Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,34,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(172.457072203\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 71909733210 x^{9} - 392361971317440 x^{8} + \cdots + 13\!\cdots\!48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{47}\cdot 3^{12}\cdot 5^{30}\cdot 7^{2}\cdot 11^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-139697.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 140551. | 1.51649 | 0.758245 | − | 0.651970i | \(-0.226057\pi\) | ||||
0.758245 | + | 0.651970i | \(0.226057\pi\) | |||||||
\(3\) | −1.29136e8 | −1.73199 | −0.865996 | − | 0.500051i | \(-0.833315\pi\) | ||||
−0.865996 | + | 0.500051i | \(0.833315\pi\) | |||||||
\(4\) | 1.11647e10 | 1.29974 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.81502e13 | −2.62655 | ||||||||
\(7\) | −4.00085e13 | −0.455025 | −0.227512 | − | 0.973775i | \(-0.573059\pi\) | ||||
−0.227512 | + | 0.973775i | \(0.573059\pi\) | |||||||
\(8\) | 3.61884e14 | 0.454553 | ||||||||
\(9\) | 1.11170e16 | 1.99980 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.48192e17 | 1.62858 | 0.814289 | − | 0.580460i | \(-0.197127\pi\) | ||||
0.814289 | + | 0.580460i | \(0.197127\pi\) | |||||||
\(12\) | −1.44176e18 | −2.25114 | ||||||||
\(13\) | 3.61009e18 | 1.50471 | 0.752356 | − | 0.658757i | \(-0.228917\pi\) | ||||
0.752356 | + | 0.658757i | \(0.228917\pi\) | |||||||
\(14\) | −5.62325e18 | −0.690040 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.50407e19 | −0.610416 | ||||||||
\(17\) | −5.03453e19 | −0.250930 | −0.125465 | − | 0.992098i | \(-0.540042\pi\) | ||||
−0.125465 | + | 0.992098i | \(0.540042\pi\) | |||||||
\(18\) | 1.56251e21 | 3.03267 | ||||||||
\(19\) | −1.19790e21 | −0.952764 | −0.476382 | − | 0.879238i | \(-0.658052\pi\) | ||||
−0.476382 | + | 0.879238i | \(0.658052\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.16654e21 | 0.788099 | ||||||||
\(22\) | 3.48837e22 | 2.46972 | ||||||||
\(23\) | −2.35311e22 | −0.800081 | −0.400040 | − | 0.916498i | \(-0.631004\pi\) | ||||
−0.400040 | + | 0.916498i | \(0.631004\pi\) | |||||||
\(24\) | −4.67322e22 | −0.787282 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.07403e23 | 2.28188 | ||||||||
\(27\) | −7.17728e23 | −1.73164 | ||||||||
\(28\) | −4.46683e23 | −0.591414 | ||||||||
\(29\) | −2.45131e24 | −1.81899 | −0.909497 | − | 0.415711i | \(-0.863533\pi\) | ||||
−0.909497 | + | 0.415711i | \(0.863533\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.88511e24 | −0.712352 | −0.356176 | − | 0.934419i | \(-0.615920\pi\) | ||||
−0.356176 | + | 0.934419i | \(0.615920\pi\) | |||||||
\(32\) | −9.43908e24 | −1.38024 | ||||||||
\(33\) | −3.20505e25 | −2.82068 | ||||||||
\(34\) | −7.07609e24 | −0.380532 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.24118e26 | 2.59922 | ||||||||
\(37\) | 3.58819e25 | 0.478131 | 0.239066 | − | 0.971003i | \(-0.423159\pi\) | ||||
0.239066 | + | 0.971003i | \(0.423159\pi\) | |||||||
\(38\) | −1.68366e26 | −1.44486 | ||||||||
\(39\) | −4.66192e26 | −2.60615 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.61568e25 | 0.162047 | 0.0810234 | − | 0.996712i | \(-0.474181\pi\) | ||||
0.0810234 | + | 0.996712i | \(0.474181\pi\) | |||||||
\(42\) | 7.26162e26 | 1.19514 | ||||||||
\(43\) | 1.70988e27 | 1.90869 | 0.954346 | − | 0.298702i | \(-0.0965538\pi\) | ||||
0.954346 | + | 0.298702i | \(0.0965538\pi\) | |||||||
\(44\) | 2.77099e27 | 2.11673 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.30733e27 | −1.21331 | ||||||||
\(47\) | 4.53211e27 | 1.16597 | 0.582983 | − | 0.812485i | \(-0.301886\pi\) | ||||
0.582983 | + | 0.812485i | \(0.301886\pi\) | |||||||
\(48\) | 5.81637e27 | 1.05724 | ||||||||
\(49\) | −6.13031e27 | −0.792952 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.50138e27 | 0.434608 | ||||||||
\(52\) | 4.03056e28 | 1.95573 | ||||||||
\(53\) | 1.11477e28 | 0.395031 | 0.197516 | − | 0.980300i | \(-0.436713\pi\) | ||||
0.197516 | + | 0.980300i | \(0.436713\pi\) | |||||||
\(54\) | −1.00877e29 | −2.62601 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.44784e28 | −0.206833 | ||||||||
\(57\) | 1.54691e29 | 1.65018 | ||||||||
\(58\) | −3.44534e29 | −2.75848 | ||||||||
\(59\) | 1.06018e29 | 0.640210 | 0.320105 | − | 0.947382i | \(-0.396282\pi\) | ||||
0.320105 | + | 0.947382i | \(0.396282\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.42654e28 | 0.328405 | 0.164203 | − | 0.986427i | \(-0.447495\pi\) | ||||
0.164203 | + | 0.986427i | \(0.447495\pi\) | |||||||
\(62\) | −4.05506e29 | −1.08027 | ||||||||
\(63\) | −4.44775e29 | −0.909957 | ||||||||
\(64\) | −9.39777e29 | −1.48271 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.50473e30 | −4.27754 | ||||||||
\(67\) | 2.59250e30 | 1.92081 | 0.960405 | − | 0.278607i | \(-0.0898727\pi\) | ||||
0.960405 | + | 0.278607i | \(0.0898727\pi\) | |||||||
\(68\) | −5.62090e29 | −0.326143 | ||||||||
\(69\) | 3.03871e30 | 1.38573 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.27372e30 | −1.21631 | −0.608153 | − | 0.793820i | \(-0.708089\pi\) | ||||
−0.608153 | + | 0.793820i | \(0.708089\pi\) | |||||||
\(72\) | 4.02306e30 | 0.909013 | ||||||||
\(73\) | 2.23754e30 | 0.402664 | 0.201332 | − | 0.979523i | \(-0.435473\pi\) | ||||
0.201332 | + | 0.979523i | \(0.435473\pi\) | |||||||
\(74\) | 5.04324e30 | 0.725081 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.33741e31 | −1.23835 | ||||||||
\(77\) | −9.92980e30 | −0.741043 | ||||||||
\(78\) | −6.55239e31 | −3.95220 | ||||||||
\(79\) | −2.21899e31 | −1.08470 | −0.542349 | − | 0.840153i | \(-0.682465\pi\) | ||||
−0.542349 | + | 0.840153i | \(0.682465\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.08843e31 | 0.999390 | ||||||||
\(82\) | 9.29841e30 | 0.245742 | ||||||||
\(83\) | 2.60461e31 | 0.563579 | 0.281790 | − | 0.959476i | \(-0.409072\pi\) | ||||
0.281790 | + | 0.959476i | \(0.409072\pi\) | |||||||
\(84\) | 5.76827e31 | 1.02432 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.40325e32 | 2.89451 | ||||||||
\(87\) | 3.16552e32 | 3.15048 | ||||||||
\(88\) | 8.98167e31 | 0.740275 | ||||||||
\(89\) | 1.65644e32 | 1.13302 | 0.566512 | − | 0.824053i | \(-0.308292\pi\) | ||||
0.566512 | + | 0.824053i | \(0.308292\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.44435e32 | −0.684681 | ||||||||
\(92\) | −2.62718e32 | −1.03990 | ||||||||
\(93\) | 3.72571e32 | 1.23379 | ||||||||
\(94\) | 6.36993e32 | 1.76817 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.21892e33 | 2.39057 | ||||||||
\(97\) | −1.37226e32 | −0.226831 | −0.113416 | − | 0.993548i | \(-0.536179\pi\) | ||||
−0.113416 | + | 0.993548i | \(0.536179\pi\) | |||||||
\(98\) | −8.61622e32 | −1.20250 | ||||||||
\(99\) | 2.75915e33 | 3.25682 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.03548e33 | 0.878698 | 0.439349 | − | 0.898317i | \(-0.355209\pi\) | ||||
0.439349 | + | 0.898317i | \(0.355209\pi\) | |||||||
\(102\) | 9.13777e32 | 0.659079 | ||||||||
\(103\) | −2.45463e33 | −1.50720 | −0.753600 | − | 0.657333i | \(-0.771684\pi\) | ||||
−0.753600 | + | 0.657333i | \(0.771684\pi\) | |||||||
\(104\) | 1.30643e33 | 0.683971 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.56681e33 | 0.599061 | ||||||||
\(107\) | 1.11407e33 | 0.364822 | 0.182411 | − | 0.983222i | \(-0.441610\pi\) | ||||
0.182411 | + | 0.983222i | \(0.441610\pi\) | |||||||
\(108\) | −8.01320e33 | −2.25068 | ||||||||
\(109\) | −2.70218e33 | −0.651894 | −0.325947 | − | 0.945388i | \(-0.605683\pi\) | ||||
−0.325947 | + | 0.945388i | \(0.605683\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.63364e33 | −0.828120 | ||||||||
\(112\) | 1.80201e33 | 0.277754 | ||||||||
\(113\) | −2.20215e33 | −0.293124 | −0.146562 | − | 0.989201i | \(-0.546821\pi\) | ||||
−0.146562 | + | 0.989201i | \(0.546821\pi\) | |||||||
\(114\) | 2.17421e34 | 2.50248 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.73681e34 | −2.36422 | ||||||||
\(117\) | 4.01334e34 | 3.00912 | ||||||||
\(118\) | 1.49010e34 | 0.970872 | ||||||||
\(119\) | 2.01424e33 | 0.114179 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.83741e34 | 1.65227 | ||||||||
\(122\) | 1.32491e34 | 0.498023 | ||||||||
\(123\) | −8.54321e33 | −0.280664 | ||||||||
\(124\) | −3.22114e34 | −0.925872 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.25136e34 | −1.37994 | ||||||||
\(127\) | 4.18545e34 | 0.810925 | 0.405463 | − | 0.914112i | \(-0.367110\pi\) | ||||
0.405463 | + | 0.914112i | \(0.367110\pi\) | |||||||
\(128\) | −5.10056e34 | −0.868267 | ||||||||
\(129\) | −2.20807e35 | −3.30584 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.65700e35 | 1.92463 | 0.962314 | − | 0.271941i | \(-0.0876655\pi\) | ||||
0.962314 | + | 0.271941i | \(0.0876655\pi\) | |||||||
\(132\) | −3.57833e35 | −3.66616 | ||||||||
\(133\) | 4.79261e34 | 0.433531 | ||||||||
\(134\) | 3.64379e35 | 2.91289 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.82192e34 | −0.114061 | ||||||||
\(137\) | −1.27396e35 | −0.706751 | −0.353375 | − | 0.935482i | \(-0.614966\pi\) | ||||
−0.353375 | + | 0.935482i | \(0.614966\pi\) | |||||||
\(138\) | 4.27094e35 | 2.10145 | ||||||||
\(139\) | −2.10212e35 | −0.918148 | −0.459074 | − | 0.888398i | \(-0.651819\pi\) | ||||
−0.459074 | + | 0.888398i | \(0.651819\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.85257e35 | −2.01944 | ||||||||
\(142\) | −6.00676e35 | −1.84452 | ||||||||
\(143\) | 8.95997e35 | 2.45054 | ||||||||
\(144\) | −5.00717e35 | −1.22071 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.14488e35 | 0.610636 | ||||||||
\(147\) | 7.91642e35 | 1.37339 | ||||||||
\(148\) | 4.00610e35 | 0.621446 | ||||||||
\(149\) | 3.92609e35 | 0.544987 | 0.272494 | − | 0.962158i | \(-0.412152\pi\) | ||||
0.272494 | + | 0.962158i | \(0.412152\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.34206e36 | 1.49504 | 0.747521 | − | 0.664239i | \(-0.231244\pi\) | ||||
0.747521 | + | 0.664239i | \(0.231244\pi\) | |||||||
\(152\) | −4.33500e35 | −0.433082 | ||||||||
\(153\) | −5.59689e35 | −0.501808 | ||||||||
\(154\) | −1.39564e36 | −1.12378 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.20489e36 | −3.38732 | ||||||||
\(157\) | 1.18714e36 | 0.695279 | 0.347640 | − | 0.937628i | \(-0.386983\pi\) | ||||
0.347640 | + | 0.937628i | \(0.386983\pi\) | |||||||
\(158\) | −3.11882e36 | −1.64493 | ||||||||
\(159\) | −1.43956e36 | −0.684191 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.41447e35 | 0.364057 | ||||||||
\(162\) | 4.34082e36 | 1.51556 | ||||||||
\(163\) | 2.79919e36 | 0.882950 | 0.441475 | − | 0.897273i | \(-0.354455\pi\) | ||||
0.441475 | + | 0.897273i | \(0.354455\pi\) | |||||||
\(164\) | 7.38619e35 | 0.210619 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.66082e36 | 0.854662 | ||||||||
\(167\) | 1.00045e36 | 0.211531 | 0.105766 | − | 0.994391i | \(-0.466271\pi\) | ||||
0.105766 | + | 0.994391i | \(0.466271\pi\) | |||||||
\(168\) | 1.86969e36 | 0.358233 | ||||||||
\(169\) | 7.27665e36 | 1.26416 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.33170e37 | −1.90533 | ||||||||
\(172\) | 1.90903e37 | 2.48080 | ||||||||
\(173\) | −3.30706e36 | −0.390554 | −0.195277 | − | 0.980748i | \(-0.562561\pi\) | ||||
−0.195277 | + | 0.980748i | \(0.562561\pi\) | |||||||
\(174\) | 4.44917e37 | 4.77767 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.11787e37 | −0.994109 | ||||||||
\(177\) | −1.36908e37 | −1.10884 | ||||||||
\(178\) | 2.32814e37 | 1.71822 | ||||||||
\(179\) | 7.68220e36 | 0.516905 | 0.258452 | − | 0.966024i | \(-0.416787\pi\) | ||||
0.258452 | + | 0.966024i | \(0.416787\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.70691e37 | 0.956123 | 0.478062 | − | 0.878326i | \(-0.341340\pi\) | ||||
0.478062 | + | 0.878326i | \(0.341340\pi\) | |||||||
\(182\) | −2.03005e37 | −1.03831 | ||||||||
\(183\) | −1.21730e37 | −0.568795 | ||||||||
\(184\) | −8.51554e36 | −0.363679 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.23653e37 | 1.87103 | ||||||||
\(187\) | −1.24953e37 | −0.408658 | ||||||||
\(188\) | 5.05995e37 | 1.51545 | ||||||||
\(189\) | 2.87152e37 | 0.787939 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.12199e37 | 0.720080 | 0.360040 | − | 0.932937i | \(-0.382763\pi\) | ||||
0.360040 | + | 0.932937i | \(0.382763\pi\) | |||||||
\(192\) | 1.21359e38 | 2.56804 | ||||||||
\(193\) | −3.37722e37 | −0.655940 | −0.327970 | − | 0.944688i | \(-0.606365\pi\) | ||||
−0.327970 | + | 0.944688i | \(0.606365\pi\) | |||||||
\(194\) | −1.92873e37 | −0.343987 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.84430e37 | −1.03063 | ||||||||
\(197\) | −1.81875e37 | −0.251814 | −0.125907 | − | 0.992042i | \(-0.540184\pi\) | ||||
−0.125907 | + | 0.992042i | \(0.540184\pi\) | |||||||
\(198\) | 3.87801e38 | 4.93894 | ||||||||
\(199\) | 1.94624e37 | 0.228098 | 0.114049 | − | 0.993475i | \(-0.463618\pi\) | ||||
0.114049 | + | 0.993475i | \(0.463618\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.34785e38 | −3.32683 | ||||||||
\(202\) | 1.45538e38 | 1.33254 | ||||||||
\(203\) | 9.80733e37 | 0.827687 | ||||||||
\(204\) | 7.25859e37 | 0.564878 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.45000e38 | −2.28565 | ||||||||
\(207\) | −2.61595e38 | −1.60000 | ||||||||
\(208\) | −1.62601e38 | −0.918499 | ||||||||
\(209\) | −2.97309e38 | −1.55165 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.61601e37 | −0.205876 | −0.102938 | − | 0.994688i | \(-0.532824\pi\) | ||||
−0.102938 | + | 0.994688i | \(0.532824\pi\) | |||||||
\(212\) | 1.24460e38 | 0.513438 | ||||||||
\(213\) | 5.51890e38 | 2.10663 | ||||||||
\(214\) | 1.56584e38 | 0.553249 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.59734e38 | −0.787122 | ||||||||
\(217\) | 1.15429e38 | 0.324138 | ||||||||
\(218\) | −3.79795e38 | −0.988591 | ||||||||
\(219\) | −2.88946e38 | −0.697411 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.81751e38 | −0.377577 | ||||||||
\(222\) | −6.51263e38 | −1.25583 | ||||||||
\(223\) | 3.65945e38 | 0.655218 | 0.327609 | − | 0.944813i | \(-0.393757\pi\) | ||||
0.327609 | + | 0.944813i | \(0.393757\pi\) | |||||||
\(224\) | 3.77644e38 | 0.628044 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.09514e38 | −0.444520 | ||||||||
\(227\) | 8.68482e38 | 1.15967 | 0.579834 | − | 0.814734i | \(-0.303117\pi\) | ||||
0.579834 | + | 0.814734i | \(0.303117\pi\) | |||||||
\(228\) | 1.72708e39 | 2.14481 | ||||||||
\(229\) | 3.80140e38 | 0.439195 | 0.219598 | − | 0.975591i | \(-0.429526\pi\) | ||||
0.219598 | + | 0.975591i | \(0.429526\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.28229e39 | 1.28348 | ||||||||
\(232\) | −8.87089e38 | −0.826829 | ||||||||
\(233\) | 7.33719e38 | 0.637026 | 0.318513 | − | 0.947918i | \(-0.396817\pi\) | ||||
0.318513 | + | 0.947918i | \(0.396817\pi\) | |||||||
\(234\) | 5.64079e39 | 4.56329 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.18366e39 | 0.832107 | ||||||||
\(237\) | 2.86551e39 | 1.87869 | ||||||||
\(238\) | 2.83104e38 | 0.173152 | ||||||||
\(239\) | −2.06579e39 | −1.17902 | −0.589509 | − | 0.807762i | \(-0.700679\pi\) | ||||
−0.589509 | + | 0.807762i | \(0.700679\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.68438e39 | 0.837833 | 0.418917 | − | 0.908025i | \(-0.362410\pi\) | ||||
0.418917 | + | 0.908025i | \(0.362410\pi\) | |||||||
\(242\) | 5.39353e39 | 2.50564 | ||||||||
\(243\) | 1.62204e36 | 0.000703975 0 | ||||||||
\(244\) | 1.05244e39 | 0.426842 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.20076e39 | −0.425624 | ||||||||
\(247\) | −4.32452e39 | −1.43364 | ||||||||
\(248\) | −1.04408e39 | −0.323802 | ||||||||
\(249\) | −3.36349e39 | −0.976115 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.13801e39 | 0.798065 | 0.399032 | − | 0.916937i | \(-0.369346\pi\) | ||||
0.399032 | + | 0.916937i | \(0.369346\pi\) | |||||||
\(252\) | −4.96577e39 | −1.18271 | ||||||||
\(253\) | −5.84024e39 | −1.30299 | ||||||||
\(254\) | 5.88270e39 | 1.22976 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.03730e38 | 0.165989 | ||||||||
\(257\) | −6.46986e39 | −1.11429 | −0.557145 | − | 0.830415i | \(-0.688103\pi\) | ||||
−0.557145 | + | 0.830415i | \(0.688103\pi\) | |||||||
\(258\) | −3.10346e40 | −5.01327 | ||||||||
\(259\) | −1.43558e39 | −0.217562 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.72512e40 | −3.63762 | ||||||||
\(262\) | 2.32894e40 | 2.91868 | ||||||||
\(263\) | 9.40764e39 | 1.10716 | 0.553581 | − | 0.832796i | \(-0.313261\pi\) | ||||
0.553581 | + | 0.832796i | \(0.313261\pi\) | |||||||
\(264\) | −1.15985e40 | −1.28215 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.73607e39 | 0.657446 | ||||||||
\(267\) | −2.13905e40 | −1.96239 | ||||||||
\(268\) | 2.89444e40 | 2.49655 | ||||||||
\(269\) | −1.06054e40 | −0.860229 | −0.430115 | − | 0.902774i | \(-0.641527\pi\) | ||||
−0.430115 | + | 0.902774i | \(0.641527\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.90847e39 | 0.424113 | 0.212057 | − | 0.977257i | \(-0.431984\pi\) | ||||
0.212057 | + | 0.977257i | \(0.431984\pi\) | |||||||
\(272\) | 2.26759e39 | 0.153171 | ||||||||
\(273\) | 1.86517e40 | 1.18586 | ||||||||
\(274\) | −1.79056e40 | −1.07178 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.39263e40 | 1.80109 | ||||||||
\(277\) | 4.69522e39 | 0.234822 | 0.117411 | − | 0.993083i | \(-0.462540\pi\) | ||||
0.117411 | + | 0.993083i | \(0.462540\pi\) | |||||||
\(278\) | −2.95455e40 | −1.39236 | ||||||||
\(279\) | −3.20738e40 | −1.42456 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.77236e40 | −1.09445 | −0.547225 | − | 0.836986i | \(-0.684316\pi\) | ||||
−0.547225 | + | 0.836986i | \(0.684316\pi\) | |||||||
\(282\) | −8.22586e40 | −3.06246 | ||||||||
\(283\) | −1.78562e40 | −0.627064 | −0.313532 | − | 0.949578i | \(-0.601512\pi\) | ||||
−0.313532 | + | 0.949578i | \(0.601512\pi\) | |||||||
\(284\) | −4.77147e40 | −1.58088 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.25933e41 | 3.71622 | ||||||||
\(287\) | −2.64684e39 | −0.0737353 | ||||||||
\(288\) | −1.04934e41 | −2.76020 | ||||||||
\(289\) | −3.77198e40 | −0.937034 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.77208e40 | 0.392870 | ||||||||
\(292\) | 2.49814e40 | 0.523359 | ||||||||
\(293\) | 7.90450e40 | 1.56516 | 0.782580 | − | 0.622551i | \(-0.213904\pi\) | ||||
0.782580 | + | 0.622551i | \(0.213904\pi\) | |||||||
\(294\) | 1.11266e41 | 2.08273 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.29851e40 | 0.217336 | ||||||||
\(297\) | −1.78134e41 | −2.82011 | ||||||||
\(298\) | 5.51816e40 | 0.826468 | ||||||||
\(299\) | −8.49496e40 | −1.20389 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.84098e40 | −0.868503 | ||||||||
\(302\) | 1.88628e41 | 2.26721 | ||||||||
\(303\) | −1.33718e41 | −1.52190 | ||||||||
\(304\) | 5.39542e40 | 0.581582 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.86649e40 | −0.760987 | ||||||||
\(307\) | 1.77046e41 | 1.62294 | 0.811471 | − | 0.584393i | \(-0.198667\pi\) | ||||
0.811471 | + | 0.584393i | \(0.198667\pi\) | |||||||
\(308\) | −1.10863e41 | −0.963164 | ||||||||
\(309\) | 3.16980e41 | 2.61046 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.58911e40 | 0.487843 | 0.243922 | − | 0.969795i | \(-0.421566\pi\) | ||||
0.243922 | + | 0.969795i | \(0.421566\pi\) | |||||||
\(312\) | −1.68707e41 | −1.18463 | ||||||||
\(313\) | −1.43570e41 | −0.956276 | −0.478138 | − | 0.878285i | \(-0.658688\pi\) | ||||
−0.478138 | + | 0.878285i | \(0.658688\pi\) | |||||||
\(314\) | 1.66854e41 | 1.05438 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.47744e41 | −1.40983 | ||||||||
\(317\) | 1.92102e41 | 1.03766 | 0.518830 | − | 0.854877i | \(-0.326368\pi\) | ||||
0.518830 | + | 0.854877i | \(0.326368\pi\) | |||||||
\(318\) | −2.02332e41 | −1.03757 | ||||||||
\(319\) | −6.08395e41 | −2.96237 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.43867e41 | −0.631869 | ||||||||
\(322\) | 1.32321e41 | 0.552088 | ||||||||
\(323\) | 6.03086e40 | 0.239077 | ||||||||
\(324\) | 3.44814e41 | 1.29895 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.93429e41 | 1.33898 | ||||||||
\(327\) | 3.48948e41 | 1.12908 | ||||||||
\(328\) | 2.39411e40 | 0.0736589 | ||||||||
\(329\) | −1.81323e41 | −0.530543 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.51390e41 | 1.72456 | 0.862282 | − | 0.506429i | \(-0.169035\pi\) | ||||
0.862282 | + | 0.506429i | \(0.169035\pi\) | |||||||
\(332\) | 2.90797e41 | 0.732507 | ||||||||
\(333\) | 3.98899e41 | 0.956165 | ||||||||
\(334\) | 1.40615e41 | 0.320785 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.32704e41 | −0.481068 | ||||||||
\(337\) | 1.11640e41 | 0.219749 | 0.109874 | − | 0.993945i | \(-0.464955\pi\) | ||||
0.109874 | + | 0.993945i | \(0.464955\pi\) | |||||||
\(338\) | 1.02274e42 | 1.91708 | ||||||||
\(339\) | 2.84376e41 | 0.507689 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.16062e41 | −1.16012 | ||||||||
\(342\) | −1.87172e42 | −2.88942 | ||||||||
\(343\) | 5.54571e41 | 0.815838 | ||||||||
\(344\) | 6.18778e41 | 0.867602 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.64810e41 | −0.592271 | ||||||||
\(347\) | 4.51461e41 | 0.548509 | 0.274255 | − | 0.961657i | \(-0.411569\pi\) | ||||
0.274255 | + | 0.961657i | \(0.411569\pi\) | |||||||
\(348\) | 3.53420e42 | 4.09481 | ||||||||
\(349\) | 1.08192e42 | 1.19557 | 0.597783 | − | 0.801658i | \(-0.296048\pi\) | ||||
0.597783 | + | 0.801658i | \(0.296048\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.59107e42 | −2.60562 | ||||||||
\(352\) | −2.34271e42 | −2.24783 | ||||||||
\(353\) | −1.02423e41 | −0.0937809 | −0.0468904 | − | 0.998900i | \(-0.514931\pi\) | ||||
−0.0468904 | + | 0.998900i | \(0.514931\pi\) | |||||||
\(354\) | −1.92425e42 | −1.68154 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.84936e42 | 1.47264 | ||||||||
\(357\) | −2.60111e41 | −0.197758 | ||||||||
\(358\) | 1.07974e42 | 0.783881 | ||||||||
\(359\) | −6.14289e40 | −0.0425907 | −0.0212953 | − | 0.999773i | \(-0.506779\pi\) | ||||
−0.0212953 | + | 0.999773i | \(0.506779\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.45811e41 | −0.0922407 | ||||||||
\(362\) | 2.39908e42 | 1.44995 | ||||||||
\(363\) | −4.95547e42 | −2.86171 | ||||||||
\(364\) | −1.61257e42 | −0.889908 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.71093e42 | −0.862572 | ||||||||
\(367\) | 2.92870e42 | 1.41151 | 0.705757 | − | 0.708454i | \(-0.250607\pi\) | ||||
0.705757 | + | 0.708454i | \(0.250607\pi\) | |||||||
\(368\) | 1.05986e42 | 0.488382 | ||||||||
\(369\) | 7.35464e41 | 0.324061 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.46001e41 | −0.179749 | ||||||||
\(372\) | 4.15964e42 | 1.60360 | ||||||||
\(373\) | −2.72869e42 | −1.00637 | −0.503186 | − | 0.864178i | \(-0.667839\pi\) | ||||
−0.503186 | + | 0.864178i | \(0.667839\pi\) | |||||||
\(374\) | −1.75623e42 | −0.619726 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.64010e42 | 0.529993 | ||||||||
\(377\) | −8.84946e42 | −2.73706 | ||||||||
\(378\) | 4.03596e42 | 1.19490 | ||||||||
\(379\) | 2.51319e42 | 0.712327 | 0.356163 | − | 0.934424i | \(-0.384085\pi\) | ||||
0.356163 | + | 0.934424i | \(0.384085\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.40492e42 | −1.40452 | ||||||||
\(382\) | 4.38799e42 | 1.09199 | ||||||||
\(383\) | 5.53799e42 | 1.31999 | 0.659997 | − | 0.751268i | \(-0.270557\pi\) | ||||
0.659997 | + | 0.751268i | \(0.270557\pi\) | |||||||
\(384\) | 6.58665e42 | 1.50383 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.74672e42 | −0.994726 | ||||||||
\(387\) | 1.90087e43 | 3.81700 | ||||||||
\(388\) | −1.53209e42 | −0.294822 | ||||||||
\(389\) | 6.43527e42 | 1.18686 | 0.593428 | − | 0.804887i | \(-0.297774\pi\) | ||||
0.593428 | + | 0.804887i | \(0.297774\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.18468e42 | 0.200764 | ||||||||
\(392\) | −2.21846e42 | −0.360439 | ||||||||
\(393\) | −2.13978e43 | −3.33344 | ||||||||
\(394\) | −2.55627e42 | −0.381873 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.08050e43 | 4.23303 | ||||||||
\(397\) | 2.59182e41 | 0.0341634 | 0.0170817 | − | 0.999854i | \(-0.494562\pi\) | ||||
0.0170817 | + | 0.999854i | \(0.494562\pi\) | |||||||
\(398\) | 2.73547e42 | 0.345908 | ||||||||
\(399\) | −6.18898e42 | −0.750873 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.15733e41 | −0.0241010 | −0.0120505 | − | 0.999927i | \(-0.503836\pi\) | ||||
−0.0120505 | + | 0.999927i | \(0.503836\pi\) | |||||||
\(402\) | −4.70543e43 | −5.04510 | ||||||||
\(403\) | −1.04155e43 | −1.07188 | ||||||||
\(404\) | 1.15608e43 | 1.14208 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.37843e43 | 1.25518 | ||||||||
\(407\) | 8.90561e42 | 0.778674 | ||||||||
\(408\) | 2.35275e42 | 0.197552 | ||||||||
\(409\) | 3.07671e42 | 0.248114 | 0.124057 | − | 0.992275i | \(-0.460409\pi\) | ||||
0.124057 | + | 0.992275i | \(0.460409\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.64514e43 | 1.22409 | ||||||||
\(412\) | −2.74051e43 | −1.95897 | ||||||||
\(413\) | −4.24164e42 | −0.291312 | ||||||||
\(414\) | −3.67675e43 | −2.42638 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.40760e43 | −2.07687 | ||||||||
\(417\) | 2.71458e43 | 1.59022 | ||||||||
\(418\) | −4.17871e43 | −2.35306 | ||||||||
\(419\) | 8.31146e42 | 0.449931 | 0.224966 | − | 0.974367i | \(-0.427773\pi\) | ||||
0.224966 | + | 0.974367i | \(0.427773\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.48499e43 | −1.24357 | −0.621786 | − | 0.783187i | \(-0.713593\pi\) | ||||
−0.621786 | + | 0.783187i | \(0.713593\pi\) | |||||||
\(422\) | −6.48786e42 | −0.312209 | ||||||||
\(423\) | 5.03834e43 | 2.33169 | ||||||||
\(424\) | 4.03415e42 | 0.179563 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.75687e43 | 3.19469 | ||||||||
\(427\) | −3.77142e42 | −0.149433 | ||||||||
\(428\) | 1.24383e43 | 0.474174 | ||||||||
\(429\) | −1.15705e44 | −4.24432 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.49619e43 | −1.86718 | −0.933591 | − | 0.358340i | \(-0.883343\pi\) | ||||
−0.933591 | + | 0.358340i | \(0.883343\pi\) | |||||||
\(432\) | 3.23270e43 | 1.05702 | ||||||||
\(433\) | 1.92976e43 | 0.607369 | 0.303685 | − | 0.952773i | \(-0.401783\pi\) | ||||
0.303685 | + | 0.952773i | \(0.401783\pi\) | |||||||
\(434\) | 1.62237e43 | 0.491552 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.01690e43 | −0.847293 | ||||||||
\(437\) | 2.81879e43 | 0.762288 | ||||||||
\(438\) | −4.06117e43 | −1.05762 | ||||||||
\(439\) | −4.45489e43 | −1.11731 | −0.558653 | − | 0.829401i | \(-0.688682\pi\) | ||||
−0.558653 | + | 0.829401i | \(0.688682\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.81506e43 | −1.58574 | ||||||||
\(442\) | −2.55454e43 | −0.572591 | ||||||||
\(443\) | −4.76827e43 | −1.02967 | −0.514837 | − | 0.857288i | \(-0.672147\pi\) | ||||
−0.514837 | + | 0.857288i | \(0.672147\pi\) | |||||||
\(444\) | −5.17331e43 | −1.07634 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.14340e43 | 0.993631 | ||||||||
\(447\) | −5.06998e43 | −0.943914 | ||||||||
\(448\) | 3.75991e43 | 0.674668 | ||||||||
\(449\) | 7.03065e43 | 1.21599 | 0.607996 | − | 0.793940i | \(-0.291974\pi\) | ||||
0.607996 | + | 0.793940i | \(0.291974\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.64196e43 | 0.263906 | ||||||||
\(452\) | −2.45863e43 | −0.380986 | ||||||||
\(453\) | −1.73308e44 | −2.58940 | ||||||||
\(454\) | 1.22066e44 | 1.75863 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.59803e43 | 0.750094 | ||||||||
\(457\) | −1.29751e44 | −1.67685 | −0.838424 | − | 0.545018i | \(-0.816523\pi\) | ||||
−0.838424 | + | 0.545018i | \(0.816523\pi\) | |||||||
\(458\) | 5.34291e43 | 0.666035 | ||||||||
\(459\) | 3.61342e43 | 0.434520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.60383e43 | −0.179512 | −0.0897561 | − | 0.995964i | \(-0.528609\pi\) | ||||
−0.0897561 | + | 0.995964i | \(0.528609\pi\) | |||||||
\(462\) | 1.80228e44 | 1.94639 | ||||||||
\(463\) | −8.21430e43 | −0.856020 | −0.428010 | − | 0.903774i | \(-0.640785\pi\) | ||||
−0.428010 | + | 0.903774i | \(0.640785\pi\) | |||||||
\(464\) | 1.10409e44 | 1.11034 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.03125e44 | 0.966044 | ||||||||
\(467\) | 2.45616e43 | 0.222089 | 0.111045 | − | 0.993815i | \(-0.464580\pi\) | ||||
0.111045 | + | 0.993815i | \(0.464580\pi\) | |||||||
\(468\) | 4.48077e44 | 3.91107 | ||||||||
\(469\) | −1.03722e44 | −0.874016 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.53303e44 | −1.20422 | ||||||||
\(472\) | 3.83663e43 | 0.291010 | ||||||||
\(473\) | 4.24378e44 | 3.10845 | ||||||||
\(474\) | 4.02751e44 | 2.84901 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.24884e43 | 0.148403 | ||||||||
\(477\) | 1.23928e44 | 0.789982 | ||||||||
\(478\) | −2.90349e44 | −1.78797 | ||||||||
\(479\) | 2.62104e44 | 1.55933 | 0.779664 | − | 0.626199i | \(-0.215390\pi\) | ||||
0.779664 | + | 0.626199i | \(0.215390\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.29537e44 | 0.719450 | ||||||||
\(482\) | 2.36741e44 | 1.27057 | ||||||||
\(483\) | −1.21574e44 | −0.630543 | ||||||||
\(484\) | 4.28435e44 | 2.14752 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.27979e41 | 0.00106757 | ||||||||
\(487\) | −1.10024e43 | −0.0498037 | −0.0249018 | − | 0.999690i | \(-0.507927\pi\) | ||||
−0.0249018 | + | 0.999690i | \(0.507927\pi\) | |||||||
\(488\) | 3.41131e43 | 0.149278 | ||||||||
\(489\) | −3.61475e44 | −1.52926 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.25640e44 | −0.892426 | −0.446213 | − | 0.894927i | \(-0.647228\pi\) | ||||
−0.446213 | + | 0.894927i | \(0.647228\pi\) | |||||||
\(492\) | −9.53822e43 | −0.364790 | ||||||||
\(493\) | 1.23412e44 | 0.456439 | ||||||||
\(494\) | −6.07817e44 | −2.17409 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.29947e44 | 0.434831 | ||||||||
\(497\) | 1.70985e44 | 0.553450 | ||||||||
\(498\) | −4.72742e44 | −1.48027 | ||||||||
\(499\) | −4.29566e44 | −1.30128 | −0.650641 | − | 0.759386i | \(-0.725500\pi\) | ||||
−0.650641 | + | 0.759386i | \(0.725500\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.29194e44 | −0.366371 | ||||||||
\(502\) | 4.41051e44 | 1.21026 | ||||||||
\(503\) | 2.02877e44 | 0.538717 | 0.269359 | − | 0.963040i | \(-0.413188\pi\) | ||||
0.269359 | + | 0.963040i | \(0.413188\pi\) | |||||||
\(504\) | −1.60957e44 | −0.413624 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.20853e44 | −1.97598 | ||||||||
\(507\) | −9.39676e44 | −2.18951 | ||||||||
\(508\) | 4.67292e44 | 1.05399 | ||||||||
\(509\) | 4.74147e44 | 1.03531 | 0.517654 | − | 0.855590i | \(-0.326806\pi\) | ||||
0.517654 | + | 0.855590i | \(0.326806\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.95206e43 | −0.183222 | ||||||||
\(512\) | 5.65155e44 | 1.11999 | ||||||||
\(513\) | 8.59764e44 | 1.64984 | ||||||||
\(514\) | −9.09346e44 | −1.68981 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.46524e45 | −4.29673 | ||||||||
\(517\) | 1.12483e45 | 1.89886 | ||||||||
\(518\) | −2.01773e44 | −0.329930 | ||||||||
\(519\) | 4.27059e44 | 0.676436 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.04032e45 | 1.54648 | 0.773240 | − | 0.634113i | \(-0.218635\pi\) | ||||
0.773240 | + | 0.634113i | \(0.218635\pi\) | |||||||
\(522\) | −3.83018e45 | −5.51641 | ||||||||
\(523\) | −7.60705e44 | −1.06154 | −0.530772 | − | 0.847514i | \(-0.678098\pi\) | ||||
−0.530772 | + | 0.847514i | \(0.678098\pi\) | |||||||
\(524\) | 1.84999e45 | 2.50152 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.32225e45 | 1.67900 | ||||||||
\(527\) | 1.45252e44 | 0.178750 | ||||||||
\(528\) | 1.44358e45 | 1.72179 | ||||||||
\(529\) | −3.11290e44 | −0.359871 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.17860e45 | 1.28029 | ||||||||
\(532\) | 5.35080e44 | 0.563478 | ||||||||
\(533\) | 2.38832e44 | 0.243834 | ||||||||
\(534\) | −3.00646e45 | −2.97594 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.38184e44 | 0.873110 | ||||||||
\(537\) | −9.92047e44 | −0.895275 | ||||||||
\(538\) | −1.49060e45 | −1.30453 | ||||||||
\(539\) | −1.52149e45 | −1.29138 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.20989e44 | 0.735359 | 0.367680 | − | 0.929953i | \(-0.380152\pi\) | ||||
0.367680 | + | 0.929953i | \(0.380152\pi\) | |||||||
\(542\) | 8.30442e44 | 0.643163 | ||||||||
\(543\) | −2.20423e45 | −1.65600 | ||||||||
\(544\) | 4.75214e44 | 0.346344 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.62151e45 | 1.79835 | ||||||||
\(547\) | 2.34454e45 | 1.56051 | 0.780254 | − | 0.625463i | \(-0.215090\pi\) | ||||
0.780254 | + | 0.625463i | \(0.215090\pi\) | |||||||
\(548\) | −1.42234e45 | −0.918593 | ||||||||
\(549\) | 1.04795e45 | 0.656744 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.93642e45 | 1.73307 | ||||||||
\(552\) | 1.09966e45 | 0.629889 | ||||||||
\(553\) | 8.87787e44 | 0.493565 | ||||||||
\(554\) | 6.59918e44 | 0.356106 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.34695e45 | −1.19335 | ||||||||
\(557\) | −9.31697e44 | −0.459900 | −0.229950 | − | 0.973202i | \(-0.573856\pi\) | ||||
−0.229950 | + | 0.973202i | \(0.573856\pi\) | |||||||
\(558\) | −4.50800e45 | −2.16033 | ||||||||
\(559\) | 6.17283e45 | 2.87203 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.61359e45 | 0.707793 | ||||||||
\(562\) | −3.89659e45 | −1.65972 | ||||||||
\(563\) | 1.76320e45 | 0.729312 | 0.364656 | − | 0.931142i | \(-0.381187\pi\) | ||||
0.364656 | + | 0.931142i | \(0.381187\pi\) | |||||||
\(564\) | −6.53421e45 | −2.62475 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.50970e45 | −0.950936 | ||||||||
\(567\) | −1.23564e45 | −0.454747 | ||||||||
\(568\) | −1.54659e45 | −0.552875 | ||||||||
\(569\) | 1.99581e45 | 0.693054 | 0.346527 | − | 0.938040i | \(-0.387361\pi\) | ||||
0.346527 | + | 0.938040i | \(0.387361\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.67320e45 | −0.548342 | −0.274171 | − | 0.961681i | \(-0.588404\pi\) | ||||
−0.274171 | + | 0.961681i | \(0.588404\pi\) | |||||||
\(572\) | 1.00035e46 | 3.18507 | ||||||||
\(573\) | −4.03161e45 | −1.24717 | ||||||||
\(574\) | −3.72016e44 | −0.111819 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.04475e46 | −2.96511 | ||||||||
\(577\) | −6.81345e44 | −0.187917 | −0.0939586 | − | 0.995576i | \(-0.529952\pi\) | ||||
−0.0939586 | + | 0.995576i | \(0.529952\pi\) | |||||||
\(578\) | −5.30157e45 | −1.42100 | ||||||||
\(579\) | 4.36120e45 | 1.13608 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.04207e45 | −0.256443 | ||||||||
\(582\) | 2.49068e45 | 0.595783 | ||||||||
\(583\) | 2.76676e45 | 0.643339 | ||||||||
\(584\) | 8.09729e44 | 0.183032 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.11099e46 | 2.37355 | ||||||||
\(587\) | −7.97410e45 | −1.65635 | −0.828176 | − | 0.560467i | \(-0.810622\pi\) | ||||
−0.828176 | + | 0.560467i | \(0.810622\pi\) | |||||||
\(588\) | 8.83844e45 | 1.78505 | ||||||||
\(589\) | 3.45607e45 | 0.678703 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.34865e45 | 0.436139 | ||||||||
\(592\) | −1.61615e45 | −0.291859 | ||||||||
\(593\) | −9.65663e45 | −1.69599 | −0.847994 | − | 0.530005i | \(-0.822190\pi\) | ||||
−0.847994 | + | 0.530005i | \(0.822190\pi\) | |||||||
\(594\) | −2.50370e46 | −4.27667 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.38335e45 | 0.708342 | ||||||||
\(597\) | −2.51330e45 | −0.395064 | ||||||||
\(598\) | −1.19398e46 | −1.82569 | ||||||||
\(599\) | −8.55789e45 | −1.27299 | −0.636494 | − | 0.771282i | \(-0.719616\pi\) | ||||
−0.636494 | + | 0.771282i | \(0.719616\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.47394e45 | −0.489095 | −0.244548 | − | 0.969637i | \(-0.578639\pi\) | ||||
−0.244548 | + | 0.969637i | \(0.578639\pi\) | |||||||
\(602\) | −9.61507e45 | −1.31707 | ||||||||
\(603\) | 2.88208e46 | 3.84123 | ||||||||
\(604\) | 1.49837e46 | 1.94317 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.87942e46 | −2.30794 | ||||||||
\(607\) | 3.78540e45 | 0.452375 | 0.226188 | − | 0.974084i | \(-0.427374\pi\) | ||||
0.226188 | + | 0.974084i | \(0.427374\pi\) | |||||||
\(608\) | 1.13071e46 | 1.31504 | ||||||||
\(609\) | −1.26648e46 | −1.43355 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.63613e46 | 1.75444 | ||||||||
\(612\) | −6.24875e45 | −0.652220 | ||||||||
\(613\) | 9.19782e45 | 0.934517 | 0.467258 | − | 0.884121i | \(-0.345242\pi\) | ||||
0.467258 | + | 0.884121i | \(0.345242\pi\) | |||||||
\(614\) | 2.48840e46 | 2.46117 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.59344e45 | −0.336843 | ||||||||
\(617\) | 3.00505e45 | 0.274250 | 0.137125 | − | 0.990554i | \(-0.456214\pi\) | ||||
0.137125 | + | 0.990554i | \(0.456214\pi\) | |||||||
\(618\) | 4.45519e46 | 3.95873 | ||||||||
\(619\) | −8.07148e45 | −0.698325 | −0.349162 | − | 0.937062i | \(-0.613534\pi\) | ||||
−0.349162 | + | 0.937062i | \(0.613534\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.68890e46 | 1.38545 | ||||||||
\(622\) | 9.26106e45 | 0.739809 | ||||||||
\(623\) | −6.62716e45 | −0.515554 | ||||||||
\(624\) | 2.09976e46 | 1.59083 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.01790e46 | −1.45018 | ||||||||
\(627\) | 3.83932e46 | 2.68745 | ||||||||
\(628\) | 1.32541e46 | 0.903682 | ||||||||
\(629\) | −1.80649e45 | −0.119977 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.34115e46 | −0.845264 | −0.422632 | − | 0.906301i | \(-0.638894\pi\) | ||||
−0.422632 | + | 0.906301i | \(0.638894\pi\) | |||||||
\(632\) | −8.03018e45 | −0.493053 | ||||||||
\(633\) | 5.96092e45 | 0.356576 | ||||||||
\(634\) | 2.70002e46 | 1.57360 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.60722e46 | −0.889271 | ||||||||
\(637\) | −2.21310e46 | −1.19316 | ||||||||
\(638\) | −8.55107e46 | −4.49241 | ||||||||
\(639\) | −4.75109e46 | −2.43237 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.68745e46 | −0.820489 | −0.410244 | − | 0.911976i | \(-0.634557\pi\) | ||||
−0.410244 | + | 0.911976i | \(0.634557\pi\) | |||||||
\(642\) | −2.02206e46 | −0.958222 | ||||||||
\(643\) | −3.29909e45 | −0.152375 | −0.0761874 | − | 0.997094i | \(-0.524275\pi\) | ||||
−0.0761874 | + | 0.997094i | \(0.524275\pi\) | |||||||
\(644\) | 1.05110e46 | 0.473179 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.47644e45 | 0.362557 | ||||||||
\(647\) | −1.31901e46 | −0.549953 | −0.274977 | − | 0.961451i | \(-0.588670\pi\) | ||||
−0.274977 | + | 0.961451i | \(0.588670\pi\) | |||||||
\(648\) | 1.11765e46 | 0.454276 | ||||||||
\(649\) | 2.63129e46 | 1.04263 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.49060e46 | −0.561404 | ||||||||
\(652\) | 3.12520e46 | 1.14761 | ||||||||
\(653\) | −3.26301e46 | −1.16829 | −0.584146 | − | 0.811649i | \(-0.698570\pi\) | ||||
−0.584146 | + | 0.811649i | \(0.698570\pi\) | |||||||
\(654\) | 4.90451e46 | 1.71223 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.97975e45 | −0.0989159 | ||||||||
\(657\) | 2.48747e46 | 0.805247 | ||||||||
\(658\) | −2.54852e46 | −0.804563 | ||||||||
\(659\) | 1.87303e46 | 0.576682 | 0.288341 | − | 0.957528i | \(-0.406896\pi\) | ||||
0.288341 | + | 0.957528i | \(0.406896\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.63902e46 | −0.480021 | −0.240011 | − | 0.970770i | \(-0.577151\pi\) | ||||
−0.240011 | + | 0.970770i | \(0.577151\pi\) | |||||||
\(662\) | 9.15536e46 | 2.61528 | ||||||||
\(663\) | 2.34706e46 | 0.653960 | ||||||||
\(664\) | 9.42568e45 | 0.256177 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.60657e46 | 1.45001 | ||||||||
\(667\) | 5.76821e46 | 1.45534 | ||||||||
\(668\) | 1.11697e46 | 0.274936 | ||||||||
\(669\) | −4.72566e46 | −1.13483 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.33959e46 | 0.534834 | ||||||||
\(672\) | −4.87674e46 | −1.08777 | ||||||||
\(673\) | 8.65953e46 | 1.88472 | 0.942358 | − | 0.334606i | \(-0.108603\pi\) | ||||
0.942358 | + | 0.334606i | \(0.108603\pi\) | |||||||
\(674\) | 1.56911e46 | 0.333246 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.12415e46 | 1.64308 | ||||||||
\(677\) | −4.79310e45 | −0.0946027 | −0.0473014 | − | 0.998881i | \(-0.515062\pi\) | ||||
−0.0473014 | + | 0.998881i | \(0.515062\pi\) | |||||||
\(678\) | 3.99694e46 | 0.769905 | ||||||||
\(679\) | 5.49021e45 | 0.103214 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.12152e47 | −2.00854 | ||||||||
\(682\) | −1.00643e47 | −1.75931 | ||||||||
\(683\) | −6.64508e46 | −1.13386 | −0.566929 | − | 0.823767i | \(-0.691869\pi\) | ||||
−0.566929 | + | 0.823767i | \(0.691869\pi\) | |||||||
\(684\) | −1.48680e47 | −2.47644 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.79455e46 | 1.23721 | ||||||||
\(687\) | −4.90896e46 | −0.760683 | ||||||||
\(688\) | −7.70142e46 | −1.16510 | ||||||||
\(689\) | 4.02441e46 | 0.594408 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.37178e46 | 0.615560 | 0.307780 | − | 0.951458i | \(-0.400414\pi\) | ||||
0.307780 | + | 0.951458i | \(0.400414\pi\) | |||||||
\(692\) | −3.69222e46 | −0.507619 | ||||||||
\(693\) | −1.10390e47 | −1.48194 | ||||||||
\(694\) | 6.34534e46 | 0.831809 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.14555e47 | 1.43206 | ||||||||
\(697\) | −3.33068e45 | −0.0406624 | ||||||||
\(698\) | 1.52064e47 | 1.81306 | ||||||||
\(699\) | −9.47494e46 | −1.10332 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.99204e46 | 1.10996 | 0.554979 | − | 0.831864i | \(-0.312726\pi\) | ||||
0.554979 | + | 0.831864i | \(0.312726\pi\) | |||||||
\(702\) | −3.64177e47 | −3.95139 | ||||||||
\(703\) | −4.29829e46 | −0.455546 | ||||||||
\(704\) | −2.33245e47 | −2.41470 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.43956e46 | −0.142218 | ||||||||
\(707\) | −4.14281e46 | −0.399829 | ||||||||
\(708\) | −1.52853e47 | −1.44120 | ||||||||
\(709\) | −3.22308e46 | −0.296898 | −0.148449 | − | 0.988920i | \(-0.547428\pi\) | ||||
−0.148449 | + | 0.988920i | \(0.547428\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.46685e47 | −2.16918 | ||||||||
\(712\) | 5.99437e46 | 0.515020 | ||||||||
\(713\) | 6.78900e46 | 0.569939 | ||||||||
\(714\) | −3.65589e46 | −0.299897 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.57693e46 | 0.671842 | ||||||||
\(717\) | 2.66767e47 | 2.04205 | ||||||||
\(718\) | −8.63391e45 | −0.0645883 | ||||||||
\(719\) | −2.25121e47 | −1.64585 | −0.822923 | − | 0.568153i | \(-0.807658\pi\) | ||||
−0.822923 | + | 0.568153i | \(0.807658\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.82060e46 | 0.685814 | ||||||||
\(722\) | −2.04940e46 | −0.139882 | ||||||||
\(723\) | −2.17513e47 | −1.45112 | ||||||||
\(724\) | 1.90571e47 | 1.24271 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.96497e47 | −4.33976 | ||||||||
\(727\) | −1.90515e46 | −0.116041 | −0.0580205 | − | 0.998315i | \(-0.518479\pi\) | ||||
−0.0580205 | + | 0.998315i | \(0.518479\pi\) | |||||||
\(728\) | −5.22686e46 | −0.311224 | ||||||||
\(729\) | −1.71897e47 | −1.00061 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.60844e46 | −0.478948 | ||||||||
\(732\) | −1.35908e47 | −0.739286 | ||||||||
\(733\) | 2.27821e47 | 1.21165 | 0.605826 | − | 0.795597i | \(-0.292843\pi\) | ||||
0.605826 | + | 0.795597i | \(0.292843\pi\) | |||||||
\(734\) | 4.11633e47 | 2.14055 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.22112e47 | 1.10430 | ||||||||
\(737\) | 6.43438e47 | 3.12819 | ||||||||
\(738\) | 1.03370e47 | 0.491435 | ||||||||
\(739\) | 3.27147e47 | 1.52093 | 0.760467 | − | 0.649377i | \(-0.224970\pi\) | ||||
0.760467 | + | 0.649377i | \(0.224970\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.58451e47 | 2.48304 | ||||||||
\(742\) | −6.26860e46 | −0.272588 | ||||||||
\(743\) | −1.23139e47 | −0.523698 | −0.261849 | − | 0.965109i | \(-0.584332\pi\) | ||||
−0.261849 | + | 0.965109i | \(0.584332\pi\) | |||||||
\(744\) | 1.34827e47 | 0.560822 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.83520e47 | −1.52615 | ||||||||
\(747\) | 2.89555e47 | 1.12704 | ||||||||
\(748\) | −1.39506e47 | −0.531150 | ||||||||
\(749\) | −4.45724e46 | −0.166003 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.24124e47 | 1.51159 | 0.755795 | − | 0.654808i | \(-0.227251\pi\) | ||||
0.755795 | + | 0.654808i | \(0.227251\pi\) | |||||||
\(752\) | −2.04129e47 | −0.711723 | ||||||||
\(753\) | −4.05230e47 | −1.38224 | ||||||||
\(754\) | −1.24380e48 | −4.15072 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.20597e47 | 1.02412 | ||||||||
\(757\) | 4.38259e47 | 1.36977 | 0.684887 | − | 0.728649i | \(-0.259852\pi\) | ||||
0.684887 | + | 0.728649i | \(0.259852\pi\) | |||||||
\(758\) | 3.53232e47 | 1.08024 | ||||||||
\(759\) | 7.54184e47 | 2.25677 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.43868e47 | −1.84480 | −0.922401 | − | 0.386232i | \(-0.873776\pi\) | ||||
−0.922401 | + | 0.386232i | \(0.873776\pi\) | |||||||
\(762\) | −7.59667e47 | −2.12993 | ||||||||
\(763\) | 1.08110e47 | 0.296628 | ||||||||
\(764\) | 3.48560e47 | 0.935918 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.78370e47 | 2.00176 | ||||||||
\(767\) | 3.82736e47 | 0.963332 | ||||||||
\(768\) | −1.16704e47 | −0.287491 | ||||||||
\(769\) | 1.83655e46 | 0.0442812 | 0.0221406 | − | 0.999755i | \(-0.492952\pi\) | ||||
0.0221406 | + | 0.999755i | \(0.492952\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.35491e47 | 1.92994 | ||||||||
\(772\) | −3.77056e47 | −0.852552 | ||||||||
\(773\) | 1.27125e47 | 0.281364 | 0.140682 | − | 0.990055i | \(-0.455070\pi\) | ||||
0.140682 | + | 0.990055i | \(0.455070\pi\) | |||||||
\(774\) | 2.67170e48 | 5.78844 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.96599e46 | −0.103107 | ||||||||
\(777\) | 1.85385e47 | 0.376815 | ||||||||
\(778\) | 9.04484e47 | 1.79986 | ||||||||
\(779\) | −7.92490e46 | −0.154392 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.06070e48 | −1.98085 | ||||||||
\(782\) | 1.66509e47 | 0.304456 | ||||||||
\(783\) | 1.75937e48 | 3.14984 | ||||||||
\(784\) | 2.76114e47 | 0.484031 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.00749e48 | −5.05513 | ||||||||
\(787\) | −1.07309e48 | −1.76626 | −0.883128 | − | 0.469133i | \(-0.844567\pi\) | ||||
−0.883128 | + | 0.469133i | \(0.844567\pi\) | |||||||
\(788\) | −2.03057e47 | −0.327292 | ||||||||
\(789\) | −1.21486e48 | −1.91759 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.81047e46 | 0.133379 | ||||||||
\(792\) | 9.98491e47 | 1.48040 | ||||||||
\(793\) | 3.40307e47 | 0.494155 | ||||||||
\(794\) | 3.64283e46 | 0.0518084 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.17292e47 | 0.296468 | ||||||||
\(797\) | −8.32944e47 | −1.11315 | −0.556575 | − | 0.830798i | \(-0.687885\pi\) | ||||
−0.556575 | + | 0.830798i | \(0.687885\pi\) | |||||||
\(798\) | −8.69868e47 | −1.13869 | ||||||||
\(799\) | −2.28170e47 | −0.292575 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.84146e48 | 2.26582 | ||||||||
\(802\) | −3.03216e46 | −0.0365489 | ||||||||
\(803\) | 5.55339e47 | 0.655770 | ||||||||
\(804\) | −3.73776e48 | −4.32401 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.46391e48 | −1.62550 | ||||||||
\(807\) | 1.36954e48 | 1.48991 | ||||||||
\(808\) | 3.74724e47 | 0.399415 | ||||||||
\(809\) | −4.91569e47 | −0.513374 | −0.256687 | − | 0.966495i | \(-0.582631\pi\) | ||||
−0.256687 | + | 0.966495i | \(0.582631\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.31202e48 | 1.31551 | 0.657757 | − | 0.753230i | \(-0.271505\pi\) | ||||
0.657757 | + | 0.753230i | \(0.271505\pi\) | |||||||
\(812\) | 1.09496e48 | 1.07578 | ||||||||
\(813\) | −7.62995e47 | −0.734560 | ||||||||
\(814\) | 1.25169e48 | 1.18085 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.92827e47 | −0.265292 | ||||||||
\(817\) | −2.04826e48 | −1.81853 | ||||||||
\(818\) | 4.32435e47 | 0.376262 | ||||||||
\(819\) | −1.60568e48 | −1.36922 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.18387e48 | −0.969711 | −0.484855 | − | 0.874594i | \(-0.661128\pi\) | ||||
−0.484855 | + | 0.874594i | \(0.661128\pi\) | |||||||
\(822\) | 2.31226e48 | 1.85631 | ||||||||
\(823\) | −1.23245e48 | −0.969776 | −0.484888 | − | 0.874576i | \(-0.661140\pi\) | ||||
−0.484888 | + | 0.874576i | \(0.661140\pi\) | |||||||
\(824\) | −8.88289e47 | −0.685102 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.96167e47 | −0.441771 | ||||||||
\(827\) | 4.69422e45 | 0.00340975 | 0.00170487 | − | 0.999999i | \(-0.499457\pi\) | ||||
0.00170487 | + | 0.999999i | \(0.499457\pi\) | |||||||
\(828\) | −2.92063e48 | −2.07958 | ||||||||
\(829\) | −4.02684e47 | −0.281070 | −0.140535 | − | 0.990076i | \(-0.544882\pi\) | ||||
−0.140535 | + | 0.990076i | \(0.544882\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.06321e47 | −0.406711 | ||||||||
\(832\) | −3.39268e48 | −2.23105 | ||||||||
\(833\) | 3.08632e47 | 0.198975 | ||||||||
\(834\) | 3.81538e48 | 2.41156 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.31936e48 | −2.01674 | ||||||||
\(837\) | 2.07072e48 | 1.23354 | ||||||||
\(838\) | 1.16819e48 | 0.682316 | ||||||||
\(839\) | 5.27811e46 | 0.0302278 | 0.0151139 | − | 0.999886i | \(-0.495189\pi\) | ||||
0.0151139 | + | 0.999886i | \(0.495189\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.19284e48 | 2.30874 | ||||||||
\(842\) | −3.49269e48 | −1.88586 | ||||||||
\(843\) | 3.58011e48 | 1.89558 | ||||||||
\(844\) | −5.15363e47 | −0.267586 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.08144e48 | 3.53599 | ||||||||
\(847\) | −1.53529e48 | −0.751822 | ||||||||
\(848\) | −5.02098e47 | −0.241133 | ||||||||
\(849\) | 2.30587e48 | 1.08607 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.44342e47 | −0.382544 | ||||||||
\(852\) | 6.16167e48 | 2.73808 | ||||||||
\(853\) | 3.55498e48 | 1.54945 | 0.774725 | − | 0.632298i | \(-0.217888\pi\) | ||||
0.774725 | + | 0.632298i | \(0.217888\pi\) | |||||||
\(854\) | −5.30078e47 | −0.226613 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.03165e47 | 0.165831 | ||||||||
\(857\) | −1.12728e48 | −0.454827 | −0.227414 | − | 0.973798i | \(-0.573027\pi\) | ||||
−0.227414 | + | 0.973798i | \(0.573027\pi\) | |||||||
\(858\) | −1.62625e49 | −6.43646 | ||||||||
\(859\) | 1.80056e48 | 0.699070 | 0.349535 | − | 0.936923i | \(-0.386340\pi\) | ||||
0.349535 | + | 0.936923i | \(0.386340\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.41801e47 | 0.127709 | ||||||||
\(862\) | −7.72496e48 | −2.83156 | ||||||||
\(863\) | 2.38697e48 | 0.858359 | 0.429180 | − | 0.903219i | \(-0.358803\pi\) | ||||
0.429180 | + | 0.903219i | \(0.358803\pi\) | |||||||
\(864\) | 6.77469e48 | 2.39008 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.71230e48 | 0.921069 | ||||||||
\(867\) | 4.87098e48 | 1.62294 | ||||||||
\(868\) | 1.28873e48 | 0.421295 | ||||||||
\(869\) | −5.50737e48 | −1.76652 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.35917e48 | 2.89027 | ||||||||
\(872\) | −9.77876e47 | −0.296320 | ||||||||
\(873\) | −1.52554e48 | −0.453616 | ||||||||
\(874\) | 3.96184e48 | 1.15600 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.22599e48 | −0.906454 | ||||||||
\(877\) | 1.44993e48 | 0.399811 | 0.199905 | − | 0.979815i | \(-0.435936\pi\) | ||||
0.199905 | + | 0.979815i | \(0.435936\pi\) | |||||||
\(878\) | −6.26140e48 | −1.69438 | ||||||||
\(879\) | −1.02075e49 | −2.71084 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.86343e48 | −1.24406 | −0.622029 | − | 0.782994i | \(-0.713691\pi\) | ||||
−0.622029 | + | 0.782994i | \(0.713691\pi\) | |||||||
\(882\) | −9.57864e48 | −2.40476 | ||||||||
\(883\) | −2.25361e48 | −0.555299 | −0.277650 | − | 0.960682i | \(-0.589555\pi\) | ||||
−0.277650 | + | 0.960682i | \(0.589555\pi\) | |||||||
\(884\) | −2.02920e48 | −0.490752 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.70186e48 | −1.56149 | ||||||||
\(887\) | 7.86411e48 | 1.79850 | 0.899248 | − | 0.437439i | \(-0.144114\pi\) | ||||
0.899248 | + | 0.437439i | \(0.144114\pi\) | |||||||
\(888\) | −1.67684e48 | −0.376424 | ||||||||
\(889\) | −1.67454e48 | −0.368991 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.66524e48 | 1.62758 | ||||||||
\(892\) | 4.08566e48 | 0.851613 | ||||||||
\(893\) | −5.42900e48 | −1.11089 | ||||||||
\(894\) | −7.12592e48 | −1.43144 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.04066e48 | 0.395083 | ||||||||
\(897\) | 1.09700e49 | 2.08513 | ||||||||
\(898\) | 9.88165e48 | 1.84404 | ||||||||
\(899\) | 7.07230e48 | 1.29576 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.61232e47 | −0.0991251 | ||||||||
\(902\) | 2.30779e48 | 0.400211 | ||||||||
\(903\) | 8.83415e48 | 1.50424 | ||||||||
\(904\) | −7.96922e47 | −0.133241 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.43587e49 | −3.92680 | ||||||||
\(907\) | 1.83168e48 | 0.289954 | 0.144977 | − | 0.989435i | \(-0.453689\pi\) | ||||
0.144977 | + | 0.989435i | \(0.453689\pi\) | |||||||
\(908\) | 9.69632e48 | 1.50727 | ||||||||
\(909\) | 1.15114e49 | 1.75722 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.44938e48 | 0.655007 | 0.327504 | − | 0.944850i | \(-0.393793\pi\) | ||||
0.327504 | + | 0.944850i | \(0.393793\pi\) | |||||||
\(912\) | −6.96742e48 | −1.00730 | ||||||||
\(913\) | 6.46445e48 | 0.917833 | ||||||||
\(914\) | −1.82367e49 | −2.54292 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.24414e48 | 0.570840 | ||||||||
\(917\) | −6.62943e48 | −0.875754 | ||||||||
\(918\) | 5.07871e48 | 0.658945 | ||||||||
\(919\) | −1.19748e49 | −1.52603 | −0.763013 | − | 0.646383i | \(-0.776281\pi\) | ||||
−0.763013 | + | 0.646383i | \(0.776281\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.28630e49 | −2.81092 | ||||||||
\(922\) | −2.25421e48 | −0.272228 | ||||||||
\(923\) | −1.54285e49 | −1.83019 | ||||||||
\(924\) | 1.43164e49 | 1.66819 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.15453e49 | −1.29815 | ||||||||
\(927\) | −2.72880e49 | −3.01409 | ||||||||
\(928\) | 2.31381e49 | 2.51065 | ||||||||
\(929\) | −6.38779e48 | −0.680912 | −0.340456 | − | 0.940260i | \(-0.610581\pi\) | ||||
−0.340456 | + | 0.940260i | \(0.610581\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.34348e48 | 0.755496 | ||||||||
\(932\) | 8.19175e48 | 0.827969 | ||||||||
\(933\) | −8.50889e48 | −0.844940 | ||||||||
\(934\) | 3.45215e48 | 0.336796 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.45236e49 | 1.36780 | ||||||||
\(937\) | −2.98186e47 | −0.0275921 | −0.0137960 | − | 0.999905i | \(-0.504392\pi\) | ||||
−0.0137960 | + | 0.999905i | \(0.504392\pi\) | |||||||
\(938\) | −1.45783e49 | −1.32544 | ||||||||
\(939\) | 1.85401e49 | 1.65626 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.14468e48 | 0.529993 | 0.264997 | − | 0.964249i | \(-0.414629\pi\) | ||||
0.264997 | + | 0.964249i | \(0.414629\pi\) | |||||||
\(942\) | −2.15469e49 | −1.82618 | ||||||||
\(943\) | −1.55674e48 | −0.129651 | ||||||||
\(944\) | −4.77514e48 | −0.390794 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.96469e49 | 4.71394 | ||||||||
\(947\) | −4.27472e46 | −0.00331996 | −0.00165998 | − | 0.999999i | \(-0.500528\pi\) | ||||
−0.00165998 | + | 0.999999i | \(0.500528\pi\) | |||||||
\(948\) | 3.19926e49 | 2.44181 | ||||||||
\(949\) | 8.07772e48 | 0.605894 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.48073e49 | −1.79722 | ||||||||
\(952\) | 7.28922e47 | 0.0519005 | ||||||||
\(953\) | −1.36139e49 | −0.952684 | −0.476342 | − | 0.879260i | \(-0.658038\pi\) | ||||
−0.476342 | + | 0.879260i | \(0.658038\pi\) | |||||||
\(954\) | 1.74183e49 | 1.19800 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.30639e49 | −1.53242 | ||||||||
\(957\) | 7.85656e49 | 5.13081 | ||||||||
\(958\) | 3.68390e49 | 2.36470 | ||||||||
\(959\) | 5.09693e48 | 0.321589 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.07961e48 | −0.492555 | ||||||||
\(962\) | 1.82066e49 | 1.09104 | ||||||||
\(963\) | 1.23851e49 | 0.729570 | ||||||||
\(964\) | 1.88055e49 | 1.08897 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.70874e49 | −0.956212 | ||||||||
\(967\) | −1.39797e49 | −0.769060 | −0.384530 | − | 0.923113i | \(-0.625636\pi\) | ||||
−0.384530 | + | 0.923113i | \(0.625636\pi\) | |||||||
\(968\) | 1.38870e49 | 0.751042 | ||||||||
\(969\) | −7.78799e48 | −0.414079 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.21572e49 | 1.13867 | 0.569334 | − | 0.822107i | \(-0.307201\pi\) | ||||
0.569334 | + | 0.822107i | \(0.307201\pi\) | |||||||
\(972\) | 1.81095e46 | 0.000914985 0 | ||||||||
\(973\) | 8.41026e48 | 0.417780 | ||||||||
\(974\) | −1.54641e48 | −0.0755268 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.24578e48 | −0.200464 | ||||||||
\(977\) | 1.12838e49 | 0.523835 | 0.261918 | − | 0.965090i | \(-0.415645\pi\) | ||||
0.261918 | + | 0.965090i | \(0.415645\pi\) | |||||||
\(978\) | −5.08057e49 | −2.31911 | ||||||||
\(979\) | 4.11114e49 | 1.84522 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.00401e49 | −1.30366 | ||||||||
\(982\) | −3.17140e49 | −1.35335 | ||||||||
\(983\) | 2.75705e49 | 1.15694 | 0.578471 | − | 0.815703i | \(-0.303650\pi\) | ||||
0.578471 | + | 0.815703i | \(0.303650\pi\) | |||||||
\(984\) | −3.09165e48 | −0.127577 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.73457e49 | 0.692185 | ||||||||
\(987\) | 2.34153e49 | 0.918896 | ||||||||
\(988\) | −4.82819e49 | −1.86335 | ||||||||
\(989\) | −4.02354e49 | −1.52711 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.93272e49 | 1.07660 | 0.538300 | − | 0.842753i | \(-0.319067\pi\) | ||||
0.538300 | + | 0.842753i | \(0.319067\pi\) | |||||||
\(992\) | 2.72328e49 | 0.983218 | ||||||||
\(993\) | −8.41178e49 | −2.98693 | ||||||||
\(994\) | 2.40322e49 | 0.839300 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.75523e49 | −1.26870 | ||||||||
\(997\) | 1.66255e49 | 0.552464 | 0.276232 | − | 0.961091i | \(-0.410914\pi\) | ||||
0.276232 | + | 0.961091i | \(0.410914\pi\) | |||||||
\(998\) | −6.03760e49 | −1.97338 | ||||||||
\(999\) | −2.57534e49 | −0.827951 |
(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 | 25.34.a.e.1.10 | yes | 11 | |
5.2 | odd | 4 | 25.34.b.d.24.19 | 22 | |||
5.3 | odd | 4 | 25.34.b.d.24.4 | 22 | |||
5.4 | even | 2 | 25.34.a.d.1.2 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.34.a.d.1.2 | ✓ | 11 | 5.4 | even | 2 | ||
25.34.a.e.1.10 | yes | 11 | 1.1 | even | 1 | trivial | |
25.34.b.d.24.4 | 22 | 5.3 | odd | 4 | |||
25.34.b.d.24.19 | 22 | 5.2 | odd | 4 |