Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,30,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 30, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 30);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 30 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(111.883889004\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.10 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.30.c.a.20.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1978.96i | 0.0854087i | 0.999088 | + | 0.0427043i | \(0.0135973\pi\) | ||||
−0.999088 | + | 0.0427043i | \(0.986403\pi\) | |||||||
\(3\) | 6.63697e6 | − | 4.95792e6i | 0.801146 | − | 0.598469i | ||||
\(4\) | 5.32955e8 | 0.992705 | ||||||||
\(5\) | −2.10087e10 | −1.53934 | −0.769669 | − | 0.638444i | \(-0.779579\pi\) | ||||
−0.769669 | + | 0.638444i | \(0.779579\pi\) | |||||||
\(6\) | 9.81152e9 | + | 1.31343e10i | 0.0511144 | + | 0.0684248i | ||||
\(7\) | 1.76916e12 | + | 2.99987e11i | 0.985927 | + | 0.167179i | ||||
\(8\) | 2.11714e12i | 0.170194i | ||||||||
\(9\) | 1.94684e13 | − | 6.58112e13i | 0.283671 | − | 0.958922i | ||||
\(10\) | − | 4.15753e13i | − | 0.131473i | ||||||
\(11\) | − | 1.97233e15i | − | 1.56598i | −0.622036 | − | 0.782989i | \(-0.713694\pi\) | ||
0.622036 | − | 0.782989i | \(-0.286306\pi\) | |||||||
\(12\) | 3.53721e15 | − | 2.64235e15i | 0.795302 | − | 0.594103i | ||||
\(13\) | − | 2.35122e16i | − | 1.65621i | −0.560577 | − | 0.828103i | \(-0.689420\pi\) | ||
0.560577 | − | 0.828103i | \(-0.310580\pi\) | |||||||
\(14\) | −5.93662e14 | + | 3.50109e15i | −0.0142785 | + | 0.0842067i | ||||
\(15\) | −1.39434e17 | + | 1.04159e17i | −1.23323 | + | 0.921245i | ||||
\(16\) | 2.81938e17 | 0.978169 | ||||||||
\(17\) | −4.82044e17 | −0.694348 | −0.347174 | − | 0.937801i | \(-0.612859\pi\) | ||||
−0.347174 | + | 0.937801i | \(0.612859\pi\) | |||||||
\(18\) | 1.30238e17 | + | 3.85272e16i | 0.0819002 | + | 0.0242279i | ||||
\(19\) | − | 5.67589e17i | − | 0.162970i | −0.996675 | − | 0.0814848i | \(-0.974034\pi\) | ||
0.996675 | − | 0.0814848i | \(-0.0259662\pi\) | |||||||
\(20\) | −1.11967e19 | −1.52811 | ||||||||
\(21\) | 1.32292e19 | − | 6.78033e18i | 0.889923 | − | 0.456112i | ||||
\(22\) | 3.90316e18 | 0.133748 | ||||||||
\(23\) | 7.46696e19i | 1.34304i | 0.740985 | + | 0.671522i | \(0.234359\pi\) | ||||
−0.740985 | + | 0.671522i | \(0.765641\pi\) | |||||||
\(24\) | 1.04966e19 | + | 1.40514e19i | 0.101856 | + | 0.136351i | ||||
\(25\) | 2.55100e20 | 1.36956 | ||||||||
\(26\) | 4.65296e19 | 0.141454 | ||||||||
\(27\) | −1.97075e20 | − | 5.33310e20i | −0.346623 | − | 0.938005i | ||||
\(28\) | 9.42880e20 | + | 1.59879e20i | 0.978735 | + | 0.165959i | ||||
\(29\) | 1.34770e21i | 0.841051i | 0.907281 | + | 0.420526i | \(0.138154\pi\) | ||||
−0.907281 | + | 0.420526i | \(0.861846\pi\) | |||||||
\(30\) | −2.06127e20 | − | 2.75934e20i | −0.0786823 | − | 0.105329i | ||||
\(31\) | 7.84435e20i | 0.186128i | 0.995660 | + | 0.0930641i | \(0.0296662\pi\) | ||||
−0.995660 | + | 0.0930641i | \(0.970334\pi\) | |||||||
\(32\) | 1.69458e21i | 0.253738i | ||||||||
\(33\) | −9.77865e21 | − | 1.30903e22i | −0.937188 | − | 1.25458i | ||||
\(34\) | − | 9.53945e20i | − | 0.0593033i | ||||||
\(35\) | −3.71676e22 | − | 6.30233e21i | −1.51767 | − | 0.257344i | ||||
\(36\) | 1.03758e22 | − | 3.50744e22i | 0.281602 | − | 0.951927i | ||||
\(37\) | −8.59247e22 | −1.56745 | −0.783723 | − | 0.621110i | \(-0.786682\pi\) | ||||
−0.783723 | + | 0.621110i | \(0.786682\pi\) | |||||||
\(38\) | 1.12324e21 | 0.0139190 | ||||||||
\(39\) | −1.16571e23 | − | 1.56050e23i | −0.991187 | − | 1.32686i | ||||
\(40\) | − | 4.44783e22i | − | 0.261986i | ||||||
\(41\) | 1.02991e23 | 0.424066 | 0.212033 | − | 0.977263i | \(-0.431992\pi\) | ||||
0.212033 | + | 0.977263i | \(0.431992\pi\) | |||||||
\(42\) | 1.34180e22 | + | 2.61800e22i | 0.0389559 | + | 0.0760071i | ||||
\(43\) | 2.29840e23 | 0.474387 | 0.237194 | − | 0.971462i | \(-0.423772\pi\) | ||||
0.237194 | + | 0.971462i | \(0.423772\pi\) | |||||||
\(44\) | − | 1.05116e24i | − | 1.55455i | ||||||
\(45\) | −4.09006e23 | + | 1.38261e24i | −0.436665 | + | 1.47610i | ||||
\(46\) | −1.47768e23 | −0.114708 | ||||||||
\(47\) | 1.10078e21 | 0.000625579 | 0.000312789 | − | 1.00000i | \(-0.499900\pi\) | ||||
0.000312789 | 1.00000i | \(0.499900\pi\) | ||||||||
\(48\) | 1.87122e24 | − | 1.39783e24i | 0.783657 | − | 0.585404i | ||||
\(49\) | 3.03992e24 | + | 1.06145e24i | 0.944103 | + | 0.329652i | ||||
\(50\) | 5.04833e23i | 0.116972i | ||||||||
\(51\) | −3.19931e24 | + | 2.38993e24i | −0.556274 | + | 0.415545i | ||||
\(52\) | − | 1.25309e25i | − | 1.64412i | ||||||
\(53\) | − | 1.34593e25i | − | 1.33975i | −0.742474 | − | 0.669875i | \(-0.766348\pi\) | ||
0.742474 | − | 0.669875i | \(-0.233652\pi\) | |||||||
\(54\) | 1.05540e24 | − | 3.90003e23i | 0.0801137 | − | 0.0296046i | ||||
\(55\) | 4.14360e25i | 2.41057i | ||||||||
\(56\) | −6.35114e23 | + | 3.74555e24i | −0.0284528 | + | 0.167799i | ||||
\(57\) | −2.81406e24 | − | 3.76707e24i | −0.0975322 | − | 0.130563i | ||||
\(58\) | −2.66705e24 | −0.0718331 | ||||||||
\(59\) | −4.98939e25 | −1.04880 | −0.524401 | − | 0.851471i | \(-0.675711\pi\) | ||||
−0.524401 | + | 0.851471i | \(0.675711\pi\) | |||||||
\(60\) | −7.43120e25 | + | 5.55122e25i | −1.22424 | + | 0.914525i | ||||
\(61\) | − | 1.41438e26i | − | 1.83351i | −0.399447 | − | 0.916756i | \(-0.630798\pi\) | ||
0.399447 | − | 0.916756i | \(-0.369202\pi\) | |||||||
\(62\) | −1.55236e24 | −0.0158970 | ||||||||
\(63\) | 5.41852e25 | − | 1.10590e26i | 0.439990 | − | 0.898003i | ||||
\(64\) | 1.48011e26 | 0.956498 | ||||||||
\(65\) | 4.93960e26i | 2.54946i | ||||||||
\(66\) | 2.59052e25 | − | 1.93516e25i | 0.107152 | − | 0.0800440i | ||||
\(67\) | 2.07066e26 | 0.688692 | 0.344346 | − | 0.938843i | \(-0.388101\pi\) | ||||
0.344346 | + | 0.938843i | \(0.388101\pi\) | |||||||
\(68\) | −2.56907e26 | −0.689283 | ||||||||
\(69\) | 3.70206e26 | + | 4.95580e26i | 0.803770 | + | 1.07597i | ||||
\(70\) | 1.24720e25 | − | 7.35532e25i | 0.0219794 | − | 0.129622i | ||||
\(71\) | − | 4.38368e24i | − | 0.00628916i | −0.999995 | − | 0.00314458i | \(-0.998999\pi\) | ||
0.999995 | − | 0.00314458i | \(-0.00100095\pi\) | |||||||
\(72\) | 1.39332e26 | + | 4.12174e25i | 0.163203 | + | 0.0482792i | ||||
\(73\) | 1.18319e27i | 1.13468i | 0.823483 | + | 0.567342i | \(0.192028\pi\) | ||||
−0.823483 | + | 0.567342i | \(0.807972\pi\) | |||||||
\(74\) | − | 1.70041e26i | − | 0.133874i | ||||||
\(75\) | 1.69309e27 | − | 1.26477e27i | 1.09722 | − | 0.819638i | ||||
\(76\) | − | 3.02499e26i | − | 0.161781i | ||||||
\(77\) | 5.91673e26 | − | 3.48936e27i | 0.261798 | − | 1.54394i | ||||
\(78\) | 3.08816e26 | − | 2.30690e26i | 0.113326 | − | 0.0846559i | ||||
\(79\) | −4.92576e27 | −1.50273 | −0.751364 | − | 0.659888i | \(-0.770604\pi\) | ||||
−0.751364 | + | 0.659888i | \(0.770604\pi\) | |||||||
\(80\) | −5.92315e27 | −1.50573 | ||||||||
\(81\) | −3.95209e27 | − | 2.56248e27i | −0.839062 | − | 0.544036i | ||||
\(82\) | 2.03815e26i | 0.0362189i | ||||||||
\(83\) | −1.26288e28 | −1.88248 | −0.941241 | − | 0.337736i | \(-0.890339\pi\) | ||||
−0.941241 | + | 0.337736i | \(0.890339\pi\) | |||||||
\(84\) | 7.05054e27 | − | 3.61361e27i | 0.883431 | − | 0.452784i | ||||
\(85\) | 1.01271e28 | 1.06884 | ||||||||
\(86\) | 4.54844e26i | 0.0405168i | ||||||||
\(87\) | 6.68179e27 | + | 8.94465e27i | 0.503343 | + | 0.673805i | ||||
\(88\) | 4.17570e27 | 0.266520 | ||||||||
\(89\) | 3.53689e27 | 0.191631 | 0.0958157 | − | 0.995399i | \(-0.469454\pi\) | ||||
0.0958157 | + | 0.995399i | \(0.469454\pi\) | |||||||
\(90\) | −2.73612e27 | − | 8.09407e26i | −0.126072 | − | 0.0372950i | ||||
\(91\) | 7.05334e27 | − | 4.15967e28i | 0.276882 | − | 1.63290i | ||||
\(92\) | 3.97955e28i | 1.33325i | ||||||||
\(93\) | 3.88916e27 | + | 5.20627e27i | 0.111392 | + | 0.149116i | ||||
\(94\) | 2.17840e24i | 5.34299e-5i | ||||||||
\(95\) | 1.19243e28i | 0.250865i | ||||||||
\(96\) | 8.40157e27 | + | 1.12469e28i | 0.151854 | + | 0.203282i | ||||
\(97\) | 6.07788e28i | 0.945283i | 0.881255 | + | 0.472642i | \(0.156700\pi\) | ||||
−0.881255 | + | 0.472642i | \(0.843300\pi\) | |||||||
\(98\) | −2.10056e27 | + | 6.01588e27i | −0.0281551 | + | 0.0806345i | ||||
\(99\) | −1.29801e29 | − | 3.83982e28i | −1.50165 | − | 0.444222i | ||||
\(100\) | 1.35957e29 | 1.35957 | ||||||||
\(101\) | −7.18680e28 | −0.622123 | −0.311061 | − | 0.950390i | \(-0.600684\pi\) | ||||
−0.311061 | + | 0.950390i | \(0.600684\pi\) | |||||||
\(102\) | −4.72958e27 | − | 6.33131e27i | −0.0354912 | − | 0.0475106i | ||||
\(103\) | − | 1.31814e29i | − | 0.858660i | −0.903148 | − | 0.429330i | \(-0.858750\pi\) | ||
0.903148 | − | 0.429330i | \(-0.141250\pi\) | |||||||
\(104\) | 4.97786e28 | 0.281877 | ||||||||
\(105\) | −2.77927e29 | + | 1.42446e29i | −1.36989 | + | 0.702109i | ||||
\(106\) | 2.66355e28 | 0.114426 | ||||||||
\(107\) | − | 2.73974e29i | − | 1.02717i | −0.858037 | − | 0.513587i | \(-0.828316\pi\) | ||
0.858037 | − | 0.513587i | \(-0.171684\pi\) | |||||||
\(108\) | −1.05032e29 | − | 2.84230e29i | −0.344094 | − | 0.931162i | ||||
\(109\) | 2.85051e28 | 0.0817030 | 0.0408515 | − | 0.999165i | \(-0.486993\pi\) | ||||
0.0408515 | + | 0.999165i | \(0.486993\pi\) | |||||||
\(110\) | −8.20002e28 | −0.205883 | ||||||||
\(111\) | −5.70280e29 | + | 4.26008e29i | −1.25575 | + | 0.938068i | ||||
\(112\) | 4.98793e29 | + | 8.45777e28i | 0.964403 | + | 0.163529i | ||||
\(113\) | − | 2.49842e29i | − | 0.424647i | −0.977199 | − | 0.212324i | \(-0.931897\pi\) | ||
0.977199 | − | 0.212324i | \(-0.0681031\pi\) | |||||||
\(114\) | 7.45488e27 | − | 5.56891e27i | 0.0111512 | − | 0.00833009i | ||||
\(115\) | − | 1.56871e30i | − | 2.06740i | ||||||
\(116\) | 7.18263e29i | 0.834916i | ||||||||
\(117\) | −1.54736e30 | − | 4.57745e29i | −1.58817 | − | 0.469817i | ||||
\(118\) | − | 9.87381e28i | − | 0.0895768i | ||||||
\(119\) | −8.52811e29 | − | 1.44607e29i | −0.684576 | − | 0.116080i | ||||
\(120\) | −2.20520e29 | − | 2.95202e29i | −0.156791 | − | 0.209889i | ||||
\(121\) | −2.30378e30 | −1.45229 | ||||||||
\(122\) | 2.79900e29 | 0.156598 | ||||||||
\(123\) | 6.83548e29 | − | 5.10621e29i | 0.339739 | − | 0.253790i | ||||
\(124\) | 4.18068e29i | 0.184770i | ||||||||
\(125\) | −1.44615e30 | −0.568875 | ||||||||
\(126\) | 2.18853e29 | + | 1.07230e29i | 0.0766972 | + | 0.0375789i | ||||
\(127\) | 1.61971e29 | 0.0506155 | 0.0253078 | − | 0.999680i | \(-0.491943\pi\) | ||||
0.0253078 | + | 0.999680i | \(0.491943\pi\) | |||||||
\(128\) | 1.20268e30i | 0.335432i | ||||||||
\(129\) | 1.52544e30 | − | 1.13953e30i | 0.380053 | − | 0.283906i | ||||
\(130\) | −9.77526e29 | −0.217746 | ||||||||
\(131\) | −4.01899e30 | −0.801093 | −0.400546 | − | 0.916276i | \(-0.631180\pi\) | ||||
−0.400546 | + | 0.916276i | \(0.631180\pi\) | |||||||
\(132\) | −5.21158e30 | − | 6.97654e30i | −0.930352 | − | 1.24543i | ||||
\(133\) | 1.70269e29 | − | 1.00415e30i | 0.0272450 | − | 0.160676i | ||||
\(134\) | 4.09776e29i | 0.0588203i | ||||||||
\(135\) | 4.14028e30 | + | 1.12041e31i | 0.533569 | + | 1.44391i | ||||
\(136\) | − | 1.02055e30i | − | 0.118174i | ||||||
\(137\) | 9.93083e30i | 1.03404i | 0.855973 | + | 0.517020i | \(0.172959\pi\) | ||||
−0.855973 | + | 0.517020i | \(0.827041\pi\) | |||||||
\(138\) | −9.80733e29 | + | 7.32623e29i | −0.0918976 | + | 0.0686489i | ||||
\(139\) | − | 1.76006e31i | − | 1.48530i | −0.669681 | − | 0.742649i | \(-0.733569\pi\) | ||
0.669681 | − | 0.742649i | \(-0.266431\pi\) | |||||||
\(140\) | −1.98087e31 | − | 3.35885e30i | −1.50660 | − | 0.255467i | ||||
\(141\) | 7.30586e27 | − | 5.45759e27i | 0.000501180 | − | 0.000374389i | ||||
\(142\) | 8.67512e27 | 0.000537149 | ||||||||
\(143\) | −4.63738e31 | −2.59358 | ||||||||
\(144\) | 5.48889e30 | − | 1.85547e31i | 0.277478 | − | 0.937988i | ||||
\(145\) | − | 2.83134e31i | − | 1.29466i | ||||||
\(146\) | −2.34149e30 | −0.0969118 | ||||||||
\(147\) | 2.54384e31 | − | 8.02689e30i | 0.953650 | − | 0.300917i | ||||
\(148\) | −4.57939e31 | −1.55601 | ||||||||
\(149\) | − | 2.16357e31i | − | 0.666759i | −0.942793 | − | 0.333380i | \(-0.891811\pi\) | ||
0.942793 | − | 0.333380i | \(-0.108189\pi\) | |||||||
\(150\) | 2.50292e30 | + | 3.35056e30i | 0.0700042 | + | 0.0937118i | ||||
\(151\) | −1.76044e28 | −0.000447151 | −0.000223576 | − | 1.00000i | \(-0.500071\pi\) | ||||
−0.000223576 | 1.00000i | \(0.500071\pi\) | ||||||||
\(152\) | 1.20167e30 | 0.0277365 | ||||||||
\(153\) | −9.38464e30 | + | 3.17239e31i | −0.196966 | + | 0.665825i | ||||
\(154\) | 6.90530e30 | + | 1.17090e30i | 0.131866 | + | 0.0223598i | ||||
\(155\) | − | 1.64799e31i | − | 0.286514i | ||||||
\(156\) | −6.21273e31 | − | 8.31674e31i | −0.983956 | − | 1.31718i | ||||
\(157\) | 6.76929e31i | 0.977233i | 0.872499 | + | 0.488617i | \(0.162498\pi\) | ||||
−0.872499 | + | 0.488617i | \(0.837502\pi\) | |||||||
\(158\) | − | 9.74788e30i | − | 0.128346i | ||||||
\(159\) | −6.67303e31 | − | 8.93293e31i | −0.801798 | − | 1.07334i | ||||
\(160\) | − | 3.56008e31i | − | 0.390589i | ||||||
\(161\) | −2.23999e31 | + | 1.32102e32i | −0.224528 | + | 1.32414i | ||||
\(162\) | 5.07105e30 | − | 7.82102e30i | 0.0464654 | − | 0.0716631i | ||||
\(163\) | 1.32662e32 | 1.11180 | 0.555900 | − | 0.831249i | \(-0.312374\pi\) | ||||
0.555900 | + | 0.831249i | \(0.312374\pi\) | |||||||
\(164\) | 5.48895e31 | 0.420972 | ||||||||
\(165\) | 2.05437e32 | + | 2.75010e32i | 1.44265 | + | 1.93122i | ||||
\(166\) | − | 2.49919e31i | − | 0.160780i | ||||||
\(167\) | 6.46226e31 | 0.381062 | 0.190531 | − | 0.981681i | \(-0.438979\pi\) | ||||
0.190531 | + | 0.981681i | \(0.438979\pi\) | |||||||
\(168\) | 1.43549e31 | + | 2.80080e31i | 0.0776276 | + | 0.151460i | ||||
\(169\) | −3.51284e32 | −1.74302 | ||||||||
\(170\) | 2.00411e31i | 0.0912878i | ||||||||
\(171\) | −3.73537e31 | − | 1.10501e31i | −0.156275 | − | 0.0462297i | ||||
\(172\) | 1.22494e32 | 0.470927 | ||||||||
\(173\) | 1.74835e32 | 0.617959 | 0.308980 | − | 0.951069i | \(-0.400012\pi\) | ||||
0.308980 | + | 0.951069i | \(0.400012\pi\) | |||||||
\(174\) | −1.77011e31 | + | 1.32230e31i | −0.0575488 | + | 0.0429898i | ||||
\(175\) | 4.51312e32 | + | 7.65267e31i | 1.35028 | + | 0.228961i | ||||
\(176\) | − | 5.56075e32i | − | 1.53179i | ||||||
\(177\) | −3.31145e32 | + | 2.47370e32i | −0.840244 | + | 0.627675i | ||||
\(178\) | 6.99936e30i | 0.0163670i | ||||||||
\(179\) | 1.94233e32i | 0.418749i | 0.977836 | + | 0.209375i | \(0.0671428\pi\) | ||||
−0.977836 | + | 0.209375i | \(0.932857\pi\) | |||||||
\(180\) | −2.17982e32 | + | 7.36866e32i | −0.433480 | + | 1.46534i | ||||
\(181\) | 2.90896e31i | 0.0533824i | 0.999644 | + | 0.0266912i | \(0.00849707\pi\) | ||||
−0.999644 | + | 0.0266912i | \(0.991503\pi\) | |||||||
\(182\) | 8.23182e31 | + | 1.39583e31i | 0.139464 | + | 0.0236481i | ||||
\(183\) | −7.01239e32 | − | 9.38721e32i | −1.09730 | − | 1.46891i | ||||
\(184\) | −1.58086e32 | −0.228578 | ||||||||
\(185\) | 1.80516e33 | 2.41283 | ||||||||
\(186\) | −1.03030e31 | + | 7.69650e30i | −0.0127358 | + | 0.00951383i | ||||
\(187\) | 9.50749e32i | 1.08733i | ||||||||
\(188\) | 5.86666e29 | 0.000621016 | ||||||||
\(189\) | −1.88670e32 | − | 1.00263e33i | −0.184930 | − | 0.982752i | ||||
\(190\) | −2.35977e31 | −0.0214261 | ||||||||
\(191\) | − | 7.24655e32i | − | 0.609744i | −0.952393 | − | 0.304872i | \(-0.901386\pi\) | ||
0.952393 | − | 0.304872i | \(-0.0986136\pi\) | |||||||
\(192\) | 9.82344e32 | − | 7.33826e32i | 0.766295 | − | 0.572434i | ||||
\(193\) | 1.23473e33 | 0.893285 | 0.446642 | − | 0.894713i | \(-0.352620\pi\) | ||||
0.446642 | + | 0.894713i | \(0.352620\pi\) | |||||||
\(194\) | −1.20279e32 | −0.0807354 | ||||||||
\(195\) | 2.44901e33 | + | 3.27840e33i | 1.52577 | + | 2.04249i | ||||
\(196\) | 1.62014e33 | + | 5.65703e32i | 0.937216 | + | 0.327247i | ||||
\(197\) | − | 3.28498e32i | − | 0.176511i | −0.996098 | − | 0.0882556i | \(-0.971871\pi\) | ||
0.996098 | − | 0.0882556i | \(-0.0281292\pi\) | |||||||
\(198\) | 7.59884e31 | − | 2.56871e32i | 0.0379404 | − | 0.128254i | ||||
\(199\) | 2.51190e33i | 1.16582i | 0.812536 | + | 0.582911i | \(0.198086\pi\) | ||||
−0.812536 | + | 0.582911i | \(0.801914\pi\) | |||||||
\(200\) | 5.40083e32i | 0.233091i | ||||||||
\(201\) | 1.37429e33 | − | 1.02662e33i | 0.551743 | − | 0.412160i | ||||
\(202\) | − | 1.42224e32i | − | 0.0531347i | ||||||
\(203\) | −4.04292e32 | + | 2.38429e33i | −0.140606 | + | 0.829215i | ||||
\(204\) | −1.70509e33 | + | 1.27373e33i | −0.552216 | + | 0.412514i | ||||
\(205\) | −2.16370e33 | −0.652780 | ||||||||
\(206\) | 2.60854e32 | 0.0733370 | ||||||||
\(207\) | 4.91409e33 | + | 1.45370e33i | 1.28787 | + | 0.380982i | ||||
\(208\) | − | 6.62898e33i | − | 1.62005i | ||||||
\(209\) | −1.11947e33 | −0.255207 | ||||||||
\(210\) | −2.81894e32 | − | 5.50006e32i | −0.0599662 | − | 0.117001i | ||||
\(211\) | −7.51239e33 | −1.49170 | −0.745852 | − | 0.666112i | \(-0.767957\pi\) | ||||
−0.745852 | + | 0.666112i | \(0.767957\pi\) | |||||||
\(212\) | − | 7.17322e33i | − | 1.32998i | ||||||
\(213\) | −2.17339e31 | − | 2.90944e31i | −0.00376386 | − | 0.00503854i | ||||
\(214\) | 5.42183e32 | 0.0877296 | ||||||||
\(215\) | −4.82863e33 | −0.730242 | ||||||||
\(216\) | 1.12909e33 | − | 4.17235e32i | 0.159643 | − | 0.0589932i | ||||
\(217\) | −2.35320e32 | + | 1.38779e33i | −0.0311166 | + | 0.183509i | ||||
\(218\) | 5.64104e31i | 0.00697814i | ||||||||
\(219\) | 5.86618e33 | + | 7.85283e33i | 0.679072 | + | 0.909047i | ||||
\(220\) | 2.20835e34i | 2.39298i | ||||||||
\(221\) | 1.13339e34i | 1.14998i | ||||||||
\(222\) | −8.43052e32 | − | 1.12856e33i | −0.0801191 | − | 0.107252i | ||||
\(223\) | − | 1.18591e34i | − | 1.05592i | −0.849268 | − | 0.527962i | \(-0.822956\pi\) | ||
0.849268 | − | 0.527962i | \(-0.177044\pi\) | |||||||
\(224\) | −5.08350e32 | + | 2.99797e33i | −0.0424196 | + | 0.250167i | ||||
\(225\) | 4.96640e33 | − | 1.67884e34i | 0.388504 | − | 1.31330i | ||||
\(226\) | 4.94427e32 | 0.0362685 | ||||||||
\(227\) | 1.14437e34 | 0.787392 | 0.393696 | − | 0.919241i | \(-0.371196\pi\) | ||||
0.393696 | + | 0.919241i | \(0.371196\pi\) | |||||||
\(228\) | −1.49977e33 | − | 2.00768e33i | −0.0968207 | − | 0.129610i | ||||
\(229\) | − | 1.47875e34i | − | 0.895941i | −0.894048 | − | 0.447971i | \(-0.852147\pi\) | ||
0.894048 | − | 0.447971i | \(-0.147853\pi\) | |||||||
\(230\) | 3.10441e33 | 0.176574 | ||||||||
\(231\) | −1.33730e34 | − | 2.60923e34i | −0.714261 | − | 1.39360i | ||||
\(232\) | −2.85327e33 | −0.143142 | ||||||||
\(233\) | − | 2.51857e34i | − | 1.18712i | −0.804791 | − | 0.593558i | \(-0.797723\pi\) | ||
0.804791 | − | 0.593558i | \(-0.202277\pi\) | |||||||
\(234\) | 9.05859e32 | − | 3.06217e33i | 0.0401265 | − | 0.135644i | ||||
\(235\) | −2.31260e31 | −0.000962977 | ||||||||
\(236\) | −2.65912e34 | −1.04115 | ||||||||
\(237\) | −3.26921e34 | + | 2.44215e34i | −1.20391 | + | 0.899336i | ||||
\(238\) | 2.86171e32 | − | 1.68768e33i | 0.00991424 | − | 0.0584687i | ||||
\(239\) | 1.71355e34i | 0.558635i | 0.960199 | + | 0.279318i | \(0.0901082\pi\) | ||||
−0.960199 | + | 0.279318i | \(0.909892\pi\) | |||||||
\(240\) | −3.93118e34 | + | 2.93665e34i | −1.20631 | + | 0.901133i | ||||
\(241\) | − | 1.04237e34i | − | 0.301145i | −0.988599 | − | 0.150573i | \(-0.951888\pi\) | ||
0.988599 | − | 0.150573i | \(-0.0481118\pi\) | |||||||
\(242\) | − | 4.55908e33i | − | 0.124038i | ||||||
\(243\) | −3.89345e34 | + | 2.58702e33i | −0.997800 | + | 0.0662993i | ||||
\(244\) | − | 7.53801e34i | − | 1.82014i | ||||||
\(245\) | −6.38647e34 | − | 2.22996e34i | −1.45329 | − | 0.507445i | ||||
\(246\) | 1.01050e33 | + | 1.35271e33i | 0.0216759 | + | 0.0290166i | ||||
\(247\) | −1.33452e34 | −0.269911 | ||||||||
\(248\) | −1.66076e33 | −0.0316780 | ||||||||
\(249\) | −8.38172e34 | + | 6.26127e34i | −1.50814 | + | 1.12661i | ||||
\(250\) | − | 2.86186e33i | − | 0.0485869i | ||||||
\(251\) | 6.64584e34 | 1.06483 | 0.532416 | − | 0.846483i | \(-0.321284\pi\) | ||||
0.532416 | + | 0.846483i | \(0.321284\pi\) | |||||||
\(252\) | 2.88782e34 | − | 5.89394e34i | 0.436780 | − | 0.891452i | ||||
\(253\) | 1.47273e35 | 2.10318 | ||||||||
\(254\) | 3.20534e32i | 0.00432300i | ||||||||
\(255\) | 6.72133e34 | − | 5.02094e34i | 0.856293 | − | 0.639664i | ||||
\(256\) | 7.70827e34 | 0.927849 | ||||||||
\(257\) | −9.04327e34 | −1.02871 | −0.514357 | − | 0.857576i | \(-0.671970\pi\) | ||||
−0.514357 | + | 0.857576i | \(0.671970\pi\) | |||||||
\(258\) | 2.25508e33 | + | 3.01879e33i | 0.0242480 | + | 0.0324599i | ||||
\(259\) | −1.52014e35 | − | 2.57763e34i | −1.54539 | − | 0.262043i | ||||
\(260\) | 2.63258e35i | 2.53086i | ||||||||
\(261\) | 8.86938e34 | + | 2.62376e34i | 0.806503 | + | 0.238582i | ||||
\(262\) | − | 7.95341e33i | − | 0.0684203i | ||||||
\(263\) | − | 6.75085e34i | − | 0.549541i | −0.961510 | − | 0.274770i | \(-0.911398\pi\) | ||
0.961510 | − | 0.274770i | \(-0.0886018\pi\) | |||||||
\(264\) | 2.77140e34 | − | 2.07028e34i | 0.213522 | − | 0.159504i | ||||
\(265\) | 2.82763e35i | 2.06233i | ||||||||
\(266\) | 1.98718e33 | + | 3.36956e32i | 0.0137231 | + | 0.00232696i | ||||
\(267\) | 2.34742e34 | − | 1.75356e34i | 0.153525 | − | 0.114685i | ||||
\(268\) | 1.10357e35 | 0.683668 | ||||||||
\(269\) | 1.02148e35 | 0.599546 | 0.299773 | − | 0.954011i | \(-0.403089\pi\) | ||||
0.299773 | + | 0.954011i | \(0.403089\pi\) | |||||||
\(270\) | −2.21725e34 | + | 8.19345e33i | −0.123322 | + | 0.0455714i | ||||
\(271\) | − | 1.68808e35i | − | 0.889896i | −0.895556 | − | 0.444948i | \(-0.853222\pi\) | ||
0.895556 | − | 0.444948i | \(-0.146778\pi\) | |||||||
\(272\) | −1.35906e35 | −0.679190 | ||||||||
\(273\) | −1.59420e35 | − | 3.11046e35i | −0.755414 | − | 1.47389i | ||||
\(274\) | −1.96527e34 | −0.0883160 | ||||||||
\(275\) | − | 5.03142e35i | − | 2.14470i | ||||||
\(276\) | 1.97303e35 | + | 2.64122e35i | 0.797906 | + | 1.06813i | ||||
\(277\) | −2.12651e35 | −0.816039 | −0.408019 | − | 0.912973i | \(-0.633780\pi\) | ||||
−0.408019 | + | 0.912973i | \(0.633780\pi\) | |||||||
\(278\) | 3.48309e34 | 0.126857 | ||||||||
\(279\) | 5.16246e34 | + | 1.52717e34i | 0.178482 | + | 0.0527992i | ||||
\(280\) | 1.33429e34 | − | 7.86891e34i | 0.0437985 | − | 0.258299i | ||||
\(281\) | 1.60703e35i | 0.500937i | 0.968125 | + | 0.250469i | \(0.0805847\pi\) | ||||
−0.968125 | + | 0.250469i | \(0.919415\pi\) | |||||||
\(282\) | 1.08003e31 | + | 1.44580e31i | 3.19761e−5 | + | 4.28051e-5i | ||||
\(283\) | 2.55313e35i | 0.718075i | 0.933323 | + | 0.359038i | \(0.116895\pi\) | ||||
−0.933323 | + | 0.359038i | \(0.883105\pi\) | |||||||
\(284\) | − | 2.33630e33i | − | 0.00624328i | ||||||
\(285\) | 5.91197e34 | + | 7.91412e34i | 0.150135 | + | 0.200980i | ||||
\(286\) | − | 9.17718e34i | − | 0.221514i | ||||||
\(287\) | 1.82207e35 | + | 3.08959e34i | 0.418098 | + | 0.0708947i | ||||
\(288\) | 1.11522e35 | + | 3.29907e34i | 0.243315 | + | 0.0719782i | ||||
\(289\) | −2.49602e35 | −0.517881 | ||||||||
\(290\) | 5.60311e34 | 0.110575 | ||||||||
\(291\) | 3.01336e35 | + | 4.03387e35i | 0.565722 | + | 0.757310i | ||||
\(292\) | 6.30589e35i | 1.12641i | ||||||||
\(293\) | 2.44043e35 | 0.414845 | 0.207422 | − | 0.978251i | \(-0.433493\pi\) | ||||
0.207422 | + | 0.978251i | \(0.433493\pi\) | |||||||
\(294\) | 1.58849e34 | + | 5.03416e34i | 0.0257009 | + | 0.0814500i | ||||
\(295\) | 1.04821e36 | 1.61446 | ||||||||
\(296\) | − | 1.81915e35i | − | 0.266771i | ||||||
\(297\) | −1.05186e36 | + | 3.88697e35i | −1.46889 | + | 0.542803i | ||||
\(298\) | 4.28161e34 | 0.0569470 | ||||||||
\(299\) | 1.75564e36 | 2.22436 | ||||||||
\(300\) | 9.02342e35 | − | 6.74063e35i | 1.08921 | − | 0.813659i | ||||
\(301\) | 4.06623e35 | + | 6.89489e34i | 0.467711 | + | 0.0793073i | ||||
\(302\) | − | 3.48383e31i | − | 3.81906e-5i | ||||||
\(303\) | −4.76986e35 | + | 3.56316e35i | −0.498411 | + | 0.372321i | ||||
\(304\) | − | 1.60025e35i | − | 0.159412i | ||||||
\(305\) | 2.97143e36i | 2.82239i | ||||||||
\(306\) | −6.27802e34 | − | 1.85718e34i | −0.0568672 | − | 0.0168226i | ||||
\(307\) | 8.70461e35i | 0.752043i | 0.926611 | + | 0.376022i | \(0.122708\pi\) | ||||
−0.926611 | + | 0.376022i | \(0.877292\pi\) | |||||||
\(308\) | 3.15335e35 | − | 1.85967e36i | 0.259888 | − | 1.53268i | ||||
\(309\) | −6.53522e35 | − | 8.74844e35i | −0.513881 | − | 0.687912i | ||||
\(310\) | 3.26131e34 | 0.0244708 | ||||||||
\(311\) | 1.19319e36 | 0.854446 | 0.427223 | − | 0.904146i | \(-0.359492\pi\) | ||||
0.427223 | + | 0.904146i | \(0.359492\pi\) | |||||||
\(312\) | 3.30379e35 | − | 2.46798e35i | 0.225824 | − | 0.168694i | ||||
\(313\) | − | 1.55805e35i | − | 0.101669i | −0.998707 | − | 0.0508345i | \(-0.983812\pi\) | ||
0.998707 | − | 0.0508345i | \(-0.0161881\pi\) | |||||||
\(314\) | −1.33961e35 | −0.0834642 | ||||||||
\(315\) | −1.13836e36 | + | 2.32335e36i | −0.677293 | + | 1.38233i | ||||
\(316\) | −2.62521e36 | −1.49177 | ||||||||
\(317\) | − | 2.35251e36i | − | 1.27694i | −0.769645 | − | 0.638472i | \(-0.779567\pi\) | ||
0.769645 | − | 0.638472i | \(-0.220433\pi\) | |||||||
\(318\) | 1.76779e35 | − | 1.32057e35i | 0.0916722 | − | 0.0684805i | ||||
\(319\) | 2.65811e36 | 1.31707 | ||||||||
\(320\) | −3.10951e36 | −1.47237 | ||||||||
\(321\) | −1.35834e36 | − | 1.81836e36i | −0.614731 | − | 0.822917i | ||||
\(322\) | −2.61425e35 | − | 4.43285e34i | −0.113093 | − | 0.0191766i | ||||
\(323\) | 2.73603e35i | 0.113158i | ||||||||
\(324\) | −2.10628e36 | − | 1.36569e36i | −0.832941 | − | 0.540068i | ||||
\(325\) | − | 5.99796e36i | − | 2.26827i | ||||||
\(326\) | 2.62533e35i | 0.0949573i | ||||||||
\(327\) | 1.89187e35 | − | 1.41326e35i | 0.0654560 | − | 0.0488967i | ||||
\(328\) | 2.18046e35i | 0.0721736i | ||||||||
\(329\) | 1.94745e33 | + | 3.30220e32i | 0.000616775 | + | 0.000104583i | ||||
\(330\) | −5.44233e35 | + | 4.06551e35i | −0.164943 | + | 0.123215i | ||||
\(331\) | 2.47394e36 | 0.717600 | 0.358800 | − | 0.933414i | \(-0.383186\pi\) | ||||
0.358800 | + | 0.933414i | \(0.383186\pi\) | |||||||
\(332\) | −6.73059e36 | −1.86875 | ||||||||
\(333\) | −1.67282e36 | + | 5.65480e36i | −0.444639 | + | 1.50306i | ||||
\(334\) | 1.27886e35i | 0.0325460i | ||||||||
\(335\) | −4.35019e36 | −1.06013 | ||||||||
\(336\) | 3.72980e36 | − | 1.91163e36i | 0.870495 | − | 0.446154i | ||||
\(337\) | 8.95109e35 | 0.200098 | 0.100049 | − | 0.994983i | \(-0.468100\pi\) | ||||
0.100049 | + | 0.994983i | \(0.468100\pi\) | |||||||
\(338\) | − | 6.95177e35i | − | 0.148869i | ||||||
\(339\) | −1.23870e36 | − | 1.65820e36i | −0.254138 | − | 0.340205i | ||||
\(340\) | 5.39729e36 | 1.06104 | ||||||||
\(341\) | 1.54716e36 | 0.291473 | ||||||||
\(342\) | 2.18676e34 | − | 7.39214e34i | 0.00394842 | − | 0.0133472i | ||||
\(343\) | 5.05968e36 | + | 2.78980e36i | 0.875705 | + | 0.482846i | ||||
\(344\) | 4.86604e35i | 0.0807380i | ||||||||
\(345\) | −7.77754e36 | − | 1.04115e37i | −1.23727 | − | 1.65629i | ||||
\(346\) | 3.45991e35i | 0.0527791i | ||||||||
\(347\) | 7.30251e36i | 1.06830i | 0.845388 | + | 0.534152i | \(0.179369\pi\) | ||||
−0.845388 | + | 0.534152i | \(0.820631\pi\) | |||||||
\(348\) | 3.56109e36 | + | 4.76710e36i | 0.499671 | + | 0.668890i | ||||
\(349\) | − | 6.48377e36i | − | 0.872688i | −0.899780 | − | 0.436344i | \(-0.856273\pi\) | ||
0.899780 | − | 0.436344i | \(-0.143727\pi\) | |||||||
\(350\) | −1.51443e35 | + | 8.93128e35i | −0.0195552 | + | 0.115326i | ||||
\(351\) | −1.25393e37 | + | 4.63366e36i | −1.55353 | + | 0.574078i | ||||
\(352\) | 3.34226e36 | 0.397349 | ||||||||
\(353\) | −7.12394e36 | −0.812806 | −0.406403 | − | 0.913694i | \(-0.633217\pi\) | ||||
−0.406403 | + | 0.913694i | \(0.633217\pi\) | |||||||
\(354\) | −4.89535e35 | − | 6.55322e35i | −0.0536089 | − | 0.0717641i | ||||
\(355\) | 9.20953e34i | 0.00968114i | ||||||||
\(356\) | 1.88500e36 | 0.190233 | ||||||||
\(357\) | −6.37703e36 | + | 3.26842e36i | −0.617916 | + | 0.316700i | ||||
\(358\) | −3.84379e35 | −0.0357648 | ||||||||
\(359\) | 9.29988e36i | 0.831013i | 0.909590 | + | 0.415507i | \(0.136396\pi\) | ||||
−0.909590 | + | 0.415507i | \(0.863604\pi\) | |||||||
\(360\) | −2.92717e36 | − | 8.65924e35i | −0.251224 | − | 0.0743179i | ||||
\(361\) | 1.18077e37 | 0.973441 | ||||||||
\(362\) | −5.75670e34 | −0.00455932 | ||||||||
\(363\) | −1.52901e37 | + | 1.14219e37i | −1.16349 | + | 0.869148i | ||||
\(364\) | 3.75911e36 | − | 2.21692e37i | 0.274862 | − | 1.62099i | ||||
\(365\) | − | 2.48574e37i | − | 1.74666i | ||||||
\(366\) | 1.85769e36 | − | 1.38772e36i | 0.125458 | − | 0.0937189i | ||||
\(367\) | 1.60683e36i | 0.104306i | 0.998639 | + | 0.0521532i | \(0.0166084\pi\) | ||||
−0.998639 | + | 0.0521532i | \(0.983392\pi\) | |||||||
\(368\) | 2.10522e37i | 1.31372i | ||||||||
\(369\) | 2.00507e36 | − | 6.77796e36i | 0.120295 | − | 0.406646i | ||||
\(370\) | 3.57235e36i | 0.206076i | ||||||||
\(371\) | 4.03763e36 | − | 2.38117e37i | 0.223977 | − | 1.32090i | ||||
\(372\) | 2.07275e36 | + | 2.77471e36i | 0.110579 | + | 0.148028i | ||||
\(373\) | −1.00669e37 | −0.516554 | −0.258277 | − | 0.966071i | \(-0.583155\pi\) | ||||
−0.258277 | + | 0.966071i | \(0.583155\pi\) | |||||||
\(374\) | −1.88149e36 | −0.0928677 | ||||||||
\(375\) | −9.59803e36 | + | 7.16988e36i | −0.455752 | + | 0.340454i | ||||
\(376\) | 2.33051e33i | 0.000106470i | ||||||||
\(377\) | 3.16874e37 | 1.39295 | ||||||||
\(378\) | 1.98416e36 | − | 3.73371e35i | 0.0839355 | − | 0.0157946i | ||||
\(379\) | 3.58578e37 | 1.45987 | 0.729937 | − | 0.683515i | \(-0.239550\pi\) | ||||
0.729937 | + | 0.683515i | \(0.239550\pi\) | |||||||
\(380\) | 6.35511e36i | 0.249035i | ||||||||
\(381\) | 1.07500e36 | − | 8.03040e35i | 0.0405504 | − | 0.0302918i | ||||
\(382\) | 1.43406e36 | 0.0520774 | ||||||||
\(383\) | 1.48831e37 | 0.520369 | 0.260184 | − | 0.965559i | \(-0.416217\pi\) | ||||
0.260184 | + | 0.965559i | \(0.416217\pi\) | |||||||
\(384\) | 5.96277e36 | + | 7.98213e36i | 0.200745 | + | 0.268730i | ||||
\(385\) | −1.24303e37 | + | 7.33068e37i | −0.402995 | + | 2.37664i | ||||
\(386\) | 2.44347e36i | 0.0762943i | ||||||||
\(387\) | 4.47462e36 | − | 1.51260e37i | 0.134570 | − | 0.454900i | ||||
\(388\) | 3.23923e37i | 0.938388i | ||||||||
\(389\) | − | 6.86856e37i | − | 1.91689i | −0.285281 | − | 0.958444i | \(-0.592087\pi\) | ||
0.285281 | − | 0.958444i | \(-0.407913\pi\) | |||||||
\(390\) | −6.48781e36 | + | 4.84650e36i | −0.174446 | + | 0.130314i | ||||
\(391\) | − | 3.59940e37i | − | 0.932540i | ||||||
\(392\) | −2.24723e36 | + | 6.43594e36i | −0.0561048 | + | 0.160681i | ||||
\(393\) | −2.66739e37 | + | 1.99258e37i | −0.641793 | + | 0.479429i | ||||
\(394\) | 6.50084e35 | 0.0150756 | ||||||||
\(395\) | 1.03484e38 | 2.31321 | ||||||||
\(396\) | −6.91782e37 | − | 2.04645e37i | −1.49070 | − | 0.440982i | ||||
\(397\) | − | 2.07347e37i | − | 0.430761i | −0.976530 | − | 0.215380i | \(-0.930901\pi\) | ||
0.976530 | − | 0.215380i | \(-0.0690992\pi\) | |||||||
\(398\) | −4.97094e36 | −0.0995712 | ||||||||
\(399\) | −3.84844e36 | − | 7.50872e36i | −0.0743323 | − | 0.145030i | ||||
\(400\) | 7.19225e37 | 1.33966 | ||||||||
\(401\) | 2.55625e37i | 0.459209i | 0.973284 | + | 0.229605i | \(0.0737433\pi\) | ||||
−0.973284 | + | 0.229605i | \(0.926257\pi\) | |||||||
\(402\) | 2.03164e36 | + | 2.71967e36i | 0.0352021 | + | 0.0471236i | ||||
\(403\) | 1.84438e37 | 0.308267 | ||||||||
\(404\) | −3.83024e37 | −0.617584 | ||||||||
\(405\) | 8.30282e37 | + | 5.38343e37i | 1.29160 | + | 0.837455i | ||||
\(406\) | −4.71842e36 | − | 8.00078e35i | −0.0708221 | − | 0.0120089i | ||||
\(407\) | 1.69472e38i | 2.45459i | ||||||||
\(408\) | −5.05983e36 | − | 6.77339e36i | −0.0707234 | − | 0.0946747i | ||||
\(409\) | 5.28502e37i | 0.712950i | 0.934305 | + | 0.356475i | \(0.116021\pi\) | ||||
−0.934305 | + | 0.356475i | \(0.883979\pi\) | |||||||
\(410\) | − | 4.28188e36i | − | 0.0557531i | ||||||
\(411\) | 4.92363e37 | + | 6.59107e37i | 0.618841 | + | 0.828418i | ||||
\(412\) | − | 7.02508e37i | − | 0.852396i | ||||||
\(413\) | −8.82702e37 | − | 1.49675e37i | −1.03404 | − | 0.175337i | ||||
\(414\) | −2.87681e36 | + | 9.72479e36i | −0.0325392 | + | 0.109996i | ||||
\(415\) | 2.65315e38 | 2.89777 | ||||||||
\(416\) | 3.98432e37 | 0.420243 | ||||||||
\(417\) | −8.72625e37 | − | 1.16815e38i | −0.888904 | − | 1.18994i | ||||
\(418\) | − | 2.21539e36i | − | 0.0217969i | ||||||
\(419\) | −5.82158e37 | −0.553271 | −0.276635 | − | 0.960975i | \(-0.589219\pi\) | ||||
−0.276635 | + | 0.960975i | \(0.589219\pi\) | |||||||
\(420\) | −1.48122e38 | + | 7.59172e37i | −1.35990 | + | 0.696988i | ||||
\(421\) | 8.94985e37 | 0.793826 | 0.396913 | − | 0.917856i | \(-0.370081\pi\) | ||||
0.396913 | + | 0.917856i | \(0.370081\pi\) | |||||||
\(422\) | − | 1.48667e37i | − | 0.127404i | ||||||
\(423\) | 2.14305e34 | − | 7.24437e34i | 0.000177459 | − | 0.000599881i | ||||
\(424\) | 2.84953e37 | 0.228018 | ||||||||
\(425\) | −1.22969e38 | −0.950950 | ||||||||
\(426\) | 5.75766e34 | − | 4.30106e34i | 0.000430335 | − | 0.000321467i | ||||
\(427\) | 4.24296e37 | − | 2.50226e38i | 0.306524 | − | 1.80771i | ||||
\(428\) | − | 1.46016e38i | − | 1.01968i | ||||||
\(429\) | −3.07781e38 | + | 2.29917e38i | −2.07784 | + | 1.55218i | ||||
\(430\) | − | 9.55567e36i | − | 0.0623690i | ||||||
\(431\) | − | 1.43236e38i | − | 0.903922i | −0.892038 | − | 0.451961i | \(-0.850725\pi\) | ||
0.892038 | − | 0.451961i | \(-0.149275\pi\) | |||||||
\(432\) | −5.55629e37 | − | 1.50360e38i | −0.339056 | − | 0.917527i | ||||
\(433\) | 1.76466e38i | 1.04132i | 0.853763 | + | 0.520662i | \(0.174315\pi\) | ||||
−0.853763 | + | 0.520662i | \(0.825685\pi\) | |||||||
\(434\) | −2.74637e36 | − | 4.65689e35i | −0.0156732 | − | 0.00265763i | ||||
\(435\) | −1.40376e38 | − | 1.87915e38i | −0.774814 | − | 1.03721i | ||||
\(436\) | 1.51919e37 | 0.0811070 | ||||||||
\(437\) | 4.23816e37 | 0.218875 | ||||||||
\(438\) | −1.55404e37 | + | 1.16089e37i | −0.0776405 | + | 0.0579986i | ||||
\(439\) | − | 4.44385e36i | − | 0.0214795i | −0.999942 | − | 0.0107397i | \(-0.996581\pi\) | ||
0.999942 | − | 0.0107397i | \(-0.00341863\pi\) | |||||||
\(440\) | −8.77260e37 | −0.410265 | ||||||||
\(441\) | 1.29038e38 | − | 1.79396e38i | 0.583924 | − | 0.811808i | ||||
\(442\) | −2.24293e37 | −0.0982185 | ||||||||
\(443\) | 5.30865e37i | 0.224973i | 0.993653 | + | 0.112486i | \(0.0358815\pi\) | ||||
−0.993653 | + | 0.112486i | \(0.964119\pi\) | |||||||
\(444\) | −3.03933e38 | + | 2.27043e38i | −1.24659 | + | 0.931225i | ||||
\(445\) | −7.43054e37 | −0.294985 | ||||||||
\(446\) | 2.34687e37 | 0.0901850 | ||||||||
\(447\) | −1.07268e38 | − | 1.43595e38i | −0.399034 | − | 0.534172i | ||||
\(448\) | 2.61854e38 | + | 4.44013e37i | 0.943037 | + | 0.159906i | ||||
\(449\) | − | 1.24111e38i | − | 0.432750i | −0.976310 | − | 0.216375i | \(-0.930577\pi\) | ||
0.976310 | − | 0.216375i | \(-0.0694234\pi\) | |||||||
\(450\) | 3.32236e37 | + | 9.82831e36i | 0.112167 | + | 0.0331816i | ||||
\(451\) | − | 2.03132e38i | − | 0.664078i | ||||||
\(452\) | − | 1.33155e38i | − | 0.421550i | ||||||
\(453\) | −1.16840e35 | + | 8.72810e34i | −0.000358234 | + | 0.000267606i | ||||
\(454\) | 2.26466e37i | 0.0672501i | ||||||||
\(455\) | −1.48181e38 | + | 8.73892e38i | −0.426215 | + | 2.51358i | ||||
\(456\) | 7.97542e36 | − | 5.95776e36i | 0.0222210 | − | 0.0165994i | ||||
\(457\) | −1.68118e38 | −0.453762 | −0.226881 | − | 0.973922i | \(-0.572853\pi\) | ||||
−0.226881 | + | 0.973922i | \(0.572853\pi\) | |||||||
\(458\) | 2.92638e37 | 0.0765212 | ||||||||
\(459\) | 9.49987e37 | + | 2.57079e38i | 0.240677 | + | 0.651302i | ||||
\(460\) | − | 8.36051e38i | − | 2.05232i | ||||||
\(461\) | 4.79870e38 | 1.14146 | 0.570729 | − | 0.821138i | \(-0.306661\pi\) | ||||
0.570729 | + | 0.821138i | \(0.306661\pi\) | |||||||
\(462\) | 5.16355e37 | − | 2.64647e37i | 0.119025 | − | 0.0610040i | ||||
\(463\) | 9.50054e37 | 0.212238 | 0.106119 | − | 0.994353i | \(-0.466158\pi\) | ||||
0.106119 | + | 0.994353i | \(0.466158\pi\) | |||||||
\(464\) | 3.79968e38i | 0.822691i | ||||||||
\(465\) | −8.17062e37 | − | 1.09377e38i | −0.171470 | − | 0.229540i | ||||
\(466\) | 4.98415e37 | 0.101390 | ||||||||
\(467\) | −5.35352e38 | −1.05571 | −0.527856 | − | 0.849334i | \(-0.677004\pi\) | ||||
−0.527856 | + | 0.849334i | \(0.677004\pi\) | |||||||
\(468\) | −8.24674e38 | − | 2.43957e38i | −1.57659 | − | 0.466390i | ||||
\(469\) | 3.66333e38 | + | 6.21172e37i | 0.679000 | + | 0.115135i | ||||
\(470\) | − | 4.57653e34i | − | 8.22466e-5i | ||||||
\(471\) | 3.35616e38 | + | 4.49276e38i | 0.584843 | + | 0.782907i | ||||
\(472\) | − | 1.05633e38i | − | 0.178500i | ||||||
\(473\) | − | 4.53320e38i | − | 0.742880i | ||||||
\(474\) | −4.83292e37 | − | 6.46964e37i | −0.0768111 | − | 0.102824i | ||||
\(475\) | − | 1.44792e38i | − | 0.223196i | ||||||
\(476\) | −4.54509e38 | − | 7.70688e37i | −0.679582 | − | 0.115233i | ||||
\(477\) | −8.85775e38 | − | 2.62032e38i | −1.28472 | − | 0.380048i | ||||
\(478\) | −3.39105e37 | −0.0477123 | ||||||||
\(479\) | 4.79011e38 | 0.653854 | 0.326927 | − | 0.945050i | \(-0.393987\pi\) | ||||
0.326927 | + | 0.945050i | \(0.393987\pi\) | |||||||
\(480\) | −1.76506e38 | − | 2.36282e38i | −0.233755 | − | 0.312919i | ||||
\(481\) | 2.02028e39i | 2.59601i | ||||||||
\(482\) | 2.06281e37 | 0.0257204 | ||||||||
\(483\) | 5.06285e38 | + | 9.87816e38i | 0.612578 | + | 1.19521i | ||||
\(484\) | −1.22781e39 | −1.44169 | ||||||||
\(485\) | − | 1.27688e39i | − | 1.45511i | ||||||
\(486\) | −5.11961e36 | − | 7.70497e37i | −0.00566253 | − | 0.0852207i | ||||
\(487\) | 8.62466e38 | 0.925917 | 0.462959 | − | 0.886380i | \(-0.346788\pi\) | ||||
0.462959 | + | 0.886380i | \(0.346788\pi\) | |||||||
\(488\) | 2.99444e38 | 0.312053 | ||||||||
\(489\) | 8.80474e38 | − | 6.57728e38i | 0.890714 | − | 0.665377i | ||||
\(490\) | 4.41300e37 | − | 1.26386e38i | 0.0433402 | − | 0.124124i | ||||
\(491\) | − | 3.03296e38i | − | 0.289191i | −0.989491 | − | 0.144596i | \(-0.953812\pi\) | ||
0.989491 | − | 0.144596i | \(-0.0461881\pi\) | |||||||
\(492\) | 3.64300e38 | − | 2.72138e38i | 0.337260 | − | 0.251939i | ||||
\(493\) | − | 6.49651e38i | − | 0.583982i | ||||||
\(494\) | − | 2.64097e37i | − | 0.0230528i | ||||||
\(495\) | 2.72695e39 | + | 8.06695e38i | 2.31155 | + | 0.683808i | ||||
\(496\) | 2.21162e38i | 0.182065i | ||||||||
\(497\) | 1.31505e36 | − | 7.75541e36i | 0.00105141 | − | 0.00620065i | ||||
\(498\) | −1.23908e38 | − | 1.65871e38i | −0.0962219 | − | 0.128809i | ||||
\(499\) | −6.83045e36 | −0.00515219 | −0.00257609 | − | 0.999997i | \(-0.500820\pi\) | ||||
−0.00257609 | + | 0.999997i | \(0.500820\pi\) | |||||||
\(500\) | −7.70730e38 | −0.564725 | ||||||||
\(501\) | 4.28898e38 | − | 3.20394e38i | 0.305286 | − | 0.228054i | ||||
\(502\) | 1.31519e38i | 0.0909459i | ||||||||
\(503\) | 1.47544e39 | 0.991257 | 0.495628 | − | 0.868535i | \(-0.334938\pi\) | ||||
0.495628 | + | 0.868535i | \(0.334938\pi\) | |||||||
\(504\) | 2.34135e38 | + | 1.14718e38i | 0.152835 | + | 0.0748838i | ||||
\(505\) | 1.50985e39 | 0.957656 | ||||||||
\(506\) | 2.91447e38i | 0.179630i | ||||||||
\(507\) | −2.33146e39 | + | 1.74164e39i | −1.39641 | + | 1.04314i | ||||
\(508\) | 8.63233e37 | 0.0502463 | ||||||||
\(509\) | −1.76025e38 | −0.0995790 | −0.0497895 | − | 0.998760i | \(-0.515855\pi\) | ||||
−0.0497895 | + | 0.998760i | \(0.515855\pi\) | |||||||
\(510\) | 9.93623e37 | + | 1.33012e38i | 0.0546329 | + | 0.0731349i | ||||
\(511\) | −3.54943e38 | + | 2.09326e39i | −0.189695 | + | 1.11871i | ||||
\(512\) | 7.98225e38i | 0.414678i | ||||||||
\(513\) | −3.02701e38 | + | 1.11858e38i | −0.152866 | + | 0.0564890i | ||||
\(514\) | − | 1.78963e38i | − | 0.0878612i | ||||||
\(515\) | 2.76923e39i | 1.32177i | ||||||||
\(516\) | 8.12991e38 | − | 6.07317e38i | 0.377281 | − | 0.281835i | ||||
\(517\) | − | 2.17110e36i | − | 0.000979643i | ||||||
\(518\) | 5.10102e37 | − | 3.00830e38i | 0.0223808 | − | 0.131989i | ||||
\(519\) | 1.16038e39 | − | 8.66818e38i | 0.495076 | − | 0.369829i | ||||
\(520\) | −1.04578e39 | −0.433903 | ||||||||
\(521\) | 4.59666e39 | 1.85479 | 0.927397 | − | 0.374079i | \(-0.122041\pi\) | ||||
0.927397 | + | 0.374079i | \(0.122041\pi\) | |||||||
\(522\) | −5.19232e37 | + | 1.75521e38i | −0.0203770 | + | 0.0688823i | ||||
\(523\) | − | 1.84113e39i | − | 0.702766i | −0.936232 | − | 0.351383i | \(-0.885712\pi\) | ||
0.936232 | − | 0.351383i | \(-0.114288\pi\) | |||||||
\(524\) | −2.14194e39 | −0.795249 | ||||||||
\(525\) | 3.37476e39 | − | 1.72966e39i | 1.21880 | − | 0.624672i | ||||
\(526\) | 1.33597e38 | 0.0469355 | ||||||||
\(527\) | − | 3.78132e38i | − | 0.129238i | ||||||
\(528\) | −2.75697e39 | − | 3.69065e39i | −0.916729 | − | 1.22719i | ||||
\(529\) | −2.48449e39 | −0.803768 | ||||||||
\(530\) | −5.59577e38 | −0.176141 | ||||||||
\(531\) | −9.71357e38 | + | 3.28358e39i | −0.297515 | + | 1.00572i | ||||
\(532\) | 9.07457e37 | − | 5.35168e38i | 0.0270463 | − | 0.159504i | ||||
\(533\) | − | 2.42154e39i | − | 0.702340i | ||||||
\(534\) | 3.47023e37 | + | 4.64546e37i | 0.00979512 | + | 0.0131123i | ||||
\(535\) | 5.75583e39i | 1.58117i | ||||||||
\(536\) | 4.38389e38i | 0.117211i | ||||||||
\(537\) | 9.62991e38 | + | 1.28912e39i | 0.250608 | + | 0.335479i | ||||
\(538\) | 2.02147e38i | 0.0512064i | ||||||||
\(539\) | 2.09352e39 | − | 5.99573e39i | 0.516227 | − | 1.47844i | ||||
\(540\) | 2.20658e39 | + | 5.97130e39i | 0.529677 | + | 1.43337i | ||||
\(541\) | −3.87248e39 | −0.904959 | −0.452479 | − | 0.891775i | \(-0.649460\pi\) | ||||
−0.452479 | + | 0.891775i | \(0.649460\pi\) | |||||||
\(542\) | 3.34065e38 | 0.0760049 | ||||||||
\(543\) | 1.44224e38 | + | 1.93067e38i | 0.0319477 | + | 0.0427671i | ||||
\(544\) | − | 8.16860e38i | − | 0.176183i | ||||||
\(545\) | −5.98854e38 | −0.125768 | ||||||||
\(546\) | 6.15548e38 | − | 3.15486e38i | 0.125883 | − | 0.0645189i | ||||
\(547\) | 1.53871e39 | 0.306436 | 0.153218 | − | 0.988192i | \(-0.451036\pi\) | ||||
0.153218 | + | 0.988192i | \(0.451036\pi\) | |||||||
\(548\) | 5.29268e39i | 1.02650i | ||||||||
\(549\) | −9.30821e39 | − | 2.75358e39i | −1.75819 | − | 0.520114i | ||||
\(550\) | 9.95697e38 | 0.183176 | ||||||||
\(551\) | 7.64940e38 | 0.137066 | ||||||||
\(552\) | −1.04921e39 | + | 7.83778e38i | −0.183125 | + | 0.136797i | ||||
\(553\) | −8.71444e39 | − | 1.47766e39i | −1.48158 | − | 0.251224i | ||||
\(554\) | − | 4.20828e38i | − | 0.0696968i | ||||||
\(555\) | 1.19808e40 | − | 8.94986e39i | 1.93303 | − | 1.44400i | ||||
\(556\) | − | 9.38033e39i | − | 1.47446i | ||||||
\(557\) | 1.96926e39i | 0.301580i | 0.988566 | + | 0.150790i | \(0.0481817\pi\) | ||||
−0.988566 | + | 0.150790i | \(0.951818\pi\) | |||||||
\(558\) | −3.02221e37 | + | 1.02163e38i | −0.00450951 | + | 0.0152439i | ||||
\(559\) | − | 5.40404e39i | − | 0.785682i | ||||||
\(560\) | −1.04790e40 | − | 1.77687e39i | −1.48454 | − | 0.251726i | ||||
\(561\) | 4.71374e39 | + | 6.31010e39i | 0.650735 | + | 0.871113i | ||||
\(562\) | −3.18025e38 | −0.0427844 | ||||||||
\(563\) | 1.17023e40 | 1.53426 | 0.767130 | − | 0.641491i | \(-0.221684\pi\) | ||||
0.767130 | + | 0.641491i | \(0.221684\pi\) | |||||||
\(564\) | 3.89369e36 | − | 2.90865e36i | 0.000497524 | − | 0.000371658i | ||||
\(565\) | 5.24885e39i | 0.653675i | ||||||||
\(566\) | −5.05255e38 | −0.0613299 | ||||||||
\(567\) | −6.22315e39 | − | 5.71900e39i | −0.736302 | − | 0.676653i | ||||
\(568\) | 9.28087e36 | 0.00107038 | ||||||||
\(569\) | − | 7.01848e39i | − | 0.789069i | −0.918881 | − | 0.394534i | \(-0.870906\pi\) | ||
0.918881 | − | 0.394534i | \(-0.129094\pi\) | |||||||
\(570\) | −1.56617e38 | + | 1.16995e38i | −0.0171654 | + | 0.0128228i | ||||
\(571\) | −1.23568e40 | −1.32033 | −0.660165 | − | 0.751121i | \(-0.729514\pi\) | ||||
−0.660165 | + | 0.751121i | \(0.729514\pi\) | |||||||
\(572\) | −2.47151e40 | −2.57466 | ||||||||
\(573\) | −3.59278e39 | − | 4.80951e39i | −0.364912 | − | 0.488494i | ||||
\(574\) | −6.11418e37 | + | 3.60580e38i | −0.00605502 | + | 0.0357092i | ||||
\(575\) | 1.90482e40i | 1.83938i | ||||||||
\(576\) | 2.88154e39 | − | 9.74077e39i | 0.271331 | − | 0.917207i | ||||
\(577\) | 1.25657e40i | 1.15381i | 0.816810 | + | 0.576907i | \(0.195741\pi\) | ||||
−0.816810 | + | 0.576907i | \(0.804259\pi\) | |||||||
\(578\) | − | 4.93953e38i | − | 0.0442315i | ||||||
\(579\) | 8.19485e39 | − | 6.12168e39i | 0.715652 | − | 0.534603i | ||||
\(580\) | − | 1.50898e40i | − | 1.28522i | ||||||
\(581\) | −2.23424e40 | − | 3.78848e39i | −1.85599 | − | 0.314711i | ||||
\(582\) | −7.98287e38 | + | 5.96333e38i | −0.0646809 | + | 0.0483176i | ||||
\(583\) | −2.65463e40 | −2.09802 | ||||||||
\(584\) | −2.50499e39 | −0.193117 | ||||||||
\(585\) | 3.25081e40 | + | 9.61662e39i | 2.44473 | + | 0.723207i | ||||
\(586\) | 4.82951e38i | 0.0354313i | ||||||||
\(587\) | 1.00668e40 | 0.720507 | 0.360254 | − | 0.932854i | \(-0.382690\pi\) | ||||
0.360254 | + | 0.932854i | \(0.382690\pi\) | |||||||
\(588\) | 1.35575e40 | − | 4.27797e39i | 0.946694 | − | 0.298722i | ||||
\(589\) | 4.45236e38 | 0.0303332 | ||||||||
\(590\) | 2.07436e39i | 0.137889i | ||||||||
\(591\) | −1.62867e39 | − | 2.18023e39i | −0.105636 | − | 0.141411i | ||||
\(592\) | −2.42254e40 | −1.53323 | ||||||||
\(593\) | 1.55472e38 | 0.00960197 | 0.00480098 | − | 0.999988i | \(-0.498472\pi\) | ||||
0.00480098 | + | 0.999988i | \(0.498472\pi\) | |||||||
\(594\) | −7.69215e38 | − | 2.08159e39i | −0.0463601 | − | 0.125456i | ||||
\(595\) | 1.79164e40 | + | 3.03800e39i | 1.05379 | + | 0.178686i | ||||
\(596\) | − | 1.15308e40i | − | 0.661896i | ||||||
\(597\) | 1.24538e40 | + | 1.66714e40i | 0.697707 | + | 0.933994i | ||||
\(598\) | 3.47435e39i | 0.189979i | ||||||||
\(599\) | 2.22330e40i | 1.18661i | 0.804976 | + | 0.593307i | \(0.202178\pi\) | ||||
−0.804976 | + | 0.593307i | \(0.797822\pi\) | |||||||
\(600\) | 2.67769e39 | + | 3.58452e39i | 0.139498 | + | 0.186740i | ||||
\(601\) | 2.95704e40i | 1.50376i | 0.659302 | + | 0.751879i | \(0.270852\pi\) | ||||
−0.659302 | + | 0.751879i | \(0.729148\pi\) | |||||||
\(602\) | −1.36447e38 | + | 8.04690e38i | −0.00677353 | + | 0.0399466i | ||||
\(603\) | 4.03126e39 | − | 1.36273e40i | 0.195362 | − | 0.660402i | ||||
\(604\) | −9.38233e36 | −0.000443890 | ||||||||
\(605\) | 4.83993e40 | 2.23556 | ||||||||
\(606\) | −7.05135e38 | − | 9.43936e38i | −0.0317994 | − | 0.0425686i | ||||
\(607\) | − | 3.19733e40i | − | 1.40783i | −0.710282 | − | 0.703917i | \(-0.751433\pi\) | ||
0.710282 | − | 0.703917i | \(-0.248567\pi\) | |||||||
\(608\) | 9.61822e38 | 0.0413517 | ||||||||
\(609\) | 9.13786e39 | + | 1.78289e40i | 0.383613 | + | 0.748471i | ||||
\(610\) | −5.88034e39 | −0.241057 | ||||||||
\(611\) | − | 2.58818e37i | − | 0.00103609i | ||||||
\(612\) | −5.00159e39 | + | 1.69074e40i | −0.195529 | + | 0.660968i | ||||
\(613\) | 3.18991e40 | 1.21787 | 0.608936 | − | 0.793220i | \(-0.291597\pi\) | ||||
0.608936 | + | 0.793220i | \(0.291597\pi\) | |||||||
\(614\) | −1.72261e39 | −0.0642310 | ||||||||
\(615\) | −1.43604e40 | + | 1.07275e40i | −0.522972 | + | 0.390668i | ||||
\(616\) | 7.38747e39 | + | 1.25265e39i | 0.262770 | + | 0.0445565i | ||||
\(617\) | − | 3.69563e40i | − | 1.28397i | −0.766719 | − | 0.641983i | \(-0.778112\pi\) | ||
0.766719 | − | 0.641983i | \(-0.221888\pi\) | |||||||
\(618\) | 1.73128e39 | − | 1.29329e39i | 0.0587536 | − | 0.0438899i | ||||
\(619\) | 2.50412e40i | 0.830118i | 0.909794 | + | 0.415059i | \(0.136239\pi\) | ||||
−0.909794 | + | 0.415059i | \(0.863761\pi\) | |||||||
\(620\) | − | 8.78306e39i | − | 0.284424i | ||||||
\(621\) | 3.98220e40 | − | 1.47155e40i | 1.25978 | − | 0.465529i | ||||
\(622\) | 2.36128e39i | 0.0729771i | ||||||||
\(623\) | 6.25731e39 | + | 1.06102e39i | 0.188934 | + | 0.0320366i | ||||
\(624\) | −3.28659e40 | − | 4.39963e40i | −0.969548 | − | 1.29790i | ||||
\(625\) | −1.71345e40 | −0.493868 | ||||||||
\(626\) | 3.08332e38 | 0.00868342 | ||||||||
\(627\) | −7.42991e39 | + | 5.55025e39i | −0.204458 | + | 0.152733i | ||||
\(628\) | 3.60772e40i | 0.970104i | ||||||||
\(629\) | 4.14194e40 | 1.08835 | ||||||||
\(630\) | −4.59781e39 | − | 2.25277e39i | −0.118063 | − | 0.0578467i | ||||
\(631\) | −4.78919e40 | −1.20181 | −0.600906 | − | 0.799320i | \(-0.705194\pi\) | ||||
−0.600906 | + | 0.799320i | \(0.705194\pi\) | |||||||
\(632\) | − | 1.04285e40i | − | 0.255756i | ||||||
\(633\) | −4.98595e40 | + | 3.72458e40i | −1.19507 | + | 0.892737i | ||||
\(634\) | 4.65552e39 | 0.109062 | ||||||||
\(635\) | −3.40280e39 | −0.0779143 | ||||||||
\(636\) | −3.55642e40 | − | 4.76085e40i | −0.795949 | − | 1.06551i | ||||
\(637\) | 2.49569e40 | − | 7.14752e40i | 0.545971 | − | 1.56363i | ||||
\(638\) | 5.26029e39i | 0.112489i | ||||||||
\(639\) | −2.88495e38 | − | 8.53434e37i | −0.00603081 | − | 0.00178405i | ||||
\(640\) | − | 2.52666e40i | − | 0.516342i | ||||||
\(641\) | − | 2.95196e40i | − | 0.589751i | −0.955536 | − | 0.294876i | \(-0.904722\pi\) | ||
0.955536 | − | 0.294876i | \(-0.0952783\pi\) | |||||||
\(642\) | 3.59845e39 | − | 2.68810e39i | 0.0702842 | − | 0.0525034i | ||||
\(643\) | 7.38431e40i | 1.41010i | 0.709156 | + | 0.705052i | \(0.249076\pi\) | ||||
−0.709156 | + | 0.705052i | \(0.750924\pi\) | |||||||
\(644\) | −1.19381e40 | + | 7.04045e40i | −0.222890 | + | 1.31448i | ||||
\(645\) | −3.20475e40 | + | 2.39400e40i | −0.585030 | + | 0.437027i | ||||
\(646\) | −5.41449e38 | −0.00966464 | ||||||||
\(647\) | 8.34491e40 | 1.45650 | 0.728248 | − | 0.685314i | \(-0.240335\pi\) | ||||
0.728248 | + | 0.685314i | \(0.240335\pi\) | |||||||
\(648\) | 5.42513e39 | − | 8.36713e39i | 0.0925919 | − | 0.142804i | ||||
\(649\) | 9.84073e40i | 1.64240i | ||||||||
\(650\) | 1.18697e40 | 0.193730 | ||||||||
\(651\) | 5.31873e39 | + | 1.03774e40i | 0.0848952 | + | 0.165640i | ||||
\(652\) | 7.07028e40 | 1.10369 | ||||||||
\(653\) | − | 7.49523e40i | − | 1.14431i | −0.820145 | − | 0.572155i | \(-0.806107\pi\) | ||
0.820145 | − | 0.572155i | \(-0.193893\pi\) | |||||||
\(654\) | 2.79678e38 | + | 3.74394e38i | 0.00417620 | + | 0.00559051i | ||||
\(655\) | 8.44336e40 | 1.23315 | ||||||||
\(656\) | 2.90371e40 | 0.414808 | ||||||||
\(657\) | 7.78674e40 | + | 2.30349e40i | 1.08807 | + | 0.321877i | ||||
\(658\) | −6.53492e35 | + | 3.85393e36i | −8.93233e−6 | + | 5.26779e-5i | ||||
\(659\) | 8.48295e40i | 1.13425i | 0.823632 | + | 0.567125i | \(0.191944\pi\) | ||||
−0.823632 | + | 0.567125i | \(0.808056\pi\) | |||||||
\(660\) | 1.09488e41 | + | 1.46568e41i | 1.43213 | + | 1.91713i | ||||
\(661\) | − | 1.12075e41i | − | 1.43413i | −0.697007 | − | 0.717065i | \(-0.745485\pi\) | ||
0.697007 | − | 0.717065i | \(-0.254515\pi\) | |||||||
\(662\) | 4.89582e39i | 0.0612893i | ||||||||
\(663\) | 5.61925e40 | + | 7.52228e40i | 0.688228 | + | 0.921304i | ||||
\(664\) | − | 2.67370e40i | − | 0.320388i | ||||||
\(665\) | −3.57713e39 | + | 2.10959e40i | −0.0419393 | + | 0.247335i | ||||
\(666\) | −1.11906e40 | − | 3.31044e39i | −0.128374 | − | 0.0379760i | ||||
\(667\) | −1.00632e41 | −1.12957 | ||||||||
\(668\) | 3.44409e40 | 0.378282 | ||||||||
\(669\) | −5.87966e40 | − | 7.87087e40i | −0.631937 | − | 0.845949i | ||||
\(670\) | − | 8.60885e39i | − | 0.0905442i | ||||||
\(671\) | −2.78963e41 | −2.87124 | ||||||||
\(672\) | 1.14898e40 | + | 2.24178e40i | 0.115733 | + | 0.225808i | ||||
\(673\) | 5.52796e40 | 0.544937 | 0.272469 | − | 0.962165i | \(-0.412160\pi\) | ||||
0.272469 | + | 0.962165i | \(0.412160\pi\) | |||||||
\(674\) | 1.77139e39i | 0.0170901i | ||||||||
\(675\) | −5.02738e40 | − | 1.36047e41i | −0.474720 | − | 1.28465i | ||||
\(676\) | −1.87219e41 | −1.73030 | ||||||||
\(677\) | −4.74373e40 | −0.429125 | −0.214563 | − | 0.976710i | \(-0.568833\pi\) | ||||
−0.214563 | + | 0.976710i | \(0.568833\pi\) | |||||||
\(678\) | 3.28150e39 | − | 2.45133e39i | 0.0290564 | − | 0.0217056i | ||||
\(679\) | −1.82328e40 | + | 1.07527e41i | −0.158031 | + | 0.931980i | ||||
\(680\) | 2.14405e40i | 0.181910i | ||||||||
\(681\) | 7.59514e40 | − | 5.67369e40i | 0.630816 | − | 0.471229i | ||||
\(682\) | 3.06177e39i | 0.0248943i | ||||||||
\(683\) | − | 1.82712e41i | − | 1.45434i | −0.686456 | − | 0.727171i | \(-0.740835\pi\) | ||
0.686456 | − | 0.727171i | \(-0.259165\pi\) | |||||||
\(684\) | −1.99078e40 | − | 5.88919e39i | −0.155135 | − | 0.0458925i | ||||
\(685\) | − | 2.08634e41i | − | 1.59174i | ||||||
\(686\) | −5.52090e39 | + | 1.00129e40i | −0.0412392 | + | 0.0747928i | ||||
\(687\) | −7.33151e40 | − | 9.81441e40i | −0.536193 | − | 0.717780i | ||||
\(688\) | 6.48006e40 | 0.464031 | ||||||||
\(689\) | −3.16458e41 | −2.21890 | ||||||||
\(690\) | 2.06039e40 | − | 1.53914e40i | 0.141461 | − | 0.105674i | ||||
\(691\) | − | 1.17641e41i | − | 0.790909i | −0.918486 | − | 0.395455i | \(-0.870587\pi\) | ||
0.918486 | − | 0.395455i | \(-0.129413\pi\) | |||||||
\(692\) | 9.31791e40 | 0.613452 | ||||||||
\(693\) | −2.18120e41 | − | 1.06871e41i | −1.40625 | − | 0.689014i | ||||
\(694\) | −1.44514e40 | −0.0912424 | ||||||||
\(695\) | 3.69766e41i | 2.28637i | ||||||||
\(696\) | −1.89371e40 | + | 1.41463e40i | −0.114678 | + | 0.0856661i | ||||
\(697\) | −4.96462e40 | −0.294449 | ||||||||
\(698\) | 1.28311e40 | 0.0745351 | ||||||||
\(699\) | −1.24869e41 | − | 1.67157e41i | −0.710452 | − | 0.951054i | ||||
\(700\) | 2.40529e41 | + | 4.07852e40i | 1.34043 | + | 0.227291i | ||||
\(701\) | − | 1.32146e41i | − | 0.721343i | −0.932693 | − | 0.360672i | \(-0.882548\pi\) | ||
0.932693 | − | 0.360672i | \(-0.117452\pi\) | |||||||
\(702\) | −9.16982e39 | − | 2.48147e40i | −0.0490312 | − | 0.132685i | ||||
\(703\) | 4.87699e40i | 0.255446i | ||||||||
\(704\) | − | 2.91926e41i | − | 1.49785i | ||||||
\(705\) | −1.53486e38 | + | 1.14657e38i | −0.000771485 | + | 0.000576311i | ||||
\(706\) | − | 1.40980e40i | − | 0.0694207i | ||||||
\(707\) | −1.27146e41 | − | 2.15595e40i | −0.613367 | − | 0.104006i | ||||
\(708\) | −1.76485e41 | + | 1.31837e41i | −0.834115 | + | 0.623097i | ||||
\(709\) | −1.20297e41 | −0.557036 | −0.278518 | − | 0.960431i | \(-0.589843\pi\) | ||||
−0.278518 | + | 0.960431i | \(0.589843\pi\) | |||||||
\(710\) | −1.82253e38 | −0.000826853 | ||||||||
\(711\) | −9.58969e40 | + | 3.24170e41i | −0.426280 | + | 1.44100i | ||||
\(712\) | 7.48810e39i | 0.0326146i | ||||||||
\(713\) | −5.85734e40 | −0.249978 | ||||||||
\(714\) | −6.46806e39 | − | 1.26199e40i | −0.0270489 | − | 0.0527754i | ||||
\(715\) | 9.74251e41 | 3.99239 | ||||||||
\(716\) | 1.03517e41i | 0.415694i | ||||||||
\(717\) | 8.49566e40 | + | 1.13728e41i | 0.334326 | + | 0.447549i | ||||
\(718\) | −1.84041e40 | −0.0709757 | ||||||||
\(719\) | 4.09014e41 | 1.54586 | 0.772929 | − | 0.634492i | \(-0.218791\pi\) | ||||
0.772929 | + | 0.634492i | \(0.218791\pi\) | |||||||
\(720\) | −1.15314e41 | + | 3.89809e41i | −0.427132 | + | 1.44388i | ||||
\(721\) | 3.95424e40 | − | 2.33199e41i | 0.143549 | − | 0.846575i | ||||
\(722\) | 2.33669e40i | 0.0831403i | ||||||||
\(723\) | −5.16800e40 | − | 6.91820e40i | −0.180226 | − | 0.241262i | ||||
\(724\) | 1.55034e40i | 0.0529929i | ||||||||
\(725\) | 3.43799e41i | 1.15187i | ||||||||
\(726\) | −2.26035e40 | − | 3.02585e40i | −0.0742327 | − | 0.0993725i | ||||
\(727\) | − | 4.68908e41i | − | 1.50952i | −0.656001 | − | 0.754760i | \(-0.727753\pi\) | ||
0.656001 | − | 0.754760i | \(-0.272247\pi\) | |||||||
\(728\) | 8.80661e40 | + | 1.49329e40i | 0.277910 | + | 0.0471237i | ||||
\(729\) | −2.45581e41 | + | 2.10204e41i | −0.759706 | + | 0.650267i | ||||
\(730\) | 4.91917e40 | 0.149180 | ||||||||
\(731\) | −1.10793e41 | −0.329390 | ||||||||
\(732\) | −3.73728e41 | − | 5.00296e41i | −1.08930 | − | 1.45820i | ||||
\(733\) | 2.91963e41i | 0.834297i | 0.908838 | + | 0.417149i | \(0.136971\pi\) | ||||
−0.908838 | + | 0.417149i | \(0.863029\pi\) | |||||||
\(734\) | −3.17984e39 | −0.00890867 | ||||||||
\(735\) | −5.34428e41 | + | 1.68634e41i | −1.46799 | + | 0.463212i | ||||
\(736\) | −1.26533e41 | −0.340782 | ||||||||
\(737\) | − | 4.08403e41i | − | 1.07848i | ||||||
\(738\) | 1.34133e40 | + | 3.96796e39i | 0.0347311 | + | 0.0102742i | ||||
\(739\) | 3.80301e41 | 0.965568 | 0.482784 | − | 0.875740i | \(-0.339626\pi\) | ||||
0.482784 | + | 0.875740i | \(0.339626\pi\) | |||||||
\(740\) | 9.62070e41 | 2.39523 | ||||||||
\(741\) | −8.85720e40 | + | 6.61647e40i | −0.216238 | + | 0.161533i | ||||
\(742\) | 4.71223e40 | + | 7.99030e39i | 0.112816 | + | 0.0191296i | ||||
\(743\) | 3.20943e41i | 0.753512i | 0.926313 | + | 0.376756i | \(0.122960\pi\) | ||||
−0.926313 | + | 0.376756i | \(0.877040\pi\) | |||||||
\(744\) | −1.10224e40 | + | 8.23391e39i | −0.0253787 | + | 0.0189583i | ||||
\(745\) | 4.54536e41i | 1.02637i | ||||||||
\(746\) | − | 1.99219e40i | − | 0.0441182i | ||||||
\(747\) | −2.45864e41 | + | 8.31118e41i | −0.534005 | + | 1.80515i | ||||
\(748\) | 5.06706e41i | 1.07940i | ||||||||
\(749\) | 8.21885e40 | − | 4.84702e41i | 0.171721 | − | 1.01272i | ||||
\(750\) | −1.41889e40 | − | 1.89941e40i | −0.0290777 | − | 0.0389252i | ||||
\(751\) | 1.32199e41 | 0.265736 | 0.132868 | − | 0.991134i | \(-0.457581\pi\) | ||||
0.132868 | + | 0.991134i | \(0.457581\pi\) | |||||||
\(752\) | 3.10352e38 | 0.000611922 | ||||||||
\(753\) | 4.41083e41 | − | 3.29496e41i | 0.853086 | − | 0.637269i | ||||
\(754\) | 6.27080e40i | 0.118970i | ||||||||
\(755\) | 3.69844e38 | 0.000688317 | ||||||||
\(756\) | −1.00553e41 | − | 5.34355e41i | −0.183581 | − | 0.975583i | ||||
\(757\) | −3.52532e41 | −0.631405 | −0.315703 | − | 0.948858i | \(-0.602240\pi\) | ||||
−0.315703 | + | 0.948858i | \(0.602240\pi\) | |||||||
\(758\) | 7.09611e40i | 0.124686i | ||||||||
\(759\) | 9.77448e41 | − | 7.30168e41i | 1.68495 | − | 1.25869i | ||||
\(760\) | −2.52454e40 | −0.0426958 | ||||||||
\(761\) | −6.34527e41 | −1.05287 | −0.526433 | − | 0.850217i | \(-0.676471\pi\) | ||||
−0.526433 | + | 0.850217i | \(0.676471\pi\) | |||||||
\(762\) | 1.58918e39 | + | 2.12738e39i | 0.00258718 | + | 0.00346336i | ||||
\(763\) | 5.04299e40 | + | 8.55114e39i | 0.0805531 | + | 0.0136590i | ||||
\(764\) | − | 3.86208e41i | − | 0.605296i | ||||||
\(765\) | 1.97159e41 | − | 6.66476e41i | 0.303197 | − | 1.02493i | ||||
\(766\) | 2.94531e40i | 0.0444440i | ||||||||
\(767\) | 1.17311e42i | 1.73703i | ||||||||
\(768\) | 5.11596e41 | − | 3.82170e41i | 0.743343 | − | 0.555288i | ||||
\(769\) | − | 3.10503e41i | − | 0.442725i | −0.975192 | − | 0.221363i | \(-0.928950\pi\) | ||
0.975192 | − | 0.221363i | \(-0.0710505\pi\) | |||||||
\(770\) | −1.45071e41 | − | 2.45990e40i | −0.202986 | − | 0.0344193i | ||||
\(771\) | −6.00199e41 | + | 4.48358e41i | −0.824151 | + | 0.615653i | ||||
\(772\) | 6.58053e41 | 0.886769 | ||||||||
\(773\) | 7.51883e41 | 0.994370 | 0.497185 | − | 0.867645i | \(-0.334367\pi\) | ||||
0.497185 | + | 0.867645i | \(0.334367\pi\) | |||||||
\(774\) | 2.99338e40 | + | 8.85510e39i | 0.0388524 | + | 0.0114934i | ||||
\(775\) | 2.00109e41i | 0.254913i | ||||||||
\(776\) | −1.28677e41 | −0.160882 | ||||||||
\(777\) | −1.13671e42 | + | 5.82598e41i | −1.39491 | + | 0.714931i | ||||
\(778\) | 1.35926e41 | 0.163719 | ||||||||
\(779\) | − | 5.84565e40i | − | 0.0691099i | ||||||
\(780\) | 1.30521e42 | + | 1.74724e42i | 1.51464 | + | 2.02759i | ||||
\(781\) | −8.64606e39 | −0.00984869 | ||||||||
\(782\) | 7.12307e40 | 0.0796470 | ||||||||
\(783\) | 7.18742e41 | − | 2.65598e41i | 0.788910 | − | 0.291527i | ||||
\(784\) | 8.57070e41 | + | 2.99262e41i | 0.923492 | + | 0.322455i | ||||
\(785\) | − | 1.42214e42i | − | 1.50429i | ||||||
\(786\) | −3.94324e40 | − | 5.27866e40i | −0.0409474 | − | 0.0548146i | ||||
\(787\) | − | 3.78389e41i | − | 0.385749i | −0.981223 | − | 0.192874i | \(-0.938219\pi\) | ||
0.981223 | − | 0.192874i | \(-0.0617810\pi\) | |||||||
\(788\) | − | 1.75075e41i | − | 0.175224i | ||||||
\(789\) | −3.34702e41 | − | 4.48052e41i | −0.328883 | − | 0.440263i | ||||
\(790\) | 2.04790e41i | 0.197568i | ||||||||
\(791\) | 7.49493e40 | − | 4.42010e41i | 0.0709919 | − | 0.418671i | ||||
\(792\) | 8.12944e40 | − | 2.74808e41i | 0.0756041 | − | 0.255572i | ||||
\(793\) | −3.32552e42 | −3.03667 | ||||||||
\(794\) | 4.10332e40 | 0.0367907 | ||||||||
\(795\) | 1.40192e42 | + | 1.87669e42i | 1.23424 | + | 1.65223i | ||||
\(796\) | 1.33873e42i | 1.15732i | ||||||||
\(797\) | −2.04749e42 | −1.73811 | −0.869053 | − | 0.494719i | \(-0.835271\pi\) | ||||
−0.869053 | + | 0.494719i | \(0.835271\pi\) | |||||||
\(798\) | 1.48595e40 | − | 7.61591e39i | 0.0123868 | − | 0.00634863i | ||||
\(799\) | −5.30625e38 | −0.000434369 | ||||||||
\(800\) | 4.32286e41i | 0.347510i | ||||||||
\(801\) | 6.88577e40 | − | 2.32767e41i | 0.0543602 | − | 0.183759i | ||||
\(802\) | −5.05872e40 | −0.0392204 | ||||||||
\(803\) | 2.33365e42 | 1.77689 | ||||||||
\(804\) | 7.32436e41 | − | 5.47141e41i | 0.547718 | − | 0.409154i | ||||
\(805\) | 4.70592e41 | − | 2.77529e42i | 0.345624 | − | 2.03830i | ||||
\(806\) | 3.64995e40i | 0.0263286i | ||||||||
\(807\) | 6.77955e41 | − | 5.06443e41i | 0.480324 | − | 0.358810i | ||||
\(808\) | − | 1.52155e41i | − | 0.105882i | ||||||
\(809\) | 2.19323e42i | 1.49910i | 0.661948 | + | 0.749550i | \(0.269730\pi\) | ||||
−0.661948 | + | 0.749550i | \(0.730270\pi\) | |||||||
\(810\) | −1.06536e41 | + | 1.64309e41i | −0.0715259 | + | 0.110314i | ||||
\(811\) | 3.40425e39i | 0.00224502i | 0.999999 | + | 0.00112251i | \(0.000357306\pi\) | ||||
−0.999999 | + | 0.00112251i | \(0.999643\pi\) | |||||||
\(812\) | −2.15470e41 | + | 1.27072e42i | −0.139580 | + | 0.823166i | ||||
\(813\) | −8.36939e41 | − | 1.12038e42i | −0.532575 | − | 0.712937i | ||||
\(814\) | −3.35378e41 | −0.209643 | ||||||||
\(815\) | −2.78705e42 | −1.71143 | ||||||||
\(816\) | −9.02008e41 | + | 6.73814e41i | −0.544130 | + | 0.406474i | ||||
\(817\) | − | 1.30455e41i | − | 0.0773107i | ||||||
\(818\) | −1.04588e41 | −0.0608921 | ||||||||
\(819\) | −2.60021e42 | − | 1.27401e42i | −1.48728 | − | 0.728713i | ||||
\(820\) | −1.15316e42 | −0.648018 | ||||||||
\(821\) | − | 2.78680e42i | − | 1.53862i | −0.638877 | − | 0.769309i | \(-0.720601\pi\) | ||
0.638877 | − | 0.769309i | \(-0.279399\pi\) | |||||||
\(822\) | −1.30435e41 | + | 9.74366e40i | −0.0707540 | + | 0.0528543i | ||||
\(823\) | 3.16453e42 | 1.68660 | 0.843300 | − | 0.537444i | \(-0.180610\pi\) | ||||
0.843300 | + | 0.537444i | \(0.180610\pi\) | |||||||
\(824\) | 2.79068e41 | 0.146139 | ||||||||
\(825\) | −2.49454e42 | − | 3.33934e42i | −1.28353 | − | 1.71822i | ||||
\(826\) | 2.96201e40 | − | 1.74683e41i | 0.0149753 | − | 0.0883162i | ||||
\(827\) | 3.51481e42i | 1.74611i | 0.487619 | + | 0.873056i | \(0.337865\pi\) | ||||
−0.487619 | + | 0.873056i | \(0.662135\pi\) | |||||||
\(828\) | 2.61899e42 | + | 7.74757e41i | 1.27848 | + | 0.378203i | ||||
\(829\) | 2.77766e42i | 1.33241i | 0.745769 | + | 0.666205i | \(0.232082\pi\) | ||||
−0.745769 | + | 0.666205i | \(0.767918\pi\) | |||||||
\(830\) | 5.25048e41i | 0.247495i | ||||||||
\(831\) | −1.41136e42 | + | 1.05431e42i | −0.653766 | + | 0.488374i | ||||
\(832\) | − | 3.48006e42i | − | 1.58416i | ||||||
\(833\) | −1.46538e42 | − | 5.11664e41i | −0.655536 | − | 0.228893i | ||||
\(834\) | 2.31172e41 | − | 1.72689e41i | 0.101631 | − | 0.0759201i | ||||
\(835\) | −1.35764e42 | −0.586583 | ||||||||
\(836\) | −5.96628e41 | −0.253345 | ||||||||
\(837\) | 4.18347e41 | − | 1.54592e41i | 0.174589 | − | 0.0645162i | ||||
\(838\) | − | 1.15207e41i | − | 0.0472541i | ||||||
\(839\) | −2.07644e42 | −0.837087 | −0.418543 | − | 0.908197i | \(-0.637459\pi\) | ||||
−0.418543 | + | 0.908197i | \(0.637459\pi\) | |||||||
\(840\) | −3.01578e41 | − | 5.88411e41i | −0.119495 | − | 0.233148i | ||||
\(841\) | 7.51388e41 | 0.292632 | ||||||||
\(842\) | 1.77114e41i | 0.0677996i | ||||||||
\(843\) | 7.96754e41 | + | 1.06658e42i | 0.299795 | + | 0.401324i | ||||
\(844\) | −4.00376e42 | −1.48082 | ||||||||
\(845\) | 7.38002e42 | 2.68309 | ||||||||
\(846\) | 1.43363e38 | + | 4.24101e37i | 5.12350e−5 | + | 1.51565e-5i | ||||
\(847\) | −4.07574e42 | − | 6.91102e41i | −1.43185 | − | 0.242791i | ||||
\(848\) | − | 3.79470e42i | − | 1.31050i | ||||||
\(849\) | 1.26582e42 | + | 1.69451e42i | 0.429746 | + | 0.575283i | ||||
\(850\) | − | 2.43351e41i | − | 0.0812194i | ||||||
\(851\) | − | 6.41596e42i | − | 2.10515i | ||||||
\(852\) | −1.15832e40 | − | 1.55060e40i | −0.00373641 | − | 0.00500178i | ||||
\(853\) | 9.65721e41i | 0.306260i | 0.988206 | + | 0.153130i | \(0.0489354\pi\) | ||||
−0.988206 | + | 0.153130i | \(0.951065\pi\) | |||||||
\(854\) | 4.95187e41 | + | 8.39664e40i | 0.154394 | + | 0.0261798i | ||||
\(855\) | 7.84752e41 | + | 2.32147e41i | 0.240560 | + | 0.0711631i | ||||
\(856\) | 5.80041e41 | 0.174819 | ||||||||
\(857\) | −1.47188e42 | −0.436165 | −0.218082 | − | 0.975930i | \(-0.569980\pi\) | ||||
−0.218082 | + | 0.975930i | \(0.569980\pi\) | |||||||
\(858\) | −4.54997e41 | − | 6.09087e41i | −0.132569 | − | 0.177465i | ||||
\(859\) | 1.39111e42i | 0.398530i | 0.979946 | + | 0.199265i | \(0.0638554\pi\) | ||||
−0.979946 | + | 0.199265i | \(0.936145\pi\) | |||||||
\(860\) | −2.57344e42 | −0.724915 | ||||||||
\(861\) | 1.36248e42 | − | 6.98313e41i | 0.377386 | − | 0.193421i | ||||
\(862\) | 2.83458e41 | 0.0772028 | ||||||||
\(863\) | − | 2.63894e42i | − | 0.706762i | −0.935480 | − | 0.353381i | \(-0.885032\pi\) | ||
0.935480 | − | 0.353381i | \(-0.114968\pi\) | |||||||
\(864\) | 9.03734e41 | − | 3.33958e41i | 0.238008 | − | 0.0879515i | ||||
\(865\) | −3.67305e42 | −0.951248 | ||||||||
\(866\) | −3.49219e41 | −0.0889382 | ||||||||
\(867\) | −1.65660e42 | + | 1.23751e42i | −0.414899 | + | 0.309936i | ||||
\(868\) | −1.25415e41 | + | 7.39628e41i | −0.0308897 | + | 0.182170i | ||||
\(869\) | 9.71523e42i | 2.35324i | ||||||||
\(870\) | 3.71877e41 | − | 2.77798e41i | 0.0885870 | − | 0.0661758i | ||||
\(871\) | − | 4.86858e42i | − | 1.14062i | ||||||
\(872\) | 6.03493e40i | 0.0139054i | ||||||||
\(873\) | 3.99992e42 | + | 1.18327e42i | 0.906453 | + | 0.268149i | ||||
\(874\) | 8.38715e40i | 0.0186939i | ||||||||
\(875\) | −2.55846e42 | − | 4.33825e41i | −0.560869 | − | 0.0951037i | ||||
\(876\) | 3.12641e42 | + | 4.18520e42i | 0.674119 | + | 0.902416i | ||||
\(877\) | 2.16209e42 | 0.458543 | 0.229271 | − | 0.973363i | \(-0.426366\pi\) | ||||
0.229271 | + | 0.973363i | \(0.426366\pi\) | |||||||
\(878\) | 8.79420e39 | 0.00183453 | ||||||||
\(879\) | 1.61971e42 | − | 1.20994e42i | 0.332351 | − | 0.248272i | ||||
\(880\) | 1.16824e43i | 2.35794i | ||||||||
\(881\) | −3.60234e42 | −0.715210 | −0.357605 | − | 0.933873i | \(-0.616407\pi\) | ||||
−0.357605 | + | 0.933873i | \(0.616407\pi\) | |||||||
\(882\) | 3.55017e41 | + | 2.55360e41i | 0.0693354 | + | 0.0498722i | ||||
\(883\) | 2.30854e42 | 0.443514 | 0.221757 | − | 0.975102i | \(-0.428821\pi\) | ||||
0.221757 | + | 0.975102i | \(0.428821\pi\) | |||||||
\(884\) | 6.04045e42i | 1.14159i | ||||||||
\(885\) | 6.95691e42 | − | 5.19692e42i | 1.29342 | − | 0.966204i | ||||
\(886\) | −1.05056e41 | −0.0192146 | ||||||||
\(887\) | 1.03993e43 | 1.87116 | 0.935580 | − | 0.353116i | \(-0.114878\pi\) | ||||
0.935580 | + | 0.353116i | \(0.114878\pi\) | |||||||
\(888\) | −9.01918e41 | − | 1.20736e42i | −0.159654 | − | 0.213722i | ||||
\(889\) | 2.86552e41 | + | 4.85892e40i | 0.0499032 | + | 0.00846183i | ||||
\(890\) | − | 1.47047e41i | − | 0.0251943i | ||||||
\(891\) | −5.05406e42 | + | 7.79482e42i | −0.851949 | + | 1.31395i | ||||
\(892\) | − | 6.32038e42i | − | 1.04822i | ||||||
\(893\) | − | 6.24791e38i | − | 0.000101950i | ||||||
\(894\) | 2.84169e41 | − | 2.12279e41i | 0.0456229 | − | 0.0340810i | ||||
\(895\) | − | 4.08058e42i | − | 0.644596i | ||||||
\(896\) | −3.60787e41 | + | 2.12772e42i | −0.0560770 | + | 0.330711i | ||||
\(897\) | 1.16522e43 | − | 8.70435e42i | 1.78204 | − | 1.33121i | ||||
\(898\) | 2.45610e41 | 0.0369606 | ||||||||
\(899\) | −1.05718e42 | −0.156543 | ||||||||
\(900\) | 2.64687e42 | − | 8.94748e42i | 0.385670 | − | 1.30372i | ||||
\(901\) | 6.48799e42i | 0.930253i | ||||||||
\(902\) | 4.01990e41 | 0.0567180 | ||||||||
\(903\) | 3.04059e42 | − | 1.55839e42i | 0.422168 | − | 0.216373i | ||||
\(904\) | 5.28951e41 | 0.0722725 | ||||||||
\(905\) | − | 6.11133e41i | − | 0.0821734i | ||||||
\(906\) | −1.72726e38 | − | 2.31221e38i | −2.28559e−5 | − | 3.05963e-5i | ||||
\(907\) | −1.35793e43 | −1.76836 | −0.884180 | − | 0.467146i | \(-0.845282\pi\) | ||||
−0.884180 | + | 0.467146i | \(0.845282\pi\) | |||||||
\(908\) | 6.09896e42 | 0.781648 | ||||||||
\(909\) | −1.39916e42 | + | 4.72972e42i | −0.176478 | + | 0.596567i | ||||
\(910\) | −1.72940e42 | − | 2.93245e41i | −0.214681 | − | 0.0364024i | ||||
\(911\) | − | 6.61361e42i | − | 0.808020i | −0.914754 | − | 0.404010i | \(-0.867616\pi\) | ||
0.914754 | − | 0.404010i | \(-0.132384\pi\) | |||||||
\(912\) | −7.93391e41 | − | 1.06208e42i | −0.0954030 | − | 0.127712i | ||||
\(913\) | 2.49082e43i | 2.94792i | ||||||||
\(914\) | − | 3.32698e41i | − | 0.0387552i | ||||||
\(915\) | 1.47321e43 | + | 1.97213e43i | 1.68911 | + | 2.26115i | ||||
\(916\) | − | 7.88106e42i | − | 0.889406i | ||||||
\(917\) | −7.11022e42 | − | 1.20564e42i | −0.789819 | − | 0.133926i | ||||
\(918\) | −5.08748e41 | + | 1.87999e41i | −0.0556268 | + | 0.0205559i | ||||
\(919\) | 1.80097e42 | 0.193835 | 0.0969176 | − | 0.995292i | \(-0.469102\pi\) | ||||
0.0969176 | + | 0.995292i | \(0.469102\pi\) | |||||||
\(920\) | 3.32118e42 | 0.351859 | ||||||||
\(921\) | 4.31568e42 | + | 5.77723e42i | 0.450074 | + | 0.602497i | ||||
\(922\) | 9.49643e41i | 0.0974904i | ||||||||
\(923\) | −1.03070e41 | −0.0104161 | ||||||||
\(924\) | −7.12723e42 | − | 1.39060e43i | −0.709050 | − | 1.38343i | ||||
\(925\) | −2.19194e43 | −2.14671 | ||||||||
\(926\) | 1.88012e41i | 0.0181270i | ||||||||
\(927\) | −8.67482e42 | − | 2.56621e42i | −0.823387 | − | 0.243577i | ||||
\(928\) | −2.28378e42 | −0.213407 | ||||||||
\(929\) | 1.40405e43 | 1.29168 | 0.645841 | − | 0.763472i | \(-0.276507\pi\) | ||||
0.645841 | + | 0.763472i | \(0.276507\pi\) | |||||||
\(930\) | 2.16452e41 | − | 1.61693e41i | 0.0196047 | − | 0.0146450i | ||||
\(931\) | 6.02465e41 | − | 1.72543e42i | 0.0537232 | − | 0.153860i | ||||
\(932\) | − | 1.34228e43i | − | 1.17846i | ||||||
\(933\) | 7.91918e42 | − | 5.91575e42i | 0.684536 | − | 0.511359i | ||||
\(934\) | − | 1.05944e42i | − | 0.0901669i | ||||||
\(935\) | − | 1.99740e43i | − | 1.67377i | ||||||
\(936\) | 9.69111e41 | − | 3.27599e42i | 0.0799602 | − | 0.270298i | ||||
\(937\) | − | 1.69093e43i | − | 1.37373i | −0.726784 | − | 0.686866i | \(-0.758986\pi\) | ||
0.726784 | − | 0.686866i | \(-0.241014\pi\) | |||||||
\(938\) | −1.22927e41 | + | 7.24958e41i | −0.00983348 | + | 0.0579925i | ||||
\(939\) | −7.72469e41 | − | 1.03407e42i | −0.0608457 | − | 0.0814518i | ||||
\(940\) | −1.23251e40 | −0.000955952 | ||||||||
\(941\) | 2.13448e43 | 1.63020 | 0.815101 | − | 0.579318i | \(-0.196681\pi\) | ||||
0.815101 | + | 0.579318i | \(0.196681\pi\) | |||||||
\(942\) | −8.89099e41 | + | 6.64170e41i | −0.0668670 | + | 0.0499507i | ||||
\(943\) | 7.69030e42i | 0.569539i | ||||||||
\(944\) | −1.40670e43 | −1.02591 | ||||||||
\(945\) | 3.96372e42 | + | 2.10639e43i | 0.284670 | + | 1.51279i | ||||
\(946\) | 8.97102e41 | 0.0634484 | ||||||||
\(947\) | 2.02683e43i | 1.41170i | 0.708362 | + | 0.705849i | \(0.249434\pi\) | ||||
−0.708362 | + | 0.705849i | \(0.750566\pi\) | |||||||
\(948\) | −1.74234e43 | + | 1.30156e43i | −1.19512 | + | 0.892775i | ||||
\(949\) | 2.78195e43 | 1.87927 | ||||||||
\(950\) | 2.86538e41 | 0.0190629 | ||||||||
\(951\) | −1.16636e43 | − | 1.56135e43i | −0.764211 | − | 1.02302i | ||||
\(952\) | 3.06153e41 | − | 1.80552e42i | 0.0197562 | − | 0.116511i | ||||
\(953\) | 1.04751e43i | 0.665748i | 0.942971 | + | 0.332874i | \(0.108018\pi\) | ||||
−0.942971 | + | 0.332874i | \(0.891982\pi\) | |||||||
\(954\) | 5.18551e41 | − | 1.75291e42i | 0.0324594 | − | 0.109726i | ||||
\(955\) | 1.52240e43i | 0.938601i | ||||||||
\(956\) | 9.13247e42i | 0.554560i | ||||||||
\(957\) | 1.76418e43 | − | 1.31787e43i | 1.05516 | − | 0.788224i | ||||
\(958\) | 9.47944e41i | 0.0558448i | ||||||||
\(959\) | −2.97912e42 | + | 1.75692e43i | −0.172869 | + | 1.01949i | ||||
\(960\) | −2.06378e43 | + | 1.54167e43i | −1.17959 | + | 0.881169i | ||||
\(961\) | 1.71465e43 | 0.965356 | ||||||||
\(962\) | −3.99804e42 | −0.221722 | ||||||||
\(963\) | −1.80305e43 | − | 5.33384e42i | −0.984980 | − | 0.291379i | ||||
\(964\) | − | 5.55538e42i | − | 0.298949i | ||||||
\(965\) | −2.59400e43 | −1.37507 | ||||||||
\(966\) | −1.95485e42 | + | 1.00192e42i | −0.102081 | + | 0.0523195i | ||||
\(967\) | 3.96273e42 | 0.203850 | 0.101925 | − | 0.994792i | \(-0.467500\pi\) | ||||
0.101925 | + | 0.994792i | \(0.467500\pi\) | |||||||
\(968\) | − | 4.87742e42i | − | 0.247171i | ||||||
\(969\) | 1.35650e42 | + | 1.81589e42i | 0.0677213 | + | 0.0906558i | ||||
\(970\) | 2.52690e42 | 0.124279 | ||||||||
\(971\) | −1.43815e43 | −0.696826 | −0.348413 | − | 0.937341i | \(-0.613279\pi\) | ||||
−0.348413 | + | 0.937341i | \(0.613279\pi\) | |||||||
\(972\) | −2.07503e43 | + | 1.37876e42i | −0.990521 | + | 0.0658157i | ||||
\(973\) | 5.27995e42 | − | 3.11383e43i | 0.248310 | − | 1.46439i | ||||
\(974\) | 1.70679e42i | 0.0790813i | ||||||||
\(975\) | −2.97374e43 | − | 3.98083e43i | −1.35749 | − | 1.81722i | ||||
\(976\) | − | 3.98768e43i | − | 1.79349i | ||||||
\(977\) | 1.83738e43i | 0.814195i | 0.913385 | + | 0.407097i | \(0.133459\pi\) | ||||
−0.913385 | + | 0.407097i | \(0.866541\pi\) | |||||||
\(978\) | 1.30162e42 | + | 1.74242e42i | 0.0568289 | + | 0.0760747i | ||||
\(979\) | − | 6.97592e42i | − | 0.300090i | ||||||
\(980\) | −3.40370e43 | − | 1.18847e43i | −1.44269 | − | 0.503743i | ||||
\(981\) | 5.54949e41 | − | 1.87595e42i | 0.0231768 | − | 0.0783468i | ||||
\(982\) | 6.00211e41 | 0.0246994 | ||||||||
\(983\) | 3.71565e43 | 1.50664 | 0.753318 | − | 0.657656i | \(-0.228452\pi\) | ||||
0.753318 | + | 0.657656i | \(0.228452\pi\) | |||||||
\(984\) | 1.08106e42 | + | 1.44717e42i | 0.0431936 | + | 0.0578216i | ||||
\(985\) | 6.90131e42i | 0.271710i | ||||||||
\(986\) | 1.28563e42 | 0.0498771 | ||||||||
\(987\) | 1.45624e40 | − | 7.46366e39i | 0.000556717 | − | 0.000285334i | ||||
\(988\) | −7.11241e42 | −0.267942 | ||||||||
\(989\) | 1.71621e43i | 0.637123i | ||||||||
\(990\) | −1.59642e42 | + | 5.39653e42i | −0.0584031 | + | 0.197426i | ||||
\(991\) | 1.40666e43 | 0.507132 | 0.253566 | − | 0.967318i | \(-0.418397\pi\) | ||||
0.253566 | + | 0.967318i | \(0.418397\pi\) | |||||||
\(992\) | −1.32928e42 | −0.0472279 | ||||||||
\(993\) | 1.64194e43 | − | 1.22656e43i | 0.574903 | − | 0.429461i | ||||
\(994\) | 1.53476e40 | + | 2.60242e39i | 0.000529589 | + | 8.97998e-5i | ||||
\(995\) | − | 5.27716e43i | − | 1.79459i | ||||||
\(996\) | −4.46708e43 | + | 3.33697e43i | −1.49714 | + | 1.11839i | ||||
\(997\) | 2.23345e43i | 0.737730i | 0.929483 | + | 0.368865i | \(0.120253\pi\) | ||||
−0.929483 | + | 0.368865i | \(0.879747\pi\) | |||||||
\(998\) | − | 1.35172e40i | − | 0.000440041i | ||||||
\(999\) | 1.69336e43 | + | 4.58245e43i | 0.543312 | + | 1.47027i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 21.30.c.a.20.10 | yes | 76 | |
3.2 | odd | 2 | inner | 21.30.c.a.20.67 | yes | 76 | |
7.6 | odd | 2 | inner | 21.30.c.a.20.68 | yes | 76 | |
21.20 | even | 2 | inner | 21.30.c.a.20.9 | ✓ | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.30.c.a.20.9 | ✓ | 76 | 21.20 | even | 2 | inner | |
21.30.c.a.20.10 | yes | 76 | 1.1 | even | 1 | trivial | |
21.30.c.a.20.67 | yes | 76 | 3.2 | odd | 2 | inner | |
21.30.c.a.20.68 | yes | 76 | 7.6 | odd | 2 | inner |