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 | 20.14 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.30.c.a.20.13 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 42628.6i | 1.83978i | 0.392175 | + | 0.919891i | \(0.371723\pi\) | ||||
−0.392175 | + | 0.919891i | \(0.628277\pi\) | |||||||
\(3\) | −4.19005e6 | − | 7.14660e6i | −0.505779 | − | 0.862663i | ||||
\(4\) | −1.28033e9 | −2.38480 | ||||||||
\(5\) | −1.62384e10 | −1.18981 | −0.594904 | − | 0.803797i | \(-0.702810\pi\) | ||||
−0.594904 | + | 0.803797i | \(0.702810\pi\) | |||||||
\(6\) | 3.04650e11 | − | 1.78616e11i | 1.58711 | − | 0.930522i | ||||
\(7\) | 1.66265e12 | − | 6.74901e11i | 0.926574 | − | 0.376113i | ||||
\(8\) | − | 3.16925e13i | − | 2.54772i | ||||||
\(9\) | −3.35174e13 | + | 5.98892e13i | −0.488376 | + | 0.872633i | ||||
\(10\) | − | 6.92219e14i | − | 2.18899i | ||||||
\(11\) | − | 1.89246e15i | − | 1.50256i | −0.659984 | − | 0.751280i | \(-0.729437\pi\) | ||
0.659984 | − | 0.751280i | \(-0.270563\pi\) | |||||||
\(12\) | 5.36463e15 | + | 9.14999e15i | 1.20618 | + | 2.05728i | ||||
\(13\) | 1.67013e16i | 1.17644i | 0.808699 | + | 0.588222i | \(0.200172\pi\) | ||||
−0.808699 | + | 0.588222i | \(0.799828\pi\) | |||||||
\(14\) | 2.87701e16 | + | 7.08766e16i | 0.691966 | + | 1.70469i | ||||
\(15\) | 6.80395e16 | + | 1.16049e17i | 0.601780 | + | 1.02640i | ||||
\(16\) | 6.63637e17 | 2.30245 | ||||||||
\(17\) | 1.70898e17 | 0.246165 | 0.123083 | − | 0.992396i | \(-0.460722\pi\) | ||||
0.123083 | + | 0.992396i | \(0.460722\pi\) | |||||||
\(18\) | −2.55299e18 | − | 1.42880e18i | −1.60545 | − | 0.898505i | ||||
\(19\) | 2.87863e18i | 0.826529i | 0.910611 | + | 0.413265i | \(0.135612\pi\) | ||||
−0.910611 | + | 0.413265i | \(0.864388\pi\) | |||||||
\(20\) | 2.07904e19 | 2.83745 | ||||||||
\(21\) | −1.17898e19 | − | 9.05445e18i | −0.793100 | − | 0.609091i | ||||
\(22\) | 8.06728e19 | 2.76438 | ||||||||
\(23\) | 8.58865e18i | 0.154480i | 0.997013 | + | 0.0772398i | \(0.0246107\pi\) | ||||
−0.997013 | + | 0.0772398i | \(0.975389\pi\) | |||||||
\(24\) | −2.26494e20 | + | 1.32793e20i | −2.19783 | + | 1.28858i | ||||
\(25\) | 7.74198e19 | 0.415644 | ||||||||
\(26\) | −7.11953e20 | −2.16440 | ||||||||
\(27\) | 5.68443e20 | − | 1.14028e19i | 0.999799 | − | 0.0200556i | ||||
\(28\) | −2.12874e21 | + | 8.64094e20i | −2.20969 | + | 0.896953i | ||||
\(29\) | − | 1.33896e21i | − | 0.835597i | −0.908540 | − | 0.417799i | \(-0.862802\pi\) | ||
0.908540 | − | 0.417799i | \(-0.137198\pi\) | |||||||
\(30\) | −4.94701e21 | + | 2.90043e21i | −1.88836 | + | 1.10714i | ||||
\(31\) | 8.21487e21i | 1.94920i | 0.223955 | + | 0.974599i | \(0.428103\pi\) | ||||
−0.223955 | + | 0.974599i | \(0.571897\pi\) | |||||||
\(32\) | 1.12751e22i | 1.68829i | ||||||||
\(33\) | −1.35246e22 | + | 7.92948e21i | −1.29620 | + | 0.759963i | ||||
\(34\) | 7.28513e21i | 0.452890i | ||||||||
\(35\) | −2.69988e22 | + | 1.09593e22i | −1.10245 | + | 0.447503i | ||||
\(36\) | 4.29133e22 | − | 7.66777e22i | 1.16468 | − | 2.08105i | ||||
\(37\) | −6.15011e22 | −1.12191 | −0.560955 | − | 0.827846i | \(-0.689566\pi\) | ||||
−0.560955 | + | 0.827846i | \(0.689566\pi\) | |||||||
\(38\) | −1.22712e23 | −1.52063 | ||||||||
\(39\) | 1.19358e23 | − | 6.99792e22i | 1.01488 | − | 0.595021i | ||||
\(40\) | 5.14634e23i | 3.03130i | ||||||||
\(41\) | −2.49794e21 | −0.0102853 | −0.00514264 | − | 0.999987i | \(-0.501637\pi\) | ||||
−0.00514264 | + | 0.999987i | \(0.501637\pi\) | |||||||
\(42\) | 3.85979e23 | − | 5.02584e23i | 1.12059 | − | 1.45913i | ||||
\(43\) | 8.52749e23 | 1.76006 | 0.880032 | − | 0.474914i | \(-0.157521\pi\) | ||||
0.880032 | + | 0.474914i | \(0.157521\pi\) | |||||||
\(44\) | 2.42296e24i | 3.58330i | ||||||||
\(45\) | 5.44268e23 | − | 9.72502e23i | 0.581074 | − | 1.03827i | ||||
\(46\) | −3.66122e23 | −0.284209 | ||||||||
\(47\) | −2.18694e24 | −1.24285 | −0.621425 | − | 0.783474i | \(-0.713446\pi\) | ||||
−0.621425 | + | 0.783474i | \(0.713446\pi\) | |||||||
\(48\) | −2.78067e24 | − | 4.74275e24i | −1.16453 | − | 1.98624i | ||||
\(49\) | 2.30892e24 | − | 2.24425e24i | 0.717078 | − | 0.696993i | ||||
\(50\) | 3.30030e24i | 0.764695i | ||||||||
\(51\) | −7.16069e23 | − | 1.22134e24i | −0.124505 | − | 0.212358i | ||||
\(52\) | − | 2.13831e25i | − | 2.80558i | ||||||
\(53\) | 1.34081e25i | 1.33465i | 0.744768 | + | 0.667323i | \(0.232560\pi\) | ||||
−0.744768 | + | 0.667323i | \(0.767440\pi\) | |||||||
\(54\) | 4.86084e23 | + | 2.42320e25i | 0.0368979 | + | 1.83941i | ||||
\(55\) | 3.07304e25i | 1.78776i | ||||||||
\(56\) | −2.13893e25 | − | 5.26936e25i | −0.958231 | − | 2.36065i | ||||
\(57\) | 2.05724e25 | − | 1.20616e25i | 0.713016 | − | 0.418041i | ||||
\(58\) | 5.70780e25 | 1.53732 | ||||||||
\(59\) | −2.12081e25 | −0.445807 | −0.222904 | − | 0.974840i | \(-0.571554\pi\) | ||||
−0.222904 | + | 0.974840i | \(0.571554\pi\) | |||||||
\(60\) | −8.71128e25 | − | 1.48581e26i | −1.43512 | − | 2.44776i | ||||
\(61\) | − | 5.23975e25i | − | 0.679247i | −0.940561 | − | 0.339623i | \(-0.889700\pi\) | ||
0.940561 | − | 0.339623i | \(-0.110300\pi\) | |||||||
\(62\) | −3.50188e26 | −3.58610 | ||||||||
\(63\) | −1.53086e25 | + | 1.22196e26i | −0.124307 | + | 0.992244i | ||||
\(64\) | −1.24356e26 | −0.803633 | ||||||||
\(65\) | − | 2.71202e26i | − | 1.39974i | ||||||
\(66\) | −3.38023e26 | − | 5.76536e26i | −1.39817 | − | 2.38473i | ||||
\(67\) | 1.73869e26 | 0.578279 | 0.289140 | − | 0.957287i | \(-0.406631\pi\) | ||||
0.289140 | + | 0.957287i | \(0.406631\pi\) | |||||||
\(68\) | −2.18805e26 | −0.587053 | ||||||||
\(69\) | 6.13796e25 | − | 3.59868e25i | 0.133264 | − | 0.0781325i | ||||
\(70\) | −4.67179e26 | − | 1.15092e27i | −0.823307 | − | 2.02826i | ||||
\(71\) | 1.36215e26i | 0.195424i | 0.995215 | + | 0.0977121i | \(0.0311524\pi\) | ||||
−0.995215 | + | 0.0977121i | \(0.968848\pi\) | |||||||
\(72\) | 1.89804e27 | + | 1.06225e27i | 2.22323 | + | 1.24425i | ||||
\(73\) | 1.03806e27i | 0.995504i | 0.867320 | + | 0.497752i | \(0.165841\pi\) | ||||
−0.867320 | + | 0.497752i | \(0.834159\pi\) | |||||||
\(74\) | − | 2.62171e27i | − | 2.06407i | ||||||
\(75\) | −3.24393e26 | − | 5.53288e26i | −0.210224 | − | 0.358561i | ||||
\(76\) | − | 3.68558e27i | − | 1.97110i | ||||||
\(77\) | −1.27722e27 | − | 3.14650e27i | −0.565133 | − | 1.39223i | ||||
\(78\) | 2.98312e27 | + | 5.08804e27i | 1.09471 | + | 1.86715i | ||||
\(79\) | 1.92827e27 | 0.588267 | 0.294133 | − | 0.955764i | \(-0.404969\pi\) | ||||
0.294133 | + | 0.955764i | \(0.404969\pi\) | |||||||
\(80\) | −1.07764e28 | −2.73948 | ||||||||
\(81\) | −2.46329e27 | − | 4.01466e27i | −0.522978 | − | 0.852346i | ||||
\(82\) | − | 1.06484e26i | − | 0.0189227i | ||||||
\(83\) | 5.55458e27 | 0.827978 | 0.413989 | − | 0.910282i | \(-0.364135\pi\) | ||||
0.413989 | + | 0.910282i | \(0.364135\pi\) | |||||||
\(84\) | 1.50949e28 | + | 1.15927e28i | 1.89138 | + | 1.45256i | ||||
\(85\) | −2.77510e27 | −0.292889 | ||||||||
\(86\) | 3.63515e28i | 3.23813i | ||||||||
\(87\) | −9.56902e27 | + | 5.61031e27i | −0.720839 | + | 0.422627i | ||||
\(88\) | −5.99767e28 | −3.82810 | ||||||||
\(89\) | −3.90521e26 | −0.0211587 | −0.0105794 | − | 0.999944i | \(-0.503368\pi\) | ||||
−0.0105794 | + | 0.999944i | \(0.503368\pi\) | |||||||
\(90\) | 4.14564e28 | + | 2.32014e28i | 1.91018 | + | 1.06905i | ||||
\(91\) | 1.12717e28 | + | 2.77685e28i | 0.442476 | + | 1.09006i | ||||
\(92\) | − | 1.09963e28i | − | 0.368402i | ||||||
\(93\) | 5.87084e28 | − | 3.44207e28i | 1.68150 | − | 0.985863i | ||||
\(94\) | − | 9.32264e28i | − | 2.28657i | ||||||
\(95\) | − | 4.67442e28i | − | 0.983411i | ||||||
\(96\) | 8.05790e28 | − | 4.72434e28i | 1.45643 | − | 0.853902i | ||||
\(97\) | 2.98614e28i | 0.464429i | 0.972665 | + | 0.232215i | \(0.0745972\pi\) | ||||
−0.972665 | + | 0.232215i | \(0.925403\pi\) | |||||||
\(98\) | 9.56693e28 | + | 9.84262e28i | 1.28231 | + | 1.31927i | ||||
\(99\) | 1.13338e29 | + | 6.34302e28i | 1.31118 | + | 0.733814i | ||||
\(100\) | −9.91227e28 | −0.991227 | ||||||||
\(101\) | 1.65441e29 | 1.43213 | 0.716066 | − | 0.698032i | \(-0.245941\pi\) | ||||
0.716066 | + | 0.698032i | \(0.245941\pi\) | |||||||
\(102\) | 5.20639e28 | − | 3.05250e28i | 0.390692 | − | 0.229062i | ||||
\(103\) | − | 4.45488e28i | − | 0.290199i | −0.989417 | − | 0.145099i | \(-0.953650\pi\) | ||
0.989417 | − | 0.145099i | \(-0.0463502\pi\) | |||||||
\(104\) | 5.29306e29 | 2.99725 | ||||||||
\(105\) | 1.91448e29 | + | 1.47029e29i | 0.943637 | + | 0.724702i | ||||
\(106\) | −5.71567e29 | −2.45546 | ||||||||
\(107\) | − | 1.85090e29i | − | 0.693933i | −0.937878 | − | 0.346966i | \(-0.887212\pi\) | ||
0.937878 | − | 0.346966i | \(-0.112788\pi\) | |||||||
\(108\) | −7.27794e29 | + | 1.45993e28i | −2.38432 | + | 0.0478285i | ||||
\(109\) | −1.95150e29 | −0.559350 | −0.279675 | − | 0.960095i | \(-0.590227\pi\) | ||||
−0.279675 | + | 0.960095i | \(0.590227\pi\) | |||||||
\(110\) | −1.30999e30 | −3.28909 | ||||||||
\(111\) | 2.57693e29 | + | 4.39524e29i | 0.567438 | + | 0.967831i | ||||
\(112\) | 1.10340e30 | − | 4.47889e29i | 2.13339 | − | 0.865983i | ||||
\(113\) | − | 8.95088e29i | − | 1.52135i | −0.649135 | − | 0.760673i | \(-0.724869\pi\) | ||
0.649135 | − | 0.760673i | \(-0.275131\pi\) | |||||||
\(114\) | 5.14168e29 | + | 8.76973e29i | 0.769104 | + | 1.31179i | ||||
\(115\) | − | 1.39466e29i | − | 0.183801i | ||||||
\(116\) | 1.71431e30i | 1.99273i | ||||||||
\(117\) | −1.00023e30 | − | 5.59784e29i | −1.02661 | − | 0.574547i | ||||
\(118\) | − | 9.04071e29i | − | 0.820188i | ||||||
\(119\) | 2.84143e29 | − | 1.15339e29i | 0.228090 | − | 0.0925859i | ||||
\(120\) | 3.67789e30 | − | 2.15634e30i | 2.61499 | − | 1.53317i | ||||
\(121\) | −1.99508e30 | −1.25769 | ||||||||
\(122\) | 2.23363e30 | 1.24967 | ||||||||
\(123\) | 1.04665e28 | + | 1.78518e28i | 0.00520208 | + | 0.00887274i | ||||
\(124\) | − | 1.05177e31i | − | 4.64844i | ||||||
\(125\) | 1.76746e30 | 0.695271 | ||||||||
\(126\) | −5.20904e30 | − | 6.52583e29i | −1.82551 | − | 0.228698i | ||||
\(127\) | 7.73525e29 | 0.241724 | 0.120862 | − | 0.992669i | \(-0.461434\pi\) | ||||
0.120862 | + | 0.992669i | \(0.461434\pi\) | |||||||
\(128\) | 7.52166e29i | 0.209782i | ||||||||
\(129\) | −3.57306e30 | − | 6.09426e30i | −0.890203 | − | 1.51834i | ||||
\(130\) | 1.15610e31 | 2.57522 | ||||||||
\(131\) | −7.88995e30 | −1.57268 | −0.786340 | − | 0.617794i | \(-0.788027\pi\) | ||||
−0.786340 | + | 0.617794i | \(0.788027\pi\) | |||||||
\(132\) | 1.73159e31 | − | 1.01523e31i | 3.09118 | − | 1.81236i | ||||
\(133\) | 1.94279e30 | + | 4.78616e30i | 0.310868 | + | 0.765840i | ||||
\(134\) | 7.41180e30i | 1.06391i | ||||||||
\(135\) | −9.23059e30 | + | 1.85162e29i | −1.18957 | + | 0.0238623i | ||||
\(136\) | − | 5.41617e30i | − | 0.627160i | ||||||
\(137\) | − | 7.65395e30i | − | 0.796962i | −0.917177 | − | 0.398481i | \(-0.869537\pi\) | ||
0.917177 | − | 0.398481i | \(-0.130463\pi\) | |||||||
\(138\) | 1.53407e30 | + | 2.61653e30i | 0.143747 | + | 0.245176i | ||||
\(139\) | 1.56074e31i | 1.31709i | 0.752540 | + | 0.658547i | \(0.228828\pi\) | ||||
−0.752540 | + | 0.658547i | \(0.771172\pi\) | |||||||
\(140\) | 3.45672e31 | − | 1.40315e31i | 2.62911 | − | 1.06720i | ||||
\(141\) | 9.16339e30 | + | 1.56292e31i | 0.628607 | + | 1.07216i | ||||
\(142\) | −5.80665e30 | −0.359538 | ||||||||
\(143\) | 3.16065e31 | 1.76768 | ||||||||
\(144\) | −2.22434e31 | + | 3.97447e31i | −1.12446 | + | 2.00920i | ||||
\(145\) | 2.17425e31i | 0.994201i | ||||||||
\(146\) | −4.42512e31 | −1.83151 | ||||||||
\(147\) | −2.57133e31 | − | 7.09743e30i | −0.963953 | − | 0.266072i | ||||
\(148\) | 7.87416e31 | 2.67553 | ||||||||
\(149\) | 3.20467e31i | 0.987603i | 0.869575 | + | 0.493801i | \(0.164393\pi\) | ||||
−0.869575 | + | 0.493801i | \(0.835607\pi\) | |||||||
\(150\) | 2.35859e31 | − | 1.38284e31i | 0.659674 | − | 0.386766i | ||||
\(151\) | −4.16619e31 | −1.05821 | −0.529107 | − | 0.848555i | \(-0.677473\pi\) | ||||
−0.529107 | + | 0.848555i | \(0.677473\pi\) | |||||||
\(152\) | 9.12309e31 | 2.10577 | ||||||||
\(153\) | −5.72804e30 | + | 1.02349e31i | −0.120221 | + | 0.214812i | ||||
\(154\) | 1.34131e32 | − | 5.44461e31i | 2.56140 | − | 1.03972i | ||||
\(155\) | − | 1.33396e32i | − | 2.31917i | ||||||
\(156\) | −1.52817e32 | + | 8.95963e31i | −2.42027 | + | 1.41900i | ||||
\(157\) | − | 5.28389e31i | − | 0.762797i | −0.924411 | − | 0.381399i | \(-0.875443\pi\) | ||
0.924411 | − | 0.381399i | \(-0.124557\pi\) | |||||||
\(158\) | 8.21993e31i | 1.08228i | ||||||||
\(159\) | 9.58221e31 | − | 5.61804e31i | 1.15135 | − | 0.675035i | ||||
\(160\) | − | 1.83090e32i | − | 2.00874i | ||||||
\(161\) | 5.79649e30 | + | 1.42799e31i | 0.0581018 | + | 0.143137i | ||||
\(162\) | 1.71139e32 | − | 1.05007e32i | 1.56813 | − | 0.962166i | ||||
\(163\) | −2.67602e31 | −0.224269 | −0.112134 | − | 0.993693i | \(-0.535769\pi\) | ||||
−0.112134 | + | 0.993693i | \(0.535769\pi\) | |||||||
\(164\) | 3.19818e30 | 0.0245283 | ||||||||
\(165\) | 2.19618e32 | − | 1.28762e32i | 1.54223 | − | 0.904210i | ||||
\(166\) | 2.36784e32i | 1.52330i | ||||||||
\(167\) | −2.65867e32 | −1.56774 | −0.783872 | − | 0.620923i | \(-0.786758\pi\) | ||||
−0.783872 | + | 0.620923i | \(0.786758\pi\) | |||||||
\(168\) | −2.86958e32 | + | 3.73650e32i | −1.55179 | + | 2.02060i | ||||
\(169\) | −7.73952e31 | −0.384023 | ||||||||
\(170\) | − | 1.18298e32i | − | 0.538852i | ||||||
\(171\) | −1.72399e32 | − | 9.64841e31i | −0.721257 | − | 0.403657i | ||||
\(172\) | −1.09180e33 | −4.19739 | ||||||||
\(173\) | 8.39332e31 | 0.296664 | 0.148332 | − | 0.988938i | \(-0.452610\pi\) | ||||
0.148332 | + | 0.988938i | \(0.452610\pi\) | |||||||
\(174\) | −2.39160e32 | − | 4.07914e32i | −0.777542 | − | 1.32619i | ||||
\(175\) | 1.28722e32 | − | 5.22507e31i | 0.385125 | − | 0.156329i | ||||
\(176\) | − | 1.25590e33i | − | 3.45958i | ||||||
\(177\) | 8.88629e31 | + | 1.51566e32i | 0.225480 | + | 0.384582i | ||||
\(178\) | − | 1.66474e31i | − | 0.0389274i | ||||||
\(179\) | − | 2.95712e32i | − | 0.637529i | −0.947834 | − | 0.318764i | \(-0.896732\pi\) | ||
0.947834 | − | 0.318764i | \(-0.103268\pi\) | |||||||
\(180\) | −6.96841e32 | + | 1.24512e33i | −1.38574 | + | 2.47605i | ||||
\(181\) | 4.15225e32i | 0.761981i | 0.924579 | + | 0.380991i | \(0.124417\pi\) | ||||
−0.924579 | + | 0.380991i | \(0.875583\pi\) | |||||||
\(182\) | −1.18373e33 | + | 4.80498e32i | −2.00548 | + | 0.814060i | ||||
\(183\) | −3.74464e32 | + | 2.19548e32i | −0.585961 | + | 0.343549i | ||||
\(184\) | 2.72196e32 | 0.393571 | ||||||||
\(185\) | 9.98678e32 | 1.33486 | ||||||||
\(186\) | 1.46731e33 | + | 2.50266e33i | 1.81377 | + | 3.09360i | ||||
\(187\) | − | 3.23416e32i | − | 0.369878i | ||||||
\(188\) | 2.80000e33 | 2.96394 | ||||||||
\(189\) | 9.37428e32 | − | 4.02602e32i | 0.918844 | − | 0.394620i | ||||
\(190\) | 1.99264e33 | 1.80926 | ||||||||
\(191\) | − | 1.57626e33i | − | 1.32631i | −0.748483 | − | 0.663154i | \(-0.769218\pi\) | ||
0.748483 | − | 0.663154i | \(-0.230782\pi\) | |||||||
\(192\) | 5.21058e32 | + | 8.88724e32i | 0.406460 | + | 0.693265i | ||||
\(193\) | −2.12406e33 | −1.53669 | −0.768343 | − | 0.640038i | \(-0.778919\pi\) | ||||
−0.768343 | + | 0.640038i | \(0.778919\pi\) | |||||||
\(194\) | −1.27295e33 | −0.854448 | ||||||||
\(195\) | −1.93817e33 | + | 1.13635e33i | −1.20751 | + | 0.707961i | ||||
\(196\) | −2.95618e33 | + | 2.87338e33i | −1.71008 | + | 1.66219i | ||||
\(197\) | 3.51020e31i | 0.0188613i | 0.999956 | + | 0.00943065i | \(0.00300191\pi\) | ||||
−0.999956 | + | 0.00943065i | \(0.996998\pi\) | |||||||
\(198\) | −2.70394e33 | + | 4.83142e33i | −1.35006 | + | 2.41229i | ||||
\(199\) | − | 4.24135e33i | − | 1.96849i | −0.176799 | − | 0.984247i | \(-0.556574\pi\) | ||
0.176799 | − | 0.984247i | \(-0.443426\pi\) | |||||||
\(200\) | − | 2.45363e33i | − | 1.05895i | ||||||
\(201\) | −7.28519e32 | − | 1.24257e33i | −0.292481 | − | 0.498860i | ||||
\(202\) | 7.05252e33i | 2.63481i | ||||||||
\(203\) | −9.03666e32 | − | 2.22623e33i | −0.314279 | − | 0.774242i | ||||
\(204\) | 9.16802e32 | + | 1.56371e33i | 0.296919 | + | 0.506429i | ||||
\(205\) | 4.05625e31 | 0.0122375 | ||||||||
\(206\) | 1.89905e33 | 0.533903 | ||||||||
\(207\) | −5.14367e32 | − | 2.87869e32i | −0.134804 | − | 0.0754441i | ||||
\(208\) | 1.10836e34i | 2.70871i | ||||||||
\(209\) | 5.44767e33 | 1.24191 | ||||||||
\(210\) | −6.26766e33 | + | 8.16115e33i | −1.33329 | + | 1.73609i | ||||
\(211\) | −9.91975e32 | −0.196972 | −0.0984861 | − | 0.995138i | \(-0.531400\pi\) | ||||
−0.0984861 | + | 0.995138i | \(0.531400\pi\) | |||||||
\(212\) | − | 1.71667e34i | − | 3.18286i | ||||||
\(213\) | 9.73473e32 | − | 5.70746e32i | 0.168585 | − | 0.0988414i | ||||
\(214\) | 7.89011e33 | 1.27668 | ||||||||
\(215\) | −1.38472e34 | −2.09414 | ||||||||
\(216\) | −3.61382e32 | − | 1.80154e34i | −0.0510961 | − | 2.54721i | ||||
\(217\) | 5.54422e33 | + | 1.36585e34i | 0.733119 | + | 1.80608i | ||||
\(218\) | − | 8.31897e33i | − | 1.02908i | ||||||
\(219\) | 7.41863e33 | − | 4.34954e33i | 0.858784 | − | 0.503505i | ||||
\(220\) | − | 3.93449e34i | − | 4.26344i | ||||||
\(221\) | 2.85421e33i | 0.289600i | ||||||||
\(222\) | −1.87363e34 | + | 1.09851e34i | −1.78060 | + | 1.04396i | ||||
\(223\) | − | 1.85405e34i | − | 1.65083i | −0.564528 | − | 0.825414i | \(-0.690942\pi\) | ||
0.564528 | − | 0.825414i | \(-0.309058\pi\) | |||||||
\(224\) | 7.60961e33 | + | 1.87467e34i | 0.634989 | + | 1.56433i | ||||
\(225\) | −2.59491e33 | + | 4.63661e33i | −0.202991 | + | 0.362705i | ||||
\(226\) | 3.81563e34 | 2.79895 | ||||||||
\(227\) | −1.20656e33 | −0.0830186 | −0.0415093 | − | 0.999138i | \(-0.513217\pi\) | ||||
−0.0415093 | + | 0.999138i | \(0.513217\pi\) | |||||||
\(228\) | −2.63394e34 | + | 1.54428e34i | −1.70040 | + | 0.996942i | ||||
\(229\) | − | 1.39988e34i | − | 0.848159i | −0.905625 | − | 0.424079i | \(-0.860598\pi\) | ||
0.905625 | − | 0.424079i | \(-0.139402\pi\) | |||||||
\(230\) | 5.94522e33 | 0.338154 | ||||||||
\(231\) | −1.71351e34 | + | 2.23117e34i | −0.915196 | + | 1.19168i | ||||
\(232\) | −4.24350e34 | −2.12887 | ||||||||
\(233\) | − | 5.02379e33i | − | 0.236794i | −0.992966 | − | 0.118397i | \(-0.962224\pi\) | ||
0.992966 | − | 0.118397i | \(-0.0377756\pi\) | |||||||
\(234\) | 2.38628e34 | − | 4.26383e34i | 1.05704 | − | 1.88873i | ||||
\(235\) | 3.55124e34 | 1.47875 | ||||||||
\(236\) | 2.71533e34 | 1.06316 | ||||||||
\(237\) | −8.07953e33 | − | 1.37806e34i | −0.297533 | − | 0.507476i | ||||
\(238\) | 4.91674e33 | + | 1.21126e34i | 0.170338 | + | 0.419636i | ||||
\(239\) | − | 2.45052e34i | − | 0.798894i | −0.916756 | − | 0.399447i | \(-0.869202\pi\) | ||
0.916756 | − | 0.399447i | \(-0.130798\pi\) | |||||||
\(240\) | 4.51535e34 | + | 7.70145e34i | 1.38557 | + | 2.36325i | ||||
\(241\) | − | 4.09826e34i | − | 1.18400i | −0.805938 | − | 0.592000i | \(-0.798338\pi\) | ||
0.805938 | − | 0.592000i | \(-0.201662\pi\) | |||||||
\(242\) | − | 8.50475e34i | − | 2.31387i | ||||||
\(243\) | −1.83698e34 | + | 3.44258e34i | −0.470776 | + | 0.882253i | ||||
\(244\) | 6.70859e34i | 1.61986i | ||||||||
\(245\) | −3.74931e34 | + | 3.64430e34i | −0.853185 | + | 0.829288i | ||||
\(246\) | −7.60997e32 | + | 4.46172e32i | −0.0163239 | + | 0.00957069i | ||||
\(247\) | −4.80768e34 | −0.972366 | ||||||||
\(248\) | 2.60350e35 | 4.96602 | ||||||||
\(249\) | −2.32739e34 | − | 3.96963e34i | −0.418774 | − | 0.714266i | ||||
\(250\) | 7.53443e34i | 1.27915i | ||||||||
\(251\) | −9.77945e34 | −1.56691 | −0.783457 | − | 0.621446i | \(-0.786546\pi\) | ||||
−0.783457 | + | 0.621446i | \(0.786546\pi\) | |||||||
\(252\) | 1.96000e34 | − | 1.56451e35i | 0.296447 | − | 2.36630i | ||||
\(253\) | 1.62536e34 | 0.232115 | ||||||||
\(254\) | 3.29743e34i | 0.444720i | ||||||||
\(255\) | 1.16278e34 | + | 1.98325e34i | 0.148137 | + | 0.252665i | ||||
\(256\) | −9.88270e34 | −1.18959 | ||||||||
\(257\) | 3.16712e34 | 0.360275 | 0.180137 | − | 0.983641i | \(-0.442346\pi\) | ||||
0.180137 | + | 0.983641i | \(0.442346\pi\) | |||||||
\(258\) | 2.59790e35 | − | 1.52314e35i | 2.79342 | − | 1.63778i | ||||
\(259\) | −1.02255e35 | + | 4.15072e34i | −1.03953 | + | 0.421965i | ||||
\(260\) | 3.47227e35i | 3.33810i | ||||||||
\(261\) | 8.01893e34 | + | 4.48785e34i | 0.729170 | + | 0.408085i | ||||
\(262\) | − | 3.36338e35i | − | 2.89339i | ||||||
\(263\) | 8.13052e34i | 0.661851i | 0.943657 | + | 0.330925i | \(0.107361\pi\) | ||||
−0.943657 | + | 0.330925i | \(0.892639\pi\) | |||||||
\(264\) | 2.51305e35 | + | 4.28629e35i | 1.93617 | + | 3.30236i | ||||
\(265\) | − | 2.17725e35i | − | 1.58797i | ||||||
\(266\) | −2.04027e35 | + | 8.28183e34i | −1.40898 | + | 0.571930i | ||||
\(267\) | 1.63630e33 | + | 2.79090e33i | 0.0107016 | + | 0.0182528i | ||||
\(268\) | −2.22609e35 | −1.37908 | ||||||||
\(269\) | −2.19676e35 | −1.28936 | −0.644679 | − | 0.764453i | \(-0.723009\pi\) | ||||
−0.644679 | + | 0.764453i | \(0.723009\pi\) | |||||||
\(270\) | −7.89321e33 | − | 3.93487e35i | −0.0439015 | − | 2.18855i | ||||
\(271\) | − | 7.81113e34i | − | 0.411774i | −0.978576 | − | 0.205887i | \(-0.933992\pi\) | ||
0.978576 | − | 0.205887i | \(-0.0660080\pi\) | |||||||
\(272\) | 1.13414e35 | 0.566784 | ||||||||
\(273\) | 1.51221e35 | − | 1.96906e35i | 0.716562 | − | 0.933039i | ||||
\(274\) | 3.26277e35 | 1.46624 | ||||||||
\(275\) | − | 1.46514e35i | − | 0.624531i | ||||||
\(276\) | −7.85860e34 | + | 4.60749e34i | −0.317807 | + | 0.186330i | ||||
\(277\) | 3.47632e35 | 1.33402 | 0.667011 | − | 0.745048i | \(-0.267573\pi\) | ||||
0.667011 | + | 0.745048i | \(0.267573\pi\) | |||||||
\(278\) | −6.65323e35 | −2.42316 | ||||||||
\(279\) | −4.91982e35 | − | 2.75341e35i | −1.70094 | − | 0.951941i | ||||
\(280\) | 3.47327e35 | + | 8.55658e35i | 1.14011 | + | 2.80872i | ||||
\(281\) | − | 3.03762e35i | − | 0.946872i | −0.880828 | − | 0.473436i | \(-0.843014\pi\) | ||
0.880828 | − | 0.473436i | \(-0.156986\pi\) | |||||||
\(282\) | −6.66252e35 | + | 3.90623e35i | −1.97254 | + | 1.15650i | ||||
\(283\) | 2.26273e35i | 0.636400i | 0.948024 | + | 0.318200i | \(0.103078\pi\) | ||||
−0.948024 | + | 0.318200i | \(0.896922\pi\) | |||||||
\(284\) | − | 1.74400e35i | − | 0.466047i | ||||||
\(285\) | −3.34062e35 | + | 1.95860e35i | −0.848353 | + | 0.497389i | ||||
\(286\) | 1.34734e36i | 3.25214i | ||||||||
\(287\) | −4.15321e33 | + | 1.68586e33i | −0.00953008 | + | 0.00386843i | ||||
\(288\) | −6.75259e35 | − | 3.77914e35i | −1.47326 | − | 0.824521i | ||||
\(289\) | −4.52763e35 | −0.939403 | ||||||||
\(290\) | −9.26854e35 | −1.82911 | ||||||||
\(291\) | 2.13407e35 | − | 1.25120e35i | 0.400646 | − | 0.234898i | ||||
\(292\) | − | 1.32906e36i | − | 2.37407i | ||||||
\(293\) | 1.20746e35 | 0.205254 | 0.102627 | − | 0.994720i | \(-0.467275\pi\) | ||||
0.102627 | + | 0.994720i | \(0.467275\pi\) | |||||||
\(294\) | 3.02554e35 | − | 1.09612e36i | 0.489515 | − | 1.77346i | ||||
\(295\) | 3.44385e35 | 0.530426 | ||||||||
\(296\) | 1.94913e36i | 2.85832i | ||||||||
\(297\) | −2.15792e34 | − | 1.07575e36i | −0.0301348 | − | 1.50226i | ||||
\(298\) | −1.36611e36 | −1.81697 | ||||||||
\(299\) | −1.43442e35 | −0.181737 | ||||||||
\(300\) | 4.15329e35 | + | 7.08390e35i | 0.501342 | + | 0.855095i | ||||
\(301\) | 1.41783e36 | − | 5.75521e35i | 1.63083 | − | 0.661983i | ||||
\(302\) | − | 1.77599e36i | − | 1.94688i | ||||||
\(303\) | −6.93205e35 | − | 1.18234e36i | −0.724342 | − | 1.23545i | ||||
\(304\) | 1.91036e36i | 1.90305i | ||||||||
\(305\) | 8.50849e35i | 0.808174i | ||||||||
\(306\) | −4.36300e35 | − | 2.44179e35i | −0.395207 | − | 0.221181i | ||||
\(307\) | 4.19561e35i | 0.362484i | 0.983439 | + | 0.181242i | \(0.0580117\pi\) | ||||
−0.983439 | + | 0.181242i | \(0.941988\pi\) | |||||||
\(308\) | 1.63526e36 | + | 4.02855e36i | 1.34773 | + | 3.32019i | ||||
\(309\) | −3.18372e35 | + | 1.86661e35i | −0.250344 | + | 0.146776i | ||||
\(310\) | 5.68649e36 | 4.26677 | ||||||||
\(311\) | 1.38364e34 | 0.00990823 | 0.00495411 | − | 0.999988i | \(-0.498423\pi\) | ||||
0.00495411 | + | 0.999988i | \(0.498423\pi\) | |||||||
\(312\) | −2.21782e36 | − | 3.78274e36i | −1.51595 | − | 2.58562i | ||||
\(313\) | 4.32475e35i | 0.282207i | 0.989995 | + | 0.141104i | \(0.0450651\pi\) | ||||
−0.989995 | + | 0.141104i | \(0.954935\pi\) | |||||||
\(314\) | 2.25245e36 | 1.40338 | ||||||||
\(315\) | 2.48586e35 | − | 1.98426e36i | 0.147902 | − | 1.18058i | ||||
\(316\) | −2.46881e36 | −1.40290 | ||||||||
\(317\) | − | 1.15872e36i | − | 0.628954i | −0.949265 | − | 0.314477i | \(-0.898171\pi\) | ||
0.949265 | − | 0.314477i | \(-0.101829\pi\) | |||||||
\(318\) | 2.39489e36 | + | 4.08476e36i | 1.24192 | + | 2.11823i | ||||
\(319\) | −2.53392e36 | −1.25553 | ||||||||
\(320\) | 2.01934e36 | 0.956169 | ||||||||
\(321\) | −1.32276e36 | + | 7.75534e35i | −0.598630 | + | 0.350976i | ||||
\(322\) | −6.08734e35 | + | 2.47096e35i | −0.263340 | + | 0.106895i | ||||
\(323\) | 4.91950e35i | 0.203463i | ||||||||
\(324\) | 3.15382e36 | + | 5.14008e36i | 1.24720 | + | 2.03267i | ||||
\(325\) | 1.29301e36i | 0.488983i | ||||||||
\(326\) | − | 1.14075e36i | − | 0.412606i | ||||||
\(327\) | 8.17687e35 | + | 1.39466e36i | 0.282908 | + | 0.482531i | ||||
\(328\) | 7.91661e34i | 0.0262041i | ||||||||
\(329\) | −3.63613e36 | + | 1.47597e36i | −1.15159 | + | 0.467452i | ||||
\(330\) | 5.48893e36 | + | 9.36200e36i | 1.66355 | + | 2.83737i | ||||
\(331\) | −3.22513e36 | −0.935494 | −0.467747 | − | 0.883863i | \(-0.654934\pi\) | ||||
−0.467747 | + | 0.883863i | \(0.654934\pi\) | |||||||
\(332\) | −7.11168e36 | −1.97456 | ||||||||
\(333\) | 2.06136e36 | − | 3.68325e36i | 0.547914 | − | 0.979017i | ||||
\(334\) | − | 1.13335e37i | − | 2.88430i | ||||||
\(335\) | −2.82335e36 | −0.688042 | ||||||||
\(336\) | −7.82418e36 | − | 6.00887e36i | −1.82608 | − | 1.40240i | ||||
\(337\) | −1.45896e36 | −0.326144 | −0.163072 | − | 0.986614i | \(-0.552140\pi\) | ||||
−0.163072 | + | 0.986614i | \(0.552140\pi\) | |||||||
\(338\) | − | 3.29925e36i | − | 0.706518i | ||||||
\(339\) | −6.39683e36 | + | 3.75046e36i | −1.31241 | + | 0.769465i | ||||
\(340\) | 3.55303e36 | 0.698481 | ||||||||
\(341\) | 1.55463e37 | 2.92879 | ||||||||
\(342\) | 4.11298e36 | − | 7.34911e36i | 0.742640 | − | 1.32695i | ||||
\(343\) | 2.32429e36 | − | 5.28971e36i | 0.402277 | − | 0.915518i | ||||
\(344\) | − | 2.70258e37i | − | 4.48415i | ||||||
\(345\) | −9.96705e35 | + | 5.84367e35i | −0.158559 | + | 0.0929627i | ||||
\(346\) | 3.57796e36i | 0.545798i | ||||||||
\(347\) | 3.82608e36i | 0.559727i | 0.960040 | + | 0.279864i | \(0.0902893\pi\) | ||||
−0.960040 | + | 0.279864i | \(0.909711\pi\) | |||||||
\(348\) | 1.22515e37 | − | 7.18303e36i | 1.71905 | − | 1.00788i | ||||
\(349\) | − | 2.85704e36i | − | 0.384545i | −0.981342 | − | 0.192272i | \(-0.938414\pi\) | ||
0.981342 | − | 0.192272i | \(-0.0615857\pi\) | |||||||
\(350\) | 2.22737e36 | + | 5.48725e36i | 0.287612 | + | 0.708546i | ||||
\(351\) | 1.90441e35 | + | 9.49374e36i | 0.0235943 | + | 1.17621i | ||||
\(352\) | 2.13377e37 | 2.53676 | ||||||||
\(353\) | 1.00942e36 | 0.115170 | 0.0575850 | − | 0.998341i | \(-0.481660\pi\) | ||||
0.0575850 | + | 0.998341i | \(0.481660\pi\) | |||||||
\(354\) | −6.46104e36 | + | 3.78810e36i | −0.707546 | + | 0.414834i | ||||
\(355\) | − | 2.21191e36i | − | 0.232517i | ||||||
\(356\) | 4.99994e35 | 0.0504592 | ||||||||
\(357\) | −2.01485e36 | − | 1.54738e36i | −0.195234 | − | 0.149937i | ||||
\(358\) | 1.26058e37 | 1.17291 | ||||||||
\(359\) | − | 9.97546e36i | − | 0.891381i | −0.895187 | − | 0.445691i | \(-0.852958\pi\) | ||
0.895187 | − | 0.445691i | \(-0.147042\pi\) | |||||||
\(360\) | −3.08210e37 | − | 1.72492e37i | −2.64521 | − | 1.48041i | ||||
\(361\) | 3.84333e36 | 0.316850 | ||||||||
\(362\) | −1.77005e37 | −1.40188 | ||||||||
\(363\) | 8.35947e36 | + | 1.42580e37i | 0.636111 | + | 1.08496i | ||||
\(364\) | −1.44315e37 | − | 3.55527e37i | −1.05522 | − | 2.59958i | ||||
\(365\) | − | 1.68565e37i | − | 1.18446i | ||||||
\(366\) | −9.35901e36 | − | 1.59629e37i | −0.632054 | − | 1.07804i | ||||
\(367\) | 1.83505e37i | 1.19122i | 0.803275 | + | 0.595608i | \(0.203089\pi\) | ||||
−0.803275 | + | 0.595608i | \(0.796911\pi\) | |||||||
\(368\) | 5.69975e36i | 0.355682i | ||||||||
\(369\) | 8.37246e34 | − | 1.49600e35i | 0.00502309 | − | 0.00897529i | ||||
\(370\) | 4.25722e37i | 2.45585i | ||||||||
\(371\) | 9.04912e36 | + | 2.22930e37i | 0.501978 | + | 1.23665i | ||||
\(372\) | −7.51660e37 | + | 4.40697e37i | −4.01004 | + | 2.35108i | ||||
\(373\) | −1.43895e37 | −0.738360 | −0.369180 | − | 0.929358i | \(-0.620361\pi\) | ||||
−0.369180 | + | 0.929358i | \(0.620361\pi\) | |||||||
\(374\) | 1.37868e37 | 0.680494 | ||||||||
\(375\) | −7.40574e36 | − | 1.26313e37i | −0.351653 | − | 0.599785i | ||||
\(376\) | 6.93097e37i | 3.16643i | ||||||||
\(377\) | 2.23624e37 | 0.983034 | ||||||||
\(378\) | 1.71624e37 | + | 3.99613e37i | 0.726015 | + | 1.69047i | ||||
\(379\) | 3.90053e37 | 1.58802 | 0.794008 | − | 0.607907i | \(-0.207991\pi\) | ||||
0.794008 | + | 0.607907i | \(0.207991\pi\) | |||||||
\(380\) | 5.98478e37i | 2.34523i | ||||||||
\(381\) | −3.24110e36 | − | 5.52807e36i | −0.122259 | − | 0.208527i | ||||
\(382\) | 6.71938e37 | 2.44012 | ||||||||
\(383\) | 5.07083e37 | 1.77295 | 0.886476 | − | 0.462775i | \(-0.153146\pi\) | ||||
0.886476 | + | 0.462775i | \(0.153146\pi\) | |||||||
\(384\) | 5.37543e36 | − | 3.15161e36i | 0.180972 | − | 0.106104i | ||||
\(385\) | 2.07400e37 | + | 5.10939e37i | 0.672399 | + | 1.65649i | ||||
\(386\) | − | 9.05456e37i | − | 2.82717i | ||||||
\(387\) | −2.85819e37 | + | 5.10704e37i | −0.859573 | + | 1.53589i | ||||
\(388\) | − | 3.82323e37i | − | 1.10757i | ||||||
\(389\) | 2.09477e37i | 0.584612i | 0.956325 | + | 0.292306i | \(0.0944225\pi\) | ||||
−0.956325 | + | 0.292306i | \(0.905578\pi\) | |||||||
\(390\) | −4.84409e37 | − | 8.26215e37i | −1.30249 | − | 2.22155i | ||||
\(391\) | 1.46778e36i | 0.0380275i | ||||||||
\(392\) | −7.11260e37 | − | 7.31756e37i | −1.77574 | − | 1.82691i | ||||
\(393\) | 3.30592e37 | + | 5.63863e37i | 0.795428 | + | 1.35669i | ||||
\(394\) | −1.49635e36 | −0.0347007 | ||||||||
\(395\) | −3.13119e37 | −0.699925 | ||||||||
\(396\) | −1.45109e38 | − | 8.12114e37i | −3.12691 | − | 1.75000i | ||||
\(397\) | 3.28408e37i | 0.682262i | 0.940016 | + | 0.341131i | \(0.110810\pi\) | ||||
−0.940016 | + | 0.341131i | \(0.889190\pi\) | |||||||
\(398\) | 1.80803e38 | 3.62160 | ||||||||
\(399\) | 2.60644e37 | − | 3.39385e37i | 0.503431 | − | 0.655520i | ||||
\(400\) | 5.13787e37 | 0.957002 | ||||||||
\(401\) | − | 5.91548e37i | − | 1.06267i | −0.847163 | − | 0.531333i | \(-0.821691\pi\) | ||
0.847163 | − | 0.531333i | \(-0.178309\pi\) | |||||||
\(402\) | 5.29691e37 | − | 3.10558e37i | 0.917794 | − | 0.538102i | ||||
\(403\) | −1.37199e38 | −2.29313 | ||||||||
\(404\) | −2.11819e38 | −3.41534 | ||||||||
\(405\) | 3.99999e37 | + | 6.51915e37i | 0.622244 | + | 1.01413i | ||||
\(406\) | 9.49010e37 | − | 3.85220e37i | 1.42444 | − | 0.578205i | ||||
\(407\) | 1.16388e38i | 1.68574i | ||||||||
\(408\) | −3.87072e37 | + | 2.26940e37i | −0.541028 | + | 0.317204i | ||||
\(409\) | − | 4.47203e37i | − | 0.603277i | −0.953422 | − | 0.301638i | \(-0.902466\pi\) | ||
0.953422 | − | 0.301638i | \(-0.0975336\pi\) | |||||||
\(410\) | 1.72912e36i | 0.0225144i | ||||||||
\(411\) | −5.46997e37 | + | 3.20704e37i | −0.687510 | + | 0.403086i | ||||
\(412\) | 5.70370e37i | 0.692065i | ||||||||
\(413\) | −3.52617e37 | + | 1.43134e37i | −0.413074 | + | 0.167674i | ||||
\(414\) | 1.22715e37 | − | 2.19267e37i | 0.138801 | − | 0.248010i | ||||
\(415\) | −9.01972e37 | −0.985135 | ||||||||
\(416\) | −1.88310e38 | −1.98618 | ||||||||
\(417\) | 1.11540e38 | − | 6.53958e37i | 1.13621 | − | 0.666158i | ||||
\(418\) | 2.32227e38i | 2.28484i | ||||||||
\(419\) | −1.08659e38 | −1.03268 | −0.516338 | − | 0.856385i | \(-0.672705\pi\) | ||||
−0.516338 | + | 0.856385i | \(0.672705\pi\) | |||||||
\(420\) | −2.45116e38 | − | 1.88246e38i | −2.25038 | − | 1.72827i | ||||
\(421\) | −1.13162e38 | −1.00372 | −0.501858 | − | 0.864950i | \(-0.667350\pi\) | ||||
−0.501858 | + | 0.864950i | \(0.667350\pi\) | |||||||
\(422\) | − | 4.22865e37i | − | 0.362386i | ||||||
\(423\) | 7.33007e37 | − | 1.30974e38i | 0.606978 | − | 1.08455i | ||||
\(424\) | 4.24935e38 | 3.40031 | ||||||||
\(425\) | 1.32309e37 | 0.102317 | ||||||||
\(426\) | 2.43301e37 | + | 4.14978e37i | 0.181847 | + | 0.310160i | ||||
\(427\) | −3.53631e37 | − | 8.71188e37i | −0.255474 | − | 0.629372i | ||||
\(428\) | 2.36975e38i | 1.65489i | ||||||||
\(429\) | −1.32433e38 | − | 2.25879e38i | −0.894054 | − | 1.52491i | ||||
\(430\) | − | 5.90289e38i | − | 3.85276i | ||||||
\(431\) | 1.11081e38i | 0.701002i | 0.936562 | + | 0.350501i | \(0.113989\pi\) | ||||
−0.936562 | + | 0.350501i | \(0.886011\pi\) | |||||||
\(432\) | 3.77240e38 | − | 7.56730e36i | 2.30199 | − | 0.0461771i | ||||
\(433\) | 5.00180e37i | 0.295156i | 0.989050 | + | 0.147578i | \(0.0471478\pi\) | ||||
−0.989050 | + | 0.147578i | \(0.952852\pi\) | |||||||
\(434\) | −5.82242e38 | + | 2.36343e38i | −3.32279 | + | 1.34878i | ||||
\(435\) | 1.55385e38 | − | 9.11022e37i | 0.857660 | − | 0.502846i | ||||
\(436\) | 2.49856e38 | 1.33394 | ||||||||
\(437\) | −2.47235e37 | −0.127682 | ||||||||
\(438\) | 1.85415e38 | + | 3.16246e38i | 0.926338 | + | 1.57998i | ||||
\(439\) | 2.71259e38i | 1.31114i | 0.755135 | + | 0.655569i | \(0.227571\pi\) | ||||
−0.755135 | + | 0.655569i | \(0.772429\pi\) | |||||||
\(440\) | 9.73923e38 | 4.55471 | ||||||||
\(441\) | 5.70172e37 | + | 2.13501e38i | 0.258016 | + | 0.966141i | ||||
\(442\) | −1.21671e38 | −0.532800 | ||||||||
\(443\) | 1.09543e38i | 0.464228i | 0.972689 | + | 0.232114i | \(0.0745643\pi\) | ||||
−0.972689 | + | 0.232114i | \(0.925436\pi\) | |||||||
\(444\) | −3.29931e38 | − | 5.62735e38i | −1.35322 | − | 2.30808i | ||||
\(445\) | 6.34142e36 | 0.0251748 | ||||||||
\(446\) | 7.90357e38 | 3.03716 | ||||||||
\(447\) | 2.29025e38 | − | 1.34277e38i | 0.851969 | − | 0.499508i | ||||
\(448\) | −2.06761e38 | + | 8.39281e37i | −0.744625 | + | 0.302257i | ||||
\(449\) | − | 2.09076e38i | − | 0.729008i | −0.931202 | − | 0.364504i | \(-0.881238\pi\) | ||
0.931202 | − | 0.364504i | \(-0.118762\pi\) | |||||||
\(450\) | −1.97652e38 | − | 1.10617e38i | −0.667298 | − | 0.373458i | ||||
\(451\) | 4.72725e36i | 0.0154543i | ||||||||
\(452\) | 1.14601e39i | 3.62810i | ||||||||
\(453\) | 1.74565e38 | + | 2.97741e38i | 0.535222 | + | 0.912882i | ||||
\(454\) | − | 5.14342e37i | − | 0.152736i | ||||||
\(455\) | −1.83034e38 | − | 4.50914e38i | −0.526462 | − | 1.29697i | ||||
\(456\) | −3.82262e38 | − | 6.51991e38i | −1.06505 | − | 1.81657i | ||||
\(457\) | 5.95107e38 | 1.60624 | 0.803119 | − | 0.595818i | \(-0.203172\pi\) | ||||
0.803119 | + | 0.595818i | \(0.203172\pi\) | |||||||
\(458\) | 5.96750e38 | 1.56043 | ||||||||
\(459\) | 9.71456e37 | − | 1.94871e36i | 0.246116 | − | 0.00493699i | ||||
\(460\) | 1.78562e38i | 0.438328i | ||||||||
\(461\) | −2.80849e38 | −0.668051 | −0.334025 | − | 0.942564i | \(-0.608407\pi\) | ||||
−0.334025 | + | 0.942564i | \(0.608407\pi\) | |||||||
\(462\) | −9.51119e38 | − | 7.30447e38i | −2.19243 | − | 1.68376i | ||||
\(463\) | 3.33521e37 | 0.0745074 | 0.0372537 | − | 0.999306i | \(-0.488139\pi\) | ||||
0.0372537 | + | 0.999306i | \(0.488139\pi\) | |||||||
\(464\) | − | 8.88584e38i | − | 1.92392i | ||||||
\(465\) | −9.53328e38 | + | 5.58935e38i | −2.00067 | + | 1.17299i | ||||
\(466\) | 2.14157e38 | 0.435649 | ||||||||
\(467\) | −4.61986e38 | −0.911034 | −0.455517 | − | 0.890227i | \(-0.650545\pi\) | ||||
−0.455517 | + | 0.890227i | \(0.650545\pi\) | |||||||
\(468\) | 1.28062e39 | + | 7.16707e38i | 2.44824 | + | 1.37018i | ||||
\(469\) | 2.89084e38 | − | 1.17344e38i | 0.535819 | − | 0.217498i | ||||
\(470\) | 1.51384e39i | 2.72058i | ||||||||
\(471\) | −3.77619e38 | + | 2.21398e38i | −0.658037 | + | 0.385807i | ||||
\(472\) | 6.72138e38i | 1.13579i | ||||||||
\(473\) | − | 1.61379e39i | − | 2.64460i | ||||||
\(474\) | 5.87446e38 | − | 3.44419e38i | 0.933645 | − | 0.547395i | ||||
\(475\) | 2.22863e38i | 0.343542i | ||||||||
\(476\) | −3.63796e38 | + | 1.47672e38i | −0.543948 | + | 0.220799i | ||||
\(477\) | −8.02998e38 | − | 4.49404e38i | −1.16466 | − | 0.651809i | ||||
\(478\) | 1.04462e39 | 1.46979 | ||||||||
\(479\) | −1.28353e39 | −1.75203 | −0.876014 | − | 0.482287i | \(-0.839806\pi\) | ||||
−0.876014 | + | 0.482287i | \(0.839806\pi\) | |||||||
\(480\) | −1.30847e39 | + | 7.67155e38i | −1.73287 | + | 1.01598i | ||||
\(481\) | − | 1.02715e39i | − | 1.31987i | ||||||
\(482\) | 1.74703e39 | 2.17830 | ||||||||
\(483\) | 7.77655e37 | − | 1.01259e38i | 0.0940922 | − | 0.122518i | ||||
\(484\) | 2.55436e39 | 2.99933 | ||||||||
\(485\) | − | 4.84900e38i | − | 0.552582i | ||||||
\(486\) | −1.46752e39 | − | 7.83081e38i | −1.62315 | − | 0.866126i | ||||
\(487\) | −7.13633e38 | −0.766135 | −0.383067 | − | 0.923720i | \(-0.625132\pi\) | ||||
−0.383067 | + | 0.923720i | \(0.625132\pi\) | |||||||
\(488\) | −1.66061e39 | −1.73053 | ||||||||
\(489\) | 1.12126e38 | + | 1.91244e38i | 0.113430 | + | 0.193469i | ||||
\(490\) | −1.55351e39 | − | 1.59828e39i | −1.52571 | − | 1.56967i | ||||
\(491\) | 7.76737e38i | 0.740615i | 0.928909 | + | 0.370307i | \(0.120748\pi\) | ||||
−0.928909 | + | 0.370307i | \(0.879252\pi\) | |||||||
\(492\) | −1.34005e37 | − | 2.28561e37i | −0.0124059 | − | 0.0211597i | ||||
\(493\) | − | 2.28825e38i | − | 0.205695i | ||||||
\(494\) | − | 2.04945e39i | − | 1.78894i | ||||||
\(495\) | −1.84042e39 | − | 1.03000e39i | −1.56006 | − | 0.873098i | ||||
\(496\) | 5.45169e39i | 4.48794i | ||||||||
\(497\) | 9.19315e37 | + | 2.26478e38i | 0.0735016 | + | 0.181075i | ||||
\(498\) | 1.69220e39 | − | 9.92135e38i | 1.31409 | − | 0.770452i | ||||
\(499\) | 9.62333e37 | 0.0725884 | 0.0362942 | − | 0.999341i | \(-0.488445\pi\) | ||||
0.0362942 | + | 0.999341i | \(0.488445\pi\) | |||||||
\(500\) | −2.26293e39 | −1.65808 | ||||||||
\(501\) | 1.11399e39 | + | 1.90004e39i | 0.792931 | + | 1.35243i | ||||
\(502\) | − | 4.16884e39i | − | 2.88278i | ||||||
\(503\) | 6.01385e38 | 0.404033 | 0.202017 | − | 0.979382i | \(-0.435251\pi\) | ||||
0.202017 | + | 0.979382i | \(0.435251\pi\) | |||||||
\(504\) | 3.87269e39 | + | 4.85167e38i | 2.52796 | + | 0.316700i | ||||
\(505\) | −2.68649e39 | −1.70396 | ||||||||
\(506\) | 6.92870e38i | 0.427041i | ||||||||
\(507\) | 3.24290e38 | + | 5.53113e38i | 0.194231 | + | 0.331282i | ||||
\(508\) | −9.90365e38 | −0.576463 | ||||||||
\(509\) | 4.89063e38 | 0.276667 | 0.138333 | − | 0.990386i | \(-0.455825\pi\) | ||||
0.138333 | + | 0.990386i | \(0.455825\pi\) | |||||||
\(510\) | −8.45432e38 | + | 4.95676e38i | −0.464848 | + | 0.272540i | ||||
\(511\) | 7.00591e38 | + | 1.72594e39i | 0.374422 | + | 0.922407i | ||||
\(512\) | − | 3.80904e39i | − | 1.97880i | ||||||
\(513\) | 3.28243e37 | + | 1.63634e39i | 0.0165765 | + | 0.826363i | ||||
\(514\) | 1.35010e39i | 0.662826i | ||||||||
\(515\) | 7.23399e38i | 0.345281i | ||||||||
\(516\) | 4.57468e39 | + | 7.80264e39i | 2.12295 | + | 3.62094i | ||||
\(517\) | 4.13869e39i | 1.86746i | ||||||||
\(518\) | −1.76939e39 | − | 4.35899e39i | −0.776324 | − | 1.91251i | ||||
\(519\) | −3.51684e38 | − | 5.99837e38i | −0.150047 | − | 0.255921i | ||||
\(520\) | −8.59506e39 | −3.56616 | ||||||||
\(521\) | −4.65997e39 | −1.88034 | −0.940170 | − | 0.340707i | \(-0.889334\pi\) | ||||
−0.940170 | + | 0.340707i | \(0.889334\pi\) | |||||||
\(522\) | −1.91311e39 | + | 3.41836e39i | −0.750788 | + | 1.34151i | ||||
\(523\) | − | 6.05568e38i | − | 0.231147i | −0.993299 | − | 0.115573i | \(-0.963129\pi\) | ||
0.993299 | − | 0.115573i | \(-0.0368706\pi\) | |||||||
\(524\) | 1.01017e40 | 3.75052 | ||||||||
\(525\) | −9.12767e38 | − | 7.00994e38i | −0.329648 | − | 0.253165i | ||||
\(526\) | −3.46593e39 | −1.21766 | ||||||||
\(527\) | 1.40390e39i | 0.479825i | ||||||||
\(528\) | −8.97545e39 | + | 5.26230e39i | −2.98445 | + | 1.74978i | ||||
\(529\) | 3.01729e39 | 0.976136 | ||||||||
\(530\) | 9.28131e39 | 2.92152 | ||||||||
\(531\) | 7.10840e38 | − | 1.27013e39i | 0.217722 | − | 0.389027i | ||||
\(532\) | −2.48740e39 | − | 6.12785e39i | −0.741358 | − | 1.82637i | ||||
\(533\) | − | 4.17189e37i | − | 0.0121001i | ||||||
\(534\) | −1.18972e38 | + | 6.97532e37i | −0.0335812 | + | 0.0196886i | ||||
\(535\) | 3.00555e39i | 0.825647i | ||||||||
\(536\) | − | 5.51035e39i | − | 1.47329i | ||||||
\(537\) | −2.11333e39 | + | 1.23905e39i | −0.549973 | + | 0.322449i | ||||
\(538\) | − | 9.36446e39i | − | 2.37214i | ||||||
\(539\) | −4.24715e39 | − | 4.36953e39i | −1.04727 | − | 1.07745i | ||||
\(540\) | 1.18182e40 | − | 2.37068e38i | 2.83688 | − | 0.0569068i | ||||
\(541\) | 3.55979e39 | 0.831886 | 0.415943 | − | 0.909391i | \(-0.363452\pi\) | ||||
0.415943 | + | 0.909391i | \(0.363452\pi\) | |||||||
\(542\) | 3.32978e39 | 0.757575 | ||||||||
\(543\) | 2.96745e39 | − | 1.73981e39i | 0.657333 | − | 0.385394i | ||||
\(544\) | 1.92689e39i | 0.415598i | ||||||||
\(545\) | 3.16891e39 | 0.665520 | ||||||||
\(546\) | 8.39381e39 | + | 6.44634e39i | 1.71659 | + | 1.31832i | ||||
\(547\) | −8.86194e39 | −1.76487 | −0.882434 | − | 0.470436i | \(-0.844097\pi\) | ||||
−0.882434 | + | 0.470436i | \(0.844097\pi\) | |||||||
\(548\) | 9.79957e39i | 1.90059i | ||||||||
\(549\) | 3.13804e39 | + | 1.75623e39i | 0.592733 | + | 0.331728i | ||||
\(550\) | 6.24567e39 | 1.14900 | ||||||||
\(551\) | 3.85437e39 | 0.690645 | ||||||||
\(552\) | −1.14051e39 | − | 1.94528e39i | −0.199060 | − | 0.339519i | ||||
\(553\) | 3.20604e39 | − | 1.30139e39i | 0.545073 | − | 0.221255i | ||||
\(554\) | 1.48191e40i | 2.45431i | ||||||||
\(555\) | −4.18451e39 | − | 7.13715e39i | −0.675143 | − | 1.15153i | ||||
\(556\) | − | 1.99826e40i | − | 3.14100i | ||||||
\(557\) | 1.32679e39i | 0.203189i | 0.994826 | + | 0.101595i | \(0.0323945\pi\) | ||||
−0.994826 | + | 0.101595i | \(0.967606\pi\) | |||||||
\(558\) | 1.17374e40 | − | 2.09725e40i | 1.75136 | − | 3.12935i | ||||
\(559\) | 1.42420e40i | 2.07062i | ||||||||
\(560\) | −1.79174e40 | + | 7.27299e39i | −2.53833 | + | 1.03035i | ||||
\(561\) | −2.31133e39 | + | 1.35513e39i | −0.319080 | + | 0.187076i | ||||
\(562\) | 1.29489e40 | 1.74204 | ||||||||
\(563\) | 8.43743e39 | 1.10621 | 0.553106 | − | 0.833111i | \(-0.313443\pi\) | ||||
0.553106 | + | 0.833111i | \(0.313443\pi\) | |||||||
\(564\) | −1.17321e40 | − | 2.00105e40i | −1.49910 | − | 2.55688i | ||||
\(565\) | 1.45348e40i | 1.81011i | ||||||||
\(566\) | −9.64572e39 | −1.17084 | ||||||||
\(567\) | −6.80510e39 | − | 5.01250e39i | −0.805156 | − | 0.593063i | ||||
\(568\) | 4.31699e39 | 0.497886 | ||||||||
\(569\) | 5.26041e39i | 0.591414i | 0.955279 | + | 0.295707i | \(0.0955553\pi\) | ||||
−0.955279 | + | 0.295707i | \(0.904445\pi\) | |||||||
\(570\) | −8.34925e39 | − | 1.42406e40i | −0.915086 | − | 1.56078i | ||||
\(571\) | −1.34038e40 | −1.43220 | −0.716099 | − | 0.697999i | \(-0.754074\pi\) | ||||
−0.716099 | + | 0.697999i | \(0.754074\pi\) | |||||||
\(572\) | −4.04666e40 | −4.21555 | ||||||||
\(573\) | −1.12649e40 | + | 6.60460e39i | −1.14416 | + | 0.670818i | ||||
\(574\) | −7.18660e37 | − | 1.77046e38i | −0.00711707 | − | 0.0175333i | ||||
\(575\) | 6.64932e38i | 0.0642086i | ||||||||
\(576\) | 4.16810e39 | − | 7.44759e39i | 0.392475 | − | 0.701277i | ||||
\(577\) | − | 1.01243e40i | − | 0.929643i | −0.885404 | − | 0.464822i | \(-0.846118\pi\) | ||
0.885404 | − | 0.464822i | \(-0.153882\pi\) | |||||||
\(578\) | − | 1.93006e40i | − | 1.72830i | ||||||
\(579\) | 8.89990e39 | + | 1.51798e40i | 0.777223 | + | 1.32564i | ||||
\(580\) | − | 2.78376e40i | − | 2.37097i | ||||||
\(581\) | 9.23533e39 | − | 3.74879e39i | 0.767182 | − | 0.311413i | ||||
\(582\) | 5.33371e39 | + | 9.09725e39i | 0.432162 | + | 0.737101i | ||||
\(583\) | 2.53742e40 | 2.00539 | ||||||||
\(584\) | 3.28989e40 | 2.53627 | ||||||||
\(585\) | 1.62420e40 | + | 9.08998e39i | 1.22146 | + | 0.683601i | ||||
\(586\) | 5.14723e39i | 0.377623i | ||||||||
\(587\) | 6.26225e39 | 0.448206 | 0.224103 | − | 0.974565i | \(-0.428055\pi\) | ||||
0.224103 | + | 0.974565i | \(0.428055\pi\) | |||||||
\(588\) | 3.29214e40 | + | 9.08704e39i | 2.29883 | + | 0.634528i | ||||
\(589\) | −2.36475e40 | −1.61107 | ||||||||
\(590\) | 1.46806e40i | 0.975867i | ||||||||
\(591\) | 2.50860e38 | − | 1.47079e38i | 0.0162710 | − | 0.00953965i | ||||
\(592\) | −4.08145e40 | −2.58315 | ||||||||
\(593\) | −1.54878e40 | −0.956527 | −0.478264 | − | 0.878216i | \(-0.658734\pi\) | ||||
−0.478264 | + | 0.878216i | \(0.658734\pi\) | |||||||
\(594\) | 4.58579e40 | − | 9.19893e38i | 2.76383 | − | 0.0554414i | ||||
\(595\) | −4.61402e39 | + | 1.87292e39i | −0.271384 | + | 0.110160i | ||||
\(596\) | − | 4.10303e40i | − | 2.35523i | ||||||
\(597\) | −3.03112e40 | + | 1.77714e40i | −1.69815 | + | 0.995622i | ||||
\(598\) | − | 6.11472e39i | − | 0.334356i | ||||||
\(599\) | − | 1.20812e39i | − | 0.0644795i | −0.999480 | − | 0.0322398i | \(-0.989736\pi\) | ||
0.999480 | − | 0.0322398i | \(-0.0102640\pi\) | |||||||
\(600\) | −1.75351e40 | + | 1.02808e40i | −0.913514 | + | 0.535592i | ||||
\(601\) | − | 2.22116e40i | − | 1.12953i | −0.825250 | − | 0.564767i | \(-0.808966\pi\) | ||
0.825250 | − | 0.564767i | \(-0.191034\pi\) | |||||||
\(602\) | 2.45337e40 | + | 6.04399e40i | 1.21790 | + | 3.00037i | ||||
\(603\) | −5.82764e39 | + | 1.04129e40i | −0.282418 | + | 0.504626i | ||||
\(604\) | 5.33408e40 | 2.52362 | ||||||||
\(605\) | 3.23968e40 | 1.49641 | ||||||||
\(606\) | 5.04015e40 | − | 2.95504e40i | 2.27295 | − | 1.33263i | ||||
\(607\) | − | 5.52437e39i | − | 0.243247i | −0.992576 | − | 0.121623i | \(-0.961190\pi\) | ||
0.992576 | − | 0.121623i | \(-0.0388100\pi\) | |||||||
\(608\) | −3.24569e40 | −1.39542 | ||||||||
\(609\) | −1.21236e40 | + | 1.57861e40i | −0.508955 | + | 0.662712i | ||||
\(610\) | −3.62705e40 | −1.48686 | ||||||||
\(611\) | − | 3.65248e40i | − | 1.46214i | ||||||
\(612\) | 7.33377e39 | − | 1.31040e40i | 0.286703 | − | 0.512282i | ||||
\(613\) | 3.71583e39 | 0.141866 | 0.0709332 | − | 0.997481i | \(-0.477402\pi\) | ||||
0.0709332 | + | 0.997481i | \(0.477402\pi\) | |||||||
\(614\) | −1.78853e40 | −0.666891 | ||||||||
\(615\) | −1.69959e38 | − | 2.89884e38i | −0.00618948 | − | 0.0105569i | ||||
\(616\) | −9.97204e40 | + | 4.04783e40i | −3.54702 | + | 1.43980i | ||||
\(617\) | 2.67277e40i | 0.928595i | 0.885679 | + | 0.464297i | \(0.153693\pi\) | ||||
−0.885679 | + | 0.464297i | \(0.846307\pi\) | |||||||
\(618\) | −7.95711e39 | − | 1.35718e40i | −0.270037 | − | 0.460578i | ||||
\(619\) | 4.32119e40i | 1.43248i | 0.697853 | + | 0.716241i | \(0.254139\pi\) | ||||
−0.697853 | + | 0.716241i | \(0.745861\pi\) | |||||||
\(620\) | 1.70791e41i | 5.53075i | ||||||||
\(621\) | 9.79344e37 | + | 4.88216e39i | 0.00309818 | + | 0.154449i | ||||
\(622\) | 5.89825e38i | 0.0182290i | ||||||||
\(623\) | −6.49301e38 | + | 2.63563e38i | −0.0196051 | + | 0.00795807i | ||||
\(624\) | 7.92101e40 | − | 4.64408e40i | 2.33671 | − | 1.37001i | ||||
\(625\) | −4.31212e40 | −1.24288 | ||||||||
\(626\) | −1.84358e40 | −0.519200 | ||||||||
\(627\) | −2.28260e40 | − | 3.89323e40i | −0.628131 | − | 1.07135i | ||||
\(628\) | 6.76512e40i | 1.81912i | ||||||||
\(629\) | −1.05104e40 | −0.276175 | ||||||||
\(630\) | 8.45862e40 | + | 1.05969e40i | 2.17201 | + | 0.272107i | ||||
\(631\) | −3.99053e40 | −1.00139 | −0.500696 | − | 0.865623i | \(-0.666923\pi\) | ||||
−0.500696 | + | 0.865623i | \(0.666923\pi\) | |||||||
\(632\) | − | 6.11116e40i | − | 1.49874i | ||||||
\(633\) | 4.15642e39 | + | 7.08925e39i | 0.0996244 | + | 0.169921i | ||||
\(634\) | 4.93946e40 | 1.15714 | ||||||||
\(635\) | −1.25608e40 | −0.287606 | ||||||||
\(636\) | −1.22684e41 | + | 7.19293e40i | −2.74573 | + | 1.60982i | ||||
\(637\) | 3.74819e40 | + | 3.85620e40i | 0.819974 | + | 0.843603i | ||||
\(638\) | − | 1.08018e41i | − | 2.30991i | ||||||
\(639\) | −8.15779e39 | − | 4.56557e39i | −0.170534 | − | 0.0954404i | ||||
\(640\) | − | 1.22139e40i | − | 0.249601i | ||||||
\(641\) | − | 4.28272e40i | − | 0.855614i | −0.903870 | − | 0.427807i | \(-0.859286\pi\) | ||
0.903870 | − | 0.427807i | \(-0.140714\pi\) | |||||||
\(642\) | −3.30599e40 | − | 5.63875e40i | −0.645720 | − | 1.10135i | ||||
\(643\) | − | 9.04997e40i | − | 1.72818i | −0.503340 | − | 0.864088i | \(-0.667896\pi\) | ||
0.503340 | − | 0.864088i | \(-0.332104\pi\) | |||||||
\(644\) | −7.42140e39 | − | 1.82830e40i | −0.138561 | − | 0.341352i | ||||
\(645\) | 5.80206e40 | + | 9.89607e40i | 1.05917 | + | 1.80654i | ||||
\(646\) | −2.09712e40 | −0.374327 | ||||||||
\(647\) | −3.67746e38 | −0.00641853 | −0.00320926 | − | 0.999995i | \(-0.501022\pi\) | ||||
−0.00320926 | + | 0.999995i | \(0.501022\pi\) | |||||||
\(648\) | −1.27235e41 | + | 7.80680e40i | −2.17154 | + | 1.33240i | ||||
\(649\) | 4.01354e40i | 0.669852i | ||||||||
\(650\) | −5.51193e40 | −0.899621 | ||||||||
\(651\) | 7.43811e40 | − | 9.68520e40i | 1.18724 | − | 1.54591i | ||||
\(652\) | 3.42618e40 | 0.534836 | ||||||||
\(653\) | 5.73825e39i | 0.0876069i | 0.999040 | + | 0.0438035i | \(0.0139475\pi\) | ||||
−0.999040 | + | 0.0438035i | \(0.986052\pi\) | |||||||
\(654\) | −5.94523e40 | + | 3.48568e40i | −0.887752 | + | 0.520488i | ||||
\(655\) | 1.28120e41 | 1.87119 | ||||||||
\(656\) | −1.65773e39 | −0.0236814 | ||||||||
\(657\) | −6.21688e40 | − | 3.47932e40i | −0.868710 | − | 0.486180i | ||||
\(658\) | −6.29186e40 | − | 1.55003e41i | −0.860010 | − | 2.11868i | ||||
\(659\) | − | 8.55947e40i | − | 1.14448i | −0.820086 | − | 0.572241i | \(-0.806074\pi\) | ||
0.820086 | − | 0.572241i | \(-0.193926\pi\) | |||||||
\(660\) | −2.81183e41 | + | 1.64857e41i | −3.67791 | + | 2.15636i | ||||
\(661\) | 3.55669e40i | 0.455119i | 0.973764 | + | 0.227560i | \(0.0730747\pi\) | ||||
−0.973764 | + | 0.227560i | \(0.926925\pi\) | |||||||
\(662\) | − | 1.37483e41i | − | 1.72110i | ||||||
\(663\) | 2.03979e40 | − | 1.19593e40i | 0.249827 | − | 0.146473i | ||||
\(664\) | − | 1.76039e41i | − | 2.10946i | ||||||
\(665\) | −3.15477e40 | − | 7.77193e40i | −0.369874 | − | 0.911203i | ||||
\(666\) | 1.57012e41 | + | 8.78729e40i | 1.80118 | + | 1.00804i | ||||
\(667\) | 1.14999e40 | 0.129083 | ||||||||
\(668\) | 3.40396e41 | 3.73875 | ||||||||
\(669\) | −1.32502e41 | + | 7.76857e40i | −1.42411 | + | 0.834954i | ||||
\(670\) | − | 1.20355e41i | − | 1.26585i | ||||||
\(671\) | −9.91599e40 | −1.02061 | ||||||||
\(672\) | 1.02090e41 | − | 1.32932e41i | 1.02832 | − | 1.33898i | ||||
\(673\) | 3.87780e40 | 0.382268 | 0.191134 | − | 0.981564i | \(-0.438784\pi\) | ||||
0.191134 | + | 0.981564i | \(0.438784\pi\) | |||||||
\(674\) | − | 6.21933e40i | − | 0.600033i | ||||||
\(675\) | 4.40088e40 | − | 8.82800e38i | 0.415561 | − | 0.00833600i | ||||
\(676\) | 9.90912e40 | 0.915816 | ||||||||
\(677\) | 8.03411e39 | 0.0726779 | 0.0363389 | − | 0.999340i | \(-0.488430\pi\) | ||||
0.0363389 | + | 0.999340i | \(0.488430\pi\) | |||||||
\(678\) | −1.59877e41 | − | 2.72688e41i | −1.41565 | − | 2.41455i | ||||
\(679\) | 2.01535e40 | + | 4.96491e40i | 0.174678 | + | 0.430328i | ||||
\(680\) | 8.79498e40i | 0.746200i | ||||||||
\(681\) | 5.05556e39 | + | 8.62283e39i | 0.0419890 | + | 0.0716171i | ||||
\(682\) | 6.62716e41i | 5.38833i | ||||||||
\(683\) | 6.79765e40i | 0.541077i | 0.962709 | + | 0.270538i | \(0.0872017\pi\) | ||||
−0.962709 | + | 0.270538i | \(0.912798\pi\) | |||||||
\(684\) | 2.20727e41 | + | 1.23531e41i | 1.72005 | + | 0.962639i | ||||
\(685\) | 1.24288e41i | 0.948232i | ||||||||
\(686\) | 2.25493e41 | + | 9.90812e40i | 1.68435 | + | 0.740102i | ||||
\(687\) | −1.00044e41 | + | 5.86557e40i | −0.731675 | + | 0.428981i | ||||
\(688\) | 5.65916e41 | 4.05247 | ||||||||
\(689\) | −2.23932e41 | −1.57014 | ||||||||
\(690\) | −2.49108e40 | − | 4.24881e40i | −0.171031 | − | 0.291713i | ||||
\(691\) | − | 2.70551e41i | − | 1.81893i | −0.415775 | − | 0.909467i | \(-0.636490\pi\) | ||
0.415775 | − | 0.909467i | \(-0.363510\pi\) | |||||||
\(692\) | −1.07462e41 | −0.707484 | ||||||||
\(693\) | 2.31250e41 | + | 2.89708e40i | 1.49091 | + | 0.186779i | ||||
\(694\) | −1.63100e41 | −1.02978 | ||||||||
\(695\) | − | 2.53439e41i | − | 1.56709i | ||||||
\(696\) | 1.77805e41 | + | 3.03266e41i | 1.07674 | + | 1.83650i | ||||
\(697\) | −4.26892e38 | −0.00253188 | ||||||||
\(698\) | 1.21791e41 | 0.707479 | ||||||||
\(699\) | −3.59030e40 | + | 2.10499e40i | −0.204274 | + | 0.119765i | ||||
\(700\) | −1.64807e41 | + | 6.68980e40i | −0.918445 | + | 0.372813i | ||||
\(701\) | 2.10589e41i | 1.14954i | 0.818314 | + | 0.574771i | \(0.194909\pi\) | ||||
−0.818314 | + | 0.574771i | \(0.805091\pi\) | |||||||
\(702\) | −4.04705e41 | + | 8.11824e39i | −2.16397 | + | 0.0434084i | ||||
\(703\) | − | 1.77039e41i | − | 0.927292i | ||||||
\(704\) | 2.35339e41i | 1.20751i | ||||||||
\(705\) | −1.48798e41 | − | 2.53793e41i | −0.747922 | − | 1.27567i | ||||
\(706\) | 4.30302e40i | 0.211888i | ||||||||
\(707\) | 2.75071e41 | − | 1.11656e41i | 1.32698 | − | 0.538644i | ||||
\(708\) | −1.13774e41 | − | 1.94054e41i | −0.537724 | − | 0.917149i | ||||
\(709\) | 1.75830e41 | 0.814183 | 0.407091 | − | 0.913387i | \(-0.366543\pi\) | ||||
0.407091 | + | 0.913387i | \(0.366543\pi\) | |||||||
\(710\) | 9.42905e40 | 0.427781 | ||||||||
\(711\) | −6.46305e40 | + | 1.15482e41i | −0.287295 | + | 0.513341i | ||||
\(712\) | 1.23766e40i | 0.0539065i | ||||||||
\(713\) | −7.05546e40 | −0.301112 | ||||||||
\(714\) | 6.59628e40 | − | 8.58905e40i | 0.275851 | − | 0.359187i | ||||
\(715\) | −5.13237e41 | −2.10320 | ||||||||
\(716\) | 3.78608e41i | 1.52038i | ||||||||
\(717\) | −1.75129e41 | + | 1.02678e41i | −0.689176 | + | 0.404063i | ||||
\(718\) | 4.25240e41 | 1.63995 | ||||||||
\(719\) | 6.69236e40 | 0.252936 | 0.126468 | − | 0.991971i | \(-0.459636\pi\) | ||||
0.126468 | + | 0.991971i | \(0.459636\pi\) | |||||||
\(720\) | 3.61196e41 | − | 6.45388e41i | 1.33790 | − | 2.39056i | ||||
\(721\) | −3.00660e40 | − | 7.40691e40i | −0.109148 | − | 0.268891i | ||||
\(722\) | 1.63836e41i | 0.582934i | ||||||||
\(723\) | −2.92886e41 | + | 1.71719e41i | −1.02139 | + | 0.598842i | ||||
\(724\) | − | 5.31624e41i | − | 1.81717i | ||||||
\(725\) | − | 1.03662e41i | − | 0.347311i | ||||||
\(726\) | −6.07800e41 | + | 3.56353e41i | −1.99609 | + | 1.17031i | ||||
\(727\) | 9.31430e40i | 0.299848i | 0.988698 | + | 0.149924i | \(0.0479029\pi\) | ||||
−0.988698 | + | 0.149924i | \(0.952097\pi\) | |||||||
\(728\) | 8.80052e41 | − | 3.57229e41i | 2.77718 | − | 1.12731i | ||||
\(729\) | 3.22998e41 | − | 1.29637e40i | 0.999196 | − | 0.0401031i | ||||
\(730\) | 7.18568e41 | 2.17914 | ||||||||
\(731\) | 1.45733e41 | 0.433266 | ||||||||
\(732\) | 4.79436e41 | − | 2.81093e41i | 1.39740 | − | 0.819293i | ||||
\(733\) | − | 2.83486e41i | − | 0.810072i | −0.914301 | − | 0.405036i | \(-0.867259\pi\) | ||
0.914301 | − | 0.405036i | \(-0.132741\pi\) | |||||||
\(734\) | −7.82258e41 | −2.19158 | ||||||||
\(735\) | 4.17541e41 | + | 1.15251e41i | 1.14692 | + | 0.316575i | ||||
\(736\) | −9.68383e40 | −0.260807 | ||||||||
\(737\) | − | 3.29040e41i | − | 0.868899i | ||||||
\(738\) | 6.37723e39 | + | 3.56906e39i | 0.0165126 | + | 0.00924138i | ||||
\(739\) | 3.16897e41 | 0.804590 | 0.402295 | − | 0.915510i | \(-0.368213\pi\) | ||||
0.402295 | + | 0.915510i | \(0.368213\pi\) | |||||||
\(740\) | −1.27863e42 | −3.18337 | ||||||||
\(741\) | 2.01444e41 | + | 3.43586e41i | 0.491802 | + | 0.838824i | ||||
\(742\) | −9.50318e41 | + | 3.85751e41i | −2.27516 | + | 0.923529i | ||||
\(743\) | − | 2.03599e41i | − | 0.478012i | −0.971018 | − | 0.239006i | \(-0.923178\pi\) | ||
0.971018 | − | 0.239006i | \(-0.0768216\pi\) | |||||||
\(744\) | −1.09088e42 | − | 1.86062e42i | −2.51170 | − | 4.28400i | ||||
\(745\) | − | 5.20386e41i | − | 1.17506i | ||||||
\(746\) | − | 6.13405e41i | − | 1.35842i | ||||||
\(747\) | −1.86175e41 | + | 3.32659e41i | −0.404364 | + | 0.722521i | ||||
\(748\) | 4.14078e41i | 0.882083i | ||||||||
\(749\) | −1.24917e41 | − | 3.07740e41i | −0.260997 | − | 0.642980i | ||||
\(750\) | 5.38456e41 | − | 3.15696e41i | 1.10347 | − | 0.646965i | ||||
\(751\) | 1.13321e41 | 0.227789 | 0.113894 | − | 0.993493i | \(-0.463667\pi\) | ||||
0.113894 | + | 0.993493i | \(0.463667\pi\) | |||||||
\(752\) | −1.45134e42 | −2.86160 | ||||||||
\(753\) | 4.09763e41 | + | 6.98898e41i | 0.792512 | + | 1.35172i | ||||
\(754\) | 9.53277e41i | 1.80857i | ||||||||
\(755\) | 6.76521e41 | 1.25907 | ||||||||
\(756\) | −1.20022e42 | + | 5.15462e41i | −2.19126 | + | 0.941089i | ||||
\(757\) | −3.74734e40 | −0.0671171 | −0.0335585 | − | 0.999437i | \(-0.510684\pi\) | ||||
−0.0335585 | + | 0.999437i | \(0.510684\pi\) | |||||||
\(758\) | 1.66274e42i | 2.92160i | ||||||||
\(759\) | −6.81035e40 | − | 1.16158e41i | −0.117399 | − | 0.200237i | ||||
\(760\) | −1.48144e42 | −2.50546 | ||||||||
\(761\) | 4.12750e41 | 0.684872 | 0.342436 | − | 0.939541i | \(-0.388748\pi\) | ||||
0.342436 | + | 0.939541i | \(0.388748\pi\) | |||||||
\(762\) | 2.35654e41 | − | 1.38164e41i | 0.383643 | − | 0.224930i | ||||
\(763\) | −3.24466e41 | + | 1.31707e41i | −0.518279 | + | 0.210379i | ||||
\(764\) | 2.01813e42i | 3.16297i | ||||||||
\(765\) | 9.30140e40 | − | 1.66198e41i | 0.143040 | − | 0.255585i | ||||
\(766\) | 2.16162e42i | 3.26184i | ||||||||
\(767\) | − | 3.54203e41i | − | 0.524468i | ||||||
\(768\) | 4.14090e41 | + | 7.06277e41i | 0.601668 | + | 1.02621i | ||||
\(769\) | − | 7.44193e41i | − | 1.06109i | −0.847656 | − | 0.530546i | \(-0.821987\pi\) | ||
0.847656 | − | 0.530546i | \(-0.178013\pi\) | |||||||
\(770\) | −2.17806e42 | + | 8.84116e41i | −3.04758 | + | 1.23707i | ||||
\(771\) | −1.32704e41 | − | 2.26341e41i | −0.182219 | − | 0.310796i | ||||
\(772\) | 2.71949e42 | 3.66468 | ||||||||
\(773\) | 1.18820e42 | 1.57141 | 0.785703 | − | 0.618604i | \(-0.212301\pi\) | ||||
0.785703 | + | 0.618604i | \(0.212301\pi\) | |||||||
\(774\) | −2.17706e42 | − | 1.21841e42i | −2.82570 | − | 1.58143i | ||||
\(775\) | 6.35994e41i | 0.810174i | ||||||||
\(776\) | 9.46382e41 | 1.18324 | ||||||||
\(777\) | 7.25089e41 | + | 5.56859e41i | 0.889787 | + | 0.683346i | ||||
\(778\) | −8.92972e41 | −1.07556 | ||||||||
\(779\) | − | 7.19064e39i | − | 0.00850109i | ||||||
\(780\) | 2.48149e42 | − | 1.45490e42i | 2.87966 | − | 1.68834i | ||||
\(781\) | 2.57781e41 | 0.293637 | ||||||||
\(782\) | −6.25694e40 | −0.0699623 | ||||||||
\(783\) | −1.52679e40 | − | 7.61124e41i | −0.0167584 | − | 0.835429i | ||||
\(784\) | 1.53229e42 | − | 1.48937e42i | 1.65104 | − | 1.60479i | ||||
\(785\) | 8.58018e41i | 0.907583i | ||||||||
\(786\) | −2.40367e42 | + | 1.40927e42i | −2.49602 | + | 1.46341i | ||||
\(787\) | − | 5.53722e41i | − | 0.564493i | −0.959342 | − | 0.282246i | \(-0.908920\pi\) | ||
0.959342 | − | 0.282246i | \(-0.0910796\pi\) | |||||||
\(788\) | − | 4.49421e40i | − | 0.0449804i | ||||||
\(789\) | 5.81056e41 | − | 3.40673e41i | 0.570954 | − | 0.334750i | ||||
\(790\) | − | 1.33478e42i | − | 1.28771i | ||||||
\(791\) | −6.04096e41 | − | 1.48822e42i | −0.572198 | − | 1.40964i | ||||
\(792\) | 2.01026e42 | − | 3.59195e42i | 1.86955 | − | 3.34053i | ||||
\(793\) | 8.75106e41 | 0.799097 | ||||||||
\(794\) | −1.39996e42 | −1.25521 | ||||||||
\(795\) | −1.55599e42 | + | 9.12278e41i | −1.36989 | + | 0.803163i | ||||
\(796\) | 5.43031e42i | 4.69446i | ||||||||
\(797\) | 1.82944e42 | 1.55300 | 0.776502 | − | 0.630114i | \(-0.216992\pi\) | ||||
0.776502 | + | 0.630114i | \(0.216992\pi\) | |||||||
\(798\) | 1.44675e42 | + | 1.11109e42i | 1.20601 | + | 0.926204i | ||||
\(799\) | −3.73743e41 | −0.305946 | ||||||||
\(800\) | 8.72920e41i | 0.701729i | ||||||||
\(801\) | 1.30892e40 | − | 2.33880e40i | 0.0103334 | − | 0.0184638i | ||||
\(802\) | 2.52169e42 | 1.95507 | ||||||||
\(803\) | 1.96449e42 | 1.49580 | ||||||||
\(804\) | 9.32743e41 | + | 1.59090e42i | 0.697508 | + | 1.18968i | ||||
\(805\) | −9.41254e40 | − | 2.31883e41i | −0.0691300 | − | 0.170305i | ||||
\(806\) | − | 5.84860e42i | − | 4.21885i | ||||||
\(807\) | 9.20450e41 | + | 1.56993e42i | 0.652130 | + | 1.11228i | ||||
\(808\) | − | 5.24324e42i | − | 3.64868i | ||||||
\(809\) | 1.31136e42i | 0.896333i | 0.893950 | + | 0.448167i | \(0.147923\pi\) | ||||
−0.893950 | + | 0.448167i | \(0.852077\pi\) | |||||||
\(810\) | −2.77902e42 | + | 1.70514e42i | −1.86577 | + | 1.14479i | ||||
\(811\) | − | 1.64058e41i | − | 0.108192i | −0.998536 | − | 0.0540959i | \(-0.982772\pi\) | ||
0.998536 | − | 0.0540959i | \(-0.0172277\pi\) | |||||||
\(812\) | 1.15699e42 | + | 2.85030e42i | 0.749491 | + | 1.84641i | ||||
\(813\) | −5.58231e41 | + | 3.27290e41i | −0.355223 | + | 0.208267i | ||||
\(814\) | −4.96147e42 | −3.10139 | ||||||||
\(815\) | 4.34542e41 | 0.266837 | ||||||||
\(816\) | −4.75210e41 | − | 8.10524e41i | −0.286667 | − | 0.488944i | ||||
\(817\) | 2.45475e42i | 1.45474i | ||||||||
\(818\) | 1.90636e42 | 1.10990 | ||||||||
\(819\) | −2.04083e42 | − | 2.55673e41i | −1.16732 | − | 0.146241i | ||||
\(820\) | −5.19333e40 | −0.0291840 | ||||||||
\(821\) | 4.86041e41i | 0.268347i | 0.990958 | + | 0.134174i | \(0.0428380\pi\) | ||||
−0.990958 | + | 0.134174i | \(0.957162\pi\) | |||||||
\(822\) | −1.36712e42 | − | 2.33177e42i | −0.741591 | − | 1.26487i | ||||
\(823\) | −2.32959e42 | −1.24160 | −0.620800 | − | 0.783969i | \(-0.713192\pi\) | ||||
−0.620800 | + | 0.783969i | \(0.713192\pi\) | |||||||
\(824\) | −1.41186e42 | −0.739346 | ||||||||
\(825\) | −1.04707e42 | + | 6.13899e41i | −0.538760 | + | 0.315874i | ||||
\(826\) | −6.10159e41 | − | 1.50316e42i | −0.308484 | − | 0.759965i | ||||
\(827\) | − | 1.76908e42i | − | 0.878857i | −0.898278 | − | 0.439428i | \(-0.855181\pi\) | ||
0.898278 | − | 0.439428i | \(-0.144819\pi\) | |||||||
\(828\) | 6.58558e41 | + | 3.68567e41i | 0.321480 | + | 0.179919i | ||||
\(829\) | 1.36122e40i | 0.00652960i | 0.999995 | + | 0.00326480i | \(0.00103922\pi\) | ||||
−0.999995 | + | 0.00326480i | \(0.998961\pi\) | |||||||
\(830\) | − | 3.84498e42i | − | 1.81243i | ||||||
\(831\) | −1.45659e42 | − | 2.48439e42i | −0.674720 | − | 1.15081i | ||||
\(832\) | − | 2.07691e42i | − | 0.945430i | ||||||
\(833\) | 3.94589e41 | − | 3.83537e41i | 0.176520 | − | 0.171575i | ||||
\(834\) | 2.78773e42 | + | 4.75479e42i | 1.22558 | + | 2.09037i | ||||
\(835\) | 4.31724e42 | 1.86531 | ||||||||
\(836\) | −6.97481e42 | −2.96170 | ||||||||
\(837\) | 9.36723e40 | + | 4.66969e42i | 0.0390924 | + | 1.94881i | ||||
\(838\) | − | 4.63200e42i | − | 1.89990i | ||||||
\(839\) | −5.08775e41 | −0.205105 | −0.102553 | − | 0.994728i | \(-0.532701\pi\) | ||||
−0.102553 | + | 0.994728i | \(0.532701\pi\) | |||||||
\(840\) | 4.65973e42 | − | 6.06746e42i | 1.84634 | − | 2.40413i | ||||
\(841\) | 7.74870e41 | 0.301777 | ||||||||
\(842\) | − | 4.82394e42i | − | 1.84662i | ||||||
\(843\) | −2.17086e42 | + | 1.27277e42i | −0.816832 | + | 0.478908i | ||||
\(844\) | 1.27005e42 | 0.469739 | ||||||||
\(845\) | 1.25677e42 | 0.456914 | ||||||||
\(846\) | 5.58325e42 | + | 3.12471e42i | 1.99534 | + | 1.11671i | ||||
\(847\) | −3.31712e42 | + | 1.34648e42i | −1.16534 | + | 0.473032i | ||||
\(848\) | 8.89809e42i | 3.07296i | ||||||||
\(849\) | 1.61708e42 | − | 9.48095e41i | 0.548999 | − | 0.321877i | ||||
\(850\) | 5.64013e41i | 0.188241i | ||||||||
\(851\) | − | 5.28212e41i | − | 0.173312i | ||||||
\(852\) | −1.24636e42 | + | 7.30742e41i | −0.402041 | + | 0.235717i | ||||
\(853\) | − | 1.46159e42i | − | 0.463517i | −0.972773 | − | 0.231758i | \(-0.925552\pi\) | ||
0.972773 | − | 0.231758i | \(-0.0744479\pi\) | |||||||
\(854\) | 3.71375e42 | − | 1.50748e42i | 1.15791 | − | 0.470016i | ||||
\(855\) | 2.79947e42 | + | 1.56674e42i | 0.858158 | + | 0.480274i | ||||
\(856\) | −5.86596e42 | −1.76795 | ||||||||
\(857\) | −2.78902e42 | −0.826474 | −0.413237 | − | 0.910624i | \(-0.635602\pi\) | ||||
−0.413237 | + | 0.910624i | \(0.635602\pi\) | |||||||
\(858\) | 9.62890e42 | − | 5.64542e42i | 2.80550 | − | 1.64486i | ||||
\(859\) | − | 4.60345e42i | − | 1.31881i | −0.751787 | − | 0.659406i | \(-0.770808\pi\) | ||
0.751787 | − | 0.659406i | \(-0.229192\pi\) | |||||||
\(860\) | 1.77290e43 | 4.99409 | ||||||||
\(861\) | 2.94503e40 | + | 2.26175e40i | 0.00815727 | + | 0.00626468i | ||||
\(862\) | −4.73522e42 | −1.28969 | ||||||||
\(863\) | − | 3.11363e42i | − | 0.833893i | −0.908931 | − | 0.416946i | \(-0.863100\pi\) | ||
0.908931 | − | 0.416946i | \(-0.136900\pi\) | |||||||
\(864\) | 1.28568e41 | + | 6.40928e42i | 0.0338597 | + | 1.68795i | ||||
\(865\) | −1.36294e42 | −0.352974 | ||||||||
\(866\) | −2.13220e42 | −0.543023 | ||||||||
\(867\) | 1.89710e42 | + | 3.23571e42i | 0.475130 | + | 0.810388i | ||||
\(868\) | −7.09842e42 | − | 1.74873e43i | −1.74834 | − | 4.30712i | ||||
\(869\) | − | 3.64916e42i | − | 0.883906i | ||||||
\(870\) | 3.88356e42 | + | 6.62385e42i | 0.925126 | + | 1.57791i | ||||
\(871\) | 2.90384e42i | 0.680314i | ||||||||
\(872\) | 6.18479e42i | 1.42507i | ||||||||
\(873\) | −1.78837e42 | − | 1.00088e42i | −0.405276 | − | 0.226816i | ||||
\(874\) | − | 1.05393e42i | − | 0.234907i | ||||||
\(875\) | 2.93867e42 | − | 1.19286e42i | 0.644220 | − | 0.261501i | ||||
\(876\) | −9.49828e42 | + | 5.56883e42i | −2.04803 | + | 1.20076i | ||||
\(877\) | −2.16367e42 | −0.458877 | −0.229438 | − | 0.973323i | \(-0.573689\pi\) | ||||
−0.229438 | + | 0.973323i | \(0.573689\pi\) | |||||||
\(878\) | −1.15634e43 | −2.41221 | ||||||||
\(879\) | −5.05931e41 | − | 8.62923e41i | −0.103813 | − | 0.177065i | ||||
\(880\) | 2.03938e43i | 4.11623i | ||||||||
\(881\) | −6.51135e42 | −1.29277 | −0.646384 | − | 0.763012i | \(-0.723720\pi\) | ||||
−0.646384 | + | 0.763012i | \(0.723720\pi\) | |||||||
\(882\) | −9.10125e42 | + | 2.43057e42i | −1.77749 | + | 0.474693i | ||||
\(883\) | 9.76807e42 | 1.87663 | 0.938314 | − | 0.345783i | \(-0.112387\pi\) | ||||
0.938314 | + | 0.345783i | \(0.112387\pi\) | |||||||
\(884\) | − | 3.65432e42i | − | 0.690636i | ||||||
\(885\) | −1.44299e42 | − | 2.46118e42i | −0.268278 | − | 0.457579i | ||||
\(886\) | −4.66968e42 | −0.854079 | ||||||||
\(887\) | −2.22619e42 | −0.400561 | −0.200281 | − | 0.979739i | \(-0.564185\pi\) | ||||
−0.200281 | + | 0.979739i | \(0.564185\pi\) | |||||||
\(888\) | 1.39296e43 | − | 8.16693e42i | 2.46576 | − | 1.44567i | ||||
\(889\) | 1.28610e42 | − | 5.22053e41i | 0.223975 | − | 0.0909157i | ||||
\(890\) | 2.70326e41i | 0.0463161i | ||||||||
\(891\) | −7.59757e42 | + | 4.66168e42i | −1.28070 | + | 0.785806i | ||||
\(892\) | 2.37380e43i | 3.93689i | ||||||||
\(893\) | − | 6.29539e42i | − | 1.02725i | ||||||
\(894\) | 5.72405e42 | + | 9.76301e42i | 0.918986 | + | 1.56744i | ||||
\(895\) | 4.80188e42i | 0.758537i | ||||||||
\(896\) | 5.07638e41 | + | 1.25059e42i | 0.0789019 | + | 0.194379i | ||||
\(897\) | 6.01027e41 | + | 1.02512e42i | 0.0919186 | + | 0.156778i | ||||
\(898\) | 8.91262e42 | 1.34122 | ||||||||
\(899\) | 1.09994e43 | 1.62875 | ||||||||
\(900\) | 3.32234e42 | − | 5.93638e42i | 0.484091 | − | 0.864978i | ||||
\(901\) | 2.29141e42i | 0.328543i | ||||||||
\(902\) | −2.01516e41 | −0.0284325 | ||||||||
\(903\) | −1.00538e43 | − | 7.72117e42i | −1.39591 | − | 1.07204i | ||||
\(904\) | −2.83676e43 | −3.87597 | ||||||||
\(905\) | − | 6.74257e42i | − | 0.906612i | ||||||
\(906\) | −1.26923e43 | + | 7.44147e42i | −1.67950 | + | 0.984691i | ||||
\(907\) | −5.32245e42 | −0.693116 | −0.346558 | − | 0.938028i | \(-0.612650\pi\) | ||||
−0.346558 | + | 0.938028i | \(0.612650\pi\) | |||||||
\(908\) | 1.54480e42 | 0.197982 | ||||||||
\(909\) | −5.54516e42 | + | 9.90812e42i | −0.699419 | + | 1.24973i | ||||
\(910\) | 1.92218e43 | − | 7.80250e42i | 2.38613 | − | 0.968575i | ||||
\(911\) | − | 1.18310e43i | − | 1.44546i | −0.691130 | − | 0.722730i | \(-0.742887\pi\) | ||
0.691130 | − | 0.722730i | \(-0.257113\pi\) | |||||||
\(912\) | 1.36526e43 | − | 8.00451e42i | 1.64169 | − | 0.962520i | ||||
\(913\) | − | 1.05118e43i | − | 1.24409i | ||||||
\(914\) | 2.53686e43i | 2.95513i | ||||||||
\(915\) | 6.08068e42 | − | 3.56510e42i | 0.697182 | − | 0.408757i | ||||
\(916\) | 1.79231e43i | 2.02268i | ||||||||
\(917\) | −1.31182e43 | + | 5.32493e42i | −1.45720 | + | 0.591506i | ||||
\(918\) | 8.30706e40 | + | 4.14118e42i | 0.00908298 | + | 0.452799i | ||||
\(919\) | 1.41281e43 | 1.52058 | 0.760290 | − | 0.649583i | \(-0.225057\pi\) | ||||
0.760290 | + | 0.649583i | \(0.225057\pi\) | |||||||
\(920\) | −4.42001e42 | −0.468274 | ||||||||
\(921\) | 2.99844e42 | − | 1.75798e42i | 0.312702 | − | 0.183337i | ||||
\(922\) | − | 1.19722e43i | − | 1.22907i | ||||||
\(923\) | −2.27496e42 | −0.229906 | ||||||||
\(924\) | 2.19386e43 | − | 2.85663e43i | 2.18256 | − | 2.84191i | ||||
\(925\) | −4.76141e42 | −0.466316 | ||||||||
\(926\) | 1.42176e42i | 0.137077i | ||||||||
\(927\) | 2.66799e42 | + | 1.49316e42i | 0.253237 | + | 0.141726i | ||||
\(928\) | 1.50970e43 | 1.41073 | ||||||||
\(929\) | −4.38245e42 | −0.403171 | −0.201586 | − | 0.979471i | \(-0.564609\pi\) | ||||
−0.201586 | + | 0.979471i | \(0.564609\pi\) | |||||||
\(930\) | −2.38266e43 | − | 4.06390e43i | −2.15804 | − | 3.68079i | ||||
\(931\) | 6.46036e42 | + | 6.64653e42i | 0.576085 | + | 0.592686i | ||||
\(932\) | 6.43210e42i | 0.564705i | ||||||||
\(933\) | −5.79750e40 | − | 9.88829e40i | −0.00501137 | − | 0.00854747i | ||||
\(934\) | − | 1.96938e43i | − | 1.67610i | ||||||
\(935\) | 5.25175e42i | 0.440084i | ||||||||
\(936\) | −1.77410e43 | + | 3.16997e43i | −1.46379 | + | 2.61550i | ||||
\(937\) | − | 1.84887e43i | − | 1.50204i | −0.660277 | − | 0.751022i | \(-0.729561\pi\) | ||
0.660277 | − | 0.751022i | \(-0.270439\pi\) | |||||||
\(938\) | 5.00223e42 | + | 1.23232e43i | 0.400150 | + | 0.985789i | ||||
\(939\) | 3.09073e42 | − | 1.81209e42i | 0.243450 | − | 0.142735i | ||||
\(940\) | −4.54675e43 | −3.52652 | ||||||||
\(941\) | −2.02949e43 | −1.55002 | −0.775009 | − | 0.631950i | \(-0.782255\pi\) | ||||
−0.775009 | + | 0.631950i | \(0.782255\pi\) | |||||||
\(942\) | −9.43787e42 | − | 1.60974e43i | −0.709800 | − | 1.21064i | ||||
\(943\) | − | 2.14540e40i | − | 0.00158887i | ||||||
\(944\) | −1.40745e43 | −1.02645 | ||||||||
\(945\) | −1.52223e43 | + | 6.53759e42i | −1.09325 | + | 0.469523i | ||||
\(946\) | 6.87936e43 | 4.86549 | ||||||||
\(947\) | − | 5.73675e42i | − | 0.399569i | −0.979840 | − | 0.199784i | \(-0.935976\pi\) | ||
0.979840 | − | 0.199784i | \(-0.0640242\pi\) | |||||||
\(948\) | 1.03444e43 | + | 1.76436e43i | 0.709555 | + | 1.21023i | ||||
\(949\) | −1.73370e43 | −1.17116 | ||||||||
\(950\) | −9.50033e42 | −0.632043 | ||||||||
\(951\) | −8.28091e42 | + | 4.85509e42i | −0.542576 | + | 0.318112i | ||||
\(952\) | −3.65538e42 | − | 9.00522e42i | −0.235883 | − | 0.581110i | ||||
\(953\) | − | 3.42786e42i | − | 0.217859i | −0.994049 | − | 0.108929i | \(-0.965258\pi\) | ||
0.994049 | − | 0.108929i | \(-0.0347423\pi\) | |||||||
\(954\) | 1.91575e43 | − | 3.42307e43i | 1.19919 | − | 2.14271i | ||||
\(955\) | 2.55959e43i | 1.57805i | ||||||||
\(956\) | 3.13747e43i | 1.90520i | ||||||||
\(957\) | 1.06173e43 | + | 1.81089e43i | 0.635023 | + | 1.08310i | ||||
\(958\) | − | 5.47151e43i | − | 3.22335i | ||||||
\(959\) | −5.16566e42 | − | 1.27259e43i | −0.299748 | − | 0.738444i | ||||
\(960\) | −8.46113e42 | − | 1.44314e43i | −0.483610 | − | 0.824852i | ||||
\(961\) | −4.97222e43 | −2.79938 | ||||||||
\(962\) | 4.37859e43 | 2.42826 | ||||||||
\(963\) | 1.10849e43 | + | 6.20373e42i | 0.605549 | + | 0.338900i | ||||
\(964\) | 5.24711e43i | 2.82360i | ||||||||
\(965\) | 3.44912e43 | 1.82836 | ||||||||
\(966\) | 4.31652e42 | + | 3.31503e42i | 0.225406 | + | 0.173109i | ||||
\(967\) | −7.51156e42 | −0.386408 | −0.193204 | − | 0.981159i | \(-0.561888\pi\) | ||||
−0.193204 | + | 0.981159i | \(0.561888\pi\) | |||||||
\(968\) | 6.32291e43i | 3.20423i | ||||||||
\(969\) | 3.51577e42 | − | 2.06129e42i | 0.175520 | − | 0.102907i | ||||
\(970\) | 2.06706e43 | 1.01663 | ||||||||
\(971\) | −2.84958e43 | −1.38071 | −0.690354 | − | 0.723472i | \(-0.742545\pi\) | ||||
−0.690354 | + | 0.723472i | \(0.742545\pi\) | |||||||
\(972\) | 2.35194e43 | − | 4.40763e43i | 1.12271 | − | 2.10399i | ||||
\(973\) | 1.05335e43 | + | 2.59497e43i | 0.495376 | + | 1.22038i | ||||
\(974\) | − | 3.04212e43i | − | 1.40952i | ||||||
\(975\) | 9.24064e42 | − | 5.41778e42i | 0.421828 | − | 0.247317i | ||||
\(976\) | − | 3.47729e43i | − | 1.56393i | ||||||
\(977\) | − | 8.83529e41i | − | 0.0391516i | −0.999808 | − | 0.0195758i | \(-0.993768\pi\) | ||
0.999808 | − | 0.0195758i | \(-0.00623157\pi\) | |||||||
\(978\) | −8.15249e42 | + | 4.77980e42i | −0.355940 | + | 0.208687i | ||||
\(979\) | 7.39043e41i | 0.0317922i | ||||||||
\(980\) | 4.80035e43 | − | 4.66589e43i | 2.03467 | − | 1.97768i | ||||
\(981\) | 6.54092e42 | − | 1.16874e43i | 0.273173 | − | 0.488108i | ||||
\(982\) | −3.31112e43 | −1.36257 | ||||||||
\(983\) | 1.12350e43 | 0.455560 | 0.227780 | − | 0.973713i | \(-0.426853\pi\) | ||||
0.227780 | + | 0.973713i | \(0.426853\pi\) | |||||||
\(984\) | 5.65768e41 | − | 3.31710e41i | 0.0226053 | − | 0.0132535i | ||||
\(985\) | − | 5.69999e41i | − | 0.0224413i | ||||||
\(986\) | 9.75450e42 | 0.378434 | ||||||||
\(987\) | 2.57837e43 | + | 1.98016e43i | 0.985704 | + | 0.757009i | ||||
\(988\) | 6.15540e43 | 2.31889 | ||||||||
\(989\) | 7.32396e42i | 0.271894i | ||||||||
\(990\) | 4.39076e43 | − | 7.84544e43i | 1.60631 | − | 2.87017i | ||||
\(991\) | −1.88068e43 | −0.678027 | −0.339014 | − | 0.940781i | \(-0.610093\pi\) | ||||
−0.339014 | + | 0.940781i | \(0.610093\pi\) | |||||||
\(992\) | −9.26239e43 | −3.29082 | ||||||||
\(993\) | 1.35134e43 | + | 2.30487e43i | 0.473153 | + | 0.807016i | ||||
\(994\) | −9.65444e42 | + | 3.91891e42i | −0.333138 | + | 0.135227i | ||||
\(995\) | 6.88725e43i | 2.34213i | ||||||||
\(996\) | 2.97983e43 | + | 5.08243e43i | 0.998689 | + | 1.70338i | ||||
\(997\) | 3.63727e42i | 0.120142i | 0.998194 | + | 0.0600711i | \(0.0191327\pi\) | ||||
−0.998194 | + | 0.0600711i | \(0.980867\pi\) | |||||||
\(998\) | 4.10229e42i | 0.133547i | ||||||||
\(999\) | −3.49599e43 | + | 7.01283e41i | −1.12168 | + | 0.0225006i |
(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.20.14 | yes | 76 | |
3.2 | odd | 2 | inner | 21.30.c.a.20.63 | yes | 76 | |
7.6 | odd | 2 | inner | 21.30.c.a.20.64 | yes | 76 | |
21.20 | even | 2 | inner | 21.30.c.a.20.13 | ✓ | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.30.c.a.20.13 | ✓ | 76 | 21.20 | even | 2 | inner | |
21.30.c.a.20.14 | yes | 76 | 1.1 | even | 1 | trivial | |
21.30.c.a.20.63 | yes | 76 | 3.2 | odd | 2 | inner | |
21.30.c.a.20.64 | yes | 76 | 7.6 | odd | 2 | inner |