Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,12,Mod(17,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.17");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.e (of order \(4\), degree \(2\), 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: | \(49.1739635558\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(21\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.8 | ||
Character | \(\chi\) | \(=\) | 64.17 |
Dual form | 64.12.e.a.49.8 |
$q$-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 \(\left(\mathbb{Z}/64\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(63\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −219.312 | − | 219.312i | −0.521069 | − | 0.521069i | 0.396825 | − | 0.917894i | \(-0.370112\pi\) |
−0.917894 | + | 0.396825i | \(0.870112\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4575.66 | + | 4575.66i | −0.654815 | + | 0.654815i | −0.954149 | − | 0.299333i | \(-0.903236\pi\) |
0.299333 | + | 0.954149i | \(0.403236\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2778.29i | 0.0624796i | 0.999512 | + | 0.0312398i | \(0.00994555\pi\) | ||||
−0.999512 | + | 0.0312398i | \(0.990054\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 80951.6i | − | 0.456974i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17312.0 | + | 17312.0i | −0.0324106 | + | 0.0324106i | −0.723126 | − | 0.690716i | \(-0.757296\pi\) |
0.690716 | + | 0.723126i | \(0.257296\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.16637e6 | − | 1.16637e6i | −0.871263 | − | 0.871263i | 0.121347 | − | 0.992610i | \(-0.461278\pi\) |
−0.992610 | + | 0.121347i | \(0.961278\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00699e6 | 0.682408 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.63947e6 | −1.30495 | −0.652475 | − | 0.757810i | \(-0.726269\pi\) | ||||
−0.652475 | + | 0.757810i | \(0.726269\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.62010e6 | − | 1.62010e6i | −0.150106 | − | 0.150106i | 0.628060 | − | 0.778165i | \(-0.283849\pi\) |
−0.778165 | + | 0.628060i | \(0.783849\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 609312. | − | 609312.i | 0.0325562 | − | 0.0325562i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.41251e7i | 1.10553i | 0.833337 | + | 0.552765i | \(0.186427\pi\) | ||||
−0.833337 | + | 0.552765i | \(0.813573\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.95479e6i | 0.142434i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.66041e7 | + | 5.66041e7i | −0.759184 | + | 0.759184i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.22501e7 | − | 5.22501e7i | −0.473041 | − | 0.473041i | 0.429856 | − | 0.902897i | \(-0.358564\pi\) |
−0.902897 | + | 0.429856i | \(0.858564\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.70466e8 | 1.06942 | 0.534710 | − | 0.845035i | \(-0.320421\pi\) | ||||
0.534710 | + | 0.845035i | \(0.320421\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.59345e6 | 0.0337763 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.27125e7 | − | 1.27125e7i | −0.0409126 | − | 0.0409126i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.36013e8 | − | 1.36013e8i | 0.322455 | − | 0.322455i | −0.527253 | − | 0.849708i | \(-0.676778\pi\) |
0.849708 | + | 0.527253i | \(0.176778\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.11599e8i | 0.907976i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.43574e8i | − | 1.27193i | −0.771716 | − | 0.635967i | \(-0.780601\pi\) | ||
0.771716 | − | 0.635967i | \(-0.219399\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.75831e8 | − | 1.75831e8i | 0.182397 | − | 0.182397i | −0.610002 | − | 0.792400i | \(-0.708831\pi\) |
0.792400 | + | 0.610002i | \(0.208831\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.70407e8 | + | 3.70407e8i | 0.299233 | + | 0.299233i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.33824e9 | 1.48714 | 0.743569 | − | 0.668660i | \(-0.233132\pi\) | ||||
0.743569 | + | 0.668660i | \(0.233132\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.96961e9 | 0.996096 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.67543e9 | + | 1.67543e9i | 0.679969 | + | 0.679969i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.13123e9 | + | 2.13123e9i | −0.700023 | + | 0.700023i | −0.964415 | − | 0.264392i | \(-0.914829\pi\) |
0.264392 | + | 0.964415i | \(0.414829\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.58428e8i | − | 0.0424459i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.10614e8i | 0.156431i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.73656e8 | − | 2.73656e8i | 0.0498333 | − | 0.0498333i | −0.681751 | − | 0.731584i | \(-0.738781\pi\) |
0.731584 | + | 0.681751i | \(0.238781\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.10089e9 | + | 7.10089e9i | 1.07646 | + | 1.07646i | 0.996824 | + | 0.0796382i | \(0.0253765\pi\) |
0.0796382 | + | 0.996824i | \(0.474624\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.24907e8 | 0.0285515 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.06739e10 | 1.14103 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.25789e9 | − | 6.25789e9i | −0.566261 | − | 0.566261i | 0.364818 | − | 0.931079i | \(-0.381131\pi\) |
−0.931079 | + | 0.364818i | \(0.881131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.48403e9 | − | 7.48403e9i | 0.576057 | − | 0.576057i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.05701e9i | − | 0.201083i | −0.994933 | − | 0.100542i | \(-0.967942\pi\) | ||
0.994933 | − | 0.100542i | \(-0.0320576\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.14465e10i | 1.77540i | 0.460420 | + | 0.887701i | \(0.347699\pi\) | ||||
−0.460420 | + | 0.887701i | \(0.652301\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.52527e9 | − | 1.52527e9i | 0.0742180 | − | 0.0742180i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.80977e7 | − | 4.80977e7i | −0.00202500 | − | 0.00202500i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.76542e10 | 1.74242 | 0.871209 | − | 0.490912i | \(-0.163336\pi\) | ||||
0.871209 | + | 0.490912i | \(0.163336\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.04876e10 | 0.334201 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.66019e10 | + | 4.66019e10i | 1.29860 | + | 1.29860i | 0.929320 | + | 0.369276i | \(0.120394\pi\) |
0.369276 | + | 0.929320i | \(0.379606\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.49556e10 | − | 3.49556e10i | 0.854501 | − | 0.854501i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.29182e10i | 0.492974i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.17108e10i | 0.222300i | 0.993804 | + | 0.111150i | \(0.0354534\pi\) | ||||
−0.993804 | + | 0.111150i | \(0.964547\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.24052e9 | − | 3.24052e9i | 0.0544361 | − | 0.0544361i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.73852e10 | − | 3.73852e10i | −0.557242 | − | 0.557242i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.48261e10 | 0.196583 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.59417e10 | 0.424966 | 0.212483 | − | 0.977165i | \(-0.431845\pi\) | ||||
0.212483 | + | 0.977165i | \(0.431845\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.40143e9 | + | 1.40143e9i | 0.0148108 | + | 0.0148108i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.25749e9 | − | 4.25749e9i | 0.0403075 | − | 0.0403075i | −0.686666 | − | 0.726973i | \(-0.740926\pi\) |
0.726973 | + | 0.686666i | \(0.240926\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.38400e10i | − | 0.712601i | −0.934371 | − | 0.356301i | \(-0.884038\pi\) | ||
0.934371 | − | 0.356301i | \(-0.115962\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.57601e9i | 0.0426366i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.39681e11 | + | 1.39681e11i | −0.962782 | + | 0.962782i | −0.999332 | − | 0.0365502i | \(-0.988363\pi\) |
0.0365502 | + | 0.999332i | \(0.488363\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.03674e11 | − | 1.03674e11i | −0.645393 | − | 0.645393i | 0.306483 | − | 0.951876i | \(-0.400848\pi\) |
−0.951876 | + | 0.306483i | \(0.900848\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.96583e10 | −0.336043 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.37338e10 | −0.223298 | −0.111649 | − | 0.993748i | \(-0.535613\pi\) | ||||
−0.111649 | + | 0.993748i | \(0.535613\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.56145e11 | − | 1.56145e11i | −0.723917 | − | 0.723917i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.44197e10 | + | 9.44197e10i | −0.398144 | + | 0.398144i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.12246e10i | − | 0.0815328i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.84712e11i | 0.997899i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.06937e11 | + | 2.06937e11i | −0.662765 | + | 0.662765i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.55244e11 | − | 2.55244e11i | −0.748083 | − | 0.748083i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00265e11 | 1.61221 | 0.806107 | − | 0.591770i | \(-0.201570\pi\) | ||||
0.806107 | + | 0.591770i | \(0.201570\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.71236e10 | −0.190083 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.08704e11 | − | 6.08704e11i | −1.37852 | − | 1.37852i | −0.847117 | − | 0.531407i | \(-0.821663\pi\) |
−0.531407 | − | 0.847117i | \(-0.678337\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.50111e9 | − | 4.50111e9i | 0.00937854 | − | 0.00937854i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 5.18002e11i | − | 0.994251i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.71507e11i | 0.657663i | 0.944389 | + | 0.328832i | \(0.106655\pi\) | ||||
−0.944389 | + | 0.328832i | \(0.893345\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.19881e11 | + | 4.19881e11i | −0.686348 | + | 0.686348i | −0.961423 | − | 0.275075i | \(-0.911297\pi\) |
0.275075 | + | 0.961423i | \(0.411297\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.12804e11 | − | 5.12804e11i | −0.774901 | − | 0.774901i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.03845e10 | 0.0564763 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.78158e11 | 0.619509 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.31958e11 | − | 4.31958e11i | −0.519035 | − | 0.519035i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.05211e11 | − | 5.05211e11i | 0.563571 | − | 0.563571i | −0.366749 | − | 0.930320i | \(-0.619529\pi\) |
0.930320 | + | 0.366749i | \(0.119529\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.08446e11i | − | 0.838065i | −0.907971 | − | 0.419033i | \(-0.862369\pi\) | ||
0.907971 | − | 0.419033i | \(-0.137631\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.18427e11i | 0.596328i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.79995e11 | + | 7.79995e11i | −0.700273 | + | 0.700273i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.30037e11 | − | 7.30037e11i | −0.610797 | − | 0.610797i | 0.332357 | − | 0.943154i | \(-0.392156\pi\) |
−0.943154 | + | 0.332357i | \(0.892156\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.34807e11 | 0.729521 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.48093e10 | −0.0690730 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.03848e11 | + | 9.03848e11i | 0.615267 | + | 0.615267i | 0.944314 | − | 0.329047i | \(-0.106727\pi\) |
−0.329047 | + | 0.944314i | \(0.606727\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.47450e10 | + | 3.47450e10i | −0.0221173 | + | 0.0221173i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.22636e12i | 1.32634i | 0.748469 | + | 0.663170i | \(0.230789\pi\) | ||||
−0.748469 | + | 0.663170i | \(0.769211\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.28692e11i | 0.518197i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.31150e11 | + | 1.31150e11i | −0.0685944 | + | 0.0685944i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.98524e11 | − | 6.98524e11i | −0.342711 | − | 0.342711i | 0.514675 | − | 0.857385i | \(-0.327913\pi\) |
−0.857385 | + | 0.514675i | \(0.827913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.93224e10 | −0.00889922 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.20032e11 | −0.0519332 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.78923e12 | + | 2.78923e12i | 1.13447 | + | 1.13447i | 0.989425 | + | 0.145044i | \(0.0463322\pi\) |
0.145044 | + | 0.989425i | \(0.453668\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.65718e11 | − | 8.65718e11i | 0.331241 | − | 0.331241i | −0.521817 | − | 0.853058i | \(-0.674745\pi\) |
0.853058 | + | 0.521817i | \(0.174745\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.11462e12i | − | 1.12182i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.24469e12i | 0.422297i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.32254e11 | − | 1.32254e11i | 0.0422942 | − | 0.0422942i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.57263e11 | − | 1.57263e11i | −0.0474335 | − | 0.0474335i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.97152e12 | 1.13051 | 0.565254 | − | 0.824917i | \(-0.308778\pi\) | ||||
0.565254 | + | 0.824917i | \(0.308778\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.02696e12 | 1.35126 | 0.675632 | − | 0.737239i | \(-0.263871\pi\) | ||||
0.675632 | + | 0.737239i | \(0.263871\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.34090e12 | − | 2.34090e12i | −0.594557 | − | 0.594557i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.21725e12 | − | 2.21725e12i | 0.532415 | − | 0.532415i | −0.388876 | − | 0.921290i | \(-0.627136\pi\) |
0.921290 | + | 0.388876i | \(0.127136\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.69752e12i | 0.385588i | 0.981239 | + | 0.192794i | \(0.0617548\pi\) | ||||
−0.981239 | + | 0.192794i | \(0.938245\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.74486e12i | 0.590122i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.45166e11 | − | 1.45166e11i | 0.0295554 | − | 0.0295554i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.31747e12 | + | 4.31747e12i | 0.832882 | + | 0.832882i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.76248e12 | 0.505198 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.60943e10 | 0.00973003 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.20649e12 | − | 1.20649e12i | −0.198596 | − | 0.198596i | 0.600802 | − | 0.799398i | \(-0.294848\pi\) |
−0.799398 | + | 0.600802i | \(0.794848\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.70439e11 | + | 6.70439e11i | −0.104778 | + | 0.104778i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.60908e12i | 0.238873i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.73604e11i | 0.0668170i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.89660e12 | − | 6.89660e12i | 0.925108 | − | 0.925108i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.91047e12 | + | 8.91047e12i | 1.13695 | + | 1.13695i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.81312e12 | −0.463025 | −0.231512 | − | 0.972832i | \(-0.574367\pi\) | ||||
−0.231512 | + | 0.972832i | \(0.574367\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.63001e11 | 0.0650887 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.20437e12 | − | 2.20437e12i | −0.242740 | − | 0.242740i | 0.575243 | − | 0.817983i | \(-0.304908\pi\) |
−0.817983 | + | 0.575243i | \(0.804908\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.95781e12 | + | 6.95781e12i | −0.730092 | + | 0.730092i | −0.970638 | − | 0.240546i | \(-0.922673\pi\) |
0.240546 | + | 0.970638i | \(0.422673\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.10968e10i | 0.00211033i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.59857e13i | − | 1.52502i | −0.646977 | − | 0.762510i | \(-0.723967\pi\) | ||
0.646977 | − | 0.762510i | \(-0.276033\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.06990e13 | + | 1.06990e13i | −0.973800 | + | 0.973800i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.04511e13 | − | 1.04511e13i | −0.907920 | − | 0.907920i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.48081e13 | −1.22831 | −0.614157 | − | 0.789184i | \(-0.710504\pi\) | ||||
−0.614157 | + | 0.789184i | \(0.710504\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00810e13 | −0.798750 | −0.399375 | − | 0.916788i | \(-0.630773\pi\) | ||||
−0.399375 | + | 0.916788i | \(0.630773\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.72719e12 | + | 7.72719e12i | 0.585042 | + | 0.585042i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.01226e12 | + | 9.01226e12i | −0.652259 | + | 0.652259i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.77928e12i | 0.261563i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 2.04407e13i | − | 1.35332i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.01824e13 | − | 2.01824e13i | 1.27870 | − | 1.27870i | 0.337302 | − | 0.941397i | \(-0.390486\pi\) |
0.941397 | − | 0.337302i | \(-0.109514\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.90772e11 | − | 5.90772e11i | −0.0358309 | − | 0.0358309i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.53324e13 | −0.890509 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.83439e13 | −1.57699 | −0.788493 | − | 0.615044i | \(-0.789138\pi\) | ||||
−0.788493 | + | 0.615044i | \(0.789138\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.77882e11 | + | 3.77882e11i | 0.0201469 | + | 0.0201469i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.22973e12 | + | 4.22973e12i | −0.216167 | + | 0.216167i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.43628e13i | 0.703855i | 0.936027 | + | 0.351928i | \(0.114474\pi\) | ||||
−0.936027 | + | 0.351928i | \(0.885526\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.95035e13i | − | 0.916772i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.56831e12 | − | 2.56831e12i | 0.115834 | − | 0.115834i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.53045e13 | + | 1.53045e13i | 0.662492 | + | 0.662492i | 0.955967 | − | 0.293475i | \(-0.0948116\pi\) |
−0.293475 | + | 0.955967i | \(0.594812\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.43046e13 | −1.42568 | −0.712838 | − | 0.701329i | \(-0.752590\pi\) | ||||
−0.712838 | + | 0.701329i | \(0.752590\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.42137e12 | −0.0567300 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.20401e11 | − | 1.20401e11i | −0.00461637 | − | 0.00461637i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.09049e13 | − | 3.09049e13i | 1.13864 | − | 1.13864i | 0.149951 | − | 0.988693i | \(-0.452088\pi\) |
0.988693 | − | 0.149951i | \(-0.0479117\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.37995e13i | − | 0.488697i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.94675e13i | 1.00336i | 0.865052 | + | 0.501682i | \(0.167285\pi\) | ||||
−0.865052 | + | 0.501682i | \(0.832715\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.63667e12 | + | 7.63667e12i | −0.250080 | + | 0.250080i | −0.821003 | − | 0.570923i | \(-0.806585\pi\) |
0.570923 | + | 0.821003i | \(0.306585\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.25153e12 | − | 3.25153e12i | −0.102433 | − | 0.102433i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.62152e12 | 0.0794699 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.40896e13 | 0.702896 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.88244e12 | − | 7.88244e12i | −0.221437 | − | 0.221437i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.88996e13 | + | 1.88996e13i | −0.511307 | + | 0.511307i | −0.914927 | − | 0.403620i | \(-0.867752\pi\) |
0.403620 | + | 0.914927i | \(0.367752\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.50432e12i | 0.0652632i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.95986e12i | − | 0.0492112i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.98025e13 | − | 3.98025e13i | 0.963206 | − | 0.963206i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.88509e11 | + | 4.88509e11i | 0.0113961 | + | 0.0113961i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.86744e12 | −0.0420060 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.49825e13 | −1.40977 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.05621e12 | + | 8.05621e12i | 0.168605 | + | 0.168605i | 0.786366 | − | 0.617761i | \(-0.211960\pi\) |
−0.617761 | + | 0.786366i | \(0.711960\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.83871e13 | + | 1.83871e13i | −0.371315 | + | 0.371315i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2.29206e13i | − | 0.446729i | −0.974735 | − | 0.223365i | \(-0.928296\pi\) | ||
0.974735 | − | 0.223365i | \(-0.0717041\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.16826e13i | − | 0.219809i | −0.993942 | − | 0.109904i | \(-0.964946\pi\) | ||
0.993942 | − | 0.109904i | \(-0.0350544\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.02910e12 | + | 1.02910e12i | −0.0186960 | + | 0.0186960i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.67319e13 | + | 4.67319e13i | 0.819950 | + | 0.819950i | 0.986100 | − | 0.166150i | \(-0.0531337\pi\) |
−0.166150 | + | 0.986100i | \(0.553134\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.80911e12 | 0.0306631 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.12676e13 | 1.00335 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.23767e13 | + | 1.23767e13i | 0.195880 | + | 0.195880i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.11188e12 | − | 8.11188e12i | 0.124097 | − | 0.124097i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.54739e13i | 0.672588i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.49631e12i | 0.0929157i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.48513e13 | + | 2.48513e13i | −0.343791 | + | 0.343791i | −0.857790 | − | 0.514000i | \(-0.828163\pi\) |
0.514000 | + | 0.857790i | \(0.328163\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.10104e13 | − | 1.10104e13i | −0.147354 | − | 0.147354i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.72680e13 | 0.741593 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.14158e14 | 1.43068 | 0.715342 | − | 0.698775i | \(-0.246271\pi\) | ||||
0.715342 | + | 0.698775i | \(0.246271\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.59133e12 | + | 9.59133e12i | 0.116354 | + | 0.116354i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.95111e12 | + | 2.95111e12i | −0.0346606 | + | 0.0346606i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.09657e13i | 0.124715i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.84888e13i | 0.754422i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.86725e13 | + | 6.86725e13i | −0.732776 | + | 0.732776i | −0.971169 | − | 0.238393i | \(-0.923379\pi\) |
0.238393 | + | 0.971169i | \(0.423379\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.60520e13 | + | 5.60520e13i | 0.579497 | + | 0.579497i | 0.934765 | − | 0.355268i | \(-0.115610\pi\) |
−0.355268 | + | 0.934765i | \(0.615610\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.32043e14 | 1.32290 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.46239e13 | 0.530423 | 0.265211 | − | 0.964190i | \(-0.414558\pi\) | ||||
0.265211 | + | 0.964190i | \(0.414558\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.39878e13 | + | 1.39878e13i | 0.131672 | + | 0.131672i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.65482e12 | + | 4.65482e12i | −0.0424842 | + | 0.0424842i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 3.93500e13i | − | 0.348278i | −0.984721 | − | 0.174139i | \(-0.944286\pi\) | ||
0.984721 | − | 0.174139i | \(-0.0557141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.11241e14i | − | 0.954937i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.24408e13 | − | 6.24408e13i | 0.519974 | − | 0.519974i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.43889e14 | − | 1.43889e14i | −1.16256 | − | 1.16256i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.36804e14 | 1.07260 | 0.536299 | − | 0.844028i | \(-0.319822\pi\) | ||||
0.536299 | + | 0.844028i | \(0.319822\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.63838e13 | −0.581241 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.92116e12 | − | 5.92116e12i | −0.0437372 | − | 0.0437372i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.67793e14 | − | 1.67793e14i | 1.20331 | − | 1.20331i | 0.230152 | − | 0.973155i | \(-0.426078\pi\) |
0.973155 | − | 0.230152i | \(-0.0739224\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.11956e14i | 0.779606i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.21886e14i | 0.824285i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.77288e13 | + | 8.77288e13i | −0.576271 | + | 0.576271i | −0.933874 | − | 0.357603i | \(-0.883594\pi\) |
0.357603 | + | 0.933874i | \(0.383594\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.31645e14 | − | 1.31645e14i | −0.840075 | − | 0.840075i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.00616e13 | 0.372395 | 0.186197 | − | 0.982512i | \(-0.440384\pi\) | ||||
0.186197 | + | 0.982512i | \(0.440384\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.40157e11 | 0.00265200 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.42338e13 | − | 1.42338e13i | −0.0833508 | − | 0.0833508i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.16819e13 | + | 3.16819e13i | −0.180339 | + | 0.180339i | −0.791503 | − | 0.611165i | \(-0.790701\pi\) |
0.611165 | + | 0.791503i | \(0.290701\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.60697e14i | − | 1.44266i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.66992e14i | 1.43661i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.18050e14 | + | 2.18050e14i | −1.14096 | + | 1.14096i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.07399e13 | − | 9.07399e13i | −0.461796 | − | 0.461796i | 0.437448 | − | 0.899244i | \(-0.355883\pi\) |
−0.899244 | + | 0.437448i | \(0.855883\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.97429e12 | −0.00977373 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.18853e14 | −0.572424 | −0.286212 | − | 0.958166i | \(-0.592396\pi\) | ||||
−0.286212 | + | 0.958166i | \(0.592396\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.98827e14 | − | 1.98827e14i | −0.931746 | − | 0.931746i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.79876e13 | + | 4.79876e13i | −0.218840 | + | 0.218840i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.70929e12i | 0.0209019i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.44879e14i | 1.05797i | 0.848631 | + | 0.528986i | \(0.177428\pi\) | ||||
−0.848631 | + | 0.528986i | \(0.822572\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.14758e13 | − | 8.14758e13i | 0.342688 | − | 0.342688i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.60297e11 | + | 7.60297e11i | 0.00311356 | + | 0.00311356i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.26469e14 | −1.70068 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.84170e14 | 0.715270 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.30256e13 | − | 2.30256e13i | −0.0871033 | − | 0.0871033i | 0.662213 | − | 0.749316i | \(-0.269618\pi\) |
−0.749316 | + | 0.662213i | \(0.769618\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.71463e13 | + | 2.71463e13i | −0.100036 | + | 0.100036i | −0.755354 | − | 0.655317i | \(-0.772535\pi\) |
0.655317 | + | 0.755354i | \(0.272535\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1.89284e14i | − | 0.679583i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 5.31309e13i | − | 0.185869i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.97283e13 | + | 1.97283e13i | −0.0672569 | + | 0.0672569i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.85680e12 | − | 8.85680e12i | −0.0294281 | − | 0.0294281i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.22363e13 | −0.136792 | −0.0683961 | − | 0.997658i | \(-0.521788\pi\) | ||||
−0.0683961 | + | 0.997658i | \(0.521788\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.22774e14 | −1.01909 | −0.509547 | − | 0.860443i | \(-0.670187\pi\) | ||||
−0.509547 | + | 0.860443i | \(0.670187\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.04866e14 | − | 1.04866e14i | −0.322807 | − | 0.322807i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.52860e13 | − | 5.52860e13i | 0.165946 | − | 0.165946i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.45795e14i | − | 0.426764i | −0.976969 | − | 0.213382i | \(-0.931552\pi\) | ||
0.976969 | − | 0.213382i | \(-0.0684479\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 1.59443e14i | − | 0.455190i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.05734e14 | + | 2.05734e14i | −0.572909 | + | 0.572909i | −0.932940 | − | 0.360031i | \(-0.882766\pi\) |
0.360031 | + | 0.932940i | \(0.382766\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.35844e13 | − | 5.35844e13i | −0.145566 | − | 0.145566i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.21598e14 | −0.587319 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.85617e13 | 0.0480024 | 0.0240012 | − | 0.999712i | \(-0.492359\pi\) | ||||
0.0240012 | + | 0.999712i | \(0.492359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.63351e13 | + | 1.63351e13i | 0.0412241 | + | 0.0412241i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.77302e14 | + | 1.77302e14i | −0.436690 | + | 0.436690i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.96551e13i | 0.0712912i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 5.36809e14i | − | 1.25974i | −0.776701 | − | 0.629869i | \(-0.783109\pi\) | ||
0.776701 | − | 0.629869i | \(-0.216891\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.32425e14 | − | 4.32425e14i | 0.990698 | − | 0.990698i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.02395e14 | − | 1.02395e14i | −0.229046 | − | 0.229046i | 0.583248 | − | 0.812294i | \(-0.301782\pi\) |
−0.812294 | + | 0.583248i | \(0.801782\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.64099e14 | 1.45057 | 0.725283 | − | 0.688451i | \(-0.241709\pi\) | ||||
0.725283 | + | 0.688451i | \(0.241709\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.42124e14 | 0.729781 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.58885e14 | + | 3.58885e14i | 0.747675 | + | 0.747675i | 0.974042 | − | 0.226367i | \(-0.0726849\pi\) |
−0.226367 | + | 0.974042i | \(0.572685\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.73862e13 | − | 1.73862e13i | 0.0353798 | − | 0.0353798i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.20212e14i | 0.636535i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.08796e12i | 0.0118232i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.12675e13 | − | 1.12675e13i | 0.0213802 | − | 0.0213802i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.72526e14 | + | 1.72526e14i | 0.319892 | + | 0.319892i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.53948e14 | 0.278951 | 0.139475 | − | 0.990226i | \(-0.455458\pi\) | ||||
0.139475 | + | 0.990226i | \(0.455458\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.17283e14 | −0.561886 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.07928e13 | + | 2.07928e13i | 0.0359918 | + | 0.0359918i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.64457e14 | + | 1.64457e14i | −0.278274 | + | 0.278274i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.15975e14i | 1.51522i | 0.652710 | + | 0.757608i | \(0.273632\pi\) | ||||
−0.652710 | + | 0.757608i | \(0.726368\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 3.96449e14i | − | 0.641193i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.86596e14 | + | 1.86596e14i | −0.295089 | + | 0.295089i | −0.839087 | − | 0.543998i | \(-0.816910\pi\) |
0.543998 | + | 0.839087i | \(0.316910\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.99163e14 | + | 3.99163e14i | 0.617295 | + | 0.617295i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.28250e13 | −0.0193967 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.49326e12 | 0.0125636 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.06833e14 | − | 1.06833e14i | −0.154580 | − | 0.154580i | 0.625580 | − | 0.780160i | \(-0.284862\pi\) |
−0.780160 | + | 0.625580i | \(0.784862\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.88267e14 | − | 4.88267e14i | 0.691114 | − | 0.691114i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.16223e14i | 0.160941i | 0.996757 | + | 0.0804706i | \(0.0256423\pi\) | ||||
−0.996757 | + | 0.0804706i | \(0.974358\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.89616e13i | 0.0527879i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.03673e14 | − | 2.03673e14i | 0.270017 | − | 0.270017i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.43081e14 | + | 8.43081e14i | 1.09376 | + | 1.09376i | 0.995124 | + | 0.0986346i | \(0.0314475\pi\) |
0.0986346 | + | 0.995124i | \(0.468552\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.73675e13 | −0.110926 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.83409e14 | 0.227916 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.83624e14 | + | 3.83624e14i | 0.466622 | + | 0.466622i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.04796e13 | + | 4.04796e13i | −0.0481990 | + | 0.0481990i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.06389e14i | 0.357152i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.87101e14i | 0.327662i | 0.986488 | + | 0.163831i | \(0.0523852\pi\) | ||||
−0.986488 | + | 0.163831i | \(0.947615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.16485e15 | − | 1.16485e15i | 1.30169 | − | 1.30169i | 0.374446 | − | 0.927249i | \(-0.377833\pi\) |
0.927249 | − | 0.374446i | \(-0.122167\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.23764e12 | + | 4.23764e12i | 0.00463711 | + | 0.00463711i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.30227e15 | −1.39554 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.11709e14 | −0.222195 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.21529e13 | − | 2.21529e13i | −0.0227725 | − | 0.0227725i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.10056e15 | + | 1.10056e15i | −1.10819 | + | 1.10819i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.27827e15i | − | 1.26089i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1.22342e15i | − | 1.18227i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.40978e13 | + | 3.40978e13i | −0.0322841 | + | 0.0322841i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.21814e14 | + | 6.21814e14i | 0.576866 | + | 0.576866i | 0.934039 | − | 0.357172i | \(-0.116259\pi\) |
−0.357172 | + | 0.934039i | \(0.616259\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.79725e14 | −0.345199 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.48754e14 | 0.845226 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.07617e14 | + | 7.07617e14i | 0.617829 | + | 0.617829i | 0.944974 | − | 0.327145i | \(-0.106087\pi\) |
−0.327145 | + | 0.944974i | \(0.606087\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.74828e14 | − | 5.74828e14i | 0.491915 | − | 0.491915i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.69301e14i | 0.142012i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.32397e14i | 0.108866i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.72976e14 | − | 2.72976e14i | 0.220046 | − | 0.220046i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.59075e14 | + | 8.59075e14i | 0.678934 | + | 0.678934i | 0.959759 | − | 0.280825i | \(-0.0906081\pi\) |
−0.280825 | + | 0.959759i | \(0.590608\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.10169e14 | −0.317832 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.80099e13 | −0.0440764 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.71752e14 | + | 9.71752e14i | 0.724034 | + | 0.724034i | 0.969424 | − | 0.245390i | \(-0.0789160\pi\) |
−0.245390 | + | 0.969424i | \(0.578916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00111e14 | − | 2.00111e14i | 0.146219 | − | 0.146219i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.91375e13i | 0.0208807i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.36146e15i | 0.956949i | 0.878102 | + | 0.478474i | \(0.158810\pi\) | ||||
−0.878102 | + | 0.478474i | \(0.841190\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.36626e15 | − | 1.36626e15i | 0.941966 | − | 0.941966i | −0.0564400 | − | 0.998406i | \(-0.517975\pi\) |
0.998406 | + | 0.0564400i | \(0.0179750\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.71002e14 | − | 8.71002e14i | −0.589072 | − | 0.589072i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.37333e14 | −0.157465 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.37482e15 | −0.894911 | −0.447456 | − | 0.894306i | \(-0.647670\pi\) | ||||
−0.447456 | + | 0.894306i | \(0.647670\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.10247e15 | − | 1.10247e15i | −0.704102 | − | 0.704102i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.29474e14 | + | 1.29474e14i | −0.0811357 | + | 0.0811357i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 7.37915e13i | − | 0.0453763i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 8.64065e14i | − | 0.521422i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.27134e15 | + | 1.27134e15i | −0.752925 | + | 0.752925i | −0.975024 | − | 0.222099i | \(-0.928709\pi\) |
0.222099 | + | 0.975024i | \(0.428709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.76172e14 | − | 2.76172e14i | −0.160526 | − | 0.160526i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.72538e14 | −0.554850 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.66805e15 | −0.934131 | −0.467066 | − | 0.884223i | \(-0.654689\pi\) | ||||
−0.467066 | + | 0.884223i | \(0.654689\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.71168e13 | + | 9.71168e13i | 0.0533889 | + | 0.0533889i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.72286e14 | − | 3.72286e14i | 0.200918 | − | 0.200918i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.85853e15i | 0.984741i | 0.870386 | + | 0.492370i | \(0.163869\pi\) | ||||
−0.870386 | + | 0.492370i | \(0.836131\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.26696e15i | − | 1.17932i | −0.807650 | − | 0.589662i | \(-0.799261\pi\) | ||
0.807650 | − | 0.589662i | \(-0.200739\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.06586e14 | + | 5.06586e14i | −0.258767 | + | 0.258767i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.30275e15 | − | 1.30275e15i | −0.653440 | − | 0.653440i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.39375e15 | 0.686508 | 0.343254 | − | 0.939243i | \(-0.388471\pi\) | ||||
0.343254 | + | 0.939243i | \(0.388471\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.36733e13 | −0.0308008 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.72726e15 | − | 2.72726e15i | −1.29569 | − | 1.29569i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.24343e13 | + | 4.24343e13i | −0.0198009 | + | 0.0198009i | −0.716938 | − | 0.697137i | \(-0.754457\pi\) |
0.697137 | + | 0.716938i | \(0.254457\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 1.89375e15i | − | 0.867978i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.15894e15i | 0.972013i | 0.873955 | + | 0.486007i | \(0.161547\pi\) | ||||
−0.873955 | + | 0.486007i | \(0.838453\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.84800e15 | + | 1.84800e15i | −0.817339 | + | 0.817339i | −0.985722 | − | 0.168382i | \(-0.946146\pi\) |
0.168382 | + | 0.985722i | \(0.446146\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.93162e15 | − | 1.93162e15i | −0.839300 | − | 0.839300i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.25359e13 | −0.0138892 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.99623e15 | 0.837278 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.23021e13 | − | 1.23021e13i | −0.00507002 | − | 0.00507002i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.03906e15 | + | 1.03906e15i | −0.420788 | + | 0.420788i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.80781e15i | − | 0.719435i | −0.933061 | − | 0.359718i | \(-0.882873\pi\) | ||
0.933061 | − | 0.359718i | \(-0.117127\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.29195e14i | 0.206964i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.74661e15 | + | 2.74661e15i | −1.05570 | + | 1.05570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.29730e15 | − | 2.29730e15i | −0.867861 | − | 0.867861i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.47470e14 | −0.0918898 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.37793e15 | −1.23291 | −0.616456 | − | 0.787389i | \(-0.711432\pi\) | ||||
−0.616456 | + | 0.787389i | \(0.711432\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.45344e15 | − | 1.45344e15i | −0.521480 | − | 0.521480i | 0.396538 | − | 0.918018i | \(-0.370211\pi\) |
−0.918018 | + | 0.396538i | \(0.870211\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.52891e14 | − | 3.52891e14i | 0.124469 | − | 0.124469i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.51422e15i | 1.56534i | 0.622436 | + | 0.782670i | \(0.286143\pi\) | ||||
−0.622436 | + | 0.782670i | \(0.713857\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.47507e12i | 0.00323025i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.03867e14 | − | 1.03867e14i | 0.0348163 | − | 0.0348163i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.89288e15 | + | 1.89288e15i | 0.623880 | + | 0.623880i | 0.946521 | − | 0.322641i | \(-0.104571\pi\) |
−0.322641 | + | 0.946521i | \(0.604571\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.57045e15 | 1.80536 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.54565e15 | 0.811313 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.29856e15 | + | 2.29856e15i | 0.720420 | + | 0.720420i | 0.968691 | − | 0.248270i | \(-0.0798621\pi\) |
−0.248270 | + | 0.968691i | \(0.579862\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.03518e13 | + | 9.03518e13i | −0.0278502 | + | 0.0278502i | −0.720895 | − | 0.693045i | \(-0.756269\pi\) |
0.693045 | + | 0.720895i | \(0.256269\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 3.90834e15i | − | 1.18486i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.11911e13i | 0.0122824i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.78304e15 | − | 1.78304e15i | 0.522960 | − | 0.522960i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.36263e14 | + | 8.36263e14i | 0.241268 | + | 0.241268i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.45861e14 | −0.0697776 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.82094e14 | 0.162521 | 0.0812606 | − | 0.996693i | \(-0.474105\pi\) | ||||
0.0812606 | + | 0.996693i | \(0.474105\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.93670e14 | − | 3.93670e14i | −0.108134 | − | 0.108134i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.51457e14 | + | 5.51457e14i | −0.149030 | + | 0.149030i | −0.777685 | − | 0.628655i | \(-0.783606\pi\) |
0.628655 | + | 0.777685i | \(0.283606\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.98564e13i | 0.0265517i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.66887e14i | 0.252969i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.35222e15 | − | 1.35222e15i | 0.348123 | − | 0.348123i | −0.511287 | − | 0.859410i | \(-0.670831\pi\) |
0.859410 | + | 0.511287i | \(0.170831\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.69989e15 | − | 1.69989e15i | −0.430648 | − | 0.430648i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.05186e15 | 0.760856 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.97161e15 | 1.21981 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.10782e15 | − | 1.10782e15i | −0.267510 | − | 0.267510i | 0.560586 | − | 0.828096i | \(-0.310576\pi\) |
−0.828096 | + | 0.560586i | \(0.810576\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.89358e12 | + | 3.89358e12i | −0.000925373 | + | 0.000925373i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 3.84246e15i | − | 0.898863i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.20840e15i | 1.65981i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.50587e15 | + | 3.50587e15i | −0.794641 | + | 0.794641i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.35478e14 | + | 2.35478e14i | 0.0525413 | + | 0.0525413i | 0.732889 | − | 0.680348i | \(-0.238171\pi\) |
−0.680348 | + | 0.732889i | \(0.738171\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.40708e14 | −0.0968047 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.69284e15 | 1.01483 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.18285e13 | + | 1.18285e13i | 0.00251840 | + | 0.00251840i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.09313e15 | − | 6.09313e15i | 1.27728 | − | 1.27728i | 0.335097 | − | 0.942184i | \(-0.391231\pi\) |
0.942184 | − | 0.335097i | \(-0.108769\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 3.85768e15i | − | 0.796240i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.81716e15i | 1.18228i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.84786e14 | + | 1.84786e14i | −0.0369815 | + | 0.0369815i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.24758e15 | + | 3.24758e15i | 0.640037 | + | 0.640037i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.52319e15 | −0.489713 | −0.244856 | − | 0.969559i | \(-0.578741\pi\) | ||||
−0.244856 | + | 0.969559i | \(0.578741\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.32932e14 | 0.0445230 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.21089e15 | + | 2.21089e15i | 0.416204 | + | 0.416204i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.63389e14 | − | 3.63389e14i | 0.0673771 | − | 0.0673771i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.17879e14i | 0.0945777i | 0.998881 | + | 0.0472888i | \(0.0150581\pi\) | ||||
−0.998881 | + | 0.0472888i | \(0.984942\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 5.24717e15i | − | 0.943896i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.34325e15 | + | 1.34325e15i | −0.238019 | + | 0.238019i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.12556e15 | − | 2.12556e15i | −0.371023 | − | 0.371023i | 0.496827 | − | 0.867850i | \(-0.334499\pi\) |
−0.867850 | + | 0.496827i | \(0.834499\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.95299e15 | 0.679744 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.16673e14 | 0.0367057 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.41609e14 | + | 5.41609e14i | 0.0903945 | + | 0.0903945i | 0.750858 | − | 0.660464i | \(-0.229640\pi\) |
−0.660464 | + | 0.750858i | \(0.729640\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.28842e14 | − | 8.28842e14i | 0.136292 | − | 0.136292i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.22006e16i | 1.97670i | 0.152185 | + | 0.988352i | \(0.451369\pi\) | ||||
−0.152185 | + | 0.988352i | \(0.548631\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.62335e15i | 0.738070i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.77250e15 | − | 3.77250e15i | 0.593424 | − | 0.593424i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.88075e14 | − | 3.88075e14i | −0.0601542 | − | 0.0601542i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.45402e15 | 0.680351 | 0.340175 | − | 0.940362i | \(-0.389514\pi\) | ||||
0.340175 | + | 0.940362i | \(0.389514\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.85250e15 | −1.33258 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.69918e15 | + | 3.69918e15i | 0.548778 | + | 0.548778i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.55016e15 | + | 1.55016e15i | −0.226646 | + | 0.226646i | −0.811290 | − | 0.584644i | \(-0.801234\pi\) |
0.584644 | + | 0.811290i | \(0.301234\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.59127e14i | 0.0373407i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 7.65104e14i | − | 0.108669i | −0.998523 | − | 0.0543344i | \(-0.982696\pi\) | ||
0.998523 | − | 0.0543344i | \(-0.0173037\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.88036e14 | − | 2.88036e14i | 0.0403239 | − | 0.0403239i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.82971e15 | − | 2.82971e15i | −0.390485 | − | 0.390485i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.38371e14 | −0.0868358 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.01633e15 | −0.672653 | −0.336327 | − | 0.941745i | \(-0.609185\pi\) | ||||
−0.336327 | + | 0.941745i | \(0.609185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.21616e15 | + | 6.21616e15i | 0.821718 | + | 0.821718i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.87468e15 | + | 2.87468e15i | −0.374630 | + | 0.374630i | −0.869160 | − | 0.494530i | \(-0.835340\pi\) |
0.494530 | + | 0.869160i | \(0.335340\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.18556e15i | 0.152322i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 1.65748e14i | − | 0.0209958i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.52868e15 | + | 1.52868e15i | −0.190924 | + | 0.190924i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.29229e13 | + | 5.29229e13i | 0.00651723 | + | 0.00651723i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.91514e15 | 0.718250 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.68081e15 | 0.799918 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.90637e15 | − | 8.90637e15i | −1.05157 | − | 1.05157i | −0.998596 | − | 0.0529775i | \(-0.983129\pi\) |
−0.0529775 | − | 0.998596i | \(-0.516871\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.14994e15 | − | 3.14994e15i | 0.366757 | − | 0.366757i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.21505e14i | − | 0.0139516i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.65646e16i | − | 1.87576i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.27736e15 | + | 4.27736e15i | −0.477701 | + | 0.477701i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.42605e13 | − | 1.42605e13i | −0.00157077 | − | 0.00157077i | 0.706321 | − | 0.707892i | \(-0.250354\pi\) |
−0.707892 | + | 0.706321i | \(0.750354\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.78629e16 | −1.94064 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.48004e14 | 0.101585 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.44402e14 | − | 5.44402e14i | −0.0575419 | − | 0.0575419i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.33815e14 | − | 4.33815e14i | 0.0452301 | − | 0.0452301i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 6.71291e15i | − | 0.690409i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1.34639e16i | − | 1.36601i | −0.730414 | − | 0.683005i | \(-0.760673\pi\) | ||
0.730414 | − | 0.683005i | \(-0.239327\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.18874e16 | − | 1.18874e16i | 1.18979 | − | 1.18979i | 0.212668 | − | 0.977125i | \(-0.431785\pi\) |
0.977125 | − | 0.212668i | \(-0.0682151\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.52340e15 | + | 7.52340e15i | 0.742876 | + | 0.742876i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.27140e15 | −0.805772 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.69727e14 | −0.0547577 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.62325e14 | − | 2.62325e14i | −0.0248759 | − | 0.0248759i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.13620e16 | + | 1.13620e16i | −1.06309 | + | 1.06309i | −0.0652148 | + | 0.997871i | \(0.520773\pi\) |
−0.997871 | + | 0.0652148i | \(0.979227\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.24911e15i | 0.115319i | 0.998336 | + | 0.0576595i | \(0.0183638\pi\) | ||||
−0.998336 | + | 0.0576595i | \(0.981636\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.28108e13i | 0.00481090i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.94453e15 | − | 4.94453e15i | 0.444472 | − | 0.444472i | −0.449040 | − | 0.893512i | \(-0.648234\pi\) |
0.893512 | + | 0.449040i | \(0.148234\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.22877e16 | + | 1.22877e16i | 1.08999 | + | 1.08999i | 0.995529 | + | 0.0944611i | \(0.0301128\pi\) |
0.0944611 | + | 0.995529i | \(0.469887\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.35556e16 | −1.18663 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.50468e16 | −1.29986 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.01871e16 | − | 1.01871e16i | −0.868507 | − | 0.868507i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.64907e15 | + | 9.64907e15i | −0.811887 | + | 0.811887i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1.84580e15i | − | 0.153283i | −0.997059 | − | 0.0766417i | \(-0.975580\pi\) | ||
0.997059 | − | 0.0766417i | \(-0.0244198\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 6.74035e15i | − | 0.552465i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.46258e15 | − | 6.46258e15i | 0.522822 | − | 0.522822i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.24938e15 | − | 4.24938e15i | −0.339323 | − | 0.339323i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.91013e14 | −0.0623483 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.34963e15 | 0.260618 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.64144e15 | + | 4.64144e15i | 0.356484 | + | 0.356484i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.94698e14 | + | 3.94698e14i | −0.0299257 | + | 0.0299257i | −0.721911 | − | 0.691986i | \(-0.756736\pi\) |
0.691986 | + | 0.721911i | \(0.256736\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.20019e15i | − | 0.0898333i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.04705e15i | 0.446837i | 0.974723 | + | 0.223418i | \(0.0717216\pi\) | ||||
−0.974723 | + | 0.223418i | \(0.928278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.24768e16 | + | 1.24768e16i | −0.910209 | + | 0.910209i | −0.996288 | − | 0.0860789i | \(-0.972566\pi\) |
0.0860789 | + | 0.996288i | \(0.472566\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.74931e14 | − | 5.74931e14i | −0.0414093 | − | 0.0414093i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.09979e15 | −0.504878 | −0.252439 | − | 0.967613i | \(-0.581233\pi\) | ||||
−0.252439 | + | 0.967613i | \(0.581233\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.39241e15 | 0.448824 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.28313e15 | − | 5.28313e15i | −0.366257 | − | 0.366257i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.24989e14 | + | 8.24989e14i | −0.0564728 | + | 0.0564728i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.45981e16i | 0.986724i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.90954e15i | − | 0.194198i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.09141e14 | − | 7.09141e14i | 0.0467399 | − | 0.0467399i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.22409e15 | + | 1.22409e15i | 0.0796738 | + | 0.0796738i | 0.745821 | − | 0.666147i | \(-0.232058\pi\) |
−0.666147 | + | 0.745821i | \(0.732058\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.28983e15 | 0.532852 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.00411e16 | −1.27219 | −0.636097 | − | 0.771609i | \(-0.719452\pi\) | ||||
−0.636097 | + | 0.771609i | \(0.719452\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.72509e15 | + | 9.72509e15i | 0.609691 | + | 0.609691i | 0.942865 | − | 0.333174i | \(-0.108120\pi\) |
−0.333174 | + | 0.942865i | \(0.608120\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.49227e14 | − | 5.49227e14i | 0.0340066 | − | 0.0340066i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.20718e16i | − | 0.738230i | −0.929384 | − | 0.369115i | \(-0.879661\pi\) | ||
0.929384 | − | 0.369115i | \(-0.120339\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.66771e15i | 0.100730i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.81561e14 | + | 1.81561e14i | −0.0108317 | + | 0.0108317i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.78818e15 | − | 3.78818e15i | −0.223228 | − | 0.223228i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.55251e16 | −1.48573 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.74583e16 | −1.00379 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.90687e15 | − | 8.90687e15i | −0.505879 | − | 0.505879i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.62814e16 | − | 1.62814e16i | 0.913496 | − | 0.913496i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2.14272e14i | − | 0.0118763i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.92246e15i | 0.433803i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.15151e16 | − | 2.15151e16i | 1.16387 | − | 1.16387i | 0.180243 | − | 0.983622i | \(-0.442312\pi\) |
0.983622 | − | 0.180243i | \(-0.0576884\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.44650e14 | − | 3.44650e14i | −0.0184195 | − | 0.0184195i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.28388e16 | 1.20593 | 0.602964 | − | 0.797768i | \(-0.293986\pi\) | ||||
0.602964 | + | 0.797768i | \(0.293986\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.61354e15 | −0.0841765 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.42514e16 | + | 1.42514e16i | 0.734586 | + | 0.734586i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.69116e15 | − | 1.69116e15i | 0.0861296 | − | 0.0861296i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.19185e16i | 1.10300i | 0.834175 | + | 0.551500i | \(0.185944\pi\) | ||||
−0.834175 | + | 0.551500i | \(0.814056\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 3.53365e15i | − | 0.175709i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.56561e15 | + | 3.56561e15i | −0.175196 | + | 0.175196i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.45938e14 | + | 9.45938e14i | 0.0459286 | + | 0.0459286i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.78698e15 | −0.325640 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.13223e16 | 1.95929 | 0.979644 | − | 0.200741i | \(-0.0643350\pi\) | ||||
0.979644 | + | 0.200741i | \(0.0643350\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.19096e15 | − | 3.19096e15i | −0.149520 | − | 0.149520i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.02677e15 | + | 5.02677e15i | −0.232777 | + | 0.232777i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.21030e15i | 0.0553898i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 9.03330e15i | − | 0.408582i | −0.978910 | − | 0.204291i | \(-0.934511\pi\) | ||
0.978910 | − | 0.204291i | \(-0.0654888\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.56213e15 | + | 2.56213e15i | −0.114535 | + | 0.114535i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.44069e15 | + | 3.44069e15i | 0.152021 | + | 0.152021i | 0.779020 | − | 0.626999i | \(-0.215717\pi\) |
−0.626999 | + | 0.779020i | \(0.715717\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.21995e16 | 1.40616 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.43916e15 | 0.0621204 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.83365e16 | + | 2.83365e16i | 1.20899 | + | 1.20899i | 0.971356 | + | 0.237630i | \(0.0763705\pi\) |
0.237630 | + | 0.971356i | \(0.423629\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.66784e16 | − | 3.66784e16i | 1.54684 | − | 1.54684i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 2.04977e16i | − | 0.854501i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.18190e16i | 0.899133i | 0.893247 | + | 0.449566i | \(0.148422\pi\) | ||||
−0.893247 | + | 0.449566i | \(0.851578\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.81723e16 | + | 1.81723e16i | −0.740273 | + | 0.740273i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.96759e14 | − | 3.96759e14i | −0.0159776 | − | 0.0159776i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.03215e15 | −0.0410905 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.65018e15 | 0.143660 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.13074e16 | + | 1.13074e16i | 0.439966 | + | 0.439966i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.30017e16 | + | 2.30017e16i | −0.884829 | + | 0.884829i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.21064e16i | 1.22109i | 0.791983 | + | 0.610543i | \(0.209049\pi\) | ||||
−0.791983 | + | 0.610543i | \(0.790951\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 5.42872e15i | − | 0.204134i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.64302e15 | − | 7.64302e15i | 0.284158 | − | 0.284158i | −0.550607 | − | 0.834765i | \(-0.685604\pi\) |
0.834765 | + | 0.550607i | \(0.185604\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.16655e15 | − | 1.16655e15i | −0.0428828 | − | 0.0428828i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.55806e15 | −0.129327 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.77134e16 | 1.71483 | 0.857413 | − | 0.514628i | \(-0.172070\pi\) | ||||
0.857413 | + | 0.514628i | \(0.172070\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.02736e14 | − | 2.02736e14i | −0.00720488 | − | 0.00720488i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.39257e15 | + | 8.39257e15i | −0.294928 | + | 0.294928i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 5.15731e16i | − | 1.79217i | −0.443884 | − | 0.896084i | \(-0.646400\pi\) | ||
0.443884 | − | 0.896084i | \(-0.353600\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.02907e16i | 0.697266i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.42472e15 | − | 1.42472e15i | 0.0484155 | − | 0.0484155i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.00024e15 | + | 6.00024e15i | 0.201646 | + | 0.201646i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.04756e16 | 1.67755 | 0.838776 | − | 0.544476i | \(-0.183272\pi\) | ||||
0.838776 | + | 0.544476i | \(0.183272\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.09004e16 | 0.358278 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.76728e15 | − | 7.76728e15i | −0.252489 | − | 0.252489i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.06141e15 | − | 5.06141e15i | 0.162723 | − | 0.162723i | −0.621049 | − | 0.783772i | \(-0.713293\pi\) |
0.783772 | + | 0.621049i | \(0.213293\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.53977e16i | 0.489606i |
(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 | 64.12.e.a.17.8 | 42 | ||
4.3 | odd | 2 | 16.12.e.a.13.6 | yes | 42 | ||
8.3 | odd | 2 | 128.12.e.b.33.8 | 42 | |||
8.5 | even | 2 | 128.12.e.a.33.14 | 42 | |||
16.3 | odd | 4 | 128.12.e.b.97.8 | 42 | |||
16.5 | even | 4 | inner | 64.12.e.a.49.8 | 42 | ||
16.11 | odd | 4 | 16.12.e.a.5.6 | ✓ | 42 | ||
16.13 | even | 4 | 128.12.e.a.97.14 | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.12.e.a.5.6 | ✓ | 42 | 16.11 | odd | 4 | ||
16.12.e.a.13.6 | yes | 42 | 4.3 | odd | 2 | ||
64.12.e.a.17.8 | 42 | 1.1 | even | 1 | trivial | ||
64.12.e.a.49.8 | 42 | 16.5 | even | 4 | inner | ||
128.12.e.a.33.14 | 42 | 8.5 | even | 2 | |||
128.12.e.a.97.14 | 42 | 16.13 | even | 4 | |||
128.12.e.b.33.8 | 42 | 8.3 | odd | 2 | |||
128.12.e.b.97.8 | 42 | 16.3 | odd | 4 |