Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,10,Mod(1,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(18.0262542657\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 35.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 28.0000 | 1.23744 | 0.618718 | − | 0.785613i | \(-0.287652\pi\) | ||||
0.618718 | + | 0.785613i | \(0.287652\pi\) | |||||||
\(3\) | −116.000 | −0.826823 | −0.413411 | − | 0.910544i | \(-0.635663\pi\) | ||||
−0.413411 | + | 0.910544i | \(0.635663\pi\) | |||||||
\(4\) | 272.000 | 0.531250 | ||||||||
\(5\) | 625.000 | 0.447214 | ||||||||
\(6\) | −3248.00 | −1.02314 | ||||||||
\(7\) | 2401.00 | 0.377964 | ||||||||
\(8\) | −6720.00 | −0.580049 | ||||||||
\(9\) | −6227.00 | −0.316364 | ||||||||
\(10\) | 17500.0 | 0.553399 | ||||||||
\(11\) | −25548.0 | −0.526126 | −0.263063 | − | 0.964779i | \(-0.584733\pi\) | ||||
−0.263063 | + | 0.964779i | \(0.584733\pi\) | |||||||
\(12\) | −31552.0 | −0.439250 | ||||||||
\(13\) | −42306.0 | −0.410825 | −0.205413 | − | 0.978675i | \(-0.565854\pi\) | ||||
−0.205413 | + | 0.978675i | \(0.565854\pi\) | |||||||
\(14\) | 67228.0 | 0.467707 | ||||||||
\(15\) | −72500.0 | −0.369766 | ||||||||
\(16\) | −327424. | −1.24902 | ||||||||
\(17\) | −526342. | −1.52844 | −0.764219 | − | 0.644957i | \(-0.776875\pi\) | ||||
−0.764219 | + | 0.644957i | \(0.776875\pi\) | |||||||
\(18\) | −174356. | −0.391481 | ||||||||
\(19\) | −350060. | −0.616242 | −0.308121 | − | 0.951347i | \(-0.599700\pi\) | ||||
−0.308121 | + | 0.951347i | \(0.599700\pi\) | |||||||
\(20\) | 170000. | 0.237582 | ||||||||
\(21\) | −278516. | −0.312510 | ||||||||
\(22\) | −715344. | −0.651048 | ||||||||
\(23\) | −621976. | −0.463445 | −0.231723 | − | 0.972782i | \(-0.574436\pi\) | ||||
−0.231723 | + | 0.972782i | \(0.574436\pi\) | |||||||
\(24\) | 779520. | 0.479597 | ||||||||
\(25\) | 390625. | 0.200000 | ||||||||
\(26\) | −1.18457e6 | −0.508370 | ||||||||
\(27\) | 3.00556e6 | 1.08840 | ||||||||
\(28\) | 653072. | 0.200794 | ||||||||
\(29\) | 6.72043e6 | 1.76444 | 0.882218 | − | 0.470841i | \(-0.156049\pi\) | ||||
0.882218 | + | 0.470841i | \(0.156049\pi\) | |||||||
\(30\) | −2.03000e6 | −0.457562 | ||||||||
\(31\) | −6.41221e6 | −1.24704 | −0.623519 | − | 0.781808i | \(-0.714298\pi\) | ||||
−0.623519 | + | 0.781808i | \(0.714298\pi\) | |||||||
\(32\) | −5.72723e6 | −0.965539 | ||||||||
\(33\) | 2.96357e6 | 0.435013 | ||||||||
\(34\) | −1.47376e7 | −1.89135 | ||||||||
\(35\) | 1.50062e6 | 0.169031 | ||||||||
\(36\) | −1.69374e6 | −0.168069 | ||||||||
\(37\) | −2.31768e6 | −0.203304 | −0.101652 | − | 0.994820i | \(-0.532413\pi\) | ||||
−0.101652 | + | 0.994820i | \(0.532413\pi\) | |||||||
\(38\) | −9.80168e6 | −0.762561 | ||||||||
\(39\) | 4.90750e6 | 0.339679 | ||||||||
\(40\) | −4.20000e6 | −0.259406 | ||||||||
\(41\) | −1.02247e7 | −0.565096 | −0.282548 | − | 0.959253i | \(-0.591180\pi\) | ||||
−0.282548 | + | 0.959253i | \(0.591180\pi\) | |||||||
\(42\) | −7.79845e6 | −0.386711 | ||||||||
\(43\) | 3.01140e7 | 1.34326 | 0.671631 | − | 0.740886i | \(-0.265594\pi\) | ||||
0.671631 | + | 0.740886i | \(0.265594\pi\) | |||||||
\(44\) | −6.94906e6 | −0.279504 | ||||||||
\(45\) | −3.89188e6 | −0.141482 | ||||||||
\(46\) | −1.74153e7 | −0.573484 | ||||||||
\(47\) | −2.36449e7 | −0.706801 | −0.353401 | − | 0.935472i | \(-0.614975\pi\) | ||||
−0.353401 | + | 0.935472i | \(0.614975\pi\) | |||||||
\(48\) | 3.79812e7 | 1.03272 | ||||||||
\(49\) | 5.76480e6 | 0.142857 | ||||||||
\(50\) | 1.09375e7 | 0.247487 | ||||||||
\(51\) | 6.10557e7 | 1.26375 | ||||||||
\(52\) | −1.15072e7 | −0.218251 | ||||||||
\(53\) | 5.72927e7 | 0.997373 | 0.498686 | − | 0.866782i | \(-0.333816\pi\) | ||||
0.498686 | + | 0.866782i | \(0.333816\pi\) | |||||||
\(54\) | 8.41557e7 | 1.34683 | ||||||||
\(55\) | −1.59675e7 | −0.235291 | ||||||||
\(56\) | −1.61347e7 | −0.219238 | ||||||||
\(57\) | 4.06070e7 | 0.509523 | ||||||||
\(58\) | 1.88172e8 | 2.18338 | ||||||||
\(59\) | 8.49348e7 | 0.912539 | 0.456270 | − | 0.889842i | \(-0.349185\pi\) | ||||
0.456270 | + | 0.889842i | \(0.349185\pi\) | |||||||
\(60\) | −1.97200e7 | −0.196438 | ||||||||
\(61\) | 1.46778e7 | 0.135730 | 0.0678652 | − | 0.997694i | \(-0.478381\pi\) | ||||
0.0678652 | + | 0.997694i | \(0.478381\pi\) | |||||||
\(62\) | −1.79542e8 | −1.54313 | ||||||||
\(63\) | −1.49510e7 | −0.119574 | ||||||||
\(64\) | 7.27859e6 | 0.0542297 | ||||||||
\(65\) | −2.64412e7 | −0.183727 | ||||||||
\(66\) | 8.29799e7 | 0.538301 | ||||||||
\(67\) | −2.44558e8 | −1.48267 | −0.741336 | − | 0.671134i | \(-0.765807\pi\) | ||||
−0.741336 | + | 0.671134i | \(0.765807\pi\) | |||||||
\(68\) | −1.43165e8 | −0.811983 | ||||||||
\(69\) | 7.21492e7 | 0.383187 | ||||||||
\(70\) | 4.20175e7 | 0.209165 | ||||||||
\(71\) | 6.19020e7 | 0.289096 | 0.144548 | − | 0.989498i | \(-0.453827\pi\) | ||||
0.144548 | + | 0.989498i | \(0.453827\pi\) | |||||||
\(72\) | 4.18454e7 | 0.183507 | ||||||||
\(73\) | −2.83764e8 | −1.16951 | −0.584755 | − | 0.811210i | \(-0.698809\pi\) | ||||
−0.584755 | + | 0.811210i | \(0.698809\pi\) | |||||||
\(74\) | −6.48951e7 | −0.251576 | ||||||||
\(75\) | −4.53125e7 | −0.165365 | ||||||||
\(76\) | −9.52163e7 | −0.327379 | ||||||||
\(77\) | −6.13407e7 | −0.198857 | ||||||||
\(78\) | 1.37410e8 | 0.420332 | ||||||||
\(79\) | 2.76107e8 | 0.797547 | 0.398773 | − | 0.917049i | \(-0.369436\pi\) | ||||
0.398773 | + | 0.917049i | \(0.369436\pi\) | |||||||
\(80\) | −2.04640e8 | −0.558580 | ||||||||
\(81\) | −2.26079e8 | −0.583549 | ||||||||
\(82\) | −2.86291e8 | −0.699271 | ||||||||
\(83\) | −7.29960e7 | −0.168829 | −0.0844146 | − | 0.996431i | \(-0.526902\pi\) | ||||
−0.0844146 | + | 0.996431i | \(0.526902\pi\) | |||||||
\(84\) | −7.57564e7 | −0.166021 | ||||||||
\(85\) | −3.28964e8 | −0.683538 | ||||||||
\(86\) | 8.43192e8 | 1.66220 | ||||||||
\(87\) | −7.79570e8 | −1.45888 | ||||||||
\(88\) | 1.71683e8 | 0.305179 | ||||||||
\(89\) | −8.96368e8 | −1.51437 | −0.757184 | − | 0.653201i | \(-0.773425\pi\) | ||||
−0.757184 | + | 0.653201i | \(0.773425\pi\) | |||||||
\(90\) | −1.08973e8 | −0.175076 | ||||||||
\(91\) | −1.01577e8 | −0.155277 | ||||||||
\(92\) | −1.69177e8 | −0.246205 | ||||||||
\(93\) | 7.43816e8 | 1.03108 | ||||||||
\(94\) | −6.62058e8 | −0.874622 | ||||||||
\(95\) | −2.18788e8 | −0.275592 | ||||||||
\(96\) | 6.64359e8 | 0.798330 | ||||||||
\(97\) | 1.20581e9 | 1.38295 | 0.691474 | − | 0.722401i | \(-0.256962\pi\) | ||||
0.691474 | + | 0.722401i | \(0.256962\pi\) | |||||||
\(98\) | 1.61414e8 | 0.176777 | ||||||||
\(99\) | 1.59087e8 | 0.166448 | ||||||||
\(100\) | 1.06250e8 | 0.106250 | ||||||||
\(101\) | −1.46021e9 | −1.39627 | −0.698136 | − | 0.715965i | \(-0.745987\pi\) | ||||
−0.698136 | + | 0.715965i | \(0.745987\pi\) | |||||||
\(102\) | 1.70956e9 | 1.56381 | ||||||||
\(103\) | 1.08009e9 | 0.945563 | 0.472782 | − | 0.881180i | \(-0.343250\pi\) | ||||
0.472782 | + | 0.881180i | \(0.343250\pi\) | |||||||
\(104\) | 2.84296e8 | 0.238298 | ||||||||
\(105\) | −1.74072e8 | −0.139759 | ||||||||
\(106\) | 1.60419e9 | 1.23419 | ||||||||
\(107\) | 3.35949e8 | 0.247769 | 0.123884 | − | 0.992297i | \(-0.460465\pi\) | ||||
0.123884 | + | 0.992297i | \(0.460465\pi\) | |||||||
\(108\) | 8.17512e8 | 0.578212 | ||||||||
\(109\) | −1.42521e9 | −0.967072 | −0.483536 | − | 0.875324i | \(-0.660648\pi\) | ||||
−0.483536 | + | 0.875324i | \(0.660648\pi\) | |||||||
\(110\) | −4.47090e8 | −0.291157 | ||||||||
\(111\) | 2.68851e8 | 0.168096 | ||||||||
\(112\) | −7.86145e8 | −0.472086 | ||||||||
\(113\) | −2.84178e9 | −1.63960 | −0.819799 | − | 0.572651i | \(-0.805915\pi\) | ||||
−0.819799 | + | 0.572651i | \(0.805915\pi\) | |||||||
\(114\) | 1.13699e9 | 0.630502 | ||||||||
\(115\) | −3.88735e8 | −0.207259 | ||||||||
\(116\) | 1.82796e9 | 0.937357 | ||||||||
\(117\) | 2.63439e8 | 0.129970 | ||||||||
\(118\) | 2.37817e9 | 1.12921 | ||||||||
\(119\) | −1.26375e9 | −0.577695 | ||||||||
\(120\) | 4.87200e8 | 0.214482 | ||||||||
\(121\) | −1.70525e9 | −0.723191 | ||||||||
\(122\) | 4.10979e8 | 0.167958 | ||||||||
\(123\) | 1.18606e9 | 0.467234 | ||||||||
\(124\) | −1.74412e9 | −0.662489 | ||||||||
\(125\) | 2.44141e8 | 0.0894427 | ||||||||
\(126\) | −4.18629e8 | −0.147966 | ||||||||
\(127\) | 3.49339e9 | 1.19160 | 0.595800 | − | 0.803133i | \(-0.296835\pi\) | ||||
0.595800 | + | 0.803133i | \(0.296835\pi\) | |||||||
\(128\) | 3.13614e9 | 1.03264 | ||||||||
\(129\) | −3.49322e9 | −1.11064 | ||||||||
\(130\) | −7.40355e8 | −0.227350 | ||||||||
\(131\) | −1.84697e9 | −0.547946 | −0.273973 | − | 0.961737i | \(-0.588338\pi\) | ||||
−0.273973 | + | 0.961737i | \(0.588338\pi\) | |||||||
\(132\) | 8.06090e8 | 0.231101 | ||||||||
\(133\) | −8.40494e8 | −0.232918 | ||||||||
\(134\) | −6.84762e9 | −1.83471 | ||||||||
\(135\) | 1.87848e9 | 0.486747 | ||||||||
\(136\) | 3.53702e9 | 0.886568 | ||||||||
\(137\) | 1.17238e9 | 0.284331 | 0.142166 | − | 0.989843i | \(-0.454593\pi\) | ||||
0.142166 | + | 0.989843i | \(0.454593\pi\) | |||||||
\(138\) | 2.02018e9 | 0.474170 | ||||||||
\(139\) | −4.89001e9 | −1.11108 | −0.555538 | − | 0.831491i | \(-0.687488\pi\) | ||||
−0.555538 | + | 0.831491i | \(0.687488\pi\) | |||||||
\(140\) | 4.08170e8 | 0.0897976 | ||||||||
\(141\) | 2.74281e9 | 0.584399 | ||||||||
\(142\) | 1.73325e9 | 0.357738 | ||||||||
\(143\) | 1.08083e9 | 0.216146 | ||||||||
\(144\) | 2.03887e9 | 0.395147 | ||||||||
\(145\) | 4.20027e9 | 0.789080 | ||||||||
\(146\) | −7.94538e9 | −1.44720 | ||||||||
\(147\) | −6.68717e8 | −0.118118 | ||||||||
\(148\) | −6.30410e8 | −0.108005 | ||||||||
\(149\) | −8.61488e9 | −1.43189 | −0.715947 | − | 0.698155i | \(-0.754005\pi\) | ||||
−0.715947 | + | 0.698155i | \(0.754005\pi\) | |||||||
\(150\) | −1.26875e9 | −0.204628 | ||||||||
\(151\) | 5.48905e9 | 0.859213 | 0.429607 | − | 0.903016i | \(-0.358652\pi\) | ||||
0.429607 | + | 0.903016i | \(0.358652\pi\) | |||||||
\(152\) | 2.35240e9 | 0.357450 | ||||||||
\(153\) | 3.27753e9 | 0.483543 | ||||||||
\(154\) | −1.71754e9 | −0.246073 | ||||||||
\(155\) | −4.00763e9 | −0.557693 | ||||||||
\(156\) | 1.33484e9 | 0.180455 | ||||||||
\(157\) | −1.33110e9 | −0.174849 | −0.0874246 | − | 0.996171i | \(-0.527864\pi\) | ||||
−0.0874246 | + | 0.996171i | \(0.527864\pi\) | |||||||
\(158\) | 7.73101e9 | 0.986914 | ||||||||
\(159\) | −6.64595e9 | −0.824650 | ||||||||
\(160\) | −3.57952e9 | −0.431802 | ||||||||
\(161\) | −1.49336e9 | −0.175166 | ||||||||
\(162\) | −6.33021e9 | −0.722105 | ||||||||
\(163\) | 1.41097e9 | 0.156557 | 0.0782786 | − | 0.996932i | \(-0.475058\pi\) | ||||
0.0782786 | + | 0.996932i | \(0.475058\pi\) | |||||||
\(164\) | −2.78111e9 | −0.300207 | ||||||||
\(165\) | 1.85223e9 | 0.194544 | ||||||||
\(166\) | −2.04389e9 | −0.208915 | ||||||||
\(167\) | 2.48555e8 | 0.0247285 | 0.0123642 | − | 0.999924i | \(-0.496064\pi\) | ||||
0.0123642 | + | 0.999924i | \(0.496064\pi\) | |||||||
\(168\) | 1.87163e9 | 0.181271 | ||||||||
\(169\) | −8.81470e9 | −0.831223 | ||||||||
\(170\) | −9.21098e9 | −0.845836 | ||||||||
\(171\) | 2.17982e9 | 0.194957 | ||||||||
\(172\) | 8.19101e9 | 0.713607 | ||||||||
\(173\) | 1.66522e10 | 1.41340 | 0.706699 | − | 0.707515i | \(-0.250184\pi\) | ||||
0.706699 | + | 0.707515i | \(0.250184\pi\) | |||||||
\(174\) | −2.18280e10 | −1.80527 | ||||||||
\(175\) | 9.37891e8 | 0.0755929 | ||||||||
\(176\) | 8.36503e9 | 0.657144 | ||||||||
\(177\) | −9.85243e9 | −0.754508 | ||||||||
\(178\) | −2.50983e10 | −1.87394 | ||||||||
\(179\) | 2.02956e10 | 1.47762 | 0.738811 | − | 0.673913i | \(-0.235388\pi\) | ||||
0.738811 | + | 0.673913i | \(0.235388\pi\) | |||||||
\(180\) | −1.05859e9 | −0.0751626 | ||||||||
\(181\) | −1.36159e10 | −0.942960 | −0.471480 | − | 0.881877i | \(-0.656280\pi\) | ||||
−0.471480 | + | 0.881877i | \(0.656280\pi\) | |||||||
\(182\) | −2.84415e9 | −0.192146 | ||||||||
\(183\) | −1.70263e9 | −0.112225 | ||||||||
\(184\) | 4.17968e9 | 0.268821 | ||||||||
\(185\) | −1.44855e9 | −0.0909203 | ||||||||
\(186\) | 2.08269e10 | 1.27590 | ||||||||
\(187\) | 1.34470e10 | 0.804151 | ||||||||
\(188\) | −6.43142e9 | −0.375488 | ||||||||
\(189\) | 7.21635e9 | 0.411376 | ||||||||
\(190\) | −6.12605e9 | −0.341027 | ||||||||
\(191\) | 1.82357e9 | 0.0991453 | 0.0495726 | − | 0.998771i | \(-0.484214\pi\) | ||||
0.0495726 | + | 0.998771i | \(0.484214\pi\) | |||||||
\(192\) | −8.44317e8 | −0.0448384 | ||||||||
\(193\) | 1.23747e10 | 0.641989 | 0.320995 | − | 0.947081i | \(-0.395983\pi\) | ||||
0.320995 | + | 0.947081i | \(0.395983\pi\) | |||||||
\(194\) | 3.37627e10 | 1.71131 | ||||||||
\(195\) | 3.06718e9 | 0.151909 | ||||||||
\(196\) | 1.56803e9 | 0.0758929 | ||||||||
\(197\) | 1.93137e10 | 0.913626 | 0.456813 | − | 0.889563i | \(-0.348991\pi\) | ||||
0.456813 | + | 0.889563i | \(0.348991\pi\) | |||||||
\(198\) | 4.45445e9 | 0.205968 | ||||||||
\(199\) | 1.52145e10 | 0.687733 | 0.343867 | − | 0.939019i | \(-0.388263\pi\) | ||||
0.343867 | + | 0.939019i | \(0.388263\pi\) | |||||||
\(200\) | −2.62500e9 | −0.116010 | ||||||||
\(201\) | 2.83687e10 | 1.22591 | ||||||||
\(202\) | −4.08860e10 | −1.72780 | ||||||||
\(203\) | 1.61358e10 | 0.666894 | ||||||||
\(204\) | 1.66071e10 | 0.671366 | ||||||||
\(205\) | −6.39042e9 | −0.252719 | ||||||||
\(206\) | 3.02424e10 | 1.17007 | ||||||||
\(207\) | 3.87304e9 | 0.146618 | ||||||||
\(208\) | 1.38520e10 | 0.513130 | ||||||||
\(209\) | 8.94333e9 | 0.324221 | ||||||||
\(210\) | −4.87403e9 | −0.172942 | ||||||||
\(211\) | −3.89626e10 | −1.35325 | −0.676624 | − | 0.736329i | \(-0.736558\pi\) | ||||
−0.676624 | + | 0.736329i | \(0.736558\pi\) | |||||||
\(212\) | 1.55836e10 | 0.529854 | ||||||||
\(213\) | −7.18063e9 | −0.239031 | ||||||||
\(214\) | 9.40658e9 | 0.306598 | ||||||||
\(215\) | 1.88213e10 | 0.600725 | ||||||||
\(216\) | −2.01974e10 | −0.631325 | ||||||||
\(217\) | −1.53957e10 | −0.471336 | ||||||||
\(218\) | −3.99058e10 | −1.19669 | ||||||||
\(219\) | 3.29166e10 | 0.966977 | ||||||||
\(220\) | −4.34316e9 | −0.124998 | ||||||||
\(221\) | 2.22674e10 | 0.627921 | ||||||||
\(222\) | 7.52783e9 | 0.208009 | ||||||||
\(223\) | 1.08324e9 | 0.0293328 | 0.0146664 | − | 0.999892i | \(-0.495331\pi\) | ||||
0.0146664 | + | 0.999892i | \(0.495331\pi\) | |||||||
\(224\) | −1.37511e10 | −0.364939 | ||||||||
\(225\) | −2.43242e9 | −0.0632729 | ||||||||
\(226\) | −7.95698e10 | −2.02890 | ||||||||
\(227\) | −4.94618e10 | −1.23639 | −0.618193 | − | 0.786027i | \(-0.712135\pi\) | ||||
−0.618193 | + | 0.786027i | \(0.712135\pi\) | |||||||
\(228\) | 1.10451e10 | 0.270684 | ||||||||
\(229\) | −4.32776e10 | −1.03993 | −0.519965 | − | 0.854188i | \(-0.674055\pi\) | ||||
−0.519965 | + | 0.854188i | \(0.674055\pi\) | |||||||
\(230\) | −1.08846e10 | −0.256470 | ||||||||
\(231\) | 7.11553e9 | 0.164419 | ||||||||
\(232\) | −4.51613e10 | −1.02346 | ||||||||
\(233\) | −7.55367e9 | −0.167902 | −0.0839511 | − | 0.996470i | \(-0.526754\pi\) | ||||
−0.0839511 | + | 0.996470i | \(0.526754\pi\) | |||||||
\(234\) | 7.37630e9 | 0.160830 | ||||||||
\(235\) | −1.47781e10 | −0.316091 | ||||||||
\(236\) | 2.31023e10 | 0.484786 | ||||||||
\(237\) | −3.20285e10 | −0.659430 | ||||||||
\(238\) | −3.53849e10 | −0.714862 | ||||||||
\(239\) | −2.76516e10 | −0.548188 | −0.274094 | − | 0.961703i | \(-0.588378\pi\) | ||||
−0.274094 | + | 0.961703i | \(0.588378\pi\) | |||||||
\(240\) | 2.37382e10 | 0.461847 | ||||||||
\(241\) | −8.26006e10 | −1.57727 | −0.788635 | − | 0.614861i | \(-0.789212\pi\) | ||||
−0.788635 | + | 0.614861i | \(0.789212\pi\) | |||||||
\(242\) | −4.77469e10 | −0.894904 | ||||||||
\(243\) | −3.29333e10 | −0.605908 | ||||||||
\(244\) | 3.99237e9 | 0.0721068 | ||||||||
\(245\) | 3.60300e9 | 0.0638877 | ||||||||
\(246\) | 3.32098e10 | 0.578173 | ||||||||
\(247\) | 1.48096e10 | 0.253168 | ||||||||
\(248\) | 4.30900e10 | 0.723343 | ||||||||
\(249\) | 8.46753e9 | 0.139592 | ||||||||
\(250\) | 6.83594e9 | 0.110680 | ||||||||
\(251\) | 2.01817e10 | 0.320942 | 0.160471 | − | 0.987041i | \(-0.448699\pi\) | ||||
0.160471 | + | 0.987041i | \(0.448699\pi\) | |||||||
\(252\) | −4.06668e9 | −0.0635240 | ||||||||
\(253\) | 1.58902e10 | 0.243831 | ||||||||
\(254\) | 9.78150e10 | 1.47453 | ||||||||
\(255\) | 3.81598e10 | 0.565165 | ||||||||
\(256\) | 8.40854e10 | 1.22360 | ||||||||
\(257\) | 2.82781e10 | 0.404344 | 0.202172 | − | 0.979350i | \(-0.435200\pi\) | ||||
0.202172 | + | 0.979350i | \(0.435200\pi\) | |||||||
\(258\) | −9.78103e10 | −1.37435 | ||||||||
\(259\) | −5.56475e9 | −0.0768417 | ||||||||
\(260\) | −7.19202e9 | −0.0976047 | ||||||||
\(261\) | −4.18481e10 | −0.558205 | ||||||||
\(262\) | −5.17150e10 | −0.678049 | ||||||||
\(263\) | 1.39139e11 | 1.79328 | 0.896642 | − | 0.442756i | \(-0.145999\pi\) | ||||
0.896642 | + | 0.442756i | \(0.145999\pi\) | |||||||
\(264\) | −1.99152e10 | −0.252329 | ||||||||
\(265\) | 3.58079e10 | 0.446039 | ||||||||
\(266\) | −2.35338e10 | −0.288221 | ||||||||
\(267\) | 1.03979e11 | 1.25211 | ||||||||
\(268\) | −6.65197e10 | −0.787669 | ||||||||
\(269\) | 5.78883e9 | 0.0674071 | 0.0337035 | − | 0.999432i | \(-0.489270\pi\) | ||||
0.0337035 | + | 0.999432i | \(0.489270\pi\) | |||||||
\(270\) | 5.25973e10 | 0.602319 | ||||||||
\(271\) | −7.46910e10 | −0.841214 | −0.420607 | − | 0.907243i | \(-0.638183\pi\) | ||||
−0.420607 | + | 0.907243i | \(0.638183\pi\) | |||||||
\(272\) | 1.72337e11 | 1.90906 | ||||||||
\(273\) | 1.17829e10 | 0.128387 | ||||||||
\(274\) | 3.28265e10 | 0.351842 | ||||||||
\(275\) | −9.97969e9 | −0.105225 | ||||||||
\(276\) | 1.96246e10 | 0.203568 | ||||||||
\(277\) | 2.22355e10 | 0.226928 | 0.113464 | − | 0.993542i | \(-0.463805\pi\) | ||||
0.113464 | + | 0.993542i | \(0.463805\pi\) | |||||||
\(278\) | −1.36920e11 | −1.37489 | ||||||||
\(279\) | 3.99288e10 | 0.394519 | ||||||||
\(280\) | −1.00842e10 | −0.0980461 | ||||||||
\(281\) | −1.36058e11 | −1.30180 | −0.650901 | − | 0.759162i | \(-0.725609\pi\) | ||||
−0.650901 | + | 0.759162i | \(0.725609\pi\) | |||||||
\(282\) | 7.67987e10 | 0.723157 | ||||||||
\(283\) | −1.71084e11 | −1.58551 | −0.792757 | − | 0.609538i | \(-0.791355\pi\) | ||||
−0.792757 | + | 0.609538i | \(0.791355\pi\) | |||||||
\(284\) | 1.68373e10 | 0.153582 | ||||||||
\(285\) | 2.53793e10 | 0.227866 | ||||||||
\(286\) | 3.02633e10 | 0.267467 | ||||||||
\(287\) | −2.45495e10 | −0.213586 | ||||||||
\(288\) | 3.56635e10 | 0.305462 | ||||||||
\(289\) | 1.58448e11 | 1.33612 | ||||||||
\(290\) | 1.17608e11 | 0.976437 | ||||||||
\(291\) | −1.39874e11 | −1.14345 | ||||||||
\(292\) | −7.71837e10 | −0.621302 | ||||||||
\(293\) | 1.05732e11 | 0.838115 | 0.419058 | − | 0.907960i | \(-0.362361\pi\) | ||||
0.419058 | + | 0.907960i | \(0.362361\pi\) | |||||||
\(294\) | −1.87241e10 | −0.146163 | ||||||||
\(295\) | 5.30842e10 | 0.408100 | ||||||||
\(296\) | 1.55748e10 | 0.117926 | ||||||||
\(297\) | −7.67860e10 | −0.572636 | ||||||||
\(298\) | −2.41217e11 | −1.77188 | ||||||||
\(299\) | 2.63133e10 | 0.190395 | ||||||||
\(300\) | −1.23250e10 | −0.0878499 | ||||||||
\(301\) | 7.23037e10 | 0.507705 | ||||||||
\(302\) | 1.53693e11 | 1.06322 | ||||||||
\(303\) | 1.69385e11 | 1.15447 | ||||||||
\(304\) | 1.14618e11 | 0.769701 | ||||||||
\(305\) | 9.17364e9 | 0.0607005 | ||||||||
\(306\) | 9.17709e10 | 0.598354 | ||||||||
\(307\) | 1.74144e11 | 1.11889 | 0.559443 | − | 0.828869i | \(-0.311015\pi\) | ||||
0.559443 | + | 0.828869i | \(0.311015\pi\) | |||||||
\(308\) | −1.66847e10 | −0.105643 | ||||||||
\(309\) | −1.25290e11 | −0.781813 | ||||||||
\(310\) | −1.12214e11 | −0.690110 | ||||||||
\(311\) | −1.05907e11 | −0.641954 | −0.320977 | − | 0.947087i | \(-0.604011\pi\) | ||||
−0.320977 | + | 0.947087i | \(0.604011\pi\) | |||||||
\(312\) | −3.29784e10 | −0.197031 | ||||||||
\(313\) | −2.43558e11 | −1.43434 | −0.717171 | − | 0.696897i | \(-0.754563\pi\) | ||||
−0.717171 | + | 0.696897i | \(0.754563\pi\) | |||||||
\(314\) | −3.72709e10 | −0.216365 | ||||||||
\(315\) | −9.34439e9 | −0.0534753 | ||||||||
\(316\) | 7.51012e10 | 0.423697 | ||||||||
\(317\) | 1.83776e11 | 1.02217 | 0.511083 | − | 0.859531i | \(-0.329245\pi\) | ||||
0.511083 | + | 0.859531i | \(0.329245\pi\) | |||||||
\(318\) | −1.86087e11 | −1.02045 | ||||||||
\(319\) | −1.71694e11 | −0.928316 | ||||||||
\(320\) | 4.54912e9 | 0.0242523 | ||||||||
\(321\) | −3.89701e10 | −0.204861 | ||||||||
\(322\) | −4.18142e10 | −0.216757 | ||||||||
\(323\) | 1.84251e11 | 0.941888 | ||||||||
\(324\) | −6.14935e10 | −0.310011 | ||||||||
\(325\) | −1.65258e10 | −0.0821650 | ||||||||
\(326\) | 3.95071e10 | 0.193730 | ||||||||
\(327\) | 1.65324e11 | 0.799597 | ||||||||
\(328\) | 6.87098e10 | 0.327783 | ||||||||
\(329\) | −5.67714e10 | −0.267146 | ||||||||
\(330\) | 5.18624e10 | 0.240736 | ||||||||
\(331\) | −5.81760e10 | −0.266390 | −0.133195 | − | 0.991090i | \(-0.542524\pi\) | ||||
−0.133195 | + | 0.991090i | \(0.542524\pi\) | |||||||
\(332\) | −1.98549e10 | −0.0896905 | ||||||||
\(333\) | 1.44322e10 | 0.0643182 | ||||||||
\(334\) | 6.95953e9 | 0.0305999 | ||||||||
\(335\) | −1.52849e11 | −0.663071 | ||||||||
\(336\) | 9.11928e10 | 0.390332 | ||||||||
\(337\) | −3.40267e11 | −1.43709 | −0.718547 | − | 0.695478i | \(-0.755193\pi\) | ||||
−0.718547 | + | 0.695478i | \(0.755193\pi\) | |||||||
\(338\) | −2.46812e11 | −1.02859 | ||||||||
\(339\) | 3.29646e11 | 1.35566 | ||||||||
\(340\) | −8.94781e10 | −0.363130 | ||||||||
\(341\) | 1.63819e11 | 0.656100 | ||||||||
\(342\) | 6.10351e10 | 0.241247 | ||||||||
\(343\) | 1.38413e10 | 0.0539949 | ||||||||
\(344\) | −2.02366e11 | −0.779157 | ||||||||
\(345\) | 4.50933e10 | 0.171366 | ||||||||
\(346\) | 4.66262e11 | 1.74899 | ||||||||
\(347\) | −5.02625e11 | −1.86107 | −0.930533 | − | 0.366208i | \(-0.880656\pi\) | ||||
−0.930533 | + | 0.366208i | \(0.880656\pi\) | |||||||
\(348\) | −2.12043e11 | −0.775028 | ||||||||
\(349\) | 7.14710e10 | 0.257879 | 0.128939 | − | 0.991652i | \(-0.458843\pi\) | ||||
0.128939 | + | 0.991652i | \(0.458843\pi\) | |||||||
\(350\) | 2.62609e10 | 0.0935414 | ||||||||
\(351\) | −1.27153e11 | −0.447142 | ||||||||
\(352\) | 1.46319e11 | 0.507995 | ||||||||
\(353\) | −2.55096e10 | −0.0874414 | −0.0437207 | − | 0.999044i | \(-0.513921\pi\) | ||||
−0.0437207 | + | 0.999044i | \(0.513921\pi\) | |||||||
\(354\) | −2.75868e11 | −0.933656 | ||||||||
\(355\) | 3.86887e10 | 0.129288 | ||||||||
\(356\) | −2.43812e11 | −0.804508 | ||||||||
\(357\) | 1.46595e11 | 0.477652 | ||||||||
\(358\) | 5.68277e11 | 1.82846 | ||||||||
\(359\) | 1.49816e11 | 0.476029 | 0.238014 | − | 0.971262i | \(-0.423503\pi\) | ||||
0.238014 | + | 0.971262i | \(0.423503\pi\) | |||||||
\(360\) | 2.61534e10 | 0.0820667 | ||||||||
\(361\) | −2.00146e11 | −0.620246 | ||||||||
\(362\) | −3.81246e11 | −1.16685 | ||||||||
\(363\) | 1.97809e11 | 0.597951 | ||||||||
\(364\) | −2.76289e10 | −0.0824910 | ||||||||
\(365\) | −1.77352e11 | −0.523021 | ||||||||
\(366\) | −4.76736e10 | −0.138871 | ||||||||
\(367\) | −4.59514e11 | −1.32221 | −0.661107 | − | 0.750291i | \(-0.729913\pi\) | ||||
−0.661107 | + | 0.750291i | \(0.729913\pi\) | |||||||
\(368\) | 2.03650e11 | 0.578854 | ||||||||
\(369\) | 6.36691e10 | 0.178776 | ||||||||
\(370\) | −4.05594e10 | −0.112508 | ||||||||
\(371\) | 1.37560e11 | 0.376971 | ||||||||
\(372\) | 2.02318e11 | 0.547761 | ||||||||
\(373\) | −5.04230e11 | −1.34877 | −0.674386 | − | 0.738379i | \(-0.735592\pi\) | ||||
−0.674386 | + | 0.738379i | \(0.735592\pi\) | |||||||
\(374\) | 3.76516e11 | 0.995086 | ||||||||
\(375\) | −2.83203e10 | −0.0739533 | ||||||||
\(376\) | 1.58894e11 | 0.409979 | ||||||||
\(377\) | −2.84315e11 | −0.724875 | ||||||||
\(378\) | 2.02058e11 | 0.509052 | ||||||||
\(379\) | −9.63136e10 | −0.239779 | −0.119889 | − | 0.992787i | \(-0.538254\pi\) | ||||
−0.119889 | + | 0.992787i | \(0.538254\pi\) | |||||||
\(380\) | −5.95102e10 | −0.146408 | ||||||||
\(381\) | −4.05234e11 | −0.985242 | ||||||||
\(382\) | 5.10599e10 | 0.122686 | ||||||||
\(383\) | 6.10835e11 | 1.45054 | 0.725269 | − | 0.688465i | \(-0.241715\pi\) | ||||
0.725269 | + | 0.688465i | \(0.241715\pi\) | |||||||
\(384\) | −3.63793e11 | −0.853814 | ||||||||
\(385\) | −3.83380e10 | −0.0889315 | ||||||||
\(386\) | 3.46492e11 | 0.794421 | ||||||||
\(387\) | −1.87520e11 | −0.424960 | ||||||||
\(388\) | 3.27980e11 | 0.734691 | ||||||||
\(389\) | −6.49908e11 | −1.43906 | −0.719530 | − | 0.694461i | \(-0.755643\pi\) | ||||
−0.719530 | + | 0.694461i | \(0.755643\pi\) | |||||||
\(390\) | 8.58812e10 | 0.187978 | ||||||||
\(391\) | 3.27372e11 | 0.708347 | ||||||||
\(392\) | −3.87395e10 | −0.0828641 | ||||||||
\(393\) | 2.14248e11 | 0.453054 | ||||||||
\(394\) | 5.40785e11 | 1.13055 | ||||||||
\(395\) | 1.72567e11 | 0.356674 | ||||||||
\(396\) | 4.32718e10 | 0.0884253 | ||||||||
\(397\) | −3.67168e11 | −0.741836 | −0.370918 | − | 0.928666i | \(-0.620957\pi\) | ||||
−0.370918 | + | 0.928666i | \(0.620957\pi\) | |||||||
\(398\) | 4.26007e11 | 0.851026 | ||||||||
\(399\) | 9.74973e10 | 0.192582 | ||||||||
\(400\) | −1.27900e11 | −0.249805 | ||||||||
\(401\) | −9.73985e11 | −1.88106 | −0.940530 | − | 0.339712i | \(-0.889670\pi\) | ||||
−0.940530 | + | 0.339712i | \(0.889670\pi\) | |||||||
\(402\) | 7.94324e11 | 1.51698 | ||||||||
\(403\) | 2.71275e11 | 0.512315 | ||||||||
\(404\) | −3.97178e11 | −0.741770 | ||||||||
\(405\) | −1.41299e11 | −0.260971 | ||||||||
\(406\) | 4.51801e11 | 0.825240 | ||||||||
\(407\) | 5.92121e10 | 0.106964 | ||||||||
\(408\) | −4.10294e11 | −0.733035 | ||||||||
\(409\) | 3.58196e11 | 0.632944 | 0.316472 | − | 0.948602i | \(-0.397502\pi\) | ||||
0.316472 | + | 0.948602i | \(0.397502\pi\) | |||||||
\(410\) | −1.78932e11 | −0.312723 | ||||||||
\(411\) | −1.35996e11 | −0.235091 | ||||||||
\(412\) | 2.93783e11 | 0.502330 | ||||||||
\(413\) | 2.03928e11 | 0.344907 | ||||||||
\(414\) | 1.08445e11 | 0.181430 | ||||||||
\(415\) | −4.56225e10 | −0.0755027 | ||||||||
\(416\) | 2.42296e11 | 0.396668 | ||||||||
\(417\) | 5.67242e11 | 0.918662 | ||||||||
\(418\) | 2.50413e11 | 0.401203 | ||||||||
\(419\) | 4.84712e11 | 0.768283 | 0.384141 | − | 0.923274i | \(-0.374498\pi\) | ||||
0.384141 | + | 0.923274i | \(0.374498\pi\) | |||||||
\(420\) | −4.73477e10 | −0.0742467 | ||||||||
\(421\) | 7.18298e11 | 1.11438 | 0.557192 | − | 0.830384i | \(-0.311879\pi\) | ||||
0.557192 | + | 0.830384i | \(0.311879\pi\) | |||||||
\(422\) | −1.09095e12 | −1.67456 | ||||||||
\(423\) | 1.47237e11 | 0.223607 | ||||||||
\(424\) | −3.85007e11 | −0.578525 | ||||||||
\(425\) | −2.05602e11 | −0.305688 | ||||||||
\(426\) | −2.01058e11 | −0.295786 | ||||||||
\(427\) | 3.52415e10 | 0.0513013 | ||||||||
\(428\) | 9.13782e10 | 0.131627 | ||||||||
\(429\) | −1.25377e11 | −0.178714 | ||||||||
\(430\) | 5.26995e11 | 0.743359 | ||||||||
\(431\) | 8.27297e11 | 1.15482 | 0.577409 | − | 0.816455i | \(-0.304064\pi\) | ||||
0.577409 | + | 0.816455i | \(0.304064\pi\) | |||||||
\(432\) | −9.84092e11 | −1.35944 | ||||||||
\(433\) | 8.73032e11 | 1.19353 | 0.596767 | − | 0.802415i | \(-0.296452\pi\) | ||||
0.596767 | + | 0.802415i | \(0.296452\pi\) | |||||||
\(434\) | −4.31080e11 | −0.583249 | ||||||||
\(435\) | −4.87231e11 | −0.652429 | ||||||||
\(436\) | −3.87657e11 | −0.513757 | ||||||||
\(437\) | 2.17729e11 | 0.285594 | ||||||||
\(438\) | 9.21665e11 | 1.19657 | ||||||||
\(439\) | 7.15061e11 | 0.918867 | 0.459433 | − | 0.888212i | \(-0.348053\pi\) | ||||
0.459433 | + | 0.888212i | \(0.348053\pi\) | |||||||
\(440\) | 1.07302e11 | 0.136480 | ||||||||
\(441\) | −3.58974e10 | −0.0451949 | ||||||||
\(442\) | 6.23488e11 | 0.777012 | ||||||||
\(443\) | 5.89691e11 | 0.727457 | 0.363729 | − | 0.931505i | \(-0.381504\pi\) | ||||
0.363729 | + | 0.931505i | \(0.381504\pi\) | |||||||
\(444\) | 7.31275e10 | 0.0893012 | ||||||||
\(445\) | −5.60230e11 | −0.677246 | ||||||||
\(446\) | 3.03308e10 | 0.0362975 | ||||||||
\(447\) | 9.99326e11 | 1.18392 | ||||||||
\(448\) | 1.74759e10 | 0.0204969 | ||||||||
\(449\) | −1.06477e12 | −1.23636 | −0.618181 | − | 0.786036i | \(-0.712130\pi\) | ||||
−0.618181 | + | 0.786036i | \(0.712130\pi\) | |||||||
\(450\) | −6.81078e10 | −0.0782962 | ||||||||
\(451\) | 2.61220e11 | 0.297312 | ||||||||
\(452\) | −7.72964e11 | −0.871037 | ||||||||
\(453\) | −6.36730e11 | −0.710417 | ||||||||
\(454\) | −1.38493e12 | −1.52995 | ||||||||
\(455\) | −6.34854e10 | −0.0694421 | ||||||||
\(456\) | −2.72879e11 | −0.295548 | ||||||||
\(457\) | 1.54296e12 | 1.65475 | 0.827374 | − | 0.561651i | \(-0.189834\pi\) | ||||
0.827374 | + | 0.561651i | \(0.189834\pi\) | |||||||
\(458\) | −1.21177e12 | −1.28685 | ||||||||
\(459\) | −1.58195e12 | −1.66355 | ||||||||
\(460\) | −1.05736e11 | −0.110106 | ||||||||
\(461\) | −8.38680e11 | −0.864852 | −0.432426 | − | 0.901669i | \(-0.642342\pi\) | ||||
−0.432426 | + | 0.901669i | \(0.642342\pi\) | |||||||
\(462\) | 1.99235e11 | 0.203459 | ||||||||
\(463\) | −8.61819e11 | −0.871569 | −0.435784 | − | 0.900051i | \(-0.643529\pi\) | ||||
−0.435784 | + | 0.900051i | \(0.643529\pi\) | |||||||
\(464\) | −2.20043e12 | −2.20382 | ||||||||
\(465\) | 4.64885e11 | 0.461113 | ||||||||
\(466\) | −2.11503e11 | −0.207768 | ||||||||
\(467\) | 1.46986e12 | 1.43005 | 0.715023 | − | 0.699101i | \(-0.246416\pi\) | ||||
0.715023 | + | 0.699101i | \(0.246416\pi\) | |||||||
\(468\) | 7.16555e10 | 0.0690468 | ||||||||
\(469\) | −5.87183e11 | −0.560397 | ||||||||
\(470\) | −4.13786e11 | −0.391143 | ||||||||
\(471\) | 1.54408e11 | 0.144569 | ||||||||
\(472\) | −5.70762e11 | −0.529317 | ||||||||
\(473\) | −7.69353e11 | −0.706725 | ||||||||
\(474\) | −8.96797e11 | −0.816003 | ||||||||
\(475\) | −1.36742e11 | −0.123248 | ||||||||
\(476\) | −3.43739e11 | −0.306901 | ||||||||
\(477\) | −3.56761e11 | −0.315533 | ||||||||
\(478\) | −7.74245e11 | −0.678348 | ||||||||
\(479\) | 2.20227e12 | 1.91144 | 0.955721 | − | 0.294275i | \(-0.0950782\pi\) | ||||
0.955721 | + | 0.294275i | \(0.0950782\pi\) | |||||||
\(480\) | 4.15224e11 | 0.357024 | ||||||||
\(481\) | 9.80519e10 | 0.0835224 | ||||||||
\(482\) | −2.31282e12 | −1.95177 | ||||||||
\(483\) | 1.73230e11 | 0.144831 | ||||||||
\(484\) | −4.63827e11 | −0.384195 | ||||||||
\(485\) | 7.53631e11 | 0.618473 | ||||||||
\(486\) | −9.22132e11 | −0.749773 | ||||||||
\(487\) | 1.30073e12 | 1.04786 | 0.523932 | − | 0.851760i | \(-0.324464\pi\) | ||||
0.523932 | + | 0.851760i | \(0.324464\pi\) | |||||||
\(488\) | −9.86350e10 | −0.0787303 | ||||||||
\(489\) | −1.63672e11 | −0.129445 | ||||||||
\(490\) | 1.00884e11 | 0.0790569 | ||||||||
\(491\) | 6.88947e11 | 0.534957 | 0.267479 | − | 0.963564i | \(-0.413810\pi\) | ||||
0.267479 | + | 0.963564i | \(0.413810\pi\) | |||||||
\(492\) | 3.22609e11 | 0.248218 | ||||||||
\(493\) | −3.53724e12 | −2.69683 | ||||||||
\(494\) | 4.14670e11 | 0.313279 | ||||||||
\(495\) | 9.94296e10 | 0.0744376 | ||||||||
\(496\) | 2.09951e12 | 1.55758 | ||||||||
\(497\) | 1.48627e11 | 0.109268 | ||||||||
\(498\) | 2.37091e11 | 0.172736 | ||||||||
\(499\) | 1.76710e12 | 1.27588 | 0.637939 | − | 0.770087i | \(-0.279787\pi\) | ||||
0.637939 | + | 0.770087i | \(0.279787\pi\) | |||||||
\(500\) | 6.64063e10 | 0.0475164 | ||||||||
\(501\) | −2.88323e10 | −0.0204461 | ||||||||
\(502\) | 5.65088e11 | 0.397145 | ||||||||
\(503\) | 2.63527e12 | 1.83556 | 0.917780 | − | 0.397089i | \(-0.129980\pi\) | ||||
0.917780 | + | 0.397089i | \(0.129980\pi\) | |||||||
\(504\) | 1.00471e11 | 0.0693590 | ||||||||
\(505\) | −9.12633e11 | −0.624432 | ||||||||
\(506\) | 4.44927e11 | 0.301725 | ||||||||
\(507\) | 1.02251e12 | 0.687274 | ||||||||
\(508\) | 9.50203e11 | 0.633038 | ||||||||
\(509\) | 2.22151e12 | 1.46696 | 0.733479 | − | 0.679712i | \(-0.237895\pi\) | ||||
0.733479 | + | 0.679712i | \(0.237895\pi\) | |||||||
\(510\) | 1.06847e12 | 0.699356 | ||||||||
\(511\) | −6.81317e11 | −0.442033 | ||||||||
\(512\) | 7.48685e11 | 0.481487 | ||||||||
\(513\) | −1.05213e12 | −0.670718 | ||||||||
\(514\) | 7.91786e11 | 0.500350 | ||||||||
\(515\) | 6.75053e11 | 0.422869 | ||||||||
\(516\) | −9.50157e11 | −0.590027 | ||||||||
\(517\) | 6.04080e11 | 0.371867 | ||||||||
\(518\) | −1.55813e11 | −0.0950868 | ||||||||
\(519\) | −1.93166e12 | −1.16863 | ||||||||
\(520\) | 1.77685e11 | 0.106570 | ||||||||
\(521\) | −1.87441e12 | −1.11454 | −0.557269 | − | 0.830332i | \(-0.688151\pi\) | ||||
−0.557269 | + | 0.830332i | \(0.688151\pi\) | |||||||
\(522\) | −1.17175e12 | −0.690743 | ||||||||
\(523\) | −1.58412e12 | −0.925828 | −0.462914 | − | 0.886403i | \(-0.653196\pi\) | ||||
−0.462914 | + | 0.886403i | \(0.653196\pi\) | |||||||
\(524\) | −5.02375e11 | −0.291096 | ||||||||
\(525\) | −1.08795e11 | −0.0625019 | ||||||||
\(526\) | 3.89590e12 | 2.21908 | ||||||||
\(527\) | 3.37501e12 | 1.90602 | ||||||||
\(528\) | −9.70343e11 | −0.543341 | ||||||||
\(529\) | −1.41430e12 | −0.785219 | ||||||||
\(530\) | 1.00262e12 | 0.551945 | ||||||||
\(531\) | −5.28889e11 | −0.288695 | ||||||||
\(532\) | −2.28614e11 | −0.123737 | ||||||||
\(533\) | 4.32565e11 | 0.232156 | ||||||||
\(534\) | 2.91140e12 | 1.54941 | ||||||||
\(535\) | 2.09968e11 | 0.110806 | ||||||||
\(536\) | 1.64343e12 | 0.860021 | ||||||||
\(537\) | −2.35429e12 | −1.22173 | ||||||||
\(538\) | 1.62087e11 | 0.0834120 | ||||||||
\(539\) | −1.47279e11 | −0.0751609 | ||||||||
\(540\) | 5.10945e11 | 0.258584 | ||||||||
\(541\) | 2.79888e12 | 1.40474 | 0.702370 | − | 0.711812i | \(-0.252125\pi\) | ||||
0.702370 | + | 0.711812i | \(0.252125\pi\) | |||||||
\(542\) | −2.09135e12 | −1.04095 | ||||||||
\(543\) | 1.57945e12 | 0.779660 | ||||||||
\(544\) | 3.01448e12 | 1.47577 | ||||||||
\(545\) | −8.90755e11 | −0.432488 | ||||||||
\(546\) | 3.29921e11 | 0.158870 | ||||||||
\(547\) | 1.16606e12 | 0.556901 | 0.278451 | − | 0.960451i | \(-0.410179\pi\) | ||||
0.278451 | + | 0.960451i | \(0.410179\pi\) | |||||||
\(548\) | 3.18886e11 | 0.151051 | ||||||||
\(549\) | −9.13988e10 | −0.0429403 | ||||||||
\(550\) | −2.79431e11 | −0.130210 | ||||||||
\(551\) | −2.35255e12 | −1.08732 | ||||||||
\(552\) | −4.84843e11 | −0.222267 | ||||||||
\(553\) | 6.62934e11 | 0.301444 | ||||||||
\(554\) | 6.22594e11 | 0.280809 | ||||||||
\(555\) | 1.68032e11 | 0.0751750 | ||||||||
\(556\) | −1.33008e12 | −0.590259 | ||||||||
\(557\) | 3.29033e12 | 1.44841 | 0.724204 | − | 0.689586i | \(-0.242207\pi\) | ||||
0.724204 | + | 0.689586i | \(0.242207\pi\) | |||||||
\(558\) | 1.11801e12 | 0.488192 | ||||||||
\(559\) | −1.27400e12 | −0.551845 | ||||||||
\(560\) | −4.91341e11 | −0.211123 | ||||||||
\(561\) | −1.55985e12 | −0.664890 | ||||||||
\(562\) | −3.80962e12 | −1.61090 | ||||||||
\(563\) | −3.63871e12 | −1.52637 | −0.763186 | − | 0.646179i | \(-0.776366\pi\) | ||||
−0.763186 | + | 0.646179i | \(0.776366\pi\) | |||||||
\(564\) | 7.46044e11 | 0.310462 | ||||||||
\(565\) | −1.77611e12 | −0.733251 | ||||||||
\(566\) | −4.79035e12 | −1.96197 | ||||||||
\(567\) | −5.42815e11 | −0.220561 | ||||||||
\(568\) | −4.15981e11 | −0.167690 | ||||||||
\(569\) | 4.35009e12 | 1.73978 | 0.869888 | − | 0.493250i | \(-0.164191\pi\) | ||||
0.869888 | + | 0.493250i | \(0.164191\pi\) | |||||||
\(570\) | 7.10622e11 | 0.281969 | ||||||||
\(571\) | −4.91136e12 | −1.93348 | −0.966739 | − | 0.255767i | \(-0.917672\pi\) | ||||
−0.966739 | + | 0.255767i | \(0.917672\pi\) | |||||||
\(572\) | 2.93987e11 | 0.114827 | ||||||||
\(573\) | −2.11534e11 | −0.0819756 | ||||||||
\(574\) | −6.87385e11 | −0.264299 | ||||||||
\(575\) | −2.42959e11 | −0.0926890 | ||||||||
\(576\) | −4.53238e10 | −0.0171564 | ||||||||
\(577\) | −1.68758e12 | −0.633830 | −0.316915 | − | 0.948454i | \(-0.602647\pi\) | ||||
−0.316915 | + | 0.948454i | \(0.602647\pi\) | |||||||
\(578\) | 4.43654e12 | 1.65337 | ||||||||
\(579\) | −1.43547e12 | −0.530811 | ||||||||
\(580\) | 1.14247e12 | 0.419199 | ||||||||
\(581\) | −1.75263e11 | −0.0638114 | ||||||||
\(582\) | −3.91647e12 | −1.41495 | ||||||||
\(583\) | −1.46371e12 | −0.524744 | ||||||||
\(584\) | 1.90689e12 | 0.678373 | ||||||||
\(585\) | 1.64650e11 | 0.0581245 | ||||||||
\(586\) | 2.96051e12 | 1.03711 | ||||||||
\(587\) | −4.82739e12 | −1.67819 | −0.839094 | − | 0.543987i | \(-0.816914\pi\) | ||||
−0.839094 | + | 0.543987i | \(0.816914\pi\) | |||||||
\(588\) | −1.81891e11 | −0.0627499 | ||||||||
\(589\) | 2.24466e12 | 0.768478 | ||||||||
\(590\) | 1.48636e12 | 0.504998 | ||||||||
\(591\) | −2.24039e12 | −0.755407 | ||||||||
\(592\) | 7.58865e11 | 0.253932 | ||||||||
\(593\) | −1.12076e12 | −0.372193 | −0.186096 | − | 0.982532i | \(-0.559584\pi\) | ||||
−0.186096 | + | 0.982532i | \(0.559584\pi\) | |||||||
\(594\) | −2.15001e12 | −0.708600 | ||||||||
\(595\) | −7.89842e11 | −0.258353 | ||||||||
\(596\) | −2.34325e12 | −0.760694 | ||||||||
\(597\) | −1.76489e12 | −0.568633 | ||||||||
\(598\) | 7.36773e11 | 0.235602 | ||||||||
\(599\) | 1.35944e12 | 0.431460 | 0.215730 | − | 0.976453i | \(-0.430787\pi\) | ||||
0.215730 | + | 0.976453i | \(0.430787\pi\) | |||||||
\(600\) | 3.04500e11 | 0.0959194 | ||||||||
\(601\) | 9.50421e11 | 0.297153 | 0.148577 | − | 0.988901i | \(-0.452531\pi\) | ||||
0.148577 | + | 0.988901i | \(0.452531\pi\) | |||||||
\(602\) | 2.02450e12 | 0.628253 | ||||||||
\(603\) | 1.52286e12 | 0.469064 | ||||||||
\(604\) | 1.49302e12 | 0.456457 | ||||||||
\(605\) | −1.06578e12 | −0.323421 | ||||||||
\(606\) | 4.74277e12 | 1.42858 | ||||||||
\(607\) | 3.35939e12 | 1.00441 | 0.502205 | − | 0.864749i | \(-0.332522\pi\) | ||||
0.502205 | + | 0.864749i | \(0.332522\pi\) | |||||||
\(608\) | 2.00487e12 | 0.595006 | ||||||||
\(609\) | −1.87175e12 | −0.551403 | ||||||||
\(610\) | 2.56862e11 | 0.0751131 | ||||||||
\(611\) | 1.00032e12 | 0.290372 | ||||||||
\(612\) | 8.91489e11 | 0.256882 | ||||||||
\(613\) | −2.62257e12 | −0.750162 | −0.375081 | − | 0.926992i | \(-0.622385\pi\) | ||||
−0.375081 | + | 0.926992i | \(0.622385\pi\) | |||||||
\(614\) | 4.87603e12 | 1.38455 | ||||||||
\(615\) | 7.41289e11 | 0.208953 | ||||||||
\(616\) | 4.12210e11 | 0.115347 | ||||||||
\(617\) | −3.35285e10 | −0.00931388 | −0.00465694 | − | 0.999989i | \(-0.501482\pi\) | ||||
−0.00465694 | + | 0.999989i | \(0.501482\pi\) | |||||||
\(618\) | −3.50812e12 | −0.967444 | ||||||||
\(619\) | 5.51587e12 | 1.51010 | 0.755051 | − | 0.655666i | \(-0.227612\pi\) | ||||
0.755051 | + | 0.655666i | \(0.227612\pi\) | |||||||
\(620\) | −1.09008e12 | −0.296274 | ||||||||
\(621\) | −1.86939e12 | −0.504414 | ||||||||
\(622\) | −2.96540e12 | −0.794377 | ||||||||
\(623\) | −2.15218e12 | −0.572377 | ||||||||
\(624\) | −1.60683e12 | −0.424268 | ||||||||
\(625\) | 1.52588e11 | 0.0400000 | ||||||||
\(626\) | −6.81962e12 | −1.77491 | ||||||||
\(627\) | −1.03743e12 | −0.268073 | ||||||||
\(628\) | −3.62060e11 | −0.0928886 | ||||||||
\(629\) | 1.21989e12 | 0.310738 | ||||||||
\(630\) | −2.61643e11 | −0.0661724 | ||||||||
\(631\) | 2.72456e12 | 0.684170 | 0.342085 | − | 0.939669i | \(-0.388867\pi\) | ||||
0.342085 | + | 0.939669i | \(0.388867\pi\) | |||||||
\(632\) | −1.85544e12 | −0.462616 | ||||||||
\(633\) | 4.51966e12 | 1.11890 | ||||||||
\(634\) | 5.14572e12 | 1.26487 | ||||||||
\(635\) | 2.18337e12 | 0.532900 | ||||||||
\(636\) | −1.80770e12 | −0.438096 | ||||||||
\(637\) | −2.43886e11 | −0.0586893 | ||||||||
\(638\) | −4.80742e12 | −1.14873 | ||||||||
\(639\) | −3.85463e11 | −0.0914596 | ||||||||
\(640\) | 1.96009e12 | 0.461813 | ||||||||
\(641\) | 3.79136e11 | 0.0887022 | 0.0443511 | − | 0.999016i | \(-0.485878\pi\) | ||||
0.0443511 | + | 0.999016i | \(0.485878\pi\) | |||||||
\(642\) | −1.09116e12 | −0.253502 | ||||||||
\(643\) | −5.15446e12 | −1.18914 | −0.594571 | − | 0.804043i | \(-0.702678\pi\) | ||||
−0.594571 | + | 0.804043i | \(0.702678\pi\) | |||||||
\(644\) | −4.06195e11 | −0.0930568 | ||||||||
\(645\) | −2.18327e12 | −0.496693 | ||||||||
\(646\) | 5.15904e12 | 1.16553 | ||||||||
\(647\) | −2.68059e12 | −0.601397 | −0.300699 | − | 0.953719i | \(-0.597220\pi\) | ||||
−0.300699 | + | 0.953719i | \(0.597220\pi\) | |||||||
\(648\) | 1.51925e12 | 0.338487 | ||||||||
\(649\) | −2.16991e12 | −0.480111 | ||||||||
\(650\) | −4.62722e11 | −0.101674 | ||||||||
\(651\) | 1.78590e12 | 0.389712 | ||||||||
\(652\) | 3.83783e11 | 0.0831710 | ||||||||
\(653\) | −6.44986e12 | −1.38816 | −0.694082 | − | 0.719896i | \(-0.744190\pi\) | ||||
−0.694082 | + | 0.719896i | \(0.744190\pi\) | |||||||
\(654\) | 4.62908e12 | 0.989451 | ||||||||
\(655\) | −1.15435e12 | −0.245049 | ||||||||
\(656\) | 3.34780e12 | 0.705818 | ||||||||
\(657\) | 1.76700e12 | 0.369991 | ||||||||
\(658\) | −1.58960e12 | −0.330576 | ||||||||
\(659\) | −2.79549e12 | −0.577396 | −0.288698 | − | 0.957420i | \(-0.593222\pi\) | ||||
−0.288698 | + | 0.957420i | \(0.593222\pi\) | |||||||
\(660\) | 5.03807e11 | 0.103351 | ||||||||
\(661\) | −4.93691e11 | −0.100589 | −0.0502943 | − | 0.998734i | \(-0.516016\pi\) | ||||
−0.0502943 | + | 0.998734i | \(0.516016\pi\) | |||||||
\(662\) | −1.62893e12 | −0.329641 | ||||||||
\(663\) | −2.58302e12 | −0.519179 | ||||||||
\(664\) | 4.90533e11 | 0.0979291 | ||||||||
\(665\) | −5.25309e11 | −0.104164 | ||||||||
\(666\) | 4.04102e11 | 0.0795897 | ||||||||
\(667\) | −4.17995e12 | −0.817720 | ||||||||
\(668\) | 6.76068e10 | 0.0131370 | ||||||||
\(669\) | −1.25656e11 | −0.0242530 | ||||||||
\(670\) | −4.27976e12 | −0.820508 | ||||||||
\(671\) | −3.74989e11 | −0.0714113 | ||||||||
\(672\) | 1.59513e12 | 0.301740 | ||||||||
\(673\) | 2.83805e12 | 0.533277 | 0.266638 | − | 0.963797i | \(-0.414087\pi\) | ||||
0.266638 | + | 0.963797i | \(0.414087\pi\) | |||||||
\(674\) | −9.52747e12 | −1.77831 | ||||||||
\(675\) | 1.17405e12 | 0.217680 | ||||||||
\(676\) | −2.39760e12 | −0.441587 | ||||||||
\(677\) | 7.71236e12 | 1.41104 | 0.705519 | − | 0.708691i | \(-0.250714\pi\) | ||||
0.705519 | + | 0.708691i | \(0.250714\pi\) | |||||||
\(678\) | 9.23010e12 | 1.67754 | ||||||||
\(679\) | 2.89515e12 | 0.522705 | ||||||||
\(680\) | 2.21064e12 | 0.396485 | ||||||||
\(681\) | 5.73757e12 | 1.02227 | ||||||||
\(682\) | 4.58693e12 | 0.811882 | ||||||||
\(683\) | 1.07677e13 | 1.89334 | 0.946670 | − | 0.322204i | \(-0.104424\pi\) | ||||
0.946670 | + | 0.322204i | \(0.104424\pi\) | |||||||
\(684\) | 5.92912e11 | 0.103571 | ||||||||
\(685\) | 7.32735e11 | 0.127157 | ||||||||
\(686\) | 3.87556e11 | 0.0668153 | ||||||||
\(687\) | 5.02021e12 | 0.859837 | ||||||||
\(688\) | −9.86005e12 | −1.67776 | ||||||||
\(689\) | −2.42382e12 | −0.409746 | ||||||||
\(690\) | 1.26261e12 | 0.212055 | ||||||||
\(691\) | 2.02298e12 | 0.337552 | 0.168776 | − | 0.985654i | \(-0.446019\pi\) | ||||
0.168776 | + | 0.985654i | \(0.446019\pi\) | |||||||
\(692\) | 4.52940e12 | 0.750867 | ||||||||
\(693\) | 3.81969e11 | 0.0629113 | ||||||||
\(694\) | −1.40735e13 | −2.30295 | ||||||||
\(695\) | −3.05626e12 | −0.496888 | ||||||||
\(696\) | 5.23871e12 | 0.846219 | ||||||||
\(697\) | 5.38168e12 | 0.863714 | ||||||||
\(698\) | 2.00119e12 | 0.319109 | ||||||||
\(699\) | 8.76226e11 | 0.138825 | ||||||||
\(700\) | 2.55106e11 | 0.0401587 | ||||||||
\(701\) | 8.66031e11 | 0.135457 | 0.0677286 | − | 0.997704i | \(-0.478425\pi\) | ||||
0.0677286 | + | 0.997704i | \(0.478425\pi\) | |||||||
\(702\) | −3.56029e12 | −0.553310 | ||||||||
\(703\) | 8.11328e11 | 0.125285 | ||||||||
\(704\) | −1.85953e11 | −0.0285317 | ||||||||
\(705\) | 1.71426e12 | 0.261351 | ||||||||
\(706\) | −7.14268e11 | −0.108203 | ||||||||
\(707\) | −3.50597e12 | −0.527741 | ||||||||
\(708\) | −2.67986e12 | −0.400832 | ||||||||
\(709\) | −3.78834e12 | −0.563042 | −0.281521 | − | 0.959555i | \(-0.590839\pi\) | ||||
−0.281521 | + | 0.959555i | \(0.590839\pi\) | |||||||
\(710\) | 1.08328e12 | 0.159985 | ||||||||
\(711\) | −1.71932e12 | −0.252315 | ||||||||
\(712\) | 6.02360e12 | 0.878407 | ||||||||
\(713\) | 3.98824e12 | 0.577934 | ||||||||
\(714\) | 4.10465e12 | 0.591064 | ||||||||
\(715\) | 6.75521e11 | 0.0966633 | ||||||||
\(716\) | 5.52040e12 | 0.784986 | ||||||||
\(717\) | 3.20758e12 | 0.453254 | ||||||||
\(718\) | 4.19485e12 | 0.589056 | ||||||||
\(719\) | 8.16972e11 | 0.114006 | 0.0570029 | − | 0.998374i | \(-0.481846\pi\) | ||||
0.0570029 | + | 0.998374i | \(0.481846\pi\) | |||||||
\(720\) | 1.27429e12 | 0.176715 | ||||||||
\(721\) | 2.59328e12 | 0.357389 | ||||||||
\(722\) | −5.60408e12 | −0.767515 | ||||||||
\(723\) | 9.58166e12 | 1.30412 | ||||||||
\(724\) | −3.70353e12 | −0.500947 | ||||||||
\(725\) | 2.62517e12 | 0.352887 | ||||||||
\(726\) | 5.53864e12 | 0.739927 | ||||||||
\(727\) | 3.13227e12 | 0.415867 | 0.207933 | − | 0.978143i | \(-0.433326\pi\) | ||||
0.207933 | + | 0.978143i | \(0.433326\pi\) | |||||||
\(728\) | 6.82595e11 | 0.0900683 | ||||||||
\(729\) | 8.27017e12 | 1.08453 | ||||||||
\(730\) | −4.96587e12 | −0.647205 | ||||||||
\(731\) | −1.58503e13 | −2.05309 | ||||||||
\(732\) | −4.63115e11 | −0.0596195 | ||||||||
\(733\) | −1.33197e13 | −1.70422 | −0.852112 | − | 0.523360i | \(-0.824678\pi\) | ||||
−0.852112 | + | 0.523360i | \(0.824678\pi\) | |||||||
\(734\) | −1.28664e13 | −1.63616 | ||||||||
\(735\) | −4.17948e11 | −0.0528238 | ||||||||
\(736\) | 3.56220e12 | 0.447474 | ||||||||
\(737\) | 6.24796e12 | 0.780072 | ||||||||
\(738\) | 1.78273e12 | 0.221224 | ||||||||
\(739\) | −1.56702e13 | −1.93274 | −0.966371 | − | 0.257154i | \(-0.917215\pi\) | ||||
−0.966371 | + | 0.257154i | \(0.917215\pi\) | |||||||
\(740\) | −3.94006e11 | −0.0483014 | ||||||||
\(741\) | −1.71792e12 | −0.209325 | ||||||||
\(742\) | 3.85167e12 | 0.466478 | ||||||||
\(743\) | 7.91108e12 | 0.952327 | 0.476164 | − | 0.879357i | \(-0.342027\pi\) | ||||
0.476164 | + | 0.879357i | \(0.342027\pi\) | |||||||
\(744\) | −4.99844e12 | −0.598076 | ||||||||
\(745\) | −5.38430e12 | −0.640362 | ||||||||
\(746\) | −1.41184e13 | −1.66902 | ||||||||
\(747\) | 4.54546e11 | 0.0534115 | ||||||||
\(748\) | 3.65758e12 | 0.427205 | ||||||||
\(749\) | 8.06614e11 | 0.0936478 | ||||||||
\(750\) | −7.92969e11 | −0.0915125 | ||||||||
\(751\) | −4.01514e12 | −0.460597 | −0.230299 | − | 0.973120i | \(-0.573970\pi\) | ||||
−0.230299 | + | 0.973120i | \(0.573970\pi\) | |||||||
\(752\) | 7.74191e12 | 0.882811 | ||||||||
\(753\) | −2.34108e12 | −0.265362 | ||||||||
\(754\) | −7.96081e12 | −0.896987 | ||||||||
\(755\) | 3.43066e12 | 0.384252 | ||||||||
\(756\) | 1.96285e12 | 0.218544 | ||||||||
\(757\) | 2.84075e12 | 0.314414 | 0.157207 | − | 0.987566i | \(-0.449751\pi\) | ||||
0.157207 | + | 0.987566i | \(0.449751\pi\) | |||||||
\(758\) | −2.69678e12 | −0.296711 | ||||||||
\(759\) | −1.84327e12 | −0.201605 | ||||||||
\(760\) | 1.47025e12 | 0.159857 | ||||||||
\(761\) | −7.10439e12 | −0.767884 | −0.383942 | − | 0.923357i | \(-0.625434\pi\) | ||||
−0.383942 | + | 0.923357i | \(0.625434\pi\) | |||||||
\(762\) | −1.13465e13 | −1.21918 | ||||||||
\(763\) | −3.42192e12 | −0.365519 | ||||||||
\(764\) | 4.96011e11 | 0.0526709 | ||||||||
\(765\) | 2.04846e12 | 0.216247 | ||||||||
\(766\) | 1.71034e13 | 1.79495 | ||||||||
\(767\) | −3.59325e12 | −0.374894 | ||||||||
\(768\) | −9.75390e12 | −1.01170 | ||||||||
\(769\) | −4.97052e12 | −0.512546 | −0.256273 | − | 0.966604i | \(-0.582495\pi\) | ||||
−0.256273 | + | 0.966604i | \(0.582495\pi\) | |||||||
\(770\) | −1.07346e12 | −0.110047 | ||||||||
\(771\) | −3.28026e12 | −0.334321 | ||||||||
\(772\) | 3.36593e12 | 0.341057 | ||||||||
\(773\) | 1.11565e13 | 1.12388 | 0.561939 | − | 0.827179i | \(-0.310056\pi\) | ||||
0.561939 | + | 0.827179i | \(0.310056\pi\) | |||||||
\(774\) | −5.25056e12 | −0.525861 | ||||||||
\(775\) | −2.50477e12 | −0.249408 | ||||||||
\(776\) | −8.10304e12 | −0.802177 | ||||||||
\(777\) | 6.45512e11 | 0.0635345 | ||||||||
\(778\) | −1.81974e13 | −1.78075 | ||||||||
\(779\) | 3.57925e12 | 0.348236 | ||||||||
\(780\) | 8.34274e11 | 0.0807018 | ||||||||
\(781\) | −1.58147e12 | −0.152101 | ||||||||
\(782\) | 9.16642e12 | 0.876535 | ||||||||
\(783\) | 2.01987e13 | 1.92041 | ||||||||
\(784\) | −1.88753e12 | −0.178432 | ||||||||
\(785\) | −8.31940e11 | −0.0781949 | ||||||||
\(786\) | 5.99894e12 | 0.560626 | ||||||||
\(787\) | −6.23763e12 | −0.579607 | −0.289803 | − | 0.957086i | \(-0.593590\pi\) | ||||
−0.289803 | + | 0.957086i | \(0.593590\pi\) | |||||||
\(788\) | 5.25334e12 | 0.485364 | ||||||||
\(789\) | −1.61402e13 | −1.48273 | ||||||||
\(790\) | 4.83188e12 | 0.441361 | ||||||||
\(791\) | −6.82311e12 | −0.619710 | ||||||||
\(792\) | −1.06907e12 | −0.0965477 | ||||||||
\(793\) | −6.20960e11 | −0.0557615 | ||||||||
\(794\) | −1.02807e13 | −0.917975 | ||||||||
\(795\) | −4.15372e12 | −0.368795 | ||||||||
\(796\) | 4.13835e12 | 0.365358 | ||||||||
\(797\) | −1.83799e12 | −0.161355 | −0.0806773 | − | 0.996740i | \(-0.525708\pi\) | ||||
−0.0806773 | + | 0.996740i | \(0.525708\pi\) | |||||||
\(798\) | 2.72992e12 | 0.238307 | ||||||||
\(799\) | 1.24453e13 | 1.08030 | ||||||||
\(800\) | −2.23720e12 | −0.193108 | ||||||||
\(801\) | 5.58169e12 | 0.479092 | ||||||||
\(802\) | −2.72716e13 | −2.32769 | ||||||||
\(803\) | 7.24960e12 | 0.615310 | ||||||||
\(804\) | 7.71629e12 | 0.651263 | ||||||||
\(805\) | −9.33353e11 | −0.0783365 | ||||||||
\(806\) | 7.59570e12 | 0.633957 | ||||||||
\(807\) | −6.71504e11 | −0.0557337 | ||||||||
\(808\) | 9.81263e12 | 0.809906 | ||||||||
\(809\) | 1.92205e13 | 1.57760 | 0.788801 | − | 0.614649i | \(-0.210702\pi\) | ||||
0.788801 | + | 0.614649i | \(0.210702\pi\) | |||||||
\(810\) | −3.95638e12 | −0.322935 | ||||||||
\(811\) | −1.70316e13 | −1.38249 | −0.691246 | − | 0.722620i | \(-0.742938\pi\) | ||||
−0.691246 | + | 0.722620i | \(0.742938\pi\) | |||||||
\(812\) | 4.38892e12 | 0.354288 | ||||||||
\(813\) | 8.66416e12 | 0.695535 | ||||||||
\(814\) | 1.65794e12 | 0.132361 | ||||||||
\(815\) | 8.81855e11 | 0.0700145 | ||||||||
\(816\) | −1.99911e13 | −1.57845 | ||||||||
\(817\) | −1.05417e13 | −0.827774 | ||||||||
\(818\) | 1.00295e13 | 0.783228 | ||||||||
\(819\) | 6.32518e11 | 0.0491242 | ||||||||
\(820\) | −1.73820e12 | −0.134257 | ||||||||
\(821\) | 1.33485e13 | 1.02539 | 0.512694 | − | 0.858572i | \(-0.328648\pi\) | ||||
0.512694 | + | 0.858572i | \(0.328648\pi\) | |||||||
\(822\) | −3.80788e12 | −0.290911 | ||||||||
\(823\) | −1.72858e13 | −1.31338 | −0.656689 | − | 0.754161i | \(-0.728044\pi\) | ||||
−0.656689 | + | 0.754161i | \(0.728044\pi\) | |||||||
\(824\) | −7.25817e12 | −0.548473 | ||||||||
\(825\) | 1.15764e12 | 0.0870026 | ||||||||
\(826\) | 5.71000e12 | 0.426801 | ||||||||
\(827\) | 1.64651e13 | 1.22402 | 0.612012 | − | 0.790849i | \(-0.290361\pi\) | ||||
0.612012 | + | 0.790849i | \(0.290361\pi\) | |||||||
\(828\) | 1.05347e12 | 0.0778906 | ||||||||
\(829\) | −5.91786e12 | −0.435181 | −0.217590 | − | 0.976040i | \(-0.569820\pi\) | ||||
−0.217590 | + | 0.976040i | \(0.569820\pi\) | |||||||
\(830\) | −1.27743e12 | −0.0934298 | ||||||||
\(831\) | −2.57932e12 | −0.187629 | ||||||||
\(832\) | −3.07928e11 | −0.0222789 | ||||||||
\(833\) | −3.03426e12 | −0.218348 | ||||||||
\(834\) | 1.58828e13 | 1.13679 | ||||||||
\(835\) | 1.55347e11 | 0.0110589 | ||||||||
\(836\) | 2.43259e12 | 0.172242 | ||||||||
\(837\) | −1.92723e13 | −1.35728 | ||||||||
\(838\) | 1.35719e13 | 0.950701 | ||||||||
\(839\) | 2.40380e13 | 1.67483 | 0.837414 | − | 0.546569i | \(-0.184066\pi\) | ||||
0.837414 | + | 0.546569i | \(0.184066\pi\) | |||||||
\(840\) | 1.16977e12 | 0.0810667 | ||||||||
\(841\) | 3.06570e13 | 2.11324 | ||||||||
\(842\) | 2.01123e13 | 1.37898 | ||||||||
\(843\) | 1.57827e13 | 1.07636 | ||||||||
\(844\) | −1.05978e13 | −0.718913 | ||||||||
\(845\) | −5.50919e12 | −0.371734 | ||||||||
\(846\) | 4.12263e12 | 0.276699 | ||||||||
\(847\) | −4.09430e12 | −0.273341 | ||||||||
\(848\) | −1.87590e13 | −1.24574 | ||||||||
\(849\) | 1.98457e13 | 1.31094 | ||||||||
\(850\) | −5.75687e12 | −0.378269 | ||||||||
\(851\) | 1.44154e12 | 0.0942203 | ||||||||
\(852\) | −1.95313e12 | −0.126985 | ||||||||
\(853\) | 2.26446e13 | 1.46452 | 0.732258 | − | 0.681027i | \(-0.238466\pi\) | ||||
0.732258 | + | 0.681027i | \(0.238466\pi\) | |||||||
\(854\) | 9.86761e11 | 0.0634821 | ||||||||
\(855\) | 1.36239e12 | 0.0871874 | ||||||||
\(856\) | −2.25758e12 | −0.143718 | ||||||||
\(857\) | −1.20223e13 | −0.761334 | −0.380667 | − | 0.924712i | \(-0.624306\pi\) | ||||
−0.380667 | + | 0.924712i | \(0.624306\pi\) | |||||||
\(858\) | −3.51055e12 | −0.221148 | ||||||||
\(859\) | −9.44258e12 | −0.591727 | −0.295864 | − | 0.955230i | \(-0.595607\pi\) | ||||
−0.295864 | + | 0.955230i | \(0.595607\pi\) | |||||||
\(860\) | 5.11938e12 | 0.319135 | ||||||||
\(861\) | 2.84774e12 | 0.176598 | ||||||||
\(862\) | 2.31643e13 | 1.42901 | ||||||||
\(863\) | 8.80380e12 | 0.540283 | 0.270142 | − | 0.962821i | \(-0.412929\pi\) | ||||
0.270142 | + | 0.962821i | \(0.412929\pi\) | |||||||
\(864\) | −1.72135e13 | −1.05089 | ||||||||
\(865\) | 1.04076e13 | 0.632090 | ||||||||
\(866\) | 2.44449e13 | 1.47692 | ||||||||
\(867\) | −1.83800e13 | −1.10474 | ||||||||
\(868\) | −4.18763e12 | −0.250397 | ||||||||
\(869\) | −7.05399e12 | −0.419610 | ||||||||
\(870\) | −1.36425e13 | −0.807340 | ||||||||
\(871\) | 1.03463e13 | 0.609119 | ||||||||
\(872\) | 9.57740e12 | 0.560949 | ||||||||
\(873\) | −7.50858e12 | −0.437516 | ||||||||
\(874\) | 6.09641e12 | 0.353405 | ||||||||
\(875\) | 5.86182e11 | 0.0338062 | ||||||||
\(876\) | 8.95331e12 | 0.513707 | ||||||||
\(877\) | 6.73513e12 | 0.384457 | 0.192229 | − | 0.981350i | \(-0.438429\pi\) | ||||
0.192229 | + | 0.981350i | \(0.438429\pi\) | |||||||
\(878\) | 2.00217e13 | 1.13704 | ||||||||
\(879\) | −1.22650e13 | −0.692973 | ||||||||
\(880\) | 5.22814e12 | 0.293884 | ||||||||
\(881\) | −7.58474e12 | −0.424179 | −0.212089 | − | 0.977250i | \(-0.568027\pi\) | ||||
−0.212089 | + | 0.977250i | \(0.568027\pi\) | |||||||
\(882\) | −1.00513e12 | −0.0559258 | ||||||||
\(883\) | −1.78234e13 | −0.986662 | −0.493331 | − | 0.869842i | \(-0.664221\pi\) | ||||
−0.493331 | + | 0.869842i | \(0.664221\pi\) | |||||||
\(884\) | 6.05674e12 | 0.333583 | ||||||||
\(885\) | −6.15777e12 | −0.337426 | ||||||||
\(886\) | 1.65113e13 | 0.900182 | ||||||||
\(887\) | −2.45177e13 | −1.32991 | −0.664956 | − | 0.746882i | \(-0.731550\pi\) | ||||
−0.664956 | + | 0.746882i | \(0.731550\pi\) | |||||||
\(888\) | −1.80668e12 | −0.0975041 | ||||||||
\(889\) | 8.38764e12 | 0.450383 | ||||||||
\(890\) | −1.56864e13 | −0.838049 | ||||||||
\(891\) | 5.77586e12 | 0.307020 | ||||||||
\(892\) | 2.94642e11 | 0.0155830 | ||||||||
\(893\) | 8.27714e12 | 0.435561 | ||||||||
\(894\) | 2.79811e13 | 1.46503 | ||||||||
\(895\) | 1.26847e13 | 0.660812 | ||||||||
\(896\) | 7.52988e12 | 0.390303 | ||||||||
\(897\) | −3.05234e12 | −0.157423 | ||||||||
\(898\) | −2.98134e13 | −1.52992 | ||||||||
\(899\) | −4.30928e13 | −2.20032 | ||||||||
\(900\) | −6.61619e11 | −0.0336137 | ||||||||
\(901\) | −3.01555e13 | −1.52442 | ||||||||
\(902\) | 7.31416e12 | 0.367905 | ||||||||
\(903\) | −8.38723e12 | −0.419782 | ||||||||
\(904\) | 1.90968e13 | 0.951047 | ||||||||
\(905\) | −8.50995e12 | −0.421704 | ||||||||
\(906\) | −1.78284e13 | −0.879096 | ||||||||
\(907\) | −8.14231e12 | −0.399498 | −0.199749 | − | 0.979847i | \(-0.564013\pi\) | ||||
−0.199749 | + | 0.979847i | \(0.564013\pi\) | |||||||
\(908\) | −1.34536e13 | −0.656830 | ||||||||
\(909\) | 9.09275e12 | 0.441731 | ||||||||
\(910\) | −1.77759e12 | −0.0859302 | ||||||||
\(911\) | −1.26965e13 | −0.610733 | −0.305367 | − | 0.952235i | \(-0.598779\pi\) | ||||
−0.305367 | + | 0.952235i | \(0.598779\pi\) | |||||||
\(912\) | −1.32957e13 | −0.636406 | ||||||||
\(913\) | 1.86490e12 | 0.0888254 | ||||||||
\(914\) | 4.32029e13 | 2.04765 | ||||||||
\(915\) | −1.06414e12 | −0.0501886 | ||||||||
\(916\) | −1.17715e13 | −0.552463 | ||||||||
\(917\) | −4.43456e12 | −0.207104 | ||||||||
\(918\) | −4.42947e13 | −2.05854 | ||||||||
\(919\) | −2.53575e13 | −1.17270 | −0.586350 | − | 0.810058i | \(-0.699436\pi\) | ||||
−0.586350 | + | 0.810058i | \(0.699436\pi\) | |||||||
\(920\) | 2.61230e12 | 0.120220 | ||||||||
\(921\) | −2.02007e13 | −0.925120 | ||||||||
\(922\) | −2.34830e13 | −1.07020 | ||||||||
\(923\) | −2.61882e12 | −0.118768 | ||||||||
\(924\) | 1.93542e12 | 0.0873478 | ||||||||
\(925\) | −9.05345e11 | −0.0406608 | ||||||||
\(926\) | −2.41309e13 | −1.07851 | ||||||||
\(927\) | −6.72569e12 | −0.299143 | ||||||||
\(928\) | −3.84895e13 | −1.70363 | ||||||||
\(929\) | 1.89611e13 | 0.835203 | 0.417602 | − | 0.908630i | \(-0.362871\pi\) | ||||
0.417602 | + | 0.908630i | \(0.362871\pi\) | |||||||
\(930\) | 1.30168e13 | 0.570598 | ||||||||
\(931\) | −2.01803e12 | −0.0880346 | ||||||||
\(932\) | −2.05460e12 | −0.0891980 | ||||||||
\(933\) | 1.22852e13 | 0.530782 | ||||||||
\(934\) | 4.11561e13 | 1.76959 | ||||||||
\(935\) | 8.40437e12 | 0.359627 | ||||||||
\(936\) | −1.77031e12 | −0.0753891 | ||||||||
\(937\) | 8.65559e12 | 0.366833 | 0.183416 | − | 0.983035i | \(-0.441284\pi\) | ||||
0.183416 | + | 0.983035i | \(0.441284\pi\) | |||||||
\(938\) | −1.64411e13 | −0.693456 | ||||||||
\(939\) | 2.82527e13 | 1.18595 | ||||||||
\(940\) | −4.01964e12 | −0.167923 | ||||||||
\(941\) | 3.42336e13 | 1.42331 | 0.711654 | − | 0.702530i | \(-0.247946\pi\) | ||||
0.711654 | + | 0.702530i | \(0.247946\pi\) | |||||||
\(942\) | 4.32343e12 | 0.178895 | ||||||||
\(943\) | 6.35950e12 | 0.261891 | ||||||||
\(944\) | −2.78097e13 | −1.13978 | ||||||||
\(945\) | 4.51022e12 | 0.183973 | ||||||||
\(946\) | −2.15419e13 | −0.874527 | ||||||||
\(947\) | 2.38597e13 | 0.964030 | 0.482015 | − | 0.876163i | \(-0.339905\pi\) | ||||
0.482015 | + | 0.876163i | \(0.339905\pi\) | |||||||
\(948\) | −8.71174e12 | −0.350322 | ||||||||
\(949\) | 1.20049e13 | 0.480464 | ||||||||
\(950\) | −3.82878e12 | −0.152512 | ||||||||
\(951\) | −2.13180e13 | −0.845150 | ||||||||
\(952\) | 8.49238e12 | 0.335091 | ||||||||
\(953\) | −4.83481e13 | −1.89872 | −0.949360 | − | 0.314189i | \(-0.898267\pi\) | ||||
−0.949360 | + | 0.314189i | \(0.898267\pi\) | |||||||
\(954\) | −9.98932e12 | −0.390452 | ||||||||
\(955\) | 1.13973e12 | 0.0443391 | ||||||||
\(956\) | −7.52123e12 | −0.291225 | ||||||||
\(957\) | 1.99165e13 | 0.767553 | ||||||||
\(958\) | 6.16636e13 | 2.36529 | ||||||||
\(959\) | 2.81488e12 | 0.107467 | ||||||||
\(960\) | −5.27698e11 | −0.0200523 | ||||||||
\(961\) | 1.46768e13 | 0.555106 | ||||||||
\(962\) | 2.74545e12 | 0.103354 | ||||||||
\(963\) | −2.09196e12 | −0.0783852 | ||||||||
\(964\) | −2.24674e13 | −0.837925 | ||||||||
\(965\) | 7.73421e12 | 0.287106 | ||||||||
\(966\) | 4.85045e12 | 0.179219 | ||||||||
\(967\) | −2.28025e13 | −0.838617 | −0.419308 | − | 0.907844i | \(-0.637727\pi\) | ||||
−0.419308 | + | 0.907844i | \(0.637727\pi\) | |||||||
\(968\) | 1.14593e13 | 0.419486 | ||||||||
\(969\) | −2.13731e13 | −0.778774 | ||||||||
\(970\) | 2.11017e13 | 0.765322 | ||||||||
\(971\) | 7.62385e12 | 0.275225 | 0.137612 | − | 0.990486i | \(-0.456057\pi\) | ||||
0.137612 | + | 0.990486i | \(0.456057\pi\) | |||||||
\(972\) | −8.95785e12 | −0.321889 | ||||||||
\(973\) | −1.17409e13 | −0.419947 | ||||||||
\(974\) | 3.64203e13 | 1.29667 | ||||||||
\(975\) | 1.91699e12 | 0.0679359 | ||||||||
\(976\) | −4.80587e12 | −0.169531 | ||||||||
\(977\) | 2.97018e13 | 1.04293 | 0.521467 | − | 0.853272i | \(-0.325385\pi\) | ||||
0.521467 | + | 0.853272i | \(0.325385\pi\) | |||||||
\(978\) | −4.58282e12 | −0.160180 | ||||||||
\(979\) | 2.29004e13 | 0.796749 | ||||||||
\(980\) | 9.80016e11 | 0.0339403 | ||||||||
\(981\) | 8.87477e12 | 0.305947 | ||||||||
\(982\) | 1.92905e13 | 0.661976 | ||||||||
\(983\) | −1.08292e13 | −0.369917 | −0.184958 | − | 0.982746i | \(-0.559215\pi\) | ||||
−0.184958 | + | 0.982746i | \(0.559215\pi\) | |||||||
\(984\) | −7.97034e12 | −0.271019 | ||||||||
\(985\) | 1.20711e13 | 0.408586 | ||||||||
\(986\) | −9.90428e13 | −3.33716 | ||||||||
\(987\) | 6.58549e12 | 0.220882 | ||||||||
\(988\) | 4.02822e12 | 0.134495 | ||||||||
\(989\) | −1.87302e13 | −0.622528 | ||||||||
\(990\) | 2.78403e12 | 0.0921118 | ||||||||
\(991\) | 5.29514e12 | 0.174400 | 0.0871999 | − | 0.996191i | \(-0.472208\pi\) | ||||
0.0871999 | + | 0.996191i | \(0.472208\pi\) | |||||||
\(992\) | 3.67242e13 | 1.20406 | ||||||||
\(993\) | 6.74842e12 | 0.220257 | ||||||||
\(994\) | 4.16154e12 | 0.135212 | ||||||||
\(995\) | 9.50909e12 | 0.307564 | ||||||||
\(996\) | 2.30317e12 | 0.0741581 | ||||||||
\(997\) | 1.64214e13 | 0.526360 | 0.263180 | − | 0.964747i | \(-0.415229\pi\) | ||||
0.263180 | + | 0.964747i | \(0.415229\pi\) | |||||||
\(998\) | 4.94788e13 | 1.57882 | ||||||||
\(999\) | −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 | 35.10.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 315.10.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 175.10.b.a.99.2 | 2 | |||
5.3 | odd | 4 | 175.10.b.a.99.1 | 2 | |||
5.4 | even | 2 | 175.10.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 245.10.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.10.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
175.10.a.a.1.1 | 1 | 5.4 | even | 2 | |||
175.10.b.a.99.1 | 2 | 5.3 | odd | 4 | |||
175.10.b.a.99.2 | 2 | 5.2 | odd | 4 | |||
245.10.a.b.1.1 | 1 | 7.6 | odd | 2 | |||
315.10.a.a.1.1 | 1 | 3.2 | odd | 2 |