Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,10,Mod(99,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.99");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(90.1312713287\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.99 |
Dual form | 175.10.b.a.99.2 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 28.0000i | − 1.23744i | −0.785613 | − | 0.618718i | \(-0.787652\pi\) | ||||
0.785613 | − | 0.618718i | \(-0.212348\pi\) | |||||||
\(3\) | − 116.000i | − 0.826823i | −0.910544 | − | 0.413411i | \(-0.864337\pi\) | ||||
0.910544 | − | 0.413411i | \(-0.135663\pi\) | |||||||
\(4\) | −272.000 | −0.531250 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3248.00 | −1.02314 | ||||||||
\(7\) | − 2401.00i | − 0.377964i | ||||||||
\(8\) | − 6720.00i | − 0.580049i | ||||||||
\(9\) | 6227.00 | 0.316364 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −25548.0 | −0.526126 | −0.263063 | − | 0.964779i | \(-0.584733\pi\) | ||||
−0.263063 | + | 0.964779i | \(0.584733\pi\) | |||||||
\(12\) | 31552.0i | 0.439250i | ||||||||
\(13\) | − 42306.0i | − 0.410825i | −0.978675 | − | 0.205413i | \(-0.934146\pi\) | ||||
0.978675 | − | 0.205413i | \(-0.0658536\pi\) | |||||||
\(14\) | −67228.0 | −0.467707 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −327424. | −1.24902 | ||||||||
\(17\) | 526342.i | 1.52844i | 0.644957 | + | 0.764219i | \(0.276875\pi\) | ||||
−0.644957 | + | 0.764219i | \(0.723125\pi\) | |||||||
\(18\) | − 174356.i | − 0.391481i | ||||||||
\(19\) | 350060. | 0.616242 | 0.308121 | − | 0.951347i | \(-0.400300\pi\) | ||||
0.308121 | + | 0.951347i | \(0.400300\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −278516. | −0.312510 | ||||||||
\(22\) | 715344.i | 0.651048i | ||||||||
\(23\) | − 621976.i | − 0.463445i | −0.972782 | − | 0.231723i | \(-0.925564\pi\) | ||||
0.972782 | − | 0.231723i | \(-0.0744362\pi\) | |||||||
\(24\) | −779520. | −0.479597 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.18457e6 | −0.508370 | ||||||||
\(27\) | − 3.00556e6i | − 1.08840i | ||||||||
\(28\) | 653072.i | 0.200794i | ||||||||
\(29\) | −6.72043e6 | −1.76444 | −0.882218 | − | 0.470841i | \(-0.843951\pi\) | ||||
−0.882218 | + | 0.470841i | \(0.843951\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.41221e6 | −1.24704 | −0.623519 | − | 0.781808i | \(-0.714298\pi\) | ||||
−0.623519 | + | 0.781808i | \(0.714298\pi\) | |||||||
\(32\) | 5.72723e6i | 0.965539i | ||||||||
\(33\) | 2.96357e6i | 0.435013i | ||||||||
\(34\) | 1.47376e7 | 1.89135 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.69374e6 | −0.168069 | ||||||||
\(37\) | 2.31768e6i | 0.203304i | 0.994820 | + | 0.101652i | \(0.0324128\pi\) | ||||
−0.994820 | + | 0.101652i | \(0.967587\pi\) | |||||||
\(38\) | − 9.80168e6i | − 0.762561i | ||||||||
\(39\) | −4.90750e6 | −0.339679 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.02247e7 | −0.565096 | −0.282548 | − | 0.959253i | \(-0.591180\pi\) | ||||
−0.282548 | + | 0.959253i | \(0.591180\pi\) | |||||||
\(42\) | 7.79845e6i | 0.386711i | ||||||||
\(43\) | 3.01140e7i | 1.34326i | 0.740886 | + | 0.671631i | \(0.234406\pi\) | ||||
−0.740886 | + | 0.671631i | \(0.765594\pi\) | |||||||
\(44\) | 6.94906e6 | 0.279504 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.74153e7 | −0.573484 | ||||||||
\(47\) | 2.36449e7i | 0.706801i | 0.935472 | + | 0.353401i | \(0.114975\pi\) | ||||
−0.935472 | + | 0.353401i | \(0.885025\pi\) | |||||||
\(48\) | 3.79812e7i | 1.03272i | ||||||||
\(49\) | −5.76480e6 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.10557e7 | 1.26375 | ||||||||
\(52\) | 1.15072e7i | 0.218251i | ||||||||
\(53\) | 5.72927e7i | 0.997373i | 0.866782 | + | 0.498686i | \(0.166184\pi\) | ||||
−0.866782 | + | 0.498686i | \(0.833816\pi\) | |||||||
\(54\) | −8.41557e7 | −1.34683 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.61347e7 | −0.219238 | ||||||||
\(57\) | − 4.06070e7i | − 0.509523i | ||||||||
\(58\) | 1.88172e8i | 2.18338i | ||||||||
\(59\) | −8.49348e7 | −0.912539 | −0.456270 | − | 0.889842i | \(-0.650815\pi\) | ||||
−0.456270 | + | 0.889842i | \(0.650815\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.46778e7 | 0.135730 | 0.0678652 | − | 0.997694i | \(-0.478381\pi\) | ||||
0.0678652 | + | 0.997694i | \(0.478381\pi\) | |||||||
\(62\) | 1.79542e8i | 1.54313i | ||||||||
\(63\) | − 1.49510e7i | − 0.119574i | ||||||||
\(64\) | −7.27859e6 | −0.0542297 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.29799e7 | 0.538301 | ||||||||
\(67\) | 2.44558e8i | 1.48267i | 0.671134 | + | 0.741336i | \(0.265807\pi\) | ||||
−0.671134 | + | 0.741336i | \(0.734193\pi\) | |||||||
\(68\) | − 1.43165e8i | − 0.811983i | ||||||||
\(69\) | −7.21492e7 | −0.383187 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.19020e7 | 0.289096 | 0.144548 | − | 0.989498i | \(-0.453827\pi\) | ||||
0.144548 | + | 0.989498i | \(0.453827\pi\) | |||||||
\(72\) | − 4.18454e7i | − 0.183507i | ||||||||
\(73\) | − 2.83764e8i | − 1.16951i | −0.811210 | − | 0.584755i | \(-0.801191\pi\) | ||||
0.811210 | − | 0.584755i | \(-0.198809\pi\) | |||||||
\(74\) | 6.48951e7 | 0.251576 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.52163e7 | −0.327379 | ||||||||
\(77\) | 6.13407e7i | 0.198857i | ||||||||
\(78\) | 1.37410e8i | 0.420332i | ||||||||
\(79\) | −2.76107e8 | −0.797547 | −0.398773 | − | 0.917049i | \(-0.630564\pi\) | ||||
−0.398773 | + | 0.917049i | \(0.630564\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.26079e8 | −0.583549 | ||||||||
\(82\) | 2.86291e8i | 0.699271i | ||||||||
\(83\) | − 7.29960e7i | − 0.168829i | −0.996431 | − | 0.0844146i | \(-0.973098\pi\) | ||||
0.996431 | − | 0.0844146i | \(-0.0269020\pi\) | |||||||
\(84\) | 7.57564e7 | 0.166021 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.43192e8 | 1.66220 | ||||||||
\(87\) | 7.79570e8i | 1.45888i | ||||||||
\(88\) | 1.71683e8i | 0.305179i | ||||||||
\(89\) | 8.96368e8 | 1.51437 | 0.757184 | − | 0.653201i | \(-0.226575\pi\) | ||||
0.757184 | + | 0.653201i | \(0.226575\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.01577e8 | −0.155277 | ||||||||
\(92\) | 1.69177e8i | 0.246205i | ||||||||
\(93\) | 7.43816e8i | 1.03108i | ||||||||
\(94\) | 6.62058e8 | 0.874622 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.64359e8 | 0.798330 | ||||||||
\(97\) | − 1.20581e9i | − 1.38295i | −0.722401 | − | 0.691474i | \(-0.756962\pi\) | ||||
0.722401 | − | 0.691474i | \(-0.243038\pi\) | |||||||
\(98\) | 1.61414e8i | 0.176777i | ||||||||
\(99\) | −1.59087e8 | −0.166448 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.46021e9 | −1.39627 | −0.698136 | − | 0.715965i | \(-0.745987\pi\) | ||||
−0.698136 | + | 0.715965i | \(0.745987\pi\) | |||||||
\(102\) | − 1.70956e9i | − 1.56381i | ||||||||
\(103\) | 1.08009e9i | 0.945563i | 0.881180 | + | 0.472782i | \(0.156750\pi\) | ||||
−0.881180 | + | 0.472782i | \(0.843250\pi\) | |||||||
\(104\) | −2.84296e8 | −0.238298 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.60419e9 | 1.23419 | ||||||||
\(107\) | − 3.35949e8i | − 0.247769i | −0.992297 | − | 0.123884i | \(-0.960465\pi\) | ||||
0.992297 | − | 0.123884i | \(-0.0395352\pi\) | |||||||
\(108\) | 8.17512e8i | 0.578212i | ||||||||
\(109\) | 1.42521e9 | 0.967072 | 0.483536 | − | 0.875324i | \(-0.339352\pi\) | ||||
0.483536 | + | 0.875324i | \(0.339352\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.68851e8 | 0.168096 | ||||||||
\(112\) | 7.86145e8i | 0.472086i | ||||||||
\(113\) | − 2.84178e9i | − 1.63960i | −0.572651 | − | 0.819799i | \(-0.694085\pi\) | ||||
0.572651 | − | 0.819799i | \(-0.305915\pi\) | |||||||
\(114\) | −1.13699e9 | −0.630502 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.82796e9 | 0.937357 | ||||||||
\(117\) | − 2.63439e8i | − 0.129970i | ||||||||
\(118\) | 2.37817e9i | 1.12921i | ||||||||
\(119\) | 1.26375e9 | 0.577695 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.70525e9 | −0.723191 | ||||||||
\(122\) | − 4.10979e8i | − 0.167958i | ||||||||
\(123\) | 1.18606e9i | 0.467234i | ||||||||
\(124\) | 1.74412e9 | 0.662489 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.18629e8 | −0.147966 | ||||||||
\(127\) | − 3.49339e9i | − 1.19160i | −0.803133 | − | 0.595800i | \(-0.796835\pi\) | ||||
0.803133 | − | 0.595800i | \(-0.203165\pi\) | |||||||
\(128\) | 3.13614e9i | 1.03264i | ||||||||
\(129\) | 3.49322e9 | 1.11064 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.84697e9 | −0.547946 | −0.273973 | − | 0.961737i | \(-0.588338\pi\) | ||||
−0.273973 | + | 0.961737i | \(0.588338\pi\) | |||||||
\(132\) | − 8.06090e8i | − 0.231101i | ||||||||
\(133\) | − 8.40494e8i | − 0.232918i | ||||||||
\(134\) | 6.84762e9 | 1.83471 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.53702e9 | 0.886568 | ||||||||
\(137\) | − 1.17238e9i | − 0.284331i | −0.989843 | − | 0.142166i | \(-0.954593\pi\) | ||||
0.989843 | − | 0.142166i | \(-0.0454066\pi\) | |||||||
\(138\) | 2.02018e9i | 0.474170i | ||||||||
\(139\) | 4.89001e9 | 1.11108 | 0.555538 | − | 0.831491i | \(-0.312512\pi\) | ||||
0.555538 | + | 0.831491i | \(0.312512\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.74281e9 | 0.584399 | ||||||||
\(142\) | − 1.73325e9i | − 0.357738i | ||||||||
\(143\) | 1.08083e9i | 0.216146i | ||||||||
\(144\) | −2.03887e9 | −0.395147 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.94538e9 | −1.44720 | ||||||||
\(147\) | 6.68717e8i | 0.118118i | ||||||||
\(148\) | − 6.30410e8i | − 0.108005i | ||||||||
\(149\) | 8.61488e9 | 1.43189 | 0.715947 | − | 0.698155i | \(-0.245995\pi\) | ||||
0.715947 | + | 0.698155i | \(0.245995\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.48905e9 | 0.859213 | 0.429607 | − | 0.903016i | \(-0.358652\pi\) | ||||
0.429607 | + | 0.903016i | \(0.358652\pi\) | |||||||
\(152\) | − 2.35240e9i | − 0.357450i | ||||||||
\(153\) | 3.27753e9i | 0.483543i | ||||||||
\(154\) | 1.71754e9 | 0.246073 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.33484e9 | 0.180455 | ||||||||
\(157\) | 1.33110e9i | 0.174849i | 0.996171 | + | 0.0874246i | \(0.0278637\pi\) | ||||
−0.996171 | + | 0.0874246i | \(0.972136\pi\) | |||||||
\(158\) | 7.73101e9i | 0.986914i | ||||||||
\(159\) | 6.64595e9 | 0.824650 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.49336e9 | −0.175166 | ||||||||
\(162\) | 6.33021e9i | 0.722105i | ||||||||
\(163\) | 1.41097e9i | 0.156557i | 0.996932 | + | 0.0782786i | \(0.0249424\pi\) | ||||
−0.996932 | + | 0.0782786i | \(0.975058\pi\) | |||||||
\(164\) | 2.78111e9 | 0.300207 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.04389e9 | −0.208915 | ||||||||
\(167\) | − 2.48555e8i | − 0.0247285i | −0.999924 | − | 0.0123642i | \(-0.996064\pi\) | ||||
0.999924 | − | 0.0123642i | \(-0.00393576\pi\) | |||||||
\(168\) | 1.87163e9i | 0.181271i | ||||||||
\(169\) | 8.81470e9 | 0.831223 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.17982e9 | 0.194957 | ||||||||
\(172\) | − 8.19101e9i | − 0.713607i | ||||||||
\(173\) | 1.66522e10i | 1.41340i | 0.707515 | + | 0.706699i | \(0.249816\pi\) | ||||
−0.707515 | + | 0.706699i | \(0.750184\pi\) | |||||||
\(174\) | 2.18280e10 | 1.80527 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.36503e9 | 0.657144 | ||||||||
\(177\) | 9.85243e9i | 0.754508i | ||||||||
\(178\) | − 2.50983e10i | − 1.87394i | ||||||||
\(179\) | −2.02956e10 | −1.47762 | −0.738811 | − | 0.673913i | \(-0.764612\pi\) | ||||
−0.738811 | + | 0.673913i | \(0.764612\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.36159e10 | −0.942960 | −0.471480 | − | 0.881877i | \(-0.656280\pi\) | ||||
−0.471480 | + | 0.881877i | \(0.656280\pi\) | |||||||
\(182\) | 2.84415e9i | 0.192146i | ||||||||
\(183\) | − 1.70263e9i | − 0.112225i | ||||||||
\(184\) | −4.17968e9 | −0.268821 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.08269e10 | 1.27590 | ||||||||
\(187\) | − 1.34470e10i | − 0.804151i | ||||||||
\(188\) | − 6.43142e9i | − 0.375488i | ||||||||
\(189\) | −7.21635e9 | −0.411376 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.82357e9 | 0.0991453 | 0.0495726 | − | 0.998771i | \(-0.484214\pi\) | ||||
0.0495726 | + | 0.998771i | \(0.484214\pi\) | |||||||
\(192\) | 8.44317e8i | 0.0448384i | ||||||||
\(193\) | 1.23747e10i | 0.641989i | 0.947081 | + | 0.320995i | \(0.104017\pi\) | ||||
−0.947081 | + | 0.320995i | \(0.895983\pi\) | |||||||
\(194\) | −3.37627e10 | −1.71131 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.56803e9 | 0.0758929 | ||||||||
\(197\) | − 1.93137e10i | − 0.913626i | −0.889563 | − | 0.456813i | \(-0.848991\pi\) | ||||
0.889563 | − | 0.456813i | \(-0.151009\pi\) | |||||||
\(198\) | 4.45445e9i | 0.205968i | ||||||||
\(199\) | −1.52145e10 | −0.687733 | −0.343867 | − | 0.939019i | \(-0.611737\pi\) | ||||
−0.343867 | + | 0.939019i | \(0.611737\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.83687e10 | 1.22591 | ||||||||
\(202\) | 4.08860e10i | 1.72780i | ||||||||
\(203\) | 1.61358e10i | 0.666894i | ||||||||
\(204\) | −1.66071e10 | −0.671366 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.02424e10 | 1.17007 | ||||||||
\(207\) | − 3.87304e9i | − 0.146618i | ||||||||
\(208\) | 1.38520e10i | 0.513130i | ||||||||
\(209\) | −8.94333e9 | −0.324221 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.89626e10 | −1.35325 | −0.676624 | − | 0.736329i | \(-0.736558\pi\) | ||||
−0.676624 | + | 0.736329i | \(0.736558\pi\) | |||||||
\(212\) | − 1.55836e10i | − 0.529854i | ||||||||
\(213\) | − 7.18063e9i | − 0.239031i | ||||||||
\(214\) | −9.40658e9 | −0.306598 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.01974e10 | −0.631325 | ||||||||
\(217\) | 1.53957e10i | 0.471336i | ||||||||
\(218\) | − 3.99058e10i | − 1.19669i | ||||||||
\(219\) | −3.29166e10 | −0.966977 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.22674e10 | 0.627921 | ||||||||
\(222\) | − 7.52783e9i | − 0.208009i | ||||||||
\(223\) | 1.08324e9i | 0.0293328i | 0.999892 | + | 0.0146664i | \(0.00466863\pi\) | ||||
−0.999892 | + | 0.0146664i | \(0.995331\pi\) | |||||||
\(224\) | 1.37511e10 | 0.364939 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.95698e10 | −2.02890 | ||||||||
\(227\) | 4.94618e10i | 1.23639i | 0.786027 | + | 0.618193i | \(0.212135\pi\) | ||||
−0.786027 | + | 0.618193i | \(0.787865\pi\) | |||||||
\(228\) | 1.10451e10i | 0.270684i | ||||||||
\(229\) | 4.32776e10 | 1.03993 | 0.519965 | − | 0.854188i | \(-0.325945\pi\) | ||||
0.519965 | + | 0.854188i | \(0.325945\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.11553e9 | 0.164419 | ||||||||
\(232\) | 4.51613e10i | 1.02346i | ||||||||
\(233\) | − 7.55367e9i | − 0.167902i | −0.996470 | − | 0.0839511i | \(-0.973246\pi\) | ||||
0.996470 | − | 0.0839511i | \(-0.0267539\pi\) | |||||||
\(234\) | −7.37630e9 | −0.160830 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.31023e10 | 0.484786 | ||||||||
\(237\) | 3.20285e10i | 0.659430i | ||||||||
\(238\) | − 3.53849e10i | − 0.714862i | ||||||||
\(239\) | 2.76516e10 | 0.548188 | 0.274094 | − | 0.961703i | \(-0.411622\pi\) | ||||
0.274094 | + | 0.961703i | \(0.411622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.26006e10 | −1.57727 | −0.788635 | − | 0.614861i | \(-0.789212\pi\) | ||||
−0.788635 | + | 0.614861i | \(0.789212\pi\) | |||||||
\(242\) | 4.77469e10i | 0.894904i | ||||||||
\(243\) | − 3.29333e10i | − 0.605908i | ||||||||
\(244\) | −3.99237e9 | −0.0721068 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.32098e10 | 0.578173 | ||||||||
\(247\) | − 1.48096e10i | − 0.253168i | ||||||||
\(248\) | 4.30900e10i | 0.723343i | ||||||||
\(249\) | −8.46753e9 | −0.139592 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.01817e10 | 0.320942 | 0.160471 | − | 0.987041i | \(-0.448699\pi\) | ||||
0.160471 | + | 0.987041i | \(0.448699\pi\) | |||||||
\(252\) | 4.06668e9i | 0.0635240i | ||||||||
\(253\) | 1.58902e10i | 0.243831i | ||||||||
\(254\) | −9.78150e10 | −1.47453 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.40854e10 | 1.22360 | ||||||||
\(257\) | − 2.82781e10i | − 0.404344i | −0.979350 | − | 0.202172i | \(-0.935200\pi\) | ||||
0.979350 | − | 0.202172i | \(-0.0648000\pi\) | |||||||
\(258\) | − 9.78103e10i | − 1.37435i | ||||||||
\(259\) | 5.56475e9 | 0.0768417 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.18481e10 | −0.558205 | ||||||||
\(262\) | 5.17150e10i | 0.678049i | ||||||||
\(263\) | 1.39139e11i | 1.79328i | 0.442756 | + | 0.896642i | \(0.354001\pi\) | ||||
−0.442756 | + | 0.896642i | \(0.645999\pi\) | |||||||
\(264\) | 1.99152e10 | 0.252329 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.35338e10 | −0.288221 | ||||||||
\(267\) | − 1.03979e11i | − 1.25211i | ||||||||
\(268\) | − 6.65197e10i | − 0.787669i | ||||||||
\(269\) | −5.78883e9 | −0.0674071 | −0.0337035 | − | 0.999432i | \(-0.510730\pi\) | ||||
−0.0337035 | + | 0.999432i | \(0.510730\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.46910e10 | −0.841214 | −0.420607 | − | 0.907243i | \(-0.638183\pi\) | ||||
−0.420607 | + | 0.907243i | \(0.638183\pi\) | |||||||
\(272\) | − 1.72337e11i | − 1.90906i | ||||||||
\(273\) | 1.17829e10i | 0.128387i | ||||||||
\(274\) | −3.28265e10 | −0.351842 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.96246e10 | 0.203568 | ||||||||
\(277\) | − 2.22355e10i | − 0.226928i | −0.993542 | − | 0.113464i | \(-0.963805\pi\) | ||||
0.993542 | − | 0.113464i | \(-0.0361947\pi\) | |||||||
\(278\) | − 1.36920e11i | − 1.37489i | ||||||||
\(279\) | −3.99288e10 | −0.394519 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.36058e11 | −1.30180 | −0.650901 | − | 0.759162i | \(-0.725609\pi\) | ||||
−0.650901 | + | 0.759162i | \(0.725609\pi\) | |||||||
\(282\) | − 7.67987e10i | − 0.723157i | ||||||||
\(283\) | − 1.71084e11i | − 1.58551i | −0.609538 | − | 0.792757i | \(-0.708645\pi\) | ||||
0.609538 | − | 0.792757i | \(-0.291355\pi\) | |||||||
\(284\) | −1.68373e10 | −0.153582 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.02633e10 | 0.267467 | ||||||||
\(287\) | 2.45495e10i | 0.213586i | ||||||||
\(288\) | 3.56635e10i | 0.305462i | ||||||||
\(289\) | −1.58448e11 | −1.33612 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.39874e11 | −1.14345 | ||||||||
\(292\) | 7.71837e10i | 0.621302i | ||||||||
\(293\) | 1.05732e11i | 0.838115i | 0.907960 | + | 0.419058i | \(0.137639\pi\) | ||||
−0.907960 | + | 0.419058i | \(0.862361\pi\) | |||||||
\(294\) | 1.87241e10 | 0.146163 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.55748e10 | 0.117926 | ||||||||
\(297\) | 7.67860e10i | 0.572636i | ||||||||
\(298\) | − 2.41217e11i | − 1.77188i | ||||||||
\(299\) | −2.63133e10 | −0.190395 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.23037e10 | 0.507705 | ||||||||
\(302\) | − 1.53693e11i | − 1.06322i | ||||||||
\(303\) | 1.69385e11i | 1.15447i | ||||||||
\(304\) | −1.14618e11 | −0.769701 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.17709e10 | 0.598354 | ||||||||
\(307\) | − 1.74144e11i | − 1.11889i | −0.828869 | − | 0.559443i | \(-0.811015\pi\) | ||||
0.828869 | − | 0.559443i | \(-0.188985\pi\) | |||||||
\(308\) | − 1.66847e10i | − 0.105643i | ||||||||
\(309\) | 1.25290e11 | 0.781813 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.05907e11 | −0.641954 | −0.320977 | − | 0.947087i | \(-0.604011\pi\) | ||||
−0.320977 | + | 0.947087i | \(0.604011\pi\) | |||||||
\(312\) | 3.29784e10i | 0.197031i | ||||||||
\(313\) | − 2.43558e11i | − 1.43434i | −0.696897 | − | 0.717171i | \(-0.745437\pi\) | ||||
0.696897 | − | 0.717171i | \(-0.254563\pi\) | |||||||
\(314\) | 3.72709e10 | 0.216365 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.51012e10 | 0.423697 | ||||||||
\(317\) | − 1.83776e11i | − 1.02217i | −0.859531 | − | 0.511083i | \(-0.829245\pi\) | ||||
0.859531 | − | 0.511083i | \(-0.170755\pi\) | |||||||
\(318\) | − 1.86087e11i | − 1.02045i | ||||||||
\(319\) | 1.71694e11 | 0.928316 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.89701e10 | −0.204861 | ||||||||
\(322\) | 4.18142e10i | 0.216757i | ||||||||
\(323\) | 1.84251e11i | 0.941888i | ||||||||
\(324\) | 6.14935e10 | 0.310011 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.95071e10 | 0.193730 | ||||||||
\(327\) | − 1.65324e11i | − 0.799597i | ||||||||
\(328\) | 6.87098e10i | 0.327783i | ||||||||
\(329\) | 5.67714e10 | 0.267146 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.81760e10 | −0.266390 | −0.133195 | − | 0.991090i | \(-0.542524\pi\) | ||||
−0.133195 | + | 0.991090i | \(0.542524\pi\) | |||||||
\(332\) | 1.98549e10i | 0.0896905i | ||||||||
\(333\) | 1.44322e10i | 0.0643182i | ||||||||
\(334\) | −6.95953e9 | −0.0305999 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.11928e10 | 0.390332 | ||||||||
\(337\) | 3.40267e11i | 1.43709i | 0.695478 | + | 0.718547i | \(0.255193\pi\) | ||||
−0.695478 | + | 0.718547i | \(0.744807\pi\) | |||||||
\(338\) | − 2.46812e11i | − 1.02859i | ||||||||
\(339\) | −3.29646e11 | −1.35566 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.63819e11 | 0.656100 | ||||||||
\(342\) | − 6.10351e10i | − 0.241247i | ||||||||
\(343\) | 1.38413e10i | 0.0539949i | ||||||||
\(344\) | 2.02366e11 | 0.779157 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.66262e11 | 1.74899 | ||||||||
\(347\) | 5.02625e11i | 1.86107i | 0.366208 | + | 0.930533i | \(0.380656\pi\) | ||||
−0.366208 | + | 0.930533i | \(0.619344\pi\) | |||||||
\(348\) | − 2.12043e11i | − 0.775028i | ||||||||
\(349\) | −7.14710e10 | −0.257879 | −0.128939 | − | 0.991652i | \(-0.541157\pi\) | ||||
−0.128939 | + | 0.991652i | \(0.541157\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.27153e11 | −0.447142 | ||||||||
\(352\) | − 1.46319e11i | − 0.507995i | ||||||||
\(353\) | − 2.55096e10i | − 0.0874414i | −0.999044 | − | 0.0437207i | \(-0.986079\pi\) | ||||
0.999044 | − | 0.0437207i | \(-0.0139212\pi\) | |||||||
\(354\) | 2.75868e11 | 0.933656 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.43812e11 | −0.804508 | ||||||||
\(357\) | − 1.46595e11i | − 0.477652i | ||||||||
\(358\) | 5.68277e11i | 1.82846i | ||||||||
\(359\) | −1.49816e11 | −0.476029 | −0.238014 | − | 0.971262i | \(-0.576497\pi\) | ||||
−0.238014 | + | 0.971262i | \(0.576497\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.00146e11 | −0.620246 | ||||||||
\(362\) | 3.81246e11i | 1.16685i | ||||||||
\(363\) | 1.97809e11i | 0.597951i | ||||||||
\(364\) | 2.76289e10 | 0.0824910 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.76736e10 | −0.138871 | ||||||||
\(367\) | 4.59514e11i | 1.32221i | 0.750291 | + | 0.661107i | \(0.229913\pi\) | ||||
−0.750291 | + | 0.661107i | \(0.770087\pi\) | |||||||
\(368\) | 2.03650e11i | 0.578854i | ||||||||
\(369\) | −6.36691e10 | −0.178776 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.37560e11 | 0.376971 | ||||||||
\(372\) | − 2.02318e11i | − 0.547761i | ||||||||
\(373\) | − 5.04230e11i | − 1.34877i | −0.738379 | − | 0.674386i | \(-0.764408\pi\) | ||||
0.738379 | − | 0.674386i | \(-0.235592\pi\) | |||||||
\(374\) | −3.76516e11 | −0.995086 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.58894e11 | 0.409979 | ||||||||
\(377\) | 2.84315e11i | 0.724875i | ||||||||
\(378\) | 2.02058e11i | 0.509052i | ||||||||
\(379\) | 9.63136e10 | 0.239779 | 0.119889 | − | 0.992787i | \(-0.461746\pi\) | ||||
0.119889 | + | 0.992787i | \(0.461746\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.05234e11 | −0.985242 | ||||||||
\(382\) | − 5.10599e10i | − 0.122686i | ||||||||
\(383\) | 6.10835e11i | 1.45054i | 0.688465 | + | 0.725269i | \(0.258285\pi\) | ||||
−0.688465 | + | 0.725269i | \(0.741715\pi\) | |||||||
\(384\) | 3.63793e11 | 0.853814 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.46492e11 | 0.794421 | ||||||||
\(387\) | 1.87520e11i | 0.424960i | ||||||||
\(388\) | 3.27980e11i | 0.734691i | ||||||||
\(389\) | 6.49908e11 | 1.43906 | 0.719530 | − | 0.694461i | \(-0.244357\pi\) | ||||
0.719530 | + | 0.694461i | \(0.244357\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.27372e11 | 0.708347 | ||||||||
\(392\) | 3.87395e10i | 0.0828641i | ||||||||
\(393\) | 2.14248e11i | 0.453054i | ||||||||
\(394\) | −5.40785e11 | −1.13055 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.32718e10 | 0.0884253 | ||||||||
\(397\) | 3.67168e11i | 0.741836i | 0.928666 | + | 0.370918i | \(0.120957\pi\) | ||||
−0.928666 | + | 0.370918i | \(0.879043\pi\) | |||||||
\(398\) | 4.26007e11i | 0.851026i | ||||||||
\(399\) | −9.74973e10 | −0.192582 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.73985e11 | −1.88106 | −0.940530 | − | 0.339712i | \(-0.889670\pi\) | ||||
−0.940530 | + | 0.339712i | \(0.889670\pi\) | |||||||
\(402\) | − 7.94324e11i | − 1.51698i | ||||||||
\(403\) | 2.71275e11i | 0.512315i | ||||||||
\(404\) | 3.97178e11 | 0.741770 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.51801e11 | 0.825240 | ||||||||
\(407\) | − 5.92121e10i | − 0.106964i | ||||||||
\(408\) | − 4.10294e11i | − 0.733035i | ||||||||
\(409\) | −3.58196e11 | −0.632944 | −0.316472 | − | 0.948602i | \(-0.602498\pi\) | ||||
−0.316472 | + | 0.948602i | \(0.602498\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.35996e11 | −0.235091 | ||||||||
\(412\) | − 2.93783e11i | − 0.502330i | ||||||||
\(413\) | 2.03928e11i | 0.344907i | ||||||||
\(414\) | −1.08445e11 | −0.181430 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.42296e11 | 0.396668 | ||||||||
\(417\) | − 5.67242e11i | − 0.918662i | ||||||||
\(418\) | 2.50413e11i | 0.401203i | ||||||||
\(419\) | −4.84712e11 | −0.768283 | −0.384141 | − | 0.923274i | \(-0.625502\pi\) | ||||
−0.384141 | + | 0.923274i | \(0.625502\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.18298e11 | 1.11438 | 0.557192 | − | 0.830384i | \(-0.311879\pi\) | ||||
0.557192 | + | 0.830384i | \(0.311879\pi\) | |||||||
\(422\) | 1.09095e12i | 1.67456i | ||||||||
\(423\) | 1.47237e11i | 0.223607i | ||||||||
\(424\) | 3.85007e11 | 0.578525 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.01058e11 | −0.295786 | ||||||||
\(427\) | − 3.52415e10i | − 0.0513013i | ||||||||
\(428\) | 9.13782e10i | 0.131627i | ||||||||
\(429\) | 1.25377e11 | 0.178714 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.27297e11 | 1.15482 | 0.577409 | − | 0.816455i | \(-0.304064\pi\) | ||||
0.577409 | + | 0.816455i | \(0.304064\pi\) | |||||||
\(432\) | 9.84092e11i | 1.35944i | ||||||||
\(433\) | 8.73032e11i | 1.19353i | 0.802415 | + | 0.596767i | \(0.203548\pi\) | ||||
−0.802415 | + | 0.596767i | \(0.796452\pi\) | |||||||
\(434\) | 4.31080e11 | 0.583249 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.87657e11 | −0.513757 | ||||||||
\(437\) | − 2.17729e11i | − 0.285594i | ||||||||
\(438\) | 9.21665e11i | 1.19657i | ||||||||
\(439\) | −7.15061e11 | −0.918867 | −0.459433 | − | 0.888212i | \(-0.651947\pi\) | ||||
−0.459433 | + | 0.888212i | \(0.651947\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.58974e10 | −0.0451949 | ||||||||
\(442\) | − 6.23488e11i | − 0.777012i | ||||||||
\(443\) | 5.89691e11i | 0.727457i | 0.931505 | + | 0.363729i | \(0.118496\pi\) | ||||
−0.931505 | + | 0.363729i | \(0.881504\pi\) | |||||||
\(444\) | −7.31275e10 | −0.0893012 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.03308e10 | 0.0362975 | ||||||||
\(447\) | − 9.99326e11i | − 1.18392i | ||||||||
\(448\) | 1.74759e10i | 0.0204969i | ||||||||
\(449\) | 1.06477e12 | 1.23636 | 0.618181 | − | 0.786036i | \(-0.287870\pi\) | ||||
0.618181 | + | 0.786036i | \(0.287870\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.61220e11 | 0.297312 | ||||||||
\(452\) | 7.72964e11i | 0.871037i | ||||||||
\(453\) | − 6.36730e11i | − 0.710417i | ||||||||
\(454\) | 1.38493e12 | 1.52995 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.72879e11 | −0.295548 | ||||||||
\(457\) | − 1.54296e12i | − 1.65475i | −0.561651 | − | 0.827374i | \(-0.689834\pi\) | ||||
0.561651 | − | 0.827374i | \(-0.310166\pi\) | |||||||
\(458\) | − 1.21177e12i | − 1.28685i | ||||||||
\(459\) | 1.58195e12 | 1.66355 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.38680e11 | −0.864852 | −0.432426 | − | 0.901669i | \(-0.642342\pi\) | ||||
−0.432426 | + | 0.901669i | \(0.642342\pi\) | |||||||
\(462\) | − 1.99235e11i | − 0.203459i | ||||||||
\(463\) | − 8.61819e11i | − 0.871569i | −0.900051 | − | 0.435784i | \(-0.856471\pi\) | ||||
0.900051 | − | 0.435784i | \(-0.143529\pi\) | |||||||
\(464\) | 2.20043e12 | 2.20382 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.11503e11 | −0.207768 | ||||||||
\(467\) | − 1.46986e12i | − 1.43005i | −0.699101 | − | 0.715023i | \(-0.746416\pi\) | ||||
0.699101 | − | 0.715023i | \(-0.253584\pi\) | |||||||
\(468\) | 7.16555e10i | 0.0690468i | ||||||||
\(469\) | 5.87183e11 | 0.560397 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.54408e11 | 0.144569 | ||||||||
\(472\) | 5.70762e11i | 0.529317i | ||||||||
\(473\) | − 7.69353e11i | − 0.706725i | ||||||||
\(474\) | 8.96797e11 | 0.816003 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.43739e11 | −0.306901 | ||||||||
\(477\) | 3.56761e11i | 0.315533i | ||||||||
\(478\) | − 7.74245e11i | − 0.678348i | ||||||||
\(479\) | −2.20227e12 | −1.91144 | −0.955721 | − | 0.294275i | \(-0.904922\pi\) | ||||
−0.955721 | + | 0.294275i | \(0.904922\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.80519e10 | 0.0835224 | ||||||||
\(482\) | 2.31282e12i | 1.95177i | ||||||||
\(483\) | 1.73230e11i | 0.144831i | ||||||||
\(484\) | 4.63827e11 | 0.384195 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.22132e11 | −0.749773 | ||||||||
\(487\) | − 1.30073e12i | − 1.04786i | −0.851760 | − | 0.523932i | \(-0.824464\pi\) | ||||
0.851760 | − | 0.523932i | \(-0.175536\pi\) | |||||||
\(488\) | − 9.86350e10i | − 0.0787303i | ||||||||
\(489\) | 1.63672e11 | 0.129445 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.88947e11 | 0.534957 | 0.267479 | − | 0.963564i | \(-0.413810\pi\) | ||||
0.267479 | + | 0.963564i | \(0.413810\pi\) | |||||||
\(492\) | − 3.22609e11i | − 0.248218i | ||||||||
\(493\) | − 3.53724e12i | − 2.69683i | ||||||||
\(494\) | −4.14670e11 | −0.313279 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.09951e12 | 1.55758 | ||||||||
\(497\) | − 1.48627e11i | − 0.109268i | ||||||||
\(498\) | 2.37091e11i | 0.172736i | ||||||||
\(499\) | −1.76710e12 | −1.27588 | −0.637939 | − | 0.770087i | \(-0.720213\pi\) | ||||
−0.637939 | + | 0.770087i | \(0.720213\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.88323e10 | −0.0204461 | ||||||||
\(502\) | − 5.65088e11i | − 0.397145i | ||||||||
\(503\) | 2.63527e12i | 1.83556i | 0.397089 | + | 0.917780i | \(0.370020\pi\) | ||||
−0.397089 | + | 0.917780i | \(0.629980\pi\) | |||||||
\(504\) | −1.00471e11 | −0.0693590 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.44927e11 | 0.301725 | ||||||||
\(507\) | − 1.02251e12i | − 0.687274i | ||||||||
\(508\) | 9.50203e11i | 0.633038i | ||||||||
\(509\) | −2.22151e12 | −1.46696 | −0.733479 | − | 0.679712i | \(-0.762105\pi\) | ||||
−0.733479 | + | 0.679712i | \(0.762105\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.81317e11 | −0.442033 | ||||||||
\(512\) | − 7.48685e11i | − 0.481487i | ||||||||
\(513\) | − 1.05213e12i | − 0.670718i | ||||||||
\(514\) | −7.91786e11 | −0.500350 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.50157e11 | −0.590027 | ||||||||
\(517\) | − 6.04080e11i | − 0.371867i | ||||||||
\(518\) | − 1.55813e11i | − 0.0950868i | ||||||||
\(519\) | 1.93166e12 | 1.16863 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.87441e12 | −1.11454 | −0.557269 | − | 0.830332i | \(-0.688151\pi\) | ||||
−0.557269 | + | 0.830332i | \(0.688151\pi\) | |||||||
\(522\) | 1.17175e12i | 0.690743i | ||||||||
\(523\) | − 1.58412e12i | − 0.925828i | −0.886403 | − | 0.462914i | \(-0.846804\pi\) | ||||
0.886403 | − | 0.462914i | \(-0.153196\pi\) | |||||||
\(524\) | 5.02375e11 | 0.291096 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.89590e12 | 2.21908 | ||||||||
\(527\) | − 3.37501e12i | − 1.90602i | ||||||||
\(528\) | − 9.70343e11i | − 0.543341i | ||||||||
\(529\) | 1.41430e12 | 0.785219 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.28889e11 | −0.288695 | ||||||||
\(532\) | 2.28614e11i | 0.123737i | ||||||||
\(533\) | 4.32565e11i | 0.232156i | ||||||||
\(534\) | −2.91140e12 | −1.54941 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.64343e12 | 0.860021 | ||||||||
\(537\) | 2.35429e12i | 1.22173i | ||||||||
\(538\) | 1.62087e11i | 0.0834120i | ||||||||
\(539\) | 1.47279e11 | 0.0751609 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.79888e12 | 1.40474 | 0.702370 | − | 0.711812i | \(-0.252125\pi\) | ||||
0.702370 | + | 0.711812i | \(0.252125\pi\) | |||||||
\(542\) | 2.09135e12i | 1.04095i | ||||||||
\(543\) | 1.57945e12i | 0.779660i | ||||||||
\(544\) | −3.01448e12 | −1.47577 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.29921e11 | 0.158870 | ||||||||
\(547\) | − 1.16606e12i | − 0.556901i | −0.960451 | − | 0.278451i | \(-0.910179\pi\) | ||||
0.960451 | − | 0.278451i | \(-0.0898209\pi\) | |||||||
\(548\) | 3.18886e11i | 0.151051i | ||||||||
\(549\) | 9.13988e10 | 0.0429403 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.35255e12 | −1.08732 | ||||||||
\(552\) | 4.84843e11i | 0.222267i | ||||||||
\(553\) | 6.62934e11i | 0.301444i | ||||||||
\(554\) | −6.22594e11 | −0.280809 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.33008e12 | −0.590259 | ||||||||
\(557\) | − 3.29033e12i | − 1.44841i | −0.689586 | − | 0.724204i | \(-0.742207\pi\) | ||||
0.689586 | − | 0.724204i | \(-0.257793\pi\) | |||||||
\(558\) | 1.11801e12i | 0.488192i | ||||||||
\(559\) | 1.27400e12 | 0.551845 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.55985e12 | −0.664890 | ||||||||
\(562\) | 3.80962e12i | 1.61090i | ||||||||
\(563\) | − 3.63871e12i | − 1.52637i | −0.646179 | − | 0.763186i | \(-0.723634\pi\) | ||||
0.646179 | − | 0.763186i | \(-0.276366\pi\) | |||||||
\(564\) | −7.46044e11 | −0.310462 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.79035e12 | −1.96197 | ||||||||
\(567\) | 5.42815e11i | 0.220561i | ||||||||
\(568\) | − 4.15981e11i | − 0.167690i | ||||||||
\(569\) | −4.35009e12 | −1.73978 | −0.869888 | − | 0.493250i | \(-0.835809\pi\) | ||||
−0.869888 | + | 0.493250i | \(0.835809\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.91136e12 | −1.93348 | −0.966739 | − | 0.255767i | \(-0.917672\pi\) | ||||
−0.966739 | + | 0.255767i | \(0.917672\pi\) | |||||||
\(572\) | − 2.93987e11i | − 0.114827i | ||||||||
\(573\) | − 2.11534e11i | − 0.0819756i | ||||||||
\(574\) | 6.87385e11 | 0.264299 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.53238e10 | −0.0171564 | ||||||||
\(577\) | 1.68758e12i | 0.633830i | 0.948454 | + | 0.316915i | \(0.102647\pi\) | ||||
−0.948454 | + | 0.316915i | \(0.897353\pi\) | |||||||
\(578\) | 4.43654e12i | 1.65337i | ||||||||
\(579\) | 1.43547e12 | 0.530811 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.75263e11 | −0.0638114 | ||||||||
\(582\) | 3.91647e12i | 1.41495i | ||||||||
\(583\) | − 1.46371e12i | − 0.524744i | ||||||||
\(584\) | −1.90689e12 | −0.678373 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.96051e12 | 1.03711 | ||||||||
\(587\) | 4.82739e12i | 1.67819i | 0.543987 | + | 0.839094i | \(0.316914\pi\) | ||||
−0.543987 | + | 0.839094i | \(0.683086\pi\) | |||||||
\(588\) | − 1.81891e11i | − 0.0627499i | ||||||||
\(589\) | −2.24466e12 | −0.768478 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.24039e12 | −0.755407 | ||||||||
\(592\) | − 7.58865e11i | − 0.253932i | ||||||||
\(593\) | − 1.12076e12i | − 0.372193i | −0.982532 | − | 0.186096i | \(-0.940416\pi\) | ||||
0.982532 | − | 0.186096i | \(-0.0595837\pi\) | |||||||
\(594\) | 2.15001e12 | 0.708600 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.34325e12 | −0.760694 | ||||||||
\(597\) | 1.76489e12i | 0.568633i | ||||||||
\(598\) | 7.36773e11i | 0.235602i | ||||||||
\(599\) | −1.35944e12 | −0.431460 | −0.215730 | − | 0.976453i | \(-0.569213\pi\) | ||||
−0.215730 | + | 0.976453i | \(0.569213\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.50421e11 | 0.297153 | 0.148577 | − | 0.988901i | \(-0.452531\pi\) | ||||
0.148577 | + | 0.988901i | \(0.452531\pi\) | |||||||
\(602\) | − 2.02450e12i | − 0.628253i | ||||||||
\(603\) | 1.52286e12i | 0.469064i | ||||||||
\(604\) | −1.49302e12 | −0.456457 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.74277e12 | 1.42858 | ||||||||
\(607\) | − 3.35939e12i | − 1.00441i | −0.864749 | − | 0.502205i | \(-0.832522\pi\) | ||||
0.864749 | − | 0.502205i | \(-0.167478\pi\) | |||||||
\(608\) | 2.00487e12i | 0.595006i | ||||||||
\(609\) | 1.87175e12 | 0.551403 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.00032e12 | 0.290372 | ||||||||
\(612\) | − 8.91489e11i | − 0.256882i | ||||||||
\(613\) | − 2.62257e12i | − 0.750162i | −0.926992 | − | 0.375081i | \(-0.877615\pi\) | ||||
0.926992 | − | 0.375081i | \(-0.122385\pi\) | |||||||
\(614\) | −4.87603e12 | −1.38455 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.12210e11 | 0.115347 | ||||||||
\(617\) | 3.35285e10i | 0.00931388i | 0.999989 | + | 0.00465694i | \(0.00148236\pi\) | ||||
−0.999989 | + | 0.00465694i | \(0.998518\pi\) | |||||||
\(618\) | − 3.50812e12i | − 0.967444i | ||||||||
\(619\) | −5.51587e12 | −1.51010 | −0.755051 | − | 0.655666i | \(-0.772388\pi\) | ||||
−0.755051 | + | 0.655666i | \(0.772388\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.86939e12 | −0.504414 | ||||||||
\(622\) | 2.96540e12i | 0.794377i | ||||||||
\(623\) | − 2.15218e12i | − 0.572377i | ||||||||
\(624\) | 1.60683e12 | 0.424268 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.81962e12 | −1.77491 | ||||||||
\(627\) | 1.03743e12i | 0.268073i | ||||||||
\(628\) | − 3.62060e11i | − 0.0928886i | ||||||||
\(629\) | −1.21989e12 | −0.310738 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.72456e12 | 0.684170 | 0.342085 | − | 0.939669i | \(-0.388867\pi\) | ||||
0.342085 | + | 0.939669i | \(0.388867\pi\) | |||||||
\(632\) | 1.85544e12i | 0.462616i | ||||||||
\(633\) | 4.51966e12i | 1.11890i | ||||||||
\(634\) | −5.14572e12 | −1.26487 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.80770e12 | −0.438096 | ||||||||
\(637\) | 2.43886e11i | 0.0586893i | ||||||||
\(638\) | − 4.80742e12i | − 1.14873i | ||||||||
\(639\) | 3.85463e11 | 0.0914596 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.79136e11 | 0.0887022 | 0.0443511 | − | 0.999016i | \(-0.485878\pi\) | ||||
0.0443511 | + | 0.999016i | \(0.485878\pi\) | |||||||
\(642\) | 1.09116e12i | 0.253502i | ||||||||
\(643\) | − 5.15446e12i | − 1.18914i | −0.804043 | − | 0.594571i | \(-0.797322\pi\) | ||||
0.804043 | − | 0.594571i | \(-0.202678\pi\) | |||||||
\(644\) | 4.06195e11 | 0.0930568 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.15904e12 | 1.16553 | ||||||||
\(647\) | 2.68059e12i | 0.601397i | 0.953719 | + | 0.300699i | \(0.0972198\pi\) | ||||
−0.953719 | + | 0.300699i | \(0.902780\pi\) | |||||||
\(648\) | 1.51925e12i | 0.338487i | ||||||||
\(649\) | 2.16991e12 | 0.480111 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.78590e12 | 0.389712 | ||||||||
\(652\) | − 3.83783e11i | − 0.0831710i | ||||||||
\(653\) | − 6.44986e12i | − 1.38816i | −0.719896 | − | 0.694082i | \(-0.755810\pi\) | ||||
0.719896 | − | 0.694082i | \(-0.244190\pi\) | |||||||
\(654\) | −4.62908e12 | −0.989451 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.34780e12 | 0.705818 | ||||||||
\(657\) | − 1.76700e12i | − 0.369991i | ||||||||
\(658\) | − 1.58960e12i | − 0.330576i | ||||||||
\(659\) | 2.79549e12 | 0.577396 | 0.288698 | − | 0.957420i | \(-0.406778\pi\) | ||||
0.288698 | + | 0.957420i | \(0.406778\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.93691e11 | −0.100589 | −0.0502943 | − | 0.998734i | \(-0.516016\pi\) | ||||
−0.0502943 | + | 0.998734i | \(0.516016\pi\) | |||||||
\(662\) | 1.62893e12i | 0.329641i | ||||||||
\(663\) | − 2.58302e12i | − 0.519179i | ||||||||
\(664\) | −4.90533e11 | −0.0979291 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.04102e11 | 0.0795897 | ||||||||
\(667\) | 4.17995e12i | 0.817720i | ||||||||
\(668\) | 6.76068e10i | 0.0131370i | ||||||||
\(669\) | 1.25656e11 | 0.0242530 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.74989e11 | −0.0714113 | ||||||||
\(672\) | − 1.59513e12i | − 0.301740i | ||||||||
\(673\) | 2.83805e12i | 0.533277i | 0.963797 | + | 0.266638i | \(0.0859130\pi\) | ||||
−0.963797 | + | 0.266638i | \(0.914087\pi\) | |||||||
\(674\) | 9.52747e12 | 1.77831 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.39760e12 | −0.441587 | ||||||||
\(677\) | − 7.71236e12i | − 1.41104i | −0.708691 | − | 0.705519i | \(-0.750714\pi\) | ||||
0.708691 | − | 0.705519i | \(-0.249286\pi\) | |||||||
\(678\) | 9.23010e12i | 1.67754i | ||||||||
\(679\) | −2.89515e12 | −0.522705 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.73757e12 | 1.02227 | ||||||||
\(682\) | − 4.58693e12i | − 0.811882i | ||||||||
\(683\) | 1.07677e13i | 1.89334i | 0.322204 | + | 0.946670i | \(0.395576\pi\) | ||||
−0.322204 | + | 0.946670i | \(0.604424\pi\) | |||||||
\(684\) | −5.92912e11 | −0.103571 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.87556e11 | 0.0668153 | ||||||||
\(687\) | − 5.02021e12i | − 0.859837i | ||||||||
\(688\) | − 9.86005e12i | − 1.67776i | ||||||||
\(689\) | 2.42382e12 | 0.409746 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.02298e12 | 0.337552 | 0.168776 | − | 0.985654i | \(-0.446019\pi\) | ||||
0.168776 | + | 0.985654i | \(0.446019\pi\) | |||||||
\(692\) | − 4.52940e12i | − 0.750867i | ||||||||
\(693\) | 3.81969e11i | 0.0629113i | ||||||||
\(694\) | 1.40735e13 | 2.30295 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.23871e12 | 0.846219 | ||||||||
\(697\) | − 5.38168e12i | − 0.863714i | ||||||||
\(698\) | 2.00119e12i | 0.319109i | ||||||||
\(699\) | −8.76226e11 | −0.138825 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.66031e11 | 0.135457 | 0.0677286 | − | 0.997704i | \(-0.478425\pi\) | ||||
0.0677286 | + | 0.997704i | \(0.478425\pi\) | |||||||
\(702\) | 3.56029e12i | 0.553310i | ||||||||
\(703\) | 8.11328e11i | 0.125285i | ||||||||
\(704\) | 1.85953e11 | 0.0285317 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.14268e11 | −0.108203 | ||||||||
\(707\) | 3.50597e12i | 0.527741i | ||||||||
\(708\) | − 2.67986e12i | − 0.400832i | ||||||||
\(709\) | 3.78834e12 | 0.563042 | 0.281521 | − | 0.959555i | \(-0.409161\pi\) | ||||
0.281521 | + | 0.959555i | \(0.409161\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.71932e12 | −0.252315 | ||||||||
\(712\) | − 6.02360e12i | − 0.878407i | ||||||||
\(713\) | 3.98824e12i | 0.577934i | ||||||||
\(714\) | −4.10465e12 | −0.591064 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.52040e12 | 0.784986 | ||||||||
\(717\) | − 3.20758e12i | − 0.453254i | ||||||||
\(718\) | 4.19485e12i | 0.589056i | ||||||||
\(719\) | −8.16972e11 | −0.114006 | −0.0570029 | − | 0.998374i | \(-0.518154\pi\) | ||||
−0.0570029 | + | 0.998374i | \(0.518154\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.59328e12 | 0.357389 | ||||||||
\(722\) | 5.60408e12i | 0.767515i | ||||||||
\(723\) | 9.58166e12i | 1.30412i | ||||||||
\(724\) | 3.70353e12 | 0.500947 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.53864e12 | 0.739927 | ||||||||
\(727\) | − 3.13227e12i | − 0.415867i | −0.978143 | − | 0.207933i | \(-0.933326\pi\) | ||||
0.978143 | − | 0.207933i | \(-0.0666737\pi\) | |||||||
\(728\) | 6.82595e11i | 0.0900683i | ||||||||
\(729\) | −8.27017e12 | −1.08453 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.58503e13 | −2.05309 | ||||||||
\(732\) | 4.63115e11i | 0.0596195i | ||||||||
\(733\) | − 1.33197e13i | − 1.70422i | −0.523360 | − | 0.852112i | \(-0.675322\pi\) | ||||
0.523360 | − | 0.852112i | \(-0.324678\pi\) | |||||||
\(734\) | 1.28664e13 | 1.63616 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.56220e12 | 0.447474 | ||||||||
\(737\) | − 6.24796e12i | − 0.780072i | ||||||||
\(738\) | 1.78273e12i | 0.221224i | ||||||||
\(739\) | 1.56702e13 | 1.93274 | 0.966371 | − | 0.257154i | \(-0.0827847\pi\) | ||||
0.966371 | + | 0.257154i | \(0.0827847\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.71792e12 | −0.209325 | ||||||||
\(742\) | − 3.85167e12i | − 0.466478i | ||||||||
\(743\) | 7.91108e12i | 0.952327i | 0.879357 | + | 0.476164i | \(0.157973\pi\) | ||||
−0.879357 | + | 0.476164i | \(0.842027\pi\) | |||||||
\(744\) | 4.99844e12 | 0.598076 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.41184e13 | −1.66902 | ||||||||
\(747\) | − 4.54546e11i | − 0.0534115i | ||||||||
\(748\) | 3.65758e12i | 0.427205i | ||||||||
\(749\) | −8.06614e11 | −0.0936478 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.01514e12 | −0.460597 | −0.230299 | − | 0.973120i | \(-0.573970\pi\) | ||||
−0.230299 | + | 0.973120i | \(0.573970\pi\) | |||||||
\(752\) | − 7.74191e12i | − 0.882811i | ||||||||
\(753\) | − 2.34108e12i | − 0.265362i | ||||||||
\(754\) | 7.96081e12 | 0.896987 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.96285e12 | 0.218544 | ||||||||
\(757\) | − 2.84075e12i | − 0.314414i | −0.987566 | − | 0.157207i | \(-0.949751\pi\) | ||||
0.987566 | − | 0.157207i | \(-0.0502489\pi\) | |||||||
\(758\) | − 2.69678e12i | − 0.296711i | ||||||||
\(759\) | 1.84327e12 | 0.201605 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.10439e12 | −0.767884 | −0.383942 | − | 0.923357i | \(-0.625434\pi\) | ||||
−0.383942 | + | 0.923357i | \(0.625434\pi\) | |||||||
\(762\) | 1.13465e13i | 1.21918i | ||||||||
\(763\) | − 3.42192e12i | − 0.365519i | ||||||||
\(764\) | −4.96011e11 | −0.0526709 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.71034e13 | 1.79495 | ||||||||
\(767\) | 3.59325e12i | 0.374894i | ||||||||
\(768\) | − 9.75390e12i | − 1.01170i | ||||||||
\(769\) | 4.97052e12 | 0.512546 | 0.256273 | − | 0.966604i | \(-0.417505\pi\) | ||||
0.256273 | + | 0.966604i | \(0.417505\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.28026e12 | −0.334321 | ||||||||
\(772\) | − 3.36593e12i | − 0.341057i | ||||||||
\(773\) | 1.11565e13i | 1.12388i | 0.827179 | + | 0.561939i | \(0.189944\pi\) | ||||
−0.827179 | + | 0.561939i | \(0.810056\pi\) | |||||||
\(774\) | 5.25056e12 | 0.525861 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.10304e12 | −0.802177 | ||||||||
\(777\) | − 6.45512e11i | − 0.0635345i | ||||||||
\(778\) | − 1.81974e13i | − 1.78075i | ||||||||
\(779\) | −3.57925e12 | −0.348236 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.58147e12 | −0.152101 | ||||||||
\(782\) | − 9.16642e12i | − 0.876535i | ||||||||
\(783\) | 2.01987e13i | 1.92041i | ||||||||
\(784\) | 1.88753e12 | 0.178432 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.99894e12 | 0.560626 | ||||||||
\(787\) | 6.23763e12i | 0.579607i | 0.957086 | + | 0.289803i | \(0.0935899\pi\) | ||||
−0.957086 | + | 0.289803i | \(0.906410\pi\) | |||||||
\(788\) | 5.25334e12i | 0.485364i | ||||||||
\(789\) | 1.61402e13 | 1.48273 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.82311e12 | −0.619710 | ||||||||
\(792\) | 1.06907e12i | 0.0965477i | ||||||||
\(793\) | − 6.20960e11i | − 0.0557615i | ||||||||
\(794\) | 1.02807e13 | 0.917975 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.13835e12 | 0.365358 | ||||||||
\(797\) | 1.83799e12i | 0.161355i | 0.996740 | + | 0.0806773i | \(0.0257083\pi\) | ||||
−0.996740 | + | 0.0806773i | \(0.974292\pi\) | |||||||
\(798\) | 2.72992e12i | 0.238307i | ||||||||
\(799\) | −1.24453e13 | −1.08030 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.58169e12 | 0.479092 | ||||||||
\(802\) | 2.72716e13i | 2.32769i | ||||||||
\(803\) | 7.24960e12i | 0.615310i | ||||||||
\(804\) | −7.71629e12 | −0.651263 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.59570e12 | 0.633957 | ||||||||
\(807\) | 6.71504e11i | 0.0557337i | ||||||||
\(808\) | 9.81263e12i | 0.809906i | ||||||||
\(809\) | −1.92205e13 | −1.57760 | −0.788801 | − | 0.614649i | \(-0.789298\pi\) | ||||
−0.788801 | + | 0.614649i | \(0.789298\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.70316e13 | −1.38249 | −0.691246 | − | 0.722620i | \(-0.742938\pi\) | ||||
−0.691246 | + | 0.722620i | \(0.742938\pi\) | |||||||
\(812\) | − 4.38892e12i | − 0.354288i | ||||||||
\(813\) | 8.66416e12i | 0.695535i | ||||||||
\(814\) | −1.65794e12 | −0.132361 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.99911e13 | −1.57845 | ||||||||
\(817\) | 1.05417e13i | 0.827774i | ||||||||
\(818\) | 1.00295e13i | 0.783228i | ||||||||
\(819\) | −6.32518e11 | −0.0491242 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.33485e13 | 1.02539 | 0.512694 | − | 0.858572i | \(-0.328648\pi\) | ||||
0.512694 | + | 0.858572i | \(0.328648\pi\) | |||||||
\(822\) | 3.80788e12i | 0.290911i | ||||||||
\(823\) | − 1.72858e13i | − 1.31338i | −0.754161 | − | 0.656689i | \(-0.771956\pi\) | ||||
0.754161 | − | 0.656689i | \(-0.228044\pi\) | |||||||
\(824\) | 7.25817e12 | 0.548473 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.71000e12 | 0.426801 | ||||||||
\(827\) | − 1.64651e13i | − 1.22402i | −0.790849 | − | 0.612012i | \(-0.790361\pi\) | ||||
0.790849 | − | 0.612012i | \(-0.209639\pi\) | |||||||
\(828\) | 1.05347e12i | 0.0778906i | ||||||||
\(829\) | 5.91786e12 | 0.435181 | 0.217590 | − | 0.976040i | \(-0.430180\pi\) | ||||
0.217590 | + | 0.976040i | \(0.430180\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.57932e12 | −0.187629 | ||||||||
\(832\) | 3.07928e11i | 0.0222789i | ||||||||
\(833\) | − 3.03426e12i | − 0.218348i | ||||||||
\(834\) | −1.58828e13 | −1.13679 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.43259e12 | 0.172242 | ||||||||
\(837\) | 1.92723e13i | 1.35728i | ||||||||
\(838\) | 1.35719e13i | 0.950701i | ||||||||
\(839\) | −2.40380e13 | −1.67483 | −0.837414 | − | 0.546569i | \(-0.815934\pi\) | ||||
−0.837414 | + | 0.546569i | \(0.815934\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.06570e13 | 2.11324 | ||||||||
\(842\) | − 2.01123e13i | − 1.37898i | ||||||||
\(843\) | 1.57827e13i | 1.07636i | ||||||||
\(844\) | 1.05978e13 | 0.718913 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.12263e12 | 0.276699 | ||||||||
\(847\) | 4.09430e12i | 0.273341i | ||||||||
\(848\) | − 1.87590e13i | − 1.24574i | ||||||||
\(849\) | −1.98457e13 | −1.31094 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.44154e12 | 0.0942203 | ||||||||
\(852\) | 1.95313e12i | 0.126985i | ||||||||
\(853\) | 2.26446e13i | 1.46452i | 0.681027 | + | 0.732258i | \(0.261534\pi\) | ||||
−0.681027 | + | 0.732258i | \(0.738466\pi\) | |||||||
\(854\) | −9.86761e11 | −0.0634821 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.25758e12 | −0.143718 | ||||||||
\(857\) | 1.20223e13i | 0.761334i | 0.924712 | + | 0.380667i | \(0.124306\pi\) | ||||
−0.924712 | + | 0.380667i | \(0.875694\pi\) | |||||||
\(858\) | − 3.51055e12i | − 0.221148i | ||||||||
\(859\) | 9.44258e12 | 0.591727 | 0.295864 | − | 0.955230i | \(-0.404393\pi\) | ||||
0.295864 | + | 0.955230i | \(0.404393\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.84774e12 | 0.176598 | ||||||||
\(862\) | − 2.31643e13i | − 1.42901i | ||||||||
\(863\) | 8.80380e12i | 0.540283i | 0.962821 | + | 0.270142i | \(0.0870705\pi\) | ||||
−0.962821 | + | 0.270142i | \(0.912929\pi\) | |||||||
\(864\) | 1.72135e13 | 1.05089 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.44449e13 | 1.47692 | ||||||||
\(867\) | 1.83800e13i | 1.10474i | ||||||||
\(868\) | − 4.18763e12i | − 0.250397i | ||||||||
\(869\) | 7.05399e12 | 0.419610 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.03463e13 | 0.609119 | ||||||||
\(872\) | − 9.57740e12i | − 0.560949i | ||||||||
\(873\) | − 7.50858e12i | − 0.437516i | ||||||||
\(874\) | −6.09641e12 | −0.353405 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.95331e12 | 0.513707 | ||||||||
\(877\) | − 6.73513e12i | − 0.384457i | −0.981350 | − | 0.192229i | \(-0.938429\pi\) | ||||
0.981350 | − | 0.192229i | \(-0.0615715\pi\) | |||||||
\(878\) | 2.00217e13i | 1.13704i | ||||||||
\(879\) | 1.22650e13 | 0.692973 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.58474e12 | −0.424179 | −0.212089 | − | 0.977250i | \(-0.568027\pi\) | ||||
−0.212089 | + | 0.977250i | \(0.568027\pi\) | |||||||
\(882\) | 1.00513e12i | 0.0559258i | ||||||||
\(883\) | − 1.78234e13i | − 0.986662i | −0.869842 | − | 0.493331i | \(-0.835779\pi\) | ||||
0.869842 | − | 0.493331i | \(-0.164221\pi\) | |||||||
\(884\) | −6.05674e12 | −0.333583 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.65113e13 | 0.900182 | ||||||||
\(887\) | 2.45177e13i | 1.32991i | 0.746882 | + | 0.664956i | \(0.231550\pi\) | ||||
−0.746882 | + | 0.664956i | \(0.768450\pi\) | |||||||
\(888\) | − 1.80668e12i | − 0.0975041i | ||||||||
\(889\) | −8.38764e12 | −0.450383 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.77586e12 | 0.307020 | ||||||||
\(892\) | − 2.94642e11i | − 0.0155830i | ||||||||
\(893\) | 8.27714e12i | 0.435561i | ||||||||
\(894\) | −2.79811e13 | −1.46503 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7.52988e12 | 0.390303 | ||||||||
\(897\) | 3.05234e12i | 0.157423i | ||||||||
\(898\) | − 2.98134e13i | − 1.52992i | ||||||||
\(899\) | 4.30928e13 | 2.20032 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.01555e13 | −1.52442 | ||||||||
\(902\) | − 7.31416e12i | − 0.367905i | ||||||||
\(903\) | − 8.38723e12i | − 0.419782i | ||||||||
\(904\) | −1.90968e13 | −0.951047 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.78284e13 | −0.879096 | ||||||||
\(907\) | 8.14231e12i | 0.399498i | 0.979847 | + | 0.199749i | \(0.0640127\pi\) | ||||
−0.979847 | + | 0.199749i | \(0.935987\pi\) | |||||||
\(908\) | − 1.34536e13i | − 0.656830i | ||||||||
\(909\) | −9.09275e12 | −0.441731 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.26965e13 | −0.610733 | −0.305367 | − | 0.952235i | \(-0.598779\pi\) | ||||
−0.305367 | + | 0.952235i | \(0.598779\pi\) | |||||||
\(912\) | 1.32957e13i | 0.636406i | ||||||||
\(913\) | 1.86490e12i | 0.0888254i | ||||||||
\(914\) | −4.32029e13 | −2.04765 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.17715e13 | −0.552463 | ||||||||
\(917\) | 4.43456e12i | 0.207104i | ||||||||
\(918\) | − 4.42947e13i | − 2.05854i | ||||||||
\(919\) | 2.53575e13 | 1.17270 | 0.586350 | − | 0.810058i | \(-0.300564\pi\) | ||||
0.586350 | + | 0.810058i | \(0.300564\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.02007e13 | −0.925120 | ||||||||
\(922\) | 2.34830e13i | 1.07020i | ||||||||
\(923\) | − 2.61882e12i | − 0.118768i | ||||||||
\(924\) | −1.93542e12 | −0.0873478 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.41309e13 | −1.07851 | ||||||||
\(927\) | 6.72569e12i | 0.299143i | ||||||||
\(928\) | − 3.84895e13i | − 1.70363i | ||||||||
\(929\) | −1.89611e13 | −0.835203 | −0.417602 | − | 0.908630i | \(-0.637129\pi\) | ||||
−0.417602 | + | 0.908630i | \(0.637129\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.01803e12 | −0.0880346 | ||||||||
\(932\) | 2.05460e12i | 0.0891980i | ||||||||
\(933\) | 1.22852e13i | 0.530782i | ||||||||
\(934\) | −4.11561e13 | −1.76959 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.77031e12 | −0.0753891 | ||||||||
\(937\) | − 8.65559e12i | − 0.366833i | −0.983035 | − | 0.183416i | \(-0.941284\pi\) | ||||
0.983035 | − | 0.183416i | \(-0.0587157\pi\) | |||||||
\(938\) | − 1.64411e13i | − 0.693456i | ||||||||
\(939\) | −2.82527e13 | −1.18595 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.42336e13 | 1.42331 | 0.711654 | − | 0.702530i | \(-0.247946\pi\) | ||||
0.711654 | + | 0.702530i | \(0.247946\pi\) | |||||||
\(942\) | − 4.32343e12i | − 0.178895i | ||||||||
\(943\) | 6.35950e12i | 0.261891i | ||||||||
\(944\) | 2.78097e13 | 1.13978 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.15419e13 | −0.874527 | ||||||||
\(947\) | − 2.38597e13i | − 0.964030i | −0.876163 | − | 0.482015i | \(-0.839905\pi\) | ||||
0.876163 | − | 0.482015i | \(-0.160095\pi\) | |||||||
\(948\) | − 8.71174e12i | − 0.350322i | ||||||||
\(949\) | −1.20049e13 | −0.480464 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.13180e13 | −0.845150 | ||||||||
\(952\) | − 8.49238e12i | − 0.335091i | ||||||||
\(953\) | − 4.83481e13i | − 1.89872i | −0.314189 | − | 0.949360i | \(-0.601733\pi\) | ||||
0.314189 | − | 0.949360i | \(-0.398267\pi\) | |||||||
\(954\) | 9.98932e12 | 0.390452 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.52123e12 | −0.291225 | ||||||||
\(957\) | − 1.99165e13i | − 0.767553i | ||||||||
\(958\) | 6.16636e13i | 2.36529i | ||||||||
\(959\) | −2.81488e12 | −0.107467 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.46768e13 | 0.555106 | ||||||||
\(962\) | − 2.74545e12i | − 0.103354i | ||||||||
\(963\) | − 2.09196e12i | − 0.0783852i | ||||||||
\(964\) | 2.24674e13 | 0.837925 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.85045e12 | 0.179219 | ||||||||
\(967\) | 2.28025e13i | 0.838617i | 0.907844 | + | 0.419308i | \(0.137727\pi\) | ||||
−0.907844 | + | 0.419308i | \(0.862273\pi\) | |||||||
\(968\) | 1.14593e13i | 0.419486i | ||||||||
\(969\) | 2.13731e13 | 0.778774 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.62385e12 | 0.275225 | 0.137612 | − | 0.990486i | \(-0.456057\pi\) | ||||
0.137612 | + | 0.990486i | \(0.456057\pi\) | |||||||
\(972\) | 8.95785e12i | 0.321889i | ||||||||
\(973\) | − 1.17409e13i | − 0.419947i | ||||||||
\(974\) | −3.64203e13 | −1.29667 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.80587e12 | −0.169531 | ||||||||
\(977\) | − 2.97018e13i | − 1.04293i | −0.853272 | − | 0.521467i | \(-0.825385\pi\) | ||||
0.853272 | − | 0.521467i | \(-0.174615\pi\) | |||||||
\(978\) | − 4.58282e12i | − 0.160180i | ||||||||
\(979\) | −2.29004e13 | −0.796749 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.87477e12 | 0.305947 | ||||||||
\(982\) | − 1.92905e13i | − 0.661976i | ||||||||
\(983\) | − 1.08292e13i | − 0.369917i | −0.982746 | − | 0.184958i | \(-0.940785\pi\) | ||||
0.982746 | − | 0.184958i | \(-0.0592150\pi\) | |||||||
\(984\) | 7.97034e12 | 0.271019 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.90428e13 | −3.33716 | ||||||||
\(987\) | − 6.58549e12i | − 0.220882i | ||||||||
\(988\) | 4.02822e12i | 0.134495i | ||||||||
\(989\) | 1.87302e13 | 0.622528 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.29514e12 | 0.174400 | 0.0871999 | − | 0.996191i | \(-0.472208\pi\) | ||||
0.0871999 | + | 0.996191i | \(0.472208\pi\) | |||||||
\(992\) | − 3.67242e13i | − 1.20406i | ||||||||
\(993\) | 6.74842e12i | 0.220257i | ||||||||
\(994\) | −4.16154e12 | −0.135212 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.30317e12 | 0.0741581 | ||||||||
\(997\) | − 1.64214e13i | − 0.526360i | −0.964747 | − | 0.263180i | \(-0.915229\pi\) | ||||
0.964747 | − | 0.263180i | \(-0.0847712\pi\) | |||||||
\(998\) | 4.94788e13i | 1.57882i | ||||||||
\(999\) | 6.96593e12 | 0.221276 |
(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 | 175.10.b.a.99.1 | 2 | ||
5.2 | odd | 4 | 35.10.a.a.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 175.10.a.a.1.1 | 1 | |||
5.4 | even | 2 | inner | 175.10.b.a.99.2 | 2 | ||
15.2 | even | 4 | 315.10.a.a.1.1 | 1 | |||
35.27 | even | 4 | 245.10.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.10.a.a.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
175.10.a.a.1.1 | 1 | 5.3 | odd | 4 | |||
175.10.b.a.99.1 | 2 | 1.1 | even | 1 | trivial | ||
175.10.b.a.99.2 | 2 | 5.4 | even | 2 | inner | ||
245.10.a.b.1.1 | 1 | 35.27 | even | 4 | |||
315.10.a.a.1.1 | 1 | 15.2 | even | 4 |