Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,22,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(58.6902423003\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.41 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.22.c.b.20.42 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1704.62i | − | 1.17710i | −0.808462 | − | 0.588548i | \(-0.799700\pi\) | ||
0.808462 | − | 0.588548i | \(-0.200300\pi\) | |||||||
\(3\) | 65800.8 | + | 78298.2i | 0.643366 | + | 0.765559i | ||||
\(4\) | −808569. | −0.385556 | ||||||||
\(5\) | 2.49846e7 | 1.14416 | 0.572082 | − | 0.820197i | \(-0.306136\pi\) | ||||
0.572082 | + | 0.820197i | \(0.306136\pi\) | |||||||
\(6\) | 1.33469e8 | − | 1.12165e8i | 0.901137 | − | 0.757303i | ||||
\(7\) | 7.21028e7 | − | 7.43873e8i | 0.0964768 | − | 0.995335i | ||||
\(8\) | − | 2.19654e9i | − | 0.723260i | ||||||
\(9\) | −1.80087e9 | + | 1.03042e10i | −0.172161 | + | 0.985069i | ||||
\(10\) | − | 4.25893e10i | − | 1.34679i | ||||||
\(11\) | − | 5.38334e10i | − | 0.625790i | −0.949788 | − | 0.312895i | \(-0.898701\pi\) | ||
0.949788 | − | 0.312895i | \(-0.101299\pi\) | |||||||
\(12\) | −5.32045e10 | − | 6.33095e10i | −0.248053 | − | 0.295166i | ||||
\(13\) | − | 8.15234e11i | − | 1.64013i | −0.572274 | − | 0.820063i | \(-0.693939\pi\) | ||
0.572274 | − | 0.820063i | \(-0.306061\pi\) | |||||||
\(14\) | −1.26802e12 | − | 1.22908e11i | −1.17161 | − | 0.113562i | ||||
\(15\) | 1.64401e12 | + | 1.95625e12i | 0.736116 | + | 0.875925i | ||||
\(16\) | −5.43995e12 | −1.23690 | ||||||||
\(17\) | −7.14032e12 | −0.859021 | −0.429510 | − | 0.903062i | \(-0.641314\pi\) | ||||
−0.429510 | + | 0.903062i | \(0.641314\pi\) | |||||||
\(18\) | 1.75647e13 | + | 3.06979e12i | 1.15952 | + | 0.202650i | ||||
\(19\) | 2.64515e13i | 0.989778i | 0.868956 | + | 0.494889i | \(0.164791\pi\) | ||||
−0.868956 | + | 0.494889i | \(0.835209\pi\) | |||||||
\(20\) | −2.02018e13 | −0.441139 | ||||||||
\(21\) | 6.29884e13 | − | 4.33019e13i | 0.824058 | − | 0.566506i | ||||
\(22\) | −9.17654e13 | −0.736616 | ||||||||
\(23\) | 9.27517e13i | 0.466852i | 0.972375 | + | 0.233426i | \(0.0749937\pi\) | ||||
−0.972375 | + | 0.233426i | \(0.925006\pi\) | |||||||
\(24\) | 1.71985e14 | − | 1.44534e14i | 0.553698 | − | 0.465321i | ||||
\(25\) | 1.47395e14 | 0.309110 | ||||||||
\(26\) | −1.38966e15 | −1.93059 | ||||||||
\(27\) | −9.25296e14 | + | 5.37017e14i | −0.864891 | + | 0.501960i | ||||
\(28\) | −5.83001e13 | + | 6.01473e14i | −0.0371972 | + | 0.383757i | ||||
\(29\) | − | 2.96948e15i | − | 1.31069i | −0.755328 | − | 0.655347i | \(-0.772522\pi\) | ||
0.755328 | − | 0.655347i | \(-0.227478\pi\) | |||||||
\(30\) | 3.33466e15 | − | 2.80241e15i | 1.03105 | − | 0.866479i | ||||
\(31\) | − | 4.95268e15i | − | 1.08528i | −0.839965 | − | 0.542641i | \(-0.817424\pi\) | ||
0.839965 | − | 0.542641i | \(-0.182576\pi\) | |||||||
\(32\) | 4.66656e15i | 0.732693i | ||||||||
\(33\) | 4.21506e15 | − | 3.54228e15i | 0.479080 | − | 0.402612i | ||||
\(34\) | 1.21715e16i | 1.01115i | ||||||||
\(35\) | 1.80146e15 | − | 1.85854e16i | 0.110385 | − | 1.13883i | ||||
\(36\) | 1.45613e15 | − | 8.33163e15i | 0.0663778 | − | 0.379799i | ||||
\(37\) | 3.48905e16 | 1.19286 | 0.596430 | − | 0.802665i | \(-0.296585\pi\) | ||||
0.596430 | + | 0.802665i | \(0.296585\pi\) | |||||||
\(38\) | 4.50897e16 | 1.16506 | ||||||||
\(39\) | 6.38314e16 | − | 5.36430e16i | 1.25561 | − | 1.05520i | ||||
\(40\) | − | 5.48798e16i | − | 0.827528i | ||||||
\(41\) | −8.41304e15 | −0.0978864 | −0.0489432 | − | 0.998802i | \(-0.515585\pi\) | ||||
−0.0489432 | + | 0.998802i | \(0.515585\pi\) | |||||||
\(42\) | −7.38132e16 | − | 1.07371e17i | −0.666832 | − | 0.969995i | ||||
\(43\) | −7.53851e15 | −0.0531945 | −0.0265973 | − | 0.999646i | \(-0.508467\pi\) | ||||
−0.0265973 | + | 0.999646i | \(0.508467\pi\) | |||||||
\(44\) | 4.35281e16i | 0.241277i | ||||||||
\(45\) | −4.49940e16 | + | 2.57446e17i | −0.196981 | + | 1.12708i | ||||
\(46\) | 1.58106e17 | 0.549530 | ||||||||
\(47\) | −2.39922e17 | −0.665337 | −0.332669 | − | 0.943044i | \(-0.607949\pi\) | ||||
−0.332669 | + | 0.943044i | \(0.607949\pi\) | |||||||
\(48\) | −3.57953e17 | − | 4.25939e17i | −0.795781 | − | 0.946922i | ||||
\(49\) | −5.48148e17 | − | 1.07271e17i | −0.981384 | − | 0.192054i | ||||
\(50\) | − | 2.51253e17i | − | 0.363853i | ||||||
\(51\) | −4.69838e17 | − | 5.59074e17i | −0.552665 | − | 0.657631i | ||||
\(52\) | 6.59173e17i | 0.632360i | ||||||||
\(53\) | 1.77085e18i | 1.39086i | 0.718592 | + | 0.695432i | \(0.244787\pi\) | ||||
−0.718592 | + | 0.695432i | \(0.755213\pi\) | |||||||
\(54\) | 9.15409e17 | + | 1.57728e18i | 0.590855 | + | 1.01806i | ||||
\(55\) | − | 1.34501e18i | − | 0.716007i | ||||||
\(56\) | −1.63395e18 | − | 1.58377e17i | −0.719886 | − | 0.0697778i | ||||
\(57\) | −2.07111e18 | + | 1.74053e18i | −0.757733 | + | 0.636789i | ||||
\(58\) | −5.06183e18 | −1.54281 | ||||||||
\(59\) | 6.53938e18 | 1.66567 | 0.832837 | − | 0.553518i | \(-0.186715\pi\) | ||||
0.832837 | + | 0.553518i | \(0.186715\pi\) | |||||||
\(60\) | −1.32929e18 | − | 1.58177e18i | −0.283814 | − | 0.337718i | ||||
\(61\) | − | 4.21755e17i | − | 0.0757003i | −0.999283 | − | 0.0378501i | \(-0.987949\pi\) | ||
0.999283 | − | 0.0378501i | \(-0.0120510\pi\) | |||||||
\(62\) | −8.44243e18 | −1.27748 | ||||||||
\(63\) | 7.53514e18 | + | 2.08258e18i | 0.963864 | + | 0.266394i | ||||
\(64\) | −3.45371e18 | −0.374452 | ||||||||
\(65\) | − | 2.03683e19i | − | 1.87657i | ||||||
\(66\) | −6.03824e18 | − | 7.18507e18i | −0.473913 | − | 0.563923i | ||||
\(67\) | −1.30627e19 | −0.875479 | −0.437740 | − | 0.899102i | \(-0.644221\pi\) | ||||
−0.437740 | + | 0.899102i | \(0.644221\pi\) | |||||||
\(68\) | 5.77344e18 | 0.331200 | ||||||||
\(69\) | −7.26229e18 | + | 6.10313e18i | −0.357403 | + | 0.300357i | ||||
\(70\) | −3.16810e19 | − | 3.07081e18i | −1.34051 | − | 0.129934i | ||||
\(71\) | − | 3.56914e19i | − | 1.30122i | −0.759411 | − | 0.650611i | \(-0.774513\pi\) | ||
0.759411 | − | 0.650611i | \(-0.225487\pi\) | |||||||
\(72\) | 2.26335e19 | + | 3.95568e18i | 0.712461 | + | 0.124517i | ||||
\(73\) | 3.10669e19i | 0.846074i | 0.906112 | + | 0.423037i | \(0.139036\pi\) | ||||
−0.906112 | + | 0.423037i | \(0.860964\pi\) | |||||||
\(74\) | − | 5.94750e19i | − | 1.40411i | ||||||
\(75\) | 9.69872e18 | + | 1.15408e19i | 0.198871 | + | 0.236642i | ||||
\(76\) | − | 2.13879e19i | − | 0.381615i | ||||||
\(77\) | −4.00452e19 | − | 3.88154e18i | −0.622871 | − | 0.0603743i | ||||
\(78\) | −9.14408e19 | − | 1.08808e20i | −1.24207 | − | 1.47798i | ||||
\(79\) | 1.16544e20 | 1.38486 | 0.692429 | − | 0.721486i | \(-0.256541\pi\) | ||||
0.692429 | + | 0.721486i | \(0.256541\pi\) | |||||||
\(80\) | −1.35915e20 | −1.41522 | ||||||||
\(81\) | −1.02933e20 | − | 3.71129e19i | −0.940721 | − | 0.339181i | ||||
\(82\) | 1.43410e19i | 0.115222i | ||||||||
\(83\) | 1.17516e19 | 0.0831339 | 0.0415670 | − | 0.999136i | \(-0.486765\pi\) | ||||
0.0415670 | + | 0.999136i | \(0.486765\pi\) | |||||||
\(84\) | −5.09304e19 | + | 3.50126e19i | −0.317720 | + | 0.218420i | ||||
\(85\) | −1.78398e20 | −0.982860 | ||||||||
\(86\) | 1.28503e19i | 0.0626151i | ||||||||
\(87\) | 2.32505e20 | − | 1.95394e20i | 1.00341 | − | 0.843256i | ||||
\(88\) | −1.18247e20 | −0.452609 | ||||||||
\(89\) | 8.40556e19 | 0.285740 | 0.142870 | − | 0.989741i | \(-0.454367\pi\) | ||||
0.142870 | + | 0.989741i | \(0.454367\pi\) | |||||||
\(90\) | 4.38847e20 | + | 7.66976e19i | 1.32668 | + | 0.231865i | ||||
\(91\) | −6.06430e20 | − | 5.87807e19i | −1.63247 | − | 0.158234i | ||||
\(92\) | − | 7.49961e19i | − | 0.179998i | ||||||
\(93\) | 3.87786e20 | − | 3.25890e20i | 0.830848 | − | 0.698234i | ||||
\(94\) | 4.08975e20i | 0.783166i | ||||||||
\(95\) | 6.60882e20i | 1.13247i | ||||||||
\(96\) | −3.65383e20 | + | 3.07063e20i | −0.560920 | + | 0.471390i | ||||
\(97\) | 4.28920e20i | 0.590573i | 0.955409 | + | 0.295286i | \(0.0954150\pi\) | ||||
−0.955409 | + | 0.295286i | \(0.904585\pi\) | |||||||
\(98\) | −1.82856e20 | + | 9.34383e20i | −0.226065 | + | 1.15518i | ||||
\(99\) | 5.54709e20 | + | 9.69469e19i | 0.616447 | + | 0.107737i | ||||
\(100\) | −1.19179e20 | −0.119179 | ||||||||
\(101\) | −9.89833e20 | −0.891636 | −0.445818 | − | 0.895124i | \(-0.647087\pi\) | ||||
−0.445818 | + | 0.895124i | \(0.647087\pi\) | |||||||
\(102\) | −9.53007e20 | + | 8.00895e20i | −0.774095 | + | 0.650539i | ||||
\(103\) | − | 2.36391e21i | − | 1.73316i | −0.499035 | − | 0.866582i | \(-0.666312\pi\) | ||
0.499035 | − | 0.866582i | \(-0.333688\pi\) | |||||||
\(104\) | −1.79069e21 | −1.18624 | ||||||||
\(105\) | 1.57374e21 | − | 1.08188e21i | 0.942857 | − | 0.648175i | ||||
\(106\) | 3.01862e21 | 1.63718 | ||||||||
\(107\) | − | 1.14232e21i | − | 0.561381i | −0.959798 | − | 0.280690i | \(-0.909437\pi\) | ||
0.959798 | − | 0.280690i | \(-0.0905634\pi\) | |||||||
\(108\) | 7.48166e20 | − | 4.34216e20i | 0.333464 | − | 0.193533i | ||||
\(109\) | 4.60801e21 | 1.86438 | 0.932192 | − | 0.361964i | \(-0.117894\pi\) | ||||
0.932192 | + | 0.361964i | \(0.117894\pi\) | |||||||
\(110\) | −2.29273e21 | −0.842809 | ||||||||
\(111\) | 2.29582e21 | + | 2.73187e21i | 0.767445 | + | 0.913204i | ||||
\(112\) | −3.92236e20 | + | 4.04664e21i | −0.119332 | + | 1.23113i | ||||
\(113\) | − | 4.28982e21i | − | 1.18882i | −0.804162 | − | 0.594410i | \(-0.797386\pi\) | ||
0.804162 | − | 0.594410i | \(-0.202614\pi\) | |||||||
\(114\) | 2.96694e21 | + | 3.53044e21i | 0.749562 | + | 0.891925i | ||||
\(115\) | 2.31737e21i | 0.534155i | ||||||||
\(116\) | 2.40103e21i | 0.505346i | ||||||||
\(117\) | 8.40031e21 | + | 1.46813e21i | 1.61564 | + | 0.282366i | ||||
\(118\) | − | 1.11471e22i | − | 1.96066i | ||||||
\(119\) | −5.14837e20 | + | 5.31149e21i | −0.0828756 | + | 0.855014i | ||||
\(120\) | 4.29699e21 | − | 3.61113e21i | 0.633521 | − | 0.532403i | ||||
\(121\) | 4.50221e21 | 0.608386 | ||||||||
\(122\) | −7.18932e20 | −0.0891065 | ||||||||
\(123\) | −5.53585e20 | − | 6.58726e20i | −0.0629768 | − | 0.0749378i | ||||
\(124\) | 4.00459e21i | 0.418437i | ||||||||
\(125\) | −8.23099e21 | −0.790491 | ||||||||
\(126\) | 3.55000e21 | − | 1.28445e22i | 0.313572 | − | 1.13456i | ||||
\(127\) | 5.81932e21 | 0.473079 | 0.236539 | − | 0.971622i | \(-0.423987\pi\) | ||||
0.236539 | + | 0.971622i | \(0.423987\pi\) | |||||||
\(128\) | 1.56737e22i | 1.17346i | ||||||||
\(129\) | −4.96040e20 | − | 5.90252e20i | −0.0342235 | − | 0.0407235i | ||||
\(130\) | −3.47202e22 | −2.20891 | ||||||||
\(131\) | −4.60586e21 | −0.270372 | −0.135186 | − | 0.990820i | \(-0.543163\pi\) | ||||
−0.135186 | + | 0.990820i | \(0.543163\pi\) | |||||||
\(132\) | −3.40817e21 | + | 2.86418e21i | −0.184712 | + | 0.155229i | ||||
\(133\) | 1.96766e22 | + | 1.90723e21i | 0.985161 | + | 0.0954906i | ||||
\(134\) | 2.22668e22i | 1.03052i | ||||||||
\(135\) | −2.31182e22 | + | 1.34172e22i | −0.989577 | + | 0.574324i | ||||
\(136\) | 1.56840e22i | 0.621296i | ||||||||
\(137\) | − | 3.64031e22i | − | 1.33528i | −0.744485 | − | 0.667640i | \(-0.767305\pi\) | ||
0.744485 | − | 0.667640i | \(-0.232695\pi\) | |||||||
\(138\) | 1.04035e22 | + | 1.23794e22i | 0.353549 | + | 0.420698i | ||||
\(139\) | 4.77330e22i | 1.50371i | 0.659329 | + | 0.751854i | \(0.270840\pi\) | ||||
−0.659329 | + | 0.751854i | \(0.729160\pi\) | |||||||
\(140\) | −1.45661e21 | + | 1.50276e22i | −0.0425597 | + | 0.439081i | ||||
\(141\) | −1.57870e22 | − | 1.87854e22i | −0.428055 | − | 0.509355i | ||||
\(142\) | −6.08402e22 | −1.53166 | ||||||||
\(143\) | −4.38868e22 | −1.02637 | ||||||||
\(144\) | 9.79664e21 | − | 5.60542e22i | 0.212947 | − | 1.21843i | ||||
\(145\) | − | 7.41914e22i | − | 1.49965i | ||||||
\(146\) | 5.29572e22 | 0.995910 | ||||||||
\(147\) | −2.76695e22 | − | 4.99775e22i | −0.484361 | − | 0.874868i | ||||
\(148\) | −2.82114e22 | −0.459914 | ||||||||
\(149\) | − | 5.73702e22i | − | 0.871426i | −0.900086 | − | 0.435713i | \(-0.856496\pi\) | ||
0.900086 | − | 0.435713i | \(-0.143504\pi\) | |||||||
\(150\) | 1.96726e22 | − | 1.65326e22i | 0.278551 | − | 0.234090i | ||||
\(151\) | 3.45094e22 | 0.455701 | 0.227850 | − | 0.973696i | \(-0.426830\pi\) | ||||
0.227850 | + | 0.973696i | \(0.426830\pi\) | |||||||
\(152\) | 5.81018e22 | 0.715867 | ||||||||
\(153\) | 1.28588e22 | − | 7.35750e22i | 0.147890 | − | 0.846195i | ||||
\(154\) | −6.61655e21 | + | 6.82618e22i | −0.0710663 | + | 0.733180i | ||||
\(155\) | − | 1.23741e23i | − | 1.24174i | ||||||
\(156\) | −5.16121e22 | + | 4.33741e22i | −0.484109 | + | 0.406838i | ||||
\(157\) | 3.31549e21i | 0.0290805i | 0.999894 | + | 0.0145402i | \(0.00462847\pi\) | ||||
−0.999894 | + | 0.0145402i | \(0.995372\pi\) | |||||||
\(158\) | − | 1.98663e23i | − | 1.63011i | ||||||
\(159\) | −1.38654e23 | + | 1.16523e23i | −1.06479 | + | 0.894834i | ||||
\(160\) | 1.16592e23i | 0.838321i | ||||||||
\(161\) | 6.89955e22 | + | 6.68766e21i | 0.464675 | + | 0.0450404i | ||||
\(162\) | −6.32633e22 | + | 1.75461e23i | −0.399249 | + | 1.10732i | ||||
\(163\) | 2.61004e23 | 1.54411 | 0.772055 | − | 0.635556i | \(-0.219229\pi\) | ||||
0.772055 | + | 0.635556i | \(0.219229\pi\) | |||||||
\(164\) | 6.80252e21 | 0.0377407 | ||||||||
\(165\) | 1.05312e23 | − | 8.85027e22i | 0.548145 | − | 0.460654i | ||||
\(166\) | − | 2.00320e22i | − | 0.0978566i | ||||||
\(167\) | 1.31835e23 | 0.604653 | 0.302327 | − | 0.953204i | \(-0.402237\pi\) | ||||
0.302327 | + | 0.953204i | \(0.402237\pi\) | |||||||
\(168\) | −9.51144e22 | − | 1.38357e23i | −0.409731 | − | 0.596008i | ||||
\(169\) | −4.17542e23 | −1.69001 | ||||||||
\(170\) | 3.04101e23i | 1.15692i | ||||||||
\(171\) | −2.72561e23 | − | 4.76357e22i | −0.974999 | − | 0.170401i | ||||
\(172\) | 6.09541e21 | 0.0205094 | ||||||||
\(173\) | 5.55338e22 | 0.175822 | 0.0879110 | − | 0.996128i | \(-0.471981\pi\) | ||||
0.0879110 | + | 0.996128i | \(0.471981\pi\) | |||||||
\(174\) | −3.33072e23 | − | 3.96332e23i | −0.992593 | − | 1.18111i | ||||
\(175\) | 1.06276e22 | − | 1.09643e23i | 0.0298220 | − | 0.307668i | ||||
\(176\) | 2.92851e23i | 0.774042i | ||||||||
\(177\) | 4.30296e23 | + | 5.12021e23i | 1.07164 | + | 1.27517i | ||||
\(178\) | − | 1.43283e23i | − | 0.336344i | ||||||
\(179\) | − | 2.31473e23i | − | 0.512323i | −0.966634 | − | 0.256162i | \(-0.917542\pi\) | ||
0.966634 | − | 0.256162i | \(-0.0824579\pi\) | |||||||
\(180\) | 3.63808e22 | − | 2.08163e23i | 0.0759470 | − | 0.434552i | ||||
\(181\) | 1.00558e24i | 1.98057i | 0.139053 | + | 0.990285i | \(0.455594\pi\) | ||||
−0.139053 | + | 0.990285i | \(0.544406\pi\) | |||||||
\(182\) | −1.00199e23 | + | 1.03373e24i | −0.186257 | + | 1.92158i | ||||
\(183\) | 3.30227e22 | − | 2.77518e22i | 0.0579530 | − | 0.0487030i | ||||
\(184\) | 2.03733e23 | 0.337656 | ||||||||
\(185\) | 8.71727e23 | 1.36483 | ||||||||
\(186\) | −5.55519e23 | − | 6.61027e23i | −0.821888 | − | 0.977988i | ||||
\(187\) | 3.84388e23i | 0.537567i | ||||||||
\(188\) | 1.93993e23 | 0.256525 | ||||||||
\(189\) | 3.32756e23 | + | 7.27024e23i | 0.416176 | + | 0.909284i | ||||
\(190\) | 1.12655e24 | 1.33302 | ||||||||
\(191\) | 9.60897e23i | 1.07604i | 0.842933 | + | 0.538018i | \(0.180827\pi\) | ||||
−0.842933 | + | 0.538018i | \(0.819173\pi\) | |||||||
\(192\) | −2.27257e23 | − | 2.70419e23i | −0.240909 | − | 0.286665i | ||||
\(193\) | 6.33104e23 | 0.635512 | 0.317756 | − | 0.948173i | \(-0.397071\pi\) | ||||
0.317756 | + | 0.948173i | \(0.397071\pi\) | |||||||
\(194\) | 7.31145e23 | 0.695161 | ||||||||
\(195\) | 1.59480e24 | − | 1.34025e24i | 1.43663 | − | 1.20732i | ||||
\(196\) | 4.43216e23 | + | 8.67358e22i | 0.378378 | + | 0.0740473i | ||||
\(197\) | − | 1.44208e24i | − | 1.16706i | −0.812091 | − | 0.583531i | \(-0.801670\pi\) | ||
0.812091 | − | 0.583531i | \(-0.198330\pi\) | |||||||
\(198\) | 1.65257e23 | − | 9.45566e23i | 0.126817 | − | 0.725617i | ||||
\(199\) | − | 7.52755e23i | − | 0.547894i | −0.961745 | − | 0.273947i | \(-0.911671\pi\) | ||
0.961745 | − | 0.273947i | \(-0.0883292\pi\) | |||||||
\(200\) | − | 3.23760e23i | − | 0.223567i | ||||||
\(201\) | −8.59533e23 | − | 1.02278e24i | −0.563253 | − | 0.670231i | ||||
\(202\) | 1.68729e24i | 1.04954i | ||||||||
\(203\) | −2.20892e24 | − | 2.14108e23i | −1.30458 | − | 0.126452i | ||||
\(204\) | 3.79897e23 | + | 4.52050e23i | 0.213083 | + | 0.253554i | ||||
\(205\) | −2.10197e23 | −0.111998 | ||||||||
\(206\) | −4.02956e24 | −2.04010 | ||||||||
\(207\) | −9.55729e23 | − | 1.67034e23i | −0.459882 | − | 0.0803739i | ||||
\(208\) | 4.43484e24i | 2.02867i | ||||||||
\(209\) | 1.42398e24 | 0.619394 | ||||||||
\(210\) | −1.84420e24 | − | 2.68263e24i | −0.762965 | − | 1.10983i | ||||
\(211\) | 2.43940e24 | 0.960100 | 0.480050 | − | 0.877241i | \(-0.340619\pi\) | ||||
0.480050 | + | 0.877241i | \(0.340619\pi\) | |||||||
\(212\) | − | 1.43185e24i | − | 0.536256i | ||||||
\(213\) | 2.79458e24 | − | 2.34852e24i | 0.996162 | − | 0.837161i | ||||
\(214\) | −1.94722e24 | −0.660799 | ||||||||
\(215\) | −1.88347e23 | −0.0608632 | ||||||||
\(216\) | 1.17958e24 | + | 2.03245e24i | 0.363047 | + | 0.625541i | ||||
\(217\) | −3.68417e24 | − | 3.57103e23i | −1.08022 | − | 0.104705i | ||||
\(218\) | − | 7.85490e24i | − | 2.19456i | ||||||
\(219\) | −2.43249e24 | + | 2.04423e24i | −0.647719 | + | 0.544335i | ||||
\(220\) | 1.08753e24i | 0.276060i | ||||||||
\(221\) | 5.82103e24i | 1.40890i | ||||||||
\(222\) | 4.65679e24 | − | 3.91350e24i | 1.07493 | − | 0.903356i | ||||
\(223\) | 4.17894e24i | 0.920164i | 0.887876 | + | 0.460082i | \(0.152180\pi\) | ||||
−0.887876 | + | 0.460082i | \(0.847820\pi\) | |||||||
\(224\) | 3.47133e24 | + | 3.36472e23i | 0.729275 | + | 0.0706879i | ||||
\(225\) | −2.65439e23 | + | 1.51879e24i | −0.0532168 | + | 0.304495i | ||||
\(226\) | −7.31251e24 | −1.39935 | ||||||||
\(227\) | −8.20116e24 | −1.49832 | −0.749159 | − | 0.662391i | \(-0.769542\pi\) | ||||
−0.749159 | + | 0.662391i | \(0.769542\pi\) | |||||||
\(228\) | 1.67463e24 | − | 1.40734e24i | 0.292148 | − | 0.245518i | ||||
\(229\) | 2.44570e24i | 0.407504i | 0.979023 | + | 0.203752i | \(0.0653136\pi\) | ||||
−0.979023 | + | 0.203752i | \(0.934686\pi\) | |||||||
\(230\) | 3.95023e24 | 0.628752 | ||||||||
\(231\) | −2.33109e24 | − | 3.39088e24i | −0.354514 | − | 0.515688i | ||||
\(232\) | −6.52259e24 | −0.947973 | ||||||||
\(233\) | 6.61945e23i | 0.0919570i | 0.998942 | + | 0.0459785i | \(0.0146406\pi\) | ||||
−0.998942 | + | 0.0459785i | \(0.985359\pi\) | |||||||
\(234\) | 2.50260e24 | − | 1.43193e25i | 0.332372 | − | 1.90176i | ||||
\(235\) | −5.99436e24 | −0.761255 | ||||||||
\(236\) | −5.28754e24 | −0.642210 | ||||||||
\(237\) | 7.66868e24 | + | 9.12519e24i | 0.890970 | + | 1.06019i | ||||
\(238\) | 9.05406e24 | + | 8.77600e23i | 1.00643 | + | 0.0975526i | ||||
\(239\) | 1.32177e25i | 1.40597i | 0.711204 | + | 0.702986i | \(0.248150\pi\) | ||||
−0.711204 | + | 0.702986i | \(0.751850\pi\) | |||||||
\(240\) | −8.94333e24 | − | 1.06419e25i | −0.910503 | − | 1.08343i | ||||
\(241\) | 1.06254e25i | 1.03554i | 0.855519 | + | 0.517772i | \(0.173238\pi\) | ||||
−0.855519 | + | 0.517772i | \(0.826762\pi\) | |||||||
\(242\) | − | 7.67455e24i | − | 0.716129i | ||||||
\(243\) | −3.86718e24 | − | 1.05015e25i | −0.345564 | − | 0.938395i | ||||
\(244\) | 3.41018e23i | 0.0291867i | ||||||||
\(245\) | −1.36953e25 | − | 2.68012e24i | −1.12286 | − | 0.219741i | ||||
\(246\) | −1.12288e24 | + | 9.43650e23i | −0.0882091 | + | 0.0741297i | ||||
\(247\) | 2.15642e25 | 1.62336 | ||||||||
\(248\) | −1.08788e25 | −0.784942 | ||||||||
\(249\) | 7.73266e23 | + | 9.20132e23i | 0.0534855 | + | 0.0636439i | ||||
\(250\) | 1.40307e25i | 0.930484i | ||||||||
\(251\) | 1.49038e25 | 0.947815 | 0.473907 | − | 0.880575i | \(-0.342843\pi\) | ||||
0.473907 | + | 0.880575i | \(0.342843\pi\) | |||||||
\(252\) | −6.09268e24 | − | 1.68391e24i | −0.371623 | − | 0.102710i | ||||
\(253\) | 4.99314e24 | 0.292152 | ||||||||
\(254\) | − | 9.91972e24i | − | 0.556859i | ||||||
\(255\) | −1.17387e25 | − | 1.39683e25i | −0.632339 | − | 0.752438i | ||||
\(256\) | 1.94748e25 | 1.00682 | ||||||||
\(257\) | 3.02992e25 | 1.50360 | 0.751801 | − | 0.659390i | \(-0.229186\pi\) | ||||
0.751801 | + | 0.659390i | \(0.229186\pi\) | |||||||
\(258\) | −1.00615e24 | + | 8.45558e23i | −0.0479355 | + | 0.0402844i | ||||
\(259\) | 2.51570e24 | − | 2.59541e25i | 0.115083 | − | 1.18730i | ||||
\(260\) | 1.64692e25i | 0.723523i | ||||||||
\(261\) | 3.05980e25 | + | 5.34764e24i | 1.29112 | + | 0.225651i | ||||
\(262\) | 7.85123e24i | 0.318254i | ||||||||
\(263\) | 2.50284e25i | 0.974760i | 0.873190 | + | 0.487380i | \(0.162047\pi\) | ||||
−0.873190 | + | 0.487380i | \(0.837953\pi\) | |||||||
\(264\) | −7.78077e24 | − | 9.25856e24i | −0.291193 | − | 0.346499i | ||||
\(265\) | 4.42440e25i | 1.59138i | ||||||||
\(266\) | 3.25110e24 | − | 3.35410e25i | 0.112402 | − | 1.15963i | ||||
\(267\) | 5.53093e24 | + | 6.58141e24i | 0.183836 | + | 0.218751i | ||||
\(268\) | 1.05621e25 | 0.337546 | ||||||||
\(269\) | −2.63526e25 | −0.809886 | −0.404943 | − | 0.914342i | \(-0.632709\pi\) | ||||
−0.404943 | + | 0.914342i | \(0.632709\pi\) | |||||||
\(270\) | 2.28712e25 | + | 3.94077e25i | 0.676035 | + | 1.16483i | ||||
\(271\) | 1.18404e25i | 0.336658i | 0.985731 | + | 0.168329i | \(0.0538371\pi\) | ||||
−0.985731 | + | 0.168329i | \(0.946163\pi\) | |||||||
\(272\) | 3.88430e25 | 1.06253 | ||||||||
\(273\) | −3.53012e25 | − | 5.13502e25i | −0.929140 | − | 1.35156i | ||||
\(274\) | −6.20533e25 | −1.57175 | ||||||||
\(275\) | − | 7.93479e24i | − | 0.193438i | ||||||
\(276\) | 5.87206e24 | − | 4.93480e24i | 0.137799 | − | 0.115804i | ||||
\(277\) | 5.94698e25 | 1.34356 | 0.671782 | − | 0.740749i | \(-0.265529\pi\) | ||||
0.671782 | + | 0.740749i | \(0.265529\pi\) | |||||||
\(278\) | 8.13666e25 | 1.77001 | ||||||||
\(279\) | 5.10333e25 | + | 8.91913e24i | 1.06908 | + | 0.186844i | ||||
\(280\) | −4.08236e25 | − | 3.95699e24i | −0.823668 | − | 0.0798372i | ||||
\(281\) | 5.39388e25i | 1.04830i | 0.851626 | + | 0.524149i | \(0.175617\pi\) | ||||
−0.851626 | + | 0.524149i | \(0.824383\pi\) | |||||||
\(282\) | −3.20220e25 | + | 2.69108e25i | −0.599560 | + | 0.503862i | ||||
\(283\) | − | 8.93895e25i | − | 1.61261i | −0.591501 | − | 0.806304i | \(-0.701465\pi\) | ||
0.591501 | − | 0.806304i | \(-0.298535\pi\) | |||||||
\(284\) | 2.88590e25i | 0.501694i | ||||||||
\(285\) | −5.17459e25 | + | 4.34865e25i | −0.866971 | + | 0.728591i | ||||
\(286\) | 7.48103e25i | 1.20814i | ||||||||
\(287\) | −6.06604e23 | + | 6.25823e24i | −0.00944377 | + | 0.0974298i | ||||
\(288\) | −4.80850e25 | − | 8.40386e24i | −0.721753 | − | 0.126141i | ||||
\(289\) | −1.81078e25 | −0.262083 | ||||||||
\(290\) | −1.26468e26 | −1.76523 | ||||||||
\(291\) | −3.35837e25 | + | 2.82233e25i | −0.452118 | + | 0.379954i | ||||
\(292\) | − | 2.51198e25i | − | 0.326209i | ||||||
\(293\) | 4.40075e25 | 0.551336 | 0.275668 | − | 0.961253i | \(-0.411101\pi\) | ||||
0.275668 | + | 0.961253i | \(0.411101\pi\) | |||||||
\(294\) | −8.51926e25 | + | 4.71659e25i | −1.02980 | + | 0.570139i | ||||
\(295\) | 1.63384e26 | 1.90580 | ||||||||
\(296\) | − | 7.66385e25i | − | 0.862748i | ||||||
\(297\) | 2.89095e25 | + | 4.98119e25i | 0.314122 | + | 0.541241i | ||||
\(298\) | −9.77942e25 | −1.02575 | ||||||||
\(299\) | 7.56143e25 | 0.765696 | ||||||||
\(300\) | −7.84209e24 | − | 9.33152e24i | −0.0766758 | − | 0.0912387i | ||||
\(301\) | −5.43548e23 | + | 5.60769e24i | −0.00513203 | + | 0.0529464i | ||||
\(302\) | − | 5.88254e25i | − | 0.536404i | ||||||
\(303\) | −6.51318e25 | − | 7.75022e25i | −0.573648 | − | 0.682600i | ||||
\(304\) | − | 1.43895e26i | − | 1.22426i | ||||||
\(305\) | − | 1.05374e25i | − | 0.0866135i | ||||||
\(306\) | −1.25417e26 | − | 2.19193e25i | −0.996053 | − | 0.174081i | ||||
\(307\) | 8.79033e25i | 0.674609i | 0.941396 | + | 0.337305i | \(0.109515\pi\) | ||||
−0.941396 | + | 0.337305i | \(0.890485\pi\) | |||||||
\(308\) | 3.23793e25 | + | 3.13850e24i | 0.240152 | + | 0.0232776i | ||||
\(309\) | 1.85090e26 | − | 1.55547e26i | 1.32684 | − | 1.11506i | ||||
\(310\) | −2.10931e26 | −1.46165 | ||||||||
\(311\) | −5.79802e25 | −0.388414 | −0.194207 | − | 0.980961i | \(-0.562213\pi\) | ||||
−0.194207 | + | 0.980961i | \(0.562213\pi\) | |||||||
\(312\) | −1.17829e26 | − | 1.40208e26i | −0.763184 | − | 0.908134i | ||||
\(313\) | − | 1.53921e26i | − | 0.964013i | −0.876168 | − | 0.482006i | \(-0.839908\pi\) | ||
0.876168 | − | 0.482006i | \(-0.160092\pi\) | |||||||
\(314\) | 5.65165e24 | 0.0342305 | ||||||||
\(315\) | 1.88263e26 | + | 5.20324e25i | 1.10282 | + | 0.304799i | ||||
\(316\) | −9.42338e25 | −0.533940 | ||||||||
\(317\) | 2.62029e24i | 0.0143624i | 0.999974 | + | 0.00718121i | \(0.00228587\pi\) | ||||
−0.999974 | + | 0.00718121i | \(0.997714\pi\) | |||||||
\(318\) | 1.98628e26 | + | 2.36353e26i | 1.05331 | + | 1.25336i | ||||
\(319\) | −1.59857e26 | −0.820220 | ||||||||
\(320\) | −8.62897e25 | −0.428434 | ||||||||
\(321\) | 8.94415e25 | − | 7.51654e25i | 0.429770 | − | 0.361173i | ||||
\(322\) | 1.13999e25 | − | 1.17611e26i | 0.0530169 | − | 0.546967i | ||||
\(323\) | − | 1.88872e26i | − | 0.850240i | ||||||
\(324\) | 8.32282e25 | + | 3.00083e25i | 0.362700 | + | 0.130773i | ||||
\(325\) | − | 1.20162e26i | − | 0.506979i | ||||||
\(326\) | − | 4.44913e26i | − | 1.81757i | ||||||
\(327\) | 3.03211e26 | + | 3.60799e26i | 1.19948 | + | 1.42730i | ||||
\(328\) | 1.84796e25i | 0.0707973i | ||||||||
\(329\) | −1.72990e25 | + | 1.78471e26i | −0.0641896 | + | 0.662234i | ||||
\(330\) | −1.50863e26 | − | 1.79516e26i | −0.542234 | − | 0.645220i | ||||
\(331\) | 4.00443e26 | 1.39427 | 0.697135 | − | 0.716940i | \(-0.254458\pi\) | ||||
0.697135 | + | 0.716940i | \(0.254458\pi\) | |||||||
\(332\) | −9.50200e24 | −0.0320528 | ||||||||
\(333\) | −6.28332e25 | + | 3.59518e26i | −0.205364 | + | 1.17505i | ||||
\(334\) | − | 2.24727e26i | − | 0.711735i | ||||||
\(335\) | −3.26366e26 | −1.00169 | ||||||||
\(336\) | −3.42654e26 | + | 2.35560e26i | −1.01928 | + | 0.700712i | ||||
\(337\) | −8.65529e25 | −0.249556 | −0.124778 | − | 0.992185i | \(-0.539822\pi\) | ||||
−0.124778 | + | 0.992185i | \(0.539822\pi\) | |||||||
\(338\) | 7.11749e26i | 1.98931i | ||||||||
\(339\) | 3.35886e26 | − | 2.82274e26i | 0.910111 | − | 0.764845i | ||||
\(340\) | 1.44247e26 | 0.378947 | ||||||||
\(341\) | −2.66620e26 | −0.679160 | ||||||||
\(342\) | −8.12006e25 | + | 4.64612e26i | −0.200579 | + | 1.14767i | ||||
\(343\) | −1.19319e26 | + | 4.00018e26i | −0.285838 | + | 0.958278i | ||||
\(344\) | 1.65586e25i | 0.0384735i | ||||||||
\(345\) | −1.81446e26 | + | 1.52485e26i | −0.408928 | + | 0.343657i | ||||
\(346\) | − | 9.46638e25i | − | 0.206959i | ||||||
\(347\) | 3.69203e26i | 0.783078i | 0.920161 | + | 0.391539i | \(0.128057\pi\) | ||||
−0.920161 | + | 0.391539i | \(0.871943\pi\) | |||||||
\(348\) | −1.87996e26 | + | 1.57990e26i | −0.386872 | + | 0.325122i | ||||
\(349\) | − | 5.13323e26i | − | 1.02500i | −0.858687 | − | 0.512500i | \(-0.828720\pi\) | ||
0.858687 | − | 0.512500i | \(-0.171280\pi\) | |||||||
\(350\) | −1.86900e26 | − | 1.81160e25i | −0.362155 | − | 0.0351033i | ||||
\(351\) | 4.37795e26 | + | 7.54333e26i | 0.823277 | + | 1.41853i | ||||
\(352\) | 2.51217e26 | 0.458513 | ||||||||
\(353\) | −7.67815e26 | −1.36026 | −0.680130 | − | 0.733091i | \(-0.738077\pi\) | ||||
−0.680130 | + | 0.733091i | \(0.738077\pi\) | |||||||
\(354\) | 8.72801e26 | − | 7.33490e26i | 1.50100 | − | 1.26142i | ||||
\(355\) | − | 8.91738e26i | − | 1.48881i | ||||||
\(356\) | −6.79648e25 | −0.110169 | ||||||||
\(357\) | −4.49757e26 | + | 3.09189e26i | −0.707883 | + | 0.486640i | ||||
\(358\) | −3.94573e26 | −0.603054 | ||||||||
\(359\) | − | 4.03983e25i | − | 0.0599614i | −0.999550 | − | 0.0299807i | \(-0.990455\pi\) | ||
0.999550 | − | 0.0299807i | \(-0.00954458\pi\) | |||||||
\(360\) | 5.65491e26 | + | 9.88313e25i | 0.815172 | + | 0.142468i | ||||
\(361\) | 1.45267e25 | 0.0203395 | ||||||||
\(362\) | 1.71412e27 | 2.33132 | ||||||||
\(363\) | 2.96249e26 | + | 3.52515e26i | 0.391415 | + | 0.465756i | ||||
\(364\) | 4.90341e26 | + | 4.75282e25i | 0.629410 | + | 0.0610080i | ||||
\(365\) | 7.76196e26i | 0.968047i | ||||||||
\(366\) | −4.73063e25 | − | 5.62911e25i | −0.0573281 | − | 0.0682163i | ||||
\(367\) | 9.04216e26i | 1.06483i | 0.846485 | + | 0.532413i | \(0.178715\pi\) | ||||
−0.846485 | + | 0.532413i | \(0.821285\pi\) | |||||||
\(368\) | − | 5.04565e26i | − | 0.577451i | ||||||
\(369\) | 1.51508e25 | − | 8.66894e25i | 0.0168523 | − | 0.0964249i | ||||
\(370\) | − | 1.48596e27i | − | 1.60653i | ||||||
\(371\) | 1.31729e27 | + | 1.27683e26i | 1.38438 | + | 0.134186i | ||||
\(372\) | −3.13552e26 | + | 2.63505e26i | −0.320338 | + | 0.269208i | ||||
\(373\) | 1.38478e27 | 1.37542 | 0.687712 | − | 0.725984i | \(-0.258615\pi\) | ||||
0.687712 | + | 0.725984i | \(0.258615\pi\) | |||||||
\(374\) | 6.55234e26 | 0.632768 | ||||||||
\(375\) | −5.41605e26 | − | 6.44472e26i | −0.508575 | − | 0.605167i | ||||
\(376\) | 5.26998e26i | 0.481212i | ||||||||
\(377\) | −2.42082e27 | −2.14970 | ||||||||
\(378\) | 1.23930e27 | − | 5.67222e26i | 1.07031 | − | 0.489880i | ||||
\(379\) | −3.97744e26 | −0.334112 | −0.167056 | − | 0.985947i | \(-0.553426\pi\) | ||||
−0.167056 | + | 0.985947i | \(0.553426\pi\) | |||||||
\(380\) | − | 5.34368e26i | − | 0.436629i | ||||||
\(381\) | 3.82916e26 | + | 4.55643e26i | 0.304363 | + | 0.362170i | ||||
\(382\) | 1.63796e27 | 1.26660 | ||||||||
\(383\) | −4.37995e25 | −0.0329520 | −0.0164760 | − | 0.999864i | \(-0.505245\pi\) | ||||
−0.0164760 | + | 0.999864i | \(0.505245\pi\) | |||||||
\(384\) | −1.22723e27 | + | 1.03134e27i | −0.898352 | + | 0.754963i | ||||
\(385\) | −1.00052e27 | − | 9.69790e25i | −0.712667 | − | 0.0690780i | ||||
\(386\) | − | 1.07920e27i | − | 0.748058i | ||||||
\(387\) | 1.35759e25 | − | 7.76781e25i | 0.00915803 | − | 0.0524002i | ||||
\(388\) | − | 3.46812e26i | − | 0.227699i | ||||||
\(389\) | − | 6.30559e26i | − | 0.402954i | −0.979493 | − | 0.201477i | \(-0.935426\pi\) | ||
0.979493 | − | 0.201477i | \(-0.0645741\pi\) | |||||||
\(390\) | −2.28462e27 | − | 2.71853e27i | −1.42113 | − | 1.69105i | ||||
\(391\) | − | 6.62276e26i | − | 0.401036i | ||||||
\(392\) | −2.35624e26 | + | 1.20403e27i | −0.138905 | + | 0.709796i | ||||
\(393\) | −3.03069e26 | − | 3.60631e26i | −0.173948 | − | 0.206986i | ||||
\(394\) | −2.45820e27 | −1.37375 | ||||||||
\(395\) | 2.91181e27 | 1.58450 | ||||||||
\(396\) | −4.48520e26 | − | 7.83883e25i | −0.237675 | − | 0.0415386i | ||||
\(397\) | − | 9.29130e26i | − | 0.479486i | −0.970836 | − | 0.239743i | \(-0.922937\pi\) | ||
0.970836 | − | 0.239743i | \(-0.0770633\pi\) | |||||||
\(398\) | −1.28316e27 | −0.644924 | ||||||||
\(399\) | 1.14540e27 | + | 1.66614e27i | 0.560715 | + | 0.815634i | ||||
\(400\) | −8.01823e26 | −0.382339 | ||||||||
\(401\) | 1.41731e27i | 0.658337i | 0.944271 | + | 0.329168i | \(0.106768\pi\) | ||||
−0.944271 | + | 0.329168i | \(0.893232\pi\) | |||||||
\(402\) | −1.74345e27 | + | 1.46517e27i | −0.788927 | + | 0.663003i | ||||
\(403\) | −4.03760e27 | −1.78000 | ||||||||
\(404\) | 8.00348e26 | 0.343775 | ||||||||
\(405\) | −2.57174e27 | − | 9.27252e26i | −1.07634 | − | 0.388079i | ||||
\(406\) | −3.64972e26 | + | 3.76536e27i | −0.148846 | + | 1.53562i | ||||
\(407\) | − | 1.87828e27i | − | 0.746480i | ||||||
\(408\) | −1.22803e27 | + | 1.03202e27i | −0.475638 | + | 0.399720i | ||||
\(409\) | 2.56372e27i | 0.967780i | 0.875129 | + | 0.483890i | \(0.160776\pi\) | ||||
−0.875129 | + | 0.483890i | \(0.839224\pi\) | |||||||
\(410\) | 3.58305e26i | 0.131833i | ||||||||
\(411\) | 2.85030e27 | − | 2.39535e27i | 1.02224 | − | 0.859073i | ||||
\(412\) | 1.91138e27i | 0.668231i | ||||||||
\(413\) | 4.71507e26 | − | 4.86447e27i | 0.160699 | − | 1.65790i | ||||
\(414\) | −2.84728e26 | + | 1.62915e27i | −0.0946078 | + | 0.541325i | ||||
\(415\) | 2.93610e26 | 0.0951188 | ||||||||
\(416\) | 3.80434e27 | 1.20171 | ||||||||
\(417\) | −3.73741e27 | + | 3.14087e27i | −1.15118 | + | 0.967435i | ||||
\(418\) | − | 2.42733e27i | − | 0.729086i | ||||||
\(419\) | 2.76286e26 | 0.0809303 | 0.0404651 | − | 0.999181i | \(-0.487116\pi\) | ||||
0.0404651 | + | 0.999181i | \(0.487116\pi\) | |||||||
\(420\) | −1.27248e27 | + | 8.74777e26i | −0.363524 | + | 0.249908i | ||||
\(421\) | 7.66524e26 | 0.213581 | 0.106791 | − | 0.994282i | \(-0.465943\pi\) | ||||
0.106791 | + | 0.994282i | \(0.465943\pi\) | |||||||
\(422\) | − | 4.15824e27i | − | 1.13013i | ||||||
\(423\) | 4.32067e26 | − | 2.47219e27i | 0.114545 | − | 0.655403i | ||||
\(424\) | 3.88974e27 | 1.00596 | ||||||||
\(425\) | −1.05245e27 | −0.265532 | ||||||||
\(426\) | −4.00334e27 | − | 4.76368e27i | −0.985420 | − | 1.17258i | ||||
\(427\) | −3.13733e26 | − | 3.04098e25i | −0.0753472 | − | 0.00730332i | ||||
\(428\) | 9.23643e26i | 0.216444i | ||||||||
\(429\) | −2.88779e27 | − | 3.43626e27i | −0.660334 | − | 0.785750i | ||||
\(430\) | 3.21060e26i | 0.0716419i | ||||||||
\(431\) | 7.46042e27i | 1.62462i | 0.583225 | + | 0.812311i | \(0.301791\pi\) | ||||
−0.583225 | + | 0.812311i | \(0.698209\pi\) | |||||||
\(432\) | 5.03357e27 | − | 2.92135e27i | 1.06979 | − | 0.620875i | ||||
\(433\) | 5.21226e27i | 1.08119i | 0.841282 | + | 0.540596i | \(0.181801\pi\) | ||||
−0.841282 | + | 0.540596i | \(0.818199\pi\) | |||||||
\(434\) | −6.08723e26 | + | 6.28010e27i | −0.123247 | + | 1.27152i | ||||
\(435\) | 5.80905e27 | − | 4.88185e27i | 1.14807 | − | 0.964823i | ||||
\(436\) | −3.72590e27 | −0.718824 | ||||||||
\(437\) | −2.45342e27 | −0.462080 | ||||||||
\(438\) | 3.48463e27 | + | 4.14646e27i | 0.640735 | + | 0.762428i | ||||
\(439\) | − | 4.85066e26i | − | 0.0870809i | −0.999052 | − | 0.0435405i | \(-0.986136\pi\) | ||
0.999052 | − | 0.0435405i | \(-0.0138637\pi\) | |||||||
\(440\) | −2.95437e27 | −0.517859 | ||||||||
\(441\) | 2.09248e27 | − | 5.45503e27i | 0.358142 | − | 0.933667i | ||||
\(442\) | 9.92262e27 | 1.65841 | ||||||||
\(443\) | − | 1.00313e28i | − | 1.63726i | −0.574324 | − | 0.818628i | \(-0.694735\pi\) | ||
0.574324 | − | 0.818628i | \(-0.305265\pi\) | |||||||
\(444\) | −1.85633e27 | − | 2.20890e27i | −0.295893 | − | 0.352091i | ||||
\(445\) | 2.10010e27 | 0.326934 | ||||||||
\(446\) | 7.12350e27 | 1.08312 | ||||||||
\(447\) | 4.49198e27 | − | 3.77500e27i | 0.667128 | − | 0.560645i | ||||
\(448\) | −2.49022e26 | + | 2.56912e27i | −0.0361259 | + | 0.372705i | ||||
\(449\) | 1.26558e27i | 0.179350i | 0.995971 | + | 0.0896752i | \(0.0285829\pi\) | ||||
−0.995971 | + | 0.0896752i | \(0.971417\pi\) | |||||||
\(450\) | 2.58895e27 | + | 4.52473e26i | 0.358420 | + | 0.0626413i | ||||
\(451\) | 4.52903e26i | 0.0612564i | ||||||||
\(452\) | 3.46862e27i | 0.458356i | ||||||||
\(453\) | 2.27075e27 | + | 2.70203e27i | 0.293182 | + | 0.348866i | ||||
\(454\) | 1.39798e28i | 1.76366i | ||||||||
\(455\) | −1.51514e28 | − | 1.46861e27i | −1.86782 | − | 0.181046i | ||||
\(456\) | 3.82315e27 | + | 4.54927e27i | 0.460564 | + | 0.548038i | ||||
\(457\) | 1.22284e28 | 1.43963 | 0.719813 | − | 0.694168i | \(-0.244227\pi\) | ||||
0.719813 | + | 0.694168i | \(0.244227\pi\) | |||||||
\(458\) | 4.16899e27 | 0.479671 | ||||||||
\(459\) | 6.60691e27 | − | 3.83447e27i | 0.742959 | − | 0.431194i | ||||
\(460\) | − | 1.87375e27i | − | 0.205947i | ||||||
\(461\) | −1.60244e28 | −1.72156 | −0.860782 | − | 0.508973i | \(-0.830025\pi\) | ||||
−0.860782 | + | 0.508973i | \(0.830025\pi\) | |||||||
\(462\) | −5.78015e27 | + | 3.97362e27i | −0.607014 | + | 0.417297i | ||||
\(463\) | −1.36001e28 | −1.39618 | −0.698092 | − | 0.716008i | \(-0.745968\pi\) | ||||
−0.698092 | + | 0.716008i | \(0.745968\pi\) | |||||||
\(464\) | 1.61538e28i | 1.62120i | ||||||||
\(465\) | 9.68870e27 | − | 8.14226e27i | 0.950626 | − | 0.798893i | ||||
\(466\) | 1.12836e27 | 0.108242 | ||||||||
\(467\) | −3.65637e27 | −0.342944 | −0.171472 | − | 0.985189i | \(-0.554852\pi\) | ||||
−0.171472 | + | 0.985189i | \(0.554852\pi\) | |||||||
\(468\) | −6.79223e27 | − | 1.18708e27i | −0.622918 | − | 0.108868i | ||||
\(469\) | −9.41854e26 | + | 9.71695e27i | −0.0844634 | + | 0.871395i | ||||
\(470\) | 1.02181e28i | 0.896070i | ||||||||
\(471\) | −2.59597e26 | + | 2.18162e26i | −0.0222628 | + | 0.0187094i | ||||
\(472\) | − | 1.43640e28i | − | 1.20472i | ||||||
\(473\) | 4.05824e26i | 0.0332886i | ||||||||
\(474\) | 1.55550e28 | − | 1.30722e28i | 1.24795 | − | 1.04876i | ||||
\(475\) | 3.89883e27i | 0.305951i | ||||||||
\(476\) | 4.16281e26 | − | 4.29470e27i | 0.0319532 | − | 0.329655i | ||||
\(477\) | −1.82471e28 | − | 3.18906e27i | −1.37010 | − | 0.239453i | ||||
\(478\) | 2.25310e28 | 1.65496 | ||||||||
\(479\) | 1.10483e28 | 0.793912 | 0.396956 | − | 0.917838i | \(-0.370067\pi\) | ||||
0.396956 | + | 0.917838i | \(0.370067\pi\) | |||||||
\(480\) | −9.12898e27 | + | 7.67187e27i | −0.641784 | + | 0.539347i | ||||
\(481\) | − | 2.84439e28i | − | 1.95644i | ||||||
\(482\) | 1.81123e28 | 1.21893 | ||||||||
\(483\) | 4.01632e27 | + | 5.84228e27i | 0.264475 | + | 0.384713i | ||||
\(484\) | −3.64035e27 | −0.234567 | ||||||||
\(485\) | 1.07164e28i | 0.675712i | ||||||||
\(486\) | −1.79011e28 | + | 6.59207e27i | −1.10458 | + | 0.406762i | ||||
\(487\) | −1.02733e28 | −0.620375 | −0.310187 | − | 0.950675i | \(-0.600392\pi\) | ||||
−0.310187 | + | 0.950675i | \(0.600392\pi\) | |||||||
\(488\) | −9.26403e26 | −0.0547510 | ||||||||
\(489\) | 1.71743e28 | + | 2.04362e28i | 0.993427 | + | 1.18211i | ||||
\(490\) | −4.56858e27 | + | 2.33452e28i | −0.258656 | + | 1.32172i | ||||
\(491\) | − | 4.32085e27i | − | 0.239450i | −0.992807 | − | 0.119725i | \(-0.961799\pi\) | ||
0.992807 | − | 0.119725i | \(-0.0382012\pi\) | |||||||
\(492\) | 4.47611e26 | + | 5.32625e26i | 0.0242811 | + | 0.0288927i | ||||
\(493\) | 2.12030e28i | 1.12591i | ||||||||
\(494\) | − | 3.67587e28i | − | 1.91085i | ||||||
\(495\) | 1.38592e28 | + | 2.42218e27i | 0.705316 | + | 0.123269i | ||||
\(496\) | 2.69424e28i | 1.34239i | ||||||||
\(497\) | −2.65499e28 | − | 2.57345e27i | −1.29515 | − | 0.125538i | ||||
\(498\) | 1.56847e27 | − | 1.31812e27i | 0.0749150 | − | 0.0629576i | ||||
\(499\) | −2.48378e28 | −1.16160 | −0.580802 | − | 0.814045i | \(-0.697261\pi\) | ||||
−0.580802 | + | 0.814045i | \(0.697261\pi\) | |||||||
\(500\) | 6.65532e27 | 0.304778 | ||||||||
\(501\) | 8.67481e27 | + | 1.03224e28i | 0.389013 | + | 0.462898i | ||||
\(502\) | − | 2.54053e28i | − | 1.11567i | ||||||
\(503\) | −1.16976e28 | −0.503074 | −0.251537 | − | 0.967848i | \(-0.580936\pi\) | ||||
−0.251537 | + | 0.967848i | \(0.580936\pi\) | |||||||
\(504\) | 4.57447e27 | − | 1.65513e28i | 0.192672 | − | 0.697124i | ||||
\(505\) | −2.47306e28 | −1.02018 | ||||||||
\(506\) | − | 8.51140e27i | − | 0.343891i | ||||||
\(507\) | −2.74746e28 | − | 3.26928e28i | −1.08729 | − | 1.29380i | ||||
\(508\) | −4.70532e27 | −0.182398 | ||||||||
\(509\) | 2.68759e28 | 1.02053 | 0.510266 | − | 0.860016i | \(-0.329547\pi\) | ||||
0.510266 | + | 0.860016i | \(0.329547\pi\) | |||||||
\(510\) | −2.38105e28 | + | 2.00101e28i | −0.885692 | + | 0.744324i | ||||
\(511\) | 2.31098e28 | + | 2.24001e27i | 0.842127 | + | 0.0816265i | ||||
\(512\) | − | 3.26836e26i | − | 0.0116680i | ||||||
\(513\) | −1.42049e28 | − | 2.44755e28i | −0.496829 | − | 0.856050i | ||||
\(514\) | − | 5.16485e28i | − | 1.76988i | ||||||
\(515\) | − | 5.90614e28i | − | 1.98302i | ||||||
\(516\) | 4.01082e26 | + | 4.77259e26i | 0.0131951 | + | 0.0157012i | ||||
\(517\) | 1.29158e28i | 0.416362i | ||||||||
\(518\) | −4.42418e28 | − | 4.28831e27i | −1.39756 | − | 0.135464i | ||||
\(519\) | 3.65416e27 | + | 4.34819e27i | 0.113118 | + | 0.134602i | ||||
\(520\) | −4.47399e28 | −1.35725 | ||||||||
\(521\) | −9.47556e27 | −0.281714 | −0.140857 | − | 0.990030i | \(-0.544986\pi\) | ||||
−0.140857 | + | 0.990030i | \(0.544986\pi\) | |||||||
\(522\) | 9.11568e27 | − | 5.21579e28i | 0.265613 | − | 1.51978i | ||||
\(523\) | − | 7.28173e27i | − | 0.207954i | −0.994580 | − | 0.103977i | \(-0.966843\pi\) | ||
0.994580 | − | 0.103977i | \(-0.0331568\pi\) | |||||||
\(524\) | 3.72416e27 | 0.104244 | ||||||||
\(525\) | 9.28418e27 | − | 6.38249e27i | 0.254725 | − | 0.175113i | ||||
\(526\) | 4.26639e28 | 1.14739 | ||||||||
\(527\) | 3.53637e28i | 0.932281i | ||||||||
\(528\) | −2.29297e28 | + | 1.92699e28i | −0.592575 | + | 0.497992i | ||||
\(529\) | 3.08687e28 | 0.782049 | ||||||||
\(530\) | 7.54191e28 | 1.87320 | ||||||||
\(531\) | −1.17766e28 | + | 6.73828e28i | −0.286765 | + | 1.64080i | ||||
\(532\) | −1.59099e28 | − | 1.54213e27i | −0.379834 | − | 0.0368170i | ||||
\(533\) | 6.85859e27i | 0.160546i | ||||||||
\(534\) | 1.12188e28 | − | 9.42811e27i | 0.257491 | − | 0.216392i | ||||
\(535\) | − | 2.85404e28i | − | 0.642311i | ||||||
\(536\) | 2.86927e28i | 0.633199i | ||||||||
\(537\) | 1.81239e28 | − | 1.52311e28i | 0.392214 | − | 0.329611i | ||||
\(538\) | 4.49210e28i | 0.953313i | ||||||||
\(539\) | −5.77475e27 | + | 2.95087e28i | −0.120185 | + | 0.614141i | ||||
\(540\) | 1.86927e28 | − | 1.08487e28i | 0.381537 | − | 0.221434i | ||||
\(541\) | −4.20480e28 | −0.841733 | −0.420867 | − | 0.907123i | \(-0.638274\pi\) | ||||
−0.420867 | + | 0.907123i | \(0.638274\pi\) | |||||||
\(542\) | 2.01833e28 | 0.396279 | ||||||||
\(543\) | −7.87349e28 | + | 6.61677e28i | −1.51624 | + | 1.27423i | ||||
\(544\) | − | 3.33207e28i | − | 0.629399i | ||||||
\(545\) | 1.15130e29 | 2.13316 | ||||||||
\(546\) | −8.75325e28 | + | 6.01750e28i | −1.59091 | + | 1.09369i | ||||
\(547\) | 4.84337e28 | 0.863537 | 0.431768 | − | 0.901984i | \(-0.357890\pi\) | ||||
0.431768 | + | 0.901984i | \(0.357890\pi\) | |||||||
\(548\) | 2.94344e28i | 0.514825i | ||||||||
\(549\) | 4.34584e27 | + | 7.59526e26i | 0.0745700 | + | 0.0130327i | ||||
\(550\) | −1.35258e28 | −0.227695 | ||||||||
\(551\) | 7.85473e28 | 1.29730 | ||||||||
\(552\) | 1.34058e28 | + | 1.59519e28i | 0.217236 | + | 0.258495i | ||||
\(553\) | 8.40315e27 | − | 8.66939e28i | 0.133607 | − | 1.37840i | ||||
\(554\) | − | 1.01373e29i | − | 1.58151i | ||||||
\(555\) | 5.73603e28 | + | 6.82547e28i | 0.878082 | + | 1.04486i | ||||
\(556\) | − | 3.85955e28i | − | 0.579764i | ||||||
\(557\) | 1.13096e28i | 0.166712i | 0.996520 | + | 0.0833560i | \(0.0265639\pi\) | ||||
−0.996520 | + | 0.0833560i | \(0.973436\pi\) | |||||||
\(558\) | 1.52037e28 | − | 8.69922e28i | 0.219933 | − | 1.25841i | ||||
\(559\) | 6.14565e27i | 0.0872456i | ||||||||
\(560\) | −9.79988e27 | + | 1.01104e29i | −0.136536 | + | 1.40862i | ||||
\(561\) | −3.00969e28 | + | 2.52930e28i | −0.411539 | + | 0.345852i | ||||
\(562\) | 9.19451e28 | 1.23395 | ||||||||
\(563\) | −1.20262e29 | −1.58412 | −0.792062 | − | 0.610441i | \(-0.790992\pi\) | ||||
−0.792062 | + | 0.610441i | \(0.790992\pi\) | |||||||
\(564\) | 1.27649e28 | + | 1.51893e28i | 0.165039 | + | 0.196385i | ||||
\(565\) | − | 1.07180e29i | − | 1.36020i | ||||||
\(566\) | −1.52375e29 | −1.89819 | ||||||||
\(567\) | −3.50290e28 | + | 7.38929e28i | −0.428357 | + | 0.903610i | ||||
\(568\) | −7.83977e28 | −0.941122 | ||||||||
\(569\) | 9.26804e28i | 1.09222i | 0.837714 | + | 0.546109i | \(0.183891\pi\) | ||||
−0.837714 | + | 0.546109i | \(0.816109\pi\) | |||||||
\(570\) | 7.41279e28 | + | 8.82069e28i | 0.857622 | + | 1.02051i | ||||
\(571\) | −9.42718e27 | −0.107079 | −0.0535393 | − | 0.998566i | \(-0.517050\pi\) | ||||
−0.0535393 | + | 0.998566i | \(0.517050\pi\) | |||||||
\(572\) | 3.54855e28 | 0.395725 | ||||||||
\(573\) | −7.52365e28 | + | 6.32278e28i | −0.823769 | + | 0.692284i | ||||
\(574\) | 1.06679e28 | + | 1.03403e27i | 0.114684 | + | 0.0111162i | ||||
\(575\) | 1.36712e28i | 0.144309i | ||||||||
\(576\) | 6.21967e27 | − | 3.55876e28i | 0.0644661 | − | 0.368861i | ||||
\(577\) | 1.82632e28i | 0.185879i | 0.995672 | + | 0.0929395i | \(0.0296263\pi\) | ||||
−0.995672 | + | 0.0929395i | \(0.970374\pi\) | |||||||
\(578\) | 3.08669e28i | 0.308497i | ||||||||
\(579\) | 4.16588e28 | + | 4.95709e28i | 0.408866 | + | 0.486522i | ||||
\(580\) | 5.99889e28i | 0.578198i | ||||||||
\(581\) | 8.47326e26 | − | 8.74172e27i | 0.00802049 | − | 0.0827461i | ||||
\(582\) | 4.81099e28 | + | 5.72473e28i | 0.447243 | + | 0.532187i | ||||
\(583\) | 9.53309e28 | 0.870390 | ||||||||
\(584\) | 6.82398e28 | 0.611931 | ||||||||
\(585\) | 2.09879e29 | + | 3.66807e28i | 1.84855 | + | 0.323073i | ||||
\(586\) | − | 7.50160e28i | − | 0.648976i | ||||||
\(587\) | −1.02461e29 | −0.870684 | −0.435342 | − | 0.900265i | \(-0.643372\pi\) | ||||
−0.435342 | + | 0.900265i | \(0.643372\pi\) | |||||||
\(588\) | 2.23727e28 | + | 4.04103e28i | 0.186748 | + | 0.337311i | ||||
\(589\) | 1.31006e29 | 1.07419 | ||||||||
\(590\) | − | 2.78507e29i | − | 2.24332i | ||||||
\(591\) | 1.12912e29 | − | 9.48901e28i | 0.893456 | − | 0.750848i | ||||
\(592\) | −1.89803e29 | −1.47545 | ||||||||
\(593\) | −9.65141e28 | −0.737084 | −0.368542 | − | 0.929611i | \(-0.620143\pi\) | ||||
−0.368542 | + | 0.929611i | \(0.620143\pi\) | |||||||
\(594\) | 8.49102e28 | − | 4.92796e28i | 0.637092 | − | 0.369751i | ||||
\(595\) | −1.28630e28 | + | 1.32706e29i | −0.0948232 | + | 0.978276i | ||||
\(596\) | 4.63877e28i | 0.335983i | ||||||||
\(597\) | 5.89394e28 | − | 4.95319e28i | 0.419445 | − | 0.352496i | ||||
\(598\) | − | 1.28893e29i | − | 0.901298i | ||||||
\(599\) | − | 1.55669e29i | − | 1.06960i | −0.844979 | − | 0.534799i | \(-0.820387\pi\) | ||
0.844979 | − | 0.534799i | \(-0.179613\pi\) | |||||||
\(600\) | 2.53498e28 | − | 2.13036e28i | 0.171154 | − | 0.143835i | ||||
\(601\) | − | 4.35706e28i | − | 0.289076i | −0.989499 | − | 0.144538i | \(-0.953830\pi\) | ||
0.989499 | − | 0.144538i | \(-0.0461695\pi\) | |||||||
\(602\) | 9.55897e27 | + | 9.26541e26i | 0.0623230 | + | 0.00604090i | ||||
\(603\) | 2.35241e28 | − | 1.34600e29i | 0.150724 | − | 0.862407i | ||||
\(604\) | −2.79033e28 | −0.175698 | ||||||||
\(605\) | 1.12486e29 | 0.696093 | ||||||||
\(606\) | −1.32112e29 | + | 1.11025e29i | −0.803486 | + | 0.675239i | ||||
\(607\) | − | 4.72217e28i | − | 0.282267i | −0.989991 | − | 0.141134i | \(-0.954925\pi\) | ||
0.989991 | − | 0.141134i | \(-0.0450747\pi\) | |||||||
\(608\) | −1.23438e29 | −0.725204 | ||||||||
\(609\) | −1.28584e29 | − | 1.87043e29i | −0.742516 | − | 1.08009i | ||||
\(610\) | −1.79623e28 | −0.101952 | ||||||||
\(611\) | 1.95592e29i | 1.09124i | ||||||||
\(612\) | −1.03972e28 | + | 5.94905e28i | −0.0570199 | + | 0.326255i | ||||
\(613\) | 2.58348e29 | 1.39274 | 0.696370 | − | 0.717682i | \(-0.254797\pi\) | ||||
0.696370 | + | 0.717682i | \(0.254797\pi\) | |||||||
\(614\) | 1.49842e29 | 0.794080 | ||||||||
\(615\) | −1.38311e28 | − | 1.64580e28i | −0.0720557 | − | 0.0857411i | ||||
\(616\) | −8.52597e27 | + | 8.79610e28i | −0.0436663 | + | 0.450498i | ||||
\(617\) | − | 4.81699e28i | − | 0.242539i | −0.992620 | − | 0.121269i | \(-0.961304\pi\) | ||
0.992620 | − | 0.121269i | \(-0.0386965\pi\) | |||||||
\(618\) | −2.65148e29 | − | 3.15507e29i | −1.31253 | − | 1.56182i | ||||
\(619\) | − | 6.83865e28i | − | 0.332827i | −0.986056 | − | 0.166414i | \(-0.946781\pi\) | ||
0.986056 | − | 0.166414i | \(-0.0532187\pi\) | |||||||
\(620\) | 1.00053e29i | 0.478760i | ||||||||
\(621\) | −4.98093e28 | − | 8.58228e28i | −0.234341 | − | 0.403776i | ||||
\(622\) | 9.88340e28i | 0.457201i | ||||||||
\(623\) | 6.06065e27 | − | 6.25267e28i | 0.0275673 | − | 0.284408i | ||||
\(624\) | −3.47240e29 | + | 2.91816e29i | −1.55307 | + | 1.30518i | ||||
\(625\) | −2.75932e29 | −1.21356 | ||||||||
\(626\) | −2.62377e29 | −1.13474 | ||||||||
\(627\) | 9.36987e28 | + | 1.11495e29i | 0.398497 | + | 0.474182i | ||||
\(628\) | − | 2.68080e27i | − | 0.0112121i | ||||||
\(629\) | −2.49129e29 | −1.02469 | ||||||||
\(630\) | 8.86954e28 | − | 3.20916e29i | 0.358778 | − | 1.29812i | ||||
\(631\) | −2.90971e29 | −1.15755 | −0.578777 | − | 0.815486i | \(-0.696470\pi\) | ||||
−0.578777 | + | 0.815486i | \(0.696470\pi\) | |||||||
\(632\) | − | 2.55994e29i | − | 1.00161i | ||||||
\(633\) | 1.60514e29 | + | 1.91000e29i | 0.617695 | + | 0.735013i | ||||
\(634\) | 4.46660e27 | 0.0169059 | ||||||||
\(635\) | 1.45394e29 | 0.541279 | ||||||||
\(636\) | 1.12112e29 | − | 9.42170e28i | 0.410535 | − | 0.345008i | ||||
\(637\) | −8.74507e28 | + | 4.46869e29i | −0.314992 | + | 1.60959i | ||||
\(638\) | 2.72496e29i | 0.965478i | ||||||||
\(639\) | 3.67770e29 | + | 6.42756e28i | 1.28179 | + | 0.224020i | ||||
\(640\) | 3.91603e29i | 1.34263i | ||||||||
\(641\) | 1.64057e29i | 0.553332i | 0.960966 | + | 0.276666i | \(0.0892296\pi\) | ||||
−0.960966 | + | 0.276666i | \(0.910770\pi\) | |||||||
\(642\) | −1.28128e29 | − | 1.52463e29i | −0.425135 | − | 0.505881i | ||||
\(643\) | − | 1.74137e29i | − | 0.568427i | −0.958761 | − | 0.284214i | \(-0.908267\pi\) | ||
0.958761 | − | 0.284214i | \(-0.0917325\pi\) | |||||||
\(644\) | −5.57876e28 | − | 5.40743e27i | −0.179158 | − | 0.0173656i | ||||
\(645\) | −1.23934e28 | − | 1.47472e28i | −0.0391573 | − | 0.0465944i | ||||
\(646\) | −3.21955e29 | −1.00081 | ||||||||
\(647\) | 8.97286e28 | 0.274433 | 0.137216 | − | 0.990541i | \(-0.456184\pi\) | ||||
0.137216 | + | 0.990541i | \(0.456184\pi\) | |||||||
\(648\) | −8.15200e28 | + | 2.26096e29i | −0.245316 | + | 0.680386i | ||||
\(649\) | − | 3.52037e29i | − | 1.04236i | ||||||
\(650\) | −2.04830e29 | −0.596764 | ||||||||
\(651\) | −2.14461e29 | − | 3.11961e29i | −0.614819 | − | 0.894336i | ||||
\(652\) | −2.11040e29 | −0.595340 | ||||||||
\(653\) | 5.20171e29i | 1.44397i | 0.691910 | + | 0.721984i | \(0.256770\pi\) | ||||
−0.691910 | + | 0.721984i | \(0.743230\pi\) | |||||||
\(654\) | 6.15025e29 | − | 5.16858e29i | 1.68007 | − | 1.41190i | ||||
\(655\) | −1.15076e29 | −0.309350 | ||||||||
\(656\) | 4.57666e28 | 0.121076 | ||||||||
\(657\) | −3.20119e29 | − | 5.59474e28i | −0.833441 | − | 0.145661i | ||||
\(658\) | 3.04225e29 | + | 2.94882e28i | 0.779513 | + | 0.0755573i | ||||
\(659\) | − | 6.00874e29i | − | 1.51526i | −0.652685 | − | 0.757629i | \(-0.726358\pi\) | ||
0.652685 | − | 0.757629i | \(-0.273642\pi\) | |||||||
\(660\) | −8.51519e28 | + | 7.15605e28i | −0.211341 | + | 0.177608i | ||||
\(661\) | 2.78191e29i | 0.679559i | 0.940505 | + | 0.339779i | \(0.110352\pi\) | ||||
−0.940505 | + | 0.339779i | \(0.889648\pi\) | |||||||
\(662\) | − | 6.82602e29i | − | 1.64119i | ||||||
\(663\) | −4.55776e29 | + | 3.83028e29i | −1.07860 | + | 0.906439i | ||||
\(664\) | − | 2.58129e28i | − | 0.0601274i | ||||||
\(665\) | 4.91612e29 | + | 4.76514e28i | 1.12719 | + | 0.109257i | ||||
\(666\) | 6.12840e29 | + | 1.07107e29i | 1.38315 | + | 0.241733i | ||||
\(667\) | 2.75424e29 | 0.611901 | ||||||||
\(668\) | −1.06597e29 | −0.233127 | ||||||||
\(669\) | −3.27204e29 | + | 2.74978e29i | −0.704440 | + | 0.592002i | ||||
\(670\) | 5.56329e29i | 1.17909i | ||||||||
\(671\) | −2.27046e28 | −0.0473725 | ||||||||
\(672\) | 2.02071e29 | + | 2.93939e29i | 0.415075 | + | 0.603782i | ||||
\(673\) | 8.91219e29 | 1.80230 | 0.901149 | − | 0.433510i | \(-0.142725\pi\) | ||||
0.901149 | + | 0.433510i | \(0.142725\pi\) | |||||||
\(674\) | 1.47540e29i | 0.293751i | ||||||||
\(675\) | −1.36384e29 | + | 7.91538e28i | −0.267347 | + | 0.155161i | ||||
\(676\) | 3.37611e29 | 0.651593 | ||||||||
\(677\) | 4.37738e29 | 0.831827 | 0.415914 | − | 0.909404i | \(-0.363462\pi\) | ||||
0.415914 | + | 0.909404i | \(0.363462\pi\) | |||||||
\(678\) | −4.81169e29 | − | 5.72556e29i | −0.900297 | − | 1.07129i | ||||
\(679\) | 3.19062e29 | + | 3.09264e28i | 0.587818 | + | 0.0569765i | ||||
\(680\) | 3.91859e29i | 0.710864i | ||||||||
\(681\) | −5.39643e29 | − | 6.42136e29i | −0.963966 | − | 1.14705i | ||||
\(682\) | 4.54485e29i | 0.799436i | ||||||||
\(683\) | − | 1.06104e30i | − | 1.83787i | −0.394414 | − | 0.918933i | \(-0.629052\pi\) | ||
0.394414 | − | 0.918933i | \(-0.370948\pi\) | |||||||
\(684\) | 2.20384e29 | + | 3.85167e28i | 0.375917 | + | 0.0656993i | ||||
\(685\) | − | 9.09518e29i | − | 1.52778i | ||||||
\(686\) | 6.81878e29 | + | 2.03393e29i | 1.12799 | + | 0.336459i | ||||
\(687\) | −1.91494e29 | + | 1.60929e29i | −0.311968 | + | 0.262174i | ||||
\(688\) | 4.10092e28 | 0.0657964 | ||||||||
\(689\) | 1.44366e30 | 2.28119 | ||||||||
\(690\) | 2.59928e29 | + | 3.09296e29i | 0.404518 | + | 0.481347i | ||||
\(691\) | − | 1.29496e29i | − | 0.198490i | −0.995063 | − | 0.0992448i | \(-0.968357\pi\) | ||
0.995063 | − | 0.0992448i | \(-0.0316427\pi\) | |||||||
\(692\) | −4.49029e28 | −0.0677891 | ||||||||
\(693\) | 1.12112e29 | − | 4.05643e29i | 0.166707 | − | 0.603177i | ||||
\(694\) | 6.29349e29 | 0.921759 | ||||||||
\(695\) | 1.19259e30i | 1.72049i | ||||||||
\(696\) | −4.29191e29 | − | 5.10707e29i | −0.609893 | − | 0.725729i | ||||
\(697\) | 6.00718e28 | 0.0840865 | ||||||||
\(698\) | −8.75019e29 | −1.20652 | ||||||||
\(699\) | −5.18291e28 | + | 4.35565e28i | −0.0703985 | + | 0.0591620i | ||||
\(700\) | −8.59316e27 | + | 8.86542e28i | −0.0114980 | + | 0.118623i | ||||
\(701\) | − | 5.98641e28i | − | 0.0789091i | −0.999221 | − | 0.0394545i | \(-0.987438\pi\) | ||
0.999221 | − | 0.0394545i | \(-0.0125620\pi\) | |||||||
\(702\) | 1.28585e30 | − | 7.46273e29i | 1.66975 | − | 0.969076i | ||||
\(703\) | 9.22907e29i | 1.18067i | ||||||||
\(704\) | 1.85925e29i | 0.234328i | ||||||||
\(705\) | −3.94433e29 | − | 4.69347e29i | −0.489765 | − | 0.582785i | ||||
\(706\) | 1.30883e30i | 1.60116i | ||||||||
\(707\) | −7.13698e28 | + | 7.36310e29i | −0.0860222 | + | 0.887476i | ||||
\(708\) | −3.47924e29 | − | 4.14005e29i | −0.413176 | − | 0.491650i | ||||
\(709\) | 3.11942e29 | 0.364996 | 0.182498 | − | 0.983206i | \(-0.441582\pi\) | ||||
0.182498 | + | 0.983206i | \(0.441582\pi\) | |||||||
\(710\) | −1.52007e30 | −1.75247 | ||||||||
\(711\) | −2.09880e29 | + | 1.20089e30i | −0.238419 | + | 1.36418i | ||||
\(712\) | − | 1.84632e29i | − | 0.206665i | ||||||
\(713\) | 4.59370e29 | 0.506667 | ||||||||
\(714\) | 5.27049e29 | + | 7.66663e29i | 0.572823 | + | 0.833246i | ||||
\(715\) | −1.09650e30 | −1.17434 | ||||||||
\(716\) | 1.87162e29i | 0.197529i | ||||||||
\(717\) | −1.03492e30 | + | 8.69732e29i | −1.07635 | + | 0.904554i | ||||
\(718\) | −6.88637e28 | −0.0705803 | ||||||||
\(719\) | −6.52660e29 | −0.659225 | −0.329613 | − | 0.944116i | \(-0.606918\pi\) | ||||
−0.329613 | + | 0.944116i | \(0.606918\pi\) | |||||||
\(720\) | 2.44766e29 | − | 1.40049e30i | 0.243646 | − | 1.39409i | ||||
\(721\) | −1.75845e30 | − | 1.70444e29i | −1.72508 | − | 0.167210i | ||||
\(722\) | − | 2.47624e28i | − | 0.0239416i | ||||||
\(723\) | −8.31953e29 | + | 6.99163e29i | −0.792769 | + | 0.666233i | ||||
\(724\) | − | 8.13078e29i | − | 0.763620i | ||||||
\(725\) | − | 4.37687e29i | − | 0.405149i | ||||||
\(726\) | 6.00903e29 | − | 5.04991e29i | 0.548239 | − | 0.460733i | ||||
\(727\) | − | 2.41749e29i | − | 0.217397i | −0.994075 | − | 0.108698i | \(-0.965332\pi\) | ||
0.994075 | − | 0.108698i | \(-0.0346682\pi\) | |||||||
\(728\) | −1.29114e29 | + | 1.33205e30i | −0.114444 | + | 1.18070i | ||||
\(729\) | 5.67786e29 | − | 9.93801e29i | 0.496073 | − | 0.868281i | ||||
\(730\) | 1.32312e30 | 1.13948 | ||||||||
\(731\) | 5.38273e28 | 0.0456952 | ||||||||
\(732\) | −2.67011e28 | + | 2.24393e28i | −0.0223441 | + | 0.0187777i | ||||
\(733\) | 1.91838e30i | 1.58250i | 0.611493 | + | 0.791250i | \(0.290569\pi\) | ||||
−0.611493 | + | 0.791250i | \(0.709431\pi\) | |||||||
\(734\) | 1.54134e30 | 1.25340 | ||||||||
\(735\) | −6.91312e29 | − | 1.24867e30i | −0.554188 | − | 1.00099i | ||||
\(736\) | −4.32832e29 | −0.342060 | ||||||||
\(737\) | 7.03208e29i | 0.547867i | ||||||||
\(738\) | −1.47772e29 | − | 2.58263e28i | −0.113501 | − | 0.0198367i | ||||
\(739\) | −1.83945e30 | −1.39290 | −0.696452 | − | 0.717604i | \(-0.745239\pi\) | ||||
−0.696452 | + | 0.717604i | \(0.745239\pi\) | |||||||
\(740\) | −7.04851e29 | −0.526217 | ||||||||
\(741\) | 1.41894e30 | + | 1.68844e30i | 1.04441 | + | 1.24278i | ||||
\(742\) | 2.17651e29 | − | 2.24547e30i | 0.157950 | − | 1.62954i | ||||
\(743\) | − | 1.87045e30i | − | 1.33833i | −0.743115 | − | 0.669164i | \(-0.766652\pi\) | ||
0.743115 | − | 0.669164i | \(-0.233348\pi\) | |||||||
\(744\) | −7.15832e29 | − | 8.51789e29i | −0.505004 | − | 0.600919i | ||||
\(745\) | − | 1.43337e30i | − | 0.997053i | ||||||
\(746\) | − | 2.36051e30i | − | 1.61901i | ||||||
\(747\) | −2.11631e28 | + | 1.21091e29i | −0.0143124 | + | 0.0818926i | ||||
\(748\) | − | 3.10804e29i | − | 0.207262i | ||||||
\(749\) | −8.49740e29 | − | 8.23644e28i | −0.558762 | − | 0.0541602i | ||||
\(750\) | −1.09858e30 | + | 9.23230e29i | −0.712340 | + | 0.598641i | ||||
\(751\) | −2.87327e29 | −0.183721 | −0.0918603 | − | 0.995772i | \(-0.529281\pi\) | ||||
−0.0918603 | + | 0.995772i | \(0.529281\pi\) | |||||||
\(752\) | 1.30516e30 | 0.822957 | ||||||||
\(753\) | 9.80683e29 | + | 1.16694e30i | 0.609791 | + | 0.725608i | ||||
\(754\) | 4.12657e30i | 2.53041i | ||||||||
\(755\) | 8.62206e29 | 0.521396 | ||||||||
\(756\) | −2.69056e29 | − | 5.87849e29i | −0.160459 | − | 0.350580i | ||||
\(757\) | −9.46707e29 | −0.556812 | −0.278406 | − | 0.960463i | \(-0.589806\pi\) | ||||
−0.278406 | + | 0.960463i | \(0.589806\pi\) | |||||||
\(758\) | 6.78001e29i | 0.393282i | ||||||||
\(759\) | 3.28553e29 | + | 3.90954e29i | 0.187960 | + | 0.223659i | ||||
\(760\) | 1.45165e30 | 0.819069 | ||||||||
\(761\) | −2.30806e30 | −1.28442 | −0.642212 | − | 0.766527i | \(-0.721983\pi\) | ||||
−0.642212 | + | 0.766527i | \(0.721983\pi\) | |||||||
\(762\) | 7.76697e29 | − | 6.52725e29i | 0.426309 | − | 0.358264i | ||||
\(763\) | 3.32251e29 | − | 3.42778e30i | 0.179870 | − | 1.85569i | ||||
\(764\) | − | 7.76952e29i | − | 0.414872i | ||||||
\(765\) | 3.21272e29 | − | 1.83825e30i | 0.169211 | − | 0.968185i | ||||
\(766\) | 7.46613e28i | 0.0387877i | ||||||||
\(767\) | − | 5.33112e30i | − | 2.73191i | ||||||
\(768\) | 1.28146e30 | + | 1.52484e30i | 0.647755 | + | 0.770782i | ||||
\(769\) | − | 2.99233e29i | − | 0.149205i | −0.997213 | − | 0.0746024i | \(-0.976231\pi\) | ||
0.997213 | − | 0.0746024i | \(-0.0237688\pi\) | |||||||
\(770\) | −1.65312e29 | + | 1.70550e30i | −0.0813115 | + | 0.838877i | ||||
\(771\) | 1.99371e30 | + | 2.37237e30i | 0.967365 | + | 1.15110i | ||||
\(772\) | −5.11909e29 | −0.245025 | ||||||||
\(773\) | −3.76572e30 | −1.77813 | −0.889065 | − | 0.457780i | \(-0.848645\pi\) | ||||
−0.889065 | + | 0.457780i | \(0.848645\pi\) | |||||||
\(774\) | −1.32411e29 | − | 2.31417e28i | −0.0616801 | − | 0.0107799i | ||||
\(775\) | − | 7.30002e29i | − | 0.335472i | ||||||
\(776\) | 9.42141e29 | 0.427138 | ||||||||
\(777\) | 2.19770e30 | − | 1.51083e30i | 0.982985 | − | 0.675762i | ||||
\(778\) | −1.07486e30 | −0.474315 | ||||||||
\(779\) | − | 2.22538e29i | − | 0.0968858i | ||||||
\(780\) | −1.28951e30 | + | 1.08369e30i | −0.553899 | + | 0.465490i | ||||
\(781\) | −1.92139e30 | −0.814292 | ||||||||
\(782\) | −1.12893e30 | −0.472058 | ||||||||
\(783\) | 1.59466e30 | + | 2.74765e30i | 0.657916 | + | 1.13361i | ||||
\(784\) | 2.98190e30 | + | 5.83548e29i | 1.21388 | + | 0.237551i | ||||
\(785\) | 8.28364e28i | 0.0332728i | ||||||||
\(786\) | −6.14738e29 | + | 5.16617e29i | −0.243642 | + | 0.204754i | ||||
\(787\) | − | 2.53125e30i | − | 0.989921i | −0.868915 | − | 0.494961i | \(-0.835183\pi\) | ||
0.868915 | − | 0.494961i | \(-0.164817\pi\) | |||||||
\(788\) | 1.16602e30i | 0.449968i | ||||||||
\(789\) | −1.95968e30 | + | 1.64689e30i | −0.746236 | + | 0.627127i | ||||
\(790\) | − | 4.96352e30i | − | 1.86511i | ||||||
\(791\) | −3.19108e30 | − | 3.09308e29i | −1.18327 | − | 0.114693i | ||||
\(792\) | 2.12948e29 | − | 1.21844e30i | 0.0779218 | − | 0.445851i | ||||
\(793\) | −3.43829e29 | −0.124158 | ||||||||
\(794\) | −1.58381e30 | −0.564402 | ||||||||
\(795\) | −3.46423e30 | + | 2.91129e30i | −1.21829 | + | 1.02384i | ||||
\(796\) | 6.08654e29i | 0.211244i | ||||||||
\(797\) | 1.37850e30 | 0.472164 | 0.236082 | − | 0.971733i | \(-0.424137\pi\) | ||||
0.236082 | + | 0.971733i | \(0.424137\pi\) | |||||||
\(798\) | 2.84013e30 | − | 1.95247e30i | 0.960080 | − | 0.660016i | ||||
\(799\) | 1.71312e30 | 0.571539 | ||||||||
\(800\) | 6.87829e29i | 0.226483i | ||||||||
\(801\) | −1.51373e29 | + | 8.66123e29i | −0.0491934 | + | 0.281474i | ||||
\(802\) | 2.41597e30 | 0.774926 | ||||||||
\(803\) | 1.67244e30 | 0.529465 | ||||||||
\(804\) | 6.94991e29 | + | 8.26990e29i | 0.217166 | + | 0.258411i | ||||
\(805\) | 1.72383e30 | + | 1.67089e29i | 0.531664 | + | 0.0515336i | ||||
\(806\) | 6.88256e30i | 2.09523i | ||||||||
\(807\) | −1.73402e30 | − | 2.06336e30i | −0.521053 | − | 0.620015i | ||||
\(808\) | 2.17421e30i | 0.644885i | ||||||||
\(809\) | 3.23821e30i | 0.948082i | 0.880503 | + | 0.474041i | \(0.157205\pi\) | ||||
−0.880503 | + | 0.474041i | \(0.842795\pi\) | |||||||
\(810\) | −1.58061e30 | + | 4.38383e30i | −0.456806 | + | 1.26695i | ||||
\(811\) | − | 9.38781e29i | − | 0.267822i | −0.990993 | − | 0.133911i | \(-0.957246\pi\) | ||
0.990993 | − | 0.133911i | \(-0.0427536\pi\) | |||||||
\(812\) | 1.78606e30 | + | 1.73121e29i | 0.502988 | + | 0.0487541i | ||||
\(813\) | −9.27082e29 | + | 7.79107e29i | −0.257731 | + | 0.216594i | ||||
\(814\) | −3.20174e30 | −0.878679 | ||||||||
\(815\) | 6.52110e30 | 1.76671 | ||||||||
\(816\) | 2.55590e30 | + | 3.04134e30i | 0.683592 | + | 0.813426i | ||||
\(817\) | − | 1.99405e29i | − | 0.0526507i | ||||||
\(818\) | 4.37017e30 | 1.13917 | ||||||||
\(819\) | 1.69779e30 | − | 6.14290e30i | 0.436920 | − | 1.58086i | ||||
\(820\) | 1.69959e29 | 0.0431815 | ||||||||
\(821\) | 6.38629e30i | 1.60194i | 0.598706 | + | 0.800969i | \(0.295682\pi\) | ||||
−0.598706 | + | 0.800969i | \(0.704318\pi\) | |||||||
\(822\) | −4.08316e30 | − | 4.85866e30i | −1.01121 | − | 1.20327i | ||||
\(823\) | 7.01330e30 | 1.71484 | 0.857421 | − | 0.514616i | \(-0.172066\pi\) | ||||
0.857421 | + | 0.514616i | \(0.172066\pi\) | |||||||
\(824\) | −5.19242e30 | −1.25353 | ||||||||
\(825\) | 6.21280e29 | − | 5.22116e29i | 0.148088 | − | 0.124452i | ||||
\(826\) | −8.29205e30 | − | 8.03740e29i | −1.95151 | − | 0.189158i | ||||
\(827\) | − | 1.77840e30i | − | 0.413259i | −0.978419 | − | 0.206630i | \(-0.933750\pi\) | ||
0.978419 | − | 0.206630i | \(-0.0662495\pi\) | |||||||
\(828\) | 7.72773e29 | + | 1.35058e29i | 0.177310 | + | 0.0309886i | ||||
\(829\) | − | 4.26678e30i | − | 0.966668i | −0.875436 | − | 0.483334i | \(-0.839426\pi\) | ||
0.875436 | − | 0.483334i | \(-0.160574\pi\) | |||||||
\(830\) | − | 5.00493e29i | − | 0.111964i | ||||||
\(831\) | 3.91316e30 | + | 4.65638e30i | 0.864403 | + | 1.02858i | ||||
\(832\) | 2.81558e30i | 0.614148i | ||||||||
\(833\) | 3.91395e30 | + | 7.65947e29i | 0.843030 | + | 0.164978i | ||||
\(834\) | 5.35398e30 | + | 6.37086e30i | 1.13876 | + | 1.35505i | ||||
\(835\) | 3.29384e30 | 0.691822 | ||||||||
\(836\) | −1.15138e30 | −0.238811 | ||||||||
\(837\) | 2.65968e30 | + | 4.58270e30i | 0.544768 | + | 0.938651i | ||||
\(838\) | − | 4.70961e29i | − | 0.0952628i | ||||||
\(839\) | 8.99381e30 | 1.79657 | 0.898283 | − | 0.439417i | \(-0.144815\pi\) | ||||
0.898283 | + | 0.439417i | \(0.144815\pi\) | |||||||
\(840\) | −2.37640e30 | − | 3.45679e30i | −0.468799 | − | 0.681931i | ||||
\(841\) | −3.68497e30 | −0.717920 | ||||||||
\(842\) | − | 1.30663e30i | − | 0.251406i | ||||||
\(843\) | −4.22331e30 | + | 3.54922e30i | −0.802535 | + | 0.674439i | ||||
\(844\) | −1.97242e30 | −0.370172 | ||||||||
\(845\) | −1.04321e31 | −1.93365 | ||||||||
\(846\) | −4.21414e30 | − | 7.36509e29i | −0.771472 | − | 0.134831i | ||||
\(847\) | 3.24622e29 | − | 3.34907e30i | 0.0586952 | − | 0.605548i | ||||
\(848\) | − | 9.63334e30i | − | 1.72036i | ||||||
\(849\) | 6.99904e30 | − | 5.88190e30i | 1.23455 | − | 1.03750i | ||||
\(850\) | 1.79402e30i | 0.312557i | ||||||||
\(851\) | 3.23615e30i | 0.556889i | ||||||||
\(852\) | −2.25961e30 | + | 1.89894e30i | −0.384076 | + | 0.322772i | ||||
\(853\) | − | 4.18128e30i | − | 0.702011i | −0.936373 | − | 0.351006i | \(-0.885840\pi\) | ||
0.936373 | − | 0.351006i | \(-0.114160\pi\) | |||||||
\(854\) | −5.18370e28 | + | 5.34794e29i | −0.00859671 | + | 0.0886909i | ||||
\(855\) | −6.80984e30 | − | 1.19016e30i | −1.11556 | − | 0.194967i | ||||
\(856\) | −2.50915e30 | −0.406024 | ||||||||
\(857\) | 1.09174e30 | 0.174510 | 0.0872548 | − | 0.996186i | \(-0.472191\pi\) | ||||
0.0872548 | + | 0.996186i | \(0.472191\pi\) | |||||||
\(858\) | −5.85751e30 | + | 4.92257e30i | −0.924904 | + | 0.777277i | ||||
\(859\) | − | 2.29470e29i | − | 0.0357929i | −0.999840 | − | 0.0178964i | \(-0.994303\pi\) | ||
0.999840 | − | 0.0178964i | \(-0.00569692\pi\) | |||||||
\(860\) | 1.52292e29 | 0.0234662 | ||||||||
\(861\) | −5.29924e29 | + | 3.64301e29i | −0.0806641 | + | 0.0554532i | ||||
\(862\) | 1.27172e31 | 1.91234 | ||||||||
\(863\) | − | 6.94201e30i | − | 1.03127i | −0.856809 | − | 0.515635i | \(-0.827556\pi\) | ||
0.856809 | − | 0.515635i | \(-0.172444\pi\) | |||||||
\(864\) | −2.50603e30 | − | 4.31795e30i | −0.367783 | − | 0.633700i | ||||
\(865\) | 1.38749e30 | 0.201169 | ||||||||
\(866\) | 8.88491e30 | 1.27267 | ||||||||
\(867\) | −1.19151e30 | − | 1.41781e30i | −0.168615 | − | 0.200640i | ||||
\(868\) | 2.97890e30 | + | 2.88742e29i | 0.416485 | + | 0.0403695i | ||||
\(869\) | − | 6.27396e30i | − | 0.866631i | ||||||
\(870\) | −8.32169e30 | − | 9.90222e30i | −1.13569 | − | 1.35139i | ||||
\(871\) | 1.06491e31i | 1.43590i | ||||||||
\(872\) | − | 1.01217e31i | − | 1.34843i | ||||||
\(873\) | −4.41966e30 | − | 7.72429e29i | −0.581755 | − | 0.101674i | ||||
\(874\) | 4.18215e30i | 0.543913i | ||||||||
\(875\) | −5.93478e29 | + | 6.12281e30i | −0.0762640 | + | 0.786803i | ||||
\(876\) | 1.96683e30 | − | 1.65290e30i | 0.249732 | − | 0.209871i | ||||
\(877\) | 9.85421e30 | 1.23631 | 0.618153 | − | 0.786058i | \(-0.287881\pi\) | ||||
0.618153 | + | 0.786058i | \(0.287881\pi\) | |||||||
\(878\) | −8.26851e29 | −0.102503 | ||||||||
\(879\) | 2.89573e30 | + | 3.44571e30i | 0.354711 | + | 0.422081i | ||||
\(880\) | 7.31679e30i | 0.885630i | ||||||||
\(881\) | −8.91446e30 | −1.06622 | −0.533111 | − | 0.846045i | \(-0.678977\pi\) | ||||
−0.533111 | + | 0.846045i | \(0.678977\pi\) | |||||||
\(882\) | −9.29874e30 | − | 3.56687e30i | −1.09902 | − | 0.421568i | ||||
\(883\) | −1.33427e31 | −1.55832 | −0.779158 | − | 0.626827i | \(-0.784353\pi\) | ||||
−0.779158 | + | 0.626827i | \(0.784353\pi\) | |||||||
\(884\) | − | 4.70670e30i | − | 0.543210i | ||||||
\(885\) | 1.07508e31 | + | 1.27927e31i | 1.22613 | + | 1.45901i | ||||
\(886\) | −1.70995e31 | −1.92721 | ||||||||
\(887\) | 3.55260e30 | 0.395683 | 0.197842 | − | 0.980234i | \(-0.436607\pi\) | ||||
0.197842 | + | 0.980234i | \(0.436607\pi\) | |||||||
\(888\) | 6.00065e30 | − | 5.04287e30i | 0.660484 | − | 0.555062i | ||||
\(889\) | 4.19590e29 | − | 4.32884e30i | 0.0456411 | − | 0.470872i | ||||
\(890\) | − | 3.57987e30i | − | 0.384833i | ||||||
\(891\) | −1.99791e30 | + | 5.54122e30i | −0.212257 | + | 0.588694i | ||||
\(892\) | − | 3.37896e30i | − | 0.354774i | ||||||
\(893\) | − | 6.34629e30i | − | 0.658536i | ||||||
\(894\) | −6.43493e30 | − | 7.65711e30i | −0.659933 | − | 0.785274i | ||||
\(895\) | − | 5.78328e30i | − | 0.586181i | ||||||
\(896\) | 1.16593e31 | + | 1.13012e30i | 1.16799 | + | 0.113212i | ||||
\(897\) | 4.97548e30 | + | 5.92047e30i | 0.492623 | + | 0.586186i | ||||
\(898\) | 2.15733e30 | 0.211113 | ||||||||
\(899\) | −1.47069e31 | −1.42247 | ||||||||
\(900\) | 2.14626e29 | − | 1.22804e30i | 0.0205181 | − | 0.117400i | ||||
\(901\) | − | 1.26444e31i | − | 1.19478i | ||||||
\(902\) | 7.72026e29 | 0.0721047 | ||||||||
\(903\) | −4.74838e29 | + | 3.26432e29i | −0.0438353 | + | 0.0301350i | ||||
\(904\) | −9.42277e30 | −0.859825 | ||||||||
\(905\) | 2.51240e31i | 2.26610i | ||||||||
\(906\) | 4.60592e30 | − | 3.87076e30i | 0.410649 | − | 0.345104i | ||||
\(907\) | −6.95111e30 | −0.612601 | −0.306300 | − | 0.951935i | \(-0.599091\pi\) | ||||
−0.306300 | + | 0.951935i | \(0.599091\pi\) | |||||||
\(908\) | 6.63120e30 | 0.577685 | ||||||||
\(909\) | 1.78256e30 | − | 1.01994e31i | 0.153505 | − | 0.878323i | ||||
\(910\) | −2.50342e30 | + | 2.58274e31i | −0.213108 | + | 2.19860i | ||||
\(911\) | 1.18167e31i | 0.994381i | 0.867641 | + | 0.497191i | \(0.165635\pi\) | ||||
−0.867641 | + | 0.497191i | \(0.834365\pi\) | |||||||
\(912\) | 1.12667e31 | − | 9.46841e30i | 0.937242 | − | 0.787646i | ||||
\(913\) | − | 6.32631e29i | − | 0.0520244i | ||||||
\(914\) | − | 2.08448e31i | − | 1.69458i | ||||||
\(915\) | 8.25060e29 | − | 6.93370e29i | 0.0663077 | − | 0.0557242i | ||||
\(916\) | − | 1.97752e30i | − | 0.157115i | ||||||
\(917\) | −3.32096e29 | + | 3.42618e30i | −0.0260847 | + | 0.269111i | ||||
\(918\) | −6.53631e30 | − | 1.12623e31i | −0.507557 | − | 0.874535i | ||||
\(919\) | −1.62113e31 | −1.24453 | −0.622263 | − | 0.782808i | \(-0.713786\pi\) | ||||
−0.622263 | + | 0.782808i | \(0.713786\pi\) | |||||||
\(920\) | 5.09019e30 | 0.386333 | ||||||||
\(921\) | −6.88267e30 | + | 5.78411e30i | −0.516453 | + | 0.434021i | ||||
\(922\) | 2.73156e31i | 2.02645i | ||||||||
\(923\) | −2.90969e31 | −2.13417 | ||||||||
\(924\) | 1.88485e30 | + | 2.74176e30i | 0.136685 | + | 0.198826i | ||||
\(925\) | 5.14270e30 | 0.368725 | ||||||||
\(926\) | 2.31830e31i | 1.64344i | ||||||||
\(927\) | 2.43581e31 | + | 4.25709e30i | 1.70729 | + | 0.298384i | ||||
\(928\) | 1.38573e31 | 0.960337 | ||||||||
\(929\) | −3.12710e30 | −0.214277 | −0.107139 | − | 0.994244i | \(-0.534169\pi\) | ||||
−0.107139 | + | 0.994244i | \(0.534169\pi\) | |||||||
\(930\) | −1.38794e31 | − | 1.65155e31i | −0.940374 | − | 1.11898i | ||||
\(931\) | 2.83747e30 | − | 1.44994e31i | 0.190090 | − | 0.971353i | ||||
\(932\) | − | 5.35228e29i | − | 0.0354545i | ||||||
\(933\) | −3.81514e30 | − | 4.53974e30i | −0.249893 | − | 0.297354i | ||||
\(934\) | 6.23271e30i | 0.403678i | ||||||||
\(935\) | 9.60379e30i | 0.615065i | ||||||||
\(936\) | 3.22480e30 | − | 1.84516e31i | 0.204224 | − | 1.16853i | ||||
\(937\) | 1.97842e31i | 1.23895i | 0.785018 | + | 0.619473i | \(0.212654\pi\) | ||||
−0.785018 | + | 0.619473i | \(0.787346\pi\) | |||||||
\(938\) | 1.65637e31 | + | 1.60550e30i | 1.02572 | + | 0.0994216i | ||||
\(939\) | 1.20518e31 | − | 1.01281e31i | 0.738009 | − | 0.620213i | ||||
\(940\) | 4.84685e30 | 0.293506 | ||||||||
\(941\) | 2.40995e31 | 1.44317 | 0.721585 | − | 0.692326i | \(-0.243414\pi\) | ||||
0.721585 | + | 0.692326i | \(0.243414\pi\) | |||||||
\(942\) | 3.71883e29 | + | 4.42514e29i | 0.0220227 | + | 0.0262055i | ||||
\(943\) | − | 7.80324e29i | − | 0.0456985i | ||||||
\(944\) | −3.55739e31 | −2.06028 | ||||||||
\(945\) | 8.31380e30 | + | 1.81644e31i | 0.476174 | + | 1.04037i | ||||
\(946\) | 6.91775e29 | 0.0391839 | ||||||||
\(947\) | − | 1.27295e31i | − | 0.713078i | −0.934281 | − | 0.356539i | \(-0.883957\pi\) | ||
0.934281 | − | 0.356539i | \(-0.116043\pi\) | |||||||
\(948\) | −6.20066e30 | − | 7.37834e30i | −0.343519 | − | 0.408763i | ||||
\(949\) | 2.53268e31 | 1.38767 | ||||||||
\(950\) | 6.64601e30 | 0.360133 | ||||||||
\(951\) | −2.05164e29 | + | 1.72417e29i | −0.0109953 | + | 0.00924028i | ||||
\(952\) | 1.16669e31 | + | 1.13086e30i | 0.618397 | + | 0.0599406i | ||||
\(953\) | 1.29646e31i | 0.679645i | 0.940490 | + | 0.339822i | \(0.110367\pi\) | ||||
−0.940490 | + | 0.339822i | \(0.889633\pi\) | |||||||
\(954\) | −5.43613e30 | + | 3.11044e31i | −0.281859 | + | 1.61274i | ||||
\(955\) | 2.40077e31i | 1.23116i | ||||||||
\(956\) | − | 1.06874e31i | − | 0.542080i | ||||||
\(957\) | −1.05187e31 | − | 1.25165e31i | −0.527701 | − | 0.627927i | ||||
\(958\) | − | 1.88331e31i | − | 0.934511i | ||||||
\(959\) | −2.70793e31 | − | 2.62476e30i | −1.32905 | − | 0.128823i | ||||
\(960\) | −5.67793e30 | − | 6.75633e30i | −0.275640 | − | 0.327992i | ||||
\(961\) | −3.70357e30 | −0.177838 | ||||||||
\(962\) | −4.84860e31 | −2.30292 | ||||||||
\(963\) | 1.17706e31 | + | 2.05716e30i | 0.552998 | + | 0.0966480i | ||||
\(964\) | − | 8.59141e30i | − | 0.399260i | ||||||
\(965\) | 1.58179e31 | 0.727129 | ||||||||
\(966\) | 9.95885e30 | − | 6.84630e30i | 0.452845 | − | 0.311312i | ||||
\(967\) | 2.95203e31 | 1.32783 | 0.663916 | − | 0.747808i | \(-0.268893\pi\) | ||||
0.663916 | + | 0.747808i | \(0.268893\pi\) | |||||||
\(968\) | − | 9.88929e30i | − | 0.440021i | ||||||
\(969\) | 1.47884e31 | − | 1.24279e31i | 0.650909 | − | 0.547015i | ||||
\(970\) | 1.82674e31 | 0.795378 | ||||||||
\(971\) | −1.92379e31 | −0.828619 | −0.414309 | − | 0.910136i | \(-0.635977\pi\) | ||||
−0.414309 | + | 0.910136i | \(0.635977\pi\) | |||||||
\(972\) | 3.12688e30 | + | 8.49119e30i | 0.133234 | + | 0.361804i | ||||
\(973\) | 3.55073e31 | + | 3.44169e30i | 1.49669 | + | 0.145073i | ||||
\(974\) | 1.75120e31i | 0.730241i | ||||||||
\(975\) | 9.40844e30 | − | 7.90673e30i | 0.388123 | − | 0.326173i | ||||
\(976\) | 2.29433e30i | 0.0936339i | ||||||||
\(977\) | − | 4.39902e31i | − | 1.77608i | −0.459764 | − | 0.888041i | \(-0.652066\pi\) | ||
0.459764 | − | 0.888041i | \(-0.347934\pi\) | |||||||
\(978\) | 3.48359e31 | − | 2.92756e31i | 1.39145 | − | 1.16936i | ||||
\(979\) | − | 4.52500e30i | − | 0.178814i | ||||||
\(980\) | 1.10736e31 | + | 2.16706e30i | 0.432927 | + | 0.0847223i | ||||
\(981\) | −8.29842e30 | + | 4.74817e31i | −0.320975 | + | 1.83655i | ||||
\(982\) | −7.36540e30 | −0.281855 | ||||||||
\(983\) | 5.07704e31 | 1.92220 | 0.961100 | − | 0.276200i | \(-0.0890752\pi\) | ||||
0.961100 | + | 0.276200i | \(0.0890752\pi\) | |||||||
\(984\) | −1.44692e30 | + | 1.21597e30i | −0.0541995 | + | 0.0455486i | ||||
\(985\) | − | 3.60299e31i | − | 1.33531i | ||||||
\(986\) | 3.61431e31 | 1.32531 | ||||||||
\(987\) | −1.51123e31 | + | 1.03891e31i | −0.548276 | + | 0.376917i | ||||
\(988\) | −1.74361e31 | −0.625896 | ||||||||
\(989\) | − | 6.99210e29i | − | 0.0248340i | ||||||
\(990\) | 4.12890e30 | − | 2.36246e31i | 0.145099 | − | 0.830225i | ||||
\(991\) | −3.70813e31 | −1.28938 | −0.644692 | − | 0.764443i | \(-0.723014\pi\) | ||||
−0.644692 | + | 0.764443i | \(0.723014\pi\) | |||||||
\(992\) | 2.31120e31 | 0.795179 | ||||||||
\(993\) | 2.63495e31 | + | 3.13540e31i | 0.897025 | + | 1.06740i | ||||
\(994\) | −4.38675e30 | + | 4.52574e31i | −0.147770 | + | 1.52452i | ||||
\(995\) | − | 1.88073e31i | − | 0.626880i | ||||||
\(996\) | −6.25239e29 | − | 7.43990e29i | −0.0206216 | − | 0.0245383i | ||||
\(997\) | 5.97176e30i | 0.194896i | 0.995241 | + | 0.0974480i | \(0.0310680\pi\) | ||||
−0.995241 | + | 0.0974480i | \(0.968932\pi\) | |||||||
\(998\) | 4.23390e31i | 1.36732i | ||||||||
\(999\) | −3.22841e31 | + | 1.87368e31i | −1.03169 | + | 0.598767i |
(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 | 21.22.c.b.20.41 | yes | 52 | |
3.2 | odd | 2 | inner | 21.22.c.b.20.12 | yes | 52 | |
7.6 | odd | 2 | inner | 21.22.c.b.20.11 | ✓ | 52 | |
21.20 | even | 2 | inner | 21.22.c.b.20.42 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.22.c.b.20.11 | ✓ | 52 | 7.6 | odd | 2 | inner | |
21.22.c.b.20.12 | yes | 52 | 3.2 | odd | 2 | inner | |
21.22.c.b.20.41 | yes | 52 | 1.1 | even | 1 | trivial | |
21.22.c.b.20.42 | yes | 52 | 21.20 | even | 2 | inner |