Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,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, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
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: | \(189.798744245\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −170.157 | −1.87999 | −0.939994 | − | 0.341192i | \(-0.889169\pi\) | ||||
−0.939994 | + | 0.341192i | \(0.889169\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 20761.4 | 2.53435 | ||||||||
\(5\) | 7033.25 | 0.201303 | 0.100652 | − | 0.994922i | \(-0.467907\pi\) | ||||
0.100652 | + | 0.994922i | \(0.467907\pi\) | |||||||
\(6\) | −124044. | −1.08541 | ||||||||
\(7\) | −166219. | −0.534004 | −0.267002 | − | 0.963696i | \(-0.586033\pi\) | ||||
−0.267002 | + | 0.963696i | \(0.586033\pi\) | |||||||
\(8\) | −2.13877e6 | −2.88456 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −1.19676e6 | −0.378448 | ||||||||
\(11\) | −2.55370e6 | −0.434628 | −0.217314 | − | 0.976102i | \(-0.569730\pi\) | ||||
−0.217314 | + | 0.976102i | \(0.569730\pi\) | |||||||
\(12\) | 1.51351e7 | 1.46321 | ||||||||
\(13\) | −9.38582e6 | −0.539312 | −0.269656 | − | 0.962957i | \(-0.586910\pi\) | ||||
−0.269656 | + | 0.962957i | \(0.586910\pi\) | |||||||
\(14\) | 2.82834e7 | 1.00392 | ||||||||
\(15\) | 5.12724e6 | 0.116223 | ||||||||
\(16\) | 1.93850e8 | 2.88859 | ||||||||
\(17\) | −4.94668e7 | −0.497045 | −0.248523 | − | 0.968626i | \(-0.579945\pi\) | ||||
−0.248523 | + | 0.968626i | \(0.579945\pi\) | |||||||
\(18\) | −9.04284e7 | −0.626662 | ||||||||
\(19\) | 8.01706e6 | 0.0390946 | 0.0195473 | − | 0.999809i | \(-0.493778\pi\) | ||||
0.0195473 | + | 0.999809i | \(0.493778\pi\) | |||||||
\(20\) | 1.46020e8 | 0.510174 | ||||||||
\(21\) | −1.21174e8 | −0.308307 | ||||||||
\(22\) | 4.34530e8 | 0.817095 | ||||||||
\(23\) | −4.03810e8 | −0.568783 | −0.284391 | − | 0.958708i | \(-0.591791\pi\) | ||||
−0.284391 | + | 0.958708i | \(0.591791\pi\) | |||||||
\(24\) | −1.55917e9 | −1.66540 | ||||||||
\(25\) | −1.17124e9 | −0.959477 | ||||||||
\(26\) | 1.59706e9 | 1.01390 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | −3.45095e9 | −1.35335 | ||||||||
\(29\) | −1.78851e9 | −0.558347 | −0.279174 | − | 0.960241i | \(-0.590060\pi\) | ||||
−0.279174 | + | 0.960241i | \(0.590060\pi\) | |||||||
\(30\) | −8.72436e8 | −0.218497 | ||||||||
\(31\) | −7.59511e9 | −1.53703 | −0.768516 | − | 0.639831i | \(-0.779005\pi\) | ||||
−0.768516 | + | 0.639831i | \(0.779005\pi\) | |||||||
\(32\) | −1.54641e10 | −2.54595 | ||||||||
\(33\) | −1.86165e9 | −0.250933 | ||||||||
\(34\) | 8.41713e9 | 0.934439 | ||||||||
\(35\) | −1.16906e9 | −0.107497 | ||||||||
\(36\) | 1.10335e10 | 0.844784 | ||||||||
\(37\) | −2.95954e10 | −1.89632 | −0.948162 | − | 0.317789i | \(-0.897060\pi\) | ||||
−0.948162 | + | 0.317789i | \(0.897060\pi\) | |||||||
\(38\) | −1.36416e9 | −0.0734974 | ||||||||
\(39\) | −6.84226e9 | −0.311372 | ||||||||
\(40\) | −1.50425e10 | −0.580672 | ||||||||
\(41\) | −1.30835e9 | −0.0430160 | −0.0215080 | − | 0.999769i | \(-0.506847\pi\) | ||||
−0.0215080 | + | 0.999769i | \(0.506847\pi\) | |||||||
\(42\) | 2.06186e10 | 0.579614 | ||||||||
\(43\) | 1.57511e9 | 0.0379986 | 0.0189993 | − | 0.999819i | \(-0.493952\pi\) | ||||
0.0189993 | + | 0.999819i | \(0.493952\pi\) | |||||||
\(44\) | −5.30185e10 | −1.10150 | ||||||||
\(45\) | 3.73776e9 | 0.0671011 | ||||||||
\(46\) | 6.87111e10 | 1.06930 | ||||||||
\(47\) | 1.19393e11 | 1.61563 | 0.807817 | − | 0.589433i | \(-0.200649\pi\) | ||||
0.807817 | + | 0.589433i | \(0.200649\pi\) | |||||||
\(48\) | 1.41317e11 | 1.66773 | ||||||||
\(49\) | −6.92602e10 | −0.714840 | ||||||||
\(50\) | 1.99294e11 | 1.80380 | ||||||||
\(51\) | −3.60613e10 | −0.286969 | ||||||||
\(52\) | −1.94863e11 | −1.36681 | ||||||||
\(53\) | 6.19930e10 | 0.384193 | 0.192097 | − | 0.981376i | \(-0.438471\pi\) | ||||
0.192097 | + | 0.981376i | \(0.438471\pi\) | |||||||
\(54\) | −6.59223e10 | −0.361804 | ||||||||
\(55\) | −1.79608e10 | −0.0874921 | ||||||||
\(56\) | 3.55506e11 | 1.54037 | ||||||||
\(57\) | 5.84444e9 | 0.0225713 | ||||||||
\(58\) | 3.04328e11 | 1.04969 | ||||||||
\(59\) | −4.21805e10 | −0.130189 | ||||||||
\(60\) | 1.06449e11 | 0.294549 | ||||||||
\(61\) | 4.65074e11 | 1.15579 | 0.577894 | − | 0.816112i | \(-0.303875\pi\) | ||||
0.577894 | + | 0.816112i | \(0.303875\pi\) | |||||||
\(62\) | 1.29236e12 | 2.88960 | ||||||||
\(63\) | −8.83358e10 | −0.178001 | ||||||||
\(64\) | 1.04331e12 | 1.89776 | ||||||||
\(65\) | −6.60128e10 | −0.108565 | ||||||||
\(66\) | 3.16773e11 | 0.471750 | ||||||||
\(67\) | 8.10106e11 | 1.09410 | 0.547048 | − | 0.837101i | \(-0.315751\pi\) | ||||
0.547048 | + | 0.837101i | \(0.315751\pi\) | |||||||
\(68\) | −1.02700e12 | −1.25969 | ||||||||
\(69\) | −2.94378e11 | −0.328387 | ||||||||
\(70\) | 1.98924e11 | 0.202092 | ||||||||
\(71\) | −2.60417e11 | −0.241263 | −0.120631 | − | 0.992697i | \(-0.538492\pi\) | ||||
−0.120631 | + | 0.992697i | \(0.538492\pi\) | |||||||
\(72\) | −1.13663e12 | −0.961521 | ||||||||
\(73\) | 4.55646e11 | 0.352395 | 0.176197 | − | 0.984355i | \(-0.443620\pi\) | ||||
0.176197 | + | 0.984355i | \(0.443620\pi\) | |||||||
\(74\) | 5.03586e12 | 3.56506 | ||||||||
\(75\) | −8.53831e11 | −0.553954 | ||||||||
\(76\) | 1.66446e11 | 0.0990796 | ||||||||
\(77\) | 4.24475e11 | 0.232093 | ||||||||
\(78\) | 1.16426e12 | 0.585376 | ||||||||
\(79\) | −3.34216e11 | −0.154686 | −0.0773429 | − | 0.997005i | \(-0.524644\pi\) | ||||
−0.0773429 | + | 0.997005i | \(0.524644\pi\) | |||||||
\(80\) | 1.36340e12 | 0.581483 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 2.22626e11 | 0.0808696 | ||||||||
\(83\) | −3.25618e12 | −1.09320 | −0.546602 | − | 0.837392i | \(-0.684079\pi\) | ||||
−0.546602 | + | 0.837392i | \(0.684079\pi\) | |||||||
\(84\) | −2.51574e12 | −0.781359 | ||||||||
\(85\) | −3.47913e11 | −0.100057 | ||||||||
\(86\) | −2.68017e11 | −0.0714368 | ||||||||
\(87\) | −1.30382e12 | −0.322362 | ||||||||
\(88\) | 5.46179e12 | 1.25371 | ||||||||
\(89\) | −5.57760e11 | −0.118963 | −0.0594816 | − | 0.998229i | \(-0.518945\pi\) | ||||
−0.0594816 | + | 0.998229i | \(0.518945\pi\) | |||||||
\(90\) | −6.36006e11 | −0.126149 | ||||||||
\(91\) | 1.56010e12 | 0.287995 | ||||||||
\(92\) | −8.38367e12 | −1.44150 | ||||||||
\(93\) | −5.53683e12 | −0.887406 | ||||||||
\(94\) | −2.03156e13 | −3.03737 | ||||||||
\(95\) | 5.63860e10 | 0.00786988 | ||||||||
\(96\) | −1.12733e13 | −1.46991 | ||||||||
\(97\) | 8.44687e12 | 1.02963 | 0.514813 | − | 0.857302i | \(-0.327861\pi\) | ||||
0.514813 | + | 0.857302i | \(0.327861\pi\) | |||||||
\(98\) | 1.17851e13 | 1.34389 | ||||||||
\(99\) | −1.35714e12 | −0.144876 | ||||||||
\(100\) | −2.43165e13 | −2.43165 | ||||||||
\(101\) | 1.23286e13 | 1.15564 | 0.577822 | − | 0.816163i | \(-0.303903\pi\) | ||||
0.577822 | + | 0.816163i | \(0.303903\pi\) | |||||||
\(102\) | 6.13609e12 | 0.539499 | ||||||||
\(103\) | −9.41263e12 | −0.776728 | −0.388364 | − | 0.921506i | \(-0.626960\pi\) | ||||
−0.388364 | + | 0.921506i | \(0.626960\pi\) | |||||||
\(104\) | 2.00741e13 | 1.55568 | ||||||||
\(105\) | −8.52246e11 | −0.0620633 | ||||||||
\(106\) | −1.05486e13 | −0.722279 | ||||||||
\(107\) | 1.46915e12 | 0.0946392 | 0.0473196 | − | 0.998880i | \(-0.484932\pi\) | ||||
0.0473196 | + | 0.998880i | \(0.484932\pi\) | |||||||
\(108\) | 8.04340e12 | 0.487736 | ||||||||
\(109\) | −4.79233e12 | −0.273700 | −0.136850 | − | 0.990592i | \(-0.543698\pi\) | ||||
−0.136850 | + | 0.990592i | \(0.543698\pi\) | |||||||
\(110\) | 3.05616e12 | 0.164484 | ||||||||
\(111\) | −2.15750e13 | −1.09484 | ||||||||
\(112\) | −3.22216e13 | −1.54252 | ||||||||
\(113\) | 3.69814e12 | 0.167099 | 0.0835495 | − | 0.996504i | \(-0.473374\pi\) | ||||
0.0835495 | + | 0.996504i | \(0.473374\pi\) | |||||||
\(114\) | −9.94473e11 | −0.0424337 | ||||||||
\(115\) | −2.84010e12 | −0.114498 | ||||||||
\(116\) | −3.71320e13 | −1.41505 | ||||||||
\(117\) | −4.98801e12 | −0.179771 | ||||||||
\(118\) | 7.17731e12 | 0.244754 | ||||||||
\(119\) | 8.22234e12 | 0.265424 | ||||||||
\(120\) | −1.09660e13 | −0.335251 | ||||||||
\(121\) | −2.80013e13 | −0.811098 | ||||||||
\(122\) | −7.91357e13 | −2.17287 | ||||||||
\(123\) | −9.53791e11 | −0.0248353 | ||||||||
\(124\) | −1.57685e14 | −3.89538 | ||||||||
\(125\) | −1.68231e13 | −0.394449 | ||||||||
\(126\) | 1.50310e13 | 0.334640 | ||||||||
\(127\) | −3.80266e13 | −0.804198 | −0.402099 | − | 0.915596i | \(-0.631719\pi\) | ||||
−0.402099 | + | 0.915596i | \(0.631719\pi\) | |||||||
\(128\) | −5.08441e13 | −1.02182 | ||||||||
\(129\) | 1.14826e12 | 0.0219385 | ||||||||
\(130\) | 1.12325e13 | 0.204102 | ||||||||
\(131\) | 5.84443e13 | 1.01037 | 0.505183 | − | 0.863012i | \(-0.331425\pi\) | ||||
0.505183 | + | 0.863012i | \(0.331425\pi\) | |||||||
\(132\) | −3.86505e13 | −0.635952 | ||||||||
\(133\) | −1.33259e12 | −0.0208767 | ||||||||
\(134\) | −1.37845e14 | −2.05689 | ||||||||
\(135\) | 2.72483e12 | 0.0387408 | ||||||||
\(136\) | 1.05798e14 | 1.43376 | ||||||||
\(137\) | 8.27578e13 | 1.06936 | 0.534682 | − | 0.845053i | \(-0.320431\pi\) | ||||
0.534682 | + | 0.845053i | \(0.320431\pi\) | |||||||
\(138\) | 5.00904e13 | 0.617363 | ||||||||
\(139\) | −5.38267e13 | −0.632997 | −0.316499 | − | 0.948593i | \(-0.602507\pi\) | ||||
−0.316499 | + | 0.948593i | \(0.602507\pi\) | |||||||
\(140\) | −2.42714e13 | −0.272435 | ||||||||
\(141\) | 8.70375e13 | 0.932787 | ||||||||
\(142\) | 4.43118e13 | 0.453571 | ||||||||
\(143\) | 2.39686e13 | 0.234400 | ||||||||
\(144\) | 1.03020e14 | 0.962864 | ||||||||
\(145\) | −1.25790e13 | −0.112397 | ||||||||
\(146\) | −7.75315e13 | −0.662498 | ||||||||
\(147\) | −5.04907e13 | −0.412713 | ||||||||
\(148\) | −6.14442e14 | −4.80595 | ||||||||
\(149\) | −2.71828e13 | −0.203509 | −0.101755 | − | 0.994810i | \(-0.532446\pi\) | ||||
−0.101755 | + | 0.994810i | \(0.532446\pi\) | |||||||
\(150\) | 1.45285e14 | 1.04143 | ||||||||
\(151\) | 1.41607e14 | 0.972151 | 0.486075 | − | 0.873917i | \(-0.338428\pi\) | ||||
0.486075 | + | 0.873917i | \(0.338428\pi\) | |||||||
\(152\) | −1.71467e13 | −0.112771 | ||||||||
\(153\) | −2.62887e13 | −0.165682 | ||||||||
\(154\) | −7.22273e13 | −0.436332 | ||||||||
\(155\) | −5.34183e13 | −0.309410 | ||||||||
\(156\) | −1.42055e14 | −0.789127 | ||||||||
\(157\) | 2.25519e14 | 1.20181 | 0.600904 | − | 0.799321i | \(-0.294807\pi\) | ||||
0.600904 | + | 0.799321i | \(0.294807\pi\) | |||||||
\(158\) | 5.68691e13 | 0.290807 | ||||||||
\(159\) | 4.51929e13 | 0.221814 | ||||||||
\(160\) | −1.08763e14 | −0.512508 | ||||||||
\(161\) | 6.71211e13 | 0.303732 | ||||||||
\(162\) | −4.80574e13 | −0.208887 | ||||||||
\(163\) | −1.83787e13 | −0.0767532 | −0.0383766 | − | 0.999263i | \(-0.512219\pi\) | ||||
−0.0383766 | + | 0.999263i | \(0.512219\pi\) | |||||||
\(164\) | −2.71633e13 | −0.109018 | ||||||||
\(165\) | −1.30934e13 | −0.0505136 | ||||||||
\(166\) | 5.54063e14 | 2.05521 | ||||||||
\(167\) | 2.25320e14 | 0.803790 | 0.401895 | − | 0.915686i | \(-0.368352\pi\) | ||||
0.401895 | + | 0.915686i | \(0.368352\pi\) | |||||||
\(168\) | 2.59164e14 | 0.889332 | ||||||||
\(169\) | −2.14782e14 | −0.709142 | ||||||||
\(170\) | 5.91998e13 | 0.188106 | ||||||||
\(171\) | 4.26060e12 | 0.0130315 | ||||||||
\(172\) | 3.27016e13 | 0.0963018 | ||||||||
\(173\) | −1.50083e14 | −0.425628 | −0.212814 | − | 0.977093i | \(-0.568263\pi\) | ||||
−0.212814 | + | 0.977093i | \(0.568263\pi\) | |||||||
\(174\) | 2.21855e14 | 0.606036 | ||||||||
\(175\) | 1.94682e14 | 0.512364 | ||||||||
\(176\) | −4.95035e14 | −1.25546 | ||||||||
\(177\) | −3.07496e13 | −0.0751646 | ||||||||
\(178\) | 9.49068e13 | 0.223649 | ||||||||
\(179\) | −3.55234e13 | −0.0807179 | −0.0403589 | − | 0.999185i | \(-0.512850\pi\) | ||||
−0.0403589 | + | 0.999185i | \(0.512850\pi\) | |||||||
\(180\) | 7.76011e13 | 0.170058 | ||||||||
\(181\) | 2.64803e14 | 0.559773 | 0.279887 | − | 0.960033i | \(-0.409703\pi\) | ||||
0.279887 | + | 0.960033i | \(0.409703\pi\) | |||||||
\(182\) | −2.65463e14 | −0.541426 | ||||||||
\(183\) | 3.39039e14 | 0.667295 | ||||||||
\(184\) | 8.63659e14 | 1.64069 | ||||||||
\(185\) | −2.08152e14 | −0.381736 | ||||||||
\(186\) | 9.42131e14 | 1.66831 | ||||||||
\(187\) | 1.26324e14 | 0.216030 | ||||||||
\(188\) | 2.47877e15 | 4.09459 | ||||||||
\(189\) | −6.43968e13 | −0.102769 | ||||||||
\(190\) | −9.59448e12 | −0.0147953 | ||||||||
\(191\) | −2.81830e14 | −0.420020 | −0.210010 | − | 0.977699i | \(-0.567350\pi\) | ||||
−0.210010 | + | 0.977699i | \(0.567350\pi\) | |||||||
\(192\) | 7.60571e14 | 1.09568 | ||||||||
\(193\) | −9.99271e14 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(194\) | −1.43729e15 | −1.93568 | ||||||||
\(195\) | −4.81233e13 | −0.0626802 | ||||||||
\(196\) | −1.43794e15 | −1.81166 | ||||||||
\(197\) | 5.75327e14 | 0.701268 | 0.350634 | − | 0.936513i | \(-0.385966\pi\) | ||||
0.350634 | + | 0.936513i | \(0.385966\pi\) | |||||||
\(198\) | 2.30927e14 | 0.272365 | ||||||||
\(199\) | −1.71490e15 | −1.95746 | −0.978732 | − | 0.205144i | \(-0.934234\pi\) | ||||
−0.978732 | + | 0.205144i | \(0.934234\pi\) | |||||||
\(200\) | 2.50501e15 | 2.76767 | ||||||||
\(201\) | 5.90567e14 | 0.631677 | ||||||||
\(202\) | −2.09779e15 | −2.17259 | ||||||||
\(203\) | 2.97285e14 | 0.298159 | ||||||||
\(204\) | −7.48684e14 | −0.727282 | ||||||||
\(205\) | −9.20198e12 | −0.00865927 | ||||||||
\(206\) | 1.60163e15 | 1.46024 | ||||||||
\(207\) | −2.14601e14 | −0.189594 | ||||||||
\(208\) | −1.81944e15 | −1.55785 | ||||||||
\(209\) | −2.04732e13 | −0.0169916 | ||||||||
\(210\) | 1.45016e14 | 0.116678 | ||||||||
\(211\) | −1.77117e15 | −1.38173 | −0.690866 | − | 0.722982i | \(-0.742771\pi\) | ||||
−0.690866 | + | 0.722982i | \(0.742771\pi\) | |||||||
\(212\) | 1.28706e15 | 0.973681 | ||||||||
\(213\) | −1.89844e14 | −0.139293 | ||||||||
\(214\) | −2.49986e14 | −0.177920 | ||||||||
\(215\) | 1.10782e13 | 0.00764924 | ||||||||
\(216\) | −8.28605e14 | −0.555135 | ||||||||
\(217\) | 1.26245e15 | 0.820781 | ||||||||
\(218\) | 8.15449e14 | 0.514552 | ||||||||
\(219\) | 3.32166e14 | 0.203455 | ||||||||
\(220\) | −3.72892e14 | −0.221736 | ||||||||
\(221\) | 4.64287e14 | 0.268063 | ||||||||
\(222\) | 3.67114e15 | 2.05829 | ||||||||
\(223\) | 9.09946e14 | 0.495489 | 0.247745 | − | 0.968825i | \(-0.420311\pi\) | ||||
0.247745 | + | 0.968825i | \(0.420311\pi\) | |||||||
\(224\) | 2.57043e15 | 1.35955 | ||||||||
\(225\) | −6.22443e14 | −0.319826 | ||||||||
\(226\) | −6.29265e14 | −0.314144 | ||||||||
\(227\) | 1.49961e15 | 0.727460 | 0.363730 | − | 0.931504i | \(-0.381503\pi\) | ||||
0.363730 | + | 0.931504i | \(0.381503\pi\) | |||||||
\(228\) | 1.21339e14 | 0.0572036 | ||||||||
\(229\) | −1.44673e14 | −0.0662914 | −0.0331457 | − | 0.999451i | \(-0.510553\pi\) | ||||
−0.0331457 | + | 0.999451i | \(0.510553\pi\) | |||||||
\(230\) | 4.83263e14 | 0.215255 | ||||||||
\(231\) | 3.09442e14 | 0.133999 | ||||||||
\(232\) | 3.82522e15 | 1.61059 | ||||||||
\(233\) | 3.68294e15 | 1.50793 | 0.753964 | − | 0.656915i | \(-0.228139\pi\) | ||||
0.753964 | + | 0.656915i | \(0.228139\pi\) | |||||||
\(234\) | 8.48745e14 | 0.337967 | ||||||||
\(235\) | 8.39721e14 | 0.325233 | ||||||||
\(236\) | −8.75728e14 | −0.329945 | ||||||||
\(237\) | −2.43643e14 | −0.0893079 | ||||||||
\(238\) | −1.39909e15 | −0.498994 | ||||||||
\(239\) | −6.02546e14 | −0.209124 | −0.104562 | − | 0.994518i | \(-0.533344\pi\) | ||||
−0.104562 | + | 0.994518i | \(0.533344\pi\) | |||||||
\(240\) | 9.93916e14 | 0.335719 | ||||||||
\(241\) | 5.03873e14 | 0.165657 | 0.0828286 | − | 0.996564i | \(-0.473605\pi\) | ||||
0.0828286 | + | 0.996564i | \(0.473605\pi\) | |||||||
\(242\) | 4.76462e15 | 1.52485 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | 9.65560e15 | 2.92918 | ||||||||
\(245\) | −4.87124e14 | −0.143900 | ||||||||
\(246\) | 1.62294e14 | 0.0466901 | ||||||||
\(247\) | −7.52467e13 | −0.0210842 | ||||||||
\(248\) | 1.62442e16 | 4.43367 | ||||||||
\(249\) | −2.37376e15 | −0.631162 | ||||||||
\(250\) | 2.86257e15 | 0.741560 | ||||||||
\(251\) | −2.48115e15 | −0.626287 | −0.313143 | − | 0.949706i | \(-0.601382\pi\) | ||||
−0.313143 | + | 0.949706i | \(0.601382\pi\) | |||||||
\(252\) | −1.83398e15 | −0.451118 | ||||||||
\(253\) | 1.03121e15 | 0.247209 | ||||||||
\(254\) | 6.47049e15 | 1.51188 | ||||||||
\(255\) | −2.53628e14 | −0.0577679 | ||||||||
\(256\) | 1.04708e14 | 0.0232498 | ||||||||
\(257\) | 7.50380e15 | 1.62449 | 0.812243 | − | 0.583319i | \(-0.198246\pi\) | ||||
0.812243 | + | 0.583319i | \(0.198246\pi\) | |||||||
\(258\) | −1.95384e14 | −0.0412441 | ||||||||
\(259\) | 4.91932e15 | 1.01264 | ||||||||
\(260\) | −1.37052e15 | −0.275143 | ||||||||
\(261\) | −9.50488e14 | −0.186116 | ||||||||
\(262\) | −9.94471e15 | −1.89948 | ||||||||
\(263\) | 6.65940e14 | 0.124086 | 0.0620430 | − | 0.998073i | \(-0.480238\pi\) | ||||
0.0620430 | + | 0.998073i | \(0.480238\pi\) | |||||||
\(264\) | 3.98165e15 | 0.723831 | ||||||||
\(265\) | 4.36013e14 | 0.0773394 | ||||||||
\(266\) | 2.26750e14 | 0.0392479 | ||||||||
\(267\) | −4.06607e14 | −0.0686834 | ||||||||
\(268\) | 1.68190e16 | 2.77283 | ||||||||
\(269\) | 3.46513e14 | 0.0557609 | 0.0278804 | − | 0.999611i | \(-0.491124\pi\) | ||||
0.0278804 | + | 0.999611i | \(0.491124\pi\) | |||||||
\(270\) | −4.63648e14 | −0.0728323 | ||||||||
\(271\) | −4.10330e15 | −0.629264 | −0.314632 | − | 0.949214i | \(-0.601881\pi\) | ||||
−0.314632 | + | 0.949214i | \(0.601881\pi\) | |||||||
\(272\) | −9.58915e15 | −1.43576 | ||||||||
\(273\) | 1.13732e15 | 0.166274 | ||||||||
\(274\) | −1.40818e16 | −2.01039 | ||||||||
\(275\) | 2.99099e15 | 0.417016 | ||||||||
\(276\) | −6.11170e15 | −0.832248 | ||||||||
\(277\) | 2.44658e15 | 0.325417 | 0.162709 | − | 0.986674i | \(-0.447977\pi\) | ||||
0.162709 | + | 0.986674i | \(0.447977\pi\) | |||||||
\(278\) | 9.15900e15 | 1.19003 | ||||||||
\(279\) | −4.03635e15 | −0.512344 | ||||||||
\(280\) | 2.50036e15 | 0.310081 | ||||||||
\(281\) | 4.71511e15 | 0.571347 | 0.285674 | − | 0.958327i | \(-0.407783\pi\) | ||||
0.285674 | + | 0.958327i | \(0.407783\pi\) | |||||||
\(282\) | −1.48100e16 | −1.75363 | ||||||||
\(283\) | −3.74240e15 | −0.433050 | −0.216525 | − | 0.976277i | \(-0.569472\pi\) | ||||
−0.216525 | + | 0.976277i | \(0.569472\pi\) | |||||||
\(284\) | −5.40662e15 | −0.611444 | ||||||||
\(285\) | 4.11054e13 | 0.00454368 | ||||||||
\(286\) | −4.07842e15 | −0.440669 | ||||||||
\(287\) | 2.17474e14 | 0.0229707 | ||||||||
\(288\) | −8.21826e15 | −0.848650 | ||||||||
\(289\) | −7.45761e15 | −0.752946 | ||||||||
\(290\) | 2.14041e15 | 0.211305 | ||||||||
\(291\) | 6.15777e15 | 0.594455 | ||||||||
\(292\) | 9.45987e15 | 0.893093 | ||||||||
\(293\) | −3.63287e15 | −0.335437 | −0.167718 | − | 0.985835i | \(-0.553640\pi\) | ||||
−0.167718 | + | 0.985835i | \(0.553640\pi\) | |||||||
\(294\) | 8.59134e15 | 0.775896 | ||||||||
\(295\) | −2.96666e14 | −0.0262075 | ||||||||
\(296\) | 6.32978e16 | 5.47007 | ||||||||
\(297\) | −9.89356e14 | −0.0836442 | ||||||||
\(298\) | 4.62535e15 | 0.382594 | ||||||||
\(299\) | 3.79009e15 | 0.306751 | ||||||||
\(300\) | −1.77268e16 | −1.40392 | ||||||||
\(301\) | −2.61814e14 | −0.0202914 | ||||||||
\(302\) | −2.40954e16 | −1.82763 | ||||||||
\(303\) | 8.98753e15 | 0.667211 | ||||||||
\(304\) | 1.55411e15 | 0.112928 | ||||||||
\(305\) | 3.27098e15 | 0.232664 | ||||||||
\(306\) | 4.47321e15 | 0.311480 | ||||||||
\(307\) | −1.47965e16 | −1.00869 | −0.504346 | − | 0.863501i | \(-0.668266\pi\) | ||||
−0.504346 | + | 0.863501i | \(0.668266\pi\) | |||||||
\(308\) | 8.81269e15 | 0.588205 | ||||||||
\(309\) | −6.86181e15 | −0.448444 | ||||||||
\(310\) | 9.08950e15 | 0.581686 | ||||||||
\(311\) | −2.91507e15 | −0.182686 | −0.0913432 | − | 0.995819i | \(-0.529116\pi\) | ||||
−0.0913432 | + | 0.995819i | \(0.529116\pi\) | |||||||
\(312\) | 1.46341e16 | 0.898173 | ||||||||
\(313\) | 1.73118e15 | 0.104065 | 0.0520323 | − | 0.998645i | \(-0.483430\pi\) | ||||
0.0520323 | + | 0.998645i | \(0.483430\pi\) | |||||||
\(314\) | −3.83736e16 | −2.25939 | ||||||||
\(315\) | −6.21287e14 | −0.0358322 | ||||||||
\(316\) | −6.93879e15 | −0.392028 | ||||||||
\(317\) | −1.45553e16 | −0.805629 | −0.402815 | − | 0.915282i | \(-0.631968\pi\) | ||||
−0.402815 | + | 0.915282i | \(0.631968\pi\) | |||||||
\(318\) | −7.68989e15 | −0.417008 | ||||||||
\(319\) | 4.56732e15 | 0.242673 | ||||||||
\(320\) | 7.33784e15 | 0.382026 | ||||||||
\(321\) | 1.07101e15 | 0.0546399 | ||||||||
\(322\) | −1.14211e16 | −0.571012 | ||||||||
\(323\) | −3.96579e14 | −0.0194318 | ||||||||
\(324\) | 5.86364e15 | 0.281595 | ||||||||
\(325\) | 1.09930e16 | 0.517458 | ||||||||
\(326\) | 3.12727e15 | 0.144295 | ||||||||
\(327\) | −3.49361e15 | −0.158021 | ||||||||
\(328\) | 2.79828e15 | 0.124083 | ||||||||
\(329\) | −1.98454e16 | −0.862754 | ||||||||
\(330\) | 2.22794e15 | 0.0949649 | ||||||||
\(331\) | 3.05897e16 | 1.27848 | 0.639239 | − | 0.769008i | \(-0.279250\pi\) | ||||
0.639239 | + | 0.769008i | \(0.279250\pi\) | |||||||
\(332\) | −6.76030e16 | −2.77057 | ||||||||
\(333\) | −1.57282e16 | −0.632108 | ||||||||
\(334\) | −3.83398e16 | −1.51111 | ||||||||
\(335\) | 5.69768e15 | 0.220245 | ||||||||
\(336\) | −2.34896e16 | −0.890573 | ||||||||
\(337\) | 1.53397e16 | 0.570455 | 0.285228 | − | 0.958460i | \(-0.407931\pi\) | ||||
0.285228 | + | 0.958460i | \(0.407931\pi\) | |||||||
\(338\) | 3.65466e16 | 1.33318 | ||||||||
\(339\) | 2.69595e15 | 0.0964746 | ||||||||
\(340\) | −7.22316e15 | −0.253580 | ||||||||
\(341\) | 1.93956e16 | 0.668037 | ||||||||
\(342\) | −7.24971e14 | −0.0244991 | ||||||||
\(343\) | 2.76172e16 | 0.915731 | ||||||||
\(344\) | −3.36882e15 | −0.109609 | ||||||||
\(345\) | −2.07043e15 | −0.0661054 | ||||||||
\(346\) | 2.55376e16 | 0.800176 | ||||||||
\(347\) | 5.54727e15 | 0.170584 | 0.0852919 | − | 0.996356i | \(-0.472818\pi\) | ||||
0.0852919 | + | 0.996356i | \(0.472818\pi\) | |||||||
\(348\) | −2.70692e16 | −0.816979 | ||||||||
\(349\) | 9.99234e14 | 0.0296007 | 0.0148003 | − | 0.999890i | \(-0.495289\pi\) | ||||
0.0148003 | + | 0.999890i | \(0.495289\pi\) | |||||||
\(350\) | −3.31265e16 | −0.963238 | ||||||||
\(351\) | −3.63626e15 | −0.103791 | ||||||||
\(352\) | 3.94907e16 | 1.10654 | ||||||||
\(353\) | −4.57025e16 | −1.25720 | −0.628600 | − | 0.777728i | \(-0.716372\pi\) | ||||
−0.628600 | + | 0.777728i | \(0.716372\pi\) | |||||||
\(354\) | 5.23226e15 | 0.141309 | ||||||||
\(355\) | −1.83158e15 | −0.0485670 | ||||||||
\(356\) | −1.15799e16 | −0.301495 | ||||||||
\(357\) | 5.99409e15 | 0.153243 | ||||||||
\(358\) | 6.04456e15 | 0.151749 | ||||||||
\(359\) | −1.82839e16 | −0.450771 | −0.225386 | − | 0.974270i | \(-0.572364\pi\) | ||||
−0.225386 | + | 0.974270i | \(0.572364\pi\) | |||||||
\(360\) | −7.99422e15 | −0.193557 | ||||||||
\(361\) | −4.19887e16 | −0.998472 | ||||||||
\(362\) | −4.50581e16 | −1.05237 | ||||||||
\(363\) | −2.04130e16 | −0.468288 | ||||||||
\(364\) | 3.23900e16 | 0.729880 | ||||||||
\(365\) | 3.20468e15 | 0.0709382 | ||||||||
\(366\) | −5.76899e16 | −1.25451 | ||||||||
\(367\) | −4.89157e16 | −1.04501 | −0.522503 | − | 0.852637i | \(-0.675002\pi\) | ||||
−0.522503 | + | 0.852637i | \(0.675002\pi\) | |||||||
\(368\) | −7.82786e16 | −1.64298 | ||||||||
\(369\) | −6.95313e14 | −0.0143387 | ||||||||
\(370\) | 3.54184e16 | 0.717659 | ||||||||
\(371\) | −1.03044e16 | −0.205161 | ||||||||
\(372\) | −1.14953e17 | −2.24900 | ||||||||
\(373\) | 1.99499e16 | 0.383560 | 0.191780 | − | 0.981438i | \(-0.438574\pi\) | ||||
0.191780 | + | 0.981438i | \(0.438574\pi\) | |||||||
\(374\) | −2.14948e16 | −0.406134 | ||||||||
\(375\) | −1.22640e16 | −0.227735 | ||||||||
\(376\) | −2.55355e17 | −4.66040 | ||||||||
\(377\) | 1.67866e16 | 0.301123 | ||||||||
\(378\) | 1.09576e16 | 0.193205 | ||||||||
\(379\) | 3.65263e16 | 0.633068 | 0.316534 | − | 0.948581i | \(-0.397481\pi\) | ||||
0.316534 | + | 0.948581i | \(0.397481\pi\) | |||||||
\(380\) | 1.17065e15 | 0.0199450 | ||||||||
\(381\) | −2.77214e16 | −0.464304 | ||||||||
\(382\) | 4.79553e16 | 0.789633 | ||||||||
\(383\) | 2.23028e16 | 0.361050 | 0.180525 | − | 0.983570i | \(-0.442220\pi\) | ||||
0.180525 | + | 0.983570i | \(0.442220\pi\) | |||||||
\(384\) | −3.70653e16 | −0.589950 | ||||||||
\(385\) | 2.98544e15 | 0.0467211 | ||||||||
\(386\) | 1.70033e17 | 2.61647 | ||||||||
\(387\) | 8.37080e14 | 0.0126662 | ||||||||
\(388\) | 1.75369e17 | 2.60944 | ||||||||
\(389\) | 5.46805e16 | 0.800129 | 0.400065 | − | 0.916487i | \(-0.368988\pi\) | ||||
0.400065 | + | 0.916487i | \(0.368988\pi\) | |||||||
\(390\) | 8.18852e15 | 0.117838 | ||||||||
\(391\) | 1.99752e16 | 0.282711 | ||||||||
\(392\) | 1.48132e17 | 2.06200 | ||||||||
\(393\) | 4.26059e16 | 0.583335 | ||||||||
\(394\) | −9.78959e16 | −1.31837 | ||||||||
\(395\) | −2.35062e15 | −0.0311388 | ||||||||
\(396\) | −2.81762e16 | −0.367167 | ||||||||
\(397\) | 1.28646e17 | 1.64914 | 0.824569 | − | 0.565761i | \(-0.191418\pi\) | ||||
0.824569 | + | 0.565761i | \(0.191418\pi\) | |||||||
\(398\) | 2.91802e17 | 3.68001 | ||||||||
\(399\) | −9.71459e14 | −0.0120531 | ||||||||
\(400\) | −2.27044e17 | −2.77154 | ||||||||
\(401\) | 3.90820e16 | 0.469394 | 0.234697 | − | 0.972069i | \(-0.424590\pi\) | ||||
0.234697 | + | 0.972069i | \(0.424590\pi\) | |||||||
\(402\) | −1.00489e17 | −1.18754 | ||||||||
\(403\) | 7.12863e16 | 0.828940 | ||||||||
\(404\) | 2.55959e17 | 2.92881 | ||||||||
\(405\) | 1.98640e15 | 0.0223670 | ||||||||
\(406\) | −5.05851e16 | −0.560536 | ||||||||
\(407\) | 7.55777e16 | 0.824195 | ||||||||
\(408\) | 7.71271e16 | 0.827781 | ||||||||
\(409\) | 1.58381e17 | 1.67302 | 0.836511 | − | 0.547949i | \(-0.184591\pi\) | ||||
0.836511 | + | 0.547949i | \(0.184591\pi\) | |||||||
\(410\) | 1.56578e15 | 0.0162793 | ||||||||
\(411\) | 6.03305e16 | 0.617397 | ||||||||
\(412\) | −1.95420e17 | −1.96850 | ||||||||
\(413\) | 7.01122e15 | 0.0695213 | ||||||||
\(414\) | 3.65159e16 | 0.356435 | ||||||||
\(415\) | −2.29016e16 | −0.220066 | ||||||||
\(416\) | 1.45143e17 | 1.37306 | ||||||||
\(417\) | −3.92397e16 | −0.365461 | ||||||||
\(418\) | 3.48366e15 | 0.0319440 | ||||||||
\(419\) | −1.75996e16 | −0.158895 | −0.0794476 | − | 0.996839i | \(-0.525316\pi\) | ||||
−0.0794476 | + | 0.996839i | \(0.525316\pi\) | |||||||
\(420\) | −1.76938e16 | −0.157290 | ||||||||
\(421\) | −6.49651e16 | −0.568652 | −0.284326 | − | 0.958728i | \(-0.591770\pi\) | ||||
−0.284326 | + | 0.958728i | \(0.591770\pi\) | |||||||
\(422\) | 3.01377e17 | 2.59764 | ||||||||
\(423\) | 6.34504e16 | 0.538545 | ||||||||
\(424\) | −1.32589e17 | −1.10823 | ||||||||
\(425\) | 5.79374e16 | 0.476904 | ||||||||
\(426\) | 3.23033e16 | 0.261869 | ||||||||
\(427\) | −7.73043e16 | −0.617195 | ||||||||
\(428\) | 3.05016e16 | 0.239849 | ||||||||
\(429\) | 1.74731e16 | 0.135331 | ||||||||
\(430\) | −1.88503e15 | −0.0143805 | ||||||||
\(431\) | 2.25555e17 | 1.69493 | 0.847463 | − | 0.530854i | \(-0.178129\pi\) | ||||
0.847463 | + | 0.530854i | \(0.178129\pi\) | |||||||
\(432\) | 7.51015e16 | 0.555910 | ||||||||
\(433\) | −7.21930e16 | −0.526410 | −0.263205 | − | 0.964740i | \(-0.584780\pi\) | ||||
−0.263205 | + | 0.964740i | \(0.584780\pi\) | |||||||
\(434\) | −2.14815e17 | −1.54306 | ||||||||
\(435\) | −9.17012e15 | −0.0648925 | ||||||||
\(436\) | −9.94956e16 | −0.693652 | ||||||||
\(437\) | −3.23737e15 | −0.0222363 | ||||||||
\(438\) | −5.65204e16 | −0.382493 | ||||||||
\(439\) | 2.09300e17 | 1.39557 | 0.697783 | − | 0.716309i | \(-0.254170\pi\) | ||||
0.697783 | + | 0.716309i | \(0.254170\pi\) | |||||||
\(440\) | 3.84142e16 | 0.252377 | ||||||||
\(441\) | −3.68077e16 | −0.238280 | ||||||||
\(442\) | −7.90016e16 | −0.503955 | ||||||||
\(443\) | 2.71262e17 | 1.70516 | 0.852578 | − | 0.522600i | \(-0.175038\pi\) | ||||
0.852578 | + | 0.522600i | \(0.175038\pi\) | |||||||
\(444\) | −4.47928e17 | −2.77472 | ||||||||
\(445\) | −3.92287e15 | −0.0239477 | ||||||||
\(446\) | −1.54834e17 | −0.931514 | ||||||||
\(447\) | −1.98163e16 | −0.117496 | ||||||||
\(448\) | −1.73418e17 | −1.01341 | ||||||||
\(449\) | 1.68893e17 | 0.972773 | 0.486386 | − | 0.873744i | \(-0.338315\pi\) | ||||
0.486386 | + | 0.873744i | \(0.338315\pi\) | |||||||
\(450\) | 1.05913e17 | 0.601268 | ||||||||
\(451\) | 3.34115e15 | 0.0186960 | ||||||||
\(452\) | 7.67787e16 | 0.423488 | ||||||||
\(453\) | 1.03231e17 | 0.561272 | ||||||||
\(454\) | −2.55168e17 | −1.36762 | ||||||||
\(455\) | 1.09726e16 | 0.0579743 | ||||||||
\(456\) | −1.24999e16 | −0.0651083 | ||||||||
\(457\) | −7.01661e16 | −0.360306 | −0.180153 | − | 0.983639i | \(-0.557659\pi\) | ||||
−0.180153 | + | 0.983639i | \(0.557659\pi\) | |||||||
\(458\) | 2.46171e16 | 0.124627 | ||||||||
\(459\) | −1.91645e16 | −0.0956564 | ||||||||
\(460\) | −5.89645e16 | −0.290178 | ||||||||
\(461\) | −2.49241e17 | −1.20938 | −0.604691 | − | 0.796460i | \(-0.706703\pi\) | ||||
−0.604691 | + | 0.796460i | \(0.706703\pi\) | |||||||
\(462\) | −5.26537e16 | −0.251916 | ||||||||
\(463\) | 9.84433e16 | 0.464419 | 0.232209 | − | 0.972666i | \(-0.425405\pi\) | ||||
0.232209 | + | 0.972666i | \(0.425405\pi\) | |||||||
\(464\) | −3.46703e17 | −1.61284 | ||||||||
\(465\) | −3.89419e16 | −0.178638 | ||||||||
\(466\) | −6.26678e17 | −2.83489 | ||||||||
\(467\) | 8.80036e16 | 0.392591 | 0.196296 | − | 0.980545i | \(-0.437109\pi\) | ||||
0.196296 | + | 0.980545i | \(0.437109\pi\) | |||||||
\(468\) | −1.03558e17 | −0.455602 | ||||||||
\(469\) | −1.34655e17 | −0.584252 | ||||||||
\(470\) | −1.42884e17 | −0.611433 | ||||||||
\(471\) | 1.64403e17 | 0.693865 | ||||||||
\(472\) | 9.02147e16 | 0.375538 | ||||||||
\(473\) | −4.02237e15 | −0.0165152 | ||||||||
\(474\) | 4.14576e16 | 0.167898 | ||||||||
\(475\) | −9.38988e15 | −0.0375104 | ||||||||
\(476\) | 1.70707e17 | 0.672678 | ||||||||
\(477\) | 3.29456e16 | 0.128064 | ||||||||
\(478\) | 1.02527e17 | 0.393151 | ||||||||
\(479\) | 9.72567e16 | 0.367907 | 0.183954 | − | 0.982935i | \(-0.441110\pi\) | ||||
0.183954 | + | 0.982935i | \(0.441110\pi\) | |||||||
\(480\) | −7.92882e16 | −0.295897 | ||||||||
\(481\) | 2.77777e17 | 1.02271 | ||||||||
\(482\) | −8.57375e16 | −0.311433 | ||||||||
\(483\) | 4.89312e16 | 0.175360 | ||||||||
\(484\) | −5.81347e17 | −2.05561 | ||||||||
\(485\) | 5.94090e16 | 0.207267 | ||||||||
\(486\) | −3.50338e16 | −0.120601 | ||||||||
\(487\) | 2.54834e17 | 0.865604 | 0.432802 | − | 0.901489i | \(-0.357525\pi\) | ||||
0.432802 | + | 0.901489i | \(0.357525\pi\) | |||||||
\(488\) | −9.94689e17 | −3.33395 | ||||||||
\(489\) | −1.33981e16 | −0.0443135 | ||||||||
\(490\) | 8.28876e16 | 0.270530 | ||||||||
\(491\) | −4.17339e17 | −1.34419 | −0.672093 | − | 0.740467i | \(-0.734605\pi\) | ||||
−0.672093 | + | 0.740467i | \(0.734605\pi\) | |||||||
\(492\) | −1.98020e16 | −0.0629415 | ||||||||
\(493\) | 8.84719e16 | 0.277524 | ||||||||
\(494\) | 1.28038e16 | 0.0396380 | ||||||||
\(495\) | −9.54512e15 | −0.0291640 | ||||||||
\(496\) | −1.47231e18 | −4.43986 | ||||||||
\(497\) | 4.32863e16 | 0.128835 | ||||||||
\(498\) | 4.03912e17 | 1.18658 | ||||||||
\(499\) | −5.29556e16 | −0.153553 | −0.0767765 | − | 0.997048i | \(-0.524463\pi\) | ||||
−0.0767765 | + | 0.997048i | \(0.524463\pi\) | |||||||
\(500\) | −3.49272e17 | −0.999674 | ||||||||
\(501\) | 1.64258e17 | 0.464068 | ||||||||
\(502\) | 4.22184e17 | 1.17741 | ||||||||
\(503\) | 3.57602e17 | 0.984483 | 0.492241 | − | 0.870459i | \(-0.336178\pi\) | ||||
0.492241 | + | 0.870459i | \(0.336178\pi\) | |||||||
\(504\) | 1.88930e17 | 0.513456 | ||||||||
\(505\) | 8.67099e16 | 0.232635 | ||||||||
\(506\) | −1.75468e17 | −0.464750 | ||||||||
\(507\) | −1.56576e17 | −0.409424 | ||||||||
\(508\) | −7.89485e17 | −2.03812 | ||||||||
\(509\) | 5.77008e17 | 1.47067 | 0.735337 | − | 0.677702i | \(-0.237024\pi\) | ||||
0.735337 | + | 0.677702i | \(0.237024\pi\) | |||||||
\(510\) | 4.31566e16 | 0.108603 | ||||||||
\(511\) | −7.57372e16 | −0.188180 | ||||||||
\(512\) | 3.98698e17 | 0.978114 | ||||||||
\(513\) | 3.10598e15 | 0.00752376 | ||||||||
\(514\) | −1.27682e18 | −3.05401 | ||||||||
\(515\) | −6.62014e16 | −0.156358 | ||||||||
\(516\) | 2.38395e16 | 0.0555998 | ||||||||
\(517\) | −3.04894e17 | −0.702200 | ||||||||
\(518\) | −8.37057e17 | −1.90376 | ||||||||
\(519\) | −1.09410e17 | −0.245737 | ||||||||
\(520\) | 1.41186e17 | 0.313164 | ||||||||
\(521\) | −4.44092e17 | −0.972810 | −0.486405 | − | 0.873733i | \(-0.661692\pi\) | ||||
−0.486405 | + | 0.873733i | \(0.661692\pi\) | |||||||
\(522\) | 1.61732e17 | 0.349895 | ||||||||
\(523\) | 6.78619e17 | 1.44999 | 0.724995 | − | 0.688755i | \(-0.241842\pi\) | ||||
0.724995 | + | 0.688755i | \(0.241842\pi\) | |||||||
\(524\) | 1.21339e18 | 2.56062 | ||||||||
\(525\) | 1.41923e17 | 0.295814 | ||||||||
\(526\) | −1.13314e17 | −0.233280 | ||||||||
\(527\) | 3.75706e17 | 0.763975 | ||||||||
\(528\) | −3.60881e17 | −0.724842 | ||||||||
\(529\) | −3.40974e17 | −0.676486 | ||||||||
\(530\) | −7.41906e16 | −0.145397 | ||||||||
\(531\) | −2.24165e16 | −0.0433963 | ||||||||
\(532\) | −2.76665e16 | −0.0529088 | ||||||||
\(533\) | 1.22800e16 | 0.0231991 | ||||||||
\(534\) | 6.91871e16 | 0.129124 | ||||||||
\(535\) | 1.03329e16 | 0.0190512 | ||||||||
\(536\) | −1.73263e18 | −3.15599 | ||||||||
\(537\) | −2.58966e16 | −0.0466025 | ||||||||
\(538\) | −5.89616e16 | −0.104830 | ||||||||
\(539\) | 1.76870e17 | 0.310690 | ||||||||
\(540\) | 5.65712e16 | 0.0981830 | ||||||||
\(541\) | 6.99335e17 | 1.19923 | 0.599616 | − | 0.800288i | \(-0.295320\pi\) | ||||
0.599616 | + | 0.800288i | \(0.295320\pi\) | |||||||
\(542\) | 6.98206e17 | 1.18301 | ||||||||
\(543\) | 1.93041e17 | 0.323185 | ||||||||
\(544\) | 7.64961e17 | 1.26545 | ||||||||
\(545\) | −3.37057e16 | −0.0550967 | ||||||||
\(546\) | −1.93522e17 | −0.312593 | ||||||||
\(547\) | 5.92322e16 | 0.0945454 | 0.0472727 | − | 0.998882i | \(-0.484947\pi\) | ||||
0.0472727 | + | 0.998882i | \(0.484947\pi\) | |||||||
\(548\) | 1.71817e18 | 2.71014 | ||||||||
\(549\) | 2.47160e17 | 0.385263 | ||||||||
\(550\) | −5.08938e17 | −0.783984 | ||||||||
\(551\) | −1.43386e16 | −0.0218284 | ||||||||
\(552\) | 6.29608e17 | 0.947253 | ||||||||
\(553\) | 5.55531e16 | 0.0826028 | ||||||||
\(554\) | −4.16303e17 | −0.611780 | ||||||||
\(555\) | −1.51742e17 | −0.220396 | ||||||||
\(556\) | −1.11752e18 | −1.60424 | ||||||||
\(557\) | 7.37090e17 | 1.04583 | 0.522916 | − | 0.852384i | \(-0.324844\pi\) | ||||
0.522916 | + | 0.852384i | \(0.324844\pi\) | |||||||
\(558\) | 6.86814e17 | 0.963200 | ||||||||
\(559\) | −1.47837e16 | −0.0204931 | ||||||||
\(560\) | −2.26623e17 | −0.310514 | ||||||||
\(561\) | 9.20899e16 | 0.124725 | ||||||||
\(562\) | −8.02308e17 | −1.07413 | ||||||||
\(563\) | −1.24785e17 | −0.165142 | −0.0825711 | − | 0.996585i | \(-0.526313\pi\) | ||||
−0.0825711 | + | 0.996585i | \(0.526313\pi\) | |||||||
\(564\) | 1.80702e18 | 2.36401 | ||||||||
\(565\) | 2.60100e16 | 0.0336376 | ||||||||
\(566\) | 6.36795e17 | 0.814128 | ||||||||
\(567\) | −4.69452e16 | −0.0593337 | ||||||||
\(568\) | 5.56973e17 | 0.695937 | ||||||||
\(569\) | −1.59085e18 | −1.96517 | −0.982584 | − | 0.185817i | \(-0.940507\pi\) | ||||
−0.982584 | + | 0.185817i | \(0.940507\pi\) | |||||||
\(570\) | −6.99437e15 | −0.00854205 | ||||||||
\(571\) | 1.47573e18 | 1.78185 | 0.890926 | − | 0.454148i | \(-0.150056\pi\) | ||||
0.890926 | + | 0.454148i | \(0.150056\pi\) | |||||||
\(572\) | 4.97622e17 | 0.594053 | ||||||||
\(573\) | −2.05454e17 | −0.242499 | ||||||||
\(574\) | −3.70047e16 | −0.0431847 | ||||||||
\(575\) | 4.72957e17 | 0.545734 | ||||||||
\(576\) | 5.54456e17 | 0.632588 | ||||||||
\(577\) | −2.17224e17 | −0.245056 | −0.122528 | − | 0.992465i | \(-0.539100\pi\) | ||||
−0.122528 | + | 0.992465i | \(0.539100\pi\) | |||||||
\(578\) | 1.26896e18 | 1.41553 | ||||||||
\(579\) | −7.28469e17 | −0.803526 | ||||||||
\(580\) | −2.61159e17 | −0.284854 | ||||||||
\(581\) | 5.41241e17 | 0.583775 | ||||||||
\(582\) | −1.04779e18 | −1.11757 | ||||||||
\(583\) | −1.58312e17 | −0.166981 | ||||||||
\(584\) | −9.74525e17 | −1.01651 | ||||||||
\(585\) | −3.50819e16 | −0.0361885 | ||||||||
\(586\) | 6.18159e17 | 0.630617 | ||||||||
\(587\) | −1.98633e17 | −0.200403 | −0.100201 | − | 0.994967i | \(-0.531949\pi\) | ||||
−0.100201 | + | 0.994967i | \(0.531949\pi\) | |||||||
\(588\) | −1.04826e18 | −1.04596 | ||||||||
\(589\) | −6.08905e16 | −0.0600897 | ||||||||
\(590\) | 5.04798e16 | 0.0492697 | ||||||||
\(591\) | 4.19413e17 | 0.404877 | ||||||||
\(592\) | −5.73706e18 | −5.47770 | ||||||||
\(593\) | −6.95171e17 | −0.656502 | −0.328251 | − | 0.944591i | \(-0.606459\pi\) | ||||
−0.328251 | + | 0.944591i | \(0.606459\pi\) | |||||||
\(594\) | 1.68346e17 | 0.157250 | ||||||||
\(595\) | 5.78298e16 | 0.0534308 | ||||||||
\(596\) | −5.64354e17 | −0.515764 | ||||||||
\(597\) | −1.25016e18 | −1.13014 | ||||||||
\(598\) | −6.44910e17 | −0.576689 | ||||||||
\(599\) | 1.54769e18 | 1.36902 | 0.684508 | − | 0.729005i | \(-0.260017\pi\) | ||||
0.684508 | + | 0.729005i | \(0.260017\pi\) | |||||||
\(600\) | 1.82615e18 | 1.59792 | ||||||||
\(601\) | −1.19539e17 | −0.103473 | −0.0517363 | − | 0.998661i | \(-0.516476\pi\) | ||||
−0.0517363 | + | 0.998661i | \(0.516476\pi\) | |||||||
\(602\) | 4.45496e16 | 0.0381475 | ||||||||
\(603\) | 4.30524e17 | 0.364699 | ||||||||
\(604\) | 2.93996e18 | 2.46377 | ||||||||
\(605\) | −1.96940e17 | −0.163277 | ||||||||
\(606\) | −1.52929e18 | −1.25435 | ||||||||
\(607\) | 9.17599e16 | 0.0744606 | 0.0372303 | − | 0.999307i | \(-0.488146\pi\) | ||||
0.0372303 | + | 0.999307i | \(0.488146\pi\) | |||||||
\(608\) | −1.23977e17 | −0.0995330 | ||||||||
\(609\) | 2.16721e17 | 0.172142 | ||||||||
\(610\) | −5.56581e17 | −0.437406 | ||||||||
\(611\) | −1.12060e18 | −0.871331 | ||||||||
\(612\) | −5.45791e17 | −0.419896 | ||||||||
\(613\) | −5.26140e17 | −0.400505 | −0.200253 | − | 0.979744i | \(-0.564176\pi\) | ||||
−0.200253 | + | 0.979744i | \(0.564176\pi\) | |||||||
\(614\) | 2.51772e18 | 1.89633 | ||||||||
\(615\) | −6.70825e15 | −0.00499943 | ||||||||
\(616\) | −9.07856e17 | −0.669487 | ||||||||
\(617\) | −6.58913e17 | −0.480811 | −0.240406 | − | 0.970673i | \(-0.577280\pi\) | ||||
−0.240406 | + | 0.970673i | \(0.577280\pi\) | |||||||
\(618\) | 1.16758e18 | 0.843070 | ||||||||
\(619\) | −5.92220e17 | −0.423150 | −0.211575 | − | 0.977362i | \(-0.567859\pi\) | ||||
−0.211575 | + | 0.977362i | \(0.567859\pi\) | |||||||
\(620\) | −1.10904e18 | −0.784153 | ||||||||
\(621\) | −1.56444e17 | −0.109462 | ||||||||
\(622\) | 4.96020e17 | 0.343448 | ||||||||
\(623\) | 9.27105e16 | 0.0635268 | ||||||||
\(624\) | −1.32637e18 | −0.899427 | ||||||||
\(625\) | 1.31141e18 | 0.880073 | ||||||||
\(626\) | −2.94572e17 | −0.195640 | ||||||||
\(627\) | −1.49250e16 | −0.00981012 | ||||||||
\(628\) | 4.68209e18 | 3.04581 | ||||||||
\(629\) | 1.46399e18 | 0.942559 | ||||||||
\(630\) | 1.05716e17 | 0.0673642 | ||||||||
\(631\) | 5.22450e17 | 0.329499 | 0.164750 | − | 0.986335i | \(-0.447318\pi\) | ||||
0.164750 | + | 0.986335i | \(0.447318\pi\) | |||||||
\(632\) | 7.14812e17 | 0.446201 | ||||||||
\(633\) | −1.29118e18 | −0.797744 | ||||||||
\(634\) | 2.47668e18 | 1.51457 | ||||||||
\(635\) | −2.67450e17 | −0.161888 | ||||||||
\(636\) | 9.38269e17 | 0.562155 | ||||||||
\(637\) | 6.50063e17 | 0.385522 | ||||||||
\(638\) | −7.77162e17 | −0.456223 | ||||||||
\(639\) | −1.38396e17 | −0.0804209 | ||||||||
\(640\) | −3.57599e17 | −0.205696 | ||||||||
\(641\) | −2.26268e18 | −1.28838 | −0.644192 | − | 0.764864i | \(-0.722806\pi\) | ||||
−0.644192 | + | 0.764864i | \(0.722806\pi\) | |||||||
\(642\) | −1.82240e17 | −0.102722 | ||||||||
\(643\) | 2.53174e18 | 1.41269 | 0.706347 | − | 0.707866i | \(-0.250342\pi\) | ||||
0.706347 | + | 0.707866i | \(0.250342\pi\) | |||||||
\(644\) | 1.39353e18 | 0.769764 | ||||||||
\(645\) | 8.07599e15 | 0.00441629 | ||||||||
\(646\) | 6.74807e16 | 0.0365315 | ||||||||
\(647\) | −2.92304e18 | −1.56660 | −0.783299 | − | 0.621645i | \(-0.786465\pi\) | ||||
−0.783299 | + | 0.621645i | \(0.786465\pi\) | |||||||
\(648\) | −6.04053e17 | −0.320507 | ||||||||
\(649\) | 1.07717e17 | 0.0565838 | ||||||||
\(650\) | −1.87054e18 | −0.972814 | ||||||||
\(651\) | 9.20329e17 | 0.473878 | ||||||||
\(652\) | −3.81569e17 | −0.194520 | ||||||||
\(653\) | 2.04456e18 | 1.03196 | 0.515981 | − | 0.856600i | \(-0.327428\pi\) | ||||
0.515981 | + | 0.856600i | \(0.327428\pi\) | |||||||
\(654\) | 5.94462e17 | 0.297077 | ||||||||
\(655\) | 4.11053e17 | 0.203390 | ||||||||
\(656\) | −2.53625e17 | −0.124256 | ||||||||
\(657\) | 2.42149e17 | 0.117465 | ||||||||
\(658\) | 3.37684e18 | 1.62197 | ||||||||
\(659\) | 2.35125e18 | 1.11826 | 0.559130 | − | 0.829080i | \(-0.311135\pi\) | ||||
0.559130 | + | 0.829080i | \(0.311135\pi\) | |||||||
\(660\) | −2.71838e17 | −0.128019 | ||||||||
\(661\) | 3.60614e18 | 1.68164 | 0.840820 | − | 0.541314i | \(-0.182073\pi\) | ||||
0.840820 | + | 0.541314i | \(0.182073\pi\) | |||||||
\(662\) | −5.20505e18 | −2.40352 | ||||||||
\(663\) | 3.38465e17 | 0.154766 | ||||||||
\(664\) | 6.96424e18 | 3.15342 | ||||||||
\(665\) | −9.37244e15 | −0.00420254 | ||||||||
\(666\) | 2.67626e18 | 1.18835 | ||||||||
\(667\) | 7.22219e17 | 0.317578 | ||||||||
\(668\) | 4.67796e18 | 2.03709 | ||||||||
\(669\) | 6.63351e17 | 0.286071 | ||||||||
\(670\) | −9.69500e17 | −0.414058 | ||||||||
\(671\) | −1.18766e18 | −0.502338 | ||||||||
\(672\) | 1.87385e18 | 0.784935 | ||||||||
\(673\) | −3.12553e17 | −0.129666 | −0.0648329 | − | 0.997896i | \(-0.520651\pi\) | ||||
−0.0648329 | + | 0.997896i | \(0.520651\pi\) | |||||||
\(674\) | −2.61015e18 | −1.07245 | ||||||||
\(675\) | −4.53761e17 | −0.184651 | ||||||||
\(676\) | −4.45917e18 | −1.79722 | ||||||||
\(677\) | −3.40538e17 | −0.135937 | −0.0679687 | − | 0.997687i | \(-0.521652\pi\) | ||||
−0.0679687 | + | 0.997687i | \(0.521652\pi\) | |||||||
\(678\) | −4.58734e17 | −0.181371 | ||||||||
\(679\) | −1.40403e18 | −0.549824 | ||||||||
\(680\) | 7.44107e17 | 0.288621 | ||||||||
\(681\) | 1.09321e18 | 0.419999 | ||||||||
\(682\) | −3.30030e18 | −1.25590 | ||||||||
\(683\) | −2.60485e17 | −0.0981858 | −0.0490929 | − | 0.998794i | \(-0.515633\pi\) | ||||
−0.0490929 | + | 0.998794i | \(0.515633\pi\) | |||||||
\(684\) | 8.84560e16 | 0.0330265 | ||||||||
\(685\) | 5.82057e17 | 0.215266 | ||||||||
\(686\) | −4.69926e18 | −1.72156 | ||||||||
\(687\) | −1.05467e17 | −0.0382734 | ||||||||
\(688\) | 3.05336e17 | 0.109762 | ||||||||
\(689\) | −5.81855e17 | −0.207200 | ||||||||
\(690\) | 3.52298e17 | 0.124277 | ||||||||
\(691\) | −4.25754e18 | −1.48782 | −0.743912 | − | 0.668278i | \(-0.767032\pi\) | ||||
−0.743912 | + | 0.668278i | \(0.767032\pi\) | |||||||
\(692\) | −3.11593e18 | −1.07869 | ||||||||
\(693\) | 2.25583e17 | 0.0773643 | ||||||||
\(694\) | −9.43907e17 | −0.320695 | ||||||||
\(695\) | −3.78577e17 | −0.127425 | ||||||||
\(696\) | 2.78859e18 | 0.929874 | ||||||||
\(697\) | 6.47202e16 | 0.0213809 | ||||||||
\(698\) | −1.70027e17 | −0.0556489 | ||||||||
\(699\) | 2.68486e18 | 0.870603 | ||||||||
\(700\) | 4.04188e18 | 1.29851 | ||||||||
\(701\) | −2.38102e17 | −0.0757871 | −0.0378935 | − | 0.999282i | \(-0.512065\pi\) | ||||
−0.0378935 | + | 0.999282i | \(0.512065\pi\) | |||||||
\(702\) | 6.18735e17 | 0.195125 | ||||||||
\(703\) | −2.37268e17 | −0.0741360 | ||||||||
\(704\) | −2.66430e18 | −0.824822 | ||||||||
\(705\) | 6.12157e17 | 0.187773 | ||||||||
\(706\) | 7.77661e18 | 2.36352 | ||||||||
\(707\) | −2.04925e18 | −0.617118 | ||||||||
\(708\) | −6.38405e17 | −0.190494 | ||||||||
\(709\) | −2.06732e18 | −0.611234 | −0.305617 | − | 0.952154i | \(-0.598863\pi\) | ||||
−0.305617 | + | 0.952154i | \(0.598863\pi\) | |||||||
\(710\) | 3.11656e17 | 0.0913053 | ||||||||
\(711\) | −1.77616e17 | −0.0515619 | ||||||||
\(712\) | 1.19292e18 | 0.343157 | ||||||||
\(713\) | 3.06698e18 | 0.874237 | ||||||||
\(714\) | −1.01994e18 | −0.288094 | ||||||||
\(715\) | 1.68577e17 | 0.0471856 | ||||||||
\(716\) | −7.37516e17 | −0.204568 | ||||||||
\(717\) | −4.39256e17 | −0.120738 | ||||||||
\(718\) | 3.11114e18 | 0.847444 | ||||||||
\(719\) | 1.41798e18 | 0.382766 | 0.191383 | − | 0.981515i | \(-0.438703\pi\) | ||||
0.191383 | + | 0.981515i | \(0.438703\pi\) | |||||||
\(720\) | 7.24564e17 | 0.193828 | ||||||||
\(721\) | 1.56456e18 | 0.414776 | ||||||||
\(722\) | 7.14467e18 | 1.87711 | ||||||||
\(723\) | 3.67323e17 | 0.0956422 | ||||||||
\(724\) | 5.49768e18 | 1.41866 | ||||||||
\(725\) | 2.09477e18 | 0.535721 | ||||||||
\(726\) | 3.47341e18 | 0.880375 | ||||||||
\(727\) | −6.93970e18 | −1.74328 | −0.871640 | − | 0.490146i | \(-0.836943\pi\) | ||||
−0.871640 | + | 0.490146i | \(0.836943\pi\) | |||||||
\(728\) | −3.33671e18 | −0.830739 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −5.45298e17 | −0.133363 | ||||||||
\(731\) | −7.79159e16 | −0.0188870 | ||||||||
\(732\) | 7.03894e18 | 1.69116 | ||||||||
\(733\) | 7.33084e18 | 1.74573 | 0.872866 | − | 0.487960i | \(-0.162259\pi\) | ||||
0.872866 | + | 0.487960i | \(0.162259\pi\) | |||||||
\(734\) | 8.32335e18 | 1.96460 | ||||||||
\(735\) | −3.55113e17 | −0.0830805 | ||||||||
\(736\) | 6.24457e18 | 1.44809 | ||||||||
\(737\) | −2.06877e18 | −0.475525 | ||||||||
\(738\) | 1.18312e17 | 0.0269565 | ||||||||
\(739\) | 5.55464e18 | 1.25449 | 0.627245 | − | 0.778822i | \(-0.284183\pi\) | ||||
0.627245 | + | 0.778822i | \(0.284183\pi\) | |||||||
\(740\) | −4.32152e18 | −0.967454 | ||||||||
\(741\) | −5.48548e16 | −0.0121730 | ||||||||
\(742\) | 1.75337e18 | 0.385699 | ||||||||
\(743\) | 4.83846e18 | 1.05507 | 0.527533 | − | 0.849534i | \(-0.323117\pi\) | ||||
0.527533 | + | 0.849534i | \(0.323117\pi\) | |||||||
\(744\) | 1.18420e19 | 2.55978 | ||||||||
\(745\) | −1.91184e17 | −0.0409671 | ||||||||
\(746\) | −3.39461e18 | −0.721087 | ||||||||
\(747\) | −1.73047e18 | −0.364401 | ||||||||
\(748\) | 2.62266e18 | 0.547496 | ||||||||
\(749\) | −2.44201e17 | −0.0505377 | ||||||||
\(750\) | 2.08681e18 | 0.428140 | ||||||||
\(751\) | −3.87384e18 | −0.787921 | −0.393960 | − | 0.919127i | \(-0.628895\pi\) | ||||
−0.393960 | + | 0.919127i | \(0.628895\pi\) | |||||||
\(752\) | 2.31444e19 | 4.66691 | ||||||||
\(753\) | −1.80876e18 | −0.361587 | ||||||||
\(754\) | −2.85636e18 | −0.566108 | ||||||||
\(755\) | 9.95955e17 | 0.195697 | ||||||||
\(756\) | −1.33697e18 | −0.260453 | ||||||||
\(757\) | 6.22964e18 | 1.20321 | 0.601603 | − | 0.798795i | \(-0.294529\pi\) | ||||
0.601603 | + | 0.798795i | \(0.294529\pi\) | |||||||
\(758\) | −6.21520e18 | −1.19016 | ||||||||
\(759\) | 7.51753e17 | 0.142726 | ||||||||
\(760\) | −1.20597e17 | −0.0227012 | ||||||||
\(761\) | 9.05244e17 | 0.168953 | 0.0844764 | − | 0.996425i | \(-0.473078\pi\) | ||||
0.0844764 | + | 0.996425i | \(0.473078\pi\) | |||||||
\(762\) | 4.71698e18 | 0.872885 | ||||||||
\(763\) | 7.96578e17 | 0.146157 | ||||||||
\(764\) | −5.85119e18 | −1.06448 | ||||||||
\(765\) | −1.84895e17 | −0.0333523 | ||||||||
\(766\) | −3.79498e18 | −0.678769 | ||||||||
\(767\) | 3.95899e17 | 0.0702125 | ||||||||
\(768\) | 7.63321e16 | 0.0134233 | ||||||||
\(769\) | 1.33698e18 | 0.233134 | 0.116567 | − | 0.993183i | \(-0.462811\pi\) | ||||
0.116567 | + | 0.993183i | \(0.462811\pi\) | |||||||
\(770\) | −5.07993e17 | −0.0878351 | ||||||||
\(771\) | 5.47027e18 | 0.937898 | ||||||||
\(772\) | −2.07463e19 | −3.52718 | ||||||||
\(773\) | −4.30300e18 | −0.725446 | −0.362723 | − | 0.931897i | \(-0.618153\pi\) | ||||
−0.362723 | + | 0.931897i | \(0.618153\pi\) | |||||||
\(774\) | −1.42435e17 | −0.0238123 | ||||||||
\(775\) | 8.89567e18 | 1.47475 | ||||||||
\(776\) | −1.80660e19 | −2.97002 | ||||||||
\(777\) | 3.58618e18 | 0.584650 | ||||||||
\(778\) | −9.30427e18 | −1.50423 | ||||||||
\(779\) | −1.04892e16 | −0.00168170 | ||||||||
\(780\) | −9.99108e17 | −0.158854 | ||||||||
\(781\) | 6.65027e17 | 0.104859 | ||||||||
\(782\) | −3.39892e18 | −0.531493 | ||||||||
\(783\) | −6.92905e17 | −0.107454 | ||||||||
\(784\) | −1.34261e19 | −2.06488 | ||||||||
\(785\) | 1.58613e18 | 0.241928 | ||||||||
\(786\) | −7.24969e18 | −1.09666 | ||||||||
\(787\) | 1.00855e19 | 1.51309 | 0.756543 | − | 0.653944i | \(-0.226887\pi\) | ||||
0.756543 | + | 0.653944i | \(0.226887\pi\) | |||||||
\(788\) | 1.19446e19 | 1.77726 | ||||||||
\(789\) | 4.85470e17 | 0.0716411 | ||||||||
\(790\) | 3.99975e17 | 0.0585405 | ||||||||
\(791\) | −6.14703e17 | −0.0892315 | ||||||||
\(792\) | 2.90262e18 | 0.417904 | ||||||||
\(793\) | −4.36510e18 | −0.623331 | ||||||||
\(794\) | −2.18900e19 | −3.10036 | ||||||||
\(795\) | 3.17853e17 | 0.0446519 | ||||||||
\(796\) | −3.56037e19 | −4.96090 | ||||||||
\(797\) | −4.37856e18 | −0.605135 | −0.302567 | − | 0.953128i | \(-0.597844\pi\) | ||||
−0.302567 | + | 0.953128i | \(0.597844\pi\) | |||||||
\(798\) | 1.65301e17 | 0.0226598 | ||||||||
\(799\) | −5.90600e18 | −0.803044 | ||||||||
\(800\) | 1.81121e19 | 2.44278 | ||||||||
\(801\) | −2.96417e17 | −0.0396544 | ||||||||
\(802\) | −6.65007e18 | −0.882455 | ||||||||
\(803\) | −1.16359e18 | −0.153161 | ||||||||
\(804\) | 1.22610e19 | 1.60089 | ||||||||
\(805\) | 4.72079e17 | 0.0611423 | ||||||||
\(806\) | −1.21299e19 | −1.55840 | ||||||||
\(807\) | 2.52608e17 | 0.0321936 | ||||||||
\(808\) | −2.63680e19 | −3.33353 | ||||||||
\(809\) | 2.23400e18 | 0.280168 | 0.140084 | − | 0.990140i | \(-0.455263\pi\) | ||||
0.140084 | + | 0.990140i | \(0.455263\pi\) | |||||||
\(810\) | −3.38000e17 | −0.0420498 | ||||||||
\(811\) | −1.91129e18 | −0.235880 | −0.117940 | − | 0.993021i | \(-0.537629\pi\) | ||||
−0.117940 | + | 0.993021i | \(0.537629\pi\) | |||||||
\(812\) | 6.17206e18 | 0.755641 | ||||||||
\(813\) | −2.99131e18 | −0.363306 | ||||||||
\(814\) | −1.28601e19 | −1.54948 | ||||||||
\(815\) | −1.29262e17 | −0.0154507 | ||||||||
\(816\) | −6.99049e18 | −0.828937 | ||||||||
\(817\) | 1.26278e16 | 0.00148554 | ||||||||
\(818\) | −2.69497e19 | −3.14526 | ||||||||
\(819\) | 8.29103e17 | 0.0959982 | ||||||||
\(820\) | −1.91046e17 | −0.0219457 | ||||||||
\(821\) | −1.04203e19 | −1.18754 | −0.593772 | − | 0.804633i | \(-0.702362\pi\) | ||||
−0.593772 | + | 0.804633i | \(0.702362\pi\) | |||||||
\(822\) | −1.02657e19 | −1.16070 | ||||||||
\(823\) | −1.25178e19 | −1.40420 | −0.702101 | − | 0.712077i | \(-0.747755\pi\) | ||||
−0.702101 | + | 0.712077i | \(0.747755\pi\) | |||||||
\(824\) | 2.01315e19 | 2.24052 | ||||||||
\(825\) | 2.18043e18 | 0.240764 | ||||||||
\(826\) | −1.19301e18 | −0.130699 | ||||||||
\(827\) | −1.03108e19 | −1.12074 | −0.560371 | − | 0.828241i | \(-0.689342\pi\) | ||||
−0.560371 | + | 0.828241i | \(0.689342\pi\) | |||||||
\(828\) | −4.45543e18 | −0.480499 | ||||||||
\(829\) | −6.34381e18 | −0.678806 | −0.339403 | − | 0.940641i | \(-0.610225\pi\) | ||||
−0.339403 | + | 0.940641i | \(0.610225\pi\) | |||||||
\(830\) | 3.89686e18 | 0.413721 | ||||||||
\(831\) | 1.78356e18 | 0.187880 | ||||||||
\(832\) | −9.79229e18 | −1.02349 | ||||||||
\(833\) | 3.42608e18 | 0.355308 | ||||||||
\(834\) | 6.67691e18 | 0.687063 | ||||||||
\(835\) | 1.58473e18 | 0.161806 | ||||||||
\(836\) | −4.25053e17 | −0.0430628 | ||||||||
\(837\) | −2.94250e18 | −0.295802 | ||||||||
\(838\) | 2.99469e18 | 0.298721 | ||||||||
\(839\) | 3.49763e18 | 0.346196 | 0.173098 | − | 0.984905i | \(-0.444622\pi\) | ||||
0.173098 | + | 0.984905i | \(0.444622\pi\) | |||||||
\(840\) | 1.82276e18 | 0.179025 | ||||||||
\(841\) | −7.06186e18 | −0.688248 | ||||||||
\(842\) | 1.10543e19 | 1.06906 | ||||||||
\(843\) | 3.43731e18 | 0.329868 | ||||||||
\(844\) | −3.67720e19 | −3.50180 | ||||||||
\(845\) | −1.51061e18 | −0.142753 | ||||||||
\(846\) | −1.07965e19 | −1.01246 | ||||||||
\(847\) | 4.65436e18 | 0.433130 | ||||||||
\(848\) | 1.20174e19 | 1.10978 | ||||||||
\(849\) | −2.72821e18 | −0.250022 | ||||||||
\(850\) | −9.85845e18 | −0.896573 | ||||||||
\(851\) | 1.19509e19 | 1.07860 | ||||||||
\(852\) | −3.94143e18 | −0.353018 | ||||||||
\(853\) | −1.01560e19 | −0.902725 | −0.451362 | − | 0.892341i | \(-0.649062\pi\) | ||||
−0.451362 | + | 0.892341i | \(0.649062\pi\) | |||||||
\(854\) | 1.31539e19 | 1.16032 | ||||||||
\(855\) | 2.99658e16 | 0.00262329 | ||||||||
\(856\) | −3.14218e18 | −0.272993 | ||||||||
\(857\) | 1.73329e19 | 1.49450 | 0.747248 | − | 0.664545i | \(-0.231375\pi\) | ||||
0.747248 | + | 0.664545i | \(0.231375\pi\) | |||||||
\(858\) | −2.97317e18 | −0.254421 | ||||||||
\(859\) | −1.00287e19 | −0.851702 | −0.425851 | − | 0.904793i | \(-0.640025\pi\) | ||||
−0.425851 | + | 0.904793i | \(0.640025\pi\) | |||||||
\(860\) | 2.29999e17 | 0.0193859 | ||||||||
\(861\) | 1.58538e17 | 0.0132622 | ||||||||
\(862\) | −3.83798e19 | −3.18644 | ||||||||
\(863\) | 1.67230e17 | 0.0137798 | 0.00688991 | − | 0.999976i | \(-0.497807\pi\) | ||||
0.00688991 | + | 0.999976i | \(0.497807\pi\) | |||||||
\(864\) | −5.99111e18 | −0.489969 | ||||||||
\(865\) | −1.05557e18 | −0.0856804 | ||||||||
\(866\) | 1.22842e19 | 0.989644 | ||||||||
\(867\) | −5.43660e18 | −0.434713 | ||||||||
\(868\) | 2.62103e19 | 2.08015 | ||||||||
\(869\) | 8.53487e17 | 0.0672308 | ||||||||
\(870\) | 1.56036e18 | 0.121997 | ||||||||
\(871\) | −7.60351e18 | −0.590060 | ||||||||
\(872\) | 1.02497e19 | 0.789505 | ||||||||
\(873\) | 4.48901e18 | 0.343209 | ||||||||
\(874\) | 5.50862e17 | 0.0418040 | ||||||||
\(875\) | 2.79633e18 | 0.210637 | ||||||||
\(876\) | 6.89624e18 | 0.515627 | ||||||||
\(877\) | −1.91325e19 | −1.41996 | −0.709978 | − | 0.704224i | \(-0.751295\pi\) | ||||
−0.709978 | + | 0.704224i | \(0.751295\pi\) | |||||||
\(878\) | −3.56139e19 | −2.62365 | ||||||||
\(879\) | −2.64836e18 | −0.193664 | ||||||||
\(880\) | −3.48171e18 | −0.252729 | ||||||||
\(881\) | −1.48458e19 | −1.06970 | −0.534849 | − | 0.844948i | \(-0.679632\pi\) | ||||
−0.534849 | + | 0.844948i | \(0.679632\pi\) | |||||||
\(882\) | 6.26309e18 | 0.447963 | ||||||||
\(883\) | 1.02434e19 | 0.727276 | 0.363638 | − | 0.931540i | \(-0.381535\pi\) | ||||
0.363638 | + | 0.931540i | \(0.381535\pi\) | |||||||
\(884\) | 9.63925e18 | 0.679365 | ||||||||
\(885\) | −2.16270e17 | −0.0151309 | ||||||||
\(886\) | −4.61571e19 | −3.20567 | ||||||||
\(887\) | −9.36638e18 | −0.645756 | −0.322878 | − | 0.946441i | \(-0.604650\pi\) | ||||
−0.322878 | + | 0.946441i | \(0.604650\pi\) | |||||||
\(888\) | 4.61441e19 | 3.15814 | ||||||||
\(889\) | 6.32075e18 | 0.429444 | ||||||||
\(890\) | 6.67503e17 | 0.0450213 | ||||||||
\(891\) | −7.21241e17 | −0.0482920 | ||||||||
\(892\) | 1.88918e19 | 1.25574 | ||||||||
\(893\) | 9.57182e17 | 0.0631626 | ||||||||
\(894\) | 3.37188e18 | 0.220891 | ||||||||
\(895\) | −2.49845e17 | −0.0162488 | ||||||||
\(896\) | 8.45127e18 | 0.545657 | ||||||||
\(897\) | 2.76297e18 | 0.177103 | ||||||||
\(898\) | −2.87384e19 | −1.82880 | ||||||||
\(899\) | 1.35839e19 | 0.858198 | ||||||||
\(900\) | −1.29228e19 | −0.810551 | ||||||||
\(901\) | −3.06660e18 | −0.190962 | ||||||||
\(902\) | −5.68520e17 | −0.0351482 | ||||||||
\(903\) | −1.90863e17 | −0.0117152 | ||||||||
\(904\) | −7.90950e18 | −0.482008 | ||||||||
\(905\) | 1.86242e18 | 0.112684 | ||||||||
\(906\) | −1.75655e19 | −1.05518 | ||||||||
\(907\) | −2.02775e18 | −0.120939 | −0.0604696 | − | 0.998170i | \(-0.519260\pi\) | ||||
−0.0604696 | + | 0.998170i | \(0.519260\pi\) | |||||||
\(908\) | 3.11339e19 | 1.84364 | ||||||||
\(909\) | 6.55191e18 | 0.385214 | ||||||||
\(910\) | −1.86707e18 | −0.108991 | ||||||||
\(911\) | 1.57823e19 | 0.914747 | 0.457374 | − | 0.889275i | \(-0.348790\pi\) | ||||
0.457374 | + | 0.889275i | \(0.348790\pi\) | |||||||
\(912\) | 1.13295e18 | 0.0651992 | ||||||||
\(913\) | 8.31532e18 | 0.475137 | ||||||||
\(914\) | 1.19392e19 | 0.677371 | ||||||||
\(915\) | 2.38455e18 | 0.134329 | ||||||||
\(916\) | −3.00362e18 | −0.168006 | ||||||||
\(917\) | −9.71457e18 | −0.539539 | ||||||||
\(918\) | 3.26097e18 | 0.179833 | ||||||||
\(919\) | 1.43504e19 | 0.785804 | 0.392902 | − | 0.919580i | \(-0.371471\pi\) | ||||
0.392902 | + | 0.919580i | \(0.371471\pi\) | |||||||
\(920\) | 6.07433e18 | 0.330276 | ||||||||
\(921\) | −1.07866e19 | −0.582369 | ||||||||
\(922\) | 4.24101e19 | 2.27362 | ||||||||
\(923\) | 2.44423e18 | 0.130116 | ||||||||
\(924\) | 6.42445e18 | 0.339601 | ||||||||
\(925\) | 3.46632e19 | 1.81948 | ||||||||
\(926\) | −1.67508e19 | −0.873101 | ||||||||
\(927\) | −5.00226e18 | −0.258909 | ||||||||
\(928\) | 2.76577e19 | 1.42152 | ||||||||
\(929\) | 1.02277e19 | 0.522006 | 0.261003 | − | 0.965338i | \(-0.415947\pi\) | ||||
0.261003 | + | 0.965338i | \(0.415947\pi\) | |||||||
\(930\) | 6.62624e18 | 0.335837 | ||||||||
\(931\) | −5.55263e17 | −0.0279464 | ||||||||
\(932\) | 7.64630e19 | 3.82162 | ||||||||
\(933\) | −2.12509e18 | −0.105474 | ||||||||
\(934\) | −1.49744e19 | −0.738067 | ||||||||
\(935\) | 8.88465e17 | 0.0434875 | ||||||||
\(936\) | 1.06682e19 | 0.518560 | ||||||||
\(937\) | −1.82906e18 | −0.0882920 | −0.0441460 | − | 0.999025i | \(-0.514057\pi\) | ||||
−0.0441460 | + | 0.999025i | \(0.514057\pi\) | |||||||
\(938\) | 2.29125e19 | 1.09839 | ||||||||
\(939\) | 1.26203e18 | 0.0600817 | ||||||||
\(940\) | 1.74338e19 | 0.824254 | ||||||||
\(941\) | −1.95860e19 | −0.919632 | −0.459816 | − | 0.888014i | \(-0.652085\pi\) | ||||
−0.459816 | + | 0.888014i | \(0.652085\pi\) | |||||||
\(942\) | −2.79744e19 | −1.30446 | ||||||||
\(943\) | 5.28327e17 | 0.0244668 | ||||||||
\(944\) | −8.17670e18 | −0.376063 | ||||||||
\(945\) | −4.52919e17 | −0.0206878 | ||||||||
\(946\) | 6.84435e17 | 0.0310484 | ||||||||
\(947\) | −3.22268e19 | −1.45192 | −0.725959 | − | 0.687738i | \(-0.758604\pi\) | ||||
−0.725959 | + | 0.687738i | \(0.758604\pi\) | |||||||
\(948\) | −5.05838e18 | −0.226338 | ||||||||
\(949\) | −4.27661e18 | −0.190051 | ||||||||
\(950\) | 1.59775e18 | 0.0705191 | ||||||||
\(951\) | −1.06108e19 | −0.465130 | ||||||||
\(952\) | −1.75857e19 | −0.765633 | ||||||||
\(953\) | 3.50779e19 | 1.51680 | 0.758402 | − | 0.651787i | \(-0.225980\pi\) | ||||
0.758402 | + | 0.651787i | \(0.225980\pi\) | |||||||
\(954\) | −5.60593e18 | −0.240760 | ||||||||
\(955\) | −1.98218e18 | −0.0845515 | ||||||||
\(956\) | −1.25097e19 | −0.529994 | ||||||||
\(957\) | 3.32958e18 | 0.140108 | ||||||||
\(958\) | −1.65489e19 | −0.691661 | ||||||||
\(959\) | −1.37559e19 | −0.571044 | ||||||||
\(960\) | 5.34929e18 | 0.220563 | ||||||||
\(961\) | 3.32681e19 | 1.36247 | ||||||||
\(962\) | −4.72656e19 | −1.92268 | ||||||||
\(963\) | 7.80765e17 | 0.0315464 | ||||||||
\(964\) | 1.04611e19 | 0.419834 | ||||||||
\(965\) | −7.02812e18 | −0.280164 | ||||||||
\(966\) | −8.32600e18 | −0.329674 | ||||||||
\(967\) | 8.43990e18 | 0.331944 | 0.165972 | − | 0.986130i | \(-0.446924\pi\) | ||||
0.165972 | + | 0.986130i | \(0.446924\pi\) | |||||||
\(968\) | 5.98885e19 | 2.33967 | ||||||||
\(969\) | −2.89106e17 | −0.0112190 | ||||||||
\(970\) | −1.01089e19 | −0.389660 | ||||||||
\(971\) | 1.46332e18 | 0.0560292 | 0.0280146 | − | 0.999608i | \(-0.491082\pi\) | ||||
0.0280146 | + | 0.999608i | \(0.491082\pi\) | |||||||
\(972\) | 4.27459e18 | 0.162579 | ||||||||
\(973\) | 8.94704e18 | 0.338023 | ||||||||
\(974\) | −4.33618e19 | −1.62732 | ||||||||
\(975\) | 8.01391e18 | 0.298754 | ||||||||
\(976\) | 9.01547e19 | 3.33860 | ||||||||
\(977\) | −2.00744e19 | −0.738460 | −0.369230 | − | 0.929338i | \(-0.620379\pi\) | ||||
−0.369230 | + | 0.929338i | \(0.620379\pi\) | |||||||
\(978\) | 2.27978e18 | 0.0833087 | ||||||||
\(979\) | 1.42435e18 | 0.0517047 | ||||||||
\(980\) | −1.01134e19 | −0.364693 | ||||||||
\(981\) | −2.54684e18 | −0.0912333 | ||||||||
\(982\) | 7.10132e19 | 2.52705 | ||||||||
\(983\) | −3.24364e19 | −1.14666 | −0.573330 | − | 0.819324i | \(-0.694349\pi\) | ||||
−0.573330 | + | 0.819324i | \(0.694349\pi\) | |||||||
\(984\) | 2.03994e18 | 0.0716391 | ||||||||
\(985\) | 4.04642e18 | 0.141168 | ||||||||
\(986\) | −1.50541e19 | −0.521742 | ||||||||
\(987\) | −1.44673e19 | −0.498111 | ||||||||
\(988\) | −1.56223e18 | −0.0534348 | ||||||||
\(989\) | −6.36047e17 | −0.0216129 | ||||||||
\(990\) | 1.62417e18 | 0.0548280 | ||||||||
\(991\) | −2.00348e19 | −0.671903 | −0.335951 | − | 0.941879i | \(-0.609058\pi\) | ||||
−0.335951 | + | 0.941879i | \(0.609058\pi\) | |||||||
\(992\) | 1.17452e20 | 3.91321 | ||||||||
\(993\) | 2.22999e19 | 0.738129 | ||||||||
\(994\) | −7.36547e18 | −0.242208 | ||||||||
\(995\) | −1.20613e19 | −0.394044 | ||||||||
\(996\) | −4.92826e19 | −1.59959 | ||||||||
\(997\) | 5.61755e19 | 1.81146 | 0.905729 | − | 0.423858i | \(-0.139325\pi\) | ||||
0.905729 | + | 0.423858i | \(0.139325\pi\) | |||||||
\(998\) | 9.01077e18 | 0.288678 | ||||||||
\(999\) | −1.14658e19 | −0.364948 |
(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 | 177.14.a.c.1.1 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.c.1.1 | ✓ | 31 | 1.1 | even | 1 | trivial |