Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(7,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.7");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.f (of order \(4\), degree \(2\), 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: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4140 x^{13} + 1109893 x^{12} - 3063780 x^{11} + 8569800 x^{10} - 2336277960 x^{9} + 311176823556 x^{8} - 1727244961920 x^{7} + \cdots + 66\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{20}\cdot 5^{8} \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.6 | ||
Root | \(-8.66090 + 8.66090i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.43 |
Dual form | 75.9.f.e.7.6 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 11.1104 | − | 11.1104i | 0.694399 | − | 0.694399i | −0.268797 | − | 0.963197i | \(-0.586626\pi\) |
0.963197 | + | 0.268797i | \(0.0866262\pi\) | |||||||
\(3\) | −33.0681 | − | 33.0681i | −0.408248 | − | 0.408248i | ||||
\(4\) | 9.11845i | 0.0356190i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −734.799 | −0.566975 | ||||||||
\(7\) | 1159.26 | − | 1159.26i | 0.482822 | − | 0.482822i | −0.423209 | − | 0.906032i | \(-0.639097\pi\) |
0.906032 | + | 0.423209i | \(0.139097\pi\) | |||||||
\(8\) | 2945.57 | + | 2945.57i | 0.719133 | + | 0.719133i | ||||
\(9\) | 2187.00i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −24937.9 | −1.70329 | −0.851644 | − | 0.524120i | \(-0.824394\pi\) | ||||
−0.851644 | + | 0.524120i | \(0.824394\pi\) | |||||||
\(12\) | 301.530 | − | 301.530i | 0.0145414 | − | 0.0145414i | ||||
\(13\) | −15387.3 | − | 15387.3i | −0.538751 | − | 0.538751i | 0.384411 | − | 0.923162i | \(-0.374405\pi\) |
−0.923162 | + | 0.384411i | \(0.874405\pi\) | |||||||
\(14\) | − | 25759.6i | − | 0.670543i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 63118.5 | 0.963112 | ||||||||
\(17\) | −68599.4 | + | 68599.4i | −0.821343 | + | 0.821343i | −0.986301 | − | 0.164958i | \(-0.947251\pi\) |
0.164958 | + | 0.986301i | \(0.447251\pi\) | |||||||
\(18\) | 24298.4 | + | 24298.4i | 0.231466 | + | 0.231466i | ||||
\(19\) | 159765.i | 1.22593i | 0.790110 | + | 0.612965i | \(0.210024\pi\) | ||||
−0.790110 | + | 0.612965i | \(0.789976\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −76668.9 | −0.394223 | ||||||||
\(22\) | −277069. | + | 277069.i | −1.18276 | + | 1.18276i | ||||
\(23\) | 112884. | + | 112884.i | 0.403385 | + | 0.403385i | 0.879424 | − | 0.476039i | \(-0.157928\pi\) |
−0.476039 | + | 0.879424i | \(0.657928\pi\) | |||||||
\(24\) | − | 194809.i | − | 0.587170i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −341917. | −0.748217 | ||||||||
\(27\) | 72320.0 | − | 72320.0i | 0.136083 | − | 0.136083i | ||||
\(28\) | 10570.6 | + | 10570.6i | 0.0171976 | + | 0.0171976i | ||||
\(29\) | 824755.i | 1.16609i | 0.812439 | + | 0.583046i | \(0.198139\pi\) | ||||
−0.812439 | + | 0.583046i | \(0.801861\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 343482. | 0.371926 | 0.185963 | − | 0.982557i | \(-0.440459\pi\) | ||||
0.185963 | + | 0.982557i | \(0.440459\pi\) | |||||||
\(32\) | −52794.3 | + | 52794.3i | −0.0503486 | + | 0.0503486i | ||||
\(33\) | 824648. | + | 824648.i | 0.695365 | + | 0.695365i | ||||
\(34\) | 1.52433e6i | 1.14068i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −19942.1 | −0.0118730 | ||||||||
\(37\) | −564458. | + | 564458.i | −0.301179 | + | 0.301179i | −0.841475 | − | 0.540296i | \(-0.818312\pi\) |
0.540296 | + | 0.841475i | \(0.318312\pi\) | |||||||
\(38\) | 1.77505e6 | + | 1.77505e6i | 0.851286 | + | 0.851286i | ||||
\(39\) | 1.01766e6i | 0.439889i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.69004e6 | 1.30586 | 0.652929 | − | 0.757420i | \(-0.273540\pi\) | ||||
0.652929 | + | 0.757420i | \(0.273540\pi\) | |||||||
\(42\) | −851821. | + | 851821.i | −0.273748 | + | 0.273748i | ||||
\(43\) | −2.72005e6 | − | 2.72005e6i | −0.795617 | − | 0.795617i | 0.186784 | − | 0.982401i | \(-0.440193\pi\) |
−0.982401 | + | 0.186784i | \(0.940193\pi\) | |||||||
\(44\) | − | 227395.i | − | 0.0606694i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.50836e6 | 0.560220 | ||||||||
\(47\) | −2.57514e6 | + | 2.57514e6i | −0.527727 | + | 0.527727i | −0.919894 | − | 0.392167i | \(-0.871725\pi\) |
0.392167 | + | 0.919894i | \(0.371725\pi\) | |||||||
\(48\) | −2.08721e6 | − | 2.08721e6i | −0.393189 | − | 0.393189i | ||||
\(49\) | 3.07705e6i | 0.533765i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.53690e6 | 0.670623 | ||||||||
\(52\) | 140308. | − | 140308.i | 0.0191898 | − | 0.0191898i | ||||
\(53\) | −993857. | − | 993857.i | −0.125957 | − | 0.125957i | 0.641318 | − | 0.767275i | \(-0.278388\pi\) |
−0.767275 | + | 0.641318i | \(0.778388\pi\) | |||||||
\(54\) | − | 1.60701e6i | − | 0.188992i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.82934e6 | 0.694427 | ||||||||
\(57\) | 5.28311e6 | − | 5.28311e6i | 0.500484 | − | 0.500484i | ||||
\(58\) | 9.16335e6 | + | 9.16335e6i | 0.809734 | + | 0.809734i | ||||
\(59\) | 8.43553e6i | 0.696152i | 0.937466 | + | 0.348076i | \(0.113165\pi\) | ||||
−0.937466 | + | 0.348076i | \(0.886835\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.18751e7 | −1.57990 | −0.789952 | − | 0.613169i | \(-0.789895\pi\) | ||||
−0.789952 | + | 0.613169i | \(0.789895\pi\) | |||||||
\(62\) | 3.81622e6 | − | 3.81622e6i | 0.258265 | − | 0.258265i | ||||
\(63\) | 2.53529e6 | + | 2.53529e6i | 0.160941 | + | 0.160941i | ||||
\(64\) | 1.73315e7i | 1.03304i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.83243e7 | 0.965722 | ||||||||
\(67\) | −1.90919e7 | + | 1.90919e7i | −0.947437 | + | 0.947437i | −0.998686 | − | 0.0512494i | \(-0.983680\pi\) |
0.0512494 | + | 0.998686i | \(0.483680\pi\) | |||||||
\(68\) | −625520. | − | 625520.i | −0.0292554 | − | 0.0292554i | ||||
\(69\) | − | 7.46570e6i | − | 0.329362i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.06339e6 | 0.238607 | 0.119303 | − | 0.992858i | \(-0.461934\pi\) | ||||
0.119303 | + | 0.992858i | \(0.461934\pi\) | |||||||
\(72\) | −6.44196e6 | + | 6.44196e6i | −0.239711 | + | 0.239711i | ||||
\(73\) | −7.87654e6 | − | 7.87654e6i | −0.277360 | − | 0.277360i | 0.554694 | − | 0.832054i | \(-0.312835\pi\) |
−0.832054 | + | 0.554694i | \(0.812835\pi\) | |||||||
\(74\) | 1.25427e7i | 0.418277i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.45681e6 | −0.0436664 | ||||||||
\(77\) | −2.89094e7 | + | 2.89094e7i | −0.822386 | + | 0.822386i | ||||
\(78\) | 1.13066e7 | + | 1.13066e7i | 0.305458 | + | 0.305458i | ||||
\(79\) | − | 2.50449e7i | − | 0.643000i | −0.946910 | − | 0.321500i | \(-0.895813\pi\) | ||
0.946910 | − | 0.321500i | \(-0.104187\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.78297e6 | −0.111111 | ||||||||
\(82\) | 4.09978e7 | − | 4.09978e7i | 0.906786 | − | 0.906786i | ||||
\(83\) | 4.76305e7 | + | 4.76305e7i | 1.00363 | + | 1.00363i | 0.999993 | + | 0.00363460i | \(0.00115693\pi\) |
0.00363460 | + | 0.999993i | \(0.498843\pi\) | |||||||
\(84\) | − | 699101.i | − | 0.0140418i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.04417e7 | −1.10495 | ||||||||
\(87\) | 2.72731e7 | − | 2.72731e7i | 0.476055 | − | 0.476055i | ||||
\(88\) | −7.34562e7 | − | 7.34562e7i | −1.22489 | − | 1.22489i | ||||
\(89\) | − | 6.58613e7i | − | 1.04971i | −0.851191 | − | 0.524856i | \(-0.824119\pi\) | ||
0.851191 | − | 0.524856i | \(-0.175881\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.56756e7 | −0.520242 | ||||||||
\(92\) | −1.02932e6 | + | 1.02932e6i | −0.0143681 | + | 0.0143681i | ||||
\(93\) | −1.13583e7 | − | 1.13583e7i | −0.151838 | − | 0.151838i | ||||
\(94\) | 5.72216e7i | 0.732906i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.49161e6 | 0.0411094 | ||||||||
\(97\) | −2.70869e7 | + | 2.70869e7i | −0.305965 | + | 0.305965i | −0.843342 | − | 0.537377i | \(-0.819415\pi\) |
0.537377 | + | 0.843342i | \(0.319415\pi\) | |||||||
\(98\) | 3.41872e7 | + | 3.41872e7i | 0.370646 | + | 0.370646i | ||||
\(99\) | − | 5.45391e7i | − | 0.567763i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.42884e7 | −0.425603 | −0.212801 | − | 0.977095i | \(-0.568259\pi\) | ||||
−0.212801 | + | 0.977095i | \(0.568259\pi\) | |||||||
\(102\) | 5.04068e7 | − | 5.04068e7i | 0.465680 | − | 0.465680i | ||||
\(103\) | −7.81171e7 | − | 7.81171e7i | −0.694061 | − | 0.694061i | 0.269062 | − | 0.963123i | \(-0.413286\pi\) |
−0.963123 | + | 0.269062i | \(0.913286\pi\) | |||||||
\(104\) | − | 9.06486e7i | − | 0.774868i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.20843e7 | −0.174928 | ||||||||
\(107\) | 1.05407e8 | − | 1.05407e8i | 0.804143 | − | 0.804143i | −0.179597 | − | 0.983740i | \(-0.557480\pi\) |
0.983740 | + | 0.179597i | \(0.0574795\pi\) | |||||||
\(108\) | 659446. | + | 659446.i | 0.00484713 | + | 0.00484713i | ||||
\(109\) | − | 2.01252e8i | − | 1.42572i | −0.701307 | − | 0.712859i | \(-0.747400\pi\) | ||
0.701307 | − | 0.712859i | \(-0.252600\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.73312e7 | 0.245912 | ||||||||
\(112\) | 7.31706e7 | − | 7.31706e7i | 0.465012 | − | 0.465012i | ||||
\(113\) | −1.56470e8 | − | 1.56470e8i | −0.959658 | − | 0.959658i | 0.0395594 | − | 0.999217i | \(-0.487405\pi\) |
−0.999217 | + | 0.0395594i | \(0.987405\pi\) | |||||||
\(114\) | − | 1.17395e8i | − | 0.695072i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.52049e6 | −0.0415350 | ||||||||
\(117\) | 3.36520e7 | − | 3.36520e7i | 0.179584 | − | 0.179584i | ||||
\(118\) | 9.37220e7 | + | 9.37220e7i | 0.483408 | + | 0.483408i | ||||
\(119\) | 1.59049e8i | 0.793125i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.07537e8 | 1.90119 | ||||||||
\(122\) | −2.43041e8 | + | 2.43041e8i | −1.09708 | + | 1.09708i | ||||
\(123\) | −1.22023e8 | − | 1.22023e8i | −0.533114 | − | 0.533114i | ||||
\(124\) | 3.13202e6i | 0.0132476i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.63362e7 | 0.223514 | ||||||||
\(127\) | 2.87409e8 | − | 2.87409e8i | 1.10480 | − | 1.10480i | 0.110982 | − | 0.993822i | \(-0.464600\pi\) |
0.993822 | − | 0.110982i | \(-0.0353995\pi\) | |||||||
\(128\) | 1.79044e8 | + | 1.79044e8i | 0.666991 | + | 0.666991i | ||||
\(129\) | 1.79894e8i | 0.649618i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.75848e8 | −1.27622 | −0.638112 | − | 0.769944i | \(-0.720284\pi\) | ||||
−0.638112 | + | 0.769944i | \(0.720284\pi\) | |||||||
\(132\) | −7.51951e6 | + | 7.51951e6i | −0.0247682 | + | 0.0247682i | ||||
\(133\) | 1.85208e8 | + | 1.85208e8i | 0.591907 | + | 0.591907i | ||||
\(134\) | 4.24237e8i | 1.31580i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.04128e8 | −1.18131 | ||||||||
\(137\) | −3.94996e8 | + | 3.94996e8i | −1.12127 | + | 1.12127i | −0.129721 | + | 0.991551i | \(0.541408\pi\) |
−0.991551 | + | 0.129721i | \(0.958592\pi\) | |||||||
\(138\) | −8.29468e7 | − | 8.29468e7i | −0.228709 | − | 0.228709i | ||||
\(139\) | − | 3.91457e8i | − | 1.04863i | −0.851523 | − | 0.524317i | \(-0.824321\pi\) | ||
0.851523 | − | 0.524317i | \(-0.175679\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.70310e8 | 0.430887 | ||||||||
\(142\) | 6.73667e7 | − | 6.73667e7i | 0.165688 | − | 0.165688i | ||||
\(143\) | 3.83726e8 | + | 3.83726e8i | 0.917649 | + | 0.917649i | ||||
\(144\) | 1.38040e8i | 0.321037i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.75023e8 | −0.385197 | ||||||||
\(147\) | 1.01752e8 | − | 1.01752e8i | 0.217909 | − | 0.217909i | ||||
\(148\) | −5.14699e6 | − | 5.14699e6i | −0.0107277 | − | 0.0107277i | ||||
\(149\) | 3.71759e8i | 0.754251i | 0.926162 | + | 0.377125i | \(0.123087\pi\) | ||||
−0.926162 | + | 0.377125i | \(0.876913\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.50632e8 | 1.05914 | 0.529570 | − | 0.848266i | \(-0.322353\pi\) | ||||
0.529570 | + | 0.848266i | \(0.322353\pi\) | |||||||
\(152\) | −4.70598e8 | + | 4.70598e8i | −0.881608 | + | 0.881608i | ||||
\(153\) | −1.50027e8 | − | 1.50027e8i | −0.273781 | − | 0.273781i | ||||
\(154\) | 6.42389e8i | 1.14213i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −9.27945e6 | −0.0156684 | ||||||||
\(157\) | −5.44897e8 | + | 5.44897e8i | −0.896842 | + | 0.896842i | −0.995156 | − | 0.0983132i | \(-0.968655\pi\) |
0.0983132 | + | 0.995156i | \(0.468655\pi\) | |||||||
\(158\) | −2.78259e8 | − | 2.78259e8i | −0.446499 | − | 0.446499i | ||||
\(159\) | 6.57300e7i | 0.102843i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.61722e8 | 0.389527 | ||||||||
\(162\) | −5.31407e7 | + | 5.31407e7i | −0.0771555 | + | 0.0771555i | ||||
\(163\) | 2.88245e8 | + | 2.88245e8i | 0.408330 | + | 0.408330i | 0.881156 | − | 0.472826i | \(-0.156766\pi\) |
−0.472826 | + | 0.881156i | \(0.656766\pi\) | |||||||
\(164\) | 3.36475e7i | 0.0465133i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.05839e9 | 1.39384 | ||||||||
\(167\) | −2.32402e8 | + | 2.32402e8i | −0.298795 | + | 0.298795i | −0.840542 | − | 0.541747i | \(-0.817763\pi\) |
0.541747 | + | 0.840542i | \(0.317763\pi\) | |||||||
\(168\) | −2.25833e8 | − | 2.25833e8i | −0.283499 | − | 0.283499i | ||||
\(169\) | − | 3.42194e8i | − | 0.419494i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.49405e8 | −0.408644 | ||||||||
\(172\) | 2.48027e7 | − | 2.48027e7i | 0.0283390 | − | 0.0283390i | ||||
\(173\) | 6.25257e8 | + | 6.25257e8i | 0.698031 | + | 0.698031i | 0.963985 | − | 0.265955i | \(-0.0856872\pi\) |
−0.265955 | + | 0.963985i | \(0.585687\pi\) | |||||||
\(174\) | − | 6.06029e8i | − | 0.661145i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.57404e9 | −1.64046 | ||||||||
\(177\) | 2.78947e8 | − | 2.78947e8i | 0.284203 | − | 0.284203i | ||||
\(178\) | −7.31745e8 | − | 7.31745e8i | −0.728920 | − | 0.728920i | ||||
\(179\) | 6.97348e8i | 0.679263i | 0.940559 | + | 0.339631i | \(0.110302\pi\) | ||||
−0.940559 | + | 0.339631i | \(0.889698\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.10377e9 | 1.02840 | 0.514202 | − | 0.857669i | \(-0.328088\pi\) | ||||
0.514202 | + | 0.857669i | \(0.328088\pi\) | |||||||
\(182\) | −3.96370e8 | + | 3.96370e8i | −0.361256 | + | 0.361256i | ||||
\(183\) | 7.23368e8 | + | 7.23368e8i | 0.644993 | + | 0.644993i | ||||
\(184\) | 6.65013e8i | 0.580175i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.52390e8 | −0.210873 | ||||||||
\(187\) | 1.71072e9 | − | 1.71072e9i | 1.39898 | − | 1.39898i | ||||
\(188\) | −2.34813e7 | − | 2.34813e7i | −0.0187971 | − | 0.0187971i | ||||
\(189\) | − | 1.67675e8i | − | 0.131408i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.04416e9 | 0.784573 | 0.392287 | − | 0.919843i | \(-0.371684\pi\) | ||||
0.392287 | + | 0.919843i | \(0.371684\pi\) | |||||||
\(192\) | 5.73119e8 | − | 5.73119e8i | 0.421735 | − | 0.421735i | ||||
\(193\) | −3.34003e8 | − | 3.34003e8i | −0.240725 | − | 0.240725i | 0.576425 | − | 0.817150i | \(-0.304447\pi\) |
−0.817150 | + | 0.576425i | \(0.804447\pi\) | |||||||
\(194\) | 6.01891e8i | 0.424924i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.80579e7 | −0.0190122 | ||||||||
\(197\) | 1.08026e9 | − | 1.08026e9i | 0.717240 | − | 0.717240i | −0.250799 | − | 0.968039i | \(-0.580693\pi\) |
0.968039 | + | 0.250799i | \(0.0806933\pi\) | |||||||
\(198\) | −6.05950e8 | − | 6.05950e8i | −0.394254 | − | 0.394254i | ||||
\(199\) | − | 7.03684e8i | − | 0.448710i | −0.974508 | − | 0.224355i | \(-0.927973\pi\) | ||
0.974508 | − | 0.224355i | \(-0.0720275\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.26267e9 | 0.773579 | ||||||||
\(202\) | −4.92062e8 | + | 4.92062e8i | −0.295538 | + | 0.295538i | ||||
\(203\) | 9.56103e8 | + | 9.56103e8i | 0.563016 | + | 0.563016i | ||||
\(204\) | 4.13695e7i | 0.0238869i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.73582e9 | −0.963911 | ||||||||
\(207\) | −2.46876e8 | + | 2.46876e8i | −0.134462 | + | 0.134462i | ||||
\(208\) | −9.71222e8 | − | 9.71222e8i | −0.518878 | − | 0.518878i | ||||
\(209\) | − | 3.98418e9i | − | 2.08811i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.56752e9 | −1.29534 | −0.647671 | − | 0.761920i | \(-0.724257\pi\) | ||||
−0.647671 | + | 0.761920i | \(0.724257\pi\) | |||||||
\(212\) | 9.06244e6 | − | 9.06244e6i | 0.00448644 | − | 0.00448644i | ||||
\(213\) | −2.00505e8 | − | 2.00505e8i | −0.0974107 | − | 0.0974107i | ||||
\(214\) | − | 2.34222e9i | − | 1.11679i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.26047e8 | 0.195723 | ||||||||
\(217\) | 3.98184e8 | − | 3.98184e8i | 0.179574 | − | 0.179574i | ||||
\(218\) | −2.23598e9 | − | 2.23598e9i | −0.990018 | − | 0.990018i | ||||
\(219\) | 5.20925e8i | 0.226464i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.11111e9 | 0.884999 | ||||||||
\(222\) | 4.14764e8 | − | 4.14764e8i | 0.170761 | − | 0.170761i | ||||
\(223\) | 9.21336e8 | + | 9.21336e8i | 0.372562 | + | 0.372562i | 0.868410 | − | 0.495848i | \(-0.165143\pi\) |
−0.495848 | + | 0.868410i | \(0.665143\pi\) | |||||||
\(224\) | 1.22404e8i | 0.0486188i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.47688e9 | −1.33277 | ||||||||
\(227\) | −2.31382e9 | + | 2.31382e9i | −0.871415 | + | 0.871415i | −0.992627 | − | 0.121211i | \(-0.961322\pi\) |
0.121211 | + | 0.992627i | \(0.461322\pi\) | |||||||
\(228\) | 4.81738e7 | + | 4.81738e7i | 0.0178267 | + | 0.0178267i | ||||
\(229\) | 1.33331e9i | 0.484830i | 0.970173 | + | 0.242415i | \(0.0779395\pi\) | ||||
−0.970173 | + | 0.242415i | \(0.922060\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.91196e9 | 0.671475 | ||||||||
\(232\) | −2.42937e9 | + | 2.42937e9i | −0.838576 | + | 0.838576i | ||||
\(233\) | −1.72769e8 | − | 1.72769e8i | −0.0586194 | − | 0.0586194i | 0.677189 | − | 0.735809i | \(-0.263198\pi\) |
−0.735809 | + | 0.677189i | \(0.763198\pi\) | |||||||
\(234\) | − | 7.47773e8i | − | 0.249406i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.69189e7 | −0.0247962 | ||||||||
\(237\) | −8.28188e8 | + | 8.28188e8i | −0.262504 | + | 0.262504i | ||||
\(238\) | 1.76709e9 | + | 1.76709e9i | 0.550746 | + | 0.550746i | ||||
\(239\) | 3.60567e9i | 1.10508i | 0.833486 | + | 0.552541i | \(0.186342\pi\) | ||||
−0.833486 | + | 0.552541i | \(0.813658\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.36725e9 | −1.59105 | −0.795525 | − | 0.605921i | \(-0.792805\pi\) | ||||
−0.795525 | + | 0.605921i | \(0.792805\pi\) | |||||||
\(242\) | 4.52790e9 | − | 4.52790e9i | 1.32019 | − | 1.32019i | ||||
\(243\) | 1.58164e8 | + | 1.58164e8i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | − | 1.99467e8i | − | 0.0562745i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.71144e9 | −0.740388 | ||||||||
\(247\) | 2.45834e9 | − | 2.45834e9i | 0.660472 | − | 0.660472i | ||||
\(248\) | 1.01175e9 | + | 1.01175e9i | 0.267465 | + | 0.267465i | ||||
\(249\) | − | 3.15010e9i | − | 0.819459i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.83207e8 | 0.172130 | 0.0860652 | − | 0.996290i | \(-0.472571\pi\) | ||||
0.0860652 | + | 0.996290i | \(0.472571\pi\) | |||||||
\(252\) | −2.31180e7 | + | 2.31180e7i | −0.00573254 | + | 0.00573254i | ||||
\(253\) | −2.81507e9 | − | 2.81507e9i | −0.687081 | − | 0.687081i | ||||
\(254\) | − | 6.38645e9i | − | 1.53435i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.58358e8 | −0.106720 | ||||||||
\(257\) | 3.17797e9 | − | 3.17797e9i | 0.728479 | − | 0.728479i | −0.241838 | − | 0.970317i | \(-0.577750\pi\) |
0.970317 | + | 0.241838i | \(0.0777501\pi\) | |||||||
\(258\) | 1.99869e9 | + | 1.99869e9i | 0.451094 | + | 0.451094i | ||||
\(259\) | 1.30870e9i | 0.290832i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.80374e9 | −0.388697 | ||||||||
\(262\) | −4.17581e9 | + | 4.17581e9i | −0.886209 | + | 0.886209i | ||||
\(263\) | 1.32078e9 | + | 1.32078e9i | 0.276063 | + | 0.276063i | 0.831535 | − | 0.555472i | \(-0.187462\pi\) |
−0.555472 | + | 0.831535i | \(0.687462\pi\) | |||||||
\(264\) | 4.85811e9i | 1.00012i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.11547e9 | 0.822040 | ||||||||
\(267\) | −2.17791e9 | + | 2.17791e9i | −0.428543 | + | 0.428543i | ||||
\(268\) | −1.74089e8 | − | 1.74089e8i | −0.0337467 | − | 0.0337467i | ||||
\(269\) | 7.27142e8i | 0.138871i | 0.997586 | + | 0.0694353i | \(0.0221197\pi\) | ||||
−0.997586 | + | 0.0694353i | \(0.977880\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.56757e9 | 1.58847 | 0.794237 | − | 0.607607i | \(-0.207871\pi\) | ||||
0.794237 | + | 0.607607i | \(0.207871\pi\) | |||||||
\(272\) | −4.32989e9 | + | 4.32989e9i | −0.791045 | + | 0.791045i | ||||
\(273\) | 1.17972e9 | + | 1.17972e9i | 0.212388 | + | 0.212388i | ||||
\(274\) | 8.77712e9i | 1.55722i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.80756e7 | 0.0117315 | ||||||||
\(277\) | −1.36868e9 | + | 1.36868e9i | −0.232478 | + | 0.232478i | −0.813726 | − | 0.581248i | \(-0.802564\pi\) |
0.581248 | + | 0.813726i | \(0.302564\pi\) | |||||||
\(278\) | −4.34923e9 | − | 4.34923e9i | −0.728172 | − | 0.728172i | ||||
\(279\) | 7.51195e8i | 0.123975i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.39746e9 | 0.705304 | 0.352652 | − | 0.935754i | \(-0.385280\pi\) | ||||
0.352652 | + | 0.935754i | \(0.385280\pi\) | |||||||
\(282\) | 1.89221e9 | − | 1.89221e9i | 0.299208 | − | 0.299208i | ||||
\(283\) | −5.43431e8 | − | 5.43431e8i | −0.0847225 | − | 0.0847225i | 0.663475 | − | 0.748198i | \(-0.269081\pi\) |
−0.748198 | + | 0.663475i | \(0.769081\pi\) | |||||||
\(284\) | 5.52888e7i | 0.00849892i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.52668e9 | 1.27443 | ||||||||
\(287\) | 4.27770e9 | − | 4.27770e9i | 0.630497 | − | 0.630497i | ||||
\(288\) | −1.15461e8 | − | 1.15461e8i | −0.0167829 | − | 0.0167829i | ||||
\(289\) | − | 2.43598e9i | − | 0.349207i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.79142e9 | 0.249819 | ||||||||
\(292\) | 7.18218e7 | − | 7.18218e7i | 0.00987928 | − | 0.00987928i | ||||
\(293\) | 1.75807e9 | + | 1.75807e9i | 0.238543 | + | 0.238543i | 0.816246 | − | 0.577704i | \(-0.196051\pi\) |
−0.577704 | + | 0.816246i | \(0.696051\pi\) | |||||||
\(294\) | − | 2.26101e9i | − | 0.302631i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.32530e9 | −0.433176 | ||||||||
\(297\) | −1.80350e9 | + | 1.80350e9i | −0.231788 | + | 0.231788i | ||||
\(298\) | 4.13038e9 | + | 4.13038e9i | 0.523751 | + | 0.523751i | ||||
\(299\) | − | 3.47394e9i | − | 0.434648i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.30648e9 | −0.768283 | ||||||||
\(302\) | 6.11773e9 | − | 6.11773e9i | 0.735466 | − | 0.735466i | ||||
\(303\) | 1.46453e9 | + | 1.46453e9i | 0.173752 | + | 0.173752i | ||||
\(304\) | 1.00841e10i | 1.18071i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.33371e9 | −0.380227 | ||||||||
\(307\) | −3.73647e9 | + | 3.73647e9i | −0.420637 | + | 0.420637i | −0.885423 | − | 0.464786i | \(-0.846131\pi\) |
0.464786 | + | 0.885423i | \(0.346131\pi\) | |||||||
\(308\) | −2.63609e8 | − | 2.63609e8i | −0.0292925 | − | 0.0292925i | ||||
\(309\) | 5.16637e9i | 0.566698i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.09667e9 | 0.758601 | 0.379300 | − | 0.925274i | \(-0.376165\pi\) | ||||
0.379300 | + | 0.925274i | \(0.376165\pi\) | |||||||
\(312\) | −2.99758e9 | + | 2.99758e9i | −0.316338 | + | 0.316338i | ||||
\(313\) | −2.46148e9 | − | 2.46148e9i | −0.256459 | − | 0.256459i | 0.567153 | − | 0.823612i | \(-0.308045\pi\) |
−0.823612 | + | 0.567153i | \(0.808045\pi\) | |||||||
\(314\) | 1.21080e10i | 1.24553i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.28371e8 | 0.0229030 | ||||||||
\(317\) | −2.29391e9 | + | 2.29391e9i | −0.227164 | + | 0.227164i | −0.811507 | − | 0.584343i | \(-0.801352\pi\) |
0.584343 | + | 0.811507i | \(0.301352\pi\) | |||||||
\(318\) | 7.30286e8 | + | 7.30286e8i | 0.0714142 | + | 0.0714142i | ||||
\(319\) | − | 2.05676e10i | − | 1.98619i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.97120e9 | −0.656580 | ||||||||
\(322\) | 2.90784e9 | − | 2.90784e9i | 0.270487 | − | 0.270487i | ||||
\(323\) | −1.09597e10 | − | 1.09597e10i | −1.00691 | − | 1.00691i | ||||
\(324\) | − | 4.36133e7i | − | 0.00395766i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.40503e9 | 0.567089 | ||||||||
\(327\) | −6.65501e9 | + | 6.65501e9i | −0.582047 | + | 0.582047i | ||||
\(328\) | 1.08693e10 | + | 1.08693e10i | 0.939085 | + | 0.939085i | ||||
\(329\) | 5.97049e9i | 0.509597i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.33975e9 | −0.528153 | −0.264077 | − | 0.964502i | \(-0.585067\pi\) | ||||
−0.264077 | + | 0.964502i | \(0.585067\pi\) | |||||||
\(332\) | −4.34316e8 | + | 4.34316e8i | −0.0357482 | + | 0.0357482i | ||||
\(333\) | −1.23447e9 | − | 1.23447e9i | −0.100393 | − | 0.100393i | ||||
\(334\) | 5.16415e9i | 0.414967i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.83923e9 | −0.379681 | ||||||||
\(337\) | −3.37261e9 | + | 3.37261e9i | −0.261485 | + | 0.261485i | −0.825657 | − | 0.564172i | \(-0.809195\pi\) |
0.564172 | + | 0.825657i | \(0.309195\pi\) | |||||||
\(338\) | −3.80191e9 | − | 3.80191e9i | −0.291297 | − | 0.291297i | ||||
\(339\) | 1.03483e10i | 0.783557i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.56570e9 | −0.633498 | ||||||||
\(342\) | −3.88203e9 | + | 3.88203e9i | −0.283762 | + | 0.283762i | ||||
\(343\) | 1.02500e10 | + | 1.02500e10i | 0.740536 | + | 0.740536i | ||||
\(344\) | − | 1.60242e10i | − | 1.14431i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.38937e10 | 0.969424 | ||||||||
\(347\) | −7.51385e9 | + | 7.51385e9i | −0.518256 | + | 0.518256i | −0.917043 | − | 0.398787i | \(-0.869431\pi\) |
0.398787 | + | 0.917043i | \(0.369431\pi\) | |||||||
\(348\) | 2.48688e8 | + | 2.48688e8i | 0.0169566 | + | 0.0169566i | ||||
\(349\) | − | 3.35120e9i | − | 0.225891i | −0.993601 | − | 0.112945i | \(-0.963972\pi\) | ||
0.993601 | − | 0.112945i | \(-0.0360285\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.22561e9 | −0.146630 | ||||||||
\(352\) | 1.31658e9 | − | 1.31658e9i | 0.0857581 | − | 0.0857581i | ||||
\(353\) | 4.76890e9 | + | 4.76890e9i | 0.307128 | + | 0.307128i | 0.843795 | − | 0.536666i | \(-0.180317\pi\) |
−0.536666 | + | 0.843795i | \(0.680317\pi\) | |||||||
\(354\) | − | 6.19842e9i | − | 0.394701i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00553e8 | 0.0373897 | ||||||||
\(357\) | 5.25943e9 | − | 5.25943e9i | 0.323792 | − | 0.323792i | ||||
\(358\) | 7.74781e9 | + | 7.74781e9i | 0.471679 | + | 0.471679i | ||||
\(359\) | 1.11490e10i | 0.671209i | 0.942003 | + | 0.335604i | \(0.108941\pi\) | ||||
−0.942003 | + | 0.335604i | \(0.891059\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.54115e9 | −0.502907 | ||||||||
\(362\) | 1.22633e10 | − | 1.22633e10i | 0.714123 | − | 0.714123i | ||||
\(363\) | −1.34765e10 | − | 1.34765e10i | −0.776159 | − | 0.776159i | ||||
\(364\) | − | 3.25306e8i | − | 0.0185305i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.60738e10 | 0.895766 | ||||||||
\(367\) | −2.39212e9 | + | 2.39212e9i | −0.131862 | + | 0.131862i | −0.769957 | − | 0.638096i | \(-0.779722\pi\) |
0.638096 | + | 0.769957i | \(0.279722\pi\) | |||||||
\(368\) | 7.12505e9 | + | 7.12505e9i | 0.388505 | + | 0.388505i | ||||
\(369\) | 8.07012e9i | 0.435286i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.30427e9 | −0.121629 | ||||||||
\(372\) | 1.03570e8 | − | 1.03570e8i | 0.00540832 | − | 0.00540832i | ||||
\(373\) | −1.75464e10 | − | 1.75464e10i | −0.906470 | − | 0.906470i | 0.0895152 | − | 0.995985i | \(-0.471468\pi\) |
−0.995985 | + | 0.0895152i | \(0.971468\pi\) | |||||||
\(374\) | − | 3.80135e10i | − | 1.94291i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.51705e10 | −0.759012 | ||||||||
\(377\) | 1.26907e10 | − | 1.26907e10i | 0.628234 | − | 0.628234i | ||||
\(378\) | −1.86293e9 | − | 1.86293e9i | −0.0912494 | − | 0.0912494i | ||||
\(379\) | 5.61785e9i | 0.272278i | 0.990690 | + | 0.136139i | \(0.0434694\pi\) | ||||
−0.990690 | + | 0.136139i | \(0.956531\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.90081e10 | −0.902069 | ||||||||
\(382\) | 1.16010e10 | − | 1.16010e10i | 0.544807 | − | 0.544807i | ||||
\(383\) | −1.04233e10 | − | 1.04233e10i | −0.484408 | − | 0.484408i | 0.422128 | − | 0.906536i | \(-0.361283\pi\) |
−0.906536 | + | 0.422128i | \(0.861283\pi\) | |||||||
\(384\) | − | 1.18413e10i | − | 0.544596i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.42181e9 | −0.334319 | ||||||||
\(387\) | 5.94876e9 | − | 5.94876e9i | 0.265206 | − | 0.265206i | ||||
\(388\) | −2.46990e8 | − | 2.46990e8i | −0.0108982 | − | 0.0108982i | ||||
\(389\) | 4.20782e9i | 0.183763i | 0.995770 | + | 0.0918817i | \(0.0292882\pi\) | ||||
−0.995770 | + | 0.0918817i | \(0.970712\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.54875e10 | −0.662634 | ||||||||
\(392\) | −9.06366e9 | + | 9.06366e9i | −0.383848 | + | 0.383848i | ||||
\(393\) | 1.24286e10 | + | 1.24286e10i | 0.521016 | + | 0.521016i | ||||
\(394\) | − | 2.40043e10i | − | 0.996102i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.97312e8 | 0.0202231 | ||||||||
\(397\) | 1.76294e10 | − | 1.76294e10i | 0.709700 | − | 0.709700i | −0.256772 | − | 0.966472i | \(-0.582659\pi\) |
0.966472 | + | 0.256772i | \(0.0826589\pi\) | |||||||
\(398\) | −7.81821e9 | − | 7.81821e9i | −0.311584 | − | 0.311584i | ||||
\(399\) | − | 1.22490e10i | − | 0.483290i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.84488e10 | −0.713496 | −0.356748 | − | 0.934201i | \(-0.616114\pi\) | ||||
−0.356748 | + | 0.934201i | \(0.616114\pi\) | |||||||
\(402\) | 1.40287e10 | − | 1.40287e10i | 0.537173 | − | 0.537173i | ||||
\(403\) | −5.28525e9 | − | 5.28525e9i | −0.200376 | − | 0.200376i | ||||
\(404\) | − | 4.03842e8i | − | 0.0151595i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.12453e10 | 0.781915 | ||||||||
\(407\) | 1.40764e10 | − | 1.40764e10i | 0.512995 | − | 0.512995i | ||||
\(408\) | 1.33638e10 | + | 1.33638e10i | 0.482268 | + | 0.482268i | ||||
\(409\) | − | 2.03359e10i | − | 0.726724i | −0.931648 | − | 0.363362i | \(-0.881629\pi\) | ||
0.931648 | − | 0.363362i | \(-0.118371\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.61236e10 | 0.915514 | ||||||||
\(412\) | 7.12307e8 | − | 7.12307e8i | 0.0247217 | − | 0.0247217i | ||||
\(413\) | 9.77894e9 | + | 9.77894e9i | 0.336118 | + | 0.336118i | ||||
\(414\) | 5.48579e9i | 0.186740i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.62472e9 | 0.0542507 | ||||||||
\(417\) | −1.29447e10 | + | 1.29447e10i | −0.428103 | + | 0.428103i | ||||
\(418\) | −4.42658e10 | − | 4.42658e10i | −1.44999 | − | 1.44999i | ||||
\(419\) | 3.97862e10i | 1.29085i | 0.763823 | + | 0.645426i | \(0.223320\pi\) | ||||
−0.763823 | + | 0.645426i | \(0.776680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.52423e10 | 1.75850 | 0.879252 | − | 0.476356i | \(-0.158043\pi\) | ||||
0.879252 | + | 0.476356i | \(0.158043\pi\) | |||||||
\(422\) | −2.85262e10 | + | 2.85262e10i | −0.899485 | + | 0.899485i | ||||
\(423\) | −5.63183e9 | − | 5.63183e9i | −0.175909 | − | 0.175909i | ||||
\(424\) | − | 5.85495e9i | − | 0.181159i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.45538e9 | −0.135284 | ||||||||
\(427\) | −2.53589e10 | + | 2.53589e10i | −0.762813 | + | 0.762813i | ||||
\(428\) | 9.61146e8 | + | 9.61146e8i | 0.0286427 | + | 0.0286427i | ||||
\(429\) | − | 2.53782e10i | − | 0.749257i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.79307e9 | 0.196860 | 0.0984299 | − | 0.995144i | \(-0.468618\pi\) | ||||
0.0984299 | + | 0.995144i | \(0.468618\pi\) | |||||||
\(432\) | 4.56473e9 | − | 4.56473e9i | 0.131063 | − | 0.131063i | ||||
\(433\) | −2.64633e10 | − | 2.64633e10i | −0.752822 | − | 0.752822i | 0.222183 | − | 0.975005i | \(-0.428682\pi\) |
−0.975005 | + | 0.222183i | \(0.928682\pi\) | |||||||
\(434\) | − | 8.84795e9i | − | 0.249393i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.83510e9 | 0.0507826 | ||||||||
\(437\) | −1.80348e10 | + | 1.80348e10i | −0.494522 | + | 0.494522i | ||||
\(438\) | 5.78767e9 | + | 5.78767e9i | 0.157256 | + | 0.157256i | ||||
\(439\) | 4.93784e10i | 1.32947i | 0.747079 | + | 0.664735i | \(0.231456\pi\) | ||||
−0.747079 | + | 0.664735i | \(0.768544\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.72951e9 | −0.177922 | ||||||||
\(442\) | 2.34553e10 | − | 2.34553e10i | 0.614542 | − | 0.614542i | ||||
\(443\) | 3.77217e10 | + | 3.77217e10i | 0.979437 | + | 0.979437i | 0.999793 | − | 0.0203558i | \(-0.00647990\pi\) |
−0.0203558 | + | 0.999793i | \(0.506480\pi\) | |||||||
\(444\) | 3.40402e8i | 0.00875912i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.04728e10 | 0.517414 | ||||||||
\(447\) | 1.22934e10 | − | 1.22934e10i | 0.307922 | − | 0.307922i | ||||
\(448\) | 2.00916e10 | + | 2.00916e10i | 0.498773 | + | 0.498773i | ||||
\(449\) | − | 4.14653e10i | − | 1.02023i | −0.860106 | − | 0.510116i | \(-0.829602\pi\) | ||
0.860106 | − | 0.510116i | \(-0.170398\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.20217e10 | −2.22425 | ||||||||
\(452\) | 1.42676e9 | − | 1.42676e9i | 0.0341820 | − | 0.0341820i | ||||
\(453\) | −1.82083e10 | − | 1.82083e10i | −0.432392 | − | 0.432392i | ||||
\(454\) | 5.14148e10i | 1.21022i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.11235e10 | 0.719830 | ||||||||
\(457\) | −2.09923e10 | + | 2.09923e10i | −0.481278 | + | 0.481278i | −0.905540 | − | 0.424262i | \(-0.860534\pi\) |
0.424262 | + | 0.905540i | \(0.360534\pi\) | |||||||
\(458\) | 1.48136e10 | + | 1.48136e10i | 0.336666 | + | 0.336666i | ||||
\(459\) | 9.92220e9i | 0.223541i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.33896e10 | −1.18210 | −0.591049 | − | 0.806636i | \(-0.701286\pi\) | ||||
−0.591049 | + | 0.806636i | \(0.701286\pi\) | |||||||
\(462\) | 2.12426e10 | − | 2.12426e10i | 0.466272 | − | 0.466272i | ||||
\(463\) | 5.09927e10 | + | 5.09927e10i | 1.10964 | + | 1.10964i | 0.993197 | + | 0.116447i | \(0.0371506\pi\) |
0.116447 | + | 0.993197i | \(0.462849\pi\) | |||||||
\(464\) | 5.20573e10i | 1.12308i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.83906e9 | −0.0814106 | ||||||||
\(467\) | −1.84770e10 | + | 1.84770e10i | −0.388475 | + | 0.388475i | −0.874143 | − | 0.485668i | \(-0.838576\pi\) |
0.485668 | + | 0.874143i | \(0.338576\pi\) | |||||||
\(468\) | 3.06854e8 | + | 3.06854e8i | 0.00639659 | + | 0.00639659i | ||||
\(469\) | 4.42648e10i | 0.914887i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.60375e10 | 0.732269 | ||||||||
\(472\) | −2.48474e10 | + | 2.48474e10i | −0.500626 | + | 0.500626i | ||||
\(473\) | 6.78323e10 | + | 6.78323e10i | 1.35516 | + | 1.35516i | ||||
\(474\) | 1.84030e10i | 0.364565i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.45028e9 | −0.0282503 | ||||||||
\(477\) | 2.17357e9 | − | 2.17357e9i | 0.0419855 | − | 0.0419855i | ||||
\(478\) | 4.00604e10 | + | 4.00604e10i | 0.767368 | + | 0.767368i | ||||
\(479\) | 7.28099e10i | 1.38308i | 0.722337 | + | 0.691542i | \(0.243068\pi\) | ||||
−0.722337 | + | 0.691542i | \(0.756932\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.73710e10 | 0.324521 | ||||||||
\(482\) | −5.96322e10 | + | 5.96322e10i | −1.10482 | + | 1.10482i | ||||
\(483\) | −8.65466e9 | − | 8.65466e9i | −0.159024 | − | 0.159024i | ||||
\(484\) | 3.71611e9i | 0.0677185i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.51452e9 | 0.0629972 | ||||||||
\(487\) | −4.95995e9 | + | 4.95995e9i | −0.0881783 | + | 0.0881783i | −0.749820 | − | 0.661642i | \(-0.769860\pi\) |
0.661642 | + | 0.749820i | \(0.269860\pi\) | |||||||
\(488\) | −6.44346e10 | − | 6.44346e10i | −1.13616 | − | 1.13616i | ||||
\(489\) | − | 1.90634e10i | − | 0.333400i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.34792e10 | 1.43632 | 0.718162 | − | 0.695876i | \(-0.244984\pi\) | ||||
0.718162 | + | 0.695876i | \(0.244984\pi\) | |||||||
\(492\) | 1.11266e9 | − | 1.11266e9i | 0.0189890 | − | 0.0189890i | ||||
\(493\) | −5.65777e10 | − | 5.65777e10i | −0.957761 | − | 0.957761i | ||||
\(494\) | − | 5.46262e10i | − | 0.917262i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.16801e10 | 0.358207 | ||||||||
\(497\) | 7.02903e9 | − | 7.02903e9i | 0.115205 | − | 0.115205i | ||||
\(498\) | −3.49989e10 | − | 3.49989e10i | −0.569032 | − | 0.569032i | ||||
\(499\) | − | 6.77551e10i | − | 1.09280i | −0.837525 | − | 0.546399i | \(-0.815998\pi\) | ||
0.837525 | − | 0.546399i | \(-0.184002\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.53702e10 | 0.243965 | ||||||||
\(502\) | 7.59070e9 | − | 7.59070e9i | 0.119527 | − | 0.119527i | ||||
\(503\) | 1.13594e10 | + | 1.13594e10i | 0.177453 | + | 0.177453i | 0.790245 | − | 0.612792i | \(-0.209953\pi\) |
−0.612792 | + | 0.790245i | \(0.709953\pi\) | |||||||
\(504\) | 1.49358e10i | 0.231476i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.25532e10 | −0.954217 | ||||||||
\(507\) | −1.13157e10 | + | 1.13157e10i | −0.171258 | + | 0.171258i | ||||
\(508\) | 2.62072e9 | + | 2.62072e9i | 0.0393520 | + | 0.0393520i | ||||
\(509\) | 1.19786e11i | 1.78458i | 0.451468 | + | 0.892288i | \(0.350901\pi\) | ||||
−0.451468 | + | 0.892288i | \(0.649099\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.82619e10 | −0.267831 | ||||||||
\(512\) | −5.09278e10 | + | 5.09278e10i | −0.741097 | + | 0.741097i | ||||
\(513\) | 1.15542e10 | + | 1.15542e10i | 0.166828 | + | 0.166828i | ||||
\(514\) | − | 7.06169e10i | − | 1.01171i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.64036e9 | −0.0231387 | ||||||||
\(517\) | 6.42184e10 | − | 6.42184e10i | 0.898871 | − | 0.898871i | ||||
\(518\) | 1.45402e10 | + | 1.45402e10i | 0.201954 | + | 0.201954i | ||||
\(519\) | − | 4.13522e10i | − | 0.569940i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.94713e10 | 0.807154 | 0.403577 | − | 0.914946i | \(-0.367767\pi\) | ||||
0.403577 | + | 0.914946i | \(0.367767\pi\) | |||||||
\(522\) | −2.00402e10 | + | 2.00402e10i | −0.269911 | + | 0.269911i | ||||
\(523\) | −2.63261e10 | − | 2.63261e10i | −0.351868 | − | 0.351868i | 0.508936 | − | 0.860804i | \(-0.330039\pi\) |
−0.860804 | + | 0.508936i | \(0.830039\pi\) | |||||||
\(524\) | − | 3.42715e9i | − | 0.0454577i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.93488e10 | 0.383396 | ||||||||
\(527\) | −2.35626e10 | + | 2.35626e10i | −0.305479 | + | 0.305479i | ||||
\(528\) | 5.20505e10 | + | 5.20505e10i | 0.669714 | + | 0.669714i | ||||
\(529\) | − | 5.28256e10i | − | 0.674561i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.84485e10 | −0.232051 | ||||||||
\(532\) | −1.68881e9 | + | 1.68881e9i | −0.0210831 | + | 0.0210831i | ||||
\(533\) | −5.67797e10 | − | 5.67797e10i | −0.703532 | − | 0.703532i | ||||
\(534\) | 4.83948e10i | 0.595160i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.12473e11 | −1.36267 | ||||||||
\(537\) | 2.30600e10 | − | 2.30600e10i | 0.277308 | − | 0.277308i | ||||
\(538\) | 8.07884e9 | + | 8.07884e9i | 0.0964317 | + | 0.0964317i | ||||
\(539\) | − | 7.67350e10i | − | 0.909156i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.20878e11 | 1.41110 | 0.705550 | − | 0.708660i | \(-0.250700\pi\) | ||||
0.705550 | + | 0.708660i | \(0.250700\pi\) | |||||||
\(542\) | 9.51890e10 | − | 9.51890e10i | 1.10304 | − | 1.10304i | ||||
\(543\) | −3.64995e10 | − | 3.64995e10i | −0.419844 | − | 0.419844i | ||||
\(544\) | − | 7.24331e9i | − | 0.0827068i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.62144e10 | 0.294964 | ||||||||
\(547\) | 7.50251e10 | − | 7.50251e10i | 0.838025 | − | 0.838025i | −0.150574 | − | 0.988599i | \(-0.548112\pi\) |
0.988599 | + | 0.150574i | \(0.0481120\pi\) | |||||||
\(548\) | −3.60175e9 | − | 3.60175e9i | −0.0399385 | − | 0.0399385i | ||||
\(549\) | − | 4.78408e10i | − | 0.526635i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.31767e11 | −1.42955 | ||||||||
\(552\) | 2.19907e10 | − | 2.19907e10i | 0.236855 | − | 0.236855i | ||||
\(553\) | −2.90335e10 | − | 2.90335e10i | −0.310455 | − | 0.310455i | ||||
\(554\) | 3.04131e10i | 0.322865i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.56948e9 | 0.0373513 | ||||||||
\(557\) | 6.33690e10 | − | 6.33690e10i | 0.658348 | − | 0.658348i | −0.296641 | − | 0.954989i | \(-0.595866\pi\) |
0.954989 | + | 0.296641i | \(0.0958664\pi\) | |||||||
\(558\) | 8.34606e9 | + | 8.34606e9i | 0.0860885 | + | 0.0860885i | ||||
\(559\) | 8.37084e10i | 0.857279i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.13141e11 | −1.14227 | ||||||||
\(562\) | 4.88575e10 | − | 4.88575e10i | 0.489763 | − | 0.489763i | ||||
\(563\) | 1.07781e10 | + | 1.07781e10i | 0.107277 | + | 0.107277i | 0.758708 | − | 0.651431i | \(-0.225831\pi\) |
−0.651431 | + | 0.758708i | \(0.725831\pi\) | |||||||
\(564\) | 1.55296e9i | 0.0153477i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.20755e10 | −0.117663 | ||||||||
\(567\) | −5.54469e9 | + | 5.54469e9i | −0.0536469 | + | 0.0536469i | ||||
\(568\) | 1.78602e10 | + | 1.78602e10i | 0.171590 | + | 0.171590i | ||||
\(569\) | − | 2.03427e11i | − | 1.94071i | −0.241685 | − | 0.970355i | \(-0.577700\pi\) | ||
0.241685 | − | 0.970355i | \(-0.422300\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.50525e10 | 0.329742 | 0.164871 | − | 0.986315i | \(-0.447279\pi\) | ||||
0.164871 | + | 0.986315i | \(0.447279\pi\) | |||||||
\(572\) | −3.49898e9 | + | 3.49898e9i | −0.0326857 | + | 0.0326857i | ||||
\(573\) | −3.45284e10 | − | 3.45284e10i | −0.320301 | − | 0.320301i | ||||
\(574\) | − | 9.50539e10i | − | 0.875634i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.79039e10 | −0.344345 | ||||||||
\(577\) | −8.96159e10 | + | 8.96159e10i | −0.808504 | + | 0.808504i | −0.984407 | − | 0.175904i | \(-0.943715\pi\) |
0.175904 | + | 0.984407i | \(0.443715\pi\) | |||||||
\(578\) | −2.70647e10 | − | 2.70647e10i | −0.242489 | − | 0.242489i | ||||
\(579\) | 2.20897e10i | 0.196551i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.10432e11 | 0.969148 | ||||||||
\(582\) | 1.99034e10 | − | 1.99034e10i | 0.173474 | − | 0.173474i | ||||
\(583\) | 2.47847e10 | + | 2.47847e10i | 0.214540 | + | 0.214540i | ||||
\(584\) | − | 4.64018e10i | − | 0.398918i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.90657e10 | 0.331288 | ||||||||
\(587\) | 3.59120e10 | − | 3.59120e10i | 0.302474 | − | 0.302474i | −0.539507 | − | 0.841981i | \(-0.681389\pi\) |
0.841981 | + | 0.539507i | \(0.181389\pi\) | |||||||
\(588\) | 9.27823e8 | + | 9.27823e8i | 0.00776168 | + | 0.00776168i | ||||
\(589\) | 5.48762e10i | 0.455956i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.14445e10 | −0.585624 | ||||||||
\(592\) | −3.56278e10 | + | 3.56278e10i | −0.290069 | + | 0.290069i | ||||
\(593\) | 7.94062e10 | + | 7.94062e10i | 0.642148 | + | 0.642148i | 0.951083 | − | 0.308935i | \(-0.0999725\pi\) |
−0.308935 | + | 0.951083i | \(0.599973\pi\) | |||||||
\(594\) | 4.00753e10i | 0.321907i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.38986e9 | −0.0268656 | ||||||||
\(597\) | −2.32695e10 | + | 2.32695e10i | −0.183185 | + | 0.183185i | ||||
\(598\) | −3.85969e10 | − | 3.85969e10i | −0.301819 | − | 0.301819i | ||||
\(599\) | 6.17729e10i | 0.479834i | 0.970793 | + | 0.239917i | \(0.0771202\pi\) | ||||
−0.970793 | + | 0.239917i | \(0.922880\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.64109e10 | −0.509028 | −0.254514 | − | 0.967069i | \(-0.581916\pi\) | ||||
−0.254514 | + | 0.967069i | \(0.581916\pi\) | |||||||
\(602\) | −7.00675e10 | + | 7.00675e10i | −0.533495 | + | 0.533495i | ||||
\(603\) | −4.17540e10 | − | 4.17540e10i | −0.315812 | − | 0.315812i | ||||
\(604\) | 5.02091e9i | 0.0377255i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.25431e10 | 0.241306 | ||||||||
\(607\) | −9.40030e10 | + | 9.40030e10i | −0.692448 | + | 0.692448i | −0.962770 | − | 0.270322i | \(-0.912870\pi\) |
0.270322 | + | 0.962770i | \(0.412870\pi\) | |||||||
\(608\) | −8.43466e9 | − | 8.43466e9i | −0.0617239 | − | 0.0617239i | ||||
\(609\) | − | 6.32330e10i | − | 0.459700i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.92487e10 | 0.568627 | ||||||||
\(612\) | 1.36801e9 | − | 1.36801e9i | 0.00975179 | − | 0.00975179i | ||||
\(613\) | 6.90775e10 | + | 6.90775e10i | 0.489209 | + | 0.489209i | 0.908057 | − | 0.418848i | \(-0.137566\pi\) |
−0.418848 | + | 0.908057i | \(0.637566\pi\) | |||||||
\(614\) | 8.30273e10i | 0.584181i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.70309e11 | −1.18281 | ||||||||
\(617\) | 3.90224e10 | − | 3.90224e10i | 0.269261 | − | 0.269261i | −0.559542 | − | 0.828802i | \(-0.689023\pi\) |
0.828802 | + | 0.559542i | \(0.189023\pi\) | |||||||
\(618\) | 5.74004e10 | + | 5.74004e10i | 0.393515 | + | 0.393515i | ||||
\(619\) | − | 1.05074e11i | − | 0.715701i | −0.933779 | − | 0.357850i | \(-0.883510\pi\) | ||
0.933779 | − | 0.357850i | \(-0.116490\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.63275e10 | 0.109787 | ||||||||
\(622\) | 7.88468e10 | − | 7.88468e10i | 0.526772 | − | 0.526772i | ||||
\(623\) | −7.63502e10 | − | 7.63502e10i | −0.506825 | − | 0.506825i | ||||
\(624\) | 6.42330e10i | 0.423662i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5.46959e10 | −0.356170 | ||||||||
\(627\) | −1.31749e11 | + | 1.31749e11i | −0.852469 | + | 0.852469i | ||||
\(628\) | −4.96862e9 | − | 4.96862e9i | −0.0319446 | − | 0.0319446i | ||||
\(629\) | − | 7.74430e10i | − | 0.494743i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.43175e11 | 0.903128 | 0.451564 | − | 0.892239i | \(-0.350866\pi\) | ||||
0.451564 | + | 0.892239i | \(0.350866\pi\) | |||||||
\(632\) | 7.37715e10 | − | 7.37715e10i | 0.462403 | − | 0.462403i | ||||
\(633\) | 8.49031e10 | + | 8.49031e10i | 0.528821 | + | 0.528821i | ||||
\(634\) | 5.09726e10i | 0.315486i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.99356e8 | −0.00366316 | ||||||||
\(637\) | 4.73474e10 | − | 4.73474e10i | 0.287566 | − | 0.287566i | ||||
\(638\) | −2.28514e11 | − | 2.28514e11i | −1.37921 | − | 1.37921i | ||||
\(639\) | 1.32606e10i | 0.0795355i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.98847e11 | −1.17784 | −0.588920 | − | 0.808191i | \(-0.700447\pi\) | ||||
−0.588920 | + | 0.808191i | \(0.700447\pi\) | |||||||
\(642\) | −7.74528e10 | + | 7.74528e10i | −0.455929 | + | 0.455929i | ||||
\(643\) | 1.71558e11 | + | 1.71558e11i | 1.00362 | + | 1.00362i | 0.999993 | + | 0.00362360i | \(0.00115343\pi\) |
0.00362360 | + | 0.999993i | \(0.498847\pi\) | |||||||
\(644\) | 2.38650e9i | 0.0138745i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.43534e11 | −1.39839 | ||||||||
\(647\) | 6.30833e9 | − | 6.30833e9i | 0.0359996 | − | 0.0359996i | −0.688878 | − | 0.724877i | \(-0.741896\pi\) |
0.724877 | + | 0.688878i | \(0.241896\pi\) | |||||||
\(648\) | −1.40886e10 | − | 1.40886e10i | −0.0799037 | − | 0.0799037i | ||||
\(649\) | − | 2.10364e11i | − | 1.18575i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.63344e10 | −0.146622 | ||||||||
\(652\) | −2.62835e9 | + | 2.62835e9i | −0.0145443 | + | 0.0145443i | ||||
\(653\) | 1.17079e9 | + | 1.17079e9i | 0.00643912 | + | 0.00643912i | 0.710319 | − | 0.703880i | \(-0.248551\pi\) |
−0.703880 | + | 0.710319i | \(0.748551\pi\) | |||||||
\(654\) | 1.47880e11i | 0.808346i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.32910e11 | 1.25769 | ||||||||
\(657\) | 1.72260e10 | − | 1.72260e10i | 0.0924534 | − | 0.0924534i | ||||
\(658\) | 6.63345e10 | + | 6.63345e10i | 0.353864 | + | 0.353864i | ||||
\(659\) | 1.23390e11i | 0.654243i | 0.944982 | + | 0.327122i | \(0.106079\pi\) | ||||
−0.944982 | + | 0.327122i | \(0.893921\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.02550e11 | −1.06103 | −0.530514 | − | 0.847676i | \(-0.678001\pi\) | ||||
−0.530514 | + | 0.847676i | \(0.678001\pi\) | |||||||
\(662\) | −7.04371e10 | + | 7.04371e10i | −0.366749 | + | 0.366749i | ||||
\(663\) | −6.98105e10 | − | 6.98105e10i | −0.361299 | − | 0.361299i | ||||
\(664\) | 2.80598e11i | 1.44348i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.74309e10 | −0.139426 | ||||||||
\(667\) | −9.31013e10 | + | 9.31013e10i | −0.470384 | + | 0.470384i | ||||
\(668\) | −2.11915e9 | − | 2.11915e9i | −0.0106428 | − | 0.0106428i | ||||
\(669\) | − | 6.09337e10i | − | 0.304196i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.45518e11 | 2.69103 | ||||||||
\(672\) | 4.04768e9 | − | 4.04768e9i | 0.0198486 | − | 0.0198486i | ||||
\(673\) | −9.90515e9 | − | 9.90515e9i | −0.0482837 | − | 0.0482837i | 0.682553 | − | 0.730836i | \(-0.260870\pi\) |
−0.730836 | + | 0.682553i | \(0.760870\pi\) | |||||||
\(674\) | 7.49420e10i | 0.363149i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.12028e9 | 0.0149419 | ||||||||
\(677\) | 2.62761e11 | − | 2.62761e11i | 1.25086 | − | 1.25086i | 0.295518 | − | 0.955337i | \(-0.404508\pi\) |
0.955337 | − | 0.295518i | \(-0.0954922\pi\) | |||||||
\(678\) | 1.14974e11 | + | 1.14974e11i | 0.544102 | + | 0.544102i | ||||
\(679\) | 6.28013e10i | 0.295454i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.53027e11 | 0.711508 | ||||||||
\(682\) | −9.51682e10 | + | 9.51682e10i | −0.439901 | + | 0.439901i | ||||
\(683\) | 1.89021e11 | + | 1.89021e11i | 0.868613 | + | 0.868613i | 0.992319 | − | 0.123706i | \(-0.0394781\pi\) |
−0.123706 | + | 0.992319i | \(0.539478\pi\) | |||||||
\(684\) | − | 3.18603e9i | − | 0.0145555i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.27762e11 | 1.02846 | ||||||||
\(687\) | 4.40901e10 | − | 4.40901e10i | 0.197931 | − | 0.197931i | ||||
\(688\) | −1.71686e11 | − | 1.71686e11i | −0.766268 | − | 0.766268i | ||||
\(689\) | 3.05855e10i | 0.135718i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.60447e11 | 1.14237 | 0.571186 | − | 0.820821i | \(-0.306483\pi\) | ||||
0.571186 | + | 0.820821i | \(0.306483\pi\) | |||||||
\(692\) | −5.70138e9 | + | 5.70138e9i | −0.0248631 | + | 0.0248631i | ||||
\(693\) | −6.32248e10 | − | 6.32248e10i | −0.274129 | − | 0.274129i | ||||
\(694\) | 1.66964e11i | 0.719753i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.60670e11 | 0.684694 | ||||||||
\(697\) | −2.53134e11 | + | 2.53134e11i | −1.07256 | + | 1.07256i | ||||
\(698\) | −3.72331e10 | − | 3.72331e10i | −0.156858 | − | 0.156858i | ||||
\(699\) | 1.14263e10i | 0.0478626i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.55285e11 | −1.05719 | −0.528594 | − | 0.848875i | \(-0.677281\pi\) | ||||
−0.528594 | + | 0.848875i | \(0.677281\pi\) | |||||||
\(702\) | −2.47274e10 | + | 2.47274e10i | −0.101819 | + | 0.101819i | ||||
\(703\) | −9.01804e10 | − | 9.01804e10i | −0.369225 | − | 0.369225i | ||||
\(704\) | − | 4.32210e11i | − | 1.75956i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.05969e11 | 0.426539 | ||||||||
\(707\) | −5.13416e10 | + | 5.13416e10i | −0.205491 | + | 0.205491i | ||||
\(708\) | 2.54356e9 | + | 2.54356e9i | 0.0101230 | + | 0.0101230i | ||||
\(709\) | 2.98420e11i | 1.18098i | 0.807044 | + | 0.590491i | \(0.201066\pi\) | ||||
−0.807044 | + | 0.590491i | \(0.798934\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.47732e10 | 0.214333 | ||||||||
\(712\) | 1.93999e11 | − | 1.93999e11i | 0.754883 | − | 0.754883i | ||||
\(713\) | 3.87735e10 | + | 3.87735e10i | 0.150029 | + | 0.150029i | ||||
\(714\) | − | 1.16869e11i | − | 0.449682i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.35874e9 | −0.0241946 | ||||||||
\(717\) | 1.19233e11 | − | 1.19233e11i | 0.451148 | − | 0.451148i | ||||
\(718\) | 1.23870e11 | + | 1.23870e11i | 0.466087 | + | 0.466087i | ||||
\(719\) | 5.68269e10i | 0.212637i | 0.994332 | + | 0.106318i | \(0.0339063\pi\) | ||||
−0.994332 | + | 0.106318i | \(0.966094\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.81116e11 | −0.670216 | ||||||||
\(722\) | −9.48955e10 | + | 9.48955e10i | −0.349218 | + | 0.349218i | ||||
\(723\) | 1.77485e11 | + | 1.77485e11i | 0.649543 | + | 0.649543i | ||||
\(724\) | 1.00647e10i | 0.0366307i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.99458e11 | −1.07793 | ||||||||
\(727\) | −2.45376e11 | + | 2.45376e11i | −0.878404 | + | 0.878404i | −0.993369 | − | 0.114966i | \(-0.963324\pi\) |
0.114966 | + | 0.993369i | \(0.463324\pi\) | |||||||
\(728\) | −1.05085e11 | − | 1.05085e11i | −0.374124 | − | 0.374124i | ||||
\(729\) | − | 1.04604e10i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.73188e11 | 1.30695 | ||||||||
\(732\) | −6.59600e9 | + | 6.59600e9i | −0.0229740 | + | 0.0229740i | ||||
\(733\) | −1.90055e11 | − | 1.90055e11i | −0.658361 | − | 0.658361i | 0.296631 | − | 0.954992i | \(-0.404137\pi\) |
−0.954992 | + | 0.296631i | \(0.904137\pi\) | |||||||
\(734\) | 5.31547e10i | 0.183129i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.19192e10 | −0.0406197 | ||||||||
\(737\) | 4.76111e11 | − | 4.76111e11i | 1.61376 | − | 1.61376i | ||||
\(738\) | 8.96622e10 | + | 8.96622e10i | 0.302262 | + | 0.302262i | ||||
\(739\) | 4.93909e11i | 1.65603i | 0.560704 | + | 0.828016i | \(0.310531\pi\) | ||||
−0.560704 | + | 0.828016i | \(0.689469\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.62585e11 | −0.539273 | ||||||||
\(742\) | −2.56014e10 | + | 2.56014e10i | −0.0844593 | + | 0.0844593i | ||||
\(743\) | 1.76600e11 | + | 1.76600e11i | 0.579474 | + | 0.579474i | 0.934758 | − | 0.355284i | \(-0.115616\pi\) |
−0.355284 | + | 0.934758i | \(0.615616\pi\) | |||||||
\(744\) | − | 6.69133e10i | − | 0.218384i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.89895e11 | −1.25890 | ||||||||
\(747\) | −1.04168e11 | + | 1.04168e11i | −0.334543 | + | 0.334543i | ||||
\(748\) | 1.55991e10 | + | 1.55991e10i | 0.0498303 | + | 0.0498303i | ||||
\(749\) | − | 2.44387e11i | − | 0.776516i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.29096e11 | 0.405839 | 0.202920 | − | 0.979195i | \(-0.434957\pi\) | ||||
0.202920 | + | 0.979195i | \(0.434957\pi\) | |||||||
\(752\) | −1.62539e11 | + | 1.62539e11i | −0.508260 | + | 0.508260i | ||||
\(753\) | −2.25924e10 | − | 2.25924e10i | −0.0702719 | − | 0.0702719i | ||||
\(754\) | − | 2.81998e11i | − | 0.872490i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.52893e9 | 0.00468060 | ||||||||
\(757\) | 2.24616e11 | − | 2.24616e11i | 0.684002 | − | 0.684002i | −0.276897 | − | 0.960899i | \(-0.589306\pi\) |
0.960899 | + | 0.276897i | \(0.0893062\pi\) | |||||||
\(758\) | 6.24165e10 | + | 6.24165e10i | 0.189070 | + | 0.189070i | ||||
\(759\) | 1.86178e11i | 0.560999i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.21683e10 | 0.215183 | 0.107591 | − | 0.994195i | \(-0.465686\pi\) | ||||
0.107591 | + | 0.994195i | \(0.465686\pi\) | |||||||
\(762\) | −2.11188e11 | + | 2.11188e11i | −0.626396 | + | 0.626396i | ||||
\(763\) | −2.33302e11 | − | 2.33302e11i | −0.688369 | − | 0.688369i | ||||
\(764\) | 9.52112e9i | 0.0279457i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.31615e11 | −0.672746 | ||||||||
\(767\) | 1.29800e11 | − | 1.29800e11i | 0.375053 | − | 0.375053i | ||||
\(768\) | 1.51570e10 | + | 1.51570e10i | 0.0435681 | + | 0.0435681i | ||||
\(769\) | − | 5.91023e11i | − | 1.69005i | −0.534729 | − | 0.845023i | \(-0.679586\pi\) | ||
0.534729 | − | 0.845023i | \(-0.320414\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.10179e11 | −0.594801 | ||||||||
\(772\) | 3.04559e9 | − | 3.04559e9i | 0.00857437 | − | 0.00857437i | ||||
\(773\) | −1.90676e11 | − | 1.90676e11i | −0.534045 | − | 0.534045i | 0.387729 | − | 0.921773i | \(-0.373260\pi\) |
−0.921773 | + | 0.387729i | \(0.873260\pi\) | |||||||
\(774\) | − | 1.32186e11i | − | 0.368317i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.59573e11 | −0.440059 | ||||||||
\(777\) | 4.32764e10 | − | 4.32764e10i | 0.118732 | − | 0.118732i | ||||
\(778\) | 4.67506e10 | + | 4.67506e10i | 0.127605 | + | 0.127605i | ||||
\(779\) | 5.89538e11i | 1.60089i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.51208e11 | −0.406416 | ||||||||
\(782\) | −1.72072e11 | + | 1.72072e11i | −0.460133 | + | 0.460133i | ||||
\(783\) | 5.96462e10 | + | 5.96462e10i | 0.158685 | + | 0.158685i | ||||
\(784\) | 1.94219e11i | 0.514076i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.76173e11 | 0.723586 | ||||||||
\(787\) | −7.13349e10 | + | 7.13349e10i | −0.185953 | + | 0.185953i | −0.793944 | − | 0.607991i | \(-0.791976\pi\) |
0.607991 | + | 0.793944i | \(0.291976\pi\) | |||||||
\(788\) | 9.85033e9 | + | 9.85033e9i | 0.0255473 | + | 0.0255473i | ||||
\(789\) | − | 8.73516e10i | − | 0.225405i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.62777e11 | −0.926689 | ||||||||
\(792\) | 1.60649e11 | − | 1.60649e11i | 0.408297 | − | 0.408297i | ||||
\(793\) | 3.36598e11 | + | 3.36598e11i | 0.851175 | + | 0.851175i | ||||
\(794\) | − | 3.91738e11i | − | 0.985631i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.41651e9 | 0.0159826 | ||||||||
\(797\) | −4.72991e11 | + | 4.72991e11i | −1.17225 | + | 1.17225i | −0.190577 | + | 0.981672i | \(0.561036\pi\) |
−0.981672 | + | 0.190577i | \(0.938964\pi\) | |||||||
\(798\) | −1.36091e11 | − | 1.36091e11i | −0.335596 | − | 0.335596i | ||||
\(799\) | − | 3.53306e11i | − | 0.866889i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.44039e11 | 0.349904 | ||||||||
\(802\) | −2.04974e11 | + | 2.04974e11i | −0.495451 | + | 0.495451i | ||||
\(803\) | 1.96424e11 | + | 1.96424e11i | 0.472424 | + | 0.472424i | ||||
\(804\) | 1.15136e10i | 0.0275541i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.17442e11 | −0.278282 | ||||||||
\(807\) | 2.40452e10 | − | 2.40452e10i | 0.0566937 | − | 0.0566937i | ||||
\(808\) | −1.30455e11 | − | 1.30455e11i | −0.306065 | − | 0.306065i | ||||
\(809\) | 2.07110e11i | 0.483511i | 0.970337 | + | 0.241756i | \(0.0777233\pi\) | ||||
−0.970337 | + | 0.241756i | \(0.922277\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.53517e11 | −0.817197 | −0.408598 | − | 0.912714i | \(-0.633982\pi\) | ||||
−0.408598 | + | 0.912714i | \(0.633982\pi\) | |||||||
\(812\) | −8.71818e9 | + | 8.71818e9i | −0.0200540 | + | 0.0200540i | ||||
\(813\) | −2.83313e11 | − | 2.83313e11i | −0.648492 | − | 0.648492i | ||||
\(814\) | − | 3.12788e11i | − | 0.712447i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.86363e11 | 0.645886 | ||||||||
\(817\) | 4.34568e11 | − | 4.34568e11i | 0.975371 | − | 0.975371i | ||||
\(818\) | −2.25939e11 | − | 2.25939e11i | −0.504636 | − | 0.504636i | ||||
\(819\) | − | 7.80225e10i | − | 0.173414i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.67064e10 | 0.0807922 | 0.0403961 | − | 0.999184i | \(-0.487138\pi\) | ||||
0.0403961 | + | 0.999184i | \(0.487138\pi\) | |||||||
\(822\) | 2.90243e11 | − | 2.90243e11i | 0.635732 | − | 0.635732i | ||||
\(823\) | −2.88642e11 | − | 2.88642e11i | −0.629158 | − | 0.629158i | 0.318698 | − | 0.947856i | \(-0.396754\pi\) |
−0.947856 | + | 0.318698i | \(0.896754\pi\) | |||||||
\(824\) | − | 4.60199e11i | − | 0.998244i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.17296e11 | 0.466800 | ||||||||
\(827\) | −1.71126e11 | + | 1.71126e11i | −0.365842 | + | 0.365842i | −0.865958 | − | 0.500117i | \(-0.833290\pi\) |
0.500117 | + | 0.865958i | \(0.333290\pi\) | |||||||
\(828\) | −2.25113e9 | − | 2.25113e9i | −0.00478938 | − | 0.00478938i | ||||
\(829\) | − | 4.90777e11i | − | 1.03912i | −0.854434 | − | 0.519561i | \(-0.826096\pi\) | ||
0.854434 | − | 0.519561i | \(-0.173904\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.05191e10 | 0.189817 | ||||||||
\(832\) | 2.66684e11 | − | 2.66684e11i | 0.556550 | − | 0.556550i | ||||
\(833\) | −2.11084e11 | − | 2.11084e11i | −0.438404 | − | 0.438404i | ||||
\(834\) | 2.87642e11i | 0.594550i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.63296e10 | 0.0743765 | ||||||||
\(837\) | 2.48406e10 | − | 2.48406e10i | 0.0506128 | − | 0.0506128i | ||||
\(838\) | 4.42040e11 | + | 4.42040e11i | 0.896366 | + | 0.896366i | ||||
\(839\) | − | 4.10905e11i | − | 0.829266i | −0.909989 | − | 0.414633i | \(-0.863910\pi\) | ||
0.909989 | − | 0.414633i | \(-0.136090\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.79974e11 | −0.359771 | ||||||||
\(842\) | 6.13764e11 | − | 6.13764e11i | 1.22110 | − | 1.22110i | ||||
\(843\) | −1.45416e11 | − | 1.45416e11i | −0.287939 | − | 0.287939i | ||||
\(844\) | − | 2.34118e10i | − | 0.0461387i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.25144e11 | −0.244302 | ||||||||
\(847\) | 4.72441e11 | − | 4.72441e11i | 0.917938 | − | 0.917938i | ||||
\(848\) | −6.27308e10 | − | 6.27308e10i | −0.121310 | − | 0.121310i | ||||
\(849\) | 3.59405e10i | 0.0691756i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.27436e11 | −0.242982 | ||||||||
\(852\) | 1.82830e9 | − | 1.82830e9i | 0.00346967 | − | 0.00346967i | ||||
\(853\) | 3.54583e11 | + | 3.54583e11i | 0.669764 | + | 0.669764i | 0.957661 | − | 0.287898i | \(-0.0929562\pi\) |
−0.287898 | + | 0.957661i | \(0.592956\pi\) | |||||||
\(854\) | 5.63494e11i | 1.05939i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.20966e11 | 1.15657 | ||||||||
\(857\) | −5.99454e11 | + | 5.99454e11i | −1.11130 | + | 1.11130i | −0.118329 | + | 0.992974i | \(0.537754\pi\) |
−0.992974 | + | 0.118329i | \(0.962246\pi\) | |||||||
\(858\) | −2.81961e11 | − | 2.81961e11i | −0.520284 | − | 0.520284i | ||||
\(859\) | 2.91954e11i | 0.536218i | 0.963389 | + | 0.268109i | \(0.0863988\pi\) | ||||
−0.963389 | + | 0.268109i | \(0.913601\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.82911e11 | −0.514799 | ||||||||
\(862\) | 7.54737e10 | − | 7.54737e10i | 0.136699 | − | 0.136699i | ||||
\(863\) | 2.27449e11 | + | 2.27449e11i | 0.410053 | + | 0.410053i | 0.881757 | − | 0.471704i | \(-0.156361\pi\) |
−0.471704 | + | 0.881757i | \(0.656361\pi\) | |||||||
\(864\) | 7.63616e9i | 0.0137031i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.88035e11 | −1.04552 | ||||||||
\(867\) | −8.05534e10 | + | 8.05534e10i | −0.142563 | + | 0.142563i | ||||
\(868\) | 3.63082e9 | + | 3.63082e9i | 0.00639625 | + | 0.00639625i | ||||
\(869\) | 6.24566e11i | 1.09522i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.87545e11 | 1.02087 | ||||||||
\(872\) | 5.92801e11 | − | 5.92801e11i | 1.02528 | − | 1.02528i | ||||
\(873\) | −5.92390e10 | − | 5.92390e10i | −0.101988 | − | 0.101988i | ||||
\(874\) | 4.00747e11i | 0.686792i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.75003e9 | −0.00806640 | ||||||||
\(877\) | 3.12100e11 | − | 3.12100e11i | 0.527589 | − | 0.527589i | −0.392264 | − | 0.919853i | \(-0.628308\pi\) |
0.919853 | + | 0.392264i | \(0.128308\pi\) | |||||||
\(878\) | 5.48613e11 | + | 5.48613e11i | 0.923183 | + | 0.923183i | ||||
\(879\) | − | 1.16272e11i | − | 0.194769i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.56713e11 | −0.924119 | −0.462059 | − | 0.886849i | \(-0.652889\pi\) | ||||
−0.462059 | + | 0.886849i | \(0.652889\pi\) | |||||||
\(882\) | −7.47674e10 | + | 7.47674e10i | −0.123549 | + | 0.123549i | ||||
\(883\) | 3.44597e11 | + | 3.44597e11i | 0.566851 | + | 0.566851i | 0.931245 | − | 0.364394i | \(-0.118724\pi\) |
−0.364394 | + | 0.931245i | \(0.618724\pi\) | |||||||
\(884\) | 1.92501e10i | 0.0315227i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.38206e11 | 1.36024 | ||||||||
\(887\) | −1.77733e11 | + | 1.77733e11i | −0.287127 | + | 0.287127i | −0.835943 | − | 0.548816i | \(-0.815079\pi\) |
0.548816 | + | 0.835943i | \(0.315079\pi\) | |||||||
\(888\) | 1.09961e11 | + | 1.09961e11i | 0.176843 | + | 0.176843i | ||||
\(889\) | − | 6.66361e11i | − | 1.06685i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.19277e11 | 0.189254 | ||||||||
\(892\) | −8.40116e9 | + | 8.40116e9i | −0.0132703 | + | 0.0132703i | ||||
\(893\) | −4.11416e11 | − | 4.11416e11i | −0.646956 | − | 0.646956i | ||||
\(894\) | − | 2.73168e11i | − | 0.427641i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.15116e11 | 0.644077 | ||||||||
\(897\) | −1.14877e11 | + | 1.14877e11i | −0.177444 | + | 0.177444i | ||||
\(898\) | −4.60695e11 | − | 4.60695e11i | −0.708449 | − | 0.708449i | ||||
\(899\) | 2.83288e11i | 0.433700i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.36356e11 | 0.206907 | ||||||||
\(902\) | −1.02240e12 | + | 1.02240e12i | −1.54452 | + | 1.54452i | ||||
\(903\) | 2.08543e11 | + | 2.08543e11i | 0.313650 | + | 0.313650i | ||||
\(904\) | − | 9.21785e11i | − | 1.38024i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.04604e11 | −0.600506 | ||||||||
\(907\) | −3.59456e11 | + | 3.59456e11i | −0.531149 | + | 0.531149i | −0.920914 | − | 0.389765i | \(-0.872556\pi\) |
0.389765 | + | 0.920914i | \(0.372556\pi\) | |||||||
\(908\) | −2.10984e10 | − | 2.10984e10i | −0.0310389 | − | 0.0310389i | ||||
\(909\) | − | 9.68588e10i | − | 0.141868i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.36965e11 | −0.634414 | −0.317207 | − | 0.948356i | \(-0.602745\pi\) | ||||
−0.317207 | + | 0.948356i | \(0.602745\pi\) | |||||||
\(912\) | 3.33462e11 | − | 3.33462e11i | 0.482023 | − | 0.482023i | ||||
\(913\) | −1.18780e12 | − | 1.18780e12i | −1.70947 | − | 1.70947i | ||||
\(914\) | 4.66466e11i | 0.668398i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.21577e10 | −0.0172691 | ||||||||
\(917\) | −4.35704e11 | + | 4.35704e11i | −0.616189 | + | 0.616189i | ||||
\(918\) | 1.10240e11 | + | 1.10240e11i | 0.155227 | + | 0.155227i | ||||
\(919\) | 1.18791e12i | 1.66542i | 0.553713 | + | 0.832708i | \(0.313211\pi\) | ||||
−0.553713 | + | 0.832708i | \(0.686789\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.47116e11 | 0.343449 | ||||||||
\(922\) | −5.93180e11 | + | 5.93180e11i | −0.820847 | + | 0.820847i | ||||
\(923\) | −9.32991e10 | − | 9.32991e10i | −0.128550 | − | 0.128550i | ||||
\(924\) | 1.74341e10i | 0.0239173i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.13310e12 | 1.54107 | ||||||||
\(927\) | 1.70842e11 | − | 1.70842e11i | 0.231354 | − | 0.231354i | ||||
\(928\) | −4.35424e10 | − | 4.35424e10i | −0.0587111 | − | 0.0587111i | ||||
\(929\) | − | 7.00667e11i | − | 0.940695i | −0.882481 | − | 0.470347i | \(-0.844129\pi\) | ||
0.882481 | − | 0.470347i | \(-0.155871\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.91603e11 | −0.654359 | ||||||||
\(932\) | 1.57538e9 | − | 1.57538e9i | 0.00208796 | − | 0.00208796i | ||||
\(933\) | −2.34674e11 | − | 2.34674e11i | −0.309697 | − | 0.309697i | ||||
\(934\) | 4.10572e11i | 0.539513i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.98248e11 | 0.258289 | ||||||||
\(937\) | 2.56761e11 | − | 2.56761e11i | 0.333097 | − | 0.333097i | −0.520664 | − | 0.853762i | \(-0.674316\pi\) |
0.853762 | + | 0.520664i | \(0.174316\pi\) | |||||||
\(938\) | 4.91800e11 | + | 4.91800e11i | 0.635297 | + | 0.635297i | ||||
\(939\) | 1.62793e11i | 0.209398i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.56412e11 | −0.199485 | −0.0997427 | − | 0.995013i | \(-0.531802\pi\) | ||||
−0.0997427 | + | 0.995013i | \(0.531802\pi\) | |||||||
\(942\) | 4.00390e11 | − | 4.00390e11i | 0.508487 | − | 0.508487i | ||||
\(943\) | 4.16545e11 | + | 4.16545e11i | 0.526763 | + | 0.526763i | ||||
\(944\) | 5.32438e11i | 0.670473i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.50729e12 | 1.88205 | ||||||||
\(947\) | −3.12048e11 | + | 3.12048e11i | −0.387990 | + | 0.387990i | −0.873970 | − | 0.485980i | \(-0.838463\pi\) |
0.485980 | + | 0.873970i | \(0.338463\pi\) | |||||||
\(948\) | −7.55179e9 | − | 7.55179e9i | −0.00935011 | − | 0.00935011i | ||||
\(949\) | 2.42397e11i | 0.298856i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.51711e11 | 0.185479 | ||||||||
\(952\) | −4.68488e11 | + | 4.68488e11i | −0.570363 | + | 0.570363i | ||||
\(953\) | 8.58235e11 | + | 8.58235e11i | 1.04048 | + | 1.04048i | 0.999145 | + | 0.0413362i | \(0.0131615\pi\) |
0.0413362 | + | 0.999145i | \(0.486839\pi\) | |||||||
\(954\) | − | 4.82983e10i | − | 0.0583094i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.28781e10 | −0.0393619 | ||||||||
\(957\) | −6.80132e11 | + | 6.80132e11i | −0.810859 | + | 0.810859i | ||||
\(958\) | 8.08946e11 | + | 8.08946e11i | 0.960412 | + | 0.960412i | ||||
\(959\) | 9.15804e11i | 1.08275i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.34911e11 | −0.861671 | ||||||||
\(962\) | 1.92998e11 | − | 1.92998e11i | 0.225347 | − | 0.225347i | ||||
\(963\) | 2.30524e11 | + | 2.30524e11i | 0.268048 | + | 0.268048i | ||||
\(964\) | − | 4.89410e10i | − | 0.0566715i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.92313e11 | −0.220852 | ||||||||
\(967\) | −5.46083e11 | + | 5.46083e11i | −0.624529 | + | 0.624529i | −0.946686 | − | 0.322157i | \(-0.895592\pi\) |
0.322157 | + | 0.946686i | \(0.395592\pi\) | |||||||
\(968\) | 1.20043e12 | + | 1.20043e12i | 1.36721 | + | 1.36721i | ||||
\(969\) | 7.24836e11i | 0.822138i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.21655e12 | −1.36853 | −0.684263 | − | 0.729235i | \(-0.739876\pi\) | ||||
−0.684263 | + | 0.729235i | \(0.739876\pi\) | |||||||
\(972\) | −1.44221e9 | + | 1.44221e9i | −0.00161571 | + | 0.00161571i | ||||
\(973\) | −4.53799e11 | − | 4.53799e11i | −0.506305 | − | 0.506305i | ||||
\(974\) | 1.10214e11i | 0.122462i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.38072e12 | −1.52163 | ||||||||
\(977\) | −3.20646e11 | + | 3.20646e11i | −0.351923 | + | 0.351923i | −0.860825 | − | 0.508902i | \(-0.830052\pi\) |
0.508902 | + | 0.860825i | \(0.330052\pi\) | |||||||
\(978\) | −2.11802e11 | − | 2.11802e11i | −0.231513 | − | 0.231513i | ||||
\(979\) | 1.64244e12i | 1.78796i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.40137e11 | 0.475239 | ||||||||
\(982\) | 9.27487e11 | − | 9.27487e11i | 0.997383 | − | 0.997383i | ||||
\(983\) | −4.05945e11 | − | 4.05945e11i | −0.434763 | − | 0.434763i | 0.455482 | − | 0.890245i | \(-0.349467\pi\) |
−0.890245 | + | 0.455482i | \(0.849467\pi\) | |||||||
\(984\) | − | 7.18852e11i | − | 0.766760i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.25720e12 | −1.33014 | ||||||||
\(987\) | 1.97433e11 | − | 1.97433e11i | 0.208042 | − | 0.208042i | ||||
\(988\) | 2.24163e10 | + | 2.24163e10i | 0.0235253 | + | 0.0235253i | ||||
\(989\) | − | 6.14099e11i | − | 0.641879i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.86193e11 | 0.504097 | 0.252049 | − | 0.967715i | \(-0.418896\pi\) | ||||
0.252049 | + | 0.967715i | \(0.418896\pi\) | |||||||
\(992\) | −1.81339e10 | + | 1.81339e10i | −0.0187260 | + | 0.0187260i | ||||
\(993\) | 2.09644e11 | + | 2.09644e11i | 0.215618 | + | 0.215618i | ||||
\(994\) | − | 1.56191e11i | − | 0.159996i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.87241e10 | 0.0291883 | ||||||||
\(997\) | −1.27343e11 | + | 1.27343e11i | −0.128883 | + | 0.128883i | −0.768606 | − | 0.639723i | \(-0.779049\pi\) |
0.639723 | + | 0.768606i | \(0.279049\pi\) | |||||||
\(998\) | −7.52785e11 | − | 7.52785e11i | −0.758838 | − | 0.758838i | ||||
\(999\) | 8.16432e10i | 0.0819706i |
(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.f.e.43.6 | 16 | ||
5.2 | odd | 4 | inner | 75.9.f.e.7.6 | 16 | ||
5.3 | odd | 4 | 15.9.f.a.7.3 | ✓ | 16 | ||
5.4 | even | 2 | 15.9.f.a.13.3 | yes | 16 | ||
15.8 | even | 4 | 45.9.g.c.37.6 | 16 | |||
15.14 | odd | 2 | 45.9.g.c.28.6 | 16 | |||
20.3 | even | 4 | 240.9.bg.d.97.4 | 16 | |||
20.19 | odd | 2 | 240.9.bg.d.193.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.9.f.a.7.3 | ✓ | 16 | 5.3 | odd | 4 | ||
15.9.f.a.13.3 | yes | 16 | 5.4 | even | 2 | ||
45.9.g.c.28.6 | 16 | 15.14 | odd | 2 | |||
45.9.g.c.37.6 | 16 | 15.8 | even | 4 | |||
75.9.f.e.7.6 | 16 | 5.2 | odd | 4 | inner | ||
75.9.f.e.43.6 | 16 | 1.1 | even | 1 | trivial | ||
240.9.bg.d.97.4 | 16 | 20.3 | even | 4 | |||
240.9.bg.d.193.4 | 16 | 20.19 | odd | 2 |