Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(91.1613430010\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −17.2166 | −0.760874 | −0.380437 | − | 0.924807i | \(-0.624226\pi\) | ||||
−0.380437 | + | 0.924807i | \(0.624226\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | −215.588 | −0.421071 | ||||||||
\(5\) | 470.596 | 0.336731 | 0.168366 | − | 0.985725i | \(-0.446151\pi\) | ||||
0.168366 | + | 0.985725i | \(0.446151\pi\) | |||||||
\(6\) | 1394.55 | 0.439291 | ||||||||
\(7\) | −5413.27 | −0.852156 | −0.426078 | − | 0.904687i | \(-0.640105\pi\) | ||||
−0.426078 | + | 0.904687i | \(0.640105\pi\) | |||||||
\(8\) | 12526.6 | 1.08126 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −8102.07 | −0.256210 | ||||||||
\(11\) | −66383.2 | −1.36707 | −0.683536 | − | 0.729917i | \(-0.739559\pi\) | ||||
−0.683536 | + | 0.729917i | \(0.739559\pi\) | |||||||
\(12\) | 17462.7 | 0.243106 | ||||||||
\(13\) | −154777. | −1.50301 | −0.751506 | − | 0.659726i | \(-0.770672\pi\) | ||||
−0.751506 | + | 0.659726i | \(0.770672\pi\) | |||||||
\(14\) | 93198.2 | 0.648383 | ||||||||
\(15\) | −38118.3 | −0.194412 | ||||||||
\(16\) | −105284. | −0.401628 | ||||||||
\(17\) | 478273. | 1.38885 | 0.694426 | − | 0.719564i | \(-0.255659\pi\) | ||||
0.694426 | + | 0.719564i | \(0.255659\pi\) | |||||||
\(18\) | −112958. | −0.253625 | ||||||||
\(19\) | 25047.4 | 0.0440933 | 0.0220466 | − | 0.999757i | \(-0.492982\pi\) | ||||
0.0220466 | + | 0.999757i | \(0.492982\pi\) | |||||||
\(20\) | −101455. | −0.141788 | ||||||||
\(21\) | 438475. | 0.491992 | ||||||||
\(22\) | 1.14289e6 | 1.04017 | ||||||||
\(23\) | 250737. | 0.186829 | 0.0934144 | − | 0.995627i | \(-0.470222\pi\) | ||||
0.0934144 | + | 0.995627i | \(0.470222\pi\) | |||||||
\(24\) | −1.01465e6 | −0.624263 | ||||||||
\(25\) | −1.73166e6 | −0.886612 | ||||||||
\(26\) | 2.66474e6 | 1.14360 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | 1.16704e6 | 0.358818 | ||||||||
\(29\) | 266117. | 0.0698684 | 0.0349342 | − | 0.999390i | \(-0.488878\pi\) | ||||
0.0349342 | + | 0.999390i | \(0.488878\pi\) | |||||||
\(30\) | 656268. | 0.147923 | ||||||||
\(31\) | −7.24334e6 | −1.40868 | −0.704338 | − | 0.709864i | \(-0.748756\pi\) | ||||
−0.704338 | + | 0.709864i | \(0.748756\pi\) | |||||||
\(32\) | −4.60098e6 | −0.775668 | ||||||||
\(33\) | 5.37704e6 | 0.789279 | ||||||||
\(34\) | −8.23424e6 | −1.05674 | ||||||||
\(35\) | −2.54747e6 | −0.286947 | ||||||||
\(36\) | −1.41448e6 | −0.140357 | ||||||||
\(37\) | −1.81489e7 | −1.59200 | −0.796000 | − | 0.605297i | \(-0.793054\pi\) | ||||
−0.796000 | + | 0.605297i | \(0.793054\pi\) | |||||||
\(38\) | −431232. | −0.0335494 | ||||||||
\(39\) | 1.25370e7 | 0.867764 | ||||||||
\(40\) | 5.89497e6 | 0.364093 | ||||||||
\(41\) | −1.23421e7 | −0.682124 | −0.341062 | − | 0.940041i | \(-0.610787\pi\) | ||||
−0.341062 | + | 0.940041i | \(0.610787\pi\) | |||||||
\(42\) | −7.54906e6 | −0.374344 | ||||||||
\(43\) | −1.58491e7 | −0.706965 | −0.353482 | − | 0.935441i | \(-0.615003\pi\) | ||||
−0.353482 | + | 0.935441i | \(0.615003\pi\) | |||||||
\(44\) | 1.43115e7 | 0.575635 | ||||||||
\(45\) | 3.08758e6 | 0.112244 | ||||||||
\(46\) | −4.31685e6 | −0.142153 | ||||||||
\(47\) | −3.87386e6 | −0.115799 | −0.0578993 | − | 0.998322i | \(-0.518440\pi\) | ||||
−0.0578993 | + | 0.998322i | \(0.518440\pi\) | |||||||
\(48\) | 8.52803e6 | 0.231880 | ||||||||
\(49\) | −1.10501e7 | −0.273831 | ||||||||
\(50\) | 2.98134e7 | 0.674600 | ||||||||
\(51\) | −3.87401e7 | −0.801854 | ||||||||
\(52\) | 3.33682e7 | 0.632875 | ||||||||
\(53\) | −2.96748e7 | −0.516591 | −0.258295 | − | 0.966066i | \(-0.583161\pi\) | ||||
−0.258295 | + | 0.966066i | \(0.583161\pi\) | |||||||
\(54\) | 9.14961e6 | 0.146430 | ||||||||
\(55\) | −3.12397e7 | −0.460336 | ||||||||
\(56\) | −6.78099e7 | −0.921398 | ||||||||
\(57\) | −2.02884e6 | −0.0254573 | ||||||||
\(58\) | −4.58162e6 | −0.0531610 | ||||||||
\(59\) | 1.21174e7 | 0.130189 | ||||||||
\(60\) | 8.21786e6 | 0.0818612 | ||||||||
\(61\) | −1.03356e8 | −0.955763 | −0.477882 | − | 0.878424i | \(-0.658595\pi\) | ||||
−0.477882 | + | 0.878424i | \(0.658595\pi\) | |||||||
\(62\) | 1.24706e8 | 1.07183 | ||||||||
\(63\) | −3.55165e7 | −0.284052 | ||||||||
\(64\) | 1.33119e8 | 0.991813 | ||||||||
\(65\) | −7.28376e7 | −0.506111 | ||||||||
\(66\) | −9.25744e7 | −0.600542 | ||||||||
\(67\) | −2.36659e8 | −1.43478 | −0.717391 | − | 0.696671i | \(-0.754664\pi\) | ||||
−0.717391 | + | 0.696671i | \(0.754664\pi\) | |||||||
\(68\) | −1.03110e8 | −0.584805 | ||||||||
\(69\) | −2.03097e7 | −0.107866 | ||||||||
\(70\) | 4.38587e7 | 0.218331 | ||||||||
\(71\) | −8.61606e7 | −0.402389 | −0.201195 | − | 0.979551i | \(-0.564482\pi\) | ||||
−0.201195 | + | 0.979551i | \(0.564482\pi\) | |||||||
\(72\) | 8.21871e7 | 0.360419 | ||||||||
\(73\) | −2.99436e8 | −1.23410 | −0.617050 | − | 0.786924i | \(-0.711672\pi\) | ||||
−0.617050 | + | 0.786924i | \(0.711672\pi\) | |||||||
\(74\) | 3.12463e8 | 1.21131 | ||||||||
\(75\) | 1.40265e8 | 0.511886 | ||||||||
\(76\) | −5.39994e6 | −0.0185664 | ||||||||
\(77\) | 3.59351e8 | 1.16496 | ||||||||
\(78\) | −2.15844e8 | −0.660259 | ||||||||
\(79\) | 2.81809e7 | 0.0814016 | 0.0407008 | − | 0.999171i | \(-0.487041\pi\) | ||||
0.0407008 | + | 0.999171i | \(0.487041\pi\) | |||||||
\(80\) | −4.95464e7 | −0.135241 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 2.12490e8 | 0.519010 | ||||||||
\(83\) | 6.97783e8 | 1.61387 | 0.806936 | − | 0.590639i | \(-0.201124\pi\) | ||||
0.806936 | + | 0.590639i | \(0.201124\pi\) | |||||||
\(84\) | −9.45302e7 | −0.207164 | ||||||||
\(85\) | 2.25073e8 | 0.467670 | ||||||||
\(86\) | 2.72868e8 | 0.537911 | ||||||||
\(87\) | −2.15554e7 | −0.0403386 | ||||||||
\(88\) | −8.31557e8 | −1.47815 | ||||||||
\(89\) | 1.72640e8 | 0.291666 | 0.145833 | − | 0.989309i | \(-0.453414\pi\) | ||||
0.145833 | + | 0.989309i | \(0.453414\pi\) | |||||||
\(90\) | −5.31577e7 | −0.0854033 | ||||||||
\(91\) | 8.37852e8 | 1.28080 | ||||||||
\(92\) | −5.40561e7 | −0.0786682 | ||||||||
\(93\) | 5.86711e8 | 0.813300 | ||||||||
\(94\) | 6.66947e7 | 0.0881082 | ||||||||
\(95\) | 1.17872e7 | 0.0148476 | ||||||||
\(96\) | 3.72680e8 | 0.447832 | ||||||||
\(97\) | −5.76011e8 | −0.660630 | −0.330315 | − | 0.943871i | \(-0.607155\pi\) | ||||
−0.330315 | + | 0.943871i | \(0.607155\pi\) | |||||||
\(98\) | 1.90245e8 | 0.208351 | ||||||||
\(99\) | −4.35540e8 | −0.455691 | ||||||||
\(100\) | 3.73327e8 | 0.373327 | ||||||||
\(101\) | −4.89774e8 | −0.468327 | −0.234164 | − | 0.972197i | \(-0.575235\pi\) | ||||
−0.234164 | + | 0.972197i | \(0.575235\pi\) | |||||||
\(102\) | 6.66973e8 | 0.610109 | ||||||||
\(103\) | 5.42890e8 | 0.475274 | 0.237637 | − | 0.971354i | \(-0.423627\pi\) | ||||
0.237637 | + | 0.971354i | \(0.423627\pi\) | |||||||
\(104\) | −1.93884e9 | −1.62514 | ||||||||
\(105\) | 2.06345e8 | 0.165669 | ||||||||
\(106\) | 5.10900e8 | 0.393060 | ||||||||
\(107\) | 8.99458e8 | 0.663367 | 0.331684 | − | 0.943391i | \(-0.392383\pi\) | ||||
0.331684 | + | 0.943391i | \(0.392383\pi\) | |||||||
\(108\) | 1.14573e8 | 0.0810352 | ||||||||
\(109\) | 8.82309e8 | 0.598689 | 0.299345 | − | 0.954145i | \(-0.403232\pi\) | ||||
0.299345 | + | 0.954145i | \(0.403232\pi\) | |||||||
\(110\) | 5.37842e8 | 0.350257 | ||||||||
\(111\) | 1.47006e9 | 0.919141 | ||||||||
\(112\) | 5.69933e8 | 0.342249 | ||||||||
\(113\) | −1.92955e9 | −1.11328 | −0.556640 | − | 0.830754i | \(-0.687910\pi\) | ||||
−0.556640 | + | 0.830754i | \(0.687910\pi\) | |||||||
\(114\) | 3.49298e7 | 0.0193698 | ||||||||
\(115\) | 1.17996e8 | 0.0629111 | ||||||||
\(116\) | −5.73717e7 | −0.0294196 | ||||||||
\(117\) | −1.01549e9 | −0.501004 | ||||||||
\(118\) | −2.08620e8 | −0.0990573 | ||||||||
\(119\) | −2.58902e9 | −1.18352 | ||||||||
\(120\) | −4.77493e8 | −0.210209 | ||||||||
\(121\) | 2.04879e9 | 0.868886 | ||||||||
\(122\) | 1.77944e9 | 0.727215 | ||||||||
\(123\) | 9.99714e8 | 0.393824 | ||||||||
\(124\) | 1.56158e9 | 0.593153 | ||||||||
\(125\) | −1.73405e9 | −0.635281 | ||||||||
\(126\) | 6.11474e8 | 0.216128 | ||||||||
\(127\) | −2.78609e7 | −0.00950340 | −0.00475170 | − | 0.999989i | \(-0.501513\pi\) | ||||
−0.00475170 | + | 0.999989i | \(0.501513\pi\) | |||||||
\(128\) | 6.38474e7 | 0.0210232 | ||||||||
\(129\) | 1.28378e9 | 0.408166 | ||||||||
\(130\) | 1.25402e9 | 0.385087 | ||||||||
\(131\) | −6.39360e8 | −0.189681 | −0.0948407 | − | 0.995492i | \(-0.530234\pi\) | ||||
−0.0948407 | + | 0.995492i | \(0.530234\pi\) | |||||||
\(132\) | −1.15923e9 | −0.332343 | ||||||||
\(133\) | −1.35589e8 | −0.0375743 | ||||||||
\(134\) | 4.07446e9 | 1.09169 | ||||||||
\(135\) | −2.50094e8 | −0.0648039 | ||||||||
\(136\) | 5.99114e9 | 1.50170 | ||||||||
\(137\) | 3.13151e9 | 0.759472 | 0.379736 | − | 0.925095i | \(-0.376015\pi\) | ||||
0.379736 | + | 0.925095i | \(0.376015\pi\) | |||||||
\(138\) | 3.49665e8 | 0.0820721 | ||||||||
\(139\) | 5.67256e9 | 1.28888 | 0.644440 | − | 0.764655i | \(-0.277090\pi\) | ||||
0.644440 | + | 0.764655i | \(0.277090\pi\) | |||||||
\(140\) | 5.49204e8 | 0.120825 | ||||||||
\(141\) | 3.13783e8 | 0.0668564 | ||||||||
\(142\) | 1.48339e9 | 0.306167 | ||||||||
\(143\) | 1.02746e10 | 2.05473 | ||||||||
\(144\) | −6.90771e8 | −0.133876 | ||||||||
\(145\) | 1.25233e8 | 0.0235269 | ||||||||
\(146\) | 5.15526e9 | 0.938995 | ||||||||
\(147\) | 8.95055e8 | 0.158096 | ||||||||
\(148\) | 3.91270e9 | 0.670345 | ||||||||
\(149\) | 6.34326e9 | 1.05432 | 0.527162 | − | 0.849765i | \(-0.323256\pi\) | ||||
0.527162 | + | 0.849765i | \(0.323256\pi\) | |||||||
\(150\) | −2.41488e9 | −0.389480 | ||||||||
\(151\) | −3.66715e9 | −0.574028 | −0.287014 | − | 0.957926i | \(-0.592663\pi\) | ||||
−0.287014 | + | 0.957926i | \(0.592663\pi\) | |||||||
\(152\) | 3.13759e8 | 0.0476761 | ||||||||
\(153\) | 3.13795e9 | 0.462950 | ||||||||
\(154\) | −6.18680e9 | −0.886386 | ||||||||
\(155\) | −3.40869e9 | −0.474345 | ||||||||
\(156\) | −2.70283e9 | −0.365391 | ||||||||
\(157\) | −4.89732e9 | −0.643295 | −0.321647 | − | 0.946859i | \(-0.604237\pi\) | ||||
−0.321647 | + | 0.946859i | \(0.604237\pi\) | |||||||
\(158\) | −4.85180e8 | −0.0619364 | ||||||||
\(159\) | 2.40366e9 | 0.298254 | ||||||||
\(160\) | −2.16520e9 | −0.261191 | ||||||||
\(161\) | −1.35731e9 | −0.159207 | ||||||||
\(162\) | −7.41118e8 | −0.0845415 | ||||||||
\(163\) | 1.47341e10 | 1.63486 | 0.817430 | − | 0.576028i | \(-0.195398\pi\) | ||||
0.817430 | + | 0.576028i | \(0.195398\pi\) | |||||||
\(164\) | 2.66082e9 | 0.287223 | ||||||||
\(165\) | 2.53042e9 | 0.265775 | ||||||||
\(166\) | −1.20135e10 | −1.22795 | ||||||||
\(167\) | −5.19742e9 | −0.517087 | −0.258543 | − | 0.966000i | \(-0.583243\pi\) | ||||
−0.258543 | + | 0.966000i | \(0.583243\pi\) | |||||||
\(168\) | 5.49261e9 | 0.531969 | ||||||||
\(169\) | 1.33515e10 | 1.25904 | ||||||||
\(170\) | −3.87500e9 | −0.355837 | ||||||||
\(171\) | 1.64336e8 | 0.0146978 | ||||||||
\(172\) | 3.41689e9 | 0.297682 | ||||||||
\(173\) | −7.79075e9 | −0.661259 | −0.330630 | − | 0.943761i | \(-0.607261\pi\) | ||||
−0.330630 | + | 0.943761i | \(0.607261\pi\) | |||||||
\(174\) | 3.71112e8 | 0.0306925 | ||||||||
\(175\) | 9.37397e9 | 0.755531 | ||||||||
\(176\) | 6.98912e9 | 0.549054 | ||||||||
\(177\) | −9.81506e8 | −0.0751646 | ||||||||
\(178\) | −2.97227e9 | −0.221921 | ||||||||
\(179\) | 2.93195e9 | 0.213461 | 0.106730 | − | 0.994288i | \(-0.465962\pi\) | ||||
0.106730 | + | 0.994288i | \(0.465962\pi\) | |||||||
\(180\) | −6.65647e8 | −0.0472626 | ||||||||
\(181\) | 1.63487e10 | 1.13222 | 0.566110 | − | 0.824330i | \(-0.308448\pi\) | ||||
0.566110 | + | 0.824330i | \(0.308448\pi\) | |||||||
\(182\) | −1.44250e10 | −0.974527 | ||||||||
\(183\) | 8.37181e9 | 0.551810 | ||||||||
\(184\) | 3.14089e9 | 0.202010 | ||||||||
\(185\) | −8.54081e9 | −0.536076 | ||||||||
\(186\) | −1.01012e10 | −0.618819 | ||||||||
\(187\) | −3.17493e10 | −1.89866 | ||||||||
\(188\) | 8.35159e8 | 0.0487595 | ||||||||
\(189\) | 2.87684e9 | 0.163997 | ||||||||
\(190\) | −2.02936e8 | −0.0112971 | ||||||||
\(191\) | 4.61139e9 | 0.250716 | 0.125358 | − | 0.992112i | \(-0.459992\pi\) | ||||
0.125358 | + | 0.992112i | \(0.459992\pi\) | |||||||
\(192\) | −1.07826e10 | −0.572623 | ||||||||
\(193\) | −1.79012e10 | −0.928700 | −0.464350 | − | 0.885652i | \(-0.653712\pi\) | ||||
−0.464350 | + | 0.885652i | \(0.653712\pi\) | |||||||
\(194\) | 9.91696e9 | 0.502656 | ||||||||
\(195\) | 5.89985e9 | 0.292203 | ||||||||
\(196\) | 2.38227e9 | 0.115302 | ||||||||
\(197\) | −1.06899e10 | −0.505678 | −0.252839 | − | 0.967508i | \(-0.581364\pi\) | ||||
−0.252839 | + | 0.967508i | \(0.581364\pi\) | |||||||
\(198\) | 7.49853e9 | 0.346723 | ||||||||
\(199\) | 3.32999e10 | 1.50523 | 0.752617 | − | 0.658458i | \(-0.228791\pi\) | ||||
0.752617 | + | 0.658458i | \(0.228791\pi\) | |||||||
\(200\) | −2.16919e10 | −0.958654 | ||||||||
\(201\) | 1.91694e10 | 0.828372 | ||||||||
\(202\) | 8.43225e9 | 0.356338 | ||||||||
\(203\) | −1.44056e9 | −0.0595388 | ||||||||
\(204\) | 8.35192e9 | 0.337637 | ||||||||
\(205\) | −5.80817e9 | −0.229692 | ||||||||
\(206\) | −9.34672e9 | −0.361624 | ||||||||
\(207\) | 1.64509e9 | 0.0622763 | ||||||||
\(208\) | 1.62956e10 | 0.603651 | ||||||||
\(209\) | −1.66273e9 | −0.0602787 | ||||||||
\(210\) | −3.55256e9 | −0.126053 | ||||||||
\(211\) | −8.48875e9 | −0.294831 | −0.147415 | − | 0.989075i | \(-0.547095\pi\) | ||||
−0.147415 | + | 0.989075i | \(0.547095\pi\) | |||||||
\(212\) | 6.39755e9 | 0.217522 | ||||||||
\(213\) | 6.97901e9 | 0.232320 | ||||||||
\(214\) | −1.54856e10 | −0.504739 | ||||||||
\(215\) | −7.45855e9 | −0.238057 | ||||||||
\(216\) | −6.65715e9 | −0.208088 | ||||||||
\(217\) | 3.92102e10 | 1.20041 | ||||||||
\(218\) | −1.51904e10 | −0.455527 | ||||||||
\(219\) | 2.42543e10 | 0.712508 | ||||||||
\(220\) | 6.73492e9 | 0.193834 | ||||||||
\(221\) | −7.40259e10 | −2.08746 | ||||||||
\(222\) | −2.53095e10 | −0.699350 | ||||||||
\(223\) | 7.04918e10 | 1.90883 | 0.954414 | − | 0.298485i | \(-0.0964814\pi\) | ||||
0.954414 | + | 0.298485i | \(0.0964814\pi\) | |||||||
\(224\) | 2.49064e10 | 0.660989 | ||||||||
\(225\) | −1.13614e10 | −0.295537 | ||||||||
\(226\) | 3.32204e10 | 0.847065 | ||||||||
\(227\) | −5.81539e10 | −1.45366 | −0.726829 | − | 0.686818i | \(-0.759007\pi\) | ||||
−0.726829 | + | 0.686818i | \(0.759007\pi\) | |||||||
\(228\) | 4.37395e8 | 0.0107193 | ||||||||
\(229\) | −6.21009e10 | −1.49224 | −0.746119 | − | 0.665813i | \(-0.768085\pi\) | ||||
−0.746119 | + | 0.665813i | \(0.768085\pi\) | |||||||
\(230\) | −2.03149e9 | −0.0478674 | ||||||||
\(231\) | −2.91074e10 | −0.672589 | ||||||||
\(232\) | 3.33354e9 | 0.0755456 | ||||||||
\(233\) | −3.61242e9 | −0.0802966 | −0.0401483 | − | 0.999194i | \(-0.512783\pi\) | ||||
−0.0401483 | + | 0.999194i | \(0.512783\pi\) | |||||||
\(234\) | 1.74834e10 | 0.381201 | ||||||||
\(235\) | −1.82302e9 | −0.0389930 | ||||||||
\(236\) | −2.61236e9 | −0.0548188 | ||||||||
\(237\) | −2.28265e9 | −0.0469973 | ||||||||
\(238\) | 4.45742e10 | 0.900507 | ||||||||
\(239\) | −2.98723e10 | −0.592214 | −0.296107 | − | 0.955155i | \(-0.595688\pi\) | ||||
−0.296107 | + | 0.955155i | \(0.595688\pi\) | |||||||
\(240\) | 4.01326e9 | 0.0780812 | ||||||||
\(241\) | −8.16207e10 | −1.55856 | −0.779280 | − | 0.626675i | \(-0.784415\pi\) | ||||
−0.779280 | + | 0.626675i | \(0.784415\pi\) | |||||||
\(242\) | −3.52732e10 | −0.661112 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 2.22823e10 | 0.402444 | ||||||||
\(245\) | −5.20012e9 | −0.0922074 | ||||||||
\(246\) | −1.72117e10 | −0.299651 | ||||||||
\(247\) | −3.87678e9 | −0.0662727 | ||||||||
\(248\) | −9.07345e10 | −1.52314 | ||||||||
\(249\) | −5.65204e10 | −0.931769 | ||||||||
\(250\) | 2.98544e10 | 0.483369 | ||||||||
\(251\) | −1.06367e11 | −1.69152 | −0.845758 | − | 0.533567i | \(-0.820851\pi\) | ||||
−0.845758 | + | 0.533567i | \(0.820851\pi\) | |||||||
\(252\) | 7.65695e9 | 0.119606 | ||||||||
\(253\) | −1.66448e10 | −0.255408 | ||||||||
\(254\) | 4.79671e8 | 0.00723089 | ||||||||
\(255\) | −1.82309e10 | −0.270009 | ||||||||
\(256\) | −6.92561e10 | −1.00781 | ||||||||
\(257\) | 4.23776e10 | 0.605951 | 0.302975 | − | 0.952998i | \(-0.402020\pi\) | ||||
0.302975 | + | 0.952998i | \(0.402020\pi\) | |||||||
\(258\) | −2.21023e10 | −0.310563 | ||||||||
\(259\) | 9.82450e10 | 1.35663 | ||||||||
\(260\) | 1.57030e10 | 0.213109 | ||||||||
\(261\) | 1.74599e9 | 0.0232895 | ||||||||
\(262\) | 1.10076e10 | 0.144324 | ||||||||
\(263\) | 6.13808e10 | 0.791101 | 0.395550 | − | 0.918444i | \(-0.370554\pi\) | ||||
0.395550 | + | 0.918444i | \(0.370554\pi\) | |||||||
\(264\) | 6.73561e10 | 0.853413 | ||||||||
\(265\) | −1.39649e10 | −0.173952 | ||||||||
\(266\) | 2.33438e9 | 0.0285893 | ||||||||
\(267\) | −1.39838e10 | −0.168394 | ||||||||
\(268\) | 5.10209e10 | 0.604145 | ||||||||
\(269\) | 5.72181e10 | 0.666266 | 0.333133 | − | 0.942880i | \(-0.391894\pi\) | ||||
0.333133 | + | 0.942880i | \(0.391894\pi\) | |||||||
\(270\) | 4.30577e9 | 0.0493076 | ||||||||
\(271\) | −1.60471e10 | −0.180732 | −0.0903661 | − | 0.995909i | \(-0.528804\pi\) | ||||
−0.0903661 | + | 0.995909i | \(0.528804\pi\) | |||||||
\(272\) | −5.03547e10 | −0.557801 | ||||||||
\(273\) | −6.78661e10 | −0.739470 | ||||||||
\(274\) | −5.39140e10 | −0.577862 | ||||||||
\(275\) | 1.14953e11 | 1.21206 | ||||||||
\(276\) | 4.37854e9 | 0.0454191 | ||||||||
\(277\) | −5.03692e10 | −0.514051 | −0.257026 | − | 0.966405i | \(-0.582742\pi\) | ||||
−0.257026 | + | 0.966405i | \(0.582742\pi\) | |||||||
\(278\) | −9.76623e10 | −0.980675 | ||||||||
\(279\) | −4.75236e10 | −0.469559 | ||||||||
\(280\) | −3.19111e10 | −0.310263 | ||||||||
\(281\) | 6.43753e10 | 0.615943 | 0.307972 | − | 0.951396i | \(-0.400350\pi\) | ||||
0.307972 | + | 0.951396i | \(0.400350\pi\) | |||||||
\(282\) | −5.40227e9 | −0.0508693 | ||||||||
\(283\) | −5.77949e10 | −0.535612 | −0.267806 | − | 0.963473i | \(-0.586299\pi\) | ||||
−0.267806 | + | 0.963473i | \(0.586299\pi\) | |||||||
\(284\) | 1.85752e10 | 0.169435 | ||||||||
\(285\) | −9.54766e8 | −0.00857225 | ||||||||
\(286\) | −1.76894e11 | −1.56339 | ||||||||
\(287\) | 6.68114e10 | 0.581276 | ||||||||
\(288\) | −3.01870e10 | −0.258556 | ||||||||
\(289\) | 1.10157e11 | 0.928908 | ||||||||
\(290\) | −2.15609e9 | −0.0179010 | ||||||||
\(291\) | 4.66569e10 | 0.381415 | ||||||||
\(292\) | 6.45548e10 | 0.519644 | ||||||||
\(293\) | 5.15641e10 | 0.408736 | 0.204368 | − | 0.978894i | \(-0.434486\pi\) | ||||
0.204368 | + | 0.978894i | \(0.434486\pi\) | |||||||
\(294\) | −1.54098e10 | −0.120291 | ||||||||
\(295\) | 5.70238e9 | 0.0438387 | ||||||||
\(296\) | −2.27344e11 | −1.72136 | ||||||||
\(297\) | 3.52788e10 | 0.263093 | ||||||||
\(298\) | −1.09209e11 | −0.802208 | ||||||||
\(299\) | −3.88085e10 | −0.280806 | ||||||||
\(300\) | −3.02395e10 | −0.215540 | ||||||||
\(301\) | 8.57958e10 | 0.602444 | ||||||||
\(302\) | 6.31359e10 | 0.436763 | ||||||||
\(303\) | 3.96717e10 | 0.270389 | ||||||||
\(304\) | −2.63710e9 | −0.0177091 | ||||||||
\(305\) | −4.86388e10 | −0.321835 | ||||||||
\(306\) | −5.40248e10 | −0.352247 | ||||||||
\(307\) | 1.84862e11 | 1.18775 | 0.593874 | − | 0.804558i | \(-0.297598\pi\) | ||||
0.593874 | + | 0.804558i | \(0.297598\pi\) | |||||||
\(308\) | −7.74719e10 | −0.490530 | ||||||||
\(309\) | −4.39741e10 | −0.274400 | ||||||||
\(310\) | 5.86861e10 | 0.360917 | ||||||||
\(311\) | 9.51423e10 | 0.576703 | 0.288351 | − | 0.957525i | \(-0.406893\pi\) | ||||
0.288351 | + | 0.957525i | \(0.406893\pi\) | |||||||
\(312\) | 1.57046e11 | 0.938275 | ||||||||
\(313\) | −1.37755e11 | −0.811255 | −0.405628 | − | 0.914038i | \(-0.632947\pi\) | ||||
−0.405628 | + | 0.914038i | \(0.632947\pi\) | |||||||
\(314\) | 8.43153e10 | 0.489466 | ||||||||
\(315\) | −1.67139e10 | −0.0956491 | ||||||||
\(316\) | −6.07548e9 | −0.0342759 | ||||||||
\(317\) | 5.17222e10 | 0.287681 | 0.143840 | − | 0.989601i | \(-0.454055\pi\) | ||||
0.143840 | + | 0.989601i | \(0.454055\pi\) | |||||||
\(318\) | −4.13829e10 | −0.226934 | ||||||||
\(319\) | −1.76657e10 | −0.0955152 | ||||||||
\(320\) | 6.26452e10 | 0.333974 | ||||||||
\(321\) | −7.28561e10 | −0.382995 | ||||||||
\(322\) | 2.33683e10 | 0.121137 | ||||||||
\(323\) | 1.19795e10 | 0.0612390 | ||||||||
\(324\) | −9.28038e9 | −0.0467857 | ||||||||
\(325\) | 2.68022e11 | 1.33259 | ||||||||
\(326\) | −2.53672e11 | −1.24392 | ||||||||
\(327\) | −7.14670e10 | −0.345653 | ||||||||
\(328\) | −1.54605e11 | −0.737550 | ||||||||
\(329\) | 2.09703e10 | 0.0986785 | ||||||||
\(330\) | −4.35652e10 | −0.202221 | ||||||||
\(331\) | 1.57884e11 | 0.722959 | 0.361479 | − | 0.932380i | \(-0.382272\pi\) | ||||
0.361479 | + | 0.932380i | \(0.382272\pi\) | |||||||
\(332\) | −1.50434e11 | −0.679555 | ||||||||
\(333\) | −1.19075e11 | −0.530666 | ||||||||
\(334\) | 8.94819e10 | 0.393438 | ||||||||
\(335\) | −1.11371e11 | −0.483136 | ||||||||
\(336\) | −4.61646e10 | −0.197598 | ||||||||
\(337\) | 1.74853e11 | 0.738480 | 0.369240 | − | 0.929334i | \(-0.379618\pi\) | ||||
0.369240 | + | 0.929334i | \(0.379618\pi\) | |||||||
\(338\) | −2.29868e11 | −0.957974 | ||||||||
\(339\) | 1.56294e11 | 0.642752 | ||||||||
\(340\) | −4.85232e10 | −0.196922 | ||||||||
\(341\) | 4.80837e11 | 1.92576 | ||||||||
\(342\) | −2.82931e9 | −0.0111831 | ||||||||
\(343\) | 2.78262e11 | 1.08550 | ||||||||
\(344\) | −1.98536e11 | −0.764410 | ||||||||
\(345\) | −9.55768e9 | −0.0363217 | ||||||||
\(346\) | 1.34130e11 | 0.503135 | ||||||||
\(347\) | −1.25277e11 | −0.463863 | −0.231931 | − | 0.972732i | \(-0.574505\pi\) | ||||
−0.231931 | + | 0.972732i | \(0.574505\pi\) | |||||||
\(348\) | 4.64710e9 | 0.0169854 | ||||||||
\(349\) | −2.06778e11 | −0.746086 | −0.373043 | − | 0.927814i | \(-0.621686\pi\) | ||||
−0.373043 | + | 0.927814i | \(0.621686\pi\) | |||||||
\(350\) | −1.61388e11 | −0.574864 | ||||||||
\(351\) | 8.22550e10 | 0.289255 | ||||||||
\(352\) | 3.05428e11 | 1.06039 | ||||||||
\(353\) | −2.24191e11 | −0.768480 | −0.384240 | − | 0.923233i | \(-0.625536\pi\) | ||||
−0.384240 | + | 0.923233i | \(0.625536\pi\) | |||||||
\(354\) | 1.68982e10 | 0.0571908 | ||||||||
\(355\) | −4.05469e10 | −0.135497 | ||||||||
\(356\) | −3.72192e10 | −0.122812 | ||||||||
\(357\) | 2.09711e11 | 0.683304 | ||||||||
\(358\) | −5.04782e10 | −0.162417 | ||||||||
\(359\) | 1.17207e10 | 0.0372416 | 0.0186208 | − | 0.999827i | \(-0.494072\pi\) | ||||
0.0186208 | + | 0.999827i | \(0.494072\pi\) | |||||||
\(360\) | 3.86769e10 | 0.121364 | ||||||||
\(361\) | −3.22060e11 | −0.998056 | ||||||||
\(362\) | −2.81470e11 | −0.861477 | ||||||||
\(363\) | −1.65952e11 | −0.501651 | ||||||||
\(364\) | −1.80631e11 | −0.539308 | ||||||||
\(365\) | −1.40913e11 | −0.415560 | ||||||||
\(366\) | −1.44134e11 | −0.419858 | ||||||||
\(367\) | 2.53136e11 | 0.728376 | 0.364188 | − | 0.931325i | \(-0.381346\pi\) | ||||
0.364188 | + | 0.931325i | \(0.381346\pi\) | |||||||
\(368\) | −2.63987e10 | −0.0750356 | ||||||||
\(369\) | −8.09768e10 | −0.227375 | ||||||||
\(370\) | 1.47044e11 | 0.407886 | ||||||||
\(371\) | 1.60638e11 | 0.440216 | ||||||||
\(372\) | −1.26488e11 | −0.342457 | ||||||||
\(373\) | −4.56903e11 | −1.22218 | −0.611089 | − | 0.791562i | \(-0.709268\pi\) | ||||
−0.611089 | + | 0.791562i | \(0.709268\pi\) | |||||||
\(374\) | 5.46615e11 | 1.44464 | ||||||||
\(375\) | 1.40458e11 | 0.366780 | ||||||||
\(376\) | −4.85263e10 | −0.125208 | ||||||||
\(377\) | −4.11888e10 | −0.105013 | ||||||||
\(378\) | −4.95294e10 | −0.124781 | ||||||||
\(379\) | 5.82504e11 | 1.45018 | 0.725090 | − | 0.688654i | \(-0.241798\pi\) | ||||
0.725090 | + | 0.688654i | \(0.241798\pi\) | |||||||
\(380\) | −2.54119e9 | −0.00625189 | ||||||||
\(381\) | 2.25674e9 | 0.00548679 | ||||||||
\(382\) | −7.93926e10 | −0.190763 | ||||||||
\(383\) | 6.37704e11 | 1.51434 | 0.757172 | − | 0.653215i | \(-0.226580\pi\) | ||||
0.757172 | + | 0.653215i | \(0.226580\pi\) | |||||||
\(384\) | −5.17164e9 | −0.0121377 | ||||||||
\(385\) | 1.69109e11 | 0.392278 | ||||||||
\(386\) | 3.08199e11 | 0.706623 | ||||||||
\(387\) | −1.03986e11 | −0.235655 | ||||||||
\(388\) | 1.24181e11 | 0.278172 | ||||||||
\(389\) | −2.82852e11 | −0.626306 | −0.313153 | − | 0.949703i | \(-0.601385\pi\) | ||||
−0.313153 | + | 0.949703i | \(0.601385\pi\) | |||||||
\(390\) | −1.01575e11 | −0.222330 | ||||||||
\(391\) | 1.19921e11 | 0.259477 | ||||||||
\(392\) | −1.38420e11 | −0.296081 | ||||||||
\(393\) | 5.17882e10 | 0.109513 | ||||||||
\(394\) | 1.84043e11 | 0.384757 | ||||||||
\(395\) | 1.32618e10 | 0.0274105 | ||||||||
\(396\) | 9.38975e10 | 0.191878 | ||||||||
\(397\) | −7.08379e8 | −0.00143123 | −0.000715613 | − | 1.00000i | \(-0.500228\pi\) | ||||
−0.000715613 | 1.00000i | \(0.500228\pi\) | ||||||||
\(398\) | −5.73312e11 | −1.14529 | ||||||||
\(399\) | 1.09827e10 | 0.0216935 | ||||||||
\(400\) | 1.82317e11 | 0.356088 | ||||||||
\(401\) | 8.61044e11 | 1.66294 | 0.831468 | − | 0.555573i | \(-0.187501\pi\) | ||||
0.831468 | + | 0.555573i | \(0.187501\pi\) | |||||||
\(402\) | −3.30031e11 | −0.630286 | ||||||||
\(403\) | 1.12111e12 | 2.11726 | ||||||||
\(404\) | 1.05590e11 | 0.197199 | ||||||||
\(405\) | 2.02576e10 | 0.0374146 | ||||||||
\(406\) | 2.48016e10 | 0.0453015 | ||||||||
\(407\) | 1.20478e12 | 2.17638 | ||||||||
\(408\) | −4.85282e11 | −0.867009 | ||||||||
\(409\) | −2.41126e11 | −0.426078 | −0.213039 | − | 0.977044i | \(-0.568336\pi\) | ||||
−0.213039 | + | 0.977044i | \(0.568336\pi\) | |||||||
\(410\) | 9.99969e10 | 0.174767 | ||||||||
\(411\) | −2.53653e11 | −0.438481 | ||||||||
\(412\) | −1.17041e11 | −0.200124 | ||||||||
\(413\) | −6.55946e10 | −0.110941 | ||||||||
\(414\) | −2.83228e10 | −0.0473844 | ||||||||
\(415\) | 3.28374e11 | 0.543441 | ||||||||
\(416\) | 7.12128e11 | 1.16584 | ||||||||
\(417\) | −4.59477e11 | −0.744135 | ||||||||
\(418\) | 2.86266e10 | 0.0458644 | ||||||||
\(419\) | −1.03648e12 | −1.64284 | −0.821421 | − | 0.570322i | \(-0.806818\pi\) | ||||
−0.821421 | + | 0.570322i | \(0.806818\pi\) | |||||||
\(420\) | −4.44855e10 | −0.0697585 | ||||||||
\(421\) | 1.50236e11 | 0.233080 | 0.116540 | − | 0.993186i | \(-0.462820\pi\) | ||||
0.116540 | + | 0.993186i | \(0.462820\pi\) | |||||||
\(422\) | 1.46147e11 | 0.224329 | ||||||||
\(423\) | −2.54164e10 | −0.0385996 | ||||||||
\(424\) | −3.71725e11 | −0.558567 | ||||||||
\(425\) | −8.28208e11 | −1.23137 | ||||||||
\(426\) | −1.20155e11 | −0.176766 | ||||||||
\(427\) | 5.59493e11 | 0.814459 | ||||||||
\(428\) | −1.93913e11 | −0.279325 | ||||||||
\(429\) | −8.32245e11 | −1.18630 | ||||||||
\(430\) | 1.28411e11 | 0.181131 | ||||||||
\(431\) | −1.15250e12 | −1.60877 | −0.804384 | − | 0.594110i | \(-0.797504\pi\) | ||||
−0.804384 | + | 0.594110i | \(0.797504\pi\) | |||||||
\(432\) | 5.59524e10 | 0.0772933 | ||||||||
\(433\) | −6.40176e11 | −0.875193 | −0.437596 | − | 0.899171i | \(-0.644170\pi\) | ||||
−0.437596 | + | 0.899171i | \(0.644170\pi\) | |||||||
\(434\) | −6.75067e11 | −0.913362 | ||||||||
\(435\) | −1.01439e10 | −0.0135832 | ||||||||
\(436\) | −1.90216e11 | −0.252091 | ||||||||
\(437\) | 6.28033e9 | 0.00823789 | ||||||||
\(438\) | −4.17576e11 | −0.542129 | ||||||||
\(439\) | −6.22464e11 | −0.799878 | −0.399939 | − | 0.916542i | \(-0.630969\pi\) | ||||
−0.399939 | + | 0.916542i | \(0.630969\pi\) | |||||||
\(440\) | −3.91327e11 | −0.497741 | ||||||||
\(441\) | −7.24995e10 | −0.0912770 | ||||||||
\(442\) | 1.27447e12 | 1.58829 | ||||||||
\(443\) | 2.06954e11 | 0.255304 | 0.127652 | − | 0.991819i | \(-0.459256\pi\) | ||||
0.127652 | + | 0.991819i | \(0.459256\pi\) | |||||||
\(444\) | −3.16928e11 | −0.387024 | ||||||||
\(445\) | 8.12436e10 | 0.0982131 | ||||||||
\(446\) | −1.21363e12 | −1.45238 | ||||||||
\(447\) | −5.13804e11 | −0.608715 | ||||||||
\(448\) | −7.20609e11 | −0.845179 | ||||||||
\(449\) | 1.49258e12 | 1.73312 | 0.866562 | − | 0.499070i | \(-0.166325\pi\) | ||||
0.866562 | + | 0.499070i | \(0.166325\pi\) | |||||||
\(450\) | 1.95606e11 | 0.224867 | ||||||||
\(451\) | 8.19311e11 | 0.932512 | ||||||||
\(452\) | 4.15990e11 | 0.468770 | ||||||||
\(453\) | 2.97039e11 | 0.331415 | ||||||||
\(454\) | 1.00121e12 | 1.10605 | ||||||||
\(455\) | 3.94290e11 | 0.431285 | ||||||||
\(456\) | −2.54145e10 | −0.0275258 | ||||||||
\(457\) | 1.39765e11 | 0.149891 | 0.0749457 | − | 0.997188i | \(-0.476122\pi\) | ||||
0.0749457 | + | 0.997188i | \(0.476122\pi\) | |||||||
\(458\) | 1.06917e12 | 1.13540 | ||||||||
\(459\) | −2.54174e11 | −0.267285 | ||||||||
\(460\) | −2.54386e10 | −0.0264900 | ||||||||
\(461\) | 1.62785e12 | 1.67865 | 0.839326 | − | 0.543628i | \(-0.182950\pi\) | ||||
0.839326 | + | 0.543628i | \(0.182950\pi\) | |||||||
\(462\) | 5.01131e11 | 0.511755 | ||||||||
\(463\) | −8.20961e9 | −0.00830249 | −0.00415124 | − | 0.999991i | \(-0.501321\pi\) | ||||
−0.00415124 | + | 0.999991i | \(0.501321\pi\) | |||||||
\(464\) | −2.80179e10 | −0.0280611 | ||||||||
\(465\) | 2.76104e11 | 0.273863 | ||||||||
\(466\) | 6.21937e10 | 0.0610955 | ||||||||
\(467\) | −2.13574e11 | −0.207789 | −0.103895 | − | 0.994588i | \(-0.533130\pi\) | ||||
−0.103895 | + | 0.994588i | \(0.533130\pi\) | |||||||
\(468\) | 2.18929e11 | 0.210958 | ||||||||
\(469\) | 1.28110e12 | 1.22266 | ||||||||
\(470\) | 3.13863e10 | 0.0296688 | ||||||||
\(471\) | 3.96683e11 | 0.371407 | ||||||||
\(472\) | 1.51789e11 | 0.140768 | ||||||||
\(473\) | 1.05212e12 | 0.966472 | ||||||||
\(474\) | 3.92996e10 | 0.0357590 | ||||||||
\(475\) | −4.33738e10 | −0.0390936 | ||||||||
\(476\) | 5.58164e11 | 0.498345 | ||||||||
\(477\) | −1.94697e11 | −0.172197 | ||||||||
\(478\) | 5.14300e11 | 0.450600 | ||||||||
\(479\) | −1.26522e11 | −0.109814 | −0.0549070 | − | 0.998491i | \(-0.517486\pi\) | ||||
−0.0549070 | + | 0.998491i | \(0.517486\pi\) | |||||||
\(480\) | 1.75382e11 | 0.150799 | ||||||||
\(481\) | 2.80904e12 | 2.39279 | ||||||||
\(482\) | 1.40523e12 | 1.18587 | ||||||||
\(483\) | 1.09942e11 | 0.0919183 | ||||||||
\(484\) | −4.41695e11 | −0.365863 | ||||||||
\(485\) | −2.71069e11 | −0.222455 | ||||||||
\(486\) | 6.00306e10 | 0.0488101 | ||||||||
\(487\) | 2.31543e12 | 1.86531 | 0.932654 | − | 0.360771i | \(-0.117486\pi\) | ||||
0.932654 | + | 0.360771i | \(0.117486\pi\) | |||||||
\(488\) | −1.29470e12 | −1.03342 | ||||||||
\(489\) | −1.19347e12 | −0.943887 | ||||||||
\(490\) | 8.95284e10 | 0.0701582 | ||||||||
\(491\) | −1.98934e12 | −1.54469 | −0.772345 | − | 0.635203i | \(-0.780916\pi\) | ||||
−0.772345 | + | 0.635203i | \(0.780916\pi\) | |||||||
\(492\) | −2.15527e11 | −0.165828 | ||||||||
\(493\) | 1.27276e11 | 0.0970369 | ||||||||
\(494\) | 6.67450e10 | 0.0504251 | ||||||||
\(495\) | −2.04964e11 | −0.153445 | ||||||||
\(496\) | 7.62611e11 | 0.565764 | ||||||||
\(497\) | 4.66411e11 | 0.342898 | ||||||||
\(498\) | 9.73090e11 | 0.708959 | ||||||||
\(499\) | −1.05952e12 | −0.764991 | −0.382496 | − | 0.923957i | \(-0.624935\pi\) | ||||
−0.382496 | + | 0.923957i | \(0.624935\pi\) | |||||||
\(500\) | 3.73841e11 | 0.267499 | ||||||||
\(501\) | 4.20991e11 | 0.298540 | ||||||||
\(502\) | 1.83128e12 | 1.28703 | ||||||||
\(503\) | −2.42824e11 | −0.169136 | −0.0845679 | − | 0.996418i | \(-0.526951\pi\) | ||||
−0.0845679 | + | 0.996418i | \(0.526951\pi\) | |||||||
\(504\) | −4.44901e11 | −0.307133 | ||||||||
\(505\) | −2.30486e11 | −0.157700 | ||||||||
\(506\) | 2.86566e11 | 0.194333 | ||||||||
\(507\) | −1.08147e12 | −0.726910 | ||||||||
\(508\) | 6.00650e9 | 0.00400161 | ||||||||
\(509\) | −1.40296e12 | −0.926439 | −0.463219 | − | 0.886244i | \(-0.653306\pi\) | ||||
−0.463219 | + | 0.886244i | \(0.653306\pi\) | |||||||
\(510\) | 3.13875e11 | 0.205443 | ||||||||
\(511\) | 1.62093e12 | 1.05165 | ||||||||
\(512\) | 1.15967e12 | 0.745792 | ||||||||
\(513\) | −1.33112e10 | −0.00848575 | ||||||||
\(514\) | −7.29599e11 | −0.461052 | ||||||||
\(515\) | 2.55482e11 | 0.160040 | ||||||||
\(516\) | −2.76768e11 | −0.171867 | ||||||||
\(517\) | 2.57159e11 | 0.158305 | ||||||||
\(518\) | −1.69145e12 | −1.03222 | ||||||||
\(519\) | 6.31051e11 | 0.381778 | ||||||||
\(520\) | −9.12408e11 | −0.547235 | ||||||||
\(521\) | 2.56574e12 | 1.52561 | 0.762804 | − | 0.646629i | \(-0.223822\pi\) | ||||
0.762804 | + | 0.646629i | \(0.223822\pi\) | |||||||
\(522\) | −3.00600e10 | −0.0177203 | ||||||||
\(523\) | −1.55421e12 | −0.908348 | −0.454174 | − | 0.890913i | \(-0.650066\pi\) | ||||
−0.454174 | + | 0.890913i | \(0.650066\pi\) | |||||||
\(524\) | 1.37839e11 | 0.0798694 | ||||||||
\(525\) | −7.59292e11 | −0.436206 | ||||||||
\(526\) | −1.05677e12 | −0.601928 | ||||||||
\(527\) | −3.46430e12 | −1.95644 | ||||||||
\(528\) | −5.66118e11 | −0.316997 | ||||||||
\(529\) | −1.73828e12 | −0.965095 | ||||||||
\(530\) | 2.40427e11 | 0.132356 | ||||||||
\(531\) | 7.95020e10 | 0.0433963 | ||||||||
\(532\) | 2.92314e10 | 0.0158215 | ||||||||
\(533\) | 1.91028e12 | 1.02524 | ||||||||
\(534\) | 2.40754e11 | 0.128126 | ||||||||
\(535\) | 4.23282e11 | 0.223376 | ||||||||
\(536\) | −2.96453e12 | −1.55137 | ||||||||
\(537\) | −2.37488e11 | −0.123242 | ||||||||
\(538\) | −9.85101e11 | −0.506945 | ||||||||
\(539\) | 7.33539e11 | 0.374347 | ||||||||
\(540\) | 5.39174e10 | 0.0272871 | ||||||||
\(541\) | 1.19331e12 | 0.598917 | 0.299459 | − | 0.954109i | \(-0.403194\pi\) | ||||
0.299459 | + | 0.954109i | \(0.403194\pi\) | |||||||
\(542\) | 2.76277e11 | 0.137514 | ||||||||
\(543\) | −1.32425e12 | −0.653688 | ||||||||
\(544\) | −2.20053e12 | −1.07729 | ||||||||
\(545\) | 4.15211e11 | 0.201597 | ||||||||
\(546\) | 1.16842e12 | 0.562643 | ||||||||
\(547\) | −2.51030e12 | −1.19890 | −0.599450 | − | 0.800412i | \(-0.704614\pi\) | ||||
−0.599450 | + | 0.800412i | \(0.704614\pi\) | |||||||
\(548\) | −6.75118e11 | −0.319792 | ||||||||
\(549\) | −6.78117e11 | −0.318588 | ||||||||
\(550\) | −1.97911e12 | −0.922227 | ||||||||
\(551\) | 6.66554e9 | 0.00308073 | ||||||||
\(552\) | −2.54412e11 | −0.116630 | ||||||||
\(553\) | −1.52551e11 | −0.0693669 | ||||||||
\(554\) | 8.67188e11 | 0.391128 | ||||||||
\(555\) | 6.91805e11 | 0.309503 | ||||||||
\(556\) | −1.22294e12 | −0.542710 | ||||||||
\(557\) | −1.61310e11 | −0.0710088 | −0.0355044 | − | 0.999370i | \(-0.511304\pi\) | ||||
−0.0355044 | + | 0.999370i | \(0.511304\pi\) | |||||||
\(558\) | 8.18195e11 | 0.357275 | ||||||||
\(559\) | 2.45309e12 | 1.06258 | ||||||||
\(560\) | 2.68208e11 | 0.115246 | ||||||||
\(561\) | 2.57169e12 | 1.09619 | ||||||||
\(562\) | −1.10832e12 | −0.468655 | ||||||||
\(563\) | −1.63046e12 | −0.683948 | −0.341974 | − | 0.939710i | \(-0.611095\pi\) | ||||
−0.341974 | + | 0.939710i | \(0.611095\pi\) | |||||||
\(564\) | −6.76479e10 | −0.0281513 | ||||||||
\(565\) | −9.08041e11 | −0.374876 | ||||||||
\(566\) | 9.95032e11 | 0.407533 | ||||||||
\(567\) | −2.33024e11 | −0.0946840 | ||||||||
\(568\) | −1.07930e12 | −0.435086 | ||||||||
\(569\) | 1.42003e12 | 0.567928 | 0.283964 | − | 0.958835i | \(-0.408350\pi\) | ||||
0.283964 | + | 0.958835i | \(0.408350\pi\) | |||||||
\(570\) | 1.64378e10 | 0.00652240 | ||||||||
\(571\) | 5.28540e11 | 0.208073 | 0.104036 | − | 0.994573i | \(-0.466824\pi\) | ||||
0.104036 | + | 0.994573i | \(0.466824\pi\) | |||||||
\(572\) | −2.21509e12 | −0.865186 | ||||||||
\(573\) | −3.73523e11 | −0.144751 | ||||||||
\(574\) | −1.15027e12 | −0.442277 | ||||||||
\(575\) | −4.34193e11 | −0.165645 | ||||||||
\(576\) | 8.73393e11 | 0.330604 | ||||||||
\(577\) | −1.43606e12 | −0.539364 | −0.269682 | − | 0.962949i | \(-0.586919\pi\) | ||||
−0.269682 | + | 0.962949i | \(0.586919\pi\) | |||||||
\(578\) | −1.89653e12 | −0.706782 | ||||||||
\(579\) | 1.45000e12 | 0.536185 | ||||||||
\(580\) | −2.69989e10 | −0.00990649 | ||||||||
\(581\) | −3.77729e12 | −1.37527 | ||||||||
\(582\) | −8.03274e11 | −0.290208 | ||||||||
\(583\) | 1.96991e12 | 0.706217 | ||||||||
\(584\) | −3.75091e12 | −1.33438 | ||||||||
\(585\) | −4.77888e11 | −0.168704 | ||||||||
\(586\) | −8.87759e11 | −0.310997 | ||||||||
\(587\) | 1.31190e12 | 0.456069 | 0.228034 | − | 0.973653i | \(-0.426770\pi\) | ||||
0.228034 | + | 0.973653i | \(0.426770\pi\) | |||||||
\(588\) | −1.92964e11 | −0.0665698 | ||||||||
\(589\) | −1.81427e11 | −0.0621132 | ||||||||
\(590\) | −9.81757e10 | −0.0333557 | ||||||||
\(591\) | 8.65879e11 | 0.291953 | ||||||||
\(592\) | 1.91080e12 | 0.639391 | ||||||||
\(593\) | −5.85336e12 | −1.94383 | −0.971917 | − | 0.235324i | \(-0.924385\pi\) | ||||
−0.971917 | + | 0.235324i | \(0.924385\pi\) | |||||||
\(594\) | −6.07381e11 | −0.200181 | ||||||||
\(595\) | −1.21838e12 | −0.398527 | ||||||||
\(596\) | −1.36753e12 | −0.443946 | ||||||||
\(597\) | −2.69729e12 | −0.869048 | ||||||||
\(598\) | 6.68150e11 | 0.213658 | ||||||||
\(599\) | −5.40235e12 | −1.71460 | −0.857298 | − | 0.514820i | \(-0.827859\pi\) | ||||
−0.857298 | + | 0.514820i | \(0.827859\pi\) | |||||||
\(600\) | 1.75704e12 | 0.553479 | ||||||||
\(601\) | −4.40596e12 | −1.37754 | −0.688772 | − | 0.724978i | \(-0.741850\pi\) | ||||
−0.688772 | + | 0.724978i | \(0.741850\pi\) | |||||||
\(602\) | −1.47711e12 | −0.458384 | ||||||||
\(603\) | −1.55272e12 | −0.478261 | ||||||||
\(604\) | 7.90596e11 | 0.241707 | ||||||||
\(605\) | 9.64151e11 | 0.292581 | ||||||||
\(606\) | −6.83012e11 | −0.205732 | ||||||||
\(607\) | 3.88829e12 | 1.16254 | 0.581272 | − | 0.813709i | \(-0.302555\pi\) | ||||
0.581272 | + | 0.813709i | \(0.302555\pi\) | |||||||
\(608\) | −1.15243e11 | −0.0342017 | ||||||||
\(609\) | 1.16686e11 | 0.0343747 | ||||||||
\(610\) | 8.37395e11 | 0.244876 | ||||||||
\(611\) | 5.99586e11 | 0.174047 | ||||||||
\(612\) | −6.76506e11 | −0.194935 | ||||||||
\(613\) | −2.22713e12 | −0.637051 | −0.318526 | − | 0.947914i | \(-0.603188\pi\) | ||||
−0.318526 | + | 0.947914i | \(0.603188\pi\) | |||||||
\(614\) | −3.18269e12 | −0.903726 | ||||||||
\(615\) | 4.70461e11 | 0.132613 | ||||||||
\(616\) | 4.50144e12 | 1.25962 | ||||||||
\(617\) | −6.19968e10 | −0.0172221 | −0.00861105 | − | 0.999963i | \(-0.502741\pi\) | ||||
−0.00861105 | + | 0.999963i | \(0.502741\pi\) | |||||||
\(618\) | 7.57084e11 | 0.208783 | ||||||||
\(619\) | 4.07655e12 | 1.11605 | 0.558027 | − | 0.829823i | \(-0.311558\pi\) | ||||
0.558027 | + | 0.829823i | \(0.311558\pi\) | |||||||
\(620\) | 7.34874e11 | 0.199733 | ||||||||
\(621\) | −1.33252e11 | −0.0359552 | ||||||||
\(622\) | −1.63803e12 | −0.438798 | ||||||||
\(623\) | −9.34547e11 | −0.248545 | ||||||||
\(624\) | −1.31995e12 | −0.348518 | ||||||||
\(625\) | 2.56612e12 | 0.672693 | ||||||||
\(626\) | 2.37167e12 | 0.617263 | ||||||||
\(627\) | 1.34681e11 | 0.0348019 | ||||||||
\(628\) | 1.05581e12 | 0.270873 | ||||||||
\(629\) | −8.68014e12 | −2.21105 | ||||||||
\(630\) | 2.87757e11 | 0.0727769 | ||||||||
\(631\) | 1.13483e12 | 0.284969 | 0.142485 | − | 0.989797i | \(-0.454491\pi\) | ||||
0.142485 | + | 0.989797i | \(0.454491\pi\) | |||||||
\(632\) | 3.53011e11 | 0.0880160 | ||||||||
\(633\) | 6.87589e11 | 0.170221 | ||||||||
\(634\) | −8.90481e11 | −0.218889 | ||||||||
\(635\) | −1.31112e10 | −0.00320009 | ||||||||
\(636\) | −5.18201e11 | −0.125586 | ||||||||
\(637\) | 1.71030e12 | 0.411571 | ||||||||
\(638\) | 3.04143e11 | 0.0726750 | ||||||||
\(639\) | −5.65300e11 | −0.134130 | ||||||||
\(640\) | 3.00463e10 | 0.00707916 | ||||||||
\(641\) | 1.03670e12 | 0.242545 | 0.121272 | − | 0.992619i | \(-0.461303\pi\) | ||||
0.121272 | + | 0.992619i | \(0.461303\pi\) | |||||||
\(642\) | 1.25433e12 | 0.291411 | ||||||||
\(643\) | −3.29334e12 | −0.759778 | −0.379889 | − | 0.925032i | \(-0.624038\pi\) | ||||
−0.379889 | + | 0.925032i | \(0.624038\pi\) | |||||||
\(644\) | 2.92620e11 | 0.0670375 | ||||||||
\(645\) | 6.04142e11 | 0.137442 | ||||||||
\(646\) | −2.06247e11 | −0.0465951 | ||||||||
\(647\) | 7.47536e12 | 1.67711 | 0.838557 | − | 0.544814i | \(-0.183400\pi\) | ||||
0.838557 | + | 0.544814i | \(0.183400\pi\) | |||||||
\(648\) | 5.39229e11 | 0.120140 | ||||||||
\(649\) | −8.04390e11 | −0.177978 | ||||||||
\(650\) | −4.61444e12 | −1.01393 | ||||||||
\(651\) | −3.17603e12 | −0.693058 | ||||||||
\(652\) | −3.17651e12 | −0.688392 | ||||||||
\(653\) | 4.84471e12 | 1.04270 | 0.521349 | − | 0.853343i | \(-0.325429\pi\) | ||||
0.521349 | + | 0.853343i | \(0.325429\pi\) | |||||||
\(654\) | 1.23042e12 | 0.262999 | ||||||||
\(655\) | −3.00880e11 | −0.0638716 | ||||||||
\(656\) | 1.29943e12 | 0.273960 | ||||||||
\(657\) | −1.96460e12 | −0.411367 | ||||||||
\(658\) | −3.61037e11 | −0.0750819 | ||||||||
\(659\) | −5.52324e12 | −1.14080 | −0.570400 | − | 0.821367i | \(-0.693212\pi\) | ||||
−0.570400 | + | 0.821367i | \(0.693212\pi\) | |||||||
\(660\) | −5.45528e11 | −0.111910 | ||||||||
\(661\) | −5.88116e12 | −1.19827 | −0.599137 | − | 0.800646i | \(-0.704490\pi\) | ||||
−0.599137 | + | 0.800646i | \(0.704490\pi\) | |||||||
\(662\) | −2.71824e12 | −0.550080 | ||||||||
\(663\) | 5.99609e12 | 1.20520 | ||||||||
\(664\) | 8.74085e12 | 1.74501 | ||||||||
\(665\) | −6.38075e10 | −0.0126524 | ||||||||
\(666\) | 2.05007e12 | 0.403770 | ||||||||
\(667\) | 6.67254e10 | 0.0130534 | ||||||||
\(668\) | 1.12050e12 | 0.217730 | ||||||||
\(669\) | −5.70984e12 | −1.10206 | ||||||||
\(670\) | 1.91743e12 | 0.367605 | ||||||||
\(671\) | 6.86109e12 | 1.30660 | ||||||||
\(672\) | −2.01742e12 | −0.381622 | ||||||||
\(673\) | 3.55154e11 | 0.0667343 | 0.0333672 | − | 0.999443i | \(-0.489377\pi\) | ||||
0.0333672 | + | 0.999443i | \(0.489377\pi\) | |||||||
\(674\) | −3.01038e12 | −0.561890 | ||||||||
\(675\) | 9.20277e11 | 0.170629 | ||||||||
\(676\) | −2.87844e12 | −0.530147 | ||||||||
\(677\) | 6.56111e12 | 1.20041 | 0.600203 | − | 0.799848i | \(-0.295086\pi\) | ||||
0.600203 | + | 0.799848i | \(0.295086\pi\) | |||||||
\(678\) | −2.69085e12 | −0.489053 | ||||||||
\(679\) | 3.11811e12 | 0.562959 | ||||||||
\(680\) | 2.81941e12 | 0.505670 | ||||||||
\(681\) | 4.71046e12 | 0.839270 | ||||||||
\(682\) | −8.27837e12 | −1.46526 | ||||||||
\(683\) | 5.91763e12 | 1.04053 | 0.520265 | − | 0.854005i | \(-0.325833\pi\) | ||||
0.520265 | + | 0.854005i | \(0.325833\pi\) | |||||||
\(684\) | −3.54290e10 | −0.00618880 | ||||||||
\(685\) | 1.47368e12 | 0.255738 | ||||||||
\(686\) | −4.79073e12 | −0.825930 | ||||||||
\(687\) | 5.03017e12 | 0.861544 | ||||||||
\(688\) | 1.66867e12 | 0.283937 | ||||||||
\(689\) | 4.59299e12 | 0.776442 | ||||||||
\(690\) | 1.64551e11 | 0.0276362 | ||||||||
\(691\) | −7.81874e12 | −1.30462 | −0.652312 | − | 0.757951i | \(-0.726201\pi\) | ||||
−0.652312 | + | 0.757951i | \(0.726201\pi\) | |||||||
\(692\) | 1.67960e12 | 0.278437 | ||||||||
\(693\) | 2.35770e12 | 0.388319 | ||||||||
\(694\) | 2.15685e12 | 0.352941 | ||||||||
\(695\) | 2.66949e12 | 0.434006 | ||||||||
\(696\) | −2.70016e11 | −0.0436163 | ||||||||
\(697\) | −5.90291e12 | −0.947369 | ||||||||
\(698\) | 3.56001e12 | 0.567678 | ||||||||
\(699\) | 2.92606e11 | 0.0463592 | ||||||||
\(700\) | −2.02092e12 | −0.318133 | ||||||||
\(701\) | −4.19167e12 | −0.655626 | −0.327813 | − | 0.944743i | \(-0.606312\pi\) | ||||
−0.327813 | + | 0.944743i | \(0.606312\pi\) | |||||||
\(702\) | −1.41615e12 | −0.220086 | ||||||||
\(703\) | −4.54584e11 | −0.0701964 | ||||||||
\(704\) | −8.83686e12 | −1.35588 | ||||||||
\(705\) | 1.47665e11 | 0.0225126 | ||||||||
\(706\) | 3.85981e12 | 0.584716 | ||||||||
\(707\) | 2.65128e12 | 0.399088 | ||||||||
\(708\) | 2.11601e11 | 0.0316496 | ||||||||
\(709\) | 4.05279e12 | 0.602345 | 0.301173 | − | 0.953570i | \(-0.402622\pi\) | ||||
0.301173 | + | 0.953570i | \(0.402622\pi\) | |||||||
\(710\) | 6.98079e11 | 0.103096 | ||||||||
\(711\) | 1.84895e11 | 0.0271339 | ||||||||
\(712\) | 2.16259e12 | 0.315366 | ||||||||
\(713\) | −1.81618e12 | −0.263181 | ||||||||
\(714\) | −3.61051e12 | −0.519908 | ||||||||
\(715\) | 4.83520e12 | 0.691890 | ||||||||
\(716\) | −6.32094e11 | −0.0898821 | ||||||||
\(717\) | 2.41966e12 | 0.341915 | ||||||||
\(718\) | −2.01791e11 | −0.0283362 | ||||||||
\(719\) | 9.83134e12 | 1.37193 | 0.685966 | − | 0.727633i | \(-0.259380\pi\) | ||||
0.685966 | + | 0.727633i | \(0.259380\pi\) | |||||||
\(720\) | −3.25074e11 | −0.0450802 | ||||||||
\(721\) | −2.93881e12 | −0.405008 | ||||||||
\(722\) | 5.54479e12 | 0.759394 | ||||||||
\(723\) | 6.61128e12 | 0.899836 | ||||||||
\(724\) | −3.52460e12 | −0.476745 | ||||||||
\(725\) | −4.60825e11 | −0.0619462 | ||||||||
\(726\) | 2.85713e12 | 0.381693 | ||||||||
\(727\) | −1.00675e13 | −1.33664 | −0.668320 | − | 0.743874i | \(-0.732986\pi\) | ||||
−0.668320 | + | 0.743874i | \(0.732986\pi\) | |||||||
\(728\) | 1.04954e13 | 1.38487 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 2.42605e12 | 0.316189 | ||||||||
\(731\) | −7.58022e12 | −0.981869 | ||||||||
\(732\) | −1.80487e12 | −0.232351 | ||||||||
\(733\) | −4.66502e12 | −0.596878 | −0.298439 | − | 0.954429i | \(-0.596466\pi\) | ||||
−0.298439 | + | 0.954429i | \(0.596466\pi\) | |||||||
\(734\) | −4.35814e12 | −0.554202 | ||||||||
\(735\) | 4.21210e11 | 0.0532360 | ||||||||
\(736\) | −1.15364e12 | −0.144917 | ||||||||
\(737\) | 1.57102e13 | 1.96145 | ||||||||
\(738\) | 1.39415e12 | 0.173003 | ||||||||
\(739\) | −1.77689e12 | −0.219159 | −0.109580 | − | 0.993978i | \(-0.534950\pi\) | ||||
−0.109580 | + | 0.993978i | \(0.534950\pi\) | |||||||
\(740\) | 1.84130e12 | 0.225726 | ||||||||
\(741\) | 3.14019e11 | 0.0382626 | ||||||||
\(742\) | −2.76564e12 | −0.334949 | ||||||||
\(743\) | 8.10862e12 | 0.976106 | 0.488053 | − | 0.872814i | \(-0.337707\pi\) | ||||
0.488053 | + | 0.872814i | \(0.337707\pi\) | |||||||
\(744\) | 7.34949e12 | 0.879385 | ||||||||
\(745\) | 2.98511e12 | 0.355024 | ||||||||
\(746\) | 7.86633e12 | 0.929923 | ||||||||
\(747\) | 4.57815e12 | 0.537957 | ||||||||
\(748\) | 6.84479e12 | 0.799471 | ||||||||
\(749\) | −4.86901e12 | −0.565292 | ||||||||
\(750\) | −2.41821e12 | −0.279073 | ||||||||
\(751\) | 1.19190e13 | 1.36729 | 0.683646 | − | 0.729814i | \(-0.260393\pi\) | ||||
0.683646 | + | 0.729814i | \(0.260393\pi\) | |||||||
\(752\) | 4.07857e11 | 0.0465080 | ||||||||
\(753\) | 8.61575e12 | 0.976597 | ||||||||
\(754\) | 7.09132e11 | 0.0799017 | ||||||||
\(755\) | −1.72575e12 | −0.193293 | ||||||||
\(756\) | −6.20213e11 | −0.0690546 | ||||||||
\(757\) | −4.03996e12 | −0.447143 | −0.223571 | − | 0.974688i | \(-0.571772\pi\) | ||||
−0.223571 | + | 0.974688i | \(0.571772\pi\) | |||||||
\(758\) | −1.00287e13 | −1.10340 | ||||||||
\(759\) | 1.34823e12 | 0.147460 | ||||||||
\(760\) | 1.47654e11 | 0.0160540 | ||||||||
\(761\) | 9.85667e12 | 1.06537 | 0.532684 | − | 0.846315i | \(-0.321184\pi\) | ||||
0.532684 | + | 0.846315i | \(0.321184\pi\) | |||||||
\(762\) | −3.88533e10 | −0.00417475 | ||||||||
\(763\) | −4.77618e12 | −0.510176 | ||||||||
\(764\) | −9.94163e11 | −0.105569 | ||||||||
\(765\) | 1.47671e12 | 0.155890 | ||||||||
\(766\) | −1.09791e13 | −1.15223 | ||||||||
\(767\) | −1.87549e12 | −0.195675 | ||||||||
\(768\) | 5.60974e12 | 0.581859 | ||||||||
\(769\) | 1.69468e13 | 1.74751 | 0.873756 | − | 0.486365i | \(-0.161677\pi\) | ||||
0.873756 | + | 0.486365i | \(0.161677\pi\) | |||||||
\(770\) | −2.91148e12 | −0.298474 | ||||||||
\(771\) | −3.43259e12 | −0.349846 | ||||||||
\(772\) | 3.85930e12 | 0.391049 | ||||||||
\(773\) | −3.18191e12 | −0.320538 | −0.160269 | − | 0.987073i | \(-0.551236\pi\) | ||||
−0.160269 | + | 0.987073i | \(0.551236\pi\) | |||||||
\(774\) | 1.79029e12 | 0.179304 | ||||||||
\(775\) | 1.25430e13 | 1.24895 | ||||||||
\(776\) | −7.21546e12 | −0.714310 | ||||||||
\(777\) | −7.95785e12 | −0.783251 | ||||||||
\(778\) | 4.86976e12 | 0.476540 | ||||||||
\(779\) | −3.09139e11 | −0.0300771 | ||||||||
\(780\) | −1.27194e12 | −0.123038 | ||||||||
\(781\) | 5.71962e12 | 0.550095 | ||||||||
\(782\) | −2.06463e12 | −0.197430 | ||||||||
\(783\) | −1.41425e11 | −0.0134462 | ||||||||
\(784\) | 1.16340e12 | 0.109978 | ||||||||
\(785\) | −2.30466e12 | −0.216617 | ||||||||
\(786\) | −8.91617e11 | −0.0833253 | ||||||||
\(787\) | −4.03160e12 | −0.374621 | −0.187310 | − | 0.982301i | \(-0.559977\pi\) | ||||
−0.187310 | + | 0.982301i | \(0.559977\pi\) | |||||||
\(788\) | 2.30461e12 | 0.212926 | ||||||||
\(789\) | −4.97185e12 | −0.456742 | ||||||||
\(790\) | −2.28324e11 | −0.0208559 | ||||||||
\(791\) | 1.04452e13 | 0.948687 | ||||||||
\(792\) | −5.45584e12 | −0.492718 | ||||||||
\(793\) | 1.59971e13 | 1.43652 | ||||||||
\(794\) | 1.21959e10 | 0.00108898 | ||||||||
\(795\) | 1.13115e12 | 0.100431 | ||||||||
\(796\) | −7.17908e12 | −0.633811 | ||||||||
\(797\) | 2.07530e13 | 1.82187 | 0.910937 | − | 0.412545i | \(-0.135360\pi\) | ||||
0.910937 | + | 0.412545i | \(0.135360\pi\) | |||||||
\(798\) | −1.89085e11 | −0.0165060 | ||||||||
\(799\) | −1.85276e12 | −0.160827 | ||||||||
\(800\) | 7.96736e12 | 0.687716 | ||||||||
\(801\) | 1.13269e12 | 0.0972220 | ||||||||
\(802\) | −1.48242e13 | −1.26528 | ||||||||
\(803\) | 1.98775e13 | 1.68710 | ||||||||
\(804\) | −4.13269e12 | −0.348804 | ||||||||
\(805\) | −6.38745e11 | −0.0536100 | ||||||||
\(806\) | −1.93016e13 | −1.61097 | ||||||||
\(807\) | −4.63466e12 | −0.384669 | ||||||||
\(808\) | −6.13521e12 | −0.506382 | ||||||||
\(809\) | −2.12249e13 | −1.74211 | −0.871056 | − | 0.491183i | \(-0.836565\pi\) | ||||
−0.871056 | + | 0.491183i | \(0.836565\pi\) | |||||||
\(810\) | −3.48767e11 | −0.0284678 | ||||||||
\(811\) | −9.19128e12 | −0.746075 | −0.373037 | − | 0.927816i | \(-0.621684\pi\) | ||||
−0.373037 | + | 0.927816i | \(0.621684\pi\) | |||||||
\(812\) | 3.10569e11 | 0.0250701 | ||||||||
\(813\) | 1.29982e12 | 0.104346 | ||||||||
\(814\) | −2.07423e13 | −1.65595 | ||||||||
\(815\) | 6.93383e12 | 0.550508 | ||||||||
\(816\) | 4.07873e12 | 0.322047 | ||||||||
\(817\) | −3.96981e11 | −0.0311724 | ||||||||
\(818\) | 4.15137e12 | 0.324191 | ||||||||
\(819\) | 5.49715e12 | 0.426933 | ||||||||
\(820\) | 1.25217e12 | 0.0967168 | ||||||||
\(821\) | −1.86206e12 | −0.143037 | −0.0715185 | − | 0.997439i | \(-0.522785\pi\) | ||||
−0.0715185 | + | 0.997439i | \(0.522785\pi\) | |||||||
\(822\) | 4.36704e12 | 0.333629 | ||||||||
\(823\) | −3.74901e12 | −0.284850 | −0.142425 | − | 0.989806i | \(-0.545490\pi\) | ||||
−0.142425 | + | 0.989806i | \(0.545490\pi\) | |||||||
\(824\) | 6.80057e12 | 0.513893 | ||||||||
\(825\) | −9.31123e12 | −0.699785 | ||||||||
\(826\) | 1.12932e12 | 0.0844122 | ||||||||
\(827\) | −1.23458e13 | −0.917790 | −0.458895 | − | 0.888491i | \(-0.651755\pi\) | ||||
−0.458895 | + | 0.888491i | \(0.651755\pi\) | |||||||
\(828\) | −3.54662e11 | −0.0262227 | ||||||||
\(829\) | −2.42543e13 | −1.78358 | −0.891790 | − | 0.452449i | \(-0.850550\pi\) | ||||
−0.891790 | + | 0.452449i | \(0.850550\pi\) | |||||||
\(830\) | −5.65349e12 | −0.413490 | ||||||||
\(831\) | 4.07991e12 | 0.296788 | ||||||||
\(832\) | −2.06038e13 | −1.49071 | ||||||||
\(833\) | −5.28495e12 | −0.380310 | ||||||||
\(834\) | 7.91064e12 | 0.566193 | ||||||||
\(835\) | −2.44588e12 | −0.174119 | ||||||||
\(836\) | 3.58465e11 | 0.0253816 | ||||||||
\(837\) | 3.84941e12 | 0.271100 | ||||||||
\(838\) | 1.78446e13 | 1.25000 | ||||||||
\(839\) | 9.09790e12 | 0.633888 | 0.316944 | − | 0.948444i | \(-0.397343\pi\) | ||||
0.316944 | + | 0.948444i | \(0.397343\pi\) | |||||||
\(840\) | 2.58480e12 | 0.179131 | ||||||||
\(841\) | −1.44363e13 | −0.995118 | ||||||||
\(842\) | −2.58656e12 | −0.177345 | ||||||||
\(843\) | −5.21440e12 | −0.355615 | ||||||||
\(844\) | 1.83008e12 | 0.124145 | ||||||||
\(845\) | 6.28318e12 | 0.423960 | ||||||||
\(846\) | 4.37584e11 | 0.0293694 | ||||||||
\(847\) | −1.10906e13 | −0.740426 | ||||||||
\(848\) | 3.12429e12 | 0.207477 | ||||||||
\(849\) | 4.68139e12 | 0.309236 | ||||||||
\(850\) | 1.42589e13 | 0.936919 | ||||||||
\(851\) | −4.55061e12 | −0.297431 | ||||||||
\(852\) | −1.50459e12 | −0.0978231 | ||||||||
\(853\) | 2.03602e13 | 1.31678 | 0.658388 | − | 0.752679i | \(-0.271239\pi\) | ||||
0.658388 | + | 0.752679i | \(0.271239\pi\) | |||||||
\(854\) | −9.63257e12 | −0.619700 | ||||||||
\(855\) | 7.73360e10 | 0.00494919 | ||||||||
\(856\) | 1.12672e13 | 0.717269 | ||||||||
\(857\) | 3.07800e13 | 1.94920 | 0.974598 | − | 0.223961i | \(-0.0718990\pi\) | ||||
0.974598 | + | 0.223961i | \(0.0718990\pi\) | |||||||
\(858\) | 1.43284e13 | 0.902622 | ||||||||
\(859\) | −1.16944e13 | −0.732837 | −0.366419 | − | 0.930450i | \(-0.619416\pi\) | ||||
−0.366419 | + | 0.930450i | \(0.619416\pi\) | |||||||
\(860\) | 1.60798e12 | 0.100239 | ||||||||
\(861\) | −5.41172e12 | −0.335600 | ||||||||
\(862\) | 1.98421e13 | 1.22407 | ||||||||
\(863\) | 5.54534e12 | 0.340314 | 0.170157 | − | 0.985417i | \(-0.445573\pi\) | ||||
0.170157 | + | 0.985417i | \(0.445573\pi\) | |||||||
\(864\) | 2.44515e12 | 0.149277 | ||||||||
\(865\) | −3.66630e12 | −0.222667 | ||||||||
\(866\) | 1.10217e13 | 0.665911 | ||||||||
\(867\) | −8.92274e12 | −0.536305 | ||||||||
\(868\) | −8.45327e12 | −0.505459 | ||||||||
\(869\) | −1.87074e12 | −0.111282 | ||||||||
\(870\) | 1.74644e11 | 0.0103351 | ||||||||
\(871\) | 3.66294e13 | 2.15649 | ||||||||
\(872\) | 1.10523e13 | 0.647336 | ||||||||
\(873\) | −3.77921e12 | −0.220210 | ||||||||
\(874\) | −1.08126e11 | −0.00626799 | ||||||||
\(875\) | 9.38688e12 | 0.541358 | ||||||||
\(876\) | −5.22894e12 | −0.300017 | ||||||||
\(877\) | −6.71347e12 | −0.383221 | −0.191610 | − | 0.981471i | \(-0.561371\pi\) | ||||
−0.191610 | + | 0.981471i | \(0.561371\pi\) | |||||||
\(878\) | 1.07167e13 | 0.608606 | ||||||||
\(879\) | −4.17669e12 | −0.235984 | ||||||||
\(880\) | 3.28905e12 | 0.184884 | ||||||||
\(881\) | −2.96798e13 | −1.65985 | −0.829926 | − | 0.557873i | \(-0.811617\pi\) | ||||
−0.829926 | + | 0.557873i | \(0.811617\pi\) | |||||||
\(882\) | 1.24819e12 | 0.0694502 | ||||||||
\(883\) | −2.19380e13 | −1.21444 | −0.607218 | − | 0.794535i | \(-0.707714\pi\) | ||||
−0.607218 | + | 0.794535i | \(0.707714\pi\) | |||||||
\(884\) | 1.59591e13 | 0.878969 | ||||||||
\(885\) | −4.61893e11 | −0.0253103 | ||||||||
\(886\) | −3.56305e12 | −0.194254 | ||||||||
\(887\) | 1.77950e13 | 0.965253 | 0.482627 | − | 0.875826i | \(-0.339683\pi\) | ||||
0.482627 | + | 0.875826i | \(0.339683\pi\) | |||||||
\(888\) | 1.84149e13 | 0.993827 | ||||||||
\(889\) | 1.50819e11 | 0.00809837 | ||||||||
\(890\) | −1.39874e12 | −0.0747278 | ||||||||
\(891\) | −2.85758e12 | −0.151897 | ||||||||
\(892\) | −1.51972e13 | −0.803753 | ||||||||
\(893\) | −9.70303e10 | −0.00510594 | ||||||||
\(894\) | 8.84597e12 | 0.463155 | ||||||||
\(895\) | 1.37976e12 | 0.0718789 | ||||||||
\(896\) | −3.45623e11 | −0.0179150 | ||||||||
\(897\) | 3.14349e12 | 0.162123 | ||||||||
\(898\) | −2.56972e13 | −1.31869 | ||||||||
\(899\) | −1.92757e12 | −0.0984220 | ||||||||
\(900\) | 2.44940e12 | 0.124442 | ||||||||
\(901\) | −1.41927e13 | −0.717468 | ||||||||
\(902\) | −1.41058e13 | −0.709524 | ||||||||
\(903\) | −6.94946e12 | −0.347821 | ||||||||
\(904\) | −2.41708e13 | −1.20374 | ||||||||
\(905\) | 7.69366e12 | 0.381254 | ||||||||
\(906\) | −5.11401e12 | −0.252165 | ||||||||
\(907\) | −3.94863e13 | −1.93737 | −0.968687 | − | 0.248285i | \(-0.920133\pi\) | ||||
−0.968687 | + | 0.248285i | \(0.920133\pi\) | |||||||
\(908\) | 1.25373e13 | 0.612093 | ||||||||
\(909\) | −3.21341e12 | −0.156109 | ||||||||
\(910\) | −6.78834e12 | −0.328154 | ||||||||
\(911\) | −5.40411e12 | −0.259951 | −0.129975 | − | 0.991517i | \(-0.541490\pi\) | ||||
−0.129975 | + | 0.991517i | \(0.541490\pi\) | |||||||
\(912\) | 2.13605e11 | 0.0102243 | ||||||||
\(913\) | −4.63211e13 | −2.20628 | ||||||||
\(914\) | −2.40629e12 | −0.114048 | ||||||||
\(915\) | 3.93974e12 | 0.185812 | ||||||||
\(916\) | 1.33882e13 | 0.628338 | ||||||||
\(917\) | 3.46103e12 | 0.161638 | ||||||||
\(918\) | 4.37601e12 | 0.203370 | ||||||||
\(919\) | 2.00688e13 | 0.928113 | 0.464056 | − | 0.885806i | \(-0.346393\pi\) | ||||
0.464056 | + | 0.885806i | \(0.346393\pi\) | |||||||
\(920\) | 1.47809e12 | 0.0680230 | ||||||||
\(921\) | −1.49738e13 | −0.685747 | ||||||||
\(922\) | −2.80261e13 | −1.27724 | ||||||||
\(923\) | 1.33357e13 | 0.604796 | ||||||||
\(924\) | 6.27522e12 | 0.283208 | ||||||||
\(925\) | 3.14278e13 | 1.41149 | ||||||||
\(926\) | 1.41342e11 | 0.00631714 | ||||||||
\(927\) | 3.56190e12 | 0.158425 | ||||||||
\(928\) | −1.22440e12 | −0.0541947 | ||||||||
\(929\) | −5.57427e12 | −0.245537 | −0.122769 | − | 0.992435i | \(-0.539177\pi\) | ||||
−0.122769 | + | 0.992435i | \(0.539177\pi\) | |||||||
\(930\) | −4.75357e12 | −0.208376 | ||||||||
\(931\) | −2.76776e11 | −0.0120741 | ||||||||
\(932\) | 7.78797e11 | 0.0338106 | ||||||||
\(933\) | −7.70653e12 | −0.332960 | ||||||||
\(934\) | 3.67703e12 | 0.158101 | ||||||||
\(935\) | −1.49411e13 | −0.639338 | ||||||||
\(936\) | −1.27207e13 | −0.541713 | ||||||||
\(937\) | −3.14621e13 | −1.33340 | −0.666698 | − | 0.745328i | \(-0.732293\pi\) | ||||
−0.666698 | + | 0.745328i | \(0.732293\pi\) | |||||||
\(938\) | −2.20562e13 | −0.930288 | ||||||||
\(939\) | 1.11581e13 | 0.468378 | ||||||||
\(940\) | 3.93023e11 | 0.0164188 | ||||||||
\(941\) | 3.85392e13 | 1.60232 | 0.801160 | − | 0.598450i | \(-0.204217\pi\) | ||||
0.801160 | + | 0.598450i | \(0.204217\pi\) | |||||||
\(942\) | −6.82954e12 | −0.282593 | ||||||||
\(943\) | −3.09464e12 | −0.127440 | ||||||||
\(944\) | −1.27577e12 | −0.0522875 | ||||||||
\(945\) | 1.35383e12 | 0.0552230 | ||||||||
\(946\) | −1.81139e13 | −0.735363 | ||||||||
\(947\) | −1.27822e13 | −0.516453 | −0.258227 | − | 0.966084i | \(-0.583138\pi\) | ||||
−0.258227 | + | 0.966084i | \(0.583138\pi\) | |||||||
\(948\) | 4.92114e11 | 0.0197892 | ||||||||
\(949\) | 4.63459e13 | 1.85487 | ||||||||
\(950\) | 7.46749e11 | 0.0297453 | ||||||||
\(951\) | −4.18950e12 | −0.166092 | ||||||||
\(952\) | −3.24317e13 | −1.27968 | ||||||||
\(953\) | −1.44419e13 | −0.567162 | −0.283581 | − | 0.958948i | \(-0.591522\pi\) | ||||
−0.283581 | + | 0.958948i | \(0.591522\pi\) | |||||||
\(954\) | 3.35201e12 | 0.131020 | ||||||||
\(955\) | 2.17010e12 | 0.0844239 | ||||||||
\(956\) | 6.44013e12 | 0.249364 | ||||||||
\(957\) | 1.43092e12 | 0.0551457 | ||||||||
\(958\) | 2.17829e12 | 0.0835546 | ||||||||
\(959\) | −1.69517e13 | −0.647188 | ||||||||
\(960\) | −5.07426e12 | −0.192820 | ||||||||
\(961\) | 2.60264e13 | 0.984371 | ||||||||
\(962\) | −4.83622e13 | −1.82061 | ||||||||
\(963\) | 5.90134e12 | 0.221122 | ||||||||
\(964\) | 1.75965e13 | 0.656265 | ||||||||
\(965\) | −8.42426e12 | −0.312722 | ||||||||
\(966\) | −1.89283e12 | −0.0699382 | ||||||||
\(967\) | −1.85584e13 | −0.682531 | −0.341266 | − | 0.939967i | \(-0.610856\pi\) | ||||
−0.341266 | + | 0.939967i | \(0.610856\pi\) | |||||||
\(968\) | 2.56643e13 | 0.939488 | ||||||||
\(969\) | −9.70341e11 | −0.0353563 | ||||||||
\(970\) | 4.66688e12 | 0.169260 | ||||||||
\(971\) | 4.55906e13 | 1.64584 | 0.822922 | − | 0.568154i | \(-0.192342\pi\) | ||||
0.822922 | + | 0.568154i | \(0.192342\pi\) | |||||||
\(972\) | 7.51710e11 | 0.0270117 | ||||||||
\(973\) | −3.07071e13 | −1.09833 | ||||||||
\(974\) | −3.98638e13 | −1.41926 | ||||||||
\(975\) | −2.17098e13 | −0.769370 | ||||||||
\(976\) | 1.08817e13 | 0.383861 | ||||||||
\(977\) | 3.06072e13 | 1.07473 | 0.537363 | − | 0.843351i | \(-0.319420\pi\) | ||||
0.537363 | + | 0.843351i | \(0.319420\pi\) | |||||||
\(978\) | 2.05474e13 | 0.718179 | ||||||||
\(979\) | −1.14604e13 | −0.398729 | ||||||||
\(980\) | 1.12109e12 | 0.0388259 | ||||||||
\(981\) | 5.78883e12 | 0.199563 | ||||||||
\(982\) | 3.42496e13 | 1.17531 | ||||||||
\(983\) | −1.41046e13 | −0.481804 | −0.240902 | − | 0.970549i | \(-0.577443\pi\) | ||||
−0.240902 | + | 0.970549i | \(0.577443\pi\) | |||||||
\(984\) | 1.25230e13 | 0.425825 | ||||||||
\(985\) | −5.03061e12 | −0.170278 | ||||||||
\(986\) | −2.19127e12 | −0.0738328 | ||||||||
\(987\) | −1.69859e12 | −0.0569720 | ||||||||
\(988\) | 8.35788e11 | 0.0279055 | ||||||||
\(989\) | −3.97397e12 | −0.132081 | ||||||||
\(990\) | 3.52878e12 | 0.116752 | ||||||||
\(991\) | −5.67071e13 | −1.86770 | −0.933848 | − | 0.357670i | \(-0.883571\pi\) | ||||
−0.933848 | + | 0.357670i | \(0.883571\pi\) | |||||||
\(992\) | 3.33265e13 | 1.09267 | ||||||||
\(993\) | −1.27886e13 | −0.417400 | ||||||||
\(994\) | −8.03002e12 | −0.260902 | ||||||||
\(995\) | 1.56708e13 | 0.506859 | ||||||||
\(996\) | 1.21851e13 | 0.392341 | ||||||||
\(997\) | 1.81463e13 | 0.581646 | 0.290823 | − | 0.956777i | \(-0.406071\pi\) | ||||
0.290823 | + | 0.956777i | \(0.406071\pi\) | |||||||
\(998\) | 1.82413e13 | 0.582062 | ||||||||
\(999\) | 9.64508e12 | 0.306380 |
(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 | 177.10.a.c.1.7 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.c.1.7 | ✓ | 22 | 1.1 | even | 1 | trivial |