Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(74,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.74");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.5533957546\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 943 x^{18} + 318815 x^{16} + 48938090 x^{14} + 3842259173 x^{12} + 159675554657 x^{10} + \cdots + 336685801 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{28}\cdot 3^{22}\cdot 5^{32} \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 74.2 | ||
Root | \(-17.2930i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.74 |
Dual form | 75.9.d.c.74.1 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −29.5009 | −1.84380 | −0.921902 | − | 0.387423i | \(-0.873365\pi\) | ||||
−0.921902 | + | 0.387423i | \(0.873365\pi\) | |||||||
\(3\) | 69.5124 | + | 41.5815i | 0.858178 | + | 0.513352i | ||||
\(4\) | 614.301 | 2.39961 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2050.68 | − | 1226.69i | −1.58231 | − | 0.946520i | ||||
\(7\) | − | 3174.27i | − | 1.32206i | −0.750359 | − | 0.661031i | \(-0.770119\pi\) | ||
0.750359 | − | 0.661031i | \(-0.229881\pi\) | |||||||
\(8\) | −10570.2 | −2.58061 | ||||||||
\(9\) | 3102.96 | + | 5780.86i | 0.472940 | + | 0.881095i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12996.3i | 0.887668i | 0.896109 | + | 0.443834i | \(0.146382\pi\) | ||||
−0.896109 | + | 0.443834i | \(0.853618\pi\) | |||||||
\(12\) | 42701.6 | + | 25543.6i | 2.05930 | + | 1.23185i | ||||
\(13\) | 8759.90i | 0.306708i | 0.988171 | + | 0.153354i | \(0.0490075\pi\) | ||||
−0.988171 | + | 0.153354i | \(0.950992\pi\) | |||||||
\(14\) | 93643.7i | 2.43762i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 154569. | 2.35853 | ||||||||
\(17\) | −108656. | −1.30094 | −0.650470 | − | 0.759532i | \(-0.725428\pi\) | ||||
−0.650470 | + | 0.759532i | \(0.725428\pi\) | |||||||
\(18\) | −91540.0 | − | 170540.i | −0.872009 | − | 1.62457i | ||||
\(19\) | 78696.7 | 0.603868 | 0.301934 | − | 0.953329i | \(-0.402368\pi\) | ||||
0.301934 | + | 0.953329i | \(0.402368\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 131991. | − | 220651.i | 0.678683 | − | 1.13456i | ||||
\(22\) | − | 383403.i | − | 1.63669i | ||||||
\(23\) | 43589.4 | 0.155765 | 0.0778825 | − | 0.996963i | \(-0.475184\pi\) | ||||
0.0778825 | + | 0.996963i | \(0.475184\pi\) | |||||||
\(24\) | −734760. | − | 439524.i | −2.21463 | − | 1.32476i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 258425.i | − | 0.565510i | ||||||
\(27\) | −24682.6 | + | 530868.i | −0.0464447 | + | 0.998921i | ||||
\(28\) | − | 1.94996e6i | − | 3.17244i | ||||||
\(29\) | 183211.i | 0.259036i | 0.991577 | + | 0.129518i | \(0.0413430\pi\) | ||||
−0.991577 | + | 0.129518i | \(0.958657\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 780664. | 0.845312 | 0.422656 | − | 0.906290i | \(-0.361098\pi\) | ||||
0.422656 | + | 0.906290i | \(0.361098\pi\) | |||||||
\(32\) | −1.85394e6 | −1.76806 | ||||||||
\(33\) | −540407. | + | 903407.i | −0.455686 | + | 0.761777i | ||||
\(34\) | 3.20544e6 | 2.39868 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.90615e6 | + | 3.55119e6i | 1.13487 | + | 2.11429i | ||||
\(37\) | − | 2.20452e6i | − | 1.17627i | −0.808763 | − | 0.588134i | \(-0.799863\pi\) | ||
0.808763 | − | 0.588134i | \(-0.200137\pi\) | |||||||
\(38\) | −2.32162e6 | −1.11341 | ||||||||
\(39\) | −364250. | + | 608922.i | −0.157449 | + | 0.263210i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.04685e6i | 1.07824i | 0.842228 | + | 0.539121i | \(0.181243\pi\) | ||||
−0.842228 | + | 0.539121i | \(0.818757\pi\) | |||||||
\(42\) | −3.89384e6 | + | 6.50940e6i | −1.25136 | + | 2.09191i | ||||
\(43\) | 4.84516e6i | 1.41721i | 0.705606 | + | 0.708605i | \(0.250675\pi\) | ||||
−0.705606 | + | 0.708605i | \(0.749325\pi\) | |||||||
\(44\) | 7.98367e6i | 2.13006i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.28593e6 | −0.287200 | ||||||||
\(47\) | 3.51057e6 | 0.719426 | 0.359713 | − | 0.933063i | \(-0.382875\pi\) | ||||
0.359713 | + | 0.933063i | \(0.382875\pi\) | |||||||
\(48\) | 1.07444e7 | + | 6.42720e6i | 2.02404 | + | 1.21076i | ||||
\(49\) | −4.31118e6 | −0.747846 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.55293e6 | − | 4.51807e6i | −1.11644 | − | 0.667840i | ||||
\(52\) | 5.38121e6i | 0.735982i | ||||||||
\(53\) | 8.64762e6 | 1.09596 | 0.547978 | − | 0.836493i | \(-0.315398\pi\) | ||||
0.547978 | + | 0.836493i | \(0.315398\pi\) | |||||||
\(54\) | 728158. | − | 1.56611e7i | 0.0856349 | − | 1.84181i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.35526e7i | 3.41173i | ||||||||
\(57\) | 5.47040e6 | + | 3.27232e6i | 0.518226 | + | 0.309997i | ||||
\(58\) | − | 5.40489e6i | − | 0.477611i | ||||||
\(59\) | 5.16824e6i | 0.426515i | 0.976996 | + | 0.213257i | \(0.0684073\pi\) | ||||
−0.976996 | + | 0.213257i | \(0.931593\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.78123e6 | 0.417543 | 0.208771 | − | 0.977964i | \(-0.433054\pi\) | ||||
0.208771 | + | 0.977964i | \(0.433054\pi\) | |||||||
\(62\) | −2.30303e7 | −1.55859 | ||||||||
\(63\) | 1.83500e7 | − | 9.84963e6i | 1.16486 | − | 0.625256i | ||||
\(64\) | 1.51233e7 | 0.901419 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.59425e7 | − | 2.66513e7i | 0.840195 | − | 1.40457i | ||||
\(67\) | 3.67916e7i | 1.82578i | 0.408202 | + | 0.912891i | \(0.366156\pi\) | ||||
−0.408202 | + | 0.912891i | \(0.633844\pi\) | |||||||
\(68\) | −6.67474e7 | −3.12175 | ||||||||
\(69\) | 3.03001e6 | + | 1.81251e6i | 0.133674 | + | 0.0799622i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 971113.i | 0.0382152i | 0.999817 | + | 0.0191076i | \(0.00608251\pi\) | ||||
−0.999817 | + | 0.0191076i | \(0.993917\pi\) | |||||||
\(72\) | −3.27989e7 | − | 6.11048e7i | −1.22048 | − | 2.27376i | ||||
\(73\) | 9.46941e6i | 0.333451i | 0.986003 | + | 0.166725i | \(0.0533193\pi\) | ||||
−0.986003 | + | 0.166725i | \(0.946681\pi\) | |||||||
\(74\) | 6.50352e7i | 2.16881i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.83434e7 | 1.44905 | ||||||||
\(77\) | 4.12539e7 | 1.17355 | ||||||||
\(78\) | 1.07457e7 | − | 1.79637e7i | 0.290306 | − | 0.485309i | ||||
\(79\) | −5.63493e7 | −1.44671 | −0.723353 | − | 0.690479i | \(-0.757400\pi\) | ||||
−0.723353 | + | 0.690479i | \(0.757400\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.37900e7 | + | 3.58756e7i | −0.552656 | + | 0.833410i | ||||
\(82\) | − | 8.98849e7i | − | 1.98807i | ||||||
\(83\) | −5.88128e7 | −1.23925 | −0.619626 | − | 0.784897i | \(-0.712716\pi\) | ||||
−0.619626 | + | 0.784897i | \(0.712716\pi\) | |||||||
\(84\) | 8.10821e7 | − | 1.35546e8i | 1.62858 | − | 2.72252i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 1.42936e8i | − | 2.61306i | ||||||
\(87\) | −7.61819e6 | + | 1.27355e7i | −0.132977 | + | 0.222299i | ||||
\(88\) | − | 1.37374e8i | − | 2.29073i | ||||||
\(89\) | 1.92128e7i | 0.306218i | 0.988209 | + | 0.153109i | \(0.0489286\pi\) | ||||
−0.988209 | + | 0.153109i | \(0.951071\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.78063e7 | 0.405487 | ||||||||
\(92\) | 2.67770e7 | 0.373776 | ||||||||
\(93\) | 5.42658e7 | + | 3.24612e7i | 0.725429 | + | 0.433943i | ||||
\(94\) | −1.03565e8 | −1.32648 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.28872e8 | − | 7.70897e7i | −1.51731 | − | 0.907635i | ||||
\(97\) | 1.42760e8i | 1.61257i | 0.591526 | + | 0.806286i | \(0.298526\pi\) | ||||
−0.591526 | + | 0.806286i | \(0.701474\pi\) | |||||||
\(98\) | 1.27184e8 | 1.37888 | ||||||||
\(99\) | −7.51301e7 | + | 4.03271e7i | −0.782119 | + | 0.419814i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.34775e7i | 0.802202i | 0.916034 | + | 0.401101i | \(0.131372\pi\) | ||||
−0.916034 | + | 0.401101i | \(0.868628\pi\) | |||||||
\(102\) | 2.22818e8 | + | 1.33287e8i | 2.05849 | + | 1.23137i | ||||
\(103\) | 1.29545e8i | 1.15099i | 0.817806 | + | 0.575494i | \(0.195190\pi\) | ||||
−0.817806 | + | 0.575494i | \(0.804810\pi\) | |||||||
\(104\) | − | 9.25938e7i | − | 0.791496i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.55112e8 | −2.02073 | ||||||||
\(107\) | 1.02862e8 | 0.784731 | 0.392365 | − | 0.919809i | \(-0.371657\pi\) | ||||
0.392365 | + | 0.919809i | \(0.371657\pi\) | |||||||
\(108\) | −1.51626e7 | + | 3.26112e8i | −0.111449 | + | 2.39702i | ||||
\(109\) | 1.82090e8 | 1.28997 | 0.644984 | − | 0.764196i | \(-0.276864\pi\) | ||||
0.644984 | + | 0.764196i | \(0.276864\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.16671e7 | − | 1.53241e8i | 0.603840 | − | 1.00945i | ||||
\(112\) | − | 4.90643e8i | − | 3.11812i | ||||||
\(113\) | −8.75507e6 | −0.0536965 | −0.0268483 | − | 0.999640i | \(-0.508547\pi\) | ||||
−0.0268483 | + | 0.999640i | \(0.508547\pi\) | |||||||
\(114\) | −1.61381e8 | − | 9.65364e7i | −0.955508 | − | 0.571573i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.12547e8i | 0.621586i | ||||||||
\(117\) | −5.06398e7 | + | 2.71816e7i | −0.270239 | + | 0.145055i | ||||
\(118\) | − | 1.52467e8i | − | 0.786410i | ||||||
\(119\) | 3.44903e8i | 1.71992i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.54540e7 | 0.212046 | ||||||||
\(122\) | −1.70551e8 | −0.769867 | ||||||||
\(123\) | −1.26693e8 | + | 2.11794e8i | −0.553518 | + | 0.925324i | ||||
\(124\) | 4.79563e8 | 2.02842 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.41341e8 | + | 2.90573e8i | −2.14778 | + | 1.15285i | ||||
\(127\) | 2.17231e7i | 0.0835040i | 0.999128 | + | 0.0417520i | \(0.0132939\pi\) | ||||
−0.999128 | + | 0.0417520i | \(0.986706\pi\) | |||||||
\(128\) | 2.84587e7 | 0.106017 | ||||||||
\(129\) | −2.01469e8 | + | 3.36799e8i | −0.727527 | + | 1.21622i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.72425e8i | − | 0.585485i | −0.956191 | − | 0.292743i | \(-0.905432\pi\) | ||
0.956191 | − | 0.292743i | \(-0.0945679\pi\) | |||||||
\(132\) | −3.31973e8 | + | 5.54964e8i | −1.09347 | + | 1.82797i | ||||
\(133\) | − | 2.49804e8i | − | 0.798350i | ||||||
\(134\) | − | 1.08538e9i | − | 3.36639i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.14851e9 | 3.35722 | ||||||||
\(137\) | 2.76036e8 | 0.783580 | 0.391790 | − | 0.920055i | \(-0.371856\pi\) | ||||
0.391790 | + | 0.920055i | \(0.371856\pi\) | |||||||
\(138\) | −8.93879e7 | − | 5.34707e7i | −0.246469 | − | 0.147435i | ||||
\(139\) | −4.04596e8 | −1.08383 | −0.541916 | − | 0.840433i | \(-0.682301\pi\) | ||||
−0.541916 | + | 0.840433i | \(0.682301\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.44028e8 | + | 1.45975e8i | 0.617396 | + | 0.369319i | ||||
\(142\) | − | 2.86487e7i | − | 0.0704614i | ||||||
\(143\) | −1.13847e8 | −0.272255 | ||||||||
\(144\) | 4.79620e8 | + | 8.93540e8i | 1.11544 | + | 2.07809i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 2.79356e8i | − | 0.614818i | ||||||
\(147\) | −2.99681e8 | − | 1.79265e8i | −0.641785 | − | 0.383908i | ||||
\(148\) | − | 1.35424e9i | − | 2.82259i | ||||||
\(149\) | − | 8.41277e8i | − | 1.70685i | −0.521219 | − | 0.853423i | \(-0.674523\pi\) | ||
0.521219 | − | 0.853423i | \(-0.325477\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.91529e8 | −0.368405 | −0.184203 | − | 0.982888i | \(-0.558970\pi\) | ||||
−0.184203 | + | 0.982888i | \(0.558970\pi\) | |||||||
\(152\) | −8.31839e8 | −1.55835 | ||||||||
\(153\) | −3.37154e8 | − | 6.28124e8i | −0.615266 | − | 1.14625i | ||||
\(154\) | −1.21703e9 | −2.16380 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.23759e8 | + | 3.74061e8i | −0.377817 | + | 0.631603i | ||||
\(157\) | − | 2.37178e8i | − | 0.390370i | −0.980766 | − | 0.195185i | \(-0.937469\pi\) | ||
0.980766 | − | 0.195185i | \(-0.0625307\pi\) | |||||||
\(158\) | 1.66235e9 | 2.66744 | ||||||||
\(159\) | 6.01117e8 | + | 3.59581e8i | 0.940525 | + | 0.562611i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.38365e8i | − | 0.205931i | ||||||
\(162\) | 7.01826e8 | − | 1.05836e9i | 1.01899 | − | 1.53664i | ||||
\(163\) | 6.29506e8i | 0.891763i | 0.895092 | + | 0.445881i | \(0.147110\pi\) | ||||
−0.895092 | + | 0.445881i | \(0.852890\pi\) | |||||||
\(164\) | 1.87169e9i | 2.58736i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.73503e9 | 2.28494 | ||||||||
\(167\) | 3.79259e7 | 0.0487607 | 0.0243803 | − | 0.999703i | \(-0.492239\pi\) | ||||
0.0243803 | + | 0.999703i | \(0.492239\pi\) | |||||||
\(168\) | −1.39517e9 | + | 2.33233e9i | −1.75142 | + | 2.92787i | ||||
\(169\) | 7.38995e8 | 0.905930 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.44193e8 | + | 4.54935e8i | 0.285593 | + | 0.532065i | ||||
\(172\) | 2.97638e9i | 3.40075i | ||||||||
\(173\) | −1.49961e9 | −1.67415 | −0.837077 | − | 0.547085i | \(-0.815737\pi\) | ||||
−0.837077 | + | 0.547085i | \(0.815737\pi\) | |||||||
\(174\) | 2.24743e8 | − | 3.75707e8i | 0.245183 | − | 0.409876i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00883e9i | 2.09359i | ||||||||
\(177\) | −2.14903e8 | + | 3.59257e8i | −0.218952 | + | 0.366026i | ||||
\(178\) | − | 5.66795e8i | − | 0.564606i | ||||||
\(179\) | 7.72267e8i | 0.752238i | 0.926571 | + | 0.376119i | \(0.122742\pi\) | ||||
−0.926571 | + | 0.376119i | \(0.877258\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.49920e8 | −0.698716 | −0.349358 | − | 0.936989i | \(-0.613600\pi\) | ||||
−0.349358 | + | 0.936989i | \(0.613600\pi\) | |||||||
\(182\) | −8.20309e8 | −0.747639 | ||||||||
\(183\) | 4.01867e8 | + | 2.40392e8i | 0.358326 | + | 0.214346i | ||||
\(184\) | −4.60749e8 | −0.401969 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.60089e9 | − | 9.57632e8i | −1.33755 | − | 0.800105i | ||||
\(187\) | − | 1.41213e9i | − | 1.15480i | ||||||
\(188\) | 2.15655e9 | 1.72635 | ||||||||
\(189\) | 1.68512e9 | + | 7.83492e7i | 1.32063 | + | 0.0614027i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.93822e7i | 0.0671611i | 0.999436 | + | 0.0335805i | \(0.0106910\pi\) | ||||
−0.999436 | + | 0.0335805i | \(0.989309\pi\) | |||||||
\(192\) | 1.05126e9 | + | 6.28849e8i | 0.773578 | + | 0.462745i | ||||
\(193\) | 8.16090e8i | 0.588178i | 0.955778 | + | 0.294089i | \(0.0950163\pi\) | ||||
−0.955778 | + | 0.294089i | \(0.904984\pi\) | |||||||
\(194\) | − | 4.21154e9i | − | 2.97327i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.64837e9 | −1.79454 | ||||||||
\(197\) | −1.32278e9 | −0.878256 | −0.439128 | − | 0.898424i | \(-0.644713\pi\) | ||||
−0.439128 | + | 0.898424i | \(0.644713\pi\) | |||||||
\(198\) | 2.21640e9 | − | 1.18968e9i | 1.44207 | − | 0.774054i | ||||
\(199\) | 1.92328e9 | 1.22639 | 0.613197 | − | 0.789930i | \(-0.289883\pi\) | ||||
0.613197 | + | 0.789930i | \(0.289883\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.52985e9 | + | 2.55747e9i | −0.937269 | + | 1.56685i | ||||
\(202\) | − | 2.46266e9i | − | 1.47910i | ||||||
\(203\) | 5.81562e8 | 0.342461 | ||||||||
\(204\) | −4.63977e9 | − | 2.77546e9i | −2.67902 | − | 1.60256i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 3.82168e9i | − | 2.12220i | ||||||
\(207\) | 1.35256e8 | + | 2.51985e8i | 0.0736675 | + | 0.137244i | ||||
\(208\) | 1.35401e9i | 0.723381i | ||||||||
\(209\) | 1.02277e9i | 0.536034i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.03655e9 | 1.02746 | 0.513729 | − | 0.857952i | \(-0.328264\pi\) | ||||
0.513729 | + | 0.857952i | \(0.328264\pi\) | |||||||
\(212\) | 5.31224e9 | 2.62987 | ||||||||
\(213\) | −4.03803e7 | + | 6.75045e7i | −0.0196179 | + | 0.0327955i | ||||
\(214\) | −3.03452e9 | −1.44689 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.60900e8 | − | 5.61137e9i | 0.119856 | − | 2.57783i | ||||
\(217\) | − | 2.47804e9i | − | 1.11755i | ||||||
\(218\) | −5.37180e9 | −2.37845 | ||||||||
\(219\) | −3.93752e8 | + | 6.58242e8i | −0.171177 | + | 0.286160i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 9.51814e8i | − | 0.399009i | ||||||
\(222\) | −2.70426e9 | + | 4.52075e9i | −1.11336 | + | 1.86122i | ||||
\(223\) | − | 4.63258e8i | − | 0.187328i | −0.995604 | − | 0.0936642i | \(-0.970142\pi\) | ||
0.995604 | − | 0.0936642i | \(-0.0298580\pi\) | |||||||
\(224\) | 5.88491e9i | 2.33748i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.58282e8 | 0.0990059 | ||||||||
\(227\) | 4.20915e9 | 1.58522 | 0.792612 | − | 0.609726i | \(-0.208721\pi\) | ||||
0.792612 | + | 0.609726i | \(0.208721\pi\) | |||||||
\(228\) | 3.36047e9 | + | 2.01019e9i | 1.24354 | + | 0.743872i | ||||
\(229\) | 4.11215e9 | 1.49530 | 0.747648 | − | 0.664095i | \(-0.231183\pi\) | ||||
0.747648 | + | 0.664095i | \(0.231183\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.86766e9 | + | 1.71540e9i | 1.00712 | + | 0.602445i | ||||
\(232\) | − | 1.93658e9i | − | 0.668471i | ||||||
\(233\) | −2.87004e9 | −0.973788 | −0.486894 | − | 0.873461i | \(-0.661870\pi\) | ||||
−0.486894 | + | 0.873461i | \(0.661870\pi\) | |||||||
\(234\) | 1.49392e9 | − | 8.01881e8i | 0.498268 | − | 0.267452i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.17485e9i | 1.02347i | ||||||||
\(237\) | −3.91698e9 | − | 2.34309e9i | −1.24153 | − | 0.742669i | ||||
\(238\) | − | 1.01749e10i | − | 3.17120i | ||||||
\(239\) | 2.06189e9i | 0.631937i | 0.948770 | + | 0.315968i | \(0.102329\pi\) | ||||
−0.948770 | + | 0.315968i | \(0.897671\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.87727e8 | 0.0556491 | 0.0278246 | − | 0.999613i | \(-0.491142\pi\) | ||||
0.0278246 | + | 0.999613i | \(0.491142\pi\) | |||||||
\(242\) | −1.34093e9 | −0.390971 | ||||||||
\(243\) | −3.14546e9 | + | 1.50457e9i | −0.902109 | + | 0.431507i | ||||
\(244\) | 3.55142e9 | 1.00194 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.73755e9 | − | 6.24812e9i | 1.02058 | − | 1.70612i | ||||
\(247\) | 6.89375e8i | 0.185211i | ||||||||
\(248\) | −8.25177e9 | −2.18142 | ||||||||
\(249\) | −4.08822e9 | − | 2.44552e9i | −1.06350 | − | 0.636172i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.87286e9i | − | 0.471856i | −0.971771 | − | 0.235928i | \(-0.924187\pi\) | ||
0.971771 | − | 0.235928i | \(-0.0758130\pi\) | |||||||
\(252\) | 1.12724e10 | − | 6.05064e9i | 2.79522 | − | 1.50037i | ||||
\(253\) | 5.66503e8i | 0.138268i | ||||||||
\(254\) | − | 6.40851e8i | − | 0.153965i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.71112e9 | −1.09689 | ||||||||
\(257\) | −2.62531e9 | −0.601795 | −0.300898 | − | 0.953656i | \(-0.597286\pi\) | ||||
−0.300898 | + | 0.953656i | \(0.597286\pi\) | |||||||
\(258\) | 5.94351e9 | − | 9.93585e9i | 1.34142 | − | 2.24247i | ||||
\(259\) | −6.99773e9 | −1.55510 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.05912e9 | + | 5.68497e8i | −0.228235 | + | 0.122508i | ||||
\(262\) | 5.08670e9i | 1.07952i | ||||||||
\(263\) | 7.30592e9 | 1.52705 | 0.763523 | − | 0.645781i | \(-0.223468\pi\) | ||||
0.763523 | + | 0.645781i | \(0.223468\pi\) | |||||||
\(264\) | 5.71221e9 | − | 9.54919e9i | 1.17595 | − | 1.96585i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.36945e9i | 1.47200i | ||||||||
\(267\) | −7.98898e8 | + | 1.33553e9i | −0.157198 | + | 0.262790i | ||||
\(268\) | 2.26011e10i | 4.38117i | ||||||||
\(269\) | − | 1.05642e9i | − | 0.201757i | −0.994899 | − | 0.100878i | \(-0.967835\pi\) | ||
0.994899 | − | 0.100878i | \(-0.0321653\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.55499e9 | −1.02993 | −0.514963 | − | 0.857212i | \(-0.672194\pi\) | ||||
−0.514963 | + | 0.857212i | \(0.672194\pi\) | |||||||
\(272\) | −1.67948e10 | −3.06831 | ||||||||
\(273\) | 1.93288e9 | + | 1.15623e9i | 0.347980 | + | 0.208158i | ||||
\(274\) | −8.14330e9 | −1.44477 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.86134e9 | + | 1.11343e9i | 0.320766 | + | 0.191878i | ||||
\(277\) | 5.81689e9i | 0.988034i | 0.869452 | + | 0.494017i | \(0.164472\pi\) | ||||
−0.869452 | + | 0.494017i | \(0.835528\pi\) | |||||||
\(278\) | 1.19359e10 | 1.99837 | ||||||||
\(279\) | 2.42237e9 | + | 4.51291e9i | 0.399782 | + | 0.744800i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7.93059e9i | − | 1.27198i | −0.771698 | − | 0.635990i | \(-0.780592\pi\) | ||
0.771698 | − | 0.635990i | \(-0.219408\pi\) | |||||||
\(282\) | −7.19905e9 | − | 4.30638e9i | −1.13836 | − | 0.680951i | ||||
\(283\) | − | 8.19763e9i | − | 1.27803i | −0.769193 | − | 0.639017i | \(-0.779341\pi\) | ||
0.769193 | − | 0.639017i | \(-0.220659\pi\) | |||||||
\(284\) | 5.96556e8i | 0.0917018i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.35857e9 | 0.501985 | ||||||||
\(287\) | 9.67154e9 | 1.42550 | ||||||||
\(288\) | −5.75271e9 | − | 1.07174e10i | −0.836185 | − | 1.55783i | ||||
\(289\) | 4.83032e9 | 0.692444 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.93617e9 | + | 9.92359e9i | −0.827817 | + | 1.38387i | ||||
\(292\) | 5.81707e9i | 0.800153i | ||||||||
\(293\) | −1.02001e10 | −1.38399 | −0.691995 | − | 0.721902i | \(-0.743268\pi\) | ||||
−0.691995 | + | 0.721902i | \(0.743268\pi\) | |||||||
\(294\) | 8.84085e9 | + | 5.28849e9i | 1.18333 | + | 0.707851i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.33022e10i | 3.03549i | ||||||||
\(297\) | −6.89934e9 | − | 3.20784e8i | −0.886710 | − | 0.0412274i | ||||
\(298\) | 2.48184e10i | 3.14709i | ||||||||
\(299\) | 3.81839e8i | 0.0477744i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.53798e10 | 1.87364 | ||||||||
\(302\) | 5.65026e9 | 0.679267 | ||||||||
\(303\) | −3.47112e9 | + | 5.80273e9i | −0.411812 | + | 0.688433i | ||||
\(304\) | 1.21640e10 | 1.42424 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.94635e9 | + | 1.85302e10i | 1.13443 | + | 2.11346i | ||||
\(307\) | 1.59327e10i | 1.79365i | 0.442389 | + | 0.896823i | \(0.354131\pi\) | ||||
−0.442389 | + | 0.896823i | \(0.645869\pi\) | |||||||
\(308\) | 2.53423e10 | 2.81607 | ||||||||
\(309\) | −5.38667e9 | + | 9.00498e9i | −0.590862 | + | 0.987754i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.47120e10i | − | 1.57265i | −0.617816 | − | 0.786323i | \(-0.711982\pi\) | ||
0.617816 | − | 0.786323i | \(-0.288018\pi\) | |||||||
\(312\) | 3.85019e9 | − | 6.43642e9i | 0.406316 | − | 0.679244i | ||||
\(313\) | 1.09163e10i | 1.13736i | 0.822560 | + | 0.568678i | \(0.192545\pi\) | ||||
−0.822560 | + | 0.568678i | \(0.807455\pi\) | |||||||
\(314\) | 6.99696e9i | 0.719765i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.46154e10 | −3.47153 | ||||||||
\(317\) | 1.31319e10 | 1.30044 | 0.650220 | − | 0.759746i | \(-0.274677\pi\) | ||||
0.650220 | + | 0.759746i | \(0.274677\pi\) | |||||||
\(318\) | −1.77335e10 | − | 1.06079e10i | −1.73414 | − | 1.03734i | ||||
\(319\) | −2.38108e9 | −0.229938 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.15020e9 | + | 4.27716e9i | 0.673439 | + | 0.402843i | ||||
\(322\) | 4.08188e9i | 0.379696i | ||||||||
\(323\) | −8.55085e9 | −0.785596 | ||||||||
\(324\) | −1.46142e10 | + | 2.20384e10i | −1.32616 | + | 1.99986i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 1.85710e10i | − | 1.64424i | ||||||
\(327\) | 1.26575e10 | + | 7.57156e9i | 1.10702 | + | 0.662208i | ||||
\(328\) | − | 3.22058e10i | − | 2.78253i | ||||||
\(329\) | − | 1.11435e10i | − | 0.951126i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.11274e9 | −0.425934 | −0.212967 | − | 0.977059i | \(-0.568313\pi\) | ||||
−0.212967 | + | 0.977059i | \(0.568313\pi\) | |||||||
\(332\) | −3.61288e10 | −2.97372 | ||||||||
\(333\) | 1.27440e10 | − | 6.84053e9i | 1.03640 | − | 0.556305i | ||||
\(334\) | −1.11885e9 | −0.0899052 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.04017e10 | − | 3.41058e10i | 1.60069 | − | 2.67591i | ||||
\(337\) | − | 2.37856e10i | − | 1.84414i | −0.387024 | − | 0.922070i | \(-0.626497\pi\) | ||
0.387024 | − | 0.922070i | \(-0.373503\pi\) | |||||||
\(338\) | −2.18010e10 | −1.67036 | ||||||||
\(339\) | −6.08587e8 | − | 3.64049e8i | −0.0460812 | − | 0.0275652i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.01458e10i | 0.750356i | ||||||||
\(342\) | −7.20389e9 | − | 1.34210e10i | −0.526578 | − | 0.981023i | ||||
\(343\) | − | 4.61417e9i | − | 0.333363i | ||||||
\(344\) | − | 5.12142e10i | − | 3.65727i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.42399e10 | 3.08681 | ||||||||
\(347\) | −3.67752e9 | −0.253652 | −0.126826 | − | 0.991925i | \(-0.540479\pi\) | ||||
−0.126826 | + | 0.991925i | \(0.540479\pi\) | |||||||
\(348\) | −4.67986e9 | + | 7.82340e9i | −0.319092 | + | 0.533432i | ||||
\(349\) | −8.39415e9 | −0.565816 | −0.282908 | − | 0.959147i | \(-0.591299\pi\) | ||||
−0.282908 | + | 0.959147i | \(0.591299\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.65034e9 | − | 2.16217e8i | −0.306377 | − | 0.0142450i | ||||
\(352\) | − | 2.40945e10i | − | 1.56945i | ||||||
\(353\) | 2.53478e10 | 1.63246 | 0.816229 | − | 0.577729i | \(-0.196061\pi\) | ||||
0.816229 | + | 0.577729i | \(0.196061\pi\) | |||||||
\(354\) | 6.33982e9 | − | 1.05984e10i | 0.403705 | − | 0.674880i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.18025e10i | 0.734805i | ||||||||
\(357\) | −1.43416e10 | + | 2.39750e10i | −0.882925 | + | 1.47600i | ||||
\(358\) | − | 2.27825e10i | − | 1.38698i | ||||||
\(359\) | − | 3.29745e9i | − | 0.198518i | −0.995062 | − | 0.0992590i | \(-0.968353\pi\) | ||
0.995062 | − | 0.0992590i | \(-0.0316472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.07904e10 | −0.635344 | ||||||||
\(362\) | 2.21233e10 | 1.28829 | ||||||||
\(363\) | 3.15962e9 | + | 1.89004e9i | 0.181973 | + | 0.108854i | ||||
\(364\) | 1.70814e10 | 0.973013 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.18554e10 | − | 7.09178e9i | −0.660683 | − | 0.395213i | ||||
\(367\) | − | 1.99945e10i | − | 1.10216i | −0.834451 | − | 0.551082i | \(-0.814215\pi\) | ||
0.834451 | − | 0.551082i | \(-0.185785\pi\) | |||||||
\(368\) | 6.73756e9 | 0.367377 | ||||||||
\(369\) | −1.76134e10 | + | 9.45427e9i | −0.950033 | + | 0.509944i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 2.74499e10i | − | 1.44892i | ||||||
\(372\) | 3.33356e10 | + | 1.99409e10i | 1.74075 | + | 1.04129i | ||||
\(373\) | − | 8.36869e9i | − | 0.432337i | −0.976356 | − | 0.216168i | \(-0.930644\pi\) | ||
0.976356 | − | 0.216168i | \(-0.0693561\pi\) | |||||||
\(374\) | 4.16590e10i | 2.12923i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.71074e10 | −1.85656 | ||||||||
\(377\) | −1.60491e9 | −0.0794485 | ||||||||
\(378\) | −4.97124e10 | − | 2.31137e9i | −2.43499 | − | 0.113215i | ||||
\(379\) | −1.46377e10 | −0.709440 | −0.354720 | − | 0.934973i | \(-0.615424\pi\) | ||||
−0.354720 | + | 0.934973i | \(0.615424\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.03280e8 | + | 1.51003e9i | −0.0428669 | + | 0.0716613i | ||||
\(382\) | − | 2.63685e9i | − | 0.123832i | ||||||
\(383\) | 9.54053e9 | 0.443381 | 0.221691 | − | 0.975117i | \(-0.428842\pi\) | ||||
0.221691 | + | 0.975117i | \(0.428842\pi\) | |||||||
\(384\) | 1.97823e9 | + | 1.18335e9i | 0.0909814 | + | 0.0544239i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 2.40754e10i | − | 1.08449i | ||||||
\(387\) | −2.80092e10 | + | 1.50343e10i | −1.24870 | + | 0.670255i | ||||
\(388\) | 8.76975e10i | 3.86955i | ||||||||
\(389\) | − | 2.67145e10i | − | 1.16667i | −0.812230 | − | 0.583337i | \(-0.801747\pi\) | ||
0.812230 | − | 0.583337i | \(-0.198253\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.73624e9 | −0.202641 | ||||||||
\(392\) | 4.55700e10 | 1.92990 | ||||||||
\(393\) | 7.16970e9 | − | 1.19857e10i | 0.300560 | − | 0.502451i | ||||
\(394\) | 3.90230e10 | 1.61933 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.61525e10 | + | 2.47730e10i | −1.87678 | + | 1.00739i | ||||
\(397\) | 7.88247e9i | 0.317322i | 0.987333 | + | 0.158661i | \(0.0507177\pi\) | ||||
−0.987333 | + | 0.158661i | \(0.949282\pi\) | |||||||
\(398\) | −5.67384e10 | −2.26123 | ||||||||
\(399\) | 1.03872e10 | − | 1.73645e10i | 0.409835 | − | 0.685127i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.90264e10i | 0.735834i | 0.929859 | + | 0.367917i | \(0.119929\pi\) | ||||
−0.929859 | + | 0.367917i | \(0.880071\pi\) | |||||||
\(402\) | 4.51319e10 | − | 7.54476e10i | 1.72814 | − | 2.88896i | ||||
\(403\) | 6.83853e9i | 0.259264i | ||||||||
\(404\) | 5.12803e10i | 1.92498i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.71566e10 | −0.631432 | ||||||||
\(407\) | 2.86507e10 | 1.04414 | ||||||||
\(408\) | 7.98359e10 | + | 4.77569e10i | 2.88110 | + | 1.72344i | ||||
\(409\) | 4.82473e9 | 0.172417 | 0.0862084 | − | 0.996277i | \(-0.472525\pi\) | ||||
0.0862084 | + | 0.996277i | \(0.472525\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.91879e10 | + | 1.14780e10i | 0.672451 | + | 0.402252i | ||||
\(412\) | 7.95795e10i | 2.76193i | ||||||||
\(413\) | 1.64054e10 | 0.563879 | ||||||||
\(414\) | −3.99018e9 | − | 7.43376e9i | −0.135828 | − | 0.253051i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 1.62403e10i | − | 0.542278i | ||||||
\(417\) | −2.81244e10 | − | 1.68237e10i | −0.930121 | − | 0.556387i | ||||
\(418\) | − | 3.01726e10i | − | 0.988342i | ||||||
\(419\) | − | 3.79749e10i | − | 1.23208i | −0.787713 | − | 0.616042i | \(-0.788735\pi\) | ||
0.787713 | − | 0.616042i | \(-0.211265\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.86781e9 | −0.186787 | −0.0933937 | − | 0.995629i | \(-0.529772\pi\) | ||||
−0.0933937 | + | 0.995629i | \(0.529772\pi\) | |||||||
\(422\) | −6.00799e10 | −1.89443 | ||||||||
\(423\) | 1.08932e10 | + | 2.02941e10i | 0.340245 | + | 0.633883i | ||||
\(424\) | −9.14070e10 | −2.82824 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.19125e9 | − | 1.99144e9i | 0.0361715 | − | 0.0604684i | ||||
\(427\) | − | 1.83512e10i | − | 0.552017i | ||||||
\(428\) | 6.31884e10 | 1.88305 | ||||||||
\(429\) | −7.91376e9 | − | 4.73391e9i | −0.233643 | − | 0.139763i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.50537e10i | 0.436250i | 0.975921 | + | 0.218125i | \(0.0699940\pi\) | ||||
−0.975921 | + | 0.218125i | \(0.930006\pi\) | |||||||
\(432\) | −3.81516e9 | + | 8.20555e10i | −0.109541 | + | 2.35599i | ||||
\(433\) | − | 2.72042e10i | − | 0.773899i | −0.922101 | − | 0.386950i | \(-0.873529\pi\) | ||
0.922101 | − | 0.386950i | \(-0.126471\pi\) | |||||||
\(434\) | 7.31042e10i | 2.06055i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.11858e11 | 3.09543 | ||||||||
\(437\) | 3.43034e9 | 0.0940615 | ||||||||
\(438\) | 1.16160e10 | − | 1.94187e10i | 0.315618 | − | 0.527623i | ||||
\(439\) | 3.48887e10 | 0.939348 | 0.469674 | − | 0.882840i | \(-0.344372\pi\) | ||||
0.469674 | + | 0.882840i | \(0.344372\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.33774e10 | − | 2.49224e10i | −0.353686 | − | 0.658923i | ||||
\(442\) | 2.80793e10i | 0.735695i | ||||||||
\(443\) | −1.32254e10 | −0.343395 | −0.171698 | − | 0.985150i | \(-0.554925\pi\) | ||||
−0.171698 | + | 0.985150i | \(0.554925\pi\) | |||||||
\(444\) | 5.63112e10 | − | 9.41363e10i | 1.44898 | − | 2.42229i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.36665e10i | 0.345397i | ||||||||
\(447\) | 3.49816e10 | − | 5.84793e10i | 0.876212 | − | 1.46478i | ||||
\(448\) | − | 4.80054e10i | − | 1.19173i | ||||||
\(449\) | 2.35824e9i | 0.0580232i | 0.999579 | + | 0.0290116i | \(0.00923598\pi\) | ||||
−0.999579 | + | 0.0290116i | \(0.990764\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.95980e10 | −0.957121 | ||||||||
\(452\) | −5.37825e9 | −0.128851 | ||||||||
\(453\) | −1.33136e10 | − | 7.96404e9i | −0.316157 | − | 0.189121i | ||||
\(454\) | −1.24174e11 | −2.92284 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.78231e10 | − | 3.45891e10i | −1.33734 | − | 0.799981i | ||||
\(457\) | − | 2.48874e10i | − | 0.570579i | −0.958441 | − | 0.285289i | \(-0.907910\pi\) | ||
0.958441 | − | 0.285289i | \(-0.0920897\pi\) | |||||||
\(458\) | −1.21312e11 | −2.75703 | ||||||||
\(459\) | 2.68191e9 | − | 5.76818e10i | 0.0604217 | − | 1.29954i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.32674e10i | 0.515163i | 0.966257 | + | 0.257581i | \(0.0829255\pi\) | ||||
−0.966257 | + | 0.257581i | \(0.917074\pi\) | |||||||
\(462\) | −8.45984e10 | − | 5.06057e10i | −1.85692 | − | 1.11079i | ||||
\(463\) | − | 3.52388e10i | − | 0.766828i | −0.923577 | − | 0.383414i | \(-0.874748\pi\) | ||
0.923577 | − | 0.383414i | \(-0.125252\pi\) | |||||||
\(464\) | 2.83187e10i | 0.610944i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.46687e10 | 1.79547 | ||||||||
\(467\) | −8.78873e10 | −1.84781 | −0.923907 | − | 0.382616i | \(-0.875023\pi\) | ||||
−0.923907 | + | 0.382616i | \(0.875023\pi\) | |||||||
\(468\) | −3.11081e10 | + | 1.66977e10i | −0.648469 | + | 0.348075i | ||||
\(469\) | 1.16786e11 | 2.41380 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.86222e9 | − | 1.64868e10i | 0.200397 | − | 0.335007i | ||||
\(472\) | − | 5.46292e10i | − | 1.10067i | ||||||
\(473\) | −6.29693e10 | −1.25801 | ||||||||
\(474\) | 1.15554e11 | + | 6.91231e10i | 2.28914 | + | 1.36934i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.11874e11i | 4.12715i | ||||||||
\(477\) | 2.68332e10 | + | 4.99907e10i | 0.518321 | + | 0.965641i | ||||
\(478\) | − | 6.08275e10i | − | 1.16517i | ||||||
\(479\) | 7.91032e10i | 1.50263i | 0.659944 | + | 0.751315i | \(0.270580\pi\) | ||||
−0.659944 | + | 0.751315i | \(0.729420\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.93113e10 | 0.360771 | ||||||||
\(482\) | −5.53811e9 | −0.102606 | ||||||||
\(483\) | 5.75341e9 | − | 9.61806e9i | 0.105715 | − | 0.176725i | ||||
\(484\) | 2.79224e10 | 0.508829 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.27938e10 | − | 4.43862e10i | 1.66331 | − | 0.795615i | ||||
\(487\) | − | 5.78470e10i | − | 1.02841i | −0.857668 | − | 0.514203i | \(-0.828088\pi\) | ||
0.857668 | − | 0.514203i | \(-0.171912\pi\) | |||||||
\(488\) | −6.11087e10 | −1.07752 | ||||||||
\(489\) | −2.61758e10 | + | 4.37585e10i | −0.457788 | + | 0.765292i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1.07166e11i | − | 1.84387i | −0.387339 | − | 0.921937i | \(-0.626606\pi\) | ||
0.387339 | − | 0.921937i | \(-0.373394\pi\) | |||||||
\(492\) | −7.78275e10 | + | 1.30105e11i | −1.32823 | + | 2.22042i | ||||
\(493\) | − | 1.99070e10i | − | 0.336990i | ||||||
\(494\) | − | 2.03371e10i | − | 0.341493i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.20666e11 | 1.99370 | ||||||||
\(497\) | 3.08257e9 | 0.0505229 | ||||||||
\(498\) | 1.20606e11 | + | 7.21451e10i | 1.96088 | + | 1.17298i | ||||
\(499\) | −2.45077e9 | −0.0395276 | −0.0197638 | − | 0.999805i | \(-0.506291\pi\) | ||||
−0.0197638 | + | 0.999805i | \(0.506291\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.63632e9 | + | 1.57701e9i | 0.0418454 | + | 0.0250314i | ||||
\(502\) | 5.52509e10i | 0.870010i | ||||||||
\(503\) | 4.84386e10 | 0.756694 | 0.378347 | − | 0.925664i | \(-0.376493\pi\) | ||||
0.378347 | + | 0.925664i | \(0.376493\pi\) | |||||||
\(504\) | −1.93963e11 | + | 1.04112e11i | −3.00606 | + | 1.61354i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 1.67123e10i | − | 0.254938i | ||||||
\(507\) | 5.13693e10 | + | 3.07285e10i | 0.777449 | + | 0.465061i | ||||
\(508\) | 1.33445e10i | 0.200377i | ||||||||
\(509\) | − | 3.20903e10i | − | 0.478082i | −0.971009 | − | 0.239041i | \(-0.923167\pi\) | ||
0.971009 | − | 0.239041i | \(-0.0768330\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.00585e10 | 0.440842 | ||||||||
\(512\) | 1.31697e11 | 1.91644 | ||||||||
\(513\) | −1.94244e9 | + | 4.17775e10i | −0.0280464 | + | 0.603216i | ||||
\(514\) | 7.74490e10 | 1.10959 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.23763e11 | + | 2.06896e11i | −1.74578 | + | 2.91845i | ||||
\(517\) | 4.56246e10i | 0.638611i | ||||||||
\(518\) | 2.06439e11 | 2.86730 | ||||||||
\(519\) | −1.04242e11 | − | 6.23562e10i | −1.43672 | − | 0.859430i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.76727e10i | 0.918465i | 0.888316 | + | 0.459232i | \(0.151875\pi\) | ||||
−0.888316 | + | 0.459232i | \(0.848125\pi\) | |||||||
\(522\) | 3.12449e10 | − | 1.67711e10i | 0.420821 | − | 0.225882i | ||||
\(523\) | − | 6.05025e10i | − | 0.808661i | −0.914613 | − | 0.404330i | \(-0.867505\pi\) | ||
0.914613 | − | 0.404330i | \(-0.132495\pi\) | |||||||
\(524\) | − | 1.05921e11i | − | 1.40494i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.15531e11 | −2.81557 | ||||||||
\(527\) | −8.48236e10 | −1.09970 | ||||||||
\(528\) | −8.35301e10 | + | 1.39639e11i | −1.07475 | + | 1.79668i | ||||
\(529\) | −7.64109e10 | −0.975737 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.98769e10 | + | 1.60368e10i | −0.375800 | + | 0.201716i | ||||
\(532\) | − | 1.53455e11i | − | 1.91573i | ||||||
\(533\) | −2.66901e10 | −0.330706 | ||||||||
\(534\) | 2.35682e10 | − | 3.93993e10i | 0.289842 | − | 0.484533i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 3.88894e11i | − | 4.71164i | ||||||
\(537\) | −3.21120e10 | + | 5.36822e10i | −0.386163 | + | 0.645555i | ||||
\(538\) | 3.11654e10i | 0.372000i | ||||||||
\(539\) | − | 5.60296e10i | − | 0.663839i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.66748e10 | −0.311396 | −0.155698 | − | 0.987805i | \(-0.549763\pi\) | ||||
−0.155698 | + | 0.987805i | \(0.549763\pi\) | |||||||
\(542\) | 1.63877e11 | 1.89898 | ||||||||
\(543\) | −5.21287e10 | − | 3.11828e10i | −0.599622 | − | 0.358687i | ||||
\(544\) | 2.01442e11 | 2.30014 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.70217e10 | − | 3.41097e10i | −0.641608 | − | 0.383802i | ||||
\(547\) | − | 1.39645e11i | − | 1.55983i | −0.625885 | − | 0.779915i | \(-0.715262\pi\) | ||
0.625885 | − | 0.779915i | \(-0.284738\pi\) | |||||||
\(548\) | 1.69569e11 | 1.88029 | ||||||||
\(549\) | 1.79389e10 | + | 3.34205e10i | 0.197473 | + | 0.367895i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.44181e10i | 0.156423i | ||||||||
\(552\) | −3.20278e10 | − | 1.91586e10i | −0.344961 | − | 0.206352i | ||||
\(553\) | 1.78868e11i | 1.91263i | ||||||||
\(554\) | − | 1.71603e11i | − | 1.82174i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.48544e11 | −2.60078 | ||||||||
\(557\) | −1.88635e10 | −0.195975 | −0.0979876 | − | 0.995188i | \(-0.531241\pi\) | ||||
−0.0979876 | + | 0.995188i | \(0.531241\pi\) | |||||||
\(558\) | −7.14619e10 | − | 1.33135e11i | −0.737120 | − | 1.37327i | ||||
\(559\) | −4.24431e10 | −0.434670 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.87184e10 | − | 9.81605e10i | 0.592820 | − | 0.991026i | ||||
\(562\) | 2.33959e11i | 2.34528i | ||||||||
\(563\) | 3.06642e10 | 0.305210 | 0.152605 | − | 0.988287i | \(-0.451234\pi\) | ||||
0.152605 | + | 0.988287i | \(0.451234\pi\) | |||||||
\(564\) | 1.49907e11 | + | 8.96725e10i | 1.48151 | + | 0.886222i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.41837e11i | 2.35644i | ||||||||
\(567\) | 1.13879e11 | + | 7.55159e10i | 1.10182 | + | 0.730645i | ||||
\(568\) | − | 1.02649e10i | − | 0.0986187i | ||||||
\(569\) | 1.85504e11i | 1.76972i | 0.465861 | + | 0.884858i | \(0.345745\pi\) | ||||
−0.465861 | + | 0.884858i | \(0.654255\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.50195e10 | 0.799786 | 0.399893 | − | 0.916562i | \(-0.369047\pi\) | ||||
0.399893 | + | 0.916562i | \(0.369047\pi\) | |||||||
\(572\) | −6.99361e10 | −0.653307 | ||||||||
\(573\) | −3.71664e9 | + | 6.21317e9i | −0.0344772 | + | 0.0576362i | ||||
\(574\) | −2.85319e11 | −2.62835 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.69270e10 | + | 8.74257e10i | 0.426317 | + | 0.794235i | ||||
\(577\) | 1.80485e11i | 1.62831i | 0.580648 | + | 0.814155i | \(0.302799\pi\) | ||||
−0.580648 | + | 0.814155i | \(0.697201\pi\) | |||||||
\(578\) | −1.42499e11 | −1.27673 | ||||||||
\(579\) | −3.39343e10 | + | 5.67284e10i | −0.301942 | + | 0.504762i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.86688e11i | 1.63837i | ||||||||
\(582\) | 1.75122e11 | − | 2.92754e11i | 1.52633 | − | 2.55159i | ||||
\(583\) | 1.12387e11i | 0.972845i | ||||||||
\(584\) | − | 1.00093e11i | − | 0.860507i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.00911e11 | 2.55181 | ||||||||
\(587\) | 3.34184e10 | 0.281471 | 0.140736 | − | 0.990047i | \(-0.455053\pi\) | ||||
0.140736 | + | 0.990047i | \(0.455053\pi\) | |||||||
\(588\) | −1.84094e11 | − | 1.10123e11i | −1.54004 | − | 0.921231i | ||||
\(589\) | 6.14356e10 | 0.510457 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.19494e10 | − | 5.50030e10i | −0.753701 | − | 0.450854i | ||||
\(592\) | − | 3.40749e11i | − | 2.77427i | ||||||
\(593\) | 1.21264e11 | 0.980647 | 0.490323 | − | 0.871541i | \(-0.336879\pi\) | ||||
0.490323 | + | 0.871541i | \(0.336879\pi\) | |||||||
\(594\) | 2.03536e11 | + | 9.46339e9i | 1.63492 | + | 0.0760153i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 5.16798e11i | − | 4.09577i | ||||||
\(597\) | 1.33692e11 | + | 7.99728e10i | 1.05246 | + | 0.629571i | ||||
\(598\) | − | 1.12646e10i | − | 0.0880867i | ||||||
\(599\) | 1.08145e11i | 0.840041i | 0.907515 | + | 0.420020i | \(0.137977\pi\) | ||||
−0.907515 | + | 0.420020i | \(0.862023\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.99467e11 | 1.52888 | 0.764440 | − | 0.644695i | \(-0.223016\pi\) | ||||
0.764440 | + | 0.644695i | \(0.223016\pi\) | |||||||
\(602\) | −4.53718e11 | −3.45462 | ||||||||
\(603\) | −2.12687e11 | + | 1.14163e11i | −1.60869 | + | 0.863486i | ||||
\(604\) | −1.17656e11 | −0.884030 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.02401e11 | − | 1.71185e11i | 0.759301 | − | 1.26934i | ||||
\(607\) | − | 7.47882e10i | − | 0.550907i | −0.961314 | − | 0.275453i | \(-0.911172\pi\) | ||
0.961314 | − | 0.275453i | \(-0.0888280\pi\) | |||||||
\(608\) | −1.45899e11 | −1.06767 | ||||||||
\(609\) | 4.04258e10 | + | 2.41822e10i | 0.293893 | + | 0.175803i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.07522e10i | 0.220654i | ||||||||
\(612\) | −2.07114e11 | − | 3.85857e11i | −1.47640 | − | 2.75056i | ||||
\(613\) | − | 2.70342e11i | − | 1.91457i | −0.289148 | − | 0.957284i | \(-0.593372\pi\) | ||
0.289148 | − | 0.957284i | \(-0.406628\pi\) | |||||||
\(614\) | − | 4.70030e11i | − | 3.30713i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.36062e11 | −3.02848 | ||||||||
\(617\) | 7.48975e10 | 0.516805 | 0.258403 | − | 0.966037i | \(-0.416804\pi\) | ||||
0.258403 | + | 0.966037i | \(0.416804\pi\) | |||||||
\(618\) | 1.58911e11 | − | 2.65655e11i | 1.08943 | − | 1.82122i | ||||
\(619\) | 9.53847e10 | 0.649705 | 0.324852 | − | 0.945765i | \(-0.394685\pi\) | ||||
0.324852 | + | 0.945765i | \(0.394685\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.07590e9 | + | 2.31402e10i | −0.00723446 | + | 0.155597i | ||||
\(622\) | 4.34018e11i | 2.89965i | ||||||||
\(623\) | 6.09867e10 | 0.404839 | ||||||||
\(624\) | −5.63016e10 | + | 9.41203e10i | −0.371349 | + | 0.620790i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 3.22039e11i | − | 2.09706i | ||||||
\(627\) | −4.25282e10 | + | 7.10951e10i | −0.275174 | + | 0.460013i | ||||
\(628\) | − | 1.45699e11i | − | 0.936736i | ||||||
\(629\) | 2.39534e11i | 1.53025i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.63469e11 | −1.66193 | −0.830965 | − | 0.556325i | \(-0.812211\pi\) | ||||
−0.830965 | + | 0.556325i | \(0.812211\pi\) | |||||||
\(632\) | 5.95623e11 | 3.73339 | ||||||||
\(633\) | 1.41565e11 | + | 8.46826e10i | 0.881743 | + | 0.527448i | ||||
\(634\) | −3.87402e11 | −2.39776 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.69267e11 | + | 2.20891e11i | 2.25690 | + | 1.35005i | ||||
\(637\) | − | 3.77655e10i | − | 0.229371i | ||||||
\(638\) | 7.02438e10 | 0.423960 | ||||||||
\(639\) | −5.61387e9 | + | 3.01332e9i | −0.0336712 | + | 0.0180735i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.27087e11i | 0.752780i | 0.926461 | + | 0.376390i | \(0.122835\pi\) | ||||
−0.926461 | + | 0.376390i | \(0.877165\pi\) | |||||||
\(642\) | −2.10937e11 | − | 1.26180e11i | −1.24169 | − | 0.742764i | ||||
\(643\) | 2.47669e11i | 1.44887i | 0.689345 | + | 0.724433i | \(0.257899\pi\) | ||||
−0.689345 | + | 0.724433i | \(0.742101\pi\) | |||||||
\(644\) | − | 8.49975e10i | − | 0.494155i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.52257e11 | 1.44848 | ||||||||
\(647\) | 1.34645e11 | 0.768374 | 0.384187 | − | 0.923255i | \(-0.374482\pi\) | ||||
0.384187 | + | 0.923255i | \(0.374482\pi\) | |||||||
\(648\) | 2.51465e11 | − | 3.79211e11i | 1.42619 | − | 2.15071i | ||||
\(649\) | −6.71682e10 | −0.378603 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.03040e11 | − | 1.72254e11i | 0.573699 | − | 0.959061i | ||||
\(652\) | 3.86706e11i | 2.13989i | ||||||||
\(653\) | −1.95881e11 | −1.07731 | −0.538655 | − | 0.842527i | \(-0.681067\pi\) | ||||
−0.538655 | + | 0.842527i | \(0.681067\pi\) | |||||||
\(654\) | −3.73407e11 | − | 2.23368e11i | −2.04113 | − | 1.22098i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.70948e11i | 2.54307i | ||||||||
\(657\) | −5.47414e10 | + | 2.93832e10i | −0.293802 | + | 0.157702i | ||||
\(658\) | 3.28743e11i | 1.75369i | ||||||||
\(659\) | − | 1.11563e11i | − | 0.591531i | −0.955261 | − | 0.295765i | \(-0.904425\pi\) | ||
0.955261 | − | 0.295765i | \(-0.0955747\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.12263e11 | −1.11191 | −0.555953 | − | 0.831214i | \(-0.687647\pi\) | ||||
−0.555953 | + | 0.831214i | \(0.687647\pi\) | |||||||
\(662\) | 1.50830e11 | 0.785338 | ||||||||
\(663\) | 3.95778e10 | − | 6.61629e10i | 0.204832 | − | 0.342421i | ||||
\(664\) | 6.21663e11 | 3.19803 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.75959e11 | + | 2.01801e11i | −1.91093 | + | 1.02572i | ||||
\(667\) | 7.98607e9i | 0.0403487i | ||||||||
\(668\) | 2.32979e10 | 0.117007 | ||||||||
\(669\) | 1.92630e10 | − | 3.22022e10i | 0.0961654 | − | 0.160761i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.51349e10i | 0.370639i | ||||||||
\(672\) | −2.44703e11 | + | 4.09075e11i | −1.19995 | + | 2.00597i | ||||
\(673\) | − | 5.44544e10i | − | 0.265444i | −0.991153 | − | 0.132722i | \(-0.957628\pi\) | ||
0.991153 | − | 0.132722i | \(-0.0423717\pi\) | |||||||
\(674\) | 7.01695e11i | 3.40023i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.53965e11 | 2.17388 | ||||||||
\(677\) | −3.73397e11 | −1.77753 | −0.888763 | − | 0.458367i | \(-0.848435\pi\) | ||||
−0.888763 | + | 0.458367i | \(0.848435\pi\) | |||||||
\(678\) | 1.79538e10 | + | 1.07398e10i | 0.0849647 | + | 0.0508248i | ||||
\(679\) | 4.53158e11 | 2.13192 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.92588e11 | + | 1.75023e11i | 1.36041 | + | 0.813778i | ||||
\(682\) | − | 2.99309e11i | − | 1.38351i | ||||||
\(683\) | −3.36543e11 | −1.54653 | −0.773263 | − | 0.634085i | \(-0.781377\pi\) | ||||
−0.773263 | + | 0.634085i | \(0.781377\pi\) | |||||||
\(684\) | 1.50008e11 | + | 2.79467e11i | 0.685313 | + | 1.27675i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.36122e11i | 0.614656i | ||||||||
\(687\) | 2.85846e11 | + | 1.70989e11i | 1.28323 | + | 0.767613i | ||||
\(688\) | 7.48910e11i | 3.34253i | ||||||||
\(689\) | 7.57523e10i | 0.336139i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.37252e11 | −0.602013 | −0.301007 | − | 0.953622i | \(-0.597323\pi\) | ||||
−0.301007 | + | 0.953622i | \(0.597323\pi\) | |||||||
\(692\) | −9.21215e11 | −4.01732 | ||||||||
\(693\) | 1.28009e11 | + | 2.38483e11i | 0.555019 | + | 1.03401i | ||||
\(694\) | 1.08490e11 | 0.467684 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.05258e10 | − | 1.34616e11i | 0.343161 | − | 0.573668i | ||||
\(697\) | − | 3.31058e11i | − | 1.40273i | ||||||
\(698\) | 2.47635e11 | 1.04325 | ||||||||
\(699\) | −1.99504e11 | − | 1.19341e11i | −0.835684 | − | 0.499896i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.12721e11i | 1.70917i | 0.519316 | + | 0.854583i | \(0.326187\pi\) | ||||
−0.519316 | + | 0.854583i | \(0.673813\pi\) | |||||||
\(702\) | 1.37189e11 | + | 6.37859e9i | 0.564900 | + | 0.0262649i | ||||
\(703\) | − | 1.73488e11i | − | 0.710311i | ||||||
\(704\) | 1.96548e11i | 0.800160i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.47783e11 | −3.00993 | ||||||||
\(707\) | 2.64980e11 | 1.06056 | ||||||||
\(708\) | −1.32015e11 | + | 2.20692e11i | −0.525401 | + | 0.878321i | ||||
\(709\) | −1.59025e11 | −0.629333 | −0.314667 | − | 0.949202i | \(-0.601893\pi\) | ||||
−0.314667 | + | 0.949202i | \(0.601893\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.74850e11 | − | 3.25747e11i | −0.684205 | − | 1.27468i | ||||
\(712\) | − | 2.03083e11i | − | 0.790231i | ||||||
\(713\) | 3.40287e10 | 0.131670 | ||||||||
\(714\) | 4.23089e11 | − | 7.07284e11i | 1.62794 | − | 2.72145i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.74405e11i | 1.80508i | ||||||||
\(717\) | −8.57364e10 | + | 1.43327e11i | −0.324406 | + | 0.542314i | ||||
\(718\) | 9.72775e10i | 0.366028i | ||||||||
\(719\) | − | 1.83117e11i | − | 0.685195i | −0.939482 | − | 0.342597i | \(-0.888693\pi\) | ||
0.939482 | − | 0.342597i | \(-0.111307\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.11210e11 | 1.52168 | ||||||||
\(722\) | 3.18326e11 | 1.17145 | ||||||||
\(723\) | 1.30494e10 | + | 7.80596e9i | 0.0477569 | + | 0.0285676i | ||||
\(724\) | −4.60676e11 | −1.67665 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −9.32114e10 | − | 5.57579e10i | −0.335523 | − | 0.200706i | ||||
\(727\) | − | 2.59798e10i | − | 0.0930032i | −0.998918 | − | 0.0465016i | \(-0.985193\pi\) | ||
0.998918 | − | 0.0465016i | \(-0.0148073\pi\) | |||||||
\(728\) | −2.93918e11 | −1.04641 | ||||||||
\(729\) | −2.81211e11 | − | 2.62064e10i | −0.995686 | − | 0.0927891i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 5.26454e11i | − | 1.84370i | ||||||
\(732\) | 2.46868e11 | + | 1.47673e11i | 0.859844 | + | 0.514348i | ||||
\(733\) | − | 6.63035e10i | − | 0.229678i | −0.993384 | − | 0.114839i | \(-0.963365\pi\) | ||
0.993384 | − | 0.114839i | \(-0.0366353\pi\) | |||||||
\(734\) | 5.89855e11i | 2.03218i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.08123e10 | −0.275401 | ||||||||
\(737\) | −4.78156e11 | −1.62069 | ||||||||
\(738\) | 5.19612e11 | − | 2.78909e11i | 1.75168 | − | 0.940237i | ||||
\(739\) | 1.53919e11 | 0.516078 | 0.258039 | − | 0.966135i | \(-0.416924\pi\) | ||||
0.258039 | + | 0.966135i | \(0.416924\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.86652e10 | + | 4.79201e10i | −0.0950785 | + | 0.158944i | ||||
\(742\) | 8.09795e11i | 2.67153i | ||||||||
\(743\) | 3.56107e9 | 0.0116849 | 0.00584246 | − | 0.999983i | \(-0.498140\pi\) | ||||
0.00584246 | + | 0.999983i | \(0.498140\pi\) | |||||||
\(744\) | −5.73600e11 | − | 3.43121e11i | −1.87205 | − | 1.11984i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.46884e11i | 0.797145i | ||||||||
\(747\) | −1.82494e11 | − | 3.39989e11i | −0.586092 | − | 1.09190i | ||||
\(748\) | − | 8.67472e11i | − | 2.77108i | ||||||
\(749\) | − | 3.26512e11i | − | 1.03746i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.54316e10 | −0.111386 | −0.0556931 | − | 0.998448i | \(-0.517737\pi\) | ||||
−0.0556931 | + | 0.998448i | \(0.517737\pi\) | |||||||
\(752\) | 5.42624e11 | 1.69679 | ||||||||
\(753\) | 7.78761e10 | − | 1.30187e11i | 0.242228 | − | 0.404937i | ||||
\(754\) | 4.73463e10 | 0.146487 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.03517e12 | + | 4.81300e10i | 3.16901 | + | 0.147343i | ||||
\(757\) | − | 3.97220e11i | − | 1.20962i | −0.796371 | − | 0.604808i | \(-0.793250\pi\) | ||
0.796371 | − | 0.604808i | \(-0.206750\pi\) | |||||||
\(758\) | 4.31824e11 | 1.30807 | ||||||||
\(759\) | −2.35560e10 | + | 3.93790e10i | −0.0709799 | + | 0.118658i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 8.97779e10i | − | 0.267689i | −0.991002 | − | 0.133845i | \(-0.957268\pi\) | ||
0.991002 | − | 0.133845i | \(-0.0427323\pi\) | |||||||
\(762\) | 2.66475e10 | − | 4.45471e10i | 0.0790382 | − | 0.132129i | ||||
\(763\) | − | 5.78002e11i | − | 1.70542i | ||||||
\(764\) | 5.49076e10i | 0.161161i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.81454e11 | −0.817508 | ||||||||
\(767\) | −4.52732e10 | −0.130816 | ||||||||
\(768\) | −3.27482e11 | − | 1.95895e11i | −0.941330 | − | 0.563092i | ||||
\(769\) | 4.29746e11 | 1.22887 | 0.614436 | − | 0.788967i | \(-0.289384\pi\) | ||||
0.614436 | + | 0.788967i | \(0.289384\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.82492e11 | − | 1.09164e11i | −0.516448 | − | 0.308933i | ||||
\(772\) | 5.01325e11i | 1.41140i | ||||||||
\(773\) | −1.11151e11 | −0.311312 | −0.155656 | − | 0.987811i | \(-0.549749\pi\) | ||||
−0.155656 | + | 0.987811i | \(0.549749\pi\) | |||||||
\(774\) | 8.26295e11 | − | 4.43526e11i | 2.30235 | − | 1.23582i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 1.50900e12i | − | 4.16142i | ||||||
\(777\) | −4.86429e11 | − | 2.90976e11i | −1.33455 | − | 0.798313i | ||||
\(778\) | 7.88102e11i | 2.15112i | ||||||||
\(779\) | 2.39777e11i | 0.651116i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.26209e10 | −0.0339224 | ||||||||
\(782\) | 1.39723e11 | 0.373630 | ||||||||
\(783\) | −9.72609e10 | − | 4.52213e9i | −0.258756 | − | 0.0120308i | ||||
\(784\) | −6.66374e11 | −1.76382 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.11512e11 | + | 3.53589e11i | −0.554173 | + | 0.926420i | ||||
\(787\) | − | 3.22875e11i | − | 0.841658i | −0.907140 | − | 0.420829i | \(-0.861739\pi\) | ||
0.907140 | − | 0.420829i | \(-0.138261\pi\) | |||||||
\(788\) | −8.12583e11 | −2.10748 | ||||||||
\(789\) | 5.07852e11 | + | 3.03791e11i | 1.31048 | + | 0.783912i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.77910e10i | 0.0709901i | ||||||||
\(792\) | 7.94139e11 | − | 4.26265e11i | 2.01835 | − | 1.08338i | ||||
\(793\) | 5.06430e10i | 0.128064i | ||||||||
\(794\) | − | 2.32540e11i | − | 0.585080i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.18147e12 | 2.94287 | ||||||||
\(797\) | 4.82426e10 | 0.119563 | 0.0597815 | − | 0.998211i | \(-0.480960\pi\) | ||||
0.0597815 | + | 0.998211i | \(0.480960\pi\) | |||||||
\(798\) | −3.06433e11 | + | 5.12268e11i | −0.755655 | + | 1.26324i | ||||
\(799\) | −3.81444e11 | −0.935930 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.11067e11 | + | 5.96166e10i | −0.269807 | + | 0.144823i | ||||
\(802\) | − | 5.61296e11i | − | 1.35673i | ||||||
\(803\) | −1.23068e11 | −0.295993 | ||||||||
\(804\) | −9.39787e11 | + | 1.57106e12i | −2.24908 | + | 3.75983i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 2.01743e11i | − | 0.478033i | ||||||
\(807\) | 4.39276e10 | − | 7.34345e10i | 0.103572 | − | 0.173143i | ||||
\(808\) | − | 8.82373e11i | − | 2.07017i | ||||||
\(809\) | 4.74471e10i | 0.110768i | 0.998465 | + | 0.0553842i | \(0.0176384\pi\) | ||||
−0.998465 | + | 0.0553842i | \(0.982362\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.83507e11 | 0.424199 | 0.212100 | − | 0.977248i | \(-0.431970\pi\) | ||||
0.212100 | + | 0.977248i | \(0.431970\pi\) | |||||||
\(812\) | 3.57254e11 | 0.821775 | ||||||||
\(813\) | −3.86141e11 | − | 2.30985e11i | −0.883861 | − | 0.528715i | ||||
\(814\) | −8.45219e11 | −1.92518 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.16745e12 | − | 6.98352e11i | −2.63315 | − | 1.57512i | ||||
\(817\) | 3.81298e11i | 0.855807i | ||||||||
\(818\) | −1.42334e11 | −0.317903 | ||||||||
\(819\) | 8.62817e10 | + | 1.60744e11i | 0.191771 | + | 0.357273i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 8.94845e10i | − | 0.196959i | −0.995139 | − | 0.0984794i | \(-0.968602\pi\) | ||
0.995139 | − | 0.0984794i | \(-0.0313978\pi\) | |||||||
\(822\) | −5.66060e11 | − | 3.38610e11i | −1.23987 | − | 0.741674i | ||||
\(823\) | 8.24619e11i | 1.79744i | 0.438524 | + | 0.898719i | \(0.355501\pi\) | ||||
−0.438524 | + | 0.898719i | \(0.644499\pi\) | |||||||
\(824\) | − | 1.36931e12i | − | 2.97026i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.83973e11 | −1.03968 | ||||||||
\(827\) | 8.26757e11 | 1.76749 | 0.883743 | − | 0.467973i | \(-0.155015\pi\) | ||||
0.883743 | + | 0.467973i | \(0.155015\pi\) | |||||||
\(828\) | 8.30880e10 | + | 1.54794e11i | 0.176774 | + | 0.329332i | ||||
\(829\) | 2.54789e11 | 0.539465 | 0.269732 | − | 0.962935i | \(-0.413065\pi\) | ||||
0.269732 | + | 0.962935i | \(0.413065\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.41875e11 | + | 4.04346e11i | −0.507209 | + | 0.847909i | ||||
\(832\) | 1.32479e11i | 0.276473i | ||||||||
\(833\) | 4.68435e11 | 0.972903 | ||||||||
\(834\) | 8.29695e11 | + | 4.96314e11i | 1.71496 | + | 1.02587i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.28288e11i | 1.28627i | ||||||||
\(837\) | −1.92688e10 | + | 4.14429e11i | −0.0392603 | + | 0.844400i | ||||
\(838\) | 1.12029e12i | 2.27172i | ||||||||
\(839\) | − | 6.07397e11i | − | 1.22581i | −0.790155 | − | 0.612907i | \(-0.790000\pi\) | ||
0.790155 | − | 0.612907i | \(-0.210000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.66680e11 | 0.932900 | ||||||||
\(842\) | 1.73106e11 | 0.344400 | ||||||||
\(843\) | 3.29766e11 | − | 5.51274e11i | 0.652973 | − | 1.09158i | ||||
\(844\) | 1.25105e12 | 2.46550 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.21358e11 | − | 5.98694e11i | −0.627346 | − | 1.16876i | ||||
\(847\) | − | 1.44283e11i | − | 0.280338i | ||||||
\(848\) | 1.33665e12 | 2.58485 | ||||||||
\(849\) | 3.40870e11 | − | 5.69837e11i | 0.656081 | − | 1.09678i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 9.60937e10i | − | 0.183222i | ||||||
\(852\) | −2.48057e10 | + | 4.14681e10i | −0.0470753 | + | 0.0786965i | ||||
\(853\) | 1.34856e11i | 0.254726i | 0.991856 | + | 0.127363i | \(0.0406514\pi\) | ||||
−0.991856 | + | 0.127363i | \(0.959349\pi\) | |||||||
\(854\) | 5.41376e11i | 1.01781i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.08727e12 | −2.02509 | ||||||||
\(857\) | −7.33386e11 | −1.35959 | −0.679797 | − | 0.733400i | \(-0.737932\pi\) | ||||
−0.679797 | + | 0.733400i | \(0.737932\pi\) | |||||||
\(858\) | 2.33463e11 | + | 1.39655e11i | 0.430793 | + | 0.257695i | ||||
\(859\) | −4.51837e11 | −0.829868 | −0.414934 | − | 0.909852i | \(-0.636195\pi\) | ||||
−0.414934 | + | 0.909852i | \(0.636195\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.72292e11 | + | 4.02157e11i | 1.22334 | + | 0.731784i | ||||
\(862\) | − | 4.44098e11i | − | 0.804359i | ||||||
\(863\) | 6.73082e11 | 1.21346 | 0.606729 | − | 0.794909i | \(-0.292481\pi\) | ||||
0.606729 | + | 0.794909i | \(0.292481\pi\) | |||||||
\(864\) | 4.57601e10 | − | 9.84198e11i | 0.0821168 | − | 1.76615i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.02548e11i | 1.42692i | ||||||||
\(867\) | 3.35768e11 | + | 2.00852e11i | 0.594241 | + | 0.355467i | ||||
\(868\) | − | 1.52226e12i | − | 2.68170i | ||||||
\(869\) | − | 7.32335e11i | − | 1.28419i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.22290e11 | −0.559983 | ||||||||
\(872\) | −1.92472e12 | −3.32891 | ||||||||
\(873\) | −8.25275e11 | + | 4.42978e11i | −1.42083 | + | 0.762650i | ||||
\(874\) | −1.01198e11 | −0.173431 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.41882e11 | + | 4.04359e11i | −0.410760 | + | 0.686674i | ||||
\(877\) | 8.29492e11i | 1.40221i | 0.713057 | + | 0.701106i | \(0.247310\pi\) | ||||
−0.713057 | + | 0.701106i | \(0.752690\pi\) | |||||||
\(878\) | −1.02925e12 | −1.73197 | ||||||||
\(879\) | −7.09033e11 | − | 4.24135e11i | −1.18771 | − | 0.710474i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.16546e11i | − | 0.193461i | −0.995311 | − | 0.0967305i | \(-0.969161\pi\) | ||
0.995311 | − | 0.0967305i | \(-0.0308385\pi\) | |||||||
\(882\) | 3.94646e11 | + | 7.35231e11i | 0.652128 | + | 1.21493i | ||||
\(883\) | − | 4.57775e11i | − | 0.753025i | −0.926412 | − | 0.376512i | \(-0.877123\pi\) | ||
0.926412 | − | 0.376512i | \(-0.122877\pi\) | |||||||
\(884\) | − | 5.84700e11i | − | 0.957468i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.90161e11 | 0.633153 | ||||||||
\(887\) | 8.01818e11 | 1.29533 | 0.647667 | − | 0.761924i | \(-0.275745\pi\) | ||||
0.647667 | + | 0.761924i | \(0.275745\pi\) | |||||||
\(888\) | −9.68939e11 | + | 1.61979e12i | −1.55828 | + | 2.60500i | ||||
\(889\) | 6.89550e10 | 0.110397 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.66251e11 | − | 3.09183e11i | −0.739791 | − | 0.490575i | ||||
\(892\) | − | 2.84580e11i | − | 0.449516i | ||||||
\(893\) | 2.76270e11 | 0.434438 | ||||||||
\(894\) | −1.03199e12 | + | 1.72519e12i | −1.61556 | + | 2.70076i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 9.03355e10i | − | 0.140161i | ||||||
\(897\) | −1.58774e10 | + | 2.65426e10i | −0.0245251 | + | 0.0409990i | ||||
\(898\) | − | 6.95700e10i | − | 0.106983i | ||||||
\(899\) | 1.43026e11i | 0.218966i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.39614e11 | −1.42577 | ||||||||
\(902\) | 1.16817e12 | 1.76474 | ||||||||
\(903\) | 1.06909e12 | + | 6.39516e11i | 1.60792 | + | 0.961835i | ||||
\(904\) | 9.25428e10 | 0.138570 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.92763e11 | + | 2.34946e11i | 0.582932 | + | 0.348703i | ||||
\(907\) | 4.83758e10i | 0.0714824i | 0.999361 | + | 0.0357412i | \(0.0113792\pi\) | ||||
−0.999361 | + | 0.0357412i | \(0.988621\pi\) | |||||||
\(908\) | 2.58568e12 | 3.80393 | ||||||||
\(909\) | −4.82572e11 | + | 2.59027e11i | −0.706816 | + | 0.379394i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 9.65899e11i | − | 1.40236i | −0.712986 | − | 0.701178i | \(-0.752658\pi\) | ||
0.712986 | − | 0.701178i | \(-0.247342\pi\) | |||||||
\(912\) | 8.45552e11 | + | 5.05799e11i | 1.22225 | + | 0.731137i | ||||
\(913\) | − | 7.64351e11i | − | 1.10004i | ||||||
\(914\) | 7.34201e11i | 1.05204i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.52610e12 | 3.58813 | ||||||||
\(917\) | −5.47324e11 | −0.774047 | ||||||||
\(918\) | −7.91186e10 | + | 1.70166e12i | −0.111406 | + | 2.39609i | ||||
\(919\) | −1.14405e12 | −1.60392 | −0.801962 | − | 0.597375i | \(-0.796211\pi\) | ||||
−0.801962 | + | 0.597375i | \(0.796211\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.62507e11 | + | 1.10752e12i | −0.920772 | + | 1.53927i | ||||
\(922\) | − | 6.86409e11i | − | 0.949859i | ||||||
\(923\) | −8.50685e9 | −0.0117209 | ||||||||
\(924\) | 1.76161e12 | + | 1.05377e12i | 2.41669 | + | 1.44563i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.03958e12i | 1.41388i | ||||||||
\(927\) | −7.48881e11 | + | 4.01972e11i | −1.01413 | + | 0.544349i | ||||
\(928\) | − | 3.39663e11i | − | 0.457990i | ||||||
\(929\) | 7.33571e11i | 0.984870i | 0.870349 | + | 0.492435i | \(0.163893\pi\) | ||||
−0.870349 | + | 0.492435i | \(0.836107\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.39276e11 | −0.451600 | ||||||||
\(932\) | −1.76307e12 | −2.33671 | ||||||||
\(933\) | 6.11748e11 | − | 1.02267e12i | 0.807321 | − | 1.34961i | ||||
\(934\) | 2.59275e12 | 3.40701 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.35272e11 | − | 2.87315e11i | 0.697383 | − | 0.374330i | ||||
\(937\) | 3.55464e11i | 0.461145i | 0.973055 | + | 0.230573i | \(0.0740599\pi\) | ||||
−0.973055 | + | 0.230573i | \(0.925940\pi\) | |||||||
\(938\) | −3.44530e12 | −4.45057 | ||||||||
\(939\) | −4.53914e11 | + | 7.58816e11i | −0.583864 | + | 0.976054i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 6.76442e11i | − | 0.862724i | −0.902179 | − | 0.431362i | \(-0.858033\pi\) | ||
0.902179 | − | 0.431362i | \(-0.141967\pi\) | |||||||
\(942\) | −2.90944e11 | + | 4.86376e11i | −0.369493 | + | 0.617687i | ||||
\(943\) | 1.32811e11i | 0.167952i | ||||||||
\(944\) | 7.98847e11i | 1.00595i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.85765e12 | 2.31953 | ||||||||
\(947\) | 1.02862e12 | 1.27896 | 0.639479 | − | 0.768809i | \(-0.279150\pi\) | ||||
0.639479 | + | 0.768809i | \(0.279150\pi\) | |||||||
\(948\) | −2.40620e12 | − | 1.43936e12i | −2.97919 | − | 1.78212i | ||||
\(949\) | −8.29511e10 | −0.102272 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.12830e11 | + | 5.46044e11i | 1.11601 | + | 0.667583i | ||||
\(952\) | − | 3.64569e12i | − | 4.43845i | ||||||
\(953\) | 1.23011e11 | 0.149132 | 0.0745661 | − | 0.997216i | \(-0.476243\pi\) | ||||
0.0745661 | + | 0.997216i | \(0.476243\pi\) | |||||||
\(954\) | −7.91603e11 | − | 1.47477e12i | −0.955683 | − | 1.78045i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.26662e12i | 1.51640i | ||||||||
\(957\) | −1.65514e11 | − | 9.90087e10i | −0.197328 | − | 0.118039i | ||||
\(958\) | − | 2.33361e12i | − | 2.77056i | ||||||
\(959\) | − | 8.76212e11i | − | 1.03594i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.43455e11 | −0.285447 | ||||||||
\(962\) | −5.69701e11 | −0.665192 | ||||||||
\(963\) | 3.19177e11 | + | 5.94632e11i | 0.371131 | + | 0.691422i | ||||
\(964\) | 1.15321e11 | 0.133536 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.69730e11 | + | 2.83741e11i | −0.194918 | + | 0.325847i | ||||
\(967\) | 2.66857e11i | 0.305191i | 0.988289 | + | 0.152596i | \(0.0487632\pi\) | ||||
−0.988289 | + | 0.152596i | \(0.951237\pi\) | |||||||
\(968\) | −4.80457e11 | −0.547209 | ||||||||
\(969\) | −5.94390e11 | − | 3.55557e11i | −0.674181 | − | 0.403287i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.52105e12i | − | 1.71106i | −0.517750 | − | 0.855532i | \(-0.673230\pi\) | ||
0.517750 | − | 0.855532i | \(-0.326770\pi\) | |||||||
\(972\) | −1.93226e12 | + | 9.24261e11i | −2.16471 | + | 1.03545i | ||||
\(973\) | 1.28430e12i | 1.43289i | ||||||||
\(974\) | 1.70654e12i | 1.89618i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.93597e11 | 0.984788 | ||||||||
\(977\) | 1.09651e12 | 1.20347 | 0.601735 | − | 0.798696i | \(-0.294476\pi\) | ||||
0.601735 | + | 0.798696i | \(0.294476\pi\) | |||||||
\(978\) | 7.72209e11 | − | 1.29091e12i | 0.844072 | − | 1.41105i | ||||
\(979\) | −2.49696e11 | −0.271820 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.65017e11 | + | 1.05264e12i | 0.610078 | + | 1.13658i | ||||
\(982\) | 3.16149e12i | 3.39974i | ||||||||
\(983\) | 4.45708e11 | 0.477349 | 0.238675 | − | 0.971100i | \(-0.423287\pi\) | ||||
0.238675 | + | 0.971100i | \(0.423287\pi\) | |||||||
\(984\) | 1.33917e12 | − | 2.23871e12i | 1.42841 | − | 2.38790i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.87272e11i | 0.621344i | ||||||||
\(987\) | 4.63363e11 | − | 7.74612e11i | 0.488262 | − | 0.816235i | ||||
\(988\) | 4.23484e11i | 0.444436i | ||||||||
\(989\) | 2.11198e11i | 0.220752i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.99867e11 | 0.621957 | 0.310979 | − | 0.950417i | \(-0.399343\pi\) | ||||
0.310979 | + | 0.950417i | \(0.399343\pi\) | |||||||
\(992\) | −1.44731e12 | −1.49456 | ||||||||
\(993\) | −3.55399e11 | − | 2.12595e11i | −0.365527 | − | 0.218654i | ||||
\(994\) | −9.09386e10 | −0.0931543 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.51140e12 | − | 1.50229e12i | −2.55199 | − | 1.52657i | ||||
\(997\) | 6.40433e11i | 0.648176i | 0.946027 | + | 0.324088i | \(0.105057\pi\) | ||||
−0.946027 | + | 0.324088i | \(0.894943\pi\) | |||||||
\(998\) | 7.22998e10 | 0.0728811 | ||||||||
\(999\) | 1.17031e12 | + | 5.44132e10i | 1.17500 | + | 0.0546314i |
(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 | 75.9.d.c.74.2 | 20 | ||
3.2 | odd | 2 | inner | 75.9.d.c.74.20 | 20 | ||
5.2 | odd | 4 | 15.9.c.a.11.1 | ✓ | 10 | ||
5.3 | odd | 4 | 75.9.c.g.26.10 | 10 | |||
5.4 | even | 2 | inner | 75.9.d.c.74.19 | 20 | ||
15.2 | even | 4 | 15.9.c.a.11.10 | yes | 10 | ||
15.8 | even | 4 | 75.9.c.g.26.1 | 10 | |||
15.14 | odd | 2 | inner | 75.9.d.c.74.1 | 20 | ||
20.7 | even | 4 | 240.9.l.b.161.4 | 10 | |||
60.47 | odd | 4 | 240.9.l.b.161.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.9.c.a.11.1 | ✓ | 10 | 5.2 | odd | 4 | ||
15.9.c.a.11.10 | yes | 10 | 15.2 | even | 4 | ||
75.9.c.g.26.1 | 10 | 15.8 | even | 4 | |||
75.9.c.g.26.10 | 10 | 5.3 | odd | 4 | |||
75.9.d.c.74.1 | 20 | 15.14 | odd | 2 | inner | ||
75.9.d.c.74.2 | 20 | 1.1 | even | 1 | trivial | ||
75.9.d.c.74.19 | 20 | 5.4 | even | 2 | inner | ||
75.9.d.c.74.20 | 20 | 3.2 | odd | 2 | inner | ||
240.9.l.b.161.3 | 10 | 60.47 | odd | 4 | |||
240.9.l.b.161.4 | 10 | 20.7 | even | 4 |