Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,11,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.3203618650\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.18 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.11.b.b.42.17 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.846054i | 0.0264392i | 0.999913 | + | 0.0132196i | \(0.00420805\pi\) | ||||
−0.999913 | + | 0.0132196i | \(0.995792\pi\) | |||||||
\(3\) | 54.5873i | 0.224639i | 0.993672 | + | 0.112320i | \(0.0358281\pi\) | ||||
−0.993672 | + | 0.112320i | \(0.964172\pi\) | |||||||
\(4\) | 1023.28 | 0.999301 | ||||||||
\(5\) | 4881.88i | 1.56220i | 0.624404 | + | 0.781101i | \(0.285342\pi\) | ||||
−0.624404 | + | 0.781101i | \(0.714658\pi\) | |||||||
\(6\) | −46.1839 | −0.00593928 | ||||||||
\(7\) | 30624.2i | 1.82211i | 0.412287 | + | 0.911054i | \(0.364730\pi\) | ||||
−0.412287 | + | 0.911054i | \(0.635270\pi\) | |||||||
\(8\) | 1732.11i | 0.0528599i | ||||||||
\(9\) | 56069.2 | 0.949537 | ||||||||
\(10\) | −4130.34 | −0.0413034 | ||||||||
\(11\) | −179422. | −1.11407 | −0.557036 | − | 0.830488i | \(-0.688061\pi\) | ||||
−0.557036 | + | 0.830488i | \(0.688061\pi\) | |||||||
\(12\) | 55858.4i | 0.224482i | ||||||||
\(13\) | −338315. | −0.911179 | −0.455590 | − | 0.890190i | \(-0.650572\pi\) | ||||
−0.455590 | + | 0.890190i | \(0.650572\pi\) | |||||||
\(14\) | −25909.7 | −0.0481751 | ||||||||
\(15\) | −266489. | −0.350932 | ||||||||
\(16\) | 1.04638e6 | 0.997903 | ||||||||
\(17\) | 766203. | 0.539634 | 0.269817 | − | 0.962912i | \(-0.413037\pi\) | ||||
0.269817 | + | 0.962912i | \(0.413037\pi\) | |||||||
\(18\) | 47437.6i | 0.0251050i | ||||||||
\(19\) | − | 3.89726e6i | − | 1.57395i | −0.616985 | − | 0.786975i | \(-0.711646\pi\) | ||
0.616985 | − | 0.786975i | \(-0.288354\pi\) | |||||||
\(20\) | 4.99555e6i | 1.56111i | ||||||||
\(21\) | −1.67169e6 | −0.409317 | ||||||||
\(22\) | − | 151801.i | − | 0.0294552i | ||||||
\(23\) | 3.13921e6 | 0.487732 | 0.243866 | − | 0.969809i | \(-0.421584\pi\) | ||||
0.243866 | + | 0.969809i | \(0.421584\pi\) | |||||||
\(24\) | −94551.5 | −0.0118744 | ||||||||
\(25\) | −1.40672e7 | −1.44048 | ||||||||
\(26\) | − | 286232.i | − | 0.0240908i | ||||||
\(27\) | 6.28400e6i | 0.437943i | ||||||||
\(28\) | 3.13372e7i | 1.82083i | ||||||||
\(29\) | − | 1.81741e7i | − | 0.886060i | −0.896507 | − | 0.443030i | \(-0.853903\pi\) | ||
0.896507 | − | 0.443030i | \(-0.146097\pi\) | |||||||
\(30\) | − | 225464.i | − | 0.00927836i | ||||||
\(31\) | −2.96757e7 | −1.03656 | −0.518278 | − | 0.855212i | \(-0.673427\pi\) | ||||
−0.518278 | + | 0.855212i | \(0.673427\pi\) | |||||||
\(32\) | 2.65898e6i | 0.0792437i | ||||||||
\(33\) | − | 9.79419e6i | − | 0.250264i | ||||||
\(34\) | 648249.i | 0.0142675i | ||||||||
\(35\) | −1.49504e8 | −2.84650 | ||||||||
\(36\) | 5.73747e7 | 0.948873 | ||||||||
\(37\) | 8.05730e7i | 1.16193i | 0.813928 | + | 0.580966i | \(0.197325\pi\) | ||||
−0.813928 | + | 0.580966i | \(0.802675\pi\) | |||||||
\(38\) | 3.29729e6 | 0.0416140 | ||||||||
\(39\) | − | 1.84677e7i | − | 0.204687i | ||||||
\(40\) | −8.45598e6 | −0.0825779 | ||||||||
\(41\) | 4.52023e7 | 0.390159 | 0.195079 | − | 0.980787i | \(-0.437504\pi\) | ||||
0.195079 | + | 0.980787i | \(0.437504\pi\) | |||||||
\(42\) | − | 1.41434e6i | − | 0.0108220i | ||||||
\(43\) | 1.20044e8 | + | 8.48586e7i | 0.816577 | + | 0.577237i | ||||
\(44\) | −1.83600e8 | −1.11329 | ||||||||
\(45\) | 2.73723e8i | 1.48337i | ||||||||
\(46\) | 2.65594e6i | 0.0128952i | ||||||||
\(47\) | 1.36443e8 | 0.594925 | 0.297463 | − | 0.954733i | \(-0.403860\pi\) | ||||
0.297463 | + | 0.954733i | \(0.403860\pi\) | |||||||
\(48\) | 5.71190e7i | 0.224168i | ||||||||
\(49\) | −6.55365e8 | −2.32008 | ||||||||
\(50\) | − | 1.19016e7i | − | 0.0380850i | ||||||
\(51\) | 4.18250e7i | 0.121223i | ||||||||
\(52\) | −3.46192e8 | −0.910542 | ||||||||
\(53\) | −3.81746e8 | −0.912842 | −0.456421 | − | 0.889764i | \(-0.650869\pi\) | ||||
−0.456421 | + | 0.889764i | \(0.650869\pi\) | |||||||
\(54\) | −5.31660e6 | −0.0115789 | ||||||||
\(55\) | − | 8.75919e8i | − | 1.74041i | ||||||
\(56\) | −5.30445e7 | −0.0963165 | ||||||||
\(57\) | 2.12741e8 | 0.353571 | ||||||||
\(58\) | 1.53763e7 | 0.0234267 | ||||||||
\(59\) | 1.06201e9 | 1.48548 | 0.742740 | − | 0.669580i | \(-0.233526\pi\) | ||||
0.742740 | + | 0.669580i | \(0.233526\pi\) | |||||||
\(60\) | −2.72694e8 | −0.350687 | ||||||||
\(61\) | 7.22078e8i | 0.854939i | 0.904030 | + | 0.427470i | \(0.140595\pi\) | ||||
−0.904030 | + | 0.427470i | \(0.859405\pi\) | |||||||
\(62\) | − | 2.51072e7i | − | 0.0274057i | ||||||
\(63\) | 1.71707e9i | 1.73016i | ||||||||
\(64\) | 1.06924e9 | 0.995808 | ||||||||
\(65\) | − | 1.65161e9i | − | 1.42345i | ||||||
\(66\) | 8.28642e6 | 0.00661679 | ||||||||
\(67\) | 1.44131e9 | 1.06753 | 0.533767 | − | 0.845631i | \(-0.320776\pi\) | ||||
0.533767 | + | 0.845631i | \(0.320776\pi\) | |||||||
\(68\) | 7.84044e8 | 0.539257 | ||||||||
\(69\) | 1.71361e8i | 0.109564i | ||||||||
\(70\) | − | 1.26488e8i | − | 0.0752592i | ||||||
\(71\) | 3.79857e8i | 0.210537i | 0.994444 | + | 0.105268i | \(0.0335702\pi\) | ||||
−0.994444 | + | 0.105268i | \(0.966430\pi\) | |||||||
\(72\) | 9.71183e7i | 0.0501925i | ||||||||
\(73\) | − | 1.13814e9i | − | 0.549013i | −0.961585 | − | 0.274507i | \(-0.911485\pi\) | ||
0.961585 | − | 0.274507i | \(-0.0885145\pi\) | |||||||
\(74\) | −6.81691e7 | −0.0307206 | ||||||||
\(75\) | − | 7.67889e8i | − | 0.323588i | ||||||
\(76\) | − | 3.98800e9i | − | 1.57285i | ||||||
\(77\) | − | 5.49466e9i | − | 2.02996i | ||||||
\(78\) | 1.56247e7 | 0.00541175 | ||||||||
\(79\) | −4.58342e9 | −1.48955 | −0.744773 | − | 0.667318i | \(-0.767442\pi\) | ||||
−0.744773 | + | 0.667318i | \(0.767442\pi\) | |||||||
\(80\) | 5.10829e9i | 1.55893i | ||||||||
\(81\) | 2.96780e9 | 0.851158 | ||||||||
\(82\) | 3.82436e7i | 0.0103155i | ||||||||
\(83\) | 6.19566e9 | 1.57289 | 0.786443 | − | 0.617663i | \(-0.211920\pi\) | ||||
0.786443 | + | 0.617663i | \(0.211920\pi\) | |||||||
\(84\) | −1.71062e9 | −0.409031 | ||||||||
\(85\) | 3.74051e9i | 0.843018i | ||||||||
\(86\) | −7.17950e7 | + | 1.01563e8i | −0.0152617 | + | 0.0215896i | ||||
\(87\) | 9.92077e8 | 0.199044 | ||||||||
\(88\) | − | 3.10780e8i | − | 0.0588898i | ||||||
\(89\) | 7.46570e9i | 1.33697i | 0.743727 | + | 0.668483i | \(0.233056\pi\) | ||||
−0.743727 | + | 0.668483i | \(0.766944\pi\) | |||||||
\(90\) | −2.31585e8 | −0.0392191 | ||||||||
\(91\) | − | 1.03606e10i | − | 1.66027i | ||||||
\(92\) | 3.21231e9 | 0.487391 | ||||||||
\(93\) | − | 1.61992e9i | − | 0.232851i | ||||||
\(94\) | 1.15438e8i | 0.0157293i | ||||||||
\(95\) | 1.90259e10 | 2.45883 | ||||||||
\(96\) | −1.45146e8 | −0.0178012 | ||||||||
\(97\) | −3.79259e9 | −0.441649 | −0.220825 | − | 0.975314i | \(-0.570875\pi\) | ||||
−0.220825 | + | 0.975314i | \(0.570875\pi\) | |||||||
\(98\) | − | 5.54474e8i | − | 0.0613410i | ||||||
\(99\) | −1.00601e10 | −1.05785 | ||||||||
\(100\) | −1.43947e10 | −1.43947 | ||||||||
\(101\) | −1.53422e9 | −0.145976 | −0.0729878 | − | 0.997333i | \(-0.523253\pi\) | ||||
−0.0729878 | + | 0.997333i | \(0.523253\pi\) | |||||||
\(102\) | −3.53862e7 | −0.00320504 | ||||||||
\(103\) | −2.62038e9 | −0.226036 | −0.113018 | − | 0.993593i | \(-0.536052\pi\) | ||||
−0.113018 | + | 0.993593i | \(0.536052\pi\) | |||||||
\(104\) | − | 5.85999e8i | − | 0.0481649i | ||||||
\(105\) | − | 8.16101e9i | − | 0.639436i | ||||||
\(106\) | − | 3.22978e8i | − | 0.0241348i | ||||||
\(107\) | −1.32447e10 | −0.944326 | −0.472163 | − | 0.881511i | \(-0.656527\pi\) | ||||
−0.472163 | + | 0.881511i | \(0.656527\pi\) | |||||||
\(108\) | 6.43032e9i | 0.437637i | ||||||||
\(109\) | −2.14660e8 | −0.0139514 | −0.00697570 | − | 0.999976i | \(-0.502220\pi\) | ||||
−0.00697570 | + | 0.999976i | \(0.502220\pi\) | |||||||
\(110\) | 7.41075e8 | 0.0460149 | ||||||||
\(111\) | −4.39827e9 | −0.261016 | ||||||||
\(112\) | 3.20444e10i | 1.81829i | ||||||||
\(113\) | 1.52894e10i | 0.829846i | 0.909857 | + | 0.414923i | \(0.136191\pi\) | ||||
−0.909857 | + | 0.414923i | \(0.863809\pi\) | |||||||
\(114\) | 1.79990e8i | 0.00934813i | ||||||||
\(115\) | 1.53253e10i | 0.761937i | ||||||||
\(116\) | − | 1.85973e10i | − | 0.885441i | ||||||
\(117\) | −1.89690e10 | −0.865199 | ||||||||
\(118\) | 8.98514e8i | 0.0392749i | ||||||||
\(119\) | 2.34643e10i | 0.983272i | ||||||||
\(120\) | − | 4.61589e8i | − | 0.0185502i | ||||||
\(121\) | 6.25498e9 | 0.241157 | ||||||||
\(122\) | −6.10918e8 | −0.0226039 | ||||||||
\(123\) | 2.46747e9i | 0.0876450i | ||||||||
\(124\) | −3.03667e10 | −1.03583 | ||||||||
\(125\) | − | 2.09996e10i | − | 0.688113i | ||||||
\(126\) | −1.45274e9 | −0.0457440 | ||||||||
\(127\) | −1.09606e10 | −0.331754 | −0.165877 | − | 0.986146i | \(-0.553045\pi\) | ||||
−0.165877 | + | 0.986146i | \(0.553045\pi\) | |||||||
\(128\) | 3.62743e9i | 0.105572i | ||||||||
\(129\) | −4.63221e9 | + | 6.55287e9i | −0.129670 | + | 0.183435i | ||||
\(130\) | 1.39735e9 | 0.0376348 | ||||||||
\(131\) | − | 4.01825e10i | − | 1.04155i | −0.853694 | − | 0.520776i | \(-0.825643\pi\) | ||
0.853694 | − | 0.520776i | \(-0.174357\pi\) | |||||||
\(132\) | − | 1.00222e10i | − | 0.250089i | ||||||
\(133\) | 1.19350e11 | 2.86791 | ||||||||
\(134\) | 1.21942e9i | 0.0282248i | ||||||||
\(135\) | −3.06777e10 | −0.684155 | ||||||||
\(136\) | 1.32715e9i | 0.0285250i | ||||||||
\(137\) | − | 1.58617e10i | − | 0.328661i | −0.986405 | − | 0.164330i | \(-0.947454\pi\) | ||
0.986405 | − | 0.164330i | \(-0.0525463\pi\) | |||||||
\(138\) | −1.44981e8 | −0.00289678 | ||||||||
\(139\) | −2.51826e10 | −0.485318 | −0.242659 | − | 0.970112i | \(-0.578020\pi\) | ||||
−0.242659 | + | 0.970112i | \(0.578020\pi\) | |||||||
\(140\) | −1.52985e11 | −2.84451 | ||||||||
\(141\) | 7.44807e9i | 0.133644i | ||||||||
\(142\) | −3.21380e8 | −0.00556643 | ||||||||
\(143\) | 6.07012e10 | 1.01512 | ||||||||
\(144\) | 5.86696e10 | 0.947546 | ||||||||
\(145\) | 8.87239e10 | 1.38421 | ||||||||
\(146\) | 9.62931e8 | 0.0145155 | ||||||||
\(147\) | − | 3.57746e10i | − | 0.521181i | ||||||
\(148\) | 8.24491e10i | 1.16112i | ||||||||
\(149\) | 2.12604e10i | 0.289495i | 0.989469 | + | 0.144747i | \(0.0462369\pi\) | ||||
−0.989469 | + | 0.144747i | \(0.953763\pi\) | |||||||
\(150\) | 6.49675e8 | 0.00855540 | ||||||||
\(151\) | − | 1.47453e10i | − | 0.187831i | −0.995580 | − | 0.0939157i | \(-0.970062\pi\) | ||
0.995580 | − | 0.0939157i | \(-0.0299384\pi\) | |||||||
\(152\) | 6.75049e9 | 0.0831988 | ||||||||
\(153\) | 4.29604e10 | 0.512403 | ||||||||
\(154\) | 4.64878e9 | 0.0536705 | ||||||||
\(155\) | − | 1.44873e11i | − | 1.61931i | ||||||
\(156\) | − | 1.88977e10i | − | 0.204544i | ||||||
\(157\) | − | 6.49091e10i | − | 0.680467i | −0.940341 | − | 0.340233i | \(-0.889494\pi\) | ||
0.940341 | − | 0.340233i | \(-0.110506\pi\) | |||||||
\(158\) | − | 3.87782e9i | − | 0.0393824i | ||||||
\(159\) | − | 2.08385e10i | − | 0.205060i | ||||||
\(160\) | −1.29808e10 | −0.123795 | ||||||||
\(161\) | 9.61358e10i | 0.888701i | ||||||||
\(162\) | 2.51092e9i | 0.0225039i | ||||||||
\(163\) | 1.68483e11i | 1.46426i | 0.681167 | + | 0.732128i | \(0.261473\pi\) | ||||
−0.681167 | + | 0.732128i | \(0.738527\pi\) | |||||||
\(164\) | 4.62548e10 | 0.389886 | ||||||||
\(165\) | 4.78141e10 | 0.390964 | ||||||||
\(166\) | 5.24186e9i | 0.0415858i | ||||||||
\(167\) | 8.66424e10 | 0.667034 | 0.333517 | − | 0.942744i | \(-0.391765\pi\) | ||||
0.333517 | + | 0.942744i | \(0.391765\pi\) | |||||||
\(168\) | − | 2.89556e9i | − | 0.0216365i | ||||||
\(169\) | −2.34018e10 | −0.169752 | ||||||||
\(170\) | −3.16468e9 | −0.0222887 | ||||||||
\(171\) | − | 2.18516e11i | − | 1.49452i | ||||||
\(172\) | 1.22839e11 | + | 8.68345e10i | 0.816006 | + | 0.576833i | ||||
\(173\) | 1.37685e11 | 0.888496 | 0.444248 | − | 0.895904i | \(-0.353471\pi\) | ||||
0.444248 | + | 0.895904i | \(0.353471\pi\) | |||||||
\(174\) | 8.39351e8i | 0.00526256i | ||||||||
\(175\) | − | 4.30795e11i | − | 2.62470i | ||||||
\(176\) | −1.87744e11 | −1.11174 | ||||||||
\(177\) | 5.79720e10i | 0.333697i | ||||||||
\(178\) | −6.31639e9 | −0.0353483 | ||||||||
\(179\) | − | 2.72920e11i | − | 1.48515i | −0.669763 | − | 0.742575i | \(-0.733604\pi\) | ||
0.669763 | − | 0.742575i | \(-0.266396\pi\) | |||||||
\(180\) | 2.80097e11i | 1.48233i | ||||||||
\(181\) | 2.81034e11 | 1.44666 | 0.723328 | − | 0.690505i | \(-0.242612\pi\) | ||||
0.723328 | + | 0.690505i | \(0.242612\pi\) | |||||||
\(182\) | 8.76563e9 | 0.0438961 | ||||||||
\(183\) | −3.94163e10 | −0.192053 | ||||||||
\(184\) | 5.43747e9i | 0.0257815i | ||||||||
\(185\) | −3.93348e11 | −1.81517 | ||||||||
\(186\) | 1.37054e9 | 0.00615639 | ||||||||
\(187\) | −1.37474e11 | −0.601191 | ||||||||
\(188\) | 1.39620e11 | 0.594509 | ||||||||
\(189\) | −1.92442e11 | −0.797979 | ||||||||
\(190\) | 1.60970e10i | 0.0650094i | ||||||||
\(191\) | 4.74206e11i | 1.86552i | 0.360495 | + | 0.932761i | \(0.382608\pi\) | ||||
−0.360495 | + | 0.932761i | \(0.617392\pi\) | |||||||
\(192\) | 5.83670e10i | 0.223698i | ||||||||
\(193\) | −3.33550e11 | −1.24559 | −0.622794 | − | 0.782386i | \(-0.714002\pi\) | ||||
−0.622794 | + | 0.782386i | \(0.714002\pi\) | |||||||
\(194\) | − | 3.20874e9i | − | 0.0116769i | ||||||
\(195\) | 9.01571e10 | 0.319762 | ||||||||
\(196\) | −6.70624e11 | −2.31846 | ||||||||
\(197\) | 4.59036e11 | 1.54709 | 0.773545 | − | 0.633742i | \(-0.218482\pi\) | ||||
0.773545 | + | 0.633742i | \(0.218482\pi\) | |||||||
\(198\) | − | 8.51137e9i | − | 0.0279688i | ||||||
\(199\) | 3.09195e11i | 0.990756i | 0.868677 | + | 0.495378i | \(0.164971\pi\) | ||||
−0.868677 | + | 0.495378i | \(0.835029\pi\) | |||||||
\(200\) | − | 2.43659e10i | − | 0.0761435i | ||||||
\(201\) | 7.86770e10i | 0.239810i | ||||||||
\(202\) | − | 1.29803e9i | − | 0.00385948i | ||||||
\(203\) | 5.56567e11 | 1.61450 | ||||||||
\(204\) | 4.27989e10i | 0.121138i | ||||||||
\(205\) | 2.20672e11i | 0.609507i | ||||||||
\(206\) | − | 2.21699e9i | − | 0.00597622i | ||||||
\(207\) | 1.76013e11 | 0.463120 | ||||||||
\(208\) | −3.54005e11 | −0.909269 | ||||||||
\(209\) | 6.99255e11i | 1.75349i | ||||||||
\(210\) | 6.90465e9 | 0.0169062 | ||||||||
\(211\) | − | 5.38365e11i | − | 1.28725i | −0.765339 | − | 0.643627i | \(-0.777429\pi\) | ||
0.765339 | − | 0.643627i | \(-0.222571\pi\) | |||||||
\(212\) | −3.90635e11 | −0.912204 | ||||||||
\(213\) | −2.07354e10 | −0.0472949 | ||||||||
\(214\) | − | 1.12057e10i | − | 0.0249672i | ||||||
\(215\) | −4.14270e11 | + | 5.86039e11i | −0.901760 | + | 1.27566i | ||||
\(216\) | −1.08846e10 | −0.0231496 | ||||||||
\(217\) | − | 9.08793e11i | − | 1.88872i | ||||||
\(218\) | − | 1.81614e8i | − | 0.000368864i | ||||||
\(219\) | 6.21283e10 | 0.123330 | ||||||||
\(220\) | − | 8.96314e11i | − | 1.73919i | ||||||
\(221\) | −2.59218e11 | −0.491703 | ||||||||
\(222\) | − | 3.72117e9i | − | 0.00690105i | ||||||
\(223\) | − | 8.51101e10i | − | 0.154332i | −0.997018 | − | 0.0771661i | \(-0.975413\pi\) | ||
0.997018 | − | 0.0771661i | \(-0.0245872\pi\) | |||||||
\(224\) | −8.14290e10 | −0.144391 | ||||||||
\(225\) | −7.88734e11 | −1.36779 | ||||||||
\(226\) | −1.29356e10 | −0.0219405 | ||||||||
\(227\) | 5.77929e11i | 0.958837i | 0.877586 | + | 0.479419i | \(0.159152\pi\) | ||||
−0.877586 | + | 0.479419i | \(0.840848\pi\) | |||||||
\(228\) | 2.17694e11 | 0.353324 | ||||||||
\(229\) | 3.46320e11 | 0.549920 | 0.274960 | − | 0.961456i | \(-0.411335\pi\) | ||||
0.274960 | + | 0.961456i | \(0.411335\pi\) | |||||||
\(230\) | −1.29660e10 | −0.0201450 | ||||||||
\(231\) | 2.99939e11 | 0.456009 | ||||||||
\(232\) | 3.14796e10 | 0.0468371 | ||||||||
\(233\) | − | 5.72808e11i | − | 0.834121i | −0.908879 | − | 0.417061i | \(-0.863060\pi\) | ||
0.908879 | − | 0.417061i | \(-0.136940\pi\) | |||||||
\(234\) | − | 1.60488e10i | − | 0.0228752i | ||||||
\(235\) | 6.66099e11i | 0.929393i | ||||||||
\(236\) | 1.08673e12 | 1.48444 | ||||||||
\(237\) | − | 2.50197e11i | − | 0.334611i | ||||||
\(238\) | −1.98521e10 | −0.0259969 | ||||||||
\(239\) | 3.40057e11 | 0.436076 | 0.218038 | − | 0.975940i | \(-0.430034\pi\) | ||||
0.218038 | + | 0.975940i | \(0.430034\pi\) | |||||||
\(240\) | −2.78848e11 | −0.350196 | ||||||||
\(241\) | 1.25721e12i | 1.54641i | 0.634158 | + | 0.773204i | \(0.281347\pi\) | ||||
−0.634158 | + | 0.773204i | \(0.718653\pi\) | |||||||
\(242\) | 5.29205e9i | 0.00637599i | ||||||||
\(243\) | 5.33068e11i | 0.629146i | ||||||||
\(244\) | 7.38891e11i | 0.854342i | ||||||||
\(245\) | − | 3.19941e12i | − | 3.62443i | ||||||
\(246\) | −2.08762e9 | −0.00231726 | ||||||||
\(247\) | 1.31850e12i | 1.43415i | ||||||||
\(248\) | − | 5.14017e10i | − | 0.0547922i | ||||||
\(249\) | 3.38205e11i | 0.353332i | ||||||||
\(250\) | 1.77668e10 | 0.0181932 | ||||||||
\(251\) | 1.80908e12 | 1.81589 | 0.907945 | − | 0.419089i | \(-0.137650\pi\) | ||||
0.907945 | + | 0.419089i | \(0.137650\pi\) | |||||||
\(252\) | 1.75705e12i | 1.72895i | ||||||||
\(253\) | −5.63245e11 | −0.543369 | ||||||||
\(254\) | − | 9.27326e9i | − | 0.00877130i | ||||||
\(255\) | −2.04185e11 | −0.189375 | ||||||||
\(256\) | 1.09183e12 | 0.993017 | ||||||||
\(257\) | − | 8.85258e11i | − | 0.789595i | −0.918768 | − | 0.394797i | \(-0.870815\pi\) | ||
0.918768 | − | 0.394797i | \(-0.129185\pi\) | |||||||
\(258\) | −5.54408e9 | − | 3.91910e9i | −0.00484988 | − | 0.00342837i | ||||
\(259\) | −2.46748e12 | −2.11717 | ||||||||
\(260\) | − | 1.69007e12i | − | 1.42245i | ||||||
\(261\) | − | 1.01901e12i | − | 0.841347i | ||||||
\(262\) | 3.39966e10 | 0.0275378 | ||||||||
\(263\) | − | 2.32424e12i | − | 1.84715i | −0.383413 | − | 0.923577i | \(-0.625252\pi\) | ||
0.383413 | − | 0.923577i | \(-0.374748\pi\) | |||||||
\(264\) | 1.69647e10 | 0.0132290 | ||||||||
\(265\) | − | 1.86364e12i | − | 1.42604i | ||||||
\(266\) | 1.00977e11i | 0.0758251i | ||||||||
\(267\) | −4.07533e11 | −0.300335 | ||||||||
\(268\) | 1.47487e12 | 1.06679 | ||||||||
\(269\) | −8.13151e10 | −0.0577311 | −0.0288656 | − | 0.999583i | \(-0.509189\pi\) | ||||
−0.0288656 | + | 0.999583i | \(0.509189\pi\) | |||||||
\(270\) | − | 2.59550e10i | − | 0.0180885i | ||||||
\(271\) | 1.01982e12 | 0.697711 | 0.348856 | − | 0.937177i | \(-0.386570\pi\) | ||||
0.348856 | + | 0.937177i | \(0.386570\pi\) | |||||||
\(272\) | 8.01738e11 | 0.538503 | ||||||||
\(273\) | 5.65558e11 | 0.372961 | ||||||||
\(274\) | 1.34199e10 | 0.00868953 | ||||||||
\(275\) | 2.52396e12 | 1.60479 | ||||||||
\(276\) | 1.75351e11i | 0.109487i | ||||||||
\(277\) | 2.04163e12i | 1.25192i | 0.779854 | + | 0.625961i | \(0.215293\pi\) | ||||
−0.779854 | + | 0.625961i | \(0.784707\pi\) | |||||||
\(278\) | − | 2.13058e10i | − | 0.0128314i | ||||||
\(279\) | −1.66389e12 | −0.984248 | ||||||||
\(280\) | − | 2.58957e11i | − | 0.150466i | ||||||
\(281\) | 1.27867e12 | 0.729836 | 0.364918 | − | 0.931040i | \(-0.381097\pi\) | ||||
0.364918 | + | 0.931040i | \(0.381097\pi\) | |||||||
\(282\) | −6.30147e9 | −0.00353343 | ||||||||
\(283\) | 7.72221e11 | 0.425412 | 0.212706 | − | 0.977116i | \(-0.431772\pi\) | ||||
0.212706 | + | 0.977116i | \(0.431772\pi\) | |||||||
\(284\) | 3.88702e11i | 0.210390i | ||||||||
\(285\) | 1.03858e12i | 0.552349i | ||||||||
\(286\) | 5.13565e10i | 0.0268389i | ||||||||
\(287\) | 1.38428e12i | 0.710911i | ||||||||
\(288\) | 1.49087e11i | 0.0752448i | ||||||||
\(289\) | −1.42893e12 | −0.708795 | ||||||||
\(290\) | 7.50652e10i | 0.0365973i | ||||||||
\(291\) | − | 2.07028e11i | − | 0.0992118i | ||||||
\(292\) | − | 1.16464e12i | − | 0.548629i | ||||||
\(293\) | −1.94950e12 | −0.902788 | −0.451394 | − | 0.892325i | \(-0.649073\pi\) | ||||
−0.451394 | + | 0.892325i | \(0.649073\pi\) | |||||||
\(294\) | 3.02673e10 | 0.0137796 | ||||||||
\(295\) | 5.18458e12i | 2.32062i | ||||||||
\(296\) | −1.39562e11 | −0.0614196 | ||||||||
\(297\) | − | 1.12749e12i | − | 0.487900i | ||||||
\(298\) | −1.79875e10 | −0.00765400 | ||||||||
\(299\) | −1.06204e12 | −0.444412 | ||||||||
\(300\) | − | 7.85768e11i | − | 0.323361i | ||||||
\(301\) | −2.59873e12 | + | 3.67624e12i | −1.05179 | + | 1.48789i | ||||
\(302\) | 1.24753e10 | 0.00496611 | ||||||||
\(303\) | − | 8.37489e10i | − | 0.0327919i | ||||||
\(304\) | − | 4.07800e12i | − | 1.57065i | ||||||
\(305\) | −3.52510e12 | −1.33559 | ||||||||
\(306\) | 3.63468e10i | 0.0135475i | ||||||||
\(307\) | 3.18628e12 | 1.16840 | 0.584201 | − | 0.811609i | \(-0.301408\pi\) | ||||
0.584201 | + | 0.811609i | \(0.301408\pi\) | |||||||
\(308\) | − | 5.62260e12i | − | 2.02854i | ||||||
\(309\) | − | 1.43040e11i | − | 0.0507767i | ||||||
\(310\) | 1.22571e11 | 0.0428132 | ||||||||
\(311\) | 2.38175e12 | 0.818641 | 0.409321 | − | 0.912391i | \(-0.365766\pi\) | ||||
0.409321 | + | 0.912391i | \(0.365766\pi\) | |||||||
\(312\) | 3.19881e10 | 0.0108197 | ||||||||
\(313\) | 1.24263e12i | 0.413638i | 0.978379 | + | 0.206819i | \(0.0663112\pi\) | ||||
−0.978379 | + | 0.206819i | \(0.933689\pi\) | |||||||
\(314\) | 5.49166e10 | 0.0179910 | ||||||||
\(315\) | −8.38255e12 | −2.70286 | ||||||||
\(316\) | −4.69014e12 | −1.48850 | ||||||||
\(317\) | −1.03858e12 | −0.324447 | −0.162224 | − | 0.986754i | \(-0.551867\pi\) | ||||
−0.162224 | + | 0.986754i | \(0.551867\pi\) | |||||||
\(318\) | 1.76305e10 | 0.00542163 | ||||||||
\(319\) | 3.26084e12i | 0.987135i | ||||||||
\(320\) | 5.21991e12i | 1.55565i | ||||||||
\(321\) | − | 7.22991e11i | − | 0.212133i | ||||||
\(322\) | −8.13361e10 | −0.0234965 | ||||||||
\(323\) | − | 2.98609e12i | − | 0.849357i | ||||||
\(324\) | 3.03691e12 | 0.850563 | ||||||||
\(325\) | 4.75912e12 | 1.31253 | ||||||||
\(326\) | −1.42545e11 | −0.0387137 | ||||||||
\(327\) | − | 1.17177e10i | − | 0.00313403i | ||||||
\(328\) | 7.82955e10i | 0.0206238i | ||||||||
\(329\) | 4.17846e12i | 1.08402i | ||||||||
\(330\) | 4.04533e10i | 0.0103368i | ||||||||
\(331\) | − | 3.52483e12i | − | 0.887153i | −0.896236 | − | 0.443577i | \(-0.853709\pi\) | ||
0.896236 | − | 0.443577i | \(-0.146291\pi\) | |||||||
\(332\) | 6.33992e12 | 1.57179 | ||||||||
\(333\) | 4.51766e12i | 1.10330i | ||||||||
\(334\) | 7.33042e10i | 0.0176358i | ||||||||
\(335\) | 7.03628e12i | 1.66771i | ||||||||
\(336\) | −1.74922e12 | −0.408459 | ||||||||
\(337\) | −6.83158e12 | −1.57171 | −0.785854 | − | 0.618412i | \(-0.787776\pi\) | ||||
−0.785854 | + | 0.618412i | \(0.787776\pi\) | |||||||
\(338\) | − | 1.97992e10i | − | 0.00448811i | ||||||
\(339\) | −8.34606e11 | −0.186416 | ||||||||
\(340\) | 3.82761e12i | 0.842428i | ||||||||
\(341\) | 5.32448e12 | 1.15480 | ||||||||
\(342\) | 1.84876e11 | 0.0395140 | ||||||||
\(343\) | − | 1.14194e13i | − | 2.40533i | ||||||
\(344\) | −1.46985e11 | + | 2.07929e11i | −0.0305127 | + | 0.0431642i | ||||
\(345\) | −8.36566e11 | −0.171161 | ||||||||
\(346\) | 1.16489e11i | 0.0234911i | ||||||||
\(347\) | − | 8.64593e12i | − | 1.71856i | −0.511507 | − | 0.859279i | \(-0.670913\pi\) | ||
0.511507 | − | 0.859279i | \(-0.329087\pi\) | |||||||
\(348\) | 1.01518e12 | 0.198905 | ||||||||
\(349\) | 5.68975e12i | 1.09892i | 0.835520 | + | 0.549460i | \(0.185166\pi\) | ||||
−0.835520 | + | 0.549460i | \(0.814834\pi\) | |||||||
\(350\) | 3.64476e11 | 0.0693951 | ||||||||
\(351\) | − | 2.12597e12i | − | 0.399044i | ||||||
\(352\) | − | 4.77080e11i | − | 0.0882832i | ||||||
\(353\) | −1.01878e12 | −0.185868 | −0.0929342 | − | 0.995672i | \(-0.529625\pi\) | ||||
−0.0929342 | + | 0.995672i | \(0.529625\pi\) | |||||||
\(354\) | −4.90475e10 | −0.00882268 | ||||||||
\(355\) | −1.85442e12 | −0.328901 | ||||||||
\(356\) | 7.63953e12i | 1.33603i | ||||||||
\(357\) | −1.28086e12 | −0.220881 | ||||||||
\(358\) | 2.30905e11 | 0.0392662 | ||||||||
\(359\) | 2.44894e12 | 0.410682 | 0.205341 | − | 0.978691i | \(-0.434170\pi\) | ||||
0.205341 | + | 0.978691i | \(0.434170\pi\) | |||||||
\(360\) | −4.74120e11 | −0.0784108 | ||||||||
\(361\) | −9.05753e12 | −1.47732 | ||||||||
\(362\) | 2.37770e11i | 0.0382484i | ||||||||
\(363\) | 3.41443e11i | 0.0541733i | ||||||||
\(364\) | − | 1.06018e13i | − | 1.65911i | ||||||
\(365\) | 5.55628e12 | 0.857670 | ||||||||
\(366\) | − | 3.33484e10i | − | 0.00507773i | ||||||
\(367\) | −5.29017e12 | −0.794584 | −0.397292 | − | 0.917692i | \(-0.630050\pi\) | ||||
−0.397292 | + | 0.917692i | \(0.630050\pi\) | |||||||
\(368\) | 3.28480e12 | 0.486710 | ||||||||
\(369\) | 2.53446e12 | 0.370470 | ||||||||
\(370\) | − | 3.32794e11i | − | 0.0479917i | ||||||
\(371\) | − | 1.16907e13i | − | 1.66330i | ||||||
\(372\) | − | 1.65764e12i | − | 0.232688i | ||||||
\(373\) | 4.24662e12i | 0.588165i | 0.955780 | + | 0.294083i | \(0.0950141\pi\) | ||||
−0.955780 | + | 0.294083i | \(0.904986\pi\) | |||||||
\(374\) | − | 1.16310e11i | − | 0.0158950i | ||||||
\(375\) | 1.14631e12 | 0.154577 | ||||||||
\(376\) | 2.36335e11i | 0.0314477i | ||||||||
\(377\) | 6.14857e12i | 0.807360i | ||||||||
\(378\) | − | 1.62817e11i | − | 0.0210979i | ||||||
\(379\) | −1.42309e13 | −1.81986 | −0.909929 | − | 0.414764i | \(-0.863864\pi\) | ||||
−0.909929 | + | 0.414764i | \(0.863864\pi\) | |||||||
\(380\) | 1.94689e13 | 2.45711 | ||||||||
\(381\) | − | 5.98310e11i | − | 0.0745249i | ||||||
\(382\) | −4.01204e11 | −0.0493229 | ||||||||
\(383\) | 4.75530e12i | 0.577011i | 0.957478 | + | 0.288505i | \(0.0931583\pi\) | ||||
−0.957478 | + | 0.288505i | \(0.906842\pi\) | |||||||
\(384\) | −1.98012e11 | −0.0237156 | ||||||||
\(385\) | 2.68243e13 | 3.17121 | ||||||||
\(386\) | − | 2.82201e11i | − | 0.0329323i | ||||||
\(387\) | 6.73076e12 | + | 4.75796e12i | 0.775370 | + | 0.548108i | ||||
\(388\) | −3.88090e12 | −0.441341 | ||||||||
\(389\) | − | 1.25209e13i | − | 1.40568i | −0.711349 | − | 0.702839i | \(-0.751915\pi\) | ||
0.711349 | − | 0.702839i | \(-0.248085\pi\) | |||||||
\(390\) | 7.62778e10i | 0.00845425i | ||||||||
\(391\) | 2.40527e12 | 0.263197 | ||||||||
\(392\) | − | 1.13517e12i | − | 0.122639i | ||||||
\(393\) | 2.19346e12 | 0.233973 | ||||||||
\(394\) | 3.88369e11i | 0.0409038i | ||||||||
\(395\) | − | 2.23757e13i | − | 2.32697i | ||||||
\(396\) | −1.02943e13 | −1.05711 | ||||||||
\(397\) | 1.80073e13 | 1.82598 | 0.912992 | − | 0.407978i | \(-0.133766\pi\) | ||||
0.912992 | + | 0.407978i | \(0.133766\pi\) | |||||||
\(398\) | −2.61596e11 | −0.0261948 | ||||||||
\(399\) | 6.51501e12i | 0.644245i | ||||||||
\(400\) | −1.47196e13 | −1.43746 | ||||||||
\(401\) | −4.77325e12 | −0.460355 | −0.230177 | − | 0.973149i | \(-0.573931\pi\) | ||||
−0.230177 | + | 0.973149i | \(0.573931\pi\) | |||||||
\(402\) | −6.65651e10 | −0.00634039 | ||||||||
\(403\) | 1.00397e13 | 0.944488 | ||||||||
\(404\) | −1.56994e12 | −0.145874 | ||||||||
\(405\) | 1.44885e13i | 1.32968i | ||||||||
\(406\) | 4.70886e11i | 0.0426860i | ||||||||
\(407\) | − | 1.44566e13i | − | 1.29448i | ||||||
\(408\) | −7.24457e10 | −0.00640784 | ||||||||
\(409\) | − | 9.20218e12i | − | 0.804034i | −0.915632 | − | 0.402017i | \(-0.868309\pi\) | ||
0.915632 | − | 0.402017i | \(-0.131691\pi\) | |||||||
\(410\) | −1.86701e11 | −0.0161149 | ||||||||
\(411\) | 8.65850e11 | 0.0738301 | ||||||||
\(412\) | −2.68140e12 | −0.225878 | ||||||||
\(413\) | 3.25230e13i | 2.70670i | ||||||||
\(414\) | 1.48917e11i | 0.0122445i | ||||||||
\(415\) | 3.02465e13i | 2.45717i | ||||||||
\(416\) | − | 8.99570e11i | − | 0.0722052i | ||||||
\(417\) | − | 1.37465e12i | − | 0.109021i | ||||||
\(418\) | −5.91608e11 | −0.0463610 | ||||||||
\(419\) | − | 1.75815e13i | − | 1.36140i | −0.732562 | − | 0.680700i | \(-0.761676\pi\) | ||
0.732562 | − | 0.680700i | \(-0.238324\pi\) | |||||||
\(420\) | − | 8.35103e12i | − | 0.638989i | ||||||
\(421\) | − | 1.52384e13i | − | 1.15220i | −0.817379 | − | 0.576100i | \(-0.804574\pi\) | ||
0.817379 | − | 0.576100i | \(-0.195426\pi\) | |||||||
\(422\) | 4.55486e11 | 0.0340340 | ||||||||
\(423\) | 7.65026e12 | 0.564904 | ||||||||
\(424\) | − | 6.61228e11i | − | 0.0482528i | ||||||
\(425\) | −1.07783e13 | −0.777330 | ||||||||
\(426\) | − | 1.75433e10i | − | 0.00125044i | ||||||
\(427\) | −2.21131e13 | −1.55779 | ||||||||
\(428\) | −1.35531e13 | −0.943666 | ||||||||
\(429\) | 3.31352e12i | 0.228036i | ||||||||
\(430\) | −4.95821e11 | − | 3.50495e11i | −0.0337274 | − | 0.0238418i | ||||
\(431\) | 8.76785e12 | 0.589531 | 0.294766 | − | 0.955570i | \(-0.404758\pi\) | ||||
0.294766 | + | 0.955570i | \(0.404758\pi\) | |||||||
\(432\) | 6.57543e12i | 0.437024i | ||||||||
\(433\) | 9.25042e12i | 0.607746i | 0.952713 | + | 0.303873i | \(0.0982798\pi\) | ||||
−0.952713 | + | 0.303873i | \(0.901720\pi\) | |||||||
\(434\) | 7.68889e11 | 0.0499361 | ||||||||
\(435\) | 4.84320e12i | 0.310947i | ||||||||
\(436\) | −2.19658e11 | −0.0139416 | ||||||||
\(437\) | − | 1.22343e13i | − | 0.767666i | ||||||
\(438\) | 5.25639e10i | 0.00326075i | ||||||||
\(439\) | 2.41481e13 | 1.48102 | 0.740510 | − | 0.672045i | \(-0.234584\pi\) | ||||
0.740510 | + | 0.672045i | \(0.234584\pi\) | |||||||
\(440\) | 1.51719e12 | 0.0919977 | ||||||||
\(441\) | −3.67458e13 | −2.20300 | ||||||||
\(442\) | − | 2.19312e11i | − | 0.0130002i | ||||||
\(443\) | −8.01561e12 | −0.469805 | −0.234903 | − | 0.972019i | \(-0.575477\pi\) | ||||
−0.234903 | + | 0.972019i | \(0.575477\pi\) | |||||||
\(444\) | −4.50068e12 | −0.260833 | ||||||||
\(445\) | −3.64467e13 | −2.08861 | ||||||||
\(446\) | 7.20077e10 | 0.00408042 | ||||||||
\(447\) | −1.16055e12 | −0.0650319 | ||||||||
\(448\) | 3.27446e13i | 1.81447i | ||||||||
\(449\) | − | 2.13102e13i | − | 1.16777i | −0.811838 | − | 0.583883i | \(-0.801533\pi\) | ||
0.811838 | − | 0.583883i | \(-0.198467\pi\) | |||||||
\(450\) | − | 6.67312e11i | − | 0.0361632i | ||||||
\(451\) | −8.11031e12 | −0.434665 | ||||||||
\(452\) | 1.56454e13i | 0.829266i | ||||||||
\(453\) | 8.04905e11 | 0.0421943 | ||||||||
\(454\) | −4.88959e11 | −0.0253509 | ||||||||
\(455\) | 5.05792e13 | 2.59367 | ||||||||
\(456\) | 3.68491e11i | 0.0186897i | ||||||||
\(457\) | − | 1.95013e13i | − | 0.978323i | −0.872193 | − | 0.489161i | \(-0.837303\pi\) | ||
0.872193 | − | 0.489161i | \(-0.162697\pi\) | |||||||
\(458\) | 2.93005e11i | 0.0145395i | ||||||||
\(459\) | 4.81482e12i | 0.236329i | ||||||||
\(460\) | 1.56821e13i | 0.761404i | ||||||||
\(461\) | 1.21083e13 | 0.581541 | 0.290770 | − | 0.956793i | \(-0.406088\pi\) | ||||
0.290770 | + | 0.956793i | \(0.406088\pi\) | |||||||
\(462\) | 2.53765e11i | 0.0120565i | ||||||||
\(463\) | − | 2.45524e13i | − | 1.15395i | −0.816761 | − | 0.576977i | \(-0.804232\pi\) | ||
0.816761 | − | 0.576977i | \(-0.195768\pi\) | |||||||
\(464\) | − | 1.90170e13i | − | 0.884202i | ||||||
\(465\) | 7.90825e12 | 0.363760 | ||||||||
\(466\) | 4.84626e11 | 0.0220535 | ||||||||
\(467\) | 1.20191e13i | 0.541113i | 0.962704 | + | 0.270556i | \(0.0872076\pi\) | ||||
−0.962704 | + | 0.270556i | \(0.912792\pi\) | |||||||
\(468\) | −1.94107e13 | −0.864594 | ||||||||
\(469\) | 4.41388e13i | 1.94516i | ||||||||
\(470\) | −5.63556e11 | −0.0245724 | ||||||||
\(471\) | 3.54321e12 | 0.152860 | ||||||||
\(472\) | 1.83951e12i | 0.0785223i | ||||||||
\(473\) | −2.15385e13 | − | 1.52255e13i | −0.909726 | − | 0.643083i | ||||
\(474\) | 2.11680e11 | 0.00884683 | ||||||||
\(475\) | 5.48233e13i | 2.26724i | ||||||||
\(476\) | 2.40107e13i | 0.982584i | ||||||||
\(477\) | −2.14042e13 | −0.866778 | ||||||||
\(478\) | 2.87707e11i | 0.0115295i | ||||||||
\(479\) | 4.15981e13 | 1.64967 | 0.824833 | − | 0.565377i | \(-0.191269\pi\) | ||||
0.824833 | + | 0.565377i | \(0.191269\pi\) | |||||||
\(480\) | − | 7.08588e11i | − | 0.0278091i | ||||||
\(481\) | − | 2.72590e13i | − | 1.05873i | ||||||
\(482\) | −1.06367e12 | −0.0408858 | ||||||||
\(483\) | −5.24780e12 | −0.199637 | ||||||||
\(484\) | 6.40062e12 | 0.240988 | ||||||||
\(485\) | − | 1.85150e13i | − | 0.689946i | ||||||
\(486\) | −4.51005e11 | −0.0166341 | ||||||||
\(487\) | −8.49956e12 | −0.310278 | −0.155139 | − | 0.987893i | \(-0.549583\pi\) | ||||
−0.155139 | + | 0.987893i | \(0.549583\pi\) | |||||||
\(488\) | −1.25072e12 | −0.0451920 | ||||||||
\(489\) | −9.19702e12 | −0.328929 | ||||||||
\(490\) | 2.70688e12 | 0.0958271 | ||||||||
\(491\) | 5.57689e12i | 0.195427i | 0.995215 | + | 0.0977135i | \(0.0311529\pi\) | ||||
−0.995215 | + | 0.0977135i | \(0.968847\pi\) | |||||||
\(492\) | 2.52493e12i | 0.0875837i | ||||||||
\(493\) | − | 1.39251e13i | − | 0.478148i | ||||||
\(494\) | −1.11552e12 | −0.0379178 | ||||||||
\(495\) | − | 4.91121e13i | − | 1.65258i | ||||||
\(496\) | −3.10520e13 | −1.03438 | ||||||||
\(497\) | −1.16328e13 | −0.383621 | ||||||||
\(498\) | −2.86139e11 | −0.00934181 | ||||||||
\(499\) | − | 2.12718e13i | − | 0.687545i | −0.939053 | − | 0.343772i | \(-0.888295\pi\) | ||
0.939053 | − | 0.343772i | \(-0.111705\pi\) | |||||||
\(500\) | − | 2.14885e13i | − | 0.687632i | ||||||
\(501\) | 4.72958e12i | 0.149842i | ||||||||
\(502\) | 1.53058e12i | 0.0480107i | ||||||||
\(503\) | 1.61237e13i | 0.500753i | 0.968148 | + | 0.250377i | \(0.0805545\pi\) | ||||
−0.968148 | + | 0.250377i | \(0.919446\pi\) | |||||||
\(504\) | −2.97417e12 | −0.0914561 | ||||||||
\(505\) | − | 7.48987e12i | − | 0.228043i | ||||||
\(506\) | − | 4.76536e11i | − | 0.0143662i | ||||||
\(507\) | − | 1.27744e12i | − | 0.0381330i | ||||||
\(508\) | −1.12158e13 | −0.331522 | ||||||||
\(509\) | 4.96346e13 | 1.45277 | 0.726383 | − | 0.687290i | \(-0.241200\pi\) | ||||
0.726383 | + | 0.687290i | \(0.241200\pi\) | |||||||
\(510\) | − | 1.72751e11i | − | 0.00500692i | ||||||
\(511\) | 3.48547e13 | 1.00036 | ||||||||
\(512\) | 4.63824e12i | 0.131827i | ||||||||
\(513\) | 2.44903e13 | 0.689300 | ||||||||
\(514\) | 7.48976e11 | 0.0208763 | ||||||||
\(515\) | − | 1.27924e13i | − | 0.353115i | ||||||
\(516\) | −4.74007e12 | + | 6.70545e12i | −0.129579 | + | 0.183307i | ||||
\(517\) | −2.44810e13 | −0.662789 | ||||||||
\(518\) | − | 2.08762e12i | − | 0.0559762i | ||||||
\(519\) | 7.51585e12i | 0.199591i | ||||||||
\(520\) | 2.86078e12 | 0.0752433 | ||||||||
\(521\) | 5.19063e13i | 1.35217i | 0.736823 | + | 0.676086i | \(0.236325\pi\) | ||||
−0.736823 | + | 0.676086i | \(0.763675\pi\) | |||||||
\(522\) | 8.62136e11 | 0.0222445 | ||||||||
\(523\) | 2.70715e13i | 0.691836i | 0.938265 | + | 0.345918i | \(0.112432\pi\) | ||||
−0.938265 | + | 0.345918i | \(0.887568\pi\) | |||||||
\(524\) | − | 4.11181e13i | − | 1.04082i | ||||||
\(525\) | 2.35160e13 | 0.589612 | ||||||||
\(526\) | 1.96644e12 | 0.0488373 | ||||||||
\(527\) | −2.27376e13 | −0.559360 | ||||||||
\(528\) | − | 1.02484e13i | − | 0.249740i | ||||||
\(529\) | −3.15719e13 | −0.762117 | ||||||||
\(530\) | 1.57674e12 | 0.0377035 | ||||||||
\(531\) | 5.95458e13 | 1.41052 | ||||||||
\(532\) | 1.22129e14 | 2.86590 | ||||||||
\(533\) | −1.52926e13 | −0.355505 | ||||||||
\(534\) | − | 3.44795e11i | − | 0.00794062i | ||||||
\(535\) | − | 6.46589e13i | − | 1.47523i | ||||||
\(536\) | 2.49650e12i | 0.0564298i | ||||||||
\(537\) | 1.48980e13 | 0.333623 | ||||||||
\(538\) | − | 6.87970e10i | − | 0.00152636i | ||||||
\(539\) | 1.17587e14 | 2.58473 | ||||||||
\(540\) | −3.13920e13 | −0.683677 | ||||||||
\(541\) | −4.82709e11 | −0.0104160 | −0.00520798 | − | 0.999986i | \(-0.501658\pi\) | ||||
−0.00520798 | + | 0.999986i | \(0.501658\pi\) | |||||||
\(542\) | 8.62820e11i | 0.0184469i | ||||||||
\(543\) | 1.53409e13i | 0.324976i | ||||||||
\(544\) | 2.03732e12i | 0.0427626i | ||||||||
\(545\) | − | 1.04794e12i | − | 0.0217949i | ||||||
\(546\) | 4.78493e11i | 0.00986080i | ||||||||
\(547\) | 5.07801e13 | 1.03695 | 0.518474 | − | 0.855093i | \(-0.326500\pi\) | ||||
0.518474 | + | 0.855093i | \(0.326500\pi\) | |||||||
\(548\) | − | 1.62311e13i | − | 0.328431i | ||||||
\(549\) | 4.04864e13i | 0.811797i | ||||||||
\(550\) | 2.13541e12i | 0.0424295i | ||||||||
\(551\) | −7.08292e13 | −1.39461 | ||||||||
\(552\) | −2.96817e11 | −0.00579153 | ||||||||
\(553\) | − | 1.40363e14i | − | 2.71411i | ||||||
\(554\) | −1.72733e12 | −0.0330998 | ||||||||
\(555\) | − | 2.14718e13i | − | 0.407759i | ||||||
\(556\) | −2.57689e13 | −0.484978 | ||||||||
\(557\) | 1.93646e13 | 0.361188 | 0.180594 | − | 0.983558i | \(-0.442198\pi\) | ||||
0.180594 | + | 0.983558i | \(0.442198\pi\) | |||||||
\(558\) | − | 1.40774e12i | − | 0.0260227i | ||||||
\(559\) | −4.06125e13 | − | 2.87089e13i | −0.744048 | − | 0.525966i | ||||
\(560\) | −1.56437e14 | −2.84053 | ||||||||
\(561\) | − | 7.50434e12i | − | 0.135051i | ||||||
\(562\) | 1.08182e12i | 0.0192963i | ||||||||
\(563\) | 1.67892e13 | 0.296817 | 0.148409 | − | 0.988926i | \(-0.452585\pi\) | ||||
0.148409 | + | 0.988926i | \(0.452585\pi\) | |||||||
\(564\) | 7.62149e12i | 0.133550i | ||||||||
\(565\) | −7.46409e13 | −1.29639 | ||||||||
\(566\) | 6.53341e11i | 0.0112475i | ||||||||
\(567\) | 9.08866e13i | 1.55090i | ||||||||
\(568\) | −6.57955e11 | −0.0111290 | ||||||||
\(569\) | −7.06796e13 | −1.18504 | −0.592520 | − | 0.805556i | \(-0.701867\pi\) | ||||
−0.592520 | + | 0.805556i | \(0.701867\pi\) | |||||||
\(570\) | −8.78692e11 | −0.0146037 | ||||||||
\(571\) | 3.18030e13i | 0.523947i | 0.965075 | + | 0.261974i | \(0.0843733\pi\) | ||||
−0.965075 | + | 0.261974i | \(0.915627\pi\) | |||||||
\(572\) | 6.21146e13 | 1.01441 | ||||||||
\(573\) | −2.58857e13 | −0.419070 | ||||||||
\(574\) | −1.17118e12 | −0.0187959 | ||||||||
\(575\) | −4.41598e13 | −0.702567 | ||||||||
\(576\) | 5.99515e13 | 0.945557 | ||||||||
\(577\) | − | 2.25287e13i | − | 0.352255i | −0.984367 | − | 0.176128i | \(-0.943643\pi\) | ||
0.984367 | − | 0.176128i | \(-0.0563571\pi\) | |||||||
\(578\) | − | 1.20895e12i | − | 0.0187400i | ||||||
\(579\) | − | 1.82076e13i | − | 0.279808i | ||||||
\(580\) | 9.07898e13 | 1.38324 | ||||||||
\(581\) | 1.89737e14i | 2.86597i | ||||||||
\(582\) | 1.75157e11 | 0.00262308 | ||||||||
\(583\) | 6.84939e13 | 1.01697 | ||||||||
\(584\) | 1.97139e12 | 0.0290208 | ||||||||
\(585\) | − | 9.26046e13i | − | 1.35162i | ||||||
\(586\) | − | 1.64939e12i | − | 0.0238690i | ||||||
\(587\) | − | 9.42670e13i | − | 1.35260i | −0.736627 | − | 0.676300i | \(-0.763582\pi\) | ||
0.736627 | − | 0.676300i | \(-0.236418\pi\) | |||||||
\(588\) | − | 3.66076e13i | − | 0.520816i | ||||||
\(589\) | 1.15654e14i | 1.63149i | ||||||||
\(590\) | −4.38644e12 | −0.0613553 | ||||||||
\(591\) | 2.50576e13i | 0.347537i | ||||||||
\(592\) | 8.43098e13i | 1.15950i | ||||||||
\(593\) | 1.31494e14i | 1.79321i | 0.442832 | + | 0.896605i | \(0.353974\pi\) | ||||
−0.442832 | + | 0.896605i | \(0.646026\pi\) | |||||||
\(594\) | 9.53918e11 | 0.0128997 | ||||||||
\(595\) | −1.14550e14 | −1.53607 | ||||||||
\(596\) | 2.17554e13i | 0.289292i | ||||||||
\(597\) | −1.68781e13 | −0.222563 | ||||||||
\(598\) | − | 8.98544e11i | − | 0.0117499i | ||||||
\(599\) | 1.15805e12 | 0.0150174 | 0.00750868 | − | 0.999972i | \(-0.497610\pi\) | ||||
0.00750868 | + | 0.999972i | \(0.497610\pi\) | |||||||
\(600\) | 1.33007e12 | 0.0171048 | ||||||||
\(601\) | 3.04760e13i | 0.388674i | 0.980935 | + | 0.194337i | \(0.0622555\pi\) | ||||
−0.980935 | + | 0.194337i | \(0.937745\pi\) | |||||||
\(602\) | −3.11030e12 | − | 2.19866e12i | −0.0393387 | − | 0.0278084i | ||||
\(603\) | 8.08129e13 | 1.01366 | ||||||||
\(604\) | − | 1.50886e13i | − | 0.187700i | ||||||
\(605\) | 3.05361e13i | 0.376735i | ||||||||
\(606\) | 7.08561e10 | 0.000866991 | ||||||||
\(607\) | − | 1.14536e14i | − | 1.38995i | −0.719035 | − | 0.694974i | \(-0.755416\pi\) | ||
0.719035 | − | 0.694974i | \(-0.244584\pi\) | |||||||
\(608\) | 1.03627e13 | 0.124726 | ||||||||
\(609\) | 3.03815e13i | 0.362680i | ||||||||
\(610\) | − | 2.98243e12i | − | 0.0353119i | ||||||
\(611\) | −4.61607e13 | −0.542083 | ||||||||
\(612\) | 4.39607e13 | 0.512044 | ||||||||
\(613\) | −3.22409e13 | −0.372481 | −0.186241 | − | 0.982504i | \(-0.559630\pi\) | ||||
−0.186241 | + | 0.982504i | \(0.559630\pi\) | |||||||
\(614\) | 2.69577e12i | 0.0308916i | ||||||||
\(615\) | −1.20459e13 | −0.136919 | ||||||||
\(616\) | 9.51738e12 | 0.107304 | ||||||||
\(617\) | −1.54437e14 | −1.72713 | −0.863567 | − | 0.504235i | \(-0.831775\pi\) | ||||
−0.863567 | + | 0.504235i | \(0.831775\pi\) | |||||||
\(618\) | 1.21019e11 | 0.00134249 | ||||||||
\(619\) | 1.73772e13 | 0.191217 | 0.0956086 | − | 0.995419i | \(-0.469520\pi\) | ||||
0.0956086 | + | 0.995419i | \(0.469520\pi\) | |||||||
\(620\) | − | 1.48246e14i | − | 1.61818i | ||||||
\(621\) | 1.97268e13i | 0.213599i | ||||||||
\(622\) | 2.01509e12i | 0.0216442i | ||||||||
\(623\) | −2.28631e14 | −2.43610 | ||||||||
\(624\) | − | 1.93242e13i | − | 0.204258i | ||||||
\(625\) | −3.48572e13 | −0.365504 | ||||||||
\(626\) | −1.05133e12 | −0.0109363 | ||||||||
\(627\) | −3.81705e13 | −0.393904 | ||||||||
\(628\) | − | 6.64204e13i | − | 0.679991i | ||||||
\(629\) | 6.17353e13i | 0.627018i | ||||||||
\(630\) | − | 7.09209e12i | − | 0.0714614i | ||||||
\(631\) | 6.14662e12i | 0.0614454i | 0.999528 | + | 0.0307227i | \(0.00978088\pi\) | ||||
−0.999528 | + | 0.0307227i | \(0.990219\pi\) | |||||||
\(632\) | − | 7.93900e12i | − | 0.0787373i | ||||||
\(633\) | 2.93879e13 | 0.289168 | ||||||||
\(634\) | − | 8.78696e11i | − | 0.00857813i | ||||||
\(635\) | − | 5.35084e13i | − | 0.518266i | ||||||
\(636\) | − | 2.13237e13i | − | 0.204917i | ||||||
\(637\) | 2.21719e14 | 2.11401 | ||||||||
\(638\) | −2.75885e12 | −0.0260991 | ||||||||
\(639\) | 2.12983e13i | 0.199913i | ||||||||
\(640\) | −1.77087e13 | −0.164925 | ||||||||
\(641\) | − | 9.01040e13i | − | 0.832633i | −0.909220 | − | 0.416317i | \(-0.863321\pi\) | ||
0.909220 | − | 0.416317i | \(-0.136679\pi\) | |||||||
\(642\) | 6.11690e11 | 0.00560862 | ||||||||
\(643\) | 5.02415e13 | 0.457096 | 0.228548 | − | 0.973533i | \(-0.426602\pi\) | ||||
0.228548 | + | 0.973533i | \(0.426602\pi\) | |||||||
\(644\) | 9.83742e13i | 0.888080i | ||||||||
\(645\) | −3.19903e13 | − | 2.26139e13i | −0.286563 | − | 0.202571i | ||||
\(646\) | 2.52639e12 | 0.0224563 | ||||||||
\(647\) | − | 1.07660e14i | − | 0.949583i | −0.880098 | − | 0.474791i | \(-0.842524\pi\) | ||
0.880098 | − | 0.474791i | \(-0.157476\pi\) | |||||||
\(648\) | 5.14057e12i | 0.0449921i | ||||||||
\(649\) | −1.90548e14 | −1.65493 | ||||||||
\(650\) | 4.02648e12i | 0.0347023i | ||||||||
\(651\) | 4.96086e13 | 0.424280 | ||||||||
\(652\) | 1.72406e14i | 1.46323i | ||||||||
\(653\) | 2.03675e14i | 1.71542i | 0.514132 | + | 0.857711i | \(0.328114\pi\) | ||||
−0.514132 | + | 0.857711i | \(0.671886\pi\) | |||||||
\(654\) | 9.91381e9 | 8.28613e−5 | ||||||||
\(655\) | 1.96166e14 | 1.62711 | ||||||||
\(656\) | 4.72987e13 | 0.389341 | ||||||||
\(657\) | − | 6.38148e13i | − | 0.521309i | ||||||
\(658\) | −3.53520e12 | −0.0286606 | ||||||||
\(659\) | 9.42998e13 | 0.758723 | 0.379362 | − | 0.925248i | \(-0.376144\pi\) | ||||
0.379362 | + | 0.925248i | \(0.376144\pi\) | |||||||
\(660\) | 4.89274e13 | 0.390690 | ||||||||
\(661\) | −2.15781e14 | −1.71004 | −0.855018 | − | 0.518598i | \(-0.826454\pi\) | ||||
−0.855018 | + | 0.518598i | \(0.826454\pi\) | |||||||
\(662\) | 2.98220e12 | 0.0234556 | ||||||||
\(663\) | − | 1.41500e13i | − | 0.110456i | ||||||
\(664\) | 1.07316e13i | 0.0831426i | ||||||||
\(665\) | 5.82654e14i | 4.48025i | ||||||||
\(666\) | −3.82219e12 | −0.0291703 | ||||||||
\(667\) | − | 5.70524e13i | − | 0.432160i | ||||||
\(668\) | 8.86598e13 | 0.666568 | ||||||||
\(669\) | 4.64593e12 | 0.0346691 | ||||||||
\(670\) | −5.95308e12 | −0.0440928 | ||||||||
\(671\) | − | 1.29557e14i | − | 0.952464i | ||||||
\(672\) | − | 4.44499e12i | − | 0.0324358i | ||||||
\(673\) | − | 1.04309e14i | − | 0.755519i | −0.925904 | − | 0.377759i | \(-0.876695\pi\) | ||
0.925904 | − | 0.377759i | \(-0.123305\pi\) | |||||||
\(674\) | − | 5.77989e12i | − | 0.0415547i | ||||||
\(675\) | − | 8.83980e13i | − | 0.630846i | ||||||
\(676\) | −2.39467e13 | −0.169634 | ||||||||
\(677\) | − | 1.52663e14i | − | 1.07347i | −0.843750 | − | 0.536737i | \(-0.819657\pi\) | ||
0.843750 | − | 0.536737i | \(-0.180343\pi\) | |||||||
\(678\) | − | 7.06122e11i | − | 0.00492869i | ||||||
\(679\) | − | 1.16145e14i | − | 0.804733i | ||||||
\(680\) | −6.47900e12 | −0.0445618 | ||||||||
\(681\) | −3.15476e13 | −0.215393 | ||||||||
\(682\) | 4.50480e12i | 0.0305319i | ||||||||
\(683\) | 7.96363e13 | 0.535806 | 0.267903 | − | 0.963446i | \(-0.413669\pi\) | ||||
0.267903 | + | 0.963446i | \(0.413669\pi\) | |||||||
\(684\) | − | 2.23604e14i | − | 1.49348i | ||||||
\(685\) | 7.74351e13 | 0.513435 | ||||||||
\(686\) | 9.66146e12 | 0.0635949 | ||||||||
\(687\) | 1.89047e13i | 0.123534i | ||||||||
\(688\) | 1.25611e14 | + | 8.87942e13i | 0.814865 | + | 0.576026i | ||||
\(689\) | 1.29150e14 | 0.831763 | ||||||||
\(690\) | − | 7.07780e11i | − | 0.00452536i | ||||||
\(691\) | 1.80567e14i | 1.14617i | 0.819496 | + | 0.573085i | \(0.194253\pi\) | ||||
−0.819496 | + | 0.573085i | \(0.805747\pi\) | |||||||
\(692\) | 1.40891e14 | 0.887875 | ||||||||
\(693\) | − | 3.08081e14i | − | 1.92752i | ||||||
\(694\) | 7.31492e12 | 0.0454373 | ||||||||
\(695\) | − | 1.22938e14i | − | 0.758164i | ||||||
\(696\) | 1.71839e12i | 0.0105214i | ||||||||
\(697\) | 3.46341e13 | 0.210543 | ||||||||
\(698\) | −4.81384e12 | −0.0290546 | ||||||||
\(699\) | 3.12681e13 | 0.187376 | ||||||||
\(700\) | − | 4.40826e14i | − | 2.62287i | ||||||
\(701\) | −6.31483e13 | −0.373054 | −0.186527 | − | 0.982450i | \(-0.559723\pi\) | ||||
−0.186527 | + | 0.982450i | \(0.559723\pi\) | |||||||
\(702\) | 1.79868e12 | 0.0105504 | ||||||||
\(703\) | 3.14014e14 | 1.82882 | ||||||||
\(704\) | −1.91846e14 | −1.10940 | ||||||||
\(705\) | −3.63606e13 | −0.208778 | ||||||||
\(706\) | − | 8.61941e11i | − | 0.00491421i | ||||||
\(707\) | − | 4.69842e13i | − | 0.265983i | ||||||
\(708\) | 5.93219e13i | 0.333464i | ||||||||
\(709\) | 1.41239e14 | 0.788358 | 0.394179 | − | 0.919034i | \(-0.371029\pi\) | ||||
0.394179 | + | 0.919034i | \(0.371029\pi\) | |||||||
\(710\) | − | 1.56894e12i | − | 0.00869589i | ||||||
\(711\) | −2.56989e14 | −1.41438 | ||||||||
\(712\) | −1.29314e13 | −0.0706719 | ||||||||
\(713\) | −9.31583e13 | −0.505561 | ||||||||
\(714\) | − | 1.08367e12i | − | 0.00583993i | ||||||
\(715\) | 2.96336e14i | 1.58582i | ||||||||
\(716\) | − | 2.79275e14i | − | 1.48411i | ||||||
\(717\) | 1.85628e13i | 0.0979599i | ||||||||
\(718\) | 2.07193e12i | 0.0108581i | ||||||||
\(719\) | −8.58193e13 | −0.446623 | −0.223311 | − | 0.974747i | \(-0.571687\pi\) | ||||
−0.223311 | + | 0.974747i | \(0.571687\pi\) | |||||||
\(720\) | 2.86418e14i | 1.48026i | ||||||||
\(721\) | − | 8.02470e13i | − | 0.411863i | ||||||
\(722\) | − | 7.66316e12i | − | 0.0390591i | ||||||
\(723\) | −6.86280e13 | −0.347384 | ||||||||
\(724\) | 2.87577e14 | 1.44564 | ||||||||
\(725\) | 2.55658e14i | 1.27635i | ||||||||
\(726\) | −2.88879e11 | −0.00143230 | ||||||||
\(727\) | − | 1.46830e14i | − | 0.723005i | −0.932371 | − | 0.361503i | \(-0.882264\pi\) | ||
0.932371 | − | 0.361503i | \(-0.117736\pi\) | |||||||
\(728\) | 1.79457e13 | 0.0877616 | ||||||||
\(729\) | 1.46147e14 | 0.709827 | ||||||||
\(730\) | 4.70092e12i | 0.0226761i | ||||||||
\(731\) | 9.19779e13 | + | 6.50190e13i | 0.440653 | + | 0.311496i | ||||
\(732\) | −4.03341e13 | −0.191919 | ||||||||
\(733\) | 6.49570e13i | 0.306977i | 0.988150 | + | 0.153488i | \(0.0490508\pi\) | ||||
−0.988150 | + | 0.153488i | \(0.950949\pi\) | |||||||
\(734\) | − | 4.47577e12i | − | 0.0210082i | ||||||
\(735\) | 1.74647e14 | 0.814190 | ||||||||
\(736\) | 8.34709e12i | 0.0386497i | ||||||||
\(737\) | −2.58603e14 | −1.18931 | ||||||||
\(738\) | 2.14429e12i | 0.00979493i | ||||||||
\(739\) | 2.94890e14i | 1.33794i | 0.743288 | + | 0.668972i | \(0.233265\pi\) | ||||
−0.743288 | + | 0.668972i | \(0.766735\pi\) | |||||||
\(740\) | −4.02507e14 | −1.81390 | ||||||||
\(741\) | −7.19733e13 | −0.322167 | ||||||||
\(742\) | 9.89094e12 | 0.0439762 | ||||||||
\(743\) | 1.44160e14i | 0.636651i | 0.947981 | + | 0.318326i | \(0.103120\pi\) | ||||
−0.947981 | + | 0.318326i | \(0.896880\pi\) | |||||||
\(744\) | 2.80588e12 | 0.0123085 | ||||||||
\(745\) | −1.03791e14 | −0.452249 | ||||||||
\(746\) | −3.59287e12 | −0.0155506 | ||||||||
\(747\) | 3.47386e14 | 1.49351 | ||||||||
\(748\) | −1.40675e14 | −0.600771 | ||||||||
\(749\) | − | 4.05607e14i | − | 1.72066i | ||||||
\(750\) | 9.69841e11i | 0.00408690i | ||||||||
\(751\) | 8.92427e12i | 0.0373571i | 0.999826 | + | 0.0186785i | \(0.00594591\pi\) | ||||
−0.999826 | + | 0.0186785i | \(0.994054\pi\) | |||||||
\(752\) | 1.42771e14 | 0.593678 | ||||||||
\(753\) | 9.87530e13i | 0.407920i | ||||||||
\(754\) | −5.20202e12 | −0.0213459 | ||||||||
\(755\) | 7.19847e13 | 0.293431 | ||||||||
\(756\) | −1.96923e14 | −0.797421 | ||||||||
\(757\) | − | 9.64872e13i | − | 0.388142i | −0.980988 | − | 0.194071i | \(-0.937831\pi\) | ||
0.980988 | − | 0.194071i | \(-0.0621691\pi\) | |||||||
\(758\) | − | 1.20401e13i | − | 0.0481156i | ||||||
\(759\) | − | 3.07461e13i | − | 0.122062i | ||||||
\(760\) | 3.29551e13i | 0.129973i | ||||||||
\(761\) | − | 1.69309e14i | − | 0.663370i | −0.943390 | − | 0.331685i | \(-0.892383\pi\) | ||
0.943390 | − | 0.331685i | \(-0.107617\pi\) | |||||||
\(762\) | 5.06203e11 | 0.00197038 | ||||||||
\(763\) | − | 6.57377e12i | − | 0.0254210i | ||||||
\(764\) | 4.85248e14i | 1.86422i | ||||||||
\(765\) | 2.09728e14i | 0.800477i | ||||||||
\(766\) | −4.02324e12 | −0.0152557 | ||||||||
\(767\) | −3.59292e14 | −1.35354 | ||||||||
\(768\) | 5.96003e13i | 0.223071i | ||||||||
\(769\) | −3.58143e14 | −1.33176 | −0.665878 | − | 0.746061i | \(-0.731943\pi\) | ||||
−0.665878 | + | 0.746061i | \(0.731943\pi\) | |||||||
\(770\) | 2.26948e13i | 0.0838442i | ||||||||
\(771\) | 4.83239e13 | 0.177374 | ||||||||
\(772\) | −3.41316e14 | −1.24472 | ||||||||
\(773\) | 1.36760e14i | 0.495522i | 0.968821 | + | 0.247761i | \(0.0796948\pi\) | ||||
−0.968821 | + | 0.247761i | \(0.920305\pi\) | |||||||
\(774\) | −4.02549e12 | + | 5.69459e12i | −0.0144915 | + | 0.0205002i | ||||
\(775\) | 4.17452e14 | 1.49313 | ||||||||
\(776\) | − | 6.56920e12i | − | 0.0233455i | ||||||
\(777\) | − | 1.34693e14i | − | 0.475599i | ||||||
\(778\) | 1.05933e13 | 0.0371650 | ||||||||
\(779\) | − | 1.76165e14i | − | 0.614090i | ||||||
\(780\) | 9.22563e13 | 0.319539 | ||||||||
\(781\) | − | 6.81548e13i | − | 0.234553i | ||||||
\(782\) | 2.03499e12i | 0.00695872i | ||||||||
\(783\) | 1.14206e14 | 0.388044 | ||||||||
\(784\) | −6.85759e14 | −2.31521 | ||||||||
\(785\) | 3.16878e14 | 1.06303 | ||||||||
\(786\) | 1.85578e12i | 0.00618607i | ||||||||
\(787\) | 1.36777e14 | 0.453042 | 0.226521 | − | 0.974006i | \(-0.427265\pi\) | ||||
0.226521 | + | 0.974006i | \(0.427265\pi\) | |||||||
\(788\) | 4.69724e14 | 1.54601 | ||||||||
\(789\) | 1.26874e14 | 0.414943 | ||||||||
\(790\) | 1.89311e13 | 0.0615233 | ||||||||
\(791\) | −4.68224e14 | −1.51207 | ||||||||
\(792\) | − | 1.74252e13i | − | 0.0559180i | ||||||
\(793\) | − | 2.44290e14i | − | 0.779003i | ||||||
\(794\) | 1.52352e13i | 0.0482775i | ||||||||
\(795\) | 1.01731e14 | 0.320346 | ||||||||
\(796\) | 3.16394e14i | 0.990064i | ||||||||
\(797\) | −5.67827e14 | −1.76573 | −0.882866 | − | 0.469626i | \(-0.844389\pi\) | ||||
−0.882866 | + | 0.469626i | \(0.844389\pi\) | |||||||
\(798\) | −5.51205e12 | −0.0170333 | ||||||||
\(799\) | 1.04543e14 | 0.321042 | ||||||||
\(800\) | − | 3.74042e13i | − | 0.114149i | ||||||
\(801\) | 4.18596e14i | 1.26950i | ||||||||
\(802\) | − | 4.03843e12i | − | 0.0121714i | ||||||
\(803\) | 2.04209e14i | 0.611640i | ||||||||
\(804\) | 8.05090e13i | 0.239643i | ||||||||
\(805\) | −4.69324e14 | −1.38833 | ||||||||
\(806\) | 8.49415e12i | 0.0249715i | ||||||||
\(807\) | − | 4.43878e12i | − | 0.0129687i | ||||||
\(808\) | − | 2.65744e12i | − | 0.00771626i | ||||||
\(809\) | 7.98438e13 | 0.230409 | 0.115204 | − | 0.993342i | \(-0.463248\pi\) | ||||
0.115204 | + | 0.993342i | \(0.463248\pi\) | |||||||
\(810\) | −1.22580e13 | −0.0351557 | ||||||||
\(811\) | − | 5.12445e14i | − | 1.46064i | −0.683106 | − | 0.730320i | \(-0.739371\pi\) | ||
0.683106 | − | 0.730320i | \(-0.260629\pi\) | |||||||
\(812\) | 5.69526e14 | 1.61337 | ||||||||
\(813\) | 5.56691e13i | 0.156733i | ||||||||
\(814\) | 1.22311e13 | 0.0342249 | ||||||||
\(815\) | −8.22512e14 | −2.28746 | ||||||||
\(816\) | 4.37647e13i | 0.120969i | ||||||||
\(817\) | 3.30716e14 | − | 4.67841e14i | 0.908541 | − | 1.28525i | ||||
\(818\) | 7.78555e12 | 0.0212580 | ||||||||
\(819\) | − | 5.80911e14i | − | 1.57649i | ||||||
\(820\) | 2.25811e14i | 0.609081i | ||||||||
\(821\) | −3.48244e14 | −0.933614 | −0.466807 | − | 0.884359i | \(-0.654596\pi\) | ||||
−0.466807 | + | 0.884359i | \(0.654596\pi\) | |||||||
\(822\) | 7.32556e11i | 0.00195201i | ||||||||
\(823\) | 4.68372e14 | 1.24049 | 0.620243 | − | 0.784409i | \(-0.287034\pi\) | ||||
0.620243 | + | 0.784409i | \(0.287034\pi\) | |||||||
\(824\) | − | 4.53880e12i | − | 0.0119483i | ||||||
\(825\) | 1.37776e14i | 0.360500i | ||||||||
\(826\) | −2.75162e13 | −0.0715631 | ||||||||
\(827\) | 6.08475e14 | 1.57295 | 0.786476 | − | 0.617621i | \(-0.211904\pi\) | ||||
0.786476 | + | 0.617621i | \(0.211904\pi\) | |||||||
\(828\) | 1.80112e14 | 0.462796 | ||||||||
\(829\) | 5.02721e14i | 1.28397i | 0.766718 | + | 0.641984i | \(0.221888\pi\) | ||||
−0.766718 | + | 0.641984i | \(0.778112\pi\) | |||||||
\(830\) | −2.55902e13 | −0.0649655 | ||||||||
\(831\) | −1.11447e14 | −0.281231 | ||||||||
\(832\) | −3.61740e14 | −0.907360 | ||||||||
\(833\) | −5.02142e14 | −1.25199 | ||||||||
\(834\) | 1.16303e12 | 0.00288244 | ||||||||
\(835\) | 4.22978e14i | 1.04204i | ||||||||
\(836\) | 7.15537e14i | 1.75227i | ||||||||
\(837\) | − | 1.86482e14i | − | 0.453952i | ||||||
\(838\) | 1.48749e13 | 0.0359943 | ||||||||
\(839\) | − | 9.63376e13i | − | 0.231732i | −0.993265 | − | 0.115866i | \(-0.963036\pi\) | ||
0.993265 | − | 0.115866i | \(-0.0369643\pi\) | |||||||
\(840\) | 1.41358e13 | 0.0338005 | ||||||||
\(841\) | 9.04089e13 | 0.214897 | ||||||||
\(842\) | 1.28925e13 | 0.0304632 | ||||||||
\(843\) | 6.97990e13i | 0.163950i | ||||||||
\(844\) | − | 5.50900e14i | − | 1.28635i | ||||||
\(845\) | − | 1.14245e14i | − | 0.265187i | ||||||
\(846\) | 6.47253e12i | 0.0149356i | ||||||||
\(847\) | 1.91554e14i | 0.439413i | ||||||||
\(848\) | −3.99451e14 | −0.910928 | ||||||||
\(849\) | 4.21535e13i | 0.0955641i | ||||||||
\(850\) | − | 9.11902e12i | − | 0.0205520i | ||||||
\(851\) | 2.52936e14i | 0.566712i | ||||||||
\(852\) | −2.12182e13 | −0.0472618 | ||||||||
\(853\) | −8.44718e13 | −0.187054 | −0.0935269 | − | 0.995617i | \(-0.529814\pi\) | ||||
−0.0935269 | + | 0.995617i | \(0.529814\pi\) | |||||||
\(854\) | − | 1.87088e13i | − | 0.0411868i | ||||||
\(855\) | 1.06677e15 | 2.33475 | ||||||||
\(856\) | − | 2.29413e13i | − | 0.0499170i | ||||||
\(857\) | 7.23095e14 | 1.56420 | 0.782098 | − | 0.623155i | \(-0.214149\pi\) | ||||
0.782098 | + | 0.623155i | \(0.214149\pi\) | |||||||
\(858\) | −2.80342e12 | −0.00602908 | ||||||||
\(859\) | − | 5.32248e14i | − | 1.13802i | −0.822332 | − | 0.569008i | \(-0.807327\pi\) | ||
0.822332 | − | 0.569008i | \(-0.192673\pi\) | |||||||
\(860\) | −4.23916e14 | + | 5.99685e14i | −0.901130 | + | 1.27477i | ||||
\(861\) | −7.55643e13 | −0.159699 | ||||||||
\(862\) | 7.41808e12i | 0.0155867i | ||||||||
\(863\) | − | 8.60293e14i | − | 1.79718i | −0.438786 | − | 0.898591i | \(-0.644591\pi\) | ||
0.438786 | − | 0.898591i | \(-0.355409\pi\) | |||||||
\(864\) | −1.67090e13 | −0.0347042 | ||||||||
\(865\) | 6.72161e14i | 1.38801i | ||||||||
\(866\) | −7.82636e12 | −0.0160683 | ||||||||
\(867\) | − | 7.80013e13i | − | 0.159223i | ||||||
\(868\) | − | 9.29954e14i | − | 1.88740i | ||||||
\(869\) | 8.22368e14 | 1.65946 | ||||||||
\(870\) | −4.09761e12 | −0.00822119 | ||||||||
\(871\) | −4.87615e14 | −0.972716 | ||||||||
\(872\) | − | 3.71815e11i | − | 0.000737470i | ||||||
\(873\) | −2.12648e14 | −0.419362 | ||||||||
\(874\) | 1.03509e13 | 0.0202965 | ||||||||
\(875\) | 6.43094e14 | 1.25382 | ||||||||
\(876\) | 6.35749e13 | 0.123244 | ||||||||
\(877\) | 9.30571e14 | 1.79371 | 0.896854 | − | 0.442327i | \(-0.145847\pi\) | ||||
0.896854 | + | 0.442327i | \(0.145847\pi\) | |||||||
\(878\) | 2.04306e13i | 0.0391570i | ||||||||
\(879\) | − | 1.06418e14i | − | 0.202802i | ||||||
\(880\) | − | 9.16542e14i | − | 1.73676i | ||||||
\(881\) | 2.02031e14 | 0.380661 | 0.190330 | − | 0.981720i | \(-0.439044\pi\) | ||||
0.190330 | + | 0.981720i | \(0.439044\pi\) | |||||||
\(882\) | − | 3.10889e13i | − | 0.0582456i | ||||||
\(883\) | 1.95016e14 | 0.363301 | 0.181651 | − | 0.983363i | \(-0.441856\pi\) | ||||
0.181651 | + | 0.983363i | \(0.441856\pi\) | |||||||
\(884\) | −2.65253e14 | −0.491360 | ||||||||
\(885\) | −2.83013e14 | −0.521302 | ||||||||
\(886\) | − | 6.78164e12i | − | 0.0124213i | ||||||
\(887\) | − | 6.85090e14i | − | 1.24775i | −0.781522 | − | 0.623877i | \(-0.785556\pi\) | ||
0.781522 | − | 0.623877i | \(-0.214444\pi\) | |||||||
\(888\) | − | 7.61830e12i | − | 0.0137973i | ||||||
\(889\) | − | 3.35659e14i | − | 0.604491i | ||||||
\(890\) | − | 3.08359e13i | − | 0.0552212i | ||||||
\(891\) | −5.32491e14 | −0.948251 | ||||||||
\(892\) | − | 8.70918e13i | − | 0.154224i | ||||||
\(893\) | − | 5.31754e14i | − | 0.936382i | ||||||
\(894\) | − | 9.81888e11i | − | 0.00171939i | ||||||
\(895\) | 1.33236e15 | 2.32011 | ||||||||
\(896\) | −1.11087e14 | −0.192364 | ||||||||
\(897\) | − | 5.79740e13i | − | 0.0998323i | ||||||
\(898\) | 1.80296e13 | 0.0308748 | ||||||||
\(899\) | 5.39329e14i | 0.918450i | ||||||||
\(900\) | −8.07099e14 | −1.36683 | ||||||||
\(901\) | −2.92495e14 | −0.492601 | ||||||||
\(902\) | − | 6.86176e12i | − | 0.0114922i | ||||||
\(903\) | −2.00676e14 | − | 1.41858e14i | −0.334239 | − | 0.236273i | ||||
\(904\) | −2.64829e13 | −0.0438656 | ||||||||
\(905\) | 1.37197e15i | 2.25997i | ||||||||
\(906\) | 6.80994e11i | 0.00111558i | ||||||||
\(907\) | 6.84032e14 | 1.11440 | 0.557199 | − | 0.830379i | \(-0.311876\pi\) | ||||
0.557199 | + | 0.830379i | \(0.311876\pi\) | |||||||
\(908\) | 5.91385e14i | 0.958167i | ||||||||
\(909\) | −8.60224e13 | −0.138609 | ||||||||
\(910\) | 4.27928e13i | 0.0685746i | ||||||||
\(911\) | − | 1.35076e14i | − | 0.215271i | −0.994190 | − | 0.107635i | \(-0.965672\pi\) | ||
0.994190 | − | 0.107635i | \(-0.0343279\pi\) | |||||||
\(912\) | 2.22607e14 | 0.352830 | ||||||||
\(913\) | −1.11164e15 | −1.75231 | ||||||||
\(914\) | 1.64991e13 | 0.0258661 | ||||||||
\(915\) | − | 1.92426e14i | − | 0.300026i | ||||||
\(916\) | 3.54383e14 | 0.549536 | ||||||||
\(917\) | 1.23056e15 | 1.89782 | ||||||||
\(918\) | −4.07360e12 | −0.00624834 | ||||||||
\(919\) | −2.36775e14 | −0.361209 | −0.180604 | − | 0.983556i | \(-0.557805\pi\) | ||||
−0.180604 | + | 0.983556i | \(0.557805\pi\) | |||||||
\(920\) | −2.65451e13 | −0.0402759 | ||||||||
\(921\) | 1.73931e14i | 0.262469i | ||||||||
\(922\) | 1.02443e13i | 0.0153755i | ||||||||
\(923\) | − | 1.28511e14i | − | 0.191837i | ||||||
\(924\) | 3.06923e14 | 0.455690 | ||||||||
\(925\) | − | 1.13343e15i | − | 1.67374i | ||||||
\(926\) | 2.07726e13 | 0.0305096 | ||||||||
\(927\) | −1.46923e14 | −0.214630 | ||||||||
\(928\) | 4.83245e13 | 0.0702147 | ||||||||
\(929\) | 5.37530e14i | 0.776827i | 0.921485 | + | 0.388413i | \(0.126977\pi\) | ||||
−0.921485 | + | 0.388413i | \(0.873023\pi\) | |||||||
\(930\) | 6.69081e12i | 0.00961753i | ||||||||
\(931\) | 2.55412e15i | 3.65169i | ||||||||
\(932\) | − | 5.86145e14i | − | 0.833538i | ||||||
\(933\) | 1.30013e14i | 0.183899i | ||||||||
\(934\) | −1.01688e13 | −0.0143066 | ||||||||
\(935\) | − | 6.71132e14i | − | 0.939182i | ||||||
\(936\) | − | 3.28565e13i | − | 0.0457343i | ||||||
\(937\) | 5.74508e14i | 0.795423i | 0.917510 | + | 0.397712i | \(0.130196\pi\) | ||||
−0.917510 | + | 0.397712i | \(0.869804\pi\) | |||||||
\(938\) | −3.73438e13 | −0.0514286 | ||||||||
\(939\) | −6.78320e13 | −0.0929194 | ||||||||
\(940\) | 6.81609e14i | 0.928744i | ||||||||
\(941\) | −1.18983e15 | −1.61264 | −0.806322 | − | 0.591477i | \(-0.798545\pi\) | ||||
−0.806322 | + | 0.591477i | \(0.798545\pi\) | |||||||
\(942\) | 2.99775e12i | 0.00404149i | ||||||||
\(943\) | 1.41900e14 | 0.190293 | ||||||||
\(944\) | 1.11126e15 | 1.48236 | ||||||||
\(945\) | − | 9.39480e14i | − | 1.24660i | ||||||
\(946\) | 1.28816e13 | − | 1.82228e13i | 0.0170026 | − | 0.0240524i | ||||
\(947\) | −1.05265e15 | −1.38208 | −0.691040 | − | 0.722817i | \(-0.742847\pi\) | ||||
−0.691040 | + | 0.722817i | \(0.742847\pi\) | |||||||
\(948\) | − | 2.56022e14i | − | 0.334377i | ||||||
\(949\) | 3.85051e14i | 0.500250i | ||||||||
\(950\) | −4.63835e13 | −0.0599439 | ||||||||
\(951\) | − | 5.66934e13i | − | 0.0728836i | ||||||
\(952\) | −4.06429e13 | −0.0519756 | ||||||||
\(953\) | − | 4.60655e14i | − | 0.586019i | −0.956110 | − | 0.293009i | \(-0.905343\pi\) | ||
0.956110 | − | 0.293009i | \(-0.0946567\pi\) | |||||||
\(954\) | − | 1.81091e13i | − | 0.0229169i | ||||||
\(955\) | −2.31502e15 | −2.91432 | ||||||||
\(956\) | 3.47975e14 | 0.435771 | ||||||||
\(957\) | −1.78001e14 | −0.221749 | ||||||||
\(958\) | 3.51942e13i | 0.0436158i | ||||||||
\(959\) | 4.85753e14 | 0.598856 | ||||||||
\(960\) | −2.84941e14 | −0.349461 | ||||||||
\(961\) | 6.10183e13 | 0.0744463 | ||||||||
\(962\) | 2.30626e13 | 0.0279919 | ||||||||
\(963\) | −7.42618e14 | −0.896673 | ||||||||
\(964\) | 1.28649e15i | 1.54533i | ||||||||
\(965\) | − | 1.62835e15i | − | 1.94586i | ||||||
\(966\) | − | 4.43992e12i | − | 0.00527825i | ||||||
\(967\) | −4.77240e14 | −0.564422 | −0.282211 | − | 0.959352i | \(-0.591068\pi\) | ||||
−0.282211 | + | 0.959352i | \(0.591068\pi\) | |||||||
\(968\) | 1.08343e13i | 0.0127475i | ||||||||
\(969\) | 1.63003e14 | 0.190799 | ||||||||
\(970\) | 1.56647e13 | 0.0182416 | ||||||||
\(971\) | −1.14694e15 | −1.32875 | −0.664377 | − | 0.747398i | \(-0.731303\pi\) | ||||
−0.664377 | + | 0.747398i | \(0.731303\pi\) | |||||||
\(972\) | 5.45480e14i | 0.628706i | ||||||||
\(973\) | − | 7.71195e14i | − | 0.884301i | ||||||
\(974\) | − | 7.19109e12i | − | 0.00820351i | ||||||
\(975\) | 2.59788e14i | 0.294846i | ||||||||
\(976\) | 7.55567e14i | 0.853147i | ||||||||
\(977\) | 1.69978e15 | 1.90950 | 0.954748 | − | 0.297417i | \(-0.0961251\pi\) | ||||
0.954748 | + | 0.297417i | \(0.0961251\pi\) | |||||||
\(978\) | − | 7.78118e12i | − | 0.00869663i | ||||||
\(979\) | − | 1.33951e15i | − | 1.48948i | ||||||
\(980\) | − | 3.27391e15i | − | 3.62190i | ||||||
\(981\) | −1.20358e13 | −0.0132474 | ||||||||
\(982\) | −4.71835e12 | −0.00516693 | ||||||||
\(983\) | 4.99631e14i | 0.544354i | 0.962247 | + | 0.272177i | \(0.0877437\pi\) | ||||
−0.962247 | + | 0.272177i | \(0.912256\pi\) | |||||||
\(984\) | −4.27395e12 | −0.00463291 | ||||||||
\(985\) | 2.24096e15i | 2.41687i | ||||||||
\(986\) | 1.17814e13 | 0.0126419 | ||||||||
\(987\) | −2.28091e14 | −0.243513 | ||||||||
\(988\) | 1.34920e15i | 1.43315i | ||||||||
\(989\) | 3.76843e14 | + | 2.66389e14i | 0.398271 | + | 0.281537i | ||||
\(990\) | 4.15515e13 | 0.0436929 | ||||||||
\(991\) | 3.18035e14i | 0.332741i | 0.986063 | + | 0.166371i | \(0.0532048\pi\) | ||||
−0.986063 | + | 0.166371i | \(0.946795\pi\) | |||||||
\(992\) | − | 7.89070e13i | − | 0.0821404i | ||||||
\(993\) | 1.92411e14 | 0.199289 | ||||||||
\(994\) | − | 9.84198e12i | − | 0.0101426i | ||||||
\(995\) | −1.50945e15 | −1.54776 | ||||||||
\(996\) | 3.46079e14i | 0.353085i | ||||||||
\(997\) | − | 8.99024e14i | − | 0.912632i | −0.889818 | − | 0.456316i | \(-0.849169\pi\) | ||
0.889818 | − | 0.456316i | \(-0.150831\pi\) | |||||||
\(998\) | 1.79971e13 | 0.0181781 | ||||||||
\(999\) | −5.06321e14 | −0.508860 |
(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 | 43.11.b.b.42.18 | yes | 34 | |
43.42 | odd | 2 | inner | 43.11.b.b.42.17 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.11.b.b.42.17 | ✓ | 34 | 43.42 | odd | 2 | inner | |
43.11.b.b.42.18 | yes | 34 | 1.1 | even | 1 | trivial |