Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,8,Mod(75,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.75");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.d (of order \(2\), degree \(1\), 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: | \(23.7412619368\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 75.20 | ||
Character | \(\chi\) | \(=\) | 76.75 |
Dual form | 76.8.d.a.75.19 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.35548 | + | 8.59633i | −0.650139 | + | 0.759816i | ||||
\(3\) | −83.0232 | −1.77531 | −0.887657 | − | 0.460505i | \(-0.847668\pi\) | ||||
−0.887657 | + | 0.460505i | \(0.847668\pi\) | |||||||
\(4\) | −19.7938 | − | 126.460i | −0.154639 | − | 0.987971i | ||||
\(5\) | −447.252 | −1.60014 | −0.800068 | − | 0.599909i | \(-0.795203\pi\) | ||||
−0.800068 | + | 0.599909i | \(0.795203\pi\) | |||||||
\(6\) | 610.676 | − | 713.695i | 1.15420 | − | 1.34891i | ||||
\(7\) | − | 106.200i | − | 0.117026i | −0.998287 | − | 0.0585130i | \(-0.981364\pi\) | ||
0.998287 | − | 0.0585130i | \(-0.0186359\pi\) | |||||||
\(8\) | 1232.69 | + | 760.022i | 0.851213 | + | 0.524821i | ||||
\(9\) | 4705.86 | 2.15174 | ||||||||
\(10\) | 3289.75 | − | 3844.72i | 1.04031 | − | 1.21581i | ||||
\(11\) | − | 7457.91i | − | 1.68944i | −0.535208 | − | 0.844720i | \(-0.679767\pi\) | ||
0.535208 | − | 0.844720i | \(-0.320233\pi\) | |||||||
\(12\) | 1643.35 | + | 10499.1i | 0.274533 | + | 1.75396i | ||||
\(13\) | − | 996.063i | − | 0.125743i | −0.998022 | − | 0.0628717i | \(-0.979974\pi\) | ||
0.998022 | − | 0.0628717i | \(-0.0200259\pi\) | |||||||
\(14\) | 912.932 | + | 781.153i | 0.0889181 | + | 0.0760831i | ||||
\(15\) | 37132.3 | 2.84074 | ||||||||
\(16\) | −15600.4 | + | 5006.27i | −0.952173 | + | 0.305558i | ||||
\(17\) | −14144.3 | −0.698249 | −0.349124 | − | 0.937076i | \(-0.613521\pi\) | ||||
−0.349124 | + | 0.937076i | \(0.613521\pi\) | |||||||
\(18\) | −34613.8 | + | 40453.1i | −1.39893 | + | 1.63493i | ||||
\(19\) | 10708.7 | − | 27914.1i | 0.358178 | − | 0.933653i | ||||
\(20\) | 8852.83 | + | 56559.6i | 0.247444 | + | 1.58089i | ||||
\(21\) | 8817.08i | 0.207758i | ||||||||
\(22\) | 64110.7 | + | 54856.5i | 1.28366 | + | 1.09837i | ||||
\(23\) | − | 49089.2i | − | 0.841276i | −0.907228 | − | 0.420638i | \(-0.861806\pi\) | ||
0.907228 | − | 0.420638i | \(-0.138194\pi\) | |||||||
\(24\) | −102342. | − | 63099.5i | −1.51117 | − | 0.931722i | ||||
\(25\) | 121909. | 1.56044 | ||||||||
\(26\) | 8562.49 | + | 7326.52i | 0.0955418 | + | 0.0817506i | ||||
\(27\) | −209124. | −2.04470 | ||||||||
\(28\) | −13430.1 | + | 2102.11i | −0.115618 | + | 0.0180968i | ||||
\(29\) | − | 195745.i | − | 1.49038i | −0.666849 | − | 0.745192i | \(-0.732358\pi\) | ||
0.666849 | − | 0.745192i | \(-0.267642\pi\) | |||||||
\(30\) | −273126. | + | 319201.i | −1.84688 | + | 2.15844i | ||||
\(31\) | −243107. | −1.46566 | −0.732828 | − | 0.680414i | \(-0.761800\pi\) | ||||
−0.732828 | + | 0.680414i | \(0.761800\pi\) | |||||||
\(32\) | 71712.9 | − | 170930.i | 0.386877 | − | 0.922131i | ||||
\(33\) | 619180.i | 2.99929i | ||||||||
\(34\) | 104038. | − | 121589.i | 0.453958 | − | 0.530540i | ||||
\(35\) | 47498.2i | 0.187257i | ||||||||
\(36\) | −93147.0 | − | 595104.i | −0.332744 | − | 2.12586i | ||||
\(37\) | 152241.i | 0.494113i | 0.969001 | + | 0.247057i | \(0.0794634\pi\) | ||||
−0.969001 | + | 0.247057i | \(0.920537\pi\) | |||||||
\(38\) | 161191. | + | 297377.i | 0.476539 | + | 0.879153i | ||||
\(39\) | 82696.4i | 0.223234i | ||||||||
\(40\) | −551322. | − | 339921.i | −1.36206 | − | 0.839785i | ||||
\(41\) | − | 581032.i | − | 1.31661i | −0.752752 | − | 0.658304i | \(-0.771274\pi\) | ||
0.752752 | − | 0.658304i | \(-0.228726\pi\) | |||||||
\(42\) | −75794.6 | − | 64853.9i | −0.157858 | − | 0.135071i | ||||
\(43\) | − | 675783.i | − | 1.29619i | −0.761561 | − | 0.648094i | \(-0.775567\pi\) | ||
0.761561 | − | 0.648094i | \(-0.224433\pi\) | |||||||
\(44\) | −943130. | + | 147621.i | −1.66912 | + | 0.261254i | ||||
\(45\) | −2.10470e6 | −3.44308 | ||||||||
\(46\) | 421987. | + | 361075.i | 0.639215 | + | 0.546946i | ||||
\(47\) | 165475.i | 0.232482i | 0.993221 | + | 0.116241i | \(0.0370844\pi\) | ||||
−0.993221 | + | 0.116241i | \(0.962916\pi\) | |||||||
\(48\) | 1.29520e6 | − | 415637.i | 1.69041 | − | 0.542462i | ||||
\(49\) | 812265. | 0.986305 | ||||||||
\(50\) | −896699. | + | 1.04797e6i | −1.01450 | + | 1.18564i | ||||
\(51\) | 1.17431e6 | 1.23961 | ||||||||
\(52\) | −125962. | + | 19715.9i | −0.124231 | + | 0.0194449i | ||||
\(53\) | 38212.1i | 0.0352562i | 0.999845 | + | 0.0176281i | \(0.00561148\pi\) | ||||
−0.999845 | + | 0.0176281i | \(0.994389\pi\) | |||||||
\(54\) | 1.53820e6 | − | 1.79770e6i | 1.32934 | − | 1.55360i | ||||
\(55\) | 3.33556e6i | 2.70333i | ||||||||
\(56\) | 80714.4 | − | 130912.i | 0.0614176 | − | 0.0996140i | ||||
\(57\) | −889070. | + | 2.31752e6i | −0.635878 | + | 1.65753i | ||||
\(58\) | 1.68269e6 | + | 1.43980e6i | 1.13242 | + | 0.968957i | ||||
\(59\) | −2.24545e6 | −1.42338 | −0.711692 | − | 0.702492i | \(-0.752071\pi\) | ||||
−0.711692 | + | 0.702492i | \(0.752071\pi\) | |||||||
\(60\) | −734990. | − | 4.69576e6i | −0.439291 | − | 2.80657i | ||||
\(61\) | 368923. | 0.208105 | 0.104052 | − | 0.994572i | \(-0.466819\pi\) | ||||
0.104052 | + | 0.994572i | \(0.466819\pi\) | |||||||
\(62\) | 1.78817e6 | − | 2.08983e6i | 0.952879 | − | 1.11363i | ||||
\(63\) | − | 499763.i | − | 0.251810i | ||||||
\(64\) | 941886. | + | 1.87374e6i | 0.449126 | + | 0.893468i | ||||
\(65\) | 445491.i | 0.201206i | ||||||||
\(66\) | −5.32268e6 | − | 4.55437e6i | −2.27891 | − | 1.94995i | ||||
\(67\) | −762681. | −0.309800 | −0.154900 | − | 0.987930i | \(-0.549505\pi\) | ||||
−0.154900 | + | 0.987930i | \(0.549505\pi\) | |||||||
\(68\) | 279970. | + | 1.78869e6i | 0.107977 | + | 0.689849i | ||||
\(69\) | 4.07555e6i | 1.49353i | ||||||||
\(70\) | −408310. | − | 349372.i | −0.142281 | − | 0.121743i | ||||
\(71\) | 336990. | 0.111741 | 0.0558705 | − | 0.998438i | \(-0.482207\pi\) | ||||
0.0558705 | + | 0.998438i | \(0.482207\pi\) | |||||||
\(72\) | 5.80085e6 | + | 3.57655e6i | 1.83159 | + | 1.12928i | ||||
\(73\) | 2.02383e6 | 0.608898 | 0.304449 | − | 0.952529i | \(-0.401528\pi\) | ||||
0.304449 | + | 0.952529i | \(0.401528\pi\) | |||||||
\(74\) | −1.30872e6 | − | 1.11981e6i | −0.375435 | − | 0.321242i | ||||
\(75\) | −1.01213e7 | −2.77026 | ||||||||
\(76\) | −3.74199e6 | − | 801697.i | −0.977811 | − | 0.209490i | ||||
\(77\) | −792032. | −0.197708 | ||||||||
\(78\) | −710885. | − | 608271.i | −0.169617 | − | 0.145133i | ||||
\(79\) | 3.58420e6 | 0.817894 | 0.408947 | − | 0.912558i | \(-0.365896\pi\) | ||||
0.408947 | + | 0.912558i | \(0.365896\pi\) | |||||||
\(80\) | 6.97731e6 | − | 2.23906e6i | 1.52361 | − | 0.488935i | ||||
\(81\) | 7.07041e6 | 1.47825 | ||||||||
\(82\) | 4.99474e6 | + | 4.27377e6i | 1.00038 | + | 0.855978i | ||||
\(83\) | − | 8.23737e6i | − | 1.58130i | −0.612266 | − | 0.790652i | \(-0.709742\pi\) | ||
0.612266 | − | 0.790652i | \(-0.290258\pi\) | |||||||
\(84\) | 1.11501e6 | − | 174524.i | 0.205259 | − | 0.0321275i | ||||
\(85\) | 6.32606e6 | 1.11729 | ||||||||
\(86\) | 5.80926e6 | + | 4.97071e6i | 0.984863 | + | 0.842701i | ||||
\(87\) | 1.62514e7i | 2.64590i | ||||||||
\(88\) | 5.66818e6 | − | 9.19328e6i | 0.886654 | − | 1.43807i | ||||
\(89\) | − | 4.68170e6i | − | 0.703945i | −0.936010 | − | 0.351973i | \(-0.885511\pi\) | ||
0.936010 | − | 0.351973i | \(-0.114489\pi\) | |||||||
\(90\) | 1.54811e7 | − | 1.80927e7i | 2.23848 | − | 2.61610i | ||||
\(91\) | −105782. | −0.0147152 | ||||||||
\(92\) | −6.20784e6 | + | 971664.i | −0.831157 | + | 0.130094i | ||||
\(93\) | 2.01835e7 | 2.60200 | ||||||||
\(94\) | −1.42247e6 | − | 1.21714e6i | −0.176643 | − | 0.151145i | ||||
\(95\) | −4.78948e6 | + | 1.24846e7i | −0.573133 | + | 1.49397i | ||||
\(96\) | −5.95384e6 | + | 1.41911e7i | −0.686828 | + | 1.63707i | ||||
\(97\) | 1.14401e7i | 1.27271i | 0.771397 | + | 0.636354i | \(0.219558\pi\) | ||||
−0.771397 | + | 0.636354i | \(0.780442\pi\) | |||||||
\(98\) | −5.97460e6 | + | 6.98250e6i | −0.641235 | + | 0.749410i | ||||
\(99\) | − | 3.50959e7i | − | 3.63524i | ||||||
\(100\) | −2.41305e6 | − | 1.54166e7i | −0.241305 | − | 1.54166i | ||||
\(101\) | −1.21597e7 | −1.17435 | −0.587176 | − | 0.809459i | \(-0.699761\pi\) | ||||
−0.587176 | + | 0.809459i | \(0.699761\pi\) | |||||||
\(102\) | −8.63758e6 | + | 1.00947e7i | −0.805919 | + | 0.941875i | ||||
\(103\) | −1.22848e7 | −1.10774 | −0.553869 | − | 0.832604i | \(-0.686849\pi\) | ||||
−0.553869 | + | 0.832604i | \(0.686849\pi\) | |||||||
\(104\) | 757029. | − | 1.22783e6i | 0.0659927 | − | 0.107034i | ||||
\(105\) | − | 3.94345e6i | − | 0.332441i | ||||||
\(106\) | −328484. | − | 281068.i | −0.0267882 | − | 0.0229214i | ||||
\(107\) | 1.66914e6 | 0.131719 | 0.0658596 | − | 0.997829i | \(-0.479021\pi\) | ||||
0.0658596 | + | 0.997829i | \(0.479021\pi\) | |||||||
\(108\) | 4.13936e6 | + | 2.64458e7i | 0.316191 | + | 2.02011i | ||||
\(109\) | − | 5.54615e6i | − | 0.410203i | −0.978741 | − | 0.205101i | \(-0.934248\pi\) | ||
0.978741 | − | 0.205101i | \(-0.0657524\pi\) | |||||||
\(110\) | −2.86736e7 | − | 2.45347e7i | −2.05404 | − | 1.75754i | ||||
\(111\) | − | 1.26396e7i | − | 0.877207i | ||||||
\(112\) | 531667. | + | 1.65677e6i | 0.0357583 | + | 0.111429i | ||||
\(113\) | − | 1.55694e7i | − | 1.01507i | −0.861630 | − | 0.507536i | \(-0.830556\pi\) | ||
0.861630 | − | 0.507536i | \(-0.169444\pi\) | |||||||
\(114\) | −1.33826e7 | − | 2.46892e7i | −0.846007 | − | 1.56077i | ||||
\(115\) | 2.19552e7i | 1.34616i | ||||||||
\(116\) | −2.47540e7 | + | 3.87455e6i | −1.47246 | + | 0.230472i | ||||
\(117\) | − | 4.68733e6i | − | 0.270567i | ||||||
\(118\) | 1.65164e7 | − | 1.93027e7i | 0.925397 | − | 1.08151i | ||||
\(119\) | 1.50213e6i | 0.0817132i | ||||||||
\(120\) | 4.57725e7 | + | 2.82213e7i | 2.41808 | + | 1.49088i | ||||
\(121\) | −3.61333e7 | −1.85421 | ||||||||
\(122\) | −2.71361e6 | + | 3.17139e6i | −0.135297 | + | 0.158121i | ||||
\(123\) | 4.82391e7i | 2.33739i | ||||||||
\(124\) | 4.81202e6 | + | 3.07434e7i | 0.226648 | + | 1.44802i | ||||
\(125\) | −1.95825e7 | −0.896772 | ||||||||
\(126\) | 4.29613e6 | + | 3.67600e6i | 0.191329 | + | 0.163711i | ||||
\(127\) | −1.65404e7 | −0.716526 | −0.358263 | − | 0.933621i | \(-0.616631\pi\) | ||||
−0.358263 | + | 0.933621i | \(0.616631\pi\) | |||||||
\(128\) | −2.30353e7 | − | 5.68548e6i | −0.970865 | − | 0.239625i | ||||
\(129\) | 5.61057e7i | 2.30114i | ||||||||
\(130\) | −3.82959e6 | − | 3.27680e6i | −0.152880 | − | 0.130812i | ||||
\(131\) | − | 2.32760e7i | − | 0.904604i | −0.891865 | − | 0.452302i | \(-0.850603\pi\) | ||
0.891865 | − | 0.452302i | \(-0.149397\pi\) | |||||||
\(132\) | 7.83017e7 | − | 1.22560e7i | 2.96321 | − | 0.463808i | ||||
\(133\) | −2.96448e6 | − | 1.13726e6i | −0.109262 | − | 0.0419161i | ||||
\(134\) | 5.60988e6 | − | 6.55626e6i | 0.201413 | − | 0.235391i | ||||
\(135\) | 9.35309e7 | 3.27180 | ||||||||
\(136\) | −1.74355e7 | − | 1.07500e7i | −0.594358 | − | 0.366455i | ||||
\(137\) | 2.59781e7 | 0.863148 | 0.431574 | − | 0.902077i | \(-0.357958\pi\) | ||||
0.431574 | + | 0.902077i | \(0.357958\pi\) | |||||||
\(138\) | −3.50347e7 | − | 2.99776e7i | −1.13481 | − | 0.971002i | ||||
\(139\) | − | 5.33514e6i | − | 0.168498i | −0.996445 | − | 0.0842488i | \(-0.973151\pi\) | ||
0.996445 | − | 0.0842488i | \(-0.0268491\pi\) | |||||||
\(140\) | 6.00664e6 | − | 940172.i | 0.185005 | − | 0.0289574i | ||||
\(141\) | − | 1.37382e7i | − | 0.412728i | ||||||
\(142\) | −2.47872e6 | + | 2.89688e6i | −0.0726472 | + | 0.0849026i | ||||
\(143\) | −7.42855e6 | −0.212436 | ||||||||
\(144\) | −7.34133e7 | + | 2.35588e7i | −2.04883 | + | 0.657483i | ||||
\(145\) | 8.75474e7i | 2.38482i | ||||||||
\(146\) | −1.48863e7 | + | 1.73975e7i | −0.395868 | + | 0.462650i | ||||
\(147\) | −6.74368e7 | −1.75100 | ||||||||
\(148\) | 1.92525e7 | − | 3.01344e6i | 0.488170 | − | 0.0764094i | ||||
\(149\) | −4.81028e7 | −1.19129 | −0.595646 | − | 0.803247i | \(-0.703104\pi\) | ||||
−0.595646 | + | 0.803247i | \(0.703104\pi\) | |||||||
\(150\) | 7.44469e7 | − | 8.70059e7i | 1.80105 | − | 2.10489i | ||||
\(151\) | −2.65180e7 | −0.626788 | −0.313394 | − | 0.949623i | \(-0.601466\pi\) | ||||
−0.313394 | + | 0.949623i | \(0.601466\pi\) | |||||||
\(152\) | 3.44158e7 | − | 2.62705e7i | 0.794886 | − | 0.606759i | ||||
\(153\) | −6.65610e7 | −1.50245 | ||||||||
\(154\) | 5.82577e6 | − | 6.80857e6i | 0.128538 | − | 0.150222i | ||||
\(155\) | 1.08730e8 | 2.34525 | ||||||||
\(156\) | 1.04578e7 | − | 1.63688e6i | 0.220549 | − | 0.0345208i | ||||
\(157\) | −2.00364e7 | −0.413211 | −0.206606 | − | 0.978424i | \(-0.566242\pi\) | ||||
−0.206606 | + | 0.978424i | \(0.566242\pi\) | |||||||
\(158\) | −2.63635e7 | + | 3.08109e7i | −0.531745 | + | 0.621449i | ||||
\(159\) | − | 3.17249e6i | − | 0.0625908i | ||||||
\(160\) | −3.20737e7 | + | 7.64486e7i | −0.619055 | + | 1.47554i | ||||
\(161\) | −5.21329e6 | −0.0984512 | ||||||||
\(162\) | −5.20063e7 | + | 6.07796e7i | −0.961066 | + | 1.12320i | ||||
\(163\) | − | 2.69656e7i | − | 0.487701i | −0.969813 | − | 0.243851i | \(-0.921589\pi\) | ||
0.969813 | − | 0.243851i | \(-0.0784107\pi\) | |||||||
\(164\) | −7.34775e7 | + | 1.15009e7i | −1.30077 | + | 0.203599i | ||||
\(165\) | − | 2.76929e8i | − | 4.79927i | ||||||
\(166\) | 7.08112e7 | + | 6.05898e7i | 1.20150 | + | 1.02807i | ||||
\(167\) | 3.10719e7 | 0.516250 | 0.258125 | − | 0.966112i | \(-0.416895\pi\) | ||||
0.258125 | + | 0.966112i | \(0.416895\pi\) | |||||||
\(168\) | −6.70117e6 | + | 1.08687e7i | −0.109036 | + | 0.176846i | ||||
\(169\) | 6.17564e7 | 0.984189 | ||||||||
\(170\) | −4.65312e7 | + | 5.43809e7i | −0.726395 | + | 0.848936i | ||||
\(171\) | 5.03935e7 | − | 1.31360e8i | 0.770706 | − | 2.00898i | ||||
\(172\) | −8.54597e7 | + | 1.33763e7i | −1.28060 | + | 0.200442i | ||||
\(173\) | − | 2.64643e7i | − | 0.388597i | −0.980942 | − | 0.194298i | \(-0.937757\pi\) | ||
0.980942 | − | 0.194298i | \(-0.0622430\pi\) | |||||||
\(174\) | −1.39703e8 | − | 1.19537e8i | −2.01040 | − | 1.72020i | ||||
\(175\) | − | 1.29468e7i | − | 0.182611i | ||||||
\(176\) | 3.73363e7 | + | 1.16346e8i | 0.516223 | + | 1.60864i | ||||
\(177\) | 1.86425e8 | 2.52695 | ||||||||
\(178\) | 4.02455e7 | + | 3.44362e7i | 0.534869 | + | 0.457662i | ||||
\(179\) | −3.02694e7 | −0.394474 | −0.197237 | − | 0.980356i | \(-0.563197\pi\) | ||||
−0.197237 | + | 0.980356i | \(0.563197\pi\) | |||||||
\(180\) | 4.16601e7 | + | 2.66161e8i | 0.532435 | + | 3.40166i | ||||
\(181\) | − | 9.65258e7i | − | 1.20995i | −0.796244 | − | 0.604976i | \(-0.793183\pi\) | ||
0.796244 | − | 0.604976i | \(-0.206817\pi\) | |||||||
\(182\) | 778078. | − | 909338.i | 0.00956694 | − | 0.0111809i | ||||
\(183\) | −3.06292e7 | −0.369451 | ||||||||
\(184\) | 3.73089e7 | − | 6.05117e7i | 0.441519 | − | 0.716105i | ||||
\(185\) | − | 6.80902e7i | − | 0.790649i | ||||||
\(186\) | −1.48460e8 | + | 1.73504e8i | −1.69166 | + | 1.97704i | ||||
\(187\) | 1.05487e8i | 1.17965i | ||||||||
\(188\) | 2.09260e7 | − | 3.27538e6i | 0.229685 | − | 0.0359508i | ||||
\(189\) | 2.22090e7i | 0.239283i | ||||||||
\(190\) | −7.20930e7 | − | 1.33002e8i | −0.762528 | − | 1.40676i | ||||
\(191\) | 1.94105e7i | 0.201567i | 0.994908 | + | 0.100784i | \(0.0321350\pi\) | ||||
−0.994908 | + | 0.100784i | \(0.967865\pi\) | |||||||
\(192\) | −7.81984e7 | − | 1.55564e8i | −0.797340 | − | 1.58619i | ||||
\(193\) | 5.06797e7i | 0.507439i | 0.967278 | + | 0.253719i | \(0.0816540\pi\) | ||||
−0.967278 | + | 0.253719i | \(0.918346\pi\) | |||||||
\(194\) | −9.83428e7 | − | 8.41474e7i | −0.967023 | − | 0.827436i | ||||
\(195\) | − | 3.69861e7i | − | 0.357205i | ||||||
\(196\) | −1.60778e7 | − | 1.02719e8i | −0.152522 | − | 0.974441i | ||||
\(197\) | 1.51253e7 | 0.140953 | 0.0704763 | − | 0.997513i | \(-0.477548\pi\) | ||||
0.0704763 | + | 0.997513i | \(0.477548\pi\) | |||||||
\(198\) | 3.01696e8 | + | 2.58147e8i | 2.76211 | + | 2.36341i | ||||
\(199\) | 1.28443e7i | 0.115538i | 0.998330 | + | 0.0577690i | \(0.0183987\pi\) | ||||
−0.998330 | + | 0.0577690i | \(0.981601\pi\) | |||||||
\(200\) | 1.50276e8 | + | 9.26535e7i | 1.32826 | + | 0.818949i | ||||
\(201\) | 6.33202e7 | 0.549992 | ||||||||
\(202\) | 8.94405e7 | − | 1.04529e8i | 0.763492 | − | 0.892292i | ||||
\(203\) | −2.07882e7 | −0.174414 | ||||||||
\(204\) | −2.32440e7 | − | 1.48503e8i | −0.191693 | − | 1.22470i | ||||
\(205\) | 2.59867e8i | 2.10675i | ||||||||
\(206\) | 9.03604e7 | − | 1.05604e8i | 0.720183 | − | 0.841677i | ||||
\(207\) | − | 2.31007e8i | − | 1.81021i | ||||||
\(208\) | 4.98656e6 | + | 1.55390e7i | 0.0384219 | + | 0.119729i | ||||
\(209\) | −2.08181e8 | − | 7.98645e7i | −1.57735 | − | 0.605120i | ||||
\(210\) | 3.38992e7 | + | 2.90060e7i | 0.252594 | + | 0.216133i | ||||
\(211\) | 1.51484e8 | 1.11014 | 0.555069 | − | 0.831804i | \(-0.312692\pi\) | ||||
0.555069 | + | 0.831804i | \(0.312692\pi\) | |||||||
\(212\) | 4.83231e6 | − | 756363.i | 0.0348321 | − | 0.00545199i | ||||
\(213\) | −2.79780e7 | −0.198375 | ||||||||
\(214\) | −1.22773e7 | + | 1.43485e7i | −0.0856358 | + | 0.100082i | ||||
\(215\) | 3.02245e8i | 2.07408i | ||||||||
\(216\) | −2.57784e8 | − | 1.58939e8i | −1.74048 | − | 1.07310i | ||||
\(217\) | 2.58180e7i | 0.171520i | ||||||||
\(218\) | 4.76765e7 | + | 4.07946e7i | 0.311679 | + | 0.266689i | ||||
\(219\) | −1.68025e8 | −1.08099 | ||||||||
\(220\) | 4.21816e8 | − | 6.60236e7i | 2.67082 | − | 0.418042i | ||||
\(221\) | 1.40886e7i | 0.0878001i | ||||||||
\(222\) | 1.08654e8 | + | 9.29701e7i | 0.666515 | + | 0.570306i | ||||
\(223\) | 2.80414e8 | 1.69329 | 0.846646 | − | 0.532156i | \(-0.178618\pi\) | ||||
0.846646 | + | 0.532156i | \(0.178618\pi\) | |||||||
\(224\) | −1.81528e7 | − | 7.61593e6i | −0.107913 | − | 0.0452746i | ||||
\(225\) | 5.73686e8 | 3.35765 | ||||||||
\(226\) | 1.33840e8 | + | 1.14520e8i | 0.771268 | + | 0.659938i | ||||
\(227\) | −1.54180e7 | −0.0874858 | −0.0437429 | − | 0.999043i | \(-0.513928\pi\) | ||||
−0.0437429 | + | 0.999043i | \(0.513928\pi\) | |||||||
\(228\) | 3.10672e8 | + | 6.65594e7i | 1.73592 | + | 0.371910i | ||||
\(229\) | 2.05480e8 | 1.13070 | 0.565349 | − | 0.824852i | \(-0.308742\pi\) | ||||
0.565349 | + | 0.824852i | \(0.308742\pi\) | |||||||
\(230\) | −1.88734e8 | − | 1.61491e8i | −1.02283 | − | 0.875189i | ||||
\(231\) | 6.57570e7 | 0.350995 | ||||||||
\(232\) | 1.48771e8 | − | 2.41293e8i | 0.782185 | − | 1.26863i | ||||
\(233\) | −3.43211e8 | −1.77752 | −0.888762 | − | 0.458369i | \(-0.848434\pi\) | ||||
−0.888762 | + | 0.458369i | \(0.848434\pi\) | |||||||
\(234\) | 4.02938e7 | + | 3.44776e7i | 0.205581 | + | 0.175906i | ||||
\(235\) | − | 7.40087e7i | − | 0.372002i | ||||||
\(236\) | 4.44461e7 | + | 2.83961e8i | 0.220111 | + | 1.40626i | ||||
\(237\) | −2.97572e8 | −1.45202 | ||||||||
\(238\) | −1.29128e7 | − | 1.10489e7i | −0.0620870 | − | 0.0531249i | ||||
\(239\) | 1.41496e8i | 0.670426i | 0.942142 | + | 0.335213i | \(0.108808\pi\) | ||||
−0.942142 | + | 0.335213i | \(0.891192\pi\) | |||||||
\(240\) | −5.79279e8 | + | 1.85894e8i | −2.70488 | + | 0.868013i | ||||
\(241\) | − | 7.11607e7i | − | 0.327477i | −0.986504 | − | 0.163738i | \(-0.947645\pi\) | ||
0.986504 | − | 0.163738i | \(-0.0523553\pi\) | |||||||
\(242\) | 2.65778e8 | − | 3.10614e8i | 1.20549 | − | 1.40886i | ||||
\(243\) | −1.29655e8 | −0.579653 | ||||||||
\(244\) | −7.30241e6 | − | 4.66542e7i | −0.0321812 | − | 0.205601i | ||||
\(245\) | −3.63287e8 | −1.57822 | ||||||||
\(246\) | −4.14680e8 | − | 3.54822e8i | −1.77599 | − | 1.51963i | ||||
\(247\) | −2.78042e7 | − | 1.06665e7i | −0.117401 | − | 0.0450385i | ||||
\(248\) | −2.99675e8 | − | 1.84767e8i | −1.24758 | − | 0.769206i | ||||
\(249\) | 6.83893e8i | 2.80731i | ||||||||
\(250\) | 1.44038e8 | − | 1.68337e8i | 0.583026 | − | 0.681381i | ||||
\(251\) | 3.40204e8i | 1.35794i | 0.734164 | + | 0.678972i | \(0.237574\pi\) | ||||
−0.734164 | + | 0.678972i | \(0.762426\pi\) | |||||||
\(252\) | −6.32002e7 | + | 9.89223e6i | −0.248780 | + | 0.0389397i | ||||
\(253\) | −3.66103e8 | −1.42129 | ||||||||
\(254\) | 1.21662e8 | − | 1.42186e8i | 0.465841 | − | 0.544428i | ||||
\(255\) | −5.25210e8 | −1.98355 | ||||||||
\(256\) | 2.18310e8 | − | 1.56200e8i | 0.813268 | − | 0.581889i | ||||
\(257\) | 4.39945e8i | 1.61671i | 0.588695 | + | 0.808355i | \(0.299642\pi\) | ||||
−0.588695 | + | 0.808355i | \(0.700358\pi\) | |||||||
\(258\) | −4.82303e8 | − | 4.12684e8i | −1.74844 | − | 1.49606i | ||||
\(259\) | 1.61681e7 | 0.0578241 | ||||||||
\(260\) | 5.63369e7 | − | 8.81797e6i | 0.198786 | − | 0.0311144i | ||||
\(261\) | − | 9.21150e8i | − | 3.20692i | ||||||
\(262\) | 2.00088e8 | + | 1.71206e8i | 0.687332 | + | 0.588118i | ||||
\(263\) | − | 6.92242e7i | − | 0.234646i | −0.993094 | − | 0.117323i | \(-0.962569\pi\) | ||
0.993094 | − | 0.117323i | \(-0.0374313\pi\) | |||||||
\(264\) | −4.70590e8 | + | 7.63256e8i | −1.57409 | + | 2.55303i | ||||
\(265\) | − | 1.70904e7i | − | 0.0564146i | ||||||
\(266\) | 3.15815e7 | − | 1.71185e7i | 0.102884 | − | 0.0557675i | ||||
\(267\) | 3.88690e8i | 1.24972i | ||||||||
\(268\) | 1.50964e7 | + | 9.64488e7i | 0.0479072 | + | 0.306073i | ||||
\(269\) | 2.17640e8i | 0.681720i | 0.940114 | + | 0.340860i | \(0.110718\pi\) | ||||
−0.940114 | + | 0.340860i | \(0.889282\pi\) | |||||||
\(270\) | −6.87965e8 | + | 8.04023e8i | −2.12712 | + | 2.48597i | ||||
\(271\) | − | 684637.i | − | 0.00208962i | −0.999999 | − | 0.00104481i | \(-0.999667\pi\) | ||
0.999999 | − | 0.00104481i | \(-0.000332574\pi\) | |||||||
\(272\) | 2.20657e8 | − | 7.08101e7i | 0.664854 | − | 0.213356i | ||||
\(273\) | 8.78237e6 | 0.0261242 | ||||||||
\(274\) | −1.91081e8 | + | 2.23316e8i | −0.561166 | + | 0.655834i | ||||
\(275\) | − | 9.09187e8i | − | 2.63626i | ||||||
\(276\) | 5.15395e8 | − | 8.06707e7i | 1.47556 | − | 0.230959i | ||||
\(277\) | 4.58005e8 | 1.29476 | 0.647382 | − | 0.762166i | \(-0.275864\pi\) | ||||
0.647382 | + | 0.762166i | \(0.275864\pi\) | |||||||
\(278\) | 4.58626e7 | + | 3.92425e7i | 0.128027 | + | 0.109547i | ||||
\(279\) | −1.14403e9 | −3.15371 | ||||||||
\(280\) | −3.60997e7 | + | 5.85505e7i | −0.0982766 | + | 0.159396i | ||||
\(281\) | − | 1.01473e8i | − | 0.272822i | −0.990652 | − | 0.136411i | \(-0.956443\pi\) | ||
0.990652 | − | 0.136411i | \(-0.0435568\pi\) | |||||||
\(282\) | 1.18098e8 | + | 1.01051e8i | 0.313597 | + | 0.268330i | ||||
\(283\) | 7.49619e8i | 1.96602i | 0.183548 | + | 0.983011i | \(0.441242\pi\) | ||||
−0.183548 | + | 0.983011i | \(0.558758\pi\) | |||||||
\(284\) | −6.67032e6 | − | 4.26158e7i | −0.0172796 | − | 0.110397i | ||||
\(285\) | 3.97638e8 | − | 1.03651e9i | 1.01749 | − | 2.65227i | ||||
\(286\) | 5.46406e7 | − | 6.38583e7i | 0.138113 | − | 0.161412i | ||||
\(287\) | −6.17057e7 | −0.154077 | ||||||||
\(288\) | 3.37471e8 | − | 8.04371e8i | 0.832458 | − | 1.98419i | ||||
\(289\) | −2.10278e8 | −0.512449 | ||||||||
\(290\) | −7.52587e8 | − | 6.43953e8i | −1.81202 | − | 1.55046i | ||||
\(291\) | − | 9.49794e8i | − | 2.25946i | ||||||
\(292\) | −4.00594e7 | − | 2.55935e8i | −0.0941597 | − | 0.601574i | ||||
\(293\) | 7.91184e8i | 1.83756i | 0.394772 | + | 0.918779i | \(0.370823\pi\) | ||||
−0.394772 | + | 0.918779i | \(0.629177\pi\) | |||||||
\(294\) | 4.96030e8 | − | 5.79709e8i | 1.13839 | − | 1.33044i | ||||
\(295\) | 1.00428e9 | 2.27761 | ||||||||
\(296\) | −1.15707e8 | + | 1.87666e8i | −0.259321 | + | 0.420596i | ||||
\(297\) | 1.55963e9i | 3.45440i | ||||||||
\(298\) | 3.53819e8 | − | 4.13507e8i | 0.774505 | − | 0.905162i | ||||
\(299\) | −4.88960e7 | −0.105785 | ||||||||
\(300\) | 2.00339e8 | + | 1.27994e9i | 0.428392 | + | 2.73694i | ||||
\(301\) | −7.17683e7 | −0.151688 | ||||||||
\(302\) | 1.95052e8 | − | 2.27957e8i | 0.407499 | − | 0.476244i | ||||
\(303\) | 1.00954e9 | 2.08485 | ||||||||
\(304\) | −2.73145e7 | + | 4.89082e8i | −0.0557616 | + | 0.998444i | ||||
\(305\) | −1.65002e8 | −0.332996 | ||||||||
\(306\) | 4.89588e8 | − | 5.72181e8i | 0.976801 | − | 1.14158i | ||||
\(307\) | −5.63617e8 | −1.11173 | −0.555865 | − | 0.831272i | \(-0.687613\pi\) | ||||
−0.555865 | + | 0.831272i | \(0.687613\pi\) | |||||||
\(308\) | 1.56774e7 | + | 1.00161e8i | 0.0305735 | + | 0.195330i | ||||
\(309\) | 1.01992e9 | 1.96658 | ||||||||
\(310\) | −7.99762e8 | + | 9.34680e8i | −1.52474 | + | 1.78196i | ||||
\(311\) | − | 7.72031e8i | − | 1.45537i | −0.685912 | − | 0.727685i | \(-0.740596\pi\) | ||
0.685912 | − | 0.727685i | \(-0.259404\pi\) | |||||||
\(312\) | −6.28510e7 | + | 1.01939e8i | −0.117158 | + | 0.190020i | ||||
\(313\) | 4.52014e8 | 0.833195 | 0.416597 | − | 0.909091i | \(-0.363223\pi\) | ||||
0.416597 | + | 0.909091i | \(0.363223\pi\) | |||||||
\(314\) | 1.47378e8 | − | 1.72240e8i | 0.268644 | − | 0.313964i | ||||
\(315\) | 2.23520e8i | 0.402929i | ||||||||
\(316\) | −7.09450e7 | − | 4.53259e8i | −0.126479 | − | 0.808056i | ||||
\(317\) | − | 7.32387e8i | − | 1.29132i | −0.763626 | − | 0.645659i | \(-0.776583\pi\) | ||
0.763626 | − | 0.645659i | \(-0.223417\pi\) | |||||||
\(318\) | 2.72718e7 | + | 2.33352e7i | 0.0475574 | + | 0.0406927i | ||||
\(319\) | −1.45985e9 | −2.51792 | ||||||||
\(320\) | −4.21260e8 | − | 8.38033e8i | −0.718663 | − | 1.42967i | ||||
\(321\) | −1.38577e8 | −0.233843 | ||||||||
\(322\) | 3.83462e7 | − | 4.48151e7i | 0.0640069 | − | 0.0748047i | ||||
\(323\) | −1.51467e8 | + | 3.94825e8i | −0.250097 | + | 0.651922i | ||||
\(324\) | −1.39951e8 | − | 8.94127e8i | −0.228595 | − | 1.46047i | ||||
\(325\) | − | 1.21429e8i | − | 0.196214i | ||||||
\(326\) | 2.31805e8 | + | 1.98345e8i | 0.370563 | + | 0.317073i | ||||
\(327\) | 4.60459e8i | 0.728239i | ||||||||
\(328\) | 4.41597e8 | − | 7.16231e8i | 0.690983 | − | 1.12071i | ||||
\(329\) | 1.75734e7 | 0.0272064 | ||||||||
\(330\) | 2.38058e9 | + | 2.03695e9i | 3.64656 | + | 3.12019i | ||||
\(331\) | −5.46189e7 | −0.0827838 | −0.0413919 | − | 0.999143i | \(-0.513179\pi\) | ||||
−0.0413919 | + | 0.999143i | \(0.513179\pi\) | |||||||
\(332\) | −1.04170e9 | + | 1.63049e8i | −1.56228 | + | 0.244532i | ||||
\(333\) | 7.16426e8i | 1.06320i | ||||||||
\(334\) | −2.28549e8 | + | 2.67104e8i | −0.335634 | + | 0.392255i | ||||
\(335\) | 3.41110e8 | 0.495722 | ||||||||
\(336\) | −4.41407e7 | − | 1.37550e8i | −0.0634822 | − | 0.197821i | ||||
\(337\) | − | 3.48422e8i | − | 0.495908i | −0.968772 | − | 0.247954i | \(-0.920242\pi\) | ||
0.968772 | − | 0.247954i | \(-0.0797581\pi\) | |||||||
\(338\) | −4.54248e8 | + | 5.30878e8i | −0.639859 | + | 0.747802i | ||||
\(339\) | 1.29262e9i | 1.80207i | ||||||||
\(340\) | −1.25217e8 | − | 7.99995e8i | −0.172777 | − | 1.10385i | ||||
\(341\) | 1.81307e9i | 2.47614i | ||||||||
\(342\) | 7.58543e8 | + | 1.39941e9i | 1.02539 | + | 1.89171i | ||||
\(343\) | − | 1.73723e8i | − | 0.232449i | ||||||
\(344\) | 5.13610e8 | − | 8.33029e8i | 0.680266 | − | 1.10333i | ||||
\(345\) | − | 1.82279e9i | − | 2.38985i | ||||||
\(346\) | 2.27496e8 | + | 1.94658e8i | 0.295262 | + | 0.252642i | ||||
\(347\) | 2.50612e8i | 0.321994i | 0.986955 | + | 0.160997i | \(0.0514710\pi\) | ||||
−0.986955 | + | 0.160997i | \(0.948529\pi\) | |||||||
\(348\) | 2.05516e9 | − | 3.21678e8i | 2.61407 | − | 0.409161i | ||||
\(349\) | −1.13646e9 | −1.43108 | −0.715542 | − | 0.698569i | \(-0.753820\pi\) | ||||
−0.715542 | + | 0.698569i | \(0.753820\pi\) | |||||||
\(350\) | 1.11295e8 | + | 9.52296e7i | 0.138751 | + | 0.118723i | ||||
\(351\) | 2.08300e8i | 0.257108i | ||||||||
\(352\) | −1.27478e9 | − | 5.34829e8i | −1.55789 | − | 0.653605i | ||||
\(353\) | 4.89645e8 | 0.592475 | 0.296237 | − | 0.955114i | \(-0.404268\pi\) | ||||
0.296237 | + | 0.955114i | \(0.404268\pi\) | |||||||
\(354\) | −1.37124e9 | + | 1.60257e9i | −1.64287 | + | 1.92002i | ||||
\(355\) | −1.50719e8 | −0.178801 | ||||||||
\(356\) | −5.92050e8 | + | 9.26689e7i | −0.695477 | + | 0.108858i | ||||
\(357\) | − | 1.24711e8i | − | 0.145067i | ||||||
\(358\) | 2.22646e8 | − | 2.60206e8i | 0.256463 | − | 0.299727i | ||||
\(359\) | 7.62380e8i | 0.869643i | 0.900517 | + | 0.434822i | \(0.143189\pi\) | ||||
−0.900517 | + | 0.434822i | \(0.856811\pi\) | |||||||
\(360\) | −2.59444e9 | − | 1.59962e9i | −2.93079 | − | 1.80700i | ||||
\(361\) | −6.64520e8 | − | 5.97846e8i | −0.743417 | − | 0.668828i | ||||
\(362\) | 8.29767e8 | + | 7.09993e8i | 0.919340 | + | 0.786637i | ||||
\(363\) | 2.99990e9 | 3.29181 | ||||||||
\(364\) | 2.09383e6 | + | 1.33772e7i | 0.00227555 | + | 0.0145382i | ||||
\(365\) | −9.05163e8 | −0.974320 | ||||||||
\(366\) | 2.25293e8 | − | 2.63299e8i | 0.240195 | − | 0.280715i | ||||
\(367\) | − | 1.43283e9i | − | 1.51309i | −0.653941 | − | 0.756545i | \(-0.726886\pi\) | ||
0.653941 | − | 0.756545i | \(-0.273114\pi\) | |||||||
\(368\) | 2.45754e8 | + | 7.65812e8i | 0.257059 | + | 0.801041i | ||||
\(369\) | − | 2.73425e9i | − | 2.83300i | ||||||
\(370\) | 5.85326e8 | + | 5.00836e8i | 0.600747 | + | 0.514031i | ||||
\(371\) | 4.05813e6 | 0.00412588 | ||||||||
\(372\) | −3.99510e8 | − | 2.55242e9i | −0.402371 | − | 2.57070i | ||||
\(373\) | − | 3.69312e8i | − | 0.368479i | −0.982881 | − | 0.184239i | \(-0.941018\pi\) | ||
0.982881 | − | 0.184239i | \(-0.0589822\pi\) | |||||||
\(374\) | −9.06801e8 | − | 7.75907e8i | −0.896316 | − | 0.766936i | ||||
\(375\) | 1.62580e9 | 1.59205 | ||||||||
\(376\) | −1.25764e8 | + | 2.03978e8i | −0.122011 | + | 0.197891i | ||||
\(377\) | −1.94975e8 | −0.187406 | ||||||||
\(378\) | −1.90916e8 | − | 1.63358e8i | −0.181811 | − | 0.155567i | ||||
\(379\) | 7.66263e8 | 0.723004 | 0.361502 | − | 0.932371i | \(-0.382264\pi\) | ||||
0.361502 | + | 0.932371i | \(0.382264\pi\) | |||||||
\(380\) | 1.67361e9 | + | 3.58560e8i | 1.56463 | + | 0.335212i | ||||
\(381\) | 1.37323e9 | 1.27206 | ||||||||
\(382\) | −1.66859e8 | − | 1.42774e8i | −0.153154 | − | 0.131047i | ||||
\(383\) | −6.19328e8 | −0.563281 | −0.281640 | − | 0.959520i | \(-0.590878\pi\) | ||||
−0.281640 | + | 0.959520i | \(0.590878\pi\) | |||||||
\(384\) | 1.91247e9 | + | 4.72027e8i | 1.72359 | + | 0.425410i | ||||
\(385\) | 3.54238e8 | 0.316360 | ||||||||
\(386\) | −4.35660e8 | − | 3.72774e8i | −0.385560 | − | 0.329906i | ||||
\(387\) | − | 3.18014e9i | − | 2.78906i | ||||||
\(388\) | 1.44672e9 | − | 2.26443e8i | 1.25740 | − | 0.196811i | ||||
\(389\) | −3.09742e8 | −0.266794 | −0.133397 | − | 0.991063i | \(-0.542589\pi\) | ||||
−0.133397 | + | 0.991063i | \(0.542589\pi\) | |||||||
\(390\) | 3.17945e8 | + | 2.72050e8i | 0.271410 | + | 0.232233i | ||||
\(391\) | 6.94332e8i | 0.587420i | ||||||||
\(392\) | 1.00127e9 | + | 6.17339e8i | 0.839555 | + | 0.517633i | ||||
\(393\) | 1.93245e9i | 1.60596i | ||||||||
\(394\) | −1.11254e8 | + | 1.30022e8i | −0.0916387 | + | 0.107098i | ||||
\(395\) | −1.60304e9 | −1.30874 | ||||||||
\(396\) | −4.43823e9 | + | 6.94682e8i | −3.59151 | + | 0.562151i | ||||
\(397\) | 1.74154e9 | 1.39690 | 0.698452 | − | 0.715657i | \(-0.253873\pi\) | ||||
0.698452 | + | 0.715657i | \(0.253873\pi\) | |||||||
\(398\) | −1.10414e8 | − | 9.44760e7i | −0.0877875 | − | 0.0751157i | ||||
\(399\) | 2.46121e8 | + | 9.44194e7i | 0.193974 | + | 0.0744142i | ||||
\(400\) | −1.90183e9 | + | 6.10309e8i | −1.48580 | + | 0.476804i | ||||
\(401\) | − | 1.11977e9i | − | 0.867212i | −0.901103 | − | 0.433606i | \(-0.857241\pi\) | ||
0.901103 | − | 0.433606i | \(-0.142759\pi\) | |||||||
\(402\) | −4.65751e8 | + | 5.44322e8i | −0.357571 | + | 0.417892i | ||||
\(403\) | 2.42150e8i | 0.184296i | ||||||||
\(404\) | 2.40687e8 | + | 1.53772e9i | 0.181601 | + | 1.16023i | ||||
\(405\) | −3.16225e9 | −2.36540 | ||||||||
\(406\) | 1.52907e8 | − | 1.78702e8i | 0.113393 | − | 0.132522i | ||||
\(407\) | 1.13540e9 | 0.834775 | ||||||||
\(408\) | 1.44755e9 | + | 8.92497e8i | 1.05517 | + | 0.650573i | ||||
\(409\) | − | 6.06144e8i | − | 0.438071i | −0.975717 | − | 0.219035i | \(-0.929709\pi\) | ||
0.975717 | − | 0.219035i | \(-0.0702910\pi\) | |||||||
\(410\) | −2.23391e9 | − | 1.91145e9i | −1.60074 | − | 1.36968i | ||||
\(411\) | −2.15679e9 | −1.53236 | ||||||||
\(412\) | 2.43163e8 | + | 1.55354e9i | 0.171300 | + | 1.09441i | ||||
\(413\) | 2.38468e8i | 0.166573i | ||||||||
\(414\) | 1.98581e9 | + | 1.69917e9i | 1.37542 | + | 1.17689i | ||||
\(415\) | 3.68418e9i | 2.53030i | ||||||||
\(416\) | −1.70257e8 | − | 7.14306e7i | −0.115952 | − | 0.0486472i | ||||
\(417\) | 4.42940e8i | 0.299136i | ||||||||
\(418\) | 2.21781e9 | − | 1.20215e9i | 1.48528 | − | 0.805085i | ||||
\(419\) | 6.76363e7i | 0.0449191i | 0.999748 | + | 0.0224595i | \(0.00714969\pi\) | ||||
−0.999748 | + | 0.0224595i | \(0.992850\pi\) | |||||||
\(420\) | −4.98690e8 | + | 7.80561e7i | −0.328442 | + | 0.0514084i | ||||
\(421\) | 2.41699e9i | 1.57866i | 0.613971 | + | 0.789329i | \(0.289571\pi\) | ||||
−0.613971 | + | 0.789329i | \(0.710429\pi\) | |||||||
\(422\) | −1.11424e9 | + | 1.30220e9i | −0.721744 | + | 0.843501i | ||||
\(423\) | 7.78699e8i | 0.500240i | ||||||||
\(424\) | −2.90420e7 | + | 4.71035e7i | −0.0185032 | + | 0.0300105i | ||||
\(425\) | −1.72432e9 | −1.08957 | ||||||||
\(426\) | 2.05792e8 | − | 2.40508e8i | 0.128972 | − | 0.150729i | ||||
\(427\) | − | 3.91797e7i | − | 0.0243537i | ||||||
\(428\) | −3.30387e7 | − | 2.11080e8i | −0.0203690 | − | 0.130135i | ||||
\(429\) | 6.16742e8 | 0.377141 | ||||||||
\(430\) | −2.59820e9 | − | 2.22316e9i | −1.57591 | − | 1.34844i | ||||
\(431\) | 1.87453e9 | 1.12778 | 0.563888 | − | 0.825851i | \(-0.309305\pi\) | ||||
0.563888 | + | 0.825851i | \(0.309305\pi\) | |||||||
\(432\) | 3.26241e9 | − | 1.04693e9i | 1.94691 | − | 0.624776i | ||||
\(433\) | − | 3.14975e9i | − | 1.86453i | −0.361780 | − | 0.932263i | \(-0.617831\pi\) | ||
0.361780 | − | 0.932263i | \(-0.382169\pi\) | |||||||
\(434\) | −2.21940e8 | − | 1.89904e8i | −0.130323 | − | 0.111512i | ||||
\(435\) | − | 7.26847e9i | − | 4.23380i | ||||||
\(436\) | −7.01367e8 | + | 1.09780e8i | −0.405269 | + | 0.0634335i | ||||
\(437\) | −1.37028e9 | − | 5.25681e8i | −0.785461 | − | 0.301326i | ||||
\(438\) | 1.23591e9 | − | 1.44440e9i | 0.702791 | − | 0.821350i | ||||
\(439\) | −3.03555e9 | −1.71243 | −0.856213 | − | 0.516623i | \(-0.827189\pi\) | ||||
−0.856213 | + | 0.516623i | \(0.827189\pi\) | |||||||
\(440\) | −2.53510e9 | + | 4.11171e9i | −1.41877 | + | 2.30111i | ||||
\(441\) | 3.82240e9 | 2.12227 | ||||||||
\(442\) | −1.21110e8 | − | 1.03628e8i | −0.0667119 | − | 0.0570823i | ||||
\(443\) | − | 1.15236e9i | − | 0.629758i | −0.949132 | − | 0.314879i | \(-0.898036\pi\) | ||
0.949132 | − | 0.314879i | \(-0.101964\pi\) | |||||||
\(444\) | −1.59840e9 | + | 2.50186e8i | −0.866655 | + | 0.135651i | ||||
\(445\) | 2.09390e9i | 1.12641i | ||||||||
\(446\) | −2.06258e9 | + | 2.41053e9i | −1.10088 | + | 1.28659i | ||||
\(447\) | 3.99365e9 | 2.11492 | ||||||||
\(448\) | 1.98991e8 | − | 1.00028e8i | 0.104559 | − | 0.0525594i | ||||
\(449\) | − | 8.59070e8i | − | 0.447885i | −0.974602 | − | 0.223942i | \(-0.928107\pi\) | ||
0.974602 | − | 0.223942i | \(-0.0718928\pi\) | |||||||
\(450\) | −4.21974e9 | + | 4.93160e9i | −2.18294 | + | 2.55120i | ||||
\(451\) | −4.33329e9 | −2.22433 | ||||||||
\(452\) | −1.96891e9 | + | 3.08178e8i | −1.00286 | + | 0.156970i | ||||
\(453\) | 2.20161e9 | 1.11275 | ||||||||
\(454\) | 1.13407e8 | − | 1.32538e8i | 0.0568779 | − | 0.0664731i | ||||
\(455\) | 4.73112e7 | 0.0235464 | ||||||||
\(456\) | −2.85731e9 | + | 2.18106e9i | −1.41117 | + | 1.07719i | ||||
\(457\) | 3.34517e9 | 1.63950 | 0.819749 | − | 0.572723i | \(-0.194113\pi\) | ||||
0.819749 | + | 0.572723i | \(0.194113\pi\) | |||||||
\(458\) | −1.51141e9 | + | 1.76638e9i | −0.735110 | + | 0.859121i | ||||
\(459\) | 2.95791e9 | 1.42771 | ||||||||
\(460\) | 2.77647e9 | − | 4.34578e8i | 1.32996 | − | 0.208169i | ||||
\(461\) | 3.27440e9 | 1.55661 | 0.778303 | − | 0.627889i | \(-0.216081\pi\) | ||||
0.778303 | + | 0.627889i | \(0.216081\pi\) | |||||||
\(462\) | −4.83675e8 | + | 5.65269e8i | −0.228195 | + | 0.266691i | ||||
\(463\) | 7.33860e8i | 0.343621i | 0.985130 | + | 0.171811i | \(0.0549617\pi\) | ||||
−0.985130 | + | 0.171811i | \(0.945038\pi\) | |||||||
\(464\) | 9.79954e8 | + | 3.05371e9i | 0.455400 | + | 1.41910i | ||||
\(465\) | −9.02712e9 | −4.16355 | ||||||||
\(466\) | 2.52448e9 | − | 2.95035e9i | 1.15564 | − | 1.35059i | ||||
\(467\) | 5.17347e8i | 0.235057i | 0.993070 | + | 0.117528i | \(0.0374971\pi\) | ||||
−0.993070 | + | 0.117528i | \(0.962503\pi\) | |||||||
\(468\) | −5.92761e8 | + | 9.27803e7i | −0.267312 | + | 0.0418403i | ||||
\(469\) | 8.09968e7i | 0.0362546i | ||||||||
\(470\) | 6.36204e8 | + | 5.44370e8i | 0.282653 | + | 0.241853i | ||||
\(471\) | 1.66349e9 | 0.733579 | ||||||||
\(472\) | −2.76794e9 | − | 1.70659e9i | −1.21160 | − | 0.747021i | ||||
\(473\) | −5.03993e9 | −2.18983 | ||||||||
\(474\) | 2.18878e9 | − | 2.55802e9i | 0.944014 | − | 1.10327i | ||||
\(475\) | 1.30548e9 | − | 3.40298e9i | 0.558913 | − | 1.45691i | ||||
\(476\) | 1.89959e8 | − | 2.97329e7i | 0.0807303 | − | 0.0126361i | ||||
\(477\) | 1.79821e8i | 0.0758621i | ||||||||
\(478\) | −1.21634e9 | − | 1.04077e9i | −0.509400 | − | 0.435870i | ||||
\(479\) | − | 3.33597e8i | − | 0.138691i | −0.997593 | − | 0.0693454i | \(-0.977909\pi\) | ||
0.997593 | − | 0.0693454i | \(-0.0220911\pi\) | |||||||
\(480\) | 2.66286e9 | − | 6.34701e9i | 1.09902 | − | 2.61954i | ||||
\(481\) | 1.51642e8 | 0.0621315 | ||||||||
\(482\) | 6.11721e8 | + | 5.23421e8i | 0.248822 | + | 0.212905i | ||||
\(483\) | 4.32824e8 | 0.174782 | ||||||||
\(484\) | 7.15217e8 | + | 4.56943e9i | 0.286734 | + | 1.83191i | ||||
\(485\) | − | 5.11660e9i | − | 2.03650i | ||||||
\(486\) | 9.53676e8 | − | 1.11456e9i | 0.376855 | − | 0.440429i | ||||
\(487\) | −1.85149e9 | −0.726390 | −0.363195 | − | 0.931713i | \(-0.618314\pi\) | ||||
−0.363195 | + | 0.931713i | \(0.618314\pi\) | |||||||
\(488\) | 4.54767e8 | + | 2.80390e8i | 0.177141 | + | 0.109218i | ||||
\(489\) | 2.23877e9i | 0.865823i | ||||||||
\(490\) | 2.67215e9 | − | 3.12293e9i | 1.02606 | − | 1.19916i | ||||
\(491\) | 1.07948e9i | 0.411557i | 0.978599 | + | 0.205778i | \(0.0659726\pi\) | ||||
−0.978599 | + | 0.205778i | \(0.934027\pi\) | |||||||
\(492\) | 6.10034e9 | − | 9.54838e8i | 2.30928 | − | 0.361453i | ||||
\(493\) | 2.76868e9i | 1.04066i | ||||||||
\(494\) | 2.96206e8 | − | 1.60557e8i | 0.110548 | − | 0.0599216i | ||||
\(495\) | 1.56967e10i | 5.81688i | ||||||||
\(496\) | 3.79257e9 | − | 1.21706e9i | 1.39556 | − | 0.447843i | ||||
\(497\) | − | 3.57884e7i | − | 0.0130766i | ||||||
\(498\) | −5.87897e9 | − | 5.03036e9i | −2.13304 | − | 1.82514i | ||||
\(499\) | − | 2.14498e9i | − | 0.772808i | −0.922330 | − | 0.386404i | \(-0.873717\pi\) | ||
0.922330 | − | 0.386404i | \(-0.126283\pi\) | |||||||
\(500\) | 3.87612e8 | + | 2.47640e9i | 0.138676 | + | 0.885985i | ||||
\(501\) | −2.57969e9 | −0.916506 | ||||||||
\(502\) | −2.92451e9 | − | 2.50237e9i | −1.03179 | − | 0.882852i | ||||
\(503\) | − | 3.18072e9i | − | 1.11439i | −0.830381 | − | 0.557196i | \(-0.811877\pi\) | ||
0.830381 | − | 0.557196i | \(-0.188123\pi\) | |||||||
\(504\) | 3.79831e8 | − | 6.16052e8i | 0.132155 | − | 0.214343i | ||||
\(505\) | 5.43845e9 | 1.87912 | ||||||||
\(506\) | 2.69286e9 | − | 3.14714e9i | 0.924033 | − | 1.07992i | ||||
\(507\) | −5.12721e9 | −1.74724 | ||||||||
\(508\) | 3.27397e8 | + | 2.09170e9i | 0.110803 | + | 0.707907i | ||||
\(509\) | 3.97902e9i | 1.33741i | 0.743529 | + | 0.668704i | \(0.233150\pi\) | ||||
−0.743529 | + | 0.668704i | \(0.766850\pi\) | |||||||
\(510\) | 3.86317e9 | − | 4.51488e9i | 1.28958 | − | 1.50713i | ||||
\(511\) | − | 2.14932e8i | − | 0.0712569i | ||||||
\(512\) | −2.63030e8 | + | 3.02559e9i | −0.0866086 | + | 0.996242i | ||||
\(513\) | −2.23944e9 | + | 5.83749e9i | −0.732367 | + | 1.90904i | ||||
\(514\) | −3.78191e9 | − | 3.23600e9i | −1.22840 | − | 1.05109i | ||||
\(515\) | 5.49439e9 | 1.77253 | ||||||||
\(516\) | 7.09514e9 | − | 1.11055e9i | 2.27346 | − | 0.355847i | ||||
\(517\) | 1.23409e9 | 0.392764 | ||||||||
\(518\) | −1.18924e8 | + | 1.38986e8i | −0.0375937 | + | 0.0439357i | ||||
\(519\) | 2.19715e9i | 0.689881i | ||||||||
\(520\) | −3.38583e8 | + | 5.49151e8i | −0.105597 | + | 0.171270i | ||||
\(521\) | − | 4.72489e9i | − | 1.46372i | −0.681453 | − | 0.731862i | \(-0.738651\pi\) | ||
0.681453 | − | 0.731862i | \(-0.261349\pi\) | |||||||
\(522\) | 7.91851e9 | + | 6.77550e9i | 2.43667 | + | 2.08494i | ||||
\(523\) | −4.12799e9 | −1.26178 | −0.630888 | − | 0.775874i | \(-0.717309\pi\) | ||||
−0.630888 | + | 0.775874i | \(0.717309\pi\) | |||||||
\(524\) | −2.94349e9 | + | 4.60721e8i | −0.893722 | + | 0.139887i | ||||
\(525\) | 1.07488e9i | 0.324193i | ||||||||
\(526\) | 5.95074e8 | + | 5.09177e8i | 0.178288 | + | 0.152552i | ||||
\(527\) | 3.43858e9 | 1.02339 | ||||||||
\(528\) | −3.09978e9 | − | 9.65946e9i | −0.916458 | − | 2.85584i | ||||
\(529\) | 9.95074e8 | 0.292254 | ||||||||
\(530\) | 1.46915e8 | + | 1.25708e8i | 0.0428647 | + | 0.0366773i | ||||
\(531\) | −1.05668e10 | −3.06275 | ||||||||
\(532\) | −8.51403e7 | + | 3.97400e8i | −0.0245157 | + | 0.114429i | ||||
\(533\) | −5.78744e8 | −0.165555 | ||||||||
\(534\) | −3.34131e9 | − | 2.85900e9i | −0.949560 | − | 0.812494i | ||||
\(535\) | −7.46525e8 | −0.210769 | ||||||||
\(536\) | −9.40147e8 | − | 5.79654e8i | −0.263705 | − | 0.162589i | ||||
\(537\) | 2.51306e9 | 0.700315 | ||||||||
\(538\) | −1.87091e9 | − | 1.60085e9i | −0.517981 | − | 0.443212i | ||||
\(539\) | − | 6.05780e9i | − | 1.66630i | ||||||
\(540\) | −1.85134e9 | − | 1.18279e10i | −0.505949 | − | 3.23244i | ||||
\(541\) | 1.99704e9 | 0.542247 | 0.271124 | − | 0.962545i | \(-0.412605\pi\) | ||||
0.271124 | + | 0.962545i | \(0.412605\pi\) | |||||||
\(542\) | 5.88537e6 | + | 5.03584e6i | 0.00158773 | + | 0.00135854i | ||||
\(543\) | 8.01388e9i | 2.14805i | ||||||||
\(544\) | −1.01433e9 | + | 2.41768e9i | −0.270136 | + | 0.643877i | ||||
\(545\) | 2.48052e9i | 0.656380i | ||||||||
\(546\) | −6.45985e7 | + | 7.54962e7i | −0.0169843 | + | 0.0198496i | ||||
\(547\) | 1.88840e9 | 0.493331 | 0.246666 | − | 0.969101i | \(-0.420665\pi\) | ||||
0.246666 | + | 0.969101i | \(0.420665\pi\) | |||||||
\(548\) | −5.14206e8 | − | 3.28520e9i | −0.133477 | − | 0.852766i | ||||
\(549\) | 1.73610e9 | 0.447787 | ||||||||
\(550\) | 7.81567e9 | + | 6.68750e9i | 2.00307 | + | 1.71394i | ||||
\(551\) | −5.46405e9 | − | 2.09618e9i | −1.39150 | − | 0.533823i | ||||
\(552\) | −3.09750e9 | + | 5.02388e9i | −0.783836 | + | 1.27131i | ||||
\(553\) | − | 3.80642e8i | − | 0.0957148i | ||||||
\(554\) | −3.36884e9 | + | 3.93716e9i | −0.841776 | + | 0.983782i | ||||
\(555\) | 5.65307e9i | 1.40365i | ||||||||
\(556\) | −6.74683e8 | + | 1.05603e8i | −0.166471 | + | 0.0260564i | ||||
\(557\) | 5.09331e9 | 1.24884 | 0.624421 | − | 0.781088i | \(-0.285335\pi\) | ||||
0.624421 | + | 0.781088i | \(0.285335\pi\) | |||||||
\(558\) | 8.41487e9 | − | 9.83444e9i | 2.05035 | − | 2.39624i | ||||
\(559\) | −6.73122e8 | −0.162987 | ||||||||
\(560\) | −2.37789e8 | − | 7.40991e8i | −0.0572181 | − | 0.178302i | ||||
\(561\) | − | 8.75787e9i | − | 2.09425i | ||||||
\(562\) | 8.72298e8 | + | 7.46385e8i | 0.207294 | + | 0.177372i | ||||
\(563\) | 8.42481e8 | 0.198967 | 0.0994834 | − | 0.995039i | \(-0.468281\pi\) | ||||
0.0994834 | + | 0.995039i | \(0.468281\pi\) | |||||||
\(564\) | −1.73734e9 | + | 2.71932e8i | −0.407763 | + | 0.0638240i | ||||
\(565\) | 6.96343e9i | 1.62425i | ||||||||
\(566\) | −6.44398e9 | − | 5.51381e9i | −1.49381 | − | 1.27819i | ||||
\(567\) | − | 7.50879e8i | − | 0.172993i | ||||||
\(568\) | 4.15403e8 | + | 2.56120e8i | 0.0951154 | + | 0.0586440i | ||||
\(569\) | − | 2.30834e9i | − | 0.525300i | −0.964891 | − | 0.262650i | \(-0.915403\pi\) | ||
0.964891 | − | 0.262650i | \(-0.0845965\pi\) | |||||||
\(570\) | 5.98539e9 | + | 1.10423e10i | 1.35373 | + | 2.49745i | ||||
\(571\) | 3.46898e8i | 0.0779785i | 0.999240 | + | 0.0389893i | \(0.0124138\pi\) | ||||
−0.999240 | + | 0.0389893i | \(0.987586\pi\) | |||||||
\(572\) | 1.47040e8 | + | 9.39417e8i | 0.0328510 | + | 0.209881i | ||||
\(573\) | − | 1.61152e9i | − | 0.357845i | ||||||
\(574\) | 4.53875e8 | − | 5.30443e8i | 0.100172 | − | 0.117070i | ||||
\(575\) | − | 5.98442e9i | − | 1.31276i | ||||||
\(576\) | 4.43238e9 | + | 8.81755e9i | 0.966403 | + | 1.92251i | ||||
\(577\) | 4.03219e9 | 0.873827 | 0.436914 | − | 0.899504i | \(-0.356072\pi\) | ||||
0.436914 | + | 0.899504i | \(0.356072\pi\) | |||||||
\(578\) | 1.54669e9 | − | 1.80762e9i | 0.333163 | − | 0.389367i | ||||
\(579\) | − | 4.20760e9i | − | 0.900864i | ||||||
\(580\) | 1.10713e10 | − | 1.73290e9i | 2.35613 | − | 0.368787i | ||||
\(581\) | −8.74810e8 | −0.185054 | ||||||||
\(582\) | 8.16474e9 | + | 6.98619e9i | 1.71677 | + | 1.46896i | ||||
\(583\) | 2.84982e8 | 0.0595632 | ||||||||
\(584\) | 2.49475e9 | + | 1.53816e9i | 0.518302 | + | 0.319562i | ||||
\(585\) | 2.09642e9i | 0.432944i | ||||||||
\(586\) | −6.80128e9 | − | 5.81954e9i | −1.39621 | − | 1.19467i | ||||
\(587\) | 3.71265e9i | 0.757618i | 0.925475 | + | 0.378809i | \(0.123666\pi\) | ||||
−0.925475 | + | 0.378809i | \(0.876334\pi\) | |||||||
\(588\) | 1.33483e9 | + | 8.52808e9i | 0.270774 | + | 1.72994i | ||||
\(589\) | −2.60336e9 | + | 6.78611e9i | −0.524965 | + | 1.36841i | ||||
\(590\) | −7.38698e9 | + | 8.63315e9i | −1.48076 | + | 1.73056i | ||||
\(591\) | −1.25575e9 | −0.250235 | ||||||||
\(592\) | −7.62161e8 | − | 2.37503e9i | −0.150981 | − | 0.470482i | ||||
\(593\) | −3.54071e9 | −0.697266 | −0.348633 | − | 0.937259i | \(-0.613354\pi\) | ||||
−0.348633 | + | 0.937259i | \(0.613354\pi\) | |||||||
\(594\) | −1.34071e10 | − | 1.14718e10i | −2.62471 | − | 2.24584i | ||||
\(595\) | − | 6.71829e8i | − | 0.130752i | ||||||
\(596\) | 9.52138e8 | + | 6.08309e9i | 0.184221 | + | 1.17696i | ||||
\(597\) | − | 1.06638e9i | − | 0.205116i | ||||||
\(598\) | 3.59653e8 | − | 4.20326e8i | 0.0687749 | − | 0.0803770i | ||||
\(599\) | 8.48019e8 | 0.161217 | 0.0806087 | − | 0.996746i | \(-0.474314\pi\) | ||||
0.0806087 | + | 0.996746i | \(0.474314\pi\) | |||||||
\(600\) | −1.24764e10 | − | 7.69239e9i | −2.35808 | − | 1.45389i | ||||
\(601\) | − | 3.01276e9i | − | 0.566114i | −0.959103 | − | 0.283057i | \(-0.908652\pi\) | ||
0.959103 | − | 0.283057i | \(-0.0913485\pi\) | |||||||
\(602\) | 5.27890e8 | − | 6.16944e8i | 0.0986179 | − | 0.115255i | ||||
\(603\) | −3.58907e9 | −0.666609 | ||||||||
\(604\) | 5.24892e8 | + | 3.35347e9i | 0.0969262 | + | 0.619249i | ||||
\(605\) | 1.61607e10 | 2.96699 | ||||||||
\(606\) | −7.42564e9 | + | 8.67833e9i | −1.35544 | + | 1.58410i | ||||
\(607\) | 2.39524e9 | 0.434700 | 0.217350 | − | 0.976094i | \(-0.430259\pi\) | ||||
0.217350 | + | 0.976094i | \(0.430259\pi\) | |||||||
\(608\) | −4.00340e9 | − | 3.83223e9i | −0.722381 | − | 0.691496i | ||||
\(609\) | 1.72590e9 | 0.309639 | ||||||||
\(610\) | 1.21367e9 | − | 1.41841e9i | 0.216493 | − | 0.253015i | ||||
\(611\) | 1.64823e8 | 0.0292330 | ||||||||
\(612\) | 1.31750e9 | + | 8.41733e9i | 0.232338 | + | 1.48438i | ||||
\(613\) | −1.02628e10 | −1.79951 | −0.899755 | − | 0.436395i | \(-0.856255\pi\) | ||||
−0.899755 | + | 0.436395i | \(0.856255\pi\) | |||||||
\(614\) | 4.14567e9 | − | 4.84503e9i | 0.722779 | − | 0.844710i | ||||
\(615\) | − | 2.15750e10i | − | 3.74015i | ||||||
\(616\) | −9.76328e8 | − | 6.01961e8i | −0.168292 | − | 0.103761i | ||||
\(617\) | 3.36122e9 | 0.576101 | 0.288051 | − | 0.957615i | \(-0.406993\pi\) | ||||
0.288051 | + | 0.957615i | \(0.406993\pi\) | |||||||
\(618\) | −7.50202e9 | + | 8.76759e9i | −1.27855 | + | 1.49424i | ||||
\(619\) | − | 6.15064e9i | − | 1.04232i | −0.853457 | − | 0.521162i | \(-0.825499\pi\) | ||
0.853457 | − | 0.521162i | \(-0.174501\pi\) | |||||||
\(620\) | −2.15219e9 | − | 1.37500e10i | −0.362668 | − | 2.31704i | ||||
\(621\) | 1.02657e10i | 1.72016i | ||||||||
\(622\) | 6.63663e9 | + | 5.67866e9i | 1.10581 | + | 0.946192i | ||||
\(623\) | −4.97198e8 | −0.0823799 | ||||||||
\(624\) | −4.14000e8 | − | 1.29010e9i | −0.0682110 | − | 0.212557i | ||||
\(625\) | −7.65854e8 | −0.125478 | ||||||||
\(626\) | −3.32478e9 | + | 3.88566e9i | −0.541692 | + | 0.633074i | ||||
\(627\) | 1.72838e10 | + | 6.63061e9i | 2.80030 | + | 1.07428i | ||||
\(628\) | 3.96598e8 | + | 2.53381e9i | 0.0638987 | + | 0.408240i | ||||
\(629\) | − | 2.15335e9i | − | 0.345014i | ||||||
\(630\) | −1.92145e9 | − | 1.64410e9i | −0.306152 | − | 0.261960i | ||||
\(631\) | 2.57771e9i | 0.408444i | 0.978925 | + | 0.204222i | \(0.0654664\pi\) | ||||
−0.978925 | + | 0.204222i | \(0.934534\pi\) | |||||||
\(632\) | 4.41820e9 | + | 2.72407e9i | 0.696202 | + | 0.429248i | ||||
\(633\) | −1.25767e10 | −1.97085 | ||||||||
\(634\) | 6.29584e9 | + | 5.38706e9i | 0.981163 | + | 0.839536i | ||||
\(635\) | 7.39770e9 | 1.14654 | ||||||||
\(636\) | −4.01194e8 | + | 6.27957e7i | −0.0618378 | + | 0.00967899i | ||||
\(637\) | − | 8.09067e8i | − | 0.124021i | ||||||
\(638\) | 1.07379e10 | − | 1.25494e10i | 1.63700 | − | 1.91315i | ||||
\(639\) | 1.58583e9 | 0.240438 | ||||||||
\(640\) | 1.03026e10 | + | 2.54284e9i | 1.55352 | + | 0.383433i | ||||
\(641\) | − | 4.66718e9i | − | 0.699924i | −0.936764 | − | 0.349962i | \(-0.886194\pi\) | ||
0.936764 | − | 0.349962i | \(-0.113806\pi\) | |||||||
\(642\) | 1.01930e9 | − | 1.19126e9i | 0.152030 | − | 0.177678i | ||||
\(643\) | 1.11696e10i | 1.65691i | 0.560058 | + | 0.828453i | \(0.310779\pi\) | ||||
−0.560058 | + | 0.828453i | \(0.689221\pi\) | |||||||
\(644\) | 1.03191e8 | + | 6.59274e8i | 0.0152244 | + | 0.0972669i | ||||
\(645\) | − | 2.50934e10i | − | 3.68214i | ||||||
\(646\) | −2.27994e9 | − | 4.20619e9i | −0.332743 | − | 0.613867i | ||||
\(647\) | 4.43545e9i | 0.643832i | 0.946768 | + | 0.321916i | \(0.104327\pi\) | ||||
−0.946768 | + | 0.321916i | \(0.895673\pi\) | |||||||
\(648\) | 8.71561e9 | + | 5.37367e9i | 1.25830 | + | 0.775815i | ||||
\(649\) | 1.67464e10i | 2.40472i | ||||||||
\(650\) | 1.04384e9 | + | 8.93169e8i | 0.149087 | + | 0.127567i | ||||
\(651\) | − | 2.14350e9i | − | 0.304501i | ||||||
\(652\) | −3.41008e9 | + | 5.33753e8i | −0.481835 | + | 0.0754178i | ||||
\(653\) | −1.23995e10 | −1.74264 | −0.871320 | − | 0.490716i | \(-0.836735\pi\) | ||||
−0.871320 | + | 0.490716i | \(0.836735\pi\) | |||||||
\(654\) | −3.95826e9 | − | 3.38690e9i | −0.553327 | − | 0.473456i | ||||
\(655\) | 1.04102e10i | 1.44749i | ||||||||
\(656\) | 2.90880e9 | + | 9.06433e9i | 0.402301 | + | 1.25364i | ||||
\(657\) | 9.52387e9 | 1.31019 | ||||||||
\(658\) | −1.29261e8 | + | 1.51067e8i | −0.0176879 | + | 0.0206718i | ||||
\(659\) | 3.16574e9 | 0.430900 | 0.215450 | − | 0.976515i | \(-0.430878\pi\) | ||||
0.215450 | + | 0.976515i | \(0.430878\pi\) | |||||||
\(660\) | −3.50206e10 | + | 5.48149e9i | −4.74154 | + | 0.742156i | ||||
\(661\) | − | 9.70152e9i | − | 1.30658i | −0.757110 | − | 0.653288i | \(-0.773389\pi\) | ||
0.757110 | − | 0.653288i | \(-0.226611\pi\) | |||||||
\(662\) | 4.01748e8 | − | 4.69523e8i | 0.0538209 | − | 0.0629004i | ||||
\(663\) | − | 1.16968e9i | − | 0.155873i | ||||||
\(664\) | 6.26058e9 | − | 1.01541e10i | 0.829901 | − | 1.34603i | ||||
\(665\) | 1.32587e9 | + | 5.08643e8i | 0.174834 | + | 0.0670714i | ||||
\(666\) | −6.15864e9 | − | 5.26966e9i | −0.807839 | − | 0.691230i | ||||
\(667\) | −9.60899e9 | −1.25383 | ||||||||
\(668\) | −6.15032e8 | − | 3.92936e9i | −0.0798326 | − | 0.510040i | ||||
\(669\) | −2.32808e10 | −3.00613 | ||||||||
\(670\) | −2.50903e9 | + | 2.93230e9i | −0.322288 | + | 0.376657i | ||||
\(671\) | − | 2.75140e9i | − | 0.351581i | ||||||
\(672\) | 1.50710e9 | + | 6.32299e8i | 0.191580 | + | 0.0803767i | ||||
\(673\) | 9.49005e9i | 1.20010i | 0.799964 | + | 0.600048i | \(0.204852\pi\) | ||||
−0.799964 | + | 0.600048i | \(0.795148\pi\) | |||||||
\(674\) | 2.99515e9 | + | 2.56281e9i | 0.376798 | + | 0.322409i | ||||
\(675\) | −2.54941e10 | −3.19062 | ||||||||
\(676\) | −1.22240e9 | − | 7.80973e9i | −0.152194 | − | 0.972350i | ||||
\(677\) | − | 6.38172e9i | − | 0.790455i | −0.918583 | − | 0.395228i | \(-0.870666\pi\) | ||
0.918583 | − | 0.395228i | \(-0.129334\pi\) | |||||||
\(678\) | −1.11118e10 | − | 9.50785e9i | −1.36924 | − | 1.17160i | ||||
\(679\) | 1.21494e9 | 0.148940 | ||||||||
\(680\) | 7.79805e9 | + | 4.80794e9i | 0.951054 | + | 0.586378i | ||||
\(681\) | 1.28005e9 | 0.155315 | ||||||||
\(682\) | −1.55858e10 | − | 1.33360e10i | −1.88141 | − | 1.60983i | ||||
\(683\) | −4.32806e9 | −0.519782 | −0.259891 | − | 0.965638i | \(-0.583687\pi\) | ||||
−0.259891 | + | 0.965638i | \(0.583687\pi\) | |||||||
\(684\) | −1.76093e10 | − | 3.77267e9i | −2.10400 | − | 0.450767i | ||||
\(685\) | −1.16187e10 | −1.38115 | ||||||||
\(686\) | 1.49338e9 | + | 1.27782e9i | 0.176619 | + | 0.151124i | ||||
\(687\) | −1.70597e10 | −2.00734 | ||||||||
\(688\) | 3.38315e9 | + | 1.05425e10i | 0.396061 | + | 1.23419i | ||||
\(689\) | 3.80616e7 | 0.00443323 | ||||||||
\(690\) | 1.56693e10 | + | 1.34075e10i | 1.81585 | + | 1.55373i | ||||
\(691\) | − | 1.20117e10i | − | 1.38495i | −0.721444 | − | 0.692473i | \(-0.756521\pi\) | ||
0.721444 | − | 0.692473i | \(-0.243479\pi\) | |||||||
\(692\) | −3.34668e9 | + | 5.23830e8i | −0.383922 | + | 0.0600923i | ||||
\(693\) | −3.72719e9 | −0.425417 | ||||||||
\(694\) | −2.15434e9 | − | 1.84337e9i | −0.244656 | − | 0.209341i | ||||
\(695\) | 2.38615e9i | 0.269619i | ||||||||
\(696\) | −1.23514e10 | + | 2.00329e10i | −1.38862 | + | 2.25223i | ||||
\(697\) | 8.21829e9i | 0.919320i | ||||||||
\(698\) | 8.35921e9 | − | 9.76939e9i | 0.930403 | − | 1.08736i | ||||
\(699\) | 2.84945e10 | 3.15566 | ||||||||
\(700\) | −1.63725e9 | + | 2.56266e8i | −0.180415 | + | 0.0282389i | ||||
\(701\) | 6.81686e9 | 0.747432 | 0.373716 | − | 0.927543i | \(-0.378084\pi\) | ||||
0.373716 | + | 0.927543i | \(0.378084\pi\) | |||||||
\(702\) | −1.79062e9 | − | 1.53215e9i | −0.195354 | − | 0.167156i | ||||
\(703\) | 4.24968e9 | + | 1.63031e9i | 0.461331 | + | 0.176980i | ||||
\(704\) | 1.39742e10 | − | 7.02451e9i | 1.50946 | − | 0.758772i | ||||
\(705\) | 6.14445e9i | 0.660421i | ||||||||
\(706\) | −3.60157e9 | + | 4.20915e9i | −0.385191 | + | 0.450171i | ||||
\(707\) | 1.29136e9i | 0.137430i | ||||||||
\(708\) | −3.69006e9 | − | 2.35753e10i | −0.390766 | − | 2.49656i | ||||
\(709\) | 3.98257e8 | 0.0419663 | 0.0209832 | − | 0.999780i | \(-0.493320\pi\) | ||||
0.0209832 | + | 0.999780i | \(0.493320\pi\) | |||||||
\(710\) | 1.10861e9 | − | 1.29563e9i | 0.116245 | − | 0.135856i | ||||
\(711\) | 1.68667e10 | 1.75990 | ||||||||
\(712\) | 3.55820e9 | − | 5.77108e9i | 0.369445 | − | 0.599207i | ||||
\(713\) | 1.19339e10i | 1.23302i | ||||||||
\(714\) | 1.07206e9 | + | 9.17312e8i | 0.110224 | + | 0.0943134i | ||||
\(715\) | 3.32243e9 | 0.339926 | ||||||||
\(716\) | 5.99148e8 | + | 3.82788e9i | 0.0610012 | + | 0.389729i | ||||
\(717\) | − | 1.17474e10i | − | 1.19022i | ||||||
\(718\) | −6.55367e9 | − | 5.60767e9i | −0.660768 | − | 0.565389i | ||||
\(719\) | 1.37676e10i | 1.38136i | 0.723162 | + | 0.690678i | \(0.242688\pi\) | ||||
−0.723162 | + | 0.690678i | \(0.757312\pi\) | |||||||
\(720\) | 3.28342e10 | − | 1.05367e10i | 3.27841 | − | 1.05206i | ||||
\(721\) | 1.30465e9i | 0.129634i | ||||||||
\(722\) | 1.00271e10 | − | 1.31499e9i | 0.991510 | − | 0.130029i | ||||
\(723\) | 5.90799e9i | 0.581374i | ||||||||
\(724\) | −1.22067e10 | + | 1.91062e9i | −1.19540 | + | 0.187106i | ||||
\(725\) | − | 2.38631e10i | − | 2.32565i | ||||||
\(726\) | −2.20657e10 | + | 2.57882e10i | −2.14013 | + | 2.50116i | ||||
\(727\) | 5.42026e9i | 0.523178i | 0.965179 | + | 0.261589i | \(0.0842465\pi\) | ||||
−0.965179 | + | 0.261589i | \(0.915753\pi\) | |||||||
\(728\) | −1.30396e8 | − | 8.03967e7i | −0.0125258 | − | 0.00772286i | ||||
\(729\) | −4.69861e9 | −0.449182 | ||||||||
\(730\) | 6.65791e9 | − | 7.78108e9i | 0.633443 | − | 0.740304i | ||||
\(731\) | 9.55847e9i | 0.905061i | ||||||||
\(732\) | 6.06270e8 | + | 3.87338e9i | 0.0571317 | + | 0.365007i | ||||
\(733\) | 6.95448e9 | 0.652230 | 0.326115 | − | 0.945330i | \(-0.394260\pi\) | ||||
0.326115 | + | 0.945330i | \(0.394260\pi\) | |||||||
\(734\) | 1.23171e10 | + | 1.05392e10i | 1.14967 | + | 0.983719i | ||||
\(735\) | 3.01612e10 | 2.80184 | ||||||||
\(736\) | −8.39081e9 | − | 3.52033e9i | −0.775767 | − | 0.325470i | ||||
\(737\) | 5.68801e9i | 0.523388i | ||||||||
\(738\) | 2.35045e10 | + | 2.01117e10i | 2.15256 | + | 1.84184i | ||||
\(739\) | − | 1.03818e10i | − | 0.946271i | −0.880990 | − | 0.473136i | \(-0.843122\pi\) | ||
0.880990 | − | 0.473136i | \(-0.156878\pi\) | |||||||
\(740\) | −8.61071e9 | + | 1.34777e9i | −0.781138 | + | 0.122265i | ||||
\(741\) | 2.30839e9 | + | 8.85569e8i | 0.208423 | + | 0.0799574i | ||||
\(742\) | −2.98495e7 | + | 3.48850e7i | −0.00268240 | + | 0.00313491i | ||||
\(743\) | −1.29366e10 | −1.15707 | −0.578536 | − | 0.815657i | \(-0.696376\pi\) | ||||
−0.578536 | + | 0.815657i | \(0.696376\pi\) | |||||||
\(744\) | 2.48800e10 | + | 1.53399e10i | 2.21485 | + | 1.36558i | ||||
\(745\) | 2.15140e10 | 1.90623 | ||||||||
\(746\) | 3.17473e9 | + | 2.71647e9i | 0.279976 | + | 0.239562i | ||||
\(747\) | − | 3.87639e10i | − | 3.40255i | ||||||
\(748\) | 1.33399e10 | − | 2.08799e9i | 1.16546 | − | 0.182420i | ||||
\(749\) | − | 1.77263e8i | − | 0.0154146i | ||||||
\(750\) | −1.19585e10 | + | 1.39759e10i | −1.03505 | + | 1.20967i | ||||
\(751\) | 1.47832e10 | 1.27358 | 0.636792 | − | 0.771036i | \(-0.280261\pi\) | ||||
0.636792 | + | 0.771036i | \(0.280261\pi\) | |||||||
\(752\) | −8.28410e8 | − | 2.58147e9i | −0.0710367 | − | 0.221363i | ||||
\(753\) | − | 2.82449e10i | − | 2.41078i | ||||||
\(754\) | 1.43413e9 | − | 1.67607e9i | 0.121840 | − | 0.142394i | ||||
\(755\) | 1.18602e10 | 1.00295 | ||||||||
\(756\) | 2.80855e9 | − | 4.39601e8i | 0.236405 | − | 0.0370026i | ||||
\(757\) | −3.97261e9 | −0.332844 | −0.166422 | − | 0.986055i | \(-0.553221\pi\) | ||||
−0.166422 | + | 0.986055i | \(0.553221\pi\) | |||||||
\(758\) | −5.63623e9 | + | 6.58705e9i | −0.470053 | + | 0.549349i | ||||
\(759\) | 3.03951e10 | 2.52323 | ||||||||
\(760\) | −1.53925e10 | + | 1.17495e10i | −1.27193 | + | 0.970896i | ||||
\(761\) | −2.76070e9 | −0.227077 | −0.113539 | − | 0.993534i | \(-0.536219\pi\) | ||||
−0.113539 | + | 0.993534i | \(0.536219\pi\) | |||||||
\(762\) | −1.01008e10 | + | 1.18048e10i | −0.827015 | + | 0.966530i | ||||
\(763\) | −5.89002e8 | −0.0480044 | ||||||||
\(764\) | 2.45466e9 | − | 3.84209e8i | 0.199143 | − | 0.0311702i | ||||
\(765\) | 2.97695e10 | 2.40412 | ||||||||
\(766\) | 4.55545e9 | − | 5.32395e9i | 0.366211 | − | 0.427989i | ||||
\(767\) | 2.23661e9i | 0.178981i | ||||||||
\(768\) | −1.81248e10 | + | 1.29682e10i | −1.44381 | + | 1.03304i | ||||
\(769\) | 3.09668e9 | 0.245558 | 0.122779 | − | 0.992434i | \(-0.460819\pi\) | ||||
0.122779 | + | 0.992434i | \(0.460819\pi\) | |||||||
\(770\) | −2.60559e9 | + | 3.04514e9i | −0.205678 | + | 0.240375i | ||||
\(771\) | − | 3.65256e10i | − | 2.87017i | ||||||
\(772\) | 6.40897e9 | − | 1.00315e9i | 0.501335 | − | 0.0784700i | ||||
\(773\) | − | 4.92236e9i | − | 0.383306i | −0.981463 | − | 0.191653i | \(-0.938615\pi\) | ||
0.981463 | − | 0.191653i | \(-0.0613848\pi\) | |||||||
\(774\) | 2.73375e10 | + | 2.33914e10i | 2.11917 | + | 1.81328i | ||||
\(775\) | −2.96369e10 | −2.28706 | ||||||||
\(776\) | −8.69472e9 | + | 1.41021e10i | −0.667943 | + | 1.08334i | ||||
\(777\) | −1.34233e9 | −0.102656 | ||||||||
\(778\) | 2.27830e9 | − | 2.66264e9i | 0.173453 | − | 0.202714i | ||||
\(779\) | −1.62190e10 | − | 6.22209e9i | −1.22926 | − | 0.471580i | ||||
\(780\) | −4.67727e9 | + | 7.32097e8i | −0.352908 | + | 0.0552379i | ||||
\(781\) | − | 2.51324e9i | − | 0.188780i | ||||||
\(782\) | −5.96871e9 | − | 5.10715e9i | −0.446331 | − | 0.381905i | ||||
\(783\) | 4.09350e10i | 3.04739i | ||||||||
\(784\) | −1.26717e10 | + | 4.06641e9i | −0.939133 | + | 0.301374i | ||||
\(785\) | 8.96133e9 | 0.661194 | ||||||||
\(786\) | −1.66120e10 | − | 1.42141e10i | −1.22023 | − | 1.04409i | ||||
\(787\) | −2.34994e10 | −1.71848 | −0.859241 | − | 0.511571i | \(-0.829064\pi\) | ||||
−0.859241 | + | 0.511571i | \(0.829064\pi\) | |||||||
\(788\) | −2.99388e8 | − | 1.91275e9i | −0.0217968 | − | 0.139257i | ||||
\(789\) | 5.74722e9i | 0.416570i | ||||||||
\(790\) | 1.17911e10 | − | 1.37802e10i | 0.850864 | − | 0.994402i | ||||
\(791\) | −1.65347e9 | −0.118790 | ||||||||
\(792\) | 2.66736e10 | − | 4.32623e10i | 1.90785 | − | 3.09436i | ||||
\(793\) | − | 3.67471e8i | − | 0.0261678i | ||||||
\(794\) | −1.28099e10 | + | 1.49709e10i | −0.908181 | + | 1.06139i | ||||
\(795\) | 1.41890e9i | 0.100154i | ||||||||
\(796\) | 1.62429e9 | − | 2.54238e8i | 0.114148 | − | 0.0178667i | ||||
\(797\) | 1.98702e10i | 1.39026i | 0.718882 | + | 0.695132i | \(0.244654\pi\) | ||||
−0.718882 | + | 0.695132i | \(0.755346\pi\) | |||||||
\(798\) | −2.62200e9 | + | 1.42124e9i | −0.182651 | + | 0.0990048i | ||||
\(799\) | − | 2.34052e9i | − | 0.162330i | ||||||
\(800\) | 8.74245e9 | − | 2.08379e10i | 0.603696 | − | 1.43893i | ||||
\(801\) | − | 2.20314e10i | − | 1.51471i | ||||||
\(802\) | 9.62595e9 | + | 8.23647e9i | 0.658921 | + | 0.563808i | ||||
\(803\) | − | 1.50936e10i | − | 1.02870i | ||||||
\(804\) | −1.25335e9 | − | 8.00749e9i | −0.0850504 | − | 0.543376i | ||||
\(805\) | 2.33165e9 | 0.157535 | ||||||||
\(806\) | −2.08160e9 | − | 1.78113e9i | −0.140031 | − | 0.119818i | ||||
\(807\) | − | 1.80692e10i | − | 1.21027i | ||||||
\(808\) | −1.49891e10 | − | 9.24165e9i | −0.999624 | − | 0.616325i | ||||
\(809\) | 1.11935e10 | 0.743270 | 0.371635 | − | 0.928379i | \(-0.378797\pi\) | ||||
0.371635 | + | 0.928379i | \(0.378797\pi\) | |||||||
\(810\) | 2.32599e10 | − | 2.71838e10i | 1.53784 | − | 1.79727i | ||||
\(811\) | −1.84475e10 | −1.21441 | −0.607203 | − | 0.794547i | \(-0.707709\pi\) | ||||
−0.607203 | + | 0.794547i | \(0.707709\pi\) | |||||||
\(812\) | 4.11478e8 | + | 2.62888e9i | 0.0269712 | + | 0.172316i | ||||
\(813\) | 5.68408e7i | 0.00370974i | ||||||||
\(814\) | −8.35143e9 | + | 9.76030e9i | −0.542720 | + | 0.634275i | ||||
\(815\) | 1.20604e10i | 0.780388i | ||||||||
\(816\) | −1.83196e10 | + | 5.87889e9i | −1.18032 | + | 0.378773i | ||||
\(817\) | −1.88639e10 | − | 7.23675e9i | −1.21019 | − | 0.464265i | ||||
\(818\) | 5.21062e9 | + | 4.45848e9i | 0.332853 | + | 0.284807i | ||||
\(819\) | −4.97795e8 | −0.0316634 | ||||||||
\(820\) | 3.28629e10 | − | 5.14377e9i | 2.08141 | − | 0.325787i | ||||
\(821\) | 8.29733e9 | 0.523284 | 0.261642 | − | 0.965165i | \(-0.415736\pi\) | ||||
0.261642 | + | 0.965165i | \(0.415736\pi\) | |||||||
\(822\) | 1.58642e10 | − | 1.85404e10i | 0.996246 | − | 1.16431i | ||||
\(823\) | 2.57639e10i | 1.61106i | 0.592552 | + | 0.805532i | \(0.298120\pi\) | ||||
−0.592552 | + | 0.805532i | \(0.701880\pi\) | |||||||
\(824\) | −1.51433e10 | − | 9.33670e9i | −0.942921 | − | 0.581364i | ||||
\(825\) | 7.54836e10i | 4.68019i | ||||||||
\(826\) | −2.04995e9 | − | 1.75404e9i | −0.126565 | − | 0.108295i | ||||
\(827\) | −1.38746e10 | −0.853007 | −0.426504 | − | 0.904486i | \(-0.640255\pi\) | ||||
−0.426504 | + | 0.904486i | \(0.640255\pi\) | |||||||
\(828\) | −2.92132e10 | + | 4.57251e9i | −1.78843 | + | 0.279930i | ||||
\(829\) | 1.91143e10i | 1.16525i | 0.812742 | + | 0.582624i | \(0.197974\pi\) | ||||
−0.812742 | + | 0.582624i | \(0.802026\pi\) | |||||||
\(830\) | −3.16704e10 | − | 2.70989e10i | −1.92256 | − | 1.64505i | ||||
\(831\) | −3.80250e10 | −2.29861 | ||||||||
\(832\) | 1.86636e9 | − | 9.38178e8i | 0.112348 | − | 0.0564747i | ||||
\(833\) | −1.14889e10 | −0.688686 | ||||||||
\(834\) | −3.80766e9 | − | 3.25804e9i | −0.227288 | − | 0.194480i | ||||
\(835\) | −1.38970e10 | −0.826070 | ||||||||
\(836\) | −5.97898e9 | + | 2.79074e10i | −0.353920 | + | 1.65195i | ||||
\(837\) | 5.08395e10 | 2.99683 | ||||||||
\(838\) | −5.81424e8 | − | 4.97497e8i | −0.0341302 | − | 0.0292036i | ||||
\(839\) | 5.76495e8 | 0.0336999 | 0.0168500 | − | 0.999858i | \(-0.494636\pi\) | ||||
0.0168500 | + | 0.999858i | \(0.494636\pi\) | |||||||
\(840\) | 2.99711e9 | − | 4.86105e9i | 0.174472 | − | 0.282978i | ||||
\(841\) | −2.10664e10 | −1.22125 | ||||||||
\(842\) | −2.07773e10 | − | 1.77781e10i | −1.19949 | − | 1.02635i | ||||
\(843\) | 8.42464e9i | 0.484345i | ||||||||
\(844\) | −2.99844e9 | − | 1.91567e10i | −0.171671 | − | 1.09679i | ||||
\(845\) | −2.76206e10 | −1.57484 | ||||||||
\(846\) | −6.69396e9 | − | 5.72771e9i | −0.380090 | − | 0.325226i | ||||
\(847\) | 3.83736e9i | 0.216991i | ||||||||
\(848\) | −1.91300e8 | − | 5.96124e8i | −0.0107728 | − | 0.0335700i | ||||
\(849\) | − | 6.22358e10i | − | 3.49031i | ||||||
\(850\) | 1.26832e10 | − | 1.48228e10i | 0.708373 | − | 0.827873i | ||||
\(851\) | 7.47341e9 | 0.415686 | ||||||||
\(852\) | 5.53792e8 | + | 3.53811e9i | 0.0306767 | + | 0.195989i | ||||
\(853\) | −2.05019e9 | −0.113102 | −0.0565512 | − | 0.998400i | \(-0.518010\pi\) | ||||
−0.0565512 | + | 0.998400i | \(0.518010\pi\) | |||||||
\(854\) | 3.36802e8 | + | 2.88186e8i | 0.0185043 | + | 0.0158333i | ||||
\(855\) | −2.25386e10 | + | 5.87508e10i | −1.23323 | + | 3.21464i | ||||
\(856\) | 2.05753e9 | + | 1.26858e9i | 0.112121 | + | 0.0691290i | ||||
\(857\) | − | 5.83437e9i | − | 0.316637i | −0.987388 | − | 0.158318i | \(-0.949393\pi\) | ||
0.987388 | − | 0.158318i | \(-0.0506072\pi\) | |||||||
\(858\) | −4.53644e9 | + | 5.30172e9i | −0.245194 | + | 0.286557i | ||||
\(859\) | 8.97485e9i | 0.483116i | 0.970386 | + | 0.241558i | \(0.0776583\pi\) | ||||
−0.970386 | + | 0.241558i | \(0.922342\pi\) | |||||||
\(860\) | 3.82220e10 | − | 5.98259e9i | 2.04913 | − | 0.320734i | ||||
\(861\) | 5.12301e9 | 0.273536 | ||||||||
\(862\) | −1.37881e10 | + | 1.61141e10i | −0.733211 | + | 0.856902i | ||||
\(863\) | 2.74440e10 | 1.45348 | 0.726742 | − | 0.686911i | \(-0.241034\pi\) | ||||
0.726742 | + | 0.686911i | \(0.241034\pi\) | |||||||
\(864\) | −1.49969e10 | + | 3.57455e10i | −0.791048 | + | 1.88548i | ||||
\(865\) | 1.18362e10i | 0.621807i | ||||||||
\(866\) | 2.70763e10 | + | 2.31679e10i | 1.41670 | + | 1.21220i | ||||
\(867\) | 1.74579e10 | 0.909758 | ||||||||
\(868\) | 3.26496e9 | − | 5.11038e8i | 0.169456 | − | 0.0265237i | ||||
\(869\) | − | 2.67306e10i | − | 1.38178i | ||||||
\(870\) | 6.24822e10 | + | 5.34631e10i | 3.21691 | + | 2.75256i | ||||
\(871\) | 7.59678e8i | 0.0389552i | ||||||||
\(872\) | 4.21519e9 | − | 6.83667e9i | 0.215283 | − | 0.349170i | ||||
\(873\) | 5.38354e10i | 2.73854i | ||||||||
\(874\) | 1.45980e10 | − | 7.91275e9i | 0.739611 | − | 0.400901i | ||||
\(875\) | 2.07966e9i | 0.104946i | ||||||||
\(876\) | 3.32586e9 | + | 2.12485e10i | 0.167163 | + | 1.06798i | ||||
\(877\) | − | 1.47541e10i | − | 0.738610i | −0.929308 | − | 0.369305i | \(-0.879596\pi\) | ||
0.929308 | − | 0.369305i | \(-0.120404\pi\) | |||||||
\(878\) | 2.23279e10 | − | 2.60946e10i | 1.11331 | − | 1.30113i | ||||
\(879\) | − | 6.56867e10i | − | 3.26224i | ||||||
\(880\) | −1.66987e10 | − | 5.20362e10i | −0.826027 | − | 2.57404i | ||||
\(881\) | 6.76561e9 | 0.333343 | 0.166672 | − | 0.986012i | \(-0.446698\pi\) | ||||
0.166672 | + | 0.986012i | \(0.446698\pi\) | |||||||
\(882\) | −2.81156e10 | + | 3.28586e10i | −1.37977 | + | 1.61254i | ||||
\(883\) | 2.06807e10i | 1.01089i | 0.862860 | + | 0.505443i | \(0.168671\pi\) | ||||
−0.862860 | + | 0.505443i | \(0.831329\pi\) | |||||||
\(884\) | 1.78165e9 | − | 2.78868e8i | 0.0867440 | − | 0.0135774i | ||||
\(885\) | −8.33788e10 | −4.04347 | ||||||||
\(886\) | 9.90604e9 | + | 8.47614e9i | 0.478500 | + | 0.409430i | ||||
\(887\) | 3.04308e10 | 1.46414 | 0.732068 | − | 0.681232i | \(-0.238555\pi\) | ||||
0.732068 | + | 0.681232i | \(0.238555\pi\) | |||||||
\(888\) | 9.60635e9 | − | 1.55806e10i | 0.460376 | − | 0.746690i | ||||
\(889\) | 1.75659e9i | 0.0838521i | ||||||||
\(890\) | −1.79999e10 | − | 1.54016e10i | −0.855862 | − | 0.732321i | ||||
\(891\) | − | 5.27305e10i | − | 2.49741i | ||||||
\(892\) | −5.55046e9 | − | 3.54612e10i | −0.261850 | − | 1.67292i | ||||
\(893\) | 4.61907e9 | + | 1.77201e9i | 0.217057 | + | 0.0832697i | ||||
\(894\) | −2.93752e10 | + | 3.43307e10i | −1.37499 | + | 1.60695i | ||||
\(895\) | 1.35380e10 | 0.631212 | ||||||||
\(896\) | −6.03799e8 | + | 2.44635e9i | −0.0280424 | + | 0.113616i | ||||
\(897\) | 4.05950e9 | 0.187801 | ||||||||
\(898\) | 7.38485e9 | + | 6.31887e9i | 0.340310 | + | 0.291187i | ||||
\(899\) | 4.75871e10i | 2.18439i | ||||||||
\(900\) | −1.13555e10 | − | 7.25485e10i | −0.519225 | − | 3.31726i | ||||
\(901\) | − | 5.40483e8i | − | 0.0246176i | ||||||
\(902\) | 3.18734e10 | − | 3.72504e10i | 1.44612 | − | 1.69008i | ||||
\(903\) | 5.95844e9 | 0.269293 | ||||||||
\(904\) | 1.18331e10 | − | 1.91922e10i | 0.532731 | − | 0.864042i | ||||
\(905\) | 4.31713e10i | 1.93609i | ||||||||
\(906\) | −1.61939e10 | + | 1.89257e10i | −0.723440 | + | 0.845482i | ||||
\(907\) | −1.08794e10 | −0.484149 | −0.242074 | − | 0.970258i | \(-0.577828\pi\) | ||||
−0.242074 | + | 0.970258i | \(0.577828\pi\) | |||||||
\(908\) | 3.05181e8 | + | 1.94976e9i | 0.0135287 | + | 0.0864334i | ||||
\(909\) | −5.72219e10 | −2.52690 | ||||||||
\(910\) | −3.47997e8 | + | 4.06703e8i | −0.0153084 | + | 0.0178909i | ||||
\(911\) | 4.07735e10 | 1.78675 | 0.893374 | − | 0.449313i | \(-0.148331\pi\) | ||||
0.893374 | + | 0.449313i | \(0.148331\pi\) | |||||||
\(912\) | 2.26774e9 | − | 4.06051e10i | 0.0989944 | − | 1.77255i | ||||
\(913\) | −6.14336e10 | −2.67152 | ||||||||
\(914\) | −2.46053e10 | + | 2.87562e10i | −1.06590 | + | 1.24572i | ||||
\(915\) | 1.36990e10 | 0.591172 | ||||||||
\(916\) | −4.06725e9 | − | 2.59851e10i | −0.174850 | − | 1.11710i | ||||
\(917\) | −2.47191e9 | −0.105862 | ||||||||
\(918\) | −2.17568e10 | + | 2.54271e10i | −0.928210 | + | 1.08480i | ||||
\(919\) | 2.57661e10i | 1.09508i | 0.836781 | + | 0.547538i | \(0.184435\pi\) | ||||
−0.836781 | + | 0.547538i | \(0.815565\pi\) | |||||||
\(920\) | −1.66865e10 | + | 2.70639e10i | −0.706491 | + | 1.14587i | ||||
\(921\) | 4.67933e10 | 1.97367 | ||||||||
\(922\) | −2.40848e10 | + | 2.81478e10i | −1.01201 | + | 1.18273i | ||||
\(923\) | − | 3.35663e8i | − | 0.0140507i | ||||||
\(924\) | −1.30158e9 | − | 8.31566e9i | −0.0542776 | − | 0.346772i | ||||
\(925\) | 1.85596e10i | 0.771032i | ||||||||
\(926\) | −6.30851e9 | − | 5.39790e9i | −0.261089 | − | 0.223401i | ||||
\(927\) | −5.78104e10 | −2.38357 | ||||||||
\(928\) | −3.34587e10 | − | 1.40375e10i | −1.37433 | − | 0.576595i | ||||
\(929\) | 1.46881e10 | 0.601050 | 0.300525 | − | 0.953774i | \(-0.402838\pi\) | ||||
0.300525 | + | 0.953774i | \(0.402838\pi\) | |||||||
\(930\) | 6.63988e10 | − | 7.76001e10i | 2.70689 | − | 3.16353i | ||||
\(931\) | 8.69829e9 | − | 2.26736e10i | 0.353272 | − | 0.920867i | ||||
\(932\) | 6.79346e9 | + | 4.34025e10i | 0.274875 | + | 1.75614i | ||||
\(933\) | 6.40965e10i | 2.58374i | ||||||||
\(934\) | −4.44729e9 | − | 3.80534e9i | −0.178600 | − | 0.152820i | ||||
\(935\) | − | 4.71792e10i | − | 1.88760i | ||||||
\(936\) | 3.56247e9 | − | 5.77801e9i | 0.141999 | − | 0.230310i | ||||
\(937\) | 2.17946e10 | 0.865487 | 0.432744 | − | 0.901517i | \(-0.357546\pi\) | ||||
0.432744 | + | 0.901517i | \(0.357546\pi\) | |||||||
\(938\) | −6.96276e8 | − | 5.95771e8i | −0.0275468 | − | 0.0235705i | ||||
\(939\) | −3.75276e10 | −1.47918 | ||||||||
\(940\) | −9.35917e9 | + | 1.46492e9i | −0.367527 | + | 0.0575262i | ||||
\(941\) | 2.95166e10i | 1.15479i | 0.816466 | + | 0.577394i | \(0.195930\pi\) | ||||
−0.816466 | + | 0.577394i | \(0.804070\pi\) | |||||||
\(942\) | −1.22358e10 | + | 1.42999e10i | −0.476928 | + | 0.557385i | ||||
\(943\) | −2.85224e10 | −1.10763 | ||||||||
\(944\) | 3.50300e10 | − | 1.12413e10i | 1.35531 | − | 0.434927i | ||||
\(945\) | − | 9.93300e9i | − | 0.382886i | ||||||
\(946\) | 3.70711e10 | − | 4.33249e10i | 1.42369 | − | 1.66387i | ||||
\(947\) | − | 1.05941e10i | − | 0.405358i | −0.979245 | − | 0.202679i | \(-0.935035\pi\) | ||
0.979245 | − | 0.202679i | \(-0.0649648\pi\) | |||||||
\(948\) | 5.89009e9 | + | 3.76310e10i | 0.224539 | + | 1.43455i | ||||
\(949\) | − | 2.01587e9i | − | 0.0765649i | ||||||
\(950\) | 1.96507e10 | + | 3.62529e10i | 0.743608 | + | 1.37186i | ||||
\(951\) | 6.08051e10i | 2.29249i | ||||||||
\(952\) | −1.14165e9 | + | 1.85165e9i | −0.0428848 | + | 0.0695553i | ||||
\(953\) | − | 2.76760e10i | − | 1.03581i | −0.855439 | − | 0.517903i | \(-0.826713\pi\) | ||
0.855439 | − | 0.517903i | \(-0.173287\pi\) | |||||||
\(954\) | −1.54580e9 | − | 1.32267e9i | −0.0576412 | − | 0.0493209i | ||||
\(955\) | − | 8.68138e9i | − | 0.322535i | ||||||
\(956\) | 1.78936e10 | − | 2.80074e9i | 0.662361 | − | 0.103674i | ||||
\(957\) | 1.21202e11 | 4.47009 | ||||||||
\(958\) | 2.86771e9 | + | 2.45376e9i | 0.105379 | + | 0.0901682i | ||||
\(959\) | − | 2.75888e9i | − | 0.101011i | ||||||
\(960\) | 3.49744e10 | + | 6.95762e10i | 1.27585 | + | 2.53811i | ||||
\(961\) | 3.15885e10 | 1.14815 | ||||||||
\(962\) | −1.11540e9 | + | 1.30357e9i | −0.0403941 | + | 0.0472085i | ||||
\(963\) | 7.85473e9 | 0.283426 | ||||||||
\(964\) | −8.99901e9 | + | 1.40854e9i | −0.323538 | + | 0.0506408i | ||||
\(965\) | − | 2.26666e10i | − | 0.811971i | ||||||
\(966\) | −3.18363e9 | + | 3.72070e9i | −0.113632 | + | 0.132802i | ||||
\(967\) | 3.10111e10i | 1.10287i | 0.834217 | + | 0.551436i | \(0.185920\pi\) | ||||
−0.834217 | + | 0.551436i | \(0.814080\pi\) | |||||||
\(968\) | −4.45411e10 | − | 2.74621e10i | −1.57833 | − | 0.973128i | ||||
\(969\) | 1.25753e10 | − | 3.27796e10i | 0.444001 | − | 1.15737i | ||||
\(970\) | 4.39840e10 | + | 3.76350e10i | 1.54737 | + | 1.32401i | ||||
\(971\) | 2.13027e10 | 0.746736 | 0.373368 | − | 0.927683i | \(-0.378203\pi\) | ||||
0.373368 | + | 0.927683i | \(0.378203\pi\) | |||||||
\(972\) | 2.56637e9 | + | 1.63962e10i | 0.0896371 | + | 0.572680i | ||||
\(973\) | −5.66593e8 | −0.0197186 | ||||||||
\(974\) | 1.36186e10 | − | 1.59160e10i | 0.472254 | − | 0.551922i | ||||
\(975\) | 1.00814e10i | 0.348342i | ||||||||
\(976\) | −5.75536e9 | + | 1.84693e9i | −0.198152 | + | 0.0635881i | ||||
\(977\) | − | 2.76538e10i | − | 0.948688i | −0.880340 | − | 0.474344i | \(-0.842685\pi\) | ||
0.880340 | − | 0.474344i | \(-0.157315\pi\) | |||||||
\(978\) | −1.92452e10 | − | 1.64673e10i | −0.657866 | − | 0.562905i | ||||
\(979\) | −3.49157e10 | −1.18927 | ||||||||
\(980\) | 7.19084e9 | + | 4.59413e10i | 0.244055 | + | 1.55924i | ||||
\(981\) | − | 2.60994e10i | − | 0.882650i | ||||||
\(982\) | −9.27957e9 | − | 7.94010e9i | −0.312707 | − | 0.267569i | ||||
\(983\) | −1.68773e10 | −0.566715 | −0.283357 | − | 0.959014i | \(-0.591448\pi\) | ||||
−0.283357 | + | 0.959014i | \(0.591448\pi\) | |||||||
\(984\) | −3.66628e10 | + | 5.94638e10i | −1.22671 | + | 1.98962i | ||||
\(985\) | −6.76483e9 | −0.225543 | ||||||||
\(986\) | −2.38005e10 | − | 2.03650e10i | −0.790709 | − | 0.676573i | ||||
\(987\) | −1.45900e9 | −0.0482999 | ||||||||
\(988\) | −7.98540e8 | + | 3.72726e9i | −0.0263419 | + | 0.122953i | ||||
\(989\) | −3.31737e10 | −1.09045 | ||||||||
\(990\) | −1.34934e11 | − | 1.15457e11i | −4.41975 | − | 3.78178i | ||||
\(991\) | −4.78133e10 | −1.56060 | −0.780299 | − | 0.625407i | \(-0.784933\pi\) | ||||
−0.780299 | + | 0.625407i | \(0.784933\pi\) | |||||||
\(992\) | −1.74339e10 | + | 4.15543e10i | −0.567028 | + | 1.35153i | ||||
\(993\) | 4.53464e9 | 0.146967 | ||||||||
\(994\) | 3.07649e8 | + | 2.63241e8i | 0.00993581 | + | 0.00850160i | ||||
\(995\) | − | 5.74463e9i | − | 0.184876i | ||||||
\(996\) | 8.64853e10 | − | 1.35369e10i | 2.77354 | − | 0.434121i | ||||
\(997\) | −1.83879e10 | −0.587623 | −0.293812 | − | 0.955863i | \(-0.594924\pi\) | ||||
−0.293812 | + | 0.955863i | \(0.594924\pi\) | |||||||
\(998\) | 1.84390e10 | + | 1.57774e10i | 0.587191 | + | 0.502432i | ||||
\(999\) | − | 3.18373e10i | − | 1.01031i |
(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 | 76.8.d.a.75.20 | yes | 68 | |
4.3 | odd | 2 | inner | 76.8.d.a.75.50 | yes | 68 | |
19.18 | odd | 2 | inner | 76.8.d.a.75.49 | yes | 68 | |
76.75 | even | 2 | inner | 76.8.d.a.75.19 | ✓ | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.8.d.a.75.19 | ✓ | 68 | 76.75 | even | 2 | inner | |
76.8.d.a.75.20 | yes | 68 | 1.1 | even | 1 | trivial | |
76.8.d.a.75.49 | yes | 68 | 19.18 | odd | 2 | inner | |
76.8.d.a.75.50 | yes | 68 | 4.3 | odd | 2 | inner |