Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,17,Mod(7,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 17, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.7");
S:= CuspForms(chi, 17);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 17 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.4789452628\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 37115 x^{14} + 433616 x^{13} + 965822723 x^{12} + 11579264195 x^{11} + \cdots + 43\!\cdots\!49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{106}\cdot 3^{51} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 7.11 | ||
Root | \(54.8669 + 95.0323i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.7 |
Dual form | 12.17.d.a.7.12 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 196.501 | − | 164.084i | 0.767581 | − | 0.640952i | ||||
\(3\) | − | 3788.00i | − | 0.577350i | ||||||
\(4\) | 11689.0 | − | 64485.1i | 0.178361 | − | 0.983965i | ||||
\(5\) | −45026.4 | −0.115268 | −0.0576338 | − | 0.998338i | \(-0.518356\pi\) | ||||
−0.0576338 | + | 0.998338i | \(0.518356\pi\) | |||||||
\(6\) | −621548. | − | 744344.i | −0.370054 | − | 0.443163i | ||||
\(7\) | − | 3.24149e6i | − | 0.562289i | −0.959665 | − | 0.281145i | \(-0.909286\pi\) | ||
0.959665 | − | 0.281145i | \(-0.0907141\pi\) | |||||||
\(8\) | −8.28406e6 | − | 1.45894e7i | −0.493768 | − | 0.869593i | ||||
\(9\) | −1.43489e7 | −0.333333 | ||||||||
\(10\) | −8.84773e6 | + | 7.38811e6i | −0.0884773 | + | 0.0738811i | ||||
\(11\) | − | 2.75960e7i | − | 0.128738i | −0.997926 | − | 0.0643688i | \(-0.979497\pi\) | ||
0.997926 | − | 0.0643688i | \(-0.0205034\pi\) | |||||||
\(12\) | −2.44269e8 | − | 4.42780e7i | −0.568093 | − | 0.102977i | ||||
\(13\) | −6.92488e8 | −0.848917 | −0.424459 | − | 0.905447i | \(-0.639536\pi\) | ||||
−0.424459 | + | 0.905447i | \(0.639536\pi\) | |||||||
\(14\) | −5.31875e8 | − | 6.36954e8i | −0.360401 | − | 0.431602i | ||||
\(15\) | 1.70560e8i | 0.0665498i | ||||||||
\(16\) | −4.02170e9 | − | 1.50754e9i | −0.936375 | − | 0.351001i | ||||
\(17\) | 2.60696e9 | 0.373718 | 0.186859 | − | 0.982387i | \(-0.440169\pi\) | ||||
0.186859 | + | 0.982387i | \(0.440169\pi\) | |||||||
\(18\) | −2.81957e9 | + | 2.35442e9i | −0.255860 | + | 0.213651i | ||||
\(19\) | 1.17841e10i | 0.693852i | 0.937892 | + | 0.346926i | \(0.112775\pi\) | ||||
−0.937892 | + | 0.346926i | \(0.887225\pi\) | |||||||
\(20\) | −5.26316e8 | + | 2.90354e9i | −0.0205592 | + | 0.113419i | ||||
\(21\) | −1.22787e10 | −0.324638 | ||||||||
\(22\) | −4.52806e9 | − | 5.42264e9i | −0.0825146 | − | 0.0988165i | ||||
\(23\) | − | 3.87992e9i | − | 0.0495451i | −0.999693 | − | 0.0247725i | \(-0.992114\pi\) | ||
0.999693 | − | 0.0247725i | \(-0.00788615\pi\) | |||||||
\(24\) | −5.52644e10 | + | 3.13800e10i | −0.502060 | + | 0.285077i | ||||
\(25\) | −1.50561e11 | −0.986713 | ||||||||
\(26\) | −1.36074e11 | + | 1.13626e11i | −0.651612 | + | 0.544115i | ||||
\(27\) | 5.43536e10i | 0.192450i | ||||||||
\(28\) | −2.09028e11 | − | 3.78899e10i | −0.553273 | − | 0.100290i | ||||
\(29\) | −6.46281e11 | −1.29193 | −0.645963 | − | 0.763369i | \(-0.723544\pi\) | ||||
−0.645963 | + | 0.763369i | \(0.723544\pi\) | |||||||
\(30\) | 2.79861e10 | + | 3.35151e10i | 0.0426553 | + | 0.0510824i | ||||
\(31\) | − | 9.55575e11i | − | 1.12040i | −0.828359 | − | 0.560198i | \(-0.810725\pi\) | ||
0.828359 | − | 0.560198i | \(-0.189275\pi\) | |||||||
\(32\) | −1.03763e12 | + | 3.63663e11i | −0.943718 | + | 0.330750i | ||||
\(33\) | −1.04534e11 | −0.0743267 | ||||||||
\(34\) | 5.12270e11 | − | 4.27761e11i | 0.286859 | − | 0.239535i | ||||
\(35\) | 1.45953e11i | 0.0648138i | ||||||||
\(36\) | −1.67725e11 | + | 9.25291e11i | −0.0594535 | + | 0.327988i | ||||
\(37\) | 6.34959e12 | 1.80772 | 0.903861 | − | 0.427826i | \(-0.140720\pi\) | ||||
0.903861 | + | 0.427826i | \(0.140720\pi\) | |||||||
\(38\) | 1.93358e12 | + | 2.31558e12i | 0.444726 | + | 0.532588i | ||||
\(39\) | 2.62314e12i | 0.490123i | ||||||||
\(40\) | 3.73002e11 | + | 6.56907e11i | 0.0569156 | + | 0.100236i | ||||
\(41\) | 1.16356e13 | 1.45720 | 0.728600 | − | 0.684939i | \(-0.240171\pi\) | ||||
0.728600 | + | 0.684939i | \(0.240171\pi\) | |||||||
\(42\) | −2.41278e12 | + | 2.01474e12i | −0.249186 | + | 0.208077i | ||||
\(43\) | − | 1.79375e13i | − | 1.53467i | −0.641246 | − | 0.767335i | \(-0.721582\pi\) | ||
0.641246 | − | 0.767335i | \(-0.278418\pi\) | |||||||
\(44\) | −1.77953e12 | − | 3.22571e11i | −0.126673 | − | 0.0229617i | ||||
\(45\) | 6.46080e11 | 0.0384226 | ||||||||
\(46\) | −6.36633e11 | − | 7.62408e11i | −0.0317560 | − | 0.0380299i | ||||
\(47\) | − | 3.29643e13i | − | 1.38440i | −0.721706 | − | 0.692200i | \(-0.756642\pi\) | ||
0.721706 | − | 0.692200i | \(-0.243358\pi\) | |||||||
\(48\) | −5.71055e12 | + | 1.52342e13i | −0.202651 | + | 0.540616i | ||||
\(49\) | 2.27257e13 | 0.683831 | ||||||||
\(50\) | −2.95852e13 | + | 2.47045e13i | −0.757382 | + | 0.632436i | ||||
\(51\) | − | 9.87517e12i | − | 0.215766i | ||||||
\(52\) | −8.09452e12 | + | 4.46552e13i | −0.151413 | + | 0.835305i | ||||
\(53\) | 5.59722e12 | 0.0899013 | 0.0449506 | − | 0.998989i | \(-0.485687\pi\) | ||||
0.0449506 | + | 0.998989i | \(0.485687\pi\) | |||||||
\(54\) | 8.91854e12 | + | 1.06805e13i | 0.123351 | + | 0.147721i | ||||
\(55\) | 1.24255e12i | 0.0148393i | ||||||||
\(56\) | −4.72912e13 | + | 2.68527e13i | −0.488963 | + | 0.277641i | ||||
\(57\) | 4.46381e13 | 0.400596 | ||||||||
\(58\) | −1.26995e14 | + | 1.06044e14i | −0.991657 | + | 0.828062i | ||||
\(59\) | − | 1.93936e14i | − | 1.32082i | −0.750906 | − | 0.660409i | \(-0.770383\pi\) | ||
0.750906 | − | 0.660409i | \(-0.229617\pi\) | |||||||
\(60\) | 1.09986e13 | + | 1.99368e12i | 0.0654827 | + | 0.0118699i | ||||
\(61\) | −1.41886e13 | −0.0740117 | −0.0370058 | − | 0.999315i | \(-0.511782\pi\) | ||||
−0.0370058 | + | 0.999315i | \(0.511782\pi\) | |||||||
\(62\) | −1.56794e14 | − | 1.87771e14i | −0.718120 | − | 0.859994i | ||||
\(63\) | 4.65118e13i | 0.187430i | ||||||||
\(64\) | −1.44224e14 | + | 2.41718e14i | −0.512385 | + | 0.858756i | ||||
\(65\) | 3.11803e13 | 0.0978527 | ||||||||
\(66\) | −2.05409e13 | + | 1.71523e13i | −0.0570517 | + | 0.0476398i | ||||
\(67\) | 3.51753e14i | 0.866242i | 0.901336 | + | 0.433121i | \(0.142588\pi\) | ||||
−0.901336 | + | 0.433121i | \(0.857412\pi\) | |||||||
\(68\) | 3.04729e13 | − | 1.68110e14i | 0.0666565 | − | 0.367725i | ||||
\(69\) | −1.46971e13 | −0.0286049 | ||||||||
\(70\) | 2.39484e13 | + | 2.86798e13i | 0.0415425 | + | 0.0497498i | ||||
\(71\) | − | 8.84835e14i | − | 1.37024i | −0.728432 | − | 0.685119i | \(-0.759750\pi\) | ||
0.728432 | − | 0.685119i | \(-0.240250\pi\) | |||||||
\(72\) | 1.18867e14 | + | 2.09341e14i | 0.164589 | + | 0.289864i | ||||
\(73\) | 1.70546e14 | 0.211475 | 0.105737 | − | 0.994394i | \(-0.466280\pi\) | ||||
0.105737 | + | 0.994394i | \(0.466280\pi\) | |||||||
\(74\) | 1.24770e15 | − | 1.04186e15i | 1.38757 | − | 1.15866i | ||||
\(75\) | 5.70322e14i | 0.569679i | ||||||||
\(76\) | 7.59898e14 | + | 1.37745e14i | 0.682727 | + | 0.123756i | ||||
\(77\) | −8.94522e13 | −0.0723878 | ||||||||
\(78\) | 4.30415e14 | + | 5.15449e14i | 0.314145 | + | 0.376209i | ||||
\(79\) | 1.50351e15i | 0.991037i | 0.868597 | + | 0.495519i | \(0.165022\pi\) | ||||
−0.868597 | + | 0.495519i | \(0.834978\pi\) | |||||||
\(80\) | 1.81083e14 | + | 6.78791e13i | 0.107934 | + | 0.0404591i | ||||
\(81\) | 2.05891e14 | 0.111111 | ||||||||
\(82\) | 2.28641e15 | − | 1.90922e15i | 1.11852 | − | 0.933996i | ||||
\(83\) | 4.88125e14i | 0.216724i | 0.994112 | + | 0.108362i | \(0.0345605\pi\) | ||||
−0.994112 | + | 0.108362i | \(0.965439\pi\) | |||||||
\(84\) | −1.43527e14 | + | 7.91796e14i | −0.0579026 | + | 0.319432i | ||||
\(85\) | −1.17382e14 | −0.0430776 | ||||||||
\(86\) | −2.94326e15 | − | 3.52474e15i | −0.983650 | − | 1.17798i | ||||
\(87\) | 2.44811e15i | 0.745893i | ||||||||
\(88\) | −4.02609e14 | + | 2.28607e14i | −0.111949 | + | 0.0635666i | ||||
\(89\) | −7.27333e15 | −1.84762 | −0.923811 | − | 0.382849i | \(-0.874943\pi\) | ||||
−0.923811 | + | 0.382849i | \(0.874943\pi\) | |||||||
\(90\) | 1.26955e14 | − | 1.06011e14i | 0.0294924 | − | 0.0246270i | ||||
\(91\) | 2.24469e15i | 0.477337i | ||||||||
\(92\) | −2.50197e14 | − | 4.53526e13i | −0.0487506 | − | 0.00883689i | ||||
\(93\) | −3.61972e15 | −0.646861 | ||||||||
\(94\) | −5.40891e15 | − | 6.47752e15i | −0.887334 | − | 1.06264i | ||||
\(95\) | − | 5.30595e14i | − | 0.0799787i | ||||||
\(96\) | 1.37755e15 | + | 3.93054e15i | 0.190958 | + | 0.544856i | ||||
\(97\) | −1.59239e15 | −0.203178 | −0.101589 | − | 0.994826i | \(-0.532393\pi\) | ||||
−0.101589 | + | 0.994826i | \(0.532393\pi\) | |||||||
\(98\) | 4.46562e15 | − | 3.72892e15i | 0.524895 | − | 0.438303i | ||||
\(99\) | 3.95973e14i | 0.0429125i | ||||||||
\(100\) | −1.75991e15 | + | 9.70892e15i | −0.175991 | + | 0.970892i | ||||
\(101\) | 7.05130e15 | 0.651176 | 0.325588 | − | 0.945512i | \(-0.394438\pi\) | ||||
0.325588 | + | 0.945512i | \(0.394438\pi\) | |||||||
\(102\) | −1.62035e15 | − | 1.94048e15i | −0.138296 | − | 0.165618i | ||||
\(103\) | 3.22497e15i | 0.254582i | 0.991865 | + | 0.127291i | \(0.0406282\pi\) | ||||
−0.991865 | + | 0.127291i | \(0.959372\pi\) | |||||||
\(104\) | 5.73661e15 | + | 1.01030e16i | 0.419169 | + | 0.738213i | ||||
\(105\) | 5.52868e14 | 0.0374203 | ||||||||
\(106\) | 1.09986e15 | − | 9.18414e14i | 0.0690065 | − | 0.0576224i | ||||
\(107\) | − | 1.41542e16i | − | 0.823785i | −0.911233 | − | 0.411892i | \(-0.864868\pi\) | ||
0.911233 | − | 0.411892i | \(-0.135132\pi\) | |||||||
\(108\) | 3.50500e15 | + | 6.35341e14i | 0.189364 | + | 0.0343255i | ||||
\(109\) | 2.21392e16 | 1.11109 | 0.555546 | − | 0.831486i | \(-0.312509\pi\) | ||||
0.555546 | + | 0.831486i | \(0.312509\pi\) | |||||||
\(110\) | 2.03883e14 | + | 2.44162e14i | 0.00951127 | + | 0.0113903i | ||||
\(111\) | − | 2.40522e16i | − | 1.04369i | ||||||
\(112\) | −4.88667e15 | + | 1.30363e16i | −0.197364 | + | 0.526514i | ||||
\(113\) | 1.02991e16 | 0.387411 | 0.193705 | − | 0.981060i | \(-0.437949\pi\) | ||||
0.193705 | + | 0.981060i | \(0.437949\pi\) | |||||||
\(114\) | 8.77141e15 | − | 7.32438e15i | 0.307490 | − | 0.256763i | ||||
\(115\) | 1.74699e14i | 0.00571095i | ||||||||
\(116\) | −7.55440e15 | + | 4.16755e16i | −0.230429 | + | 1.27121i | ||||
\(117\) | 9.93644e15 | 0.282972 | ||||||||
\(118\) | −3.18218e16 | − | 3.81086e16i | −0.846581 | − | 1.01383i | ||||
\(119\) | − | 8.45044e15i | − | 0.210138i | ||||||
\(120\) | 2.48836e15 | − | 1.41293e15i | 0.0578713 | − | 0.0328602i | ||||
\(121\) | 4.51882e16 | 0.983427 | ||||||||
\(122\) | −2.78807e15 | + | 2.32812e15i | −0.0568099 | + | 0.0474379i | ||||
\(123\) | − | 4.40757e16i | − | 0.841315i | ||||||
\(124\) | −6.16204e16 | − | 1.11698e16i | −1.10243 | − | 0.199834i | ||||
\(125\) | 1.36497e16 | 0.229004 | ||||||||
\(126\) | 7.63183e15 | + | 9.13960e15i | 0.120134 | + | 0.143867i | ||||
\(127\) | − | 2.78419e15i | − | 0.0411404i | −0.999788 | − | 0.0205702i | \(-0.993452\pi\) | ||
0.999788 | − | 0.0205702i | \(-0.00654816\pi\) | |||||||
\(128\) | 1.13220e16 | + | 7.11626e16i | 0.157124 | + | 0.987579i | ||||
\(129\) | −6.79473e16 | −0.886042 | ||||||||
\(130\) | 6.12694e15 | − | 5.11617e15i | 0.0751099 | − | 0.0627189i | ||||
\(131\) | 8.46988e16i | 0.976577i | 0.872682 | + | 0.488289i | \(0.162379\pi\) | ||||
−0.872682 | + | 0.488289i | \(0.837621\pi\) | |||||||
\(132\) | −1.22190e15 | + | 6.74087e15i | −0.0132569 | + | 0.0731349i | ||||
\(133\) | 3.81979e16 | 0.390146 | ||||||||
\(134\) | 5.77170e16 | + | 6.91197e16i | 0.555220 | + | 0.664911i | ||||
\(135\) | − | 2.44735e15i | − | 0.0221833i | ||||||
\(136\) | −2.15963e16 | − | 3.80339e16i | −0.184530 | − | 0.324983i | ||||
\(137\) | −1.59917e17 | −1.28863 | −0.644317 | − | 0.764758i | \(-0.722858\pi\) | ||||
−0.644317 | + | 0.764758i | \(0.722858\pi\) | |||||||
\(138\) | −2.88800e15 | + | 2.41156e15i | −0.0219565 | + | 0.0183344i | ||||
\(139\) | 4.46000e15i | 0.0320049i | 0.999872 | + | 0.0160024i | \(0.00509395\pi\) | ||||
−0.999872 | + | 0.0160024i | \(0.994906\pi\) | |||||||
\(140\) | 9.41177e15 | + | 1.70605e15i | 0.0637745 | + | 0.0115602i | ||||
\(141\) | −1.24869e17 | −0.799284 | ||||||||
\(142\) | −1.45187e17 | − | 1.73871e17i | −0.878256 | − | 1.05177i | ||||
\(143\) | 1.91099e16i | 0.109288i | ||||||||
\(144\) | 5.77070e16 | + | 2.16315e16i | 0.312125 | + | 0.117000i | ||||
\(145\) | 2.90997e16 | 0.148917 | ||||||||
\(146\) | 3.35124e16 | − | 2.79838e16i | 0.162324 | − | 0.135545i | ||||
\(147\) | − | 8.60848e16i | − | 0.394810i | ||||||
\(148\) | 7.42206e16 | − | 4.09454e17i | 0.322426 | − | 1.77874i | ||||
\(149\) | −1.63558e17 | −0.673259 | −0.336629 | − | 0.941637i | \(-0.609287\pi\) | ||||
−0.336629 | + | 0.941637i | \(0.609287\pi\) | |||||||
\(150\) | 9.35807e16 | + | 1.12069e17i | 0.365137 | + | 0.437275i | ||||
\(151\) | 4.45986e17i | 1.65008i | 0.565074 | + | 0.825041i | \(0.308848\pi\) | ||||
−0.565074 | + | 0.825041i | \(0.691152\pi\) | |||||||
\(152\) | 1.71922e17 | − | 9.76201e16i | 0.603369 | − | 0.342602i | ||||
\(153\) | −3.74071e16 | −0.124573 | ||||||||
\(154\) | −1.75774e16 | + | 1.46777e16i | −0.0555635 | + | 0.0463971i | ||||
\(155\) | 4.30262e16i | 0.129145i | ||||||||
\(156\) | 1.69154e17 | + | 3.06620e16i | 0.482263 | + | 0.0874185i | ||||
\(157\) | 6.72606e17 | 1.82206 | 0.911031 | − | 0.412337i | \(-0.135288\pi\) | ||||
0.911031 | + | 0.412337i | \(0.135288\pi\) | |||||||
\(158\) | 2.46702e17 | + | 2.95441e17i | 0.635208 | + | 0.760701i | ||||
\(159\) | − | 2.12023e16i | − | 0.0519045i | ||||||
\(160\) | 4.67208e16 | − | 1.63745e16i | 0.108780 | − | 0.0381248i | ||||
\(161\) | −1.25767e16 | −0.0278587 | ||||||||
\(162\) | 4.04577e16 | − | 3.37834e16i | 0.0852868 | − | 0.0712169i | ||||
\(163\) | 6.97357e17i | 1.39944i | 0.714417 | + | 0.699720i | \(0.246692\pi\) | ||||
−0.714417 | + | 0.699720i | \(0.753308\pi\) | |||||||
\(164\) | 1.36009e17 | − | 7.50326e17i | 0.259907 | − | 1.43383i | ||||
\(165\) | 4.70678e15 | 0.00856746 | ||||||||
\(166\) | 8.00934e16 | + | 9.59169e16i | 0.138909 | + | 0.166353i | ||||
\(167\) | − | 1.02388e18i | − | 1.69246i | −0.532818 | − | 0.846230i | \(-0.678867\pi\) | ||
0.532818 | − | 0.846230i | \(-0.321133\pi\) | |||||||
\(168\) | 1.01718e17 | + | 1.79139e17i | 0.160296 | + | 0.282303i | ||||
\(169\) | −1.85877e17 | −0.279340 | ||||||||
\(170\) | −2.30657e16 | + | 1.92605e16i | −0.0330655 | + | 0.0276107i | ||||
\(171\) | − | 1.69089e17i | − | 0.231284i | ||||||
\(172\) | −1.15670e18 | − | 2.09673e17i | −1.51006 | − | 0.273725i | ||||
\(173\) | −4.70521e17 | −0.586423 | −0.293211 | − | 0.956048i | \(-0.594724\pi\) | ||||
−0.293211 | + | 0.956048i | \(0.594724\pi\) | |||||||
\(174\) | 4.01695e17 | + | 4.81055e17i | 0.478082 | + | 0.572533i | ||||
\(175\) | 4.88040e17i | 0.554818i | ||||||||
\(176\) | −4.16021e16 | + | 1.10983e17i | −0.0451870 | + | 0.120547i | ||||
\(177\) | −7.34630e17 | −0.762575 | ||||||||
\(178\) | −1.42921e18 | + | 1.19343e18i | −1.41820 | + | 1.18424i | ||||
\(179\) | − | 1.41139e18i | − | 1.33913i | −0.742755 | − | 0.669564i | \(-0.766481\pi\) | ||
0.742755 | − | 0.669564i | \(-0.233519\pi\) | |||||||
\(180\) | 7.55206e15 | − | 4.16626e16i | 0.00685307 | − | 0.0378065i | ||||
\(181\) | 5.45235e17 | 0.473320 | 0.236660 | − | 0.971592i | \(-0.423947\pi\) | ||||
0.236660 | + | 0.971592i | \(0.423947\pi\) | |||||||
\(182\) | 3.68317e17 | + | 4.41083e17i | 0.305950 | + | 0.366395i | ||||
\(183\) | 5.37463e16i | 0.0427307i | ||||||||
\(184\) | −5.66056e16 | + | 3.21415e16i | −0.0430841 | + | 0.0244638i | ||||
\(185\) | −2.85899e17 | −0.208372 | ||||||||
\(186\) | −7.11276e17 | + | 5.93936e17i | −0.496518 | + | 0.414607i | ||||
\(187\) | − | 7.19419e16i | − | 0.0481115i | ||||||
\(188\) | −2.12571e18 | − | 3.85322e17i | −1.36220 | − | 0.246922i | ||||
\(189\) | 1.76186e17 | 0.108213 | ||||||||
\(190\) | −8.70621e16 | − | 1.04262e17i | −0.0512626 | − | 0.0613902i | ||||
\(191\) | − | 5.83418e17i | − | 0.329392i | −0.986344 | − | 0.164696i | \(-0.947336\pi\) | ||
0.986344 | − | 0.164696i | \(-0.0526643\pi\) | |||||||
\(192\) | 9.15627e17 | + | 5.46319e17i | 0.495803 | + | 0.295826i | ||||
\(193\) | 3.06897e18 | 1.59417 | 0.797083 | − | 0.603870i | \(-0.206375\pi\) | ||||
0.797083 | + | 0.603870i | \(0.206375\pi\) | |||||||
\(194\) | −3.12907e17 | + | 2.61286e17i | −0.155956 | + | 0.130227i | ||||
\(195\) | − | 1.18111e17i | − | 0.0564953i | ||||||
\(196\) | 2.65642e17 | − | 1.46547e18i | 0.121968 | − | 0.672866i | ||||
\(197\) | 1.15460e18 | 0.508982 | 0.254491 | − | 0.967075i | \(-0.418092\pi\) | ||||
0.254491 | + | 0.967075i | \(0.418092\pi\) | |||||||
\(198\) | 6.49728e16 | + | 7.78090e16i | 0.0275049 | + | 0.0329388i | ||||
\(199\) | − | 1.38254e18i | − | 0.562149i | −0.959686 | − | 0.281075i | \(-0.909309\pi\) | ||
0.959686 | − | 0.281075i | \(-0.0906909\pi\) | |||||||
\(200\) | 1.24725e18 | + | 2.19658e18i | 0.487208 | + | 0.858039i | ||||
\(201\) | 1.33244e18 | 0.500125 | ||||||||
\(202\) | 1.38559e18 | − | 1.15700e18i | 0.499830 | − | 0.417373i | ||||
\(203\) | 2.09491e18i | 0.726436i | ||||||||
\(204\) | −6.36802e17 | − | 1.15431e17i | −0.212306 | − | 0.0384842i | ||||
\(205\) | −5.23911e17 | −0.167968 | ||||||||
\(206\) | 5.29165e17 | + | 6.33709e17i | 0.163175 | + | 0.195412i | ||||
\(207\) | 5.56727e16i | 0.0165150i | ||||||||
\(208\) | 2.78498e18 | + | 1.04395e18i | 0.794905 | + | 0.297971i | ||||
\(209\) | 3.25194e17 | 0.0893249 | ||||||||
\(210\) | 1.08639e17 | − | 9.07166e16i | 0.0287231 | − | 0.0239846i | ||||
\(211\) | − | 1.48026e18i | − | 0.376771i | −0.982095 | − | 0.188385i | \(-0.939675\pi\) | ||
0.982095 | − | 0.188385i | \(-0.0603254\pi\) | |||||||
\(212\) | 6.54262e16 | − | 3.60938e17i | 0.0160348 | − | 0.0884597i | ||||
\(213\) | −3.35175e18 | −0.791107 | ||||||||
\(214\) | −2.32247e18 | − | 2.78130e18i | −0.528007 | − | 0.632321i | ||||
\(215\) | 8.07663e17i | 0.176898i | ||||||||
\(216\) | 7.92984e17 | − | 4.50268e17i | 0.167353 | − | 0.0950258i | ||||
\(217\) | −3.09748e18 | −0.629987 | ||||||||
\(218\) | 4.35037e18 | − | 3.63268e18i | 0.852853 | − | 0.712157i | ||||
\(219\) | − | 6.46027e17i | − | 0.122095i | ||||||
\(220\) | 8.01261e16 | + | 1.45242e16i | 0.0146013 | + | 0.00264674i | ||||
\(221\) | −1.80529e18 | −0.317255 | ||||||||
\(222\) | −3.94658e18 | − | 4.72627e18i | −0.668955 | − | 0.801116i | ||||
\(223\) | 6.05000e17i | 0.0989274i | 0.998776 | + | 0.0494637i | \(0.0157512\pi\) | ||||
−0.998776 | + | 0.0494637i | \(0.984249\pi\) | |||||||
\(224\) | 1.17881e18 | + | 3.36346e18i | 0.185977 | + | 0.530643i | ||||
\(225\) | 2.16038e18 | 0.328904 | ||||||||
\(226\) | 2.02378e18 | − | 1.68991e18i | 0.297369 | − | 0.248312i | ||||
\(227\) | 1.25176e19i | 1.77547i | 0.460356 | + | 0.887734i | \(0.347722\pi\) | ||||
−0.460356 | + | 0.887734i | \(0.652278\pi\) | |||||||
\(228\) | 5.21776e17 | − | 2.87849e18i | 0.0714505 | − | 0.394172i | ||||
\(229\) | −1.23160e19 | −1.62849 | −0.814245 | − | 0.580521i | \(-0.802849\pi\) | ||||
−0.814245 | + | 0.580521i | \(0.802849\pi\) | |||||||
\(230\) | 2.86653e16 | + | 3.43285e16i | 0.00366044 | + | 0.00438361i | ||||
\(231\) | 3.38844e17i | 0.0417931i | ||||||||
\(232\) | 5.35383e18 | + | 9.42882e18i | 0.637912 | + | 1.12345i | ||||
\(233\) | 1.37425e18 | 0.158205 | 0.0791024 | − | 0.996866i | \(-0.474795\pi\) | ||||
0.0791024 | + | 0.996866i | \(0.474795\pi\) | |||||||
\(234\) | 1.95252e18 | − | 1.63041e18i | 0.217204 | − | 0.181372i | ||||
\(235\) | 1.48427e18i | 0.159577i | ||||||||
\(236\) | −1.25060e19 | − | 2.26693e18i | −1.29964 | − | 0.235582i | ||||
\(237\) | 5.69529e18 | 0.572176 | ||||||||
\(238\) | −1.38658e18 | − | 1.66052e18i | −0.134688 | − | 0.161298i | ||||
\(239\) | 9.58646e18i | 0.900482i | 0.892907 | + | 0.450241i | \(0.148662\pi\) | ||||
−0.892907 | + | 0.450241i | \(0.851338\pi\) | |||||||
\(240\) | 2.57126e17 | − | 6.85941e17i | 0.0233591 | − | 0.0623156i | ||||
\(241\) | −8.84376e18 | −0.777142 | −0.388571 | − | 0.921419i | \(-0.627031\pi\) | ||||
−0.388571 | + | 0.921419i | \(0.627031\pi\) | |||||||
\(242\) | 8.87951e18 | − | 7.41465e18i | 0.754859 | − | 0.630329i | ||||
\(243\) | − | 7.79915e17i | − | 0.0641500i | ||||||
\(244\) | −1.65851e17 | + | 9.14953e17i | −0.0132008 | + | 0.0728249i | ||||
\(245\) | −1.02326e18 | −0.0788236 | ||||||||
\(246\) | −7.23211e18 | − | 8.66091e18i | −0.539243 | − | 0.645777i | ||||
\(247\) | − | 8.16033e18i | − | 0.589023i | ||||||
\(248\) | −1.39412e19 | + | 7.91604e18i | −0.974289 | + | 0.553216i | ||||
\(249\) | 1.84901e18 | 0.125125 | ||||||||
\(250\) | 2.68217e18 | − | 2.23969e18i | 0.175779 | − | 0.146781i | ||||
\(251\) | − | 1.29171e19i | − | 0.819928i | −0.912102 | − | 0.409964i | \(-0.865541\pi\) | ||
0.912102 | − | 0.409964i | \(-0.134459\pi\) | |||||||
\(252\) | 2.99932e18 | + | 5.43678e17i | 0.184424 | + | 0.0334301i | ||||
\(253\) | −1.07071e17 | −0.00637831 | ||||||||
\(254\) | −4.56840e17 | − | 5.47095e17i | −0.0263690 | − | 0.0315786i | ||||
\(255\) | 4.44644e17i | 0.0248709i | ||||||||
\(256\) | 1.39014e19 | + | 1.21257e19i | 0.753596 | + | 0.657338i | ||||
\(257\) | 2.12187e19 | 1.11495 | 0.557474 | − | 0.830195i | \(-0.311771\pi\) | ||||
0.557474 | + | 0.830195i | \(0.311771\pi\) | |||||||
\(258\) | −1.33517e19 | + | 1.11490e19i | −0.680109 | + | 0.567911i | ||||
\(259\) | − | 2.05821e19i | − | 1.01646i | ||||||
\(260\) | 3.64467e17 | − | 2.01066e18i | 0.0174531 | − | 0.0962837i | ||||
\(261\) | 9.27343e18 | 0.430642 | ||||||||
\(262\) | 1.38977e19 | + | 1.66434e19i | 0.625939 | + | 0.749602i | ||||
\(263\) | − | 1.52461e19i | − | 0.666060i | −0.942916 | − | 0.333030i | \(-0.891929\pi\) | ||
0.942916 | − | 0.333030i | \(-0.108071\pi\) | |||||||
\(264\) | 8.65963e17 | + | 1.52508e18i | 0.0367002 | + | 0.0646340i | ||||
\(265\) | −2.52023e17 | −0.0103627 | ||||||||
\(266\) | 7.50592e18 | − | 6.26766e18i | 0.299468 | − | 0.250065i | ||||
\(267\) | 2.75513e19i | 1.06672i | ||||||||
\(268\) | 2.26828e19 | + | 4.11165e18i | 0.852352 | + | 0.154503i | ||||
\(269\) | 2.80251e19 | 1.02218 | 0.511092 | − | 0.859526i | \(-0.329241\pi\) | ||||
0.511092 | + | 0.859526i | \(0.329241\pi\) | |||||||
\(270\) | −4.01570e17 | − | 4.80906e17i | −0.0142184 | − | 0.0170275i | ||||
\(271\) | − | 4.19385e19i | − | 1.44165i | −0.693119 | − | 0.720824i | \(-0.743764\pi\) | ||
0.693119 | − | 0.720824i | \(-0.256236\pi\) | |||||||
\(272\) | −1.04844e19 | − | 3.93010e18i | −0.349940 | − | 0.131175i | ||||
\(273\) | 8.50287e18 | 0.275591 | ||||||||
\(274\) | −3.14238e19 | + | 2.62398e19i | −0.989131 | + | 0.825953i | ||||
\(275\) | 4.15487e18i | 0.127027i | ||||||||
\(276\) | −1.71795e17 | + | 9.47747e17i | −0.00510198 | + | 0.0281462i | ||||
\(277\) | 2.75902e19 | 0.796006 | 0.398003 | − | 0.917384i | \(-0.369703\pi\) | ||||
0.398003 | + | 0.917384i | \(0.369703\pi\) | |||||||
\(278\) | 7.31813e17 | + | 8.76393e17i | 0.0205136 | + | 0.0245663i | ||||
\(279\) | 1.37115e19i | 0.373465i | ||||||||
\(280\) | 2.12935e18 | − | 1.20908e18i | 0.0563616 | − | 0.0320030i | ||||
\(281\) | −1.24012e19 | −0.319017 | −0.159508 | − | 0.987197i | \(-0.550991\pi\) | ||||
−0.159508 | + | 0.987197i | \(0.550991\pi\) | |||||||
\(282\) | −2.45368e19 | + | 2.04889e19i | −0.613515 | + | 0.512303i | ||||
\(283\) | 2.72260e19i | 0.661748i | 0.943675 | + | 0.330874i | \(0.107344\pi\) | ||||
−0.943675 | + | 0.330874i | \(0.892656\pi\) | |||||||
\(284\) | −5.70587e19 | − | 1.03429e19i | −1.34827 | − | 0.244396i | ||||
\(285\) | −2.00989e18 | −0.0461758 | ||||||||
\(286\) | 3.13563e18 | + | 3.75511e18i | 0.0700481 | + | 0.0838870i | ||||
\(287\) | − | 3.77167e19i | − | 0.819368i | ||||||
\(288\) | 1.48888e19 | − | 5.21817e18i | 0.314573 | − | 0.110250i | ||||
\(289\) | −4.18649e19 | −0.860335 | ||||||||
\(290\) | 5.71812e18 | − | 4.77479e18i | 0.114306 | − | 0.0954488i | ||||
\(291\) | 6.03198e18i | 0.117305i | ||||||||
\(292\) | 1.99352e18 | − | 1.09977e19i | 0.0377187 | − | 0.208084i | ||||
\(293\) | −7.20983e19 | −1.32735 | −0.663673 | − | 0.748023i | \(-0.731003\pi\) | ||||
−0.663673 | + | 0.748023i | \(0.731003\pi\) | |||||||
\(294\) | −1.41251e19 | − | 1.69157e19i | −0.253054 | − | 0.303048i | ||||
\(295\) | 8.73226e18i | 0.152248i | ||||||||
\(296\) | −5.26004e19 | − | 9.26364e19i | −0.892596 | − | 1.57198i | ||||
\(297\) | 1.49994e18 | 0.0247756 | ||||||||
\(298\) | −3.21393e19 | + | 2.68372e19i | −0.516781 | + | 0.431527i | ||||
\(299\) | 2.68680e18i | 0.0420597i | ||||||||
\(300\) | 3.67773e19 | + | 6.66652e18i | 0.560545 | + | 0.101608i | ||||
\(301\) | −5.81443e19 | −0.862929 | ||||||||
\(302\) | 7.31790e19 | + | 8.76365e19i | 1.05762 | + | 1.26657i | ||||
\(303\) | − | 2.67103e19i | − | 0.375956i | ||||||
\(304\) | 1.77650e19 | − | 4.73921e19i | 0.243543 | − | 0.649706i | ||||
\(305\) | 6.38861e17 | 0.00853116 | ||||||||
\(306\) | −7.35052e18 | + | 6.13790e18i | −0.0956195 | + | 0.0798451i | ||||
\(307\) | 1.20412e20i | 1.52603i | 0.646383 | + | 0.763013i | \(0.276281\pi\) | ||||
−0.646383 | + | 0.763013i | \(0.723719\pi\) | |||||||
\(308\) | −1.04561e18 | + | 5.76834e18i | −0.0129111 | + | 0.0712270i | ||||
\(309\) | 1.22162e19 | 0.146983 | ||||||||
\(310\) | 7.05989e18 | + | 8.45467e18i | 0.0827760 | + | 0.0991295i | ||||
\(311\) | 5.06945e19i | 0.579266i | 0.957138 | + | 0.289633i | \(0.0935332\pi\) | ||||
−0.957138 | + | 0.289633i | \(0.906467\pi\) | |||||||
\(312\) | 3.82699e19 | − | 2.17303e19i | 0.426207 | − | 0.242007i | ||||
\(313\) | 4.30599e18 | 0.0467432 | 0.0233716 | − | 0.999727i | \(-0.492560\pi\) | ||||
0.0233716 | + | 0.999727i | \(0.492560\pi\) | |||||||
\(314\) | 1.32167e20 | − | 1.10364e20i | 1.39858 | − | 1.16785i | ||||
\(315\) | − | 2.09426e18i | − | 0.0216046i | ||||||
\(316\) | 9.69542e19 | + | 1.75746e19i | 0.975146 | + | 0.176762i | ||||
\(317\) | 9.98544e19 | 0.979249 | 0.489624 | − | 0.871934i | \(-0.337134\pi\) | ||||
0.489624 | + | 0.871934i | \(0.337134\pi\) | |||||||
\(318\) | −3.47895e18 | − | 4.16626e18i | −0.0332683 | − | 0.0398409i | ||||
\(319\) | 1.78348e19i | 0.166319i | ||||||||
\(320\) | 6.49388e18 | − | 1.08837e19i | 0.0590615 | − | 0.0989868i | ||||
\(321\) | −5.36159e19 | −0.475612 | ||||||||
\(322\) | −2.47133e18 | + | 2.06364e18i | −0.0213838 | + | 0.0178561i | ||||
\(323\) | 3.07207e19i | 0.259305i | ||||||||
\(324\) | 2.40667e18 | − | 1.32769e19i | 0.0198178 | − | 0.109329i | ||||
\(325\) | 1.04261e20 | 0.837638 | ||||||||
\(326\) | 1.14425e20 | + | 1.37031e20i | 0.896975 | + | 1.07418i | ||||
\(327\) | − | 8.38632e19i | − | 0.641489i | ||||||
\(328\) | −9.63903e19 | − | 1.69756e20i | −0.719520 | − | 1.26717i | ||||
\(329\) | −1.06853e20 | −0.778433 | ||||||||
\(330\) | 9.24885e17 | − | 7.72306e17i | 0.00657622 | − | 0.00549133i | ||||
\(331\) | 3.89785e19i | 0.270521i | 0.990810 | + | 0.135260i | \(0.0431871\pi\) | ||||
−0.990810 | + | 0.135260i | \(0.956813\pi\) | |||||||
\(332\) | 3.14768e19 | + | 5.70571e18i | 0.213249 | + | 0.0386550i | ||||
\(333\) | −9.11096e19 | −0.602574 | ||||||||
\(334\) | −1.68002e20 | − | 2.01194e20i | −1.08479 | − | 1.29910i | ||||
\(335\) | − | 1.58382e19i | − | 0.0998498i | ||||||
\(336\) | 4.93814e19 | + | 1.85107e19i | 0.303983 | + | 0.113948i | ||||
\(337\) | 1.58332e20 | 0.951767 | 0.475883 | − | 0.879508i | \(-0.342128\pi\) | ||||
0.475883 | + | 0.879508i | \(0.342128\pi\) | |||||||
\(338\) | −3.65250e19 | + | 3.04994e19i | −0.214416 | + | 0.179043i | ||||
\(339\) | − | 3.90129e19i | − | 0.223672i | ||||||
\(340\) | −1.37209e18 | + | 7.56942e18i | −0.00768334 | + | 0.0423868i | ||||
\(341\) | −2.63701e19 | −0.144237 | ||||||||
\(342\) | −2.77447e19 | − | 3.32261e19i | −0.148242 | − | 0.177529i | ||||
\(343\) | − | 1.81389e20i | − | 0.946800i | ||||||
\(344\) | −2.61697e20 | + | 1.48596e20i | −1.33454 | + | 0.757772i | ||||
\(345\) | 6.61760e17 | 0.00329722 | ||||||||
\(346\) | −9.24578e19 | + | 7.72049e19i | −0.450127 | + | 0.375869i | ||||
\(347\) | 3.30940e20i | 1.57439i | 0.616701 | + | 0.787197i | \(0.288469\pi\) | ||||
−0.616701 | + | 0.787197i | \(0.711531\pi\) | |||||||
\(348\) | 1.57867e20 | + | 2.86160e19i | 0.733933 | + | 0.133038i | ||||
\(349\) | 1.03699e20 | 0.471164 | 0.235582 | − | 0.971854i | \(-0.424300\pi\) | ||||
0.235582 | + | 0.971854i | \(0.424300\pi\) | |||||||
\(350\) | 8.00794e19 | + | 9.59002e19i | 0.355612 | + | 0.425868i | ||||
\(351\) | − | 3.76392e19i | − | 0.163374i | ||||||
\(352\) | 1.00357e19 | + | 2.86345e19i | 0.0425799 | + | 0.121492i | ||||
\(353\) | −1.73945e20 | −0.721465 | −0.360733 | − | 0.932669i | \(-0.617473\pi\) | ||||
−0.360733 | + | 0.932669i | \(0.617473\pi\) | |||||||
\(354\) | −1.44355e20 | + | 1.20541e20i | −0.585338 | + | 0.488774i | ||||
\(355\) | 3.98410e19i | 0.157944i | ||||||||
\(356\) | −8.50182e19 | + | 4.69022e20i | −0.329543 | + | 1.81800i | ||||
\(357\) | −3.20102e19 | −0.121323 | ||||||||
\(358\) | −2.31586e20 | − | 2.77339e20i | −0.858317 | − | 1.02789i | ||||
\(359\) | − | 5.26548e20i | − | 1.90846i | −0.299079 | − | 0.954228i | \(-0.596679\pi\) | ||
0.299079 | − | 0.954228i | \(-0.403321\pi\) | |||||||
\(360\) | −5.35217e18 | − | 9.42589e18i | −0.0189719 | − | 0.0334120i | ||||
\(361\) | 1.49577e20 | 0.518569 | ||||||||
\(362\) | 1.07139e20 | − | 8.94642e19i | 0.363312 | − | 0.303376i | ||||
\(363\) | − | 1.71173e20i | − | 0.567782i | ||||||
\(364\) | 1.44749e20 | + | 2.62383e19i | 0.469683 | + | 0.0851381i | ||||
\(365\) | −7.67907e18 | −0.0243762 | ||||||||
\(366\) | 8.81889e18 | + | 1.05612e19i | 0.0273883 | + | 0.0327992i | ||||
\(367\) | − | 1.15856e20i | − | 0.352039i | −0.984387 | − | 0.176019i | \(-0.943678\pi\) | ||
0.984387 | − | 0.176019i | \(-0.0563222\pi\) | |||||||
\(368\) | −5.84914e18 | + | 1.56039e19i | −0.0173904 | + | 0.0463928i | ||||
\(369\) | −1.66959e20 | −0.485733 | ||||||||
\(370\) | −5.61794e19 | + | 4.69114e19i | −0.159942 | + | 0.133556i | ||||
\(371\) | − | 1.81433e19i | − | 0.0505505i | ||||||
\(372\) | −4.23110e19 | + | 2.33418e20i | −0.115374 | + | 0.636488i | ||||
\(373\) | 1.79070e20 | 0.477916 | 0.238958 | − | 0.971030i | \(-0.423194\pi\) | ||||
0.238958 | + | 0.971030i | \(0.423194\pi\) | |||||||
\(374\) | −1.18045e19 | − | 1.41366e19i | −0.0308372 | − | 0.0369295i | ||||
\(375\) | − | 5.17050e19i | − | 0.132215i | ||||||
\(376\) | −4.80929e20 | + | 2.73079e20i | −1.20387 | + | 0.683573i | ||||
\(377\) | 4.47542e20 | 1.09674 | ||||||||
\(378\) | 3.46207e19 | − | 2.89093e19i | 0.0830619 | − | 0.0693591i | ||||
\(379\) | 5.63500e20i | 1.32367i | 0.749649 | + | 0.661836i | \(0.230222\pi\) | ||||
−0.749649 | + | 0.661836i | \(0.769778\pi\) | |||||||
\(380\) | −3.42155e19 | − | 6.20215e18i | −0.0786963 | − | 0.0142651i | ||||
\(381\) | −1.05465e19 | −0.0237524 | ||||||||
\(382\) | −9.57294e19 | − | 1.14642e20i | −0.211124 | − | 0.252835i | ||||
\(383\) | − | 3.70048e20i | − | 0.799222i | −0.916685 | − | 0.399611i | \(-0.869145\pi\) | ||
0.916685 | − | 0.399611i | \(-0.130855\pi\) | |||||||
\(384\) | 2.69563e20 | − | 4.28876e19i | 0.570179 | − | 0.0907157i | ||||
\(385\) | 4.02771e18 | 0.00834397 | ||||||||
\(386\) | 6.03054e20 | − | 5.03568e20i | 1.22365 | − | 1.02178i | ||||
\(387\) | 2.57384e20i | 0.511557i | ||||||||
\(388\) | −1.86136e19 | + | 1.02686e20i | −0.0362390 | + | 0.199920i | ||||
\(389\) | −1.44538e20 | −0.275666 | −0.137833 | − | 0.990455i | \(-0.544014\pi\) | ||||
−0.137833 | + | 0.990455i | \(0.544014\pi\) | |||||||
\(390\) | −1.93800e19 | − | 2.32088e19i | −0.0362108 | − | 0.0433647i | ||||
\(391\) | − | 1.01148e19i | − | 0.0185159i | ||||||
\(392\) | −1.88261e20 | − | 3.31553e20i | −0.337654 | − | 0.594655i | ||||
\(393\) | 3.20838e20 | 0.563827 | ||||||||
\(394\) | 2.26880e20 | − | 1.89451e20i | 0.390685 | − | 0.326233i | ||||
\(395\) | − | 6.76978e19i | − | 0.114235i | ||||||
\(396\) | 2.55344e19 | + | 4.62854e18i | 0.0422244 | + | 0.00765390i | ||||
\(397\) | −8.04793e19 | −0.130425 | −0.0652124 | − | 0.997871i | \(-0.520772\pi\) | ||||
−0.0652124 | + | 0.997871i | \(0.520772\pi\) | |||||||
\(398\) | −2.26852e20 | − | 2.71669e20i | −0.360311 | − | 0.431495i | ||||
\(399\) | − | 1.44694e20i | − | 0.225251i | ||||||
\(400\) | 6.05509e20 | + | 2.26976e20i | 0.923934 | + | 0.346338i | ||||
\(401\) | −1.41133e20 | −0.211093 | −0.105546 | − | 0.994414i | \(-0.533659\pi\) | ||||
−0.105546 | + | 0.994414i | \(0.533659\pi\) | |||||||
\(402\) | 2.61825e20 | − | 2.18632e20i | 0.383887 | − | 0.320556i | ||||
\(403\) | 6.61724e20i | 0.951123i | ||||||||
\(404\) | 8.24229e19 | − | 4.54704e20i | 0.116144 | − | 0.640734i | ||||
\(405\) | −9.27054e18 | −0.0128075 | ||||||||
\(406\) | 3.43741e20 | + | 4.11651e20i | 0.465611 | + | 0.557598i | ||||
\(407\) | − | 1.75223e20i | − | 0.232722i | ||||||
\(408\) | −1.44072e20 | + | 8.18065e19i | −0.187629 | + | 0.106538i | ||||
\(409\) | 1.27269e20 | 0.162531 | 0.0812654 | − | 0.996693i | \(-0.474104\pi\) | ||||
0.0812654 | + | 0.996693i | \(0.474104\pi\) | |||||||
\(410\) | −1.02949e20 | + | 8.59653e19i | −0.128929 | + | 0.107660i | ||||
\(411\) | 6.05764e20i | 0.743993i | ||||||||
\(412\) | 2.07963e20 | + | 3.76968e19i | 0.250500 | + | 0.0454074i | ||||
\(413\) | −6.28642e20 | −0.742682 | ||||||||
\(414\) | 9.13498e18 | + | 1.09397e19i | 0.0105853 | + | 0.0126766i | ||||
\(415\) | − | 2.19785e19i | − | 0.0249812i | ||||||
\(416\) | 7.18546e20 | − | 2.51832e20i | 0.801139 | − | 0.280779i | ||||
\(417\) | 1.68944e19 | 0.0184780 | ||||||||
\(418\) | 6.39009e19 | − | 5.33591e19i | 0.0685641 | − | 0.0572530i | ||||
\(419\) | 1.22983e21i | 1.29459i | 0.762240 | + | 0.647295i | \(0.224100\pi\) | ||||
−0.762240 | + | 0.647295i | \(0.775900\pi\) | |||||||
\(420\) | 6.46249e18 | − | 3.56517e19i | 0.00667430 | − | 0.0368202i | ||||
\(421\) | −1.70492e21 | −1.72762 | −0.863810 | − | 0.503818i | \(-0.831928\pi\) | ||||
−0.863810 | + | 0.503818i | \(0.831928\pi\) | |||||||
\(422\) | −2.42886e20 | − | 2.90871e20i | −0.241492 | − | 0.289202i | ||||
\(423\) | 4.73002e20i | 0.461467i | ||||||||
\(424\) | −4.63677e19 | − | 8.16599e19i | −0.0443904 | − | 0.0781775i | ||||
\(425\) | −3.92506e20 | −0.368752 | ||||||||
\(426\) | −6.58622e20 | + | 5.49968e20i | −0.607238 | + | 0.507062i | ||||
\(427\) | 4.59921e19i | 0.0416160i | ||||||||
\(428\) | −9.12733e20 | − | 1.65448e20i | −0.810575 | − | 0.146931i | ||||
\(429\) | 7.23883e19 | 0.0630972 | ||||||||
\(430\) | 1.32524e20 | + | 1.58706e20i | 0.113383 | + | 0.135783i | ||||
\(431\) | − | 1.28885e21i | − | 1.08239i | −0.840896 | − | 0.541197i | \(-0.817971\pi\) | ||
0.840896 | − | 0.541197i | \(-0.182029\pi\) | |||||||
\(432\) | 8.19401e19 | − | 2.18594e20i | 0.0675502 | − | 0.180205i | ||||
\(433\) | −1.15744e21 | −0.936686 | −0.468343 | − | 0.883547i | \(-0.655149\pi\) | ||||
−0.468343 | + | 0.883547i | \(0.655149\pi\) | |||||||
\(434\) | −6.08658e20 | + | 5.08247e20i | −0.483566 | + | 0.403791i | ||||
\(435\) | − | 1.10230e20i | − | 0.0859774i | ||||||
\(436\) | 2.58786e20 | − | 1.42765e21i | 0.198175 | − | 1.09328i | ||||
\(437\) | 4.57214e19 | 0.0343770 | ||||||||
\(438\) | −1.06002e20 | − | 1.26945e20i | −0.0782570 | − | 0.0937177i | ||||
\(439\) | − | 2.49135e21i | − | 1.80600i | −0.429639 | − | 0.903001i | \(-0.641359\pi\) | ||
0.429639 | − | 0.903001i | \(-0.358641\pi\) | |||||||
\(440\) | 1.81280e19 | − | 1.02934e19i | 0.0129041 | − | 0.00732717i | ||||
\(441\) | −3.26089e20 | −0.227944 | ||||||||
\(442\) | −3.54741e20 | + | 2.96219e20i | −0.243519 | + | 0.203346i | ||||
\(443\) | 2.09067e21i | 1.40947i | 0.709472 | + | 0.704734i | \(0.248934\pi\) | ||||
−0.709472 | + | 0.704734i | \(0.751066\pi\) | |||||||
\(444\) | −1.55101e21 | − | 2.81147e20i | −1.02695 | − | 0.186153i | ||||
\(445\) | 3.27492e20 | 0.212971 | ||||||||
\(446\) | 9.92707e19 | + | 1.18883e20i | 0.0634078 | + | 0.0759348i | ||||
\(447\) | 6.19557e20i | 0.388706i | ||||||||
\(448\) | 7.83526e20 | + | 4.67499e20i | 0.482869 | + | 0.288109i | ||||
\(449\) | 2.29386e21 | 1.38866 | 0.694331 | − | 0.719656i | \(-0.255700\pi\) | ||||
0.694331 | + | 0.719656i | \(0.255700\pi\) | |||||||
\(450\) | 4.24516e20 | − | 3.54483e20i | 0.252461 | − | 0.210812i | ||||
\(451\) | − | 3.21097e20i | − | 0.187596i | ||||||
\(452\) | 1.20386e20 | − | 6.64138e20i | 0.0690988 | − | 0.381198i | ||||
\(453\) | 1.68939e21 | 0.952675 | ||||||||
\(454\) | 2.05393e21 | + | 2.45971e21i | 1.13799 | + | 1.36282i | ||||
\(455\) | − | 1.01070e20i | − | 0.0550215i | ||||||
\(456\) | −3.69784e20 | − | 6.51240e20i | −0.197802 | − | 0.348355i | ||||
\(457\) | 1.45139e21 | 0.762876 | 0.381438 | − | 0.924394i | \(-0.375429\pi\) | ||||
0.381438 | + | 0.924394i | \(0.375429\pi\) | |||||||
\(458\) | −2.42010e21 | + | 2.02085e21i | −1.25000 | + | 1.04378i | ||||
\(459\) | 1.41698e20i | 0.0719220i | ||||||||
\(460\) | 1.12655e19 | + | 2.04207e18i | 0.00561937 | + | 0.00101861i | ||||
\(461\) | 2.70680e21 | 1.32693 | 0.663466 | − | 0.748207i | \(-0.269085\pi\) | ||||
0.663466 | + | 0.748207i | \(0.269085\pi\) | |||||||
\(462\) | 5.55989e19 | + | 6.65832e19i | 0.0267874 | + | 0.0320796i | ||||
\(463\) | − | 2.77293e21i | − | 1.31308i | −0.754291 | − | 0.656540i | \(-0.772019\pi\) | ||
0.754291 | − | 0.656540i | \(-0.227981\pi\) | |||||||
\(464\) | 2.59915e21 | + | 9.74294e20i | 1.20973 | + | 0.453467i | ||||
\(465\) | 1.62983e20 | 0.0745621 | ||||||||
\(466\) | 2.70042e20 | − | 2.25493e20i | 0.121435 | − | 0.101402i | ||||
\(467\) | 1.65320e21i | 0.730785i | 0.930853 | + | 0.365393i | \(0.119065\pi\) | ||||
−0.930853 | + | 0.365393i | \(0.880935\pi\) | |||||||
\(468\) | 1.16147e20 | − | 6.40753e20i | 0.0504711 | − | 0.278435i | ||||
\(469\) | 1.14020e21 | 0.487079 | ||||||||
\(470\) | 2.43544e20 | + | 2.91660e20i | 0.102281 | + | 0.122488i | ||||
\(471\) | − | 2.54783e21i | − | 1.05197i | ||||||
\(472\) | −2.82941e21 | + | 1.60658e21i | −1.14857 | + | 0.652179i | ||||
\(473\) | −4.95005e20 | −0.197570 | ||||||||
\(474\) | 1.11913e21 | − | 9.34505e20i | 0.439191 | − | 0.366737i | ||||
\(475\) | − | 1.77422e21i | − | 0.684633i | ||||||
\(476\) | −5.44928e20 | − | 9.87775e19i | −0.206768 | − | 0.0374803i | ||||
\(477\) | −8.03141e19 | −0.0299671 | ||||||||
\(478\) | 1.57298e21 | + | 1.88375e21i | 0.577166 | + | 0.691193i | ||||
\(479\) | − | 9.34864e20i | − | 0.337337i | −0.985673 | − | 0.168669i | \(-0.946053\pi\) | ||
0.985673 | − | 0.168669i | \(-0.0539468\pi\) | |||||||
\(480\) | −6.20264e19 | − | 1.76978e20i | −0.0220113 | − | 0.0628043i | ||||
\(481\) | −4.39701e21 | −1.53461 | ||||||||
\(482\) | −1.73780e21 | + | 1.45112e21i | −0.596520 | + | 0.498111i | ||||
\(483\) | 4.76406e19i | 0.0160842i | ||||||||
\(484\) | 5.28206e20 | − | 2.91397e21i | 0.175405 | − | 0.967658i | ||||
\(485\) | 7.16999e19 | 0.0234199 | ||||||||
\(486\) | −1.27971e20 | − | 1.53254e20i | −0.0411171 | − | 0.0492403i | ||||
\(487\) | − | 1.25840e20i | − | 0.0397729i | −0.999802 | − | 0.0198864i | \(-0.993670\pi\) | ||
0.999802 | − | 0.0198864i | \(-0.00633047\pi\) | |||||||
\(488\) | 1.17539e20 | + | 2.07002e20i | 0.0365446 | + | 0.0643601i | ||||
\(489\) | 2.64159e21 | 0.807968 | ||||||||
\(490\) | −2.01071e20 | + | 1.67900e20i | −0.0605035 | + | 0.0505221i | ||||
\(491\) | − | 1.35029e21i | − | 0.399737i | −0.979823 | − | 0.199868i | \(-0.935949\pi\) | ||
0.979823 | − | 0.199868i | \(-0.0640515\pi\) | |||||||
\(492\) | −2.84223e21 | − | 5.15203e20i | −0.827825 | − | 0.150057i | ||||
\(493\) | −1.68483e21 | −0.482815 | ||||||||
\(494\) | −1.33898e21 | − | 1.60351e21i | −0.377536 | − | 0.452123i | ||||
\(495\) | − | 1.78293e19i | − | 0.00494643i | ||||||
\(496\) | −1.44057e21 | + | 3.84304e21i | −0.393260 | + | 1.04911i | ||||
\(497\) | −2.86818e21 | −0.770470 | ||||||||
\(498\) | 3.63333e20 | − | 3.03393e20i | 0.0960439 | − | 0.0801994i | ||||
\(499\) | 5.21112e21i | 1.35559i | 0.735253 | + | 0.677793i | \(0.237063\pi\) | ||||
−0.735253 | + | 0.677793i | \(0.762937\pi\) | |||||||
\(500\) | 1.59552e20 | − | 8.80202e20i | 0.0408453 | − | 0.225332i | ||||
\(501\) | −3.87846e21 | −0.977142 | ||||||||
\(502\) | −2.11949e21 | − | 2.53822e21i | −0.525535 | − | 0.629361i | ||||
\(503\) | 3.67581e21i | 0.897036i | 0.893774 | + | 0.448518i | \(0.148048\pi\) | ||||
−0.893774 | + | 0.448518i | \(0.851952\pi\) | |||||||
\(504\) | 6.78577e20 | − | 3.85306e20i | 0.162988 | − | 0.0925469i | ||||
\(505\) | −3.17495e20 | −0.0750595 | ||||||||
\(506\) | −2.10394e19 | + | 1.75685e19i | −0.00489587 | + | 0.00408819i | ||||
\(507\) | 7.04102e20i | 0.161277i | ||||||||
\(508\) | −1.79539e20 | − | 3.25445e19i | −0.0404807 | − | 0.00733783i | ||||
\(509\) | 3.70215e21 | 0.821698 | 0.410849 | − | 0.911703i | \(-0.365232\pi\) | ||||
0.410849 | + | 0.911703i | \(0.365232\pi\) | |||||||
\(510\) | 7.29588e19 | + | 8.73728e19i | 0.0159410 | + | 0.0190904i | ||||
\(511\) | − | 5.52822e20i | − | 0.118910i | ||||||
\(512\) | 4.72127e21 | + | 1.01722e20i | 0.999768 | + | 0.0215405i | ||||
\(513\) | −6.40507e20 | −0.133532 | ||||||||
\(514\) | 4.16950e21 | − | 3.48165e21i | 0.855812 | − | 0.714628i | ||||
\(515\) | − | 1.45209e20i | − | 0.0293451i | ||||||
\(516\) | −7.94239e20 | + | 4.38159e21i | −0.158035 | + | 0.871835i | ||||
\(517\) | −9.09686e20 | −0.178224 | ||||||||
\(518\) | −3.37719e21 | − | 4.04440e21i | −0.651504 | − | 0.780217i | ||||
\(519\) | 1.78233e21i | 0.338571i | ||||||||
\(520\) | −2.58299e20 | − | 4.54900e20i | −0.0483166 | − | 0.0850921i | ||||
\(521\) | −4.65046e21 | −0.856631 | −0.428316 | − | 0.903629i | \(-0.640893\pi\) | ||||
−0.428316 | + | 0.903629i | \(0.640893\pi\) | |||||||
\(522\) | 1.82223e21 | − | 1.52162e21i | 0.330552 | − | 0.276021i | ||||
\(523\) | 7.31101e21i | 1.30606i | 0.757331 | + | 0.653031i | \(0.226503\pi\) | ||||
−0.757331 | + | 0.653031i | \(0.773497\pi\) | |||||||
\(524\) | 5.46181e21 | + | 9.90047e20i | 0.960918 | + | 0.174183i | ||||
\(525\) | 1.84869e21 | 0.320325 | ||||||||
\(526\) | −2.50164e21 | − | 2.99587e21i | −0.426913 | − | 0.511255i | ||||
\(527\) | − | 2.49115e21i | − | 0.418712i | ||||||
\(528\) | 4.20403e20 | + | 1.57589e20i | 0.0695976 | + | 0.0260888i | ||||
\(529\) | 6.11756e21 | 0.997545 | ||||||||
\(530\) | −4.95227e19 | + | 4.13529e19i | −0.00795422 | + | 0.00664200i | ||||
\(531\) | 2.78277e21i | 0.440273i | ||||||||
\(532\) | 4.46497e20 | − | 2.46320e21i | 0.0695866 | − | 0.383890i | ||||
\(533\) | −8.05753e21 | −1.23704 | ||||||||
\(534\) | 4.52073e21 | + | 5.41385e21i | 0.683720 | + | 0.818798i | ||||
\(535\) | 6.37311e20i | 0.0949557i | ||||||||
\(536\) | 5.13185e21 | − | 2.91394e21i | 0.753279 | − | 0.427723i | ||||
\(537\) | −5.34633e21 | −0.773146 | ||||||||
\(538\) | 5.50696e21 | − | 4.59847e21i | 0.784609 | − | 0.655171i | ||||
\(539\) | − | 6.27139e20i | − | 0.0880347i | ||||||
\(540\) | −1.57818e20 | − | 2.86072e19i | −0.0218276 | − | 0.00395662i | ||||
\(541\) | 8.52511e21 | 1.16178 | 0.580888 | − | 0.813984i | \(-0.302706\pi\) | ||||
0.580888 | + | 0.813984i | \(0.302706\pi\) | |||||||
\(542\) | −6.88143e21 | − | 8.24095e21i | −0.924027 | − | 1.10658i | ||||
\(543\) | − | 2.06535e21i | − | 0.273272i | ||||||
\(544\) | −2.70506e21 | + | 9.48057e20i | −0.352684 | + | 0.123607i | ||||
\(545\) | −9.96849e20 | −0.128073 | ||||||||
\(546\) | 1.67082e21 | − | 1.39518e21i | 0.211538 | − | 0.176640i | ||||
\(547\) | − | 7.69610e21i | − | 0.960223i | −0.877208 | − | 0.480111i | \(-0.840596\pi\) | ||
0.877208 | − | 0.480111i | \(-0.159404\pi\) | |||||||
\(548\) | −1.86927e21 | + | 1.03123e22i | −0.229842 | + | 1.26797i | ||||
\(549\) | 2.03591e20 | 0.0246706 | ||||||||
\(550\) | 6.81747e20 | + | 8.16436e20i | 0.0814183 | + | 0.0975036i | ||||
\(551\) | − | 7.61583e21i | − | 0.896405i | ||||||
\(552\) | 1.21752e20 | + | 2.14422e20i | 0.0141242 | + | 0.0248746i | ||||
\(553\) | 4.87361e21 | 0.557250 | ||||||||
\(554\) | 5.42149e21 | − | 4.52710e21i | 0.610999 | − | 0.510202i | ||||
\(555\) | 1.08299e21i | 0.120304i | ||||||||
\(556\) | 2.87604e20 | + | 5.21331e19i | 0.0314917 | + | 0.00570841i | ||||
\(557\) | −4.62948e21 | −0.499678 | −0.249839 | − | 0.968287i | \(-0.580378\pi\) | ||||
−0.249839 | + | 0.968287i | \(0.580378\pi\) | |||||||
\(558\) | 2.24983e21 | + | 2.69431e21i | 0.239373 | + | 0.286665i | ||||
\(559\) | 1.24215e22i | 1.30281i | ||||||||
\(560\) | 2.20029e20 | − | 5.86977e20i | 0.0227497 | − | 0.0606900i | ||||
\(561\) | −2.72516e20 | −0.0277772 | ||||||||
\(562\) | −2.43685e21 | + | 2.03484e21i | −0.244871 | + | 0.204475i | ||||
\(563\) | − | 8.89108e21i | − | 0.880820i | −0.897797 | − | 0.440410i | \(-0.854833\pi\) | ||
0.897797 | − | 0.440410i | \(-0.145167\pi\) | |||||||
\(564\) | −1.45960e21 | + | 8.05218e21i | −0.142561 | + | 0.786467i | ||||
\(565\) | −4.63731e20 | −0.0446559 | ||||||||
\(566\) | 4.46735e21 | + | 5.34993e21i | 0.424149 | + | 0.507945i | ||||
\(567\) | − | 6.67393e20i | − | 0.0624766i | ||||||
\(568\) | −1.29092e22 | + | 7.33003e21i | −1.19155 | + | 0.676580i | ||||
\(569\) | 1.92778e22 | 1.75452 | 0.877261 | − | 0.480014i | \(-0.159368\pi\) | ||||
0.877261 | + | 0.480014i | \(0.159368\pi\) | |||||||
\(570\) | −3.94945e20 | + | 3.29791e20i | −0.0354436 | + | 0.0295964i | ||||
\(571\) | 9.49922e21i | 0.840619i | 0.907381 | + | 0.420309i | \(0.138078\pi\) | ||||
−0.907381 | + | 0.420309i | \(0.861922\pi\) | |||||||
\(572\) | 1.23231e21 | + | 2.23377e20i | 0.107535 | + | 0.0194926i | ||||
\(573\) | −2.20998e21 | −0.190174 | ||||||||
\(574\) | −6.18871e21 | − | 7.41137e21i | −0.525176 | − | 0.628931i | ||||
\(575\) | 5.84163e20i | 0.0488868i | ||||||||
\(576\) | 2.06945e21 | − | 3.46839e21i | 0.170795 | − | 0.286252i | ||||
\(577\) | 3.93866e20 | 0.0320584 | 0.0160292 | − | 0.999872i | \(-0.494898\pi\) | ||||
0.0160292 | + | 0.999872i | \(0.494898\pi\) | |||||||
\(578\) | −8.22649e21 | + | 6.86935e21i | −0.660377 | + | 0.551434i | ||||
\(579\) | − | 1.16252e22i | − | 0.920392i | ||||||
\(580\) | 3.40148e20 | − | 1.87650e21i | 0.0265610 | − | 0.146529i | ||||
\(581\) | 1.58225e21 | 0.121861 | ||||||||
\(582\) | 9.89750e20 | + | 1.18529e21i | 0.0751868 | + | 0.0900410i | ||||
\(583\) | − | 1.54461e20i | − | 0.0115737i | ||||||
\(584\) | −1.41281e21 | − | 2.48815e21i | −0.104419 | − | 0.183897i | ||||
\(585\) | −4.47403e20 | −0.0326176 | ||||||||
\(586\) | −1.41674e22 | + | 1.18302e22i | −1.01885 | + | 0.850766i | ||||
\(587\) | − | 1.14484e22i | − | 0.812156i | −0.913838 | − | 0.406078i | \(-0.866896\pi\) | ||
0.913838 | − | 0.406078i | \(-0.133104\pi\) | |||||||
\(588\) | −5.55119e21 | − | 1.00625e21i | −0.388479 | − | 0.0704185i | ||||
\(589\) | 1.12606e22 | 0.777389 | ||||||||
\(590\) | 1.43282e21 | + | 1.71590e21i | 0.0975835 | + | 0.116862i | ||||
\(591\) | − | 4.37363e21i | − | 0.293861i | ||||||
\(592\) | −2.55361e22 | − | 9.57225e21i | −1.69271 | − | 0.634513i | ||||
\(593\) | −2.05167e22 | −1.34175 | −0.670874 | − | 0.741572i | \(-0.734081\pi\) | ||||
−0.670874 | + | 0.741572i | \(0.734081\pi\) | |||||||
\(594\) | 2.94740e20 | − | 2.46116e20i | 0.0190172 | − | 0.0158799i | ||||
\(595\) | 3.80493e20i | 0.0242221i | ||||||||
\(596\) | −1.91184e21 | + | 1.05471e22i | −0.120083 | + | 0.662463i | ||||
\(597\) | −5.23704e21 | −0.324557 | ||||||||
\(598\) | 4.40860e20 | + | 5.27958e20i | 0.0269582 | + | 0.0322842i | ||||
\(599\) | − | 5.38868e20i | − | 0.0325138i | −0.999868 | − | 0.0162569i | \(-0.994825\pi\) | ||
0.999868 | − | 0.0162569i | \(-0.00517496\pi\) | |||||||
\(600\) | 8.32064e21 | − | 4.72459e21i | 0.495389 | − | 0.281290i | ||||
\(601\) | −5.44089e21 | −0.319650 | −0.159825 | − | 0.987145i | \(-0.551093\pi\) | ||||
−0.159825 | + | 0.987145i | \(0.551093\pi\) | |||||||
\(602\) | −1.14254e22 | + | 9.54053e21i | −0.662368 | + | 0.553096i | ||||
\(603\) | − | 5.04727e21i | − | 0.288747i | ||||||
\(604\) | 2.87594e22 | + | 5.21314e21i | 1.62362 | + | 0.294309i | ||||
\(605\) | −2.03466e21 | −0.113357 | ||||||||
\(606\) | −4.38272e21 | − | 5.24859e21i | −0.240970 | − | 0.288577i | ||||
\(607\) | − | 5.75755e21i | − | 0.312412i | −0.987724 | − | 0.156206i | \(-0.950074\pi\) | ||
0.987724 | − | 0.156206i | \(-0.0499264\pi\) | |||||||
\(608\) | −4.28544e21 | − | 1.22275e22i | −0.229492 | − | 0.654801i | ||||
\(609\) | 7.93551e21 | 0.419408 | ||||||||
\(610\) | 1.25537e20 | − | 1.04827e20i | 0.00654835 | − | 0.00546806i | ||||
\(611\) | 2.28274e22i | 1.17524i | ||||||||
\(612\) | −4.37253e20 | + | 2.41220e21i | −0.0222188 | + | 0.122575i | ||||
\(613\) | −9.14430e21 | −0.458635 | −0.229317 | − | 0.973352i | \(-0.573649\pi\) | ||||
−0.229317 | + | 0.973352i | \(0.573649\pi\) | |||||||
\(614\) | 1.97576e22 | + | 2.36610e22i | 0.978109 | + | 1.17135i | ||||
\(615\) | 1.98457e21i | 0.0969764i | ||||||||
\(616\) | 7.41027e20 | + | 1.30505e21i | 0.0357428 | + | 0.0629479i | ||||
\(617\) | 1.03301e22 | 0.491841 | 0.245920 | − | 0.969290i | \(-0.420910\pi\) | ||||
0.245920 | + | 0.969290i | \(0.420910\pi\) | |||||||
\(618\) | 2.40049e21 | − | 2.00448e21i | 0.112821 | − | 0.0942092i | ||||
\(619\) | − | 4.25685e22i | − | 1.97498i | −0.157681 | − | 0.987490i | \(-0.550402\pi\) | ||
0.157681 | − | 0.987490i | \(-0.449598\pi\) | |||||||
\(620\) | 2.77455e21 | + | 5.02934e20i | 0.127075 | + | 0.0230345i | ||||
\(621\) | 2.10888e20 | 0.00953496 | ||||||||
\(622\) | 8.31815e21 | + | 9.96151e21i | 0.371282 | + | 0.444633i | ||||
\(623\) | 2.35764e22i | 1.03890i | ||||||||
\(624\) | 3.95449e21 | − | 1.05495e22i | 0.172034 | − | 0.458938i | ||||
\(625\) | 2.23591e22 | 0.960317 | ||||||||
\(626\) | 8.46131e20 | − | 7.06544e20i | 0.0358792 | − | 0.0299602i | ||||
\(627\) | − | 1.23183e21i | − | 0.0515717i | ||||||
\(628\) | 7.86211e21 | − | 4.33731e22i | 0.324984 | − | 1.79285i | ||||
\(629\) | 1.65531e22 | 0.675578 | ||||||||
\(630\) | −3.43634e20 | − | 4.11524e20i | −0.0138475 | − | 0.0165833i | ||||
\(631\) | 2.86017e22i | 1.13804i | 0.822324 | + | 0.569020i | \(0.192677\pi\) | ||||
−0.822324 | + | 0.569020i | \(0.807323\pi\) | |||||||
\(632\) | 2.19353e22 | − | 1.24552e22i | 0.861800 | − | 0.489343i | ||||
\(633\) | −5.60720e21 | −0.217529 | ||||||||
\(634\) | 1.96215e22 | − | 1.63845e22i | 0.751652 | − | 0.627651i | ||||
\(635\) | 1.25362e20i | 0.00474216i | ||||||||
\(636\) | −1.36723e21 | − | 2.47834e20i | −0.0510722 | − | 0.00925772i | ||||
\(637\) | −1.57373e22 | −0.580516 | ||||||||
\(638\) | 2.92640e21 | + | 3.50455e21i | 0.106603 | + | 0.127664i | ||||
\(639\) | 1.26964e22i | 0.456746i | ||||||||
\(640\) | −5.09789e20 | − | 3.20420e21i | −0.0181113 | − | 0.113836i | ||||
\(641\) | −5.68766e21 | −0.199558 | −0.0997791 | − | 0.995010i | \(-0.531814\pi\) | ||||
−0.0997791 | + | 0.995010i | \(0.531814\pi\) | |||||||
\(642\) | −1.05356e22 | + | 8.79749e21i | −0.365071 | + | 0.304845i | ||||
\(643\) | − | 9.58453e21i | − | 0.328007i | −0.986460 | − | 0.164003i | \(-0.947559\pi\) | ||
0.986460 | − | 0.164003i | \(-0.0524408\pi\) | |||||||
\(644\) | −1.47010e20 | + | 8.11012e20i | −0.00496889 | + | 0.0274120i | ||||
\(645\) | 3.05943e21 | 0.102132 | ||||||||
\(646\) | 5.04077e21 | + | 6.03664e21i | 0.166202 | + | 0.199038i | ||||
\(647\) | 4.46026e22i | 1.45253i | 0.687414 | + | 0.726266i | \(0.258746\pi\) | ||||
−0.687414 | + | 0.726266i | \(0.741254\pi\) | |||||||
\(648\) | −1.70561e21 | − | 3.00382e21i | −0.0548632 | − | 0.0966215i | ||||
\(649\) | −5.35188e21 | −0.170039 | ||||||||
\(650\) | 2.04874e22 | − | 1.71076e22i | 0.642955 | − | 0.536886i | ||||
\(651\) | 1.17333e22i | 0.363723i | ||||||||
\(652\) | 4.49692e22 | + | 8.15144e21i | 1.37700 | + | 0.249605i | ||||
\(653\) | −4.48623e21 | −0.135699 | −0.0678494 | − | 0.997696i | \(-0.521614\pi\) | ||||
−0.0678494 | + | 0.997696i | \(0.521614\pi\) | |||||||
\(654\) | −1.37606e22 | − | 1.64792e22i | −0.411164 | − | 0.492395i | ||||
\(655\) | − | 3.81368e21i | − | 0.112568i | ||||||
\(656\) | −4.67950e22 | − | 1.75412e22i | −1.36449 | − | 0.511479i | ||||
\(657\) | −2.44715e21 | −0.0704915 | ||||||||
\(658\) | −2.09968e22 | + | 1.75329e22i | −0.597511 | + | 0.498939i | ||||
\(659\) | − | 5.30196e21i | − | 0.149057i | −0.997219 | − | 0.0745286i | \(-0.976255\pi\) | ||
0.997219 | − | 0.0745286i | \(-0.0237452\pi\) | |||||||
\(660\) | 5.50177e19 | − | 3.03517e20i | 0.00152810 | − | 0.00843009i | ||||
\(661\) | −5.01176e22 | −1.37524 | −0.687620 | − | 0.726070i | \(-0.741345\pi\) | ||||
−0.687620 | + | 0.726070i | \(0.741345\pi\) | |||||||
\(662\) | 6.39573e21 | + | 7.65929e21i | 0.173391 | + | 0.207647i | ||||
\(663\) | 6.83843e21i | 0.183168i | ||||||||
\(664\) | 7.12143e21 | − | 4.04366e21i | 0.188461 | − | 0.107011i | ||||
\(665\) | −1.71992e21 | −0.0449712 | ||||||||
\(666\) | −1.79031e22 | + | 1.49496e22i | −0.462524 | + | 0.386221i | ||||
\(667\) | 2.50752e21i | 0.0640085i | ||||||||
\(668\) | −6.60252e22 | − | 1.19682e22i | −1.66532 | − | 0.301868i | ||||
\(669\) | 2.29174e21 | 0.0571158 | ||||||||
\(670\) | −2.59879e21 | − | 3.11221e21i | −0.0639989 | − | 0.0766428i | ||||
\(671\) | 3.91549e20i | 0.00952808i | ||||||||
\(672\) | 1.27408e22 | − | 4.46532e21i | 0.306367 | − | 0.107374i | ||||
\(673\) | −7.45742e22 | −1.77202 | −0.886009 | − | 0.463668i | \(-0.846533\pi\) | ||||
−0.886009 | + | 0.463668i | \(0.846533\pi\) | |||||||
\(674\) | 3.11124e22 | − | 2.59798e22i | 0.730558 | − | 0.610037i | ||||
\(675\) | − | 8.18350e21i | − | 0.189893i | ||||||
\(676\) | −2.17273e21 | + | 1.19863e22i | −0.0498232 | + | 0.274861i | ||||
\(677\) | −1.34138e22 | −0.303979 | −0.151989 | − | 0.988382i | \(-0.548568\pi\) | ||||
−0.151989 | + | 0.988382i | \(0.548568\pi\) | |||||||
\(678\) | −6.40139e21 | − | 7.66606e21i | −0.143363 | − | 0.171686i | ||||
\(679\) | 5.16172e21i | 0.114245i | ||||||||
\(680\) | 9.72402e20 | + | 1.71253e21i | 0.0212704 | + | 0.0374600i | ||||
\(681\) | 4.74165e22 | 1.02507 | ||||||||
\(682\) | −5.18174e21 | + | 4.32691e21i | −0.110714 | + | 0.0924490i | ||||
\(683\) | − | 6.68422e22i | − | 1.41151i | −0.708454 | − | 0.705757i | \(-0.750607\pi\) | ||
0.708454 | − | 0.705757i | \(-0.249393\pi\) | |||||||
\(684\) | −1.09037e22 | − | 1.97648e21i | −0.227576 | − | 0.0412520i | ||||
\(685\) | 7.20049e21 | 0.148538 | ||||||||
\(686\) | −2.97630e22 | − | 3.56431e22i | −0.606854 | − | 0.726746i | ||||
\(687\) | 4.66529e22i | 0.940210i | ||||||||
\(688\) | −2.70415e22 | + | 7.21394e22i | −0.538671 | + | 1.43703i | ||||
\(689\) | −3.87601e21 | −0.0763187 | ||||||||
\(690\) | 1.30036e20 | − | 1.08584e20i | 0.00253088 | − | 0.00211336i | ||||
\(691\) | − | 7.61674e22i | − | 1.46536i | −0.680572 | − | 0.732681i | \(-0.738269\pi\) | ||
0.680572 | − | 0.732681i | \(-0.261731\pi\) | |||||||
\(692\) | −5.49994e21 | + | 3.03416e22i | −0.104595 | + | 0.577019i | ||||
\(693\) | 1.28354e21 | 0.0241293 | ||||||||
\(694\) | 5.43019e22 | + | 6.50300e22i | 1.00911 | + | 1.20848i | ||||
\(695\) | − | 2.00818e20i | − | 0.00368913i | ||||||
\(696\) | 3.57163e22 | − | 2.02803e22i | 0.648624 | − | 0.368299i | ||||
\(697\) | 3.03337e22 | 0.544582 | ||||||||
\(698\) | 2.03770e22 | − | 1.70154e22i | 0.361657 | − | 0.301994i | ||||
\(699\) | − | 5.20567e21i | − | 0.0913396i | ||||||
\(700\) | 3.14713e22 | + | 5.70472e21i | 0.545922 | + | 0.0989577i | ||||
\(701\) | 6.67032e22 | 1.14394 | 0.571969 | − | 0.820275i | \(-0.306180\pi\) | ||||
0.571969 | + | 0.820275i | \(0.306180\pi\) | |||||||
\(702\) | −6.17598e21 | − | 7.39613e21i | −0.104715 | − | 0.125403i | ||||
\(703\) | 7.48241e22i | 1.25429i | ||||||||
\(704\) | 6.67047e21 | + | 3.98000e21i | 0.110554 | + | 0.0659633i | ||||
\(705\) | 5.62240e21 | 0.0921316 | ||||||||
\(706\) | −3.41804e22 | + | 2.85416e22i | −0.553783 | + | 0.462425i | ||||
\(707\) | − | 2.28567e22i | − | 0.366149i | ||||||
\(708\) | −8.58712e21 | + | 4.73727e22i | −0.136013 | + | 0.750347i | ||||
\(709\) | 6.94725e22 | 1.08803 | 0.544017 | − | 0.839074i | \(-0.316903\pi\) | ||||
0.544017 | + | 0.839074i | \(0.316903\pi\) | |||||||
\(710\) | 6.53726e21 | + | 7.82878e21i | 0.101235 | + | 0.121235i | ||||
\(711\) | − | 2.15737e22i | − | 0.330346i | ||||||
\(712\) | 6.02527e22 | + | 1.06113e23i | 0.912297 | + | 1.60668i | ||||
\(713\) | −3.70756e21 | −0.0555101 | ||||||||
\(714\) | −6.29003e21 | + | 5.25236e21i | −0.0931252 | + | 0.0777622i | ||||
\(715\) | − | 8.60452e20i | − | 0.0125973i | ||||||
\(716\) | −9.10135e22 | − | 1.64978e22i | −1.31766 | − | 0.238848i | ||||
\(717\) | 3.63135e22 | 0.519894 | ||||||||
\(718\) | −8.63980e22 | − | 1.03467e23i | −1.22323 | − | 1.46489i | ||||
\(719\) | − | 7.93076e22i | − | 1.11041i | −0.831713 | − | 0.555205i | \(-0.812640\pi\) | ||
0.831713 | − | 0.555205i | \(-0.187360\pi\) | |||||||
\(720\) | −2.59834e21 | − | 9.73991e20i | −0.0359779 | − | 0.0134864i | ||||
\(721\) | 1.04537e22 | 0.143149 | ||||||||
\(722\) | 2.93919e22 | − | 2.45431e22i | 0.398044 | − | 0.332378i | ||||
\(723\) | 3.35001e22i | 0.448683i | ||||||||
\(724\) | 6.37327e21 | − | 3.51596e22i | 0.0844217 | − | 0.465731i | ||||
\(725\) | 9.73044e22 | 1.27476 | ||||||||
\(726\) | −2.80866e22 | − | 3.36355e22i | −0.363921 | − | 0.435818i | ||||
\(727\) | − | 1.18224e23i | − | 1.51506i | −0.652802 | − | 0.757528i | \(-0.726407\pi\) | ||
0.652802 | − | 0.757528i | \(-0.273593\pi\) | |||||||
\(728\) | 3.27486e22 | − | 1.85951e22i | 0.415089 | − | 0.235694i | ||||
\(729\) | −2.95431e21 | −0.0370370 | ||||||||
\(730\) | −1.50894e21 | + | 1.26001e21i | −0.0187107 | + | 0.0156240i | ||||
\(731\) | − | 4.67625e22i | − | 0.573534i | ||||||
\(732\) | 3.46584e21 | + | 6.28242e20i | 0.0420455 | + | 0.00762147i | ||||
\(733\) | −7.24896e22 | −0.869849 | −0.434925 | − | 0.900467i | \(-0.643225\pi\) | ||||
−0.434925 | + | 0.900467i | \(0.643225\pi\) | |||||||
\(734\) | −1.90101e22 | − | 2.27658e22i | −0.225640 | − | 0.270218i | ||||
\(735\) | 3.87609e21i | 0.0455088i | ||||||||
\(736\) | 1.41099e21 | + | 4.02592e21i | 0.0163870 | + | 0.0467566i | ||||
\(737\) | 9.70699e21 | 0.111518 | ||||||||
\(738\) | −3.28075e22 | + | 2.73952e22i | −0.372840 | + | 0.311332i | ||||
\(739\) | 4.36734e21i | 0.0490978i | 0.999699 | + | 0.0245489i | \(0.00781494\pi\) | ||||
−0.999699 | + | 0.0245489i | \(0.992185\pi\) | |||||||
\(740\) | −3.34189e21 | + | 1.84363e22i | −0.0371653 | + | 0.205031i | ||||
\(741\) | −3.09113e22 | −0.340073 | ||||||||
\(742\) | −2.97703e21 | − | 3.56518e21i | −0.0324005 | − | 0.0388016i | ||||
\(743\) | 1.41363e23i | 1.52204i | 0.648728 | + | 0.761020i | \(0.275301\pi\) | ||||
−0.648728 | + | 0.761020i | \(0.724699\pi\) | |||||||
\(744\) | 2.99859e22 | + | 5.28093e22i | 0.319399 | + | 0.562506i | ||||
\(745\) | 7.36444e21 | 0.0776050 | ||||||||
\(746\) | 3.51873e22 | − | 2.93824e22i | 0.366839 | − | 0.306321i | ||||
\(747\) | − | 7.00406e21i | − | 0.0722412i | ||||||
\(748\) | −4.63918e21 | − | 8.40932e20i | −0.0473401 | − | 0.00858120i | ||||
\(749\) | −4.58805e22 | −0.463205 | ||||||||
\(750\) | −8.48395e21 | − | 1.01601e22i | −0.0847438 | − | 0.101486i | ||||
\(751\) | 8.90798e22i | 0.880358i | 0.897910 | + | 0.440179i | \(0.145085\pi\) | ||||
−0.897910 | + | 0.440179i | \(0.854915\pi\) | |||||||
\(752\) | −4.96950e22 | + | 1.32573e23i | −0.485926 | + | 1.29632i | ||||
\(753\) | −4.89300e22 | −0.473386 | ||||||||
\(754\) | 8.79422e22 | − | 7.34343e22i | 0.841835 | − | 0.702956i | ||||
\(755\) | − | 2.00811e22i | − | 0.190201i | ||||||
\(756\) | 2.05945e21 | − | 1.13614e22i | 0.0193009 | − | 0.106477i | ||||
\(757\) | 4.63034e22 | 0.429384 | 0.214692 | − | 0.976682i | \(-0.431125\pi\) | ||||
0.214692 | + | 0.976682i | \(0.431125\pi\) | |||||||
\(758\) | 9.24612e22 | + | 1.10728e23i | 0.848410 | + | 1.01602i | ||||
\(759\) | 4.05583e20i | 0.00368252i | ||||||||
\(760\) | −7.74104e21 | + | 4.39548e21i | −0.0695490 | + | 0.0394910i | ||||
\(761\) | −1.56378e23 | −1.39026 | −0.695132 | − | 0.718882i | \(-0.744654\pi\) | ||||
−0.695132 | + | 0.718882i | \(0.744654\pi\) | |||||||
\(762\) | −2.07239e21 | + | 1.73051e21i | −0.0182319 | + | 0.0152242i | ||||
\(763\) | − | 7.17639e22i | − | 0.624755i | ||||||
\(764\) | −3.76218e22 | − | 6.81959e21i | −0.324110 | − | 0.0587505i | ||||
\(765\) | 1.68431e21 | 0.0143592 | ||||||||
\(766\) | −6.07188e22 | − | 7.27146e22i | −0.512263 | − | 0.613467i | ||||
\(767\) | 1.34299e23i | 1.12127i | ||||||||
\(768\) | 4.59322e22 | − | 5.26584e22i | 0.379514 | − | 0.435089i | ||||
\(769\) | 2.59960e22 | 0.212567 | 0.106283 | − | 0.994336i | \(-0.466105\pi\) | ||||
0.106283 | + | 0.994336i | \(0.466105\pi\) | |||||||
\(770\) | 7.91449e20 | − | 6.60882e20i | 0.00640467 | − | 0.00534809i | ||||
\(771\) | − | 8.03765e22i | − | 0.643715i | ||||||
\(772\) | 3.58733e22 | − | 1.97903e23i | 0.284336 | − | 1.56860i | ||||
\(773\) | −1.28175e23 | −1.00546 | −0.502732 | − | 0.864442i | \(-0.667672\pi\) | ||||
−0.502732 | + | 0.864442i | \(0.667672\pi\) | |||||||
\(774\) | 4.22325e22 | + | 5.05761e22i | 0.327883 | + | 0.392661i | ||||
\(775\) | 1.43872e23i | 1.10551i | ||||||||
\(776\) | 1.31915e22 | + | 2.32320e22i | 0.100323 | + | 0.176682i | ||||
\(777\) | −7.79649e22 | −0.586855 | ||||||||
\(778\) | −2.84017e22 | + | 2.37163e22i | −0.211596 | + | 0.176689i | ||||
\(779\) | 1.37115e23i | 1.01108i | ||||||||
\(780\) | −7.61638e21 | − | 1.38060e21i | −0.0555894 | − | 0.0100765i | ||||
\(781\) | −2.44180e22 | −0.176401 | ||||||||
\(782\) | −1.65968e21 | − | 1.98757e21i | −0.0118678 | − | 0.0142124i | ||||
\(783\) | − | 3.51277e22i | − | 0.248631i | ||||||
\(784\) | −9.13959e22 | − | 3.42599e22i | −0.640322 | − | 0.240025i | ||||
\(785\) | −3.02850e22 | −0.210025 | ||||||||
\(786\) | 6.30450e22 | − | 5.26444e22i | 0.432783 | − | 0.361386i | ||||
\(787\) | 3.96418e22i | 0.269374i | 0.990888 | + | 0.134687i | \(0.0430029\pi\) | ||||
−0.990888 | + | 0.134687i | \(0.956997\pi\) | |||||||
\(788\) | 1.34962e22 | − | 7.44547e22i | 0.0907823 | − | 0.500821i | ||||
\(789\) | −5.77523e22 | −0.384550 | ||||||||
\(790\) | −1.11081e22 | − | 1.33027e22i | −0.0732189 | − | 0.0876843i | ||||
\(791\) | − | 3.33844e22i | − | 0.217837i | ||||||
\(792\) | 5.77699e21 | − | 3.28026e21i | 0.0373165 | − | 0.0211889i | ||||
\(793\) | 9.82542e21 | 0.0628298 | ||||||||
\(794\) | −1.58142e22 | + | 1.32054e22i | −0.100112 | + | 0.0835961i | ||||
\(795\) | 9.54662e20i | 0.00598291i | ||||||||
\(796\) | −8.91530e22 | − | 1.61605e22i | −0.553135 | − | 0.100265i | ||||
\(797\) | 2.13798e21 | 0.0131322 | 0.00656609 | − | 0.999978i | \(-0.497910\pi\) | ||||
0.00656609 | + | 0.999978i | \(0.497910\pi\) | |||||||
\(798\) | −2.37419e22 | − | 2.84324e22i | −0.144375 | − | 0.172898i | ||||
\(799\) | − | 8.59369e22i | − | 0.517375i | ||||||
\(800\) | 1.56226e23 | − | 5.47533e22i | 0.931180 | − | 0.326355i | ||||
\(801\) | 1.04364e23 | 0.615874 | ||||||||
\(802\) | −2.77327e22 | + | 2.31576e22i | −0.162031 | + | 0.135300i | ||||
\(803\) | − | 4.70639e21i | − | 0.0272247i | ||||||
\(804\) | 1.55749e22 | − | 8.59225e22i | 0.0892026 | − | 0.492106i | ||||
\(805\) | 5.66285e20 | 0.00321120 | ||||||||
\(806\) | 1.08578e23 | + | 1.30029e23i | 0.609624 | + | 0.730064i | ||||
\(807\) | − | 1.06159e23i | − | 0.590158i | ||||||
\(808\) | −5.84134e22 | − | 1.02874e23i | −0.321530 | − | 0.566258i | ||||
\(809\) | 1.44463e23 | 0.787351 | 0.393675 | − | 0.919250i | \(-0.371203\pi\) | ||||
0.393675 | + | 0.919250i | \(0.371203\pi\) | |||||||
\(810\) | −1.82167e21 | + | 1.52115e21i | −0.00983081 | + | 0.00820901i | ||||
\(811\) | 3.08751e23i | 1.64984i | 0.565249 | + | 0.824920i | \(0.308780\pi\) | ||||
−0.565249 | + | 0.824920i | \(0.691220\pi\) | |||||||
\(812\) | 1.35091e23 | + | 2.44875e22i | 0.714788 | + | 0.129568i | ||||
\(813\) | −1.58863e23 | −0.832335 | ||||||||
\(814\) | −2.87513e22 | − | 3.44315e22i | −0.149164 | − | 0.178633i | ||||
\(815\) | − | 3.13995e22i | − | 0.161310i | ||||||
\(816\) | −1.48872e22 | + | 3.97150e22i | −0.0757342 | + | 0.202038i | ||||
\(817\) | 2.11377e23 | 1.06483 | ||||||||
\(818\) | 2.50084e22 | − | 2.08827e22i | 0.124755 | − | 0.104174i | ||||
\(819\) | − | 3.22088e22i | − | 0.159112i | ||||||
\(820\) | −6.12402e21 | + | 3.37845e22i | −0.0299589 | + | 0.165275i | ||||
\(821\) | 1.09914e23 | 0.532484 | 0.266242 | − | 0.963906i | \(-0.414218\pi\) | ||||
0.266242 | + | 0.963906i | \(0.414218\pi\) | |||||||
\(822\) | 9.93961e22 | + | 1.19033e23i | 0.476864 | + | 0.571075i | ||||
\(823\) | 7.16721e22i | 0.340527i | 0.985399 | + | 0.170263i | \(0.0544618\pi\) | ||||
−0.985399 | + | 0.170263i | \(0.945538\pi\) | |||||||
\(824\) | 4.70503e22 | − | 2.67159e22i | 0.221383 | − | 0.125705i | ||||
\(825\) | 1.57386e22 | 0.0733391 | ||||||||
\(826\) | −1.23529e23 | + | 1.03150e23i | −0.570069 | + | 0.476024i | ||||
\(827\) | − | 2.00338e23i | − | 0.915628i | −0.889048 | − | 0.457814i | \(-0.848633\pi\) | ||
0.889048 | − | 0.457814i | \(-0.151367\pi\) | |||||||
\(828\) | 3.59006e21 | + | 6.50760e20i | 0.0162502 | + | 0.00294563i | ||||
\(829\) | 1.46109e23 | 0.654999 | 0.327499 | − | 0.944851i | \(-0.393794\pi\) | ||||
0.327499 | + | 0.944851i | \(0.393794\pi\) | |||||||
\(830\) | −3.60632e21 | − | 4.31880e21i | −0.0160118 | − | 0.0191751i | ||||
\(831\) | − | 1.04511e23i | − | 0.459574i | ||||||
\(832\) | 9.98731e22 | − | 1.67387e23i | 0.434973 | − | 0.729012i | ||||
\(833\) | 5.92451e22 | 0.255560 | ||||||||
\(834\) | 3.31977e21 | − | 2.77210e21i | 0.0141834 | − | 0.0118435i | ||||
\(835\) | 4.61018e22i | 0.195086i | ||||||||
\(836\) | 3.80121e21 | − | 2.09702e22i | 0.0159320 | − | 0.0878926i | ||||
\(837\) | 5.19390e22 | 0.215620 | ||||||||
\(838\) | 2.01795e23 | + | 2.41662e23i | 0.829770 | + | 0.993702i | ||||
\(839\) | − | 2.64414e23i | − | 1.07693i | −0.842647 | − | 0.538466i | \(-0.819004\pi\) | ||
0.842647 | − | 0.538466i | \(-0.180996\pi\) | |||||||
\(840\) | −4.57999e21 | − | 8.06598e21i | −0.0184769 | − | 0.0325404i | ||||
\(841\) | 1.67433e23 | 0.669071 | ||||||||
\(842\) | −3.35019e23 | + | 2.79750e23i | −1.32609 | + | 1.10732i | ||||
\(843\) | 4.69758e22i | 0.184185i | ||||||||
\(844\) | −9.54545e22 | − | 1.73028e22i | −0.370729 | − | 0.0672011i | ||||
\(845\) | 8.36939e21 | 0.0321988 | ||||||||
\(846\) | 7.76120e22 | + | 9.29453e22i | 0.295778 | + | 0.354213i | ||||
\(847\) | − | 1.46477e23i | − | 0.552970i | ||||||
\(848\) | −2.25104e22 | − | 8.43803e21i | −0.0841813 | − | 0.0315555i | ||||
\(849\) | 1.03132e23 | 0.382060 | ||||||||
\(850\) | −7.71277e22 | + | 6.44039e22i | −0.283047 | + | 0.236353i | ||||
\(851\) | − | 2.46359e22i | − | 0.0895637i | ||||||
\(852\) | −3.91788e22 | + | 2.16138e23i | −0.141102 | + | 0.778422i | ||||
\(853\) | −1.71142e23 | −0.610609 | −0.305305 | − | 0.952255i | \(-0.598758\pi\) | ||||
−0.305305 | + | 0.952255i | \(0.598758\pi\) | |||||||
\(854\) | 7.54655e21 | + | 9.03748e21i | 0.0266739 | + | 0.0319436i | ||||
\(855\) | 7.61346e21i | 0.0266596i | ||||||||
\(856\) | −2.06500e23 | + | 1.17254e23i | −0.716358 | + | 0.406759i | ||||
\(857\) | −4.71695e23 | −1.62112 | −0.810559 | − | 0.585657i | \(-0.800836\pi\) | ||||
−0.810559 | + | 0.585657i | \(0.800836\pi\) | |||||||
\(858\) | 1.42243e22 | − | 1.18777e22i | 0.0484322 | − | 0.0404423i | ||||
\(859\) | − | 1.89722e23i | − | 0.639988i | −0.947420 | − | 0.319994i | \(-0.896319\pi\) | ||
0.947420 | − | 0.319994i | \(-0.103681\pi\) | |||||||
\(860\) | 5.20823e22 | + | 9.44081e21i | 0.174061 | + | 0.0315516i | ||||
\(861\) | −1.42871e23 | −0.473062 | ||||||||
\(862\) | −2.11480e23 | − | 2.53260e23i | −0.693762 | − | 0.830824i | ||||
\(863\) | − | 1.25778e23i | − | 0.408806i | −0.978887 | − | 0.204403i | \(-0.934475\pi\) | ||
0.978887 | − | 0.204403i | \(-0.0655254\pi\) | |||||||
\(864\) | −1.97664e22 | − | 5.63989e22i | −0.0636528 | − | 0.181619i | ||||
\(865\) | 2.11859e22 | 0.0675956 | ||||||||
\(866\) | −2.27437e23 | + | 1.89916e23i | −0.718982 | + | 0.600371i | ||||
\(867\) | 1.58584e23i | 0.496715i | ||||||||
\(868\) | −3.62066e22 | + | 1.99742e23i | −0.112365 | + | 0.619885i | ||||
\(869\) | 4.14910e22 | 0.127584 | ||||||||
\(870\) | −1.80869e22 | − | 2.16602e22i | −0.0551074 | − | 0.0659946i | ||||
\(871\) | − | 2.43585e23i | − | 0.735368i | ||||||
\(872\) | −1.83402e23 | − | 3.22997e23i | −0.548622 | − | 0.966198i | ||||
\(873\) | 2.28491e22 | 0.0677260 | ||||||||
\(874\) | 8.98428e21 | − | 7.50213e21i | 0.0263871 | − | 0.0220340i | ||||
\(875\) | − | 4.42453e22i | − | 0.128766i | ||||||
\(876\) | −4.16591e22 | − | 7.55143e21i | −0.120137 | − | 0.0217769i | ||||
\(877\) | −1.17923e22 | −0.0336977 | −0.0168489 | − | 0.999858i | \(-0.505363\pi\) | ||||
−0.0168489 | + | 0.999858i | \(0.505363\pi\) | |||||||
\(878\) | −4.08790e23 | − | 4.89551e23i | −1.15756 | − | 1.38625i | ||||
\(879\) | 2.73108e23i | 0.766344i | ||||||||
\(880\) | 1.87319e21 | − | 4.99717e21i | 0.00520861 | − | 0.0138951i | ||||
\(881\) | −3.20332e22 | −0.0882661 | −0.0441330 | − | 0.999026i | \(-0.514053\pi\) | ||||
−0.0441330 | + | 0.999026i | \(0.514053\pi\) | |||||||
\(882\) | −6.40767e22 | + | 5.35059e22i | −0.174965 | + | 0.146101i | ||||
\(883\) | 1.83970e23i | 0.497808i | 0.968528 | + | 0.248904i | \(0.0800704\pi\) | ||||
−0.968528 | + | 0.248904i | \(0.919930\pi\) | |||||||
\(884\) | −2.11021e22 | + | 1.16414e23i | −0.0565859 | + | 0.312168i | ||||
\(885\) | 3.30778e22 | 0.0879002 | ||||||||
\(886\) | 3.43045e23 | + | 4.10818e23i | 0.903401 | + | 1.08188i | ||||
\(887\) | − | 1.11278e23i | − | 0.290416i | −0.989401 | − | 0.145208i | \(-0.953615\pi\) | ||
0.989401 | − | 0.145208i | \(-0.0463851\pi\) | |||||||
\(888\) | −3.50906e23 | + | 1.99250e23i | −0.907585 | + | 0.515341i | ||||
\(889\) | −9.02490e21 | −0.0231328 | ||||||||
\(890\) | 6.43524e22 | − | 5.37361e22i | 0.163473 | − | 0.136504i | ||||
\(891\) | − | 5.68178e21i | − | 0.0143042i | ||||||
\(892\) | 3.90135e22 | + | 7.07187e21i | 0.0973412 | + | 0.0176448i | ||||
\(893\) | 3.88455e23 | 0.960569 | ||||||||
\(894\) | 1.01659e23 | + | 1.21743e23i | 0.249142 | + | 0.298363i | ||||
\(895\) | 6.35497e22i | 0.154358i | ||||||||
\(896\) | 2.30672e23 | − | 3.67001e22i | 0.555305 | − | 0.0883492i | ||||
\(897\) | 1.01776e22 | 0.0242832 | ||||||||
\(898\) | 4.50745e23 | − | 3.76386e23i | 1.06591 | − | 0.890066i | ||||
\(899\) | 6.17570e23i | 1.44747i | ||||||||
\(900\) | 2.52528e22 | − | 1.39312e23i | 0.0586636 | − | 0.323631i | ||||
\(901\) | 1.45918e22 | 0.0335977 | ||||||||
\(902\) | −5.26869e22 | − | 6.30959e22i | −0.120240 | − | 0.143995i | ||||
\(903\) | 2.20250e23i | 0.498212i | ||||||||
\(904\) | −8.53183e22 | − | 1.50257e23i | −0.191291 | − | 0.336890i | ||||
\(905\) | −2.45500e22 | −0.0545585 | ||||||||
\(906\) | 3.31967e23 | − | 2.77202e23i | 0.731255 | − | 0.610619i | ||||
\(907\) | 7.45124e22i | 0.162693i | 0.996686 | + | 0.0813467i | \(0.0259221\pi\) | ||||
−0.996686 | + | 0.0813467i | \(0.974078\pi\) | |||||||
\(908\) | 8.07197e23 | + | 1.46318e23i | 1.74700 | + | 0.316674i | ||||
\(909\) | −1.01178e23 | −0.217059 | ||||||||
\(910\) | −1.65840e22 | − | 1.98604e22i | −0.0352662 | − | 0.0422335i | ||||
\(911\) | − | 6.10002e23i | − | 1.28583i | −0.765936 | − | 0.642916i | \(-0.777724\pi\) | ||
0.765936 | − | 0.642916i | \(-0.222276\pi\) | |||||||
\(912\) | −1.79521e23 | − | 6.72936e22i | −0.375108 | − | 0.140610i | ||||
\(913\) | 1.34703e22 | 0.0279005 | ||||||||
\(914\) | 2.85199e23 | − | 2.38149e23i | 0.585569 | − | 0.488967i | ||||
\(915\) | − | 2.42000e21i | − | 0.00492546i | ||||||
\(916\) | −1.43962e23 | + | 7.94198e23i | −0.290459 | + | 1.60238i | ||||
\(917\) | 2.74550e23 | 0.549119 | ||||||||
\(918\) | 2.32503e22 | + | 2.78437e22i | 0.0460986 | + | 0.0552060i | ||||
\(919\) | − | 2.84863e23i | − | 0.559901i | −0.960014 | − | 0.279951i | \(-0.909682\pi\) | ||
0.960014 | − | 0.279951i | \(-0.0903181\pi\) | |||||||
\(920\) | 2.54875e21 | − | 1.44722e21i | 0.00496620 | − | 0.00281989i | ||||
\(921\) | 4.56119e23 | 0.881051 | ||||||||
\(922\) | 5.31888e23 | − | 4.44142e23i | 1.01853 | − | 0.850499i | ||||
\(923\) | 6.12738e23i | 1.16322i | ||||||||
\(924\) | 2.18504e22 | + | 3.96077e21i | 0.0411230 | + | 0.00745424i | ||||
\(925\) | −9.55997e23 | −1.78370 | ||||||||
\(926\) | −4.54993e23 | − | 5.44883e23i | −0.841621 | − | 1.00789i | ||||
\(927\) | − | 4.62748e22i | − | 0.0848607i | ||||||
\(928\) | 6.70600e23 | − | 2.35029e23i | 1.21921 | − | 0.427304i | ||||
\(929\) | −2.66657e23 | −0.480649 | −0.240324 | − | 0.970693i | \(-0.577254\pi\) | ||||
−0.240324 | + | 0.970693i | \(0.577254\pi\) | |||||||
\(930\) | 3.20262e22 | − | 2.67428e22i | 0.0572325 | − | 0.0477908i | ||||
\(931\) | 2.67802e23i | 0.474478i | ||||||||
\(932\) | 1.60637e22 | − | 8.86190e22i | 0.0282175 | − | 0.155668i | ||||
\(933\) | 1.92031e23 | 0.334439 | ||||||||
\(934\) | 2.71263e23 | + | 3.24854e23i | 0.468398 | + | 0.560937i | ||||
\(935\) | 3.23929e21i | 0.00554570i | ||||||||
\(936\) | −8.23141e22 | − | 1.44966e23i | −0.139723 | − | 0.246071i | ||||
\(937\) | −6.92827e23 | −1.16603 | −0.583013 | − | 0.812463i | \(-0.698126\pi\) | ||||
−0.583013 | + | 0.812463i | \(0.698126\pi\) | |||||||
\(938\) | 2.24051e23 | − | 1.87089e23i | 0.373872 | − | 0.312194i | ||||
\(939\) | − | 1.63111e22i | − | 0.0269872i | ||||||
\(940\) | 9.57132e22 | + | 1.73497e22i | 0.157018 | + | 0.0284622i | ||||
\(941\) | 5.28516e23 | 0.859689 | 0.429845 | − | 0.902903i | \(-0.358568\pi\) | ||||
0.429845 | + | 0.902903i | \(0.358568\pi\) | |||||||
\(942\) | −4.18057e23 | − | 5.00650e23i | −0.674261 | − | 0.807471i | ||||
\(943\) | − | 4.51454e22i | − | 0.0721971i | ||||||
\(944\) | −2.92367e23 | + | 7.79954e23i | −0.463609 | + | 1.23678i | ||||
\(945\) | −7.93305e21 | −0.0124734 | ||||||||
\(946\) | −9.72688e22 | + | 8.12223e22i | −0.151651 | + | 0.126633i | ||||
\(947\) | 6.74753e23i | 1.04315i | 0.853207 | + | 0.521573i | \(0.174655\pi\) | ||||
−0.853207 | + | 0.521573i | \(0.825345\pi\) | |||||||
\(948\) | 6.65725e22 | − | 3.67262e23i | 0.102054 | − | 0.563001i | ||||
\(949\) | −1.18101e23 | −0.179524 | ||||||||
\(950\) | −2.91120e23 | − | 3.48635e23i | −0.438817 | − | 0.525511i | ||||
\(951\) | − | 3.78248e23i | − | 0.565369i | ||||||
\(952\) | −1.23286e23 | + | 7.00040e22i | −0.182734 | + | 0.103759i | ||||
\(953\) | −7.56472e23 | −1.11186 | −0.555929 | − | 0.831229i | \(-0.687638\pi\) | ||||
−0.555929 | + | 0.831229i | \(0.687638\pi\) | |||||||
\(954\) | −1.57818e22 | + | 1.31782e22i | −0.0230022 | + | 0.0192075i | ||||
\(955\) | 2.62692e22i | 0.0379682i | ||||||||
\(956\) | 6.18185e23 | + | 1.12057e23i | 0.886043 | + | 0.160611i | ||||
\(957\) | 6.75581e22 | 0.0960245 | ||||||||
\(958\) | −1.53396e23 | − | 1.83701e23i | −0.216217 | − | 0.258934i | ||||
\(959\) | 5.18368e23i | 0.724585i | ||||||||
\(960\) | −4.12274e22 | − | 2.45988e22i | −0.0571500 | − | 0.0340992i | ||||
\(961\) | −1.85701e23 | −0.255286 | ||||||||
\(962\) | −8.64016e23 | + | 7.21478e23i | −1.17793 | + | 0.983609i | ||||
\(963\) | 2.03097e23i | 0.274595i | ||||||||
\(964\) | −1.03375e23 | + | 5.70291e23i | −0.138612 | + | 0.764681i | ||||
\(965\) | −1.38185e23 | −0.183756 | ||||||||
\(966\) | 7.81704e21 | + | 9.36140e21i | 0.0103092 | + | 0.0123459i | ||||
\(967\) | − | 1.04571e24i | − | 1.36773i | −0.729608 | − | 0.683866i | \(-0.760297\pi\) | ||
0.729608 | − | 0.683866i | \(-0.239703\pi\) | |||||||
\(968\) | −3.74342e23 | − | 6.59267e23i | −0.485585 | − | 0.855181i | ||||
\(969\) | 1.16370e23 | 0.149710 | ||||||||
\(970\) | 1.40891e22 | − | 1.17648e22i | 0.0179766 | − | 0.0150110i | ||||
\(971\) | 1.34646e23i | 0.170388i | 0.996364 | + | 0.0851941i | \(0.0271510\pi\) | ||||
−0.996364 | + | 0.0851941i | \(0.972849\pi\) | |||||||
\(972\) | −5.02929e22 | − | 9.11645e21i | −0.0631214 | − | 0.0114418i | ||||
\(973\) | 1.44570e22 | 0.0179960 | ||||||||
\(974\) | −2.06483e22 | − | 2.47277e22i | −0.0254925 | − | 0.0305289i | ||||
\(975\) | − | 3.94941e23i | − | 0.483610i | ||||||
\(976\) | 5.70622e22 | + | 2.13898e22i | 0.0693027 | + | 0.0259782i | ||||
\(977\) | 1.14732e24 | 1.38207 | 0.691034 | − | 0.722822i | \(-0.257156\pi\) | ||||
0.691034 | + | 0.722822i | \(0.257156\pi\) | |||||||
\(978\) | 5.19074e23 | − | 4.33441e23i | 0.620180 | − | 0.517869i | ||||
\(979\) | 2.00715e23i | 0.237858i | ||||||||
\(980\) | −1.19609e22 | + | 6.59849e22i | −0.0140590 | + | 0.0775597i | ||||
\(981\) | −3.17673e23 | −0.370364 | ||||||||
\(982\) | −2.21560e23 | − | 2.65332e23i | −0.256212 | − | 0.306830i | ||||
\(983\) | 1.23621e23i | 0.141796i | 0.997484 | + | 0.0708980i | \(0.0225865\pi\) | ||||
−0.997484 | + | 0.0708980i | \(0.977414\pi\) | |||||||
\(984\) | −6.43036e23 | + | 3.65126e23i | −0.731602 | + | 0.415415i | ||||
\(985\) | −5.19876e22 | −0.0586692 | ||||||||
\(986\) | −3.31071e23 | + | 2.76454e23i | −0.370600 | + | 0.309462i | ||||
\(987\) | 4.04760e23i | 0.449429i | ||||||||
\(988\) | −5.26220e23 | − | 9.53865e22i | −0.579578 | − | 0.105058i | ||||
\(989\) | −6.95963e22 | −0.0760354 | ||||||||
\(990\) | −2.92549e21 | − | 3.50346e21i | −0.00317042 | − | 0.00379678i | ||||
\(991\) | − | 1.00814e24i | − | 1.08376i | −0.840456 | − | 0.541879i | \(-0.817713\pi\) | ||
0.840456 | − | 0.541879i | \(-0.182287\pi\) | |||||||
\(992\) | 3.47508e23 | + | 9.91533e23i | 0.370571 | + | 1.05734i | ||||
\(993\) | 1.47650e23 | 0.156185 | ||||||||
\(994\) | −5.63600e23 | + | 4.70622e23i | −0.591398 | + | 0.493834i | ||||
\(995\) | 6.22506e22i | 0.0647976i | ||||||||
\(996\) | 2.16132e22 | − | 1.19234e23i | 0.0223174 | − | 0.123119i | ||||
\(997\) | 9.03998e23 | 0.925990 | 0.462995 | − | 0.886361i | \(-0.346775\pi\) | ||||
0.462995 | + | 0.886361i | \(0.346775\pi\) | |||||||
\(998\) | 8.55060e23 | + | 1.02399e24i | 0.868865 | + | 1.04052i | ||||
\(999\) | 3.45123e23i | 0.347896i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 12.17.d.a.7.11 | ✓ | 16 | |
3.2 | odd | 2 | 36.17.d.d.19.6 | 16 | |||
4.3 | odd | 2 | inner | 12.17.d.a.7.12 | yes | 16 | |
12.11 | even | 2 | 36.17.d.d.19.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.17.d.a.7.11 | ✓ | 16 | 1.1 | even | 1 | trivial | |
12.17.d.a.7.12 | yes | 16 | 4.3 | odd | 2 | inner | |
36.17.d.d.19.5 | 16 | 12.11 | even | 2 | |||
36.17.d.d.19.6 | 16 | 3.2 | odd | 2 |