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: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 43.5631 | 0.481309 | 0.240654 | − | 0.970611i | \(-0.422638\pi\) | ||||
0.240654 | + | 0.970611i | \(0.422638\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | −6294.26 | −0.768342 | ||||||||
\(5\) | −53819.8 | −1.54041 | −0.770207 | − | 0.637794i | \(-0.779847\pi\) | ||||
−0.770207 | + | 0.637794i | \(0.779847\pi\) | |||||||
\(6\) | 31757.5 | 0.277884 | ||||||||
\(7\) | −600256. | −1.92841 | −0.964205 | − | 0.265158i | \(-0.914576\pi\) | ||||
−0.964205 | + | 0.265158i | \(0.914576\pi\) | |||||||
\(8\) | −631066. | −0.851118 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −2.34456e6 | −0.741415 | ||||||||
\(11\) | 4.53623e6 | 0.772044 | 0.386022 | − | 0.922489i | \(-0.373849\pi\) | ||||
0.386022 | + | 0.922489i | \(0.373849\pi\) | |||||||
\(12\) | −4.58851e6 | −0.443602 | ||||||||
\(13\) | 1.89968e7 | 1.09156 | 0.545780 | − | 0.837928i | \(-0.316233\pi\) | ||||
0.545780 | + | 0.837928i | \(0.316233\pi\) | |||||||
\(14\) | −2.61490e7 | −0.928161 | ||||||||
\(15\) | −3.92347e7 | −0.889358 | ||||||||
\(16\) | 2.40714e7 | 0.358691 | ||||||||
\(17\) | 5.77965e7 | 0.580743 | 0.290371 | − | 0.956914i | \(-0.406221\pi\) | ||||
0.290371 | + | 0.956914i | \(0.406221\pi\) | |||||||
\(18\) | 2.31512e7 | 0.160436 | ||||||||
\(19\) | −1.29263e7 | −0.0630341 | −0.0315171 | − | 0.999503i | \(-0.510034\pi\) | ||||
−0.0315171 | + | 0.999503i | \(0.510034\pi\) | |||||||
\(20\) | 3.38756e8 | 1.18356 | ||||||||
\(21\) | −4.37587e8 | −1.11337 | ||||||||
\(22\) | 1.97612e8 | 0.371592 | ||||||||
\(23\) | 5.60284e8 | 0.789183 | 0.394591 | − | 0.918857i | \(-0.370886\pi\) | ||||
0.394591 | + | 0.918857i | \(0.370886\pi\) | |||||||
\(24\) | −4.60047e8 | −0.491393 | ||||||||
\(25\) | 1.67587e9 | 1.37287 | ||||||||
\(26\) | 8.27558e8 | 0.525378 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | 3.77817e9 | 1.48168 | ||||||||
\(29\) | −4.37208e9 | −1.36490 | −0.682451 | − | 0.730931i | \(-0.739086\pi\) | ||||
−0.682451 | + | 0.730931i | \(0.739086\pi\) | |||||||
\(30\) | −1.70918e9 | −0.428056 | ||||||||
\(31\) | −7.07112e9 | −1.43099 | −0.715496 | − | 0.698617i | \(-0.753799\pi\) | ||||
−0.715496 | + | 0.698617i | \(0.753799\pi\) | |||||||
\(32\) | 6.21832e9 | 1.02376 | ||||||||
\(33\) | 3.30691e9 | 0.445740 | ||||||||
\(34\) | 2.51780e9 | 0.279516 | ||||||||
\(35\) | 3.23057e10 | 2.97055 | ||||||||
\(36\) | −3.34503e9 | −0.256114 | ||||||||
\(37\) | 1.95842e10 | 1.25486 | 0.627428 | − | 0.778675i | \(-0.284108\pi\) | ||||
0.627428 | + | 0.778675i | \(0.284108\pi\) | |||||||
\(38\) | −5.63110e8 | −0.0303389 | ||||||||
\(39\) | 1.38486e10 | 0.630213 | ||||||||
\(40\) | 3.39639e10 | 1.31107 | ||||||||
\(41\) | 1.43851e10 | 0.472952 | 0.236476 | − | 0.971637i | \(-0.424008\pi\) | ||||
0.236476 | + | 0.971637i | \(0.424008\pi\) | |||||||
\(42\) | −1.90626e10 | −0.535874 | ||||||||
\(43\) | 1.26442e10 | 0.305033 | 0.152517 | − | 0.988301i | \(-0.451262\pi\) | ||||
0.152517 | + | 0.988301i | \(0.451262\pi\) | |||||||
\(44\) | −2.85522e10 | −0.593194 | ||||||||
\(45\) | −2.86021e10 | −0.513471 | ||||||||
\(46\) | 2.44077e10 | 0.379841 | ||||||||
\(47\) | −2.13046e10 | −0.288295 | −0.144148 | − | 0.989556i | \(-0.546044\pi\) | ||||
−0.144148 | + | 0.989556i | \(0.546044\pi\) | |||||||
\(48\) | 1.75480e10 | 0.207090 | ||||||||
\(49\) | 2.63418e11 | 2.71876 | ||||||||
\(50\) | 7.30062e10 | 0.660776 | ||||||||
\(51\) | 4.21337e10 | 0.335292 | ||||||||
\(52\) | −1.19570e11 | −0.838692 | ||||||||
\(53\) | 1.08144e11 | 0.670205 | 0.335102 | − | 0.942182i | \(-0.391229\pi\) | ||||
0.335102 | + | 0.942182i | \(0.391229\pi\) | |||||||
\(54\) | 1.68772e10 | 0.0926279 | ||||||||
\(55\) | −2.44139e11 | −1.18927 | ||||||||
\(56\) | 3.78801e11 | 1.64131 | ||||||||
\(57\) | −9.42327e9 | −0.0363928 | ||||||||
\(58\) | −1.90462e11 | −0.656939 | ||||||||
\(59\) | 4.21805e10 | 0.130189 | ||||||||
\(60\) | 2.46953e11 | 0.683331 | ||||||||
\(61\) | −6.15544e11 | −1.52973 | −0.764866 | − | 0.644190i | \(-0.777195\pi\) | ||||
−0.764866 | + | 0.644190i | \(0.777195\pi\) | |||||||
\(62\) | −3.08040e11 | −0.688749 | ||||||||
\(63\) | −3.19001e11 | −0.642803 | ||||||||
\(64\) | 7.36966e10 | 0.134053 | ||||||||
\(65\) | −1.02240e12 | −1.68145 | ||||||||
\(66\) | 1.44059e11 | 0.214539 | ||||||||
\(67\) | 2.30947e11 | 0.311907 | 0.155954 | − | 0.987764i | \(-0.450155\pi\) | ||||
0.155954 | + | 0.987764i | \(0.450155\pi\) | |||||||
\(68\) | −3.63786e11 | −0.446209 | ||||||||
\(69\) | 4.08447e11 | 0.455635 | ||||||||
\(70\) | 1.40734e12 | 1.42975 | ||||||||
\(71\) | −4.88923e10 | −0.0452961 | −0.0226481 | − | 0.999743i | \(-0.507210\pi\) | ||||
−0.0226481 | + | 0.999743i | \(0.507210\pi\) | |||||||
\(72\) | −3.35374e11 | −0.283706 | ||||||||
\(73\) | 2.23802e12 | 1.73087 | 0.865435 | − | 0.501021i | \(-0.167042\pi\) | ||||
0.865435 | + | 0.501021i | \(0.167042\pi\) | |||||||
\(74\) | 8.53146e11 | 0.603973 | ||||||||
\(75\) | 1.22171e12 | 0.792629 | ||||||||
\(76\) | 8.13615e10 | 0.0484318 | ||||||||
\(77\) | −2.72290e12 | −1.48882 | ||||||||
\(78\) | 6.03290e11 | 0.303327 | ||||||||
\(79\) | −3.41626e12 | −1.58116 | −0.790579 | − | 0.612361i | \(-0.790220\pi\) | ||||
−0.790579 | + | 0.612361i | \(0.790220\pi\) | |||||||
\(80\) | −1.29552e12 | −0.552533 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 6.26658e11 | 0.227636 | ||||||||
\(83\) | 2.93065e12 | 0.983911 | 0.491955 | − | 0.870620i | \(-0.336282\pi\) | ||||
0.491955 | + | 0.870620i | \(0.336282\pi\) | |||||||
\(84\) | 2.75428e12 | 0.855447 | ||||||||
\(85\) | −3.11060e12 | −0.894584 | ||||||||
\(86\) | 5.50822e11 | 0.146815 | ||||||||
\(87\) | −3.18725e12 | −0.788027 | ||||||||
\(88\) | −2.86266e12 | −0.657101 | ||||||||
\(89\) | 4.55708e12 | 0.971967 | 0.485984 | − | 0.873968i | \(-0.338461\pi\) | ||||
0.485984 | + | 0.873968i | \(0.338461\pi\) | |||||||
\(90\) | −1.24599e12 | −0.247138 | ||||||||
\(91\) | −1.14029e13 | −2.10498 | ||||||||
\(92\) | −3.52657e12 | −0.606362 | ||||||||
\(93\) | −5.15484e12 | −0.826183 | ||||||||
\(94\) | −9.28094e11 | −0.138759 | ||||||||
\(95\) | 6.95691e11 | 0.0970987 | ||||||||
\(96\) | 4.53315e12 | 0.591068 | ||||||||
\(97\) | −8.26454e12 | −1.00740 | −0.503701 | − | 0.863878i | \(-0.668028\pi\) | ||||
−0.503701 | + | 0.863878i | \(0.668028\pi\) | |||||||
\(98\) | 1.14753e13 | 1.30857 | ||||||||
\(99\) | 2.41074e12 | 0.257348 | ||||||||
\(100\) | −1.05484e13 | −1.05484 | ||||||||
\(101\) | 5.40578e12 | 0.506722 | 0.253361 | − | 0.967372i | \(-0.418464\pi\) | ||||
0.253361 | + | 0.967372i | \(0.418464\pi\) | |||||||
\(102\) | 1.83547e12 | 0.161379 | ||||||||
\(103\) | −6.54245e11 | −0.0539881 | −0.0269941 | − | 0.999636i | \(-0.508594\pi\) | ||||
−0.0269941 | + | 0.999636i | \(0.508594\pi\) | |||||||
\(104\) | −1.19882e13 | −0.929047 | ||||||||
\(105\) | 2.35508e13 | 1.71505 | ||||||||
\(106\) | 4.71107e12 | 0.322575 | ||||||||
\(107\) | −2.01968e13 | −1.30103 | −0.650515 | − | 0.759494i | \(-0.725447\pi\) | ||||
−0.650515 | + | 0.759494i | \(0.725447\pi\) | |||||||
\(108\) | −2.43852e12 | −0.147867 | ||||||||
\(109\) | −3.14736e13 | −1.79752 | −0.898762 | − | 0.438437i | \(-0.855532\pi\) | ||||
−0.898762 | + | 0.438437i | \(0.855532\pi\) | |||||||
\(110\) | −1.06354e13 | −0.572405 | ||||||||
\(111\) | 1.42769e13 | 0.724491 | ||||||||
\(112\) | −1.44490e13 | −0.691704 | ||||||||
\(113\) | −2.69712e13 | −1.21868 | −0.609341 | − | 0.792909i | \(-0.708566\pi\) | ||||
−0.609341 | + | 0.792909i | \(0.708566\pi\) | |||||||
\(114\) | −4.10507e11 | −0.0175162 | ||||||||
\(115\) | −3.01544e13 | −1.21567 | ||||||||
\(116\) | 2.75190e13 | 1.04871 | ||||||||
\(117\) | 1.00957e13 | 0.363853 | ||||||||
\(118\) | 1.83751e12 | 0.0626611 | ||||||||
\(119\) | −3.46927e13 | −1.11991 | ||||||||
\(120\) | 2.47597e13 | 0.756949 | ||||||||
\(121\) | −1.39454e13 | −0.403947 | ||||||||
\(122\) | −2.68150e13 | −0.736273 | ||||||||
\(123\) | 1.04867e13 | 0.273059 | ||||||||
\(124\) | 4.45074e13 | 1.09949 | ||||||||
\(125\) | −2.44971e13 | −0.574381 | ||||||||
\(126\) | −1.38967e13 | −0.309387 | ||||||||
\(127\) | 6.52454e13 | 1.37983 | 0.689915 | − | 0.723890i | \(-0.257648\pi\) | ||||
0.689915 | + | 0.723890i | \(0.257648\pi\) | |||||||
\(128\) | −4.77300e13 | −0.959239 | ||||||||
\(129\) | 9.21764e12 | 0.176111 | ||||||||
\(130\) | −4.45390e13 | −0.809299 | ||||||||
\(131\) | 1.69094e13 | 0.292324 | 0.146162 | − | 0.989261i | \(-0.453308\pi\) | ||||
0.146162 | + | 0.989261i | \(0.453308\pi\) | |||||||
\(132\) | −2.08145e13 | −0.342481 | ||||||||
\(133\) | 7.75909e12 | 0.121556 | ||||||||
\(134\) | 1.00608e13 | 0.150124 | ||||||||
\(135\) | −2.08509e13 | −0.296453 | ||||||||
\(136\) | −3.64734e13 | −0.494281 | ||||||||
\(137\) | −6.34715e13 | −0.820154 | −0.410077 | − | 0.912051i | \(-0.634498\pi\) | ||||
−0.410077 | + | 0.912051i | \(0.634498\pi\) | |||||||
\(138\) | 1.77932e13 | 0.219301 | ||||||||
\(139\) | 4.11242e13 | 0.483617 | 0.241809 | − | 0.970324i | \(-0.422259\pi\) | ||||
0.241809 | + | 0.970324i | \(0.422259\pi\) | |||||||
\(140\) | −2.03340e14 | −2.28240 | ||||||||
\(141\) | −1.55311e13 | −0.166447 | ||||||||
\(142\) | −2.12990e12 | −0.0218014 | ||||||||
\(143\) | 8.61736e13 | 0.842733 | ||||||||
\(144\) | 1.27925e13 | 0.119564 | ||||||||
\(145\) | 2.35305e14 | 2.10251 | ||||||||
\(146\) | 9.74949e13 | 0.833083 | ||||||||
\(147\) | 1.92032e14 | 1.56968 | ||||||||
\(148\) | −1.23268e14 | −0.964158 | ||||||||
\(149\) | 1.82687e14 | 1.36772 | 0.683859 | − | 0.729614i | \(-0.260300\pi\) | ||||
0.683859 | + | 0.729614i | \(0.260300\pi\) | |||||||
\(150\) | 5.32215e13 | 0.381499 | ||||||||
\(151\) | 3.11847e13 | 0.214087 | 0.107044 | − | 0.994254i | \(-0.465862\pi\) | ||||
0.107044 | + | 0.994254i | \(0.465862\pi\) | |||||||
\(152\) | 8.15735e12 | 0.0536495 | ||||||||
\(153\) | 3.07154e13 | 0.193581 | ||||||||
\(154\) | −1.18618e14 | −0.716581 | ||||||||
\(155\) | 3.80566e14 | 2.20432 | ||||||||
\(156\) | −8.71669e13 | −0.484219 | ||||||||
\(157\) | 1.19492e14 | 0.636784 | 0.318392 | − | 0.947959i | \(-0.396857\pi\) | ||||
0.318392 | + | 0.947959i | \(0.396857\pi\) | |||||||
\(158\) | −1.48823e14 | −0.761025 | ||||||||
\(159\) | 7.88367e13 | 0.386943 | ||||||||
\(160\) | −3.34669e14 | −1.57701 | ||||||||
\(161\) | −3.36314e14 | −1.52187 | ||||||||
\(162\) | 1.23035e13 | 0.0534787 | ||||||||
\(163\) | 3.35984e14 | 1.40313 | 0.701566 | − | 0.712604i | \(-0.252484\pi\) | ||||
0.701566 | + | 0.712604i | \(0.252484\pi\) | |||||||
\(164\) | −9.05433e13 | −0.363389 | ||||||||
\(165\) | −1.77977e14 | −0.686624 | ||||||||
\(166\) | 1.27668e14 | 0.473565 | ||||||||
\(167\) | −1.48112e14 | −0.528365 | −0.264183 | − | 0.964473i | \(-0.585102\pi\) | ||||
−0.264183 | + | 0.964473i | \(0.585102\pi\) | |||||||
\(168\) | 2.76146e14 | 0.947608 | ||||||||
\(169\) | 5.80018e13 | 0.191504 | ||||||||
\(170\) | −1.35507e14 | −0.430571 | ||||||||
\(171\) | −6.86957e12 | −0.0210114 | ||||||||
\(172\) | −7.95860e13 | −0.234370 | ||||||||
\(173\) | −4.96846e13 | −0.140904 | −0.0704518 | − | 0.997515i | \(-0.522444\pi\) | ||||
−0.0704518 | + | 0.997515i | \(0.522444\pi\) | |||||||
\(174\) | −1.38846e14 | −0.379284 | ||||||||
\(175\) | −1.00595e15 | −2.64746 | ||||||||
\(176\) | 1.09193e14 | 0.276925 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | 1.98521e14 | 0.467816 | ||||||||
\(179\) | −2.02867e14 | −0.460963 | −0.230481 | − | 0.973077i | \(-0.574030\pi\) | ||||
−0.230481 | + | 0.973077i | \(0.574030\pi\) | |||||||
\(180\) | 1.80029e14 | 0.394521 | ||||||||
\(181\) | 3.87973e14 | 0.820146 | 0.410073 | − | 0.912053i | \(-0.365503\pi\) | ||||
0.410073 | + | 0.912053i | \(0.365503\pi\) | |||||||
\(182\) | −4.96747e14 | −1.01314 | ||||||||
\(183\) | −4.48732e14 | −0.883191 | ||||||||
\(184\) | −3.53577e14 | −0.671688 | ||||||||
\(185\) | −1.05402e15 | −1.93300 | ||||||||
\(186\) | −2.24561e14 | −0.397649 | ||||||||
\(187\) | 2.62178e14 | 0.448359 | ||||||||
\(188\) | 1.34097e14 | 0.221509 | ||||||||
\(189\) | −2.32552e14 | −0.371123 | ||||||||
\(190\) | 3.03065e13 | 0.0467344 | ||||||||
\(191\) | 2.70789e14 | 0.403565 | 0.201782 | − | 0.979430i | \(-0.435327\pi\) | ||||
0.201782 | + | 0.979430i | \(0.435327\pi\) | |||||||
\(192\) | 5.37248e13 | 0.0773957 | ||||||||
\(193\) | 6.36613e14 | 0.886652 | 0.443326 | − | 0.896360i | \(-0.353798\pi\) | ||||
0.443326 | + | 0.896360i | \(0.353798\pi\) | |||||||
\(194\) | −3.60029e14 | −0.484871 | ||||||||
\(195\) | −7.45332e14 | −0.970788 | ||||||||
\(196\) | −1.65802e15 | −2.08894 | ||||||||
\(197\) | 1.08435e15 | 1.32172 | 0.660858 | − | 0.750511i | \(-0.270193\pi\) | ||||
0.660858 | + | 0.750511i | \(0.270193\pi\) | |||||||
\(198\) | 1.05019e14 | 0.123864 | ||||||||
\(199\) | −1.40793e15 | −1.60708 | −0.803540 | − | 0.595251i | \(-0.797053\pi\) | ||||
−0.803540 | + | 0.595251i | \(0.797053\pi\) | |||||||
\(200\) | −1.05759e15 | −1.16848 | ||||||||
\(201\) | 1.68360e14 | 0.180080 | ||||||||
\(202\) | 2.35493e14 | 0.243890 | ||||||||
\(203\) | 2.62437e15 | 2.63209 | ||||||||
\(204\) | −2.65200e14 | −0.257619 | ||||||||
\(205\) | −7.74202e14 | −0.728541 | ||||||||
\(206\) | −2.85009e13 | −0.0259850 | ||||||||
\(207\) | 2.97758e14 | 0.263061 | ||||||||
\(208\) | 4.57278e14 | 0.391533 | ||||||||
\(209\) | −5.86366e13 | −0.0486652 | ||||||||
\(210\) | 1.02595e15 | 0.825467 | ||||||||
\(211\) | −2.07296e15 | −1.61717 | −0.808583 | − | 0.588382i | \(-0.799765\pi\) | ||||
−0.808583 | + | 0.588382i | \(0.799765\pi\) | |||||||
\(212\) | −6.80684e14 | −0.514947 | ||||||||
\(213\) | −3.56425e13 | −0.0261517 | ||||||||
\(214\) | −8.79833e14 | −0.626197 | ||||||||
\(215\) | −6.80510e14 | −0.469878 | ||||||||
\(216\) | −2.44488e14 | −0.163798 | ||||||||
\(217\) | 4.24448e15 | 2.75954 | ||||||||
\(218\) | −1.37109e15 | −0.865164 | ||||||||
\(219\) | 1.63151e15 | 0.999318 | ||||||||
\(220\) | 1.53667e15 | 0.913764 | ||||||||
\(221\) | 1.09795e15 | 0.633916 | ||||||||
\(222\) | 6.21944e14 | 0.348704 | ||||||||
\(223\) | −7.10419e14 | −0.386842 | −0.193421 | − | 0.981116i | \(-0.561958\pi\) | ||||
−0.193421 | + | 0.981116i | \(0.561958\pi\) | |||||||
\(224\) | −3.73258e15 | −1.97423 | ||||||||
\(225\) | 8.90627e14 | 0.457625 | ||||||||
\(226\) | −1.17495e15 | −0.586562 | ||||||||
\(227\) | −1.65843e15 | −0.804507 | −0.402254 | − | 0.915528i | \(-0.631773\pi\) | ||||
−0.402254 | + | 0.915528i | \(0.631773\pi\) | |||||||
\(228\) | 5.93125e13 | 0.0279621 | ||||||||
\(229\) | −1.29550e15 | −0.593617 | −0.296808 | − | 0.954937i | \(-0.595922\pi\) | ||||
−0.296808 | + | 0.954937i | \(0.595922\pi\) | |||||||
\(230\) | −1.31362e15 | −0.585112 | ||||||||
\(231\) | −1.98499e15 | −0.859569 | ||||||||
\(232\) | 2.75907e15 | 1.16169 | ||||||||
\(233\) | 4.69091e15 | 1.92063 | 0.960315 | − | 0.278918i | \(-0.0899758\pi\) | ||||
0.960315 | + | 0.278918i | \(0.0899758\pi\) | |||||||
\(234\) | 4.39798e14 | 0.175126 | ||||||||
\(235\) | 1.14661e15 | 0.444094 | ||||||||
\(236\) | −2.65495e14 | −0.100030 | ||||||||
\(237\) | −2.49045e15 | −0.912882 | ||||||||
\(238\) | −1.51132e15 | −0.539022 | ||||||||
\(239\) | 3.18696e15 | 1.10609 | 0.553044 | − | 0.833152i | \(-0.313466\pi\) | ||||
0.553044 | + | 0.833152i | \(0.313466\pi\) | |||||||
\(240\) | −9.44432e14 | −0.319005 | ||||||||
\(241\) | −2.57566e15 | −0.846794 | −0.423397 | − | 0.905944i | \(-0.639162\pi\) | ||||
−0.423397 | + | 0.905944i | \(0.639162\pi\) | |||||||
\(242\) | −6.07503e14 | −0.194423 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | 3.87439e15 | 1.17536 | ||||||||
\(245\) | −1.41771e16 | −4.18802 | ||||||||
\(246\) | 4.56834e14 | 0.131426 | ||||||||
\(247\) | −2.45558e14 | −0.0688056 | ||||||||
\(248\) | 4.46234e15 | 1.21794 | ||||||||
\(249\) | 2.13644e15 | 0.568061 | ||||||||
\(250\) | −1.06717e15 | −0.276454 | ||||||||
\(251\) | −3.49703e15 | −0.882714 | −0.441357 | − | 0.897332i | \(-0.645503\pi\) | ||||
−0.441357 | + | 0.897332i | \(0.645503\pi\) | |||||||
\(252\) | 2.00787e15 | 0.493893 | ||||||||
\(253\) | 2.54158e15 | 0.609284 | ||||||||
\(254\) | 2.84229e15 | 0.664124 | ||||||||
\(255\) | −2.26763e15 | −0.516488 | ||||||||
\(256\) | −2.68299e15 | −0.595743 | ||||||||
\(257\) | 8.78471e15 | 1.90179 | 0.950895 | − | 0.309515i | \(-0.100167\pi\) | ||||
0.950895 | + | 0.309515i | \(0.100167\pi\) | |||||||
\(258\) | 4.01549e14 | 0.0847638 | ||||||||
\(259\) | −1.17555e16 | −2.41988 | ||||||||
\(260\) | 6.43526e15 | 1.29193 | ||||||||
\(261\) | −2.32350e15 | −0.454967 | ||||||||
\(262\) | 7.36625e14 | 0.140698 | ||||||||
\(263\) | −5.03607e15 | −0.938382 | −0.469191 | − | 0.883097i | \(-0.655454\pi\) | ||||
−0.469191 | + | 0.883097i | \(0.655454\pi\) | |||||||
\(264\) | −2.08688e15 | −0.379378 | ||||||||
\(265\) | −5.82027e15 | −1.03239 | ||||||||
\(266\) | 3.38010e14 | 0.0585058 | ||||||||
\(267\) | 3.32211e15 | 0.561166 | ||||||||
\(268\) | −1.45364e15 | −0.239652 | ||||||||
\(269\) | −8.65542e15 | −1.39283 | −0.696415 | − | 0.717639i | \(-0.745223\pi\) | ||||
−0.696415 | + | 0.717639i | \(0.745223\pi\) | |||||||
\(270\) | −9.08330e14 | −0.142685 | ||||||||
\(271\) | −8.30355e15 | −1.27340 | −0.636698 | − | 0.771113i | \(-0.719700\pi\) | ||||
−0.636698 | + | 0.771113i | \(0.719700\pi\) | |||||||
\(272\) | 1.39124e15 | 0.208307 | ||||||||
\(273\) | −8.31273e15 | −1.21531 | ||||||||
\(274\) | −2.76502e15 | −0.394747 | ||||||||
\(275\) | 7.60213e15 | 1.05992 | ||||||||
\(276\) | −2.57087e15 | −0.350083 | ||||||||
\(277\) | 1.70303e15 | 0.226518 | 0.113259 | − | 0.993565i | \(-0.463871\pi\) | ||||
0.113259 | + | 0.993565i | \(0.463871\pi\) | |||||||
\(278\) | 1.79150e15 | 0.232769 | ||||||||
\(279\) | −3.75788e15 | −0.476997 | ||||||||
\(280\) | −2.03870e16 | −2.52829 | ||||||||
\(281\) | 3.42250e15 | 0.414717 | 0.207359 | − | 0.978265i | \(-0.433513\pi\) | ||||
0.207359 | + | 0.978265i | \(0.433513\pi\) | |||||||
\(282\) | −6.76581e14 | −0.0801125 | ||||||||
\(283\) | 6.86754e15 | 0.794675 | 0.397338 | − | 0.917673i | \(-0.369934\pi\) | ||||
0.397338 | + | 0.917673i | \(0.369934\pi\) | |||||||
\(284\) | 3.07741e14 | 0.0348029 | ||||||||
\(285\) | 5.07159e14 | 0.0560599 | ||||||||
\(286\) | 3.75399e15 | 0.405615 | ||||||||
\(287\) | −8.63473e15 | −0.912045 | ||||||||
\(288\) | 3.30467e15 | 0.341253 | ||||||||
\(289\) | −6.56414e15 | −0.662738 | ||||||||
\(290\) | 1.02506e16 | 1.01196 | ||||||||
\(291\) | −6.02485e15 | −0.581623 | ||||||||
\(292\) | −1.40866e16 | −1.32990 | ||||||||
\(293\) | −1.51715e16 | −1.40084 | −0.700422 | − | 0.713729i | \(-0.747005\pi\) | ||||
−0.700422 | + | 0.713729i | \(0.747005\pi\) | |||||||
\(294\) | 8.36551e15 | 0.755501 | ||||||||
\(295\) | −2.27015e15 | −0.200545 | ||||||||
\(296\) | −1.23589e16 | −1.06803 | ||||||||
\(297\) | 1.75743e15 | 0.148580 | ||||||||
\(298\) | 7.95841e15 | 0.658295 | ||||||||
\(299\) | 1.06436e16 | 0.861441 | ||||||||
\(300\) | −7.68976e15 | −0.609010 | ||||||||
\(301\) | −7.58977e15 | −0.588229 | ||||||||
\(302\) | 1.35850e15 | 0.103042 | ||||||||
\(303\) | 3.94082e15 | 0.292556 | ||||||||
\(304\) | −3.11154e14 | −0.0226098 | ||||||||
\(305\) | 3.31285e16 | 2.35642 | ||||||||
\(306\) | 1.33806e15 | 0.0931722 | ||||||||
\(307\) | −1.24999e16 | −0.852132 | −0.426066 | − | 0.904692i | \(-0.640101\pi\) | ||||
−0.426066 | + | 0.904692i | \(0.640101\pi\) | |||||||
\(308\) | 1.71386e16 | 1.14392 | ||||||||
\(309\) | −4.76944e14 | −0.0311701 | ||||||||
\(310\) | 1.65786e16 | 1.06096 | ||||||||
\(311\) | 1.61408e16 | 1.01154 | 0.505770 | − | 0.862668i | \(-0.331208\pi\) | ||||
0.505770 | + | 0.862668i | \(0.331208\pi\) | |||||||
\(312\) | −8.73941e15 | −0.536386 | ||||||||
\(313\) | −3.98009e15 | −0.239252 | −0.119626 | − | 0.992819i | \(-0.538169\pi\) | ||||
−0.119626 | + | 0.992819i | \(0.538169\pi\) | |||||||
\(314\) | 5.20545e15 | 0.306490 | ||||||||
\(315\) | 1.71686e16 | 0.990183 | ||||||||
\(316\) | 2.15028e16 | 1.21487 | ||||||||
\(317\) | −5.32616e15 | −0.294801 | −0.147400 | − | 0.989077i | \(-0.547091\pi\) | ||||
−0.147400 | + | 0.989077i | \(0.547091\pi\) | |||||||
\(318\) | 3.43437e15 | 0.186239 | ||||||||
\(319\) | −1.98328e16 | −1.05377 | ||||||||
\(320\) | −3.96634e15 | −0.206498 | ||||||||
\(321\) | −1.47234e16 | −0.751150 | ||||||||
\(322\) | −1.46509e16 | −0.732488 | ||||||||
\(323\) | −7.47095e14 | −0.0366066 | ||||||||
\(324\) | −1.77768e15 | −0.0853713 | ||||||||
\(325\) | 3.18361e16 | 1.49858 | ||||||||
\(326\) | 1.46365e16 | 0.675340 | ||||||||
\(327\) | −2.29443e16 | −1.03780 | ||||||||
\(328\) | −9.07793e15 | −0.402538 | ||||||||
\(329\) | 1.27882e16 | 0.555951 | ||||||||
\(330\) | −7.75324e15 | −0.330478 | ||||||||
\(331\) | −2.46478e16 | −1.03014 | −0.515070 | − | 0.857148i | \(-0.672234\pi\) | ||||
−0.515070 | + | 0.857148i | \(0.672234\pi\) | |||||||
\(332\) | −1.84462e16 | −0.755980 | ||||||||
\(333\) | 1.04078e16 | 0.418285 | ||||||||
\(334\) | −6.45223e15 | −0.254307 | ||||||||
\(335\) | −1.24295e16 | −0.480467 | ||||||||
\(336\) | −1.05333e16 | −0.399355 | ||||||||
\(337\) | 3.07147e16 | 1.14223 | 0.571113 | − | 0.820871i | \(-0.306512\pi\) | ||||
0.571113 | + | 0.820871i | \(0.306512\pi\) | |||||||
\(338\) | 2.52674e15 | 0.0921726 | ||||||||
\(339\) | −1.96620e16 | −0.703606 | ||||||||
\(340\) | 1.95789e16 | 0.687346 | ||||||||
\(341\) | −3.20762e16 | −1.10479 | ||||||||
\(342\) | −2.99260e14 | −0.0101130 | ||||||||
\(343\) | −9.99603e16 | −3.31448 | ||||||||
\(344\) | −7.97934e15 | −0.259619 | ||||||||
\(345\) | −2.19826e16 | −0.701866 | ||||||||
\(346\) | −2.16441e15 | −0.0678181 | ||||||||
\(347\) | −2.76500e16 | −0.850263 | −0.425132 | − | 0.905132i | \(-0.639772\pi\) | ||||
−0.425132 | + | 0.905132i | \(0.639772\pi\) | |||||||
\(348\) | 2.00614e16 | 0.605474 | ||||||||
\(349\) | 4.40754e16 | 1.30566 | 0.652831 | − | 0.757504i | \(-0.273581\pi\) | ||||
0.652831 | + | 0.757504i | \(0.273581\pi\) | |||||||
\(350\) | −4.38224e16 | −1.27425 | ||||||||
\(351\) | 7.35973e15 | 0.210071 | ||||||||
\(352\) | 2.82077e16 | 0.790388 | ||||||||
\(353\) | 4.03066e16 | 1.10877 | 0.554384 | − | 0.832261i | \(-0.312954\pi\) | ||||
0.554384 | + | 0.832261i | \(0.312954\pi\) | |||||||
\(354\) | 1.33955e15 | 0.0361774 | ||||||||
\(355\) | 2.63137e15 | 0.0697748 | ||||||||
\(356\) | −2.86834e16 | −0.746803 | ||||||||
\(357\) | −2.52910e16 | −0.646580 | ||||||||
\(358\) | −8.83750e15 | −0.221865 | ||||||||
\(359\) | −7.41685e15 | −0.182854 | −0.0914272 | − | 0.995812i | \(-0.529143\pi\) | ||||
−0.0914272 | + | 0.995812i | \(0.529143\pi\) | |||||||
\(360\) | 1.80498e16 | 0.437025 | ||||||||
\(361\) | −4.18859e16 | −0.996027 | ||||||||
\(362\) | 1.69013e16 | 0.394743 | ||||||||
\(363\) | −1.01662e16 | −0.233219 | ||||||||
\(364\) | 7.17729e16 | 1.61734 | ||||||||
\(365\) | −1.20450e17 | −2.66626 | ||||||||
\(366\) | −1.95481e16 | −0.425088 | ||||||||
\(367\) | 4.32762e16 | 0.924527 | 0.462263 | − | 0.886743i | \(-0.347037\pi\) | ||||
0.462263 | + | 0.886743i | \(0.347037\pi\) | |||||||
\(368\) | 1.34868e16 | 0.283073 | ||||||||
\(369\) | 7.64482e15 | 0.157651 | ||||||||
\(370\) | −4.59162e16 | −0.930368 | ||||||||
\(371\) | −6.49139e16 | −1.29243 | ||||||||
\(372\) | 3.24459e16 | 0.634791 | ||||||||
\(373\) | 4.41744e16 | 0.849303 | 0.424652 | − | 0.905357i | \(-0.360397\pi\) | ||||
0.424652 | + | 0.905357i | \(0.360397\pi\) | |||||||
\(374\) | 1.14213e16 | 0.215799 | ||||||||
\(375\) | −1.78584e16 | −0.331619 | ||||||||
\(376\) | 1.34446e16 | 0.245373 | ||||||||
\(377\) | −8.30554e16 | −1.48987 | ||||||||
\(378\) | −1.01307e16 | −0.178625 | ||||||||
\(379\) | −6.14710e16 | −1.06541 | −0.532703 | − | 0.846302i | \(-0.678824\pi\) | ||||
−0.532703 | + | 0.846302i | \(0.678824\pi\) | |||||||
\(380\) | −4.37886e15 | −0.0746050 | ||||||||
\(381\) | 4.75639e16 | 0.796645 | ||||||||
\(382\) | 1.17964e16 | 0.194239 | ||||||||
\(383\) | 3.73747e16 | 0.605043 | 0.302521 | − | 0.953143i | \(-0.402172\pi\) | ||||
0.302521 | + | 0.953143i | \(0.402172\pi\) | |||||||
\(384\) | −3.47952e16 | −0.553817 | ||||||||
\(385\) | 1.46546e17 | 2.29340 | ||||||||
\(386\) | 2.77328e16 | 0.426753 | ||||||||
\(387\) | 6.71966e15 | 0.101678 | ||||||||
\(388\) | 5.20191e16 | 0.774028 | ||||||||
\(389\) | 4.71503e16 | 0.689942 | 0.344971 | − | 0.938613i | \(-0.387889\pi\) | ||||
0.344971 | + | 0.938613i | \(0.387889\pi\) | |||||||
\(390\) | −3.24689e16 | −0.467249 | ||||||||
\(391\) | 3.23825e16 | 0.458312 | ||||||||
\(392\) | −1.66234e17 | −2.31399 | ||||||||
\(393\) | 1.23269e16 | 0.168773 | ||||||||
\(394\) | 4.72375e16 | 0.636153 | ||||||||
\(395\) | 1.83863e17 | 2.43564 | ||||||||
\(396\) | −1.51738e16 | −0.197731 | ||||||||
\(397\) | 4.60714e16 | 0.590600 | 0.295300 | − | 0.955405i | \(-0.404580\pi\) | ||||
0.295300 | + | 0.955405i | \(0.404580\pi\) | |||||||
\(398\) | −6.13340e16 | −0.773502 | ||||||||
\(399\) | 5.65638e15 | 0.0701802 | ||||||||
\(400\) | 4.03405e16 | 0.492438 | ||||||||
\(401\) | −1.17360e17 | −1.40956 | −0.704779 | − | 0.709427i | \(-0.748954\pi\) | ||||
−0.704779 | + | 0.709427i | \(0.748954\pi\) | |||||||
\(402\) | 7.33429e15 | 0.0866740 | ||||||||
\(403\) | −1.34328e17 | −1.56201 | ||||||||
\(404\) | −3.40254e16 | −0.389336 | ||||||||
\(405\) | −1.52003e16 | −0.171157 | ||||||||
\(406\) | 1.14326e17 | 1.26685 | ||||||||
\(407\) | 8.88382e16 | 0.968804 | ||||||||
\(408\) | −2.65891e16 | −0.285373 | ||||||||
\(409\) | 1.18336e17 | 1.25001 | 0.625006 | − | 0.780620i | \(-0.285097\pi\) | ||||
0.625006 | + | 0.780620i | \(0.285097\pi\) | |||||||
\(410\) | −3.37266e16 | −0.350653 | ||||||||
\(411\) | −4.62707e16 | −0.473516 | ||||||||
\(412\) | 4.11798e15 | 0.0414813 | ||||||||
\(413\) | −2.53191e16 | −0.251058 | ||||||||
\(414\) | 1.29713e16 | 0.126614 | ||||||||
\(415\) | −1.57727e17 | −1.51563 | ||||||||
\(416\) | 1.18128e17 | 1.11750 | ||||||||
\(417\) | 2.99796e16 | 0.279216 | ||||||||
\(418\) | −2.55439e15 | −0.0234230 | ||||||||
\(419\) | 9.40473e16 | 0.849093 | 0.424546 | − | 0.905406i | \(-0.360434\pi\) | ||||
0.424546 | + | 0.905406i | \(0.360434\pi\) | |||||||
\(420\) | −1.48235e17 | −1.31774 | ||||||||
\(421\) | 1.34689e17 | 1.17896 | 0.589478 | − | 0.807784i | \(-0.299333\pi\) | ||||
0.589478 | + | 0.807784i | \(0.299333\pi\) | |||||||
\(422\) | −9.03045e16 | −0.778356 | ||||||||
\(423\) | −1.13221e16 | −0.0960984 | ||||||||
\(424\) | −6.82458e16 | −0.570424 | ||||||||
\(425\) | 9.68596e16 | 0.797287 | ||||||||
\(426\) | −1.55270e15 | −0.0125871 | ||||||||
\(427\) | 3.69484e17 | 2.94995 | ||||||||
\(428\) | 1.27124e17 | 0.999635 | ||||||||
\(429\) | 6.28206e16 | 0.486552 | ||||||||
\(430\) | −2.96451e16 | −0.226156 | ||||||||
\(431\) | −8.81796e16 | −0.662622 | −0.331311 | − | 0.943522i | \(-0.607491\pi\) | ||||
−0.331311 | + | 0.943522i | \(0.607491\pi\) | |||||||
\(432\) | 9.32574e15 | 0.0690301 | ||||||||
\(433\) | −4.42402e15 | −0.0322586 | −0.0161293 | − | 0.999870i | \(-0.505134\pi\) | ||||
−0.0161293 | + | 0.999870i | \(0.505134\pi\) | |||||||
\(434\) | 1.84903e17 | 1.32819 | ||||||||
\(435\) | 1.71537e17 | 1.21389 | ||||||||
\(436\) | 1.98103e17 | 1.38111 | ||||||||
\(437\) | −7.24241e15 | −0.0497455 | ||||||||
\(438\) | 7.10738e16 | 0.480981 | ||||||||
\(439\) | −2.17504e17 | −1.45027 | −0.725133 | − | 0.688609i | \(-0.758222\pi\) | ||||
−0.725133 | + | 0.688609i | \(0.758222\pi\) | |||||||
\(440\) | 1.54068e17 | 1.01221 | ||||||||
\(441\) | 1.39991e17 | 0.906255 | ||||||||
\(442\) | 4.78300e16 | 0.305109 | ||||||||
\(443\) | 2.88824e17 | 1.81555 | 0.907777 | − | 0.419454i | \(-0.137778\pi\) | ||||
0.907777 | + | 0.419454i | \(0.137778\pi\) | |||||||
\(444\) | −8.98622e16 | −0.556657 | ||||||||
\(445\) | −2.45261e17 | −1.49723 | ||||||||
\(446\) | −3.09481e16 | −0.186190 | ||||||||
\(447\) | 1.33179e17 | 0.789653 | ||||||||
\(448\) | −4.42368e16 | −0.258510 | ||||||||
\(449\) | 2.73967e16 | 0.157796 | 0.0788981 | − | 0.996883i | \(-0.474860\pi\) | ||||
0.0788981 | + | 0.996883i | \(0.474860\pi\) | |||||||
\(450\) | 3.87985e16 | 0.220259 | ||||||||
\(451\) | 6.52539e16 | 0.365140 | ||||||||
\(452\) | 1.69764e17 | 0.936364 | ||||||||
\(453\) | 2.27336e16 | 0.123603 | ||||||||
\(454\) | −7.22465e16 | −0.387216 | ||||||||
\(455\) | 6.13703e17 | 3.24253 | ||||||||
\(456\) | 5.94671e15 | 0.0309746 | ||||||||
\(457\) | −1.46978e17 | −0.754737 | −0.377368 | − | 0.926063i | \(-0.623171\pi\) | ||||
−0.377368 | + | 0.926063i | \(0.623171\pi\) | |||||||
\(458\) | −5.64359e16 | −0.285713 | ||||||||
\(459\) | 2.23916e16 | 0.111764 | ||||||||
\(460\) | 1.89800e17 | 0.934049 | ||||||||
\(461\) | −3.03380e17 | −1.47208 | −0.736038 | − | 0.676940i | \(-0.763306\pi\) | ||||
−0.736038 | + | 0.676940i | \(0.763306\pi\) | |||||||
\(462\) | −8.64724e16 | −0.413718 | ||||||||
\(463\) | −1.61846e17 | −0.763528 | −0.381764 | − | 0.924260i | \(-0.624683\pi\) | ||||
−0.381764 | + | 0.924260i | \(0.624683\pi\) | |||||||
\(464\) | −1.05242e17 | −0.489578 | ||||||||
\(465\) | 2.77433e17 | 1.27266 | ||||||||
\(466\) | 2.04351e17 | 0.924416 | ||||||||
\(467\) | 1.95192e17 | 0.870766 | 0.435383 | − | 0.900245i | \(-0.356613\pi\) | ||||
0.435383 | + | 0.900245i | \(0.356613\pi\) | |||||||
\(468\) | −6.35447e16 | −0.279564 | ||||||||
\(469\) | −1.38627e17 | −0.601485 | ||||||||
\(470\) | 4.99499e16 | 0.213746 | ||||||||
\(471\) | 8.71098e16 | 0.367647 | ||||||||
\(472\) | −2.66187e16 | −0.110806 | ||||||||
\(473\) | 5.73571e16 | 0.235499 | ||||||||
\(474\) | −1.08492e17 | −0.439378 | ||||||||
\(475\) | −2.16628e16 | −0.0865380 | ||||||||
\(476\) | 2.18365e17 | 0.860474 | ||||||||
\(477\) | 5.74719e16 | 0.223402 | ||||||||
\(478\) | 1.38834e17 | 0.532370 | ||||||||
\(479\) | −1.50312e17 | −0.568608 | −0.284304 | − | 0.958734i | \(-0.591763\pi\) | ||||
−0.284304 | + | 0.958734i | \(0.591763\pi\) | |||||||
\(480\) | −2.43974e17 | −0.910489 | ||||||||
\(481\) | 3.72036e17 | 1.36975 | ||||||||
\(482\) | −1.12204e17 | −0.407569 | ||||||||
\(483\) | −2.45173e17 | −0.878651 | ||||||||
\(484\) | 8.77757e16 | 0.310370 | ||||||||
\(485\) | 4.44796e17 | 1.55181 | ||||||||
\(486\) | 8.96925e15 | 0.0308760 | ||||||||
\(487\) | −5.73308e16 | −0.194738 | −0.0973688 | − | 0.995248i | \(-0.531043\pi\) | ||||
−0.0973688 | + | 0.995248i | \(0.531043\pi\) | |||||||
\(488\) | 3.88449e17 | 1.30198 | ||||||||
\(489\) | 2.44932e17 | 0.810099 | ||||||||
\(490\) | −6.17600e17 | −2.01573 | ||||||||
\(491\) | −4.00825e17 | −1.29100 | −0.645498 | − | 0.763762i | \(-0.723350\pi\) | ||||
−0.645498 | + | 0.763762i | \(0.723350\pi\) | |||||||
\(492\) | −6.60061e16 | −0.209803 | ||||||||
\(493\) | −2.52691e17 | −0.792657 | ||||||||
\(494\) | −1.06973e16 | −0.0331167 | ||||||||
\(495\) | −1.29745e17 | −0.396423 | ||||||||
\(496\) | −1.70211e17 | −0.513284 | ||||||||
\(497\) | 2.93479e16 | 0.0873495 | ||||||||
\(498\) | 9.30700e16 | 0.273413 | ||||||||
\(499\) | 6.00021e17 | 1.73985 | 0.869927 | − | 0.493181i | \(-0.164166\pi\) | ||||
0.869927 | + | 0.493181i | \(0.164166\pi\) | |||||||
\(500\) | 1.54191e17 | 0.441321 | ||||||||
\(501\) | −1.07974e17 | −0.305052 | ||||||||
\(502\) | −1.52341e17 | −0.424858 | ||||||||
\(503\) | −1.77486e17 | −0.488620 | −0.244310 | − | 0.969697i | \(-0.578561\pi\) | ||||
−0.244310 | + | 0.969697i | \(0.578561\pi\) | |||||||
\(504\) | 2.01311e17 | 0.547102 | ||||||||
\(505\) | −2.90938e17 | −0.780561 | ||||||||
\(506\) | 1.10719e17 | 0.293254 | ||||||||
\(507\) | 4.22833e16 | 0.110565 | ||||||||
\(508\) | −4.10671e17 | −1.06018 | ||||||||
\(509\) | −1.45247e17 | −0.370204 | −0.185102 | − | 0.982719i | \(-0.559262\pi\) | ||||
−0.185102 | + | 0.982719i | \(0.559262\pi\) | |||||||
\(510\) | −9.87848e16 | −0.248590 | ||||||||
\(511\) | −1.34338e18 | −3.33783 | ||||||||
\(512\) | 2.74125e17 | 0.672502 | ||||||||
\(513\) | −5.00791e15 | −0.0121309 | ||||||||
\(514\) | 3.82689e17 | 0.915348 | ||||||||
\(515\) | 3.52113e16 | 0.0831641 | ||||||||
\(516\) | −5.80182e16 | −0.135314 | ||||||||
\(517\) | −9.66425e16 | −0.222577 | ||||||||
\(518\) | −5.12106e17 | −1.16471 | ||||||||
\(519\) | −3.62201e16 | −0.0813507 | ||||||||
\(520\) | 6.45204e17 | 1.43112 | ||||||||
\(521\) | −6.85604e17 | −1.50186 | −0.750928 | − | 0.660384i | \(-0.770393\pi\) | ||||
−0.750928 | + | 0.660384i | \(0.770393\pi\) | |||||||
\(522\) | −1.01219e17 | −0.218980 | ||||||||
\(523\) | −4.89577e17 | −1.04607 | −0.523035 | − | 0.852311i | \(-0.675200\pi\) | ||||
−0.523035 | + | 0.852311i | \(0.675200\pi\) | |||||||
\(524\) | −1.06432e17 | −0.224605 | ||||||||
\(525\) | −7.33339e17 | −1.52851 | ||||||||
\(526\) | −2.19387e17 | −0.451651 | ||||||||
\(527\) | −4.08686e17 | −0.831038 | ||||||||
\(528\) | 7.96018e16 | 0.159883 | ||||||||
\(529\) | −1.90118e17 | −0.377190 | ||||||||
\(530\) | −2.53549e17 | −0.496900 | ||||||||
\(531\) | 2.24165e16 | 0.0433963 | ||||||||
\(532\) | −4.88377e16 | −0.0933963 | ||||||||
\(533\) | 2.73270e17 | 0.516255 | ||||||||
\(534\) | 1.44721e17 | 0.270094 | ||||||||
\(535\) | 1.08699e18 | 2.00412 | ||||||||
\(536\) | −1.45743e17 | −0.265470 | ||||||||
\(537\) | −1.47890e17 | −0.266137 | ||||||||
\(538\) | −3.77057e17 | −0.670382 | ||||||||
\(539\) | 1.19493e18 | 2.09901 | ||||||||
\(540\) | 1.31241e17 | 0.227777 | ||||||||
\(541\) | −2.74375e16 | −0.0470503 | −0.0235251 | − | 0.999723i | \(-0.507489\pi\) | ||||
−0.0235251 | + | 0.999723i | \(0.507489\pi\) | |||||||
\(542\) | −3.61728e17 | −0.612897 | ||||||||
\(543\) | 2.82833e17 | 0.473511 | ||||||||
\(544\) | 3.59397e17 | 0.594541 | ||||||||
\(545\) | 1.69391e18 | 2.76893 | ||||||||
\(546\) | −3.62128e17 | −0.584939 | ||||||||
\(547\) | −6.61230e16 | −0.105544 | −0.0527721 | − | 0.998607i | \(-0.516806\pi\) | ||||
−0.0527721 | + | 0.998607i | \(0.516806\pi\) | |||||||
\(548\) | 3.99506e17 | 0.630159 | ||||||||
\(549\) | −3.27125e17 | −0.509911 | ||||||||
\(550\) | 3.31173e17 | 0.510149 | ||||||||
\(551\) | 5.65149e16 | 0.0860354 | ||||||||
\(552\) | −2.57757e17 | −0.387799 | ||||||||
\(553\) | 2.05063e18 | 3.04912 | ||||||||
\(554\) | 7.41891e16 | 0.109025 | ||||||||
\(555\) | −7.68378e17 | −1.11602 | ||||||||
\(556\) | −2.58847e17 | −0.371583 | ||||||||
\(557\) | −6.62052e17 | −0.939363 | −0.469681 | − | 0.882836i | \(-0.655631\pi\) | ||||
−0.469681 | + | 0.882836i | \(0.655631\pi\) | |||||||
\(558\) | −1.63705e17 | −0.229583 | ||||||||
\(559\) | 2.40199e17 | 0.332962 | ||||||||
\(560\) | 7.77642e17 | 1.06551 | ||||||||
\(561\) | 1.91128e17 | 0.258860 | ||||||||
\(562\) | 1.49095e17 | 0.199607 | ||||||||
\(563\) | 3.84925e17 | 0.509415 | 0.254708 | − | 0.967018i | \(-0.418021\pi\) | ||||
0.254708 | + | 0.967018i | \(0.418021\pi\) | |||||||
\(564\) | 9.77564e16 | 0.127888 | ||||||||
\(565\) | 1.45158e18 | 1.87727 | ||||||||
\(566\) | 2.99171e17 | 0.382484 | ||||||||
\(567\) | −1.69530e17 | −0.214268 | ||||||||
\(568\) | 3.08543e16 | 0.0385524 | ||||||||
\(569\) | 1.27520e17 | 0.157525 | 0.0787624 | − | 0.996893i | \(-0.474903\pi\) | ||||
0.0787624 | + | 0.996893i | \(0.474903\pi\) | |||||||
\(570\) | 2.20934e16 | 0.0269821 | ||||||||
\(571\) | 9.82029e17 | 1.18574 | 0.592870 | − | 0.805298i | \(-0.297995\pi\) | ||||
0.592870 | + | 0.805298i | \(0.297995\pi\) | |||||||
\(572\) | −5.42399e17 | −0.647507 | ||||||||
\(573\) | 1.97405e17 | 0.232998 | ||||||||
\(574\) | −3.76155e17 | −0.438975 | ||||||||
\(575\) | 9.38965e17 | 1.08345 | ||||||||
\(576\) | 3.91654e16 | 0.0446844 | ||||||||
\(577\) | −9.32031e16 | −0.105145 | −0.0525724 | − | 0.998617i | \(-0.516742\pi\) | ||||
−0.0525724 | + | 0.998617i | \(0.516742\pi\) | |||||||
\(578\) | −2.85954e17 | −0.318982 | ||||||||
\(579\) | 4.64091e17 | 0.511909 | ||||||||
\(580\) | −1.48107e18 | −1.61545 | ||||||||
\(581\) | −1.75914e18 | −1.89738 | ||||||||
\(582\) | −2.62461e17 | −0.279940 | ||||||||
\(583\) | 4.90564e17 | 0.517428 | ||||||||
\(584\) | −1.41234e18 | −1.47318 | ||||||||
\(585\) | −5.43347e17 | −0.560485 | ||||||||
\(586\) | −6.60918e17 | −0.674238 | ||||||||
\(587\) | −1.88941e18 | −1.90625 | −0.953124 | − | 0.302580i | \(-0.902152\pi\) | ||||
−0.953124 | + | 0.302580i | \(0.902152\pi\) | |||||||
\(588\) | −1.20870e18 | −1.20605 | ||||||||
\(589\) | 9.14034e16 | 0.0902013 | ||||||||
\(590\) | −9.88947e16 | −0.0965240 | ||||||||
\(591\) | 7.90489e17 | 0.763093 | ||||||||
\(592\) | 4.71417e17 | 0.450106 | ||||||||
\(593\) | 6.06244e16 | 0.0572521 | 0.0286261 | − | 0.999590i | \(-0.490887\pi\) | ||||
0.0286261 | + | 0.999590i | \(0.490887\pi\) | |||||||
\(594\) | 7.65590e16 | 0.0715129 | ||||||||
\(595\) | 1.86716e18 | 1.72512 | ||||||||
\(596\) | −1.14988e18 | −1.05088 | ||||||||
\(597\) | −1.02638e18 | −0.927848 | ||||||||
\(598\) | 4.63668e17 | 0.414619 | ||||||||
\(599\) | −1.04909e18 | −0.927977 | −0.463988 | − | 0.885841i | \(-0.653582\pi\) | ||||
−0.463988 | + | 0.885841i | \(0.653582\pi\) | |||||||
\(600\) | −7.70980e17 | −0.674621 | ||||||||
\(601\) | −1.45304e18 | −1.25775 | −0.628874 | − | 0.777507i | \(-0.716484\pi\) | ||||
−0.628874 | + | 0.777507i | \(0.716484\pi\) | |||||||
\(602\) | −3.30634e17 | −0.283120 | ||||||||
\(603\) | 1.22735e17 | 0.103969 | ||||||||
\(604\) | −1.96284e17 | −0.164492 | ||||||||
\(605\) | 7.50537e17 | 0.622246 | ||||||||
\(606\) | 1.71674e17 | 0.140810 | ||||||||
\(607\) | −1.18656e18 | −0.962863 | −0.481432 | − | 0.876484i | \(-0.659883\pi\) | ||||
−0.481432 | + | 0.876484i | \(0.659883\pi\) | |||||||
\(608\) | −8.03798e16 | −0.0645318 | ||||||||
\(609\) | 1.91317e18 | 1.51964 | ||||||||
\(610\) | 1.44318e18 | 1.13417 | ||||||||
\(611\) | −4.04718e17 | −0.314692 | ||||||||
\(612\) | −1.93331e17 | −0.148736 | ||||||||
\(613\) | 1.12742e16 | 0.00858211 | 0.00429105 | − | 0.999991i | \(-0.498634\pi\) | ||||
0.00429105 | + | 0.999991i | \(0.498634\pi\) | |||||||
\(614\) | −5.44534e17 | −0.410138 | ||||||||
\(615\) | −5.64393e17 | −0.420624 | ||||||||
\(616\) | 1.71833e18 | 1.26716 | ||||||||
\(617\) | −1.04678e18 | −0.763838 | −0.381919 | − | 0.924196i | \(-0.624737\pi\) | ||||
−0.381919 | + | 0.924196i | \(0.624737\pi\) | |||||||
\(618\) | −2.07772e16 | −0.0150024 | ||||||||
\(619\) | 1.54959e17 | 0.110720 | 0.0553601 | − | 0.998466i | \(-0.482369\pi\) | ||||
0.0553601 | + | 0.998466i | \(0.482369\pi\) | |||||||
\(620\) | −2.39538e18 | −1.69367 | ||||||||
\(621\) | 2.17066e17 | 0.151878 | ||||||||
\(622\) | 7.03144e17 | 0.486863 | ||||||||
\(623\) | −2.73542e18 | −1.87435 | ||||||||
\(624\) | 3.33356e17 | 0.226052 | ||||||||
\(625\) | −7.27311e17 | −0.488090 | ||||||||
\(626\) | −1.73385e17 | −0.115154 | ||||||||
\(627\) | −4.27461e16 | −0.0280968 | ||||||||
\(628\) | −7.52115e17 | −0.489268 | ||||||||
\(629\) | 1.13190e18 | 0.728748 | ||||||||
\(630\) | 7.47916e17 | 0.476584 | ||||||||
\(631\) | −7.67258e17 | −0.483894 | −0.241947 | − | 0.970289i | \(-0.577786\pi\) | ||||
−0.241947 | + | 0.970289i | \(0.577786\pi\) | |||||||
\(632\) | 2.15589e18 | 1.34575 | ||||||||
\(633\) | −1.51119e18 | −0.933672 | ||||||||
\(634\) | −2.32024e17 | −0.141890 | ||||||||
\(635\) | −3.51150e18 | −2.12551 | ||||||||
\(636\) | −4.96218e17 | −0.297305 | ||||||||
\(637\) | 5.00410e18 | 2.96770 | ||||||||
\(638\) | −8.63977e17 | −0.507186 | ||||||||
\(639\) | −2.59834e16 | −0.0150987 | ||||||||
\(640\) | 2.56882e18 | 1.47762 | ||||||||
\(641\) | 1.31735e18 | 0.750110 | 0.375055 | − | 0.927003i | \(-0.377624\pi\) | ||||
0.375055 | + | 0.927003i | \(0.377624\pi\) | |||||||
\(642\) | −6.41399e17 | −0.361535 | ||||||||
\(643\) | −1.05245e18 | −0.587261 | −0.293631 | − | 0.955919i | \(-0.594864\pi\) | ||||
−0.293631 | + | 0.955919i | \(0.594864\pi\) | |||||||
\(644\) | 2.11685e18 | 1.16932 | ||||||||
\(645\) | −4.96092e17 | −0.271284 | ||||||||
\(646\) | −3.25458e16 | −0.0176191 | ||||||||
\(647\) | −2.85595e18 | −1.53064 | −0.765319 | − | 0.643652i | \(-0.777419\pi\) | ||||
−0.765319 | + | 0.643652i | \(0.777419\pi\) | |||||||
\(648\) | −1.78232e17 | −0.0945687 | ||||||||
\(649\) | 1.91340e17 | 0.100512 | ||||||||
\(650\) | 1.38688e18 | 0.721277 | ||||||||
\(651\) | 3.09423e18 | 1.59322 | ||||||||
\(652\) | −2.11477e18 | −1.07809 | ||||||||
\(653\) | −3.54567e18 | −1.78963 | −0.894814 | − | 0.446439i | \(-0.852692\pi\) | ||||
−0.894814 | + | 0.446439i | \(0.852692\pi\) | |||||||
\(654\) | −9.99524e17 | −0.499503 | ||||||||
\(655\) | −9.10060e17 | −0.450299 | ||||||||
\(656\) | 3.46268e17 | 0.169644 | ||||||||
\(657\) | 1.18937e18 | 0.576957 | ||||||||
\(658\) | 5.57094e17 | 0.267584 | ||||||||
\(659\) | 1.44324e18 | 0.686412 | 0.343206 | − | 0.939260i | \(-0.388487\pi\) | ||||
0.343206 | + | 0.939260i | \(0.388487\pi\) | |||||||
\(660\) | 1.12023e18 | 0.527562 | ||||||||
\(661\) | −6.17628e17 | −0.288017 | −0.144008 | − | 0.989576i | \(-0.545999\pi\) | ||||
−0.144008 | + | 0.989576i | \(0.545999\pi\) | |||||||
\(662\) | −1.07374e18 | −0.495816 | ||||||||
\(663\) | 8.00403e17 | 0.365991 | ||||||||
\(664\) | −1.84943e18 | −0.837425 | ||||||||
\(665\) | −4.17593e17 | −0.187246 | ||||||||
\(666\) | 4.53397e17 | 0.201324 | ||||||||
\(667\) | −2.44961e18 | −1.07716 | ||||||||
\(668\) | 9.32257e17 | 0.405965 | ||||||||
\(669\) | −5.17896e17 | −0.223343 | ||||||||
\(670\) | −5.41468e17 | −0.231253 | ||||||||
\(671\) | −2.79225e18 | −1.18102 | ||||||||
\(672\) | −2.72105e18 | −1.13982 | ||||||||
\(673\) | 4.31364e18 | 1.78956 | 0.894780 | − | 0.446508i | \(-0.147332\pi\) | ||||
0.894780 | + | 0.446508i | \(0.147332\pi\) | |||||||
\(674\) | 1.33803e18 | 0.549763 | ||||||||
\(675\) | 6.49267e17 | 0.264210 | ||||||||
\(676\) | −3.65078e17 | −0.147141 | ||||||||
\(677\) | −2.55818e18 | −1.02119 | −0.510593 | − | 0.859823i | \(-0.670574\pi\) | ||||
−0.510593 | + | 0.859823i | \(0.670574\pi\) | |||||||
\(678\) | −8.56537e17 | −0.338652 | ||||||||
\(679\) | 4.96084e18 | 1.94268 | ||||||||
\(680\) | 1.96299e18 | 0.761397 | ||||||||
\(681\) | −1.20900e18 | −0.464483 | ||||||||
\(682\) | −1.39734e18 | −0.531744 | ||||||||
\(683\) | −9.84128e17 | −0.370952 | −0.185476 | − | 0.982649i | \(-0.559383\pi\) | ||||
−0.185476 | + | 0.982649i | \(0.559383\pi\) | |||||||
\(684\) | 4.32388e16 | 0.0161439 | ||||||||
\(685\) | 3.41603e18 | 1.26338 | ||||||||
\(686\) | −4.35458e18 | −1.59529 | ||||||||
\(687\) | −9.44418e17 | −0.342725 | ||||||||
\(688\) | 3.04364e17 | 0.109413 | ||||||||
\(689\) | 2.05438e18 | 0.731569 | ||||||||
\(690\) | −9.57629e17 | −0.337814 | ||||||||
\(691\) | −2.51089e18 | −0.877447 | −0.438723 | − | 0.898622i | \(-0.644569\pi\) | ||||
−0.438723 | + | 0.898622i | \(0.644569\pi\) | |||||||
\(692\) | 3.12728e17 | 0.108262 | ||||||||
\(693\) | −1.44706e18 | −0.496273 | ||||||||
\(694\) | −1.20452e18 | −0.409239 | ||||||||
\(695\) | −2.21330e18 | −0.744970 | ||||||||
\(696\) | 2.01137e18 | 0.670704 | ||||||||
\(697\) | 8.31407e17 | 0.274663 | ||||||||
\(698\) | 1.92006e18 | 0.628426 | ||||||||
\(699\) | 3.41967e18 | 1.10888 | ||||||||
\(700\) | 6.33172e18 | 2.03416 | ||||||||
\(701\) | −2.20623e18 | −0.702238 | −0.351119 | − | 0.936331i | \(-0.614199\pi\) | ||||
−0.351119 | + | 0.936331i | \(0.614199\pi\) | |||||||
\(702\) | 3.20613e17 | 0.101109 | ||||||||
\(703\) | −2.53151e17 | −0.0790987 | ||||||||
\(704\) | 3.34304e17 | 0.103495 | ||||||||
\(705\) | 8.35879e17 | 0.256398 | ||||||||
\(706\) | 1.75588e18 | 0.533659 | ||||||||
\(707\) | −3.24485e18 | −0.977167 | ||||||||
\(708\) | −1.93546e17 | −0.0577521 | ||||||||
\(709\) | 3.00415e18 | 0.888222 | 0.444111 | − | 0.895972i | \(-0.353520\pi\) | ||||
0.444111 | + | 0.895972i | \(0.353520\pi\) | |||||||
\(710\) | 1.14631e17 | 0.0335832 | ||||||||
\(711\) | −1.81554e18 | −0.527052 | ||||||||
\(712\) | −2.87582e18 | −0.827259 | ||||||||
\(713\) | −3.96184e18 | −1.12931 | ||||||||
\(714\) | −1.10175e18 | −0.311205 | ||||||||
\(715\) | −4.63785e18 | −1.29816 | ||||||||
\(716\) | 1.27689e18 | 0.354177 | ||||||||
\(717\) | 2.32329e18 | 0.638600 | ||||||||
\(718\) | −3.23101e17 | −0.0880095 | ||||||||
\(719\) | −4.12082e18 | −1.11236 | −0.556181 | − | 0.831061i | \(-0.687734\pi\) | ||||
−0.556181 | + | 0.831061i | \(0.687734\pi\) | |||||||
\(720\) | −6.88491e17 | −0.184178 | ||||||||
\(721\) | 3.92714e17 | 0.104111 | ||||||||
\(722\) | −1.82468e18 | −0.479396 | ||||||||
\(723\) | −1.87766e18 | −0.488897 | ||||||||
\(724\) | −2.44200e18 | −0.630153 | ||||||||
\(725\) | −7.32705e18 | −1.87384 | ||||||||
\(726\) | −4.42870e17 | −0.112250 | ||||||||
\(727\) | 6.30968e18 | 1.58502 | 0.792508 | − | 0.609862i | \(-0.208775\pi\) | ||||
0.792508 | + | 0.609862i | \(0.208775\pi\) | |||||||
\(728\) | 7.19600e18 | 1.79158 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −5.24716e18 | −1.28329 | ||||||||
\(731\) | 7.30792e17 | 0.177146 | ||||||||
\(732\) | 2.82443e18 | 0.678593 | ||||||||
\(733\) | 1.02753e18 | 0.244691 | 0.122346 | − | 0.992488i | \(-0.460958\pi\) | ||||
0.122346 | + | 0.992488i | \(0.460958\pi\) | |||||||
\(734\) | 1.88524e18 | 0.444983 | ||||||||
\(735\) | −1.03351e19 | −2.41796 | ||||||||
\(736\) | 3.48403e18 | 0.807934 | ||||||||
\(737\) | 1.04763e18 | 0.240806 | ||||||||
\(738\) | 3.33032e17 | 0.0758786 | ||||||||
\(739\) | −3.32865e18 | −0.751760 | −0.375880 | − | 0.926668i | \(-0.622660\pi\) | ||||
−0.375880 | + | 0.926668i | \(0.622660\pi\) | |||||||
\(740\) | 6.63425e18 | 1.48520 | ||||||||
\(741\) | −1.79012e17 | −0.0397249 | ||||||||
\(742\) | −2.82785e18 | −0.622058 | ||||||||
\(743\) | −6.32750e18 | −1.37976 | −0.689882 | − | 0.723922i | \(-0.742338\pi\) | ||||
−0.689882 | + | 0.723922i | \(0.742338\pi\) | |||||||
\(744\) | 3.25305e18 | 0.703180 | ||||||||
\(745\) | −9.83218e18 | −2.10685 | ||||||||
\(746\) | 1.92437e18 | 0.408777 | ||||||||
\(747\) | 1.55747e18 | 0.327970 | ||||||||
\(748\) | −1.65022e18 | −0.344493 | ||||||||
\(749\) | 1.21232e19 | 2.50892 | ||||||||
\(750\) | −7.77967e17 | −0.159611 | ||||||||
\(751\) | 9.28701e18 | 1.88893 | 0.944466 | − | 0.328608i | \(-0.106579\pi\) | ||||
0.944466 | + | 0.328608i | \(0.106579\pi\) | |||||||
\(752\) | −5.12831e17 | −0.103409 | ||||||||
\(753\) | −2.54933e18 | −0.509635 | ||||||||
\(754\) | −3.61815e18 | −0.717089 | ||||||||
\(755\) | −1.67835e18 | −0.329783 | ||||||||
\(756\) | 1.46374e18 | 0.285149 | ||||||||
\(757\) | 2.46880e17 | 0.0476829 | 0.0238415 | − | 0.999716i | \(-0.492410\pi\) | ||||
0.0238415 | + | 0.999716i | \(0.492410\pi\) | |||||||
\(758\) | −2.67786e18 | −0.512789 | ||||||||
\(759\) | 1.85281e18 | 0.351770 | ||||||||
\(760\) | −4.39027e17 | −0.0826425 | ||||||||
\(761\) | −1.27339e18 | −0.237663 | −0.118832 | − | 0.992914i | \(-0.537915\pi\) | ||||
−0.118832 | + | 0.992914i | \(0.537915\pi\) | |||||||
\(762\) | 2.07203e18 | 0.383432 | ||||||||
\(763\) | 1.88922e19 | 3.46636 | ||||||||
\(764\) | −1.70441e18 | −0.310076 | ||||||||
\(765\) | −1.65310e18 | −0.298195 | ||||||||
\(766\) | 1.62816e18 | 0.291212 | ||||||||
\(767\) | 8.01294e17 | 0.142109 | ||||||||
\(768\) | −1.95590e18 | −0.343953 | ||||||||
\(769\) | 1.14083e18 | 0.198930 | 0.0994649 | − | 0.995041i | \(-0.468287\pi\) | ||||
0.0994649 | + | 0.995041i | \(0.468287\pi\) | |||||||
\(770\) | 6.38399e18 | 1.10383 | ||||||||
\(771\) | 6.40406e18 | 1.09800 | ||||||||
\(772\) | −4.00701e18 | −0.681252 | ||||||||
\(773\) | −2.80195e18 | −0.472382 | −0.236191 | − | 0.971707i | \(-0.575899\pi\) | ||||
−0.236191 | + | 0.971707i | \(0.575899\pi\) | |||||||
\(774\) | 2.92729e17 | 0.0489384 | ||||||||
\(775\) | −1.18503e19 | −1.96457 | ||||||||
\(776\) | 5.21547e18 | 0.857418 | ||||||||
\(777\) | −8.56977e18 | −1.39712 | ||||||||
\(778\) | 2.05401e18 | 0.332075 | ||||||||
\(779\) | −1.85946e17 | −0.0298121 | ||||||||
\(780\) | 4.69131e18 | 0.745897 | ||||||||
\(781\) | −2.21786e17 | −0.0349706 | ||||||||
\(782\) | 1.41068e18 | 0.220590 | ||||||||
\(783\) | −1.69383e18 | −0.262676 | ||||||||
\(784\) | 6.34084e18 | 0.975197 | ||||||||
\(785\) | −6.43105e18 | −0.980910 | ||||||||
\(786\) | 5.36999e17 | 0.0812320 | ||||||||
\(787\) | 1.01329e19 | 1.52019 | 0.760097 | − | 0.649810i | \(-0.225152\pi\) | ||||
0.760097 | + | 0.649810i | \(0.225152\pi\) | |||||||
\(788\) | −6.82516e18 | −1.01553 | ||||||||
\(789\) | −3.67130e18 | −0.541775 | ||||||||
\(790\) | 8.00963e18 | 1.17229 | ||||||||
\(791\) | 1.61896e19 | 2.35012 | ||||||||
\(792\) | −1.52133e18 | −0.219034 | ||||||||
\(793\) | −1.16933e19 | −1.66979 | ||||||||
\(794\) | 2.00701e18 | 0.284261 | ||||||||
\(795\) | −4.24298e18 | −0.596052 | ||||||||
\(796\) | 8.86190e18 | 1.23479 | ||||||||
\(797\) | −5.39744e18 | −0.745948 | −0.372974 | − | 0.927842i | \(-0.621662\pi\) | ||||
−0.372974 | + | 0.927842i | \(0.621662\pi\) | |||||||
\(798\) | 2.46409e17 | 0.0337783 | ||||||||
\(799\) | −1.23133e18 | −0.167425 | ||||||||
\(800\) | 1.04211e19 | 1.40549 | ||||||||
\(801\) | 2.42182e18 | 0.323989 | ||||||||
\(802\) | −5.11258e18 | −0.678432 | ||||||||
\(803\) | 1.01521e19 | 1.33631 | ||||||||
\(804\) | −1.05970e18 | −0.138363 | ||||||||
\(805\) | 1.81004e19 | 2.34431 | ||||||||
\(806\) | −5.85176e18 | −0.751811 | ||||||||
\(807\) | −6.30980e18 | −0.804151 | ||||||||
\(808\) | −3.41141e18 | −0.431280 | ||||||||
\(809\) | −1.37848e19 | −1.72876 | −0.864379 | − | 0.502841i | \(-0.832288\pi\) | ||||
−0.864379 | + | 0.502841i | \(0.832288\pi\) | |||||||
\(810\) | −6.62173e17 | −0.0823794 | ||||||||
\(811\) | 7.86660e18 | 0.970849 | 0.485424 | − | 0.874279i | \(-0.338665\pi\) | ||||
0.485424 | + | 0.874279i | \(0.338665\pi\) | |||||||
\(812\) | −1.65185e19 | −2.02235 | ||||||||
\(813\) | −6.05329e18 | −0.735196 | ||||||||
\(814\) | 3.87007e18 | 0.466294 | ||||||||
\(815\) | −1.80826e19 | −2.16140 | ||||||||
\(816\) | 1.01421e18 | 0.120266 | ||||||||
\(817\) | −1.63443e17 | −0.0192275 | ||||||||
\(818\) | 5.15507e18 | 0.601642 | ||||||||
\(819\) | −6.05998e18 | −0.701659 | ||||||||
\(820\) | 4.87303e18 | 0.559769 | ||||||||
\(821\) | −1.12256e18 | −0.127932 | −0.0639661 | − | 0.997952i | \(-0.520375\pi\) | ||||
−0.0639661 | + | 0.997952i | \(0.520375\pi\) | |||||||
\(822\) | −2.01570e18 | −0.227907 | ||||||||
\(823\) | −5.31478e18 | −0.596193 | −0.298096 | − | 0.954536i | \(-0.596352\pi\) | ||||
−0.298096 | + | 0.954536i | \(0.596352\pi\) | |||||||
\(824\) | 4.12872e17 | 0.0459503 | ||||||||
\(825\) | 5.54196e18 | 0.611945 | ||||||||
\(826\) | −1.10298e18 | −0.120836 | ||||||||
\(827\) | −1.51535e19 | −1.64712 | −0.823562 | − | 0.567226i | \(-0.808017\pi\) | ||||
−0.823562 | + | 0.567226i | \(0.808017\pi\) | |||||||
\(828\) | −1.87417e18 | −0.202121 | ||||||||
\(829\) | −1.13320e19 | −1.21256 | −0.606280 | − | 0.795251i | \(-0.707339\pi\) | ||||
−0.606280 | + | 0.795251i | \(0.707339\pi\) | |||||||
\(830\) | −6.87107e18 | −0.729486 | ||||||||
\(831\) | 1.24151e18 | 0.130780 | ||||||||
\(832\) | 1.40000e18 | 0.146327 | ||||||||
\(833\) | 1.52247e19 | 1.57890 | ||||||||
\(834\) | 1.30600e18 | 0.134389 | ||||||||
\(835\) | 7.97138e18 | 0.813901 | ||||||||
\(836\) | 3.69074e17 | 0.0373915 | ||||||||
\(837\) | −2.73950e18 | −0.275394 | ||||||||
\(838\) | 4.09699e18 | 0.408676 | ||||||||
\(839\) | −5.77180e18 | −0.571292 | −0.285646 | − | 0.958335i | \(-0.592208\pi\) | ||||
−0.285646 | + | 0.958335i | \(0.592208\pi\) | |||||||
\(840\) | −1.48621e19 | −1.45971 | ||||||||
\(841\) | 8.85449e18 | 0.862958 | ||||||||
\(842\) | 5.86746e18 | 0.567442 | ||||||||
\(843\) | 2.49500e18 | 0.239437 | ||||||||
\(844\) | 1.30477e19 | 1.24254 | ||||||||
\(845\) | −3.12165e18 | −0.294995 | ||||||||
\(846\) | −4.93227e17 | −0.0462530 | ||||||||
\(847\) | 8.37079e18 | 0.778976 | ||||||||
\(848\) | 2.60316e18 | 0.240397 | ||||||||
\(849\) | 5.00644e18 | 0.458806 | ||||||||
\(850\) | 4.21950e18 | 0.383741 | ||||||||
\(851\) | 1.09727e19 | 0.990310 | ||||||||
\(852\) | 2.24343e17 | 0.0200935 | ||||||||
\(853\) | −1.09086e18 | −0.0969615 | −0.0484807 | − | 0.998824i | \(-0.515438\pi\) | ||||
−0.0484807 | + | 0.998824i | \(0.515438\pi\) | |||||||
\(854\) | 1.60959e19 | 1.41984 | ||||||||
\(855\) | 3.69719e17 | 0.0323662 | ||||||||
\(856\) | 1.27455e19 | 1.10733 | ||||||||
\(857\) | 1.02647e19 | 0.885059 | 0.442530 | − | 0.896754i | \(-0.354081\pi\) | ||||
0.442530 | + | 0.896754i | \(0.354081\pi\) | |||||||
\(858\) | 2.73666e18 | 0.234182 | ||||||||
\(859\) | −7.39090e18 | −0.627685 | −0.313842 | − | 0.949475i | \(-0.601616\pi\) | ||||
−0.313842 | + | 0.949475i | \(0.601616\pi\) | |||||||
\(860\) | 4.28331e18 | 0.361027 | ||||||||
\(861\) | −6.29472e18 | −0.526569 | ||||||||
\(862\) | −3.84138e18 | −0.318926 | ||||||||
\(863\) | 5.38961e18 | 0.444107 | 0.222053 | − | 0.975034i | \(-0.428724\pi\) | ||||
0.222053 | + | 0.975034i | \(0.428724\pi\) | |||||||
\(864\) | 2.40910e18 | 0.197023 | ||||||||
\(865\) | 2.67402e18 | 0.217050 | ||||||||
\(866\) | −1.92724e17 | −0.0155264 | ||||||||
\(867\) | −4.78526e18 | −0.382632 | ||||||||
\(868\) | −2.67159e19 | −2.12027 | ||||||||
\(869\) | −1.54969e19 | −1.22072 | ||||||||
\(870\) | 7.47269e18 | 0.584254 | ||||||||
\(871\) | 4.38724e18 | 0.340466 | ||||||||
\(872\) | 1.98620e19 | 1.52991 | ||||||||
\(873\) | −4.39212e18 | −0.335800 | ||||||||
\(874\) | −3.15502e17 | −0.0239429 | ||||||||
\(875\) | 1.47045e19 | 1.10764 | ||||||||
\(876\) | −1.02692e19 | −0.767818 | ||||||||
\(877\) | −1.44805e19 | −1.07470 | −0.537348 | − | 0.843361i | \(-0.680574\pi\) | ||||
−0.537348 | + | 0.843361i | \(0.680574\pi\) | |||||||
\(878\) | −9.47514e18 | −0.698025 | ||||||||
\(879\) | −1.10600e19 | −0.808777 | ||||||||
\(880\) | −5.87676e18 | −0.426580 | ||||||||
\(881\) | −1.69980e19 | −1.22477 | −0.612385 | − | 0.790560i | \(-0.709790\pi\) | ||||
−0.612385 | + | 0.790560i | \(0.709790\pi\) | |||||||
\(882\) | 6.09846e18 | 0.436188 | ||||||||
\(883\) | 7.63222e18 | 0.541884 | 0.270942 | − | 0.962596i | \(-0.412665\pi\) | ||||
0.270942 | + | 0.962596i | \(0.412665\pi\) | |||||||
\(884\) | −6.91076e18 | −0.487064 | ||||||||
\(885\) | −1.65494e18 | −0.115785 | ||||||||
\(886\) | 1.25821e19 | 0.873842 | ||||||||
\(887\) | −5.94311e18 | −0.409741 | −0.204871 | − | 0.978789i | \(-0.565677\pi\) | ||||
−0.204871 | + | 0.978789i | \(0.565677\pi\) | |||||||
\(888\) | −9.00964e18 | −0.616628 | ||||||||
\(889\) | −3.91639e19 | −2.66088 | ||||||||
\(890\) | −1.06843e19 | −0.720631 | ||||||||
\(891\) | 1.28116e18 | 0.0857827 | ||||||||
\(892\) | 4.47156e18 | 0.297227 | ||||||||
\(893\) | 2.75390e17 | 0.0181724 | ||||||||
\(894\) | 5.80168e18 | 0.380067 | ||||||||
\(895\) | 1.09183e19 | 0.710074 | ||||||||
\(896\) | 2.86502e19 | 1.84981 | ||||||||
\(897\) | 7.75918e18 | 0.497353 | ||||||||
\(898\) | 1.19348e18 | 0.0759486 | ||||||||
\(899\) | 3.09155e19 | 1.95316 | ||||||||
\(900\) | −5.60584e18 | −0.351612 | ||||||||
\(901\) | 6.25032e18 | 0.389217 | ||||||||
\(902\) | 2.84266e18 | 0.175745 | ||||||||
\(903\) | −5.53295e18 | −0.339614 | ||||||||
\(904\) | 1.70206e19 | 1.03724 | ||||||||
\(905\) | −2.08807e19 | −1.26336 | ||||||||
\(906\) | 9.90347e17 | 0.0594914 | ||||||||
\(907\) | 1.52905e19 | 0.911957 | 0.455978 | − | 0.889991i | \(-0.349289\pi\) | ||||
0.455978 | + | 0.889991i | \(0.349289\pi\) | |||||||
\(908\) | 1.04386e19 | 0.618137 | ||||||||
\(909\) | 2.87285e18 | 0.168907 | ||||||||
\(910\) | 2.67348e19 | 1.56066 | ||||||||
\(911\) | 1.71685e19 | 0.995092 | 0.497546 | − | 0.867438i | \(-0.334235\pi\) | ||||
0.497546 | + | 0.867438i | \(0.334235\pi\) | |||||||
\(912\) | −2.26831e17 | −0.0130538 | ||||||||
\(913\) | 1.32941e19 | 0.759623 | ||||||||
\(914\) | −6.40280e18 | −0.363262 | ||||||||
\(915\) | 2.41507e19 | 1.36048 | ||||||||
\(916\) | 8.15420e18 | 0.456101 | ||||||||
\(917\) | −1.01500e19 | −0.563720 | ||||||||
\(918\) | 9.75445e17 | 0.0537930 | ||||||||
\(919\) | 2.99876e19 | 1.64207 | 0.821034 | − | 0.570879i | \(-0.193397\pi\) | ||||
0.821034 | + | 0.570879i | \(0.193397\pi\) | |||||||
\(920\) | 1.90294e19 | 1.03468 | ||||||||
\(921\) | −9.11242e18 | −0.491978 | ||||||||
\(922\) | −1.32162e19 | −0.708523 | ||||||||
\(923\) | −9.28795e17 | −0.0494434 | ||||||||
\(924\) | 1.24941e19 | 0.660443 | ||||||||
\(925\) | 3.28205e19 | 1.72276 | ||||||||
\(926\) | −7.05050e18 | −0.367493 | ||||||||
\(927\) | −3.47692e17 | −0.0179960 | ||||||||
\(928\) | −2.71870e19 | −1.39733 | ||||||||
\(929\) | −2.16193e19 | −1.10342 | −0.551710 | − | 0.834036i | \(-0.686024\pi\) | ||||
−0.551710 | + | 0.834036i | \(0.686024\pi\) | |||||||
\(930\) | 1.20858e19 | 0.612544 | ||||||||
\(931\) | −3.40503e18 | −0.171375 | ||||||||
\(932\) | −2.95258e19 | −1.47570 | ||||||||
\(933\) | 1.17667e19 | 0.584013 | ||||||||
\(934\) | 8.50315e18 | 0.419107 | ||||||||
\(935\) | −1.41104e19 | −0.690658 | ||||||||
\(936\) | −6.37103e18 | −0.309682 | ||||||||
\(937\) | −1.19127e19 | −0.575045 | −0.287523 | − | 0.957774i | \(-0.592832\pi\) | ||||
−0.287523 | + | 0.957774i | \(0.592832\pi\) | |||||||
\(938\) | −6.03903e18 | −0.289500 | ||||||||
\(939\) | −2.90149e18 | −0.138132 | ||||||||
\(940\) | −7.21706e18 | −0.341216 | ||||||||
\(941\) | −2.08670e19 | −0.979776 | −0.489888 | − | 0.871785i | \(-0.662962\pi\) | ||||
−0.489888 | + | 0.871785i | \(0.662962\pi\) | |||||||
\(942\) | 3.79477e18 | 0.176952 | ||||||||
\(943\) | 8.05973e18 | 0.373245 | ||||||||
\(944\) | 1.01534e18 | 0.0466976 | ||||||||
\(945\) | 1.25159e19 | 0.571682 | ||||||||
\(946\) | 2.49865e18 | 0.113348 | ||||||||
\(947\) | 2.59334e19 | 1.16838 | 0.584190 | − | 0.811617i | \(-0.301412\pi\) | ||||
0.584190 | + | 0.811617i | \(0.301412\pi\) | |||||||
\(948\) | 1.56756e19 | 0.701405 | ||||||||
\(949\) | 4.25150e19 | 1.88935 | ||||||||
\(950\) | −9.43700e17 | −0.0416515 | ||||||||
\(951\) | −3.88277e18 | −0.170203 | ||||||||
\(952\) | 2.18934e19 | 0.953176 | ||||||||
\(953\) | 2.69420e19 | 1.16500 | 0.582501 | − | 0.812830i | \(-0.302074\pi\) | ||||
0.582501 | + | 0.812830i | \(0.302074\pi\) | |||||||
\(954\) | 2.50366e18 | 0.107525 | ||||||||
\(955\) | −1.45738e19 | −0.621657 | ||||||||
\(956\) | −2.00595e19 | −0.849854 | ||||||||
\(957\) | −1.44581e19 | −0.608392 | ||||||||
\(958\) | −6.54806e18 | −0.273676 | ||||||||
\(959\) | 3.80992e19 | 1.58159 | ||||||||
\(960\) | −2.89146e18 | −0.119221 | ||||||||
\(961\) | 2.55831e19 | 1.04774 | ||||||||
\(962\) | 1.62070e19 | 0.659273 | ||||||||
\(963\) | −1.07334e19 | −0.433676 | ||||||||
\(964\) | 1.62119e19 | 0.650627 | ||||||||
\(965\) | −3.42624e19 | −1.36581 | ||||||||
\(966\) | −1.06805e19 | −0.422902 | ||||||||
\(967\) | 2.00944e19 | 0.790320 | 0.395160 | − | 0.918612i | \(-0.370689\pi\) | ||||
0.395160 | + | 0.918612i | \(0.370689\pi\) | |||||||
\(968\) | 8.80045e18 | 0.343807 | ||||||||
\(969\) | −5.44632e17 | −0.0211348 | ||||||||
\(970\) | 1.93767e19 | 0.746902 | ||||||||
\(971\) | 1.08762e19 | 0.416441 | 0.208221 | − | 0.978082i | \(-0.433233\pi\) | ||||
0.208221 | + | 0.978082i | \(0.433233\pi\) | |||||||
\(972\) | −1.29593e18 | −0.0492892 | ||||||||
\(973\) | −2.46851e19 | −0.932612 | ||||||||
\(974\) | −2.49751e18 | −0.0937289 | ||||||||
\(975\) | 2.32085e19 | 0.865203 | ||||||||
\(976\) | −1.48170e19 | −0.548701 | ||||||||
\(977\) | −1.60956e19 | −0.592098 | −0.296049 | − | 0.955173i | \(-0.595669\pi\) | ||||
−0.296049 | + | 0.955173i | \(0.595669\pi\) | |||||||
\(978\) | 1.06700e19 | 0.389908 | ||||||||
\(979\) | 2.06719e19 | 0.750402 | ||||||||
\(980\) | 8.92345e19 | 3.21783 | ||||||||
\(981\) | −1.67264e19 | −0.599175 | ||||||||
\(982\) | −1.74612e19 | −0.621368 | ||||||||
\(983\) | 1.76692e19 | 0.624623 | 0.312312 | − | 0.949980i | \(-0.398897\pi\) | ||||
0.312312 | + | 0.949980i | \(0.398897\pi\) | |||||||
\(984\) | −6.61781e18 | −0.232405 | ||||||||
\(985\) | −5.83594e19 | −2.03599 | ||||||||
\(986\) | −1.10080e19 | −0.381513 | ||||||||
\(987\) | 9.32261e18 | 0.320979 | ||||||||
\(988\) | 1.54560e18 | 0.0528662 | ||||||||
\(989\) | 7.08436e18 | 0.240727 | ||||||||
\(990\) | −5.65211e18 | −0.190802 | ||||||||
\(991\) | −3.77816e19 | −1.26707 | −0.633536 | − | 0.773713i | \(-0.718397\pi\) | ||||
−0.633536 | + | 0.773713i | \(0.718397\pi\) | |||||||
\(992\) | −4.39704e19 | −1.46499 | ||||||||
\(993\) | −1.79683e19 | −0.594752 | ||||||||
\(994\) | 1.27848e18 | 0.0420421 | ||||||||
\(995\) | 7.57748e19 | 2.47557 | ||||||||
\(996\) | −1.34473e19 | −0.436465 | ||||||||
\(997\) | 4.25387e19 | 1.37172 | 0.685860 | − | 0.727733i | \(-0.259426\pi\) | ||||
0.685860 | + | 0.727733i | \(0.259426\pi\) | |||||||
\(998\) | 2.61388e19 | 0.837407 | ||||||||
\(999\) | 7.58730e18 | 0.241497 |
(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.a.1.20 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.a.1.20 | ✓ | 30 | 1.1 | even | 1 | trivial |