Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,12,Mod(1,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.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: | \(11.5251477084\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1801}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 450 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-20.7191\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 14.7191 | 0.325249 | 0.162625 | − | 0.986688i | \(-0.448004\pi\) | ||||
0.162625 | + | 0.986688i | \(0.448004\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | −1831.35 | −0.894213 | ||||||||
\(5\) | −3125.00 | −0.447214 | ||||||||
\(6\) | −3576.74 | −0.187783 | ||||||||
\(7\) | 79941.2 | 1.79776 | 0.898880 | − | 0.438195i | \(-0.144382\pi\) | ||||
0.898880 | + | 0.438195i | \(0.144382\pi\) | |||||||
\(8\) | −57100.5 | −0.616091 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −45997.2 | −0.145456 | ||||||||
\(11\) | 805067. | 1.50720 | 0.753602 | − | 0.657331i | \(-0.228315\pi\) | ||||
0.753602 | + | 0.657331i | \(0.228315\pi\) | |||||||
\(12\) | 445018. | 0.516274 | ||||||||
\(13\) | −1.19767e6 | −0.894641 | −0.447321 | − | 0.894374i | \(-0.647622\pi\) | ||||
−0.447321 | + | 0.894374i | \(0.647622\pi\) | |||||||
\(14\) | 1.17666e6 | 0.584720 | ||||||||
\(15\) | 759375. | 0.258199 | ||||||||
\(16\) | 2.91013e6 | 0.693830 | ||||||||
\(17\) | 2.63319e6 | 0.449793 | 0.224896 | − | 0.974383i | \(-0.427796\pi\) | ||||
0.224896 | + | 0.974383i | \(0.427796\pi\) | |||||||
\(18\) | 869148. | 0.108416 | ||||||||
\(19\) | 1.16061e7 | 1.07533 | 0.537664 | − | 0.843159i | \(-0.319307\pi\) | ||||
0.537664 | + | 0.843159i | \(0.319307\pi\) | |||||||
\(20\) | 5.72296e6 | 0.399904 | ||||||||
\(21\) | −1.94257e7 | −1.03794 | ||||||||
\(22\) | 1.18499e7 | 0.490217 | ||||||||
\(23\) | 1.84216e7 | 0.596794 | 0.298397 | − | 0.954442i | \(-0.403548\pi\) | ||||
0.298397 | + | 0.954442i | \(0.403548\pi\) | |||||||
\(24\) | 1.38754e7 | 0.355700 | ||||||||
\(25\) | 9.76562e6 | 0.200000 | ||||||||
\(26\) | −1.76286e7 | −0.290981 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | −1.46400e8 | −1.60758 | ||||||||
\(29\) | −1.90527e8 | −1.72491 | −0.862457 | − | 0.506130i | \(-0.831076\pi\) | ||||
−0.862457 | + | 0.506130i | \(0.831076\pi\) | |||||||
\(30\) | 1.11773e7 | 0.0839790 | ||||||||
\(31\) | 1.01127e8 | 0.634419 | 0.317209 | − | 0.948356i | \(-0.397254\pi\) | ||||
0.317209 | + | 0.948356i | \(0.397254\pi\) | |||||||
\(32\) | 1.59776e8 | 0.841759 | ||||||||
\(33\) | −1.95631e8 | −0.870185 | ||||||||
\(34\) | 3.87581e7 | 0.146295 | ||||||||
\(35\) | −2.49816e8 | −0.803983 | ||||||||
\(36\) | −1.08139e8 | −0.298071 | ||||||||
\(37\) | 8.06675e7 | 0.191245 | 0.0956223 | − | 0.995418i | \(-0.469516\pi\) | ||||
0.0956223 | + | 0.995418i | \(0.469516\pi\) | |||||||
\(38\) | 1.70831e8 | 0.349749 | ||||||||
\(39\) | 2.91034e8 | 0.516522 | ||||||||
\(40\) | 1.78439e8 | 0.275524 | ||||||||
\(41\) | 2.26316e8 | 0.305073 | 0.152537 | − | 0.988298i | \(-0.451256\pi\) | ||||
0.152537 | + | 0.988298i | \(0.451256\pi\) | |||||||
\(42\) | −2.85929e8 | −0.337588 | ||||||||
\(43\) | 1.67149e9 | 1.73391 | 0.866956 | − | 0.498385i | \(-0.166073\pi\) | ||||
0.866956 | + | 0.498385i | \(0.166073\pi\) | |||||||
\(44\) | −1.47436e9 | −1.34776 | ||||||||
\(45\) | −1.84528e8 | −0.149071 | ||||||||
\(46\) | 2.71150e8 | 0.194107 | ||||||||
\(47\) | 8.58507e8 | 0.546016 | 0.273008 | − | 0.962012i | \(-0.411981\pi\) | ||||
0.273008 | + | 0.962012i | \(0.411981\pi\) | |||||||
\(48\) | −7.07162e8 | −0.400583 | ||||||||
\(49\) | 4.41327e9 | 2.23194 | ||||||||
\(50\) | 1.43741e8 | 0.0650498 | ||||||||
\(51\) | −6.39864e8 | −0.259688 | ||||||||
\(52\) | 2.19335e9 | 0.800000 | ||||||||
\(53\) | −3.52750e9 | −1.15864 | −0.579322 | − | 0.815099i | \(-0.696683\pi\) | ||||
−0.579322 | + | 0.815099i | \(0.696683\pi\) | |||||||
\(54\) | −2.11203e8 | −0.0625942 | ||||||||
\(55\) | −2.51583e9 | −0.674042 | ||||||||
\(56\) | −4.56468e9 | −1.10758 | ||||||||
\(57\) | −2.82028e9 | −0.620841 | ||||||||
\(58\) | −2.80438e9 | −0.561027 | ||||||||
\(59\) | 4.35760e9 | 0.793527 | 0.396763 | − | 0.917921i | \(-0.370133\pi\) | ||||
0.396763 | + | 0.917921i | \(0.370133\pi\) | |||||||
\(60\) | −1.39068e9 | −0.230885 | ||||||||
\(61\) | −1.65393e9 | −0.250727 | −0.125364 | − | 0.992111i | \(-0.540010\pi\) | ||||
−0.125364 | + | 0.992111i | \(0.540010\pi\) | |||||||
\(62\) | 1.48849e9 | 0.206344 | ||||||||
\(63\) | 4.72045e9 | 0.599253 | ||||||||
\(64\) | −3.60819e9 | −0.420049 | ||||||||
\(65\) | 3.74272e9 | 0.400096 | ||||||||
\(66\) | −2.87951e9 | −0.283027 | ||||||||
\(67\) | 7.58610e9 | 0.686447 | 0.343224 | − | 0.939254i | \(-0.388481\pi\) | ||||
0.343224 | + | 0.939254i | \(0.388481\pi\) | |||||||
\(68\) | −4.82228e9 | −0.402211 | ||||||||
\(69\) | −4.47645e9 | −0.344559 | ||||||||
\(70\) | −3.67707e9 | −0.261495 | ||||||||
\(71\) | −2.75809e10 | −1.81421 | −0.907104 | − | 0.420905i | \(-0.861712\pi\) | ||||
−0.907104 | + | 0.420905i | \(0.861712\pi\) | |||||||
\(72\) | −3.37173e9 | −0.205364 | ||||||||
\(73\) | 3.22368e10 | 1.82002 | 0.910011 | − | 0.414584i | \(-0.136073\pi\) | ||||
0.910011 | + | 0.414584i | \(0.136073\pi\) | |||||||
\(74\) | 1.18735e9 | 0.0622022 | ||||||||
\(75\) | −2.37305e9 | −0.115470 | ||||||||
\(76\) | −2.12548e10 | −0.961572 | ||||||||
\(77\) | 6.43580e10 | 2.70959 | ||||||||
\(78\) | 4.28376e9 | 0.167998 | ||||||||
\(79\) | −2.43149e9 | −0.0889046 | −0.0444523 | − | 0.999012i | \(-0.514154\pi\) | ||||
−0.0444523 | + | 0.999012i | \(0.514154\pi\) | |||||||
\(80\) | −9.09417e9 | −0.310290 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 3.33116e9 | 0.0992247 | ||||||||
\(83\) | 1.20729e10 | 0.336421 | 0.168210 | − | 0.985751i | \(-0.446201\pi\) | ||||
0.168210 | + | 0.985751i | \(0.446201\pi\) | |||||||
\(84\) | 3.55753e10 | 0.928137 | ||||||||
\(85\) | −8.22871e9 | −0.201154 | ||||||||
\(86\) | 2.46028e10 | 0.563953 | ||||||||
\(87\) | 4.62981e10 | 0.995880 | ||||||||
\(88\) | −4.59697e10 | −0.928575 | ||||||||
\(89\) | 4.44073e9 | 0.0842964 | 0.0421482 | − | 0.999111i | \(-0.486580\pi\) | ||||
0.0421482 | + | 0.999111i | \(0.486580\pi\) | |||||||
\(90\) | −2.71609e9 | −0.0484853 | ||||||||
\(91\) | −9.57433e10 | −1.60835 | ||||||||
\(92\) | −3.37364e10 | −0.533661 | ||||||||
\(93\) | −2.45737e10 | −0.366282 | ||||||||
\(94\) | 1.26364e10 | 0.177591 | ||||||||
\(95\) | −3.62690e10 | −0.480901 | ||||||||
\(96\) | −3.88257e10 | −0.485990 | ||||||||
\(97\) | −2.04453e10 | −0.241740 | −0.120870 | − | 0.992668i | \(-0.538568\pi\) | ||||
−0.120870 | + | 0.992668i | \(0.538568\pi\) | |||||||
\(98\) | 6.49594e10 | 0.725937 | ||||||||
\(99\) | 4.75384e10 | 0.502401 | ||||||||
\(100\) | −1.78843e10 | −0.178843 | ||||||||
\(101\) | −1.55947e11 | −1.47642 | −0.738209 | − | 0.674572i | \(-0.764328\pi\) | ||||
−0.738209 | + | 0.674572i | \(0.764328\pi\) | |||||||
\(102\) | −9.41823e9 | −0.0844633 | ||||||||
\(103\) | −5.10325e10 | −0.433752 | −0.216876 | − | 0.976199i | \(-0.569587\pi\) | ||||
−0.216876 | + | 0.976199i | \(0.569587\pi\) | |||||||
\(104\) | 6.83876e10 | 0.551181 | ||||||||
\(105\) | 6.07054e10 | 0.464180 | ||||||||
\(106\) | −5.19217e10 | −0.376848 | ||||||||
\(107\) | 1.06665e10 | 0.0735207 | 0.0367603 | − | 0.999324i | \(-0.488296\pi\) | ||||
0.0367603 | + | 0.999324i | \(0.488296\pi\) | |||||||
\(108\) | 2.62778e10 | 0.172091 | ||||||||
\(109\) | −3.12513e10 | −0.194546 | −0.0972729 | − | 0.995258i | \(-0.531012\pi\) | ||||
−0.0972729 | + | 0.995258i | \(0.531012\pi\) | |||||||
\(110\) | −3.70308e10 | −0.219232 | ||||||||
\(111\) | −1.96022e10 | −0.110415 | ||||||||
\(112\) | 2.32640e11 | 1.24734 | ||||||||
\(113\) | −3.96346e10 | −0.202369 | −0.101184 | − | 0.994868i | \(-0.532263\pi\) | ||||
−0.101184 | + | 0.994868i | \(0.532263\pi\) | |||||||
\(114\) | −4.15119e10 | −0.201928 | ||||||||
\(115\) | −5.75676e10 | −0.266895 | ||||||||
\(116\) | 3.48921e11 | 1.54244 | ||||||||
\(117\) | −7.07213e10 | −0.298214 | ||||||||
\(118\) | 6.41400e10 | 0.258094 | ||||||||
\(119\) | 2.10500e11 | 0.808620 | ||||||||
\(120\) | −4.33607e10 | −0.159074 | ||||||||
\(121\) | 3.62821e11 | 1.27166 | ||||||||
\(122\) | −2.43443e10 | −0.0815489 | ||||||||
\(123\) | −5.49948e10 | −0.176134 | ||||||||
\(124\) | −1.85198e11 | −0.567305 | ||||||||
\(125\) | −3.05176e10 | −0.0894427 | ||||||||
\(126\) | 6.94808e10 | 0.194907 | ||||||||
\(127\) | 2.63460e10 | 0.0707611 | 0.0353806 | − | 0.999374i | \(-0.488736\pi\) | ||||
0.0353806 | + | 0.999374i | \(0.488736\pi\) | |||||||
\(128\) | −3.80331e11 | −0.978379 | ||||||||
\(129\) | −4.06172e11 | −1.00107 | ||||||||
\(130\) | 5.50895e10 | 0.130131 | ||||||||
\(131\) | −2.19917e11 | −0.498044 | −0.249022 | − | 0.968498i | \(-0.580109\pi\) | ||||
−0.249022 | + | 0.968498i | \(0.580109\pi\) | |||||||
\(132\) | 3.58269e11 | 0.778131 | ||||||||
\(133\) | 9.27805e11 | 1.93318 | ||||||||
\(134\) | 1.11661e11 | 0.223266 | ||||||||
\(135\) | 4.48403e10 | 0.0860663 | ||||||||
\(136\) | −1.50356e11 | −0.277113 | ||||||||
\(137\) | −5.54041e11 | −0.980795 | −0.490398 | − | 0.871499i | \(-0.663148\pi\) | ||||
−0.490398 | + | 0.871499i | \(0.663148\pi\) | |||||||
\(138\) | −6.58894e10 | −0.112068 | ||||||||
\(139\) | −6.17540e11 | −1.00945 | −0.504723 | − | 0.863281i | \(-0.668406\pi\) | ||||
−0.504723 | + | 0.863281i | \(0.668406\pi\) | |||||||
\(140\) | 4.57501e11 | 0.718932 | ||||||||
\(141\) | −2.08617e11 | −0.315243 | ||||||||
\(142\) | −4.05966e11 | −0.590070 | ||||||||
\(143\) | −9.64205e11 | −1.34841 | ||||||||
\(144\) | 1.71840e11 | 0.231277 | ||||||||
\(145\) | 5.95397e11 | 0.771405 | ||||||||
\(146\) | 4.74497e11 | 0.591961 | ||||||||
\(147\) | −1.07243e12 | −1.28861 | ||||||||
\(148\) | −1.47730e11 | −0.171013 | ||||||||
\(149\) | −6.68742e11 | −0.745992 | −0.372996 | − | 0.927833i | \(-0.621670\pi\) | ||||
−0.372996 | + | 0.927833i | \(0.621670\pi\) | |||||||
\(150\) | −3.49291e10 | −0.0375565 | ||||||||
\(151\) | 1.38243e12 | 1.43308 | 0.716541 | − | 0.697545i | \(-0.245724\pi\) | ||||
0.716541 | + | 0.697545i | \(0.245724\pi\) | |||||||
\(152\) | −6.62713e11 | −0.662500 | ||||||||
\(153\) | 1.55487e11 | 0.149931 | ||||||||
\(154\) | 9.47292e11 | 0.881292 | ||||||||
\(155\) | −3.16020e11 | −0.283721 | ||||||||
\(156\) | −5.32985e11 | −0.461880 | ||||||||
\(157\) | −7.93661e11 | −0.664029 | −0.332014 | − | 0.943274i | \(-0.607728\pi\) | ||||
−0.332014 | + | 0.943274i | \(0.607728\pi\) | |||||||
\(158\) | −3.57894e10 | −0.0289161 | ||||||||
\(159\) | 8.57184e11 | 0.668944 | ||||||||
\(160\) | −4.99301e11 | −0.376446 | ||||||||
\(161\) | 1.47265e12 | 1.07289 | ||||||||
\(162\) | 5.13223e10 | 0.0361388 | ||||||||
\(163\) | −4.67399e11 | −0.318168 | −0.159084 | − | 0.987265i | \(-0.550854\pi\) | ||||
−0.159084 | + | 0.987265i | \(0.550854\pi\) | |||||||
\(164\) | −4.14463e11 | −0.272800 | ||||||||
\(165\) | 6.11348e11 | 0.389158 | ||||||||
\(166\) | 1.77702e11 | 0.109421 | ||||||||
\(167\) | 2.87482e12 | 1.71266 | 0.856328 | − | 0.516432i | \(-0.172740\pi\) | ||||
0.856328 | + | 0.516432i | \(0.172740\pi\) | |||||||
\(168\) | 1.10922e12 | 0.639464 | ||||||||
\(169\) | −3.57745e11 | −0.199617 | ||||||||
\(170\) | −1.21119e11 | −0.0654250 | ||||||||
\(171\) | 6.85328e11 | 0.358443 | ||||||||
\(172\) | −3.06108e12 | −1.55049 | ||||||||
\(173\) | 1.53085e12 | 0.751068 | 0.375534 | − | 0.926809i | \(-0.377459\pi\) | ||||
0.375534 | + | 0.926809i | \(0.377459\pi\) | |||||||
\(174\) | 6.81465e11 | 0.323909 | ||||||||
\(175\) | 7.80676e11 | 0.359552 | ||||||||
\(176\) | 2.34285e12 | 1.04574 | ||||||||
\(177\) | −1.05890e12 | −0.458143 | ||||||||
\(178\) | 6.53635e10 | 0.0274173 | ||||||||
\(179\) | −1.91337e12 | −0.778228 | −0.389114 | − | 0.921190i | \(-0.627219\pi\) | ||||
−0.389114 | + | 0.921190i | \(0.627219\pi\) | |||||||
\(180\) | 3.37935e11 | 0.133301 | ||||||||
\(181\) | −1.70819e12 | −0.653587 | −0.326794 | − | 0.945096i | \(-0.605968\pi\) | ||||
−0.326794 | + | 0.945096i | \(0.605968\pi\) | |||||||
\(182\) | −1.40925e12 | −0.523115 | ||||||||
\(183\) | 4.01904e11 | 0.144758 | ||||||||
\(184\) | −1.05188e12 | −0.367680 | ||||||||
\(185\) | −2.52086e11 | −0.0855272 | ||||||||
\(186\) | −3.61703e11 | −0.119133 | ||||||||
\(187\) | 2.11989e12 | 0.677930 | ||||||||
\(188\) | −1.57223e12 | −0.488255 | ||||||||
\(189\) | −1.14707e12 | −0.345979 | ||||||||
\(190\) | −5.33847e11 | −0.156413 | ||||||||
\(191\) | 3.16020e12 | 0.899562 | 0.449781 | − | 0.893139i | \(-0.351502\pi\) | ||||
0.449781 | + | 0.893139i | \(0.351502\pi\) | |||||||
\(192\) | 8.76790e11 | 0.242515 | ||||||||
\(193\) | 2.77296e12 | 0.745382 | 0.372691 | − | 0.927956i | \(-0.378435\pi\) | ||||
0.372691 | + | 0.927956i | \(0.378435\pi\) | |||||||
\(194\) | −3.00936e11 | −0.0786256 | ||||||||
\(195\) | −9.09481e11 | −0.230995 | ||||||||
\(196\) | −8.08224e12 | −1.99583 | ||||||||
\(197\) | 3.86504e12 | 0.928089 | 0.464044 | − | 0.885812i | \(-0.346398\pi\) | ||||
0.464044 | + | 0.885812i | \(0.346398\pi\) | |||||||
\(198\) | 6.99722e11 | 0.163406 | ||||||||
\(199\) | −1.01839e12 | −0.231325 | −0.115663 | − | 0.993289i | \(-0.536899\pi\) | ||||
−0.115663 | + | 0.993289i | \(0.536899\pi\) | |||||||
\(200\) | −5.57622e11 | −0.123218 | ||||||||
\(201\) | −1.84342e12 | −0.396321 | ||||||||
\(202\) | −2.29540e12 | −0.480204 | ||||||||
\(203\) | −1.52310e13 | −3.10098 | ||||||||
\(204\) | 1.17181e12 | 0.232216 | ||||||||
\(205\) | −7.07237e11 | −0.136433 | ||||||||
\(206\) | −7.51152e11 | −0.141078 | ||||||||
\(207\) | 1.08778e12 | 0.198931 | ||||||||
\(208\) | −3.48538e12 | −0.620729 | ||||||||
\(209\) | 9.34367e12 | 1.62074 | ||||||||
\(210\) | 8.93528e11 | 0.150974 | ||||||||
\(211\) | 2.05668e12 | 0.338543 | 0.169271 | − | 0.985569i | \(-0.445859\pi\) | ||||
0.169271 | + | 0.985569i | \(0.445859\pi\) | |||||||
\(212\) | 6.46009e12 | 1.03608 | ||||||||
\(213\) | 6.70216e12 | 1.04743 | ||||||||
\(214\) | 1.57001e11 | 0.0239125 | ||||||||
\(215\) | −5.22340e12 | −0.775429 | ||||||||
\(216\) | 8.19330e11 | 0.118567 | ||||||||
\(217\) | 8.08418e12 | 1.14053 | ||||||||
\(218\) | −4.59990e11 | −0.0632759 | ||||||||
\(219\) | −7.83355e12 | −1.05079 | ||||||||
\(220\) | 4.60737e12 | 0.602737 | ||||||||
\(221\) | −3.15369e12 | −0.402403 | ||||||||
\(222\) | −2.88527e11 | −0.0359124 | ||||||||
\(223\) | 9.99986e12 | 1.21428 | 0.607138 | − | 0.794597i | \(-0.292318\pi\) | ||||
0.607138 | + | 0.794597i | \(0.292318\pi\) | |||||||
\(224\) | 1.27727e13 | 1.51328 | ||||||||
\(225\) | 5.76650e11 | 0.0666667 | ||||||||
\(226\) | −5.83386e11 | −0.0658202 | ||||||||
\(227\) | −6.77123e12 | −0.745634 | −0.372817 | − | 0.927905i | \(-0.621608\pi\) | ||||
−0.372817 | + | 0.927905i | \(0.621608\pi\) | |||||||
\(228\) | 5.16491e12 | 0.555164 | ||||||||
\(229\) | 1.01933e13 | 1.06959 | 0.534796 | − | 0.844981i | \(-0.320389\pi\) | ||||
0.534796 | + | 0.844981i | \(0.320389\pi\) | |||||||
\(230\) | −8.47343e11 | −0.0868072 | ||||||||
\(231\) | −1.56390e13 | −1.56438 | ||||||||
\(232\) | 1.08792e13 | 1.06270 | ||||||||
\(233\) | 6.74446e12 | 0.643412 | 0.321706 | − | 0.946840i | \(-0.395744\pi\) | ||||
0.321706 | + | 0.946840i | \(0.395744\pi\) | |||||||
\(234\) | −1.04095e12 | −0.0969938 | ||||||||
\(235\) | −2.68283e12 | −0.244186 | ||||||||
\(236\) | −7.98029e12 | −0.709582 | ||||||||
\(237\) | 5.90853e11 | 0.0513291 | ||||||||
\(238\) | 3.09837e12 | 0.263003 | ||||||||
\(239\) | −1.76501e13 | −1.46406 | −0.732030 | − | 0.681272i | \(-0.761427\pi\) | ||||
−0.732030 | + | 0.681272i | \(0.761427\pi\) | |||||||
\(240\) | 2.20988e12 | 0.179146 | ||||||||
\(241\) | −1.37662e13 | −1.09074 | −0.545369 | − | 0.838196i | \(-0.683611\pi\) | ||||
−0.545369 | + | 0.838196i | \(0.683611\pi\) | |||||||
\(242\) | 5.34039e12 | 0.413608 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | 3.02891e12 | 0.224204 | ||||||||
\(245\) | −1.37915e13 | −0.998154 | ||||||||
\(246\) | −8.09473e11 | −0.0572874 | ||||||||
\(247\) | −1.39003e13 | −0.962033 | ||||||||
\(248\) | −5.77438e12 | −0.390860 | ||||||||
\(249\) | −2.93372e12 | −0.194233 | ||||||||
\(250\) | −4.49191e11 | −0.0290912 | ||||||||
\(251\) | 3.02252e13 | 1.91498 | 0.957490 | − | 0.288467i | \(-0.0931454\pi\) | ||||
0.957490 | + | 0.288467i | \(0.0931454\pi\) | |||||||
\(252\) | −8.64479e12 | −0.535860 | ||||||||
\(253\) | 1.48306e13 | 0.899491 | ||||||||
\(254\) | 3.87790e11 | 0.0230150 | ||||||||
\(255\) | 1.99958e12 | 0.116136 | ||||||||
\(256\) | 1.79144e12 | 0.101832 | ||||||||
\(257\) | 6.88263e12 | 0.382933 | 0.191466 | − | 0.981499i | \(-0.438676\pi\) | ||||
0.191466 | + | 0.981499i | \(0.438676\pi\) | |||||||
\(258\) | −5.97848e12 | −0.325599 | ||||||||
\(259\) | 6.44866e12 | 0.343812 | ||||||||
\(260\) | −6.85423e12 | −0.357771 | ||||||||
\(261\) | −1.12504e13 | −0.574971 | ||||||||
\(262\) | −3.23698e12 | −0.161988 | ||||||||
\(263\) | −3.29948e13 | −1.61692 | −0.808462 | − | 0.588549i | \(-0.799699\pi\) | ||||
−0.808462 | + | 0.588549i | \(0.799699\pi\) | |||||||
\(264\) | 1.11706e13 | 0.536113 | ||||||||
\(265\) | 1.10235e13 | 0.518162 | ||||||||
\(266\) | 1.36564e13 | 0.628765 | ||||||||
\(267\) | −1.07910e12 | −0.0486686 | ||||||||
\(268\) | −1.38928e13 | −0.613830 | ||||||||
\(269\) | −2.97478e13 | −1.28771 | −0.643855 | − | 0.765148i | \(-0.722666\pi\) | ||||
−0.643855 | + | 0.765148i | \(0.722666\pi\) | |||||||
\(270\) | 6.60009e11 | 0.0279930 | ||||||||
\(271\) | −4.30410e13 | −1.78876 | −0.894378 | − | 0.447312i | \(-0.852381\pi\) | ||||
−0.894378 | + | 0.447312i | \(0.852381\pi\) | |||||||
\(272\) | 7.66293e12 | 0.312080 | ||||||||
\(273\) | 2.32656e13 | 0.928582 | ||||||||
\(274\) | −8.15498e12 | −0.319003 | ||||||||
\(275\) | 7.86198e12 | 0.301441 | ||||||||
\(276\) | 8.19795e12 | 0.308110 | ||||||||
\(277\) | 1.46706e13 | 0.540518 | 0.270259 | − | 0.962788i | \(-0.412891\pi\) | ||||
0.270259 | + | 0.962788i | \(0.412891\pi\) | |||||||
\(278\) | −9.08963e12 | −0.328322 | ||||||||
\(279\) | 5.97142e12 | 0.211473 | ||||||||
\(280\) | 1.42646e13 | 0.495327 | ||||||||
\(281\) | 4.18378e13 | 1.42457 | 0.712286 | − | 0.701890i | \(-0.247660\pi\) | ||||
0.712286 | + | 0.701890i | \(0.247660\pi\) | |||||||
\(282\) | −3.07066e12 | −0.102532 | ||||||||
\(283\) | 2.34242e13 | 0.767078 | 0.383539 | − | 0.923525i | \(-0.374705\pi\) | ||||
0.383539 | + | 0.923525i | \(0.374705\pi\) | |||||||
\(284\) | 5.05102e13 | 1.62229 | ||||||||
\(285\) | 8.81337e12 | 0.277648 | ||||||||
\(286\) | −1.41922e13 | −0.438568 | ||||||||
\(287\) | 1.80920e13 | 0.548448 | ||||||||
\(288\) | 9.43463e12 | 0.280586 | ||||||||
\(289\) | −2.73382e13 | −0.797686 | ||||||||
\(290\) | 8.76370e12 | 0.250899 | ||||||||
\(291\) | 4.96820e12 | 0.139568 | ||||||||
\(292\) | −5.90369e13 | −1.62749 | ||||||||
\(293\) | −7.31258e12 | −0.197833 | −0.0989166 | − | 0.995096i | \(-0.531538\pi\) | ||||
−0.0989166 | + | 0.995096i | \(0.531538\pi\) | |||||||
\(294\) | −1.57851e13 | −0.419120 | ||||||||
\(295\) | −1.36175e13 | −0.354876 | ||||||||
\(296\) | −4.60616e12 | −0.117824 | ||||||||
\(297\) | −1.15518e13 | −0.290062 | ||||||||
\(298\) | −9.84328e12 | −0.242633 | ||||||||
\(299\) | −2.20630e13 | −0.533917 | ||||||||
\(300\) | 4.34588e12 | 0.103255 | ||||||||
\(301\) | 1.33621e14 | 3.11716 | ||||||||
\(302\) | 2.03482e13 | 0.466109 | ||||||||
\(303\) | 3.78951e13 | 0.852410 | ||||||||
\(304\) | 3.37752e13 | 0.746094 | ||||||||
\(305\) | 5.16852e12 | 0.112129 | ||||||||
\(306\) | 2.28863e12 | 0.0487649 | ||||||||
\(307\) | −5.37239e13 | −1.12436 | −0.562181 | − | 0.827014i | \(-0.690038\pi\) | ||||
−0.562181 | + | 0.827014i | \(0.690038\pi\) | |||||||
\(308\) | −1.17862e14 | −2.42295 | ||||||||
\(309\) | 1.24009e13 | 0.250427 | ||||||||
\(310\) | −4.65154e12 | −0.0922799 | ||||||||
\(311\) | 5.41406e13 | 1.05521 | 0.527607 | − | 0.849489i | \(-0.323089\pi\) | ||||
0.527607 | + | 0.849489i | \(0.323089\pi\) | |||||||
\(312\) | −1.66182e13 | −0.318224 | ||||||||
\(313\) | −4.29721e12 | −0.0808524 | −0.0404262 | − | 0.999183i | \(-0.512872\pi\) | ||||
−0.0404262 | + | 0.999183i | \(0.512872\pi\) | |||||||
\(314\) | −1.16820e13 | −0.215975 | ||||||||
\(315\) | −1.47514e13 | −0.267994 | ||||||||
\(316\) | 4.45291e12 | 0.0794996 | ||||||||
\(317\) | −2.81928e13 | −0.494666 | −0.247333 | − | 0.968931i | \(-0.579554\pi\) | ||||
−0.247333 | + | 0.968931i | \(0.579554\pi\) | |||||||
\(318\) | 1.26170e13 | 0.217573 | ||||||||
\(319\) | −1.53387e14 | −2.59980 | ||||||||
\(320\) | 1.12756e13 | 0.187851 | ||||||||
\(321\) | −2.59195e12 | −0.0424472 | ||||||||
\(322\) | 2.16760e13 | 0.348958 | ||||||||
\(323\) | 3.05610e13 | 0.483675 | ||||||||
\(324\) | −6.38552e12 | −0.0993570 | ||||||||
\(325\) | −1.16960e13 | −0.178928 | ||||||||
\(326\) | −6.87969e12 | −0.103484 | ||||||||
\(327\) | 7.59406e12 | 0.112321 | ||||||||
\(328\) | −1.29227e13 | −0.187953 | ||||||||
\(329\) | 6.86301e13 | 0.981606 | ||||||||
\(330\) | 8.99848e12 | 0.126573 | ||||||||
\(331\) | −9.95469e13 | −1.37713 | −0.688563 | − | 0.725176i | \(-0.741758\pi\) | ||||
−0.688563 | + | 0.725176i | \(0.741758\pi\) | |||||||
\(332\) | −2.21097e13 | −0.300832 | ||||||||
\(333\) | 4.76334e12 | 0.0637482 | ||||||||
\(334\) | 4.23148e13 | 0.557040 | ||||||||
\(335\) | −2.37066e13 | −0.306989 | ||||||||
\(336\) | −5.65314e13 | −0.720152 | ||||||||
\(337\) | −9.05175e13 | −1.13440 | −0.567202 | − | 0.823579i | \(-0.691974\pi\) | ||||
−0.567202 | + | 0.823579i | \(0.691974\pi\) | |||||||
\(338\) | −5.26568e12 | −0.0649251 | ||||||||
\(339\) | 9.63121e12 | 0.116838 | ||||||||
\(340\) | 1.50696e13 | 0.179874 | ||||||||
\(341\) | 8.14136e13 | 0.956198 | ||||||||
\(342\) | 1.00874e13 | 0.116583 | ||||||||
\(343\) | 1.94733e14 | 2.21473 | ||||||||
\(344\) | −9.54428e13 | −1.06825 | ||||||||
\(345\) | 1.39889e13 | 0.154092 | ||||||||
\(346\) | 2.25327e13 | 0.244284 | ||||||||
\(347\) | −6.36892e13 | −0.679601 | −0.339801 | − | 0.940498i | \(-0.610360\pi\) | ||||
−0.339801 | + | 0.940498i | \(0.610360\pi\) | |||||||
\(348\) | −8.47879e13 | −0.890529 | ||||||||
\(349\) | 7.08598e13 | 0.732588 | 0.366294 | − | 0.930499i | \(-0.380626\pi\) | ||||
0.366294 | + | 0.930499i | \(0.380626\pi\) | |||||||
\(350\) | 1.14908e13 | 0.116944 | ||||||||
\(351\) | 1.71853e13 | 0.172174 | ||||||||
\(352\) | 1.28631e14 | 1.26870 | ||||||||
\(353\) | 6.62893e13 | 0.643699 | 0.321849 | − | 0.946791i | \(-0.395696\pi\) | ||||
0.321849 | + | 0.946791i | \(0.395696\pi\) | |||||||
\(354\) | −1.55860e13 | −0.149011 | ||||||||
\(355\) | 8.61903e13 | 0.811339 | ||||||||
\(356\) | −8.13252e12 | −0.0753790 | ||||||||
\(357\) | −5.11516e13 | −0.466857 | ||||||||
\(358\) | −2.81630e13 | −0.253118 | ||||||||
\(359\) | 6.80217e13 | 0.602044 | 0.301022 | − | 0.953617i | \(-0.402672\pi\) | ||||
0.301022 | + | 0.953617i | \(0.402672\pi\) | |||||||
\(360\) | 1.05366e13 | 0.0918414 | ||||||||
\(361\) | 1.82109e13 | 0.156330 | ||||||||
\(362\) | −2.51430e13 | −0.212579 | ||||||||
\(363\) | −8.81654e13 | −0.734196 | ||||||||
\(364\) | 1.75339e14 | 1.43821 | ||||||||
\(365\) | −1.00740e14 | −0.813939 | ||||||||
\(366\) | 5.91566e12 | 0.0470823 | ||||||||
\(367\) | 2.19771e14 | 1.72309 | 0.861543 | − | 0.507685i | \(-0.169499\pi\) | ||||
0.861543 | + | 0.507685i | \(0.169499\pi\) | |||||||
\(368\) | 5.36094e13 | 0.414074 | ||||||||
\(369\) | 1.33637e13 | 0.101691 | ||||||||
\(370\) | −3.71048e12 | −0.0278177 | ||||||||
\(371\) | −2.81993e14 | −2.08296 | ||||||||
\(372\) | 4.50031e13 | 0.327534 | ||||||||
\(373\) | −1.67232e14 | −1.19928 | −0.599639 | − | 0.800271i | \(-0.704689\pi\) | ||||
−0.599639 | + | 0.800271i | \(0.704689\pi\) | |||||||
\(374\) | 3.12029e13 | 0.220496 | ||||||||
\(375\) | 7.41577e12 | 0.0516398 | ||||||||
\(376\) | −4.90212e13 | −0.336396 | ||||||||
\(377\) | 2.28189e14 | 1.54318 | ||||||||
\(378\) | −1.68838e13 | −0.112529 | ||||||||
\(379\) | −1.57778e14 | −1.03641 | −0.518205 | − | 0.855256i | \(-0.673400\pi\) | ||||
−0.518205 | + | 0.855256i | \(0.673400\pi\) | |||||||
\(380\) | 6.64212e13 | 0.430028 | ||||||||
\(381\) | −6.40209e12 | −0.0408540 | ||||||||
\(382\) | 4.65153e13 | 0.292582 | ||||||||
\(383\) | 5.49255e13 | 0.340550 | 0.170275 | − | 0.985397i | \(-0.445534\pi\) | ||||
0.170275 | + | 0.985397i | \(0.445534\pi\) | |||||||
\(384\) | 9.24205e13 | 0.564867 | ||||||||
\(385\) | −2.01119e14 | −1.21177 | ||||||||
\(386\) | 4.08155e13 | 0.242435 | ||||||||
\(387\) | 9.86997e13 | 0.577971 | ||||||||
\(388\) | 3.74424e13 | 0.216167 | ||||||||
\(389\) | −2.32940e14 | −1.32593 | −0.662965 | − | 0.748650i | \(-0.730702\pi\) | ||||
−0.662965 | + | 0.748650i | \(0.730702\pi\) | |||||||
\(390\) | −1.33867e13 | −0.0751311 | ||||||||
\(391\) | 4.85076e13 | 0.268434 | ||||||||
\(392\) | −2.52000e14 | −1.37508 | ||||||||
\(393\) | 5.34399e13 | 0.287546 | ||||||||
\(394\) | 5.68899e13 | 0.301860 | ||||||||
\(395\) | 7.59842e12 | 0.0397593 | ||||||||
\(396\) | −8.70593e13 | −0.449254 | ||||||||
\(397\) | −4.76134e13 | −0.242316 | −0.121158 | − | 0.992633i | \(-0.538661\pi\) | ||||
−0.121158 | + | 0.992633i | \(0.538661\pi\) | |||||||
\(398\) | −1.49898e13 | −0.0752383 | ||||||||
\(399\) | −2.25456e14 | −1.11612 | ||||||||
\(400\) | 2.84193e13 | 0.138766 | ||||||||
\(401\) | −2.99074e14 | −1.44040 | −0.720202 | − | 0.693764i | \(-0.755951\pi\) | ||||
−0.720202 | + | 0.693764i | \(0.755951\pi\) | |||||||
\(402\) | −2.71335e13 | −0.128903 | ||||||||
\(403\) | −1.21116e14 | −0.567577 | ||||||||
\(404\) | 2.85593e14 | 1.32023 | ||||||||
\(405\) | −1.08962e13 | −0.0496904 | ||||||||
\(406\) | −2.24186e14 | −1.00859 | ||||||||
\(407\) | 6.49428e13 | 0.288245 | ||||||||
\(408\) | 3.65366e13 | 0.159992 | ||||||||
\(409\) | −2.55879e14 | −1.10550 | −0.552748 | − | 0.833349i | \(-0.686421\pi\) | ||||
−0.552748 | + | 0.833349i | \(0.686421\pi\) | |||||||
\(410\) | −1.04099e13 | −0.0443747 | ||||||||
\(411\) | 1.34632e14 | 0.566262 | ||||||||
\(412\) | 9.34582e13 | 0.387867 | ||||||||
\(413\) | 3.48352e14 | 1.42657 | ||||||||
\(414\) | 1.60111e13 | 0.0647023 | ||||||||
\(415\) | −3.77279e13 | −0.150452 | ||||||||
\(416\) | −1.91359e14 | −0.753072 | ||||||||
\(417\) | 1.50062e14 | 0.582804 | ||||||||
\(418\) | 1.37530e14 | 0.527144 | ||||||||
\(419\) | 2.21825e14 | 0.839139 | 0.419570 | − | 0.907723i | \(-0.362181\pi\) | ||||
0.419570 | + | 0.907723i | \(0.362181\pi\) | |||||||
\(420\) | −1.11173e14 | −0.415075 | ||||||||
\(421\) | 9.78949e13 | 0.360752 | 0.180376 | − | 0.983598i | \(-0.442269\pi\) | ||||
0.180376 | + | 0.983598i | \(0.442269\pi\) | |||||||
\(422\) | 3.02725e13 | 0.110111 | ||||||||
\(423\) | 5.06940e13 | 0.182005 | ||||||||
\(424\) | 2.01422e14 | 0.713831 | ||||||||
\(425\) | 2.57147e13 | 0.0899586 | ||||||||
\(426\) | 9.86497e13 | 0.340677 | ||||||||
\(427\) | −1.32217e14 | −0.450748 | ||||||||
\(428\) | −1.95340e13 | −0.0657432 | ||||||||
\(429\) | 2.34302e14 | 0.778503 | ||||||||
\(430\) | −7.68838e13 | −0.252208 | ||||||||
\(431\) | 1.11415e14 | 0.360842 | 0.180421 | − | 0.983589i | \(-0.442254\pi\) | ||||
0.180421 | + | 0.983589i | \(0.442254\pi\) | |||||||
\(432\) | −4.17572e13 | −0.133528 | ||||||||
\(433\) | −3.42045e14 | −1.07994 | −0.539970 | − | 0.841684i | \(-0.681564\pi\) | ||||
−0.539970 | + | 0.841684i | \(0.681564\pi\) | |||||||
\(434\) | 1.18992e14 | 0.370957 | ||||||||
\(435\) | −1.44681e14 | −0.445371 | ||||||||
\(436\) | 5.72320e13 | 0.173965 | ||||||||
\(437\) | 2.13803e14 | 0.641750 | ||||||||
\(438\) | −1.15303e14 | −0.341769 | ||||||||
\(439\) | 1.20947e14 | 0.354029 | 0.177015 | − | 0.984208i | \(-0.443356\pi\) | ||||
0.177015 | + | 0.984208i | \(0.443356\pi\) | |||||||
\(440\) | 1.43655e14 | 0.415271 | ||||||||
\(441\) | 2.60599e14 | 0.743980 | ||||||||
\(442\) | −4.64195e13 | −0.130881 | ||||||||
\(443\) | −1.27316e14 | −0.354539 | −0.177270 | − | 0.984162i | \(-0.556726\pi\) | ||||
−0.177270 | + | 0.984162i | \(0.556726\pi\) | |||||||
\(444\) | 3.58985e13 | 0.0987347 | ||||||||
\(445\) | −1.38773e13 | −0.0376985 | ||||||||
\(446\) | 1.47189e14 | 0.394942 | ||||||||
\(447\) | 1.62504e14 | 0.430699 | ||||||||
\(448\) | −2.88443e14 | −0.755147 | ||||||||
\(449\) | −1.61837e14 | −0.418526 | −0.209263 | − | 0.977859i | \(-0.567106\pi\) | ||||
−0.209263 | + | 0.977859i | \(0.567106\pi\) | |||||||
\(450\) | 8.48777e12 | 0.0216833 | ||||||||
\(451\) | 1.82199e14 | 0.459807 | ||||||||
\(452\) | 7.25848e13 | 0.180961 | ||||||||
\(453\) | −3.35931e14 | −0.827390 | ||||||||
\(454\) | −9.96664e13 | −0.242517 | ||||||||
\(455\) | 2.99198e14 | 0.719276 | ||||||||
\(456\) | 1.61039e14 | 0.382494 | ||||||||
\(457\) | −3.49165e14 | −0.819391 | −0.409696 | − | 0.912222i | \(-0.634365\pi\) | ||||
−0.409696 | + | 0.912222i | \(0.634365\pi\) | |||||||
\(458\) | 1.50036e14 | 0.347884 | ||||||||
\(459\) | −3.77834e13 | −0.0865627 | ||||||||
\(460\) | 1.05426e14 | 0.238661 | ||||||||
\(461\) | −4.49619e14 | −1.00575 | −0.502875 | − | 0.864359i | \(-0.667724\pi\) | ||||
−0.502875 | + | 0.864359i | \(0.667724\pi\) | |||||||
\(462\) | −2.30192e14 | −0.508814 | ||||||||
\(463\) | 4.21098e13 | 0.0919787 | 0.0459894 | − | 0.998942i | \(-0.485356\pi\) | ||||
0.0459894 | + | 0.998942i | \(0.485356\pi\) | |||||||
\(464\) | −5.54459e14 | −1.19680 | ||||||||
\(465\) | 7.67930e13 | 0.163806 | ||||||||
\(466\) | 9.92723e13 | 0.209269 | ||||||||
\(467\) | −7.91358e13 | −0.164866 | −0.0824328 | − | 0.996597i | \(-0.526269\pi\) | ||||
−0.0824328 | + | 0.996597i | \(0.526269\pi\) | |||||||
\(468\) | 1.29515e14 | 0.266667 | ||||||||
\(469\) | 6.06442e14 | 1.23407 | ||||||||
\(470\) | −3.94889e13 | −0.0794213 | ||||||||
\(471\) | 1.92860e14 | 0.383377 | ||||||||
\(472\) | −2.48821e14 | −0.488885 | ||||||||
\(473\) | 1.34566e15 | 2.61336 | ||||||||
\(474\) | 8.69682e12 | 0.0166947 | ||||||||
\(475\) | 1.13341e14 | 0.215066 | ||||||||
\(476\) | −3.85499e14 | −0.723078 | ||||||||
\(477\) | −2.08296e14 | −0.386215 | ||||||||
\(478\) | −2.59794e14 | −0.476184 | ||||||||
\(479\) | −9.62318e14 | −1.74371 | −0.871853 | − | 0.489768i | \(-0.837081\pi\) | ||||
−0.871853 | + | 0.489768i | \(0.837081\pi\) | |||||||
\(480\) | 1.21330e14 | 0.217341 | ||||||||
\(481\) | −9.66132e13 | −0.171095 | ||||||||
\(482\) | −2.02626e14 | −0.354762 | ||||||||
\(483\) | −3.57853e14 | −0.619435 | ||||||||
\(484\) | −6.64451e14 | −1.13714 | ||||||||
\(485\) | 6.38914e13 | 0.108109 | ||||||||
\(486\) | −1.24713e13 | −0.0208647 | ||||||||
\(487\) | 4.57117e14 | 0.756168 | 0.378084 | − | 0.925771i | \(-0.376583\pi\) | ||||
0.378084 | + | 0.925771i | \(0.376583\pi\) | |||||||
\(488\) | 9.44399e13 | 0.154471 | ||||||||
\(489\) | 1.13578e14 | 0.183694 | ||||||||
\(490\) | −2.02998e14 | −0.324649 | ||||||||
\(491\) | 4.40122e14 | 0.696025 | 0.348013 | − | 0.937490i | \(-0.386857\pi\) | ||||
0.348013 | + | 0.937490i | \(0.386857\pi\) | |||||||
\(492\) | 1.00715e14 | 0.157501 | ||||||||
\(493\) | −5.01693e14 | −0.775854 | ||||||||
\(494\) | −2.04599e14 | −0.312900 | ||||||||
\(495\) | −1.48557e14 | −0.224681 | ||||||||
\(496\) | 2.94292e14 | 0.440179 | ||||||||
\(497\) | −2.20485e15 | −3.26151 | ||||||||
\(498\) | −4.31817e13 | −0.0631740 | ||||||||
\(499\) | 6.36085e14 | 0.920369 | 0.460185 | − | 0.887823i | \(-0.347783\pi\) | ||||
0.460185 | + | 0.887823i | \(0.347783\pi\) | |||||||
\(500\) | 5.58883e13 | 0.0799808 | ||||||||
\(501\) | −6.98581e14 | −0.988802 | ||||||||
\(502\) | 4.44888e14 | 0.622846 | ||||||||
\(503\) | −4.81639e12 | −0.00666957 | −0.00333478 | − | 0.999994i | \(-0.501061\pi\) | ||||
−0.00333478 | + | 0.999994i | \(0.501061\pi\) | |||||||
\(504\) | −2.69540e14 | −0.369195 | ||||||||
\(505\) | 4.87334e14 | 0.660274 | ||||||||
\(506\) | 2.18294e14 | 0.292559 | ||||||||
\(507\) | 8.69320e13 | 0.115249 | ||||||||
\(508\) | −4.82488e13 | −0.0632755 | ||||||||
\(509\) | −5.73829e14 | −0.744449 | −0.372224 | − | 0.928143i | \(-0.621405\pi\) | ||||
−0.372224 | + | 0.928143i | \(0.621405\pi\) | |||||||
\(510\) | 2.94320e13 | 0.0377731 | ||||||||
\(511\) | 2.57705e15 | 3.27196 | ||||||||
\(512\) | 8.05287e14 | 1.01150 | ||||||||
\(513\) | −1.66535e14 | −0.206947 | ||||||||
\(514\) | 1.01306e14 | 0.124548 | ||||||||
\(515\) | 1.59476e14 | 0.193980 | ||||||||
\(516\) | 7.43842e14 | 0.895174 | ||||||||
\(517\) | 6.91155e14 | 0.822958 | ||||||||
\(518\) | 9.49185e13 | 0.111825 | ||||||||
\(519\) | −3.71997e14 | −0.433630 | ||||||||
\(520\) | −2.13711e14 | −0.246495 | ||||||||
\(521\) | 5.14705e14 | 0.587422 | 0.293711 | − | 0.955894i | \(-0.405110\pi\) | ||||
0.293711 | + | 0.955894i | \(0.405110\pi\) | |||||||
\(522\) | −1.65596e14 | −0.187009 | ||||||||
\(523\) | 1.20146e15 | 1.34261 | 0.671304 | − | 0.741182i | \(-0.265735\pi\) | ||||
0.671304 | + | 0.741182i | \(0.265735\pi\) | |||||||
\(524\) | 4.02745e14 | 0.445357 | ||||||||
\(525\) | −1.89704e14 | −0.207587 | ||||||||
\(526\) | −4.85654e14 | −0.525903 | ||||||||
\(527\) | 2.66285e14 | 0.285357 | ||||||||
\(528\) | −5.69313e14 | −0.603760 | ||||||||
\(529\) | −6.13454e14 | −0.643836 | ||||||||
\(530\) | 1.62255e14 | 0.168532 | ||||||||
\(531\) | 2.57312e14 | 0.264509 | ||||||||
\(532\) | −1.69913e15 | −1.72868 | ||||||||
\(533\) | −2.71052e14 | −0.272931 | ||||||||
\(534\) | −1.58833e13 | −0.0158294 | ||||||||
\(535\) | −3.33327e13 | −0.0328795 | ||||||||
\(536\) | −4.33170e14 | −0.422914 | ||||||||
\(537\) | 4.64948e14 | 0.449310 | ||||||||
\(538\) | −4.37861e14 | −0.418826 | ||||||||
\(539\) | 3.55298e15 | 3.36399 | ||||||||
\(540\) | −8.21183e13 | −0.0769616 | ||||||||
\(541\) | −1.89107e15 | −1.75438 | −0.877190 | − | 0.480143i | \(-0.840585\pi\) | ||||
−0.877190 | + | 0.480143i | \(0.840585\pi\) | |||||||
\(542\) | −6.33524e14 | −0.581791 | ||||||||
\(543\) | 4.15090e14 | 0.377349 | ||||||||
\(544\) | 4.20721e14 | 0.378617 | ||||||||
\(545\) | 9.76602e13 | 0.0870035 | ||||||||
\(546\) | 3.42449e14 | 0.302020 | ||||||||
\(547\) | 1.37400e14 | 0.119966 | 0.0599830 | − | 0.998199i | \(-0.480895\pi\) | ||||
0.0599830 | + | 0.998199i | \(0.480895\pi\) | |||||||
\(548\) | 1.01464e15 | 0.877040 | ||||||||
\(549\) | −9.76626e13 | −0.0835758 | ||||||||
\(550\) | 1.15721e14 | 0.0980434 | ||||||||
\(551\) | −2.21127e15 | −1.85485 | ||||||||
\(552\) | 2.55608e14 | 0.212280 | ||||||||
\(553\) | −1.94377e14 | −0.159829 | ||||||||
\(554\) | 2.15939e14 | 0.175803 | ||||||||
\(555\) | 6.12569e13 | 0.0493792 | ||||||||
\(556\) | 1.13093e15 | 0.902661 | ||||||||
\(557\) | −1.18622e15 | −0.937483 | −0.468742 | − | 0.883335i | \(-0.655292\pi\) | ||||
−0.468742 | + | 0.883335i | \(0.655292\pi\) | |||||||
\(558\) | 8.78939e13 | 0.0687814 | ||||||||
\(559\) | −2.00189e15 | −1.55123 | ||||||||
\(560\) | −7.26999e14 | −0.557827 | ||||||||
\(561\) | −5.15134e14 | −0.391403 | ||||||||
\(562\) | 6.15815e14 | 0.463340 | ||||||||
\(563\) | −2.58208e15 | −1.92386 | −0.961929 | − | 0.273298i | \(-0.911885\pi\) | ||||
−0.961929 | + | 0.273298i | \(0.911885\pi\) | |||||||
\(564\) | 3.82051e14 | 0.281894 | ||||||||
\(565\) | 1.23858e14 | 0.0905020 | ||||||||
\(566\) | 3.44783e14 | 0.249491 | ||||||||
\(567\) | 2.78738e14 | 0.199751 | ||||||||
\(568\) | 1.57488e15 | 1.11772 | ||||||||
\(569\) | 6.86455e13 | 0.0482497 | 0.0241249 | − | 0.999709i | \(-0.492320\pi\) | ||||
0.0241249 | + | 0.999709i | \(0.492320\pi\) | |||||||
\(570\) | 1.29725e14 | 0.0903049 | ||||||||
\(571\) | −1.48521e15 | −1.02397 | −0.511986 | − | 0.858994i | \(-0.671090\pi\) | ||||
−0.511986 | + | 0.858994i | \(0.671090\pi\) | |||||||
\(572\) | 1.76579e15 | 1.20576 | ||||||||
\(573\) | −7.67929e14 | −0.519363 | ||||||||
\(574\) | 2.66297e14 | 0.178382 | ||||||||
\(575\) | 1.79899e14 | 0.119359 | ||||||||
\(576\) | −2.13060e14 | −0.140016 | ||||||||
\(577\) | −1.11682e14 | −0.0726966 | −0.0363483 | − | 0.999339i | \(-0.511573\pi\) | ||||
−0.0363483 | + | 0.999339i | \(0.511573\pi\) | |||||||
\(578\) | −4.02394e14 | −0.259447 | ||||||||
\(579\) | −6.73830e14 | −0.430346 | ||||||||
\(580\) | −1.09038e15 | −0.689800 | ||||||||
\(581\) | 9.65124e14 | 0.604803 | ||||||||
\(582\) | 7.31274e13 | 0.0453945 | ||||||||
\(583\) | −2.83988e15 | −1.74631 | ||||||||
\(584\) | −1.84074e15 | −1.12130 | ||||||||
\(585\) | 2.21004e14 | 0.133365 | ||||||||
\(586\) | −1.07635e14 | −0.0643450 | ||||||||
\(587\) | 1.03228e15 | 0.611347 | 0.305673 | − | 0.952136i | \(-0.401118\pi\) | ||||
0.305673 | + | 0.952136i | \(0.401118\pi\) | |||||||
\(588\) | 1.96398e15 | 1.15229 | ||||||||
\(589\) | 1.17368e15 | 0.682208 | ||||||||
\(590\) | −2.00437e14 | −0.115423 | ||||||||
\(591\) | −9.39204e14 | −0.535832 | ||||||||
\(592\) | 2.34753e14 | 0.132691 | ||||||||
\(593\) | 5.05946e14 | 0.283337 | 0.141668 | − | 0.989914i | \(-0.454753\pi\) | ||||
0.141668 | + | 0.989914i | \(0.454753\pi\) | |||||||
\(594\) | −1.70032e14 | −0.0943423 | ||||||||
\(595\) | −6.57813e14 | −0.361626 | ||||||||
\(596\) | 1.22470e15 | 0.667076 | ||||||||
\(597\) | 2.47469e14 | 0.133556 | ||||||||
\(598\) | −3.24748e14 | −0.173656 | ||||||||
\(599\) | −1.86439e14 | −0.0987846 | −0.0493923 | − | 0.998779i | \(-0.515728\pi\) | ||||
−0.0493923 | + | 0.998779i | \(0.515728\pi\) | |||||||
\(600\) | 1.35502e14 | 0.0711401 | ||||||||
\(601\) | −6.39018e14 | −0.332433 | −0.166216 | − | 0.986089i | \(-0.553155\pi\) | ||||
−0.166216 | + | 0.986089i | \(0.553155\pi\) | |||||||
\(602\) | 1.96678e15 | 1.01385 | ||||||||
\(603\) | 4.47952e14 | 0.228816 | ||||||||
\(604\) | −2.53172e15 | −1.28148 | ||||||||
\(605\) | −1.13381e15 | −0.568706 | ||||||||
\(606\) | 5.57782e14 | 0.277246 | ||||||||
\(607\) | 3.07440e15 | 1.51434 | 0.757169 | − | 0.653219i | \(-0.226582\pi\) | ||||
0.757169 | + | 0.653219i | \(0.226582\pi\) | |||||||
\(608\) | 1.85438e15 | 0.905166 | ||||||||
\(609\) | 3.70112e15 | 1.79035 | ||||||||
\(610\) | 7.60759e13 | 0.0364698 | ||||||||
\(611\) | −1.02821e15 | −0.488489 | ||||||||
\(612\) | −2.84751e14 | −0.134070 | ||||||||
\(613\) | 1.45823e15 | 0.680447 | 0.340223 | − | 0.940345i | \(-0.389497\pi\) | ||||
0.340223 | + | 0.940345i | \(0.389497\pi\) | |||||||
\(614\) | −7.90767e14 | −0.365698 | ||||||||
\(615\) | 1.71859e14 | 0.0787695 | ||||||||
\(616\) | −3.67488e15 | −1.66935 | ||||||||
\(617\) | 2.52038e15 | 1.13474 | 0.567372 | − | 0.823462i | \(-0.307960\pi\) | ||||
0.567372 | + | 0.823462i | \(0.307960\pi\) | |||||||
\(618\) | 1.82530e14 | 0.0814512 | ||||||||
\(619\) | 2.76117e15 | 1.22122 | 0.610612 | − | 0.791930i | \(-0.290924\pi\) | ||||
0.610612 | + | 0.791930i | \(0.290924\pi\) | |||||||
\(620\) | 5.78743e14 | 0.253707 | ||||||||
\(621\) | −2.64330e14 | −0.114853 | ||||||||
\(622\) | 7.96900e14 | 0.343207 | ||||||||
\(623\) | 3.54997e14 | 0.151545 | ||||||||
\(624\) | 8.46948e14 | 0.358378 | ||||||||
\(625\) | 9.53674e13 | 0.0400000 | ||||||||
\(626\) | −6.32511e13 | −0.0262972 | ||||||||
\(627\) | −2.27051e15 | −0.935734 | ||||||||
\(628\) | 1.45347e15 | 0.593783 | ||||||||
\(629\) | 2.12413e14 | 0.0860205 | ||||||||
\(630\) | −2.17127e14 | −0.0871649 | ||||||||
\(631\) | −5.89126e14 | −0.234448 | −0.117224 | − | 0.993105i | \(-0.537400\pi\) | ||||
−0.117224 | + | 0.993105i | \(0.537400\pi\) | |||||||
\(632\) | 1.38839e14 | 0.0547733 | ||||||||
\(633\) | −4.99774e14 | −0.195458 | ||||||||
\(634\) | −4.14972e14 | −0.160890 | ||||||||
\(635\) | −8.23314e13 | −0.0316453 | ||||||||
\(636\) | −1.56980e15 | −0.598178 | ||||||||
\(637\) | −5.28565e15 | −1.99679 | ||||||||
\(638\) | −2.25772e15 | −0.845582 | ||||||||
\(639\) | −1.62862e15 | −0.604736 | ||||||||
\(640\) | 1.18854e15 | 0.437544 | ||||||||
\(641\) | 1.59787e15 | 0.583208 | 0.291604 | − | 0.956539i | \(-0.405811\pi\) | ||||
0.291604 | + | 0.956539i | \(0.405811\pi\) | |||||||
\(642\) | −3.81512e13 | −0.0138059 | ||||||||
\(643\) | 4.44445e15 | 1.59462 | 0.797310 | − | 0.603569i | \(-0.206255\pi\) | ||||
0.797310 | + | 0.603569i | \(0.206255\pi\) | |||||||
\(644\) | −2.69693e15 | −0.959395 | ||||||||
\(645\) | 1.26929e15 | 0.447694 | ||||||||
\(646\) | 4.49830e14 | 0.157315 | ||||||||
\(647\) | −8.54247e14 | −0.296217 | −0.148108 | − | 0.988971i | \(-0.547318\pi\) | ||||
−0.148108 | + | 0.988971i | \(0.547318\pi\) | |||||||
\(648\) | −1.99097e14 | −0.0684546 | ||||||||
\(649\) | 3.50816e15 | 1.19601 | ||||||||
\(650\) | −1.72155e14 | −0.0581963 | ||||||||
\(651\) | −1.96446e15 | −0.658486 | ||||||||
\(652\) | 8.55971e14 | 0.284510 | ||||||||
\(653\) | −2.86428e15 | −0.944045 | −0.472022 | − | 0.881587i | \(-0.656476\pi\) | ||||
−0.472022 | + | 0.881587i | \(0.656476\pi\) | |||||||
\(654\) | 1.11778e14 | 0.0365323 | ||||||||
\(655\) | 6.87242e14 | 0.222732 | ||||||||
\(656\) | 6.58609e14 | 0.211669 | ||||||||
\(657\) | 1.90355e15 | 0.606674 | ||||||||
\(658\) | 1.01017e15 | 0.319267 | ||||||||
\(659\) | 4.78135e15 | 1.49858 | 0.749291 | − | 0.662241i | \(-0.230394\pi\) | ||||
0.749291 | + | 0.662241i | \(0.230394\pi\) | |||||||
\(660\) | −1.11959e15 | −0.347991 | ||||||||
\(661\) | −5.52275e14 | −0.170234 | −0.0851172 | − | 0.996371i | \(-0.527126\pi\) | ||||
−0.0851172 | + | 0.996371i | \(0.527126\pi\) | |||||||
\(662\) | −1.46524e15 | −0.447909 | ||||||||
\(663\) | 7.66347e14 | 0.232328 | ||||||||
\(664\) | −6.89369e14 | −0.207266 | ||||||||
\(665\) | −2.89939e15 | −0.864545 | ||||||||
\(666\) | 7.01120e13 | 0.0207341 | ||||||||
\(667\) | −3.50982e15 | −1.02942 | ||||||||
\(668\) | −5.26480e15 | −1.53148 | ||||||||
\(669\) | −2.42997e15 | −0.701062 | ||||||||
\(670\) | −3.48939e14 | −0.0998478 | ||||||||
\(671\) | −1.33152e15 | −0.377897 | ||||||||
\(672\) | −3.10377e15 | −0.873693 | ||||||||
\(673\) | −3.31175e15 | −0.924645 | −0.462323 | − | 0.886712i | \(-0.652984\pi\) | ||||
−0.462323 | + | 0.886712i | \(0.652984\pi\) | |||||||
\(674\) | −1.33234e15 | −0.368964 | ||||||||
\(675\) | −1.40126e14 | −0.0384900 | ||||||||
\(676\) | 6.55156e14 | 0.178500 | ||||||||
\(677\) | 6.69181e15 | 1.80845 | 0.904223 | − | 0.427060i | \(-0.140451\pi\) | ||||
0.904223 | + | 0.427060i | \(0.140451\pi\) | |||||||
\(678\) | 1.41763e14 | 0.0380013 | ||||||||
\(679\) | −1.63442e15 | −0.434590 | ||||||||
\(680\) | 4.69863e14 | 0.123929 | ||||||||
\(681\) | 1.64541e15 | 0.430492 | ||||||||
\(682\) | 1.19833e15 | 0.311003 | ||||||||
\(683\) | −7.20810e15 | −1.85570 | −0.927848 | − | 0.372959i | \(-0.878343\pi\) | ||||
−0.927848 | + | 0.372959i | \(0.878343\pi\) | |||||||
\(684\) | −1.25507e15 | −0.320524 | ||||||||
\(685\) | 1.73138e15 | 0.438625 | ||||||||
\(686\) | 2.86629e15 | 0.720340 | ||||||||
\(687\) | −2.47696e15 | −0.617529 | ||||||||
\(688\) | 4.86426e15 | 1.20304 | ||||||||
\(689\) | 4.22479e15 | 1.03657 | ||||||||
\(690\) | 2.05904e14 | 0.0501182 | ||||||||
\(691\) | 7.79467e15 | 1.88221 | 0.941106 | − | 0.338112i | \(-0.109788\pi\) | ||||
0.941106 | + | 0.338112i | \(0.109788\pi\) | |||||||
\(692\) | −2.80352e15 | −0.671615 | ||||||||
\(693\) | 3.80028e15 | 0.903197 | ||||||||
\(694\) | −9.37448e14 | −0.221040 | ||||||||
\(695\) | 1.92981e15 | 0.451438 | ||||||||
\(696\) | −2.64364e15 | −0.613553 | ||||||||
\(697\) | 5.95932e14 | 0.137220 | ||||||||
\(698\) | 1.04299e15 | 0.238274 | ||||||||
\(699\) | −1.63890e15 | −0.371474 | ||||||||
\(700\) | −1.42969e15 | −0.321516 | ||||||||
\(701\) | 6.71290e15 | 1.49782 | 0.748912 | − | 0.662669i | \(-0.230577\pi\) | ||||
0.748912 | + | 0.662669i | \(0.230577\pi\) | |||||||
\(702\) | 2.52952e14 | 0.0559994 | ||||||||
\(703\) | 9.36234e14 | 0.205651 | ||||||||
\(704\) | −2.90483e15 | −0.633099 | ||||||||
\(705\) | 6.51929e14 | 0.140981 | ||||||||
\(706\) | 9.75719e14 | 0.209362 | ||||||||
\(707\) | −1.24666e16 | −2.65424 | ||||||||
\(708\) | 1.93921e15 | 0.409677 | ||||||||
\(709\) | −4.10214e15 | −0.859917 | −0.429959 | − | 0.902849i | \(-0.641472\pi\) | ||||
−0.429959 | + | 0.902849i | \(0.641472\pi\) | |||||||
\(710\) | 1.26864e15 | 0.263887 | ||||||||
\(711\) | −1.43577e14 | −0.0296349 | ||||||||
\(712\) | −2.53568e14 | −0.0519343 | ||||||||
\(713\) | 1.86291e15 | 0.378617 | ||||||||
\(714\) | −7.52905e14 | −0.151845 | ||||||||
\(715\) | 3.01314e15 | 0.603026 | ||||||||
\(716\) | 3.50404e15 | 0.695902 | ||||||||
\(717\) | 4.28898e15 | 0.845276 | ||||||||
\(718\) | 1.00122e15 | 0.195814 | ||||||||
\(719\) | −3.31818e15 | −0.644008 | −0.322004 | − | 0.946738i | \(-0.604356\pi\) | ||||
−0.322004 | + | 0.946738i | \(0.604356\pi\) | |||||||
\(720\) | −5.37001e14 | −0.103430 | ||||||||
\(721\) | −4.07960e15 | −0.779783 | ||||||||
\(722\) | 2.68047e14 | 0.0508460 | ||||||||
\(723\) | 3.34519e15 | 0.629738 | ||||||||
\(724\) | 3.12829e15 | 0.584446 | ||||||||
\(725\) | −1.86061e15 | −0.344983 | ||||||||
\(726\) | −1.29772e15 | −0.238797 | ||||||||
\(727\) | 3.34273e15 | 0.610467 | 0.305233 | − | 0.952278i | \(-0.401266\pi\) | ||||
0.305233 | + | 0.952278i | \(0.401266\pi\) | |||||||
\(728\) | 5.46699e15 | 0.990890 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −1.48280e15 | −0.264733 | ||||||||
\(731\) | 4.40134e15 | 0.779901 | ||||||||
\(732\) | −7.36026e14 | −0.129444 | ||||||||
\(733\) | −6.14966e15 | −1.07344 | −0.536722 | − | 0.843759i | \(-0.680338\pi\) | ||||
−0.536722 | + | 0.843759i | \(0.680338\pi\) | |||||||
\(734\) | 3.23483e15 | 0.560432 | ||||||||
\(735\) | 3.35133e15 | 0.576284 | ||||||||
\(736\) | 2.94334e15 | 0.502357 | ||||||||
\(737\) | 6.10732e15 | 1.03462 | ||||||||
\(738\) | 1.96702e14 | 0.0330749 | ||||||||
\(739\) | −4.15701e15 | −0.693804 | −0.346902 | − | 0.937901i | \(-0.612766\pi\) | ||||
−0.346902 | + | 0.937901i | \(0.612766\pi\) | |||||||
\(740\) | 4.61657e14 | 0.0764795 | ||||||||
\(741\) | 3.37776e15 | 0.555430 | ||||||||
\(742\) | −4.15068e15 | −0.677482 | ||||||||
\(743\) | −4.90364e15 | −0.794474 | −0.397237 | − | 0.917716i | \(-0.630031\pi\) | ||||
−0.397237 | + | 0.917716i | \(0.630031\pi\) | |||||||
\(744\) | 1.40317e15 | 0.225663 | ||||||||
\(745\) | 2.08982e15 | 0.333618 | ||||||||
\(746\) | −2.46150e15 | −0.390064 | ||||||||
\(747\) | 7.12893e14 | 0.112140 | ||||||||
\(748\) | −3.88226e15 | −0.606214 | ||||||||
\(749\) | 8.52690e14 | 0.132173 | ||||||||
\(750\) | 1.09153e14 | 0.0167958 | ||||||||
\(751\) | −2.00580e15 | −0.306385 | −0.153192 | − | 0.988196i | \(-0.548955\pi\) | ||||
−0.153192 | + | 0.988196i | \(0.548955\pi\) | |||||||
\(752\) | 2.49837e15 | 0.378842 | ||||||||
\(753\) | −7.34473e15 | −1.10561 | ||||||||
\(754\) | 3.35873e15 | 0.501918 | ||||||||
\(755\) | −4.32010e15 | −0.640894 | ||||||||
\(756\) | 2.10068e15 | 0.309379 | ||||||||
\(757\) | 2.85016e15 | 0.416718 | 0.208359 | − | 0.978052i | \(-0.433188\pi\) | ||||
0.208359 | + | 0.978052i | \(0.433188\pi\) | |||||||
\(758\) | −2.32235e15 | −0.337091 | ||||||||
\(759\) | −3.60384e15 | −0.519321 | ||||||||
\(760\) | 2.07098e15 | 0.296279 | ||||||||
\(761\) | 8.65962e15 | 1.22994 | 0.614969 | − | 0.788551i | \(-0.289168\pi\) | ||||
0.614969 | + | 0.788551i | \(0.289168\pi\) | |||||||
\(762\) | −9.42329e13 | −0.0132877 | ||||||||
\(763\) | −2.49827e15 | −0.349747 | ||||||||
\(764\) | −5.78743e15 | −0.804400 | ||||||||
\(765\) | −4.85897e14 | −0.0670512 | ||||||||
\(766\) | 8.08453e14 | 0.110763 | ||||||||
\(767\) | −5.21897e15 | −0.709922 | ||||||||
\(768\) | −4.35320e14 | −0.0587925 | ||||||||
\(769\) | −7.49727e15 | −1.00533 | −0.502665 | − | 0.864481i | \(-0.667647\pi\) | ||||
−0.502665 | + | 0.864481i | \(0.667647\pi\) | |||||||
\(770\) | −2.96029e15 | −0.394126 | ||||||||
\(771\) | −1.67248e15 | −0.221086 | ||||||||
\(772\) | −5.07826e15 | −0.666530 | ||||||||
\(773\) | 2.07867e15 | 0.270894 | 0.135447 | − | 0.990785i | \(-0.456753\pi\) | ||||
0.135447 | + | 0.990785i | \(0.456753\pi\) | |||||||
\(774\) | 1.45277e15 | 0.187984 | ||||||||
\(775\) | 9.87564e14 | 0.126884 | ||||||||
\(776\) | 1.16743e15 | 0.148934 | ||||||||
\(777\) | −1.56703e15 | −0.198500 | ||||||||
\(778\) | −3.42866e15 | −0.431258 | ||||||||
\(779\) | 2.62664e15 | 0.328053 | ||||||||
\(780\) | 1.66558e15 | 0.206559 | ||||||||
\(781\) | −2.22045e16 | −2.73438 | ||||||||
\(782\) | 7.13988e14 | 0.0873079 | ||||||||
\(783\) | 2.73385e15 | 0.331960 | ||||||||
\(784\) | 1.28432e16 | 1.54859 | ||||||||
\(785\) | 2.48019e15 | 0.296963 | ||||||||
\(786\) | 7.86587e14 | 0.0935239 | ||||||||
\(787\) | −1.58421e16 | −1.87047 | −0.935235 | − | 0.354026i | \(-0.884812\pi\) | ||||
−0.935235 | + | 0.354026i | \(0.884812\pi\) | |||||||
\(788\) | −7.07823e15 | −0.829909 | ||||||||
\(789\) | 8.01774e15 | 0.933531 | ||||||||
\(790\) | 1.11842e14 | 0.0129317 | ||||||||
\(791\) | −3.16844e15 | −0.363810 | ||||||||
\(792\) | −2.71447e15 | −0.309525 | ||||||||
\(793\) | 1.98086e15 | 0.224311 | ||||||||
\(794\) | −7.00826e14 | −0.0788129 | ||||||||
\(795\) | −2.67870e15 | −0.299161 | ||||||||
\(796\) | 1.86503e15 | 0.206854 | ||||||||
\(797\) | −4.58469e15 | −0.504997 | −0.252499 | − | 0.967597i | \(-0.581252\pi\) | ||||
−0.252499 | + | 0.967597i | \(0.581252\pi\) | |||||||
\(798\) | −3.31852e15 | −0.363018 | ||||||||
\(799\) | 2.26061e15 | 0.245594 | ||||||||
\(800\) | 1.56032e15 | 0.168352 | ||||||||
\(801\) | 2.62221e14 | 0.0280988 | ||||||||
\(802\) | −4.40210e15 | −0.468490 | ||||||||
\(803\) | 2.59528e16 | 2.74315 | ||||||||
\(804\) | 3.37595e15 | 0.354395 | ||||||||
\(805\) | −4.60202e15 | −0.479812 | ||||||||
\(806\) | −1.78272e15 | −0.184604 | ||||||||
\(807\) | 7.22872e15 | 0.743459 | ||||||||
\(808\) | 8.90465e15 | 0.909608 | ||||||||
\(809\) | −1.72813e15 | −0.175331 | −0.0876656 | − | 0.996150i | \(-0.527941\pi\) | ||||
−0.0876656 | + | 0.996150i | \(0.527941\pi\) | |||||||
\(810\) | −1.60382e14 | −0.0161618 | ||||||||
\(811\) | 4.24638e14 | 0.0425015 | 0.0212507 | − | 0.999774i | \(-0.493235\pi\) | ||||
0.0212507 | + | 0.999774i | \(0.493235\pi\) | |||||||
\(812\) | 2.78932e16 | 2.77294 | ||||||||
\(813\) | 1.04590e16 | 1.03274 | ||||||||
\(814\) | 9.55899e14 | 0.0937514 | ||||||||
\(815\) | 1.46062e15 | 0.142289 | ||||||||
\(816\) | −1.86209e15 | −0.180179 | ||||||||
\(817\) | 1.93994e16 | 1.86452 | ||||||||
\(818\) | −3.76631e15 | −0.359561 | ||||||||
\(819\) | −5.65355e15 | −0.536117 | ||||||||
\(820\) | 1.29520e15 | 0.122000 | ||||||||
\(821\) | −1.96517e16 | −1.83871 | −0.919354 | − | 0.393431i | \(-0.871288\pi\) | ||||
−0.919354 | + | 0.393431i | \(0.871288\pi\) | |||||||
\(822\) | 1.98166e15 | 0.184176 | ||||||||
\(823\) | 5.95701e14 | 0.0549957 | 0.0274979 | − | 0.999622i | \(-0.491246\pi\) | ||||
0.0274979 | + | 0.999622i | \(0.491246\pi\) | |||||||
\(824\) | 2.91398e15 | 0.267231 | ||||||||
\(825\) | −1.91046e15 | −0.174037 | ||||||||
\(826\) | 5.12743e15 | 0.463991 | ||||||||
\(827\) | −1.40975e16 | −1.26725 | −0.633626 | − | 0.773639i | \(-0.718434\pi\) | ||||
−0.633626 | + | 0.773639i | \(0.718434\pi\) | |||||||
\(828\) | −1.99210e15 | −0.177887 | ||||||||
\(829\) | −7.87187e15 | −0.698277 | −0.349139 | − | 0.937071i | \(-0.613526\pi\) | ||||
−0.349139 | + | 0.937071i | \(0.613526\pi\) | |||||||
\(830\) | −5.55320e14 | −0.0489343 | ||||||||
\(831\) | −3.56497e15 | −0.312068 | ||||||||
\(832\) | 4.32142e15 | 0.375793 | ||||||||
\(833\) | 1.16210e16 | 1.00391 | ||||||||
\(834\) | 2.20878e15 | 0.189557 | ||||||||
\(835\) | −8.98381e15 | −0.765923 | ||||||||
\(836\) | −1.71115e16 | −1.44929 | ||||||||
\(837\) | −1.45106e15 | −0.122094 | ||||||||
\(838\) | 3.26507e15 | 0.272929 | ||||||||
\(839\) | 6.12117e15 | 0.508327 | 0.254164 | − | 0.967161i | \(-0.418200\pi\) | ||||
0.254164 | + | 0.967161i | \(0.418200\pi\) | |||||||
\(840\) | −3.46631e15 | −0.285977 | ||||||||
\(841\) | 2.41000e16 | 1.97533 | ||||||||
\(842\) | 1.44092e15 | 0.117334 | ||||||||
\(843\) | −1.01666e16 | −0.822476 | ||||||||
\(844\) | −3.76650e15 | −0.302729 | ||||||||
\(845\) | 1.11795e15 | 0.0892713 | ||||||||
\(846\) | 7.46170e14 | 0.0591971 | ||||||||
\(847\) | 2.90043e16 | 2.28615 | ||||||||
\(848\) | −1.02655e16 | −0.803902 | ||||||||
\(849\) | −5.69208e15 | −0.442873 | ||||||||
\(850\) | 3.78497e14 | 0.0292590 | ||||||||
\(851\) | 1.48603e15 | 0.114134 | ||||||||
\(852\) | −1.22740e16 | −0.936629 | ||||||||
\(853\) | 2.83032e15 | 0.214594 | 0.107297 | − | 0.994227i | \(-0.465781\pi\) | ||||
0.107297 | + | 0.994227i | \(0.465781\pi\) | |||||||
\(854\) | −1.94611e15 | −0.146605 | ||||||||
\(855\) | −2.14165e15 | −0.160300 | ||||||||
\(856\) | −6.09060e14 | −0.0452954 | ||||||||
\(857\) | −4.83193e14 | −0.0357048 | −0.0178524 | − | 0.999841i | \(-0.505683\pi\) | ||||
−0.0178524 | + | 0.999841i | \(0.505683\pi\) | |||||||
\(858\) | 3.44871e15 | 0.253208 | ||||||||
\(859\) | 1.23886e16 | 0.903775 | 0.451888 | − | 0.892075i | \(-0.350751\pi\) | ||||
0.451888 | + | 0.892075i | \(0.350751\pi\) | |||||||
\(860\) | 9.56587e15 | 0.693399 | ||||||||
\(861\) | −4.39635e15 | −0.316647 | ||||||||
\(862\) | 1.63992e15 | 0.117364 | ||||||||
\(863\) | −2.26458e16 | −1.61038 | −0.805191 | − | 0.593016i | \(-0.797937\pi\) | ||||
−0.805191 | + | 0.593016i | \(0.797937\pi\) | |||||||
\(864\) | −2.29262e15 | −0.161997 | ||||||||
\(865\) | −4.78391e15 | −0.335888 | ||||||||
\(866\) | −5.03459e15 | −0.351249 | ||||||||
\(867\) | 6.64319e15 | 0.460544 | ||||||||
\(868\) | −1.48050e16 | −1.01988 | ||||||||
\(869\) | −1.95751e15 | −0.133997 | ||||||||
\(870\) | −2.12958e15 | −0.144857 | ||||||||
\(871\) | −9.08565e15 | −0.614124 | ||||||||
\(872\) | 1.78446e15 | 0.119858 | ||||||||
\(873\) | −1.20727e15 | −0.0805799 | ||||||||
\(874\) | 3.14698e15 | 0.208728 | ||||||||
\(875\) | −2.43961e15 | −0.160797 | ||||||||
\(876\) | 1.43460e16 | 0.939630 | ||||||||
\(877\) | −8.89622e15 | −0.579039 | −0.289519 | − | 0.957172i | \(-0.593495\pi\) | ||||
−0.289519 | + | 0.957172i | \(0.593495\pi\) | |||||||
\(878\) | 1.78023e15 | 0.115148 | ||||||||
\(879\) | 1.77696e15 | 0.114219 | ||||||||
\(880\) | −7.32141e15 | −0.467671 | ||||||||
\(881\) | −1.82720e16 | −1.15989 | −0.579946 | − | 0.814655i | \(-0.696927\pi\) | ||||
−0.579946 | + | 0.814655i | \(0.696927\pi\) | |||||||
\(882\) | 3.83579e15 | 0.241979 | ||||||||
\(883\) | 8.75758e15 | 0.549035 | 0.274518 | − | 0.961582i | \(-0.411482\pi\) | ||||
0.274518 | + | 0.961582i | \(0.411482\pi\) | |||||||
\(884\) | 5.77551e15 | 0.359834 | ||||||||
\(885\) | 3.30905e15 | 0.204888 | ||||||||
\(886\) | −1.87398e15 | −0.115314 | ||||||||
\(887\) | 8.52159e15 | 0.521124 | 0.260562 | − | 0.965457i | \(-0.416092\pi\) | ||||
0.260562 | + | 0.965457i | \(0.416092\pi\) | |||||||
\(888\) | 1.11930e15 | 0.0680258 | ||||||||
\(889\) | 2.10613e15 | 0.127212 | ||||||||
\(890\) | −2.04261e14 | −0.0122614 | ||||||||
\(891\) | 2.80709e15 | 0.167467 | ||||||||
\(892\) | −1.83132e16 | −1.08582 | ||||||||
\(893\) | 9.96390e15 | 0.587146 | ||||||||
\(894\) | 2.39192e15 | 0.140084 | ||||||||
\(895\) | 5.97928e15 | 0.348034 | ||||||||
\(896\) | −3.04042e16 | −1.75889 | ||||||||
\(897\) | 5.36132e15 | 0.308257 | ||||||||
\(898\) | −2.38209e15 | −0.136125 | ||||||||
\(899\) | −1.92673e16 | −1.09432 | ||||||||
\(900\) | −1.05605e15 | −0.0596142 | ||||||||
\(901\) | −9.28858e15 | −0.521150 | ||||||||
\(902\) | 2.68181e15 | 0.149552 | ||||||||
\(903\) | −3.24699e16 | −1.79969 | ||||||||
\(904\) | 2.26316e15 | 0.124677 | ||||||||
\(905\) | 5.33809e15 | 0.292293 | ||||||||
\(906\) | −4.94461e15 | −0.269108 | ||||||||
\(907\) | 2.10550e16 | 1.13898 | 0.569490 | − | 0.821998i | \(-0.307141\pi\) | ||||
0.569490 | + | 0.821998i | \(0.307141\pi\) | |||||||
\(908\) | 1.24005e16 | 0.666756 | ||||||||
\(909\) | −9.20851e15 | −0.492139 | ||||||||
\(910\) | 4.40392e15 | 0.233944 | ||||||||
\(911\) | 3.04479e16 | 1.60771 | 0.803854 | − | 0.594827i | \(-0.202780\pi\) | ||||
0.803854 | + | 0.594827i | \(0.202780\pi\) | |||||||
\(912\) | −8.20739e15 | −0.430758 | ||||||||
\(913\) | 9.71950e15 | 0.507055 | ||||||||
\(914\) | −5.13939e15 | −0.266506 | ||||||||
\(915\) | −1.25595e15 | −0.0647375 | ||||||||
\(916\) | −1.86674e16 | −0.956443 | ||||||||
\(917\) | −1.75805e16 | −0.895363 | ||||||||
\(918\) | −5.56137e14 | −0.0281544 | ||||||||
\(919\) | −4.47695e15 | −0.225293 | −0.112646 | − | 0.993635i | \(-0.535933\pi\) | ||||
−0.112646 | + | 0.993635i | \(0.535933\pi\) | |||||||
\(920\) | 3.28714e15 | 0.164431 | ||||||||
\(921\) | 1.30549e16 | 0.649151 | ||||||||
\(922\) | −6.61799e15 | −0.327119 | ||||||||
\(923\) | 3.30328e16 | 1.62307 | ||||||||
\(924\) | 2.86405e16 | 1.39889 | ||||||||
\(925\) | 7.87769e14 | 0.0382489 | ||||||||
\(926\) | 6.19818e14 | 0.0299160 | ||||||||
\(927\) | −3.01342e15 | −0.144584 | ||||||||
\(928\) | −3.04417e16 | −1.45196 | ||||||||
\(929\) | 2.63310e16 | 1.24848 | 0.624238 | − | 0.781234i | \(-0.285409\pi\) | ||||
0.624238 | + | 0.781234i | \(0.285409\pi\) | |||||||
\(930\) | 1.13032e15 | 0.0532778 | ||||||||
\(931\) | 5.12208e16 | 2.40007 | ||||||||
\(932\) | −1.23515e16 | −0.575348 | ||||||||
\(933\) | −1.31562e16 | −0.609228 | ||||||||
\(934\) | −1.16481e15 | −0.0536224 | ||||||||
\(935\) | −6.62466e15 | −0.303179 | ||||||||
\(936\) | 4.03822e15 | 0.183727 | ||||||||
\(937\) | 1.18259e16 | 0.534894 | 0.267447 | − | 0.963573i | \(-0.413820\pi\) | ||||
0.267447 | + | 0.963573i | \(0.413820\pi\) | |||||||
\(938\) | 8.92628e15 | 0.401379 | ||||||||
\(939\) | 1.04422e15 | 0.0466802 | ||||||||
\(940\) | 4.91320e15 | 0.218354 | ||||||||
\(941\) | 6.96003e15 | 0.307517 | 0.153758 | − | 0.988108i | \(-0.450862\pi\) | ||||
0.153758 | + | 0.988108i | \(0.450862\pi\) | |||||||
\(942\) | 2.83872e15 | 0.124693 | ||||||||
\(943\) | 4.16911e15 | 0.182066 | ||||||||
\(944\) | 1.26812e16 | 0.550573 | ||||||||
\(945\) | 3.58459e15 | 0.154727 | ||||||||
\(946\) | 1.98069e16 | 0.849993 | ||||||||
\(947\) | −3.38501e16 | −1.44423 | −0.722113 | − | 0.691775i | \(-0.756829\pi\) | ||||
−0.722113 | + | 0.691775i | \(0.756829\pi\) | |||||||
\(948\) | −1.08206e15 | −0.0458991 | ||||||||
\(949\) | −3.86091e16 | −1.62827 | ||||||||
\(950\) | 1.66827e15 | 0.0699499 | ||||||||
\(951\) | 6.85084e15 | 0.285595 | ||||||||
\(952\) | −1.20197e16 | −0.498183 | ||||||||
\(953\) | 4.50062e16 | 1.85465 | 0.927323 | − | 0.374262i | \(-0.122104\pi\) | ||||
0.927323 | + | 0.374262i | \(0.122104\pi\) | |||||||
\(954\) | −3.06592e15 | −0.125616 | ||||||||
\(955\) | −9.87563e15 | −0.402297 | ||||||||
\(956\) | 3.23235e16 | 1.30918 | ||||||||
\(957\) | 3.72730e16 | 1.50099 | ||||||||
\(958\) | −1.41644e16 | −0.567139 | ||||||||
\(959\) | −4.42907e16 | −1.76323 | ||||||||
\(960\) | −2.73997e15 | −0.108456 | ||||||||
\(961\) | −1.51819e16 | −0.597513 | ||||||||
\(962\) | −1.42206e15 | −0.0556486 | ||||||||
\(963\) | 6.29844e14 | 0.0245069 | ||||||||
\(964\) | 2.52107e16 | 0.975353 | ||||||||
\(965\) | −8.66551e15 | −0.333345 | ||||||||
\(966\) | −5.26728e15 | −0.201471 | ||||||||
\(967\) | −1.48359e16 | −0.564246 | −0.282123 | − | 0.959378i | \(-0.591039\pi\) | ||||
−0.282123 | + | 0.959378i | \(0.591039\pi\) | |||||||
\(968\) | −2.07172e16 | −0.783461 | ||||||||
\(969\) | −7.42632e15 | −0.279250 | ||||||||
\(970\) | 9.40424e14 | 0.0351624 | ||||||||
\(971\) | 1.14414e16 | 0.425378 | 0.212689 | − | 0.977120i | \(-0.431778\pi\) | ||||
0.212689 | + | 0.977120i | \(0.431778\pi\) | |||||||
\(972\) | 1.55168e15 | 0.0573638 | ||||||||
\(973\) | −4.93669e16 | −1.81474 | ||||||||
\(974\) | 6.72835e15 | 0.245943 | ||||||||
\(975\) | 2.84213e15 | 0.103304 | ||||||||
\(976\) | −4.81314e15 | −0.173962 | ||||||||
\(977\) | −2.64437e16 | −0.950390 | −0.475195 | − | 0.879881i | \(-0.657622\pi\) | ||||
−0.475195 | + | 0.879881i | \(0.657622\pi\) | |||||||
\(978\) | 1.67177e15 | 0.0597464 | ||||||||
\(979\) | 3.57508e15 | 0.127052 | ||||||||
\(980\) | 2.52570e16 | 0.892562 | ||||||||
\(981\) | −1.84536e15 | −0.0648486 | ||||||||
\(982\) | 6.47820e15 | 0.226382 | ||||||||
\(983\) | 3.63656e16 | 1.26371 | 0.631854 | − | 0.775088i | \(-0.282294\pi\) | ||||
0.631854 | + | 0.775088i | \(0.282294\pi\) | |||||||
\(984\) | 3.14023e15 | 0.108515 | ||||||||
\(985\) | −1.20782e16 | −0.415054 | ||||||||
\(986\) | −7.38447e15 | −0.252346 | ||||||||
\(987\) | −1.66771e16 | −0.566731 | ||||||||
\(988\) | 2.54562e16 | 0.860262 | ||||||||
\(989\) | 3.07915e16 | 1.03479 | ||||||||
\(990\) | −2.18663e15 | −0.0730772 | ||||||||
\(991\) | 5.09067e16 | 1.69188 | 0.845941 | − | 0.533276i | \(-0.179039\pi\) | ||||
0.845941 | + | 0.533276i | \(0.179039\pi\) | |||||||
\(992\) | 1.61576e16 | 0.534027 | ||||||||
\(993\) | 2.41899e16 | 0.795084 | ||||||||
\(994\) | −3.24534e16 | −1.06080 | ||||||||
\(995\) | 3.18247e15 | 0.103452 | ||||||||
\(996\) | 5.37266e15 | 0.173685 | ||||||||
\(997\) | −4.28291e16 | −1.37694 | −0.688471 | − | 0.725264i | \(-0.741718\pi\) | ||||
−0.688471 | + | 0.725264i | \(0.741718\pi\) | |||||||
\(998\) | 9.36259e15 | 0.299349 | ||||||||
\(999\) | −1.15749e15 | −0.0368051 |
(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 | 15.12.a.c.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 45.12.a.c.1.1 | 2 | |||
4.3 | odd | 2 | 240.12.a.m.1.1 | 2 | |||
5.2 | odd | 4 | 75.12.b.d.49.3 | 4 | |||
5.3 | odd | 4 | 75.12.b.d.49.2 | 4 | |||
5.4 | even | 2 | 75.12.a.c.1.1 | 2 | |||
15.2 | even | 4 | 225.12.b.i.199.2 | 4 | |||
15.8 | even | 4 | 225.12.b.i.199.3 | 4 | |||
15.14 | odd | 2 | 225.12.a.i.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.12.a.c.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
45.12.a.c.1.1 | 2 | 3.2 | odd | 2 | |||
75.12.a.c.1.1 | 2 | 5.4 | even | 2 | |||
75.12.b.d.49.2 | 4 | 5.3 | odd | 4 | |||
75.12.b.d.49.3 | 4 | 5.2 | odd | 4 | |||
225.12.a.i.1.2 | 2 | 15.14 | odd | 2 | |||
225.12.b.i.199.2 | 4 | 15.2 | even | 4 | |||
225.12.b.i.199.3 | 4 | 15.8 | even | 4 | |||
240.12.a.m.1.1 | 2 | 4.3 | odd | 2 |