Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,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, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
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: | \(135.996742959\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −47.6933 | −1.05388 | −0.526942 | − | 0.849901i | \(-0.676661\pi\) | ||||
−0.526942 | + | 0.849901i | \(0.676661\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | 226.652 | 0.110670 | ||||||||
\(5\) | 10067.2 | 1.44070 | 0.720352 | − | 0.693609i | \(-0.243980\pi\) | ||||
0.720352 | + | 0.693609i | \(0.243980\pi\) | |||||||
\(6\) | −11589.5 | −0.608460 | ||||||||
\(7\) | 19897.8 | 0.447472 | 0.223736 | − | 0.974650i | \(-0.428175\pi\) | ||||
0.223736 | + | 0.974650i | \(0.428175\pi\) | |||||||
\(8\) | 86866.1 | 0.937250 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −480139. | −1.51833 | ||||||||
\(11\) | −256850. | −0.480860 | −0.240430 | − | 0.970666i | \(-0.577289\pi\) | ||||
−0.240430 | + | 0.970666i | \(0.577289\pi\) | |||||||
\(12\) | 55076.4 | 0.0638953 | ||||||||
\(13\) | 1.87281e6 | 1.39896 | 0.699478 | − | 0.714654i | \(-0.253416\pi\) | ||||
0.699478 | + | 0.714654i | \(0.253416\pi\) | |||||||
\(14\) | −948992. | −0.471583 | ||||||||
\(15\) | 2.44633e6 | 0.831790 | ||||||||
\(16\) | −4.60712e6 | −1.09842 | ||||||||
\(17\) | 3.91960e6 | 0.669534 | 0.334767 | − | 0.942301i | \(-0.391342\pi\) | ||||
0.334767 | + | 0.942301i | \(0.391342\pi\) | |||||||
\(18\) | −2.81624e6 | −0.351294 | ||||||||
\(19\) | −1.36502e7 | −1.26472 | −0.632361 | − | 0.774674i | \(-0.717914\pi\) | ||||
−0.632361 | + | 0.774674i | \(0.717914\pi\) | |||||||
\(20\) | 2.28175e6 | 0.159442 | ||||||||
\(21\) | 4.83516e6 | 0.258348 | ||||||||
\(22\) | 1.22500e7 | 0.506771 | ||||||||
\(23\) | 4.09884e7 | 1.32788 | 0.663939 | − | 0.747786i | \(-0.268883\pi\) | ||||
0.663939 | + | 0.747786i | \(0.268883\pi\) | |||||||
\(24\) | 2.11085e7 | 0.541122 | ||||||||
\(25\) | 5.25208e7 | 1.07563 | ||||||||
\(26\) | −8.93203e7 | −1.47434 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | 4.50987e6 | 0.0495217 | ||||||||
\(29\) | −2.21762e7 | −0.200769 | −0.100385 | − | 0.994949i | \(-0.532007\pi\) | ||||
−0.100385 | + | 0.994949i | \(0.532007\pi\) | |||||||
\(30\) | −1.16674e8 | −0.876610 | ||||||||
\(31\) | 2.03908e8 | 1.27922 | 0.639608 | − | 0.768701i | \(-0.279097\pi\) | ||||
0.639608 | + | 0.768701i | \(0.279097\pi\) | |||||||
\(32\) | 4.18268e7 | 0.220359 | ||||||||
\(33\) | −6.24144e7 | −0.277625 | ||||||||
\(34\) | −1.86939e8 | −0.705611 | ||||||||
\(35\) | 2.00315e8 | 0.644674 | ||||||||
\(36\) | 1.33836e7 | 0.0368900 | ||||||||
\(37\) | 7.60284e8 | 1.80246 | 0.901231 | − | 0.433339i | \(-0.142665\pi\) | ||||
0.901231 | + | 0.433339i | \(0.142665\pi\) | |||||||
\(38\) | 6.51025e8 | 1.33287 | ||||||||
\(39\) | 4.55092e8 | 0.807688 | ||||||||
\(40\) | 8.74500e8 | 1.35030 | ||||||||
\(41\) | −1.05040e9 | −1.41593 | −0.707966 | − | 0.706246i | \(-0.750387\pi\) | ||||
−0.707966 | + | 0.706246i | \(0.750387\pi\) | |||||||
\(42\) | −2.30605e8 | −0.272269 | ||||||||
\(43\) | 6.64995e8 | 0.689830 | 0.344915 | − | 0.938634i | \(-0.387908\pi\) | ||||
0.344915 | + | 0.938634i | \(0.387908\pi\) | |||||||
\(44\) | −5.82155e7 | −0.0532168 | ||||||||
\(45\) | 5.94459e8 | 0.480234 | ||||||||
\(46\) | −1.95487e9 | −1.39943 | ||||||||
\(47\) | 1.48540e9 | 0.944725 | 0.472363 | − | 0.881404i | \(-0.343401\pi\) | ||||
0.472363 | + | 0.881404i | \(0.343401\pi\) | |||||||
\(48\) | −1.11953e9 | −0.634174 | ||||||||
\(49\) | −1.58140e9 | −0.799769 | ||||||||
\(50\) | −2.50489e9 | −1.13358 | ||||||||
\(51\) | 9.52463e8 | 0.386556 | ||||||||
\(52\) | 4.24475e8 | 0.154822 | ||||||||
\(53\) | 9.91182e8 | 0.325564 | 0.162782 | − | 0.986662i | \(-0.447953\pi\) | ||||
0.162782 | + | 0.986662i | \(0.447953\pi\) | |||||||
\(54\) | −6.84347e8 | −0.202820 | ||||||||
\(55\) | −2.58576e9 | −0.692777 | ||||||||
\(56\) | 1.72844e9 | 0.419393 | ||||||||
\(57\) | −3.31701e9 | −0.730188 | ||||||||
\(58\) | 1.05765e9 | 0.211587 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | 5.54466e8 | 0.0920542 | ||||||||
\(61\) | 8.36215e9 | 1.26766 | 0.633832 | − | 0.773471i | \(-0.281481\pi\) | ||||
0.633832 | + | 0.773471i | \(0.281481\pi\) | |||||||
\(62\) | −9.72503e9 | −1.34814 | ||||||||
\(63\) | 1.17494e9 | 0.149157 | ||||||||
\(64\) | 7.44051e9 | 0.866190 | ||||||||
\(65\) | 1.88539e10 | 2.01548 | ||||||||
\(66\) | 2.97675e9 | 0.292584 | ||||||||
\(67\) | −1.21766e10 | −1.10183 | −0.550913 | − | 0.834563i | \(-0.685720\pi\) | ||||
−0.550913 | + | 0.834563i | \(0.685720\pi\) | |||||||
\(68\) | 8.88385e8 | 0.0740973 | ||||||||
\(69\) | 9.96019e9 | 0.766651 | ||||||||
\(70\) | −9.55371e9 | −0.679411 | ||||||||
\(71\) | 4.45588e9 | 0.293098 | 0.146549 | − | 0.989203i | \(-0.453183\pi\) | ||||
0.146549 | + | 0.989203i | \(0.453183\pi\) | |||||||
\(72\) | 5.12936e9 | 0.312417 | ||||||||
\(73\) | 6.92941e9 | 0.391219 | 0.195610 | − | 0.980682i | \(-0.437331\pi\) | ||||
0.195610 | + | 0.980682i | \(0.437331\pi\) | |||||||
\(74\) | −3.62604e10 | −1.89958 | ||||||||
\(75\) | 1.27626e10 | 0.621013 | ||||||||
\(76\) | −3.09385e9 | −0.139967 | ||||||||
\(77\) | −5.11074e9 | −0.215172 | ||||||||
\(78\) | −2.17048e10 | −0.851209 | ||||||||
\(79\) | −1.11775e9 | −0.0408693 | −0.0204346 | − | 0.999791i | \(-0.506505\pi\) | ||||
−0.0204346 | + | 0.999791i | \(0.506505\pi\) | |||||||
\(80\) | −4.63809e10 | −1.58250 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 5.00969e10 | 1.49223 | ||||||||
\(83\) | −6.93121e10 | −1.93143 | −0.965716 | − | 0.259600i | \(-0.916409\pi\) | ||||
−0.965716 | + | 0.259600i | \(0.916409\pi\) | |||||||
\(84\) | 1.09590e9 | 0.0285913 | ||||||||
\(85\) | 3.94595e10 | 0.964600 | ||||||||
\(86\) | −3.17158e10 | −0.727000 | ||||||||
\(87\) | −5.38881e9 | −0.115914 | ||||||||
\(88\) | −2.23115e10 | −0.450687 | ||||||||
\(89\) | −4.21667e10 | −0.800432 | −0.400216 | − | 0.916421i | \(-0.631065\pi\) | ||||
−0.400216 | + | 0.916421i | \(0.631065\pi\) | |||||||
\(90\) | −2.83517e10 | −0.506111 | ||||||||
\(91\) | 3.72647e10 | 0.625994 | ||||||||
\(92\) | 9.29011e9 | 0.146956 | ||||||||
\(93\) | 4.95495e10 | 0.738556 | ||||||||
\(94\) | −7.08437e10 | −0.995630 | ||||||||
\(95\) | −1.37420e11 | −1.82209 | ||||||||
\(96\) | 1.01639e10 | 0.127224 | ||||||||
\(97\) | −7.55087e10 | −0.892796 | −0.446398 | − | 0.894835i | \(-0.647293\pi\) | ||||
−0.446398 | + | 0.894835i | \(0.647293\pi\) | |||||||
\(98\) | 7.54224e10 | 0.842863 | ||||||||
\(99\) | −1.51667e10 | −0.160287 | ||||||||
\(100\) | 1.19039e10 | 0.119039 | ||||||||
\(101\) | −1.30355e11 | −1.23413 | −0.617065 | − | 0.786912i | \(-0.711679\pi\) | ||||
−0.617065 | + | 0.786912i | \(0.711679\pi\) | |||||||
\(102\) | −4.54261e10 | −0.407385 | ||||||||
\(103\) | −1.76189e11 | −1.49752 | −0.748762 | − | 0.662839i | \(-0.769351\pi\) | ||||
−0.748762 | + | 0.662839i | \(0.769351\pi\) | |||||||
\(104\) | 1.62683e11 | 1.31117 | ||||||||
\(105\) | 4.86767e10 | 0.372203 | ||||||||
\(106\) | −4.72728e10 | −0.343106 | ||||||||
\(107\) | 1.22677e11 | 0.845573 | 0.422787 | − | 0.906229i | \(-0.361052\pi\) | ||||
0.422787 | + | 0.906229i | \(0.361052\pi\) | |||||||
\(108\) | 3.25221e9 | 0.0212984 | ||||||||
\(109\) | 6.96262e10 | 0.433438 | 0.216719 | − | 0.976234i | \(-0.430464\pi\) | ||||
0.216719 | + | 0.976234i | \(0.430464\pi\) | |||||||
\(110\) | 1.23324e11 | 0.730106 | ||||||||
\(111\) | 1.84749e11 | 1.04065 | ||||||||
\(112\) | −9.16715e10 | −0.491513 | ||||||||
\(113\) | 8.22738e10 | 0.420078 | 0.210039 | − | 0.977693i | \(-0.432641\pi\) | ||||
0.210039 | + | 0.977693i | \(0.432641\pi\) | |||||||
\(114\) | 1.58199e11 | 0.769533 | ||||||||
\(115\) | 4.12640e11 | 1.91308 | ||||||||
\(116\) | −5.02627e9 | −0.0222191 | ||||||||
\(117\) | 1.10587e11 | 0.466319 | ||||||||
\(118\) | −3.40971e10 | −0.137204 | ||||||||
\(119\) | 7.79914e10 | 0.299598 | ||||||||
\(120\) | 2.12504e11 | 0.779596 | ||||||||
\(121\) | −2.19340e11 | −0.768773 | ||||||||
\(122\) | −3.98819e11 | −1.33597 | ||||||||
\(123\) | −2.55247e11 | −0.817489 | ||||||||
\(124\) | 4.62161e10 | 0.141571 | ||||||||
\(125\) | 3.71749e10 | 0.108954 | ||||||||
\(126\) | −5.60370e10 | −0.157194 | ||||||||
\(127\) | 3.47214e10 | 0.0932560 | 0.0466280 | − | 0.998912i | \(-0.485152\pi\) | ||||
0.0466280 | + | 0.998912i | \(0.485152\pi\) | |||||||
\(128\) | −4.40524e11 | −1.13322 | ||||||||
\(129\) | 1.61594e11 | 0.398273 | ||||||||
\(130\) | −8.99207e11 | −2.12408 | ||||||||
\(131\) | 3.74267e11 | 0.847598 | 0.423799 | − | 0.905756i | \(-0.360696\pi\) | ||||
0.423799 | + | 0.905756i | \(0.360696\pi\) | |||||||
\(132\) | −1.41464e10 | −0.0307247 | ||||||||
\(133\) | −2.71609e11 | −0.565928 | ||||||||
\(134\) | 5.80740e11 | 1.16120 | ||||||||
\(135\) | 1.44454e11 | 0.277263 | ||||||||
\(136\) | 3.40481e11 | 0.627521 | ||||||||
\(137\) | −8.59009e11 | −1.52067 | −0.760334 | − | 0.649532i | \(-0.774965\pi\) | ||||
−0.760334 | + | 0.649532i | \(0.774965\pi\) | |||||||
\(138\) | −4.75035e11 | −0.807961 | ||||||||
\(139\) | 6.85989e11 | 1.12134 | 0.560668 | − | 0.828040i | \(-0.310544\pi\) | ||||
0.560668 | + | 0.828040i | \(0.310544\pi\) | |||||||
\(140\) | 4.54019e10 | 0.0713460 | ||||||||
\(141\) | 3.60952e11 | 0.545437 | ||||||||
\(142\) | −2.12516e11 | −0.308891 | ||||||||
\(143\) | −4.81029e11 | −0.672703 | ||||||||
\(144\) | −2.72046e11 | −0.366141 | ||||||||
\(145\) | −2.23252e11 | −0.289249 | ||||||||
\(146\) | −3.30486e11 | −0.412300 | ||||||||
\(147\) | −3.84281e11 | −0.461747 | ||||||||
\(148\) | 1.72320e11 | 0.199478 | ||||||||
\(149\) | 1.04015e12 | 1.16030 | 0.580152 | − | 0.814508i | \(-0.302993\pi\) | ||||
0.580152 | + | 0.814508i | \(0.302993\pi\) | |||||||
\(150\) | −6.08688e11 | −0.654475 | ||||||||
\(151\) | 5.73329e11 | 0.594335 | 0.297167 | − | 0.954825i | \(-0.403958\pi\) | ||||
0.297167 | + | 0.954825i | \(0.403958\pi\) | |||||||
\(152\) | −1.18574e12 | −1.18536 | ||||||||
\(153\) | 2.31449e11 | 0.223178 | ||||||||
\(154\) | 2.43748e11 | 0.226766 | ||||||||
\(155\) | 2.05278e12 | 1.84297 | ||||||||
\(156\) | 1.03147e11 | 0.0893867 | ||||||||
\(157\) | −1.08917e10 | −0.00911269 | −0.00455635 | − | 0.999990i | \(-0.501450\pi\) | ||||
−0.00455635 | + | 0.999990i | \(0.501450\pi\) | |||||||
\(158\) | 5.33094e10 | 0.0430714 | ||||||||
\(159\) | 2.40857e11 | 0.187964 | ||||||||
\(160\) | 4.21080e11 | 0.317471 | ||||||||
\(161\) | 8.15580e11 | 0.594188 | ||||||||
\(162\) | −1.66296e11 | −0.117098 | ||||||||
\(163\) | 2.44839e12 | 1.66667 | 0.833335 | − | 0.552769i | \(-0.186429\pi\) | ||||
0.833335 | + | 0.552769i | \(0.186429\pi\) | |||||||
\(164\) | −2.38075e11 | −0.156701 | ||||||||
\(165\) | −6.28340e11 | −0.399975 | ||||||||
\(166\) | 3.30572e12 | 2.03550 | ||||||||
\(167\) | 2.37729e12 | 1.41625 | 0.708127 | − | 0.706085i | \(-0.249540\pi\) | ||||
0.708127 | + | 0.706085i | \(0.249540\pi\) | |||||||
\(168\) | 4.20012e11 | 0.242137 | ||||||||
\(169\) | 1.71524e12 | 0.957080 | ||||||||
\(170\) | −1.88195e12 | −1.01658 | ||||||||
\(171\) | −8.06032e11 | −0.421574 | ||||||||
\(172\) | 1.50722e11 | 0.0763434 | ||||||||
\(173\) | 7.48267e11 | 0.367116 | 0.183558 | − | 0.983009i | \(-0.441239\pi\) | ||||
0.183558 | + | 0.983009i | \(0.441239\pi\) | |||||||
\(174\) | 2.57010e11 | 0.122160 | ||||||||
\(175\) | 1.04505e12 | 0.481312 | ||||||||
\(176\) | 1.18334e12 | 0.528188 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | 2.01107e12 | 0.843562 | ||||||||
\(179\) | −1.89651e11 | −0.0771372 | −0.0385686 | − | 0.999256i | \(-0.512280\pi\) | ||||
−0.0385686 | + | 0.999256i | \(0.512280\pi\) | |||||||
\(180\) | 1.34735e11 | 0.0531475 | ||||||||
\(181\) | −1.13759e12 | −0.435266 | −0.217633 | − | 0.976031i | \(-0.569834\pi\) | ||||
−0.217633 | + | 0.976031i | \(0.569834\pi\) | |||||||
\(182\) | −1.77728e12 | −0.659724 | ||||||||
\(183\) | 2.03200e12 | 0.731886 | ||||||||
\(184\) | 3.56051e12 | 1.24455 | ||||||||
\(185\) | 7.65394e12 | 2.59681 | ||||||||
\(186\) | −2.36318e12 | −0.778352 | ||||||||
\(187\) | −1.00675e12 | −0.321953 | ||||||||
\(188\) | 3.36669e11 | 0.104553 | ||||||||
\(189\) | 2.85512e11 | 0.0861160 | ||||||||
\(190\) | 6.55401e12 | 1.92027 | ||||||||
\(191\) | 2.41641e12 | 0.687839 | 0.343920 | − | 0.938999i | \(-0.388245\pi\) | ||||
0.343920 | + | 0.938999i | \(0.388245\pi\) | |||||||
\(192\) | 1.80805e12 | 0.500095 | ||||||||
\(193\) | −1.61769e12 | −0.434841 | −0.217421 | − | 0.976078i | \(-0.569764\pi\) | ||||
−0.217421 | + | 0.976078i | \(0.569764\pi\) | |||||||
\(194\) | 3.60126e12 | 0.940903 | ||||||||
\(195\) | 4.58151e12 | 1.16364 | ||||||||
\(196\) | −3.58428e11 | −0.0885103 | ||||||||
\(197\) | 3.30183e12 | 0.792850 | 0.396425 | − | 0.918067i | \(-0.370251\pi\) | ||||
0.396425 | + | 0.918067i | \(0.370251\pi\) | |||||||
\(198\) | 7.23351e11 | 0.168924 | ||||||||
\(199\) | −6.57007e12 | −1.49238 | −0.746188 | − | 0.665736i | \(-0.768118\pi\) | ||||
−0.746188 | + | 0.665736i | \(0.768118\pi\) | |||||||
\(200\) | 4.56228e12 | 1.00813 | ||||||||
\(201\) | −2.95890e12 | −0.636139 | ||||||||
\(202\) | 6.21707e12 | 1.30063 | ||||||||
\(203\) | −4.41257e11 | −0.0898386 | ||||||||
\(204\) | 2.15878e11 | 0.0427801 | ||||||||
\(205\) | −1.05746e13 | −2.03994 | ||||||||
\(206\) | 8.40303e12 | 1.57822 | ||||||||
\(207\) | 2.42033e12 | 0.442626 | ||||||||
\(208\) | −8.62823e12 | −1.53664 | ||||||||
\(209\) | 3.50606e12 | 0.608155 | ||||||||
\(210\) | −2.32155e12 | −0.392258 | ||||||||
\(211\) | 9.22870e12 | 1.51910 | 0.759551 | − | 0.650447i | \(-0.225419\pi\) | ||||
0.759551 | + | 0.650447i | \(0.225419\pi\) | |||||||
\(212\) | 2.24653e11 | 0.0360301 | ||||||||
\(213\) | 1.08278e12 | 0.169220 | ||||||||
\(214\) | −5.85086e12 | −0.891136 | ||||||||
\(215\) | 6.69465e12 | 0.993840 | ||||||||
\(216\) | 1.24643e12 | 0.180374 | ||||||||
\(217\) | 4.05731e12 | 0.572413 | ||||||||
\(218\) | −3.32070e12 | −0.456793 | ||||||||
\(219\) | 1.68385e12 | 0.225871 | ||||||||
\(220\) | −5.86068e11 | −0.0766696 | ||||||||
\(221\) | 7.34065e12 | 0.936649 | ||||||||
\(222\) | −8.81129e12 | −1.09673 | ||||||||
\(223\) | −4.71766e12 | −0.572862 | −0.286431 | − | 0.958101i | \(-0.592469\pi\) | ||||
−0.286431 | + | 0.958101i | \(0.592469\pi\) | |||||||
\(224\) | 8.32261e11 | 0.0986042 | ||||||||
\(225\) | 3.10130e12 | 0.358542 | ||||||||
\(226\) | −3.92391e12 | −0.442713 | ||||||||
\(227\) | 1.08803e13 | 1.19812 | 0.599059 | − | 0.800705i | \(-0.295542\pi\) | ||||
0.599059 | + | 0.800705i | \(0.295542\pi\) | |||||||
\(228\) | −7.51806e11 | −0.0808098 | ||||||||
\(229\) | −6.39892e12 | −0.671446 | −0.335723 | − | 0.941961i | \(-0.608981\pi\) | ||||
−0.335723 | + | 0.941961i | \(0.608981\pi\) | |||||||
\(230\) | −1.96802e13 | −2.01616 | ||||||||
\(231\) | −1.24191e12 | −0.124229 | ||||||||
\(232\) | −1.92636e12 | −0.188171 | ||||||||
\(233\) | 6.18274e12 | 0.589826 | 0.294913 | − | 0.955524i | \(-0.404709\pi\) | ||||
0.294913 | + | 0.955524i | \(0.404709\pi\) | |||||||
\(234\) | −5.27427e12 | −0.491446 | ||||||||
\(235\) | 1.49539e13 | 1.36107 | ||||||||
\(236\) | 1.62039e11 | 0.0144080 | ||||||||
\(237\) | −2.71614e11 | −0.0235959 | ||||||||
\(238\) | −3.71967e12 | −0.315741 | ||||||||
\(239\) | 7.82182e12 | 0.648813 | 0.324406 | − | 0.945918i | \(-0.394835\pi\) | ||||
0.324406 | + | 0.945918i | \(0.394835\pi\) | |||||||
\(240\) | −1.12705e13 | −0.913657 | ||||||||
\(241\) | −2.29486e13 | −1.81829 | −0.909145 | − | 0.416480i | \(-0.863264\pi\) | ||||
−0.909145 | + | 0.416480i | \(0.863264\pi\) | |||||||
\(242\) | 1.04610e13 | 0.810197 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | 1.89530e12 | 0.140292 | ||||||||
\(245\) | −1.59203e13 | −1.15223 | ||||||||
\(246\) | 1.21736e13 | 0.861538 | ||||||||
\(247\) | −2.55642e13 | −1.76929 | ||||||||
\(248\) | 1.77127e13 | 1.19895 | ||||||||
\(249\) | −1.68428e13 | −1.11511 | ||||||||
\(250\) | −1.77299e12 | −0.114825 | ||||||||
\(251\) | 1.14535e13 | 0.725660 | 0.362830 | − | 0.931855i | \(-0.381810\pi\) | ||||
0.362830 | + | 0.931855i | \(0.381810\pi\) | |||||||
\(252\) | 2.66304e11 | 0.0165072 | ||||||||
\(253\) | −1.05279e13 | −0.638524 | ||||||||
\(254\) | −1.65598e12 | −0.0982810 | ||||||||
\(255\) | 9.58866e12 | 0.556912 | ||||||||
\(256\) | 5.77188e12 | 0.328093 | ||||||||
\(257\) | 1.26561e13 | 0.704155 | 0.352077 | − | 0.935971i | \(-0.385475\pi\) | ||||
0.352077 | + | 0.935971i | \(0.385475\pi\) | |||||||
\(258\) | −7.70694e12 | −0.419734 | ||||||||
\(259\) | 1.51280e13 | 0.806551 | ||||||||
\(260\) | 4.27328e12 | 0.223053 | ||||||||
\(261\) | −1.30948e12 | −0.0669231 | ||||||||
\(262\) | −1.78501e13 | −0.893269 | ||||||||
\(263\) | −3.37616e13 | −1.65450 | −0.827248 | − | 0.561837i | \(-0.810095\pi\) | ||||
−0.827248 | + | 0.561837i | \(0.810095\pi\) | |||||||
\(264\) | −5.42170e12 | −0.260204 | ||||||||
\(265\) | 9.97845e12 | 0.469041 | ||||||||
\(266\) | 1.29540e13 | 0.596422 | ||||||||
\(267\) | −1.02465e13 | −0.462130 | ||||||||
\(268\) | −2.75984e12 | −0.121939 | ||||||||
\(269\) | 2.88764e13 | 1.24999 | 0.624993 | − | 0.780630i | \(-0.285102\pi\) | ||||
0.624993 | + | 0.780630i | \(0.285102\pi\) | |||||||
\(270\) | −6.88947e12 | −0.292203 | ||||||||
\(271\) | 6.85896e12 | 0.285054 | 0.142527 | − | 0.989791i | \(-0.454477\pi\) | ||||
0.142527 | + | 0.989791i | \(0.454477\pi\) | |||||||
\(272\) | −1.80581e13 | −0.735431 | ||||||||
\(273\) | 9.05532e12 | 0.361418 | ||||||||
\(274\) | 4.09690e13 | 1.60261 | ||||||||
\(275\) | −1.34899e13 | −0.517226 | ||||||||
\(276\) | 2.25750e12 | 0.0848452 | ||||||||
\(277\) | −8.47203e11 | −0.0312139 | −0.0156070 | − | 0.999878i | \(-0.504968\pi\) | ||||
−0.0156070 | + | 0.999878i | \(0.504968\pi\) | |||||||
\(278\) | −3.27171e13 | −1.18176 | ||||||||
\(279\) | 1.20405e13 | 0.426406 | ||||||||
\(280\) | 1.74006e13 | 0.604221 | ||||||||
\(281\) | −3.05709e13 | −1.04093 | −0.520467 | − | 0.853882i | \(-0.674242\pi\) | ||||
−0.520467 | + | 0.853882i | \(0.674242\pi\) | |||||||
\(282\) | −1.72150e13 | −0.574827 | ||||||||
\(283\) | 7.56230e12 | 0.247644 | 0.123822 | − | 0.992304i | \(-0.460485\pi\) | ||||
0.123822 | + | 0.992304i | \(0.460485\pi\) | |||||||
\(284\) | 1.00993e12 | 0.0324371 | ||||||||
\(285\) | −3.33930e13 | −1.05198 | ||||||||
\(286\) | 2.29419e13 | 0.708950 | ||||||||
\(287\) | −2.09006e13 | −0.633590 | ||||||||
\(288\) | 2.46983e12 | 0.0734528 | ||||||||
\(289\) | −1.89086e13 | −0.551724 | ||||||||
\(290\) | 1.06476e13 | 0.304835 | ||||||||
\(291\) | −1.83486e13 | −0.515456 | ||||||||
\(292\) | 1.57056e12 | 0.0432962 | ||||||||
\(293\) | 6.01099e13 | 1.62620 | 0.813101 | − | 0.582123i | \(-0.197778\pi\) | ||||
0.813101 | + | 0.582123i | \(0.197778\pi\) | |||||||
\(294\) | 1.83276e13 | 0.486627 | ||||||||
\(295\) | 7.19730e12 | 0.187564 | ||||||||
\(296\) | 6.60429e13 | 1.68936 | ||||||||
\(297\) | −3.68551e12 | −0.0925416 | ||||||||
\(298\) | −4.96082e13 | −1.22283 | ||||||||
\(299\) | 7.67634e13 | 1.85764 | ||||||||
\(300\) | 2.89266e12 | 0.0687274 | ||||||||
\(301\) | 1.32319e13 | 0.308679 | ||||||||
\(302\) | −2.73440e13 | −0.626359 | ||||||||
\(303\) | −3.16763e13 | −0.712526 | ||||||||
\(304\) | 6.28882e13 | 1.38920 | ||||||||
\(305\) | 8.41836e13 | 1.82633 | ||||||||
\(306\) | −1.10385e13 | −0.235204 | ||||||||
\(307\) | −4.07056e13 | −0.851910 | −0.425955 | − | 0.904744i | \(-0.640062\pi\) | ||||
−0.425955 | + | 0.904744i | \(0.640062\pi\) | |||||||
\(308\) | −1.15836e12 | −0.0238130 | ||||||||
\(309\) | −4.28139e13 | −0.864596 | ||||||||
\(310\) | −9.79040e13 | −1.94228 | ||||||||
\(311\) | −1.69524e13 | −0.330408 | −0.165204 | − | 0.986259i | \(-0.552828\pi\) | ||||
−0.165204 | + | 0.986259i | \(0.552828\pi\) | |||||||
\(312\) | 3.95321e13 | 0.757006 | ||||||||
\(313\) | −4.57468e13 | −0.860730 | −0.430365 | − | 0.902655i | \(-0.641615\pi\) | ||||
−0.430365 | + | 0.902655i | \(0.641615\pi\) | |||||||
\(314\) | 5.19460e11 | 0.00960372 | ||||||||
\(315\) | 1.18284e13 | 0.214891 | ||||||||
\(316\) | −2.53341e11 | −0.00452300 | ||||||||
\(317\) | −9.76435e13 | −1.71324 | −0.856619 | − | 0.515950i | \(-0.827439\pi\) | ||||
−0.856619 | + | 0.515950i | \(0.827439\pi\) | |||||||
\(318\) | −1.14873e13 | −0.198093 | ||||||||
\(319\) | 5.69594e12 | 0.0965420 | ||||||||
\(320\) | 7.49053e13 | 1.24792 | ||||||||
\(321\) | 2.98104e13 | 0.488192 | ||||||||
\(322\) | −3.88977e13 | −0.626205 | ||||||||
\(323\) | −5.35035e13 | −0.846775 | ||||||||
\(324\) | 7.90286e11 | 0.0122967 | ||||||||
\(325\) | 9.83612e13 | 1.50475 | ||||||||
\(326\) | −1.16772e14 | −1.75648 | ||||||||
\(327\) | 1.69192e13 | 0.250246 | ||||||||
\(328\) | −9.12440e13 | −1.32708 | ||||||||
\(329\) | 2.95562e13 | 0.422738 | ||||||||
\(330\) | 2.99676e13 | 0.421527 | ||||||||
\(331\) | 7.91062e13 | 1.09435 | 0.547176 | − | 0.837018i | \(-0.315703\pi\) | ||||
0.547176 | + | 0.837018i | \(0.315703\pi\) | |||||||
\(332\) | −1.57097e13 | −0.213751 | ||||||||
\(333\) | 4.48940e13 | 0.600821 | ||||||||
\(334\) | −1.13381e14 | −1.49257 | ||||||||
\(335\) | −1.22584e14 | −1.58740 | ||||||||
\(336\) | −2.22762e13 | −0.283775 | ||||||||
\(337\) | −6.52137e13 | −0.817287 | −0.408643 | − | 0.912694i | \(-0.633998\pi\) | ||||
−0.408643 | + | 0.912694i | \(0.633998\pi\) | |||||||
\(338\) | −8.18055e13 | −1.00865 | ||||||||
\(339\) | 1.99925e13 | 0.242532 | ||||||||
\(340\) | 8.94357e12 | 0.106752 | ||||||||
\(341\) | −5.23736e13 | −0.615125 | ||||||||
\(342\) | 3.84424e13 | 0.444290 | ||||||||
\(343\) | −7.08109e13 | −0.805346 | ||||||||
\(344\) | 5.77655e13 | 0.646543 | ||||||||
\(345\) | 1.00271e14 | 1.10452 | ||||||||
\(346\) | −3.56873e13 | −0.386897 | ||||||||
\(347\) | 1.40426e14 | 1.49843 | 0.749215 | − | 0.662327i | \(-0.230431\pi\) | ||||
0.749215 | + | 0.662327i | \(0.230431\pi\) | |||||||
\(348\) | −1.22138e12 | −0.0128282 | ||||||||
\(349\) | −9.96355e13 | −1.03009 | −0.515044 | − | 0.857164i | \(-0.672224\pi\) | ||||
−0.515044 | + | 0.857164i | \(0.672224\pi\) | |||||||
\(350\) | −4.98418e13 | −0.507247 | ||||||||
\(351\) | 2.68727e13 | 0.269229 | ||||||||
\(352\) | −1.07432e13 | −0.105962 | ||||||||
\(353\) | −1.16903e13 | −0.113518 | −0.0567591 | − | 0.998388i | \(-0.518077\pi\) | ||||
−0.0567591 | + | 0.998388i | \(0.518077\pi\) | |||||||
\(354\) | −8.28560e12 | −0.0792147 | ||||||||
\(355\) | 4.48583e13 | 0.422267 | ||||||||
\(356\) | −9.55716e12 | −0.0885837 | ||||||||
\(357\) | 1.89519e13 | 0.172973 | ||||||||
\(358\) | 9.04509e12 | 0.0812936 | ||||||||
\(359\) | 1.09916e14 | 0.972840 | 0.486420 | − | 0.873725i | \(-0.338302\pi\) | ||||
0.486420 | + | 0.873725i | \(0.338302\pi\) | |||||||
\(360\) | 5.16384e13 | 0.450100 | ||||||||
\(361\) | 6.98385e13 | 0.599522 | ||||||||
\(362\) | 5.42555e13 | 0.458719 | ||||||||
\(363\) | −5.32996e13 | −0.443851 | ||||||||
\(364\) | 8.44612e12 | 0.0692787 | ||||||||
\(365\) | 6.97599e13 | 0.563631 | ||||||||
\(366\) | −9.69129e13 | −0.771322 | ||||||||
\(367\) | 1.86818e14 | 1.46472 | 0.732361 | − | 0.680917i | \(-0.238418\pi\) | ||||
0.732361 | + | 0.680917i | \(0.238418\pi\) | |||||||
\(368\) | −1.88839e14 | −1.45857 | ||||||||
\(369\) | −6.20249e13 | −0.471978 | ||||||||
\(370\) | −3.65042e14 | −2.73674 | ||||||||
\(371\) | 1.97223e13 | 0.145681 | ||||||||
\(372\) | 1.12305e13 | 0.0817359 | ||||||||
\(373\) | −1.50943e14 | −1.08247 | −0.541233 | − | 0.840873i | \(-0.682042\pi\) | ||||
−0.541233 | + | 0.840873i | \(0.682042\pi\) | |||||||
\(374\) | 4.80151e13 | 0.339300 | ||||||||
\(375\) | 9.03350e12 | 0.0629048 | ||||||||
\(376\) | 1.29031e14 | 0.885444 | ||||||||
\(377\) | −4.15316e13 | −0.280868 | ||||||||
\(378\) | −1.36170e13 | −0.0907562 | ||||||||
\(379\) | 6.75399e13 | 0.443654 | 0.221827 | − | 0.975086i | \(-0.428798\pi\) | ||||
0.221827 | + | 0.975086i | \(0.428798\pi\) | |||||||
\(380\) | −3.11465e13 | −0.201650 | ||||||||
\(381\) | 8.43730e12 | 0.0538414 | ||||||||
\(382\) | −1.15247e14 | −0.724902 | ||||||||
\(383\) | 1.30035e14 | 0.806245 | 0.403123 | − | 0.915146i | \(-0.367925\pi\) | ||||
0.403123 | + | 0.915146i | \(0.367925\pi\) | |||||||
\(384\) | −1.07047e14 | −0.654266 | ||||||||
\(385\) | −5.14509e13 | −0.309998 | ||||||||
\(386\) | 7.71531e13 | 0.458272 | ||||||||
\(387\) | 3.92673e13 | 0.229943 | ||||||||
\(388\) | −1.71142e13 | −0.0988056 | ||||||||
\(389\) | 2.60472e13 | 0.148265 | 0.0741325 | − | 0.997248i | \(-0.476381\pi\) | ||||
0.0741325 | + | 0.997248i | \(0.476381\pi\) | |||||||
\(390\) | −2.18507e14 | −1.22634 | ||||||||
\(391\) | 1.60658e14 | 0.889060 | ||||||||
\(392\) | −1.37370e14 | −0.749583 | ||||||||
\(393\) | 9.09470e13 | 0.489361 | ||||||||
\(394\) | −1.57475e14 | −0.835571 | ||||||||
\(395\) | −1.12527e13 | −0.0588805 | ||||||||
\(396\) | −3.43756e12 | −0.0177389 | ||||||||
\(397\) | 3.22209e14 | 1.63980 | 0.819899 | − | 0.572508i | \(-0.194029\pi\) | ||||
0.819899 | + | 0.572508i | \(0.194029\pi\) | |||||||
\(398\) | 3.13348e14 | 1.57279 | ||||||||
\(399\) | −6.60011e13 | −0.326738 | ||||||||
\(400\) | −2.41969e14 | −1.18149 | ||||||||
\(401\) | 3.46864e14 | 1.67057 | 0.835286 | − | 0.549815i | \(-0.185302\pi\) | ||||
0.835286 | + | 0.549815i | \(0.185302\pi\) | |||||||
\(402\) | 1.41120e14 | 0.670417 | ||||||||
\(403\) | 3.81879e14 | 1.78957 | ||||||||
\(404\) | −2.95453e13 | −0.136581 | ||||||||
\(405\) | 3.51022e13 | 0.160078 | ||||||||
\(406\) | 2.10450e13 | 0.0946794 | ||||||||
\(407\) | −1.95278e14 | −0.866733 | ||||||||
\(408\) | 8.27368e13 | 0.362299 | ||||||||
\(409\) | −1.91290e14 | −0.826447 | −0.413224 | − | 0.910630i | \(-0.635597\pi\) | ||||
−0.413224 | + | 0.910630i | \(0.635597\pi\) | |||||||
\(410\) | 5.04337e14 | 2.14986 | ||||||||
\(411\) | −2.08739e14 | −0.877959 | ||||||||
\(412\) | −3.99336e13 | −0.165731 | ||||||||
\(413\) | 1.42254e13 | 0.0582559 | ||||||||
\(414\) | −1.15433e14 | −0.466476 | ||||||||
\(415\) | −6.97780e14 | −2.78262 | ||||||||
\(416\) | 7.83335e13 | 0.308272 | ||||||||
\(417\) | 1.66695e14 | 0.647404 | ||||||||
\(418\) | −1.67215e14 | −0.640924 | ||||||||
\(419\) | 2.19873e14 | 0.831755 | 0.415877 | − | 0.909421i | \(-0.363475\pi\) | ||||
0.415877 | + | 0.909421i | \(0.363475\pi\) | |||||||
\(420\) | 1.10327e13 | 0.0411916 | ||||||||
\(421\) | −1.43384e14 | −0.528384 | −0.264192 | − | 0.964470i | \(-0.585105\pi\) | ||||
−0.264192 | + | 0.964470i | \(0.585105\pi\) | |||||||
\(422\) | −4.40147e14 | −1.60096 | ||||||||
\(423\) | 8.77115e13 | 0.314908 | ||||||||
\(424\) | 8.61002e13 | 0.305135 | ||||||||
\(425\) | 2.05861e14 | 0.720168 | ||||||||
\(426\) | −5.16413e13 | −0.178338 | ||||||||
\(427\) | 1.66388e14 | 0.567244 | ||||||||
\(428\) | 2.78049e13 | 0.0935795 | ||||||||
\(429\) | −1.16890e14 | −0.388385 | ||||||||
\(430\) | −3.19290e14 | −1.04739 | ||||||||
\(431\) | 5.57672e13 | 0.180615 | 0.0903076 | − | 0.995914i | \(-0.471215\pi\) | ||||
0.0903076 | + | 0.995914i | \(0.471215\pi\) | |||||||
\(432\) | −6.61071e13 | −0.211391 | ||||||||
\(433\) | −3.40207e14 | −1.07414 | −0.537069 | − | 0.843538i | \(-0.680468\pi\) | ||||
−0.537069 | + | 0.843538i | \(0.680468\pi\) | |||||||
\(434\) | −1.93507e14 | −0.603257 | ||||||||
\(435\) | −5.42503e13 | −0.166998 | ||||||||
\(436\) | 1.57809e13 | 0.0479685 | ||||||||
\(437\) | −5.59502e14 | −1.67940 | ||||||||
\(438\) | −8.03082e13 | −0.238041 | ||||||||
\(439\) | 3.95069e14 | 1.15643 | 0.578213 | − | 0.815886i | \(-0.303750\pi\) | ||||
0.578213 | + | 0.815886i | \(0.303750\pi\) | |||||||
\(440\) | −2.24615e14 | −0.649306 | ||||||||
\(441\) | −9.33804e13 | −0.266590 | ||||||||
\(442\) | −3.50100e14 | −0.987119 | ||||||||
\(443\) | −6.07338e14 | −1.69126 | −0.845629 | − | 0.533771i | \(-0.820774\pi\) | ||||
−0.845629 | + | 0.533771i | \(0.820774\pi\) | |||||||
\(444\) | 4.18737e13 | 0.115169 | ||||||||
\(445\) | −4.24501e14 | −1.15318 | ||||||||
\(446\) | 2.25001e14 | 0.603730 | ||||||||
\(447\) | 2.52757e14 | 0.669902 | ||||||||
\(448\) | 1.48050e14 | 0.387596 | ||||||||
\(449\) | 6.28780e14 | 1.62609 | 0.813043 | − | 0.582203i | \(-0.197809\pi\) | ||||
0.813043 | + | 0.582203i | \(0.197809\pi\) | |||||||
\(450\) | −1.47911e14 | −0.377861 | ||||||||
\(451\) | 2.69794e14 | 0.680866 | ||||||||
\(452\) | 1.86475e13 | 0.0464900 | ||||||||
\(453\) | 1.39319e14 | 0.343139 | ||||||||
\(454\) | −5.18918e14 | −1.26268 | ||||||||
\(455\) | 3.75152e14 | 0.901871 | ||||||||
\(456\) | −2.88135e14 | −0.684368 | ||||||||
\(457\) | 8.41019e13 | 0.197363 | 0.0986817 | − | 0.995119i | \(-0.468537\pi\) | ||||
0.0986817 | + | 0.995119i | \(0.468537\pi\) | |||||||
\(458\) | 3.05185e14 | 0.707626 | ||||||||
\(459\) | 5.62420e13 | 0.128852 | ||||||||
\(460\) | 9.35256e13 | 0.211720 | ||||||||
\(461\) | −5.29887e14 | −1.18530 | −0.592650 | − | 0.805460i | \(-0.701918\pi\) | ||||
−0.592650 | + | 0.805460i | \(0.701918\pi\) | |||||||
\(462\) | 5.92308e13 | 0.130923 | ||||||||
\(463\) | −5.25570e14 | −1.14798 | −0.573991 | − | 0.818862i | \(-0.694606\pi\) | ||||
−0.573991 | + | 0.818862i | \(0.694606\pi\) | |||||||
\(464\) | 1.02168e14 | 0.220529 | ||||||||
\(465\) | 4.98826e14 | 1.06404 | ||||||||
\(466\) | −2.94876e14 | −0.621607 | ||||||||
\(467\) | −7.96126e13 | −0.165859 | −0.0829295 | − | 0.996555i | \(-0.526428\pi\) | ||||
−0.0829295 | + | 0.996555i | \(0.526428\pi\) | |||||||
\(468\) | 2.50648e13 | 0.0516075 | ||||||||
\(469\) | −2.42287e14 | −0.493036 | ||||||||
\(470\) | −7.13199e14 | −1.43441 | ||||||||
\(471\) | −2.64668e12 | −0.00526122 | ||||||||
\(472\) | 6.21027e13 | 0.122020 | ||||||||
\(473\) | −1.70804e14 | −0.331712 | ||||||||
\(474\) | 1.29542e13 | 0.0248673 | ||||||||
\(475\) | −7.16921e14 | −1.36037 | ||||||||
\(476\) | 1.76769e13 | 0.0331565 | ||||||||
\(477\) | 5.85283e13 | 0.108521 | ||||||||
\(478\) | −3.73048e14 | −0.683773 | ||||||||
\(479\) | 3.82897e14 | 0.693803 | 0.346902 | − | 0.937902i | \(-0.387234\pi\) | ||||
0.346902 | + | 0.937902i | \(0.387234\pi\) | |||||||
\(480\) | 1.02322e14 | 0.183292 | ||||||||
\(481\) | 1.42386e15 | 2.52157 | ||||||||
\(482\) | 1.09450e15 | 1.91627 | ||||||||
\(483\) | 1.98186e14 | 0.343055 | ||||||||
\(484\) | −4.97138e13 | −0.0850801 | ||||||||
\(485\) | −7.60162e14 | −1.28625 | ||||||||
\(486\) | −4.04100e13 | −0.0676066 | ||||||||
\(487\) | 1.08358e15 | 1.79246 | 0.896231 | − | 0.443587i | \(-0.146294\pi\) | ||||
0.896231 | + | 0.443587i | \(0.146294\pi\) | |||||||
\(488\) | 7.26388e14 | 1.18812 | ||||||||
\(489\) | 5.94960e14 | 0.962252 | ||||||||
\(490\) | 7.59294e14 | 1.21432 | ||||||||
\(491\) | −6.31358e14 | −0.998453 | −0.499226 | − | 0.866472i | \(-0.666382\pi\) | ||||
−0.499226 | + | 0.866472i | \(0.666382\pi\) | |||||||
\(492\) | −5.78521e13 | −0.0904714 | ||||||||
\(493\) | −8.69217e13 | −0.134422 | ||||||||
\(494\) | 1.21924e15 | 1.86463 | ||||||||
\(495\) | −1.52687e14 | −0.230926 | ||||||||
\(496\) | −9.39426e14 | −1.40512 | ||||||||
\(497\) | 8.86622e13 | 0.131153 | ||||||||
\(498\) | 8.03291e14 | 1.17520 | ||||||||
\(499\) | 2.71326e14 | 0.392589 | 0.196295 | − | 0.980545i | \(-0.437109\pi\) | ||||
0.196295 | + | 0.980545i | \(0.437109\pi\) | |||||||
\(500\) | 8.42576e12 | 0.0120580 | ||||||||
\(501\) | 5.77681e14 | 0.817675 | ||||||||
\(502\) | −5.46256e14 | −0.764761 | ||||||||
\(503\) | 2.14150e14 | 0.296547 | 0.148274 | − | 0.988946i | \(-0.452628\pi\) | ||||
0.148274 | + | 0.988946i | \(0.452628\pi\) | |||||||
\(504\) | 1.02063e14 | 0.139798 | ||||||||
\(505\) | −1.31232e15 | −1.77802 | ||||||||
\(506\) | 5.02109e14 | 0.672930 | ||||||||
\(507\) | 4.16803e14 | 0.552570 | ||||||||
\(508\) | 7.86968e12 | 0.0103206 | ||||||||
\(509\) | −7.12359e13 | −0.0924168 | −0.0462084 | − | 0.998932i | \(-0.514714\pi\) | ||||
−0.0462084 | + | 0.998932i | \(0.514714\pi\) | |||||||
\(510\) | −4.57315e14 | −0.586920 | ||||||||
\(511\) | 1.37880e14 | 0.175060 | ||||||||
\(512\) | 6.26913e14 | 0.787450 | ||||||||
\(513\) | −1.95866e14 | −0.243396 | ||||||||
\(514\) | −6.03612e14 | −0.742097 | ||||||||
\(515\) | −1.77373e15 | −2.15749 | ||||||||
\(516\) | 3.66255e13 | 0.0440769 | ||||||||
\(517\) | −3.81525e14 | −0.454281 | ||||||||
\(518\) | −7.21503e14 | −0.850011 | ||||||||
\(519\) | 1.81829e14 | 0.211954 | ||||||||
\(520\) | 1.63777e15 | 1.88901 | ||||||||
\(521\) | 5.83431e14 | 0.665859 | 0.332929 | − | 0.942952i | \(-0.391963\pi\) | ||||
0.332929 | + | 0.942952i | \(0.391963\pi\) | |||||||
\(522\) | 6.24534e13 | 0.0705291 | ||||||||
\(523\) | −8.94909e14 | −1.00005 | −0.500023 | − | 0.866012i | \(-0.666675\pi\) | ||||
−0.500023 | + | 0.866012i | \(0.666675\pi\) | |||||||
\(524\) | 8.48284e13 | 0.0938036 | ||||||||
\(525\) | 2.53947e14 | 0.277886 | ||||||||
\(526\) | 1.61020e15 | 1.74365 | ||||||||
\(527\) | 7.99236e14 | 0.856479 | ||||||||
\(528\) | 2.87551e14 | 0.304949 | ||||||||
\(529\) | 7.27243e14 | 0.763262 | ||||||||
\(530\) | −4.75905e14 | −0.494314 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | −6.15608e13 | −0.0626311 | ||||||||
\(533\) | −1.96719e15 | −1.98083 | ||||||||
\(534\) | 4.88690e14 | 0.487031 | ||||||||
\(535\) | 1.23501e15 | 1.21822 | ||||||||
\(536\) | −1.05773e15 | −1.03269 | ||||||||
\(537\) | −4.60852e13 | −0.0445352 | ||||||||
\(538\) | −1.37721e15 | −1.31734 | ||||||||
\(539\) | 4.06183e14 | 0.384577 | ||||||||
\(540\) | 3.27407e13 | 0.0306847 | ||||||||
\(541\) | 1.14946e15 | 1.06637 | 0.533186 | − | 0.845998i | \(-0.320994\pi\) | ||||
0.533186 | + | 0.845998i | \(0.320994\pi\) | |||||||
\(542\) | −3.27127e14 | −0.300414 | ||||||||
\(543\) | −2.76435e14 | −0.251301 | ||||||||
\(544\) | 1.63944e14 | 0.147538 | ||||||||
\(545\) | 7.00942e14 | 0.624456 | ||||||||
\(546\) | −4.31878e14 | −0.380892 | ||||||||
\(547\) | 1.43162e15 | 1.24996 | 0.624982 | − | 0.780639i | \(-0.285106\pi\) | ||||
0.624982 | + | 0.780639i | \(0.285106\pi\) | |||||||
\(548\) | −1.94696e14 | −0.168292 | ||||||||
\(549\) | 4.93777e14 | 0.422554 | ||||||||
\(550\) | 6.43380e14 | 0.545096 | ||||||||
\(551\) | 3.02710e14 | 0.253917 | ||||||||
\(552\) | 8.65203e14 | 0.718544 | ||||||||
\(553\) | −2.22408e13 | −0.0182879 | ||||||||
\(554\) | 4.04059e13 | 0.0328958 | ||||||||
\(555\) | 1.85991e15 | 1.49927 | ||||||||
\(556\) | 1.55481e14 | 0.124098 | ||||||||
\(557\) | 1.90773e15 | 1.50770 | 0.753848 | − | 0.657049i | \(-0.228196\pi\) | ||||
0.753848 | + | 0.657049i | \(0.228196\pi\) | |||||||
\(558\) | −5.74253e14 | −0.449382 | ||||||||
\(559\) | 1.24541e15 | 0.965042 | ||||||||
\(560\) | −9.22877e14 | −0.708124 | ||||||||
\(561\) | −2.44640e14 | −0.185879 | ||||||||
\(562\) | 1.45803e15 | 1.09702 | ||||||||
\(563\) | −1.75838e15 | −1.31014 | −0.655070 | − | 0.755568i | \(-0.727361\pi\) | ||||
−0.655070 | + | 0.755568i | \(0.727361\pi\) | |||||||
\(564\) | 8.18106e13 | 0.0603635 | ||||||||
\(565\) | 8.28269e14 | 0.605208 | ||||||||
\(566\) | −3.60671e14 | −0.260988 | ||||||||
\(567\) | 6.93793e13 | 0.0497191 | ||||||||
\(568\) | 3.87065e14 | 0.274706 | ||||||||
\(569\) | 1.20198e15 | 0.844853 | 0.422426 | − | 0.906397i | \(-0.361178\pi\) | ||||
0.422426 | + | 0.906397i | \(0.361178\pi\) | |||||||
\(570\) | 1.59262e15 | 1.10867 | ||||||||
\(571\) | −2.41179e15 | −1.66280 | −0.831402 | − | 0.555672i | \(-0.812461\pi\) | ||||
−0.831402 | + | 0.555672i | \(0.812461\pi\) | |||||||
\(572\) | −1.09026e14 | −0.0744480 | ||||||||
\(573\) | 5.87187e14 | 0.397124 | ||||||||
\(574\) | 9.96819e14 | 0.667730 | ||||||||
\(575\) | 2.15275e15 | 1.42830 | ||||||||
\(576\) | 4.39355e14 | 0.288730 | ||||||||
\(577\) | 1.37637e15 | 0.895915 | 0.447957 | − | 0.894055i | \(-0.352152\pi\) | ||||
0.447957 | + | 0.894055i | \(0.352152\pi\) | |||||||
\(578\) | 9.01815e14 | 0.581453 | ||||||||
\(579\) | −3.93099e14 | −0.251056 | ||||||||
\(580\) | −5.06006e13 | −0.0320112 | ||||||||
\(581\) | −1.37916e15 | −0.864262 | ||||||||
\(582\) | 8.75106e14 | 0.543230 | ||||||||
\(583\) | −2.54585e14 | −0.156551 | ||||||||
\(584\) | 6.01931e14 | 0.366671 | ||||||||
\(585\) | 1.11331e15 | 0.671827 | ||||||||
\(586\) | −2.86684e15 | −1.71383 | ||||||||
\(587\) | −3.61030e14 | −0.213813 | −0.106906 | − | 0.994269i | \(-0.534095\pi\) | ||||
−0.106906 | + | 0.994269i | \(0.534095\pi\) | |||||||
\(588\) | −8.70981e13 | −0.0511015 | ||||||||
\(589\) | −2.78339e15 | −1.61785 | ||||||||
\(590\) | −3.43263e14 | −0.197670 | ||||||||
\(591\) | 8.02346e14 | 0.457752 | ||||||||
\(592\) | −3.50271e15 | −1.97986 | ||||||||
\(593\) | 5.56473e14 | 0.311633 | 0.155817 | − | 0.987786i | \(-0.450199\pi\) | ||||
0.155817 | + | 0.987786i | \(0.450199\pi\) | |||||||
\(594\) | 1.75774e14 | 0.0975281 | ||||||||
\(595\) | 7.85157e14 | 0.431631 | ||||||||
\(596\) | 2.35752e14 | 0.128411 | ||||||||
\(597\) | −1.59653e15 | −0.861623 | ||||||||
\(598\) | −3.66110e15 | −1.95774 | ||||||||
\(599\) | −2.56924e15 | −1.36131 | −0.680656 | − | 0.732603i | \(-0.738305\pi\) | ||||
−0.680656 | + | 0.732603i | \(0.738305\pi\) | |||||||
\(600\) | 1.10863e15 | 0.582044 | ||||||||
\(601\) | −2.73554e15 | −1.42309 | −0.711547 | − | 0.702638i | \(-0.752005\pi\) | ||||
−0.711547 | + | 0.702638i | \(0.752005\pi\) | |||||||
\(602\) | −6.31075e14 | −0.325312 | ||||||||
\(603\) | −7.19013e14 | −0.367275 | ||||||||
\(604\) | 1.29946e14 | 0.0657750 | ||||||||
\(605\) | −2.20814e15 | −1.10757 | ||||||||
\(606\) | 1.51075e15 | 0.750919 | ||||||||
\(607\) | 2.21689e15 | 1.09196 | 0.545980 | − | 0.837798i | \(-0.316158\pi\) | ||||
0.545980 | + | 0.837798i | \(0.316158\pi\) | |||||||
\(608\) | −5.70945e14 | −0.278692 | ||||||||
\(609\) | −1.07225e14 | −0.0518684 | ||||||||
\(610\) | −4.01500e15 | −1.92474 | ||||||||
\(611\) | 2.78187e15 | 1.32163 | ||||||||
\(612\) | 5.24583e13 | 0.0246991 | ||||||||
\(613\) | 3.99454e15 | 1.86395 | 0.931974 | − | 0.362524i | \(-0.118085\pi\) | ||||
0.931974 | + | 0.362524i | \(0.118085\pi\) | |||||||
\(614\) | 1.94139e15 | 0.897813 | ||||||||
\(615\) | −2.56962e15 | −1.17776 | ||||||||
\(616\) | −4.43950e14 | −0.201670 | ||||||||
\(617\) | 4.38705e14 | 0.197517 | 0.0987585 | − | 0.995111i | \(-0.468513\pi\) | ||||
0.0987585 | + | 0.995111i | \(0.468513\pi\) | |||||||
\(618\) | 2.04194e15 | 0.911183 | ||||||||
\(619\) | −3.34765e14 | −0.148061 | −0.0740306 | − | 0.997256i | \(-0.523586\pi\) | ||||
−0.0740306 | + | 0.997256i | \(0.523586\pi\) | |||||||
\(620\) | 4.65267e14 | 0.203961 | ||||||||
\(621\) | 5.88139e14 | 0.255550 | ||||||||
\(622\) | 8.08518e14 | 0.348211 | ||||||||
\(623\) | −8.39024e14 | −0.358171 | ||||||||
\(624\) | −2.09666e15 | −0.887182 | ||||||||
\(625\) | −2.19024e15 | −0.918655 | ||||||||
\(626\) | 2.18182e15 | 0.907109 | ||||||||
\(627\) | 8.51971e14 | 0.351118 | ||||||||
\(628\) | −2.46862e12 | −0.00100850 | ||||||||
\(629\) | 2.98001e15 | 1.20681 | ||||||||
\(630\) | −5.64137e14 | −0.226470 | ||||||||
\(631\) | 1.03484e15 | 0.411823 | 0.205911 | − | 0.978571i | \(-0.433984\pi\) | ||||
0.205911 | + | 0.978571i | \(0.433984\pi\) | |||||||
\(632\) | −9.70949e13 | −0.0383047 | ||||||||
\(633\) | 2.24257e15 | 0.877054 | ||||||||
\(634\) | 4.65694e15 | 1.80555 | ||||||||
\(635\) | 3.49548e14 | 0.134354 | ||||||||
\(636\) | 5.45908e13 | 0.0208020 | ||||||||
\(637\) | −2.96166e15 | −1.11884 | ||||||||
\(638\) | −2.71658e14 | −0.101744 | ||||||||
\(639\) | 2.63115e14 | 0.0976993 | ||||||||
\(640\) | −4.43485e15 | −1.63264 | ||||||||
\(641\) | −2.48580e15 | −0.907291 | −0.453646 | − | 0.891182i | \(-0.649877\pi\) | ||||
−0.453646 | + | 0.891182i | \(0.649877\pi\) | |||||||
\(642\) | −1.42176e15 | −0.514497 | ||||||||
\(643\) | 4.42130e15 | 1.58632 | 0.793158 | − | 0.609016i | \(-0.208436\pi\) | ||||
0.793158 | + | 0.609016i | \(0.208436\pi\) | |||||||
\(644\) | 1.84853e14 | 0.0657588 | ||||||||
\(645\) | 1.62680e15 | 0.573794 | ||||||||
\(646\) | 2.55176e15 | 0.892402 | ||||||||
\(647\) | 1.68139e15 | 0.583037 | 0.291518 | − | 0.956565i | \(-0.405840\pi\) | ||||
0.291518 | + | 0.956565i | \(0.405840\pi\) | |||||||
\(648\) | 3.02883e14 | 0.104139 | ||||||||
\(649\) | −1.83628e14 | −0.0626027 | ||||||||
\(650\) | −4.69117e15 | −1.58583 | ||||||||
\(651\) | 9.85927e14 | 0.330483 | ||||||||
\(652\) | 5.54933e14 | 0.184450 | ||||||||
\(653\) | 2.19708e15 | 0.724142 | 0.362071 | − | 0.932151i | \(-0.382070\pi\) | ||||
0.362071 | + | 0.932151i | \(0.382070\pi\) | |||||||
\(654\) | −8.06931e14 | −0.263730 | ||||||||
\(655\) | 3.76783e15 | 1.22114 | ||||||||
\(656\) | 4.83930e15 | 1.55529 | ||||||||
\(657\) | 4.09175e14 | 0.130406 | ||||||||
\(658\) | −1.40963e15 | −0.445516 | ||||||||
\(659\) | 5.21720e15 | 1.63519 | 0.817594 | − | 0.575795i | \(-0.195307\pi\) | ||||
0.817594 | + | 0.575795i | \(0.195307\pi\) | |||||||
\(660\) | −1.42414e14 | −0.0442652 | ||||||||
\(661\) | 5.47364e13 | 0.0168721 | 0.00843603 | − | 0.999964i | \(-0.497315\pi\) | ||||
0.00843603 | + | 0.999964i | \(0.497315\pi\) | |||||||
\(662\) | −3.77284e15 | −1.15332 | ||||||||
\(663\) | 1.78378e15 | 0.540775 | ||||||||
\(664\) | −6.02087e15 | −1.81024 | ||||||||
\(665\) | −2.73435e15 | −0.815334 | ||||||||
\(666\) | −2.14114e15 | −0.633195 | ||||||||
\(667\) | −9.08966e14 | −0.266597 | ||||||||
\(668\) | 5.38817e14 | 0.156737 | ||||||||
\(669\) | −1.14639e15 | −0.330742 | ||||||||
\(670\) | 5.84644e15 | 1.67294 | ||||||||
\(671\) | −2.14782e15 | −0.609569 | ||||||||
\(672\) | 2.02239e14 | 0.0569292 | ||||||||
\(673\) | −7.52893e14 | −0.210208 | −0.105104 | − | 0.994461i | \(-0.533518\pi\) | ||||
−0.105104 | + | 0.994461i | \(0.533518\pi\) | |||||||
\(674\) | 3.11026e15 | 0.861325 | ||||||||
\(675\) | 7.53616e14 | 0.207004 | ||||||||
\(676\) | 3.88762e14 | 0.105920 | ||||||||
\(677\) | −5.26803e15 | −1.42368 | −0.711838 | − | 0.702344i | \(-0.752137\pi\) | ||||
−0.711838 | + | 0.702344i | \(0.752137\pi\) | |||||||
\(678\) | −9.53510e14 | −0.255601 | ||||||||
\(679\) | −1.50246e15 | −0.399501 | ||||||||
\(680\) | 3.42769e15 | 0.904072 | ||||||||
\(681\) | 2.64392e15 | 0.691733 | ||||||||
\(682\) | 2.49787e15 | 0.648270 | ||||||||
\(683\) | −2.69775e15 | −0.694525 | −0.347262 | − | 0.937768i | \(-0.612889\pi\) | ||||
−0.347262 | + | 0.937768i | \(0.612889\pi\) | |||||||
\(684\) | −1.82689e14 | −0.0466556 | ||||||||
\(685\) | −8.64783e15 | −2.19083 | ||||||||
\(686\) | 3.37721e15 | 0.848741 | ||||||||
\(687\) | −1.55494e15 | −0.387660 | ||||||||
\(688\) | −3.06371e15 | −0.757724 | ||||||||
\(689\) | 1.85629e15 | 0.455450 | ||||||||
\(690\) | −4.78228e15 | −1.16403 | ||||||||
\(691\) | −8.85718e14 | −0.213878 | −0.106939 | − | 0.994266i | \(-0.534105\pi\) | ||||
−0.106939 | + | 0.994266i | \(0.534105\pi\) | |||||||
\(692\) | 1.69596e14 | 0.0406287 | ||||||||
\(693\) | −3.01784e14 | −0.0717238 | ||||||||
\(694\) | −6.69740e15 | −1.57917 | ||||||||
\(695\) | 6.90601e15 | 1.61551 | ||||||||
\(696\) | −4.68105e14 | −0.108641 | ||||||||
\(697\) | −4.11714e15 | −0.948015 | ||||||||
\(698\) | 4.75195e15 | 1.08559 | ||||||||
\(699\) | 1.50241e15 | 0.340536 | ||||||||
\(700\) | 2.36862e14 | 0.0532668 | ||||||||
\(701\) | −1.95996e15 | −0.437319 | −0.218659 | − | 0.975801i | \(-0.570168\pi\) | ||||
−0.218659 | + | 0.975801i | \(0.570168\pi\) | |||||||
\(702\) | −1.28165e15 | −0.283736 | ||||||||
\(703\) | −1.03780e16 | −2.27961 | ||||||||
\(704\) | −1.91109e15 | −0.416516 | ||||||||
\(705\) | 3.63379e15 | 0.785813 | ||||||||
\(706\) | 5.57550e14 | 0.119635 | ||||||||
\(707\) | −2.59378e15 | −0.552239 | ||||||||
\(708\) | 3.93755e13 | 0.00831846 | ||||||||
\(709\) | −5.58013e15 | −1.16974 | −0.584871 | − | 0.811126i | \(-0.698855\pi\) | ||||
−0.584871 | + | 0.811126i | \(0.698855\pi\) | |||||||
\(710\) | −2.13944e15 | −0.445020 | ||||||||
\(711\) | −6.60022e13 | −0.0136231 | ||||||||
\(712\) | −3.66286e15 | −0.750205 | ||||||||
\(713\) | 8.35786e15 | 1.69864 | ||||||||
\(714\) | −9.03880e14 | −0.182293 | ||||||||
\(715\) | −4.84263e15 | −0.969165 | ||||||||
\(716\) | −4.29848e13 | −0.00853676 | ||||||||
\(717\) | 1.90070e15 | 0.374592 | ||||||||
\(718\) | −5.24226e15 | −1.02526 | ||||||||
\(719\) | −8.80656e15 | −1.70922 | −0.854609 | − | 0.519272i | \(-0.826203\pi\) | ||||
−0.854609 | + | 0.519272i | \(0.826203\pi\) | |||||||
\(720\) | −2.73874e15 | −0.527500 | ||||||||
\(721\) | −3.50577e15 | −0.670100 | ||||||||
\(722\) | −3.33083e15 | −0.631826 | ||||||||
\(723\) | −5.57652e15 | −1.04979 | ||||||||
\(724\) | −2.57837e14 | −0.0481708 | ||||||||
\(725\) | −1.16471e15 | −0.215953 | ||||||||
\(726\) | 2.54204e15 | 0.467768 | ||||||||
\(727\) | −1.26060e15 | −0.230217 | −0.115109 | − | 0.993353i | \(-0.536722\pi\) | ||||
−0.115109 | + | 0.993353i | \(0.536722\pi\) | |||||||
\(728\) | 3.23704e15 | 0.586713 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −3.32708e15 | −0.594001 | ||||||||
\(731\) | 2.60651e15 | 0.461865 | ||||||||
\(732\) | 4.60557e14 | 0.0809977 | ||||||||
\(733\) | 1.28404e15 | 0.224134 | 0.112067 | − | 0.993701i | \(-0.464253\pi\) | ||||
0.112067 | + | 0.993701i | \(0.464253\pi\) | |||||||
\(734\) | −8.90997e15 | −1.54365 | ||||||||
\(735\) | −3.86864e15 | −0.665240 | ||||||||
\(736\) | 1.71442e15 | 0.292609 | ||||||||
\(737\) | 3.12754e15 | 0.529824 | ||||||||
\(738\) | 2.95817e15 | 0.497409 | ||||||||
\(739\) | −1.92179e15 | −0.320746 | −0.160373 | − | 0.987056i | \(-0.551270\pi\) | ||||
−0.160373 | + | 0.987056i | \(0.551270\pi\) | |||||||
\(740\) | 1.73478e15 | 0.287389 | ||||||||
\(741\) | −6.21211e15 | −1.02150 | ||||||||
\(742\) | −9.40624e14 | −0.153530 | ||||||||
\(743\) | 4.74326e15 | 0.768491 | 0.384245 | − | 0.923231i | \(-0.374462\pi\) | ||||
0.384245 | + | 0.923231i | \(0.374462\pi\) | |||||||
\(744\) | 4.30418e15 | 0.692212 | ||||||||
\(745\) | 1.04714e16 | 1.67165 | ||||||||
\(746\) | 7.19897e15 | 1.14079 | ||||||||
\(747\) | −4.09281e15 | −0.643811 | ||||||||
\(748\) | −2.28181e14 | −0.0356305 | ||||||||
\(749\) | 2.44100e15 | 0.378370 | ||||||||
\(750\) | −4.30837e14 | −0.0662943 | ||||||||
\(751\) | −4.09969e15 | −0.626226 | −0.313113 | − | 0.949716i | \(-0.601372\pi\) | ||||
−0.313113 | + | 0.949716i | \(0.601372\pi\) | |||||||
\(752\) | −6.84342e15 | −1.03771 | ||||||||
\(753\) | 2.78321e15 | 0.418960 | ||||||||
\(754\) | 1.98078e15 | 0.296002 | ||||||||
\(755\) | 5.77183e15 | 0.856260 | ||||||||
\(756\) | 6.47118e13 | 0.00953045 | ||||||||
\(757\) | −1.11823e16 | −1.63495 | −0.817476 | − | 0.575963i | \(-0.804627\pi\) | ||||
−0.817476 | + | 0.575963i | \(0.804627\pi\) | |||||||
\(758\) | −3.22120e15 | −0.467560 | ||||||||
\(759\) | −2.55827e15 | −0.368652 | ||||||||
\(760\) | −1.19371e16 | −1.70775 | ||||||||
\(761\) | −1.23688e16 | −1.75676 | −0.878379 | − | 0.477964i | \(-0.841375\pi\) | ||||
−0.878379 | + | 0.477964i | \(0.841375\pi\) | |||||||
\(762\) | −4.02403e14 | −0.0567425 | ||||||||
\(763\) | 1.38541e15 | 0.193951 | ||||||||
\(764\) | 5.47684e14 | 0.0761231 | ||||||||
\(765\) | 2.33004e15 | 0.321533 | ||||||||
\(766\) | −6.20180e15 | −0.849688 | ||||||||
\(767\) | 1.33891e15 | 0.182129 | ||||||||
\(768\) | 1.40257e15 | 0.189425 | ||||||||
\(769\) | −2.71460e14 | −0.0364008 | −0.0182004 | − | 0.999834i | \(-0.505794\pi\) | ||||
−0.0182004 | + | 0.999834i | \(0.505794\pi\) | |||||||
\(770\) | 2.45387e15 | 0.326702 | ||||||||
\(771\) | 3.07543e15 | 0.406544 | ||||||||
\(772\) | −3.66653e14 | −0.0481238 | ||||||||
\(773\) | −7.15121e15 | −0.931949 | −0.465974 | − | 0.884798i | \(-0.654296\pi\) | ||||
−0.465974 | + | 0.884798i | \(0.654296\pi\) | |||||||
\(774\) | −1.87279e15 | −0.242333 | ||||||||
\(775\) | 1.07094e16 | 1.37596 | ||||||||
\(776\) | −6.55914e15 | −0.836773 | ||||||||
\(777\) | 3.67610e15 | 0.465662 | ||||||||
\(778\) | −1.24228e15 | −0.156254 | ||||||||
\(779\) | 1.43382e16 | 1.79076 | ||||||||
\(780\) | 1.03841e15 | 0.128780 | ||||||||
\(781\) | −1.14449e15 | −0.140939 | ||||||||
\(782\) | −7.66233e15 | −0.936966 | ||||||||
\(783\) | −3.18204e14 | −0.0386381 | ||||||||
\(784\) | 7.28571e15 | 0.878484 | ||||||||
\(785\) | −1.09649e14 | −0.0131287 | ||||||||
\(786\) | −4.33756e15 | −0.515729 | ||||||||
\(787\) | 5.43037e15 | 0.641163 | 0.320581 | − | 0.947221i | \(-0.396122\pi\) | ||||
0.320581 | + | 0.947221i | \(0.396122\pi\) | |||||||
\(788\) | 7.48367e14 | 0.0877446 | ||||||||
\(789\) | −8.20406e15 | −0.955224 | ||||||||
\(790\) | 5.36677e14 | 0.0620532 | ||||||||
\(791\) | 1.63707e15 | 0.187973 | ||||||||
\(792\) | −1.31747e15 | −0.150229 | ||||||||
\(793\) | 1.56607e16 | 1.77341 | ||||||||
\(794\) | −1.53672e16 | −1.72816 | ||||||||
\(795\) | 2.42476e15 | 0.270801 | ||||||||
\(796\) | −1.48912e15 | −0.165161 | ||||||||
\(797\) | 2.89325e15 | 0.318688 | 0.159344 | − | 0.987223i | \(-0.449062\pi\) | ||||
0.159344 | + | 0.987223i | \(0.449062\pi\) | |||||||
\(798\) | 3.14781e15 | 0.344344 | ||||||||
\(799\) | 5.82218e15 | 0.632526 | ||||||||
\(800\) | 2.19678e15 | 0.237023 | ||||||||
\(801\) | −2.48990e15 | −0.266811 | ||||||||
\(802\) | −1.65431e16 | −1.76059 | ||||||||
\(803\) | −1.77982e15 | −0.188122 | ||||||||
\(804\) | −6.70641e14 | −0.0704015 | ||||||||
\(805\) | 8.21062e15 | 0.856049 | ||||||||
\(806\) | −1.82131e16 | −1.88600 | ||||||||
\(807\) | 7.01696e15 | 0.721680 | ||||||||
\(808\) | −1.13235e16 | −1.15669 | ||||||||
\(809\) | 7.66943e14 | 0.0778120 | 0.0389060 | − | 0.999243i | \(-0.487613\pi\) | ||||
0.0389060 | + | 0.999243i | \(0.487613\pi\) | |||||||
\(810\) | −1.67414e15 | −0.168704 | ||||||||
\(811\) | 2.35899e15 | 0.236108 | 0.118054 | − | 0.993007i | \(-0.462334\pi\) | ||||
0.118054 | + | 0.993007i | \(0.462334\pi\) | |||||||
\(812\) | −1.00012e14 | −0.00994243 | ||||||||
\(813\) | 1.66673e15 | 0.164576 | ||||||||
\(814\) | 9.31348e15 | 0.913435 | ||||||||
\(815\) | 2.46485e16 | 2.40118 | ||||||||
\(816\) | −4.38811e15 | −0.424601 | ||||||||
\(817\) | −9.07733e15 | −0.872443 | ||||||||
\(818\) | 9.12327e15 | 0.870979 | ||||||||
\(819\) | 2.20044e15 | 0.208665 | ||||||||
\(820\) | −2.39675e15 | −0.225760 | ||||||||
\(821\) | −1.62872e16 | −1.52391 | −0.761955 | − | 0.647630i | \(-0.775760\pi\) | ||||
−0.761955 | + | 0.647630i | \(0.775760\pi\) | |||||||
\(822\) | 9.95546e15 | 0.925266 | ||||||||
\(823\) | −3.12466e15 | −0.288472 | −0.144236 | − | 0.989543i | \(-0.546073\pi\) | ||||
−0.144236 | + | 0.989543i | \(0.546073\pi\) | |||||||
\(824\) | −1.53048e16 | −1.40355 | ||||||||
\(825\) | −3.27806e15 | −0.298621 | ||||||||
\(826\) | −6.78457e14 | −0.0613949 | ||||||||
\(827\) | −8.65810e14 | −0.0778291 | −0.0389146 | − | 0.999243i | \(-0.512390\pi\) | ||||
−0.0389146 | + | 0.999243i | \(0.512390\pi\) | |||||||
\(828\) | 5.48572e14 | 0.0489854 | ||||||||
\(829\) | 1.32091e16 | 1.17171 | 0.585857 | − | 0.810414i | \(-0.300758\pi\) | ||||
0.585857 | + | 0.810414i | \(0.300758\pi\) | |||||||
\(830\) | 3.32794e16 | 2.93256 | ||||||||
\(831\) | −2.05870e14 | −0.0180214 | ||||||||
\(832\) | 1.39346e16 | 1.21176 | ||||||||
\(833\) | −6.19847e15 | −0.535473 | ||||||||
\(834\) | −7.95026e15 | −0.682288 | ||||||||
\(835\) | 2.39327e16 | 2.04040 | ||||||||
\(836\) | 7.94654e14 | 0.0673044 | ||||||||
\(837\) | 2.92585e15 | 0.246185 | ||||||||
\(838\) | −1.04865e16 | −0.876572 | ||||||||
\(839\) | 1.47090e16 | 1.22149 | 0.610747 | − | 0.791826i | \(-0.290869\pi\) | ||||
0.610747 | + | 0.791826i | \(0.290869\pi\) | |||||||
\(840\) | 4.22835e15 | 0.348847 | ||||||||
\(841\) | −1.17087e16 | −0.959692 | ||||||||
\(842\) | 6.83846e15 | 0.556855 | ||||||||
\(843\) | −7.42872e15 | −0.600983 | ||||||||
\(844\) | 2.09170e15 | 0.168119 | ||||||||
\(845\) | 1.72677e16 | 1.37887 | ||||||||
\(846\) | −4.18325e15 | −0.331877 | ||||||||
\(847\) | −4.36438e15 | −0.344004 | ||||||||
\(848\) | −4.56649e15 | −0.357607 | ||||||||
\(849\) | 1.83764e15 | 0.142978 | ||||||||
\(850\) | −9.81817e15 | −0.758973 | ||||||||
\(851\) | 3.11628e16 | 2.39345 | ||||||||
\(852\) | 2.45414e14 | 0.0187276 | ||||||||
\(853\) | 9.35697e15 | 0.709440 | 0.354720 | − | 0.934973i | \(-0.384576\pi\) | ||||
0.354720 | + | 0.934973i | \(0.384576\pi\) | |||||||
\(854\) | −7.93561e15 | −0.597809 | ||||||||
\(855\) | −8.11450e15 | −0.607363 | ||||||||
\(856\) | 1.06564e16 | 0.792514 | ||||||||
\(857\) | 1.71450e16 | 1.26690 | 0.633451 | − | 0.773783i | \(-0.281638\pi\) | ||||
0.633451 | + | 0.773783i | \(0.281638\pi\) | |||||||
\(858\) | 5.57488e15 | 0.409313 | ||||||||
\(859\) | 2.02187e16 | 1.47499 | 0.737496 | − | 0.675351i | \(-0.236008\pi\) | ||||
0.737496 | + | 0.675351i | \(0.236008\pi\) | |||||||
\(860\) | 1.51736e15 | 0.109988 | ||||||||
\(861\) | −5.07885e15 | −0.365803 | ||||||||
\(862\) | −2.65972e15 | −0.190347 | ||||||||
\(863\) | −2.31489e16 | −1.64615 | −0.823077 | − | 0.567930i | \(-0.807744\pi\) | ||||
−0.823077 | + | 0.567930i | \(0.807744\pi\) | |||||||
\(864\) | 6.00169e14 | 0.0424080 | ||||||||
\(865\) | 7.53297e15 | 0.528905 | ||||||||
\(866\) | 1.62256e16 | 1.13202 | ||||||||
\(867\) | −4.59480e15 | −0.318538 | ||||||||
\(868\) | 9.19598e14 | 0.0633489 | ||||||||
\(869\) | 2.87094e14 | 0.0196524 | ||||||||
\(870\) | 2.58738e15 | 0.175996 | ||||||||
\(871\) | −2.28043e16 | −1.54141 | ||||||||
\(872\) | 6.04816e15 | 0.406240 | ||||||||
\(873\) | −4.45871e15 | −0.297599 | ||||||||
\(874\) | 2.66845e16 | 1.76989 | ||||||||
\(875\) | 7.39698e14 | 0.0487540 | ||||||||
\(876\) | 3.81647e14 | 0.0249971 | ||||||||
\(877\) | −1.34296e16 | −0.874110 | −0.437055 | − | 0.899435i | \(-0.643979\pi\) | ||||
−0.437055 | + | 0.899435i | \(0.643979\pi\) | |||||||
\(878\) | −1.88421e16 | −1.21874 | ||||||||
\(879\) | 1.46067e16 | 0.938888 | ||||||||
\(880\) | 1.19129e16 | 0.760962 | ||||||||
\(881\) | 1.10383e16 | 0.700705 | 0.350352 | − | 0.936618i | \(-0.386062\pi\) | ||||
0.350352 | + | 0.936618i | \(0.386062\pi\) | |||||||
\(882\) | 4.45362e15 | 0.280954 | ||||||||
\(883\) | −2.83712e16 | −1.77866 | −0.889331 | − | 0.457264i | \(-0.848830\pi\) | ||||
−0.889331 | + | 0.457264i | \(0.848830\pi\) | |||||||
\(884\) | 1.66377e15 | 0.103659 | ||||||||
\(885\) | 1.74894e15 | 0.108290 | ||||||||
\(886\) | 2.89660e16 | 1.78239 | ||||||||
\(887\) | 6.60674e15 | 0.404024 | 0.202012 | − | 0.979383i | \(-0.435252\pi\) | ||||
0.202012 | + | 0.979383i | \(0.435252\pi\) | |||||||
\(888\) | 1.60484e16 | 0.975351 | ||||||||
\(889\) | 6.90880e14 | 0.0417295 | ||||||||
\(890\) | 2.02459e16 | 1.21532 | ||||||||
\(891\) | −8.95579e14 | −0.0534289 | ||||||||
\(892\) | −1.06927e15 | −0.0633986 | ||||||||
\(893\) | −2.02761e16 | −1.19481 | ||||||||
\(894\) | −1.20548e16 | −0.705999 | ||||||||
\(895\) | −1.90926e15 | −0.111132 | ||||||||
\(896\) | −8.76546e15 | −0.507085 | ||||||||
\(897\) | 1.86535e16 | 1.07251 | ||||||||
\(898\) | −2.99886e16 | −1.71371 | ||||||||
\(899\) | −4.52189e15 | −0.256827 | ||||||||
\(900\) | 7.02916e14 | 0.0396798 | ||||||||
\(901\) | 3.88504e15 | 0.217976 | ||||||||
\(902\) | −1.28674e16 | −0.717553 | ||||||||
\(903\) | 3.21536e15 | 0.178216 | ||||||||
\(904\) | 7.14681e15 | 0.393718 | ||||||||
\(905\) | −1.14524e16 | −0.627089 | ||||||||
\(906\) | −6.64459e15 | −0.361629 | ||||||||
\(907\) | −2.35979e16 | −1.27654 | −0.638269 | − | 0.769813i | \(-0.720349\pi\) | ||||
−0.638269 | + | 0.769813i | \(0.720349\pi\) | |||||||
\(908\) | 2.46605e15 | 0.132596 | ||||||||
\(909\) | −7.69735e15 | −0.411377 | ||||||||
\(910\) | −1.78922e16 | −0.950467 | ||||||||
\(911\) | −1.51944e15 | −0.0802294 | −0.0401147 | − | 0.999195i | \(-0.512772\pi\) | ||||
−0.0401147 | + | 0.999195i | \(0.512772\pi\) | |||||||
\(912\) | 1.52818e16 | 0.802054 | ||||||||
\(913\) | 1.78028e16 | 0.928750 | ||||||||
\(914\) | −4.01110e15 | −0.207998 | ||||||||
\(915\) | 2.04566e16 | 1.05443 | ||||||||
\(916\) | −1.45033e15 | −0.0743089 | ||||||||
\(917\) | 7.44710e15 | 0.379276 | ||||||||
\(918\) | −2.68237e15 | −0.135795 | ||||||||
\(919\) | 3.25419e16 | 1.63760 | 0.818799 | − | 0.574080i | \(-0.194640\pi\) | ||||
0.818799 | + | 0.574080i | \(0.194640\pi\) | |||||||
\(920\) | 3.58444e16 | 1.79303 | ||||||||
\(921\) | −9.89147e15 | −0.491850 | ||||||||
\(922\) | 2.52721e16 | 1.24917 | ||||||||
\(923\) | 8.34500e15 | 0.410031 | ||||||||
\(924\) | −2.81481e14 | −0.0137484 | ||||||||
\(925\) | 3.99307e16 | 1.93877 | ||||||||
\(926\) | 2.50662e16 | 1.20984 | ||||||||
\(927\) | −1.04038e16 | −0.499175 | ||||||||
\(928\) | −9.27558e14 | −0.0442412 | ||||||||
\(929\) | 1.52117e16 | 0.721261 | 0.360630 | − | 0.932709i | \(-0.382562\pi\) | ||||
0.360630 | + | 0.932709i | \(0.382562\pi\) | |||||||
\(930\) | −2.37907e16 | −1.12137 | ||||||||
\(931\) | 2.15865e16 | 1.01149 | ||||||||
\(932\) | 1.40133e15 | 0.0652759 | ||||||||
\(933\) | −4.11944e15 | −0.190761 | ||||||||
\(934\) | 3.79699e15 | 0.174796 | ||||||||
\(935\) | −1.01352e16 | −0.463838 | ||||||||
\(936\) | 9.60629e15 | 0.437057 | ||||||||
\(937\) | −2.78623e16 | −1.26023 | −0.630114 | − | 0.776503i | \(-0.716992\pi\) | ||||
−0.630114 | + | 0.776503i | \(0.716992\pi\) | |||||||
\(938\) | 1.15554e16 | 0.519602 | ||||||||
\(939\) | −1.11165e16 | −0.496943 | ||||||||
\(940\) | 3.38932e15 | 0.150629 | ||||||||
\(941\) | 3.85825e15 | 0.170470 | 0.0852349 | − | 0.996361i | \(-0.472836\pi\) | ||||
0.0852349 | + | 0.996361i | \(0.472836\pi\) | |||||||
\(942\) | 1.26229e14 | 0.00554471 | ||||||||
\(943\) | −4.30542e16 | −1.88019 | ||||||||
\(944\) | −3.29374e15 | −0.143002 | ||||||||
\(945\) | 2.87431e15 | 0.124068 | ||||||||
\(946\) | 8.14619e15 | 0.349585 | ||||||||
\(947\) | 9.91197e15 | 0.422897 | 0.211449 | − | 0.977389i | \(-0.432182\pi\) | ||||
0.211449 | + | 0.977389i | \(0.432182\pi\) | |||||||
\(948\) | −6.15619e13 | −0.00261135 | ||||||||
\(949\) | 1.29774e16 | 0.547299 | ||||||||
\(950\) | 3.41923e16 | 1.43367 | ||||||||
\(951\) | −2.37274e16 | −0.989138 | ||||||||
\(952\) | 6.77481e15 | 0.280798 | ||||||||
\(953\) | −7.57779e15 | −0.312271 | −0.156135 | − | 0.987736i | \(-0.549904\pi\) | ||||
−0.156135 | + | 0.987736i | \(0.549904\pi\) | |||||||
\(954\) | −2.79141e15 | −0.114369 | ||||||||
\(955\) | 2.43265e16 | 0.990972 | ||||||||
\(956\) | 1.77283e15 | 0.0718040 | ||||||||
\(957\) | 1.38411e15 | 0.0557386 | ||||||||
\(958\) | −1.82616e16 | −0.731188 | ||||||||
\(959\) | −1.70924e16 | −0.680457 | ||||||||
\(960\) | 1.82020e16 | 0.720488 | ||||||||
\(961\) | 1.61698e16 | 0.636395 | ||||||||
\(962\) | −6.79087e16 | −2.65744 | ||||||||
\(963\) | 7.24394e15 | 0.281858 | ||||||||
\(964\) | −5.20135e15 | −0.201230 | ||||||||
\(965\) | −1.62857e16 | −0.626477 | ||||||||
\(966\) | −9.45214e15 | −0.361540 | ||||||||
\(967\) | −3.22702e16 | −1.22731 | −0.613657 | − | 0.789573i | \(-0.710302\pi\) | ||||
−0.613657 | + | 0.789573i | \(0.710302\pi\) | |||||||
\(968\) | −1.90532e16 | −0.720533 | ||||||||
\(969\) | −1.30013e16 | −0.488886 | ||||||||
\(970\) | 3.62547e16 | 1.35556 | ||||||||
\(971\) | −4.14383e16 | −1.54062 | −0.770312 | − | 0.637667i | \(-0.779900\pi\) | ||||
−0.770312 | + | 0.637667i | \(0.779900\pi\) | |||||||
\(972\) | 1.92040e14 | 0.00709948 | ||||||||
\(973\) | 1.36497e16 | 0.501767 | ||||||||
\(974\) | −5.16793e16 | −1.88905 | ||||||||
\(975\) | 2.39018e16 | 0.868770 | ||||||||
\(976\) | −3.85254e16 | −1.39243 | ||||||||
\(977\) | 2.39601e16 | 0.861128 | 0.430564 | − | 0.902560i | \(-0.358315\pi\) | ||||
0.430564 | + | 0.902560i | \(0.358315\pi\) | |||||||
\(978\) | −2.83756e16 | −1.01410 | ||||||||
\(979\) | 1.08305e16 | 0.384896 | ||||||||
\(980\) | −3.60838e15 | −0.127517 | ||||||||
\(981\) | 4.11136e15 | 0.144479 | ||||||||
\(982\) | 3.01116e16 | 1.05225 | ||||||||
\(983\) | −5.49845e16 | −1.91072 | −0.955358 | − | 0.295452i | \(-0.904530\pi\) | ||||
−0.955358 | + | 0.295452i | \(0.904530\pi\) | |||||||
\(984\) | −2.21723e16 | −0.766192 | ||||||||
\(985\) | 3.32403e16 | 1.14226 | ||||||||
\(986\) | 4.14558e15 | 0.141665 | ||||||||
\(987\) | 7.18216e15 | 0.244068 | ||||||||
\(988\) | −5.79418e15 | −0.195807 | ||||||||
\(989\) | 2.72571e16 | 0.916010 | ||||||||
\(990\) | 7.28213e15 | 0.243369 | ||||||||
\(991\) | −2.23721e16 | −0.743534 | −0.371767 | − | 0.928326i | \(-0.621248\pi\) | ||||
−0.371767 | + | 0.928326i | \(0.621248\pi\) | |||||||
\(992\) | 8.52880e15 | 0.281886 | ||||||||
\(993\) | 1.92228e16 | 0.631824 | ||||||||
\(994\) | −4.22860e15 | −0.138220 | ||||||||
\(995\) | −6.61423e16 | −2.15007 | ||||||||
\(996\) | −3.81746e15 | −0.123409 | ||||||||
\(997\) | 1.06303e15 | 0.0341760 | 0.0170880 | − | 0.999854i | \(-0.494560\pi\) | ||||
0.0170880 | + | 0.999854i | \(0.494560\pi\) | |||||||
\(998\) | −1.29404e16 | −0.413743 | ||||||||
\(999\) | 1.09092e16 | 0.346884 |
(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 | 177.12.a.d.1.6 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.d.1.6 | ✓ | 28 | 1.1 | even | 1 | trivial |