Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,8,Mod(75,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.75");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.d (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: | \(23.7412619368\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 75.6 | ||
Character | \(\chi\) | \(=\) | 76.75 |
Dual form | 76.8.d.a.75.5 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.9753 | + | 2.74630i | −0.970091 | + | 0.242741i | ||||
\(3\) | −8.30507 | −0.177590 | −0.0887951 | − | 0.996050i | \(-0.528302\pi\) | ||||
−0.0887951 | + | 0.996050i | \(0.528302\pi\) | |||||||
\(4\) | 112.916 | − | 60.2831i | 0.882154 | − | 0.470961i | ||||
\(5\) | −360.155 | −1.28853 | −0.644266 | − | 0.764802i | \(-0.722837\pi\) | ||||
−0.644266 | + | 0.764802i | \(0.722837\pi\) | |||||||
\(6\) | 91.1509 | − | 22.8082i | 0.172279 | − | 0.0431084i | ||||
\(7\) | − | 965.147i | − | 1.06353i | −0.846892 | − | 0.531766i | \(-0.821529\pi\) | ||
0.846892 | − | 0.531766i | \(-0.178471\pi\) | |||||||
\(8\) | −1073.73 | + | 971.727i | −0.741448 | + | 0.671010i | ||||
\(9\) | −2118.03 | −0.968462 | ||||||||
\(10\) | 3952.82 | − | 989.094i | 1.24999 | − | 0.312779i | ||||
\(11\) | 3964.61i | 0.898104i | 0.893506 | + | 0.449052i | \(0.148238\pi\) | ||||
−0.893506 | + | 0.449052i | \(0.851762\pi\) | |||||||
\(12\) | −937.773 | + | 500.655i | −0.156662 | + | 0.0836381i | ||||
\(13\) | − | 11892.9i | − | 1.50137i | −0.660662 | − | 0.750684i | \(-0.729724\pi\) | ||
0.660662 | − | 0.750684i | \(-0.270276\pi\) | |||||||
\(14\) | 2650.58 | + | 10592.8i | 0.258162 | + | 1.03172i | ||||
\(15\) | 2991.12 | 0.228831 | ||||||||
\(16\) | 9115.91 | − | 13613.8i | 0.556391 | − | 0.830921i | ||||
\(17\) | −33048.5 | −1.63148 | −0.815739 | − | 0.578420i | \(-0.803669\pi\) | ||||
−0.815739 | + | 0.578420i | \(0.803669\pi\) | |||||||
\(18\) | 23246.0 | − | 5816.73i | 0.939496 | − | 0.235085i | ||||
\(19\) | 22720.7 | − | 19433.0i | 0.759948 | − | 0.649983i | ||||
\(20\) | −40667.2 | + | 21711.3i | −1.13668 | + | 0.606848i | ||||
\(21\) | 8015.61i | 0.188873i | ||||||||
\(22\) | −10888.0 | − | 43512.9i | −0.218006 | − | 0.871243i | ||||
\(23\) | − | 20031.3i | − | 0.343290i | −0.985159 | − | 0.171645i | \(-0.945092\pi\) | ||
0.985159 | − | 0.171645i | \(-0.0549082\pi\) | |||||||
\(24\) | 8917.42 | − | 8070.26i | 0.131674 | − | 0.119165i | ||||
\(25\) | 51586.9 | 0.660313 | ||||||||
\(26\) | 32661.5 | + | 130529.i | 0.364443 | + | 1.45646i | ||||
\(27\) | 35753.5 | 0.349580 | ||||||||
\(28\) | −58182.0 | − | 108980.i | −0.500882 | − | 0.938198i | ||||
\(29\) | 6526.34i | 0.0496909i | 0.999691 | + | 0.0248454i | \(0.00790936\pi\) | ||||
−0.999691 | + | 0.0248454i | \(0.992091\pi\) | |||||||
\(30\) | −32828.5 | + | 8214.50i | −0.221986 | + | 0.0555465i | ||||
\(31\) | 56888.3 | 0.342971 | 0.171485 | − | 0.985187i | \(-0.445143\pi\) | ||||
0.171485 | + | 0.985187i | \(0.445143\pi\) | |||||||
\(32\) | −62662.5 | + | 174451.i | −0.338051 | + | 0.941128i | ||||
\(33\) | − | 32926.4i | − | 0.159494i | ||||||
\(34\) | 362719. | − | 90761.2i | 1.58268 | − | 0.396026i | ||||
\(35\) | 347603.i | 1.37039i | ||||||||
\(36\) | −239158. | + | 127681.i | −0.854332 | + | 0.456108i | ||||
\(37\) | 468695.i | 1.52119i | 0.649224 | + | 0.760597i | \(0.275094\pi\) | ||||
−0.649224 | + | 0.760597i | \(0.724906\pi\) | |||||||
\(38\) | −195998. | + | 275681.i | −0.579442 | + | 0.815014i | ||||
\(39\) | 98771.6i | 0.266628i | ||||||||
\(40\) | 386710. | − | 349973.i | 0.955379 | − | 0.864618i | ||||
\(41\) | 668641.i | 1.51513i | 0.652760 | + | 0.757564i | \(0.273611\pi\) | ||||
−0.652760 | + | 0.757564i | \(0.726389\pi\) | |||||||
\(42\) | −22013.3 | − | 87974.0i | −0.0458471 | − | 0.183224i | ||||
\(43\) | 932141.i | 1.78790i | 0.448171 | + | 0.893948i | \(0.352075\pi\) | ||||
−0.448171 | + | 0.893948i | \(0.647925\pi\) | |||||||
\(44\) | 238999. | + | 447667.i | 0.422972 | + | 0.792266i | ||||
\(45\) | 762818. | 1.24789 | ||||||||
\(46\) | 55011.8 | + | 219850.i | 0.0833304 | + | 0.333022i | ||||
\(47\) | − | 378820.i | − | 0.532219i | −0.963943 | − | 0.266110i | \(-0.914262\pi\) | ||
0.963943 | − | 0.266110i | \(-0.0857383\pi\) | |||||||
\(48\) | −75708.2 | + | 113064.i | −0.0988095 | + | 0.147563i | ||||
\(49\) | −107965. | −0.131098 | ||||||||
\(50\) | −566184. | + | 141673.i | −0.640564 | + | 0.160285i | ||||
\(51\) | 274471. | 0.289734 | ||||||||
\(52\) | −716942. | − | 1.34290e6i | −0.707086 | − | 1.32444i | ||||
\(53\) | − | 1.24150e6i | − | 1.14547i | −0.819742 | − | 0.572733i | \(-0.805883\pi\) | ||
0.819742 | − | 0.572733i | \(-0.194117\pi\) | |||||||
\(54\) | −392407. | + | 98189.9i | −0.339124 | + | 0.0848572i | ||||
\(55\) | − | 1.42788e6i | − | 1.15723i | ||||||
\(56\) | 937859. | + | 1.03631e6i | 0.713640 | + | 0.788553i | ||||
\(57\) | −188697. | + | 161392.i | −0.134959 | + | 0.115431i | ||||
\(58\) | −17923.3 | − | 71628.7i | −0.0120620 | − | 0.0482047i | ||||
\(59\) | 1.58920e6 | 1.00739 | 0.503694 | − | 0.863882i | \(-0.331974\pi\) | ||||
0.503694 | + | 0.863882i | \(0.331974\pi\) | |||||||
\(60\) | 337744. | − | 180314.i | 0.201864 | − | 0.107770i | ||||
\(61\) | 423764. | 0.239040 | 0.119520 | − | 0.992832i | \(-0.461864\pi\) | ||||
0.119520 | + | 0.992832i | \(0.461864\pi\) | |||||||
\(62\) | −624368. | + | 156232.i | −0.332713 | + | 0.0832530i | ||||
\(63\) | 2.04421e6i | 1.02999i | ||||||||
\(64\) | 208647. | − | 2.08675e6i | 0.0994905 | − | 0.995039i | ||||
\(65\) | 4.28330e6i | 1.93456i | ||||||||
\(66\) | 90425.7 | + | 361378.i | 0.0387158 | + | 0.154724i | ||||
\(67\) | −3.95935e6 | −1.60828 | −0.804140 | − | 0.594440i | \(-0.797374\pi\) | ||||
−0.804140 | + | 0.594440i | \(0.797374\pi\) | |||||||
\(68\) | −3.73170e6 | + | 1.99227e6i | −1.43921 | + | 0.768363i | ||||
\(69\) | 166361.i | 0.0609649i | ||||||||
\(70\) | −954621. | − | 3.81506e6i | −0.332650 | − | 1.32941i | ||||
\(71\) | 2.83400e6 | 0.939713 | 0.469856 | − | 0.882743i | \(-0.344306\pi\) | ||||
0.469856 | + | 0.882743i | \(0.344306\pi\) | |||||||
\(72\) | 2.27419e6 | − | 2.05814e6i | 0.718064 | − | 0.649848i | ||||
\(73\) | 582613. | 0.175287 | 0.0876436 | − | 0.996152i | \(-0.472066\pi\) | ||||
0.0876436 | + | 0.996152i | \(0.472066\pi\) | |||||||
\(74\) | −1.28718e6 | − | 5.14408e6i | −0.369256 | − | 1.47570i | ||||
\(75\) | −428433. | −0.117265 | ||||||||
\(76\) | 1.39404e6 | − | 3.56396e6i | 0.364274 | − | 0.931292i | ||||
\(77\) | 3.82643e6 | 0.955161 | ||||||||
\(78\) | −271256. | − | 1.08405e6i | −0.0647215 | − | 0.258654i | ||||
\(79\) | −4.06561e6 | −0.927749 | −0.463875 | − | 0.885901i | \(-0.653541\pi\) | ||||
−0.463875 | + | 0.885901i | \(0.653541\pi\) | |||||||
\(80\) | −3.28314e6 | + | 4.90309e6i | −0.716927 | + | 1.07067i | ||||
\(81\) | 4.33519e6 | 0.906380 | ||||||||
\(82\) | −1.83629e6 | − | 7.33856e6i | −0.367784 | − | 1.46981i | ||||
\(83\) | − | 4.76177e6i | − | 0.914102i | −0.889440 | − | 0.457051i | \(-0.848906\pi\) | ||
0.889440 | − | 0.457051i | \(-0.151094\pi\) | |||||||
\(84\) | 483206. | + | 905088.i | 0.0889518 | + | 0.166615i | ||||
\(85\) | 1.19026e7 | 2.10221 | ||||||||
\(86\) | −2.55994e6 | − | 1.02306e7i | −0.433995 | − | 1.73442i | ||||
\(87\) | − | 54201.7i | − | 0.00882461i | ||||||
\(88\) | −3.85252e6 | − | 4.25693e6i | −0.602637 | − | 0.665897i | ||||
\(89\) | 3.77882e6i | 0.568187i | 0.958797 | + | 0.284093i | \(0.0916926\pi\) | ||||
−0.958797 | + | 0.284093i | \(0.908307\pi\) | |||||||
\(90\) | −8.37218e6 | + | 2.09493e6i | −1.21057 | + | 0.302915i | ||||
\(91\) | −1.14784e7 | −1.59675 | ||||||||
\(92\) | −1.20755e6 | − | 2.26184e6i | −0.161676 | − | 0.302834i | ||||
\(93\) | −472462. | −0.0609083 | ||||||||
\(94\) | 1.04035e6 | + | 4.15768e6i | 0.129191 | + | 0.516301i | ||||
\(95\) | −8.18298e6 | + | 6.99890e6i | −0.979217 | + | 0.837524i | ||||
\(96\) | 520416. | − | 1.44883e6i | 0.0600346 | − | 0.167135i | ||||
\(97\) | 6.84934e6i | 0.761987i | 0.924578 | + | 0.380993i | \(0.124418\pi\) | ||||
−0.924578 | + | 0.380993i | \(0.875582\pi\) | |||||||
\(98\) | 1.18495e6 | − | 296505.i | 0.127177 | − | 0.0318229i | ||||
\(99\) | − | 8.39716e6i | − | 0.869779i | ||||||
\(100\) | 5.82497e6 | − | 3.10982e6i | 0.582497 | − | 0.310982i | ||||
\(101\) | −3.81550e6 | −0.368491 | −0.184246 | − | 0.982880i | \(-0.558984\pi\) | ||||
−0.184246 | + | 0.982880i | \(0.558984\pi\) | |||||||
\(102\) | −3.01240e6 | + | 753778.i | −0.281069 | + | 0.0703304i | ||||
\(103\) | 1.28044e7 | 1.15460 | 0.577298 | − | 0.816533i | \(-0.304107\pi\) | ||||
0.577298 | + | 0.816533i | \(0.304107\pi\) | |||||||
\(104\) | 1.15567e7 | + | 1.27698e7i | 1.00743 | + | 1.11319i | ||||
\(105\) | − | 2.88687e6i | − | 0.243368i | ||||||
\(106\) | 3.40954e6 | + | 1.36259e7i | 0.278051 | + | 1.11121i | ||||
\(107\) | 9.00442e6 | 0.710579 | 0.355290 | − | 0.934756i | \(-0.384382\pi\) | ||||
0.355290 | + | 0.934756i | \(0.384382\pi\) | |||||||
\(108\) | 4.03714e6 | − | 2.15533e6i | 0.308383 | − | 0.164638i | ||||
\(109\) | − | 6.98563e6i | − | 0.516670i | −0.966055 | − | 0.258335i | \(-0.916826\pi\) | ||
0.966055 | − | 0.258335i | \(-0.0831738\pi\) | |||||||
\(110\) | 3.92138e6 | + | 1.56714e7i | 0.280908 | + | 1.12262i | ||||
\(111\) | − | 3.89255e6i | − | 0.270149i | ||||||
\(112\) | −1.31393e7 | − | 8.79819e6i | −0.883710 | − | 0.591739i | ||||
\(113\) | − | 2.32744e6i | − | 0.151742i | −0.997118 | − | 0.0758708i | \(-0.975826\pi\) | ||
0.997118 | − | 0.0758708i | \(-0.0241737\pi\) | |||||||
\(114\) | 1.62778e6 | − | 2.28955e6i | 0.102903 | − | 0.144738i | ||||
\(115\) | 7.21437e6i | 0.442340i | ||||||||
\(116\) | 393428. | + | 736926.i | 0.0234025 | + | 0.0438350i | ||||
\(117\) | 2.51895e7i | 1.45402i | ||||||||
\(118\) | −1.74420e7 | + | 4.36442e6i | −0.977259 | + | 0.244534i | ||||
\(119\) | 3.18967e7i | 1.73513i | ||||||||
\(120\) | −3.21166e6 | + | 2.90655e6i | −0.169666 | + | 0.153548i | ||||
\(121\) | 3.76900e6 | 0.193409 | ||||||||
\(122\) | −4.65095e6 | + | 1.16378e6i | −0.231890 | + | 0.0580247i | ||||
\(123\) | − | 5.55311e6i | − | 0.269072i | ||||||
\(124\) | 6.42359e6 | − | 3.42940e6i | 0.302553 | − | 0.161526i | ||||
\(125\) | 9.55783e6 | 0.437698 | ||||||||
\(126\) | −5.61400e6 | − | 2.24358e7i | −0.250020 | − | 0.999183i | ||||
\(127\) | −709860. | −0.0307511 | −0.0153755 | − | 0.999882i | \(-0.504894\pi\) | ||||
−0.0153755 | + | 0.999882i | \(0.504894\pi\) | |||||||
\(128\) | 3.44086e6 | + | 2.34757e7i | 0.145022 | + | 0.989428i | ||||
\(129\) | − | 7.74150e6i | − | 0.317513i | ||||||
\(130\) | −1.17632e7 | − | 4.70107e7i | −0.469596 | − | 1.87670i | ||||
\(131\) | − | 3.97921e7i | − | 1.54649i | −0.634108 | − | 0.773245i | \(-0.718632\pi\) | ||
0.634108 | − | 0.773245i | \(-0.281368\pi\) | |||||||
\(132\) | −1.98490e6 | − | 3.71791e6i | −0.0751157 | − | 0.140699i | ||||
\(133\) | −1.87557e7 | − | 2.19288e7i | −0.691278 | − | 0.808229i | ||||
\(134\) | 4.34551e7 | − | 1.08735e7i | 1.56018 | − | 0.390395i | ||||
\(135\) | −1.28768e7 | −0.450444 | ||||||||
\(136\) | 3.54853e7 | − | 3.21142e7i | 1.20966 | − | 1.09474i | ||||
\(137\) | −3.43128e7 | −1.14008 | −0.570039 | − | 0.821618i | \(-0.693072\pi\) | ||||
−0.570039 | + | 0.821618i | \(0.693072\pi\) | |||||||
\(138\) | −456877. | − | 1.82587e6i | −0.0147987 | − | 0.0591415i | ||||
\(139\) | 3.76453e7i | 1.18894i | 0.804118 | + | 0.594469i | \(0.202638\pi\) | ||||
−0.804118 | + | 0.594469i | \(0.797362\pi\) | |||||||
\(140\) | 2.09546e7 | + | 3.92498e7i | 0.645402 | + | 1.20890i | ||||
\(141\) | 3.14613e6i | 0.0945169i | ||||||||
\(142\) | −3.11040e7 | + | 7.78300e6i | −0.911607 | + | 0.228107i | ||||
\(143\) | 4.71509e7 | 1.34838 | ||||||||
\(144\) | −1.93077e7 | + | 2.88344e7i | −0.538843 | + | 0.804715i | ||||
\(145\) | − | 2.35050e6i | − | 0.0640282i | ||||||
\(146\) | −6.39437e6 | + | 1.60003e6i | −0.170044 | + | 0.0425493i | ||||
\(147\) | 896658. | 0.0232818 | ||||||||
\(148\) | 2.82544e7 | + | 5.29230e7i | 0.716424 | + | 1.34193i | ||||
\(149\) | −5.87834e7 | −1.45580 | −0.727902 | − | 0.685682i | \(-0.759504\pi\) | ||||
−0.727902 | + | 0.685682i | \(0.759504\pi\) | |||||||
\(150\) | 4.70219e6 | − | 1.17661e6i | 0.113758 | − | 0.0284650i | ||||
\(151\) | 7.70255e7 | 1.82060 | 0.910302 | − | 0.413945i | \(-0.135849\pi\) | ||||
0.910302 | + | 0.413945i | \(0.135849\pi\) | |||||||
\(152\) | −5.51236e6 | + | 4.29441e7i | −0.127317 | + | 0.991862i | ||||
\(153\) | 6.99977e7 | 1.58002 | ||||||||
\(154\) | −4.19964e7 | + | 1.05085e7i | −0.926594 | + | 0.231857i | ||||
\(155\) | −2.04886e7 | −0.441929 | ||||||||
\(156\) | 5.95426e6 | + | 1.11529e7i | 0.125572 | + | 0.235207i | ||||
\(157\) | −1.81922e7 | −0.375176 | −0.187588 | − | 0.982248i | \(-0.560067\pi\) | ||||
−0.187588 | + | 0.982248i | \(0.560067\pi\) | |||||||
\(158\) | 4.46214e7 | − | 1.11654e7i | 0.900002 | − | 0.225203i | ||||
\(159\) | 1.03108e7i | 0.203423i | ||||||||
\(160\) | 2.25682e7 | − | 6.28295e7i | 0.435590 | − | 1.21267i | ||||
\(161\) | −1.93331e7 | −0.365099 | ||||||||
\(162\) | −4.75801e7 | + | 1.19057e7i | −0.879271 | + | 0.220015i | ||||
\(163\) | − | 3.88437e7i | − | 0.702528i | −0.936276 | − | 0.351264i | \(-0.885752\pi\) | ||
0.936276 | − | 0.351264i | \(-0.114248\pi\) | |||||||
\(164\) | 4.03077e7 | + | 7.55001e7i | 0.713567 | + | 1.33658i | ||||
\(165\) | 1.18586e7i | 0.205514i | ||||||||
\(166\) | 1.30772e7 | + | 5.22619e7i | 0.221890 | + | 0.886762i | ||||
\(167\) | 2.26519e7 | 0.376354 | 0.188177 | − | 0.982135i | \(-0.439742\pi\) | ||||
0.188177 | + | 0.982135i | \(0.439742\pi\) | |||||||
\(168\) | −7.78898e6 | − | 8.60662e6i | −0.126736 | − | 0.140039i | ||||
\(169\) | −7.86933e7 | −1.25411 | ||||||||
\(170\) | −1.30635e8 | + | 3.26881e7i | −2.03934 | + | 0.510292i | ||||
\(171\) | −4.81230e7 | + | 4.11596e7i | −0.735981 | + | 0.629484i | ||||
\(172\) | 5.61923e7 | + | 1.05253e8i | 0.842030 | + | 1.57720i | ||||
\(173\) | − | 1.21339e8i | − | 1.78172i | −0.454273 | − | 0.890862i | \(-0.650101\pi\) | ||
0.454273 | − | 0.890862i | \(-0.349899\pi\) | |||||||
\(174\) | 148854. | + | 594881.i | 0.00214209 | + | 0.00856068i | ||||
\(175\) | − | 4.97890e7i | − | 0.702263i | ||||||
\(176\) | 5.39735e7 | + | 3.61411e7i | 0.746253 | + | 0.499697i | ||||
\(177\) | −1.31984e7 | −0.178902 | ||||||||
\(178\) | −1.03778e7 | − | 4.14738e7i | −0.137922 | − | 0.551193i | ||||
\(179\) | −1.47765e8 | −1.92569 | −0.962844 | − | 0.270057i | \(-0.912957\pi\) | ||||
−0.962844 | + | 0.270057i | \(0.912957\pi\) | |||||||
\(180\) | 8.61342e7 | − | 4.59850e7i | 1.10083 | − | 0.587710i | ||||
\(181\) | 8.83586e7i | 1.10758i | 0.832657 | + | 0.553788i | \(0.186818\pi\) | ||||
−0.832657 | + | 0.553788i | \(0.813182\pi\) | |||||||
\(182\) | 1.25979e8 | − | 3.15232e7i | 1.54899 | − | 0.387597i | ||||
\(183\) | −3.51939e6 | −0.0424511 | ||||||||
\(184\) | 1.94649e7 | + | 2.15082e7i | 0.230351 | + | 0.254532i | ||||
\(185\) | − | 1.68803e8i | − | 1.96011i | ||||||
\(186\) | 5.18542e6 | − | 1.29752e6i | 0.0590866 | − | 0.0147849i | ||||
\(187\) | − | 1.31025e8i | − | 1.46524i | ||||||
\(188\) | −2.28364e7 | − | 4.27747e7i | −0.250655 | − | 0.469499i | ||||
\(189\) | − | 3.45074e7i | − | 0.371789i | ||||||
\(190\) | 7.05899e7 | − | 9.92882e7i | 0.746629 | − | 1.05017i | ||||
\(191\) | 1.40988e8i | 1.46408i | 0.681261 | + | 0.732041i | \(0.261432\pi\) | ||||
−0.681261 | + | 0.732041i | \(0.738568\pi\) | |||||||
\(192\) | −1.73283e6 | + | 1.73306e7i | −0.0176685 | + | 0.176709i | ||||
\(193\) | 5.03272e7i | 0.503909i | 0.967739 | + | 0.251955i | \(0.0810733\pi\) | ||||
−0.967739 | + | 0.251955i | \(0.918927\pi\) | |||||||
\(194\) | −1.88103e7 | − | 7.51737e7i | −0.184965 | − | 0.739197i | ||||
\(195\) | − | 3.55731e7i | − | 0.343559i | ||||||
\(196\) | −1.21910e7 | + | 6.50847e6i | −0.115649 | + | 0.0617423i | ||||
\(197\) | −4.41428e7 | −0.411366 | −0.205683 | − | 0.978619i | \(-0.565942\pi\) | ||||
−0.205683 | + | 0.978619i | \(0.565942\pi\) | |||||||
\(198\) | 2.30611e7 | + | 9.21615e7i | 0.211131 | + | 0.843765i | ||||
\(199\) | − | 1.14883e7i | − | 0.103341i | −0.998664 | − | 0.0516703i | \(-0.983546\pi\) | ||
0.998664 | − | 0.0516703i | \(-0.0164545\pi\) | |||||||
\(200\) | −5.53905e7 | + | 5.01284e7i | −0.489588 | + | 0.443077i | ||||
\(201\) | 3.28826e7 | 0.285615 | ||||||||
\(202\) | 4.18764e7 | − | 1.04785e7i | 0.357470 | − | 0.0894478i | ||||
\(203\) | 6.29887e6 | 0.0528478 | ||||||||
\(204\) | 3.09920e7 | − | 1.65459e7i | 0.255590 | − | 0.136454i | ||||
\(205\) | − | 2.40815e8i | − | 1.95229i | ||||||
\(206\) | −1.40533e8 | + | 3.51648e7i | −1.12006 | + | 0.280268i | ||||
\(207\) | 4.24267e7i | 0.332463i | ||||||||
\(208\) | −1.61908e8 | − | 1.08415e8i | −1.24752 | − | 0.835347i | ||||
\(209\) | 7.70444e7 | + | 9.00788e7i | 0.583753 | + | 0.682513i | ||||
\(210\) | 7.92820e6 | + | 3.16843e7i | 0.0590754 | + | 0.236090i | ||||
\(211\) | 7.95830e7 | 0.583219 | 0.291610 | − | 0.956537i | \(-0.405809\pi\) | ||||
0.291610 | + | 0.956537i | \(0.405809\pi\) | |||||||
\(212\) | −7.48415e7 | − | 1.40185e8i | −0.539470 | − | 1.01048i | ||||
\(213\) | −2.35365e7 | −0.166884 | ||||||||
\(214\) | −9.88264e7 | + | 2.47288e7i | −0.689326 | + | 0.172487i | ||||
\(215\) | − | 3.35716e8i | − | 2.30376i | ||||||
\(216\) | −3.83897e7 | + | 3.47427e7i | −0.259195 | + | 0.234571i | ||||
\(217\) | − | 5.49056e7i | − | 0.364760i | ||||||
\(218\) | 1.91846e7 | + | 7.66696e7i | 0.125417 | + | 0.501217i | ||||
\(219\) | −4.83864e6 | −0.0311293 | ||||||||
\(220\) | −8.60768e7 | − | 1.61230e8i | −0.545013 | − | 1.02086i | ||||
\(221\) | 3.93044e8i | 2.44945i | ||||||||
\(222\) | 1.06901e7 | + | 4.27220e7i | 0.0655762 | + | 0.262069i | ||||
\(223\) | −1.80079e8 | −1.08742 | −0.543708 | − | 0.839275i | \(-0.682980\pi\) | ||||
−0.543708 | + | 0.839275i | \(0.682980\pi\) | |||||||
\(224\) | 1.68371e8 | + | 6.04785e7i | 1.00092 | + | 0.359528i | ||||
\(225\) | −1.09262e8 | −0.639488 | ||||||||
\(226\) | 6.39186e6 | + | 2.55445e7i | 0.0368339 | + | 0.147203i | ||||
\(227\) | 3.27877e8 | 1.86046 | 0.930230 | − | 0.366976i | \(-0.119607\pi\) | ||||
0.930230 | + | 0.366976i | \(0.119607\pi\) | |||||||
\(228\) | −1.15776e7 | + | 2.95990e7i | −0.0646915 | + | 0.165388i | ||||
\(229\) | 1.98216e7 | 0.109072 | 0.0545362 | − | 0.998512i | \(-0.482632\pi\) | ||||
0.0545362 | + | 0.998512i | \(0.482632\pi\) | |||||||
\(230\) | −1.98128e7 | − | 7.91801e7i | −0.107374 | − | 0.429110i | ||||
\(231\) | −3.17788e7 | −0.169627 | ||||||||
\(232\) | −6.34182e6 | − | 7.00753e6i | −0.0333431 | − | 0.0368432i | ||||
\(233\) | 1.59540e8 | 0.826272 | 0.413136 | − | 0.910669i | \(-0.364433\pi\) | ||||
0.413136 | + | 0.910669i | \(0.364433\pi\) | |||||||
\(234\) | −6.91780e7 | − | 2.76463e8i | −0.352949 | − | 1.41053i | ||||
\(235\) | 1.36434e8i | 0.685781i | ||||||||
\(236\) | 1.79446e8 | − | 9.58020e7i | 0.888672 | − | 0.474441i | ||||
\(237\) | 3.37652e7 | 0.164759 | ||||||||
\(238\) | −8.75979e7 | − | 3.50077e8i | −0.421186 | − | 1.68323i | ||||
\(239\) | 2.64735e8i | 1.25435i | 0.778878 | + | 0.627176i | \(0.215789\pi\) | ||||
−0.778878 | + | 0.627176i | \(0.784211\pi\) | |||||||
\(240\) | 2.72667e7 | − | 4.07205e7i | 0.127319 | − | 0.190140i | ||||
\(241\) | − | 8.30066e7i | − | 0.381991i | −0.981591 | − | 0.190995i | \(-0.938828\pi\) | ||
0.981591 | − | 0.190995i | \(-0.0611716\pi\) | |||||||
\(242\) | −4.13660e7 | + | 1.03508e7i | −0.187625 | + | 0.0469484i | ||||
\(243\) | −1.14197e8 | −0.510544 | ||||||||
\(244\) | 4.78497e7 | − | 2.55458e7i | 0.210870 | − | 0.112578i | ||||
\(245\) | 3.88842e7 | 0.168924 | ||||||||
\(246\) | 1.52505e7 | + | 6.09472e7i | 0.0653148 | + | 0.261024i | ||||
\(247\) | −2.31115e8 | − | 2.70216e8i | −0.975864 | − | 1.14096i | ||||
\(248\) | −6.10828e7 | + | 5.52799e7i | −0.254295 | + | 0.230137i | ||||
\(249\) | 3.95468e7i | 0.162336i | ||||||||
\(250\) | −1.04900e8 | + | 2.62487e7i | −0.424607 | + | 0.106247i | ||||
\(251\) | 3.61723e8i | 1.44384i | 0.691978 | + | 0.721919i | \(0.256740\pi\) | ||||
−0.691978 | + | 0.721919i | \(0.743260\pi\) | |||||||
\(252\) | 1.23231e8 | + | 2.30823e8i | 0.485085 | + | 0.908609i | ||||
\(253\) | 7.94162e7 | 0.308310 | ||||||||
\(254\) | 7.79095e6 | − | 1.94949e6i | 0.0298313 | − | 0.00746453i | ||||
\(255\) | −9.88521e7 | −0.373332 | ||||||||
\(256\) | −1.02236e8 | − | 2.48204e8i | −0.380859 | − | 0.924633i | ||||
\(257\) | − | 2.17294e8i | − | 0.798511i | −0.916840 | − | 0.399256i | \(-0.869269\pi\) | ||
0.916840 | − | 0.399256i | \(-0.130731\pi\) | |||||||
\(258\) | 2.12605e7 | + | 8.49655e7i | 0.0770733 | + | 0.308016i | ||||
\(259\) | 4.52360e8 | 1.61784 | ||||||||
\(260\) | 2.58211e8 | + | 4.83652e8i | 0.911103 | + | 1.70658i | ||||
\(261\) | − | 1.38230e7i | − | 0.0481237i | ||||||
\(262\) | 1.09281e8 | + | 4.36731e8i | 0.375396 | + | 1.50024i | ||||
\(263\) | 1.68696e8i | 0.571820i | 0.958256 | + | 0.285910i | \(0.0922959\pi\) | ||||
−0.958256 | + | 0.285910i | \(0.907704\pi\) | |||||||
\(264\) | 3.19955e7 | + | 3.53541e7i | 0.107022 | + | 0.118257i | ||||
\(265\) | 4.47134e8i | 1.47597i | ||||||||
\(266\) | 2.66073e8 | + | 1.89167e8i | 0.866792 | + | 0.616254i | ||||
\(267\) | − | 3.13834e7i | − | 0.100904i | ||||||
\(268\) | −4.47072e8 | + | 2.38681e8i | −1.41875 | + | 0.757438i | ||||
\(269\) | 1.58558e8i | 0.496657i | 0.968676 | + | 0.248328i | \(0.0798812\pi\) | ||||
−0.968676 | + | 0.248328i | \(0.920119\pi\) | |||||||
\(270\) | 1.41327e8 | − | 3.53636e7i | 0.436972 | − | 0.109341i | ||||
\(271\) | 9.95154e7i | 0.303737i | 0.988401 | + | 0.151869i | \(0.0485290\pi\) | ||||
−0.988401 | + | 0.151869i | \(0.951471\pi\) | |||||||
\(272\) | −3.01267e8 | + | 4.49917e8i | −0.907739 | + | 1.35563i | ||||
\(273\) | 9.53291e7 | 0.283567 | ||||||||
\(274\) | 3.76594e8 | − | 9.42332e7i | 1.10598 | − | 0.276743i | ||||
\(275\) | 2.04522e8i | 0.593029i | ||||||||
\(276\) | 1.00288e7 | + | 1.87848e7i | 0.0287121 | + | 0.0537804i | ||||
\(277\) | −2.17548e8 | −0.615002 | −0.307501 | − | 0.951548i | \(-0.599493\pi\) | ||||
−0.307501 | + | 0.951548i | \(0.599493\pi\) | |||||||
\(278\) | −1.03385e8 | − | 4.13170e8i | −0.288604 | − | 1.15338i | ||||
\(279\) | −1.20491e8 | −0.332154 | ||||||||
\(280\) | −3.37775e8 | − | 3.73232e8i | −0.919548 | − | 1.01608i | ||||
\(281\) | 5.39415e8i | 1.45028i | 0.688603 | + | 0.725138i | \(0.258224\pi\) | ||||
−0.688603 | + | 0.725138i | \(0.741776\pi\) | |||||||
\(282\) | −8.64021e6 | − | 3.45298e7i | −0.0229431 | − | 0.0916900i | ||||
\(283\) | − | 6.70172e6i | − | 0.0175765i | −0.999961 | − | 0.00878827i | \(-0.997203\pi\) | ||
0.999961 | − | 0.00878827i | \(-0.00279743\pi\) | |||||||
\(284\) | 3.20003e8 | − | 1.70842e8i | 0.828971 | − | 0.442568i | ||||
\(285\) | 6.79603e7 | − | 5.81264e7i | 0.173899 | − | 0.148736i | ||||
\(286\) | −5.17496e8 | + | 1.29490e8i | −1.30806 | + | 0.327308i | ||||
\(287\) | 6.45337e8 | 1.61139 | ||||||||
\(288\) | 1.32721e8 | − | 3.69492e8i | 0.327390 | − | 0.911446i | ||||
\(289\) | 6.81868e8 | 1.66172 | ||||||||
\(290\) | 6.45516e6 | + | 2.57975e7i | 0.0155423 | + | 0.0621132i | ||||
\(291\) | − | 5.68842e7i | − | 0.135321i | ||||||
\(292\) | 6.57861e7 | − | 3.51217e7i | 0.154630 | − | 0.0825535i | ||||
\(293\) | 4.38051e8i | 1.01739i | 0.860947 | + | 0.508695i | \(0.169872\pi\) | ||||
−0.860947 | + | 0.508695i | \(0.830128\pi\) | |||||||
\(294\) | −9.84112e6 | + | 2.46249e6i | −0.0225855 | + | 0.00565144i | ||||
\(295\) | −5.72360e8 | −1.29805 | ||||||||
\(296\) | −4.55444e8 | − | 5.03253e8i | −1.02074 | − | 1.12789i | ||||
\(297\) | 1.41749e8i | 0.313959i | ||||||||
\(298\) | 6.45167e8 | − | 1.61437e8i | 1.41226 | − | 0.353383i | ||||
\(299\) | −2.38230e8 | −0.515404 | ||||||||
\(300\) | −4.83768e7 | + | 2.58273e7i | −0.103446 | + | 0.0552273i | ||||
\(301\) | 8.99653e8 | 1.90148 | ||||||||
\(302\) | −8.45381e8 | + | 2.11535e8i | −1.76615 | + | 0.441935i | ||||
\(303\) | 3.16880e7 | 0.0654404 | ||||||||
\(304\) | −5.74374e7 | − | 4.86465e8i | −0.117257 | − | 0.993102i | ||||
\(305\) | −1.52621e8 | −0.308010 | ||||||||
\(306\) | −7.68248e8 | + | 1.92235e8i | −1.53277 | + | 0.383536i | ||||
\(307\) | 3.46252e8 | 0.682980 | 0.341490 | − | 0.939885i | \(-0.389069\pi\) | ||||
0.341490 | + | 0.939885i | \(0.389069\pi\) | |||||||
\(308\) | 4.32065e8 | − | 2.30669e8i | 0.842599 | − | 0.449844i | ||||
\(309\) | −1.06342e8 | −0.205045 | ||||||||
\(310\) | 2.24870e8 | − | 5.62679e7i | 0.428711 | − | 0.107274i | ||||
\(311\) | 1.84289e7i | 0.0347407i | 0.999849 | + | 0.0173703i | \(0.00552943\pi\) | ||||
−0.999849 | + | 0.0173703i | \(0.994471\pi\) | |||||||
\(312\) | −9.59790e7 | − | 1.06054e8i | −0.178910 | − | 0.197691i | ||||
\(313\) | −2.62310e8 | −0.483515 | −0.241758 | − | 0.970337i | \(-0.577724\pi\) | ||||
−0.241758 | + | 0.970337i | \(0.577724\pi\) | |||||||
\(314\) | 1.99665e8 | − | 4.99611e7i | 0.363955 | − | 0.0910706i | ||||
\(315\) | − | 7.36232e8i | − | 1.32717i | ||||||
\(316\) | −4.59071e8 | + | 2.45087e8i | −0.818418 | + | 0.436934i | ||||
\(317\) | − | 1.06461e8i | − | 0.187708i | −0.995586 | − | 0.0938541i | \(-0.970081\pi\) | ||
0.995586 | − | 0.0938541i | \(-0.0299187\pi\) | |||||||
\(318\) | −2.83164e7 | − | 1.13164e8i | −0.0493792 | − | 0.197339i | ||||
\(319\) | −2.58744e7 | −0.0446276 | ||||||||
\(320\) | −7.51453e7 | + | 7.51553e8i | −0.128197 | + | 1.28214i | ||||
\(321\) | −7.47823e7 | −0.126192 | ||||||||
\(322\) | 2.12187e8 | − | 5.30945e7i | 0.354180 | − | 0.0886245i | ||||
\(323\) | −7.50886e8 | + | 6.42233e8i | −1.23984 | + | 1.06043i | ||||
\(324\) | 4.89511e8 | − | 2.61338e8i | 0.799566 | − | 0.426870i | ||||
\(325\) | − | 6.13520e8i | − | 0.991372i | ||||||
\(326\) | 1.06676e8 | + | 4.26322e8i | 0.170532 | + | 0.681516i | ||||
\(327\) | 5.80162e7i | 0.0917555i | ||||||||
\(328\) | −6.49736e8 | − | 7.17941e8i | −1.01667 | − | 1.12339i | ||||
\(329\) | −3.65617e8 | −0.566032 | ||||||||
\(330\) | −3.25673e7 | − | 1.30152e8i | −0.0498865 | − | 0.199367i | ||||
\(331\) | −6.30158e8 | −0.955106 | −0.477553 | − | 0.878603i | \(-0.658476\pi\) | ||||
−0.477553 | + | 0.878603i | \(0.658476\pi\) | |||||||
\(332\) | −2.87054e8 | − | 5.37678e8i | −0.430507 | − | 0.806379i | ||||
\(333\) | − | 9.92709e8i | − | 1.47322i | ||||||
\(334\) | −2.48612e8 | + | 6.22089e7i | −0.365098 | + | 0.0913565i | ||||
\(335\) | 1.42598e9 | 2.07232 | ||||||||
\(336\) | 1.09123e8 | + | 7.30696e7i | 0.156938 | + | 0.105087i | ||||
\(337\) | 2.99624e8i | 0.426454i | 0.977003 | + | 0.213227i | \(0.0683973\pi\) | ||||
−0.977003 | + | 0.213227i | \(0.931603\pi\) | |||||||
\(338\) | 8.63684e8 | − | 2.16115e8i | 1.21660 | − | 0.304423i | ||||
\(339\) | 1.93296e7i | 0.0269478i | ||||||||
\(340\) | 1.34399e9 | − | 7.17526e8i | 1.85447 | − | 0.990060i | ||||
\(341\) | 2.25540e8i | 0.308024i | ||||||||
\(342\) | 4.15129e8 | − | 5.83900e8i | 0.561167 | − | 0.789310i | ||||
\(343\) | − | 6.90638e8i | − | 0.924104i | ||||||
\(344\) | −9.05786e8 | − | 1.00087e9i | −1.19970 | − | 1.32563i | ||||
\(345\) | − | 5.99158e7i | − | 0.0785552i | ||||||
\(346\) | 3.33234e8 | + | 1.33174e9i | 0.432497 | + | 1.72844i | ||||
\(347\) | − | 8.25153e8i | − | 1.06018i | −0.847940 | − | 0.530092i | \(-0.822157\pi\) | ||
0.847940 | − | 0.530092i | \(-0.177843\pi\) | |||||||
\(348\) | −3.26744e6 | − | 6.12022e6i | −0.00415605 | − | 0.00778466i | ||||
\(349\) | −5.77527e8 | −0.727250 | −0.363625 | − | 0.931545i | \(-0.618461\pi\) | ||||
−0.363625 | + | 0.931545i | \(0.618461\pi\) | |||||||
\(350\) | 1.36735e8 | + | 5.46450e8i | 0.170468 | + | 0.681259i | ||||
\(351\) | − | 4.25214e8i | − | 0.524847i | ||||||
\(352\) | −6.91631e8 | − | 2.48433e8i | −0.845230 | − | 0.303605i | ||||
\(353\) | −1.55713e8 | −0.188414 | −0.0942069 | − | 0.995553i | \(-0.530032\pi\) | ||||
−0.0942069 | + | 0.995553i | \(0.530032\pi\) | |||||||
\(354\) | 1.44857e8 | − | 3.62469e7i | 0.173552 | − | 0.0434269i | ||||
\(355\) | −1.02068e9 | −1.21085 | ||||||||
\(356\) | 2.27799e8 | + | 4.26688e8i | 0.267594 | + | 0.501228i | ||||
\(357\) | − | 2.64904e8i | − | 0.308142i | ||||||
\(358\) | 1.62177e9 | − | 4.05807e8i | 1.86809 | − | 0.467443i | ||||
\(359\) | 2.95213e7i | 0.0336748i | 0.999858 | + | 0.0168374i | \(0.00535977\pi\) | ||||
−0.999858 | + | 0.0168374i | \(0.994640\pi\) | |||||||
\(360\) | −8.19062e8 | + | 7.41251e8i | −0.925248 | + | 0.837349i | ||||
\(361\) | 1.38589e8 | − | 8.83063e8i | 0.155043 | − | 0.987908i | ||||
\(362\) | −2.42659e8 | − | 9.69765e8i | −0.268854 | − | 1.07445i | ||||
\(363\) | −3.13018e7 | −0.0343476 | ||||||||
\(364\) | −1.29609e9 | + | 6.91954e8i | −1.40858 | + | 0.752008i | ||||
\(365\) | −2.09831e8 | −0.225863 | ||||||||
\(366\) | 3.86265e7 | − | 9.66531e6i | 0.0411814 | − | 0.0103046i | ||||
\(367\) | 1.48210e9i | 1.56512i | 0.622577 | + | 0.782559i | \(0.286086\pi\) | ||||
−0.622577 | + | 0.782559i | \(0.713914\pi\) | |||||||
\(368\) | −2.72702e8 | − | 1.82603e8i | −0.285247 | − | 0.191003i | ||||
\(369\) | − | 1.41620e9i | − | 1.46734i | ||||||
\(370\) | 4.63584e8 | + | 1.85267e9i | 0.475798 | + | 1.90148i | ||||
\(371\) | −1.19823e9 | −1.21824 | ||||||||
\(372\) | −5.33483e7 | + | 2.84814e7i | −0.0537305 | + | 0.0286854i | ||||
\(373\) | 1.26382e9i | 1.26097i | 0.776202 | + | 0.630484i | \(0.217144\pi\) | ||||
−0.776202 | + | 0.630484i | \(0.782856\pi\) | |||||||
\(374\) | 3.59833e8 | + | 1.43804e9i | 0.355673 | + | 1.42141i | ||||
\(375\) | −7.93785e7 | −0.0777308 | ||||||||
\(376\) | 3.68110e8 | + | 4.06751e8i | 0.357125 | + | 0.394613i | ||||
\(377\) | 7.76173e7 | 0.0746043 | ||||||||
\(378\) | 9.47677e7 | + | 3.78730e8i | 0.0902483 | + | 0.360669i | ||||
\(379\) | 2.55223e7 | 0.0240814 | 0.0120407 | − | 0.999928i | \(-0.496167\pi\) | ||||
0.0120407 | + | 0.999928i | \(0.496167\pi\) | |||||||
\(380\) | −5.02072e8 | + | 1.28358e9i | −0.469379 | + | 1.20000i | ||||
\(381\) | 5.89544e6 | 0.00546109 | ||||||||
\(382\) | −3.87195e8 | − | 1.54739e9i | −0.355392 | − | 1.42029i | ||||
\(383\) | 1.64139e9 | 1.49285 | 0.746424 | − | 0.665471i | \(-0.231769\pi\) | ||||
0.746424 | + | 0.665471i | \(0.231769\pi\) | |||||||
\(384\) | −2.85766e7 | − | 1.94968e8i | −0.0257544 | − | 0.175713i | ||||
\(385\) | −1.37811e9 | −1.23076 | ||||||||
\(386\) | −1.38214e8 | − | 5.52358e8i | −0.122319 | − | 0.488838i | ||||
\(387\) | − | 1.97430e9i | − | 1.73151i | ||||||
\(388\) | 4.12899e8 | + | 7.73398e8i | 0.358866 | + | 0.672190i | ||||
\(389\) | 2.02068e8 | 0.174050 | 0.0870250 | − | 0.996206i | \(-0.472264\pi\) | ||||
0.0870250 | + | 0.996206i | \(0.472264\pi\) | |||||||
\(390\) | 9.76945e7 | + | 3.90427e8i | 0.0833957 | + | 0.333283i | ||||
\(391\) | 6.62004e8i | 0.560070i | ||||||||
\(392\) | 1.15926e8 | − | 1.04913e8i | 0.0972026 | − | 0.0879683i | ||||
\(393\) | 3.30476e8i | 0.274641i | ||||||||
\(394\) | 4.84482e8 | − | 1.21229e8i | 0.399062 | − | 0.0998553i | ||||
\(395\) | 1.46425e9 | 1.19543 | ||||||||
\(396\) | −5.06206e8 | − | 9.48171e8i | −0.409632 | − | 0.767279i | ||||
\(397\) | 1.46254e9 | 1.17311 | 0.586557 | − | 0.809908i | \(-0.300483\pi\) | ||||
0.586557 | + | 0.809908i | \(0.300483\pi\) | |||||||
\(398\) | 3.15504e7 | + | 1.26088e8i | 0.0250850 | + | 0.100250i | ||||
\(399\) | 1.55767e8 | + | 1.82120e8i | 0.122764 | + | 0.143533i | ||||
\(400\) | 4.70262e8 | − | 7.02294e8i | 0.367392 | − | 0.548668i | ||||
\(401\) | − | 3.44403e7i | − | 0.0266724i | −0.999911 | − | 0.0133362i | \(-0.995755\pi\) | ||
0.999911 | − | 0.0133362i | \(-0.00424517\pi\) | |||||||
\(402\) | −3.60898e8 | + | 9.03056e7i | −0.277072 | + | 0.0693303i | ||||
\(403\) | − | 6.76569e8i | − | 0.514926i | ||||||
\(404\) | −4.30830e8 | + | 2.30010e8i | −0.325066 | + | 0.173545i | ||||
\(405\) | −1.56134e9 | −1.16790 | ||||||||
\(406\) | −6.91322e7 | + | 1.72986e7i | −0.0512672 | + | 0.0128283i | ||||
\(407\) | −1.85820e9 | −1.36619 | ||||||||
\(408\) | −2.94708e8 | + | 2.66710e8i | −0.214823 | + | 0.194415i | ||||
\(409\) | 4.84225e8i | 0.349958i | 0.984572 | + | 0.174979i | \(0.0559857\pi\) | ||||
−0.984572 | + | 0.174979i | \(0.944014\pi\) | |||||||
\(410\) | 6.61349e8 | + | 2.64302e9i | 0.473901 | + | 1.89390i | ||||
\(411\) | 2.84970e8 | 0.202467 | ||||||||
\(412\) | 1.44582e9 | − | 7.71891e8i | 1.01853 | − | 0.543770i | ||||
\(413\) | − | 1.53381e9i | − | 1.07139i | ||||||
\(414\) | −1.16516e8 | − | 4.65647e8i | −0.0807023 | − | 0.322519i | ||||
\(415\) | 1.71498e9i | 1.17785i | ||||||||
\(416\) | 2.07473e9 | + | 7.45240e8i | 1.41298 | + | 0.507539i | ||||
\(417\) | − | 3.12647e8i | − | 0.211144i | ||||||
\(418\) | −1.09297e9 | − | 7.77058e8i | −0.731967 | − | 0.520399i | ||||
\(419\) | 1.25832e8i | 0.0835682i | 0.999127 | + | 0.0417841i | \(0.0133042\pi\) | ||||
−0.999127 | + | 0.0417841i | \(0.986696\pi\) | |||||||
\(420\) | −1.74029e8 | − | 3.25972e8i | −0.114617 | − | 0.214688i | ||||
\(421\) | 2.64151e7i | 0.0172530i | 0.999963 | + | 0.00862650i | \(0.00274594\pi\) | ||||
−0.999963 | + | 0.00862650i | \(0.997254\pi\) | |||||||
\(422\) | −8.73450e8 | + | 2.18559e8i | −0.565776 | + | 0.141571i | ||||
\(423\) | 8.02351e8i | 0.515434i | ||||||||
\(424\) | 1.20640e9 | + | 1.33304e9i | 0.768619 | + | 0.849303i | ||||
\(425\) | −1.70487e9 | −1.07729 | ||||||||
\(426\) | 2.58321e8 | − | 6.46384e7i | 0.161892 | − | 0.0405095i | ||||
\(427\) | − | 4.08995e8i | − | 0.254226i | ||||||
\(428\) | 1.01674e9 | − | 5.42814e8i | 0.626840 | − | 0.334655i | ||||
\(429\) | −3.91591e8 | −0.239460 | ||||||||
\(430\) | 9.21976e8 | + | 3.68459e9i | 0.559216 | + | 2.23486i | ||||
\(431\) | 1.99243e9 | 1.19870 | 0.599352 | − | 0.800486i | \(-0.295425\pi\) | ||||
0.599352 | + | 0.800486i | \(0.295425\pi\) | |||||||
\(432\) | 3.25926e8 | − | 4.86742e8i | 0.194503 | − | 0.290473i | ||||
\(433\) | 1.61300e9i | 0.954834i | 0.878677 | + | 0.477417i | \(0.158427\pi\) | ||||
−0.878677 | + | 0.477417i | \(0.841573\pi\) | |||||||
\(434\) | 1.50787e8 | + | 6.02607e8i | 0.0885422 | + | 0.353851i | ||||
\(435\) | 1.95210e7i | 0.0113708i | ||||||||
\(436\) | −4.21115e8 | − | 7.88787e8i | −0.243331 | − | 0.455782i | ||||
\(437\) | −3.89268e8 | − | 4.55124e8i | −0.223133 | − | 0.260883i | ||||
\(438\) | 5.31057e7 | − | 1.32884e7i | 0.0301982 | − | 0.00755634i | ||||
\(439\) | 4.42728e7 | 0.0249753 | 0.0124877 | − | 0.999922i | \(-0.496025\pi\) | ||||
0.0124877 | + | 0.999922i | \(0.496025\pi\) | |||||||
\(440\) | 1.38751e9 | + | 1.53316e9i | 0.776516 | + | 0.858030i | ||||
\(441\) | 2.28673e8 | 0.126964 | ||||||||
\(442\) | −1.07942e9 | − | 4.31379e9i | −0.594581 | − | 2.37619i | ||||
\(443\) | 2.34668e8i | 0.128245i | 0.997942 | + | 0.0641226i | \(0.0204249\pi\) | ||||
−0.997942 | + | 0.0641226i | \(0.979575\pi\) | |||||||
\(444\) | −2.34655e8 | − | 4.39530e8i | −0.127230 | − | 0.238313i | ||||
\(445\) | − | 1.36096e9i | − | 0.732126i | ||||||
\(446\) | 1.97642e9 | − | 4.94550e8i | 1.05489 | − | 0.263960i | ||||
\(447\) | 4.88200e8 | 0.258536 | ||||||||
\(448\) | −2.01402e9 | − | 2.01375e8i | −1.05825 | − | 0.105811i | ||||
\(449\) | − | 2.40151e9i | − | 1.25205i | −0.779802 | − | 0.626026i | \(-0.784680\pi\) | ||
0.779802 | − | 0.626026i | \(-0.215320\pi\) | |||||||
\(450\) | 1.19919e9 | − | 3.00067e8i | 0.620361 | − | 0.155230i | ||||
\(451\) | −2.65090e9 | −1.36074 | ||||||||
\(452\) | −1.40305e8 | − | 2.62805e8i | −0.0714645 | − | 0.133859i | ||||
\(453\) | −6.39703e8 | −0.323321 | ||||||||
\(454\) | −3.59856e9 | + | 9.00448e8i | −1.80482 | + | 0.451610i | ||||
\(455\) | 4.13402e9 | 2.05746 | ||||||||
\(456\) | 4.57806e7 | − | 3.56654e8i | 0.0226102 | − | 0.176145i | ||||
\(457\) | 1.41435e9 | 0.693188 | 0.346594 | − | 0.938015i | \(-0.387338\pi\) | ||||
0.346594 | + | 0.938015i | \(0.387338\pi\) | |||||||
\(458\) | −2.17549e8 | + | 5.44361e7i | −0.105810 | + | 0.0264763i | ||||
\(459\) | −1.18160e9 | −0.570331 | ||||||||
\(460\) | 4.34904e8 | + | 8.14615e8i | 0.208325 | + | 0.390212i | ||||
\(461\) | −2.77312e9 | −1.31830 | −0.659152 | − | 0.752010i | \(-0.729085\pi\) | ||||
−0.659152 | + | 0.752010i | \(0.729085\pi\) | |||||||
\(462\) | 3.48783e8 | − | 8.72741e7i | 0.164554 | − | 0.0411755i | ||||
\(463\) | 1.11850e8i | 0.0523725i | 0.999657 | + | 0.0261863i | \(0.00833630\pi\) | ||||
−0.999657 | + | 0.0261863i | \(0.991664\pi\) | |||||||
\(464\) | 8.88483e7 | + | 5.94935e7i | 0.0412892 | + | 0.0276475i | ||||
\(465\) | 1.70160e8 | 0.0784822 | ||||||||
\(466\) | −1.75100e9 | + | 4.38144e8i | −0.801560 | + | 0.200570i | ||||
\(467\) | − | 1.47119e9i | − | 0.668434i | −0.942496 | − | 0.334217i | \(-0.891528\pi\) | ||
0.942496 | − | 0.334217i | \(-0.108472\pi\) | |||||||
\(468\) | 1.51850e9 | + | 2.84429e9i | 0.684786 | + | 1.28267i | ||||
\(469\) | 3.82135e9i | 1.71046i | ||||||||
\(470\) | −3.74689e8 | − | 1.49741e9i | −0.166467 | − | 0.665270i | ||||
\(471\) | 1.51087e8 | 0.0666276 | ||||||||
\(472\) | −1.70638e9 | + | 1.54427e9i | −0.746927 | + | 0.675968i | ||||
\(473\) | −3.69558e9 | −1.60572 | ||||||||
\(474\) | −3.70584e8 | + | 9.27292e7i | −0.159831 | + | 0.0399938i | ||||
\(475\) | 1.17209e9 | − | 1.00249e9i | 0.501804 | − | 0.429192i | ||||
\(476\) | 1.92283e9 | + | 3.60164e9i | 0.817178 | + | 1.53065i | ||||
\(477\) | 2.62953e9i | 1.10934i | ||||||||
\(478\) | −7.27042e8 | − | 2.90556e9i | −0.304482 | − | 1.21684i | ||||
\(479\) | − | 3.39386e7i | − | 0.0141097i | −0.999975 | − | 0.00705487i | \(-0.997754\pi\) | ||
0.999975 | − | 0.00705487i | \(-0.00224565\pi\) | |||||||
\(480\) | −1.87431e8 | + | 5.21803e8i | −0.0773565 | + | 0.215359i | ||||
\(481\) | 5.57416e9 | 2.28387 | ||||||||
\(482\) | 2.27961e8 | + | 9.11025e8i | 0.0927248 | + | 0.370566i | ||||
\(483\) | 1.60563e8 | 0.0648381 | ||||||||
\(484\) | 4.25579e8 | − | 2.27207e8i | 0.170617 | − | 0.0910884i | ||||
\(485\) | − | 2.46683e9i | − | 0.981844i | ||||||
\(486\) | 1.25335e9 | − | 3.13619e8i | 0.495274 | − | 0.123930i | ||||
\(487\) | 8.44255e8 | 0.331224 | 0.165612 | − | 0.986191i | \(-0.447040\pi\) | ||||
0.165612 | + | 0.986191i | \(0.447040\pi\) | |||||||
\(488\) | −4.55009e8 | + | 4.11783e8i | −0.177236 | + | 0.160398i | ||||
\(489\) | 3.22600e8i | 0.124762i | ||||||||
\(490\) | −4.26767e8 | + | 1.06788e8i | −0.163872 | + | 0.0410048i | ||||
\(491\) | 5.23656e8i | 0.199646i | 0.995005 | + | 0.0998231i | \(0.0318277\pi\) | ||||
−0.995005 | + | 0.0998231i | \(0.968172\pi\) | |||||||
\(492\) | −3.34759e8 | − | 6.27033e8i | −0.126723 | − | 0.237363i | ||||
\(493\) | − | 2.15686e8i | − | 0.0810695i | ||||||
\(494\) | 3.27866e9 | + | 2.33099e9i | 1.22364 | + | 0.869955i | ||||
\(495\) | 3.02428e9i | 1.12074i | ||||||||
\(496\) | 5.18589e8 | − | 7.74467e8i | 0.190826 | − | 0.284982i | ||||
\(497\) | − | 2.73522e9i | − | 0.999414i | ||||||
\(498\) | −1.08607e8 | − | 4.34039e8i | −0.0394055 | − | 0.157480i | ||||
\(499\) | − | 3.55186e9i | − | 1.27969i | −0.768505 | − | 0.639844i | \(-0.778999\pi\) | ||
0.768505 | − | 0.639844i | \(-0.221001\pi\) | |||||||
\(500\) | 1.07923e9 | − | 5.76175e8i | 0.386117 | − | 0.206139i | ||||
\(501\) | −1.88126e8 | −0.0668368 | ||||||||
\(502\) | −9.93400e8 | − | 3.97003e9i | −0.350478 | − | 1.40065i | ||||
\(503\) | 3.25375e9i | 1.13998i | 0.821653 | + | 0.569988i | \(0.193052\pi\) | ||||
−0.821653 | + | 0.569988i | \(0.806948\pi\) | |||||||
\(504\) | −1.98641e9 | − | 2.19493e9i | −0.691133 | − | 0.763683i | ||||
\(505\) | 1.37417e9 | 0.474812 | ||||||||
\(506\) | −8.71619e8 | + | 2.18101e8i | −0.299089 | + | 0.0748394i | ||||
\(507\) | 6.53553e8 | 0.222717 | ||||||||
\(508\) | −8.01544e7 | + | 4.27926e7i | −0.0271272 | + | 0.0144826i | ||||
\(509\) | 5.07091e9i | 1.70441i | 0.523209 | + | 0.852204i | \(0.324735\pi\) | ||||
−0.523209 | + | 0.852204i | \(0.675265\pi\) | |||||||
\(510\) | 1.08493e9 | − | 2.71477e8i | 0.362166 | − | 0.0906229i | ||||
\(511\) | − | 5.62307e8i | − | 0.186423i | ||||||
\(512\) | 1.80372e9 | + | 2.44335e9i | 0.593914 | + | 0.804529i | ||||
\(513\) | 8.12346e8 | − | 6.94799e8i | 0.265662 | − | 0.227221i | ||||
\(514\) | 5.96753e8 | + | 2.38487e9i | 0.193831 | + | 0.774629i | ||||
\(515\) | −4.61159e9 | −1.48773 | ||||||||
\(516\) | −4.66681e8 | − | 8.74137e8i | −0.149536 | − | 0.280095i | ||||
\(517\) | 1.50188e9 | 0.477988 | ||||||||
\(518\) | −4.96480e9 | + | 1.24231e9i | −1.56945 | + | 0.392715i | ||||
\(519\) | 1.00773e9i | 0.316417i | ||||||||
\(520\) | −4.16220e9 | − | 4.59912e9i | −1.29811 | − | 1.43438i | ||||
\(521\) | 1.53300e9i | 0.474910i | 0.971399 | + | 0.237455i | \(0.0763132\pi\) | ||||
−0.971399 | + | 0.237455i | \(0.923687\pi\) | |||||||
\(522\) | 3.79620e7 | + | 1.51711e8i | 0.0116816 | + | 0.0466844i | ||||
\(523\) | −2.40775e9 | −0.735961 | −0.367980 | − | 0.929834i | \(-0.619951\pi\) | ||||
−0.367980 | + | 0.929834i | \(0.619951\pi\) | |||||||
\(524\) | −2.39879e9 | − | 4.49315e9i | −0.728337 | − | 1.36424i | ||||
\(525\) | 4.13501e8i | 0.124715i | ||||||||
\(526\) | −4.63289e8 | − | 1.85149e9i | −0.138804 | − | 0.554718i | ||||
\(527\) | −1.88008e9 | −0.559549 | ||||||||
\(528\) | −4.48254e8 | − | 3.00154e8i | −0.132527 | − | 0.0887412i | ||||
\(529\) | 3.00357e9 | 0.882152 | ||||||||
\(530\) | −1.22796e9 | − | 4.90744e9i | −0.358278 | − | 1.43182i | ||||
\(531\) | −3.36597e9 | −0.975618 | ||||||||
\(532\) | −3.43975e9 | − | 1.34546e9i | −0.990458 | − | 0.387417i | ||||
\(533\) | 7.95210e9 | 2.27477 | ||||||||
\(534\) | 8.61881e7 | + | 3.44443e8i | 0.0244936 | + | 0.0978865i | ||||
\(535\) | −3.24299e9 | −0.915603 | ||||||||
\(536\) | 4.25127e9 | − | 3.84740e9i | 1.19246 | − | 1.07917i | ||||
\(537\) | 1.22720e9 | 0.341983 | ||||||||
\(538\) | −4.35449e8 | − | 1.74023e9i | −0.120559 | − | 0.481802i | ||||
\(539\) | − | 4.28040e8i | − | 0.117740i | ||||||
\(540\) | −1.45400e9 | + | 7.76255e8i | −0.397361 | + | 0.212142i | ||||
\(541\) | 6.65433e9 | 1.80682 | 0.903408 | − | 0.428782i | \(-0.141057\pi\) | ||||
0.903408 | + | 0.428782i | \(0.141057\pi\) | |||||||
\(542\) | −2.73299e8 | − | 1.09221e9i | −0.0737294 | − | 0.294653i | ||||
\(543\) | − | 7.33824e8i | − | 0.196695i | ||||||
\(544\) | 2.07090e9 | − | 5.76535e9i | 0.551523 | − | 1.53543i | ||||
\(545\) | 2.51591e9i | 0.665745i | ||||||||
\(546\) | −1.04627e9 | + | 2.61802e8i | −0.275086 | + | 0.0688334i | ||||
\(547\) | −5.23461e9 | −1.36750 | −0.683752 | − | 0.729714i | \(-0.739653\pi\) | ||||
−0.683752 | + | 0.729714i | \(0.739653\pi\) | |||||||
\(548\) | −3.87445e9 | + | 2.06848e9i | −1.00572 | + | 0.536932i | ||||
\(549\) | −8.97544e8 | −0.231501 | ||||||||
\(550\) | −5.61679e8 | − | 2.24470e9i | −0.143952 | − | 0.575293i | ||||
\(551\) | 1.26826e8 | + | 1.48283e8i | 0.0322982 | + | 0.0377625i | ||||
\(552\) | −1.61657e8 | − | 1.78627e8i | −0.0409081 | − | 0.0452023i | ||||
\(553\) | 3.92391e9i | 0.986690i | ||||||||
\(554\) | 2.38766e9 | − | 5.97452e8i | 0.596608 | − | 0.149286i | ||||
\(555\) | 1.40192e9i | 0.348096i | ||||||||
\(556\) | 2.26938e9 | + | 4.25075e9i | 0.559944 | + | 1.04883i | ||||
\(557\) | −3.43562e9 | −0.842387 | −0.421193 | − | 0.906971i | \(-0.638389\pi\) | ||||
−0.421193 | + | 0.906971i | \(0.638389\pi\) | |||||||
\(558\) | 1.32243e9 | − | 3.30904e8i | 0.322220 | − | 0.0806274i | ||||
\(559\) | 1.10859e10 | 2.68429 | ||||||||
\(560\) | 4.73220e9 | + | 3.16871e9i | 1.13869 | + | 0.762474i | ||||
\(561\) | 1.08817e9i | 0.260212i | ||||||||
\(562\) | −1.48139e9 | − | 5.92026e9i | −0.352041 | − | 1.40690i | ||||
\(563\) | −1.27168e9 | −0.300329 | −0.150164 | − | 0.988661i | \(-0.547980\pi\) | ||||
−0.150164 | + | 0.988661i | \(0.547980\pi\) | |||||||
\(564\) | 1.89658e8 | + | 3.55247e8i | 0.0445138 | + | 0.0833785i | ||||
\(565\) | 8.38242e8i | 0.195524i | ||||||||
\(566\) | 1.84049e7 | + | 7.35536e7i | 0.00426655 | + | 0.0170509i | ||||
\(567\) | − | 4.18409e9i | − | 0.963963i | ||||||
\(568\) | −3.04295e9 | + | 2.75387e9i | −0.696748 | + | 0.630557i | ||||
\(569\) | 1.21543e9i | 0.276590i | 0.990391 | + | 0.138295i | \(0.0441621\pi\) | ||||
−0.990391 | + | 0.138295i | \(0.955838\pi\) | |||||||
\(570\) | −5.86254e8 | + | 8.24595e8i | −0.132594 | + | 0.186500i | ||||
\(571\) | 4.02806e9i | 0.905460i | 0.891648 | + | 0.452730i | \(0.149550\pi\) | ||||
−0.891648 | + | 0.452730i | \(0.850450\pi\) | |||||||
\(572\) | 5.32407e9 | − | 2.84240e9i | 1.18948 | − | 0.635037i | ||||
\(573\) | − | 1.17092e9i | − | 0.260007i | ||||||
\(574\) | −7.08278e9 | + | 1.77229e9i | −1.56319 | + | 0.391149i | ||||
\(575\) | − | 1.03335e9i | − | 0.226679i | ||||||
\(576\) | −4.41919e8 | + | 4.41978e9i | −0.0963528 | + | 0.963657i | ||||
\(577\) | −7.38889e9 | −1.60127 | −0.800634 | − | 0.599154i | \(-0.795504\pi\) | ||||
−0.800634 | + | 0.599154i | \(0.795504\pi\) | |||||||
\(578\) | −7.48372e9 | + | 1.87261e9i | −1.61202 | + | 0.403367i | ||||
\(579\) | − | 4.17971e8i | − | 0.0894893i | ||||||
\(580\) | −1.41695e8 | − | 2.65408e8i | −0.0301548 | − | 0.0564827i | ||||
\(581\) | −4.59580e9 | −0.972176 | ||||||||
\(582\) | 1.56221e8 | + | 6.24323e8i | 0.0328480 | + | 0.131274i | ||||
\(583\) | 4.92208e9 | 1.02875 | ||||||||
\(584\) | −6.25570e8 | + | 5.66140e8i | −0.129966 | + | 0.117619i | ||||
\(585\) | − | 9.07215e9i | − | 1.87355i | ||||||
\(586\) | −1.20302e9 | − | 4.80775e9i | −0.246962 | − | 0.986962i | ||||
\(587\) | − | 2.35339e8i | − | 0.0480242i | −0.999712 | − | 0.0240121i | \(-0.992356\pi\) | ||
0.999712 | − | 0.0240121i | \(-0.00764402\pi\) | |||||||
\(588\) | 1.01247e8 | − | 5.40533e7i | 0.0205381 | − | 0.0109648i | ||||
\(589\) | 1.29254e9 | − | 1.10551e9i | 0.260640 | − | 0.222925i | ||||
\(590\) | 6.28184e9 | − | 1.57187e9i | 1.25923 | − | 0.315090i | ||||
\(591\) | 3.66609e8 | 0.0730545 | ||||||||
\(592\) | 6.38073e9 | + | 4.27258e9i | 1.26399 | + | 0.846378i | ||||
\(593\) | 3.76769e9 | 0.741965 | 0.370983 | − | 0.928640i | \(-0.379021\pi\) | ||||
0.370983 | + | 0.928640i | \(0.379021\pi\) | |||||||
\(594\) | −3.89285e8 | − | 1.55574e9i | −0.0762106 | − | 0.304569i | ||||
\(595\) | − | 1.14878e10i | − | 2.23577i | ||||||
\(596\) | −6.63757e9 | + | 3.54364e9i | −1.28424 | + | 0.685627i | ||||
\(597\) | 9.54113e7i | 0.0183523i | ||||||||
\(598\) | 2.61466e9 | − | 6.54252e8i | 0.499989 | − | 0.125110i | ||||
\(599\) | −1.38664e9 | −0.263616 | −0.131808 | − | 0.991275i | \(-0.542078\pi\) | ||||
−0.131808 | + | 0.991275i | \(0.542078\pi\) | |||||||
\(600\) | 4.60022e8 | − | 4.16320e8i | 0.0869460 | − | 0.0786861i | ||||
\(601\) | 3.07925e9i | 0.578608i | 0.957237 | + | 0.289304i | \(0.0934239\pi\) | ||||
−0.957237 | + | 0.289304i | \(0.906576\pi\) | |||||||
\(602\) | −9.87399e9 | + | 2.47072e9i | −1.84461 | + | 0.461567i | ||||
\(603\) | 8.38600e9 | 1.55756 | ||||||||
\(604\) | 8.69739e9 | − | 4.64334e9i | 1.60605 | − | 0.857434i | ||||
\(605\) | −1.35743e9 | −0.249214 | ||||||||
\(606\) | −3.47786e8 | + | 8.70248e7i | −0.0634832 | + | 0.0158851i | ||||
\(607\) | −4.43504e9 | −0.804892 | −0.402446 | − | 0.915444i | \(-0.631840\pi\) | ||||
−0.402446 | + | 0.915444i | \(0.631840\pi\) | |||||||
\(608\) | 1.96637e9 | + | 5.18137e9i | 0.354816 | + | 0.934936i | ||||
\(609\) | −5.23126e7 | −0.00938525 | ||||||||
\(610\) | 1.67507e9 | − | 4.19143e8i | 0.298798 | − | 0.0747666i | ||||
\(611\) | −4.50528e9 | −0.799057 | ||||||||
\(612\) | 7.90384e9 | − | 4.21967e9i | 1.39382 | − | 0.744130i | ||||
\(613\) | 2.20653e9 | 0.386899 | 0.193450 | − | 0.981110i | \(-0.438032\pi\) | ||||
0.193450 | + | 0.981110i | \(0.438032\pi\) | |||||||
\(614\) | −3.80023e9 | + | 9.50911e8i | −0.662552 | + | 0.165787i | ||||
\(615\) | 1.99998e9i | 0.346708i | ||||||||
\(616\) | −4.10856e9 | + | 3.71825e9i | −0.708203 | + | 0.640923i | ||||
\(617\) | −2.90373e8 | −0.0497689 | −0.0248844 | − | 0.999690i | \(-0.507922\pi\) | ||||
−0.0248844 | + | 0.999690i | \(0.507922\pi\) | |||||||
\(618\) | 1.16714e9 | − | 2.92046e8i | 0.198912 | − | 0.0497728i | ||||
\(619\) | 4.84893e9i | 0.821729i | 0.911696 | + | 0.410865i | \(0.134773\pi\) | ||||
−0.911696 | + | 0.410865i | \(0.865227\pi\) | |||||||
\(620\) | −2.31349e9 | + | 1.23512e9i | −0.389849 | + | 0.208131i | ||||
\(621\) | − | 7.16189e8i | − | 0.120007i | ||||||
\(622\) | −5.06113e7 | − | 2.02263e8i | −0.00843298 | − | 0.0337016i | ||||
\(623\) | 3.64712e9 | 0.604284 | ||||||||
\(624\) | 1.34466e9 | + | 9.00393e8i | 0.221547 | + | 0.148349i | ||||
\(625\) | −7.47253e9 | −1.22430 | ||||||||
\(626\) | 2.87894e9 | − | 7.20383e8i | 0.469054 | − | 0.117369i | ||||
\(627\) | −6.39859e8 | − | 7.48111e8i | −0.103669 | − | 0.121208i | ||||
\(628\) | −2.05418e9 | + | 1.09668e9i | −0.330963 | + | 0.176694i | ||||
\(629\) | − | 1.54897e10i | − | 2.48179i | ||||||
\(630\) | 2.02191e9 | + | 8.08039e9i | 0.322159 | + | 1.28748i | ||||
\(631\) | 8.68083e9i | 1.37549i | 0.725951 | + | 0.687747i | \(0.241400\pi\) | ||||
−0.725951 | + | 0.687747i | \(0.758600\pi\) | |||||||
\(632\) | 4.36537e9 | − | 3.95066e9i | 0.687878 | − | 0.622529i | ||||
\(633\) | −6.60943e8 | −0.103574 | ||||||||
\(634\) | 2.92374e8 | + | 1.16845e9i | 0.0455645 | + | 0.182094i | ||||
\(635\) | 2.55660e8 | 0.0396237 | ||||||||
\(636\) | 6.21564e8 | + | 1.16425e9i | 0.0958046 | + | 0.179451i | ||||
\(637\) | 1.28402e9i | 0.196827i | ||||||||
\(638\) | 2.83980e8 | − | 7.10589e7i | 0.0432928 | − | 0.0108329i | ||||
\(639\) | −6.00248e9 | −0.910076 | ||||||||
\(640\) | −1.23925e9 | − | 8.45492e9i | −0.186865 | − | 1.27491i | ||||
\(641\) | 4.15561e9i | 0.623205i | 0.950212 | + | 0.311603i | \(0.100866\pi\) | ||||
−0.950212 | + | 0.311603i | \(0.899134\pi\) | |||||||
\(642\) | 8.20761e8 | − | 2.05375e8i | 0.122418 | − | 0.0306319i | ||||
\(643\) | − | 3.22611e9i | − | 0.478565i | −0.970950 | − | 0.239282i | \(-0.923088\pi\) | ||
0.970950 | − | 0.239282i | \(-0.0769121\pi\) | |||||||
\(644\) | −2.18301e9 | + | 1.16546e9i | −0.322074 | + | 0.171948i | ||||
\(645\) | 2.78814e9i | 0.409125i | ||||||||
\(646\) | 6.47746e9 | − | 9.11087e9i | 0.945346 | − | 1.32968i | ||||
\(647\) | 1.44465e9i | 0.209700i | 0.994488 | + | 0.104850i | \(0.0334362\pi\) | ||||
−0.994488 | + | 0.104850i | \(0.966564\pi\) | |||||||
\(648\) | −4.65483e9 | + | 4.21262e9i | −0.672034 | + | 0.608190i | ||||
\(649\) | 6.30057e9i | 0.904740i | ||||||||
\(650\) | 1.68491e9 | + | 6.73358e9i | 0.240646 | + | 0.961722i | ||||
\(651\) | 4.55995e8i | 0.0647778i | ||||||||
\(652\) | −2.34162e9 | − | 4.38606e9i | −0.330864 | − | 0.619738i | ||||
\(653\) | −3.36633e9 | −0.473108 | −0.236554 | − | 0.971618i | \(-0.576018\pi\) | ||||
−0.236554 | + | 0.971618i | \(0.576018\pi\) | |||||||
\(654\) | −1.59330e8 | − | 6.36747e8i | −0.0222728 | − | 0.0890112i | ||||
\(655\) | 1.43313e10i | 1.99270i | ||||||||
\(656\) | 9.10275e9 | + | 6.09527e9i | 1.25895 | + | 0.843004i | ||||
\(657\) | −1.23399e9 | −0.169759 | ||||||||
\(658\) | 4.01277e9 | − | 1.00409e9i | 0.549102 | − | 0.137399i | ||||
\(659\) | 8.36290e9 | 1.13830 | 0.569152 | − | 0.822232i | \(-0.307272\pi\) | ||||
0.569152 | + | 0.822232i | \(0.307272\pi\) | |||||||
\(660\) | 7.14874e8 | + | 1.33902e9i | 0.0967890 | + | 0.181295i | ||||
\(661\) | 4.13787e9i | 0.557277i | 0.960396 | + | 0.278639i | \(0.0898832\pi\) | ||||
−0.960396 | + | 0.278639i | \(0.910117\pi\) | |||||||
\(662\) | 6.91620e9 | − | 1.73060e9i | 0.926540 | − | 0.231843i | ||||
\(663\) | − | 3.26426e9i | − | 0.434998i | ||||||
\(664\) | 4.62713e9 | + | 5.11286e9i | 0.613372 | + | 0.677759i | ||||
\(665\) | 6.75497e9 | + | 7.89778e9i | 0.890733 | + | 1.04143i | ||||
\(666\) | 2.72627e9 | + | 1.08953e10i | 0.357610 | + | 1.42916i | ||||
\(667\) | 1.30731e8 | 0.0170584 | ||||||||
\(668\) | 2.55775e9 | − | 1.36553e9i | 0.332002 | − | 0.177248i | ||||
\(669\) | 1.49557e9 | 0.193114 | ||||||||
\(670\) | −1.56506e10 | + | 3.91617e9i | −2.01034 | + | 0.503036i | ||||
\(671\) | 1.68006e9i | 0.214682i | ||||||||
\(672\) | −1.39833e9 | − | 5.02278e8i | −0.177753 | − | 0.0638487i | ||||
\(673\) | 1.32538e10i | 1.67605i | 0.545629 | + | 0.838027i | \(0.316291\pi\) | ||||
−0.545629 | + | 0.838027i | \(0.683709\pi\) | |||||||
\(674\) | −8.22857e8 | − | 3.28847e9i | −0.103518 | − | 0.413699i | ||||
\(675\) | 1.84442e9 | 0.230832 | ||||||||
\(676\) | −8.88570e9 | + | 4.74387e9i | −1.10631 | + | 0.590635i | ||||
\(677\) | − | 8.35900e9i | − | 1.03537i | −0.855573 | − | 0.517683i | \(-0.826795\pi\) | ||
0.855573 | − | 0.517683i | \(-0.173205\pi\) | |||||||
\(678\) | −5.30848e7 | − | 2.12149e8i | −0.00654134 | − | 0.0261419i | ||||
\(679\) | 6.61062e9 | 0.810397 | ||||||||
\(680\) | −1.27802e10 | + | 1.15661e10i | −1.55868 | + | 1.41060i | ||||
\(681\) | −2.72304e9 | −0.330400 | ||||||||
\(682\) | −6.19401e8 | − | 2.47538e9i | −0.0747699 | − | 0.298811i | ||||
\(683\) | −1.24346e9 | −0.149334 | −0.0746671 | − | 0.997209i | \(-0.523789\pi\) | ||||
−0.0746671 | + | 0.997209i | \(0.523789\pi\) | |||||||
\(684\) | −2.95262e9 | + | 7.54857e9i | −0.352786 | + | 0.901920i | ||||
\(685\) | 1.23579e10 | 1.46903 | ||||||||
\(686\) | 1.89670e9 | + | 7.57997e9i | 0.224318 | + | 0.896465i | ||||
\(687\) | −1.64620e8 | −0.0193702 | ||||||||
\(688\) | 1.26900e10 | + | 8.49731e9i | 1.48560 | + | 0.994768i | ||||
\(689\) | −1.47651e10 | −1.71976 | ||||||||
\(690\) | 1.64547e8 | + | 6.57596e8i | 0.0190685 | + | 0.0762057i | ||||
\(691\) | − | 4.21392e9i | − | 0.485863i | −0.970043 | − | 0.242931i | \(-0.921891\pi\) | ||
0.970043 | − | 0.242931i | \(-0.0781090\pi\) | |||||||
\(692\) | −7.31471e9 | − | 1.37011e10i | −0.839124 | − | 1.57176i | ||||
\(693\) | −8.10449e9 | −0.925037 | ||||||||
\(694\) | 2.26612e9 | + | 9.05632e9i | 0.257350 | + | 1.02847i | ||||
\(695\) | − | 1.35582e10i | − | 1.53198i | ||||||
\(696\) | 5.26692e7 | + | 5.81981e7i | 0.00592140 | + | 0.00654299i | ||||
\(697\) | − | 2.20976e10i | − | 2.47190i | ||||||
\(698\) | 6.33855e9 | − | 1.58606e9i | 0.705499 | − | 0.176533i | ||||
\(699\) | −1.32499e9 | −0.146738 | ||||||||
\(700\) | −3.00143e9 | − | 5.62195e9i | −0.330739 | − | 0.619504i | ||||
\(701\) | 6.46782e9 | 0.709161 | 0.354580 | − | 0.935026i | \(-0.384624\pi\) | ||||
0.354580 | + | 0.935026i | \(0.384624\pi\) | |||||||
\(702\) | 1.16777e9 | + | 4.66687e9i | 0.127402 | + | 0.509150i | ||||
\(703\) | 9.10816e9 | + | 1.06491e10i | 0.988751 | + | 1.15603i | ||||
\(704\) | 8.27315e9 | + | 8.27204e8i | 0.893648 | + | 0.0893528i | ||||
\(705\) | − | 1.13310e9i | − | 0.121788i | ||||||
\(706\) | 1.70900e9 | − | 4.27634e8i | 0.182778 | − | 0.0457357i | ||||
\(707\) | 3.68252e9i | 0.391902i | ||||||||
\(708\) | −1.49031e9 | + | 7.95642e8i | −0.157819 | + | 0.0842561i | ||||
\(709\) | −1.57425e10 | −1.65887 | −0.829433 | − | 0.558606i | \(-0.811336\pi\) | ||||
−0.829433 | + | 0.558606i | \(0.811336\pi\) | |||||||
\(710\) | 1.12023e10 | − | 2.80309e9i | 1.17463 | − | 0.293923i | ||||
\(711\) | 8.61106e9 | 0.898490 | ||||||||
\(712\) | −3.67198e9 | − | 4.05744e9i | −0.381259 | − | 0.421281i | ||||
\(713\) | − | 1.13955e9i | − | 0.117738i | ||||||
\(714\) | 7.27506e8 | + | 2.90741e9i | 0.0747985 | + | 0.298925i | ||||
\(715\) | −1.69816e10 | −1.73744 | ||||||||
\(716\) | −1.66850e10 | + | 8.90773e9i | −1.69875 | + | 0.906925i | ||||
\(717\) | − | 2.19865e9i | − | 0.222760i | ||||||
\(718\) | −8.10744e7 | − | 3.24006e8i | −0.00817426 | − | 0.0326677i | ||||
\(719\) | 6.96744e9i | 0.699072i | 0.936923 | + | 0.349536i | \(0.113661\pi\) | ||||
−0.936923 | + | 0.349536i | \(0.886339\pi\) | |||||||
\(720\) | 6.95378e9 | − | 1.03849e10i | 0.694316 | − | 1.03690i | ||||
\(721\) | − | 1.23582e10i | − | 1.22795i | ||||||
\(722\) | 9.04100e8 | + | 1.00725e10i | 0.0893997 | + | 0.995996i | ||||
\(723\) | 6.89376e8i | 0.0678378i | ||||||||
\(724\) | 5.32653e9 | + | 9.97707e9i | 0.521626 | + | 0.977053i | ||||
\(725\) | 3.36674e8i | 0.0328115i | ||||||||
\(726\) | 3.43548e8 | − | 8.59642e7i | 0.0333203 | − | 0.00833757i | ||||
\(727\) | − | 3.61410e9i | − | 0.348843i | −0.984671 | − | 0.174422i | \(-0.944194\pi\) | ||
0.984671 | − | 0.174422i | \(-0.0558056\pi\) | |||||||
\(728\) | 1.23247e10 | − | 1.11539e10i | 1.18391 | − | 1.07144i | ||||
\(729\) | −8.53264e9 | −0.815712 | ||||||||
\(730\) | 2.30297e9 | − | 5.76259e8i | 0.219108 | − | 0.0548261i | ||||
\(731\) | − | 3.08059e10i | − | 2.91691i | ||||||
\(732\) | −3.97395e8 | + | 2.12160e8i | −0.0374484 | + | 0.0199928i | ||||
\(733\) | −1.90486e10 | −1.78649 | −0.893243 | − | 0.449575i | \(-0.851575\pi\) | ||||
−0.893243 | + | 0.449575i | \(0.851575\pi\) | |||||||
\(734\) | −4.07030e9 | − | 1.62666e10i | −0.379918 | − | 1.51831i | ||||
\(735\) | −3.22936e8 | −0.0299993 | ||||||||
\(736\) | 3.49447e9 | + | 1.25521e9i | 0.323080 | + | 0.116050i | ||||
\(737\) | − | 1.56973e10i | − | 1.44440i | ||||||
\(738\) | 3.88931e9 | + | 1.55432e10i | 0.356184 | + | 1.42346i | ||||
\(739\) | − | 1.51227e10i | − | 1.37839i | −0.724575 | − | 0.689196i | \(-0.757964\pi\) | ||
0.724575 | − | 0.689196i | \(-0.242036\pi\) | |||||||
\(740\) | −1.01760e10 | − | 1.90605e10i | −0.923134 | − | 1.72911i | ||||
\(741\) | 1.91943e9 | + | 2.24416e9i | 0.173304 | + | 0.202624i | ||||
\(742\) | 1.31510e10 | − | 3.29070e9i | 1.18180 | − | 0.295716i | ||||
\(743\) | −9.37736e8 | −0.0838725 | −0.0419363 | − | 0.999120i | \(-0.513353\pi\) | ||||
−0.0419363 | + | 0.999120i | \(0.513353\pi\) | |||||||
\(744\) | 5.07297e8 | − | 4.59104e8i | 0.0451603 | − | 0.0408701i | ||||
\(745\) | 2.11712e10 | 1.87585 | ||||||||
\(746\) | −3.47083e9 | − | 1.38708e10i | −0.306088 | − | 1.22325i | ||||
\(747\) | 1.00855e10i | 0.885273i | ||||||||
\(748\) | −7.89857e9 | − | 1.47948e10i | −0.690070 | − | 1.29256i | ||||
\(749\) | − | 8.69058e9i | − | 0.755723i | ||||||
\(750\) | 8.71205e8 | − | 2.17997e8i | 0.0754060 | − | 0.0188684i | ||||
\(751\) | 7.92462e9 | 0.682714 | 0.341357 | − | 0.939934i | \(-0.389113\pi\) | ||||
0.341357 | + | 0.939934i | \(0.389113\pi\) | |||||||
\(752\) | −5.15718e9 | − | 3.45329e9i | −0.442232 | − | 0.296122i | ||||
\(753\) | − | 3.00414e9i | − | 0.256411i | ||||||
\(754\) | −8.51875e8 | + | 2.13160e8i | −0.0723729 | + | 0.0181095i | ||||
\(755\) | −2.77412e10 | −2.34590 | ||||||||
\(756\) | −2.08021e9 | − | 3.89643e9i | −0.175098 | − | 0.327975i | ||||
\(757\) | 1.25260e10 | 1.04949 | 0.524744 | − | 0.851260i | \(-0.324161\pi\) | ||||
0.524744 | + | 0.851260i | \(0.324161\pi\) | |||||||
\(758\) | −2.80115e8 | + | 7.00918e7i | −0.0233612 | + | 0.00584555i | ||||
\(759\) | −6.59558e8 | −0.0547528 | ||||||||
\(760\) | 1.98531e9 | − | 1.54666e10i | 0.164052 | − | 1.27805i | ||||
\(761\) | 4.74611e8 | 0.0390383 | 0.0195192 | − | 0.999809i | \(-0.493786\pi\) | ||||
0.0195192 | + | 0.999809i | \(0.493786\pi\) | |||||||
\(762\) | −6.47044e7 | + | 1.61906e7i | −0.00529775 | + | 0.00132563i | ||||
\(763\) | −6.74216e9 | −0.549494 | ||||||||
\(764\) | 8.49919e9 | + | 1.59198e10i | 0.689526 | + | 1.29154i | ||||
\(765\) | −2.52100e10 | −2.03591 | ||||||||
\(766\) | −1.80148e10 | + | 4.50774e9i | −1.44820 | + | 0.362375i | ||||
\(767\) | − | 1.89003e10i | − | 1.51246i | ||||||
\(768\) | 8.49077e8 | + | 2.06135e9i | 0.0676368 | + | 0.164206i | ||||
\(769\) | 1.98171e9 | 0.157144 | 0.0785719 | − | 0.996908i | \(-0.474964\pi\) | ||||
0.0785719 | + | 0.996908i | \(0.474964\pi\) | |||||||
\(770\) | 1.51252e10 | − | 3.78470e9i | 1.19394 | − | 0.298755i | ||||
\(771\) | 1.80464e9i | 0.141808i | ||||||||
\(772\) | 3.03388e9 | + | 5.68273e9i | 0.237322 | + | 0.444525i | ||||
\(773\) | 5.26122e9i | 0.409693i | 0.978794 | + | 0.204846i | \(0.0656695\pi\) | ||||
−0.978794 | + | 0.204846i | \(0.934330\pi\) | |||||||
\(774\) | 5.42201e9 | + | 2.16686e10i | 0.420308 | + | 1.67972i | ||||
\(775\) | 2.93469e9 | 0.226468 | ||||||||
\(776\) | −6.65568e9 | − | 7.35435e9i | −0.511301 | − | 0.564974i | ||||
\(777\) | −3.75688e9 | −0.287312 | ||||||||
\(778\) | −2.21776e9 | + | 5.54939e8i | −0.168844 | + | 0.0422490i | ||||
\(779\) | 1.29937e10 | + | 1.51920e10i | 0.984809 | + | 1.15142i | ||||
\(780\) | −2.14446e9 | − | 4.01677e9i | −0.161803 | − | 0.303072i | ||||
\(781\) | 1.12357e10i | 0.843960i | ||||||||
\(782\) | −1.81806e9 | − | 7.26571e9i | −0.135952 | − | 0.543319i | ||||
\(783\) | 2.33340e8i | 0.0173709i | ||||||||
\(784\) | −9.84200e8 | + | 1.46982e9i | −0.0729419 | + | 0.108932i | ||||
\(785\) | 6.55200e9 | 0.483426 | ||||||||
\(786\) | −9.07586e8 | − | 3.62708e9i | −0.0666667 | − | 0.266427i | ||||
\(787\) | 9.21236e9 | 0.673689 | 0.336844 | − | 0.941560i | \(-0.390640\pi\) | ||||
0.336844 | + | 0.941560i | \(0.390640\pi\) | |||||||
\(788\) | −4.98442e9 | + | 2.66106e9i | −0.362888 | + | 0.193737i | ||||
\(789\) | − | 1.40103e9i | − | 0.101550i | ||||||
\(790\) | −1.60706e10 | + | 4.02127e9i | −1.15968 | + | 0.290181i | ||||
\(791\) | −2.24633e9 | −0.161382 | ||||||||
\(792\) | 8.15974e9 | + | 9.01629e9i | 0.583631 | + | 0.644896i | ||||
\(793\) | − | 5.03980e9i | − | 0.358887i | ||||||
\(794\) | −1.60518e10 | + | 4.01656e9i | −1.13803 | + | 0.284762i | ||||
\(795\) | − | 3.71348e9i | − | 0.262117i | ||||||
\(796\) | −6.92551e8 | − | 1.29721e9i | −0.0486694 | − | 0.0911622i | ||||
\(797\) | 1.08189e10i | 0.756974i | 0.925607 | + | 0.378487i | \(0.123555\pi\) | ||||
−0.925607 | + | 0.378487i | \(0.876445\pi\) | |||||||
\(798\) | −2.20976e9 | − | 1.57105e9i | −0.153934 | − | 0.109441i | ||||
\(799\) | 1.25195e10i | 0.868304i | ||||||||
\(800\) | −3.23256e9 | + | 8.99939e9i | −0.223220 | + | 0.621439i | ||||
\(801\) | − | 8.00364e9i | − | 0.550267i | ||||||
\(802\) | 9.45835e7 | + | 3.77994e8i | 0.00647448 | + | 0.0258747i | ||||
\(803\) | 2.30984e9i | 0.157426i | ||||||||
\(804\) | 3.71297e9 | − | 1.98227e9i | 0.251956 | − | 0.134514i | ||||
\(805\) | 6.96292e9 | 0.470442 | ||||||||
\(806\) | 1.85806e9 | + | 7.42557e9i | 0.124993 | + | 0.499525i | ||||
\(807\) | − | 1.31684e9i | − | 0.0882014i | ||||||
\(808\) | 4.09683e9 | − | 3.70763e9i | 0.273217 | − | 0.247261i | ||||
\(809\) | 1.44475e9 | 0.0959338 | 0.0479669 | − | 0.998849i | \(-0.484726\pi\) | ||||
0.0479669 | + | 0.998849i | \(0.484726\pi\) | |||||||
\(810\) | 1.71362e10 | − | 4.28791e9i | 1.13297 | − | 0.283497i | ||||
\(811\) | −2.67454e10 | −1.76066 | −0.880332 | − | 0.474357i | \(-0.842680\pi\) | ||||
−0.880332 | + | 0.474357i | \(0.842680\pi\) | |||||||
\(812\) | 7.11242e8 | − | 3.79715e8i | 0.0466199 | − | 0.0248893i | ||||
\(813\) | − | 8.26483e8i | − | 0.0539407i | ||||||
\(814\) | 2.03943e10 | − | 5.10316e9i | 1.32533 | − | 0.331630i | ||||
\(815\) | 1.39898e10i | 0.905230i | ||||||||
\(816\) | 2.50205e9 | − | 3.73659e9i | 0.161206 | − | 0.240746i | ||||
\(817\) | 1.81143e10 | + | 2.11789e10i | 1.16210 | + | 1.35871i | ||||
\(818\) | −1.32983e9 | − | 5.31453e9i | −0.0849490 | − | 0.339491i | ||||
\(819\) | 2.43116e10 | 1.54639 | ||||||||
\(820\) | −1.45170e10 | − | 2.71918e10i | −0.919454 | − | 1.72222i | ||||
\(821\) | 7.52716e9 | 0.474712 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(822\) | −3.12764e9 | + | 7.82614e8i | −0.196411 | + | 0.0491469i | ||||
\(823\) | 8.01305e8i | 0.0501070i | 0.999686 | + | 0.0250535i | \(0.00797561\pi\) | ||||
−0.999686 | + | 0.0250535i | \(0.992024\pi\) | |||||||
\(824\) | −1.37485e10 | + | 1.24424e10i | −0.856073 | + | 0.774746i | ||||
\(825\) | − | 1.69857e9i | − | 0.105316i | ||||||
\(826\) | 4.21231e9 | + | 1.68341e10i | 0.260070 | + | 1.03935i | ||||
\(827\) | −2.45940e10 | −1.51203 | −0.756014 | − | 0.654556i | \(-0.772856\pi\) | ||||
−0.756014 | + | 0.654556i | \(0.772856\pi\) | |||||||
\(828\) | 2.55761e9 | + | 4.79064e9i | 0.156577 | + | 0.293284i | ||||
\(829\) | 2.17049e10i | 1.32317i | 0.749869 | + | 0.661586i | \(0.230116\pi\) | ||||
−0.749869 | + | 0.661586i | \(0.769884\pi\) | |||||||
\(830\) | −4.70984e9 | − | 1.88224e10i | −0.285912 | − | 1.14262i | ||||
\(831\) | 1.80675e9 | 0.109218 | ||||||||
\(832\) | −2.48175e10 | − | 2.48142e9i | −1.49392 | − | 0.149372i | ||||
\(833\) | 3.56809e9 | 0.213884 | ||||||||
\(834\) | 8.58623e8 | + | 3.43141e9i | 0.0512532 | + | 0.204829i | ||||
\(835\) | −8.15820e9 | −0.484944 | ||||||||
\(836\) | 1.41297e10 | + | 5.52684e9i | 0.836397 | + | 0.327156i | ||||
\(837\) | 2.03396e9 | 0.119896 | ||||||||
\(838\) | −3.45571e8 | − | 1.38104e9i | −0.0202854 | − | 0.0810688i | ||||
\(839\) | −1.03002e10 | −0.602114 | −0.301057 | − | 0.953606i | \(-0.597339\pi\) | ||||
−0.301057 | + | 0.953606i | \(0.597339\pi\) | |||||||
\(840\) | 2.80524e9 | + | 3.09972e9i | 0.163303 | + | 0.180445i | ||||
\(841\) | 1.72073e10 | 0.997531 | ||||||||
\(842\) | −7.25437e7 | − | 2.89914e8i | −0.00418801 | − | 0.0167370i | ||||
\(843\) | − | 4.47988e9i | − | 0.257555i | ||||||
\(844\) | 8.98617e9 | − | 4.79751e9i | 0.514489 | − | 0.274674i | ||||
\(845\) | 2.83418e10 | 1.61595 | ||||||||
\(846\) | −2.20349e9 | − | 8.80606e9i | −0.125117 | − | 0.500018i | ||||
\(847\) | − | 3.63764e9i | − | 0.205697i | ||||||
\(848\) | −1.69016e10 | − | 1.13174e10i | −0.951791 | − | 0.637326i | ||||
\(849\) | 5.56582e7i | 0.00312142i | ||||||||
\(850\) | 1.87115e10 | − | 4.68209e9i | 1.04507 | − | 0.261501i | ||||
\(851\) | 9.38856e9 | 0.522210 | ||||||||
\(852\) | −2.65765e9 | + | 1.41886e9i | −0.147217 | + | 0.0785958i | ||||
\(853\) | 7.96085e9 | 0.439175 | 0.219588 | − | 0.975593i | \(-0.429529\pi\) | ||||
0.219588 | + | 0.975593i | \(0.429529\pi\) | |||||||
\(854\) | 1.12322e9 | + | 4.48885e9i | 0.0617111 | + | 0.246623i | ||||
\(855\) | 1.73318e10 | − | 1.48239e10i | 0.948334 | − | 0.811110i | ||||
\(856\) | −9.66833e9 | + | 8.74983e9i | −0.526857 | + | 0.476806i | ||||
\(857\) | 2.11539e10i | 1.14804i | 0.818840 | + | 0.574021i | \(0.194617\pi\) | ||||
−0.818840 | + | 0.574021i | \(0.805383\pi\) | |||||||
\(858\) | 4.29784e9 | − | 1.07543e9i | 0.232298 | − | 0.0581267i | ||||
\(859\) | − | 1.99252e10i | − | 1.07257i | −0.844036 | − | 0.536286i | \(-0.819827\pi\) | ||
0.844036 | − | 0.536286i | \(-0.180173\pi\) | |||||||
\(860\) | −2.02380e10 | − | 3.79076e10i | −1.08498 | − | 2.03227i | ||||
\(861\) | −5.35957e9 | −0.286166 | ||||||||
\(862\) | −2.18675e10 | + | 5.47180e9i | −1.16285 | + | 0.290974i | ||||
\(863\) | 8.56324e8 | 0.0453524 | 0.0226762 | − | 0.999743i | \(-0.492781\pi\) | ||||
0.0226762 | + | 0.999743i | \(0.492781\pi\) | |||||||
\(864\) | −2.24041e9 | + | 6.23724e9i | −0.118176 | + | 0.328999i | ||||
\(865\) | 4.37011e10i | 2.29581i | ||||||||
\(866\) | −4.42979e9 | − | 1.77033e10i | −0.231777 | − | 0.926276i | ||||
\(867\) | −5.66296e9 | −0.295105 | ||||||||
\(868\) | −3.30988e9 | − | 6.19970e9i | −0.171788 | − | 0.321775i | ||||
\(869\) | − | 1.61186e10i | − | 0.833215i | ||||||
\(870\) | −5.36106e7 | − | 2.14250e8i | −0.00276015 | − | 0.0110307i | ||||
\(871\) | 4.70882e10i | 2.41462i | ||||||||
\(872\) | 6.78812e9 | + | 7.50069e9i | 0.346691 | + | 0.383084i | ||||
\(873\) | − | 1.45071e10i | − | 0.737955i | ||||||
\(874\) | 5.52225e9 | + | 3.92609e9i | 0.279786 | + | 0.198916i | ||||
\(875\) | − | 9.22471e9i | − | 0.465505i | ||||||
\(876\) | −5.46358e8 | + | 2.91688e8i | −0.0274608 | + | 0.0146607i | ||||
\(877\) | − | 9.40744e9i | − | 0.470948i | −0.971881 | − | 0.235474i | \(-0.924336\pi\) | ||
0.971881 | − | 0.235474i | \(-0.0756642\pi\) | |||||||
\(878\) | −4.85908e8 | + | 1.21586e8i | −0.0242283 | + | 0.00606253i | ||||
\(879\) | − | 3.63804e9i | − | 0.180679i | ||||||
\(880\) | −1.94388e10 | − | 1.30164e10i | −0.961571 | − | 0.643875i | ||||
\(881\) | −3.05311e10 | −1.50427 | −0.752137 | − | 0.659007i | \(-0.770977\pi\) | ||||
−0.752137 | + | 0.659007i | \(0.770977\pi\) | |||||||
\(882\) | −2.50976e9 | + | 6.28004e8i | −0.123166 | + | 0.0308193i | ||||
\(883\) | 3.85968e10i | 1.88664i | 0.331884 | + | 0.943320i | \(0.392316\pi\) | ||||
−0.331884 | + | 0.943320i | \(0.607684\pi\) | |||||||
\(884\) | 2.36939e10 | + | 4.43808e10i | 1.15360 | + | 2.16079i | ||||
\(885\) | 4.75349e9 | 0.230521 | ||||||||
\(886\) | −6.44469e8 | − | 2.57556e9i | −0.0311304 | − | 0.124410i | ||||
\(887\) | 1.44349e9 | 0.0694514 | 0.0347257 | − | 0.999397i | \(-0.488944\pi\) | ||||
0.0347257 | + | 0.999397i | \(0.488944\pi\) | |||||||
\(888\) | 3.78249e9 | + | 4.17955e9i | 0.181273 | + | 0.200302i | ||||
\(889\) | 6.85119e8i | 0.0327047i | ||||||||
\(890\) | 3.73761e9 | + | 1.49370e10i | 0.177717 | + | 0.710229i | ||||
\(891\) | 1.71873e10i | 0.814023i | ||||||||
\(892\) | −2.03337e10 | + | 1.08557e10i | −0.959268 | + | 0.512131i | ||||
\(893\) | −7.36161e9 | − | 8.60706e9i | −0.345934 | − | 0.404459i | ||||
\(894\) | −5.35816e9 | + | 1.34074e9i | −0.250804 | + | 0.0627573i | ||||
\(895\) | 5.32184e10 | 2.48131 | ||||||||
\(896\) | 2.26575e10 | − | 3.32094e9i | 1.05229 | − | 0.154235i | ||||
\(897\) | 1.97852e9 | 0.0915307 | ||||||||
\(898\) | 6.59527e9 | + | 2.63574e10i | 0.303924 | + | 1.21460i | ||||
\(899\) | 3.71272e8i | 0.0170425i | ||||||||
\(900\) | −1.23374e10 | + | 6.58667e9i | −0.564126 | + | 0.301174i | ||||
\(901\) | 4.10298e10i | 1.86880i | ||||||||
\(902\) | 2.90945e10 | − | 7.28017e9i | 1.32004 | − | 0.330308i | ||||
\(903\) | −7.47168e9 | −0.337685 | ||||||||
\(904\) | 2.26164e9 | + | 2.49905e9i | 0.101820 | + | 0.112509i | ||||
\(905\) | − | 3.18228e10i | − | 1.42715i | ||||||
\(906\) | 7.02095e9 | − | 1.75681e9i | 0.313651 | − | 0.0784833i | ||||
\(907\) | −7.77220e9 | −0.345875 | −0.172937 | − | 0.984933i | \(-0.555326\pi\) | ||||
−0.172937 | + | 0.984933i | \(0.555326\pi\) | |||||||
\(908\) | 3.70225e10 | − | 1.97654e10i | 1.64121 | − | 0.876205i | ||||
\(909\) | 8.08133e9 | 0.356869 | ||||||||
\(910\) | −4.53722e10 | + | 1.13532e10i | −1.99593 | + | 0.499430i | ||||
\(911\) | 2.17755e10 | 0.954232 | 0.477116 | − | 0.878840i | \(-0.341682\pi\) | ||||
0.477116 | + | 0.878840i | \(0.341682\pi\) | |||||||
\(912\) | 4.77022e8 | + | 4.04012e9i | 0.0208236 | + | 0.176365i | ||||
\(913\) | 1.88786e10 | 0.820959 | ||||||||
\(914\) | −1.55230e10 | + | 3.88424e9i | −0.672456 | + | 0.168265i | ||||
\(915\) | 1.26753e9 | 0.0546996 | ||||||||
\(916\) | 2.23817e9 | − | 1.19491e9i | 0.0962187 | − | 0.0513689i | ||||
\(917\) | −3.84052e10 | −1.64474 | ||||||||
\(918\) | 1.29685e10 | − | 3.24503e9i | 0.553273 | − | 0.138443i | ||||
\(919\) | 1.80795e10i | 0.768390i | 0.923252 | + | 0.384195i | \(0.125521\pi\) | ||||
−0.923252 | + | 0.384195i | \(0.874479\pi\) | |||||||
\(920\) | −7.01039e9 | − | 7.74629e9i | −0.296814 | − | 0.327972i | ||||
\(921\) | −2.87565e9 | −0.121290 | ||||||||
\(922\) | 3.04359e10 | − | 7.61582e9i | 1.27888 | − | 0.320006i | ||||
\(923\) | − | 3.37045e10i | − | 1.41085i | ||||||
\(924\) | −3.58833e9 | + | 1.91572e9i | −0.149637 | + | 0.0798879i | ||||
\(925\) | 2.41786e10i | 1.00446i | ||||||||
\(926\) | −3.07174e8 | − | 1.22759e9i | −0.0127130 | − | 0.0508061i | ||||
\(927\) | −2.71201e10 | −1.11818 | ||||||||
\(928\) | −1.13853e9 | − | 4.08956e8i | −0.0467654 | − | 0.0167981i | ||||
\(929\) | −2.99533e10 | −1.22572 | −0.612858 | − | 0.790193i | \(-0.709980\pi\) | ||||
−0.612858 | + | 0.790193i | \(0.709980\pi\) | |||||||
\(930\) | −1.86756e9 | + | 4.67309e8i | −0.0761349 | + | 0.0190508i | ||||
\(931\) | −2.45304e9 | + | 2.09809e9i | −0.0996280 | + | 0.0852118i | ||||
\(932\) | 1.80145e10 | − | 9.61755e9i | 0.728899 | − | 0.389142i | ||||
\(933\) | − | 1.53053e8i | − | 0.00616960i | ||||||
\(934\) | 4.04032e9 | + | 1.61468e10i | 0.162256 | + | 0.648442i | ||||
\(935\) | 4.71893e10i | 1.88800i | ||||||||
\(936\) | −2.44773e10 | − | 2.70468e10i | −0.975660 | − | 1.07808i | ||||
\(937\) | 2.33735e10 | 0.928188 | 0.464094 | − | 0.885786i | \(-0.346380\pi\) | ||||
0.464094 | + | 0.885786i | \(0.346380\pi\) | |||||||
\(938\) | −1.04946e10 | − | 4.19406e10i | −0.415197 | − | 1.65930i | ||||
\(939\) | 2.17851e9 | 0.0858676 | ||||||||
\(940\) | 8.22467e9 | + | 1.54056e10i | 0.322976 | + | 0.604964i | ||||
\(941\) | − | 4.03649e10i | − | 1.57921i | −0.613615 | − | 0.789606i | \(-0.710285\pi\) | ||
0.613615 | − | 0.789606i | \(-0.289715\pi\) | |||||||
\(942\) | −1.65823e9 | + | 4.14930e8i | −0.0646349 | + | 0.0161732i | ||||
\(943\) | 1.33937e10 | 0.520128 | ||||||||
\(944\) | 1.44870e10 | − | 2.16351e10i | 0.560502 | − | 0.837060i | ||||
\(945\) | 1.24280e10i | 0.479061i | ||||||||
\(946\) | 4.05602e10 | − | 1.01492e10i | 1.55769 | − | 0.389773i | ||||
\(947\) | − | 4.50109e10i | − | 1.72224i | −0.508405 | − | 0.861118i | \(-0.669765\pi\) | ||
0.508405 | − | 0.861118i | \(-0.330235\pi\) | |||||||
\(948\) | 3.81262e9 | − | 2.03547e9i | 0.145343 | − | 0.0775952i | ||||
\(949\) | − | 6.92897e9i | − | 0.263170i | ||||||
\(950\) | −1.01110e10 | + | 1.42216e10i | −0.382613 | + | 0.538164i | ||||
\(951\) | 8.84167e8i | 0.0333351i | ||||||||
\(952\) | −3.09949e10 | − | 3.42485e10i | −1.16429 | − | 1.28651i | ||||
\(953\) | 4.53955e10i | 1.69898i | 0.527607 | + | 0.849488i | \(0.323089\pi\) | ||||
−0.527607 | + | 0.849488i | \(0.676911\pi\) | |||||||
\(954\) | −7.22148e9 | − | 2.88600e10i | −0.269282 | − | 1.07616i | ||||
\(955\) | − | 5.07776e10i | − | 1.88651i | ||||||
\(956\) | 1.59591e10 | + | 2.98928e10i | 0.590751 | + | 1.10653i | ||||
\(957\) | 2.14889e8 | 0.00792542 | ||||||||
\(958\) | 9.32054e7 | + | 3.72487e8i | 0.00342501 | + | 0.0136877i | ||||
\(959\) | 3.31169e10i | 1.21251i | ||||||||
\(960\) | 6.24087e8 | − | 6.24170e9i | 0.0227665 | − | 0.227695i | ||||
\(961\) | −2.42763e10 | −0.882371 | ||||||||
\(962\) | −6.11782e10 | + | 1.53083e10i | −2.21556 | + | 0.554389i | ||||
\(963\) | −1.90716e10 | −0.688169 | ||||||||
\(964\) | −5.00389e9 | − | 9.37275e9i | −0.179903 | − | 0.336975i | ||||
\(965\) | − | 1.81256e10i | − | 0.649303i | ||||||
\(966\) | −1.76223e9 | + | 4.40953e8i | −0.0628988 | + | 0.0157388i | ||||
\(967\) | − | 4.26740e10i | − | 1.51765i | −0.651296 | − | 0.758824i | \(-0.725774\pi\) | ||
0.651296 | − | 0.758824i | \(-0.274226\pi\) | |||||||
\(968\) | −4.04690e9 | + | 3.66244e9i | −0.143403 | + | 0.129780i | ||||
\(969\) | 6.23616e9 | − | 5.33379e9i | 0.220183 | − | 0.188323i | ||||
\(970\) | 6.77464e9 | + | 2.70742e10i | 0.238334 | + | 0.952478i | ||||
\(971\) | 2.37027e10 | 0.830864 | 0.415432 | − | 0.909624i | \(-0.363630\pi\) | ||||
0.415432 | + | 0.909624i | \(0.363630\pi\) | |||||||
\(972\) | −1.28946e10 | + | 6.88415e9i | −0.450378 | + | 0.240446i | ||||
\(973\) | 3.63333e10 | 1.26447 | ||||||||
\(974\) | −9.26598e9 | + | 2.31858e9i | −0.321318 | + | 0.0804017i | ||||
\(975\) | 5.09533e9i | 0.176058i | ||||||||
\(976\) | 3.86300e9 | − | 5.76905e9i | 0.132999 | − | 0.198623i | ||||
\(977\) | − | 2.06467e10i | − | 0.708305i | −0.935188 | − | 0.354152i | \(-0.884769\pi\) | ||
0.935188 | − | 0.354152i | \(-0.115231\pi\) | |||||||
\(978\) | −8.85955e8 | − | 3.54064e9i | −0.0302849 | − | 0.121031i | ||||
\(979\) | −1.49816e10 | −0.510291 | ||||||||
\(980\) | 4.39064e9 | − | 2.34406e9i | 0.149017 | − | 0.0795568i | ||||
\(981\) | 1.47957e10i | 0.500375i | ||||||||
\(982\) | −1.43812e9 | − | 5.74730e9i | −0.0484623 | − | 0.193675i | ||||
\(983\) | −7.69478e9 | −0.258380 | −0.129190 | − | 0.991620i | \(-0.541238\pi\) | ||||
−0.129190 | + | 0.991620i | \(0.541238\pi\) | |||||||
\(984\) | 5.39611e9 | + | 5.96255e9i | 0.180550 | + | 0.199503i | ||||
\(985\) | 1.58983e10 | 0.530058 | ||||||||
\(986\) | 5.92338e8 | + | 2.36722e9i | 0.0196789 | + | 0.0786448i | ||||
\(987\) | 3.03648e9 | 0.100522 | ||||||||
\(988\) | −4.23860e10 | − | 1.65792e10i | −1.39821 | − | 0.546910i | ||||
\(989\) | 1.86720e10 | 0.613766 | ||||||||
\(990\) | −8.30558e9 | − | 3.31925e10i | −0.272049 | − | 1.08722i | ||||
\(991\) | −4.90220e9 | −0.160005 | −0.0800024 | − | 0.996795i | \(-0.525493\pi\) | ||||
−0.0800024 | + | 0.996795i | \(0.525493\pi\) | |||||||
\(992\) | −3.56476e9 | + | 9.92423e9i | −0.115942 | + | 0.322779i | ||||
\(993\) | 5.23351e9 | 0.169618 | ||||||||
\(994\) | 7.51174e9 | + | 3.00200e10i | 0.242598 | + | 0.969522i | ||||
\(995\) | 4.13758e9i | 0.133157i | ||||||||
\(996\) | 2.38400e9 | + | 4.46545e9i | 0.0764538 | + | 0.143205i | ||||
\(997\) | 3.98588e10 | 1.27377 | 0.636885 | − | 0.770959i | \(-0.280223\pi\) | ||||
0.636885 | + | 0.770959i | \(0.280223\pi\) | |||||||
\(998\) | 9.75448e9 | + | 3.89829e10i | 0.310633 | + | 1.24141i | ||||
\(999\) | 1.67575e10i | 0.531778i |
(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 | 76.8.d.a.75.6 | yes | 68 | |
4.3 | odd | 2 | inner | 76.8.d.a.75.64 | yes | 68 | |
19.18 | odd | 2 | inner | 76.8.d.a.75.63 | yes | 68 | |
76.75 | even | 2 | inner | 76.8.d.a.75.5 | ✓ | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.8.d.a.75.5 | ✓ | 68 | 76.75 | even | 2 | inner | |
76.8.d.a.75.6 | yes | 68 | 1.1 | even | 1 | trivial | |
76.8.d.a.75.63 | yes | 68 | 19.18 | odd | 2 | inner | |
76.8.d.a.75.64 | yes | 68 | 4.3 | odd | 2 | inner |