748 | 0.563739 | − | 0.825953i | \(-0.309362\pi\) | ||||
0.563739 | + | 0.825953i | \(0.309362\pi\) | |||||||
\(462\) | −8.29922e24 | − | 4.79549e25i | −0.0187334 | − | 0.108246i | ||||
\(463\) | − | 5.75750e26i | − | 1.27182i | −0.771765 | − | 0.635908i | \(-0.780626\pi\) | ||
0.771765 | − | 0.635908i | \(-0.219374\pi\) | |||||||
\(464\) | −4.99515e26 | + | 4.08471e26i | −1.07986 | + | 0.883043i | ||||
\(465\) | 3.26417e26 | 0.690626 | ||||||||
\(466\) | −3.92897e25 | + | 6.79959e24i | −0.0813616 | + | 0.0140807i | ||||
\(467\) | 9.45663e26i | 1.91676i | 0.285496 | + | 0.958380i | \(0.407842\pi\) | ||||
−0.285496 | + | 0.958380i | \(0.592158\pi\) | |||||||
\(468\) | −1.44931e25 | + | 5.17134e24i | −0.0287544 | + | 0.0102599i | ||||
\(469\) | −6.15710e26 | −1.19577 | ||||||||
\(470\) | −5.15596e25 | − | 2.97924e26i | −0.0980237 | − | 0.566404i | ||||
\(471\) | 2.39758e26i | 0.446235i | ||||||||
\(472\) | 2.73504e26 | + | 4.84292e26i | 0.498360 | + | 0.882444i | ||||
\(473\) | −1.41734e26 | −0.252850 | ||||||||
\(474\) | −4.02254e26 | + | 6.96154e25i | −0.702615 | + | 0.121597i | ||||
\(475\) | 1.45991e26i | 0.249683i | ||||||||
\(476\) | −3.07643e25 | − | 8.62197e25i | −0.0515202 | − | 0.144390i | ||||
\(477\) | 2.48797e26 | 0.408000 | ||||||||
\(478\) | −2.52800e25 | − | 1.46074e26i | −0.0405974 | − | 0.234582i | ||||
\(479\) | − | 1.12306e27i | − | 1.76624i | −0.469150 | − | 0.883118i | \(-0.655440\pi\) | ||
0.469150 | − | 0.883118i | \(-0.344560\pi\) | |||||||
\(480\) | 1.71318e26 | + | 1.48439e26i | 0.263870 | + | 0.228631i | ||||
\(481\) | 2.98192e25 | 0.0449827 | ||||||||
\(482\) | −5.20524e25 | + | 9.00835e24i | −0.0769078 | + | 0.0133099i | ||||
\(483\) | − | 1.52074e26i | − | 0.220082i | ||||||
\(484\) | 6.19151e26 | − | 2.20921e26i | 0.877694 | − | 0.313173i | ||||
\(485\) | 1.46922e26 | 0.204018 | ||||||||
\(486\) | 8.04184e24 | + | 4.64677e25i | 0.0109394 | + | 0.0632104i | ||||
\(487\) | 1.00388e26i | 0.133780i | 0.997760 | + | 0.0668901i | \(0.0213077\pi\) | ||||
−0.997760 | + | 0.0668901i | \(0.978692\pi\) | |||||||
\(488\) | −1.01086e27 | + | 5.70884e26i | −1.31975 | + | 0.745331i | ||||
\(489\) | 4.73524e26 | 0.605694 | ||||||||
\(490\) | −2.22714e26 | + | 3.85436e25i | −0.279118 | + | 0.0483050i | ||||
\(491\) | − | 8.18959e26i | − | 1.00565i | −0.864388 | − | 0.502825i | \(-0.832294\pi\) | ||
0.864388 | − | 0.502825i | \(-0.167706\pi\) | |||||||
\(492\) | 6.62449e25 | + | 1.85657e26i | 0.0797080 | + | 0.223389i | ||||
\(493\) | 2.48772e26 | 0.293313 | ||||||||
\(494\) | 5.32117e24 | + | 3.07470e25i | 0.00614805 | + | 0.0355249i | ||||
\(495\) | − | 4.64611e25i | − | 0.0526062i | ||||||
\(496\) | 1.12845e27 | + | 1.37997e27i | 1.25218 | + | 1.53128i | ||||
\(497\) | −1.26328e27 | −1.37384 | ||||||||
\(498\) | −6.00679e26 | + | 1.03955e26i | −0.640249 | + | 0.110804i | ||||
\(499\) | 4.06033e26i | 0.424185i | 0.977250 | + | 0.212093i | \(0.0680279\pi\) | ||||
−0.977250 | + | 0.212093i | \(0.931972\pi\) | |||||||
\(500\) | −9.09015e26 | + | 3.24348e26i | −0.930831 | + | 0.332133i | ||||
\(501\) | 6.38796e26 | 0.641187 | ||||||||
\(502\) | 2.15922e26 | + | 1.24765e27i | 0.212451 | + | 1.22760i | ||||
\(503\) | 9.34933e25i | 0.0901780i | 0.998983 | + | 0.0450890i | \(0.0143571\pi\) | ||||
−0.998983 | + | 0.0450890i | \(0.985643\pi\) | |||||||
\(504\) | 1.26390e26 | + | 2.23798e26i | 0.119511 | + | 0.211617i | ||||
\(505\) | −1.55964e26 | −0.144581 | ||||||||
\(506\) | −1.47929e26 | + | 2.56011e25i | −0.134446 | + | 0.0232677i | ||||
\(507\) | 6.42481e26i | 0.572507i | ||||||||
\(508\) | 7.40660e25 | + | 2.07576e26i | 0.0647115 | + | 0.181360i | ||||
\(509\) | −1.37706e27 | −1.17971 | −0.589853 | − | 0.807511i | \(-0.700814\pi\) | ||||
−0.589853 | + | 0.807511i | \(0.700814\pi\) | |||||||
\(510\) | −1.49030e25 | − | 8.61131e25i | −0.0125191 | − | 0.0723382i | ||||
\(511\) | − | 9.19024e26i | − | 0.757038i | ||||||
\(512\) | −3.52831e25 | + | 1.23744e27i | −0.0285015 | + | 0.999594i | ||||
\(513\) | 9.56279e25 | 0.0757550 | ||||||||
\(514\) | 8.67939e26 | − | 1.50208e26i | 0.674308 | − | 0.116698i | ||||
\(515\) | − | 2.35064e26i | − | 0.179108i | ||||||
\(516\) | 7.04985e26 | − | 2.51548e26i | 0.526845 | − | 0.187985i | ||||
\(517\) | −3.38435e26 | −0.248068 | ||||||||
\(518\) | −8.49330e25 | − | 4.90763e26i | −0.0610631 | − | 0.352837i | ||||
\(519\) | − | 1.21403e27i | − | 0.856165i | ||||||
\(520\) | −6.97156e25 | + | 3.93719e25i | −0.0482277 | + | 0.0272366i | ||||
\(521\) | 1.85746e27 | 1.26050 | 0.630248 | − | 0.776394i | \(-0.282953\pi\) | ||||
0.630248 | + | 0.776394i | \(0.282953\pi\) | |||||||
\(522\) | −6.88228e26 | + | 1.19107e26i | −0.458170 | + | 0.0792924i | ||||
\(523\) | − | 1.77848e26i | − | 0.116154i | −0.998312 | − | 0.0580768i | \(-0.981503\pi\) | ||
0.998312 | − | 0.0580768i | \(-0.0184968\pi\) | |||||||
\(524\) | −5.57179e26 | − | 1.56154e27i | −0.357011 | − | 1.00056i | ||||
\(525\) | −4.24730e26 | −0.267005 | ||||||||
\(526\) | −3.01733e26 | − | 1.74348e27i | −0.186108 | − | 1.07538i | ||||
\(527\) | − | 6.87263e26i | − | 0.415927i | ||||||
\(528\) | 1.96421e26 | − | 1.60620e26i | 0.116640 | − | 0.0953809i | ||||
\(529\) | 1.24704e27 | 0.726650 | ||||||||
\(530\) | 1.27554e27 | − | 2.20749e26i | 0.729348 | − | 0.126223i | ||||
\(531\) | 6.02038e26i | 0.337815i | ||||||||
\(532\) | 4.90876e26 | − | 1.75151e26i | 0.270306 | − | 0.0964486i | ||||
\(533\) | −6.96249e25 | −0.0376264 | ||||||||
\(534\) | −2.16696e26 | − | 1.25212e27i | −0.114931 | − | 0.664100i | ||||
\(535\) | − | 1.78900e27i | − | 0.931263i | ||||||
\(536\) | −1.57854e27 | − | 2.79511e27i | −0.806504 | − | 1.42807i | ||||
\(537\) | −9.45079e25 | −0.0473942 | ||||||||
\(538\) | −2.22098e26 | + | 3.84370e25i | −0.109326 | + | 0.0189202i | ||||
\(539\) | 2.52999e26i | 0.122245i | ||||||||
\(540\) | 8.24584e25 | + | 2.31097e26i | 0.0391109 | + | 0.109612i | ||||
\(541\) | 1.96989e27 | 0.917212 | 0.458606 | − | 0.888640i | \(-0.348349\pi\) | ||||
0.458606 | + | 0.888640i | \(0.348349\pi\) | |||||||
\(542\) | 1.18703e26 | + | 6.85892e26i | 0.0542584 | + | 0.313518i | ||||
\(543\) | 3.15208e26i | 0.141449i | ||||||||
\(544\) | 3.12534e26 | − | 3.60706e26i | 0.137692 | − | 0.158915i | ||||
\(545\) | 8.01394e26 | 0.346642 | ||||||||
\(546\) | −8.94521e25 | + | 1.54809e25i | −0.0379896 | + | 0.00657459i | ||||
\(547\) | 3.47749e27i | 1.45008i | 0.688706 | + | 0.725040i | \(0.258179\pi\) | ||||
−0.688706 | + | 0.725040i | \(0.741821\pi\) | |||||||
\(548\) | 2.22192e26 | − | 7.92810e25i | 0.0909752 | − | 0.0324611i | ||||
\(549\) | −1.25663e27 | −0.505225 | ||||||||
\(550\) | 7.15016e25 | + | 4.13154e26i | 0.0282286 | + | 0.163112i | ||||
\(551\) | 1.41633e27i | 0.549098i | ||||||||
\(552\) | 6.90362e26 | − | 3.89882e26i | 0.262837 | − | 0.148437i | ||||
\(553\) | −2.40837e27 | −0.900474 | ||||||||
\(554\) | 2.15788e27 | − | 3.73450e26i | 0.792374 | − | 0.137131i | ||||
\(555\) | − | 4.75476e26i | − | 0.171474i | ||||||
\(556\) | −6.47006e26 | − | 1.81329e27i | −0.229171 | − | 0.642273i | ||||
\(557\) | 1.20852e26 | 0.0420438 | 0.0210219 | − | 0.999779i | \(-0.493308\pi\) | ||||
0.0210219 | + | 0.999779i | \(0.493308\pi\) | |||||||
\(558\) | 3.29048e26 | + | 1.90132e27i | 0.112439 | + | 0.649699i | ||||
\(559\) | 2.64382e26i | 0.0887390i | ||||||||
\(560\) | 8.46548e26 | + | 1.03523e27i | 0.279108 | + | 0.341317i | ||||
\(561\) | −9.78228e25 | −0.0316819 | ||||||||
\(562\) | −2.83206e27 | + | 4.90126e26i | −0.901031 | + | 0.155935i | ||||
\(563\) | 3.65310e27i | 1.14177i | 0.821031 | + | 0.570884i | \(0.193399\pi\) | ||||
−0.821031 | + | 0.570884i | \(0.806601\pi\) | |||||||
\(564\) | 1.68338e27 | − | 6.00650e26i | 0.516880 | − | 0.184430i | ||||
\(565\) | −2.19036e27 | −0.660741 | ||||||||
\(566\) | 5.94868e26 | + | 3.43729e27i | 0.176301 | + | 1.01871i | ||||
\(567\) | 2.78210e26i | 0.0810107i | ||||||||
\(568\) | −3.23874e27 | − | 5.73483e27i | −0.926602 | − | 1.64073i | ||||
\(569\) | −1.09913e27 | −0.308976 | −0.154488 | − | 0.987995i | \(-0.549373\pi\) | ||||
−0.154488 | + | 0.987995i | \(0.549373\pi\) | |||||||
\(570\) | 4.90269e26 | − | 8.48474e25i | 0.135421 | − | 0.0234364i | ||||
\(571\) | 5.14817e27i | 1.39731i | 0.715461 | + | 0.698653i | \(0.246217\pi\) | ||||
−0.715461 | + | 0.698653i | \(0.753783\pi\) | |||||||
\(572\) | 3.01178e25 | + | 8.44078e25i | 0.00803273 | + | 0.0225124i | ||||
\(573\) | −1.46556e27 | −0.384112 | ||||||||
\(574\) | 1.98310e26 | + | 1.14588e27i | 0.0510770 | + | 0.295135i | ||||
\(575\) | 1.31019e27i | 0.331632i | ||||||||
\(576\) | −6.91929e26 | + | 1.14753e27i | −0.172122 | + | 0.285456i | ||||
\(577\) | 3.58695e26 | 0.0876934 | 0.0438467 | − | 0.999038i | \(-0.486039\pi\) | ||||
0.0438467 | + | 0.999038i | \(0.486039\pi\) | |||||||
\(578\) | 3.91951e27 | − | 6.78322e26i | 0.941787 | − | 0.162989i | ||||
\(579\) | 3.07165e27i | 0.725414i | ||||||||
\(580\) | −3.42275e27 | + | 1.22128e27i | −0.794503 | + | 0.283489i | ||||
\(581\) | −3.59637e27 | −0.820546 | ||||||||
\(582\) | 1.48106e26 | + | 8.55792e26i | 0.0332157 | + | 0.191928i | ||||
\(583\) | − | 1.44899e27i | − | 0.319432i | ||||||
\(584\) | 4.17204e27 | − | 2.35616e27i | 0.904107 | − | 0.510595i | ||||
\(585\) | −8.66657e25 | −0.0184624 | ||||||||
\(586\) | −7.08984e27 | + | 1.22699e27i | −1.48477 | + | 0.256959i | ||||
\(587\) | 4.41382e27i | 0.908728i | 0.890816 | + | 0.454364i | \(0.150133\pi\) | ||||
−0.890816 | + | 0.454364i | \(0.849867\pi\) | |||||||
\(588\) | −4.49019e26 | − | 1.25842e27i | −0.0908848 | − | 0.254713i | ||||
\(589\) | 3.91280e27 | 0.778637 | ||||||||
\(590\) | 5.34168e26 | + | 3.08655e27i | 0.104510 | + | 0.603884i | ||||
\(591\) | − | 3.95339e27i | − | 0.760493i | ||||||
\(592\) | 2.01014e27 | − | 1.64377e27i | 0.380198 | − | 0.310902i | ||||
\(593\) | 5.21372e27 | 0.969618 | 0.484809 | − | 0.874620i | \(-0.338889\pi\) | ||||
0.484809 | + | 0.874620i | \(0.338889\pi\) | |||||||
\(594\) | 2.70627e26 | − | 4.68356e25i | 0.0494888 | − | 0.00856468i | ||||
\(595\) | − | 5.15574e26i | − | 0.0927089i | ||||||
\(596\) | 4.18896e26 | − | 1.49467e26i | 0.0740702 | − | 0.0264292i | ||||
\(597\) | −5.32615e27 | −0.926125 | ||||||||
\(598\) | 4.77547e25 | + | 2.75938e26i | 0.00816590 | + | 0.0471845i | ||||
\(599\) | − | 1.17097e28i | − | 1.96914i | −0.174994 | − | 0.984569i | \(-0.555991\pi\) | ||
0.174994 | − | 0.984569i | \(-0.444009\pi\) | |||||||
\(600\) | −1.08891e27 | − | 1.92812e27i | −0.180085 | − | 0.318876i | ||||
\(601\) | 6.38551e27 | 1.03861 | 0.519303 | − | 0.854590i | \(-0.326192\pi\) | ||||
0.519303 | + | 0.854590i | \(0.326192\pi\) | |||||||
\(602\) | 4.35119e27 | − | 7.53030e26i | 0.696054 | − | 0.120461i | ||||
\(603\) | − | 3.47468e27i | − | 0.546691i | ||||||
\(604\) | 7.76450e26 | + | 2.17607e27i | 0.120156 | + | 0.336747i | ||||
\(605\) | 3.70238e27 | 0.563543 | ||||||||
\(606\) | −1.57221e26 | − | 9.08461e26i | −0.0235388 | − | 0.136013i | ||||
\(607\) | − | 1.18450e28i | − | 1.74441i | −0.489136 | − | 0.872207i | \(-0.662688\pi\) | ||
0.489136 | − | 0.872207i | \(-0.337312\pi\) | |||||||
\(608\) | 2.05361e27 | + | 1.77936e27i | 0.297497 | + | 0.257767i | ||||
\(609\) | −4.12054e27 | −0.587193 | ||||||||
\(610\) | −6.44255e27 | + | 1.11497e27i | −0.903149 | + | 0.156302i | ||||
\(611\) | 6.31297e26i | 0.0870606i | ||||||||
\(612\) | 4.86570e26 | − | 1.73614e26i | 0.0660132 | − | 0.0235544i | ||||
\(613\) | 1.20216e28 | 1.60456 | 0.802281 | − | 0.596947i | \(-0.203620\pi\) | ||||
0.802281 | + | 0.596947i | \(0.203620\pi\) | |||||||
\(614\) | −2.90509e26 | − | 1.67863e27i | −0.0381483 | − | 0.220430i | ||||
\(615\) | 1.11019e27i | 0.143432i | ||||||||
\(616\) | 1.30340e27 | − | 7.36092e26i | 0.165680 | − | 0.0935675i | ||||
\(617\) | −7.64204e27 | −0.955779 | −0.477889 | − | 0.878420i | \(-0.658598\pi\) | ||||
−0.477889 | + | 0.878420i | \(0.658598\pi\) | |||||||
\(618\) | 1.36920e27 | − | 2.36959e26i | 0.168494 | − | 0.0291600i | ||||
\(619\) | − | 2.55907e26i | − | 0.0309867i | −0.999880 | − | 0.0154934i | \(-0.995068\pi\) | ||
0.999880 | − | 0.0154934i | \(-0.00493188\pi\) | |||||||
\(620\) | 3.37395e27 | + | 9.45578e27i | 0.401996 | + | 1.12663i | ||||
\(621\) | 8.58211e26 | 0.100619 | ||||||||
\(622\) | 4.27834e26 | + | 2.47213e27i | 0.0493596 | + | 0.285211i | ||||
\(623\) | − | 7.49666e27i | − | 0.851114i | ||||||
\(624\) | −2.99612e26 | − | 3.66391e26i | −0.0334744 | − | 0.0409354i | ||||
\(625\) | 3.33242e26 | 0.0366403 | ||||||||
\(626\) | −1.52326e28 | + | 2.63620e27i | −1.64828 | + | 0.285256i | ||||
\(627\) | − | 5.56935e26i | − | 0.0593102i | ||||||
\(628\) | −6.94540e27 | + | 2.47821e27i | −0.727949 | + | 0.259742i | ||||
\(629\) | −1.00110e27 | −0.103270 | ||||||||
\(630\) | 2.46846e26 | + | 1.42634e27i | 0.0250623 | + | 0.144816i | ||||
\(631\) | 1.32161e27i | 0.132072i | 0.997817 | + | 0.0660358i | \(0.0210352\pi\) | ||||
−0.997817 | + | 0.0660358i | \(0.978965\pi\) | |||||||
\(632\) | −6.17448e27 | − | 1.09331e28i | −0.607337 | − | 1.07541i | ||||
\(633\) | −3.99405e27 | −0.386702 | ||||||||
\(634\) | 1.25724e28 | − | 2.17583e27i | 1.19819 | − | 0.207363i | ||||
\(635\) | 1.24126e27i | 0.116446i | ||||||||
\(636\) | 2.57164e27 | + | 7.20725e27i | 0.237487 | + | 0.665577i | ||||
\(637\) | 4.71929e26 | 0.0429025 | ||||||||
\(638\) | 6.93676e26 | + | 4.00823e27i | 0.0620797 | + | 0.358712i | ||||
\(639\) | − | 7.12914e27i | − | 0.628100i | ||||||
\(640\) | −2.52924e27 | + | 6.49712e27i | −0.219377 | + | 0.563535i | ||||
\(641\) | −1.25919e28 | −1.07526 | −0.537629 | − | 0.843182i | \(-0.680680\pi\) | ||||
−0.537629 | + | 0.843182i | \(0.680680\pi\) | |||||||
\(642\) | 1.04206e28 | − | 1.80342e27i | 0.876076 | − | 0.151616i | ||||
\(643\) | 1.36334e28i | 1.12848i | 0.825611 | + | 0.564240i | \(0.190831\pi\) | ||||
−0.825611 | + | 0.564240i | \(0.809169\pi\) | |||||||
\(644\) | 4.40535e27 | − | 1.57189e27i | 0.359023 | − | 0.128104i | ||||
\(645\) | 4.21565e27 | 0.338273 | ||||||||
\(646\) | −1.78644e26 | − | 1.03225e27i | −0.0141145 | − | 0.0815567i | ||||
\(647\) | − | 1.73575e28i | − | 1.35034i | −0.737660 | − | 0.675172i | \(-0.764069\pi\) | ||
0.737660 | − | 0.675172i | \(-0.235931\pi\) | |||||||
\(648\) | −1.26297e27 | + | 7.13265e26i | −0.0967486 | + | 0.0546388i | ||||
\(649\) | 3.50626e27 | 0.264483 | ||||||||
\(650\) | 7.70672e26 | − | 1.33375e26i | 0.0572448 | − | 0.00990695i | ||||
\(651\) | 1.13835e28i | 0.832657i | ||||||||
\(652\) | 4.89449e27 | + | 1.37173e28i | 0.352559 | + | 0.988078i | ||||
\(653\) | −2.24570e27 | −0.159301 | −0.0796507 | − | 0.996823i | \(-0.525381\pi\) | ||||
−0.0796507 | + | 0.996823i | \(0.525381\pi\) | |||||||
\(654\) | 8.07853e26 | + | 4.66797e27i | 0.0564358 | + | 0.326100i | ||||
\(655\) | − | 9.33767e27i | − | 0.642430i | ||||||
\(656\) | −4.69348e27 | + | 3.83803e27i | −0.318021 | + | 0.260058i | ||||
\(657\) | 5.18639e27 | 0.346108 | ||||||||
\(658\) | 1.03898e28 | − | 1.79810e27i | 0.682889 | − | 0.118183i | ||||
\(659\) | 1.47202e28i | 0.952925i | 0.879195 | + | 0.476463i | \(0.158081\pi\) | ||||
−0.879195 | + | 0.476463i | \(0.841919\pi\) | |||||||
\(660\) | 1.34591e27 | − | 4.80236e26i | 0.0858174 | − | 0.0306207i | ||||
\(661\) | 4.08923e27 | 0.256819 | 0.128409 | − | 0.991721i | \(-0.459013\pi\) | ||||
0.128409 | + | 0.991721i | \(0.459013\pi\) | |||||||
\(662\) | −3.15475e27 | − | 1.82289e28i | −0.195158 | − | 1.12767i | ||||
\(663\) | 1.82473e26i | 0.0111189i | ||||||||
\(664\) | −9.22024e27 | − | 1.63262e28i | −0.553428 | − | 0.979953i | ||||
\(665\) | 2.93532e27 | 0.173556 | ||||||||
\(666\) | 2.76956e27 | − | 4.79308e26i | 0.161313 | − | 0.0279172i | ||||
\(667\) | 1.27109e28i | 0.729317i | ||||||||
\(668\) | 6.60279e27 | + | 1.85049e28i | 0.373218 | + | 1.04598i | ||||
\(669\) | 8.25194e27 | 0.459510 | ||||||||
\(670\) | −3.08297e27 | − | 1.78141e28i | −0.169130 | − | 0.977274i | ||||
\(671\) | 7.31861e27i | 0.395552i | ||||||||
\(672\) | −5.17667e27 | + | 5.97457e27i | −0.275650 | + | 0.318137i | ||||
\(673\) | −2.80038e28 | −1.46915 | −0.734576 | − | 0.678527i | \(-0.762619\pi\) | ||||
−0.734576 | + | 0.678527i | \(0.762619\pi\) | |||||||
\(674\) | −3.02063e28 | + | 5.22759e27i | −1.56134 | + | 0.270211i | ||||
\(675\) | − | 2.39691e27i | − | 0.122071i | ||||||
\(676\) | −1.86117e28 | + | 6.64089e27i | −0.933939 | + | 0.333242i | ||||
\(677\) | −4.33444e27 | −0.214312 | −0.107156 | − | 0.994242i | \(-0.534174\pi\) | ||||
−0.107156 | + | 0.994242i | \(0.534174\pi\) | |||||||
\(678\) | −2.20802e27 | − | 1.27585e28i | −0.107574 | − | 0.621586i | ||||
\(679\) | 5.12377e27i | 0.245976i | ||||||||
\(680\) | 2.34052e27 | − | 1.32181e27i | 0.110719 | − | 0.0625287i | ||||
\(681\) | 1.18460e28 | 0.552207 | ||||||||
\(682\) | 1.10732e28 | − | 1.91637e27i | 0.508664 | − | 0.0880309i | ||||
\(683\) | 3.99129e28i | 1.80678i | 0.428815 | + | 0.903392i | \(0.358931\pi\) | ||||
−0.428815 | + | 0.903392i | \(0.641069\pi\) | |||||||
\(684\) | 9.88441e26 | + | 2.77019e27i | 0.0440950 | + | 0.123580i | ||||
\(685\) | 1.32866e27 | 0.0584127 | ||||||||
\(686\) | −4.21378e27 | − | 2.43482e28i | −0.182571 | − | 1.05494i | ||||
\(687\) | 2.34996e28i | 1.00345i | ||||||||
\(688\) | 1.45739e28 | + | 1.78222e28i | 0.613326 | + | 0.750029i | ||||
\(689\) | −2.70285e27 | −0.112106 | ||||||||
\(690\) | 4.39991e27 | − | 7.61461e26i | 0.179867 | − | 0.0311284i | ||||
\(691\) | − | 5.95285e26i | − | 0.0239852i | −0.999928 | − | 0.0119926i | \(-0.996183\pi\) | ||
0.999928 | − | 0.0119926i | \(-0.00381746\pi\) | |||||||
\(692\) | 3.51687e28 | − | 1.25486e28i | 1.39667 | − | 0.498352i | ||||
\(693\) | 1.62029e27 | 0.0634250 | ||||||||
\(694\) | −2.49965e27 | − | 1.44436e28i | −0.0964461 | − | 0.557289i | ||||
\(695\) | − | 1.08431e28i | − | 0.412386i | ||||||
\(696\) | −1.05641e28 | − | 1.87058e28i | −0.396040 | − | 0.701266i | ||||
\(697\) | 2.33748e27 | 0.0863812 | ||||||||
\(698\) | −6.30845e27 | + | 1.09176e27i | −0.229810 | + | 0.0397716i | ||||
\(699\) | − | 1.32751e27i | − | 0.0476724i | ||||||
\(700\) | −4.39015e27 | − | 1.23038e28i | −0.155417 | − | 0.435570i | ||||
\(701\) | −3.68199e27 | −0.128500 | −0.0642498 | − | 0.997934i | \(-0.520465\pi\) | ||||
−0.0642498 | + | 0.997934i | \(0.520465\pi\) | |||||||
\(702\) | −8.73642e25 | − | 5.04811e26i | −0.00300582 | − | 0.0173683i | ||||
\(703\) | − | 5.69960e27i | − | 0.193326i | ||||||
\(704\) | 6.68319e27 | + | 4.02978e27i | 0.223490 | + | 0.134758i | ||||
\(705\) | 1.00662e28 | 0.331875 | ||||||||
\(706\) | 3.57637e28 | − | 6.18938e27i | 1.16251 | − | 0.201187i | ||||
\(707\) | − | 5.43911e27i | − | 0.174315i | ||||||
\(708\) | −1.74401e28 | + | 6.22286e27i | −0.551083 | + | 0.196633i | ||||
\(709\) | −4.99831e28 | −1.55726 | −0.778629 | − | 0.627485i | \(-0.784084\pi\) | ||||
−0.778629 | + | 0.627485i | \(0.784084\pi\) | |||||||
\(710\) | −6.32545e27 | − | 3.65500e28i | −0.194316 | − | 1.12280i | ||||
\(711\) | − | 1.35913e28i | − | 0.411685i | ||||||
\(712\) | 3.40322e28 | − | 1.92197e28i | 1.01646 | − | 0.574045i | ||||
\(713\) | 3.51154e28 | 1.03419 | ||||||||
\(714\) | 3.00312e27 | − | 5.19730e26i | 0.0872150 | − | 0.0150937i | ||||
\(715\) | 5.04739e26i | 0.0144546i | ||||||||
\(716\) | −9.76863e26 | − | 2.73775e27i | −0.0275869 | − | 0.0773149i | ||||
\(717\) | 4.93552e27 | 0.137449 | ||||||||
\(718\) | 3.68954e27 | + | 2.13190e28i | 0.101328 | + | 0.585495i | ||||
\(719\) | − | 3.72480e28i | − | 1.00882i | −0.863464 | − | 0.504410i | \(-0.831710\pi\) | ||
0.863464 | − | 0.504410i | \(-0.168290\pi\) | |||||||
\(720\) | −5.84221e27 | + | 4.77739e27i | −0.156046 | + | 0.127604i | ||||
\(721\) | 8.19766e27 | 0.215942 | ||||||||
\(722\) | −3.20514e28 | + | 5.54692e27i | −0.832674 | + | 0.144105i | ||||
\(723\) | − | 1.75874e27i | − | 0.0450628i | ||||||
\(724\) | −9.13109e27 | + | 3.25809e27i | −0.230747 | + | 0.0823337i | ||||
\(725\) | 3.55003e28 | 0.884815 | ||||||||
\(726\) | 3.73222e27 | + | 2.15657e28i | 0.0917490 | + | 0.530148i | ||||
\(727\) | − | 3.79351e28i | − | 0.919809i | −0.887968 | − | 0.459904i | \(-0.847884\pi\) | ||
0.887968 | − | 0.459904i | \(-0.152116\pi\) | |||||||
\(728\) | −1.37306e27 | − | 2.43127e27i | −0.0328380 | − | 0.0581460i | ||||
\(729\) | −1.57004e27 | −0.0370370 | ||||||||
\(730\) | 2.65898e28 | − | 4.60171e27i | 0.618709 | − | 0.107076i | ||||
\(731\) | − | 8.87595e27i | − | 0.203724i | ||||||
\(732\) | −1.29890e28 | − | 3.64027e28i | −0.294079 | − | 0.824181i | ||||
\(733\) | −4.54335e28 | −1.01470 | −0.507349 | − | 0.861741i | \(-0.669374\pi\) | ||||
−0.507349 | + | 0.861741i | \(0.669374\pi\) | |||||||
\(734\) | 6.25697e27 | + | 3.61543e28i | 0.137849 | + | 0.796524i | ||||
\(735\) | − | 7.52503e27i | − | 0.163544i | ||||||
\(736\) | 1.84301e28 | + | 1.59688e28i | 0.395138 | + | 0.342368i | ||||
\(737\) | −2.02365e28 | −0.428016 | ||||||||
\(738\) | −6.46664e27 | + | 1.11914e27i | −0.134932 | + | 0.0233517i | ||||
\(739\) | 1.16698e28i | 0.240226i | 0.992760 | + | 0.120113i | \(0.0383257\pi\) | ||||
−0.992760 | + | 0.120113i | \(0.961674\pi\) | |||||||
\(740\) | 1.37738e28 | − | 4.91467e27i | 0.279728 | − | 0.0998107i | ||||
\(741\) | −1.03887e27 | −0.0208152 | ||||||||
\(742\) | 7.69843e27 | + | 4.44834e28i | 0.152182 | + | 0.879343i | ||||
\(743\) | 3.71645e28i | 0.724837i | 0.932015 | + | 0.362419i | \(0.118049\pi\) | ||||
−0.932015 | + | 0.362419i | \(0.881951\pi\) | |||||||
\(744\) | −5.16770e28 | + | 2.91846e28i | −0.994416 | + | 0.561597i | ||||
\(745\) | 2.50490e27 | 0.0475585 | ||||||||
\(746\) | −7.12061e28 | + | 1.23231e28i | −1.33392 | + | 0.230852i | ||||
\(747\) | − | 2.02956e28i | − | 0.375143i | ||||||
\(748\) | −1.01113e27 | − | 2.83377e27i | −0.0184412 | − | 0.0516832i | ||||
\(749\) | 6.23898e28 | 1.12278 | ||||||||
\(750\) | −5.47951e27 | − | 3.16619e28i | −0.0973037 | − | 0.562244i | ||||
\(751\) | 1.05584e28i | 0.185011i | 0.995712 | + | 0.0925056i | \(0.0294876\pi\) | ||||
−0.995712 | + | 0.0925056i | \(0.970512\pi\) | |||||||
\(752\) | 3.47998e28 | + | 4.25563e28i | 0.601726 | + | 0.735843i | ||||
\(753\) | −4.21554e28 | −0.719288 | ||||||||
\(754\) | 7.47670e27 | − | 1.29394e27i | 0.125892 | − | 0.0217872i | ||||
\(755\) | 1.30124e28i | 0.216216i | ||||||||
\(756\) | −8.05932e27 | + | 2.87567e27i | −0.132154 | + | 0.0471543i | ||||
\(757\) | −3.28744e28 | −0.531984 | −0.265992 | − | 0.963975i | \(-0.585700\pi\) | ||||
−0.265992 | + | 0.963975i | \(0.585700\pi\) | |||||||
\(758\) | 2.10748e28 | + | 1.21775e29i | 0.336567 | + | 1.94477i | ||||
\(759\) | − | 4.99821e27i | − | 0.0787764i | ||||||
\(760\) | 7.52547e27 | + | 1.33253e28i | 0.117057 | + | 0.207272i | ||||
\(761\) | 1.00236e29 | 1.53879 | 0.769394 | − | 0.638775i | \(-0.220558\pi\) | ||||
0.769394 | + | 0.638775i | \(0.220558\pi\) | |||||||
\(762\) | −7.23010e27 | + | 1.25126e27i | −0.109546 | + | 0.0189583i | ||||
\(763\) | 2.79479e28i | 0.417931i | ||||||||
\(764\) | −1.51485e28 | − | 4.24550e28i | −0.223582 | − | 0.626607i | ||||
\(765\) | 2.90957e27 | 0.0423853 | ||||||||
\(766\) | 1.72344e28 | + | 9.95845e28i | 0.247804 | + | 1.43187i | ||||
\(767\) | − | 6.54036e27i | − | 0.0928214i | ||||||
\(768\) | −4.03942e28 | − | 8.18287e27i | −0.565856 | − | 0.114629i | ||||
\(769\) | −2.66201e28 | −0.368084 | −0.184042 | − | 0.982918i | \(-0.558918\pi\) | ||||
−0.184042 | + | 0.982918i | \(0.558918\pi\) | |||||||
\(770\) | 8.30697e27 | − | 1.43763e27i | 0.113380 | − | 0.0196218i | ||||
\(771\) | 2.93258e28i | 0.395099i | ||||||||
\(772\) | −8.89809e28 | + | 3.17495e28i | −1.18338 | + | 0.422245i | ||||
\(773\) | −2.90154e28 | −0.380919 | −0.190460 | − | 0.981695i | \(-0.560998\pi\) | ||||
−0.190460 | + | 0.981695i | \(0.560998\pi\) | |||||||
\(774\) | 4.24963e27 | + | 2.45554e28i | 0.0550733 | + | 0.318227i | ||||
\(775\) | − | 9.80742e28i | − | 1.25469i | ||||||
\(776\) | −2.32601e28 | + | 1.31361e28i | −0.293761 | + | 0.165902i | ||||
\(777\) | 1.65818e28 | 0.206739 | ||||||||
\(778\) | −4.75218e28 | + | 8.22427e27i | −0.584920 | + | 0.101228i | ||||
\(779\) | 1.33080e28i | 0.161710i | ||||||||
\(780\) | −8.95804e26 | − | 2.51057e27i | −0.0107465 | − | 0.0301180i | ||||
\(781\) | −4.15200e28 | −0.491753 | ||||||||
\(782\) | −1.60324e27 | − | 9.26391e27i | −0.0187470 | − | 0.108324i | ||||
\(783\) | − | 2.32537e28i | − | 0.268457i | ||||||
\(784\) | 3.18131e28 | − | 2.60148e28i | 0.362615 | − | 0.296524i | ||||
\(785\) | −4.15319e28 | −0.467396 | ||||||||
\(786\) | 5.43902e28 | − | 9.41294e27i | 0.604359 | − | 0.104592i | ||||
\(787\) | − | 1.18527e29i | − | 1.30038i | −0.759771 | − | 0.650191i | \(-0.774689\pi\) | ||
0.759771 | − | 0.650191i | \(-0.225311\pi\) | |||||||
\(788\) | 1.14524e29 | − | 4.08635e28i | 1.24060 | − | 0.442664i | ||||
\(789\) | 5.89085e28 | 0.630098 | ||||||||
\(790\) | −1.20591e28 | − | 6.96804e28i | −0.127363 | − | 0.735935i | ||||
\(791\) | − | 7.63870e28i | − | 0.796627i | ||||||
\(792\) | 4.15404e27 | + | 7.35554e27i | 0.0427779 | + | 0.0757465i | ||||
\(793\) | 1.36517e28 | 0.138821 | ||||||||
\(794\) | 5.07728e28 | − | 8.78690e27i | 0.509831 | − | 0.0882329i | ||||
\(795\) | 4.30977e28i | 0.427349i | ||||||||
\(796\) | −5.50527e28 | − | 1.54290e29i | −0.539074 | − | 1.51080i | ||||
\(797\) | 1.66328e28 | 0.160835 | 0.0804177 | − | 0.996761i | \(-0.474375\pi\) | ||||
0.0804177 | + | 0.996761i | \(0.474375\pi\) | |||||||
\(798\) | 2.95898e27 | + | 1.70977e28i | 0.0282562 | + | 0.163271i | ||||
\(799\) | − | 2.11942e28i | − | 0.199870i | ||||||
\(800\) | 4.45994e28 | − | 5.14737e28i | 0.415365 | − | 0.479386i | ||||
\(801\) | 4.23064e28 | 0.389118 | ||||||||
\(802\) | 1.04554e29 | − | 1.80945e28i | 0.949725 | − | 0.164362i | ||||
\(803\) | − | 3.02055e28i | − | 0.270976i | ||||||
\(804\) | 1.00656e29 | − | 3.59154e28i | 0.891825 | − | 0.318215i | ||||
\(805\) | 2.63430e28 | 0.230519 | ||||||||
\(806\) | −3.57467e27 | − | 2.06553e28i | −0.0308949 | − | 0.178518i | ||||
\(807\) | − | 7.50421e27i | − | 0.0640575i | ||||||
\(808\) | 2.46916e28 | − | 1.39446e28i | 0.208179 | − | 0.117569i | ||||
\(809\) | −1.08111e29 | −0.900295 | −0.450147 | − | 0.892954i | \(-0.648629\pi\) | ||||
−0.450147 | + | 0.892954i | \(0.648629\pi\) | |||||||
\(810\) | −8.04935e27 | + | 1.39305e27i | −0.0662080 | + | 0.0114582i | ||||
\(811\) | 1.49142e29i | 1.21169i | 0.795581 | + | 0.605847i | \(0.207166\pi\) | ||||
−0.795581 | + | 0.605847i | \(0.792834\pi\) | |||||||
\(812\) | −4.25912e28 | − | 1.19366e29i | −0.341790 | − | 0.957897i | ||||
\(813\) | −2.31748e28 | −0.183701 | ||||||||
\(814\) | −2.79148e27 | − | 1.61299e28i | −0.0218570 | − | 0.126295i | ||||
\(815\) | 8.20260e28i | 0.634418i | ||||||||
\(816\) | 1.00587e28 | + | 1.23006e28i | 0.0768492 | + | 0.0939780i | ||||
\(817\) | 5.05336e28 | 0.381381 | ||||||||
\(818\) | −1.70908e29 | + | 2.95779e28i | −1.27418 | + | 0.220513i | ||||
\(819\) | − | 3.02239e27i | − | 0.0222593i | ||||||
\(820\) | −3.21604e28 | + | 1.14753e28i | −0.233982 | + | 0.0834880i | ||||
\(821\) | −1.28207e29 | −0.921465 | −0.460733 | − | 0.887539i | \(-0.652413\pi\) | ||||
−0.460733 | + | 0.887539i | \(0.652413\pi\) | |||||||
\(822\) | 1.33937e27 | + | 7.73918e27i | 0.00951002 | + | 0.0549512i | ||||
\(823\) | 1.98827e29i | 1.39469i | 0.716737 | + | 0.697343i | \(0.245635\pi\) | ||||
−0.716737 | + | 0.697343i | \(0.754365\pi\) | |||||||
\(824\) | 2.10169e28 | + | 3.72144e28i | 0.145645 | + | 0.257893i | ||||
\(825\) | −1.39596e28 | −0.0955724 | ||||||||
\(826\) | −1.07641e29 | + | 1.86287e28i | −0.728076 | + | 0.126003i | ||||
\(827\) | 3.50038e28i | 0.233916i | 0.993137 | + | 0.116958i | \(0.0373143\pi\) | ||||
−0.993137 | + | 0.116958i | \(0.962686\pi\) | |||||||
\(828\) | 8.87074e27 | + | 2.48610e28i | 0.0585675 | + | 0.164141i | ||||
\(829\) | 2.08460e29 | 1.35981 | 0.679904 | − | 0.733301i | \(-0.262021\pi\) | ||||
0.679904 | + | 0.733301i | \(0.262021\pi\) | |||||||
\(830\) | −1.80076e28 | − | 1.04052e29i | −0.116058 | − | 0.670612i | ||||
\(831\) | 7.29102e28i | 0.464278i | ||||||||
\(832\) | 7.51691e27 | − | 1.24664e28i | 0.0472940 | − | 0.0784347i | ||||
\(833\) | −1.58438e28 | −0.0984938 | ||||||||
\(834\) | 6.31588e28 | − | 1.09305e28i | 0.387948 | − | 0.0671395i | ||||
\(835\) | 1.10655e29i | 0.671594i | ||||||||
\(836\) | 1.61336e28 | − | 5.75666e27i | 0.0967537 | − | 0.0345230i | ||||
\(837\) | −6.42413e28 | −0.380680 | ||||||||
\(838\) | −1.33223e28 | − | 7.69792e28i | −0.0780077 | − | 0.450747i | ||||
\(839\) | 2.15016e28i | 0.124409i | 0.998063 | + | 0.0622043i | \(0.0198130\pi\) | ||||
−0.998063 | + | 0.0622043i | \(0.980187\pi\) | |||||||
\(840\) | −3.87673e28 | + | 2.18938e28i | −0.221653 | + | 0.125178i | ||||
\(841\) | 1.67413e29 | 0.945867 | ||||||||
\(842\) | 1.33096e28 | − | 2.30341e27i | 0.0743097 | − | 0.0128603i | ||||
\(843\) | − | 9.56892e28i | − | 0.527943i | ||||||
\(844\) | −4.12837e28 | − | 1.15701e29i | −0.225089 | − | 0.630832i | ||||
\(845\) | −1.11294e29 | −0.599657 | ||||||||
\(846\) | 1.01473e28 | + | 5.86337e28i | 0.0540317 | + | 0.312208i | ||||
\(847\) | 1.29117e29i | 0.679439i | ||||||||
\(848\) | −1.82202e29 | + | 1.48993e29i | −0.947531 | + | 0.774831i | ||||
\(849\) | −1.16138e29 | −0.596897 | ||||||||
\(850\) | −2.58733e28 | + | 4.47771e27i | −0.131420 | + | 0.0227440i | ||||
\(851\) | − | 5.11509e28i | − | 0.256778i | ||||||
\(852\) | 2.06520e29 | − | 7.36891e28i | 1.02463 | − | 0.365601i | ||||
\(853\) | −9.99709e28 | −0.490211 | −0.245106 | − | 0.969496i | \(-0.578823\pi\) | ||||
−0.245106 | + | 0.969496i | \(0.578823\pi\) | |||||||
\(854\) | −3.88836e28 | − | 2.24679e29i | −0.188446 | − | 1.08889i | ||||
\(855\) | 1.65651e28i | 0.0793475i | ||||||||
\(856\) | 1.59953e29 | + | 2.83228e29i | 0.757276 | + | 1.34090i | ||||
\(857\) | −6.23666e28 | −0.291839 | −0.145920 | − | 0.989296i | \(-0.546614\pi\) | ||||
−0.145920 | + | 0.989296i | \(0.546614\pi\) | |||||||
\(858\) | −2.94001e27 | + | 5.08808e26i | −0.0135980 | + | 0.00235332i | ||||
\(859\) | − | 1.81838e29i | − | 0.831291i | −0.909527 | − | 0.415646i | \(-0.863556\pi\) | ||
0.909527 | − | 0.415646i | \(-0.136444\pi\) | |||||||
\(860\) | 4.35743e28 | + | 1.22121e29i | 0.196900 | + | 0.551830i | ||||
\(861\) | −3.87169e28 | −0.172929 | ||||||||
\(862\) | −5.79641e27 | − | 3.34931e28i | −0.0255910 | − | 0.147871i | ||||
\(863\) | 2.84892e29i | 1.24329i | 0.783299 | + | 0.621645i | \(0.213535\pi\) | ||||
−0.783299 | + | 0.621645i | \(0.786465\pi\) | |||||||
\(864\) | −3.37167e28 | − | 2.92139e28i | −0.145448 | − | 0.126024i | ||||
\(865\) | 2.10301e29 | 0.896767 | ||||||||
\(866\) | 2.93704e29 | − | 5.08294e28i | 1.23803 | − | 0.214257i | ||||
\(867\) | 1.32432e29i | 0.551824i | ||||||||
\(868\) | −3.29763e29 | + | 1.17664e29i | −1.35833 | + | 0.484668i | ||||
\(869\) | −7.91555e28 | −0.322317 | ||||||||
\(870\) | −2.06322e28 | − | 1.19218e29i | −0.0830527 | − | 0.479898i | ||||
\(871\) | 3.77479e28i | 0.150214i | ||||||||
\(872\) | −1.26874e29 | + | 7.16519e28i | −0.499122 | + | 0.281879i | ||||
\(873\) | −2.89154e28 | −0.112457 | ||||||||
\(874\) | 5.27423e28 | − | 9.12774e27i | 0.202789 | − | 0.0350953i | ||||
\(875\) | − | 1.89565e29i | − | 0.720574i | ||||||
\(876\) | 5.36082e28 | + | 1.50242e29i | 0.201461 | + | 0.564611i | ||||
\(877\) | 4.00375e29 | 1.48755 | 0.743773 | − | 0.668432i | \(-0.233034\pi\) | ||||
0.743773 | + | 0.668432i | \(0.233034\pi\) | |||||||
\(878\) | 2.11563e28 | + | 1.22246e29i | 0.0777133 | + | 0.449046i | ||||
\(879\) | − | 2.39550e29i | − | 0.869977i | ||||||
\(880\) | 2.78234e28 | + | 3.40249e28i | 0.0999042 | + | 0.122172i | ||||
\(881\) | −2.97318e29 | −1.05551 | −0.527754 | − | 0.849397i | \(-0.676966\pi\) | ||||
−0.527754 | + | 0.849397i | \(0.676966\pi\) | |||||||
\(882\) | 4.38319e28 | − | 7.58569e27i | 0.153853 | − | 0.0266262i | ||||
\(883\) | 2.28684e28i | 0.0793649i | 0.999212 | + | 0.0396825i | \(0.0126346\pi\) | ||||
−0.999212 | + | 0.0396825i | \(0.987365\pi\) | |||||||
\(884\) | −5.28595e27 | + | 1.88610e27i | −0.0181385 | + | 0.00647204i | ||||
\(885\) | −1.04288e29 | −0.353835 | ||||||||
\(886\) | −2.35189e28 | − | 1.35898e29i | −0.0789005 | − | 0.455906i | ||||
\(887\) | − | 2.10400e28i | − | 0.0697926i | −0.999391 | − | 0.0348963i | \(-0.988890\pi\) | ||
0.999391 | − | 0.0348963i | \(-0.0111101\pi\) | |||||||
\(888\) | 4.25119e28 | + | 7.52755e28i | 0.139438 | + | 0.246902i | ||||
\(889\) | −4.32879e28 | −0.140394 | ||||||||
\(890\) | 2.16898e29 | − | 3.75371e28i | 0.695594 | − | 0.120382i | ||||
\(891\) | 9.14390e27i | 0.0289971i | ||||||||
\(892\) | 8.52946e28 | + | 2.39046e29i | 0.267469 | + | 0.749605i | ||||
\(893\) | 1.20665e29 | 0.374168 | ||||||||
\(894\) | 2.52509e27 | + | 1.45906e28i | 0.00774287 | + | 0.0447401i | ||||
\(895\) | − | 1.63711e28i | − | 0.0496418i | ||||||
\(896\) | −2.26582e29 | − | 8.82052e28i | −0.679430 | − | 0.264493i | ||||
\(897\) | −9.32335e27 | −0.0276470 | ||||||||
\(898\) | −5.52397e29 | + | 9.55996e28i | −1.61990 | + | 0.280345i | ||||
\(899\) | − | 9.51470e29i | − | 2.75930i | ||||||
\(900\) | 6.94348e28 | − | 2.47752e28i | 0.199137 | − | 0.0710547i | ||||
\(901\) | 9.07412e28 | 0.257369 | ||||||||
\(902\) | 6.51783e27 | + | 3.76616e28i | 0.0182826 | + | 0.105641i | ||||
\(903\) | 1.47017e29i | 0.407841i | ||||||||
\(904\) | 3.46770e29 | − | 1.95838e29i | 0.951386 | − | 0.537295i | ||||
\(905\) | −5.46018e28 | −0.148157 | ||||||||
\(906\) | −7.57948e28 | + | 1.31173e28i | −0.203403 | + | 0.0352015i | ||||
\(907\) | − | 6.83150e29i | − | 1.81319i | −0.422004 | − | 0.906594i | \(-0.638673\pi\) | ||
0.422004 | − | 0.906594i | \(-0.361327\pi\) | |||||||
\(908\) | 1.22445e29 | + | 3.43162e29i | 0.321426 | + | 0.900824i | ||||
\(909\) | 3.06949e28 | 0.0796944 | ||||||||
\(910\) | −2.68167e27 | − | 1.54953e28i | −0.00688637 | − | 0.0397911i | ||||
\(911\) | 2.83829e29i | 0.720897i | 0.932779 | + | 0.360449i | \(0.117376\pi\) | ||||
−0.932779 | + | 0.360449i | \(0.882624\pi\) | |||||||
\(912\) | −7.00314e28 | + | 5.72672e28i | −0.175932 | + | 0.143866i | ||||
\(913\) | −1.18201e29 | −0.293708 | ||||||||
\(914\) | 4.66261e29 | − | 8.06925e28i | 1.14595 | − | 0.198322i | ||||
\(915\) | − | 2.17680e29i | − | 0.529184i | ||||||
\(916\) | −6.80748e29 | + | 2.42900e29i | −1.63694 | + | 0.584080i | ||||
\(917\) | 3.25644e29 | 0.774549 | ||||||||
\(918\) | 2.93303e27 | + | 1.69477e28i | 0.00690064 | + | 0.0398735i | ||||
\(919\) | − | 1.08421e28i | − | 0.0252324i | −0.999920 | − | 0.0126162i | \(-0.995984\pi\) | ||
0.999920 | − | 0.0126162i | \(-0.00401596\pi\) | |||||||
\(920\) | 6.75372e28 | + | 1.19588e29i | 0.155476 | + | 0.275301i | ||||
\(921\) | 5.67172e28 | 0.129157 | ||||||||
\(922\) | −4.93184e29 | + | 8.53520e28i | −1.11096 | + | 0.192267i | ||||
\(923\) | 7.74489e28i | 0.172583i | ||||||||
\(924\) | 1.67478e28 | + | 4.69373e28i | 0.0369181 | + | 0.103466i | ||||
\(925\) | −1.42860e29 | −0.311526 | ||||||||
\(926\) | 1.00538e29 | + | 5.80933e29i | 0.216880 | + | 1.25319i | ||||
\(927\) | 4.62624e28i | 0.0987259i | ||||||||
\(928\) | 4.32683e29 | − | 4.99374e29i | 0.913462 | − | 1.05426i | ||||
\(929\) | 6.85256e29 | 1.43118 | 0.715592 | − | 0.698518i | \(-0.246157\pi\) | ||||
0.715592 | + | 0.698518i | \(0.246157\pi\) | |||||||
\(930\) | −3.29355e29 | + | 5.69991e28i | −0.680510 | + | 0.117771i | ||||
\(931\) | − | 9.02036e28i | − | 0.184386i | ||||||
\(932\) | 3.84560e28 | − | 1.37216e28i | 0.0777687 | − | 0.0277489i | ||||
\(933\) | −8.35278e28 | −0.167115 | ||||||||
\(934\) | −1.65133e29 | − | 9.54175e29i | −0.326862 | − | 1.88868i | ||||
\(935\) | − | 1.69453e28i | − | 0.0331844i | ||||||
\(936\) | 1.37206e28 | − | 7.74870e27i | 0.0265836 | − | 0.0150131i | ||||
\(937\) | −1.50628e29 | −0.288741 | −0.144371 | − | 0.989524i | \(-0.546116\pi\) | ||||
−0.144371 | + | 0.989524i | \(0.546116\pi\) | |||||||
\(938\) | 6.21253e29 | − | 1.07516e29i | 1.17826 | − | 0.203913i | ||||
\(939\) | − | 5.14676e29i | − | 0.965780i | ||||||
\(940\) | 1.04047e29 | + | 2.91602e29i | 0.193176 | + | 0.541392i | ||||
\(941\) | 3.69077e29 | 0.677986 | 0.338993 | − | 0.940789i | \(-0.389914\pi\) | ||||
0.338993 | + | 0.940789i | \(0.389914\pi\) | |||||||
\(942\) | −4.18667e28 | − | 2.41916e29i | −0.0760956 | − | 0.439698i | ||||
\(943\) | 1.19432e29i | 0.214785i | ||||||||
\(944\) | −3.60533e29 | − | 4.40892e29i | −0.641542 | − | 0.784534i | ||||
\(945\) | −4.81928e28 | −0.0848525 | ||||||||
\(946\) | 1.43010e29 | − | 2.47497e28i | 0.249147 | − | 0.0431181i | ||||
\(947\) | 8.71665e29i | 1.50262i | 0.659948 | + | 0.751311i | \(0.270578\pi\) | ||||
−0.659948 | + | 0.751311i | \(0.729422\pi\) | |||||||
\(948\) | 3.93719e29 | − | 1.40484e29i | 0.671588 | − | 0.239631i | ||||
\(949\) | −5.63434e28 | −0.0951001 | ||||||||
\(950\) | −2.54930e28 | − | 1.47305e29i | −0.0425780 | − | 0.246026i | ||||
\(951\) | 4.24795e29i | 0.702061i | ||||||||
\(952\) | 4.60970e28 | + | 8.16237e28i | 0.0753882 | + | 0.133489i | ||||
\(953\) | 2.74118e29 | 0.443618 | 0.221809 | − | 0.975090i | \(-0.428804\pi\) | ||||
0.221809 | + | 0.975090i | \(0.428804\pi\) | |||||||
\(954\) | −2.51036e29 | + | 4.34451e28i | −0.402024 | + | 0.0695756i | ||||
\(955\) | − | 2.53871e29i | − | 0.402328i | ||||||
\(956\) | 5.10151e28 | + | 1.42974e29i | 0.0800056 | + | 0.224223i | ||||
\(957\) | −1.35429e29 | −0.210181 | ||||||||
\(958\) | 1.96110e29 | + | 1.13317e30i | 0.301193 | + | 1.74037i | ||||
\(959\) | 4.63358e28i | 0.0704256i | ||||||||
\(960\) | −1.98780e29 | − | 1.19859e29i | −0.298993 | − | 0.180285i | ||||
\(961\) | −1.95677e30 | −2.91276 | ||||||||
\(962\) | −3.00877e28 | + | 5.20706e27i | −0.0443239 | + | 0.00767082i | ||||
\(963\) | 3.52089e29i | 0.513322i | ||||||||
\(964\) | 5.09479e28 | − | 1.81789e28i | 0.0735116 | − | 0.0262299i | ||||
\(965\) | −5.32085e29 | −0.759815 | ||||||||
\(966\) | 2.65553e28 | + | 1.53443e29i | 0.0375302 | + | 0.216858i | ||||
\(967\) | 1.35076e30i | 1.88936i | 0.327998 | + | 0.944678i | \(0.393626\pi\) | ||||
−0.327998 | + | 0.944678i | \(0.606374\pi\) | |||||||
\(968\) | −5.86147e29 | + | 3.31026e29i | −0.811434 | + | 0.458257i | ||||
\(969\) | 3.48775e28 | 0.0477867 | ||||||||
\(970\) | −1.48244e29 | + | 2.56556e28i | −0.201030 | + | 0.0347908i | ||||
\(971\) | 7.41402e29i | 0.995087i | 0.867439 | + | 0.497544i | \(0.165765\pi\) | ||||
−0.867439 | + | 0.497544i | \(0.834235\pi\) | |||||||
\(972\) | −1.62285e28 | − | 4.54817e28i | −0.0215583 | − | 0.0604191i | ||||
\(973\) | 3.78143e29 | 0.497196 | ||||||||
\(974\) | −1.75298e28 | − | 1.01292e29i | −0.0228133 | − | 0.131821i | ||||
\(975\) | 2.60393e28i | 0.0335416i | ||||||||
\(976\) | 9.20272e29 | − | 7.52540e29i | 1.17332 | − | 0.959470i | ||||
\(977\) | −4.07488e29 | −0.514244 | −0.257122 | − | 0.966379i | \(-0.582774\pi\) | ||||
−0.257122 | + | 0.966379i | \(0.582774\pi\) | |||||||
\(978\) | −4.77786e29 | + | 8.26871e28i | −0.596822 | + | 0.103288i | ||||
\(979\) | − | 2.46392e29i | − | 0.304649i | ||||||
\(980\) | 2.17988e29 | − | 7.77811e28i | 0.266792 | − | 0.0951948i | ||||
\(981\) | −1.57721e29 | −0.191073 | ||||||||
\(982\) | 1.43007e29 | + | 8.26331e29i | 0.171492 | + | 0.990921i | ||||
\(983\) | 4.08949e29i | 0.485438i | 0.970097 | + | 0.242719i | \(0.0780393\pi\) | ||||
−0.970097 | + | 0.242719i | \(0.921961\pi\) | |||||||
\(984\) | −9.92609e28 | − | 1.75761e29i | −0.116635 | − | 0.206524i | ||||
\(985\) | 6.84825e29 | 0.796558 | ||||||||
\(986\) | −2.51011e29 | + | 4.34407e28i | −0.289017 | + | 0.0500181i | ||||
\(987\) | 3.51050e29i | 0.400127i | ||||||||
\(988\) | −1.07381e28 | − | 3.00946e28i | −0.0121160 | − | 0.0339562i | ||||
\(989\) | 4.53512e29 | 0.506554 | ||||||||
\(990\) | 8.11307e27 | + | 4.68793e28i | 0.00897085 | + | 0.0518357i | ||||
\(991\) | 6.06373e29i | 0.663749i | 0.943324 | + | 0.331874i | \(0.107681\pi\) | ||||
−0.943324 | + | 0.331874i | \(0.892319\pi\) | |||||||
\(992\) | −1.37958e30 | − | 1.19534e30i | −1.49497 | − | 1.29532i | ||||
\(993\) | 6.15915e29 | 0.660737 | ||||||||
\(994\) | 1.27465e30 | − | 2.20595e29i | 1.35371 | − | 0.234278i | ||||
\(995\) | − | 9.22620e29i | − | 0.970045i | ||||||
\(996\) | 5.87933e29 | − | 2.09782e29i | 0.611976 | − | 0.218361i | ||||
\(997\) | −9.60862e29 | −0.990169 | −0.495085 | − | 0.868845i | \(-0.664863\pi\) | ||||
−0.495085 | + | 0.868845i | \(0.664863\pi\) | |||||||
\(998\) | −7.09018e28 | − | 4.09688e29i | −0.0723356 | − | 0.417972i | ||||
\(999\) | 9.35774e28i | 0.0945183i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 12.21.d.a.7.2 | yes | 20 | |
3.2 | odd | 2 | 36.21.d.c.19.19 | 20 | |||
4.3 | odd | 2 | inner | 12.21.d.a.7.1 | ✓ | 20 | |
12.11 | even | 2 | 36.21.d.c.19.20 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.21.d.a.7.1 | ✓ | 20 | 4.3 | odd | 2 | inner | |
12.21.d.a.7.2 | yes | 20 | 1.1 | even | 1 | trivial | |
36.21.d.c.19.19 | 20 | 3.2 | odd | 2 | |||
36.21.d.c.19.20 | 20 | 12.11 | even | 2 |