Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,10,Mod(49,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.49");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(38.6276877123\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{241})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 121x^{2} + 3600 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(8.26209i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.49 |
Dual form | 75.10.b.f.49.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 7.78626i | − 0.344107i | −0.985088 | − | 0.172054i | \(-0.944960\pi\) | ||||
0.985088 | − | 0.172054i | \(-0.0550403\pi\) | |||||||
\(3\) | 81.0000i | 0.577350i | ||||||||
\(4\) | 451.374 | 0.881590 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 630.687 | 0.198671 | ||||||||
\(7\) | 1839.88i | 0.289633i | 0.989459 | + | 0.144816i | \(0.0462591\pi\) | ||||
−0.989459 | + | 0.144816i | \(0.953741\pi\) | |||||||
\(8\) | − 7501.08i | − 0.647469i | ||||||||
\(9\) | −6561.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 44385.9 | 0.914066 | 0.457033 | − | 0.889450i | \(-0.348912\pi\) | ||||
0.457033 | + | 0.889450i | \(0.348912\pi\) | |||||||
\(12\) | 36561.3i | 0.508986i | ||||||||
\(13\) | − 136584.i | − 1.32634i | −0.748470 | − | 0.663169i | \(-0.769211\pi\) | ||||
0.748470 | − | 0.663169i | \(-0.230789\pi\) | |||||||
\(14\) | 14325.8 | 0.0996648 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 172698. | 0.658791 | ||||||||
\(17\) | − 253591.i | − 0.736399i | −0.929747 | − | 0.368199i | \(-0.879974\pi\) | ||||
0.929747 | − | 0.368199i | \(-0.120026\pi\) | |||||||
\(18\) | 51085.7i | 0.114702i | ||||||||
\(19\) | −85435.7 | −0.150400 | −0.0752001 | − | 0.997168i | \(-0.523960\pi\) | ||||
−0.0752001 | + | 0.997168i | \(0.523960\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −149030. | −0.167220 | ||||||||
\(22\) | − 345600.i | − 0.314537i | ||||||||
\(23\) | 979409.i | 0.729775i | 0.931052 | + | 0.364887i | \(0.118892\pi\) | ||||
−0.931052 | + | 0.364887i | \(0.881108\pi\) | |||||||
\(24\) | 607588. | 0.373816 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.06348e6 | −0.456403 | ||||||||
\(27\) | − 531441.i | − 0.192450i | ||||||||
\(28\) | 830473.i | 0.255337i | ||||||||
\(29\) | −2.58640e6 | −0.679054 | −0.339527 | − | 0.940596i | \(-0.610267\pi\) | ||||
−0.339527 | + | 0.940596i | \(0.610267\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.94787e6 | 1.74017 | 0.870085 | − | 0.492901i | \(-0.164064\pi\) | ||||
0.870085 | + | 0.492901i | \(0.164064\pi\) | |||||||
\(32\) | − 5.18523e6i | − 0.874164i | ||||||||
\(33\) | 3.59526e6i | 0.527736i | ||||||||
\(34\) | −1.97452e6 | −0.253400 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.96147e6 | −0.293863 | ||||||||
\(37\) | 1.56064e7i | 1.36897i | 0.729026 | + | 0.684486i | \(0.239974\pi\) | ||||
−0.729026 | + | 0.684486i | \(0.760026\pi\) | |||||||
\(38\) | 665225.i | 0.0517538i | ||||||||
\(39\) | 1.10633e7 | 0.765761 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.44893e7 | 1.35347 | 0.676735 | − | 0.736227i | \(-0.263394\pi\) | ||||
0.676735 | + | 0.736227i | \(0.263394\pi\) | |||||||
\(42\) | 1.16039e6i | 0.0575415i | ||||||||
\(43\) | − 1.27592e7i | − 0.569135i | −0.958656 | − | 0.284568i | \(-0.908150\pi\) | ||||
0.958656 | − | 0.284568i | \(-0.0918500\pi\) | |||||||
\(44\) | 2.00346e7 | 0.805832 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.62593e6 | 0.251121 | ||||||||
\(47\) | − 6.16764e7i | − 1.84365i | −0.387607 | − | 0.921825i | \(-0.626698\pi\) | ||||
0.387607 | − | 0.921825i | \(-0.373302\pi\) | |||||||
\(48\) | 1.39886e7i | 0.380353i | ||||||||
\(49\) | 3.69685e7 | 0.916113 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.05408e7 | 0.425160 | ||||||||
\(52\) | − 6.16504e7i | − 1.16929i | ||||||||
\(53\) | − 5.70418e6i | − 0.0993006i | −0.998767 | − | 0.0496503i | \(-0.984189\pi\) | ||||
0.998767 | − | 0.0496503i | \(-0.0158107\pi\) | |||||||
\(54\) | −4.13794e6 | −0.0662235 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.38011e7 | 0.187528 | ||||||||
\(57\) | − 6.92029e6i | − 0.0868336i | ||||||||
\(58\) | 2.01384e7i | 0.233668i | ||||||||
\(59\) | −8.35095e7 | −0.897226 | −0.448613 | − | 0.893726i | \(-0.648082\pi\) | ||||
−0.448613 | + | 0.893726i | \(0.648082\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.48622e8 | 1.37435 | 0.687177 | − | 0.726490i | \(-0.258850\pi\) | ||||
0.687177 | + | 0.726490i | \(0.258850\pi\) | |||||||
\(62\) | − 6.96704e7i | − 0.598806i | ||||||||
\(63\) | − 1.20714e7i | − 0.0965443i | ||||||||
\(64\) | 4.80479e7 | 0.357985 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.79936e7 | 0.181598 | ||||||||
\(67\) | − 1.68003e8i | − 1.01854i | −0.860606 | − | 0.509272i | \(-0.829915\pi\) | ||||
0.860606 | − | 0.509272i | \(-0.170085\pi\) | |||||||
\(68\) | − 1.14464e8i | − 0.649202i | ||||||||
\(69\) | −7.93321e7 | −0.421336 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.10986e8 | 0.985349 | 0.492675 | − | 0.870214i | \(-0.336019\pi\) | ||||
0.492675 | + | 0.870214i | \(0.336019\pi\) | |||||||
\(72\) | 4.92146e7i | 0.215823i | ||||||||
\(73\) | 1.43534e8i | 0.591566i | 0.955255 | + | 0.295783i | \(0.0955805\pi\) | ||||
−0.955255 | + | 0.295783i | \(0.904420\pi\) | |||||||
\(74\) | 1.21515e8 | 0.471074 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.85635e7 | −0.132591 | ||||||||
\(77\) | 8.16646e7i | 0.264744i | ||||||||
\(78\) | − 8.61416e7i | − 0.263504i | ||||||||
\(79\) | 4.55960e8 | 1.31706 | 0.658529 | − | 0.752555i | \(-0.271179\pi\) | ||||
0.658529 | + | 0.752555i | \(0.271179\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | − 1.90680e8i | − 0.465739i | ||||||||
\(83\) | 3.55106e8i | 0.821309i | 0.911791 | + | 0.410655i | \(0.134700\pi\) | ||||
−0.911791 | + | 0.410655i | \(0.865300\pi\) | |||||||
\(84\) | −6.72683e7 | −0.147419 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.93465e7 | −0.195844 | ||||||||
\(87\) | − 2.09498e8i | − 0.392052i | ||||||||
\(88\) | − 3.32942e8i | − 0.591830i | ||||||||
\(89\) | 4.24540e8 | 0.717239 | 0.358620 | − | 0.933484i | \(-0.383248\pi\) | ||||
0.358620 | + | 0.933484i | \(0.383248\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.51297e8 | 0.384151 | ||||||||
\(92\) | 4.42080e8i | 0.643362i | ||||||||
\(93\) | 7.24777e8i | 1.00469i | ||||||||
\(94\) | −4.80228e8 | −0.634413 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.20003e8 | 0.504699 | ||||||||
\(97\) | 1.19905e9i | 1.37520i | 0.726092 | + | 0.687598i | \(0.241335\pi\) | ||||
−0.726092 | + | 0.687598i | \(0.758665\pi\) | |||||||
\(98\) | − 2.87846e8i | − 0.315241i | ||||||||
\(99\) | −2.91216e8 | −0.304689 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.77085e9 | −1.69331 | −0.846654 | − | 0.532144i | \(-0.821387\pi\) | ||||
−0.846654 | + | 0.532144i | \(0.821387\pi\) | |||||||
\(102\) | − 1.59936e8i | − 0.146301i | ||||||||
\(103\) | − 3.03322e8i | − 0.265544i | −0.991147 | − | 0.132772i | \(-0.957612\pi\) | ||||
0.991147 | − | 0.132772i | \(-0.0423878\pi\) | |||||||
\(104\) | −1.02453e9 | −0.858763 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.44142e7 | −0.0341701 | ||||||||
\(107\) | − 1.95414e8i | − 0.144121i | −0.997400 | − | 0.0720607i | \(-0.977042\pi\) | ||||
0.997400 | − | 0.0720607i | \(-0.0229575\pi\) | |||||||
\(108\) | − 2.39879e8i | − 0.169662i | ||||||||
\(109\) | −2.31494e9 | −1.57080 | −0.785401 | − | 0.618988i | \(-0.787543\pi\) | ||||
−0.785401 | + | 0.618988i | \(0.787543\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.26412e9 | −0.790377 | ||||||||
\(112\) | 3.17743e8i | 0.190808i | ||||||||
\(113\) | − 1.31945e9i | − 0.761270i | −0.924725 | − | 0.380635i | \(-0.875706\pi\) | ||||
0.924725 | − | 0.380635i | \(-0.124294\pi\) | |||||||
\(114\) | −5.38832e7 | −0.0298801 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.16743e9 | −0.598648 | ||||||||
\(117\) | 8.96126e8i | 0.442113i | ||||||||
\(118\) | 6.50227e8i | 0.308742i | ||||||||
\(119\) | 4.66576e8 | 0.213285 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.87842e8 | −0.164483 | ||||||||
\(122\) | − 1.15721e9i | − 0.472925i | ||||||||
\(123\) | 1.98363e9i | 0.781426i | ||||||||
\(124\) | 4.03884e9 | 1.53412 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9.39914e7 | −0.0332216 | ||||||||
\(127\) | 3.18960e9i | 1.08798i | 0.839093 | + | 0.543988i | \(0.183086\pi\) | ||||
−0.839093 | + | 0.543988i | \(0.816914\pi\) | |||||||
\(128\) | − 3.02895e9i | − 0.997349i | ||||||||
\(129\) | 1.03350e9 | 0.328590 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.40115e9 | −1.60238 | −0.801190 | − | 0.598410i | \(-0.795799\pi\) | ||||
−0.801190 | + | 0.598410i | \(0.795799\pi\) | |||||||
\(132\) | 1.62281e9i | 0.465247i | ||||||||
\(133\) | − 1.57191e8i | − 0.0435608i | ||||||||
\(134\) | −1.30811e9 | −0.350488 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.90220e9 | −0.476796 | ||||||||
\(137\) | 1.19903e7i | 0.00290795i | 0.999999 | + | 0.00145398i | \(0.000462815\pi\) | ||||
−0.999999 | + | 0.00145398i | \(0.999537\pi\) | |||||||
\(138\) | 6.17701e8i | 0.144985i | ||||||||
\(139\) | −9.15482e8 | −0.208010 | −0.104005 | − | 0.994577i | \(-0.533166\pi\) | ||||
−0.104005 | + | 0.994577i | \(0.533166\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.99578e9 | 1.06443 | ||||||||
\(142\) | − 1.64279e9i | − 0.339066i | ||||||||
\(143\) | − 6.06239e9i | − 1.21236i | ||||||||
\(144\) | −1.13307e9 | −0.219597 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.11760e9 | 0.203562 | ||||||||
\(147\) | 2.99445e9i | 0.528918i | ||||||||
\(148\) | 7.04432e9i | 1.20687i | ||||||||
\(149\) | −5.00462e9 | −0.831827 | −0.415913 | − | 0.909404i | \(-0.636538\pi\) | ||||
−0.415913 | + | 0.909404i | \(0.636538\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.20554e9 | 0.501770 | 0.250885 | − | 0.968017i | \(-0.419278\pi\) | ||||
0.250885 | + | 0.968017i | \(0.419278\pi\) | |||||||
\(152\) | 6.40860e8i | 0.0973794i | ||||||||
\(153\) | 1.66381e9i | 0.245466i | ||||||||
\(154\) | 6.35862e8 | 0.0911002 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.99368e9 | 0.675088 | ||||||||
\(157\) | − 4.63430e8i | − 0.0608745i | −0.999537 | − | 0.0304373i | \(-0.990310\pi\) | ||||
0.999537 | − | 0.0304373i | \(-0.00968998\pi\) | |||||||
\(158\) | − 3.55023e9i | − 0.453210i | ||||||||
\(159\) | 4.62038e8 | 0.0573312 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.80199e9 | −0.211367 | ||||||||
\(162\) | − 3.35173e8i | − 0.0382342i | ||||||||
\(163\) | 1.27948e10i | 1.41968i | 0.704363 | + | 0.709840i | \(0.251233\pi\) | ||||
−0.704363 | + | 0.709840i | \(0.748767\pi\) | |||||||
\(164\) | 1.10538e10 | 1.19320 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.76495e9 | 0.282619 | ||||||||
\(167\) | − 1.85699e10i | − 1.84750i | −0.382992 | − | 0.923752i | \(-0.625106\pi\) | ||||
0.382992 | − | 0.923752i | \(-0.374894\pi\) | |||||||
\(168\) | 1.11789e9i | 0.108269i | ||||||||
\(169\) | −8.05063e9 | −0.759171 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.60544e8 | 0.0501334 | ||||||||
\(172\) | − 5.75917e9i | − 0.501744i | ||||||||
\(173\) | − 4.90746e9i | − 0.416533i | −0.978072 | − | 0.208266i | \(-0.933218\pi\) | ||||
0.978072 | − | 0.208266i | \(-0.0667821\pi\) | |||||||
\(174\) | −1.63121e9 | −0.134908 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.66536e9 | 0.602179 | ||||||||
\(177\) | − 6.76427e9i | − 0.518014i | ||||||||
\(178\) | − 3.30558e9i | − 0.246807i | ||||||||
\(179\) | 1.28930e10 | 0.938678 | 0.469339 | − | 0.883018i | \(-0.344492\pi\) | ||||
0.469339 | + | 0.883018i | \(0.344492\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.66233e10 | 1.84378 | 0.921889 | − | 0.387453i | \(-0.126645\pi\) | ||||
0.921889 | + | 0.387453i | \(0.126645\pi\) | |||||||
\(182\) | − 1.95667e9i | − 0.132189i | ||||||||
\(183\) | 1.20384e10i | 0.793483i | ||||||||
\(184\) | 7.34663e9 | 0.472506 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.64331e9 | 0.345721 | ||||||||
\(187\) | − 1.12558e10i | − 0.673117i | ||||||||
\(188\) | − 2.78391e10i | − 1.62534i | ||||||||
\(189\) | 9.77786e8 | 0.0557399 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.72802e10 | −1.48319 | −0.741595 | − | 0.670848i | \(-0.765930\pi\) | ||||
−0.741595 | + | 0.670848i | \(0.765930\pi\) | |||||||
\(192\) | 3.89188e9i | 0.206683i | ||||||||
\(193\) | 9.65442e9i | 0.500862i | 0.968134 | + | 0.250431i | \(0.0805723\pi\) | ||||
−0.968134 | + | 0.250431i | \(0.919428\pi\) | |||||||
\(194\) | 9.33612e9 | 0.473215 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.66866e10 | 0.807636 | ||||||||
\(197\) | 1.21091e10i | 0.572812i | 0.958108 | + | 0.286406i | \(0.0924606\pi\) | ||||
−0.958108 | + | 0.286406i | \(0.907539\pi\) | |||||||
\(198\) | 2.26748e9i | 0.104846i | ||||||||
\(199\) | −1.89741e10 | −0.857673 | −0.428837 | − | 0.903382i | \(-0.641076\pi\) | ||||
−0.428837 | + | 0.903382i | \(0.641076\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.36082e10 | 0.588056 | ||||||||
\(202\) | 1.37883e10i | 0.582680i | ||||||||
\(203\) | − 4.75866e9i | − 0.196676i | ||||||||
\(204\) | 9.27161e9 | 0.374817 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.36174e9 | −0.0913757 | ||||||||
\(207\) | − 6.42590e9i | − 0.243258i | ||||||||
\(208\) | − 2.35878e10i | − 0.873779i | ||||||||
\(209\) | −3.79214e9 | −0.137476 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.91928e9 | −0.309784 | −0.154892 | − | 0.987931i | \(-0.549503\pi\) | ||||
−0.154892 | + | 0.987931i | \(0.549503\pi\) | |||||||
\(212\) | − 2.57472e9i | − 0.0875424i | ||||||||
\(213\) | 1.70898e10i | 0.568892i | ||||||||
\(214\) | −1.52154e9 | −0.0495933 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.98638e9 | −0.124605 | ||||||||
\(217\) | 1.64630e10i | 0.504010i | ||||||||
\(218\) | 1.80248e10i | 0.540524i | ||||||||
\(219\) | −1.16263e10 | −0.341541 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.46364e10 | −0.976714 | ||||||||
\(222\) | 9.84275e9i | 0.271975i | ||||||||
\(223\) | 4.42755e10i | 1.19892i | 0.800403 | + | 0.599462i | \(0.204619\pi\) | ||||
−0.800403 | + | 0.599462i | \(0.795381\pi\) | |||||||
\(224\) | 9.54018e9 | 0.253187 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.02735e10 | −0.261959 | ||||||||
\(227\) | − 5.40045e10i | − 1.34994i | −0.737847 | − | 0.674968i | \(-0.764157\pi\) | ||||
0.737847 | − | 0.674968i | \(-0.235843\pi\) | |||||||
\(228\) | − 3.12364e9i | − 0.0765516i | ||||||||
\(229\) | −5.80250e9 | −0.139430 | −0.0697149 | − | 0.997567i | \(-0.522209\pi\) | ||||
−0.0697149 | + | 0.997567i | \(0.522209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.61483e9 | −0.152850 | ||||||||
\(232\) | 1.94008e10i | 0.439667i | ||||||||
\(233\) | − 5.41865e10i | − 1.20445i | −0.798326 | − | 0.602226i | \(-0.794281\pi\) | ||||
0.798326 | − | 0.602226i | \(-0.205719\pi\) | |||||||
\(234\) | 6.97747e9 | 0.152134 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.76940e10 | −0.790986 | ||||||||
\(237\) | 3.69328e10i | 0.760404i | ||||||||
\(238\) | − 3.63288e9i | − 0.0733930i | ||||||||
\(239\) | −7.91761e10 | −1.56965 | −0.784826 | − | 0.619716i | \(-0.787248\pi\) | ||||
−0.784826 | + | 0.619716i | \(0.787248\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.14920e10 | −1.17420 | −0.587100 | − | 0.809514i | \(-0.699730\pi\) | ||||
−0.587100 | + | 0.809514i | \(0.699730\pi\) | |||||||
\(242\) | 3.01984e9i | 0.0565998i | ||||||||
\(243\) | 3.48678e9i | 0.0641500i | ||||||||
\(244\) | 6.70841e10 | 1.21162 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.54451e10 | 0.268894 | ||||||||
\(247\) | 1.16691e10i | 0.199481i | ||||||||
\(248\) | − 6.71187e10i | − 1.12671i | ||||||||
\(249\) | −2.87636e10 | −0.474183 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.89319e10 | 0.460093 | 0.230046 | − | 0.973180i | \(-0.426112\pi\) | ||||
0.230046 | + | 0.973180i | \(0.426112\pi\) | |||||||
\(252\) | − 5.44873e9i | − 0.0851125i | ||||||||
\(253\) | 4.34719e10i | 0.667062i | ||||||||
\(254\) | 2.48350e10 | 0.374381 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.01633e9 | 0.0147896 | ||||||||
\(257\) | 1.22388e11i | 1.75001i | 0.484114 | + | 0.875005i | \(0.339142\pi\) | ||||
−0.484114 | + | 0.875005i | \(0.660858\pi\) | |||||||
\(258\) | − 8.04706e9i | − 0.113070i | ||||||||
\(259\) | −2.87139e10 | −0.396499 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.69694e10 | 0.226351 | ||||||||
\(262\) | 4.20548e10i | 0.551391i | ||||||||
\(263\) | 6.24892e10i | 0.805386i | 0.915335 | + | 0.402693i | \(0.131926\pi\) | ||||
−0.915335 | + | 0.402693i | \(0.868074\pi\) | |||||||
\(264\) | 2.69683e10 | 0.341693 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.22393e9 | −0.0149896 | ||||||||
\(267\) | 3.43878e10i | 0.414098i | ||||||||
\(268\) | − 7.58321e10i | − 0.897938i | ||||||||
\(269\) | −1.27214e11 | −1.48132 | −0.740659 | − | 0.671881i | \(-0.765487\pi\) | ||||
−0.740659 | + | 0.671881i | \(0.765487\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.54116e10 | 0.173574 | 0.0867871 | − | 0.996227i | \(-0.472340\pi\) | ||||
0.0867871 | + | 0.996227i | \(0.472340\pi\) | |||||||
\(272\) | − 4.37946e10i | − 0.485133i | ||||||||
\(273\) | 2.03551e10i | 0.221790i | ||||||||
\(274\) | 9.33596e7 | 0.00100065 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.58085e10 | −0.371445 | ||||||||
\(277\) | − 9.20867e10i | − 0.939806i | −0.882718 | − | 0.469903i | \(-0.844289\pi\) | ||||
0.882718 | − | 0.469903i | \(-0.155711\pi\) | |||||||
\(278\) | 7.12818e9i | 0.0715776i | ||||||||
\(279\) | −5.87070e10 | −0.580057 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.78782e10 | −0.745139 | −0.372570 | − | 0.928004i | \(-0.621523\pi\) | ||||
−0.372570 | + | 0.928004i | \(0.621523\pi\) | |||||||
\(282\) | − 3.88985e10i | − 0.366279i | ||||||||
\(283\) | − 2.92463e10i | − 0.271039i | −0.990775 | − | 0.135520i | \(-0.956730\pi\) | ||||
0.990775 | − | 0.135520i | \(-0.0432704\pi\) | |||||||
\(284\) | 9.52334e10 | 0.868674 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.72034e10 | −0.417182 | ||||||||
\(287\) | 4.50572e10i | 0.392009i | ||||||||
\(288\) | 3.40203e10i | 0.291388i | ||||||||
\(289\) | 5.42796e10 | 0.457717 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.71231e10 | −0.793970 | ||||||||
\(292\) | 6.47877e10i | 0.521519i | ||||||||
\(293\) | 2.27403e11i | 1.80257i | 0.433227 | + | 0.901285i | \(0.357375\pi\) | ||||
−0.433227 | + | 0.901285i | \(0.642625\pi\) | |||||||
\(294\) | 2.33155e10 | 0.182005 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.17065e11 | 0.886368 | ||||||||
\(297\) | − 2.35885e10i | − 0.175912i | ||||||||
\(298\) | 3.89673e10i | 0.286238i | ||||||||
\(299\) | 1.33771e11 | 0.967927 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.34754e10 | 0.164840 | ||||||||
\(302\) | − 2.49592e10i | − 0.172663i | ||||||||
\(303\) | − 1.43439e11i | − 0.977632i | ||||||||
\(304\) | −1.47546e10 | −0.0990823 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.29548e10 | 0.0844668 | ||||||||
\(307\) | − 6.02579e10i | − 0.387160i | −0.981084 | − | 0.193580i | \(-0.937990\pi\) | ||||
0.981084 | − | 0.193580i | \(-0.0620100\pi\) | |||||||
\(308\) | 3.68613e10i | 0.233395i | ||||||||
\(309\) | 2.45691e10 | 0.153312 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.36816e11 | 0.829308 | 0.414654 | − | 0.909979i | \(-0.363903\pi\) | ||||
0.414654 | + | 0.909979i | \(0.363903\pi\) | |||||||
\(312\) | − 8.29866e10i | − 0.495807i | ||||||||
\(313\) | − 2.25535e11i | − 1.32820i | −0.747643 | − | 0.664101i | \(-0.768815\pi\) | ||||
0.747643 | − | 0.664101i | \(-0.231185\pi\) | |||||||
\(314\) | −3.60839e9 | −0.0209474 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.05809e11 | 1.16111 | ||||||||
\(317\) | − 1.28386e11i | − 0.714089i | −0.934087 | − | 0.357045i | \(-0.883784\pi\) | ||||
0.934087 | − | 0.357045i | \(-0.116216\pi\) | |||||||
\(318\) | − 3.59755e9i | − 0.0197281i | ||||||||
\(319\) | −1.14800e11 | −0.620701 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.58285e10 | 0.0832086 | ||||||||
\(322\) | 1.40308e10i | 0.0727328i | ||||||||
\(323\) | 2.16657e10i | 0.110755i | ||||||||
\(324\) | 1.94302e10 | 0.0979545 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.96239e10 | 0.488522 | ||||||||
\(327\) | − 1.87510e11i | − 0.906902i | ||||||||
\(328\) | − 1.83696e11i | − 0.876329i | ||||||||
\(329\) | 1.13477e11 | 0.533981 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.15018e10 | 0.0526673 | 0.0263337 | − | 0.999653i | \(-0.491617\pi\) | ||||
0.0263337 | + | 0.999653i | \(0.491617\pi\) | |||||||
\(332\) | 1.60286e11i | 0.724058i | ||||||||
\(333\) | − 1.02394e11i | − 0.456324i | ||||||||
\(334\) | −1.44590e11 | −0.635740 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.57372e10 | −0.110163 | ||||||||
\(337\) | − 2.79631e11i | − 1.18100i | −0.807036 | − | 0.590502i | \(-0.798930\pi\) | ||||
0.807036 | − | 0.590502i | \(-0.201070\pi\) | |||||||
\(338\) | 6.26843e10i | 0.261236i | ||||||||
\(339\) | 1.06875e11 | 0.439519 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.97159e11 | 1.59063 | ||||||||
\(342\) | − 4.36454e9i | − 0.0172513i | ||||||||
\(343\) | 1.42263e11i | 0.554969i | ||||||||
\(344\) | −9.57078e10 | −0.368497 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.82107e10 | −0.143332 | ||||||||
\(347\) | 9.07088e10i | 0.335867i | 0.985798 | + | 0.167933i | \(0.0537093\pi\) | ||||
−0.985798 | + | 0.167933i | \(0.946291\pi\) | |||||||
\(348\) | − 9.45621e10i | − 0.345629i | ||||||||
\(349\) | 3.98825e11 | 1.43902 | 0.719511 | − | 0.694481i | \(-0.244366\pi\) | ||||
0.719511 | + | 0.694481i | \(0.244366\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.25862e10 | −0.255254 | ||||||||
\(352\) | − 2.30151e11i | − 0.799044i | ||||||||
\(353\) | 4.56192e11i | 1.56373i | 0.623448 | + | 0.781865i | \(0.285731\pi\) | ||||
−0.623448 | + | 0.781865i | \(0.714269\pi\) | |||||||
\(354\) | −5.26684e10 | −0.178252 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.91627e11 | 0.632311 | ||||||||
\(357\) | 3.77926e10i | 0.123140i | ||||||||
\(358\) | − 1.00389e11i | − 0.323006i | ||||||||
\(359\) | −1.89176e11 | −0.601094 | −0.300547 | − | 0.953767i | \(-0.597169\pi\) | ||||
−0.300547 | + | 0.953767i | \(0.597169\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.15388e11 | −0.977380 | ||||||||
\(362\) | − 2.07296e11i | − 0.634458i | ||||||||
\(363\) | − 3.14152e10i | − 0.0949643i | ||||||||
\(364\) | 1.13429e11 | 0.338664 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.37339e10 | 0.273044 | ||||||||
\(367\) | − 3.17920e10i | − 0.0914787i | −0.998953 | − | 0.0457394i | \(-0.985436\pi\) | ||||
0.998953 | − | 0.0457394i | \(-0.0145644\pi\) | |||||||
\(368\) | 1.69142e11i | 0.480769i | ||||||||
\(369\) | −1.60674e11 | −0.451156 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.04950e10 | 0.0287607 | ||||||||
\(372\) | 3.27146e11i | 0.885723i | ||||||||
\(373\) | 4.46388e11i | 1.19405i | 0.802222 | + | 0.597025i | \(0.203651\pi\) | ||||
−0.802222 | + | 0.597025i | \(0.796349\pi\) | |||||||
\(374\) | −8.76409e10 | −0.231625 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.62639e11 | −1.19371 | ||||||||
\(377\) | 3.53260e11i | 0.900655i | ||||||||
\(378\) | − 7.61330e9i | − 0.0191805i | ||||||||
\(379\) | −3.53467e11 | −0.879978 | −0.439989 | − | 0.898003i | \(-0.645018\pi\) | ||||
−0.439989 | + | 0.898003i | \(0.645018\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.58357e11 | −0.628143 | ||||||||
\(382\) | 2.12411e11i | 0.510377i | ||||||||
\(383\) | − 3.14974e11i | − 0.747963i | −0.927436 | − | 0.373981i | \(-0.877992\pi\) | ||||
0.927436 | − | 0.373981i | \(-0.122008\pi\) | |||||||
\(384\) | 2.45345e11 | 0.575820 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.51718e10 | 0.172350 | ||||||||
\(387\) | 8.37131e10i | 0.189712i | ||||||||
\(388\) | 5.41220e11i | 1.21236i | ||||||||
\(389\) | 4.20729e11 | 0.931600 | 0.465800 | − | 0.884890i | \(-0.345767\pi\) | ||||
0.465800 | + | 0.884890i | \(0.345767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.48369e11 | 0.537405 | ||||||||
\(392\) | − 2.77303e11i | − 0.593155i | ||||||||
\(393\) | − 4.37493e11i | − 0.925134i | ||||||||
\(394\) | 9.42843e10 | 0.197109 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.31447e11 | −0.268611 | ||||||||
\(397\) | 5.63093e11i | 1.13769i | 0.822446 | + | 0.568844i | \(0.192609\pi\) | ||||
−0.822446 | + | 0.568844i | \(0.807391\pi\) | |||||||
\(398\) | 1.47737e11i | 0.295132i | ||||||||
\(399\) | 1.27325e10 | 0.0251498 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.75897e11 | 0.532841 | 0.266420 | − | 0.963857i | \(-0.414159\pi\) | ||||
0.266420 | + | 0.963857i | \(0.414159\pi\) | |||||||
\(402\) | − 1.05957e11i | − 0.202355i | ||||||||
\(403\) | − 1.22213e12i | − 2.30805i | ||||||||
\(404\) | −7.99317e11 | −1.49280 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.70521e10 | −0.0676778 | ||||||||
\(407\) | 6.92703e11i | 1.25133i | ||||||||
\(408\) | − 1.54079e11i | − 0.275278i | ||||||||
\(409\) | 6.54552e10 | 0.115662 | 0.0578308 | − | 0.998326i | \(-0.481582\pi\) | ||||
0.0578308 | + | 0.998326i | \(0.481582\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.71214e8 | −0.00167891 | ||||||||
\(412\) | − 1.36912e11i | − 0.234101i | ||||||||
\(413\) | − 1.53647e11i | − 0.259866i | ||||||||
\(414\) | −5.00337e10 | −0.0837069 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.08218e11 | −1.15944 | ||||||||
\(417\) | − 7.41541e10i | − 0.120094i | ||||||||
\(418\) | 2.95266e10i | 0.0473064i | ||||||||
\(419\) | −2.70250e10 | −0.0428354 | −0.0214177 | − | 0.999771i | \(-0.506818\pi\) | ||||
−0.0214177 | + | 0.999771i | \(0.506818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.29698e11 | −0.666644 | −0.333322 | − | 0.942813i | \(-0.608170\pi\) | ||||
−0.333322 | + | 0.942813i | \(0.608170\pi\) | |||||||
\(422\) | 6.94478e10i | 0.106599i | ||||||||
\(423\) | 4.04659e11i | 0.614550i | ||||||||
\(424\) | −4.27875e10 | −0.0642940 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.33066e11 | 0.195760 | ||||||||
\(427\) | 2.73446e11i | 0.398058i | ||||||||
\(428\) | − 8.82048e10i | − 0.127056i | ||||||||
\(429\) | 4.91054e11 | 0.699957 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.44700e11 | −1.31870 | −0.659350 | − | 0.751836i | \(-0.729169\pi\) | ||||
−0.659350 | + | 0.751836i | \(0.729169\pi\) | |||||||
\(432\) | − 9.17789e10i | − 0.126784i | ||||||||
\(433\) | − 2.10762e11i | − 0.288136i | −0.989568 | − | 0.144068i | \(-0.953982\pi\) | ||||
0.989568 | − | 0.144068i | \(-0.0460184\pi\) | |||||||
\(434\) | 1.28185e11 | 0.173434 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.04491e12 | −1.38480 | ||||||||
\(437\) | − 8.36765e10i | − 0.109758i | ||||||||
\(438\) | 9.05253e10i | 0.117527i | ||||||||
\(439\) | −7.69079e11 | −0.988282 | −0.494141 | − | 0.869382i | \(-0.664517\pi\) | ||||
−0.494141 | + | 0.869382i | \(0.664517\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.42550e11 | −0.305371 | ||||||||
\(442\) | 2.69688e11i | 0.336094i | ||||||||
\(443\) | 6.49894e11i | 0.801726i | 0.916138 | + | 0.400863i | \(0.131290\pi\) | ||||
−0.916138 | + | 0.400863i | \(0.868710\pi\) | |||||||
\(444\) | −5.70590e11 | −0.696788 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.44741e11 | 0.412559 | ||||||||
\(447\) | − 4.05374e11i | − 0.480255i | ||||||||
\(448\) | 8.84023e10i | 0.103684i | ||||||||
\(449\) | 4.51858e11 | 0.524679 | 0.262339 | − | 0.964976i | \(-0.415506\pi\) | ||||
0.262339 | + | 0.964976i | \(0.415506\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.08698e12 | 1.23716 | ||||||||
\(452\) | − 5.95564e11i | − 0.671128i | ||||||||
\(453\) | 2.59649e11i | 0.289697i | ||||||||
\(454\) | −4.20493e11 | −0.464523 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.19097e10 | −0.0562220 | ||||||||
\(457\) | − 6.18434e11i | − 0.663240i | −0.943413 | − | 0.331620i | \(-0.892405\pi\) | ||||
0.943413 | − | 0.331620i | \(-0.107595\pi\) | |||||||
\(458\) | 4.51798e10i | 0.0479788i | ||||||||
\(459\) | −1.34768e11 | −0.141720 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.76450e11 | −0.285078 | −0.142539 | − | 0.989789i | \(-0.545527\pi\) | ||||
−0.142539 | + | 0.989789i | \(0.545527\pi\) | |||||||
\(462\) | 5.15048e10i | 0.0525967i | ||||||||
\(463\) | − 6.09969e11i | − 0.616870i | −0.951245 | − | 0.308435i | \(-0.900195\pi\) | ||||
0.951245 | − | 0.308435i | \(-0.0998052\pi\) | |||||||
\(464\) | −4.46666e11 | −0.447355 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.21910e11 | −0.414461 | ||||||||
\(467\) | 2.83260e11i | 0.275587i | 0.990461 | + | 0.137794i | \(0.0440011\pi\) | ||||
−0.990461 | + | 0.137794i | \(0.955999\pi\) | |||||||
\(468\) | 4.04488e11i | 0.389762i | ||||||||
\(469\) | 3.09104e11 | 0.295004 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.75378e10 | 0.0351459 | ||||||||
\(472\) | 6.26412e11i | 0.580926i | ||||||||
\(473\) | − 5.66328e11i | − 0.520227i | ||||||||
\(474\) | 2.87568e11 | 0.261661 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.10600e11 | 0.188030 | ||||||||
\(477\) | 3.74251e10i | 0.0331002i | ||||||||
\(478\) | 6.16485e11i | 0.540129i | ||||||||
\(479\) | 1.39149e12 | 1.20773 | 0.603865 | − | 0.797087i | \(-0.293627\pi\) | ||||
0.603865 | + | 0.797087i | \(0.293627\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.13158e12 | 1.81572 | ||||||||
\(482\) | 4.78793e11i | 0.404051i | ||||||||
\(483\) | − 1.45961e11i | − 0.122033i | ||||||||
\(484\) | −1.75062e11 | −0.145007 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.71490e10 | 0.0220745 | ||||||||
\(487\) | − 1.41532e11i | − 0.114018i | −0.998374 | − | 0.0570092i | \(-0.981844\pi\) | ||||
0.998374 | − | 0.0570092i | \(-0.0181564\pi\) | |||||||
\(488\) | − 1.11483e12i | − 0.889851i | ||||||||
\(489\) | −1.03638e12 | −0.819652 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.66246e11 | −0.362034 | −0.181017 | − | 0.983480i | \(-0.557939\pi\) | ||||
−0.181017 | + | 0.983480i | \(0.557939\pi\) | |||||||
\(492\) | 8.95359e11i | 0.688897i | ||||||||
\(493\) | 6.55887e11i | 0.500055i | ||||||||
\(494\) | 9.08589e10 | 0.0686430 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.54528e12 | 1.14641 | ||||||||
\(497\) | 3.88188e11i | 0.285389i | ||||||||
\(498\) | 2.23961e11i | 0.163170i | ||||||||
\(499\) | 2.21254e12 | 1.59749 | 0.798746 | − | 0.601668i | \(-0.205497\pi\) | ||||
0.798746 | + | 0.601668i | \(0.205497\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.50416e12 | 1.06666 | ||||||||
\(502\) | − 2.25271e11i | − 0.158321i | ||||||||
\(503\) | − 3.39574e11i | − 0.236526i | −0.992982 | − | 0.118263i | \(-0.962267\pi\) | ||||
0.992982 | − | 0.118263i | \(-0.0377326\pi\) | |||||||
\(504\) | −9.05488e10 | −0.0625094 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.38484e11 | 0.229541 | ||||||||
\(507\) | − 6.52101e11i | − 0.438308i | ||||||||
\(508\) | 1.43970e12i | 0.959149i | ||||||||
\(509\) | 5.66691e11 | 0.374211 | 0.187106 | − | 0.982340i | \(-0.440089\pi\) | ||||
0.187106 | + | 0.982340i | \(0.440089\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.64086e11 | −0.171337 | ||||||||
\(512\) | − 1.55874e12i | − 1.00244i | ||||||||
\(513\) | 4.54040e10i | 0.0289445i | ||||||||
\(514\) | 9.52947e11 | 0.602191 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.66493e11 | 0.289682 | ||||||||
\(517\) | − 2.73756e12i | − 1.68522i | ||||||||
\(518\) | 2.23574e11i | 0.136438i | ||||||||
\(519\) | 3.97504e11 | 0.240485 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.42970e11 | 0.263393 | 0.131697 | − | 0.991290i | \(-0.457958\pi\) | ||||
0.131697 | + | 0.991290i | \(0.457958\pi\) | |||||||
\(522\) | − 1.32128e11i | − 0.0778892i | ||||||||
\(523\) | 1.44683e11i | 0.0845591i | 0.999106 | + | 0.0422796i | \(0.0134620\pi\) | ||||
−0.999106 | + | 0.0422796i | \(0.986538\pi\) | |||||||
\(524\) | −2.43794e12 | −1.41264 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.86557e11 | 0.277139 | ||||||||
\(527\) | − 2.26910e12i | − 1.28146i | ||||||||
\(528\) | 6.20894e11i | 0.347668i | ||||||||
\(529\) | 8.41911e11 | 0.467429 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.47906e11 | 0.299075 | ||||||||
\(532\) | − 7.09520e10i | − 0.0384028i | ||||||||
\(533\) | − 3.34484e12i | − 1.79516i | ||||||||
\(534\) | 2.67752e11 | 0.142494 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.26020e12 | −0.659475 | ||||||||
\(537\) | 1.04434e12i | 0.541946i | ||||||||
\(538\) | 9.90519e11i | 0.509733i | ||||||||
\(539\) | 1.64088e12 | 0.837388 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.10308e11 | −0.155742 | −0.0778710 | − | 0.996963i | \(-0.524812\pi\) | ||||
−0.0778710 | + | 0.996963i | \(0.524812\pi\) | |||||||
\(542\) | − 1.19999e11i | − 0.0597281i | ||||||||
\(543\) | 2.15649e12i | 1.06451i | ||||||||
\(544\) | −1.31493e12 | −0.643733 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.58490e11 | 0.0763194 | ||||||||
\(547\) | 1.68502e12i | 0.804750i | 0.915475 | + | 0.402375i | \(0.131815\pi\) | ||||
−0.915475 | + | 0.402375i | \(0.868185\pi\) | |||||||
\(548\) | 5.41211e9i | 0.00256362i | ||||||||
\(549\) | −9.75108e11 | −0.458118 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.20971e11 | 0.102130 | ||||||||
\(552\) | 5.95077e11i | 0.272802i | ||||||||
\(553\) | 8.38911e11i | 0.381463i | ||||||||
\(554\) | −7.17011e11 | −0.323394 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.13225e11 | −0.183379 | ||||||||
\(557\) | − 2.31328e12i | − 1.01831i | −0.860674 | − | 0.509156i | \(-0.829958\pi\) | ||||
0.860674 | − | 0.509156i | \(-0.170042\pi\) | |||||||
\(558\) | 4.57108e11i | 0.199602i | ||||||||
\(559\) | −1.74270e12 | −0.754865 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.11723e11 | 0.388624 | ||||||||
\(562\) | 6.06380e11i | 0.256408i | ||||||||
\(563\) | − 7.03648e11i | − 0.295167i | −0.989050 | − | 0.147583i | \(-0.952850\pi\) | ||||
0.989050 | − | 0.147583i | \(-0.0471495\pi\) | |||||||
\(564\) | 2.25497e12 | 0.938392 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.27720e11 | −0.0932666 | ||||||||
\(567\) | 7.92007e10i | 0.0321814i | ||||||||
\(568\) | − 1.58262e12i | − 0.637983i | ||||||||
\(569\) | −3.21997e12 | −1.28779 | −0.643896 | − | 0.765113i | \(-0.722683\pi\) | ||||
−0.643896 | + | 0.765113i | \(0.722683\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.21116e12 | −0.476801 | −0.238401 | − | 0.971167i | \(-0.576623\pi\) | ||||
−0.238401 | + | 0.971167i | \(0.576623\pi\) | |||||||
\(572\) | − 2.73641e12i | − 1.06880i | ||||||||
\(573\) | − 2.20969e12i | − 0.856320i | ||||||||
\(574\) | 3.50827e11 | 0.134893 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.15242e11 | −0.119328 | ||||||||
\(577\) | 7.30673e11i | 0.274430i | 0.990541 | + | 0.137215i | \(0.0438151\pi\) | ||||
−0.990541 | + | 0.137215i | \(0.956185\pi\) | |||||||
\(578\) | − 4.22635e11i | − 0.157504i | ||||||||
\(579\) | −7.82008e11 | −0.289173 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.53352e11 | −0.237878 | ||||||||
\(582\) | 7.56226e11i | 0.273211i | ||||||||
\(583\) | − 2.53185e11i | − 0.0907673i | ||||||||
\(584\) | 1.07666e12 | 0.383021 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.77062e12 | 0.620278 | ||||||||
\(587\) | 4.55331e12i | 1.58291i | 0.611230 | + | 0.791453i | \(0.290675\pi\) | ||||
−0.611230 | + | 0.791453i | \(0.709325\pi\) | |||||||
\(588\) | 1.35162e12i | 0.466289i | ||||||||
\(589\) | −7.64467e11 | −0.261722 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.80833e11 | −0.330713 | ||||||||
\(592\) | 2.69520e12i | 0.901867i | ||||||||
\(593\) | − 3.00074e12i | − 0.996510i | −0.867030 | − | 0.498255i | \(-0.833974\pi\) | ||||
0.867030 | − | 0.498255i | \(-0.166026\pi\) | |||||||
\(594\) | −1.83666e11 | −0.0605327 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.25896e12 | −0.733330 | ||||||||
\(597\) | − 1.53690e12i | − 0.495178i | ||||||||
\(598\) | − 1.04158e12i | − 0.333071i | ||||||||
\(599\) | 4.03514e12 | 1.28067 | 0.640336 | − | 0.768095i | \(-0.278795\pi\) | ||||
0.640336 | + | 0.768095i | \(0.278795\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.04760e12 | 0.640192 | 0.320096 | − | 0.947385i | \(-0.396285\pi\) | ||||
0.320096 | + | 0.947385i | \(0.396285\pi\) | |||||||
\(602\) | − 1.82785e11i | − 0.0567227i | ||||||||
\(603\) | 1.10227e12i | 0.339514i | ||||||||
\(604\) | 1.44690e12 | 0.442355 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.11685e12 | −0.336410 | ||||||||
\(607\) | 3.15792e12i | 0.944175i | 0.881552 | + | 0.472088i | \(0.156499\pi\) | ||||
−0.881552 | + | 0.472088i | \(0.843501\pi\) | |||||||
\(608\) | 4.43004e11i | 0.131474i | ||||||||
\(609\) | 3.85451e11 | 0.113551 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.42399e12 | −2.44530 | ||||||||
\(612\) | 7.51000e11i | 0.216401i | ||||||||
\(613\) | 2.89302e12i | 0.827520i | 0.910386 | + | 0.413760i | \(0.135785\pi\) | ||||
−0.910386 | + | 0.413760i | \(0.864215\pi\) | |||||||
\(614\) | −4.69183e11 | −0.133225 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.12573e11 | 0.171413 | ||||||||
\(617\) | 6.03603e12i | 1.67675i | 0.545094 | + | 0.838375i | \(0.316494\pi\) | ||||
−0.545094 | + | 0.838375i | \(0.683506\pi\) | |||||||
\(618\) | − 1.91301e11i | − 0.0527558i | ||||||||
\(619\) | −4.05606e12 | −1.11044 | −0.555222 | − | 0.831702i | \(-0.687367\pi\) | ||||
−0.555222 | + | 0.831702i | \(0.687367\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.20498e11 | 0.140445 | ||||||||
\(622\) | − 1.06529e12i | − 0.285371i | ||||||||
\(623\) | 7.81102e11i | 0.207736i | ||||||||
\(624\) | 1.91061e12 | 0.504477 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.75607e12 | −0.457044 | ||||||||
\(627\) | − 3.07163e11i | − 0.0793716i | ||||||||
\(628\) | − 2.09180e11i | − 0.0536664i | ||||||||
\(629\) | 3.95764e12 | 1.00811 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.34498e12 | −1.34219 | −0.671095 | − | 0.741372i | \(-0.734176\pi\) | ||||
−0.671095 | + | 0.741372i | \(0.734176\pi\) | |||||||
\(632\) | − 3.42020e12i | − 0.852755i | ||||||||
\(633\) | − 7.22461e11i | − 0.178854i | ||||||||
\(634\) | −9.99651e11 | −0.245723 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.08552e11 | 0.0505426 | ||||||||
\(637\) | − 5.04929e12i | − 1.21507i | ||||||||
\(638\) | 8.93859e11i | 0.213588i | ||||||||
\(639\) | −1.38428e12 | −0.328450 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.81739e12 | 1.12707 | 0.563534 | − | 0.826093i | \(-0.309441\pi\) | ||||
0.563534 | + | 0.826093i | \(0.309441\pi\) | |||||||
\(642\) | − 1.23245e11i | − 0.0286327i | ||||||||
\(643\) | 5.85505e11i | 0.135077i | 0.997717 | + | 0.0675385i | \(0.0215145\pi\) | ||||
−0.997717 | + | 0.0675385i | \(0.978485\pi\) | |||||||
\(644\) | −8.13372e11 | −0.186339 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.68695e11 | 0.0381114 | ||||||||
\(647\) | 4.54903e12i | 1.02059i | 0.860001 | + | 0.510293i | \(0.170463\pi\) | ||||
−0.860001 | + | 0.510293i | \(0.829537\pi\) | |||||||
\(648\) | − 3.22897e11i | − 0.0719410i | ||||||||
\(649\) | −3.70664e12 | −0.820124 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.33350e12 | −0.290991 | ||||||||
\(652\) | 5.77526e12i | 1.25158i | ||||||||
\(653\) | 7.04350e12i | 1.51593i | 0.652295 | + | 0.757965i | \(0.273806\pi\) | ||||
−0.652295 | + | 0.757965i | \(0.726194\pi\) | |||||||
\(654\) | −1.46001e12 | −0.312072 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.22925e12 | 0.891653 | ||||||||
\(657\) | − 9.41729e11i | − 0.197189i | ||||||||
\(658\) | − 8.83561e11i | − 0.183747i | ||||||||
\(659\) | −5.23559e12 | −1.08139 | −0.540694 | − | 0.841219i | \(-0.681838\pi\) | ||||
−0.540694 | + | 0.841219i | \(0.681838\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.79017e12 | −1.17974 | −0.589868 | − | 0.807500i | \(-0.700820\pi\) | ||||
−0.589868 | + | 0.807500i | \(0.700820\pi\) | |||||||
\(662\) | − 8.95563e10i | − 0.0181232i | ||||||||
\(663\) | − 2.80555e12i | − 0.563906i | ||||||||
\(664\) | 2.66368e12 | 0.531772 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.97263e11 | −0.157025 | ||||||||
\(667\) | − 2.53314e12i | − 0.495557i | ||||||||
\(668\) | − 8.38197e12i | − 1.62874i | ||||||||
\(669\) | −3.58632e12 | −0.692199 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.59671e12 | 1.25625 | ||||||||
\(672\) | 7.72755e11i | 0.146177i | ||||||||
\(673\) | 5.92328e10i | 0.0111300i | 0.999985 | + | 0.00556499i | \(0.00177140\pi\) | ||||
−0.999985 | + | 0.00556499i | \(0.998229\pi\) | |||||||
\(674\) | −2.17728e12 | −0.406392 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.63385e12 | −0.669278 | ||||||||
\(677\) | 4.57177e12i | 0.836440i | 0.908346 | + | 0.418220i | \(0.137346\pi\) | ||||
−0.908346 | + | 0.418220i | \(0.862654\pi\) | |||||||
\(678\) | − 8.32157e11i | − 0.151242i | ||||||||
\(679\) | −2.20611e12 | −0.398302 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.37436e12 | 0.779386 | ||||||||
\(682\) | − 3.09238e12i | − 0.547348i | ||||||||
\(683\) | 9.71286e12i | 1.70787i | 0.520382 | + | 0.853934i | \(0.325790\pi\) | ||||
−0.520382 | + | 0.853934i | \(0.674210\pi\) | |||||||
\(684\) | 2.53015e11 | 0.0441971 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.10770e12 | 0.190969 | ||||||||
\(687\) | − 4.70003e11i | − 0.0804998i | ||||||||
\(688\) | − 2.20349e12i | − 0.374941i | ||||||||
\(689\) | −7.79098e11 | −0.131706 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.23726e12 | 0.373306 | 0.186653 | − | 0.982426i | \(-0.440236\pi\) | ||||
0.186653 | + | 0.982426i | \(0.440236\pi\) | |||||||
\(692\) | − 2.21510e12i | − 0.367211i | ||||||||
\(693\) | − 5.35801e11i | − 0.0882478i | ||||||||
\(694\) | 7.06282e11 | 0.115574 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.57146e12 | −0.253842 | ||||||||
\(697\) | − 6.21025e12i | − 0.996693i | ||||||||
\(698\) | − 3.10535e12i | − 0.495178i | ||||||||
\(699\) | 4.38911e12 | 0.695391 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.29477e10 | −0.00358929 | −0.00179464 | − | 0.999998i | \(-0.500571\pi\) | ||||
−0.00179464 | + | 0.999998i | \(0.500571\pi\) | |||||||
\(702\) | 5.65175e11i | 0.0878347i | ||||||||
\(703\) | − 1.33334e12i | − 0.205894i | ||||||||
\(704\) | 2.13265e12 | 0.327222 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.55203e12 | 0.538091 | ||||||||
\(707\) | − 3.25815e12i | − 0.490438i | ||||||||
\(708\) | − 3.05322e12i | − 0.456676i | ||||||||
\(709\) | 9.57637e12 | 1.42329 | 0.711644 | − | 0.702540i | \(-0.247951\pi\) | ||||
0.711644 | + | 0.702540i | \(0.247951\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.99156e12 | −0.439020 | ||||||||
\(712\) | − 3.18451e12i | − 0.464390i | ||||||||
\(713\) | 8.76362e12i | 1.26993i | ||||||||
\(714\) | 2.94263e11 | 0.0423735 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.81959e12 | 0.827529 | ||||||||
\(717\) | − 6.41326e12i | − 0.906239i | ||||||||
\(718\) | 1.47298e12i | 0.206841i | ||||||||
\(719\) | 5.46390e12 | 0.762469 | 0.381235 | − | 0.924478i | \(-0.375499\pi\) | ||||
0.381235 | + | 0.924478i | \(0.375499\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.58075e11 | 0.0769102 | ||||||||
\(722\) | 2.45570e12i | 0.336324i | ||||||||
\(723\) | − 4.98085e12i | − 0.677925i | ||||||||
\(724\) | 1.20171e13 | 1.62546 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.44607e11 | −0.0326779 | ||||||||
\(727\) | 6.59842e12i | 0.876062i | 0.898960 | + | 0.438031i | \(0.144324\pi\) | ||||
−0.898960 | + | 0.438031i | \(0.855676\pi\) | |||||||
\(728\) | − 1.88500e12i | − 0.248726i | ||||||||
\(729\) | −2.82430e11 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.23561e12 | −0.419111 | ||||||||
\(732\) | 5.43381e12i | 0.699527i | ||||||||
\(733\) | − 6.91041e11i | − 0.0884170i | −0.999022 | − | 0.0442085i | \(-0.985923\pi\) | ||||
0.999022 | − | 0.0442085i | \(-0.0140766\pi\) | |||||||
\(734\) | −2.47541e11 | −0.0314785 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.07846e12 | 0.637943 | ||||||||
\(737\) | − 7.45694e12i | − 0.931016i | ||||||||
\(738\) | 1.25105e12i | 0.155246i | ||||||||
\(739\) | −7.60189e12 | −0.937608 | −0.468804 | − | 0.883302i | \(-0.655315\pi\) | ||||
−0.468804 | + | 0.883302i | \(0.655315\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.45200e11 | −0.115171 | ||||||||
\(742\) | − 8.17167e10i | − 0.00989677i | ||||||||
\(743\) | 2.23002e12i | 0.268448i | 0.990951 | + | 0.134224i | \(0.0428541\pi\) | ||||
−0.990951 | + | 0.134224i | \(0.957146\pi\) | |||||||
\(744\) | 5.43661e12 | 0.650504 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.47569e12 | 0.410882 | ||||||||
\(747\) | − 2.32985e12i | − 0.273770i | ||||||||
\(748\) | − 5.08060e12i | − 0.593414i | ||||||||
\(749\) | 3.59538e11 | 0.0417423 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.65708e12 | 0.190092 | 0.0950459 | − | 0.995473i | \(-0.469700\pi\) | ||||
0.0950459 | + | 0.995473i | \(0.469700\pi\) | |||||||
\(752\) | − 1.06514e13i | − 1.21458i | ||||||||
\(753\) | 2.34348e12i | 0.265635i | ||||||||
\(754\) | 2.75058e12 | 0.309922 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.41347e11 | 0.0491397 | ||||||||
\(757\) | − 1.28420e13i | − 1.42135i | −0.703521 | − | 0.710675i | \(-0.748390\pi\) | ||||
0.703521 | − | 0.710675i | \(-0.251610\pi\) | |||||||
\(758\) | 2.75218e12i | 0.302807i | ||||||||
\(759\) | −3.52122e12 | −0.385129 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.61852e13 | 1.74939 | 0.874694 | − | 0.484676i | \(-0.161063\pi\) | ||||
0.874694 | + | 0.484676i | \(0.161063\pi\) | |||||||
\(762\) | 2.01164e12i | 0.216149i | ||||||||
\(763\) | − 4.25921e12i | − 0.454955i | ||||||||
\(764\) | −1.23136e13 | −1.30757 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.45247e12 | −0.257380 | ||||||||
\(767\) | 1.14060e13i | 1.19002i | ||||||||
\(768\) | 8.23228e10i | 0.00853875i | ||||||||
\(769\) | −5.30462e12 | −0.546998 | −0.273499 | − | 0.961872i | \(-0.588181\pi\) | ||||
−0.273499 | + | 0.961872i | \(0.588181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.91345e12 | −1.01037 | ||||||||
\(772\) | 4.35775e12i | 0.441555i | ||||||||
\(773\) | 1.26188e13i | 1.27119i | 0.772022 | + | 0.635596i | \(0.219245\pi\) | ||||
−0.772022 | + | 0.635596i | \(0.780755\pi\) | |||||||
\(774\) | 6.51812e11 | 0.0652812 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.99418e12 | 0.890397 | ||||||||
\(777\) | − 2.32582e12i | − 0.228919i | ||||||||
\(778\) | − 3.27591e12i | − 0.320571i | ||||||||
\(779\) | −2.09226e12 | −0.203562 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.36478e12 | 0.900675 | ||||||||
\(782\) | − 1.93387e12i | − 0.184925i | ||||||||
\(783\) | 1.37452e12i | 0.130684i | ||||||||
\(784\) | 6.38438e12 | 0.603527 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.40644e12 | −0.318346 | ||||||||
\(787\) | 1.22887e13i | 1.14188i | 0.820991 | + | 0.570941i | \(0.193421\pi\) | ||||
−0.820991 | + | 0.570941i | \(0.806579\pi\) | |||||||
\(788\) | 5.46571e12i | 0.504985i | ||||||||
\(789\) | −5.06162e12 | −0.464990 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.42762e12 | 0.220489 | ||||||||
\(792\) | 2.18443e12i | 0.197277i | ||||||||
\(793\) | − 2.02993e13i | − 1.82286i | ||||||||
\(794\) | 4.38439e12 | 0.391487 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.56441e12 | −0.756116 | ||||||||
\(797\) | − 3.56495e12i | − 0.312962i | −0.987681 | − | 0.156481i | \(-0.949985\pi\) | ||||
0.987681 | − | 0.156481i | \(-0.0500150\pi\) | |||||||
\(798\) | − 9.91385e10i | − 0.00865425i | ||||||||
\(799\) | −1.56405e13 | −1.35766 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.78541e12 | −0.239080 | ||||||||
\(802\) | − 2.14821e12i | − 0.183354i | ||||||||
\(803\) | 6.37090e12i | 0.540730i | ||||||||
\(804\) | 6.14240e12 | 0.518425 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.51585e12 | −0.794218 | ||||||||
\(807\) | − 1.03043e13i | − 0.855239i | ||||||||
\(808\) | 1.32833e13i | 1.09636i | ||||||||
\(809\) | 3.11624e12 | 0.255778 | 0.127889 | − | 0.991789i | \(-0.459180\pi\) | ||||
0.127889 | + | 0.991789i | \(0.459180\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.30256e12 | −0.186904 | −0.0934518 | − | 0.995624i | \(-0.529790\pi\) | ||||
−0.0934518 | + | 0.995624i | \(0.529790\pi\) | |||||||
\(812\) | − 2.14793e12i | − 0.173388i | ||||||||
\(813\) | 1.24834e12i | 0.100213i | ||||||||
\(814\) | 5.39357e12 | 0.430593 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.54737e12 | 0.280092 | ||||||||
\(817\) | 1.09009e12i | 0.0855980i | ||||||||
\(818\) | − 5.09651e11i | − 0.0398000i | ||||||||
\(819\) | −1.64876e12 | −0.128050 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.28720e12 | −0.482962 | −0.241481 | − | 0.970406i | \(-0.577633\pi\) | ||||
−0.241481 | + | 0.970406i | \(0.577633\pi\) | |||||||
\(822\) | 7.56212e9i | 0 0.000577724i | ||||||||
\(823\) | − 3.76056e12i | − 0.285728i | −0.989742 | − | 0.142864i | \(-0.954369\pi\) | ||||
0.989742 | − | 0.142864i | \(-0.0456312\pi\) | |||||||
\(824\) | −2.27524e12 | −0.171932 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.19634e12 | −0.0894219 | ||||||||
\(827\) | 1.75054e13i | 1.30136i | 0.759353 | + | 0.650679i | \(0.225516\pi\) | ||||
−0.759353 | + | 0.650679i | \(0.774484\pi\) | |||||||
\(828\) | − 2.90049e12i | − 0.214454i | ||||||||
\(829\) | 2.42570e12 | 0.178378 | 0.0891891 | − | 0.996015i | \(-0.471572\pi\) | ||||
0.0891891 | + | 0.996015i | \(0.471572\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.45902e12 | 0.542597 | ||||||||
\(832\) | − 6.56257e12i | − 0.474809i | ||||||||
\(833\) | − 9.37486e12i | − 0.674625i | ||||||||
\(834\) | −5.77383e11 | −0.0413254 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.71167e12 | −0.121197 | ||||||||
\(837\) | − 4.75526e12i | − 0.334896i | ||||||||
\(838\) | 2.10424e11i | 0.0147400i | ||||||||
\(839\) | −9.69596e11 | −0.0675557 | −0.0337778 | − | 0.999429i | \(-0.510754\pi\) | ||||
−0.0337778 | + | 0.999429i | \(0.510754\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.81769e12 | −0.538885 | ||||||||
\(842\) | 3.34574e12i | 0.229397i | ||||||||
\(843\) | − 6.30813e12i | − 0.430206i | ||||||||
\(844\) | −4.02593e12 | −0.273102 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.15078e12 | 0.211471 | ||||||||
\(847\) | − 7.13582e11i | − 0.0476397i | ||||||||
\(848\) | − 9.85101e11i | − 0.0654183i | ||||||||
\(849\) | 2.36895e12 | 0.156485 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.52850e13 | −0.999042 | ||||||||
\(852\) | 7.71391e12i | 0.501529i | ||||||||
\(853\) | 2.11898e13i | 1.37043i | 0.728340 | + | 0.685215i | \(0.240292\pi\) | ||||
−0.728340 | + | 0.685215i | \(0.759708\pi\) | |||||||
\(854\) | 2.12912e12 | 0.136975 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.46582e12 | −0.0933142 | ||||||||
\(857\) | 8.34904e12i | 0.528717i | 0.964425 | + | 0.264358i | \(0.0851602\pi\) | ||||
−0.964425 | + | 0.264358i | \(0.914840\pi\) | |||||||
\(858\) | − 3.82347e12i | − 0.240860i | ||||||||
\(859\) | 8.24621e12 | 0.516755 | 0.258378 | − | 0.966044i | \(-0.416812\pi\) | ||||
0.258378 | + | 0.966044i | \(0.416812\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.64964e12 | −0.226326 | ||||||||
\(862\) | 7.35568e12i | 0.453775i | ||||||||
\(863\) | − 4.35663e12i | − 0.267364i | −0.991024 | − | 0.133682i | \(-0.957320\pi\) | ||||
0.991024 | − | 0.133682i | \(-0.0426800\pi\) | |||||||
\(864\) | −2.75564e12 | −0.168233 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.64105e12 | −0.0991497 | ||||||||
\(867\) | 4.39665e12i | 0.264263i | ||||||||
\(868\) | 7.43096e12i | 0.444331i | ||||||||
\(869\) | 2.02382e13 | 1.20388 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.29464e13 | −1.35093 | ||||||||
\(872\) | 1.73646e13i | 1.01705i | ||||||||
\(873\) | − 7.86697e12i | − 0.458399i | ||||||||
\(874\) | −6.51527e11 | −0.0377686 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.24780e12 | −0.301099 | ||||||||
\(877\) | − 1.21873e12i | − 0.0695680i | −0.999395 | − | 0.0347840i | \(-0.988926\pi\) | ||||
0.999395 | − | 0.0347840i | \(-0.0110743\pi\) | |||||||
\(878\) | 5.98825e12i | 0.340075i | ||||||||
\(879\) | −1.84197e13 | −1.04071 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.98577e12 | 0.222905 | 0.111453 | − | 0.993770i | \(-0.464450\pi\) | ||||
0.111453 | + | 0.993770i | \(0.464450\pi\) | |||||||
\(882\) | 1.88856e12i | 0.105080i | ||||||||
\(883\) | − 2.19963e13i | − 1.21766i | −0.793300 | − | 0.608831i | \(-0.791639\pi\) | ||||
0.793300 | − | 0.608831i | \(-0.208361\pi\) | |||||||
\(884\) | −1.56340e13 | −0.861061 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.06025e12 | 0.275880 | ||||||||
\(887\) | 1.39860e13i | 0.758640i | 0.925266 | + | 0.379320i | \(0.123842\pi\) | ||||
−0.925266 | + | 0.379320i | \(0.876158\pi\) | |||||||
\(888\) | 9.48226e12i | 0.511745i | ||||||||
\(889\) | −5.86847e12 | −0.315113 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.91067e12 | 0.101563 | ||||||||
\(892\) | 1.99848e13i | 1.05696i | ||||||||
\(893\) | 5.26936e12i | 0.277285i | ||||||||
\(894\) | −3.15635e12 | −0.165259 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5.57290e12 | 0.288865 | ||||||||
\(897\) | 1.08355e13i | 0.558833i | ||||||||
\(898\) | − 3.51829e12i | − 0.180546i | ||||||||
\(899\) | −2.31428e13 | −1.18167 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.44653e12 | −0.0731248 | ||||||||
\(902\) | − 8.46349e12i | − 0.425716i | ||||||||
\(903\) | 1.90150e12i | 0.0951705i | ||||||||
\(904\) | −9.89727e12 | −0.492899 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.02169e12 | 0.0996869 | ||||||||
\(907\) | − 8.00749e12i | − 0.392884i | −0.980515 | − | 0.196442i | \(-0.937061\pi\) | ||||
0.980515 | − | 0.196442i | \(-0.0629387\pi\) | |||||||
\(908\) | − 2.43762e13i | − 1.19009i | ||||||||
\(909\) | 1.16186e13 | 0.564436 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.09248e13 | −1.96858 | −0.984291 | − | 0.176555i | \(-0.943505\pi\) | ||||
−0.984291 | + | 0.176555i | \(0.943505\pi\) | |||||||
\(912\) | − 1.19512e12i | − 0.0572052i | ||||||||
\(913\) | 1.57617e13i | 0.750731i | ||||||||
\(914\) | −4.81529e12 | −0.228226 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.61910e12 | −0.122920 | ||||||||
\(917\) | − 9.93745e12i | − 0.464102i | ||||||||
\(918\) | 1.04934e12i | 0.0487669i | ||||||||
\(919\) | −8.12730e12 | −0.375860 | −0.187930 | − | 0.982182i | \(-0.560178\pi\) | ||||
−0.187930 | + | 0.982182i | \(0.560178\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.88089e12 | 0.223527 | ||||||||
\(922\) | 2.15252e12i | 0.0980973i | ||||||||
\(923\) | − 2.88172e13i | − 1.30691i | ||||||||
\(924\) | −2.98576e12 | −0.134751 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.74938e12 | −0.212269 | ||||||||
\(927\) | 1.99010e12i | 0.0885147i | ||||||||
\(928\) | 1.34111e13i | 0.593605i | ||||||||
\(929\) | 4.43436e13 | 1.95326 | 0.976631 | − | 0.214923i | \(-0.0689500\pi\) | ||||
0.976631 | + | 0.214923i | \(0.0689500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.15843e12 | −0.137783 | ||||||||
\(932\) | − 2.44584e13i | − 1.06183i | ||||||||
\(933\) | 1.10821e13i | 0.478801i | ||||||||
\(934\) | 2.20554e12 | 0.0948317 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.72192e12 | 0.286254 | ||||||||
\(937\) | − 3.56882e13i | − 1.51250i | −0.654281 | − | 0.756251i | \(-0.727029\pi\) | ||||
0.654281 | − | 0.756251i | \(-0.272971\pi\) | |||||||
\(938\) | − 2.40677e12i | − 0.101513i | ||||||||
\(939\) | 1.82683e13 | 0.766838 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.76351e13 | 1.56473 | 0.782366 | − | 0.622818i | \(-0.214012\pi\) | ||||
0.782366 | + | 0.622818i | \(0.214012\pi\) | |||||||
\(942\) | − 2.92279e11i | − 0.0120940i | ||||||||
\(943\) | 2.39850e13i | 0.987727i | ||||||||
\(944\) | −1.44219e13 | −0.591085 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.40958e12 | −0.179014 | ||||||||
\(947\) | − 1.01014e13i | − 0.408139i | −0.978956 | − | 0.204070i | \(-0.934583\pi\) | ||||
0.978956 | − | 0.204070i | \(-0.0654169\pi\) | |||||||
\(948\) | 1.66705e13i | 0.670365i | ||||||||
\(949\) | 1.96045e13 | 0.784616 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.03993e13 | 0.412280 | ||||||||
\(952\) | − 3.49982e12i | − 0.138096i | ||||||||
\(953\) | − 1.49469e13i | − 0.586993i | −0.955960 | − | 0.293497i | \(-0.905181\pi\) | ||||
0.955960 | − | 0.293497i | \(-0.0948190\pi\) | |||||||
\(954\) | 2.91402e11 | 0.0113900 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.57380e13 | −1.38379 | ||||||||
\(957\) | − 9.29876e12i | − 0.358362i | ||||||||
\(958\) | − 1.08345e13i | − 0.415589i | ||||||||
\(959\) | −2.20607e10 | −0.000842238 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.36247e13 | 2.02819 | ||||||||
\(962\) | − 1.65970e13i | − 0.624803i | ||||||||
\(963\) | 1.28211e12i | 0.0480405i | ||||||||
\(964\) | −2.77559e13 | −1.03516 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.13649e12 | −0.0419923 | ||||||||
\(967\) | 2.42942e13i | 0.893475i | 0.894665 | + | 0.446738i | \(0.147414\pi\) | ||||
−0.894665 | + | 0.446738i | \(0.852586\pi\) | |||||||
\(968\) | 2.90924e12i | 0.106498i | ||||||||
\(969\) | −1.75492e12 | −0.0639441 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.07032e13 | −0.386392 | −0.193196 | − | 0.981160i | \(-0.561885\pi\) | ||||
−0.193196 | + | 0.981160i | \(0.561885\pi\) | |||||||
\(972\) | 1.57384e12i | 0.0565540i | ||||||||
\(973\) | − 1.68437e12i | − 0.0602464i | ||||||||
\(974\) | −1.10201e12 | −0.0392346 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.56667e13 | 0.905412 | ||||||||
\(977\) | − 1.53038e13i | − 0.537372i | −0.963228 | − | 0.268686i | \(-0.913411\pi\) | ||||
0.963228 | − | 0.268686i | \(-0.0865894\pi\) | |||||||
\(978\) | 8.06954e12i | 0.282048i | ||||||||
\(979\) | 1.88436e13 | 0.655604 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.51883e13 | 0.523600 | ||||||||
\(982\) | 3.63032e12i | 0.124578i | ||||||||
\(983\) | − 3.27251e13i | − 1.11787i | −0.829212 | − | 0.558934i | \(-0.811210\pi\) | ||||
0.829212 | − | 0.558934i | \(-0.188790\pi\) | |||||||
\(984\) | 1.48794e13 | 0.505949 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.10691e12 | 0.172073 | ||||||||
\(987\) | 9.19163e12i | 0.308294i | ||||||||
\(988\) | 5.26714e12i | 0.175861i | ||||||||
\(989\) | 1.24965e13 | 0.415340 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.05488e13 | 1.00615 | 0.503075 | − | 0.864243i | \(-0.332202\pi\) | ||||
0.503075 | + | 0.864243i | \(0.332202\pi\) | |||||||
\(992\) | − 4.63967e13i | − 1.52119i | ||||||||
\(993\) | 9.31649e11i | 0.0304075i | ||||||||
\(994\) | 3.02253e12 | 0.0982046 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.29831e13 | −0.418035 | ||||||||
\(997\) | 4.87857e13i | 1.56374i | 0.623441 | + | 0.781870i | \(0.285734\pi\) | ||||
−0.623441 | + | 0.781870i | \(0.714266\pi\) | |||||||
\(998\) | − 1.72274e13i | − 0.549709i | ||||||||
\(999\) | 8.29388e12 | 0.263459 |
(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 | 75.10.b.f.49.2 | 4 | ||
3.2 | odd | 2 | 225.10.b.i.199.3 | 4 | |||
5.2 | odd | 4 | 75.10.a.f.1.2 | 2 | |||
5.3 | odd | 4 | 15.10.a.d.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 75.10.b.f.49.3 | 4 | ||
15.2 | even | 4 | 225.10.a.k.1.1 | 2 | |||
15.8 | even | 4 | 45.10.a.d.1.2 | 2 | |||
15.14 | odd | 2 | 225.10.b.i.199.2 | 4 | |||
20.3 | even | 4 | 240.10.a.r.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.10.a.d.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
45.10.a.d.1.2 | 2 | 15.8 | even | 4 | |||
75.10.a.f.1.2 | 2 | 5.2 | odd | 4 | |||
75.10.b.f.49.2 | 4 | 1.1 | even | 1 | trivial | ||
75.10.b.f.49.3 | 4 | 5.4 | even | 2 | inner | ||
225.10.a.k.1.1 | 2 | 15.2 | even | 4 | |||
225.10.b.i.199.2 | 4 | 15.14 | odd | 2 | |||
225.10.b.i.199.3 | 4 | 3.2 | odd | 2 | |||
240.10.a.r.1.2 | 2 | 20.3 | even | 4 |