Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,11,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (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: | \(27.3203618650\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.33 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.11.b.b.42.2 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 58.7853i | 1.83704i | 0.395372 | + | 0.918521i | \(0.370616\pi\) | ||||
−0.395372 | + | 0.918521i | \(0.629384\pi\) | |||||||
\(3\) | 301.513i | 1.24080i | 0.784287 | + | 0.620398i | \(0.213029\pi\) | ||||
−0.784287 | + | 0.620398i | \(0.786971\pi\) | |||||||
\(4\) | −2431.72 | −2.37472 | ||||||||
\(5\) | 2781.13i | 0.889960i | 0.895540 | + | 0.444980i | \(0.146789\pi\) | ||||
−0.895540 | + | 0.444980i | \(0.853211\pi\) | |||||||
\(6\) | −17724.6 | −2.27939 | ||||||||
\(7\) | − | 4095.06i | − | 0.243652i | −0.992551 | − | 0.121826i | \(-0.961125\pi\) | ||
0.992551 | − | 0.121826i | \(-0.0388750\pi\) | |||||||
\(8\) | − | 82753.1i | − | 2.52543i | ||||||
\(9\) | −31861.2 | −0.539573 | ||||||||
\(10\) | −163489. | −1.63489 | ||||||||
\(11\) | −123581. | −0.767340 | −0.383670 | − | 0.923470i | \(-0.625340\pi\) | ||||
−0.383670 | + | 0.923470i | \(0.625340\pi\) | |||||||
\(12\) | − | 733195.i | − | 2.94655i | ||||||
\(13\) | 347183. | 0.935065 | 0.467533 | − | 0.883976i | \(-0.345143\pi\) | ||||
0.467533 | + | 0.883976i | \(0.345143\pi\) | |||||||
\(14\) | 240730. | 0.447599 | ||||||||
\(15\) | −838546. | −1.10426 | ||||||||
\(16\) | 2.37459e6 | 2.26459 | ||||||||
\(17\) | −82597.3 | −0.0581730 | −0.0290865 | − | 0.999577i | \(-0.509260\pi\) | ||||
−0.0290865 | + | 0.999577i | \(0.509260\pi\) | |||||||
\(18\) | − | 1.87297e6i | − | 0.991218i | ||||||
\(19\) | − | 1.73289e6i | − | 0.699846i | −0.936779 | − | 0.349923i | \(-0.886208\pi\) | ||
0.936779 | − | 0.349923i | \(-0.113792\pi\) | |||||||
\(20\) | − | 6.76291e6i | − | 2.11341i | ||||||
\(21\) | 1.23471e6 | 0.302322 | ||||||||
\(22\) | − | 7.26474e6i | − | 1.40964i | ||||||
\(23\) | −1.02592e7 | −1.59395 | −0.796974 | − | 0.604013i | \(-0.793567\pi\) | ||||
−0.796974 | + | 0.604013i | \(0.793567\pi\) | |||||||
\(24\) | 2.49512e7 | 3.13354 | ||||||||
\(25\) | 2.03096e6 | 0.207970 | ||||||||
\(26\) | 2.04093e7i | 1.71775i | ||||||||
\(27\) | 8.19747e6i | 0.571296i | ||||||||
\(28\) | 9.95803e6i | 0.578606i | ||||||||
\(29\) | 6.06720e6i | 0.295800i | 0.989002 | + | 0.147900i | \(0.0472514\pi\) | ||||
−0.989002 | + | 0.147900i | \(0.952749\pi\) | |||||||
\(30\) | − | 4.92942e7i | − | 2.02857i | ||||||
\(31\) | −4.26574e7 | −1.49000 | −0.745000 | − | 0.667064i | \(-0.767551\pi\) | ||||
−0.745000 | + | 0.667064i | \(0.767551\pi\) | |||||||
\(32\) | 5.48521e7i | 1.63472i | ||||||||
\(33\) | − | 3.72613e7i | − | 0.952112i | ||||||
\(34\) | − | 4.85551e6i | − | 0.106866i | ||||||
\(35\) | 1.13889e7 | 0.216841 | ||||||||
\(36\) | 7.74775e7 | 1.28134 | ||||||||
\(37\) | 1.00476e8i | 1.44895i | 0.689301 | + | 0.724475i | \(0.257918\pi\) | ||||
−0.689301 | + | 0.724475i | \(0.742082\pi\) | |||||||
\(38\) | 1.01868e8 | 1.28565 | ||||||||
\(39\) | 1.04680e8i | 1.16022i | ||||||||
\(40\) | 2.30147e8 | 2.24753 | ||||||||
\(41\) | 9.51556e7 | 0.821325 | 0.410662 | − | 0.911787i | \(-0.365298\pi\) | ||||
0.410662 | + | 0.911787i | \(0.365298\pi\) | |||||||
\(42\) | 7.25831e7i | 0.555379i | ||||||||
\(43\) | −1.46887e8 | + | 5.98259e6i | −0.999172 | + | 0.0406956i | ||||
\(44\) | 3.00514e8 | 1.82222 | ||||||||
\(45\) | − | 8.86101e7i | − | 0.480198i | ||||||
\(46\) | − | 6.03091e8i | − | 2.92815i | ||||||
\(47\) | 6.18096e6 | 0.0269505 | 0.0134752 | − | 0.999909i | \(-0.495711\pi\) | ||||
0.0134752 | + | 0.999909i | \(0.495711\pi\) | |||||||
\(48\) | 7.15971e8i | 2.80989i | ||||||||
\(49\) | 2.65706e8 | 0.940634 | ||||||||
\(50\) | 1.19391e8i | 0.382050i | ||||||||
\(51\) | − | 2.49042e7i | − | 0.0721808i | ||||||
\(52\) | −8.44251e8 | −2.22052 | ||||||||
\(53\) | −3.72498e8 | −0.890726 | −0.445363 | − | 0.895350i | \(-0.646925\pi\) | ||||
−0.445363 | + | 0.895350i | \(0.646925\pi\) | |||||||
\(54\) | −4.81891e8 | −1.04949 | ||||||||
\(55\) | − | 3.43694e8i | − | 0.682902i | ||||||
\(56\) | −3.38879e8 | −0.615325 | ||||||||
\(57\) | 5.22488e8 | 0.868365 | ||||||||
\(58\) | −3.56662e8 | −0.543397 | ||||||||
\(59\) | 7.30905e8 | 1.02235 | 0.511177 | − | 0.859476i | \(-0.329210\pi\) | ||||
0.511177 | + | 0.859476i | \(0.329210\pi\) | |||||||
\(60\) | 2.03911e9 | 2.62231 | ||||||||
\(61\) | − | 5.55615e8i | − | 0.657847i | −0.944357 | − | 0.328924i | \(-0.893314\pi\) | ||
0.944357 | − | 0.328924i | \(-0.106686\pi\) | |||||||
\(62\) | − | 2.50763e9i | − | 2.73719i | ||||||
\(63\) | 1.30474e8i | 0.131468i | ||||||||
\(64\) | −7.92916e8 | −0.738460 | ||||||||
\(65\) | 9.65560e8i | 0.832171i | ||||||||
\(66\) | 2.19042e9 | 1.74907 | ||||||||
\(67\) | −1.30656e9 | −0.967734 | −0.483867 | − | 0.875142i | \(-0.660768\pi\) | ||||
−0.483867 | + | 0.875142i | \(0.660768\pi\) | |||||||
\(68\) | 2.00853e8 | 0.138145 | ||||||||
\(69\) | − | 3.09328e9i | − | 1.97776i | ||||||
\(70\) | 6.69499e8i | 0.398345i | ||||||||
\(71\) | − | 2.26506e9i | − | 1.25541i | −0.778449 | − | 0.627707i | \(-0.783993\pi\) | ||
0.778449 | − | 0.627707i | \(-0.216007\pi\) | |||||||
\(72\) | 2.63662e9i | 1.36265i | ||||||||
\(73\) | 1.19629e9i | 0.577062i | 0.957471 | + | 0.288531i | \(0.0931668\pi\) | ||||
−0.957471 | + | 0.288531i | \(0.906833\pi\) | |||||||
\(74\) | −5.90651e9 | −2.66178 | ||||||||
\(75\) | 6.12362e8i | 0.258049i | ||||||||
\(76\) | 4.21389e9i | 1.66194i | ||||||||
\(77\) | 5.06071e8i | 0.186964i | ||||||||
\(78\) | −6.15367e9 | −2.13138 | ||||||||
\(79\) | −5.10251e9 | −1.65824 | −0.829122 | − | 0.559067i | \(-0.811159\pi\) | ||||
−0.829122 | + | 0.559067i | \(0.811159\pi\) | |||||||
\(80\) | 6.60404e9i | 2.01539i | ||||||||
\(81\) | −4.35302e9 | −1.24843 | ||||||||
\(82\) | 5.59375e9i | 1.50881i | ||||||||
\(83\) | 7.51268e9 | 1.90724 | 0.953618 | − | 0.301020i | \(-0.0973272\pi\) | ||||
0.953618 | + | 0.301020i | \(0.0973272\pi\) | |||||||
\(84\) | −3.00248e9 | −0.717932 | ||||||||
\(85\) | − | 2.29714e8i | − | 0.0517716i | ||||||
\(86\) | −3.51689e8 | − | 8.63478e9i | −0.0747595 | − | 1.83552i | ||||
\(87\) | −1.82934e9 | −0.367027 | ||||||||
\(88\) | 1.02267e10i | 1.93786i | ||||||||
\(89\) | − | 5.82403e9i | − | 1.04297i | −0.853259 | − | 0.521487i | \(-0.825377\pi\) | ||
0.853259 | − | 0.521487i | \(-0.174623\pi\) | |||||||
\(90\) | 5.20898e9 | 0.882145 | ||||||||
\(91\) | − | 1.42174e9i | − | 0.227831i | ||||||
\(92\) | 2.49475e10 | 3.78519 | ||||||||
\(93\) | − | 1.28618e10i | − | 1.84879i | ||||||
\(94\) | 3.63350e8i | 0.0495092i | ||||||||
\(95\) | 4.81938e9 | 0.622835 | ||||||||
\(96\) | −1.65386e10 | −2.02835 | ||||||||
\(97\) | −8.05991e9 | −0.938580 | −0.469290 | − | 0.883044i | \(-0.655490\pi\) | ||||
−0.469290 | + | 0.883044i | \(0.655490\pi\) | |||||||
\(98\) | 1.56196e10i | 1.72798i | ||||||||
\(99\) | 3.93744e9 | 0.414036 | ||||||||
\(100\) | −4.93872e9 | −0.493872 | ||||||||
\(101\) | 4.21055e8 | 0.0400620 | 0.0200310 | − | 0.999799i | \(-0.493624\pi\) | ||||
0.0200310 | + | 0.999799i | \(0.493624\pi\) | |||||||
\(102\) | 1.46400e9 | 0.132599 | ||||||||
\(103\) | 2.05118e9 | 0.176936 | 0.0884682 | − | 0.996079i | \(-0.471803\pi\) | ||||
0.0884682 | + | 0.996079i | \(0.471803\pi\) | |||||||
\(104\) | − | 2.87305e10i | − | 2.36144i | ||||||
\(105\) | 3.43390e9i | 0.269055i | ||||||||
\(106\) | − | 2.18974e10i | − | 1.63630i | ||||||
\(107\) | 1.77156e10 | 1.26309 | 0.631547 | − | 0.775337i | \(-0.282420\pi\) | ||||
0.631547 | + | 0.775337i | \(0.282420\pi\) | |||||||
\(108\) | − | 1.99339e10i | − | 1.35667i | ||||||
\(109\) | 1.07286e10 | 0.697288 | 0.348644 | − | 0.937255i | \(-0.386642\pi\) | ||||
0.348644 | + | 0.937255i | \(0.386642\pi\) | |||||||
\(110\) | 2.02042e10 | 1.25452 | ||||||||
\(111\) | −3.02948e10 | −1.79785 | ||||||||
\(112\) | − | 9.72410e9i | − | 0.551772i | ||||||
\(113\) | − | 2.05731e10i | − | 1.11663i | −0.829630 | − | 0.558314i | \(-0.811449\pi\) | ||
0.829630 | − | 0.558314i | \(-0.188551\pi\) | |||||||
\(114\) | 3.07147e10i | 1.59522i | ||||||||
\(115\) | − | 2.85321e10i | − | 1.41855i | ||||||
\(116\) | − | 1.47537e10i | − | 0.702443i | ||||||
\(117\) | −1.10617e10 | −0.504536 | ||||||||
\(118\) | 4.29665e10i | 1.87811i | ||||||||
\(119\) | 3.38241e8i | 0.0141740i | ||||||||
\(120\) | 6.93923e10i | 2.78872i | ||||||||
\(121\) | −1.06652e10 | −0.411190 | ||||||||
\(122\) | 3.26620e10 | 1.20849 | ||||||||
\(123\) | 2.86907e10i | 1.01910i | ||||||||
\(124\) | 1.03731e11 | 3.53834 | ||||||||
\(125\) | 3.28078e10i | 1.07505i | ||||||||
\(126\) | −7.66994e9 | −0.241512 | ||||||||
\(127\) | −1.51740e10 | −0.459283 | −0.229641 | − | 0.973275i | \(-0.573755\pi\) | ||||
−0.229641 | + | 0.973275i | \(0.573755\pi\) | |||||||
\(128\) | 9.55672e9i | 0.278137i | ||||||||
\(129\) | −1.80383e9 | − | 4.42883e10i | −0.0504949 | − | 1.23977i | ||||
\(130\) | −5.67608e10 | −1.52873 | ||||||||
\(131\) | 1.12052e10i | 0.290443i | 0.989399 | + | 0.145222i | \(0.0463895\pi\) | ||||
−0.989399 | + | 0.145222i | \(0.953610\pi\) | |||||||
\(132\) | 9.06088e10i | 2.26100i | ||||||||
\(133\) | −7.09628e9 | −0.170519 | ||||||||
\(134\) | − | 7.68067e10i | − | 1.77777i | ||||||
\(135\) | −2.27982e10 | −0.508431 | ||||||||
\(136\) | 6.83519e9i | 0.146912i | ||||||||
\(137\) | 7.63190e10i | 1.58136i | 0.612231 | + | 0.790679i | \(0.290272\pi\) | ||||
−0.612231 | + | 0.790679i | \(0.709728\pi\) | |||||||
\(138\) | 1.81840e11 | 3.63324 | ||||||||
\(139\) | −7.87273e10 | −1.51723 | −0.758615 | − | 0.651539i | \(-0.774123\pi\) | ||||
−0.758615 | + | 0.651539i | \(0.774123\pi\) | |||||||
\(140\) | −2.76945e10 | −0.514937 | ||||||||
\(141\) | 1.86364e9i | 0.0334400i | ||||||||
\(142\) | 1.33152e11 | 2.30625 | ||||||||
\(143\) | −4.29052e10 | −0.717513 | ||||||||
\(144\) | −7.56575e10 | −1.22191 | ||||||||
\(145\) | −1.68736e10 | −0.263250 | ||||||||
\(146\) | −7.03244e10 | −1.06009 | ||||||||
\(147\) | 8.01138e10i | 1.16713i | ||||||||
\(148\) | − | 2.44329e11i | − | 3.44086i | ||||||
\(149\) | 3.16960e10i | 0.431592i | 0.976438 | + | 0.215796i | \(0.0692346\pi\) | ||||
−0.976438 | + | 0.215796i | \(0.930765\pi\) | |||||||
\(150\) | −3.59979e10 | −0.474046 | ||||||||
\(151\) | 1.06479e11i | 1.35638i | 0.734888 | + | 0.678188i | \(0.237234\pi\) | ||||
−0.734888 | + | 0.678188i | \(0.762766\pi\) | |||||||
\(152\) | −1.43402e11 | −1.76741 | ||||||||
\(153\) | 2.63165e9 | 0.0313886 | ||||||||
\(154\) | −2.97496e10 | −0.343461 | ||||||||
\(155\) | − | 1.18636e11i | − | 1.32604i | ||||||
\(156\) | − | 2.54553e11i | − | 2.75521i | ||||||
\(157\) | 1.03422e11i | 1.08421i | 0.840311 | + | 0.542105i | \(0.182372\pi\) | ||||
−0.840311 | + | 0.542105i | \(0.817628\pi\) | |||||||
\(158\) | − | 2.99953e11i | − | 3.04626i | ||||||
\(159\) | − | 1.12313e11i | − | 1.10521i | ||||||
\(160\) | −1.52551e11 | −1.45484 | ||||||||
\(161\) | 4.20120e10i | 0.388369i | ||||||||
\(162\) | − | 2.55894e11i | − | 2.29343i | ||||||
\(163\) | 1.65963e11i | 1.44236i | 0.692748 | + | 0.721180i | \(0.256400\pi\) | ||||
−0.692748 | + | 0.721180i | \(0.743600\pi\) | |||||||
\(164\) | −2.31391e11 | −1.95042 | ||||||||
\(165\) | 1.03628e11 | 0.847342 | ||||||||
\(166\) | 4.41635e11i | 3.50367i | ||||||||
\(167\) | −1.88099e10 | −0.144812 | −0.0724061 | − | 0.997375i | \(-0.523068\pi\) | ||||
−0.0724061 | + | 0.997375i | \(0.523068\pi\) | |||||||
\(168\) | − | 1.02177e11i | − | 0.763492i | ||||||
\(169\) | −1.73223e10 | −0.125653 | ||||||||
\(170\) | 1.35038e10 | 0.0951067 | ||||||||
\(171\) | 5.52119e10i | 0.377618i | ||||||||
\(172\) | 3.57187e11 | − | 1.45480e10i | 2.37276 | − | 0.0966408i | ||||
\(173\) | 3.76642e10 | 0.243052 | 0.121526 | − | 0.992588i | \(-0.461221\pi\) | ||||
0.121526 | + | 0.992588i | \(0.461221\pi\) | |||||||
\(174\) | − | 1.07538e11i | − | 0.674245i | ||||||
\(175\) | − | 8.31691e9i | − | 0.0506724i | ||||||
\(176\) | −2.93454e11 | −1.73771 | ||||||||
\(177\) | 2.20378e11i | 1.26853i | ||||||||
\(178\) | 3.42368e11 | 1.91599 | ||||||||
\(179\) | − | 1.05319e11i | − | 0.573116i | −0.958063 | − | 0.286558i | \(-0.907489\pi\) | ||
0.958063 | − | 0.286558i | \(-0.0925111\pi\) | |||||||
\(180\) | 2.15475e11i | 1.14034i | ||||||||
\(181\) | −9.42249e10 | −0.485035 | −0.242517 | − | 0.970147i | \(-0.577973\pi\) | ||||
−0.242517 | + | 0.970147i | \(0.577973\pi\) | |||||||
\(182\) | 8.35773e10 | 0.418534 | ||||||||
\(183\) | 1.67525e11 | 0.816254 | ||||||||
\(184\) | 8.48981e11i | 4.02540i | ||||||||
\(185\) | −2.79436e11 | −1.28951 | ||||||||
\(186\) | 7.56084e11 | 3.39630 | ||||||||
\(187\) | 1.02074e10 | 0.0446384 | ||||||||
\(188\) | −1.50303e10 | −0.0639999 | ||||||||
\(189\) | 3.35691e10 | 0.139197 | ||||||||
\(190\) | 2.83309e11i | 1.14417i | ||||||||
\(191\) | − | 2.21542e10i | − | 0.0871542i | −0.999050 | − | 0.0435771i | \(-0.986125\pi\) | ||
0.999050 | − | 0.0435771i | \(-0.0138754\pi\) | |||||||
\(192\) | − | 2.39075e11i | − | 0.916278i | ||||||
\(193\) | −3.99665e11 | −1.49248 | −0.746241 | − | 0.665676i | \(-0.768143\pi\) | ||||
−0.746241 | + | 0.665676i | \(0.768143\pi\) | |||||||
\(194\) | − | 4.73804e11i | − | 1.72421i | ||||||
\(195\) | −2.91129e11 | −1.03255 | ||||||||
\(196\) | −6.46121e11 | −2.23375 | ||||||||
\(197\) | −2.90810e11 | −0.980117 | −0.490059 | − | 0.871689i | \(-0.663025\pi\) | ||||
−0.490059 | + | 0.871689i | \(0.663025\pi\) | |||||||
\(198\) | 2.31464e11i | 0.760601i | ||||||||
\(199\) | − | 4.67310e11i | − | 1.49741i | −0.662904 | − | 0.748704i | \(-0.730676\pi\) | ||
0.662904 | − | 0.748704i | \(-0.269324\pi\) | |||||||
\(200\) | − | 1.68068e11i | − | 0.525214i | ||||||
\(201\) | − | 3.93946e11i | − | 1.20076i | ||||||
\(202\) | 2.47519e10i | 0.0735955i | ||||||||
\(203\) | 2.48455e10 | 0.0720723 | ||||||||
\(204\) | 6.05599e10i | 0.171409i | ||||||||
\(205\) | 2.64640e11i | 0.730946i | ||||||||
\(206\) | 1.20579e11i | 0.325040i | ||||||||
\(207\) | 3.26871e11 | 0.860051 | ||||||||
\(208\) | 8.24419e11 | 2.11754 | ||||||||
\(209\) | 2.14152e11i | 0.537019i | ||||||||
\(210\) | −2.01863e11 | −0.494265 | ||||||||
\(211\) | − | 6.62830e11i | − | 1.58486i | −0.609965 | − | 0.792428i | \(-0.708817\pi\) | ||
0.609965 | − | 0.792428i | \(-0.291183\pi\) | |||||||
\(212\) | 9.05809e11 | 2.11523 | ||||||||
\(213\) | 6.82944e11 | 1.55771 | ||||||||
\(214\) | 1.04141e12i | 2.32036i | ||||||||
\(215\) | −1.66384e10 | − | 4.08510e11i | −0.0362175 | − | 0.889223i | ||||
\(216\) | 6.78367e11 | 1.44277 | ||||||||
\(217\) | 1.74685e11i | 0.363042i | ||||||||
\(218\) | 6.30687e11i | 1.28095i | ||||||||
\(219\) | −3.60697e11 | −0.716016 | ||||||||
\(220\) | 8.35766e11i | 1.62170i | ||||||||
\(221\) | −2.86764e10 | −0.0543955 | ||||||||
\(222\) | − | 1.78089e12i | − | 3.30273i | ||||||
\(223\) | − | 2.54463e11i | − | 0.461424i | −0.973022 | − | 0.230712i | \(-0.925894\pi\) | ||
0.973022 | − | 0.230712i | \(-0.0741056\pi\) | |||||||
\(224\) | 2.24623e11 | 0.398303 | ||||||||
\(225\) | −6.47089e10 | −0.112215 | ||||||||
\(226\) | 1.20940e12 | 2.05129 | ||||||||
\(227\) | − | 8.55296e11i | − | 1.41902i | −0.704698 | − | 0.709508i | \(-0.748917\pi\) | ||
0.704698 | − | 0.709508i | \(-0.251083\pi\) | |||||||
\(228\) | −1.27054e12 | −2.06213 | ||||||||
\(229\) | −1.39540e11 | −0.221575 | −0.110787 | − | 0.993844i | \(-0.535337\pi\) | ||||
−0.110787 | + | 0.993844i | \(0.535337\pi\) | |||||||
\(230\) | 1.67727e12 | 2.60594 | ||||||||
\(231\) | −1.52587e11 | −0.231984 | ||||||||
\(232\) | 5.02080e11 | 0.747021 | ||||||||
\(233\) | 4.38920e11i | 0.639154i | 0.947560 | + | 0.319577i | \(0.103541\pi\) | ||||
−0.947560 | + | 0.319577i | \(0.896459\pi\) | |||||||
\(234\) | − | 6.50265e11i | − | 0.926854i | ||||||
\(235\) | 1.71900e10i | 0.0239849i | ||||||||
\(236\) | −1.77735e12 | −2.42781 | ||||||||
\(237\) | − | 1.53847e12i | − | 2.05754i | ||||||
\(238\) | −1.98836e10 | −0.0260382 | ||||||||
\(239\) | −1.22437e12 | −1.57008 | −0.785041 | − | 0.619444i | \(-0.787358\pi\) | ||||
−0.785041 | + | 0.619444i | \(0.787358\pi\) | |||||||
\(240\) | −1.99121e12 | −2.50069 | ||||||||
\(241\) | − | 1.20039e11i | − | 0.147652i | −0.997271 | − | 0.0738259i | \(-0.976479\pi\) | ||
0.997271 | − | 0.0738259i | \(-0.0235209\pi\) | |||||||
\(242\) | − | 6.26958e11i | − | 0.755373i | ||||||
\(243\) | − | 8.28441e11i | − | 0.977755i | ||||||
\(244\) | 1.35110e12i | 1.56221i | ||||||||
\(245\) | 7.38961e11i | 0.837127i | ||||||||
\(246\) | −1.68659e12 | −1.87212 | ||||||||
\(247\) | − | 6.01629e11i | − | 0.654401i | ||||||
\(248\) | 3.53004e12i | 3.76288i | ||||||||
\(249\) | 2.26517e12i | 2.36649i | ||||||||
\(250\) | −1.92862e12 | −1.97490 | ||||||||
\(251\) | 8.36159e11 | 0.839306 | 0.419653 | − | 0.907685i | \(-0.362152\pi\) | ||||
0.419653 | + | 0.907685i | \(0.362152\pi\) | |||||||
\(252\) | − | 3.17275e11i | − | 0.312200i | ||||||
\(253\) | 1.26784e12 | 1.22310 | ||||||||
\(254\) | − | 8.92006e11i | − | 0.843722i | ||||||
\(255\) | 6.92617e10 | 0.0642380 | ||||||||
\(256\) | −1.37374e12 | −1.24941 | ||||||||
\(257\) | − | 5.72904e10i | − | 0.0510994i | −0.999674 | − | 0.0255497i | \(-0.991866\pi\) | ||
0.999674 | − | 0.0255497i | \(-0.00813361\pi\) | |||||||
\(258\) | 2.60350e12 | − | 1.06039e11i | 2.27750 | − | 0.0927612i | ||||
\(259\) | 4.11455e11 | 0.353040 | ||||||||
\(260\) | − | 2.34797e12i | − | 1.97618i | ||||||
\(261\) | − | 1.93308e11i | − | 0.159606i | ||||||
\(262\) | −6.58699e11 | −0.533557 | ||||||||
\(263\) | 1.94524e12i | 1.54594i | 0.634441 | + | 0.772971i | \(0.281230\pi\) | ||||
−0.634441 | + | 0.772971i | \(0.718770\pi\) | |||||||
\(264\) | −3.08349e12 | −2.40449 | ||||||||
\(265\) | − | 1.03596e12i | − | 0.792711i | ||||||
\(266\) | − | 4.17157e11i | − | 0.313250i | ||||||
\(267\) | 1.75602e12 | 1.29412 | ||||||||
\(268\) | 3.17719e12 | 2.29810 | ||||||||
\(269\) | −2.22693e11 | −0.158105 | −0.0790525 | − | 0.996870i | \(-0.525189\pi\) | ||||
−0.0790525 | + | 0.996870i | \(0.525189\pi\) | |||||||
\(270\) | − | 1.34020e12i | − | 0.934009i | ||||||
\(271\) | 1.96371e12 | 1.34348 | 0.671741 | − | 0.740786i | \(-0.265547\pi\) | ||||
0.671741 | + | 0.740786i | \(0.265547\pi\) | |||||||
\(272\) | −1.96135e11 | −0.131738 | ||||||||
\(273\) | 4.28672e11 | 0.282691 | ||||||||
\(274\) | −4.48644e12 | −2.90502 | ||||||||
\(275\) | −2.50988e11 | −0.159584 | ||||||||
\(276\) | 7.52199e12i | 4.69664i | ||||||||
\(277\) | 2.96481e12i | 1.81802i | 0.416774 | + | 0.909010i | \(0.363160\pi\) | ||||
−0.416774 | + | 0.909010i | \(0.636840\pi\) | |||||||
\(278\) | − | 4.62801e12i | − | 2.78721i | ||||||
\(279\) | 1.35912e12 | 0.803963 | ||||||||
\(280\) | − | 9.42466e11i | − | 0.547615i | ||||||
\(281\) | 1.19276e12 | 0.680803 | 0.340401 | − | 0.940280i | \(-0.389437\pi\) | ||||
0.340401 | + | 0.940280i | \(0.389437\pi\) | |||||||
\(282\) | −1.09555e11 | −0.0614307 | ||||||||
\(283\) | −1.85174e12 | −1.02011 | −0.510056 | − | 0.860141i | \(-0.670375\pi\) | ||||
−0.510056 | + | 0.860141i | \(0.670375\pi\) | |||||||
\(284\) | 5.50798e12i | 2.98126i | ||||||||
\(285\) | 1.45311e12i | 0.772810i | ||||||||
\(286\) | − | 2.52220e12i | − | 1.31810i | ||||||
\(287\) | − | 3.89668e11i | − | 0.200117i | ||||||
\(288\) | − | 1.74766e12i | − | 0.882050i | ||||||
\(289\) | −2.00917e12 | −0.996616 | ||||||||
\(290\) | − | 9.91923e11i | − | 0.483602i | ||||||
\(291\) | − | 2.43017e12i | − | 1.16459i | ||||||
\(292\) | − | 2.90904e12i | − | 1.37036i | ||||||
\(293\) | 1.59940e12 | 0.740662 | 0.370331 | − | 0.928900i | \(-0.379244\pi\) | ||||
0.370331 | + | 0.928900i | \(0.379244\pi\) | |||||||
\(294\) | −4.70952e12 | −2.14407 | ||||||||
\(295\) | 2.03274e12i | 0.909854i | ||||||||
\(296\) | 8.31470e12 | 3.65921 | ||||||||
\(297\) | − | 1.01305e12i | − | 0.438378i | ||||||
\(298\) | −1.86326e12 | −0.792853 | ||||||||
\(299\) | −3.56182e12 | −1.49045 | ||||||||
\(300\) | − | 1.48909e12i | − | 0.612794i | ||||||
\(301\) | 2.44991e10 | + | 6.01510e11i | 0.00991556 | + | 0.243450i | ||||
\(302\) | −6.25942e12 | −2.49172 | ||||||||
\(303\) | 1.26954e11i | 0.0497087i | ||||||||
\(304\) | − | 4.11490e12i | − | 1.58486i | ||||||
\(305\) | 1.54524e12 | 0.585458 | ||||||||
\(306\) | 1.54703e11i | 0.0576621i | ||||||||
\(307\) | −4.23749e12 | −1.55388 | −0.776938 | − | 0.629577i | \(-0.783228\pi\) | ||||
−0.776938 | + | 0.629577i | \(0.783228\pi\) | |||||||
\(308\) | − | 1.23062e12i | − | 0.443988i | ||||||
\(309\) | 6.18457e11i | 0.219542i | ||||||||
\(310\) | 6.97404e12 | 2.43599 | ||||||||
\(311\) | 1.81080e12 | 0.622400 | 0.311200 | − | 0.950345i | \(-0.399269\pi\) | ||||
0.311200 | + | 0.950345i | \(0.399269\pi\) | |||||||
\(312\) | 8.66263e12 | 2.93006 | ||||||||
\(313\) | − | 2.35705e12i | − | 0.784597i | −0.919838 | − | 0.392299i | \(-0.871680\pi\) | ||
0.919838 | − | 0.392299i | \(-0.128320\pi\) | |||||||
\(314\) | −6.07968e12 | −1.99174 | ||||||||
\(315\) | −3.62864e11 | −0.117001 | ||||||||
\(316\) | 1.24079e13 | 3.93787 | ||||||||
\(317\) | −2.44343e11 | −0.0763315 | −0.0381657 | − | 0.999271i | \(-0.512151\pi\) | ||||
−0.0381657 | + | 0.999271i | \(0.512151\pi\) | |||||||
\(318\) | 6.60236e12 | 2.03032 | ||||||||
\(319\) | − | 7.49789e11i | − | 0.226979i | ||||||
\(320\) | − | 2.20520e12i | − | 0.657201i | ||||||
\(321\) | 5.34147e12i | 1.56724i | ||||||||
\(322\) | −2.46969e12 | −0.713450 | ||||||||
\(323\) | 1.43132e11i | 0.0407121i | ||||||||
\(324\) | 1.05853e13 | 2.96469 | ||||||||
\(325\) | 7.05116e11 | 0.194466 | ||||||||
\(326\) | −9.75620e12 | −2.64968 | ||||||||
\(327\) | 3.23483e12i | 0.865192i | ||||||||
\(328\) | − | 7.87442e12i | − | 2.07419i | ||||||
\(329\) | − | 2.53114e10i | − | 0.00656654i | ||||||
\(330\) | 6.09182e12i | 1.55660i | ||||||||
\(331\) | 4.84332e12i | 1.21900i | 0.792787 | + | 0.609499i | \(0.208629\pi\) | ||||
−0.792787 | + | 0.609499i | \(0.791371\pi\) | |||||||
\(332\) | −1.82687e13 | −4.52916 | ||||||||
\(333\) | − | 3.20129e12i | − | 0.781814i | ||||||
\(334\) | − | 1.10575e12i | − | 0.266026i | ||||||
\(335\) | − | 3.63371e12i | − | 0.861245i | ||||||
\(336\) | 2.93195e12 | 0.684636 | ||||||||
\(337\) | 1.12548e12 | 0.258934 | 0.129467 | − | 0.991584i | \(-0.458673\pi\) | ||||
0.129467 | + | 0.991584i | \(0.458673\pi\) | |||||||
\(338\) | − | 1.01830e12i | − | 0.230829i | ||||||
\(339\) | 6.20307e12 | 1.38551 | ||||||||
\(340\) | 5.58598e11i | 0.122943i | ||||||||
\(341\) | 5.27164e12 | 1.14334 | ||||||||
\(342\) | −3.24565e12 | −0.693699 | ||||||||
\(343\) | − | 2.24483e12i | − | 0.472839i | ||||||
\(344\) | 4.95078e11 | + | 1.21553e13i | 0.102774 | + | 2.52333i | ||||
\(345\) | 8.60282e12 | 1.76013 | ||||||||
\(346\) | 2.21410e12i | 0.446496i | ||||||||
\(347\) | 7.96450e12i | 1.58311i | 0.611098 | + | 0.791555i | \(0.290728\pi\) | ||||
−0.611098 | + | 0.791555i | \(0.709272\pi\) | |||||||
\(348\) | 4.44844e12 | 0.871588 | ||||||||
\(349\) | − | 6.88437e12i | − | 1.32965i | −0.747000 | − | 0.664825i | \(-0.768506\pi\) | ||
0.747000 | − | 0.664825i | \(-0.231494\pi\) | |||||||
\(350\) | 4.88912e11 | 0.0930874 | ||||||||
\(351\) | 2.84602e12i | 0.534199i | ||||||||
\(352\) | − | 6.77867e12i | − | 1.25439i | ||||||
\(353\) | −7.60397e12 | −1.38729 | −0.693644 | − | 0.720318i | \(-0.743996\pi\) | ||||
−0.693644 | + | 0.720318i | \(0.743996\pi\) | |||||||
\(354\) | −1.29550e13 | −2.33035 | ||||||||
\(355\) | 6.29941e12 | 1.11727 | ||||||||
\(356\) | 1.41624e13i | 2.47678i | ||||||||
\(357\) | −1.01984e11 | −0.0175870 | ||||||||
\(358\) | 6.19123e12 | 1.05284 | ||||||||
\(359\) | 1.16452e12 | 0.195287 | 0.0976434 | − | 0.995221i | \(-0.468870\pi\) | ||||
0.0976434 | + | 0.995221i | \(0.468870\pi\) | |||||||
\(360\) | −7.33276e12 | −1.21271 | ||||||||
\(361\) | 3.12817e12 | 0.510216 | ||||||||
\(362\) | − | 5.53904e12i | − | 0.891029i | ||||||
\(363\) | − | 3.21570e12i | − | 0.510202i | ||||||
\(364\) | 3.45726e12i | 0.541035i | ||||||||
\(365\) | −3.32704e12 | −0.513562 | ||||||||
\(366\) | 9.84804e12i | 1.49949i | ||||||||
\(367\) | −2.37467e11 | −0.0356675 | −0.0178338 | − | 0.999841i | \(-0.505677\pi\) | ||||
−0.0178338 | + | 0.999841i | \(0.505677\pi\) | |||||||
\(368\) | −2.43614e13 | −3.60964 | ||||||||
\(369\) | −3.03177e12 | −0.443164 | ||||||||
\(370\) | − | 1.64268e13i | − | 2.36888i | ||||||
\(371\) | 1.52540e12i | 0.217027i | ||||||||
\(372\) | 3.12762e13i | 4.39035i | ||||||||
\(373\) | − | 7.65200e12i | − | 1.05982i | −0.848055 | − | 0.529908i | \(-0.822226\pi\) | ||
0.848055 | − | 0.529908i | \(-0.177774\pi\) | |||||||
\(374\) | 6.00048e11i | 0.0820027i | ||||||||
\(375\) | −9.89199e12 | −1.33391 | ||||||||
\(376\) | − | 5.11494e11i | − | 0.0680614i | ||||||
\(377\) | 2.10643e12i | 0.276592i | ||||||||
\(378\) | 1.97337e12i | 0.255712i | ||||||||
\(379\) | 2.37829e12 | 0.304136 | 0.152068 | − | 0.988370i | \(-0.451407\pi\) | ||||
0.152068 | + | 0.988370i | \(0.451407\pi\) | |||||||
\(380\) | −1.17194e13 | −1.47906 | ||||||||
\(381\) | − | 4.57515e12i | − | 0.569876i | ||||||
\(382\) | 1.30234e12 | 0.160106 | ||||||||
\(383\) | 1.19635e13i | 1.45166i | 0.687876 | + | 0.725829i | \(0.258543\pi\) | ||||
−0.687876 | + | 0.725829i | \(0.741457\pi\) | |||||||
\(384\) | −2.88148e12 | −0.345111 | ||||||||
\(385\) | −1.40745e12 | −0.166390 | ||||||||
\(386\) | − | 2.34944e13i | − | 2.74175i | ||||||
\(387\) | 4.67999e12 | − | 1.90613e11i | 0.539126 | − | 0.0219582i | ||||
\(388\) | 1.95994e13 | 2.22887 | ||||||||
\(389\) | − | 3.01793e12i | − | 0.338814i | −0.985546 | − | 0.169407i | \(-0.945815\pi\) | ||
0.985546 | − | 0.169407i | \(-0.0541853\pi\) | |||||||
\(390\) | − | 1.71141e13i | − | 1.89685i | ||||||
\(391\) | 8.47382e11 | 0.0927247 | ||||||||
\(392\) | − | 2.19880e13i | − | 2.37550i | ||||||
\(393\) | −3.37850e12 | −0.360381 | ||||||||
\(394\) | − | 1.70954e13i | − | 1.80052i | ||||||
\(395\) | − | 1.41907e13i | − | 1.47577i | ||||||
\(396\) | −9.57473e12 | −0.983220 | ||||||||
\(397\) | −3.39287e12 | −0.344045 | −0.172022 | − | 0.985093i | \(-0.555030\pi\) | ||||
−0.172022 | + | 0.985093i | \(0.555030\pi\) | |||||||
\(398\) | 2.74710e13 | 2.75080 | ||||||||
\(399\) | − | 2.13962e12i | − | 0.211579i | ||||||
\(400\) | 4.82271e12 | 0.470968 | ||||||||
\(401\) | 1.35236e13 | 1.30428 | 0.652141 | − | 0.758098i | \(-0.273871\pi\) | ||||
0.652141 | + | 0.758098i | \(0.273871\pi\) | |||||||
\(402\) | 2.31582e13 | 2.20585 | ||||||||
\(403\) | −1.48099e13 | −1.39325 | ||||||||
\(404\) | −1.02389e12 | −0.0951361 | ||||||||
\(405\) | − | 1.21063e13i | − | 1.11106i | ||||||
\(406\) | 1.46055e12i | 0.132400i | ||||||||
\(407\) | − | 1.24169e13i | − | 1.11184i | ||||||
\(408\) | −2.06090e12 | −0.182287 | ||||||||
\(409\) | 8.00571e12i | 0.699493i | 0.936844 | + | 0.349746i | \(0.113732\pi\) | ||||
−0.936844 | + | 0.349746i | \(0.886268\pi\) | |||||||
\(410\) | −1.55569e13 | −1.34278 | ||||||||
\(411\) | −2.30112e13 | −1.96214 | ||||||||
\(412\) | −4.98789e12 | −0.420175 | ||||||||
\(413\) | − | 2.99310e12i | − | 0.249099i | ||||||
\(414\) | 1.92152e13i | 1.57995i | ||||||||
\(415\) | 2.08937e13i | 1.69736i | ||||||||
\(416\) | 1.90437e13i | 1.52857i | ||||||||
\(417\) | − | 2.37373e13i | − | 1.88257i | ||||||
\(418\) | −1.25890e13 | −0.986527 | ||||||||
\(419\) | 2.17731e13i | 1.68597i | 0.537936 | + | 0.842986i | \(0.319204\pi\) | ||||
−0.537936 | + | 0.842986i | \(0.680796\pi\) | |||||||
\(420\) | − | 8.35027e12i | − | 0.638931i | ||||||
\(421\) | − | 3.22439e11i | − | 0.0243802i | −0.999926 | − | 0.0121901i | \(-0.996120\pi\) | ||
0.999926 | − | 0.0121901i | \(-0.00388033\pi\) | |||||||
\(422\) | 3.89647e13 | 2.91145 | ||||||||
\(423\) | −1.96933e11 | −0.0145417 | ||||||||
\(424\) | 3.08254e13i | 2.24946i | ||||||||
\(425\) | −1.67752e11 | −0.0120983 | ||||||||
\(426\) | 4.01471e13i | 2.86158i | ||||||||
\(427\) | −2.27528e12 | −0.160286 | ||||||||
\(428\) | −4.30792e13 | −2.99950 | ||||||||
\(429\) | − | 1.29365e13i | − | 0.890287i | ||||||
\(430\) | 2.40144e13 | − | 9.78091e11i | 1.63354 | − | 0.0665330i | ||||
\(431\) | −1.35035e13 | −0.907947 | −0.453974 | − | 0.891015i | \(-0.649994\pi\) | ||||
−0.453974 | + | 0.891015i | \(0.649994\pi\) | |||||||
\(432\) | 1.94657e13i | 1.29375i | ||||||||
\(433\) | − | 8.25814e12i | − | 0.542554i | −0.962501 | − | 0.271277i | \(-0.912554\pi\) | ||
0.962501 | − | 0.271277i | \(-0.0874459\pi\) | |||||||
\(434\) | −1.02689e13 | −0.666923 | ||||||||
\(435\) | − | 5.08763e12i | − | 0.326640i | ||||||
\(436\) | −2.60890e13 | −1.65587 | ||||||||
\(437\) | 1.77780e13i | 1.11552i | ||||||||
\(438\) | − | 2.12037e13i | − | 1.31535i | ||||||
\(439\) | 7.62272e12 | 0.467506 | 0.233753 | − | 0.972296i | \(-0.424899\pi\) | ||||
0.233753 | + | 0.972296i | \(0.424899\pi\) | |||||||
\(440\) | −2.84418e13 | −1.72462 | ||||||||
\(441\) | −8.46571e12 | −0.507540 | ||||||||
\(442\) | − | 1.68575e12i | − | 0.0999269i | ||||||
\(443\) | 2.83041e13 | 1.65894 | 0.829469 | − | 0.558553i | \(-0.188643\pi\) | ||||
0.829469 | + | 0.558553i | \(0.188643\pi\) | |||||||
\(444\) | 7.36684e13 | 4.26940 | ||||||||
\(445\) | 1.61974e13 | 0.928206 | ||||||||
\(446\) | 1.49587e13 | 0.847656 | ||||||||
\(447\) | −9.55677e12 | −0.535518 | ||||||||
\(448\) | 3.24704e12i | 0.179927i | ||||||||
\(449\) | − | 1.76773e13i | − | 0.968690i | −0.874877 | − | 0.484345i | \(-0.839058\pi\) | ||
0.874877 | − | 0.484345i | \(-0.160942\pi\) | |||||||
\(450\) | − | 3.80394e12i | − | 0.206144i | ||||||
\(451\) | −1.17594e13 | −0.630235 | ||||||||
\(452\) | 5.00280e13i | 2.65168i | ||||||||
\(453\) | −3.21049e13 | −1.68298 | ||||||||
\(454\) | 5.02789e13 | 2.60679 | ||||||||
\(455\) | 3.95403e12 | 0.202760 | ||||||||
\(456\) | − | 4.32375e13i | − | 2.19299i | ||||||
\(457\) | 3.19607e13i | 1.60338i | 0.597742 | + | 0.801689i | \(0.296065\pi\) | ||||
−0.597742 | + | 0.801689i | \(0.703935\pi\) | |||||||
\(458\) | − | 8.20289e12i | − | 0.407042i | ||||||
\(459\) | − | 6.77089e11i | − | 0.0332340i | ||||||
\(460\) | 6.93821e13i | 3.36867i | ||||||||
\(461\) | 2.66536e13 | 1.28012 | 0.640061 | − | 0.768324i | \(-0.278909\pi\) | ||||
0.640061 | + | 0.768324i | \(0.278909\pi\) | |||||||
\(462\) | − | 8.96989e12i | − | 0.426164i | ||||||
\(463\) | 8.75833e12i | 0.411639i | 0.978590 | + | 0.205820i | \(0.0659860\pi\) | ||||
−0.978590 | + | 0.205820i | \(0.934014\pi\) | |||||||
\(464\) | 1.44071e13i | 0.669865i | ||||||||
\(465\) | 3.57702e13 | 1.64535 | ||||||||
\(466\) | −2.58021e13 | −1.17415 | ||||||||
\(467\) | − | 2.30755e13i | − | 1.03889i | −0.854505 | − | 0.519443i | \(-0.826140\pi\) | ||
0.854505 | − | 0.519443i | \(-0.173860\pi\) | |||||||
\(468\) | 2.68989e13 | 1.19813 | ||||||||
\(469\) | 5.35045e12i | 0.235790i | ||||||||
\(470\) | −1.01052e12 | −0.0440612 | ||||||||
\(471\) | −3.11830e13 | −1.34528 | ||||||||
\(472\) | − | 6.04847e13i | − | 2.58188i | ||||||
\(473\) | 1.81524e13 | − | 7.39334e11i | 0.766704 | − | 0.0312273i | ||||
\(474\) | 9.04398e13 | 3.77979 | ||||||||
\(475\) | − | 3.51943e12i | − | 0.145547i | ||||||
\(476\) | − | 8.22506e11i | − | 0.0336593i | ||||||
\(477\) | 1.18682e13 | 0.480612 | ||||||||
\(478\) | − | 7.19749e13i | − | 2.88431i | ||||||
\(479\) | −2.26972e13 | −0.900110 | −0.450055 | − | 0.893001i | \(-0.648596\pi\) | ||||
−0.450055 | + | 0.893001i | \(0.648596\pi\) | |||||||
\(480\) | − | 4.59960e13i | − | 1.80515i | ||||||
\(481\) | 3.48836e13i | 1.35486i | ||||||||
\(482\) | 7.05656e12 | 0.271242 | ||||||||
\(483\) | −1.26672e13 | −0.481886 | ||||||||
\(484\) | 2.59348e13 | 0.976462 | ||||||||
\(485\) | − | 2.24156e13i | − | 0.835299i | ||||||
\(486\) | 4.87002e13 | 1.79618 | ||||||||
\(487\) | −3.49809e13 | −1.27698 | −0.638492 | − | 0.769628i | \(-0.720442\pi\) | ||||
−0.638492 | + | 0.769628i | \(0.720442\pi\) | |||||||
\(488\) | −4.59789e13 | −1.66134 | ||||||||
\(489\) | −5.00401e13 | −1.78967 | ||||||||
\(490\) | −4.34401e13 | −1.53784 | ||||||||
\(491\) | − | 1.18333e13i | − | 0.414666i | −0.978270 | − | 0.207333i | \(-0.933522\pi\) | ||
0.978270 | − | 0.207333i | \(-0.0664784\pi\) | |||||||
\(492\) | − | 6.97676e13i | − | 2.42007i | ||||||
\(493\) | − | 5.01134e11i | − | 0.0172076i | ||||||
\(494\) | 3.53670e13 | 1.20216 | ||||||||
\(495\) | 1.09505e13i | 0.368475i | ||||||||
\(496\) | −1.01294e14 | −3.37424 | ||||||||
\(497\) | −9.27554e12 | −0.305884 | ||||||||
\(498\) | −1.33159e14 | −4.34734 | ||||||||
\(499\) | 2.21676e13i | 0.716501i | 0.933625 | + | 0.358251i | \(0.116627\pi\) | ||||
−0.933625 | + | 0.358251i | \(0.883373\pi\) | |||||||
\(500\) | − | 7.97793e13i | − | 2.55294i | ||||||
\(501\) | − | 5.67145e12i | − | 0.179682i | ||||||
\(502\) | 4.91539e13i | 1.54184i | ||||||||
\(503\) | 4.12286e12i | 0.128044i | 0.997948 | + | 0.0640220i | \(0.0203928\pi\) | ||||
−0.997948 | + | 0.0640220i | \(0.979607\pi\) | |||||||
\(504\) | 1.07971e13 | 0.332013 | ||||||||
\(505\) | 1.17101e12i | 0.0356536i | ||||||||
\(506\) | 7.45305e13i | 2.24689i | ||||||||
\(507\) | − | 5.22290e12i | − | 0.155909i | ||||||
\(508\) | 3.68988e13 | 1.09067 | ||||||||
\(509\) | −2.25492e13 | −0.659997 | −0.329999 | − | 0.943981i | \(-0.607048\pi\) | ||||
−0.329999 | + | 0.943981i | \(0.607048\pi\) | |||||||
\(510\) | 4.07157e12i | 0.118008i | ||||||||
\(511\) | 4.89888e12 | 0.140602 | ||||||||
\(512\) | − | 7.09697e13i | − | 2.01708i | ||||||
\(513\) | 1.42053e13 | 0.399819 | ||||||||
\(514\) | 3.36783e12 | 0.0938718 | ||||||||
\(515\) | 5.70459e12i | 0.157466i | ||||||||
\(516\) | 4.38641e12 | + | 1.07697e14i | 0.119911 | + | 2.94410i | ||||
\(517\) | −7.63848e11 | −0.0206802 | ||||||||
\(518\) | 2.41875e13i | 0.648549i | ||||||||
\(519\) | 1.13563e13i | 0.301577i | ||||||||
\(520\) | 7.99032e13 | 2.10159 | ||||||||
\(521\) | 2.68827e13i | 0.700299i | 0.936694 | + | 0.350150i | \(0.113869\pi\) | ||||
−0.936694 | + | 0.350150i | \(0.886131\pi\) | |||||||
\(522\) | 1.13637e13 | 0.293202 | ||||||||
\(523\) | − | 2.93357e13i | − | 0.749700i | −0.927085 | − | 0.374850i | \(-0.877694\pi\) | ||
0.927085 | − | 0.374850i | \(-0.122306\pi\) | |||||||
\(524\) | − | 2.72478e13i | − | 0.689723i | ||||||
\(525\) | 2.50766e12 | 0.0628741 | ||||||||
\(526\) | −1.14351e14 | −2.83996 | ||||||||
\(527\) | 3.52339e12 | 0.0866777 | ||||||||
\(528\) | − | 8.84803e13i | − | 2.15614i | ||||||
\(529\) | 6.38247e13 | 1.54067 | ||||||||
\(530\) | 6.08995e13 | 1.45624 | ||||||||
\(531\) | −2.32875e13 | −0.551634 | ||||||||
\(532\) | 1.72561e13 | 0.404935 | ||||||||
\(533\) | 3.30364e13 | 0.767992 | ||||||||
\(534\) | 1.03228e14i | 2.37735i | ||||||||
\(535\) | 4.92692e13i | 1.12410i | ||||||||
\(536\) | 1.08122e14i | 2.44394i | ||||||||
\(537\) | 3.17552e13 | 0.711120 | ||||||||
\(538\) | − | 1.30911e13i | − | 0.290445i | ||||||
\(539\) | −3.28361e13 | −0.721786 | ||||||||
\(540\) | 5.54388e13 | 1.20738 | ||||||||
\(541\) | 1.04143e13 | 0.224722 | 0.112361 | − | 0.993667i | \(-0.464159\pi\) | ||||
0.112361 | + | 0.993667i | \(0.464159\pi\) | |||||||
\(542\) | 1.15438e14i | 2.46803i | ||||||||
\(543\) | − | 2.84101e13i | − | 0.601829i | ||||||
\(544\) | − | 4.53064e12i | − | 0.0950965i | ||||||
\(545\) | 2.98377e13i | 0.620559i | ||||||||
\(546\) | 2.51997e13i | 0.519316i | ||||||||
\(547\) | −2.26544e13 | −0.462611 | −0.231306 | − | 0.972881i | \(-0.574300\pi\) | ||||
−0.231306 | + | 0.972881i | \(0.574300\pi\) | |||||||
\(548\) | − | 1.85586e14i | − | 3.75529i | ||||||
\(549\) | 1.77026e13i | 0.354957i | ||||||||
\(550\) | − | 1.47544e13i | − | 0.293163i | ||||||
\(551\) | 1.05138e13 | 0.207014 | ||||||||
\(552\) | −2.55979e14 | −4.99470 | ||||||||
\(553\) | 2.08951e13i | 0.404035i | ||||||||
\(554\) | −1.74288e14 | −3.33978 | ||||||||
\(555\) | − | 8.42537e13i | − | 1.60002i | ||||||
\(556\) | 1.91442e14 | 3.60300 | ||||||||
\(557\) | −7.42359e13 | −1.38464 | −0.692322 | − | 0.721589i | \(-0.743412\pi\) | ||||
−0.692322 | + | 0.721589i | \(0.743412\pi\) | |||||||
\(558\) | 7.98963e13i | 1.47691i | ||||||||
\(559\) | −5.09966e13 | + | 2.07706e12i | −0.934291 | + | 0.0380530i | ||||
\(560\) | 2.70440e13 | 0.491055 | ||||||||
\(561\) | 3.07768e12i | 0.0553872i | ||||||||
\(562\) | 7.01168e13i | 1.25066i | ||||||||
\(563\) | 6.40693e13 | 1.13268 | 0.566341 | − | 0.824171i | \(-0.308359\pi\) | ||||
0.566341 | + | 0.824171i | \(0.308359\pi\) | |||||||
\(564\) | − | 4.53185e12i | − | 0.0794108i | ||||||
\(565\) | 5.72165e13 | 0.993754 | ||||||||
\(566\) | − | 1.08855e14i | − | 1.87399i | ||||||
\(567\) | 1.78259e13i | 0.304184i | ||||||||
\(568\) | −1.87441e14 | −3.17046 | ||||||||
\(569\) | −3.19302e13 | −0.535352 | −0.267676 | − | 0.963509i | \(-0.586256\pi\) | ||||
−0.267676 | + | 0.963509i | \(0.586256\pi\) | |||||||
\(570\) | −8.54213e13 | −1.41969 | ||||||||
\(571\) | 9.43273e13i | 1.55402i | 0.629488 | + | 0.777011i | \(0.283265\pi\) | ||||
−0.629488 | + | 0.777011i | \(0.716735\pi\) | |||||||
\(572\) | 1.04333e14 | 1.70389 | ||||||||
\(573\) | 6.67977e12 | 0.108141 | ||||||||
\(574\) | 2.29068e13 | 0.367624 | ||||||||
\(575\) | −2.08360e13 | −0.331494 | ||||||||
\(576\) | 2.52633e13 | 0.398453 | ||||||||
\(577\) | 6.67376e13i | 1.04350i | 0.853099 | + | 0.521749i | \(0.174720\pi\) | ||||
−0.853099 | + | 0.521749i | \(0.825280\pi\) | |||||||
\(578\) | − | 1.18110e14i | − | 1.83083i | ||||||
\(579\) | − | 1.20504e14i | − | 1.85186i | ||||||
\(580\) | 4.10319e13 | 0.625147 | ||||||||
\(581\) | − | 3.07649e13i | − | 0.464702i | ||||||
\(582\) | 1.42858e14 | 2.13939 | ||||||||
\(583\) | 4.60336e13 | 0.683490 | ||||||||
\(584\) | 9.89968e13 | 1.45733 | ||||||||
\(585\) | − | 3.07639e13i | − | 0.449017i | ||||||
\(586\) | 9.40215e13i | 1.36063i | ||||||||
\(587\) | − | 3.87372e13i | − | 0.555825i | −0.960606 | − | 0.277912i | \(-0.910357\pi\) | ||
0.960606 | − | 0.277912i | \(-0.0896425\pi\) | |||||||
\(588\) | − | 1.94814e14i | − | 2.77162i | ||||||
\(589\) | 7.39205e13i | 1.04277i | ||||||||
\(590\) | −1.19495e14 | −1.67144 | ||||||||
\(591\) | − | 8.76830e13i | − | 1.21612i | ||||||
\(592\) | 2.38589e14i | 3.28128i | ||||||||
\(593\) | 2.58904e13i | 0.353073i | 0.984294 | + | 0.176537i | \(0.0564894\pi\) | ||||
−0.984294 | + | 0.176537i | \(0.943511\pi\) | |||||||
\(594\) | 5.95525e13 | 0.805319 | ||||||||
\(595\) | −9.40691e11 | −0.0126143 | ||||||||
\(596\) | − | 7.70758e13i | − | 1.02491i | ||||||
\(597\) | 1.40900e14 | 1.85798 | ||||||||
\(598\) | − | 2.09383e14i | − | 2.73801i | ||||||
\(599\) | 3.67692e12 | 0.0476815 | 0.0238407 | − | 0.999716i | \(-0.492411\pi\) | ||||
0.0238407 | + | 0.999716i | \(0.492411\pi\) | |||||||
\(600\) | 5.06749e13 | 0.651683 | ||||||||
\(601\) | 1.31596e14i | 1.67830i | 0.543902 | + | 0.839148i | \(0.316946\pi\) | ||||
−0.543902 | + | 0.839148i | \(0.683054\pi\) | |||||||
\(602\) | −3.53600e13 | + | 1.44019e12i | −0.447228 | + | 0.0182153i | ||||
\(603\) | 4.16287e13 | 0.522163 | ||||||||
\(604\) | − | 2.58927e14i | − | 3.22102i | ||||||
\(605\) | − | 2.96613e13i | − | 0.365943i | ||||||
\(606\) | −7.46302e12 | −0.0913170 | ||||||||
\(607\) | − | 9.60688e12i | − | 0.116584i | −0.998300 | − | 0.0582920i | \(-0.981435\pi\) | ||
0.998300 | − | 0.0582920i | \(-0.0185654\pi\) | |||||||
\(608\) | 9.50525e13 | 1.14405 | ||||||||
\(609\) | 7.49126e12i | 0.0894269i | ||||||||
\(610\) | 9.08373e13i | 1.07551i | ||||||||
\(611\) | 2.14593e12 | 0.0252005 | ||||||||
\(612\) | −6.39943e12 | −0.0745391 | ||||||||
\(613\) | 5.67285e12 | 0.0655388 | 0.0327694 | − | 0.999463i | \(-0.489567\pi\) | ||||
0.0327694 | + | 0.999463i | \(0.489567\pi\) | |||||||
\(614\) | − | 2.49102e14i | − | 2.85454i | ||||||
\(615\) | −7.97924e13 | −0.906955 | ||||||||
\(616\) | 4.18790e13 | 0.472163 | ||||||||
\(617\) | 6.89629e13 | 0.771240 | 0.385620 | − | 0.922658i | \(-0.373988\pi\) | ||||
0.385620 | + | 0.922658i | \(0.373988\pi\) | |||||||
\(618\) | −3.63562e13 | −0.403308 | ||||||||
\(619\) | 8.35140e13 | 0.918980 | 0.459490 | − | 0.888183i | \(-0.348032\pi\) | ||||
0.459490 | + | 0.888183i | \(0.348032\pi\) | |||||||
\(620\) | 2.88489e14i | 3.14898i | ||||||||
\(621\) | − | 8.40995e13i | − | 0.910616i | ||||||
\(622\) | 1.06449e14i | 1.14337i | ||||||||
\(623\) | −2.38498e13 | −0.254123 | ||||||||
\(624\) | 2.48573e14i | 2.62743i | ||||||||
\(625\) | −7.14090e13 | −0.748778 | ||||||||
\(626\) | 1.38560e14 | 1.44134 | ||||||||
\(627\) | −6.45695e13 | −0.666331 | ||||||||
\(628\) | − | 2.51492e14i | − | 2.57470i | ||||||
\(629\) | − | 8.29904e12i | − | 0.0842897i | ||||||
\(630\) | − | 2.13311e13i | − | 0.214936i | ||||||
\(631\) | − | 1.17694e13i | − | 0.117654i | −0.998268 | − | 0.0588271i | \(-0.981264\pi\) | ||
0.998268 | − | 0.0588271i | \(-0.0187361\pi\) | |||||||
\(632\) | 4.22249e14i | 4.18777i | ||||||||
\(633\) | 1.99852e14 | 1.96648 | ||||||||
\(634\) | − | 1.43638e13i | − | 0.140224i | ||||||
\(635\) | − | 4.22007e13i | − | 0.408743i | ||||||
\(636\) | 2.73113e14i | 2.62457i | ||||||||
\(637\) | 9.22486e13 | 0.879554 | ||||||||
\(638\) | 4.40766e13 | 0.416970 | ||||||||
\(639\) | 7.21675e13i | 0.677388i | ||||||||
\(640\) | −2.65784e13 | −0.247531 | ||||||||
\(641\) | − | 1.39288e14i | − | 1.28713i | −0.765392 | − | 0.643565i | \(-0.777455\pi\) | ||
0.765392 | − | 0.643565i | \(-0.222545\pi\) | |||||||
\(642\) | −3.14000e14 | −2.87909 | ||||||||
\(643\) | −8.45328e13 | −0.769078 | −0.384539 | − | 0.923109i | \(-0.625640\pi\) | ||||
−0.384539 | + | 0.923109i | \(0.625640\pi\) | |||||||
\(644\) | − | 1.02161e14i | − | 0.922269i | ||||||
\(645\) | 1.23171e14 | − | 5.01668e12i | 1.10334 | − | 0.0449385i | ||||
\(646\) | −8.41405e12 | −0.0747898 | ||||||||
\(647\) | 7.54213e13i | 0.665231i | 0.943063 | + | 0.332615i | \(0.107931\pi\) | ||||
−0.943063 | + | 0.332615i | \(0.892069\pi\) | |||||||
\(648\) | 3.60226e14i | 3.15283i | ||||||||
\(649\) | −9.03259e13 | −0.784492 | ||||||||
\(650\) | 4.14505e13i | 0.357242i | ||||||||
\(651\) | −5.26698e13 | −0.450460 | ||||||||
\(652\) | − | 4.03575e14i | − | 3.42521i | ||||||
\(653\) | − | 5.99341e13i | − | 0.504787i | −0.967625 | − | 0.252393i | \(-0.918782\pi\) | ||
0.967625 | − | 0.252393i | \(-0.0812177\pi\) | |||||||
\(654\) | −1.90161e14 | −1.58939 | ||||||||
\(655\) | −3.11630e13 | −0.258483 | ||||||||
\(656\) | 2.25956e14 | 1.85996 | ||||||||
\(657\) | − | 3.81153e13i | − | 0.311367i | ||||||
\(658\) | 1.48794e12 | 0.0120630 | ||||||||
\(659\) | −2.14727e14 | −1.72766 | −0.863832 | − | 0.503781i | \(-0.831942\pi\) | ||||
−0.863832 | + | 0.503781i | \(0.831942\pi\) | |||||||
\(660\) | −2.51995e14 | −2.01220 | ||||||||
\(661\) | 4.43828e13 | 0.351728 | 0.175864 | − | 0.984414i | \(-0.443728\pi\) | ||||
0.175864 | + | 0.984414i | \(0.443728\pi\) | |||||||
\(662\) | −2.84716e14 | −2.23935 | ||||||||
\(663\) | − | 8.64632e12i | − | 0.0674937i | ||||||
\(664\) | − | 6.21698e14i | − | 4.81658i | ||||||
\(665\) | − | 1.97356e13i | − | 0.151755i | ||||||
\(666\) | 1.88189e14 | 1.43622 | ||||||||
\(667\) | − | 6.22446e13i | − | 0.471490i | ||||||
\(668\) | 4.57404e13 | 0.343889 | ||||||||
\(669\) | 7.67240e13 | 0.572533 | ||||||||
\(670\) | 2.13609e14 | 1.58214 | ||||||||
\(671\) | 6.86634e13i | 0.504792i | ||||||||
\(672\) | 6.77267e13i | 0.494212i | ||||||||
\(673\) | 2.10395e13i | 0.152392i | 0.997093 | + | 0.0761958i | \(0.0242774\pi\) | ||||
−0.997093 | + | 0.0761958i | \(0.975723\pi\) | |||||||
\(674\) | 6.61617e13i | 0.475672i | ||||||||
\(675\) | 1.66487e13i | 0.118813i | ||||||||
\(676\) | 4.21229e13 | 0.298390 | ||||||||
\(677\) | 1.41079e14i | 0.992018i | 0.868317 | + | 0.496009i | \(0.165202\pi\) | ||||
−0.868317 | + | 0.496009i | \(0.834798\pi\) | |||||||
\(678\) | 3.64650e14i | 2.54523i | ||||||||
\(679\) | 3.30058e13i | 0.228687i | ||||||||
\(680\) | −1.90095e13 | −0.130745 | ||||||||
\(681\) | 2.57883e14 | 1.76071 | ||||||||
\(682\) | 3.09895e14i | 2.10036i | ||||||||
\(683\) | −9.61331e13 | −0.646799 | −0.323400 | − | 0.946263i | \(-0.604826\pi\) | ||||
−0.323400 | + | 0.946263i | \(0.604826\pi\) | |||||||
\(684\) | − | 1.34260e14i | − | 0.896737i | ||||||
\(685\) | −2.12253e14 | −1.40735 | ||||||||
\(686\) | 1.31963e14 | 0.868626 | ||||||||
\(687\) | − | 4.20731e13i | − | 0.274929i | ||||||
\(688\) | −3.48796e14 | + | 1.42062e13i | −2.26271 | + | 0.0921588i | ||||
\(689\) | −1.29325e14 | −0.832887 | ||||||||
\(690\) | 5.05720e14i | 3.23344i | ||||||||
\(691\) | − | 2.58847e14i | − | 1.64306i | −0.570168 | − | 0.821528i | \(-0.693122\pi\) | ||
0.570168 | − | 0.821528i | \(-0.306878\pi\) | |||||||
\(692\) | −9.15887e13 | −0.577180 | ||||||||
\(693\) | − | 1.61240e13i | − | 0.100881i | ||||||
\(694\) | −4.68196e14 | −2.90824 | ||||||||
\(695\) | − | 2.18951e14i | − | 1.35027i | ||||||
\(696\) | 1.51384e14i | 0.926900i | ||||||||
\(697\) | −7.85959e12 | −0.0477789 | ||||||||
\(698\) | 4.04700e14 | 2.44262 | ||||||||
\(699\) | −1.32340e14 | −0.793060 | ||||||||
\(700\) | 2.02244e13i | 0.120333i | ||||||||
\(701\) | 2.64616e14 | 1.56324 | 0.781621 | − | 0.623753i | \(-0.214393\pi\) | ||||
0.781621 | + | 0.623753i | \(0.214393\pi\) | |||||||
\(702\) | −1.67305e14 | −0.981346 | ||||||||
\(703\) | 1.74113e14 | 1.01404 | ||||||||
\(704\) | 9.79892e13 | 0.566650 | ||||||||
\(705\) | −5.18302e12 | −0.0297603 | ||||||||
\(706\) | − | 4.47002e14i | − | 2.54851i | ||||||
\(707\) | − | 1.72425e12i | − | 0.00976118i | ||||||
\(708\) | − | 5.35896e14i | − | 3.01241i | ||||||
\(709\) | −1.70519e14 | −0.951790 | −0.475895 | − | 0.879502i | \(-0.657876\pi\) | ||||
−0.475895 | + | 0.879502i | \(0.657876\pi\) | |||||||
\(710\) | 3.70313e14i | 2.05247i | ||||||||
\(711\) | 1.62572e14 | 0.894744 | ||||||||
\(712\) | −4.81957e14 | −2.63395 | ||||||||
\(713\) | 4.37631e14 | 2.37498 | ||||||||
\(714\) | − | 5.99517e12i | − | 0.0323080i | ||||||
\(715\) | − | 1.19325e14i | − | 0.638558i | ||||||
\(716\) | 2.56107e14i | 1.36099i | ||||||||
\(717\) | − | 3.69163e14i | − | 1.94815i | ||||||
\(718\) | 6.84564e13i | 0.358750i | ||||||||
\(719\) | 5.08876e13 | 0.264830 | 0.132415 | − | 0.991194i | \(-0.457727\pi\) | ||||
0.132415 | + | 0.991194i | \(0.457727\pi\) | |||||||
\(720\) | − | 2.10413e14i | − | 1.08745i | ||||||
\(721\) | − | 8.39970e12i | − | 0.0431109i | ||||||
\(722\) | 1.83891e14i | 0.937289i | ||||||||
\(723\) | 3.61935e13 | 0.183206 | ||||||||
\(724\) | 2.29128e14 | 1.15182 | ||||||||
\(725\) | 1.23222e13i | 0.0615177i | ||||||||
\(726\) | 1.89036e14 | 0.937263 | ||||||||
\(727\) | 1.03917e14i | 0.511700i | 0.966716 | + | 0.255850i | \(0.0823554\pi\) | ||||
−0.966716 | + | 0.255850i | \(0.917645\pi\) | |||||||
\(728\) | −1.17653e14 | −0.575369 | ||||||||
\(729\) | −7.25565e12 | −0.0352402 | ||||||||
\(730\) | − | 1.95581e14i | − | 0.943435i | ||||||
\(731\) | 1.21324e13 | − | 4.94146e11i | 0.0581248 | − | 0.00236738i | ||||
\(732\) | −4.07374e14 | −1.93838 | ||||||||
\(733\) | 3.08035e14i | 1.45573i | 0.685722 | + | 0.727863i | \(0.259486\pi\) | ||||
−0.685722 | + | 0.727863i | \(0.740514\pi\) | |||||||
\(734\) | − | 1.39596e13i | − | 0.0655227i | ||||||
\(735\) | −2.22807e14 | −1.03870 | ||||||||
\(736\) | − | 5.62739e14i | − | 2.60566i | ||||||
\(737\) | 1.61466e14 | 0.742581 | ||||||||
\(738\) | − | 1.78224e14i | − | 0.814112i | ||||||
\(739\) | 2.65696e14i | 1.20549i | 0.797934 | + | 0.602744i | \(0.205926\pi\) | ||||
−0.797934 | + | 0.602744i | \(0.794074\pi\) | |||||||
\(740\) | 6.79510e14 | 3.06222 | ||||||||
\(741\) | 1.81399e14 | 0.811978 | ||||||||
\(742\) | −8.96712e13 | −0.398688 | ||||||||
\(743\) | 4.04479e13i | 0.178629i | 0.996003 | + | 0.0893145i | \(0.0284676\pi\) | ||||
−0.996003 | + | 0.0893145i | \(0.971532\pi\) | |||||||
\(744\) | −1.06435e15 | −4.66897 | ||||||||
\(745\) | −8.81507e13 | −0.384100 | ||||||||
\(746\) | 4.49826e14 | 1.94693 | ||||||||
\(747\) | −2.39363e14 | −1.02909 | ||||||||
\(748\) | −2.48216e13 | −0.106004 | ||||||||
\(749\) | − | 7.25462e13i | − | 0.307756i | ||||||
\(750\) | − | 5.81504e14i | − | 2.45045i | ||||||
\(751\) | 4.55885e14i | 1.90834i | 0.299267 | + | 0.954169i | \(0.403258\pi\) | ||||
−0.299267 | + | 0.954169i | \(0.596742\pi\) | |||||||
\(752\) | 1.46773e13 | 0.0610318 | ||||||||
\(753\) | 2.52113e14i | 1.04141i | ||||||||
\(754\) | −1.23827e14 | −0.508112 | ||||||||
\(755\) | −2.96132e14 | −1.20712 | ||||||||
\(756\) | −8.16307e13 | −0.330555 | ||||||||
\(757\) | − | 1.68937e14i | − | 0.679589i | −0.940500 | − | 0.339794i | \(-0.889643\pi\) | ||
0.940500 | − | 0.339794i | \(-0.110357\pi\) | |||||||
\(758\) | 1.39808e14i | 0.558711i | ||||||||
\(759\) | 3.82271e14i | 1.51762i | ||||||||
\(760\) | − | 3.98819e14i | − | 1.57292i | ||||||
\(761\) | − | 1.58991e14i | − | 0.622944i | −0.950255 | − | 0.311472i | \(-0.899178\pi\) | ||
0.950255 | − | 0.311472i | \(-0.100822\pi\) | |||||||
\(762\) | 2.68952e14 | 1.04689 | ||||||||
\(763\) | − | 4.39345e13i | − | 0.169896i | ||||||
\(764\) | 5.38726e13i | 0.206967i | ||||||||
\(765\) | 7.31896e12i | 0.0279346i | ||||||||
\(766\) | −7.03278e14 | −2.66676 | ||||||||
\(767\) | 2.53758e14 | 0.955967 | ||||||||
\(768\) | − | 4.14201e14i | − | 1.55026i | ||||||
\(769\) | −5.15268e13 | −0.191603 | −0.0958013 | − | 0.995400i | \(-0.530541\pi\) | ||||
−0.0958013 | + | 0.995400i | \(0.530541\pi\) | |||||||
\(770\) | − | 8.27373e13i | − | 0.305666i | ||||||
\(771\) | 1.72738e13 | 0.0634039 | ||||||||
\(772\) | 9.71871e14 | 3.54423 | ||||||||
\(773\) | 1.55645e14i | 0.563944i | 0.959423 | + | 0.281972i | \(0.0909886\pi\) | ||||
−0.959423 | + | 0.281972i | \(0.909011\pi\) | |||||||
\(774\) | 1.12052e13 | + | 2.75115e14i | 0.0403382 | + | 0.990397i | ||||
\(775\) | −8.66356e13 | −0.309876 | ||||||||
\(776\) | 6.66983e14i | 2.37031i | ||||||||
\(777\) | 1.24059e14i | 0.438050i | ||||||||
\(778\) | 1.77410e14 | 0.622416 | ||||||||
\(779\) | − | 1.64894e14i | − | 0.574800i | ||||||
\(780\) | 7.07944e14 | 2.45203 | ||||||||
\(781\) | 2.79918e14i | 0.963330i | ||||||||
\(782\) | 4.98137e13i | 0.170339i | ||||||||
\(783\) | −4.97357e13 | −0.168989 | ||||||||
\(784\) | 6.30943e14 | 2.13015 | ||||||||
\(785\) | −2.87629e14 | −0.964903 | ||||||||
\(786\) | − | 1.98607e14i | − | 0.662035i | ||||||
\(787\) | −3.72738e14 | −1.23461 | −0.617306 | − | 0.786723i | \(-0.711776\pi\) | ||||
−0.617306 | + | 0.786723i | \(0.711776\pi\) | |||||||
\(788\) | 7.07167e14 | 2.32751 | ||||||||
\(789\) | −5.86514e14 | −1.91820 | ||||||||
\(790\) | 8.34207e14 | 2.71106 | ||||||||
\(791\) | −8.42482e13 | −0.272069 | ||||||||
\(792\) | − | 3.25835e14i | − | 1.04562i | ||||||
\(793\) | − | 1.92900e14i | − | 0.615130i | ||||||
\(794\) | − | 1.99451e14i | − | 0.632025i | ||||||
\(795\) | 3.12357e14 | 0.983592 | ||||||||
\(796\) | 1.13637e15i | 3.55593i | ||||||||
\(797\) | 4.58075e14 | 1.42444 | 0.712221 | − | 0.701955i | \(-0.247689\pi\) | ||||
0.712221 | + | 0.701955i | \(0.247689\pi\) | |||||||
\(798\) | 1.25778e14 | 0.388679 | ||||||||
\(799\) | −5.10530e11 | −0.00156779 | ||||||||
\(800\) | 1.11402e14i | 0.339973i | ||||||||
\(801\) | 1.85561e14i | 0.562761i | ||||||||
\(802\) | 7.94991e14i | 2.39602i | ||||||||
\(803\) | − | 1.47839e14i | − | 0.442803i | ||||||
\(804\) | 9.57964e14i | 2.85147i | ||||||||
\(805\) | −1.16841e14 | −0.345633 | ||||||||
\(806\) | − | 8.70608e14i | − | 2.55945i | ||||||
\(807\) | − | 6.71449e13i | − | 0.196176i | ||||||
\(808\) | − | 3.48436e13i | − | 0.101174i | ||||||
\(809\) | −3.19110e14 | −0.920870 | −0.460435 | − | 0.887693i | \(-0.652307\pi\) | ||||
−0.460435 | + | 0.887693i | \(0.652307\pi\) | |||||||
\(810\) | 7.11673e14 | 2.04106 | ||||||||
\(811\) | 6.85724e14i | 1.95454i | 0.211994 | + | 0.977271i | \(0.432004\pi\) | ||||
−0.211994 | + | 0.977271i | \(0.567996\pi\) | |||||||
\(812\) | −6.04173e13 | −0.171152 | ||||||||
\(813\) | 5.92086e14i | 1.66699i | ||||||||
\(814\) | 7.29932e14 | 2.04249 | ||||||||
\(815\) | −4.61565e14 | −1.28364 | ||||||||
\(816\) | − | 5.91373e13i | − | 0.163460i | ||||||
\(817\) | 1.03672e13 | + | 2.54538e14i | 0.0284806 | + | 0.699266i | ||||
\(818\) | −4.70618e14 | −1.28500 | ||||||||
\(819\) | 4.52983e13i | 0.122931i | ||||||||
\(820\) | − | 6.43529e14i | − | 1.73580i | ||||||
\(821\) | −5.04315e14 | −1.35203 | −0.676014 | − | 0.736889i | \(-0.736294\pi\) | ||||
−0.676014 | + | 0.736889i | \(0.736294\pi\) | |||||||
\(822\) | − | 1.35272e15i | − | 3.60453i | ||||||
\(823\) | 1.37810e14 | 0.364989 | 0.182495 | − | 0.983207i | \(-0.441583\pi\) | ||||
0.182495 | + | 0.983207i | \(0.441583\pi\) | |||||||
\(824\) | − | 1.69741e14i | − | 0.446840i | ||||||
\(825\) | − | 7.56762e13i | − | 0.198011i | ||||||
\(826\) | 1.75950e14 | 0.457604 | ||||||||
\(827\) | 5.27371e13 | 0.136329 | 0.0681646 | − | 0.997674i | \(-0.478286\pi\) | ||||
0.0681646 | + | 0.997674i | \(0.478286\pi\) | |||||||
\(828\) | −7.94857e14 | −2.04238 | ||||||||
\(829\) | − | 5.77696e14i | − | 1.47546i | −0.675097 | − | 0.737729i | \(-0.735898\pi\) | ||
0.675097 | − | 0.737729i | \(-0.264102\pi\) | |||||||
\(830\) | −1.22824e15 | −3.11813 | ||||||||
\(831\) | −8.93931e14 | −2.25579 | ||||||||
\(832\) | −2.75287e14 | −0.690509 | ||||||||
\(833\) | −2.19466e13 | −0.0547195 | ||||||||
\(834\) | 1.39541e15 | 3.45836 | ||||||||
\(835\) | − | 5.23128e13i | − | 0.128877i | ||||||
\(836\) | − | 5.20756e14i | − | 1.27527i | ||||||
\(837\) | − | 3.49683e14i | − | 0.851231i | ||||||
\(838\) | −1.27994e15 | −3.09720 | ||||||||
\(839\) | 6.52424e14i | 1.56935i | 0.619906 | + | 0.784676i | \(0.287171\pi\) | ||||
−0.619906 | + | 0.784676i | \(0.712829\pi\) | |||||||
\(840\) | 2.84166e14 | 0.679478 | ||||||||
\(841\) | 3.83896e14 | 0.912502 | ||||||||
\(842\) | 1.89547e13 | 0.0447875 | ||||||||
\(843\) | 3.59633e14i | 0.844737i | ||||||||
\(844\) | 1.61182e15i | 3.76360i | ||||||||
\(845\) | − | 4.81754e13i | − | 0.111826i | ||||||
\(846\) | − | 1.15768e13i | − | 0.0267138i | ||||||
\(847\) | 4.36746e13i | 0.100187i | ||||||||
\(848\) | −8.84531e14 | −2.01713 | ||||||||
\(849\) | − | 5.58325e14i | − | 1.26575i | ||||||
\(850\) | − | 9.86136e12i | − | 0.0222250i | ||||||
\(851\) | − | 1.03080e15i | − | 2.30955i | ||||||
\(852\) | −1.66073e15 | −3.69914 | ||||||||
\(853\) | 6.82643e14 | 1.51164 | 0.755820 | − | 0.654780i | \(-0.227239\pi\) | ||||
0.755820 | + | 0.654780i | \(0.227239\pi\) | |||||||
\(854\) | − | 1.33753e14i | − | 0.294452i | ||||||
\(855\) | −1.53551e14 | −0.336065 | ||||||||
\(856\) | − | 1.46602e15i | − | 3.18985i | ||||||
\(857\) | 6.37037e14 | 1.37804 | 0.689018 | − | 0.724744i | \(-0.258042\pi\) | ||||
0.689018 | + | 0.724744i | \(0.258042\pi\) | |||||||
\(858\) | 7.60476e14 | 1.63549 | ||||||||
\(859\) | − | 8.80906e14i | − | 1.88349i | −0.336324 | − | 0.941746i | \(-0.609184\pi\) | ||
0.336324 | − | 0.941746i | \(-0.390816\pi\) | |||||||
\(860\) | 4.04598e13 | + | 9.93382e14i | 0.0860065 | + | 2.11166i | ||||
\(861\) | 1.17490e14 | 0.248305 | ||||||||
\(862\) | − | 7.93809e14i | − | 1.66794i | ||||||
\(863\) | − | 6.01567e13i | − | 0.125669i | −0.998024 | − | 0.0628347i | \(-0.979986\pi\) | ||
0.998024 | − | 0.0628347i | \(-0.0200141\pi\) | |||||||
\(864\) | −4.49649e14 | −0.933909 | ||||||||
\(865\) | 1.04749e14i | 0.216306i | ||||||||
\(866\) | 4.85458e14 | 0.996694 | ||||||||
\(867\) | − | 6.05792e14i | − | 1.23660i | ||||||
\(868\) | − | 4.24784e14i | − | 0.862123i | ||||||
\(869\) | 6.30573e14 | 1.27244 | ||||||||
\(870\) | 2.99078e14 | 0.600051 | ||||||||
\(871\) | −4.53616e14 | −0.904895 | ||||||||
\(872\) | − | 8.87829e14i | − | 1.76095i | ||||||
\(873\) | 2.56799e14 | 0.506432 | ||||||||
\(874\) | −1.04509e15 | −2.04925 | ||||||||
\(875\) | 1.34350e14 | 0.261937 | ||||||||
\(876\) | 8.77114e14 | 1.70034 | ||||||||
\(877\) | 5.17228e13 | 0.0996975 | 0.0498488 | − | 0.998757i | \(-0.484126\pi\) | ||||
0.0498488 | + | 0.998757i | \(0.484126\pi\) | |||||||
\(878\) | 4.48104e14i | 0.858828i | ||||||||
\(879\) | 4.82241e14i | 0.919009i | ||||||||
\(880\) | − | 8.16133e14i | − | 1.54649i | ||||||
\(881\) | −2.76177e14 | −0.520365 | −0.260183 | − | 0.965559i | \(-0.583783\pi\) | ||||
−0.260183 | + | 0.965559i | \(0.583783\pi\) | |||||||
\(882\) | − | 4.97660e14i | − | 0.932373i | ||||||
\(883\) | 8.44714e14 | 1.57364 | 0.786821 | − | 0.617181i | \(-0.211725\pi\) | ||||
0.786821 | + | 0.617181i | \(0.211725\pi\) | |||||||
\(884\) | 6.97329e13 | 0.129174 | ||||||||
\(885\) | −6.12898e14 | −1.12894 | ||||||||
\(886\) | 1.66386e15i | 3.04754i | ||||||||
\(887\) | 8.28143e14i | 1.50830i | 0.656703 | + | 0.754149i | \(0.271951\pi\) | ||||
−0.656703 | + | 0.754149i | \(0.728049\pi\) | |||||||
\(888\) | 2.50699e15i | 4.54034i | ||||||||
\(889\) | 6.21383e13i | 0.111905i | ||||||||
\(890\) | 9.52168e14i | 1.70515i | ||||||||
\(891\) | 5.37950e14 | 0.957973 | ||||||||
\(892\) | 6.18782e14i | 1.09576i | ||||||||
\(893\) | − | 1.07109e13i | − | 0.0188612i | ||||||
\(894\) | − | 5.61798e14i | − | 0.983768i | ||||||
\(895\) | 2.92906e14 | 0.510051 | ||||||||
\(896\) | 3.91353e13 | 0.0677687 | ||||||||
\(897\) | − | 1.07394e15i | − | 1.84934i | ||||||
\(898\) | 1.03917e15 | 1.77952 | ||||||||
\(899\) | − | 2.58811e14i | − | 0.440742i | ||||||
\(900\) | 1.57354e14 | 0.266480 | ||||||||
\(901\) | 3.07673e13 | 0.0518162 | ||||||||
\(902\) | − | 6.91281e14i | − | 1.15777i | ||||||
\(903\) | −1.81363e14 | + | 7.38680e12i | −0.302072 | + | 0.0123032i | ||||
\(904\) | −1.70249e15 | −2.81996 | ||||||||
\(905\) | − | 2.62051e14i | − | 0.431662i | ||||||
\(906\) | − | 1.88730e15i | − | 3.09171i | ||||||
\(907\) | −4.46460e14 | −0.727355 | −0.363677 | − | 0.931525i | \(-0.618479\pi\) | ||||
−0.363677 | + | 0.931525i | \(0.618479\pi\) | |||||||
\(908\) | 2.07984e15i | 3.36977i | ||||||||
\(909\) | −1.34153e13 | −0.0216163 | ||||||||
\(910\) | 2.32439e14i | 0.372479i | ||||||||
\(911\) | − | 4.71740e14i | − | 0.751815i | −0.926657 | − | 0.375907i | \(-0.877331\pi\) | ||
0.926657 | − | 0.375907i | \(-0.122669\pi\) | |||||||
\(912\) | 1.24070e15 | 1.96649 | ||||||||
\(913\) | −9.28423e14 | −1.46350 | ||||||||
\(914\) | −1.87882e15 | −2.94547 | ||||||||
\(915\) | 4.65909e14i | 0.726434i | ||||||||
\(916\) | 3.39321e14 | 0.526179 | ||||||||
\(917\) | 4.58858e13 | 0.0707671 | ||||||||
\(918\) | 3.98029e13 | 0.0610522 | ||||||||
\(919\) | −5.22957e14 | −0.797790 | −0.398895 | − | 0.916997i | \(-0.630606\pi\) | ||||
−0.398895 | + | 0.916997i | \(0.630606\pi\) | |||||||
\(920\) | −2.36112e15 | −3.58245 | ||||||||
\(921\) | − | 1.27766e15i | − | 1.92804i | ||||||
\(922\) | 1.56684e15i | 2.35164i | ||||||||
\(923\) | − | 7.86390e14i | − | 1.17390i | ||||||
\(924\) | 3.71049e14 | 0.550898 | ||||||||
\(925\) | 2.04063e14i | 0.301339i | ||||||||
\(926\) | −5.14862e14 | −0.756198 | ||||||||
\(927\) | −6.53531e13 | −0.0954701 | ||||||||
\(928\) | −3.32799e14 | −0.483550 | ||||||||
\(929\) | − | 3.65317e13i | − | 0.0527949i | −0.999652 | − | 0.0263974i | \(-0.991596\pi\) | ||
0.999652 | − | 0.0263974i | \(-0.00840354\pi\) | |||||||
\(930\) | 2.10277e15i | 3.02257i | ||||||||
\(931\) | − | 4.60438e14i | − | 0.658298i | ||||||
\(932\) | − | 1.06733e15i | − | 1.51781i | ||||||
\(933\) | 5.45981e14i | 0.772270i | ||||||||
\(934\) | 1.35650e15 | 1.90848 | ||||||||
\(935\) | 2.83882e13i | 0.0397264i | ||||||||
\(936\) | 9.15389e14i | 1.27417i | ||||||||
\(937\) | 7.96238e14i | 1.10242i | 0.834368 | + | 0.551208i | \(0.185833\pi\) | ||||
−0.834368 | + | 0.551208i | \(0.814167\pi\) | |||||||
\(938\) | −3.14528e14 | −0.433157 | ||||||||
\(939\) | 7.10681e14 | 0.973525 | ||||||||
\(940\) | − | 4.18013e13i | − | 0.0569574i | ||||||
\(941\) | −8.04190e14 | −1.08996 | −0.544980 | − | 0.838449i | \(-0.683463\pi\) | ||||
−0.544980 | + | 0.838449i | \(0.683463\pi\) | |||||||
\(942\) | − | 1.83310e15i | − | 2.47134i | ||||||
\(943\) | −9.76220e14 | −1.30915 | ||||||||
\(944\) | 1.73560e15 | 2.31521 | ||||||||
\(945\) | 9.33600e13i | 0.123880i | ||||||||
\(946\) | 4.34620e13 | + | 1.06709e15i | 0.0573659 | + | 1.40847i | ||||
\(947\) | −8.33991e14 | −1.09499 | −0.547497 | − | 0.836808i | \(-0.684419\pi\) | ||||
−0.547497 | + | 0.836808i | \(0.684419\pi\) | |||||||
\(948\) | 3.74114e15i | 4.88609i | ||||||||
\(949\) | 4.15332e14i | 0.539591i | ||||||||
\(950\) | 2.06891e14 | 0.267376 | ||||||||
\(951\) | − | 7.36727e13i | − | 0.0947117i | ||||||
\(952\) | 2.79905e13 | 0.0357953 | ||||||||
\(953\) | − | 1.28028e14i | − | 0.162870i | −0.996679 | − | 0.0814349i | \(-0.974050\pi\) | ||
0.996679 | − | 0.0814349i | \(-0.0259503\pi\) | |||||||
\(954\) | 6.97678e14i | 0.882904i | ||||||||
\(955\) | 6.16135e13 | 0.0775638 | ||||||||
\(956\) | 2.97731e15 | 3.72851 | ||||||||
\(957\) | 2.26071e14 | 0.281635 | ||||||||
\(958\) | − | 1.33426e15i | − | 1.65354i | ||||||
\(959\) | 3.12531e14 | 0.385301 | ||||||||
\(960\) | 6.64897e14 | 0.815451 | ||||||||
\(961\) | 1.00003e15 | 1.22010 | ||||||||
\(962\) | −2.05064e15 | −2.48894 | ||||||||
\(963\) | −5.64439e14 | −0.681531 | ||||||||
\(964\) | 2.91902e14i | 0.350632i | ||||||||
\(965\) | − | 1.11152e15i | − | 1.32825i | ||||||
\(966\) | − | 7.44645e14i | − | 0.885245i | ||||||
\(967\) | 8.55354e14 | 1.01161 | 0.505806 | − | 0.862647i | \(-0.331195\pi\) | ||||
0.505806 | + | 0.862647i | \(0.331195\pi\) | |||||||
\(968\) | 8.82579e14i | 1.03843i | ||||||||
\(969\) | −4.31561e13 | −0.0505154 | ||||||||
\(970\) | 1.31771e15 | 1.53448 | ||||||||
\(971\) | 1.44645e15 | 1.67575 | 0.837873 | − | 0.545866i | \(-0.183799\pi\) | ||||
0.837873 | + | 0.545866i | \(0.183799\pi\) | |||||||
\(972\) | 2.01453e15i | 2.32190i | ||||||||
\(973\) | 3.22393e14i | 0.369676i | ||||||||
\(974\) | − | 2.05636e15i | − | 2.34587i | ||||||
\(975\) | 2.12602e14i | 0.241292i | ||||||||
\(976\) | − | 1.31936e15i | − | 1.48975i | ||||||
\(977\) | −7.97820e13 | −0.0896256 | −0.0448128 | − | 0.998995i | \(-0.514269\pi\) | ||||
−0.0448128 | + | 0.998995i | \(0.514269\pi\) | |||||||
\(978\) | − | 2.94162e15i | − | 3.28771i | ||||||
\(979\) | 7.19739e14i | 0.800316i | ||||||||
\(980\) | − | 1.79694e15i | − | 1.98794i | ||||||
\(981\) | −3.41828e14 | −0.376238 | ||||||||
\(982\) | 6.95625e14 | 0.761760 | ||||||||
\(983\) | − | 2.94771e14i | − | 0.321157i | −0.987023 | − | 0.160578i | \(-0.948664\pi\) | ||
0.987023 | − | 0.160578i | \(-0.0513359\pi\) | |||||||
\(984\) | 2.37424e15 | 2.57365 | ||||||||
\(985\) | − | 8.08779e14i | − | 0.872266i | ||||||
\(986\) | 2.94594e13 | 0.0316110 | ||||||||
\(987\) | 7.63172e12 | 0.00814773 | ||||||||
\(988\) | 1.46299e15i | 1.55402i | ||||||||
\(989\) | 1.50694e15 | − | 6.13766e13i | 1.59263 | − | 0.0648667i | ||||
\(990\) | −6.43730e14 | −0.676905 | ||||||||
\(991\) | 2.67544e13i | 0.0279915i | 0.999902 | + | 0.0139958i | \(0.00445513\pi\) | ||||
−0.999902 | + | 0.0139958i | \(0.995545\pi\) | |||||||
\(992\) | − | 2.33985e15i | − | 2.43573i | ||||||
\(993\) | −1.46032e15 | −1.51253 | ||||||||
\(994\) | − | 5.45266e14i | − | 0.561923i | ||||||
\(995\) | 1.29965e15 | 1.33263 | ||||||||
\(996\) | − | 5.50826e15i | − | 5.61976i | ||||||
\(997\) | 7.46679e13i | 0.0757980i | 0.999282 | + | 0.0378990i | \(0.0120665\pi\) | ||||
−0.999282 | + | 0.0378990i | \(0.987933\pi\) | |||||||
\(998\) | −1.30313e15 | −1.31624 | ||||||||
\(999\) | −8.23648e14 | −0.827779 |
(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 | 43.11.b.b.42.33 | yes | 34 | |
43.42 | odd | 2 | inner | 43.11.b.b.42.2 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.11.b.b.42.2 | ✓ | 34 | 43.42 | odd | 2 | inner | |
43.11.b.b.42.33 | yes | 34 | 1.1 | even | 1 | trivial |