Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,10,Mod(67,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.67");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(50.4735119441\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 4038x^{4} - 137923x^{3} + 16368349x^{2} - 286546260x + 5038160400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.1 | ||
Root | \(-35.2598 + 61.0717i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.79 |
Dual form | 98.10.c.l.67.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | − | 13.8564i | 0.353553 | − | 0.612372i | ||||
\(3\) | −86.7292 | − | 150.219i | −0.618187 | − | 1.07073i | −0.989816 | − | 0.142350i | \(-0.954534\pi\) |
0.371629 | − | 0.928381i | \(-0.378799\pi\) | |||||||
\(4\) | −128.000 | − | 221.703i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1172.77 | − | 2031.30i | 0.839169 | − | 1.45348i | −0.0514219 | − | 0.998677i | \(-0.516375\pi\) |
0.890591 | − | 0.454806i | \(-0.150291\pi\) | |||||||
\(6\) | −2775.34 | −0.874248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | −5202.42 | + | 9010.85i | −0.264310 | + | 0.457799i | ||||
\(10\) | −18764.4 | − | 32500.9i | −0.593382 | − | 1.02777i | ||||
\(11\) | 35554.8 | + | 61582.8i | 0.732203 | + | 1.26821i | 0.955940 | + | 0.293563i | \(0.0948410\pi\) |
−0.223737 | + | 0.974650i | \(0.571826\pi\) | |||||||
\(12\) | −22202.7 | + | 38456.2i | −0.309093 | + | 0.535366i | ||||
\(13\) | −89420.8 | −0.868347 | −0.434174 | − | 0.900829i | \(-0.642960\pi\) | ||||
−0.434174 | + | 0.900829i | \(0.642960\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −406855. | −2.07505 | ||||||||
\(16\) | −32768.0 | + | 56755.8i | −0.125000 | + | 0.216506i | ||||
\(17\) | 16147.2 | + | 27967.9i | 0.0468898 | + | 0.0812155i | 0.888518 | − | 0.458842i | \(-0.151736\pi\) |
−0.841628 | + | 0.540058i | \(0.818402\pi\) | |||||||
\(18\) | 83238.7 | + | 144174.i | 0.186896 | + | 0.323713i | ||||
\(19\) | −389534. | + | 674693.i | −0.685732 | + | 1.18772i | 0.287475 | + | 0.957788i | \(0.407184\pi\) |
−0.973206 | + | 0.229934i | \(0.926149\pi\) | |||||||
\(20\) | −600460. | −0.839169 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.13775e6 | 1.03549 | ||||||||
\(23\) | −886420. | + | 1.53532e6i | −0.660487 | + | 1.14400i | 0.320001 | + | 0.947417i | \(0.396317\pi\) |
−0.980488 | + | 0.196580i | \(0.937016\pi\) | |||||||
\(24\) | 355243. | + | 615299.i | 0.218562 | + | 0.378561i | ||||
\(25\) | −1.77424e6 | − | 3.07307e6i | −0.908408 | − | 1.57341i | ||||
\(26\) | −715366. | + | 1.23905e6i | −0.307007 | + | 0.531752i | ||||
\(27\) | −1.60938e6 | −0.582801 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −212075. | −0.0556799 | −0.0278399 | − | 0.999612i | \(-0.508863\pi\) | ||||
−0.0278399 | + | 0.999612i | \(0.508863\pi\) | |||||||
\(30\) | −3.25484e6 | + | 5.63755e6i | −0.733642 | + | 1.27071i | ||||
\(31\) | −2.15631e6 | − | 3.73483e6i | −0.419356 | − | 0.726346i | 0.576519 | − | 0.817084i | \(-0.304411\pi\) |
−0.995875 | + | 0.0907380i | \(0.971077\pi\) | |||||||
\(32\) | 524288. | + | 908093.i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 6.16728e6 | − | 1.06821e7i | 0.905277 | − | 1.56799i | ||||
\(34\) | 516712. | 0.0663122 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.66364e6 | 0.264310 | ||||||||
\(37\) | −3.10051e6 | + | 5.37024e6i | −0.271973 | + | 0.471071i | −0.969367 | − | 0.245617i | \(-0.921009\pi\) |
0.697394 | + | 0.716688i | \(0.254343\pi\) | |||||||
\(38\) | 6.23254e6 | + | 1.07951e7i | 0.484886 | + | 0.839846i | ||||
\(39\) | 7.75540e6 | + | 1.34327e7i | 0.536801 | + | 0.929766i | ||||
\(40\) | −4.80368e6 | + | 8.32022e6i | −0.296691 | + | 0.513884i | ||||
\(41\) | −6.40835e6 | −0.354176 | −0.177088 | − | 0.984195i | \(-0.556668\pi\) | ||||
−0.177088 | + | 0.984195i | \(0.556668\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.99951e6 | −0.312219 | −0.156110 | − | 0.987740i | \(-0.549895\pi\) | ||||
−0.156110 | + | 0.987740i | \(0.549895\pi\) | |||||||
\(44\) | 9.10203e6 | − | 1.57652e7i | 0.366101 | − | 0.634106i | ||||
\(45\) | 1.22025e7 | + | 2.11354e7i | 0.443602 | + | 0.768341i | ||||
\(46\) | 1.41827e7 | + | 2.45652e7i | 0.467035 | + | 0.808928i | ||||
\(47\) | −1.75422e7 | + | 3.03840e7i | −0.524377 | + | 0.908248i | 0.475220 | + | 0.879867i | \(0.342368\pi\) |
−0.999597 | + | 0.0283808i | \(0.990965\pi\) | |||||||
\(48\) | 1.13678e7 | 0.309093 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.67755e7 | −1.28468 | ||||||||
\(51\) | 2.80088e6 | − | 4.85126e6i | 0.0579733 | − | 0.100413i | ||||
\(52\) | 1.14459e7 | + | 1.98248e7i | 0.217087 | + | 0.376005i | ||||
\(53\) | 2.13451e7 | + | 3.69707e7i | 0.371583 | + | 0.643601i | 0.989809 | − | 0.142400i | \(-0.0454818\pi\) |
−0.618226 | + | 0.786000i | \(0.712148\pi\) | |||||||
\(54\) | −1.28750e7 | + | 2.23002e7i | −0.206051 | + | 0.356891i | ||||
\(55\) | 1.66791e8 | 2.45777 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.35136e8 | 1.69564 | ||||||||
\(58\) | −1.69660e6 | + | 2.93860e6i | −0.0196858 | + | 0.0340968i | ||||
\(59\) | −1.45327e7 | − | 2.51714e7i | −0.156139 | − | 0.270441i | 0.777334 | − | 0.629088i | \(-0.216572\pi\) |
−0.933473 | + | 0.358647i | \(0.883238\pi\) | |||||||
\(60\) | 5.20775e7 | + | 9.02008e7i | 0.518763 | + | 0.898524i | ||||
\(61\) | 3.09391e7 | − | 5.35880e7i | 0.286103 | − | 0.495546i | −0.686773 | − | 0.726872i | \(-0.740973\pi\) |
0.972876 | + | 0.231327i | \(0.0743066\pi\) | |||||||
\(62\) | −6.90018e7 | −0.593059 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | −1.04870e8 | + | 1.81641e8i | −0.728690 | + | 1.26213i | ||||
\(66\) | −9.86766e7 | − | 1.70913e8i | −0.640127 | − | 1.10873i | ||||
\(67\) | −1.00325e8 | − | 1.73767e8i | −0.608234 | − | 1.05349i | −0.991531 | − | 0.129867i | \(-0.958545\pi\) |
0.383297 | − | 0.923625i | \(-0.374789\pi\) | |||||||
\(68\) | 4.13370e6 | − | 7.15977e6i | 0.0234449 | − | 0.0406078i | ||||
\(69\) | 3.07514e8 | 1.63322 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.03014e7 | 0.141514 | 0.0707571 | − | 0.997494i | \(-0.477458\pi\) | ||||
0.0707571 | + | 0.997494i | \(0.477458\pi\) | |||||||
\(72\) | 2.13091e7 | − | 3.69085e7i | 0.0934478 | − | 0.161856i | ||||
\(73\) | −1.45923e8 | − | 2.52746e8i | −0.601411 | − | 1.04167i | −0.992608 | − | 0.121367i | \(-0.961272\pi\) |
0.391197 | − | 0.920307i | \(-0.372061\pi\) | |||||||
\(74\) | 4.96082e7 | + | 8.59239e7i | 0.192314 | + | 0.333097i | ||||
\(75\) | −3.07756e8 | + | 5.33049e8i | −1.12313 | + | 1.94532i | ||||
\(76\) | 1.99441e8 | 0.685732 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.48173e8 | 0.759151 | ||||||||
\(79\) | 5.44357e7 | − | 9.42854e7i | 0.157240 | − | 0.272347i | −0.776633 | − | 0.629954i | \(-0.783074\pi\) |
0.933872 | + | 0.357607i | \(0.116407\pi\) | |||||||
\(80\) | 7.68589e7 | + | 1.33124e8i | 0.209792 | + | 0.363371i | ||||
\(81\) | 2.41979e8 | + | 4.19120e8i | 0.624590 | + | 1.08182i | ||||
\(82\) | −5.12668e7 | + | 8.87966e7i | −0.125220 | + | 0.216887i | ||||
\(83\) | −2.16661e8 | −0.501106 | −0.250553 | − | 0.968103i | \(-0.580612\pi\) | ||||
−0.250553 | + | 0.968103i | \(0.580612\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.57483e7 | 0.157394 | ||||||||
\(86\) | −5.59961e7 | + | 9.69880e7i | −0.110386 | + | 0.191194i | ||||
\(87\) | 1.83931e7 | + | 3.18578e7i | 0.0344206 | + | 0.0596182i | ||||
\(88\) | −1.45633e8 | − | 2.52243e8i | −0.258873 | − | 0.448381i | ||||
\(89\) | −9.32523e7 | + | 1.61518e8i | −0.157545 | + | 0.272876i | −0.933983 | − | 0.357318i | \(-0.883691\pi\) |
0.776438 | + | 0.630194i | \(0.217025\pi\) | |||||||
\(90\) | 3.90481e8 | 0.627348 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.53847e8 | 0.660487 | ||||||||
\(93\) | −3.74030e8 | + | 6.47838e8i | −0.518481 | + | 0.898035i | ||||
\(94\) | 2.80675e8 | + | 4.86144e8i | 0.370791 | + | 0.642228i | ||||
\(95\) | 9.13671e8 | + | 1.58252e9i | 1.15089 | + | 1.99340i | ||||
\(96\) | 9.09422e7 | − | 1.57516e8i | 0.109281 | − | 0.189280i | ||||
\(97\) | 9.53814e8 | 1.09393 | 0.546966 | − | 0.837155i | \(-0.315783\pi\) | ||||
0.546966 | + | 0.837155i | \(0.315783\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.39884e8 | −0.774115 | ||||||||
\(100\) | −4.54204e8 | + | 7.86705e8i | −0.454204 | + | 0.786705i | ||||
\(101\) | −9.73745e8 | − | 1.68657e9i | −0.931105 | − | 1.61272i | −0.781436 | − | 0.623986i | \(-0.785512\pi\) |
−0.149670 | − | 0.988736i | \(-0.547821\pi\) | |||||||
\(102\) | −4.48140e7 | − | 7.76202e7i | −0.0409933 | − | 0.0710025i | ||||
\(103\) | −6.91594e8 | + | 1.19788e9i | −0.605458 | + | 1.04868i | 0.386521 | + | 0.922281i | \(0.373677\pi\) |
−0.991979 | + | 0.126403i | \(0.959657\pi\) | |||||||
\(104\) | 3.66268e8 | 0.307007 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.83042e8 | 0.525498 | ||||||||
\(107\) | 9.59157e8 | − | 1.66131e9i | 0.707396 | − | 1.22525i | −0.258424 | − | 0.966032i | \(-0.583203\pi\) |
0.965820 | − | 0.259214i | \(-0.0834636\pi\) | |||||||
\(108\) | 2.06000e8 | + | 3.56803e8i | 0.145700 | + | 0.252360i | ||||
\(109\) | −9.42525e8 | − | 1.63250e9i | −0.639548 | − | 1.10773i | −0.985532 | − | 0.169490i | \(-0.945788\pi\) |
0.345983 | − | 0.938241i | \(-0.387545\pi\) | |||||||
\(110\) | 1.33433e9 | − | 2.31113e9i | 0.868952 | − | 1.50507i | ||||
\(111\) | 1.07562e9 | 0.672520 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.65917e9 | −0.957277 | −0.478639 | − | 0.878012i | \(-0.658870\pi\) | ||||
−0.478639 | + | 0.878012i | \(0.658870\pi\) | |||||||
\(114\) | 1.08109e9 | − | 1.87250e9i | 0.599500 | − | 1.03836i | ||||
\(115\) | 2.07914e9 | + | 3.60118e9i | 1.10852 | + | 1.92001i | ||||
\(116\) | 2.71456e7 | + | 4.70175e7i | 0.0139200 | + | 0.0241101i | ||||
\(117\) | 4.65204e8 | − | 8.05758e8i | 0.229513 | − | 0.397528i | ||||
\(118\) | −4.65046e8 | −0.220814 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.66648e9 | 0.733642 | ||||||||
\(121\) | −1.34932e9 | + | 2.33709e9i | −0.572242 | + | 0.991152i | ||||
\(122\) | −4.95025e8 | − | 8.57409e8i | −0.202306 | − | 0.350404i | ||||
\(123\) | 5.55791e8 | + | 9.62658e8i | 0.218947 | + | 0.379227i | ||||
\(124\) | −5.52014e8 | + | 9.56117e8i | −0.209678 | + | 0.363173i | ||||
\(125\) | −3.74196e9 | −1.37089 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.50752e9 | −0.855319 | −0.427659 | − | 0.903940i | \(-0.640662\pi\) | ||||
−0.427659 | + | 0.903940i | \(0.640662\pi\) | |||||||
\(128\) | 1.34218e8 | − | 2.32472e8i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 6.07062e8 | + | 1.05146e9i | 0.193010 | + | 0.334303i | ||||
\(130\) | 1.67793e9 | + | 2.90625e9i | 0.515261 | + | 0.892459i | ||||
\(131\) | −1.52573e9 | + | 2.64265e9i | −0.452645 | + | 0.784004i | −0.998549 | − | 0.0538433i | \(-0.982853\pi\) |
0.545904 | + | 0.837848i | \(0.316186\pi\) | |||||||
\(132\) | −3.15765e9 | −0.905277 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.21039e9 | −0.860173 | ||||||||
\(135\) | −1.88743e9 | + | 3.26913e9i | −0.489069 | + | 0.847092i | ||||
\(136\) | −6.61391e7 | − | 1.14556e8i | −0.0165780 | − | 0.0287140i | ||||
\(137\) | −3.65274e9 | − | 6.32673e9i | −0.885882 | − | 1.53439i | −0.844699 | − | 0.535242i | \(-0.820221\pi\) |
−0.0411834 | − | 0.999152i | \(-0.513113\pi\) | |||||||
\(138\) | 2.46011e9 | − | 4.26104e9i | 0.577430 | − | 1.00014i | ||||
\(139\) | −2.79289e9 | −0.634581 | −0.317290 | − | 0.948328i | \(-0.602773\pi\) | ||||
−0.317290 | + | 0.948328i | \(0.602773\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.08569e9 | 1.29665 | ||||||||
\(142\) | 2.42411e8 | − | 4.19868e8i | 0.0500328 | − | 0.0866594i | ||||
\(143\) | −3.17934e9 | − | 5.50678e9i | −0.635806 | − | 1.10125i | ||||
\(144\) | −3.40946e8 | − | 5.90535e8i | −0.0660776 | − | 0.114450i | ||||
\(145\) | −2.48716e8 | + | 4.30789e8i | −0.0467248 | + | 0.0809298i | ||||
\(146\) | −4.66954e9 | −0.850523 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.58746e9 | 0.271973 | ||||||||
\(149\) | 1.26713e9 | − | 2.19473e9i | 0.210611 | − | 0.364789i | −0.741295 | − | 0.671180i | \(-0.765788\pi\) |
0.951906 | + | 0.306390i | \(0.0991212\pi\) | |||||||
\(150\) | 4.92410e9 | + | 8.52879e9i | 0.794175 | + | 1.37555i | ||||
\(151\) | −1.55428e9 | − | 2.69210e9i | −0.243295 | − | 0.421400i | 0.718356 | − | 0.695676i | \(-0.244895\pi\) |
−0.961651 | + | 0.274276i | \(0.911562\pi\) | |||||||
\(152\) | 1.59553e9 | − | 2.76354e9i | 0.242443 | − | 0.419923i | ||||
\(153\) | −3.36019e8 | −0.0495738 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.01154e10 | −1.40764 | ||||||||
\(156\) | 1.98538e9 | − | 3.43878e9i | 0.268400 | − | 0.464883i | ||||
\(157\) | −5.81990e9 | − | 1.00804e10i | −0.764481 | − | 1.32412i | −0.940520 | − | 0.339737i | \(-0.889662\pi\) |
0.176039 | − | 0.984383i | \(-0.443671\pi\) | |||||||
\(158\) | −8.70971e8 | − | 1.50857e9i | −0.111185 | − | 0.192578i | ||||
\(159\) | 3.70248e9 | − | 6.41288e9i | 0.459415 | − | 0.795731i | ||||
\(160\) | 2.45949e9 | 0.296691 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.74333e9 | 0.883304 | ||||||||
\(163\) | 6.18632e9 | − | 1.07150e10i | 0.686417 | − | 1.18891i | −0.286572 | − | 0.958059i | \(-0.592516\pi\) |
0.972989 | − | 0.230851i | \(-0.0741510\pi\) | |||||||
\(164\) | 8.20268e8 | + | 1.42075e9i | 0.0885439 | + | 0.153363i | ||||
\(165\) | −1.44657e10 | − | 2.50553e10i | −1.51936 | − | 2.63161i | ||||
\(166\) | −1.73329e9 | + | 3.00215e9i | −0.177168 | + | 0.306864i | ||||
\(167\) | −6.26181e9 | −0.622982 | −0.311491 | − | 0.950249i | \(-0.600828\pi\) | ||||
−0.311491 | + | 0.950249i | \(0.600828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.60842e9 | −0.245973 | ||||||||
\(170\) | 6.05986e8 | − | 1.04960e9i | 0.0556471 | − | 0.0963836i | ||||
\(171\) | −4.05304e9 | − | 7.02007e9i | −0.362492 | − | 0.627854i | ||||
\(172\) | 8.95937e8 | + | 1.55181e9i | 0.0780548 | + | 0.135195i | ||||
\(173\) | −4.39565e8 | + | 7.61348e8i | −0.0373091 | + | 0.0646213i | −0.884077 | − | 0.467341i | \(-0.845212\pi\) |
0.846768 | + | 0.531963i | \(0.178545\pi\) | |||||||
\(174\) | 5.88579e8 | 0.0486780 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.66024e9 | −0.366101 | ||||||||
\(177\) | −2.52082e9 | + | 4.36619e9i | −0.193047 | + | 0.334367i | ||||
\(178\) | 1.49204e9 | + | 2.58428e9i | 0.111401 | + | 0.192952i | ||||
\(179\) | 8.36715e9 | + | 1.44923e10i | 0.609170 | + | 1.05511i | 0.991377 | + | 0.131037i | \(0.0418308\pi\) |
−0.382207 | + | 0.924077i | \(0.624836\pi\) | |||||||
\(180\) | 3.12385e9 | − | 5.41066e9i | 0.221801 | − | 0.384170i | ||||
\(181\) | 3.33844e9 | 0.231201 | 0.115601 | − | 0.993296i | \(-0.463121\pi\) | ||||
0.115601 | + | 0.993296i | \(0.463121\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.07333e10 | −0.707462 | ||||||||
\(184\) | 3.63078e9 | − | 6.28869e9i | 0.233517 | − | 0.404464i | ||||
\(185\) | 7.27240e9 | + | 1.25962e10i | 0.456462 | + | 0.790616i | ||||
\(186\) | 5.98447e9 | + | 1.03654e10i | 0.366621 | + | 0.635007i | ||||
\(187\) | −1.14823e9 | + | 1.98878e9i | −0.0686657 | + | 0.118932i | ||||
\(188\) | 8.98161e9 | 0.524377 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.92375e10 | 1.62760 | ||||||||
\(191\) | 5.89031e9 | − | 1.02023e10i | 0.320249 | − | 0.554688i | −0.660290 | − | 0.751011i | \(-0.729567\pi\) |
0.980539 | + | 0.196323i | \(0.0629000\pi\) | |||||||
\(192\) | −1.45508e9 | − | 2.52026e9i | −0.0772734 | − | 0.133841i | ||||
\(193\) | 1.60936e10 | + | 2.78750e10i | 0.834923 | + | 1.44613i | 0.894093 | + | 0.447881i | \(0.147821\pi\) |
−0.0591699 | + | 0.998248i | \(0.518845\pi\) | |||||||
\(194\) | 7.63051e9 | − | 1.32164e10i | 0.386764 | − | 0.669894i | ||||
\(195\) | 3.63813e10 | 1.80187 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.41075e10 | −1.14039 | −0.570195 | − | 0.821509i | \(-0.693132\pi\) | ||||
−0.570195 | + | 0.821509i | \(0.693132\pi\) | |||||||
\(198\) | −5.91908e9 | + | 1.02521e10i | −0.273691 | + | 0.474047i | ||||
\(199\) | 5.72788e9 | + | 9.92098e9i | 0.258914 | + | 0.448452i | 0.965951 | − | 0.258724i | \(-0.0833021\pi\) |
−0.707037 | + | 0.707176i | \(0.749969\pi\) | |||||||
\(200\) | 7.26727e9 | + | 1.25873e10i | 0.321171 | + | 0.556284i | ||||
\(201\) | −1.74022e10 | + | 3.01414e10i | −0.752005 | + | 1.30251i | ||||
\(202\) | −3.11598e10 | −1.31678 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.43405e9 | −0.0579733 | ||||||||
\(205\) | −7.51554e9 | + | 1.30173e10i | −0.297213 | + | 0.514788i | ||||
\(206\) | 1.10655e10 | + | 1.91660e10i | 0.428123 | + | 0.741531i | ||||
\(207\) | −9.22306e9 | − | 1.59748e10i | −0.349147 | − | 0.604740i | ||||
\(208\) | 2.93014e9 | − | 5.07515e9i | 0.108543 | − | 0.188003i | ||||
\(209\) | −5.53993e10 | −2.00838 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.03945e10 | 0.708339 | 0.354169 | − | 0.935181i | \(-0.384764\pi\) | ||||
0.354169 | + | 0.935181i | \(0.384764\pi\) | |||||||
\(212\) | 5.46433e9 | − | 9.46450e9i | 0.185791 | − | 0.321800i | ||||
\(213\) | −2.62802e9 | − | 4.55186e9i | −0.0874822 | − | 0.151524i | ||||
\(214\) | −1.53465e10 | − | 2.65809e10i | −0.500205 | − | 0.866380i | ||||
\(215\) | −8.20884e9 | + | 1.42181e10i | −0.262005 | + | 0.453805i | ||||
\(216\) | 6.59200e9 | 0.206051 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.01608e10 | −0.904458 | ||||||||
\(219\) | −2.53116e10 | + | 4.38410e10i | −0.743568 | + | 1.28790i | ||||
\(220\) | −2.13493e10 | − | 3.69780e10i | −0.614442 | − | 1.06424i | ||||
\(221\) | −1.44390e9 | − | 2.50091e9i | −0.0407166 | − | 0.0705233i | ||||
\(222\) | 8.60496e9 | − | 1.49042e10i | 0.237772 | − | 0.411833i | ||||
\(223\) | 5.72310e10 | 1.54974 | 0.774871 | − | 0.632119i | \(-0.217815\pi\) | ||||
0.774871 | + | 0.632119i | \(0.217815\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.69213e10 | 0.960407 | ||||||||
\(226\) | −1.32734e10 | + | 2.29901e10i | −0.338449 | + | 0.586210i | ||||
\(227\) | 7.62484e9 | + | 1.32066e10i | 0.190596 | + | 0.330122i | 0.945448 | − | 0.325773i | \(-0.105625\pi\) |
−0.754852 | + | 0.655895i | \(0.772291\pi\) | |||||||
\(228\) | −1.72974e10 | − | 2.99600e10i | −0.423910 | − | 0.734234i | ||||
\(229\) | −1.74014e10 | + | 3.01402e10i | −0.418144 | + | 0.724246i | −0.995753 | − | 0.0920674i | \(-0.970652\pi\) |
0.577609 | + | 0.816313i | \(0.303986\pi\) | |||||||
\(230\) | 6.65325e10 | 1.56768 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.68659e8 | 0.0196858 | ||||||||
\(233\) | −3.71391e10 | + | 6.43268e10i | −0.825524 | + | 1.42985i | 0.0759945 | + | 0.997108i | \(0.475787\pi\) |
−0.901518 | + | 0.432741i | \(0.857546\pi\) | |||||||
\(234\) | −7.44327e9 | − | 1.28921e10i | −0.162290 | − | 0.281095i | ||||
\(235\) | 4.11461e10 | + | 7.12671e10i | 0.880082 | + | 1.52435i | ||||
\(236\) | −3.72037e9 | + | 6.44387e9i | −0.0780697 | + | 0.135221i | ||||
\(237\) | −1.88847e10 | −0.388814 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.12890e10 | 1.21504 | 0.607522 | − | 0.794303i | \(-0.292164\pi\) | ||||
0.607522 | + | 0.794303i | \(0.292164\pi\) | |||||||
\(240\) | 1.33318e10 | − | 2.30914e10i | 0.259382 | − | 0.449262i | ||||
\(241\) | −2.14369e10 | − | 3.71299e10i | −0.409342 | − | 0.709001i | 0.585474 | − | 0.810691i | \(-0.300908\pi\) |
−0.994816 | + | 0.101690i | \(0.967575\pi\) | |||||||
\(242\) | 2.15891e10 | + | 3.73934e10i | 0.404636 | + | 0.700851i | ||||
\(243\) | 2.61347e10 | − | 4.52666e10i | 0.480827 | − | 0.832816i | ||||
\(244\) | −1.58408e10 | −0.286103 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.77853e10 | 0.309637 | ||||||||
\(247\) | 3.48324e10 | − | 6.03315e10i | 0.595453 | − | 1.03136i | ||||
\(248\) | 8.83223e9 | + | 1.52979e10i | 0.148265 | + | 0.256802i | ||||
\(249\) | 1.87909e10 | + | 3.25467e10i | 0.309777 | + | 0.536550i | ||||
\(250\) | −2.99357e10 | + | 5.18501e10i | −0.484684 | + | 0.839498i | ||||
\(251\) | 2.70921e10 | 0.430835 | 0.215417 | − | 0.976522i | \(-0.430889\pi\) | ||||
0.215417 | + | 0.976522i | \(0.430889\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.26066e11 | −1.93444 | ||||||||
\(254\) | −2.00602e10 | + | 3.47452e10i | −0.302401 | + | 0.523774i | ||||
\(255\) | −6.56959e9 | − | 1.13789e10i | −0.0972988 | − | 0.168526i | ||||
\(256\) | −2.14748e9 | − | 3.71955e9i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −4.17372e10 | + | 7.22909e10i | −0.596793 | + | 1.03368i | 0.396498 | + | 0.918036i | \(0.370225\pi\) |
−0.993291 | + | 0.115641i | \(0.963108\pi\) | |||||||
\(258\) | 1.94260e10 | 0.272957 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.36936e10 | 0.728690 | ||||||||
\(261\) | 1.10330e9 | − | 1.91098e9i | 0.0147168 | − | 0.0254902i | ||||
\(262\) | 2.44117e10 | + | 4.22824e10i | 0.320068 | + | 0.554375i | ||||
\(263\) | −2.51663e10 | − | 4.35893e10i | −0.324354 | − | 0.561797i | 0.657028 | − | 0.753866i | \(-0.271813\pi\) |
−0.981381 | + | 0.192070i | \(0.938480\pi\) | |||||||
\(264\) | −2.52612e10 | + | 4.37537e10i | −0.320064 | + | 0.554366i | ||||
\(265\) | 1.00132e11 | 1.24728 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.23508e10 | 0.389569 | ||||||||
\(268\) | −2.56831e10 | + | 4.44844e10i | −0.304117 | + | 0.526746i | ||||
\(269\) | 1.64843e10 | + | 2.85517e10i | 0.191949 | + | 0.332466i | 0.945896 | − | 0.324470i | \(-0.105186\pi\) |
−0.753947 | + | 0.656935i | \(0.771852\pi\) | |||||||
\(270\) | 3.01989e10 | + | 5.23061e10i | 0.345824 | + | 0.598984i | ||||
\(271\) | 1.18673e10 | − | 2.05547e10i | 0.133656 | − | 0.231499i | −0.791427 | − | 0.611263i | \(-0.790662\pi\) |
0.925083 | + | 0.379764i | \(0.123995\pi\) | |||||||
\(272\) | −2.11645e9 | −0.0234449 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.16888e11 | −1.25283 | ||||||||
\(275\) | 1.26165e11 | − | 2.18525e11i | 1.33028 | − | 2.30411i | ||||
\(276\) | −3.93618e10 | − | 6.81767e10i | −0.408305 | − | 0.707204i | ||||
\(277\) | 4.15751e10 | + | 7.20101e10i | 0.424301 | + | 0.734911i | 0.996355 | − | 0.0853053i | \(-0.0271866\pi\) |
−0.572054 | + | 0.820216i | \(0.693853\pi\) | |||||||
\(278\) | −2.23431e10 | + | 3.86994e10i | −0.224358 | + | 0.388600i | ||||
\(279\) | 4.48720e10 | 0.443360 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.48862e11 | 1.42431 | 0.712154 | − | 0.702023i | \(-0.247720\pi\) | ||||
0.712154 | + | 0.702023i | \(0.247720\pi\) | |||||||
\(282\) | 4.86855e10 | − | 8.43257e10i | 0.458436 | − | 0.794034i | ||||
\(283\) | 2.96776e10 | + | 5.14031e10i | 0.275036 | + | 0.476377i | 0.970144 | − | 0.242529i | \(-0.0779769\pi\) |
−0.695108 | + | 0.718905i | \(0.744644\pi\) | |||||||
\(284\) | −3.87858e9 | − | 6.71789e9i | −0.0353785 | − | 0.0612774i | ||||
\(285\) | 1.58484e11 | − | 2.74502e11i | 1.42293 | − | 2.46459i | ||||
\(286\) | −1.01739e11 | −0.899166 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.09103e10 | −0.0934478 | ||||||||
\(289\) | 5.87725e10 | − | 1.01797e11i | 0.495603 | − | 0.858409i | ||||
\(290\) | 3.97946e9 | + | 6.89262e9i | 0.0330394 | + | 0.0572260i | ||||
\(291\) | −8.27235e10 | − | 1.43281e11i | −0.676255 | − | 1.17131i | ||||
\(292\) | −3.73563e10 | + | 6.47030e10i | −0.300705 | + | 0.520837i | ||||
\(293\) | −9.10565e10 | −0.721783 | −0.360892 | − | 0.932608i | \(-0.617528\pi\) | ||||
−0.360892 | + | 0.932608i | \(0.617528\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.81743e10 | −0.524109 | ||||||||
\(296\) | 1.26997e10 | − | 2.19965e10i | 0.0961569 | − | 0.166549i | ||||
\(297\) | −5.72211e10 | − | 9.91098e10i | −0.426729 | − | 0.739116i | ||||
\(298\) | −2.02740e10 | − | 3.51156e10i | −0.148925 | − | 0.257945i | ||||
\(299\) | 7.92644e10 | − | 1.37290e11i | 0.573532 | − | 0.993387i | ||||
\(300\) | 1.57571e11 | 1.12313 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4.97370e10 | −0.344071 | ||||||||
\(303\) | −1.68904e11 | + | 2.92551e11i | −1.15119 | + | 1.99393i | ||||
\(304\) | −2.55285e10 | − | 4.42167e10i | −0.171433 | − | 0.296931i | ||||
\(305\) | −7.25691e10 | − | 1.25693e11i | −0.480178 | − | 0.831693i | ||||
\(306\) | −2.68815e9 | + | 4.65602e9i | −0.0175270 | + | 0.0303576i | ||||
\(307\) | −6.61649e10 | −0.425114 | −0.212557 | − | 0.977149i | \(-0.568179\pi\) | ||||
−0.212557 | + | 0.977149i | \(0.568179\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.39926e11 | 1.49714 | ||||||||
\(310\) | −8.09235e10 | + | 1.40164e11i | −0.497676 | + | 0.862001i | ||||
\(311\) | 4.42158e9 | + | 7.65840e9i | 0.0268013 | + | 0.0464212i | 0.879115 | − | 0.476610i | \(-0.158135\pi\) |
−0.852314 | + | 0.523031i | \(0.824801\pi\) | |||||||
\(312\) | −3.17661e10 | − | 5.50205e10i | −0.189788 | − | 0.328722i | ||||
\(313\) | 7.90785e9 | − | 1.36968e10i | 0.0465703 | − | 0.0806621i | −0.841801 | − | 0.539789i | \(-0.818504\pi\) |
0.888371 | + | 0.459126i | \(0.151838\pi\) | |||||||
\(314\) | −1.86237e11 | −1.08114 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.78711e10 | −0.157240 | ||||||||
\(317\) | −1.07701e11 | + | 1.86544e11i | −0.599039 | + | 1.03757i | 0.393924 | + | 0.919143i | \(0.371117\pi\) |
−0.992963 | + | 0.118423i | \(0.962216\pi\) | |||||||
\(318\) | −5.92397e10 | − | 1.02606e11i | −0.324856 | − | 0.562667i | ||||
\(319\) | −7.54029e9 | − | 1.30602e10i | −0.0407690 | − | 0.0706139i | ||||
\(320\) | 1.96759e10 | − | 3.40796e10i | 0.104896 | − | 0.181685i | ||||
\(321\) | −3.32748e11 | −1.74921 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.51596e10 | −0.128615 | ||||||||
\(324\) | 6.19467e10 | − | 1.07295e11i | 0.312295 | − | 0.540911i | ||||
\(325\) | 1.58653e11 | + | 2.74796e11i | 0.788814 | + | 1.36627i | ||||
\(326\) | −9.89812e10 | − | 1.71440e11i | −0.485370 | − | 0.840686i | ||||
\(327\) | −1.63489e11 | + | 2.83171e11i | −0.790721 | + | 1.36957i | ||||
\(328\) | 2.62486e10 | 0.125220 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.62901e11 | −2.14870 | ||||||||
\(331\) | 2.01566e10 | − | 3.49123e10i | 0.0922980 | − | 0.159865i | −0.816180 | − | 0.577798i | \(-0.803912\pi\) |
0.908478 | + | 0.417933i | \(0.137245\pi\) | |||||||
\(332\) | 2.77326e10 | + | 4.80343e10i | 0.125277 | + | 0.216985i | ||||
\(333\) | −3.22603e10 | − | 5.58765e10i | −0.143770 | − | 0.249018i | ||||
\(334\) | −5.00945e10 | + | 8.67662e10i | −0.220258 | + | 0.381497i | ||||
\(335\) | −4.70632e11 | −2.04164 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.47587e11 | −0.623324 | −0.311662 | − | 0.950193i | \(-0.600886\pi\) | ||||
−0.311662 | + | 0.950193i | \(0.600886\pi\) | |||||||
\(338\) | −2.08674e10 | + | 3.61434e10i | −0.0869647 | + | 0.150627i | ||||
\(339\) | 1.43898e11 | + | 2.49239e11i | 0.591776 | + | 1.02499i | ||||
\(340\) | −9.69578e9 | − | 1.67936e10i | −0.0393485 | − | 0.0681535i | ||||
\(341\) | 1.53334e11 | − | 2.65583e11i | 0.614107 | − | 1.06367i | ||||
\(342\) | −1.29697e11 | −0.512641 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.86700e10 | 0.110386 | ||||||||
\(345\) | 3.60645e11 | − | 6.24655e11i | 1.37055 | − | 2.37385i | ||||
\(346\) | 7.03303e9 | + | 1.21816e10i | 0.0263816 | + | 0.0456942i | ||||
\(347\) | 1.95063e11 | + | 3.37860e11i | 0.722259 | + | 1.25099i | 0.960092 | + | 0.279683i | \(0.0902295\pi\) |
−0.237833 | + | 0.971306i | \(0.576437\pi\) | |||||||
\(348\) | 4.70863e9 | − | 8.15559e9i | 0.0172103 | − | 0.0298091i | ||||
\(349\) | 2.60554e10 | 0.0940119 | 0.0470059 | − | 0.998895i | \(-0.485032\pi\) | ||||
0.0470059 | + | 0.998895i | \(0.485032\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.43912e11 | 0.506074 | ||||||||
\(352\) | −3.72819e10 | + | 6.45742e10i | −0.129436 | + | 0.224190i | ||||
\(353\) | 3.75792e10 | + | 6.50892e10i | 0.128814 | + | 0.223112i | 0.923217 | − | 0.384279i | \(-0.125550\pi\) |
−0.794404 | + | 0.607390i | \(0.792216\pi\) | |||||||
\(354\) | 4.03331e10 | + | 6.98590e10i | 0.136505 | + | 0.236433i | ||||
\(355\) | 3.55367e10 | − | 6.15513e10i | 0.118754 | − | 0.205688i | ||||
\(356\) | 4.77452e10 | 0.157545 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.67749e11 | 0.861497 | ||||||||
\(359\) | −1.43619e11 | + | 2.48755e11i | −0.456338 | + | 0.790400i | −0.998764 | − | 0.0497032i | \(-0.984172\pi\) |
0.542426 | + | 0.840103i | \(0.317506\pi\) | |||||||
\(360\) | −4.99815e10 | − | 8.65706e10i | −0.156837 | − | 0.271650i | ||||
\(361\) | −1.42130e11 | − | 2.46176e11i | −0.440456 | − | 0.762892i | ||||
\(362\) | 2.67075e10 | − | 4.62588e10i | 0.0817420 | − | 0.141581i | ||||
\(363\) | 4.68101e11 | 1.41501 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.84539e11 | −2.01874 | ||||||||
\(366\) | −8.58663e10 | + | 1.48725e11i | −0.250125 | + | 0.433230i | ||||
\(367\) | −2.54453e11 | − | 4.40726e11i | −0.732168 | − | 1.26815i | −0.955955 | − | 0.293514i | \(-0.905175\pi\) |
0.223787 | − | 0.974638i | \(-0.428158\pi\) | |||||||
\(368\) | −5.80924e10 | − | 1.00619e11i | −0.165122 | − | 0.285999i | ||||
\(369\) | 3.33389e10 | − | 5.77447e10i | 0.0936122 | − | 0.162141i | ||||
\(370\) | 2.32717e11 | 0.645535 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.91503e11 | 0.518481 | ||||||||
\(373\) | −5.17260e10 | + | 8.95921e10i | −0.138363 | + | 0.239651i | −0.926877 | − | 0.375365i | \(-0.877517\pi\) |
0.788514 | + | 0.615016i | \(0.210851\pi\) | |||||||
\(374\) | 1.83716e10 | + | 3.18205e10i | 0.0485540 | + | 0.0840980i | ||||
\(375\) | 3.24537e11 | + | 5.62115e11i | 0.847469 | + | 1.46786i | ||||
\(376\) | 7.18528e10 | − | 1.24453e11i | 0.185395 | − | 0.321114i | ||||
\(377\) | 1.89639e10 | 0.0483495 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.10894e11 | 0.276078 | 0.138039 | − | 0.990427i | \(-0.455920\pi\) | ||||
0.138039 | + | 0.990427i | \(0.455920\pi\) | |||||||
\(380\) | 2.33900e11 | − | 4.05126e11i | 0.575445 | − | 0.996699i | ||||
\(381\) | 2.17475e11 | + | 3.76679e11i | 0.528747 | + | 0.915817i | ||||
\(382\) | −9.42450e10 | − | 1.63237e11i | −0.226450 | − | 0.392224i | ||||
\(383\) | 1.29972e11 | − | 2.25118e11i | 0.308642 | − | 0.534584i | −0.669424 | − | 0.742881i | \(-0.733459\pi\) |
0.978066 | + | 0.208297i | \(0.0667922\pi\) | |||||||
\(384\) | −4.65624e10 | −0.109281 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.14997e11 | 1.18076 | ||||||||
\(387\) | 3.64144e10 | − | 6.30716e10i | 0.0825227 | − | 0.142934i | ||||
\(388\) | −1.22088e11 | − | 2.11463e11i | −0.273483 | − | 0.473687i | ||||
\(389\) | −2.91278e11 | − | 5.04508e11i | −0.644963 | − | 1.11711i | −0.984310 | − | 0.176447i | \(-0.943540\pi\) |
0.339347 | − | 0.940661i | \(-0.389794\pi\) | |||||||
\(390\) | 2.91050e11 | − | 5.04114e11i | 0.637056 | − | 1.10341i | ||||
\(391\) | −5.72530e10 | −0.123880 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.29303e11 | 1.11928 | ||||||||
\(394\) | −1.92860e11 | + | 3.34043e11i | −0.403189 | + | 0.698343i | ||||
\(395\) | −1.27682e11 | − | 2.21151e11i | −0.263901 | − | 0.457090i | ||||
\(396\) | 9.47052e10 | + | 1.64034e11i | 0.193529 | + | 0.335202i | ||||
\(397\) | −9.35365e10 | + | 1.62010e11i | −0.188983 | + | 0.327329i | −0.944912 | − | 0.327326i | \(-0.893853\pi\) |
0.755928 | + | 0.654655i | \(0.227186\pi\) | |||||||
\(398\) | 1.83292e11 | 0.366159 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.32553e11 | 0.454204 | ||||||||
\(401\) | 4.41371e11 | − | 7.64477e11i | 0.852420 | − | 1.47644i | −0.0265971 | − | 0.999646i | \(-0.508467\pi\) |
0.879018 | − | 0.476789i | \(-0.158200\pi\) | |||||||
\(402\) | 2.78434e11 | + | 4.82263e11i | 0.531748 | + | 0.921014i | ||||
\(403\) | 1.92819e11 | + | 3.33972e11i | 0.364147 | + | 0.630720i | ||||
\(404\) | −2.49279e11 | + | 4.31763e11i | −0.465553 | + | 0.806361i | ||||
\(405\) | 1.13515e12 | 2.09655 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.40953e11 | −0.796557 | ||||||||
\(408\) | −1.14724e10 | + | 1.98708e10i | −0.0204967 | + | 0.0355013i | ||||
\(409\) | −1.97162e11 | − | 3.41495e11i | −0.348393 | − | 0.603434i | 0.637571 | − | 0.770391i | \(-0.279939\pi\) |
−0.985964 | + | 0.166957i | \(0.946606\pi\) | |||||||
\(410\) | 1.20249e11 | + | 2.08277e11i | 0.210161 | + | 0.364010i | ||||
\(411\) | −6.33598e11 | + | 1.09742e12i | −1.09528 | + | 1.89708i | ||||
\(412\) | 3.54096e11 | 0.605458 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.95138e11 | −0.493769 | ||||||||
\(415\) | −2.54095e11 | + | 4.40105e11i | −0.420513 | + | 0.728349i | ||||
\(416\) | −4.68822e10 | − | 8.12024e10i | −0.0767518 | − | 0.132938i | ||||
\(417\) | 2.42225e11 | + | 4.19546e11i | 0.392290 | + | 0.679465i | ||||
\(418\) | −4.43194e11 | + | 7.67635e11i | −0.710069 | + | 1.22988i | ||||
\(419\) | 1.77960e11 | 0.282072 | 0.141036 | − | 0.990004i | \(-0.454957\pi\) | ||||
0.141036 | + | 0.990004i | \(0.454957\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.94445e11 | 0.611952 | 0.305976 | − | 0.952039i | \(-0.401017\pi\) | ||||
0.305976 | + | 0.952039i | \(0.401017\pi\) | |||||||
\(422\) | 1.63156e11 | − | 2.82594e11i | 0.250436 | − | 0.433767i | ||||
\(423\) | −1.82524e11 | − | 3.16140e11i | −0.277196 | − | 0.480118i | ||||
\(424\) | −8.74293e10 | − | 1.51432e11i | −0.131374 | − | 0.227547i | ||||
\(425\) | 5.72980e10 | − | 9.92431e10i | 0.0851902 | − | 0.147554i | ||||
\(426\) | −8.40965e10 | −0.123719 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.91088e11 | −0.707396 | ||||||||
\(429\) | −5.51483e11 | + | 9.55197e11i | −0.786094 | + | 1.36156i | ||||
\(430\) | 1.31341e11 | + | 2.27490e11i | 0.185265 | + | 0.320889i | ||||
\(431\) | −4.03895e11 | − | 6.99567e11i | −0.563795 | − | 0.976521i | −0.997161 | − | 0.0753033i | \(-0.976008\pi\) |
0.433366 | − | 0.901218i | \(-0.357326\pi\) | |||||||
\(432\) | 5.27360e10 | − | 9.13415e10i | 0.0728502 | − | 0.126180i | ||||
\(433\) | −5.77686e11 | −0.789763 | −0.394881 | − | 0.918732i | \(-0.629214\pi\) | ||||
−0.394881 | + | 0.918732i | \(0.629214\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.62838e10 | 0.115539 | ||||||||
\(436\) | −2.41286e11 | + | 4.17920e11i | −0.319774 | + | 0.553865i | ||||
\(437\) | −6.90582e11 | − | 1.19612e12i | −0.905834 | − | 1.56895i | ||||
\(438\) | 4.04985e11 | + | 7.01455e11i | 0.525782 | + | 0.910682i | ||||
\(439\) | −6.64142e11 | + | 1.15033e12i | −0.853436 | + | 1.47819i | 0.0246530 | + | 0.999696i | \(0.492152\pi\) |
−0.878089 | + | 0.478498i | \(0.841181\pi\) | |||||||
\(440\) | −6.83176e11 | −0.868952 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.62048e10 | −0.0575820 | ||||||||
\(443\) | −2.49733e11 | + | 4.32551e11i | −0.308077 | + | 0.533606i | −0.977942 | − | 0.208878i | \(-0.933019\pi\) |
0.669864 | + | 0.742483i | \(0.266352\pi\) | |||||||
\(444\) | −1.37679e11 | − | 2.38468e11i | −0.168130 | − | 0.291210i | ||||
\(445\) | 2.18728e11 | + | 3.78848e11i | 0.264414 | + | 0.457978i | ||||
\(446\) | 4.57848e11 | − | 7.93016e11i | 0.547917 | − | 0.949020i | ||||
\(447\) | −4.39588e11 | −0.520789 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.51211e10 | −0.0523927 | −0.0261964 | − | 0.999657i | \(-0.508340\pi\) | ||||
−0.0261964 | + | 0.999657i | \(0.508340\pi\) | |||||||
\(450\) | 2.95370e11 | − | 5.11596e11i | 0.339555 | − | 0.588127i | ||||
\(451\) | −2.27848e11 | − | 3.94644e11i | −0.259328 | − | 0.449170i | ||||
\(452\) | 2.12374e11 | + | 3.67842e11i | 0.239319 | + | 0.414513i | ||||
\(453\) | −2.69603e11 | + | 4.66967e11i | −0.300804 | + | 0.521008i | ||||
\(454\) | 2.43995e11 | 0.269544 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.53517e11 | −0.599500 | ||||||||
\(457\) | −3.17610e11 | + | 5.50117e11i | −0.340621 | + | 0.589973i | −0.984548 | − | 0.175114i | \(-0.943971\pi\) |
0.643927 | + | 0.765087i | \(0.277304\pi\) | |||||||
\(458\) | 2.78423e11 | + | 4.82243e11i | 0.295672 | + | 0.512119i | ||||
\(459\) | −2.59870e10 | − | 4.50108e10i | −0.0273274 | − | 0.0473325i | ||||
\(460\) | 5.32260e11 | − | 9.21901e11i | 0.554260 | − | 0.960007i | ||||
\(461\) | 1.21010e12 | 1.24786 | 0.623932 | − | 0.781479i | \(-0.285534\pi\) | ||||
0.623932 | + | 0.781479i | \(0.285534\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.73087e11 | 0.984095 | 0.492047 | − | 0.870568i | \(-0.336249\pi\) | ||||
0.492047 | + | 0.870568i | \(0.336249\pi\) | |||||||
\(464\) | 6.94927e9 | − | 1.20365e10i | 0.00695999 | − | 0.0120550i | ||||
\(465\) | 8.77304e11 | + | 1.51954e12i | 0.870186 | + | 1.50721i | ||||
\(466\) | 5.94225e11 | + | 1.02923e12i | 0.583733 | + | 1.01106i | ||||
\(467\) | 8.41530e11 | − | 1.45757e12i | 0.818735 | − | 1.41809i | −0.0878789 | − | 0.996131i | \(-0.528009\pi\) |
0.906614 | − | 0.421960i | \(-0.138658\pi\) | |||||||
\(468\) | −2.38185e11 | −0.229513 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.31667e12 | 1.24462 | ||||||||
\(471\) | −1.00951e12 | + | 1.74852e12i | −0.945185 | + | 1.63711i | ||||
\(472\) | 5.95259e10 | + | 1.03102e11i | 0.0552036 | + | 0.0956154i | ||||
\(473\) | −2.48866e11 | − | 4.31049e11i | −0.228608 | − | 0.395960i | ||||
\(474\) | −1.51077e11 | + | 2.61674e11i | −0.137466 | + | 0.238099i | ||||
\(475\) | 2.76450e12 | 2.49170 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.44184e11 | −0.392853 | ||||||||
\(478\) | 4.90312e11 | − | 8.49245e11i | 0.429583 | − | 0.744059i | ||||
\(479\) | 5.82335e11 | + | 1.00863e12i | 0.505432 | + | 0.875434i | 0.999980 | + | 0.00628383i | \(0.00200022\pi\) |
−0.494548 | + | 0.869150i | \(0.664666\pi\) | |||||||
\(480\) | −2.13309e11 | − | 3.69462e11i | −0.183410 | − | 0.317676i | ||||
\(481\) | 2.77250e11 | − | 4.80211e11i | 0.236167 | − | 0.409053i | ||||
\(482\) | −6.85982e11 | −0.578897 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.90850e11 | 0.572242 | ||||||||
\(485\) | 1.11861e12 | − | 1.93749e12i | 0.917994 | − | 1.59001i | ||||
\(486\) | −4.18155e11 | − | 7.24265e11i | −0.339996 | − | 0.588890i | ||||
\(487\) | −1.12077e12 | − | 1.94123e12i | −0.902891 | − | 1.56385i | −0.823723 | − | 0.566992i | \(-0.808107\pi\) |
−0.0791677 | − | 0.996861i | \(-0.525226\pi\) | |||||||
\(488\) | −1.26726e11 | + | 2.19497e11i | −0.101153 | + | 0.175202i | ||||
\(489\) | −2.14614e12 | −1.69734 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.65508e11 | 0.128515 | 0.0642573 | − | 0.997933i | \(-0.479532\pi\) | ||||
0.0642573 | + | 0.997933i | \(0.479532\pi\) | |||||||
\(492\) | 1.42282e11 | − | 2.46440e11i | 0.109473 | − | 0.189613i | ||||
\(493\) | −3.42443e9 | − | 5.93128e9i | −0.00261082 | − | 0.00452207i | ||||
\(494\) | −5.57319e11 | − | 9.65305e11i | −0.421049 | − | 0.729278i | ||||
\(495\) | −8.67717e11 | + | 1.50293e12i | −0.649613 | + | 1.12516i | ||||
\(496\) | 2.82631e11 | 0.209678 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.01307e11 | 0.438091 | ||||||||
\(499\) | 6.06773e11 | − | 1.05096e12i | 0.438100 | − | 0.758812i | −0.559443 | − | 0.828869i | \(-0.688985\pi\) |
0.997543 | + | 0.0700572i | \(0.0223182\pi\) | |||||||
\(500\) | 4.78971e11 | + | 8.29602e11i | 0.342724 | + | 0.593615i | ||||
\(501\) | 5.43082e11 | + | 9.40646e11i | 0.385120 | + | 0.667047i | ||||
\(502\) | 2.16737e11 | − | 3.75399e11i | 0.152323 | − | 0.263831i | ||||
\(503\) | −8.95258e10 | −0.0623580 | −0.0311790 | − | 0.999514i | \(-0.509926\pi\) | ||||
−0.0311790 | + | 0.999514i | \(0.509926\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.56793e12 | −3.12542 | ||||||||
\(506\) | −1.00853e12 | + | 1.74682e12i | −0.683929 | + | 1.18460i | ||||
\(507\) | 2.26227e11 | + | 3.91836e11i | 0.152058 | + | 0.263371i | ||||
\(508\) | 3.20963e11 | + | 5.55924e11i | 0.213830 | + | 0.370364i | ||||
\(509\) | 6.66954e11 | − | 1.15520e12i | 0.440419 | − | 0.762828i | −0.557302 | − | 0.830310i | \(-0.688163\pi\) |
0.997720 | + | 0.0674822i | \(0.0214966\pi\) | |||||||
\(510\) | −2.10227e11 | −0.137601 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | 6.26907e11 | − | 1.08583e12i | 0.399645 | − | 0.692206i | ||||
\(514\) | 6.67795e11 | + | 1.15665e12i | 0.421997 | + | 0.730919i | ||||
\(515\) | 1.62217e12 | + | 2.80968e12i | 1.01616 | + | 1.76005i | ||||
\(516\) | 1.55408e11 | − | 2.69174e11i | 0.0965049 | − | 0.167151i | ||||
\(517\) | −2.49484e12 | −1.53580 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.52492e11 | 0.0922561 | ||||||||
\(520\) | 4.29549e11 | − | 7.44001e11i | 0.257631 | − | 0.446230i | ||||
\(521\) | −2.86045e11 | − | 4.95444e11i | −0.170084 | − | 0.294595i | 0.768365 | − | 0.640012i | \(-0.221071\pi\) |
−0.938449 | + | 0.345417i | \(0.887737\pi\) | |||||||
\(522\) | −1.76528e10 | − | 3.05756e10i | −0.0104063 | − | 0.0180243i | ||||
\(523\) | −1.25008e12 | + | 2.16521e12i | −0.730602 | + | 1.26544i | 0.226024 | + | 0.974122i | \(0.427427\pi\) |
−0.956626 | + | 0.291318i | \(0.905906\pi\) | |||||||
\(524\) | 7.81175e11 | 0.452645 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.05322e11 | −0.458705 | ||||||||
\(527\) | 6.96368e10 | − | 1.20615e11i | 0.0393270 | − | 0.0681164i | ||||
\(528\) | 4.04179e11 | + | 7.00059e11i | 0.226319 | + | 0.391996i | ||||
\(529\) | −6.70905e11 | − | 1.16204e12i | −0.372486 | − | 0.645165i | ||||
\(530\) | 8.01053e11 | − | 1.38747e12i | 0.440981 | − | 0.763802i | ||||
\(531\) | 3.02421e11 | 0.165077 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.73039e11 | 0.307547 | ||||||||
\(534\) | 2.58806e11 | − | 4.48266e11i | 0.137733 | − | 0.238561i | ||||
\(535\) | −2.24975e12 | − | 3.89668e12i | −1.18725 | − | 2.05638i | ||||
\(536\) | 4.10930e11 | + | 7.11751e11i | 0.215043 | + | 0.372466i | ||||
\(537\) | 1.45135e12 | − | 2.51382e12i | 0.753162 | − | 1.30452i | ||||
\(538\) | 5.27499e11 | 0.271457 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.66366e11 | 0.489069 | ||||||||
\(541\) | −5.24154e11 | + | 9.07861e11i | −0.263070 | + | 0.455650i | −0.967056 | − | 0.254563i | \(-0.918068\pi\) |
0.703986 | + | 0.710213i | \(0.251402\pi\) | |||||||
\(542\) | −1.89876e11 | − | 3.28875e11i | −0.0945091 | − | 0.163694i | ||||
\(543\) | −2.89541e11 | − | 5.01499e11i | −0.142926 | − | 0.247554i | ||||
\(544\) | −1.69316e10 | + | 2.93264e10i | −0.00828902 | + | 0.0143570i | ||||
\(545\) | −4.42147e12 | −2.14676 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.50622e12 | −1.67454 | −0.837272 | − | 0.546786i | \(-0.815851\pi\) | ||||
−0.837272 | + | 0.546786i | \(0.815851\pi\) | |||||||
\(548\) | −9.35101e11 | + | 1.61964e12i | −0.442941 | + | 0.767197i | ||||
\(549\) | 3.21916e11 | + | 5.57575e11i | 0.151240 | + | 0.261956i | ||||
\(550\) | −2.01864e12 | − | 3.49639e12i | −0.940649 | − | 1.62925i | ||||
\(551\) | 8.26104e10 | − | 1.43085e11i | 0.0381815 | − | 0.0661322i | ||||
\(552\) | −1.25958e12 | −0.577430 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.33040e12 | 0.600052 | ||||||||
\(555\) | 1.26146e12 | − | 2.18491e12i | 0.564358 | − | 0.977497i | ||||
\(556\) | 3.57490e11 | + | 6.19190e11i | 0.158645 | + | 0.274782i | ||||
\(557\) | −1.12138e12 | − | 1.94228e12i | −0.493631 | − | 0.854994i | 0.506342 | − | 0.862333i | \(-0.330997\pi\) |
−0.999973 | + | 0.00733847i | \(0.997664\pi\) | |||||||
\(558\) | 3.58976e11 | − | 6.21765e11i | 0.156752 | − | 0.271502i | ||||
\(559\) | 6.25901e11 | 0.271115 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.98339e11 | 0.169793 | ||||||||
\(562\) | 1.19089e12 | − | 2.06269e12i | 0.503569 | − | 0.872207i | ||||
\(563\) | 1.01923e12 | + | 1.76536e12i | 0.427547 | + | 0.740533i | 0.996655 | − | 0.0817298i | \(-0.0260445\pi\) |
−0.569107 | + | 0.822263i | \(0.692711\pi\) | |||||||
\(564\) | −7.78968e11 | − | 1.34921e12i | −0.324163 | − | 0.561467i | ||||
\(565\) | −1.94583e12 | + | 3.37028e12i | −0.803317 | + | 1.39139i | ||||
\(566\) | 9.49683e11 | 0.388960 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.24114e11 | −0.0500328 | ||||||||
\(569\) | −6.24361e11 | + | 1.08142e12i | −0.249707 | + | 0.432505i | −0.963444 | − | 0.267908i | \(-0.913668\pi\) |
0.713738 | + | 0.700413i | \(0.247001\pi\) | |||||||
\(570\) | −2.53574e12 | − | 4.39204e12i | −1.00616 | − | 1.74273i | ||||
\(571\) | −1.14336e12 | − | 1.98036e12i | −0.450113 | − | 0.779619i | 0.548280 | − | 0.836295i | \(-0.315283\pi\) |
−0.998393 | + | 0.0566765i | \(0.981950\pi\) | |||||||
\(572\) | −8.13911e11 | + | 1.40974e12i | −0.317903 | + | 0.550624i | ||||
\(573\) | −2.04345e12 | −0.791896 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.29087e12 | 2.39997 | ||||||||
\(576\) | −8.72821e10 | + | 1.51177e11i | −0.0330388 | + | 0.0572249i | ||||
\(577\) | −1.30799e12 | − | 2.26550e12i | −0.491260 | − | 0.850888i | 0.508689 | − | 0.860950i | \(-0.330130\pi\) |
−0.999949 | + | 0.0100624i | \(0.996797\pi\) | |||||||
\(578\) | −9.40360e11 | − | 1.62875e12i | −0.350444 | − | 0.606987i | ||||
\(579\) | 2.79158e12 | − | 4.83516e12i | 1.03228 | − | 1.78796i | ||||
\(580\) | 1.27343e11 | 0.0467248 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.64715e12 | −0.956369 | ||||||||
\(583\) | −1.51784e12 | + | 2.62897e12i | −0.544148 | + | 0.942492i | ||||
\(584\) | 5.97701e11 | + | 1.03525e12i | 0.212631 | + | 0.368287i | ||||
\(585\) | −1.09116e12 | − | 1.88994e12i | −0.385200 | − | 0.667187i | ||||
\(586\) | −7.28452e11 | + | 1.26172e12i | −0.255189 | + | 0.442000i | ||||
\(587\) | 3.09779e12 | 1.07691 | 0.538457 | − | 0.842653i | \(-0.319007\pi\) | ||||
0.538457 | + | 0.842653i | \(0.319007\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.35982e12 | 1.15026 | ||||||||
\(590\) | −5.45394e11 | + | 9.44651e11i | −0.185301 | + | 0.320950i | ||||
\(591\) | 2.09082e12 | + | 3.62141e12i | 0.704974 | + | 1.22105i | ||||
\(592\) | −2.03195e11 | − | 3.51944e11i | −0.0679932 | − | 0.117768i | ||||
\(593\) | −1.31976e12 | + | 2.28590e12i | −0.438278 | + | 0.759120i | −0.997557 | − | 0.0698599i | \(-0.977745\pi\) |
0.559279 | + | 0.828980i | \(0.311078\pi\) | |||||||
\(594\) | −1.83107e12 | −0.603486 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.48769e11 | −0.210611 | ||||||||
\(597\) | 9.93550e11 | − | 1.72088e12i | 0.320114 | − | 0.554454i | ||||
\(598\) | −1.26823e12 | − | 2.19664e12i | −0.405548 | − | 0.702430i | ||||
\(599\) | 1.89224e12 | + | 3.27745e12i | 0.600558 | + | 1.04020i | 0.992737 | + | 0.120308i | \(0.0383882\pi\) |
−0.392178 | + | 0.919889i | \(0.628278\pi\) | |||||||
\(600\) | 1.26057e12 | − | 2.18337e12i | 0.397087 | − | 0.687775i | ||||
\(601\) | 5.10190e11 | 0.159513 | 0.0797567 | − | 0.996814i | \(-0.474586\pi\) | ||||
0.0797567 | + | 0.996814i | \(0.474586\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.08772e12 | 0.643050 | ||||||||
\(604\) | −3.97896e11 | + | 6.89177e11i | −0.121648 | + | 0.210700i | ||||
\(605\) | 3.16489e12 | + | 5.48175e12i | 0.960415 | + | 1.66349i | ||||
\(606\) | 2.70247e12 | + | 4.68081e12i | 0.814017 | + | 1.40992i | ||||
\(607\) | 2.44927e12 | − | 4.24227e12i | 0.732299 | − | 1.26838i | −0.223600 | − | 0.974681i | \(-0.571781\pi\) |
0.955898 | − | 0.293697i | \(-0.0948858\pi\) | |||||||
\(608\) | −8.16912e11 | −0.242443 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.32221e12 | −0.679074 | ||||||||
\(611\) | 1.56864e12 | − | 2.71696e12i | 0.455341 | − | 0.788674i | ||||
\(612\) | 4.30104e10 | + | 7.44963e10i | 0.0123935 | + | 0.0214661i | ||||
\(613\) | −2.18246e12 | − | 3.78013e12i | −0.624272 | − | 1.08127i | −0.988681 | − | 0.150032i | \(-0.952062\pi\) |
0.364409 | − | 0.931239i | \(-0.381271\pi\) | |||||||
\(614\) | −5.29319e11 | + | 9.16808e11i | −0.150300 | + | 0.260328i | ||||
\(615\) | 2.60727e12 | 0.734933 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.81081e12 | −1.05861 | −0.529303 | − | 0.848433i | \(-0.677547\pi\) | ||||
−0.529303 | + | 0.848433i | \(0.677547\pi\) | |||||||
\(618\) | 1.91941e12 | − | 3.32451e12i | 0.529321 | − | 0.916810i | ||||
\(619\) | −7.62819e11 | − | 1.32124e12i | −0.208840 | − | 0.361721i | 0.742509 | − | 0.669836i | \(-0.233635\pi\) |
−0.951349 | + | 0.308114i | \(0.900302\pi\) | |||||||
\(620\) | 1.29478e12 | + | 2.24262e12i | 0.351910 | + | 0.609527i | ||||
\(621\) | 1.42658e12 | − | 2.47091e12i | 0.384933 | − | 0.666723i | ||||
\(622\) | 1.41491e11 | 0.0379028 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.01652e12 | −0.268400 | ||||||||
\(625\) | −9.23168e11 | + | 1.59897e12i | −0.242003 | + | 0.419162i | ||||
\(626\) | −1.26526e11 | − | 2.19149e11i | −0.0329302 | − | 0.0570367i | ||||
\(627\) | 4.80473e12 | + | 8.32204e12i | 1.24155 | + | 2.15043i | ||||
\(628\) | −1.48989e12 | + | 2.58057e12i | −0.382241 | + | 0.662060i | ||||
\(629\) | −2.00259e11 | −0.0510110 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.08153e12 | −1.52715 | −0.763573 | − | 0.645721i | \(-0.776557\pi\) | ||||
−0.763573 | + | 0.645721i | \(0.776557\pi\) | |||||||
\(632\) | −2.22969e11 | + | 3.86193e11i | −0.0555926 | + | 0.0962892i | ||||
\(633\) | −1.76880e12 | − | 3.06364e12i | −0.437886 | − | 0.758441i | ||||
\(634\) | 1.72322e12 | + | 2.98471e12i | 0.423584 | + | 0.733670i | ||||
\(635\) | −2.94076e12 | + | 5.09354e12i | −0.717757 | + | 1.24319i | ||||
\(636\) | −1.89567e12 | −0.459415 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.41289e11 | −0.0576560 | ||||||||
\(639\) | −1.57640e11 | + | 2.73041e11i | −0.0374036 | + | 0.0647850i | ||||
\(640\) | −3.14814e11 | − | 5.45274e11i | −0.0741727 | − | 0.128471i | ||||
\(641\) | 6.84081e11 | + | 1.18486e12i | 0.160047 | + | 0.277209i | 0.934885 | − | 0.354950i | \(-0.115502\pi\) |
−0.774839 | + | 0.632159i | \(0.782169\pi\) | |||||||
\(642\) | −2.66198e12 | + | 4.61069e12i | −0.618440 | + | 1.07117i | ||||
\(643\) | 2.94301e12 | 0.678958 | 0.339479 | − | 0.940614i | \(-0.389749\pi\) | ||||
0.339479 | + | 0.940614i | \(0.389749\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.84779e12 | 0.647871 | ||||||||
\(646\) | −2.01277e11 | + | 3.48622e11i | −0.0454724 | + | 0.0787605i | ||||
\(647\) | −2.20167e12 | − | 3.81341e12i | −0.493951 | − | 0.855547i | 0.506025 | − | 0.862519i | \(-0.331114\pi\) |
−0.999976 | + | 0.00697131i | \(0.997781\pi\) | |||||||
\(648\) | −9.91147e11 | − | 1.71672e12i | −0.220826 | − | 0.382482i | ||||
\(649\) | 1.03342e12 | − | 1.78993e12i | 0.228651 | − | 0.396036i | ||||
\(650\) | 5.07691e12 | 1.11555 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.16740e12 | −0.686417 | ||||||||
\(653\) | −3.43720e11 | + | 5.95340e11i | −0.0739767 | + | 0.128131i | −0.900641 | − | 0.434564i | \(-0.856902\pi\) |
0.826664 | + | 0.562696i | \(0.190236\pi\) | |||||||
\(654\) | 2.61582e12 | + | 4.53074e12i | 0.559124 | + | 0.968432i | ||||
\(655\) | 3.57868e12 | + | 6.19846e12i | 0.759691 | + | 1.31582i | ||||
\(656\) | 2.09989e11 | − | 3.63711e11i | 0.0442719 | − | 0.0766813i | ||||
\(657\) | 3.03661e12 | 0.635836 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.48190e12 | 1.54535 | 0.772676 | − | 0.634800i | \(-0.218918\pi\) | ||||
0.772676 | + | 0.634800i | \(0.218918\pi\) | |||||||
\(660\) | −3.70321e12 | + | 6.41415e12i | −0.759680 | + | 1.31580i | ||||
\(661\) | 4.14386e12 | + | 7.17738e12i | 0.844303 | + | 1.46238i | 0.886225 | + | 0.463255i | \(0.153319\pi\) |
−0.0419217 | + | 0.999121i | \(0.513348\pi\) | |||||||
\(662\) | −3.22506e11 | − | 5.58597e11i | −0.0652645 | − | 0.113041i | ||||
\(663\) | −2.50457e11 | + | 4.33804e11i | −0.0503410 | + | 0.0871931i | ||||
\(664\) | 8.87444e11 | 0.177168 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.03233e12 | −0.203322 | ||||||||
\(667\) | 1.87987e11 | − | 3.25604e11i | 0.0367758 | − | 0.0636976i | ||||
\(668\) | 8.01512e11 | + | 1.38826e12i | 0.155746 | + | 0.269759i | ||||
\(669\) | −4.96360e12 | − | 8.59721e12i | −0.958031 | − | 1.65936i | ||||
\(670\) | −3.76506e12 | + | 6.52127e12i | −0.721830 | + | 1.25025i | ||||
\(671\) | 4.40013e12 | 0.837943 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.54077e11 | −0.0477416 | −0.0238708 | − | 0.999715i | \(-0.507599\pi\) | ||||
−0.0238708 | + | 0.999715i | \(0.507599\pi\) | |||||||
\(674\) | −1.18070e12 | + | 2.04503e12i | −0.220378 | + | 0.381707i | ||||
\(675\) | 2.85541e12 | + | 4.94572e12i | 0.529422 | + | 0.916985i | ||||
\(676\) | 3.33878e11 | + | 5.78294e11i | 0.0614933 | + | 0.106510i | ||||
\(677\) | 4.85902e12 | − | 8.41607e12i | 0.888995 | − | 1.53979i | 0.0479305 | − | 0.998851i | \(-0.484737\pi\) |
0.841065 | − | 0.540934i | \(-0.181929\pi\) | |||||||
\(678\) | 4.60475e12 | 0.836898 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.10265e11 | −0.0556471 | ||||||||
\(681\) | 1.32259e12 | − | 2.29080e12i | 0.235648 | − | 0.408155i | ||||
\(682\) | −2.45335e12 | − | 4.24932e12i | −0.434239 | − | 0.752125i | ||||
\(683\) | 3.77058e12 | + | 6.53084e12i | 0.663003 | + | 1.14835i | 0.979823 | + | 0.199869i | \(0.0640515\pi\) |
−0.316820 | + | 0.948486i | \(0.602615\pi\) | |||||||
\(684\) | −1.03758e12 | + | 1.79714e12i | −0.181246 | + | 0.313927i | ||||
\(685\) | −1.71353e13 | −2.97362 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.03685e12 | 1.03396 | ||||||||
\(688\) | 2.29360e11 | − | 3.97263e11i | 0.0390274 | − | 0.0675974i | ||||
\(689\) | −1.90869e12 | − | 3.30595e12i | −0.322663 | − | 0.558869i | ||||
\(690\) | −5.77031e12 | − | 9.99448e12i | −0.969122 | − | 1.67857i | ||||
\(691\) | −5.14662e12 | + | 8.91420e12i | −0.858758 | + | 1.48741i | 0.0143570 | + | 0.999897i | \(0.495430\pi\) |
−0.873115 | + | 0.487515i | \(0.837903\pi\) | |||||||
\(692\) | 2.25057e11 | 0.0373091 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.24203e12 | 1.02143 | ||||||||
\(695\) | −3.27543e12 | + | 5.67320e12i | −0.532520 | + | 0.922352i | ||||
\(696\) | −7.53381e10 | − | 1.30489e11i | −0.0121695 | − | 0.0210782i | ||||
\(697\) | −1.03477e11 | − | 1.79228e11i | −0.0166072 | − | 0.0287646i | ||||
\(698\) | 2.08443e11 | − | 3.61034e11i | 0.0332382 | − | 0.0575703i | ||||
\(699\) | 1.28842e13 | 2.04131 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.10623e12 | 1.42432 | 0.712160 | − | 0.702017i | \(-0.247717\pi\) | ||||
0.712160 | + | 0.702017i | \(0.247717\pi\) | |||||||
\(702\) | 1.15129e12 | − | 1.99410e12i | 0.178924 | − | 0.309906i | ||||
\(703\) | −2.41551e12 | − | 4.18378e12i | −0.373001 | − | 0.646056i | ||||
\(704\) | 5.96511e11 | + | 1.03319e12i | 0.0915254 | + | 0.158527i | ||||
\(705\) | 7.13713e12 | − | 1.23619e13i | 1.08811 | − | 1.88466i | ||||
\(706\) | 1.20254e12 | 0.182170 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.29066e12 | 0.193047 | ||||||||
\(709\) | −3.26486e12 | + | 5.65491e12i | −0.485240 | + | 0.840461i | −0.999856 | − | 0.0169599i | \(-0.994601\pi\) |
0.514616 | + | 0.857421i | \(0.327935\pi\) | |||||||
\(710\) | −5.68587e11 | − | 9.84821e11i | −0.0839719 | − | 0.145444i | ||||
\(711\) | 5.66395e11 | + | 9.81025e11i | 0.0831201 | + | 0.143968i | ||||
\(712\) | 3.81961e11 | − | 6.61577e11i | 0.0557005 | − | 0.0964762i | ||||
\(713\) | 7.64557e12 | 1.10792 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.49146e13 | −2.13419 | ||||||||
\(716\) | 2.14199e12 | − | 3.71004e12i | 0.304585 | − | 0.527557i | ||||
\(717\) | −5.31555e12 | − | 9.20680e12i | −0.751124 | − | 1.30098i | ||||
\(718\) | 2.29790e12 | + | 3.98008e12i | 0.322680 | + | 0.558897i | ||||
\(719\) | −5.24753e12 | + | 9.08899e12i | −0.732276 | + | 1.26834i | 0.223632 | + | 0.974674i | \(0.428209\pi\) |
−0.955908 | + | 0.293666i | \(0.905125\pi\) | |||||||
\(720\) | −1.59941e12 | −0.221801 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −4.54815e12 | −0.622899 | ||||||||
\(723\) | −3.71842e12 | + | 6.44049e12i | −0.506099 | + | 0.876590i | ||||
\(724\) | −4.27321e11 | − | 7.40141e11i | −0.0578003 | − | 0.100113i | ||||
\(725\) | 3.76271e11 | + | 6.51720e11i | 0.0505801 | + | 0.0876073i | ||||
\(726\) | 3.74481e12 | − | 6.48620e12i | 0.500282 | − | 0.866513i | ||||
\(727\) | −3.77271e12 | −0.500898 | −0.250449 | − | 0.968130i | \(-0.580578\pi\) | ||||
−0.250449 | + | 0.968130i | \(0.580578\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.59195e11 | 0.0602176 | ||||||||
\(730\) | −5.47631e12 | + | 9.48525e12i | −0.713732 | + | 1.23622i | ||||
\(731\) | −1.13023e11 | − | 1.95761e11i | −0.0146399 | − | 0.0253570i | ||||
\(732\) | 1.37386e12 | + | 2.37960e12i | 0.176865 | + | 0.306340i | ||||
\(733\) | −6.93047e12 | + | 1.20039e13i | −0.886737 | + | 1.53587i | −0.0430263 | + | 0.999074i | \(0.513700\pi\) |
−0.843710 | + | 0.536799i | \(0.819633\pi\) | |||||||
\(734\) | −8.14250e12 | −1.03544 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.85896e12 | −0.233517 | ||||||||
\(737\) | 7.13405e12 | − | 1.23565e13i | 0.890702 | − | 1.54274i | ||||
\(738\) | −5.33422e11 | − | 9.23915e11i | −0.0661939 | − | 0.114651i | ||||
\(739\) | 7.34297e11 | + | 1.27184e12i | 0.0905673 | + | 0.156867i | 0.907750 | − | 0.419512i | \(-0.137799\pi\) |
−0.817183 | + | 0.576379i | \(0.804465\pi\) | |||||||
\(740\) | 1.86173e12 | − | 3.22462e12i | 0.228231 | − | 0.395308i | ||||
\(741\) | −1.20840e13 | −1.47241 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.86883e12 | −0.586104 | −0.293052 | − | 0.956096i | \(-0.594671\pi\) | ||||
−0.293052 | + | 0.956096i | \(0.594671\pi\) | |||||||
\(744\) | 1.53203e12 | − | 2.65355e12i | 0.183311 | − | 0.317503i | ||||
\(745\) | −2.97211e12 | − | 5.14784e12i | −0.353477 | − | 0.612240i | ||||
\(746\) | 8.27616e11 | + | 1.43347e12i | 0.0978372 | + | 0.169459i | ||||
\(747\) | 1.12716e12 | − | 1.95230e12i | 0.132447 | − | 0.229406i | ||||
\(748\) | 5.87891e11 | 0.0686657 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.03852e13 | 1.19850 | ||||||||
\(751\) | 5.71359e12 | − | 9.89624e12i | 0.655435 | − | 1.13525i | −0.326349 | − | 0.945249i | \(-0.605819\pi\) |
0.981785 | − | 0.189998i | \(-0.0608481\pi\) | |||||||
\(752\) | −1.14965e12 | − | 1.99124e12i | −0.131094 | − | 0.227062i | ||||
\(753\) | −2.34968e12 | − | 4.06976e12i | −0.266336 | − | 0.461308i | ||||
\(754\) | 1.51711e11 | − | 2.62772e11i | 0.0170941 | − | 0.0296079i | ||||
\(755\) | −7.29129e12 | −0.816663 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.87971e12 | 0.540085 | 0.270043 | − | 0.962848i | \(-0.412962\pi\) | ||||
0.270043 | + | 0.962848i | \(0.412962\pi\) | |||||||
\(758\) | 8.87152e11 | − | 1.53659e12i | 0.0976083 | − | 0.169063i | ||||
\(759\) | 1.09336e13 | + | 1.89376e13i | 1.19585 | + | 2.07127i | ||||
\(760\) | −3.74240e12 | − | 6.48202e12i | −0.406901 | − | 0.704773i | ||||
\(761\) | 5.62833e12 | − | 9.74856e12i | 0.608343 | − | 1.05368i | −0.383170 | − | 0.923678i | \(-0.625168\pi\) |
0.991514 | − | 0.130004i | \(-0.0414989\pi\) | |||||||
\(762\) | 6.95922e12 | 0.747761 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.01584e12 | −0.320249 | ||||||||
\(765\) | −3.94074e11 | + | 6.82557e11i | −0.0416008 | + | 0.0720547i | ||||
\(766\) | −2.07955e12 | − | 3.60189e12i | −0.218243 | − | 0.378008i | ||||
\(767\) | 1.29953e12 | + | 2.25084e12i | 0.135583 | + | 0.234837i | ||||
\(768\) | −3.72499e11 | + | 6.45188e11i | −0.0386367 | + | 0.0669207i | ||||
\(769\) | 1.61412e13 | 1.66444 | 0.832220 | − | 0.554446i | \(-0.187070\pi\) | ||||
0.832220 | + | 0.554446i | \(0.187070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.44793e13 | 1.47572 | ||||||||
\(772\) | 4.11997e12 | − | 7.13600e12i | 0.417462 | − | 0.723065i | ||||
\(773\) | 7.01910e12 | + | 1.21574e13i | 0.707089 | + | 1.22471i | 0.965932 | + | 0.258794i | \(0.0833252\pi\) |
−0.258844 | + | 0.965919i | \(0.583342\pi\) | |||||||
\(774\) | −5.82630e11 | − | 1.00914e12i | −0.0583524 | − | 0.101069i | ||||
\(775\) | −7.65159e12 | + | 1.32529e13i | −0.761893 | + | 1.31964i | ||||
\(776\) | −3.90682e12 | −0.386764 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.32090e12 | −0.912115 | ||||||||
\(779\) | 2.49627e12 | − | 4.32366e12i | 0.242869 | − | 0.420662i | ||||
\(780\) | −4.65681e12 | − | 8.06583e12i | −0.450467 | − | 0.780231i | ||||
\(781\) | 1.07736e12 | + | 1.86604e12i | 0.103617 | + | 0.179470i | ||||
\(782\) | −4.58024e11 | + | 7.93321e11i | −0.0437983 | + | 0.0758610i | ||||
\(783\) | 3.41308e11 | 0.0324503 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.73017e13 | −2.56612 | ||||||||
\(786\) | 4.23442e12 | − | 7.33423e12i | 0.395724 | − | 0.685414i | ||||
\(787\) | 6.72141e11 | + | 1.16418e12i | 0.0624560 | + | 0.108177i | 0.895563 | − | 0.444935i | \(-0.146773\pi\) |
−0.833107 | + | 0.553112i | \(0.813440\pi\) | |||||||
\(788\) | 3.08575e12 | + | 5.34468e12i | 0.285097 | + | 0.493803i | ||||
\(789\) | −4.36531e12 | + | 7.56094e12i | −0.401022 | + | 0.694591i | ||||
\(790\) | −4.08581e12 | −0.373213 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.03057e12 | 0.273691 | ||||||||
\(793\) | −2.76660e12 | + | 4.79188e12i | −0.248437 | + | 0.430306i | ||||
\(794\) | 1.49658e12 | + | 2.59216e12i | 0.133631 | + | 0.231456i | ||||
\(795\) | −8.68434e12 | − | 1.50417e13i | −0.771054 | − | 1.33551i | ||||
\(796\) | 1.46634e12 | − | 2.53977e12i | 0.129457 | − | 0.224226i | ||||
\(797\) | 9.34992e12 | 0.820815 | 0.410408 | − | 0.911902i | \(-0.365386\pi\) | ||||
0.410408 | + | 0.911902i | \(0.365386\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.13303e12 | −0.0983517 | ||||||||
\(800\) | 1.86042e12 | − | 3.22234e12i | 0.160585 | − | 0.278142i | ||||
\(801\) | −9.70275e11 | − | 1.68057e12i | −0.0832815 | − | 0.144248i | ||||
\(802\) | −7.06193e12 | − | 1.22316e13i | −0.602752 | − | 1.04400i | ||||
\(803\) | 1.03765e13 | − | 1.79727e13i | 0.880709 | − | 1.52543i | ||||
\(804\) | 8.90990e12 | 0.752005 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.17019e12 | 0.514981 | ||||||||
\(807\) | 2.85935e12 | − | 4.95253e12i | 0.237321 | − | 0.411052i | ||||
\(808\) | 3.98846e12 | + | 6.90821e12i | 0.329195 | + | 0.570183i | ||||
\(809\) | 2.73458e12 | + | 4.73643e12i | 0.224451 | + | 0.388761i | 0.956155 | − | 0.292862i | \(-0.0946077\pi\) |
−0.731703 | + | 0.681623i | \(0.761274\pi\) | |||||||
\(810\) | 9.08118e12 | − | 1.57291e13i | 0.741241 | − | 1.28387i | ||||
\(811\) | −6.82318e12 | −0.553851 | −0.276925 | − | 0.960891i | \(-0.589315\pi\) | ||||
−0.276925 | + | 0.960891i | \(0.589315\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.11695e12 | −0.330498 | ||||||||
\(814\) | −3.52762e12 | + | 6.11002e12i | −0.281626 | + | 0.487790i | ||||
\(815\) | −1.45103e13 | − | 2.51326e13i | −1.15204 | − | 1.99539i | ||||
\(816\) | 1.83558e11 | + | 3.17932e11i | 0.0144933 | + | 0.0251032i | ||||
\(817\) | 2.72655e12 | − | 4.72252e12i | 0.214099 | − | 0.370830i | ||||
\(818\) | −6.30919e12 | −0.492702 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.84796e12 | 0.297213 | ||||||||
\(821\) | −1.13840e12 | + | 1.97176e12i | −0.0874479 | + | 0.151464i | −0.906432 | − | 0.422352i | \(-0.861204\pi\) |
0.818984 | + | 0.573817i | \(0.194538\pi\) | |||||||
\(822\) | 1.01376e13 | + | 1.75588e13i | 0.774481 | + | 1.34144i | ||||
\(823\) | −1.08962e13 | − | 1.88728e13i | −0.827897 | − | 1.43396i | −0.899685 | − | 0.436541i | \(-0.856204\pi\) |
0.0717871 | − | 0.997420i | \(-0.477130\pi\) | |||||||
\(824\) | 2.83277e12 | − | 4.90650e12i | 0.214062 | − | 0.370766i | ||||
\(825\) | −4.37689e13 | −3.28944 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.32468e13 | 0.984772 | 0.492386 | − | 0.870377i | \(-0.336125\pi\) | ||||
0.492386 | + | 0.870377i | \(0.336125\pi\) | |||||||
\(828\) | −2.36110e12 | + | 4.08955e12i | −0.174574 | + | 0.302370i | ||||
\(829\) | 3.21919e12 | + | 5.57580e12i | 0.236729 | + | 0.410026i | 0.959774 | − | 0.280775i | \(-0.0905914\pi\) |
−0.723045 | + | 0.690801i | \(0.757258\pi\) | |||||||
\(830\) | 4.06551e12 | + | 7.04168e12i | 0.297347 | + | 0.515021i | ||||
\(831\) | 7.21155e12 | − | 1.24908e13i | 0.524595 | − | 0.908624i | ||||
\(832\) | −1.50023e12 | −0.108543 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7.75120e12 | 0.554781 | ||||||||
\(835\) | −7.34369e12 | + | 1.27196e13i | −0.522787 | + | 0.905494i | ||||
\(836\) | 7.09110e12 | + | 1.22822e13i | 0.502095 | + | 0.869654i | ||||
\(837\) | 3.47031e12 | + | 6.01075e12i | 0.244401 | + | 0.423315i | ||||
\(838\) | 1.42368e12 | − | 2.46589e12i | 0.0997274 | − | 0.172733i | ||||
\(839\) | −2.25634e12 | −0.157208 | −0.0786041 | − | 0.996906i | \(-0.525046\pi\) | ||||
−0.0786041 | + | 0.996906i | \(0.525046\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.44622e13 | −0.996900 | ||||||||
\(842\) | 3.15556e12 | − | 5.46559e12i | 0.216358 | − | 0.374742i | ||||
\(843\) | −1.29106e13 | − | 2.23619e13i | −0.880489 | − | 1.52505i | ||||
\(844\) | −2.61049e12 | − | 4.52150e12i | −0.177085 | − | 0.306720i | ||||
\(845\) | −3.05909e12 | + | 5.29850e12i | −0.206413 | + | 0.357518i | ||||
\(846\) | −5.84076e12 | −0.392015 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.79774e12 | −0.185791 | ||||||||
\(849\) | 5.14783e12 | − | 8.91630e12i | 0.340047 | − | 0.588980i | ||||
\(850\) | −9.16768e11 | − | 1.58789e12i | −0.0602385 | − | 0.104336i | ||||
\(851\) | −5.49671e12 | − | 9.52058e12i | −0.359269 | − | 0.622272i | ||||
\(852\) | −6.72772e11 | + | 1.16528e12i | −0.0437411 | + | 0.0757618i | ||||
\(853\) | 2.07580e13 | 1.34250 | 0.671252 | − | 0.741229i | \(-0.265757\pi\) | ||||
0.671252 | + | 0.741229i | \(0.265757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.90132e13 | −1.21677 | ||||||||
\(856\) | −3.92871e12 | + | 6.80472e12i | −0.250102 | + | 0.433190i | ||||
\(857\) | 1.58626e12 | + | 2.74749e12i | 0.100453 | + | 0.173989i | 0.911871 | − | 0.410476i | \(-0.134638\pi\) |
−0.811419 | + | 0.584466i | \(0.801304\pi\) | |||||||
\(858\) | 8.82373e12 | + | 1.52832e13i | 0.555853 | + | 0.962765i | ||||
\(859\) | −1.46559e11 | + | 2.53848e11i | −0.00918426 | + | 0.0159076i | −0.870581 | − | 0.492025i | \(-0.836257\pi\) |
0.861397 | + | 0.507933i | \(0.169590\pi\) | |||||||
\(860\) | 4.20293e12 | 0.262005 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.29247e13 | −0.797326 | ||||||||
\(863\) | −6.09714e12 | + | 1.05606e13i | −0.374178 | + | 0.648095i | −0.990204 | − | 0.139631i | \(-0.955408\pi\) |
0.616026 | + | 0.787726i | \(0.288742\pi\) | |||||||
\(864\) | −8.43776e11 | − | 1.46146e12i | −0.0515128 | − | 0.0892229i | ||||
\(865\) | 1.03102e12 | + | 1.78578e12i | 0.0626173 | + | 0.108456i | ||||
\(866\) | −4.62149e12 | + | 8.00466e12i | −0.279223 | + | 0.483629i | ||||
\(867\) | −2.03892e13 | −1.22550 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.74181e12 | 0.460525 | ||||||||
\(870\) | 6.90270e11 | − | 1.19558e12i | 0.0408491 | − | 0.0707527i | ||||
\(871\) | 8.97110e12 | + | 1.55384e13i | 0.528158 | + | 0.914797i | ||||
\(872\) | 3.86058e12 | + | 6.68672e12i | 0.226115 | + | 0.391642i | ||||
\(873\) | −4.96214e12 | + | 8.59468e12i | −0.289138 | + | 0.500801i | ||||
\(874\) | −2.20986e13 | −1.28104 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.29595e13 | 0.743568 | ||||||||
\(877\) | 9.23674e12 | − | 1.59985e13i | 0.527255 | − | 0.913233i | −0.472240 | − | 0.881470i | \(-0.656555\pi\) |
0.999495 | − | 0.0317628i | \(-0.0101121\pi\) | |||||||
\(878\) | 1.06263e13 | + | 1.84053e13i | 0.603470 | + | 1.04524i | ||||
\(879\) | 7.89726e12 | + | 1.36785e13i | 0.446197 | + | 0.772836i | ||||
\(880\) | −5.46541e12 | + | 9.46637e12i | −0.307221 | + | 0.532122i | ||||
\(881\) | −2.16016e13 | −1.20808 | −0.604039 | − | 0.796955i | \(-0.706443\pi\) | ||||
−0.604039 | + | 0.796955i | \(0.706443\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.00085e13 | −0.554043 | −0.277022 | − | 0.960864i | \(-0.589347\pi\) | ||||
−0.277022 | + | 0.960864i | \(0.589347\pi\) | |||||||
\(884\) | −3.69638e11 | + | 6.40232e11i | −0.0203583 | + | 0.0352616i | ||||
\(885\) | 5.91270e12 | + | 1.02411e13i | 0.323997 | + | 0.561180i | ||||
\(886\) | 3.99573e12 | + | 6.92081e12i | 0.217844 | + | 0.377316i | ||||
\(887\) | −7.52738e12 | + | 1.30378e13i | −0.408307 | + | 0.707209i | −0.994700 | − | 0.102818i | \(-0.967214\pi\) |
0.586393 | + | 0.810027i | \(0.300548\pi\) | |||||||
\(888\) | −4.40574e12 | −0.237772 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.99929e12 | 0.373937 | ||||||||
\(891\) | −1.72071e13 | + | 2.98035e13i | −0.914654 | + | 1.58423i | ||||
\(892\) | −7.32557e12 | − | 1.26883e13i | −0.387436 | − | 0.671058i | ||||
\(893\) | −1.36666e13 | − | 2.36712e13i | −0.719164 | − | 1.24563i | ||||
\(894\) | −3.51670e12 | + | 6.09110e12i | −0.184127 | + | 0.318917i | ||||
\(895\) | 3.92511e13 | 2.04479 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.74982e13 | −1.41820 | ||||||||
\(898\) | −3.60969e11 | + | 6.25216e11i | −0.0185236 | + | 0.0320839i | ||||
\(899\) | 4.57298e11 | + | 7.92064e11i | 0.0233497 | + | 0.0404429i | ||||
\(900\) | −4.72592e12 | − | 8.18554e12i | −0.240102 | − | 0.415868i | ||||
\(901\) | −6.89328e11 | + | 1.19395e12i | −0.0348469 | + | 0.0603566i | ||||
\(902\) | −7.29112e12 | −0.366746 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.79596e12 | 0.338449 | ||||||||
\(905\) | 3.91524e12 | − | 6.78139e12i | 0.194017 | − | 0.336047i | ||||
\(906\) | 4.31366e12 | + | 7.47147e12i | 0.212701 | + | 0.368408i | ||||
\(907\) | −1.14679e13 | − | 1.98630e13i | −0.562668 | − | 0.974569i | −0.997262 | − | 0.0739431i | \(-0.976442\pi\) |
0.434595 | − | 0.900626i | \(-0.356892\pi\) | |||||||
\(908\) | 1.95196e12 | − | 3.38089e12i | 0.0952981 | − | 0.165061i | ||||
\(909\) | 2.02633e13 | 0.984403 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.04241e13 | 1.94450 | 0.972248 | − | 0.233952i | \(-0.0751657\pi\) | ||||
0.972248 | + | 0.233952i | \(0.0751657\pi\) | |||||||
\(912\) | −4.42813e12 | + | 7.66975e12i | −0.211955 | + | 0.367117i | ||||
\(913\) | −7.70335e12 | − | 1.33426e13i | −0.366911 | − | 0.635509i | ||||
\(914\) | 5.08176e12 | + | 8.80187e12i | 0.240856 | + | 0.417174i | ||||
\(915\) | −1.25877e13 | + | 2.18026e13i | −0.593680 | + | 1.02828i | ||||
\(916\) | 8.90954e12 | 0.418144 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −8.31584e11 | −0.0386468 | ||||||||
\(919\) | −2.09498e12 | + | 3.62862e12i | −0.0968859 | + | 0.167811i | −0.910394 | − | 0.413742i | \(-0.864222\pi\) |
0.813508 | + | 0.581553i | \(0.197555\pi\) | |||||||
\(920\) | −8.51616e12 | − | 1.47504e13i | −0.391921 | − | 0.678827i | ||||
\(921\) | 5.73843e12 | + | 9.93925e12i | 0.262800 | + | 0.455182i | ||||
\(922\) | 9.68080e12 | − | 1.67676e13i | 0.441186 | − | 0.764157i | ||||
\(923\) | −2.70957e12 | −0.122883 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.20041e13 | 0.988250 | ||||||||
\(926\) | 7.78469e12 | − | 1.34835e13i | 0.347930 | − | 0.602633i | ||||
\(927\) | −7.19593e12 | − | 1.24637e13i | −0.320057 | − | 0.554356i | ||||
\(928\) | −1.11188e11 | − | 1.92584e11i | −0.00492145 | − | 0.00852421i | ||||
\(929\) | 2.41805e12 | − | 4.18818e12i | 0.106511 | − | 0.184482i | −0.807844 | − | 0.589397i | \(-0.799365\pi\) |
0.914355 | + | 0.404915i | \(0.132699\pi\) | |||||||
\(930\) | 2.80737e13 | 1.23063 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.90152e13 | 0.825524 | ||||||||
\(933\) | 7.66961e11 | − | 1.32841e12i | 0.0331364 | − | 0.0573940i | ||||
\(934\) | −1.34645e13 | − | 2.33212e13i | −0.578933 | − | 1.00274i | ||||
\(935\) | 2.69322e12 | + | 4.66479e12i | 0.115244 | + | 0.199609i | ||||
\(936\) | −1.90548e12 | + | 3.30038e12i | −0.0811451 | + | 0.140547i | ||||
\(937\) | 1.70190e12 | 0.0721282 | 0.0360641 | − | 0.999349i | \(-0.488518\pi\) | ||||
0.0360641 | + | 0.999349i | \(0.488518\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.74337e12 | −0.115157 | ||||||||
\(940\) | 1.05334e13 | − | 1.82444e13i | 0.440041 | − | 0.762173i | ||||
\(941\) | 1.41493e12 | + | 2.45074e12i | 0.0588278 | + | 0.101893i | 0.893939 | − | 0.448188i | \(-0.147930\pi\) |
−0.835112 | + | 0.550080i | \(0.814597\pi\) | |||||||
\(942\) | 1.61522e13 | + | 2.79764e13i | 0.668347 | + | 1.15761i | ||||
\(943\) | 5.68049e12 | − | 9.83889e12i | 0.233928 | − | 0.405176i | ||||
\(944\) | 1.90483e12 | 0.0780697 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.96372e12 | −0.323300 | ||||||||
\(947\) | −1.85318e13 | + | 3.20981e13i | −0.748761 | + | 1.29689i | 0.199656 | + | 0.979866i | \(0.436018\pi\) |
−0.948417 | + | 0.317026i | \(0.897316\pi\) | |||||||
\(948\) | 2.41724e12 | + | 4.18678e12i | 0.0972035 | + | 0.168361i | ||||
\(949\) | 1.30486e13 | + | 2.26008e13i | 0.522233 | + | 0.904534i | ||||
\(950\) | 2.21160e13 | − | 3.83060e13i | 0.880948 | − | 1.52585i | ||||
\(951\) | 3.73635e13 | 1.48127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.53995e12 | −0.0604768 | −0.0302384 | − | 0.999543i | \(-0.509627\pi\) | ||||
−0.0302384 | + | 0.999543i | \(0.509627\pi\) | |||||||
\(954\) | −3.55347e12 | + | 6.15479e12i | −0.138894 | + | 0.240572i | ||||
\(955\) | −1.38160e13 | − | 2.39300e13i | −0.537486 | − | 0.930953i | ||||
\(956\) | −7.84499e12 | − | 1.35879e13i | −0.303761 | − | 0.526129i | ||||
\(957\) | −1.30793e12 | + | 2.26540e12i | −0.0504057 | + | 0.0873052i | ||||
\(958\) | 1.86347e13 | 0.714789 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −6.82590e12 | −0.259382 | ||||||||
\(961\) | 3.92050e12 | − | 6.79050e12i | 0.148281 | − | 0.256830i | ||||
\(962\) | −4.43600e12 | − | 7.68338e12i | −0.166995 | − | 0.289244i | ||||
\(963\) | 9.97987e12 | + | 1.72856e13i | 0.373944 | + | 0.647690i | ||||
\(964\) | −5.48786e12 | + | 9.50524e12i | −0.204671 | + | 0.354500i | ||||
\(965\) | 7.54968e13 | 2.80257 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.09919e13 | −0.404254 | −0.202127 | − | 0.979359i | \(-0.564785\pi\) | ||||
−0.202127 | + | 0.979359i | \(0.564785\pi\) | |||||||
\(968\) | 5.52680e12 | − | 9.57270e12i | 0.202318 | − | 0.350425i | ||||
\(969\) | 2.18207e12 | + | 3.77946e12i | 0.0795083 | + | 0.137712i | ||||
\(970\) | −1.78977e13 | − | 3.09998e13i | −0.649120 | − | 1.12431i | ||||
\(971\) | −6.62794e11 | + | 1.14799e12i | −0.0239272 | + | 0.0414432i | −0.877741 | − | 0.479135i | \(-0.840950\pi\) |
0.853814 | + | 0.520578i | \(0.174284\pi\) | |||||||
\(972\) | −1.33809e13 | −0.480827 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.58646e13 | −1.27688 | ||||||||
\(975\) | 2.75198e13 | − | 4.76657e13i | 0.975269 | − | 1.68922i | ||||
\(976\) | 2.02762e12 | + | 3.51195e12i | 0.0715258 | + | 0.123886i | ||||
\(977\) | 1.36658e12 | + | 2.36699e12i | 0.0479856 | + | 0.0831135i | 0.889021 | − | 0.457867i | \(-0.151387\pi\) |
−0.841035 | + | 0.540981i | \(0.818053\pi\) | |||||||
\(978\) | −1.71691e13 | + | 2.97378e13i | −0.600099 | + | 1.03940i | ||||
\(979\) | −1.32623e13 | −0.461419 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.96136e13 | 0.676157 | ||||||||
\(982\) | 1.32407e12 | − | 2.29335e12i | 0.0454368 | − | 0.0786988i | ||||
\(983\) | 3.24327e11 | + | 5.61751e11i | 0.0110788 | + | 0.0191890i | 0.871512 | − | 0.490375i | \(-0.163140\pi\) |
−0.860433 | + | 0.509564i | \(0.829807\pi\) | |||||||
\(984\) | −2.27652e12 | − | 3.94305e12i | −0.0774094 | − | 0.134077i | ||||
\(985\) | −2.82726e13 | + | 4.89696e13i | −0.956980 | + | 1.65754i | ||||
\(986\) | −1.09582e11 | −0.00369226 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.78342e13 | −0.595453 | ||||||||
\(989\) | 6.20451e12 | − | 1.07465e13i | 0.206217 | − | 0.357178i | ||||
\(990\) | 1.38835e13 | + | 2.40469e13i | 0.459346 | + | 0.795610i | ||||
\(991\) | 1.97923e13 | + | 3.42812e13i | 0.651874 | + | 1.12908i | 0.982668 | + | 0.185376i | \(0.0593504\pi\) |
−0.330793 | + | 0.943703i | \(0.607316\pi\) | |||||||
\(992\) | 2.26105e12 | − | 3.91626e12i | 0.0741324 | − | 0.128401i | ||||
\(993\) | −6.99268e12 | −0.228230 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.68700e13 | 0.869090 | ||||||||
\(996\) | 4.81046e12 | − | 8.33196e12i | 0.154889 | − | 0.268275i | ||||
\(997\) | 1.05624e13 | + | 1.82947e13i | 0.338560 | + | 0.586404i | 0.984162 | − | 0.177270i | \(-0.0567267\pi\) |
−0.645602 | + | 0.763674i | \(0.723393\pi\) | |||||||
\(998\) | −9.70836e12 | − | 1.68154e13i | −0.309784 | − | 0.536561i | ||||
\(999\) | 4.98989e12 | − | 8.64274e12i | 0.158506 | − | 0.274541i |
(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 | 98.10.c.l.79.1 | 6 | ||
7.2 | even | 3 | 98.10.a.h.1.3 | 3 | |||
7.3 | odd | 6 | 14.10.c.b.11.3 | yes | 6 | ||
7.4 | even | 3 | inner | 98.10.c.l.67.1 | 6 | ||
7.5 | odd | 6 | 98.10.a.g.1.1 | 3 | |||
7.6 | odd | 2 | 14.10.c.b.9.3 | ✓ | 6 | ||
21.17 | even | 6 | 126.10.g.e.109.3 | 6 | |||
21.20 | even | 2 | 126.10.g.e.37.3 | 6 | |||
28.3 | even | 6 | 112.10.i.a.81.1 | 6 | |||
28.27 | even | 2 | 112.10.i.a.65.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.10.c.b.9.3 | ✓ | 6 | 7.6 | odd | 2 | ||
14.10.c.b.11.3 | yes | 6 | 7.3 | odd | 6 | ||
98.10.a.g.1.1 | 3 | 7.5 | odd | 6 | |||
98.10.a.h.1.3 | 3 | 7.2 | even | 3 | |||
98.10.c.l.67.1 | 6 | 7.4 | even | 3 | inner | ||
98.10.c.l.79.1 | 6 | 1.1 | even | 1 | trivial | ||
112.10.i.a.65.1 | 6 | 28.27 | even | 2 | |||
112.10.i.a.81.1 | 6 | 28.3 | even | 6 | |||
126.10.g.e.37.3 | 6 | 21.20 | even | 2 | |||
126.10.g.e.109.3 | 6 | 21.17 | even | 6 |