Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,44,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 44, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 44);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 44 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.a (trivial) |
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: | yes |
Analytic conductor: | \(35.1331186037\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 886516819907x^{2} - 42308083143723387x + 94580276745082867224894 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{10}\cdot 5^{2}\cdot 7\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-388484.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.91590e6 | −0.645995 | −0.322997 | − | 0.946400i | \(-0.604691\pi\) | ||||
−0.322997 | + | 0.946400i | \(0.604691\pi\) | |||||||
\(3\) | −1.04604e10 | −0.577350 | ||||||||
\(4\) | −5.12540e12 | −0.582691 | ||||||||
\(5\) | 2.05854e15 | 1.93065 | 0.965326 | − | 0.261047i | \(-0.0840678\pi\) | ||||
0.965326 | + | 0.261047i | \(0.0840678\pi\) | |||||||
\(6\) | 2.00410e16 | 0.372965 | ||||||||
\(7\) | 1.37114e18 | 0.927844 | 0.463922 | − | 0.885876i | \(-0.346442\pi\) | ||||
0.463922 | + | 0.885876i | \(0.346442\pi\) | |||||||
\(8\) | 2.66723e19 | 1.02241 | ||||||||
\(9\) | 1.09419e20 | 0.333333 | ||||||||
\(10\) | −3.94396e21 | −1.24719 | ||||||||
\(11\) | −2.95641e22 | −1.20454 | −0.602271 | − | 0.798292i | \(-0.705737\pi\) | ||||
−0.602271 | + | 0.798292i | \(0.705737\pi\) | |||||||
\(12\) | 5.36135e22 | 0.336417 | ||||||||
\(13\) | 4.85026e23 | 0.544481 | 0.272241 | − | 0.962229i | \(-0.412235\pi\) | ||||
0.272241 | + | 0.962229i | \(0.412235\pi\) | |||||||
\(14\) | −2.62698e24 | −0.599383 | ||||||||
\(15\) | −2.15330e25 | −1.11466 | ||||||||
\(16\) | −6.01799e24 | −0.0777807 | ||||||||
\(17\) | 2.08153e26 | 0.730686 | 0.365343 | − | 0.930873i | \(-0.380952\pi\) | ||||
0.365343 | + | 0.930873i | \(0.380952\pi\) | |||||||
\(18\) | −2.09636e26 | −0.215332 | ||||||||
\(19\) | −1.07725e27 | −0.346029 | −0.173015 | − | 0.984919i | \(-0.555351\pi\) | ||||
−0.173015 | + | 0.984919i | \(0.555351\pi\) | |||||||
\(20\) | −1.05508e28 | −1.12497 | ||||||||
\(21\) | −1.43426e28 | −0.535691 | ||||||||
\(22\) | 5.66420e28 | 0.778128 | ||||||||
\(23\) | −2.47106e29 | −1.30537 | −0.652686 | − | 0.757628i | \(-0.726358\pi\) | ||||
−0.652686 | + | 0.757628i | \(0.726358\pi\) | |||||||
\(24\) | −2.79001e29 | −0.590289 | ||||||||
\(25\) | 3.10071e30 | 2.72742 | ||||||||
\(26\) | −9.29263e29 | −0.351732 | ||||||||
\(27\) | −1.14456e30 | −0.192450 | ||||||||
\(28\) | −7.02766e30 | −0.540646 | ||||||||
\(29\) | 1.39089e31 | 0.503195 | 0.251597 | − | 0.967832i | \(-0.419044\pi\) | ||||
0.251597 | + | 0.967832i | \(0.419044\pi\) | |||||||
\(30\) | 4.12553e31 | 0.720066 | ||||||||
\(31\) | 1.48976e31 | 0.128481 | 0.0642406 | − | 0.997934i | \(-0.479537\pi\) | ||||
0.0642406 | + | 0.997934i | \(0.479537\pi\) | |||||||
\(32\) | −2.23082e32 | −0.972164 | ||||||||
\(33\) | 3.09251e32 | 0.695443 | ||||||||
\(34\) | −3.98801e32 | −0.472020 | ||||||||
\(35\) | 2.82255e33 | 1.79134 | ||||||||
\(36\) | −5.60816e32 | −0.194230 | ||||||||
\(37\) | 9.02009e33 | 1.73330 | 0.866651 | − | 0.498916i | \(-0.166268\pi\) | ||||
0.866651 | + | 0.498916i | \(0.166268\pi\) | |||||||
\(38\) | 2.06390e33 | 0.223533 | ||||||||
\(39\) | −5.07354e33 | −0.314356 | ||||||||
\(40\) | 5.49059e34 | 1.97392 | ||||||||
\(41\) | 5.58080e34 | 1.17989 | 0.589947 | − | 0.807442i | \(-0.299148\pi\) | ||||
0.589947 | + | 0.807442i | \(0.299148\pi\) | |||||||
\(42\) | 2.74791e34 | 0.346054 | ||||||||
\(43\) | −2.06648e35 | −1.56913 | −0.784565 | − | 0.620047i | \(-0.787113\pi\) | ||||
−0.784565 | + | 0.620047i | \(0.787113\pi\) | |||||||
\(44\) | 1.51528e35 | 0.701876 | ||||||||
\(45\) | 2.25243e35 | 0.643551 | ||||||||
\(46\) | 4.73431e35 | 0.843264 | ||||||||
\(47\) | 6.46223e35 | 0.724901 | 0.362450 | − | 0.932003i | \(-0.381940\pi\) | ||||
0.362450 | + | 0.932003i | \(0.381940\pi\) | |||||||
\(48\) | 6.29503e34 | 0.0449067 | ||||||||
\(49\) | −3.03780e35 | −0.139105 | ||||||||
\(50\) | −5.94067e36 | −1.76190 | ||||||||
\(51\) | −2.17735e36 | −0.421862 | ||||||||
\(52\) | −2.48595e36 | −0.317264 | ||||||||
\(53\) | −4.21095e36 | −0.356820 | −0.178410 | − | 0.983956i | \(-0.557095\pi\) | ||||
−0.178410 | + | 0.983956i | \(0.557095\pi\) | |||||||
\(54\) | 2.19287e36 | 0.124322 | ||||||||
\(55\) | −6.08589e37 | −2.32555 | ||||||||
\(56\) | 3.65715e37 | 0.948637 | ||||||||
\(57\) | 1.12684e37 | 0.199780 | ||||||||
\(58\) | −2.66481e37 | −0.325061 | ||||||||
\(59\) | 4.40127e37 | 0.371757 | 0.185879 | − | 0.982573i | \(-0.440487\pi\) | ||||
0.185879 | + | 0.982573i | \(0.440487\pi\) | |||||||
\(60\) | 1.10366e38 | 0.649504 | ||||||||
\(61\) | 4.53571e37 | 0.187091 | 0.0935457 | − | 0.995615i | \(-0.470180\pi\) | ||||
0.0935457 | + | 0.995615i | \(0.470180\pi\) | |||||||
\(62\) | −2.85424e37 | −0.0829982 | ||||||||
\(63\) | 1.50029e38 | 0.309281 | ||||||||
\(64\) | 4.80338e38 | 0.705794 | ||||||||
\(65\) | 9.98445e38 | 1.05120 | ||||||||
\(66\) | −5.92495e38 | −0.449252 | ||||||||
\(67\) | −1.64891e37 | −0.00904878 | −0.00452439 | − | 0.999990i | \(-0.501440\pi\) | ||||
−0.00452439 | + | 0.999990i | \(0.501440\pi\) | |||||||
\(68\) | −1.06687e39 | −0.425764 | ||||||||
\(69\) | 2.58481e39 | 0.753657 | ||||||||
\(70\) | −5.40774e39 | −1.15720 | ||||||||
\(71\) | 6.75118e39 | 1.06494 | 0.532470 | − | 0.846449i | \(-0.321264\pi\) | ||||
0.532470 | + | 0.846449i | \(0.321264\pi\) | |||||||
\(72\) | 2.91845e39 | 0.340803 | ||||||||
\(73\) | −5.28077e39 | −0.458412 | −0.229206 | − | 0.973378i | \(-0.573613\pi\) | ||||
−0.229206 | + | 0.973378i | \(0.573613\pi\) | |||||||
\(74\) | −1.72816e40 | −1.11970 | ||||||||
\(75\) | −3.24346e40 | −1.57468 | ||||||||
\(76\) | 5.52132e39 | 0.201628 | ||||||||
\(77\) | −4.05366e40 | −1.11763 | ||||||||
\(78\) | 9.72042e39 | 0.203073 | ||||||||
\(79\) | 1.01508e41 | 1.61257 | 0.806286 | − | 0.591526i | \(-0.201474\pi\) | ||||
0.806286 | + | 0.591526i | \(0.201474\pi\) | |||||||
\(80\) | −1.23883e40 | −0.150167 | ||||||||
\(81\) | 1.19725e40 | 0.111111 | ||||||||
\(82\) | −1.06923e41 | −0.762206 | ||||||||
\(83\) | 2.11545e41 | 1.16205 | 0.581024 | − | 0.813886i | \(-0.302652\pi\) | ||||
0.581024 | + | 0.813886i | \(0.302652\pi\) | |||||||
\(84\) | 7.35118e40 | 0.312142 | ||||||||
\(85\) | 4.28491e41 | 1.41070 | ||||||||
\(86\) | 3.95917e41 | 1.01365 | ||||||||
\(87\) | −1.45492e41 | −0.290520 | ||||||||
\(88\) | −7.88542e41 | −1.23154 | ||||||||
\(89\) | −7.34681e41 | −0.899940 | −0.449970 | − | 0.893044i | \(-0.648565\pi\) | ||||
−0.449970 | + | 0.893044i | \(0.648565\pi\) | |||||||
\(90\) | −4.31545e41 | −0.415730 | ||||||||
\(91\) | 6.65040e41 | 0.505194 | ||||||||
\(92\) | 1.26652e42 | 0.760629 | ||||||||
\(93\) | −1.55834e41 | −0.0741787 | ||||||||
\(94\) | −1.23810e42 | −0.468282 | ||||||||
\(95\) | −2.21755e42 | −0.668062 | ||||||||
\(96\) | 2.33351e42 | 0.561279 | ||||||||
\(97\) | −6.37472e42 | −1.22707 | −0.613534 | − | 0.789668i | \(-0.710253\pi\) | ||||
−0.613534 | + | 0.789668i | \(0.710253\pi\) | |||||||
\(98\) | 5.82013e41 | 0.0898611 | ||||||||
\(99\) | −3.23487e42 | −0.401514 | ||||||||
\(100\) | −1.58924e43 | −1.58924 | ||||||||
\(101\) | 1.97674e43 | 1.59602 | 0.798012 | − | 0.602642i | \(-0.205885\pi\) | ||||
0.798012 | + | 0.602642i | \(0.205885\pi\) | |||||||
\(102\) | 4.17160e42 | 0.272521 | ||||||||
\(103\) | 2.37782e43 | 1.25944 | 0.629721 | − | 0.776821i | \(-0.283169\pi\) | ||||
0.629721 | + | 0.776821i | \(0.283169\pi\) | |||||||
\(104\) | 1.29367e43 | 0.556683 | ||||||||
\(105\) | −2.95249e43 | −1.03423 | ||||||||
\(106\) | 8.06778e42 | 0.230504 | ||||||||
\(107\) | 1.70071e41 | 0.00397081 | 0.00198541 | − | 0.999998i | \(-0.499368\pi\) | ||||
0.00198541 | + | 0.999998i | \(0.499368\pi\) | |||||||
\(108\) | 5.86634e42 | 0.112139 | ||||||||
\(109\) | 5.49545e43 | 0.861656 | 0.430828 | − | 0.902434i | \(-0.358222\pi\) | ||||
0.430828 | + | 0.902434i | \(0.358222\pi\) | |||||||
\(110\) | 1.16600e44 | 1.50229 | ||||||||
\(111\) | −9.43534e43 | −1.00072 | ||||||||
\(112\) | −8.25153e42 | −0.0721683 | ||||||||
\(113\) | 5.69482e43 | 0.411427 | 0.205714 | − | 0.978612i | \(-0.434048\pi\) | ||||
0.205714 | + | 0.978612i | \(0.434048\pi\) | |||||||
\(114\) | −2.15891e43 | −0.129057 | ||||||||
\(115\) | −5.08677e44 | −2.52022 | ||||||||
\(116\) | −7.12888e43 | −0.293207 | ||||||||
\(117\) | 5.30710e43 | 0.181494 | ||||||||
\(118\) | −8.43241e43 | −0.240153 | ||||||||
\(119\) | 2.85408e44 | 0.677963 | ||||||||
\(120\) | −5.74335e44 | −1.13964 | ||||||||
\(121\) | 2.71636e44 | 0.450922 | ||||||||
\(122\) | −8.68999e43 | −0.120860 | ||||||||
\(123\) | −5.83771e44 | −0.681213 | ||||||||
\(124\) | −7.63561e43 | −0.0748648 | ||||||||
\(125\) | 4.04265e45 | 3.33504 | ||||||||
\(126\) | −2.87442e44 | −0.199794 | ||||||||
\(127\) | −1.89728e45 | −1.11263 | −0.556316 | − | 0.830971i | \(-0.687786\pi\) | ||||
−0.556316 | + | 0.830971i | \(0.687786\pi\) | |||||||
\(128\) | 1.04197e45 | 0.516225 | ||||||||
\(129\) | 2.16161e45 | 0.905937 | ||||||||
\(130\) | −1.91292e45 | −0.679072 | ||||||||
\(131\) | 1.03358e45 | 0.311179 | 0.155590 | − | 0.987822i | \(-0.450272\pi\) | ||||
0.155590 | + | 0.987822i | \(0.450272\pi\) | |||||||
\(132\) | −1.58504e45 | −0.405228 | ||||||||
\(133\) | −1.47706e45 | −0.321061 | ||||||||
\(134\) | 3.15916e43 | 0.00584546 | ||||||||
\(135\) | −2.35612e45 | −0.371554 | ||||||||
\(136\) | 5.55191e45 | 0.747061 | ||||||||
\(137\) | 7.28740e45 | 0.837684 | 0.418842 | − | 0.908059i | \(-0.362436\pi\) | ||||
0.418842 | + | 0.908059i | \(0.362436\pi\) | |||||||
\(138\) | −4.95226e45 | −0.486859 | ||||||||
\(139\) | −6.85030e44 | −0.0576622 | −0.0288311 | − | 0.999584i | \(-0.509178\pi\) | ||||
−0.0288311 | + | 0.999584i | \(0.509178\pi\) | |||||||
\(140\) | −1.44667e46 | −1.04380 | ||||||||
\(141\) | −6.75972e45 | −0.418522 | ||||||||
\(142\) | −1.29346e46 | −0.687945 | ||||||||
\(143\) | −1.43394e46 | −0.655851 | ||||||||
\(144\) | −6.58482e44 | −0.0259269 | ||||||||
\(145\) | 2.86320e46 | 0.971494 | ||||||||
\(146\) | 1.01175e46 | 0.296132 | ||||||||
\(147\) | 3.17764e45 | 0.0803123 | ||||||||
\(148\) | −4.62316e46 | −1.00998 | ||||||||
\(149\) | −8.50711e45 | −0.160797 | −0.0803984 | − | 0.996763i | \(-0.525619\pi\) | ||||
−0.0803984 | + | 0.996763i | \(0.525619\pi\) | |||||||
\(150\) | 6.21415e46 | 1.01723 | ||||||||
\(151\) | 8.58237e46 | 1.21788 | 0.608938 | − | 0.793218i | \(-0.291596\pi\) | ||||
0.608938 | + | 0.793218i | \(0.291596\pi\) | |||||||
\(152\) | −2.87326e46 | −0.353784 | ||||||||
\(153\) | 2.27759e46 | 0.243562 | ||||||||
\(154\) | 7.76643e46 | 0.721982 | ||||||||
\(155\) | 3.06673e46 | 0.248053 | ||||||||
\(156\) | 2.60039e46 | 0.183173 | ||||||||
\(157\) | 2.17438e47 | 1.33504 | 0.667519 | − | 0.744593i | \(-0.267356\pi\) | ||||
0.667519 | + | 0.744593i | \(0.267356\pi\) | |||||||
\(158\) | −1.94480e47 | −1.04171 | ||||||||
\(159\) | 4.40480e46 | 0.206010 | ||||||||
\(160\) | −4.59223e47 | −1.87691 | ||||||||
\(161\) | −3.38818e47 | −1.21118 | ||||||||
\(162\) | −2.29382e46 | −0.0717772 | ||||||||
\(163\) | 2.10328e47 | 0.576584 | 0.288292 | − | 0.957543i | \(-0.406913\pi\) | ||||
0.288292 | + | 0.957543i | \(0.406913\pi\) | |||||||
\(164\) | −2.86038e47 | −0.687514 | ||||||||
\(165\) | 6.36605e47 | 1.34266 | ||||||||
\(166\) | −4.05300e47 | −0.750677 | ||||||||
\(167\) | 4.19368e47 | 0.682639 | 0.341320 | − | 0.939947i | \(-0.389126\pi\) | ||||
0.341320 | + | 0.939947i | \(0.389126\pi\) | |||||||
\(168\) | −3.82551e47 | −0.547696 | ||||||||
\(169\) | −5.58281e47 | −0.703540 | ||||||||
\(170\) | −8.20948e47 | −0.911305 | ||||||||
\(171\) | −1.17871e47 | −0.115343 | ||||||||
\(172\) | 1.05915e48 | 0.914317 | ||||||||
\(173\) | −2.43273e47 | −0.185397 | −0.0926983 | − | 0.995694i | \(-0.529549\pi\) | ||||
−0.0926983 | + | 0.995694i | \(0.529549\pi\) | |||||||
\(174\) | 2.78749e47 | 0.187674 | ||||||||
\(175\) | 4.25153e48 | 2.53062 | ||||||||
\(176\) | 1.77916e47 | 0.0936901 | ||||||||
\(177\) | −4.60388e47 | −0.214634 | ||||||||
\(178\) | 1.40758e48 | 0.581357 | ||||||||
\(179\) | 3.65334e47 | 0.133767 | 0.0668836 | − | 0.997761i | \(-0.478694\pi\) | ||||
0.0668836 | + | 0.997761i | \(0.478694\pi\) | |||||||
\(180\) | −1.15446e48 | −0.374991 | ||||||||
\(181\) | −4.64912e48 | −1.34054 | −0.670272 | − | 0.742115i | \(-0.733823\pi\) | ||||
−0.670272 | + | 0.742115i | \(0.733823\pi\) | |||||||
\(182\) | −1.27415e48 | −0.326352 | ||||||||
\(183\) | −4.74451e47 | −0.108017 | ||||||||
\(184\) | −6.59087e48 | −1.33463 | ||||||||
\(185\) | 1.85682e49 | 3.34640 | ||||||||
\(186\) | 2.98563e47 | 0.0479190 | ||||||||
\(187\) | −6.15386e48 | −0.880143 | ||||||||
\(188\) | −3.31215e48 | −0.422393 | ||||||||
\(189\) | −1.56936e48 | −0.178564 | ||||||||
\(190\) | 4.24862e48 | 0.431565 | ||||||||
\(191\) | −1.11668e49 | −1.01324 | −0.506621 | − | 0.862169i | \(-0.669106\pi\) | ||||
−0.506621 | + | 0.862169i | \(0.669106\pi\) | |||||||
\(192\) | −5.02451e48 | −0.407490 | ||||||||
\(193\) | −8.49609e48 | −0.616222 | −0.308111 | − | 0.951350i | \(-0.599697\pi\) | ||||
−0.308111 | + | 0.951350i | \(0.599697\pi\) | |||||||
\(194\) | 1.22134e49 | 0.792680 | ||||||||
\(195\) | −1.04441e49 | −0.606913 | ||||||||
\(196\) | 1.55699e48 | 0.0810552 | ||||||||
\(197\) | −2.47958e49 | −1.15706 | −0.578529 | − | 0.815662i | \(-0.696373\pi\) | ||||
−0.578529 | + | 0.815662i | \(0.696373\pi\) | |||||||
\(198\) | 6.19771e48 | 0.259376 | ||||||||
\(199\) | −1.43615e49 | −0.539336 | −0.269668 | − | 0.962953i | \(-0.586914\pi\) | ||||
−0.269668 | + | 0.962953i | \(0.586914\pi\) | |||||||
\(200\) | 8.27031e49 | 2.78854 | ||||||||
\(201\) | 1.72482e47 | 0.00522431 | ||||||||
\(202\) | −3.78724e49 | −1.03102 | ||||||||
\(203\) | 1.90711e49 | 0.466886 | ||||||||
\(204\) | 1.11598e49 | 0.245815 | ||||||||
\(205\) | 1.14883e50 | 2.27797 | ||||||||
\(206\) | −4.55567e49 | −0.813593 | ||||||||
\(207\) | −2.70381e49 | −0.435124 | ||||||||
\(208\) | −2.91888e48 | −0.0423501 | ||||||||
\(209\) | 3.18478e49 | 0.416807 | ||||||||
\(210\) | 5.65669e49 | 0.668109 | ||||||||
\(211\) | −1.63599e49 | −0.174464 | −0.0872322 | − | 0.996188i | \(-0.527802\pi\) | ||||
−0.0872322 | + | 0.996188i | \(0.527802\pi\) | |||||||
\(212\) | 2.15828e49 | 0.207916 | ||||||||
\(213\) | −7.06197e49 | −0.614843 | ||||||||
\(214\) | −3.25840e47 | −0.00256512 | ||||||||
\(215\) | −4.25392e50 | −3.02944 | ||||||||
\(216\) | −3.05280e49 | −0.196763 | ||||||||
\(217\) | 2.04267e49 | 0.119211 | ||||||||
\(218\) | −1.05288e50 | −0.556625 | ||||||||
\(219\) | 5.52387e49 | 0.264664 | ||||||||
\(220\) | 3.11926e50 | 1.35508 | ||||||||
\(221\) | 1.00960e50 | 0.397845 | ||||||||
\(222\) | 1.80772e50 | 0.646461 | ||||||||
\(223\) | −3.73988e50 | −1.21424 | −0.607118 | − | 0.794612i | \(-0.707674\pi\) | ||||
−0.607118 | + | 0.794612i | \(0.707674\pi\) | |||||||
\(224\) | −3.05877e50 | −0.902017 | ||||||||
\(225\) | 3.39277e50 | 0.909139 | ||||||||
\(226\) | −1.09107e50 | −0.265780 | ||||||||
\(227\) | 8.48595e49 | 0.187994 | 0.0939972 | − | 0.995572i | \(-0.470036\pi\) | ||||
0.0939972 | + | 0.995572i | \(0.470036\pi\) | |||||||
\(228\) | −5.77550e49 | −0.116410 | ||||||||
\(229\) | −7.41729e49 | −0.136076 | −0.0680381 | − | 0.997683i | \(-0.521674\pi\) | ||||
−0.0680381 | + | 0.997683i | \(0.521674\pi\) | |||||||
\(230\) | 9.74577e50 | 1.62805 | ||||||||
\(231\) | 4.24028e50 | 0.645263 | ||||||||
\(232\) | 3.70982e50 | 0.514471 | ||||||||
\(233\) | −1.00178e51 | −1.26654 | −0.633269 | − | 0.773932i | \(-0.718287\pi\) | ||||
−0.633269 | + | 0.773932i | \(0.718287\pi\) | |||||||
\(234\) | −1.01679e50 | −0.117244 | ||||||||
\(235\) | 1.33028e51 | 1.39953 | ||||||||
\(236\) | −2.25583e50 | −0.216620 | ||||||||
\(237\) | −1.06181e51 | −0.931019 | ||||||||
\(238\) | −5.46814e50 | −0.437961 | ||||||||
\(239\) | 8.73908e50 | 0.639604 | 0.319802 | − | 0.947484i | \(-0.396384\pi\) | ||||
0.319802 | + | 0.947484i | \(0.396384\pi\) | |||||||
\(240\) | 1.29586e50 | 0.0866992 | ||||||||
\(241\) | −3.95900e50 | −0.242225 | −0.121112 | − | 0.992639i | \(-0.538646\pi\) | ||||
−0.121112 | + | 0.992639i | \(0.538646\pi\) | |||||||
\(242\) | −5.20428e50 | −0.291293 | ||||||||
\(243\) | −1.25237e50 | −0.0641500 | ||||||||
\(244\) | −2.32473e50 | −0.109016 | ||||||||
\(245\) | −6.25342e50 | −0.268563 | ||||||||
\(246\) | 1.11845e51 | 0.440060 | ||||||||
\(247\) | −5.22493e50 | −0.188406 | ||||||||
\(248\) | 3.97352e50 | 0.131360 | ||||||||
\(249\) | −2.21284e51 | −0.670909 | ||||||||
\(250\) | −7.74534e51 | −2.15442 | ||||||||
\(251\) | 1.46542e51 | 0.374090 | 0.187045 | − | 0.982351i | \(-0.440109\pi\) | ||||
0.187045 | + | 0.982351i | \(0.440109\pi\) | |||||||
\(252\) | −7.68960e50 | −0.180215 | ||||||||
\(253\) | 7.30546e51 | 1.57238 | ||||||||
\(254\) | 3.63501e51 | 0.718755 | ||||||||
\(255\) | −4.48217e51 | −0.814469 | ||||||||
\(256\) | −6.22141e51 | −1.03927 | ||||||||
\(257\) | 1.09888e52 | 1.68806 | 0.844030 | − | 0.536296i | \(-0.180177\pi\) | ||||
0.844030 | + | 0.536296i | \(0.180177\pi\) | |||||||
\(258\) | −4.14143e51 | −0.585231 | ||||||||
\(259\) | 1.23678e52 | 1.60823 | ||||||||
\(260\) | −5.11743e51 | −0.612527 | ||||||||
\(261\) | 1.52190e51 | 0.167732 | ||||||||
\(262\) | −1.98024e51 | −0.201020 | ||||||||
\(263\) | 1.90424e51 | 0.178104 | 0.0890519 | − | 0.996027i | \(-0.471616\pi\) | ||||
0.0890519 | + | 0.996027i | \(0.471616\pi\) | |||||||
\(264\) | 8.24842e51 | 0.711028 | ||||||||
\(265\) | −8.66841e51 | −0.688895 | ||||||||
\(266\) | 2.82991e51 | 0.207404 | ||||||||
\(267\) | 7.68502e51 | 0.519581 | ||||||||
\(268\) | 8.45135e49 | 0.00527264 | ||||||||
\(269\) | 2.81599e52 | 1.62165 | 0.810826 | − | 0.585287i | \(-0.199018\pi\) | ||||
0.810826 | + | 0.585287i | \(0.199018\pi\) | |||||||
\(270\) | 4.51411e51 | 0.240022 | ||||||||
\(271\) | −1.50188e52 | −0.737558 | −0.368779 | − | 0.929517i | \(-0.620224\pi\) | ||||
−0.368779 | + | 0.929517i | \(0.620224\pi\) | |||||||
\(272\) | −1.25266e51 | −0.0568333 | ||||||||
\(273\) | −6.95655e51 | −0.291674 | ||||||||
\(274\) | −1.39620e52 | −0.541140 | ||||||||
\(275\) | −9.16699e52 | −3.28529 | ||||||||
\(276\) | −1.32482e52 | −0.439149 | ||||||||
\(277\) | −2.09522e52 | −0.642561 | −0.321280 | − | 0.946984i | \(-0.604113\pi\) | ||||
−0.321280 | + | 0.946984i | \(0.604113\pi\) | |||||||
\(278\) | 1.31245e51 | 0.0372495 | ||||||||
\(279\) | 1.63008e51 | 0.0428271 | ||||||||
\(280\) | 7.52839e52 | 1.83149 | ||||||||
\(281\) | −1.94351e52 | −0.437926 | −0.218963 | − | 0.975733i | \(-0.570267\pi\) | ||||
−0.218963 | + | 0.975733i | \(0.570267\pi\) | |||||||
\(282\) | 1.29510e52 | 0.270363 | ||||||||
\(283\) | 5.63973e52 | 1.09106 | 0.545532 | − | 0.838090i | \(-0.316328\pi\) | ||||
0.545532 | + | 0.838090i | \(0.316328\pi\) | |||||||
\(284\) | −3.46025e52 | −0.620531 | ||||||||
\(285\) | 2.31964e52 | 0.385706 | ||||||||
\(286\) | 2.74728e52 | 0.423676 | ||||||||
\(287\) | 7.65207e52 | 1.09476 | ||||||||
\(288\) | −2.44094e52 | −0.324055 | ||||||||
\(289\) | −3.78251e52 | −0.466098 | ||||||||
\(290\) | −5.48562e52 | −0.627580 | ||||||||
\(291\) | 6.66818e52 | 0.708448 | ||||||||
\(292\) | 2.70661e52 | 0.267112 | ||||||||
\(293\) | −1.38284e53 | −1.26800 | −0.633998 | − | 0.773334i | \(-0.718587\pi\) | ||||
−0.633998 | + | 0.773334i | \(0.718587\pi\) | |||||||
\(294\) | −6.08806e51 | −0.0518813 | ||||||||
\(295\) | 9.06018e52 | 0.717734 | ||||||||
\(296\) | 2.40586e53 | 1.77214 | ||||||||
\(297\) | 3.38379e52 | 0.231814 | ||||||||
\(298\) | 1.62988e52 | 0.103874 | ||||||||
\(299\) | −1.19853e53 | −0.710751 | ||||||||
\(300\) | 1.66240e53 | 0.917549 | ||||||||
\(301\) | −2.83344e53 | −1.45591 | ||||||||
\(302\) | −1.64430e53 | −0.786742 | ||||||||
\(303\) | −2.06774e53 | −0.921465 | ||||||||
\(304\) | 6.48286e51 | 0.0269144 | ||||||||
\(305\) | 9.33693e52 | 0.361208 | ||||||||
\(306\) | −4.36364e52 | −0.157340 | ||||||||
\(307\) | 1.55833e53 | 0.523822 | 0.261911 | − | 0.965092i | \(-0.415647\pi\) | ||||
0.261911 | + | 0.965092i | \(0.415647\pi\) | |||||||
\(308\) | 2.07767e53 | 0.651231 | ||||||||
\(309\) | −2.48728e53 | −0.727139 | ||||||||
\(310\) | −5.87556e52 | −0.160241 | ||||||||
\(311\) | 3.09503e53 | 0.787620 | 0.393810 | − | 0.919192i | \(-0.371157\pi\) | ||||
0.393810 | + | 0.919192i | \(0.371157\pi\) | |||||||
\(312\) | −1.35323e53 | −0.321401 | ||||||||
\(313\) | −6.06624e53 | −1.34498 | −0.672490 | − | 0.740106i | \(-0.734775\pi\) | ||||
−0.672490 | + | 0.740106i | \(0.734775\pi\) | |||||||
\(314\) | −4.16591e53 | −0.862428 | ||||||||
\(315\) | 3.08841e53 | 0.597115 | ||||||||
\(316\) | −5.20271e53 | −0.939631 | ||||||||
\(317\) | 7.12220e53 | 1.20182 | 0.600911 | − | 0.799316i | \(-0.294805\pi\) | ||||
0.600911 | + | 0.799316i | \(0.294805\pi\) | |||||||
\(318\) | −8.43919e52 | −0.133081 | ||||||||
\(319\) | −4.11204e53 | −0.606119 | ||||||||
\(320\) | 9.88795e53 | 1.36264 | ||||||||
\(321\) | −1.77900e51 | −0.00229255 | ||||||||
\(322\) | 6.49142e53 | 0.782418 | ||||||||
\(323\) | −2.24232e53 | −0.252839 | ||||||||
\(324\) | −6.13640e52 | −0.0647434 | ||||||||
\(325\) | 1.50393e54 | 1.48503 | ||||||||
\(326\) | −4.02968e53 | −0.372470 | ||||||||
\(327\) | −5.74844e53 | −0.497477 | ||||||||
\(328\) | 1.48852e54 | 1.20634 | ||||||||
\(329\) | 8.86065e53 | 0.672595 | ||||||||
\(330\) | −1.21968e54 | −0.867350 | ||||||||
\(331\) | −2.21005e53 | −0.147265 | −0.0736325 | − | 0.997285i | \(-0.523459\pi\) | ||||
−0.0736325 | + | 0.997285i | \(0.523459\pi\) | |||||||
\(332\) | −1.08425e54 | −0.677115 | ||||||||
\(333\) | 9.86970e53 | 0.577767 | ||||||||
\(334\) | −8.03469e53 | −0.440981 | ||||||||
\(335\) | −3.39435e52 | −0.0174700 | ||||||||
\(336\) | 8.63139e52 | 0.0416664 | ||||||||
\(337\) | −9.92988e53 | −0.449678 | −0.224839 | − | 0.974396i | \(-0.572186\pi\) | ||||
−0.224839 | + | 0.974396i | \(0.572186\pi\) | |||||||
\(338\) | 1.06961e54 | 0.454483 | ||||||||
\(339\) | −5.95698e53 | −0.237538 | ||||||||
\(340\) | −2.19619e54 | −0.822002 | ||||||||
\(341\) | −4.40434e53 | −0.154761 | ||||||||
\(342\) | 2.25830e53 | 0.0745110 | ||||||||
\(343\) | −3.41085e54 | −1.05691 | ||||||||
\(344\) | −5.51176e54 | −1.60429 | ||||||||
\(345\) | 5.32094e54 | 1.45505 | ||||||||
\(346\) | 4.66087e53 | 0.119765 | ||||||||
\(347\) | −2.14712e53 | −0.0518530 | −0.0259265 | − | 0.999664i | \(-0.508254\pi\) | ||||
−0.0259265 | + | 0.999664i | \(0.508254\pi\) | |||||||
\(348\) | 7.45706e53 | 0.169283 | ||||||||
\(349\) | 2.01754e53 | 0.0430601 | 0.0215300 | − | 0.999768i | \(-0.493146\pi\) | ||||
0.0215300 | + | 0.999768i | \(0.493146\pi\) | |||||||
\(350\) | −8.14552e54 | −1.63477 | ||||||||
\(351\) | −5.55142e53 | −0.104785 | ||||||||
\(352\) | 6.59521e54 | 1.17101 | ||||||||
\(353\) | 7.42627e54 | 1.24055 | 0.620275 | − | 0.784384i | \(-0.287021\pi\) | ||||
0.620275 | + | 0.784384i | \(0.287021\pi\) | |||||||
\(354\) | 8.82060e53 | 0.138653 | ||||||||
\(355\) | 1.38976e55 | 2.05603 | ||||||||
\(356\) | 3.76554e54 | 0.524387 | ||||||||
\(357\) | −2.98547e54 | −0.391422 | ||||||||
\(358\) | −6.99945e53 | −0.0864129 | ||||||||
\(359\) | −8.85340e54 | −1.02939 | −0.514694 | − | 0.857374i | \(-0.672095\pi\) | ||||
−0.514694 | + | 0.857374i | \(0.672095\pi\) | |||||||
\(360\) | 6.00775e54 | 0.657973 | ||||||||
\(361\) | −8.53135e54 | −0.880264 | ||||||||
\(362\) | 8.90727e54 | 0.865985 | ||||||||
\(363\) | −2.84141e54 | −0.260340 | ||||||||
\(364\) | −3.40860e54 | −0.294372 | ||||||||
\(365\) | −1.08707e55 | −0.885034 | ||||||||
\(366\) | 9.09003e53 | 0.0697786 | ||||||||
\(367\) | 2.72584e55 | 1.97324 | 0.986620 | − | 0.163035i | \(-0.0521283\pi\) | ||||
0.986620 | + | 0.163035i | \(0.0521283\pi\) | |||||||
\(368\) | 1.48708e54 | 0.101533 | ||||||||
\(369\) | 6.10645e54 | 0.393298 | ||||||||
\(370\) | −3.55749e55 | −2.16176 | ||||||||
\(371\) | −5.77382e54 | −0.331073 | ||||||||
\(372\) | 7.98712e53 | 0.0432232 | ||||||||
\(373\) | −2.12458e55 | −1.08526 | −0.542628 | − | 0.839973i | \(-0.682571\pi\) | ||||
−0.542628 | + | 0.839973i | \(0.682571\pi\) | |||||||
\(374\) | 1.17902e55 | 0.568567 | ||||||||
\(375\) | −4.22876e55 | −1.92549 | ||||||||
\(376\) | 1.72362e55 | 0.741146 | ||||||||
\(377\) | 6.74618e54 | 0.273980 | ||||||||
\(378\) | 3.00674e54 | 0.115351 | ||||||||
\(379\) | 2.08438e55 | 0.755499 | 0.377750 | − | 0.925908i | \(-0.376698\pi\) | ||||
0.377750 | + | 0.925908i | \(0.376698\pi\) | |||||||
\(380\) | 1.13659e55 | 0.389274 | ||||||||
\(381\) | 1.98462e55 | 0.642379 | ||||||||
\(382\) | 2.13946e55 | 0.654549 | ||||||||
\(383\) | −1.15099e55 | −0.332889 | −0.166444 | − | 0.986051i | \(-0.553229\pi\) | ||||
−0.166444 | + | 0.986051i | \(0.553229\pi\) | |||||||
\(384\) | −1.08993e55 | −0.298043 | ||||||||
\(385\) | −8.34463e55 | −2.15775 | ||||||||
\(386\) | 1.62777e55 | 0.398076 | ||||||||
\(387\) | −2.26112e55 | −0.523043 | ||||||||
\(388\) | 3.26730e55 | 0.715001 | ||||||||
\(389\) | 2.58934e54 | 0.0536132 | 0.0268066 | − | 0.999641i | \(-0.491466\pi\) | ||||
0.0268066 | + | 0.999641i | \(0.491466\pi\) | |||||||
\(390\) | 2.00099e55 | 0.392062 | ||||||||
\(391\) | −5.14358e55 | −0.953818 | ||||||||
\(392\) | −8.10249e54 | −0.142222 | ||||||||
\(393\) | −1.08116e55 | −0.179659 | ||||||||
\(394\) | 4.75065e55 | 0.747453 | ||||||||
\(395\) | 2.08959e56 | 3.11331 | ||||||||
\(396\) | 1.65800e55 | 0.233959 | ||||||||
\(397\) | −4.99618e55 | −0.667793 | −0.333897 | − | 0.942610i | \(-0.608364\pi\) | ||||
−0.333897 | + | 0.942610i | \(0.608364\pi\) | |||||||
\(398\) | 2.75153e55 | 0.348408 | ||||||||
\(399\) | 1.54506e55 | 0.185365 | ||||||||
\(400\) | −1.86601e55 | −0.212140 | ||||||||
\(401\) | 5.05004e55 | 0.544115 | 0.272058 | − | 0.962281i | \(-0.412296\pi\) | ||||
0.272058 | + | 0.962281i | \(0.412296\pi\) | |||||||
\(402\) | −3.30460e53 | −0.00337488 | ||||||||
\(403\) | 7.22572e54 | 0.0699556 | ||||||||
\(404\) | −1.01316e56 | −0.929988 | ||||||||
\(405\) | 2.46459e55 | 0.214517 | ||||||||
\(406\) | −3.65384e55 | −0.301606 | ||||||||
\(407\) | −2.66671e56 | −2.08783 | ||||||||
\(408\) | −5.80750e55 | −0.431316 | ||||||||
\(409\) | 2.15446e56 | 1.51806 | 0.759028 | − | 0.651058i | \(-0.225674\pi\) | ||||
0.759028 | + | 0.651058i | \(0.225674\pi\) | |||||||
\(410\) | −2.20105e56 | −1.47155 | ||||||||
\(411\) | −7.62288e55 | −0.483637 | ||||||||
\(412\) | −1.21873e56 | −0.733866 | ||||||||
\(413\) | 6.03477e55 | 0.344933 | ||||||||
\(414\) | 5.18024e55 | 0.281088 | ||||||||
\(415\) | 4.35474e56 | 2.24351 | ||||||||
\(416\) | −1.08200e56 | −0.529325 | ||||||||
\(417\) | 7.16566e54 | 0.0332913 | ||||||||
\(418\) | −6.10174e55 | −0.269255 | ||||||||
\(419\) | −3.43101e56 | −1.43820 | −0.719102 | − | 0.694904i | \(-0.755447\pi\) | ||||
−0.719102 | + | 0.694904i | \(0.755447\pi\) | |||||||
\(420\) | 1.51327e56 | 0.602638 | ||||||||
\(421\) | −4.45367e56 | −1.68521 | −0.842603 | − | 0.538536i | \(-0.818978\pi\) | ||||
−0.842603 | + | 0.538536i | \(0.818978\pi\) | |||||||
\(422\) | 3.13439e55 | 0.112703 | ||||||||
\(423\) | 7.07091e55 | 0.241634 | ||||||||
\(424\) | −1.12316e56 | −0.364816 | ||||||||
\(425\) | 6.45423e56 | 1.99289 | ||||||||
\(426\) | 1.35301e56 | 0.397185 | ||||||||
\(427\) | 6.21911e55 | 0.173592 | ||||||||
\(428\) | −8.71683e53 | −0.00231376 | ||||||||
\(429\) | 1.49995e56 | 0.378656 | ||||||||
\(430\) | 8.15011e56 | 1.95700 | ||||||||
\(431\) | −1.15170e56 | −0.263074 | −0.131537 | − | 0.991311i | \(-0.541991\pi\) | ||||
−0.131537 | + | 0.991311i | \(0.541991\pi\) | |||||||
\(432\) | 6.88796e54 | 0.0149689 | ||||||||
\(433\) | 2.47297e56 | 0.511362 | 0.255681 | − | 0.966761i | \(-0.417700\pi\) | ||||
0.255681 | + | 0.966761i | \(0.417700\pi\) | |||||||
\(434\) | −3.91357e55 | −0.0770094 | ||||||||
\(435\) | −2.99501e56 | −0.560892 | ||||||||
\(436\) | −2.81664e56 | −0.502079 | ||||||||
\(437\) | 2.66194e56 | 0.451697 | ||||||||
\(438\) | −1.05832e56 | −0.170972 | ||||||||
\(439\) | 4.99561e55 | 0.0768424 | 0.0384212 | − | 0.999262i | \(-0.487767\pi\) | ||||
0.0384212 | + | 0.999262i | \(0.487767\pi\) | |||||||
\(440\) | −1.62324e57 | −2.37767 | ||||||||
\(441\) | −3.32393e55 | −0.0463683 | ||||||||
\(442\) | −1.93429e56 | −0.257006 | ||||||||
\(443\) | 1.10930e57 | 1.40401 | 0.702003 | − | 0.712174i | \(-0.252289\pi\) | ||||
0.702003 | + | 0.712174i | \(0.252289\pi\) | |||||||
\(444\) | 4.83599e56 | 0.583111 | ||||||||
\(445\) | −1.51237e57 | −1.73747 | ||||||||
\(446\) | 7.16525e56 | 0.784389 | ||||||||
\(447\) | 8.89874e55 | 0.0928360 | ||||||||
\(448\) | 6.58613e56 | 0.654866 | ||||||||
\(449\) | −4.08332e55 | −0.0387005 | −0.0193503 | − | 0.999813i | \(-0.506160\pi\) | ||||
−0.0193503 | + | 0.999813i | \(0.506160\pi\) | |||||||
\(450\) | −6.50023e56 | −0.587299 | ||||||||
\(451\) | −1.64991e57 | −1.42123 | ||||||||
\(452\) | −2.91882e56 | −0.239735 | ||||||||
\(453\) | −8.97747e56 | −0.703141 | ||||||||
\(454\) | −1.62583e56 | −0.121443 | ||||||||
\(455\) | 1.36901e57 | 0.975353 | ||||||||
\(456\) | 3.00553e56 | 0.204257 | ||||||||
\(457\) | −1.23487e57 | −0.800611 | −0.400305 | − | 0.916382i | \(-0.631096\pi\) | ||||
−0.400305 | + | 0.916382i | \(0.631096\pi\) | |||||||
\(458\) | 1.42108e56 | 0.0879045 | ||||||||
\(459\) | −2.38244e56 | −0.140621 | ||||||||
\(460\) | 2.60717e57 | 1.46851 | ||||||||
\(461\) | 1.83528e57 | 0.986580 | 0.493290 | − | 0.869865i | \(-0.335794\pi\) | ||||
0.493290 | + | 0.869865i | \(0.335794\pi\) | |||||||
\(462\) | −8.12396e56 | −0.416836 | ||||||||
\(463\) | 8.87478e56 | 0.434677 | 0.217338 | − | 0.976096i | \(-0.430262\pi\) | ||||
0.217338 | + | 0.976096i | \(0.430262\pi\) | |||||||
\(464\) | −8.37036e55 | −0.0391388 | ||||||||
\(465\) | −3.20790e56 | −0.143213 | ||||||||
\(466\) | 1.91931e57 | 0.818177 | ||||||||
\(467\) | −9.54635e56 | −0.388620 | −0.194310 | − | 0.980940i | \(-0.562247\pi\) | ||||
−0.194310 | + | 0.980940i | \(0.562247\pi\) | |||||||
\(468\) | −2.72010e56 | −0.105755 | ||||||||
\(469\) | −2.26090e55 | −0.00839586 | ||||||||
\(470\) | −2.54868e57 | −0.904090 | ||||||||
\(471\) | −2.27448e57 | −0.770785 | ||||||||
\(472\) | 1.17392e57 | 0.380089 | ||||||||
\(473\) | 6.10935e57 | 1.89008 | ||||||||
\(474\) | 2.03433e57 | 0.601433 | ||||||||
\(475\) | −3.34024e57 | −0.943766 | ||||||||
\(476\) | −1.46283e57 | −0.395043 | ||||||||
\(477\) | −4.60758e56 | −0.118940 | ||||||||
\(478\) | −1.67432e57 | −0.413181 | ||||||||
\(479\) | 1.34733e57 | 0.317877 | 0.158939 | − | 0.987288i | \(-0.449193\pi\) | ||||
0.158939 | + | 0.987288i | \(0.449193\pi\) | |||||||
\(480\) | 4.80363e57 | 1.08363 | ||||||||
\(481\) | 4.37498e57 | 0.943750 | ||||||||
\(482\) | 7.58506e56 | 0.156476 | ||||||||
\(483\) | 3.54415e57 | 0.699277 | ||||||||
\(484\) | −1.39224e57 | −0.262748 | ||||||||
\(485\) | −1.31226e58 | −2.36904 | ||||||||
\(486\) | 2.39942e56 | 0.0414406 | ||||||||
\(487\) | −9.08466e57 | −1.50119 | −0.750596 | − | 0.660762i | \(-0.770233\pi\) | ||||
−0.750596 | + | 0.660762i | \(0.770233\pi\) | |||||||
\(488\) | 1.20978e57 | 0.191284 | ||||||||
\(489\) | −2.20010e57 | −0.332891 | ||||||||
\(490\) | 1.19810e57 | 0.173491 | ||||||||
\(491\) | −8.89699e57 | −1.23308 | −0.616540 | − | 0.787324i | \(-0.711466\pi\) | ||||
−0.616540 | + | 0.787324i | \(0.711466\pi\) | |||||||
\(492\) | 2.99206e57 | 0.396936 | ||||||||
\(493\) | 2.89518e57 | 0.367677 | ||||||||
\(494\) | 1.00105e57 | 0.121710 | ||||||||
\(495\) | −6.65912e57 | −0.775184 | ||||||||
\(496\) | −8.96535e55 | −0.00999335 | ||||||||
\(497\) | 9.25683e57 | 0.988098 | ||||||||
\(498\) | 4.23958e57 | 0.433404 | ||||||||
\(499\) | −7.85254e56 | −0.0768862 | −0.0384431 | − | 0.999261i | \(-0.512240\pi\) | ||||
−0.0384431 | + | 0.999261i | \(0.512240\pi\) | |||||||
\(500\) | −2.07202e58 | −1.94330 | ||||||||
\(501\) | −4.38674e57 | −0.394122 | ||||||||
\(502\) | −2.80760e57 | −0.241660 | ||||||||
\(503\) | 2.18276e58 | 1.80009 | 0.900044 | − | 0.435800i | \(-0.143534\pi\) | ||||
0.900044 | + | 0.435800i | \(0.143534\pi\) | |||||||
\(504\) | 4.00162e57 | 0.316212 | ||||||||
\(505\) | 4.06919e58 | 3.08137 | ||||||||
\(506\) | −1.39966e58 | −1.01575 | ||||||||
\(507\) | 5.83982e57 | 0.406189 | ||||||||
\(508\) | 9.72433e57 | 0.648321 | ||||||||
\(509\) | −9.01858e57 | −0.576376 | −0.288188 | − | 0.957574i | \(-0.593053\pi\) | ||||
−0.288188 | + | 0.957574i | \(0.593053\pi\) | |||||||
\(510\) | 8.58741e57 | 0.526142 | ||||||||
\(511\) | −7.24069e57 | −0.425335 | ||||||||
\(512\) | 2.75439e57 | 0.155139 | ||||||||
\(513\) | 1.23297e57 | 0.0665934 | ||||||||
\(514\) | −2.10535e58 | −1.09048 | ||||||||
\(515\) | 4.89483e58 | 2.43155 | ||||||||
\(516\) | −1.10791e58 | −0.527881 | ||||||||
\(517\) | −1.91050e58 | −0.873174 | ||||||||
\(518\) | −2.36956e58 | −1.03891 | ||||||||
\(519\) | 2.54472e57 | 0.107039 | ||||||||
\(520\) | 2.66308e58 | 1.07476 | ||||||||
\(521\) | −4.86422e57 | −0.188366 | −0.0941829 | − | 0.995555i | \(-0.530024\pi\) | ||||
−0.0941829 | + | 0.995555i | \(0.530024\pi\) | |||||||
\(522\) | −2.91581e57 | −0.108354 | ||||||||
\(523\) | −4.83195e58 | −1.72320 | −0.861601 | − | 0.507586i | \(-0.830538\pi\) | ||||
−0.861601 | + | 0.507586i | \(0.830538\pi\) | |||||||
\(524\) | −5.29750e57 | −0.181321 | ||||||||
\(525\) | −4.44725e58 | −1.46105 | ||||||||
\(526\) | −3.64834e57 | −0.115054 | ||||||||
\(527\) | 3.10098e57 | 0.0938795 | ||||||||
\(528\) | −1.86107e57 | −0.0540920 | ||||||||
\(529\) | 2.52272e58 | 0.703998 | ||||||||
\(530\) | 1.66078e58 | 0.445023 | ||||||||
\(531\) | 4.81582e57 | 0.123919 | ||||||||
\(532\) | 7.57053e57 | 0.187079 | ||||||||
\(533\) | 2.70683e58 | 0.642430 | ||||||||
\(534\) | −1.47238e58 | −0.335647 | ||||||||
\(535\) | 3.50098e56 | 0.00766626 | ||||||||
\(536\) | −4.39803e56 | −0.00925156 | ||||||||
\(537\) | −3.82152e57 | −0.0772305 | ||||||||
\(538\) | −5.39517e58 | −1.04758 | ||||||||
\(539\) | 8.98097e57 | 0.167558 | ||||||||
\(540\) | 1.20761e58 | 0.216501 | ||||||||
\(541\) | −8.31551e58 | −1.43267 | −0.716337 | − | 0.697754i | \(-0.754183\pi\) | ||||
−0.716337 | + | 0.697754i | \(0.754183\pi\) | |||||||
\(542\) | 2.87746e58 | 0.476458 | ||||||||
\(543\) | 4.86314e58 | 0.773964 | ||||||||
\(544\) | −4.64351e58 | −0.710347 | ||||||||
\(545\) | 1.13126e59 | 1.66356 | ||||||||
\(546\) | 1.33281e58 | 0.188420 | ||||||||
\(547\) | −1.45905e58 | −0.198310 | −0.0991548 | − | 0.995072i | \(-0.531614\pi\) | ||||
−0.0991548 | + | 0.995072i | \(0.531614\pi\) | |||||||
\(548\) | −3.73508e58 | −0.488111 | ||||||||
\(549\) | 4.96293e57 | 0.0623638 | ||||||||
\(550\) | 1.75631e59 | 2.12228 | ||||||||
\(551\) | −1.49833e58 | −0.174120 | ||||||||
\(552\) | 6.89428e58 | 0.770547 | ||||||||
\(553\) | 1.39182e59 | 1.49622 | ||||||||
\(554\) | 4.01424e58 | 0.415091 | ||||||||
\(555\) | −1.94230e59 | −1.93205 | ||||||||
\(556\) | 3.51105e57 | 0.0335992 | ||||||||
\(557\) | −1.75662e59 | −1.61730 | −0.808650 | − | 0.588290i | \(-0.799801\pi\) | ||||
−0.808650 | + | 0.588290i | \(0.799801\pi\) | |||||||
\(558\) | −3.12308e57 | −0.0276661 | ||||||||
\(559\) | −1.00229e59 | −0.854361 | ||||||||
\(560\) | −1.69861e58 | −0.139332 | ||||||||
\(561\) | 6.43715e58 | 0.508151 | ||||||||
\(562\) | 3.72358e58 | 0.282898 | ||||||||
\(563\) | −1.51361e59 | −1.10684 | −0.553418 | − | 0.832903i | \(-0.686677\pi\) | ||||
−0.553418 | + | 0.832903i | \(0.686677\pi\) | |||||||
\(564\) | 3.46463e58 | 0.243869 | ||||||||
\(565\) | 1.17230e59 | 0.794323 | ||||||||
\(566\) | −1.08052e59 | −0.704821 | ||||||||
\(567\) | 1.64160e58 | 0.103094 | ||||||||
\(568\) | 1.80069e59 | 1.08880 | ||||||||
\(569\) | 2.44840e59 | 1.42550 | 0.712752 | − | 0.701417i | \(-0.247449\pi\) | ||||
0.712752 | + | 0.701417i | \(0.247449\pi\) | |||||||
\(570\) | −4.44421e58 | −0.249164 | ||||||||
\(571\) | −2.27586e59 | −1.22877 | −0.614384 | − | 0.789007i | \(-0.710595\pi\) | ||||
−0.614384 | + | 0.789007i | \(0.710595\pi\) | |||||||
\(572\) | 7.34950e58 | 0.382158 | ||||||||
\(573\) | 1.16809e59 | 0.584995 | ||||||||
\(574\) | −1.46606e59 | −0.707208 | ||||||||
\(575\) | −7.66205e59 | −3.56030 | ||||||||
\(576\) | 5.25581e58 | 0.235265 | ||||||||
\(577\) | −5.18881e58 | −0.223763 | −0.111881 | − | 0.993722i | \(-0.535688\pi\) | ||||
−0.111881 | + | 0.993722i | \(0.535688\pi\) | |||||||
\(578\) | 7.24693e58 | 0.301097 | ||||||||
\(579\) | 8.88721e58 | 0.355776 | ||||||||
\(580\) | −1.46751e59 | −0.566081 | ||||||||
\(581\) | 2.90059e59 | 1.07820 | ||||||||
\(582\) | −1.27756e59 | −0.457654 | ||||||||
\(583\) | 1.24493e59 | 0.429805 | ||||||||
\(584\) | −1.40850e59 | −0.468685 | ||||||||
\(585\) | 1.09249e59 | 0.350401 | ||||||||
\(586\) | 2.64939e59 | 0.819119 | ||||||||
\(587\) | 2.57601e59 | 0.767764 | 0.383882 | − | 0.923382i | \(-0.374587\pi\) | ||||
0.383882 | + | 0.923382i | \(0.374587\pi\) | |||||||
\(588\) | −1.62867e58 | −0.0467973 | ||||||||
\(589\) | −1.60484e58 | −0.0444583 | ||||||||
\(590\) | −1.73585e59 | −0.463653 | ||||||||
\(591\) | 2.59373e59 | 0.668028 | ||||||||
\(592\) | −5.42828e58 | −0.134817 | ||||||||
\(593\) | 3.64832e59 | 0.873810 | 0.436905 | − | 0.899508i | \(-0.356075\pi\) | ||||
0.436905 | + | 0.899508i | \(0.356075\pi\) | |||||||
\(594\) | −6.48303e58 | −0.149751 | ||||||||
\(595\) | 5.87523e59 | 1.30891 | ||||||||
\(596\) | 4.36023e58 | 0.0936948 | ||||||||
\(597\) | 1.50227e59 | 0.311386 | ||||||||
\(598\) | 2.29626e59 | 0.459141 | ||||||||
\(599\) | −3.13536e58 | −0.0604798 | −0.0302399 | − | 0.999543i | \(-0.509627\pi\) | ||||
−0.0302399 | + | 0.999543i | \(0.509627\pi\) | |||||||
\(600\) | −8.65103e59 | −1.60996 | ||||||||
\(601\) | −5.61238e59 | −1.00773 | −0.503867 | − | 0.863781i | \(-0.668090\pi\) | ||||
−0.503867 | + | 0.863781i | \(0.668090\pi\) | |||||||
\(602\) | 5.42859e59 | 0.940509 | ||||||||
\(603\) | −1.80423e57 | −0.00301626 | ||||||||
\(604\) | −4.39881e59 | −0.709645 | ||||||||
\(605\) | 5.59173e59 | 0.870574 | ||||||||
\(606\) | 3.96159e59 | 0.595261 | ||||||||
\(607\) | −4.58204e59 | −0.664511 | −0.332255 | − | 0.943189i | \(-0.607810\pi\) | ||||
−0.332255 | + | 0.943189i | \(0.607810\pi\) | |||||||
\(608\) | 2.40314e59 | 0.336397 | ||||||||
\(609\) | −1.99491e59 | −0.269557 | ||||||||
\(610\) | −1.78887e59 | −0.233339 | ||||||||
\(611\) | 3.13435e59 | 0.394695 | ||||||||
\(612\) | −1.16736e59 | −0.141921 | ||||||||
\(613\) | −1.17245e60 | −1.37624 | −0.688118 | − | 0.725599i | \(-0.741563\pi\) | ||||
−0.688118 | + | 0.725599i | \(0.741563\pi\) | |||||||
\(614\) | −2.98561e59 | −0.338387 | ||||||||
\(615\) | −1.20172e60 | −1.31518 | ||||||||
\(616\) | −1.08120e60 | −1.14267 | ||||||||
\(617\) | −1.43564e60 | −1.46526 | −0.732628 | − | 0.680629i | \(-0.761707\pi\) | ||||
−0.732628 | + | 0.680629i | \(0.761707\pi\) | |||||||
\(618\) | 4.76540e59 | 0.469728 | ||||||||
\(619\) | 1.66096e60 | 1.58129 | 0.790644 | − | 0.612276i | \(-0.209746\pi\) | ||||
0.790644 | + | 0.612276i | \(0.209746\pi\) | |||||||
\(620\) | −1.57182e59 | −0.144538 | ||||||||
\(621\) | 2.82828e59 | 0.251219 | ||||||||
\(622\) | −5.92978e59 | −0.508798 | ||||||||
\(623\) | −1.00735e60 | −0.835005 | ||||||||
\(624\) | 3.05325e58 | 0.0244508 | ||||||||
\(625\) | 4.79686e60 | 3.71139 | ||||||||
\(626\) | 1.16223e60 | 0.868850 | ||||||||
\(627\) | −3.33140e59 | −0.240644 | ||||||||
\(628\) | −1.11446e60 | −0.777914 | ||||||||
\(629\) | 1.87756e60 | 1.26650 | ||||||||
\(630\) | −5.91710e59 | −0.385733 | ||||||||
\(631\) | −5.47413e59 | −0.344892 | −0.172446 | − | 0.985019i | \(-0.555167\pi\) | ||||
−0.172446 | + | 0.985019i | \(0.555167\pi\) | |||||||
\(632\) | 2.70745e60 | 1.64871 | ||||||||
\(633\) | 1.71130e59 | 0.100727 | ||||||||
\(634\) | −1.36455e60 | −0.776371 | ||||||||
\(635\) | −3.90563e60 | −2.14811 | ||||||||
\(636\) | −2.25764e59 | −0.120040 | ||||||||
\(637\) | −1.47341e59 | −0.0757401 | ||||||||
\(638\) | 7.87829e59 | 0.391550 | ||||||||
\(639\) | 7.38707e59 | 0.354980 | ||||||||
\(640\) | 2.14493e60 | 0.996651 | ||||||||
\(641\) | −3.66398e59 | −0.164628 | −0.0823142 | − | 0.996606i | \(-0.526231\pi\) | ||||
−0.0823142 | + | 0.996606i | \(0.526231\pi\) | |||||||
\(642\) | 3.40840e57 | 0.00148098 | ||||||||
\(643\) | −2.84143e60 | −1.19399 | −0.596995 | − | 0.802245i | \(-0.703639\pi\) | ||||
−0.596995 | + | 0.802245i | \(0.703639\pi\) | |||||||
\(644\) | 1.73658e60 | 0.705745 | ||||||||
\(645\) | 4.44975e60 | 1.74905 | ||||||||
\(646\) | 4.29608e59 | 0.163333 | ||||||||
\(647\) | −1.01042e60 | −0.371585 | −0.185793 | − | 0.982589i | \(-0.559485\pi\) | ||||
−0.185793 | + | 0.982589i | \(0.559485\pi\) | |||||||
\(648\) | 3.19334e59 | 0.113601 | ||||||||
\(649\) | −1.30120e60 | −0.447798 | ||||||||
\(650\) | −2.88138e60 | −0.959320 | ||||||||
\(651\) | −2.13671e59 | −0.0688262 | ||||||||
\(652\) | −1.07801e60 | −0.335970 | ||||||||
\(653\) | −4.87378e59 | −0.146971 | −0.0734857 | − | 0.997296i | \(-0.523412\pi\) | ||||
−0.0734857 | + | 0.997296i | \(0.523412\pi\) | |||||||
\(654\) | 1.10135e60 | 0.321368 | ||||||||
\(655\) | 2.12766e60 | 0.600779 | ||||||||
\(656\) | −3.35852e59 | −0.0917730 | ||||||||
\(657\) | −5.77816e59 | −0.152804 | ||||||||
\(658\) | −1.69762e60 | −0.434493 | ||||||||
\(659\) | −7.34783e60 | −1.82022 | −0.910108 | − | 0.414371i | \(-0.864002\pi\) | ||||
−0.910108 | + | 0.414371i | \(0.864002\pi\) | |||||||
\(660\) | −3.26286e60 | −0.782355 | ||||||||
\(661\) | 6.39610e60 | 1.48451 | 0.742256 | − | 0.670116i | \(-0.233756\pi\) | ||||
0.742256 | + | 0.670116i | \(0.233756\pi\) | |||||||
\(662\) | 4.23424e59 | 0.0951324 | ||||||||
\(663\) | −1.05607e60 | −0.229696 | ||||||||
\(664\) | 5.64239e60 | 1.18809 | ||||||||
\(665\) | −3.04059e60 | −0.619858 | ||||||||
\(666\) | −1.89094e60 | −0.373234 | ||||||||
\(667\) | −3.43697e60 | −0.656857 | ||||||||
\(668\) | −2.14943e60 | −0.397768 | ||||||||
\(669\) | 3.91204e60 | 0.701039 | ||||||||
\(670\) | 6.50326e58 | 0.0112856 | ||||||||
\(671\) | −1.34094e60 | −0.225359 | ||||||||
\(672\) | 3.19958e60 | 0.520780 | ||||||||
\(673\) | −5.66196e60 | −0.892571 | −0.446285 | − | 0.894891i | \(-0.647253\pi\) | ||||
−0.446285 | + | 0.894891i | \(0.647253\pi\) | |||||||
\(674\) | 1.90247e60 | 0.290489 | ||||||||
\(675\) | −3.54896e60 | −0.524892 | ||||||||
\(676\) | 2.86142e60 | 0.409946 | ||||||||
\(677\) | 8.79026e60 | 1.21996 | 0.609980 | − | 0.792417i | \(-0.291177\pi\) | ||||
0.609980 | + | 0.792417i | \(0.291177\pi\) | |||||||
\(678\) | 1.14130e60 | 0.153448 | ||||||||
\(679\) | −8.74065e60 | −1.13853 | ||||||||
\(680\) | 1.14288e61 | 1.44231 | ||||||||
\(681\) | −8.87661e59 | −0.108539 | ||||||||
\(682\) | 8.43830e59 | 0.0999748 | ||||||||
\(683\) | 1.82024e60 | 0.208969 | 0.104485 | − | 0.994526i | \(-0.466681\pi\) | ||||
0.104485 | + | 0.994526i | \(0.466681\pi\) | |||||||
\(684\) | 6.04138e59 | 0.0672093 | ||||||||
\(685\) | 1.50014e61 | 1.61728 | ||||||||
\(686\) | 6.53486e60 | 0.682760 | ||||||||
\(687\) | 7.75875e59 | 0.0785636 | ||||||||
\(688\) | 1.24360e60 | 0.122048 | ||||||||
\(689\) | −2.04242e60 | −0.194282 | ||||||||
\(690\) | −1.01944e61 | −0.939955 | ||||||||
\(691\) | −9.14476e60 | −0.817324 | −0.408662 | − | 0.912686i | \(-0.634005\pi\) | ||||
−0.408662 | + | 0.912686i | \(0.634005\pi\) | |||||||
\(692\) | 1.24687e60 | 0.108029 | ||||||||
\(693\) | −4.43548e60 | −0.372543 | ||||||||
\(694\) | 4.11369e59 | 0.0334967 | ||||||||
\(695\) | −1.41016e60 | −0.111326 | ||||||||
\(696\) | −3.88060e60 | −0.297030 | ||||||||
\(697\) | 1.16166e61 | 0.862133 | ||||||||
\(698\) | −3.86541e59 | −0.0278166 | ||||||||
\(699\) | 1.04789e61 | 0.731236 | ||||||||
\(700\) | −2.17908e61 | −1.47457 | ||||||||
\(701\) | 1.07211e61 | 0.703560 | 0.351780 | − | 0.936083i | \(-0.385577\pi\) | ||||
0.351780 | + | 0.936083i | \(0.385577\pi\) | |||||||
\(702\) | 1.06360e60 | 0.0676908 | ||||||||
\(703\) | −9.71687e60 | −0.599773 | ||||||||
\(704\) | −1.42008e61 | −0.850158 | ||||||||
\(705\) | −1.39152e61 | −0.808020 | ||||||||
\(706\) | −1.42280e61 | −0.801389 | ||||||||
\(707\) | 2.71039e61 | 1.48086 | ||||||||
\(708\) | 2.35968e60 | 0.125065 | ||||||||
\(709\) | 6.45364e60 | 0.331826 | 0.165913 | − | 0.986140i | \(-0.446943\pi\) | ||||
0.165913 | + | 0.986140i | \(0.446943\pi\) | |||||||
\(710\) | −2.66264e61 | −1.32818 | ||||||||
\(711\) | 1.11069e61 | 0.537524 | ||||||||
\(712\) | −1.95956e61 | −0.920108 | ||||||||
\(713\) | −3.68128e60 | −0.167716 | ||||||||
\(714\) | 5.71987e60 | 0.252857 | ||||||||
\(715\) | −2.95181e61 | −1.26622 | ||||||||
\(716\) | −1.87248e60 | −0.0779449 | ||||||||
\(717\) | −9.14139e60 | −0.369275 | ||||||||
\(718\) | 1.69623e61 | 0.664980 | ||||||||
\(719\) | −4.63987e60 | −0.176537 | −0.0882683 | − | 0.996097i | \(-0.528133\pi\) | ||||
−0.0882683 | + | 0.996097i | \(0.528133\pi\) | |||||||
\(720\) | −1.35551e60 | −0.0500558 | ||||||||
\(721\) | 3.26033e61 | 1.16857 | ||||||||
\(722\) | 1.63452e61 | 0.568646 | ||||||||
\(723\) | 4.14125e60 | 0.139849 | ||||||||
\(724\) | 2.38286e61 | 0.781123 | ||||||||
\(725\) | 4.31276e61 | 1.37242 | ||||||||
\(726\) | 5.44387e60 | 0.168178 | ||||||||
\(727\) | 1.44955e61 | 0.434753 | 0.217376 | − | 0.976088i | \(-0.430250\pi\) | ||||
0.217376 | + | 0.976088i | \(0.430250\pi\) | |||||||
\(728\) | 1.77381e61 | 0.516515 | ||||||||
\(729\) | 1.31002e60 | 0.0370370 | ||||||||
\(730\) | 2.08272e61 | 0.571727 | ||||||||
\(731\) | −4.30143e61 | −1.14654 | ||||||||
\(732\) | 2.43175e60 | 0.0629406 | ||||||||
\(733\) | 2.28885e61 | 0.575282 | 0.287641 | − | 0.957738i | \(-0.407129\pi\) | ||||
0.287641 | + | 0.957738i | \(0.407129\pi\) | |||||||
\(734\) | −5.22245e61 | −1.27470 | ||||||||
\(735\) | 6.54130e60 | 0.155055 | ||||||||
\(736\) | 5.51248e61 | 1.26904 | ||||||||
\(737\) | 4.87487e59 | 0.0108996 | ||||||||
\(738\) | −1.16994e61 | −0.254069 | ||||||||
\(739\) | −1.52004e61 | −0.320628 | −0.160314 | − | 0.987066i | \(-0.551251\pi\) | ||||
−0.160314 | + | 0.987066i | \(0.551251\pi\) | |||||||
\(740\) | −9.51696e61 | −1.94992 | ||||||||
\(741\) | 5.46546e60 | 0.108776 | ||||||||
\(742\) | 1.10621e61 | 0.213872 | ||||||||
\(743\) | −7.23666e61 | −1.35919 | −0.679593 | − | 0.733589i | \(-0.737844\pi\) | ||||
−0.679593 | + | 0.733589i | \(0.737844\pi\) | |||||||
\(744\) | −4.15645e60 | −0.0758410 | ||||||||
\(745\) | −1.75122e61 | −0.310443 | ||||||||
\(746\) | 4.07049e61 | 0.701070 | ||||||||
\(747\) | 2.31471e61 | 0.387349 | ||||||||
\(748\) | 3.15410e61 | 0.512851 | ||||||||
\(749\) | 2.33192e59 | 0.00368430 | ||||||||
\(750\) | 8.10190e61 | 1.24385 | ||||||||
\(751\) | −1.13301e62 | −1.69034 | −0.845171 | − | 0.534496i | \(-0.820502\pi\) | ||||
−0.845171 | + | 0.534496i | \(0.820502\pi\) | |||||||
\(752\) | −3.88896e60 | −0.0563833 | ||||||||
\(753\) | −1.53288e61 | −0.215981 | ||||||||
\(754\) | −1.29250e61 | −0.176990 | ||||||||
\(755\) | 1.76672e62 | 2.35129 | ||||||||
\(756\) | 8.04359e60 | 0.104047 | ||||||||
\(757\) | −1.15154e62 | −1.44783 | −0.723916 | − | 0.689888i | \(-0.757660\pi\) | ||||
−0.723916 | + | 0.689888i | \(0.757660\pi\) | |||||||
\(758\) | −3.99348e61 | −0.488049 | ||||||||
\(759\) | −7.64177e61 | −0.907812 | ||||||||
\(760\) | −5.91472e61 | −0.683033 | ||||||||
\(761\) | −1.34334e62 | −1.50805 | −0.754025 | − | 0.656845i | \(-0.771890\pi\) | ||||
−0.754025 | + | 0.656845i | \(0.771890\pi\) | |||||||
\(762\) | −3.80235e61 | −0.414973 | ||||||||
\(763\) | 7.53505e61 | 0.799482 | ||||||||
\(764\) | 5.72346e61 | 0.590407 | ||||||||
\(765\) | 4.68851e61 | 0.470234 | ||||||||
\(766\) | 2.20519e61 | 0.215044 | ||||||||
\(767\) | 2.13473e61 | 0.202415 | ||||||||
\(768\) | 6.50781e61 | 0.600024 | ||||||||
\(769\) | 9.50818e61 | 0.852474 | 0.426237 | − | 0.904612i | \(-0.359839\pi\) | ||||
0.426237 | + | 0.904612i | \(0.359839\pi\) | |||||||
\(770\) | 1.59875e62 | 1.39390 | ||||||||
\(771\) | −1.14947e62 | −0.974602 | ||||||||
\(772\) | 4.35459e61 | 0.359067 | ||||||||
\(773\) | 2.61737e61 | 0.209897 | 0.104949 | − | 0.994478i | \(-0.466532\pi\) | ||||
0.104949 | + | 0.994478i | \(0.466532\pi\) | |||||||
\(774\) | 4.33209e61 | 0.337883 | ||||||||
\(775\) | 4.61932e61 | 0.350422 | ||||||||
\(776\) | −1.70028e62 | −1.25457 | ||||||||
\(777\) | −1.29372e62 | −0.928514 | ||||||||
\(778\) | −4.96092e60 | −0.0346339 | ||||||||
\(779\) | −6.01190e61 | −0.408278 | ||||||||
\(780\) | 5.35301e61 | 0.353642 | ||||||||
\(781\) | −1.99593e62 | −1.28276 | ||||||||
\(782\) | 9.85461e61 | 0.616161 | ||||||||
\(783\) | −1.59196e61 | −0.0968399 | ||||||||
\(784\) | 1.82814e60 | 0.0108197 | ||||||||
\(785\) | 4.47605e62 | 2.57749 | ||||||||
\(786\) | 2.07140e61 | 0.116059 | ||||||||
\(787\) | 3.01082e62 | 1.64145 | 0.820726 | − | 0.571322i | \(-0.193569\pi\) | ||||
0.820726 | + | 0.571322i | \(0.193569\pi\) | |||||||
\(788\) | 1.27089e62 | 0.674207 | ||||||||
\(789\) | −1.99190e61 | −0.102828 | ||||||||
\(790\) | −4.00345e62 | −2.01118 | ||||||||
\(791\) | 7.80841e61 | 0.381741 | ||||||||
\(792\) | −8.62814e61 | −0.410512 | ||||||||
\(793\) | 2.19994e61 | 0.101868 | ||||||||
\(794\) | 9.57220e61 | 0.431391 | ||||||||
\(795\) | 9.06746e61 | 0.397734 | ||||||||
\(796\) | 7.36086e61 | 0.314266 | ||||||||
\(797\) | −2.40878e62 | −1.00102 | −0.500511 | − | 0.865730i | \(-0.666855\pi\) | ||||
−0.500511 | + | 0.865730i | \(0.666855\pi\) | |||||||
\(798\) | −2.96018e61 | −0.119745 | ||||||||
\(799\) | 1.34513e62 | 0.529675 | ||||||||
\(800\) | −6.91713e62 | −2.65150 | ||||||||
\(801\) | −8.03881e61 | −0.299980 | ||||||||
\(802\) | −9.67540e61 | −0.351496 | ||||||||
\(803\) | 1.56121e62 | 0.552176 | ||||||||
\(804\) | −8.84041e59 | −0.00304416 | ||||||||
\(805\) | −6.97469e62 | −2.33837 | ||||||||
\(806\) | −1.38438e61 | −0.0451909 | ||||||||
\(807\) | −2.94563e62 | −0.936261 | ||||||||
\(808\) | 5.27240e62 | 1.63179 | ||||||||
\(809\) | −1.56406e62 | −0.471369 | −0.235685 | − | 0.971830i | \(-0.575733\pi\) | ||||
−0.235685 | + | 0.971830i | \(0.575733\pi\) | |||||||
\(810\) | −4.72192e61 | −0.138577 | ||||||||
\(811\) | 1.12549e62 | 0.321656 | 0.160828 | − | 0.986982i | \(-0.448584\pi\) | ||||
0.160828 | + | 0.986982i | \(0.448584\pi\) | |||||||
\(812\) | −9.77471e61 | −0.272050 | ||||||||
\(813\) | 1.57102e62 | 0.425829 | ||||||||
\(814\) | 5.10916e62 | 1.34873 | ||||||||
\(815\) | 4.32967e62 | 1.11318 | ||||||||
\(816\) | 1.31033e61 | 0.0328127 | ||||||||
\(817\) | 2.22611e62 | 0.542965 | ||||||||
\(818\) | −4.12775e62 | −0.980657 | ||||||||
\(819\) | 7.27680e61 | 0.168398 | ||||||||
\(820\) | −5.88821e62 | −1.32735 | ||||||||
\(821\) | 5.96819e61 | 0.131058 | 0.0655291 | − | 0.997851i | \(-0.479126\pi\) | ||||
0.0655291 | + | 0.997851i | \(0.479126\pi\) | |||||||
\(822\) | 1.46047e62 | 0.312427 | ||||||||
\(823\) | −4.06781e62 | −0.847743 | −0.423872 | − | 0.905722i | \(-0.639329\pi\) | ||||
−0.423872 | + | 0.905722i | \(0.639329\pi\) | |||||||
\(824\) | 6.34218e62 | 1.28767 | ||||||||
\(825\) | 9.58899e62 | 1.89676 | ||||||||
\(826\) | −1.15620e62 | −0.222825 | ||||||||
\(827\) | −4.41980e61 | −0.0829915 | −0.0414958 | − | 0.999139i | \(-0.513212\pi\) | ||||
−0.0414958 | + | 0.999139i | \(0.513212\pi\) | |||||||
\(828\) | 1.38581e62 | 0.253543 | ||||||||
\(829\) | 1.49177e62 | 0.265937 | 0.132969 | − | 0.991120i | \(-0.457549\pi\) | ||||
0.132969 | + | 0.991120i | \(0.457549\pi\) | |||||||
\(830\) | −8.34327e62 | −1.44930 | ||||||||
\(831\) | 2.19167e62 | 0.370983 | ||||||||
\(832\) | 2.32976e62 | 0.384291 | ||||||||
\(833\) | −6.32326e61 | −0.101642 | ||||||||
\(834\) | −1.37287e61 | −0.0215060 | ||||||||
\(835\) | 8.63286e62 | 1.31794 | ||||||||
\(836\) | −1.63233e62 | −0.242870 | ||||||||
\(837\) | −1.70512e61 | −0.0247262 | ||||||||
\(838\) | 6.57349e62 | 0.929072 | ||||||||
\(839\) | 1.09602e62 | 0.150986 | 0.0754930 | − | 0.997146i | \(-0.475947\pi\) | ||||
0.0754930 | + | 0.997146i | \(0.475947\pi\) | |||||||
\(840\) | −7.87496e62 | −1.05741 | ||||||||
\(841\) | −5.70578e62 | −0.746795 | ||||||||
\(842\) | 8.53281e62 | 1.08863 | ||||||||
\(843\) | 2.03298e62 | 0.252837 | ||||||||
\(844\) | 8.38508e61 | 0.101659 | ||||||||
\(845\) | −1.14924e63 | −1.35829 | ||||||||
\(846\) | −1.35472e62 | −0.156094 | ||||||||
\(847\) | 3.72452e62 | 0.418386 | ||||||||
\(848\) | 2.53415e61 | 0.0277537 | ||||||||
\(849\) | −5.89936e62 | −0.629926 | ||||||||
\(850\) | −1.23657e63 | −1.28739 | ||||||||
\(851\) | −2.22892e63 | −2.26260 | ||||||||
\(852\) | 3.61954e62 | 0.358263 | ||||||||
\(853\) | −5.00803e61 | −0.0483351 | −0.0241675 | − | 0.999708i | \(-0.507694\pi\) | ||||
−0.0241675 | + | 0.999708i | \(0.507694\pi\) | |||||||
\(854\) | −1.19152e62 | −0.112139 | ||||||||
\(855\) | −2.42643e62 | −0.222687 | ||||||||
\(856\) | 4.53618e60 | 0.00405980 | ||||||||
\(857\) | 1.37674e63 | 1.20161 | 0.600805 | − | 0.799396i | \(-0.294847\pi\) | ||||
0.600805 | + | 0.799396i | \(0.294847\pi\) | |||||||
\(858\) | −2.87376e62 | −0.244609 | ||||||||
\(859\) | 1.75498e62 | 0.145687 | 0.0728434 | − | 0.997343i | \(-0.476793\pi\) | ||||
0.0728434 | + | 0.997343i | \(0.476793\pi\) | |||||||
\(860\) | 2.18031e63 | 1.76523 | ||||||||
\(861\) | −8.00434e62 | −0.632059 | ||||||||
\(862\) | 2.20655e62 | 0.169944 | ||||||||
\(863\) | 2.82644e62 | 0.212328 | 0.106164 | − | 0.994349i | \(-0.466143\pi\) | ||||
0.106164 | + | 0.994349i | \(0.466143\pi\) | |||||||
\(864\) | 2.55331e62 | 0.187093 | ||||||||
\(865\) | −5.00786e62 | −0.357936 | ||||||||
\(866\) | −4.73797e62 | −0.330337 | ||||||||
\(867\) | 3.95664e62 | 0.269102 | ||||||||
\(868\) | −1.04695e62 | −0.0694629 | ||||||||
\(869\) | −3.00100e63 | −1.94241 | ||||||||
\(870\) | 5.73816e62 | 0.362333 | ||||||||
\(871\) | −7.99766e60 | −0.00492689 | ||||||||
\(872\) | 1.46576e63 | 0.880965 | ||||||||
\(873\) | −6.97515e62 | −0.409023 | ||||||||
\(874\) | −5.10002e62 | −0.291794 | ||||||||
\(875\) | 5.54306e63 | 3.09440 | ||||||||
\(876\) | −2.83121e62 | −0.154217 | ||||||||
\(877\) | −6.64060e62 | −0.352952 | −0.176476 | − | 0.984305i | \(-0.556470\pi\) | ||||
−0.176476 | + | 0.984305i | \(0.556470\pi\) | |||||||
\(878\) | −9.57111e61 | −0.0496398 | ||||||||
\(879\) | 1.44650e63 | 0.732078 | ||||||||
\(880\) | 3.66248e62 | 0.180883 | ||||||||
\(881\) | 3.34334e62 | 0.161138 | 0.0805690 | − | 0.996749i | \(-0.474326\pi\) | ||||
0.0805690 | + | 0.996749i | \(0.474326\pi\) | |||||||
\(882\) | 6.36832e61 | 0.0299537 | ||||||||
\(883\) | 2.18835e63 | 1.00453 | 0.502263 | − | 0.864715i | \(-0.332501\pi\) | ||||
0.502263 | + | 0.864715i | \(0.332501\pi\) | |||||||
\(884\) | −5.17459e62 | −0.231821 | ||||||||
\(885\) | −9.47727e62 | −0.414384 | ||||||||
\(886\) | −2.12531e63 | −0.906980 | ||||||||
\(887\) | −1.17168e63 | −0.488034 | −0.244017 | − | 0.969771i | \(-0.578465\pi\) | ||||
−0.244017 | + | 0.969771i | \(0.578465\pi\) | |||||||
\(888\) | −2.51662e63 | −1.02315 | ||||||||
\(889\) | −2.60144e63 | −1.03235 | ||||||||
\(890\) | 2.89756e63 | 1.12240 | ||||||||
\(891\) | −3.53957e62 | −0.133838 | ||||||||
\(892\) | 1.91684e63 | 0.707524 | ||||||||
\(893\) | −6.96142e62 | −0.250837 | ||||||||
\(894\) | −1.70491e62 | −0.0599716 | ||||||||
\(895\) | 7.52054e62 | 0.258258 | ||||||||
\(896\) | 1.42868e63 | 0.478977 | ||||||||
\(897\) | 1.25370e63 | 0.410352 | ||||||||
\(898\) | 7.82325e61 | 0.0250003 | ||||||||
\(899\) | 2.07209e62 | 0.0646511 | ||||||||
\(900\) | −1.73893e63 | −0.529747 | ||||||||
\(901\) | −8.76523e62 | −0.260723 | ||||||||
\(902\) | 3.16108e63 | 0.918109 | ||||||||
\(903\) | 2.96387e63 | 0.840569 | ||||||||
\(904\) | 1.51894e63 | 0.420647 | ||||||||
\(905\) | −9.57039e63 | −2.58813 | ||||||||
\(906\) | 1.72000e63 | 0.454225 | ||||||||
\(907\) | −1.34194e63 | −0.346081 | −0.173041 | − | 0.984915i | \(-0.555359\pi\) | ||||
−0.173041 | + | 0.984915i | \(0.555359\pi\) | |||||||
\(908\) | −4.34939e62 | −0.109543 | ||||||||
\(909\) | 2.16293e63 | 0.532008 | ||||||||
\(910\) | −2.62289e63 | −0.630073 | ||||||||
\(911\) | −4.78106e63 | −1.12171 | −0.560853 | − | 0.827915i | \(-0.689527\pi\) | ||||
−0.560853 | + | 0.827915i | \(0.689527\pi\) | |||||||
\(912\) | −6.78130e61 | −0.0155390 | ||||||||
\(913\) | −6.25414e63 | −1.39974 | ||||||||
\(914\) | 2.36588e63 | 0.517190 | ||||||||
\(915\) | −9.76676e62 | −0.208544 | ||||||||
\(916\) | 3.80166e62 | 0.0792904 | ||||||||
\(917\) | 1.41718e63 | 0.288726 | ||||||||
\(918\) | 4.56453e62 | 0.0908402 | ||||||||
\(919\) | 3.81921e63 | 0.742489 | 0.371245 | − | 0.928535i | \(-0.378931\pi\) | ||||
0.371245 | + | 0.928535i | \(0.378931\pi\) | |||||||
\(920\) | −1.35676e64 | −2.57670 | ||||||||
\(921\) | −1.63007e63 | −0.302429 | ||||||||
\(922\) | −3.51622e63 | −0.637326 | ||||||||
\(923\) | 3.27450e63 | 0.579840 | ||||||||
\(924\) | −2.17331e63 | −0.375989 | ||||||||
\(925\) | 2.79687e64 | 4.72744 | ||||||||
\(926\) | −1.70032e63 | −0.280799 | ||||||||
\(927\) | 2.60178e63 | 0.419814 | ||||||||
\(928\) | −3.10282e63 | −0.489188 | ||||||||
\(929\) | 6.39575e63 | 0.985266 | 0.492633 | − | 0.870237i | \(-0.336035\pi\) | ||||
0.492633 | + | 0.870237i | \(0.336035\pi\) | |||||||
\(930\) | 6.14604e62 | 0.0925150 | ||||||||
\(931\) | 3.27246e62 | 0.0481344 | ||||||||
\(932\) | 5.13450e63 | 0.738000 | ||||||||
\(933\) | −3.23751e63 | −0.454732 | ||||||||
\(934\) | 1.82899e63 | 0.251046 | ||||||||
\(935\) | −1.26680e64 | −1.69925 | ||||||||
\(936\) | 1.41552e63 | 0.185561 | ||||||||
\(937\) | 1.49402e64 | 1.91405 | 0.957027 | − | 0.290000i | \(-0.0936554\pi\) | ||||
0.957027 | + | 0.290000i | \(0.0936554\pi\) | |||||||
\(938\) | 4.33167e61 | 0.00542368 | ||||||||
\(939\) | 6.34550e63 | 0.776525 | ||||||||
\(940\) | −6.81820e63 | −0.815494 | ||||||||
\(941\) | 3.85740e63 | 0.450939 | 0.225469 | − | 0.974250i | \(-0.427608\pi\) | ||||
0.225469 | + | 0.974250i | \(0.427608\pi\) | |||||||
\(942\) | 4.35769e63 | 0.497923 | ||||||||
\(943\) | −1.37905e64 | −1.54020 | ||||||||
\(944\) | −2.64868e62 | −0.0289155 | ||||||||
\(945\) | −3.23058e63 | −0.344744 | ||||||||
\(946\) | −1.17049e64 | −1.22098 | ||||||||
\(947\) | 1.02507e64 | 1.04527 | 0.522633 | − | 0.852558i | \(-0.324950\pi\) | ||||
0.522633 | + | 0.852558i | \(0.324950\pi\) | |||||||
\(948\) | 5.44222e63 | 0.542496 | ||||||||
\(949\) | −2.56131e63 | −0.249597 | ||||||||
\(950\) | 6.39957e63 | 0.609668 | ||||||||
\(951\) | −7.45008e63 | −0.693872 | ||||||||
\(952\) | 7.61247e63 | 0.693156 | ||||||||
\(953\) | −1.69549e63 | −0.150938 | −0.0754689 | − | 0.997148i | \(-0.524045\pi\) | ||||
−0.0754689 | + | 0.997148i | \(0.524045\pi\) | |||||||
\(954\) | 8.82769e62 | 0.0768346 | ||||||||
\(955\) | −2.29874e64 | −1.95622 | ||||||||
\(956\) | −4.47913e63 | −0.372691 | ||||||||
\(957\) | 4.30134e63 | 0.349943 | ||||||||
\(958\) | −2.58135e63 | −0.205347 | ||||||||
\(959\) | 9.99207e63 | 0.777240 | ||||||||
\(960\) | −1.03431e64 | −0.786722 | ||||||||
\(961\) | −1.32228e64 | −0.983493 | ||||||||
\(962\) | −8.38204e63 | −0.609657 | ||||||||
\(963\) | 1.86090e61 | 0.00132360 | ||||||||
\(964\) | 2.02915e63 | 0.141142 | ||||||||
\(965\) | −1.74895e64 | −1.18971 | ||||||||
\(966\) | −6.79026e63 | −0.451729 | ||||||||
\(967\) | 4.59701e63 | 0.299093 | 0.149546 | − | 0.988755i | \(-0.452219\pi\) | ||||
0.149546 | + | 0.988755i | \(0.452219\pi\) | |||||||
\(968\) | 7.24514e63 | 0.461027 | ||||||||
\(969\) | 2.34555e63 | 0.145977 | ||||||||
\(970\) | 2.51417e64 | 1.53039 | ||||||||
\(971\) | −3.19574e63 | −0.190265 | −0.0951324 | − | 0.995465i | \(-0.530327\pi\) | ||||
−0.0951324 | + | 0.995465i | \(0.530327\pi\) | |||||||
\(972\) | 6.41889e62 | 0.0373796 | ||||||||
\(973\) | −9.39274e62 | −0.0535016 | ||||||||
\(974\) | 1.74053e64 | 0.969762 | ||||||||
\(975\) | −1.57316e64 | −0.857381 | ||||||||
\(976\) | −2.72958e62 | −0.0145521 | ||||||||
\(977\) | 5.68464e63 | 0.296462 | 0.148231 | − | 0.988953i | \(-0.452642\pi\) | ||||
0.148231 | + | 0.988953i | \(0.452642\pi\) | |||||||
\(978\) | 4.21518e63 | 0.215046 | ||||||||
\(979\) | 2.17202e64 | 1.08402 | ||||||||
\(980\) | 3.20513e63 | 0.156489 | ||||||||
\(981\) | 6.01307e63 | 0.287219 | ||||||||
\(982\) | 1.70458e64 | 0.796563 | ||||||||
\(983\) | 2.85765e64 | 1.30650 | 0.653249 | − | 0.757143i | \(-0.273406\pi\) | ||||
0.653249 | + | 0.757143i | \(0.273406\pi\) | |||||||
\(984\) | −1.55705e64 | −0.696479 | ||||||||
\(985\) | −5.10432e64 | −2.23388 | ||||||||
\(986\) | −5.54689e63 | −0.237518 | ||||||||
\(987\) | −9.26855e63 | −0.388323 | ||||||||
\(988\) | 2.67798e63 | 0.109783 | ||||||||
\(989\) | 5.10638e64 | 2.04830 | ||||||||
\(990\) | 1.27582e64 | 0.500765 | ||||||||
\(991\) | −3.67835e64 | −1.41276 | −0.706381 | − | 0.707832i | \(-0.749674\pi\) | ||||
−0.706381 | + | 0.707832i | \(0.749674\pi\) | |||||||
\(992\) | −3.32338e63 | −0.124905 | ||||||||
\(993\) | 2.31179e63 | 0.0850234 | ||||||||
\(994\) | −1.77352e64 | −0.638306 | ||||||||
\(995\) | −2.95638e64 | −1.04127 | ||||||||
\(996\) | 1.13417e64 | 0.390932 | ||||||||
\(997\) | 2.35927e64 | 0.795850 | 0.397925 | − | 0.917418i | \(-0.369730\pi\) | ||||
0.397925 | + | 0.917418i | \(0.369730\pi\) | |||||||
\(998\) | 1.50447e63 | 0.0496681 | ||||||||
\(999\) | −1.03241e64 | −0.333574 |
(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 | 3.44.a.b.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 9.44.a.c.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.44.a.b.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
9.44.a.c.1.3 | 4 | 3.2 | odd | 2 |