Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,17,Mod(5,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 17, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.5");
S:= CuspForms(chi, 17);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 17 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.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: | \(9.73947263140\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 55116x^{4} + 758395257x^{2} + 123254139008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{27}\cdot 3^{13} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(12.8250i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.5 |
Dual form | 6.17.b.a.5.4 |
$q$-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 \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 181.019i | − | 0.707107i | ||||||
\(3\) | −4654.10 | + | 4624.51i | −0.709358 | + | 0.704848i | ||||
\(4\) | −32768.0 | −0.500000 | ||||||||
\(5\) | 1539.79i | 0.00394186i | 0.999998 | + | 0.00197093i | \(0.000627366\pi\) | ||||
−0.999998 | + | 0.00197093i | \(0.999373\pi\) | |||||||
\(6\) | 837125. | + | 842482.i | 0.498403 | + | 0.501592i | ||||
\(7\) | 5.92137e6 | 1.02716 | 0.513580 | − | 0.858042i | \(-0.328319\pi\) | ||||
0.513580 | + | 0.858042i | \(0.328319\pi\) | |||||||
\(8\) | 5.93164e6i | 0.353553i | ||||||||
\(9\) | 274580. | − | 4.30458e7i | 0.00637865 | − | 0.999980i | ||||
\(10\) | 278731. | 0.00278731 | ||||||||
\(11\) | − | 2.30420e8i | − | 1.07493i | −0.843287 | − | 0.537463i | \(-0.819383\pi\) | ||
0.843287 | − | 0.537463i | \(-0.180617\pi\) | |||||||
\(12\) | 1.52506e8 | − | 1.51536e8i | 0.354679 | − | 0.352424i | ||||
\(13\) | 1.44595e9 | 1.77258 | 0.886290 | − | 0.463131i | \(-0.153274\pi\) | ||||
0.886290 | + | 0.463131i | \(0.153274\pi\) | |||||||
\(14\) | − | 1.07188e9i | − | 0.726312i | ||||||
\(15\) | −7.12076e6 | − | 7.16633e6i | −0.00277841 | − | 0.00279619i | ||||
\(16\) | 1.07374e9 | 0.250000 | ||||||||
\(17\) | 1.68474e8i | 0.0241513i | 0.999927 | + | 0.0120757i | \(0.00384390\pi\) | ||||
−0.999927 | + | 0.0120757i | \(0.996156\pi\) | |||||||
\(18\) | −7.79213e9 | − | 4.97043e7i | −0.707092 | − | 0.00451039i | ||||
\(19\) | 4.32262e9 | 0.254518 | 0.127259 | − | 0.991870i | \(-0.459382\pi\) | ||||
0.127259 | + | 0.991870i | \(0.459382\pi\) | |||||||
\(20\) | − | 5.04558e7i | − | 0.00197093i | ||||||
\(21\) | −2.75587e10 | + | 2.73834e10i | −0.728625 | + | 0.723992i | ||||
\(22\) | −4.17105e10 | −0.760088 | ||||||||
\(23\) | 9.99787e10i | 1.27669i | 0.769751 | + | 0.638344i | \(0.220380\pi\) | ||||
−0.769751 | + | 0.638344i | \(0.779620\pi\) | |||||||
\(24\) | −2.74309e10 | − | 2.76065e10i | −0.249201 | − | 0.250796i | ||||
\(25\) | 1.52586e11 | 0.999984 | ||||||||
\(26\) | − | 2.61744e11i | − | 1.25340i | ||||||
\(27\) | 1.97788e11 | + | 2.01609e11i | 0.700309 | + | 0.713840i | ||||
\(28\) | −1.94032e11 | −0.513580 | ||||||||
\(29\) | − | 7.44960e11i | − | 1.48919i | −0.667519 | − | 0.744593i | \(-0.732644\pi\) | ||
0.667519 | − | 0.744593i | \(-0.267356\pi\) | |||||||
\(30\) | −1.29724e9 | + | 1.28900e9i | −0.00197720 | + | 0.00196463i | ||||
\(31\) | 1.99388e11 | 0.233779 | 0.116889 | − | 0.993145i | \(-0.462708\pi\) | ||||
0.116889 | + | 0.993145i | \(0.462708\pi\) | |||||||
\(32\) | − | 1.94368e11i | − | 0.176777i | ||||||
\(33\) | 1.06558e12 | + | 1.07240e12i | 0.757660 | + | 0.762508i | ||||
\(34\) | 3.04970e10 | 0.0170776 | ||||||||
\(35\) | 9.11766e9i | 0.00404892i | ||||||||
\(36\) | −8.99744e9 | + | 1.41053e12i | −0.00318933 | + | 0.499990i | ||||
\(37\) | −3.98927e12 | −1.13574 | −0.567871 | − | 0.823118i | \(-0.692233\pi\) | ||||
−0.567871 | + | 0.823118i | \(0.692233\pi\) | |||||||
\(38\) | − | 7.82478e11i | − | 0.179971i | ||||||
\(39\) | −6.72958e12 | + | 6.68679e12i | −1.25739 | + | 1.24940i | ||||
\(40\) | −9.13347e9 | −0.00139366 | ||||||||
\(41\) | − | 1.34623e13i | − | 1.68596i | −0.537943 | − | 0.842981i | \(-0.680798\pi\) | ||
0.537943 | − | 0.842981i | \(-0.319202\pi\) | |||||||
\(42\) | 4.95693e12 | + | 4.98865e12i | 0.511939 | + | 0.515215i | ||||
\(43\) | 9.66403e12 | 0.826819 | 0.413410 | − | 0.910545i | \(-0.364338\pi\) | ||||
0.413410 | + | 0.910545i | \(0.364338\pi\) | |||||||
\(44\) | 7.55040e12i | 0.537463i | ||||||||
\(45\) | 6.62815e10 | + | 4.22795e8i | 0.00394178 | + | 2.51437e-5i | ||||
\(46\) | 1.80981e13 | 0.902755 | ||||||||
\(47\) | − | 2.89266e13i | − | 1.21483i | −0.794385 | − | 0.607415i | \(-0.792207\pi\) | ||
0.794385 | − | 0.607415i | \(-0.207793\pi\) | |||||||
\(48\) | −4.99730e12 | + | 4.96553e12i | −0.177340 | + | 0.176212i | ||||
\(49\) | 1.82973e12 | 0.0550576 | ||||||||
\(50\) | − | 2.76209e13i | − | 0.707096i | ||||||
\(51\) | −7.79109e11 | − | 7.84094e11i | −0.0170230 | − | 0.0171320i | ||||
\(52\) | −4.73808e13 | −0.886290 | ||||||||
\(53\) | 8.03602e13i | 1.29073i | 0.763876 | + | 0.645363i | \(0.223294\pi\) | ||||
−0.763876 | + | 0.645363i | \(0.776706\pi\) | |||||||
\(54\) | 3.64952e13 | − | 3.58034e13i | 0.504761 | − | 0.495193i | ||||
\(55\) | 3.54798e11 | 0.00423721 | ||||||||
\(56\) | 3.51235e13i | 0.363156i | ||||||||
\(57\) | −2.01179e13 | + | 1.99900e13i | −0.180544 | + | 0.179396i | ||||
\(58\) | −1.34852e14 | −1.05301 | ||||||||
\(59\) | 1.63088e14i | 1.11072i | 0.831610 | + | 0.555360i | \(0.187420\pi\) | ||||
−0.831610 | + | 0.555360i | \(0.812580\pi\) | |||||||
\(60\) | 2.33333e11 | + | 2.34826e11i | 0.00138920 | + | 0.00139809i | ||||
\(61\) | 8.55778e13 | 0.446398 | 0.223199 | − | 0.974773i | \(-0.428350\pi\) | ||||
0.223199 | + | 0.974773i | \(0.428350\pi\) | |||||||
\(62\) | − | 3.60931e13i | − | 0.165307i | ||||||
\(63\) | 1.62589e12 | − | 2.54891e14i | 0.00655189 | − | 1.02714i | ||||
\(64\) | −3.51844e13 | −0.125000 | ||||||||
\(65\) | 2.22645e12i | 0.00698725i | ||||||||
\(66\) | 1.94125e14 | − | 1.92890e14i | 0.539175 | − | 0.535746i | ||||
\(67\) | 5.13528e14 | 1.26464 | 0.632319 | − | 0.774709i | \(-0.282103\pi\) | ||||
0.632319 | + | 0.774709i | \(0.282103\pi\) | |||||||
\(68\) | − | 5.52055e12i | − | 0.0120757i | ||||||
\(69\) | −4.62352e14 | − | 4.65311e14i | −0.899871 | − | 0.905630i | ||||
\(70\) | 1.65047e12 | 0.00286302 | ||||||||
\(71\) | 3.19873e14i | 0.495349i | 0.968843 | + | 0.247675i | \(0.0796664\pi\) | ||||
−0.968843 | + | 0.247675i | \(0.920334\pi\) | |||||||
\(72\) | 2.55333e14 | + | 1.62871e12i | 0.353546 | + | 0.00225519i | ||||
\(73\) | 2.79061e13 | 0.0346032 | 0.0173016 | − | 0.999850i | \(-0.494492\pi\) | ||||
0.0173016 | + | 0.999850i | \(0.494492\pi\) | |||||||
\(74\) | 7.22134e14i | 0.803090i | ||||||||
\(75\) | −7.10148e14 | + | 7.05633e14i | −0.709347 | + | 0.704837i | ||||
\(76\) | −1.41644e14 | −0.127259 | ||||||||
\(77\) | − | 1.36440e15i | − | 1.10412i | ||||||
\(78\) | 1.21044e15 | + | 1.21818e15i | 0.883458 | + | 0.889112i | ||||
\(79\) | −4.23333e14 | −0.279040 | −0.139520 | − | 0.990219i | \(-0.544556\pi\) | ||||
−0.139520 | + | 0.990219i | \(0.544556\pi\) | |||||||
\(80\) | 1.65333e12i | 0.000985464i | ||||||||
\(81\) | −1.85287e15 | − | 2.36391e13i | −0.999919 | − | 0.0127570i | ||||
\(82\) | −2.43693e15 | −1.19216 | ||||||||
\(83\) | 6.58853e14i | 0.292525i | 0.989246 | + | 0.146263i | \(0.0467245\pi\) | ||||
−0.989246 | + | 0.146263i | \(0.953276\pi\) | |||||||
\(84\) | 9.03042e14 | − | 8.97300e14i | 0.364312 | − | 0.361996i | ||||
\(85\) | −2.59414e11 | −9.52011e−5 | ||||||||
\(86\) | − | 1.74938e15i | − | 0.584650i | ||||||
\(87\) | 3.44507e15 | + | 3.46712e15i | 1.04965 | + | 1.05637i | ||||
\(88\) | 1.36677e15 | 0.380044 | ||||||||
\(89\) | − | 4.19706e15i | − | 1.06617i | −0.846062 | − | 0.533084i | \(-0.821033\pi\) | ||
0.846062 | − | 0.533084i | \(-0.178967\pi\) | |||||||
\(90\) | 7.65340e10 | − | 1.19982e13i | 1.77793e−5 | − | 0.00278726i | ||||
\(91\) | 8.56199e15 | 1.82072 | ||||||||
\(92\) | − | 3.27610e15i | − | 0.638344i | ||||||
\(93\) | −9.27971e14 | + | 9.22071e14i | −0.165833 | + | 0.164779i | ||||
\(94\) | −5.23628e15 | −0.859014 | ||||||||
\(95\) | 6.65591e12i | 0.00100327i | ||||||||
\(96\) | 8.98856e14 | + | 9.04608e14i | 0.124601 | + | 0.125398i | ||||
\(97\) | −3.81842e15 | −0.487202 | −0.243601 | − | 0.969875i | \(-0.578329\pi\) | ||||
−0.243601 | + | 0.969875i | \(0.578329\pi\) | |||||||
\(98\) | − | 3.31216e14i | − | 0.0389316i | ||||||
\(99\) | −9.91863e15 | − | 6.32687e13i | −1.07490 | − | 0.00685658i | ||||
\(100\) | −4.99992e15 | −0.499992 | ||||||||
\(101\) | 3.95394e15i | 0.365140i | 0.983193 | + | 0.182570i | \(0.0584415\pi\) | ||||
−0.983193 | + | 0.182570i | \(0.941558\pi\) | |||||||
\(102\) | −1.41936e14 | + | 1.41034e14i | −0.0121141 | + | 0.0120371i | ||||
\(103\) | 9.78409e15 | 0.772365 | 0.386182 | − | 0.922422i | \(-0.373794\pi\) | ||||
0.386182 | + | 0.922422i | \(0.373794\pi\) | |||||||
\(104\) | 8.57684e15i | 0.626701i | ||||||||
\(105\) | −4.21647e13 | − | 4.24345e13i | −0.00285387 | − | 0.00287213i | ||||
\(106\) | 1.45468e16 | 0.912681 | ||||||||
\(107\) | 2.46522e16i | 1.43478i | 0.696671 | + | 0.717390i | \(0.254664\pi\) | ||||
−0.696671 | + | 0.717390i | \(0.745336\pi\) | |||||||
\(108\) | −6.48111e15 | − | 6.60634e15i | −0.350154 | − | 0.356920i | ||||
\(109\) | −3.20807e16 | −1.61002 | −0.805012 | − | 0.593258i | \(-0.797841\pi\) | ||||
−0.805012 | + | 0.593258i | \(0.797841\pi\) | |||||||
\(110\) | − | 6.42253e13i | − | 0.00299616i | ||||||
\(111\) | 1.85664e16 | − | 1.84484e16i | 0.805647 | − | 0.800525i | ||||
\(112\) | 6.35803e15 | 0.256790 | ||||||||
\(113\) | − | 2.62806e16i | − | 0.988572i | −0.869299 | − | 0.494286i | \(-0.835430\pi\) | ||
0.869299 | − | 0.494286i | \(-0.164570\pi\) | |||||||
\(114\) | 3.61857e15 | + | 3.64173e15i | 0.126852 | + | 0.127664i | ||||
\(115\) | −1.53946e14 | −0.00503252 | ||||||||
\(116\) | 2.44108e16i | 0.744593i | ||||||||
\(117\) | 3.97028e14 | − | 6.22420e16i | 0.0113067 | − | 1.77254i | ||||
\(118\) | 2.95220e16 | 0.785398 | ||||||||
\(119\) | 9.97597e14i | 0.0248073i | ||||||||
\(120\) | 4.25081e13 | − | 4.22378e13i | 0.000988602 | − | 0.000982316i | ||||
\(121\) | −7.14366e15 | −0.155467 | ||||||||
\(122\) | − | 1.54912e16i | − | 0.315651i | ||||||
\(123\) | 6.22564e16 | + | 6.26548e16i | 1.18835 | + | 1.19595i | ||||
\(124\) | −6.53354e15 | −0.116889 | ||||||||
\(125\) | 4.69902e14i | 0.00788365i | ||||||||
\(126\) | −4.61401e16 | − | 2.94318e14i | −0.726297 | − | 0.00463289i | ||||
\(127\) | −5.11153e16 | −0.755303 | −0.377652 | − | 0.925948i | \(-0.623268\pi\) | ||||
−0.377652 | + | 0.925948i | \(0.623268\pi\) | |||||||
\(128\) | 6.36905e15i | 0.0883883i | ||||||||
\(129\) | −4.49774e16 | + | 4.46914e16i | −0.586511 | + | 0.582782i | ||||
\(130\) | 4.03031e14 | 0.00494073 | ||||||||
\(131\) | 1.07461e17i | 1.23903i | 0.784985 | + | 0.619515i | \(0.212671\pi\) | ||||
−0.784985 | + | 0.619515i | \(0.787329\pi\) | |||||||
\(132\) | −3.49169e16 | − | 3.51403e16i | −0.378830 | − | 0.381254i | ||||
\(133\) | 2.55958e16 | 0.261430 | ||||||||
\(134\) | − | 9.29585e16i | − | 0.894233i | ||||||
\(135\) | −3.10436e14 | + | 3.04551e14i | −0.00281385 | + | 0.00276052i | ||||
\(136\) | −9.99327e14 | −0.00853879 | ||||||||
\(137\) | − | 5.88231e16i | − | 0.474006i | −0.971509 | − | 0.237003i | \(-0.923835\pi\) | ||
0.971509 | − | 0.237003i | \(-0.0761651\pi\) | |||||||
\(138\) | −8.42303e16 | + | 8.36947e16i | −0.640377 | + | 0.636305i | ||||
\(139\) | 3.28378e16 | 0.235643 | 0.117822 | − | 0.993035i | \(-0.462409\pi\) | ||||
0.117822 | + | 0.993035i | \(0.462409\pi\) | |||||||
\(140\) | − | 2.98767e14i | − | 0.00202446i | ||||||
\(141\) | 1.33771e17 | + | 1.34628e17i | 0.856270 | + | 0.861749i | ||||
\(142\) | 5.79033e16 | 0.350265 | ||||||||
\(143\) | − | 3.33175e17i | − | 1.90539i | ||||||
\(144\) | 2.94828e14 | − | 4.62201e16i | 0.00159466 | − | 0.249995i | ||||
\(145\) | 1.14708e15 | 0.00587016 | ||||||||
\(146\) | − | 5.05155e15i | − | 0.0244682i | ||||||
\(147\) | −8.51573e15 | + | 8.46158e15i | −0.0390556 | + | 0.0388073i | ||||
\(148\) | 1.30720e17 | 0.567871 | ||||||||
\(149\) | 1.74764e16i | 0.0719384i | 0.999353 | + | 0.0359692i | \(0.0114518\pi\) | ||||
−0.999353 | + | 0.0359692i | \(0.988548\pi\) | |||||||
\(150\) | 1.27733e17 | + | 1.28551e17i | 0.498395 | + | 0.501584i | ||||
\(151\) | 3.48492e16 | 0.128937 | 0.0644685 | − | 0.997920i | \(-0.479465\pi\) | ||||
0.0644685 | + | 0.997920i | \(0.479465\pi\) | |||||||
\(152\) | 2.56402e16i | 0.0899856i | ||||||||
\(153\) | 7.25210e15 | + | 4.62596e13i | 0.0241508 | + | 0.000154053i | ||||
\(154\) | −2.46983e17 | −0.780732 | ||||||||
\(155\) | 3.07015e14i | 0.000921523i | ||||||||
\(156\) | 2.20515e17 | − | 2.19113e17i | 0.628697 | − | 0.624699i | ||||
\(157\) | −1.85733e17 | −0.503144 | −0.251572 | − | 0.967839i | \(-0.580948\pi\) | ||||
−0.251572 | + | 0.967839i | \(0.580948\pi\) | |||||||
\(158\) | 7.66315e16i | 0.197311i | ||||||||
\(159\) | −3.71626e17 | − | 3.74005e17i | −0.909766 | − | 0.915588i | ||||
\(160\) | 2.99285e14 | 0.000696828 | ||||||||
\(161\) | 5.92011e17i | 1.31136i | ||||||||
\(162\) | −4.27913e15 | + | 3.35405e17i | −0.00902059 | + | 0.707049i | ||||
\(163\) | −8.14420e17 | −1.63436 | −0.817180 | − | 0.576383i | \(-0.804464\pi\) | ||||
−0.817180 | + | 0.576383i | \(0.804464\pi\) | |||||||
\(164\) | 4.41132e17i | 0.842981i | ||||||||
\(165\) | −1.65126e15 | + | 1.64077e15i | −0.00300570 | + | 0.00298659i | ||||
\(166\) | 1.19265e17 | 0.206847 | ||||||||
\(167\) | − | 1.51746e17i | − | 0.250834i | −0.992104 | − | 0.125417i | \(-0.959973\pi\) | ||
0.992104 | − | 0.125417i | \(-0.0400268\pi\) | |||||||
\(168\) | −1.62429e17 | − | 1.63468e17i | −0.255970 | − | 0.257608i | ||||
\(169\) | 1.42535e18 | 2.14204 | ||||||||
\(170\) | 4.69589e13i | 6.73173e-5i | ||||||||
\(171\) | 1.18690e15 | − | 1.86071e17i | 0.00162348 | − | 0.254513i | ||||
\(172\) | −3.16671e17 | −0.413410 | ||||||||
\(173\) | 4.17219e17i | 0.519990i | 0.965610 | + | 0.259995i | \(0.0837210\pi\) | ||||
−0.965610 | + | 0.259995i | \(0.916279\pi\) | |||||||
\(174\) | 6.27615e17 | − | 6.23625e17i | 0.746964 | − | 0.742214i | ||||
\(175\) | 9.03516e17 | 1.02714 | ||||||||
\(176\) | − | 2.47412e17i | − | 0.268732i | ||||||
\(177\) | −7.54199e17 | − | 7.59026e17i | −0.782889 | − | 0.787899i | ||||
\(178\) | −7.59750e17 | −0.753895 | ||||||||
\(179\) | 1.38626e17i | 0.131529i | 0.997835 | + | 0.0657645i | \(0.0209486\pi\) | ||||
−0.997835 | + | 0.0657645i | \(0.979051\pi\) | |||||||
\(180\) | −2.17191e15 | − | 1.38541e13i | −0.00197089 | − | 1.25719e-5i | ||||
\(181\) | 6.47300e17 | 0.561923 | 0.280961 | − | 0.959719i | \(-0.409347\pi\) | ||||
0.280961 | + | 0.959719i | \(0.409347\pi\) | |||||||
\(182\) | − | 1.54989e18i | − | 1.28745i | ||||||
\(183\) | −3.98288e17 | + | 3.95755e17i | −0.316656 | + | 0.314643i | ||||
\(184\) | −5.93038e17 | −0.451377 | ||||||||
\(185\) | − | 6.14262e15i | − | 0.00447693i | ||||||
\(186\) | 1.66913e17 | + | 1.67981e17i | 0.116516 | + | 0.117262i | ||||
\(187\) | 3.88198e16 | 0.0259609 | ||||||||
\(188\) | 9.47868e17i | 0.607415i | ||||||||
\(189\) | 1.17118e18 | + | 1.19380e18i | 0.719329 | + | 0.733228i | ||||
\(190\) | 1.20485e15 | 0.000709421 | ||||||||
\(191\) | 7.46429e17i | 0.421426i | 0.977548 | + | 0.210713i | \(0.0675786\pi\) | ||||
−0.977548 | + | 0.210713i | \(0.932421\pi\) | |||||||
\(192\) | 1.63752e17 | − | 1.62710e17i | 0.0886698 | − | 0.0881060i | ||||
\(193\) | −2.21274e17 | −0.114940 | −0.0574700 | − | 0.998347i | \(-0.518303\pi\) | ||||
−0.0574700 | + | 0.998347i | \(0.518303\pi\) | |||||||
\(194\) | 6.91207e17i | 0.344504i | ||||||||
\(195\) | −1.02962e16 | − | 1.03621e16i | −0.00492495 | − | 0.00495647i | ||||
\(196\) | −5.99565e16 | −0.0275288 | ||||||||
\(197\) | − | 1.21371e18i | − | 0.535041i | −0.963552 | − | 0.267520i | \(-0.913796\pi\) | ||
0.963552 | − | 0.267520i | \(-0.0862043\pi\) | |||||||
\(198\) | −1.14529e16 | + | 1.79546e18i | −0.00484833 | + | 0.760072i | ||||
\(199\) | −4.59820e18 | −1.86966 | −0.934832 | − | 0.355090i | \(-0.884450\pi\) | ||||
−0.934832 | + | 0.355090i | \(0.884450\pi\) | |||||||
\(200\) | 9.05083e17i | 0.353548i | ||||||||
\(201\) | −2.39001e18 | + | 2.37482e18i | −0.897081 | + | 0.891377i | ||||
\(202\) | 7.15739e17 | 0.258193 | ||||||||
\(203\) | − | 4.41119e18i | − | 1.52963i | ||||||
\(204\) | 2.55298e16 | + | 2.56932e16i | 0.00851151 | + | 0.00856598i | ||||
\(205\) | 2.07291e16 | 0.00664582 | ||||||||
\(206\) | − | 1.77111e18i | − | 0.546144i | ||||||
\(207\) | 4.30367e18 | + | 2.74522e16i | 1.27666 | + | 0.00814355i | ||||
\(208\) | 1.55257e18 | 0.443145 | ||||||||
\(209\) | − | 9.96018e17i | − | 0.273588i | ||||||
\(210\) | −7.68146e15 | + | 7.63262e15i | −0.00203090 | + | 0.00201799i | ||||
\(211\) | 3.18692e18 | 0.811169 | 0.405585 | − | 0.914057i | \(-0.367068\pi\) | ||||
0.405585 | + | 0.914057i | \(0.367068\pi\) | |||||||
\(212\) | − | 2.63324e18i | − | 0.645363i | ||||||
\(213\) | −1.47926e18 | − | 1.48872e18i | −0.349146 | − | 0.351380i | ||||
\(214\) | 4.46253e18 | 1.01454 | ||||||||
\(215\) | 1.48806e16i | 0.00325920i | ||||||||
\(216\) | −1.19588e18 | + | 1.17321e18i | −0.252381 | + | 0.247597i | ||||
\(217\) | 1.18065e18 | 0.240128 | ||||||||
\(218\) | 5.80723e18i | 1.13846i | ||||||||
\(219\) | −1.29878e17 | + | 1.29052e17i | −0.0245461 | + | 0.0243900i | ||||
\(220\) | −1.16260e16 | −0.00211860 | ||||||||
\(221\) | 2.43604e17i | 0.0428102i | ||||||||
\(222\) | −3.33952e18 | − | 3.36089e18i | −0.566056 | − | 0.569679i | ||||
\(223\) | −7.13227e17 | −0.116624 | −0.0583121 | − | 0.998298i | \(-0.518572\pi\) | ||||
−0.0583121 | + | 0.998298i | \(0.518572\pi\) | |||||||
\(224\) | − | 1.15093e18i | − | 0.181578i | ||||||
\(225\) | 4.18969e16 | − | 6.56817e18i | 0.00637855 | − | 0.999964i | ||||
\(226\) | −4.75730e18 | −0.699026 | ||||||||
\(227\) | 9.97663e18i | 1.41507i | 0.706680 | + | 0.707534i | \(0.250192\pi\) | ||||
−0.706680 | + | 0.707534i | \(0.749808\pi\) | |||||||
\(228\) | 6.59223e17 | − | 6.55032e17i | 0.0902722 | − | 0.0896982i | ||||
\(229\) | −7.93251e18 | −1.04888 | −0.524441 | − | 0.851447i | \(-0.675726\pi\) | ||||
−0.524441 | + | 0.851447i | \(0.675726\pi\) | |||||||
\(230\) | 2.78672e16i | 0.00355853i | ||||||||
\(231\) | 6.30969e18 | + | 6.35007e18i | 0.778238 | + | 0.783218i | ||||
\(232\) | 4.41884e18 | 0.526507 | ||||||||
\(233\) | 8.97259e16i | 0.0103293i | 0.999987 | + | 0.00516465i | \(0.00164397\pi\) | ||||
−0.999987 | + | 0.00516465i | \(0.998356\pi\) | |||||||
\(234\) | −1.12670e19 | − | 7.18698e16i | −1.25338 | − | 0.00799502i | ||||
\(235\) | 4.45409e16 | 0.00478868 | ||||||||
\(236\) | − | 5.34405e18i | − | 0.555360i | ||||||
\(237\) | 1.97024e18 | − | 1.95771e18i | 0.197939 | − | 0.196680i | ||||
\(238\) | 1.80584e17 | 0.0175414 | ||||||||
\(239\) | 1.76298e19i | 1.65602i | 0.560716 | + | 0.828008i | \(0.310526\pi\) | ||||
−0.560716 | + | 0.828008i | \(0.689474\pi\) | |||||||
\(240\) | −7.64586e15 | − | 7.69478e15i | −0.000694602 | − | 0.000699047i | ||||
\(241\) | −7.62250e18 | −0.669825 | −0.334912 | − | 0.942249i | \(-0.608707\pi\) | ||||
−0.334912 | + | 0.942249i | \(0.608707\pi\) | |||||||
\(242\) | 1.29314e18i | 0.109932i | ||||||||
\(243\) | 8.73276e18 | − | 8.45859e18i | 0.718292 | − | 0.695741i | ||||
\(244\) | −2.80421e18 | −0.223199 | ||||||||
\(245\) | 2.81739e15i | 0.000217029i | ||||||||
\(246\) | 1.13417e19 | − | 1.12696e19i | 0.845666 | − | 0.840288i | ||||
\(247\) | 6.25028e18 | 0.451153 | ||||||||
\(248\) | 1.18270e18i | 0.0826533i | ||||||||
\(249\) | −3.04687e18 | − | 3.06637e18i | −0.206186 | − | 0.207505i | ||||
\(250\) | 8.50614e16 | 0.00557458 | ||||||||
\(251\) | − | 1.50703e19i | − | 0.956606i | −0.878195 | − | 0.478303i | \(-0.841252\pi\) | ||
0.878195 | − | 0.478303i | \(-0.158748\pi\) | |||||||
\(252\) | −5.32772e16 | + | 8.35225e18i | −0.00327595 | + | 0.513570i | ||||
\(253\) | 2.30371e19 | 1.37235 | ||||||||
\(254\) | 9.25286e18i | 0.534080i | ||||||||
\(255\) | 1.20734e15 | − | 1.19966e15i | 6.75317e−5 | − | 6.71023e-5i | ||||
\(256\) | 1.15292e18 | 0.0625000 | ||||||||
\(257\) | − | 3.63998e19i | − | 1.91265i | −0.292313 | − | 0.956323i | \(-0.594425\pi\) | ||
0.292313 | − | 0.956323i | \(-0.405575\pi\) | |||||||
\(258\) | 8.09000e18 | + | 8.14177e18i | 0.412089 | + | 0.414726i | ||||
\(259\) | −2.36219e19 | −1.16659 | ||||||||
\(260\) | − | 7.29564e16i | − | 0.00349363i | ||||||
\(261\) | −3.20674e19 | − | 2.04551e17i | −1.48916 | − | 0.00949900i | ||||
\(262\) | 1.94526e19 | 0.876126 | ||||||||
\(263\) | 6.06063e18i | 0.264772i | 0.991198 | + | 0.132386i | \(0.0422638\pi\) | ||||
−0.991198 | + | 0.132386i | \(0.957736\pi\) | |||||||
\(264\) | −6.36108e18 | + | 6.32063e18i | −0.269587 | + | 0.267873i | ||||
\(265\) | −1.23738e17 | −0.00508786 | ||||||||
\(266\) | − | 4.63334e18i | − | 0.184859i | ||||||
\(267\) | 1.94094e19 | + | 1.95336e19i | 0.751486 | + | 0.756295i | ||||
\(268\) | −1.68273e19 | −0.632319 | ||||||||
\(269\) | 2.59397e19i | 0.946122i | 0.881030 | + | 0.473061i | \(0.156851\pi\) | ||||
−0.881030 | + | 0.473061i | \(0.843149\pi\) | |||||||
\(270\) | 5.51297e16 | + | 5.61949e16i | 0.00195198 | + | 0.00198970i | ||||
\(271\) | −1.40860e19 | −0.484208 | −0.242104 | − | 0.970250i | \(-0.577838\pi\) | ||||
−0.242104 | + | 0.970250i | \(0.577838\pi\) | |||||||
\(272\) | 1.80897e17i | 0.00603783i | ||||||||
\(273\) | −3.98484e19 | + | 3.95950e19i | −1.29154 | + | 1.28333i | ||||
\(274\) | −1.06481e19 | −0.335173 | ||||||||
\(275\) | − | 3.51588e19i | − | 1.07491i | ||||||
\(276\) | 1.51504e19 | + | 1.52473e19i | 0.449936 | + | 0.452815i | ||||
\(277\) | 6.17005e19 | 1.78013 | 0.890063 | − | 0.455838i | \(-0.150660\pi\) | ||||
0.890063 | + | 0.455838i | \(0.150660\pi\) | |||||||
\(278\) | − | 5.94427e18i | − | 0.166625i | ||||||
\(279\) | 5.47479e16 | − | 8.58282e18i | 0.00149119 | − | 0.233774i | ||||
\(280\) | −5.40827e16 | −0.00143151 | ||||||||
\(281\) | 3.85570e19i | 0.991866i | 0.868361 | + | 0.495933i | \(0.165174\pi\) | ||||
−0.868361 | + | 0.495933i | \(0.834826\pi\) | |||||||
\(282\) | 2.43702e19 | − | 2.42152e19i | 0.609349 | − | 0.605474i | ||||
\(283\) | −3.08609e19 | −0.750096 | −0.375048 | − | 0.927005i | \(-0.622374\pi\) | ||||
−0.375048 | + | 0.927005i | \(0.622374\pi\) | |||||||
\(284\) | − | 1.04816e19i | − | 0.247675i | ||||||
\(285\) | −3.07803e16 | − | 3.09773e16i | −0.000707155 | − | 0.000711680i | ||||
\(286\) | −6.03112e19 | −1.34732 | ||||||||
\(287\) | − | 7.97152e19i | − | 1.73175i | ||||||
\(288\) | −8.36674e18 | − | 5.33696e16i | −0.176773 | − | 0.00112760i | ||||
\(289\) | 4.86328e19 | 0.999417 | ||||||||
\(290\) | − | 2.07644e17i | − | 0.00415083i | ||||||
\(291\) | 1.77713e19 | − | 1.76583e19i | 0.345601 | − | 0.343404i | ||||
\(292\) | −9.14428e17 | −0.0173016 | ||||||||
\(293\) | 9.45764e18i | 0.174117i | 0.996203 | + | 0.0870586i | \(0.0277468\pi\) | ||||
−0.996203 | + | 0.0870586i | \(0.972253\pi\) | |||||||
\(294\) | 1.53171e18 | + | 1.54151e18i | 0.0274409 | + | 0.0276165i | ||||
\(295\) | −2.51120e17 | −0.00437830 | ||||||||
\(296\) | − | 2.36629e19i | − | 0.401545i | ||||||
\(297\) | 4.64549e19 | − | 4.55743e19i | 0.767325 | − | 0.752781i | ||||
\(298\) | 3.16356e18 | 0.0508681 | ||||||||
\(299\) | 1.44564e20i | 2.26303i | ||||||||
\(300\) | 2.32701e19 | − | 2.31222e19i | 0.354674 | − | 0.352419i | ||||
\(301\) | 5.72243e19 | 0.849276 | ||||||||
\(302\) | − | 6.30838e18i | − | 0.0911722i | ||||||
\(303\) | −1.82850e19 | − | 1.84020e19i | −0.257368 | − | 0.259015i | ||||
\(304\) | 4.64138e18 | 0.0636294 | ||||||||
\(305\) | 1.31772e17i | 0.00175964i | ||||||||
\(306\) | 8.37387e15 | − | 1.31277e18i | 0.000108932 | − | 0.0170772i | ||||
\(307\) | −3.19426e19 | −0.404821 | −0.202411 | − | 0.979301i | \(-0.564878\pi\) | ||||
−0.202411 | + | 0.979301i | \(0.564878\pi\) | |||||||
\(308\) | 4.47088e19i | 0.552061i | ||||||||
\(309\) | −4.55361e19 | + | 4.52466e19i | −0.547883 | + | 0.544400i | ||||
\(310\) | 5.55757e16 | 0.000651615 | ||||||||
\(311\) | − | 5.04871e19i | − | 0.576895i | −0.957496 | − | 0.288448i | \(-0.906861\pi\) | ||
0.957496 | − | 0.288448i | \(-0.0931391\pi\) | |||||||
\(312\) | −3.96637e19 | − | 3.99175e19i | −0.441729 | − | 0.444556i | ||||
\(313\) | −9.61081e19 | −1.04329 | −0.521645 | − | 0.853163i | \(-0.674681\pi\) | ||||
−0.521645 | + | 0.853163i | \(0.674681\pi\) | |||||||
\(314\) | 3.36213e19i | 0.355777i | ||||||||
\(315\) | 3.92477e17 | + | 2.50353e15i | 0.00404883 | + | 2.58266e-5i | ||||
\(316\) | 1.38718e19 | 0.139520 | ||||||||
\(317\) | 1.08055e20i | 1.05967i | 0.848101 | + | 0.529834i | \(0.177746\pi\) | ||||
−0.848101 | + | 0.529834i | \(0.822254\pi\) | |||||||
\(318\) | −6.77021e19 | + | 6.72716e19i | −0.647418 | + | 0.643302i | ||||
\(319\) | −1.71654e20 | −1.60077 | ||||||||
\(320\) | − | 5.41765e16i | − | 0.000492732i | ||||||
\(321\) | −1.14004e20 | − | 1.14734e20i | −1.01130 | − | 1.01777i | ||||
\(322\) | 1.07165e20 | 0.927274 | ||||||||
\(323\) | 7.28248e17i | 0.00614694i | ||||||||
\(324\) | 6.07148e19 | + | 7.74605e17i | 0.499959 | + | 0.00637852i | ||||
\(325\) | 2.20631e20 | 1.77255 | ||||||||
\(326\) | 1.47426e20i | 1.15567i | ||||||||
\(327\) | 1.49307e20 | − | 1.48358e20i | 1.14208 | − | 1.13482i | ||||
\(328\) | 7.98535e19 | 0.596078 | ||||||||
\(329\) | − | 1.71285e20i | − | 1.24782i | ||||||
\(330\) | 2.97010e17 | + | 2.98911e17i | 0.00211183 | + | 0.00212535i | ||||
\(331\) | −5.10944e19 | −0.354608 | −0.177304 | − | 0.984156i | \(-0.556738\pi\) | ||||
−0.177304 | + | 0.984156i | \(0.556738\pi\) | |||||||
\(332\) | − | 2.15893e19i | − | 0.146263i | ||||||
\(333\) | −1.09537e18 | + | 1.71721e20i | −0.00724449 | + | 1.13572i | ||||
\(334\) | −2.74690e19 | −0.177366 | ||||||||
\(335\) | 7.90724e17i | 0.00498502i | ||||||||
\(336\) | −2.95909e19 | + | 2.94027e19i | −0.182156 | + | 0.180998i | ||||
\(337\) | 5.25258e19 | 0.315743 | 0.157871 | − | 0.987460i | \(-0.449537\pi\) | ||||
0.157871 | + | 0.987460i | \(0.449537\pi\) | |||||||
\(338\) | − | 2.58015e20i | − | 1.51465i | ||||||
\(339\) | 1.21535e20 | + | 1.22313e20i | 0.696793 | + | 0.701252i | ||||
\(340\) | 8.50048e15 | 4.76005e−5 | ||||||||
\(341\) | − | 4.59430e19i | − | 0.251295i | ||||||
\(342\) | −3.36824e19 | − | 2.14853e17i | −0.179968 | − | 0.00114797i | ||||
\(343\) | −1.85950e20 | −0.970607 | ||||||||
\(344\) | 5.73236e19i | 0.292325i | ||||||||
\(345\) | 7.16480e17 | − | 7.11924e17i | 0.00356986 | − | 0.00354716i | ||||
\(346\) | 7.55247e19 | 0.367689 | ||||||||
\(347\) | − | 3.17727e20i | − | 1.51154i | −0.654839 | − | 0.755768i | \(-0.727264\pi\) | ||
0.654839 | − | 0.755768i | \(-0.272736\pi\) | |||||||
\(348\) | −1.12888e20 | − | 1.13611e20i | −0.524825 | − | 0.528183i | ||||
\(349\) | −7.84605e19 | −0.356490 | −0.178245 | − | 0.983986i | \(-0.557042\pi\) | ||||
−0.178245 | + | 0.983986i | \(0.557042\pi\) | |||||||
\(350\) | − | 1.63554e20i | − | 0.726301i | ||||||
\(351\) | 2.85991e20 | + | 2.91517e20i | 1.24135 | + | 1.26534i | ||||
\(352\) | −4.47863e19 | −0.190022 | ||||||||
\(353\) | 2.44715e20i | 1.01499i | 0.861653 | + | 0.507497i | \(0.169429\pi\) | ||||
−0.861653 | + | 0.507497i | \(0.830571\pi\) | |||||||
\(354\) | −1.37398e20 | + | 1.36525e20i | −0.557128 | + | 0.553586i | ||||
\(355\) | −4.92537e17 | −0.00195260 | ||||||||
\(356\) | 1.37529e20i | 0.533084i | ||||||||
\(357\) | −4.61339e18 | − | 4.64292e18i | −0.0174854 | − | 0.0175973i | ||||
\(358\) | 2.50941e19 | 0.0930051 | ||||||||
\(359\) | 1.77162e20i | 0.642119i | 0.947059 | + | 0.321060i | \(0.104039\pi\) | ||||
−0.947059 | + | 0.321060i | \(0.895961\pi\) | |||||||
\(360\) | −2.50787e15 | + | 3.93158e17i | −8.88965e−6 | + | 0.00139363i | ||||
\(361\) | −2.69756e20 | −0.935221 | ||||||||
\(362\) | − | 1.17174e20i | − | 0.397340i | ||||||
\(363\) | 3.32473e19 | − | 3.30359e19i | 0.110282 | − | 0.109581i | ||||
\(364\) | −2.80559e20 | −0.910361 | ||||||||
\(365\) | 4.29695e16i | 0.000136401i | ||||||||
\(366\) | 7.16393e19 | + | 7.20977e19i | 0.222486 | + | 0.223910i | ||||
\(367\) | 3.41194e20 | 1.03675 | 0.518373 | − | 0.855154i | \(-0.326538\pi\) | ||||
0.518373 | + | 0.855154i | \(0.326538\pi\) | |||||||
\(368\) | 1.07351e20i | 0.319172i | ||||||||
\(369\) | −5.79495e20 | − | 3.69647e18i | −1.68593 | − | 0.0107542i | ||||
\(370\) | −1.11193e18 | −0.00316567 | ||||||||
\(371\) | 4.75843e20i | 1.32578i | ||||||||
\(372\) | 3.04078e19 | − | 3.02144e19i | 0.0829165 | − | 0.0823893i | ||||
\(373\) | 4.31198e20 | 1.15082 | 0.575409 | − | 0.817866i | \(-0.304843\pi\) | ||||
0.575409 | + | 0.817866i | \(0.304843\pi\) | |||||||
\(374\) | − | 7.02713e18i | − | 0.0183571i | ||||||
\(375\) | −2.17307e18 | − | 2.18697e18i | −0.00555678 | − | 0.00559233i | ||||
\(376\) | 1.71583e20 | 0.429507 | ||||||||
\(377\) | − | 1.07717e21i | − | 2.63970i | ||||||
\(378\) | 2.16102e20 | − | 2.12006e20i | 0.518470 | − | 0.508643i | ||||
\(379\) | −9.46277e19 | −0.222282 | −0.111141 | − | 0.993805i | \(-0.535451\pi\) | ||||
−0.111141 | + | 0.993805i | \(0.535451\pi\) | |||||||
\(380\) | − | 2.18101e17i | − | 0.000501636i | ||||||
\(381\) | 2.37896e20 | − | 2.36383e20i | 0.535781 | − | 0.532374i | ||||
\(382\) | 1.35118e20 | 0.297993 | ||||||||
\(383\) | 1.63118e20i | 0.352300i | 0.984363 | + | 0.176150i | \(0.0563643\pi\) | ||||
−0.984363 | + | 0.176150i | \(0.943636\pi\) | |||||||
\(384\) | −2.94537e19 | − | 2.96422e19i | −0.0623003 | − | 0.0626990i | ||||
\(385\) | 2.10089e18 | 0.00435229 | ||||||||
\(386\) | 4.00548e19i | 0.0812749i | ||||||||
\(387\) | 2.65355e18 | − | 4.15996e20i | 0.00527399 | − | 0.826803i | ||||
\(388\) | 1.25122e20 | 0.243601 | ||||||||
\(389\) | 7.07561e20i | 1.34948i | 0.738055 | + | 0.674741i | \(0.235745\pi\) | ||||
−0.738055 | + | 0.674741i | \(0.764255\pi\) | |||||||
\(390\) | −1.87575e18 | + | 1.86382e18i | −0.00350475 | + | 0.00348247i | ||||
\(391\) | −1.68438e19 | −0.0308337 | ||||||||
\(392\) | 1.08533e19i | 0.0194658i | ||||||||
\(393\) | −4.96955e20 | − | 5.00135e20i | −0.873327 | − | 0.878916i | ||||
\(394\) | −2.19706e20 | −0.378331 | ||||||||
\(395\) | − | 6.51843e17i | − | 0.00109993i | ||||||
\(396\) | 3.25014e20 | + | 2.07319e18i | 0.537452 | + | 0.00342829i | ||||
\(397\) | −7.54229e19 | −0.122230 | −0.0611152 | − | 0.998131i | \(-0.519466\pi\) | ||||
−0.0611152 | + | 0.998131i | \(0.519466\pi\) | |||||||
\(398\) | 8.32364e20i | 1.32205i | ||||||||
\(399\) | −1.19126e20 | + | 1.18368e20i | −0.185448 | + | 0.184269i | ||||
\(400\) | 1.63837e20 | 0.249996 | ||||||||
\(401\) | − | 5.73495e20i | − | 0.857777i | −0.903357 | − | 0.428889i | \(-0.858905\pi\) | ||
0.903357 | − | 0.428889i | \(-0.141095\pi\) | |||||||
\(402\) | 4.29887e20 | + | 4.32638e20i | 0.630299 | + | 0.634332i | ||||
\(403\) | 2.88304e20 | 0.414392 | ||||||||
\(404\) | − | 1.29563e20i | − | 0.182570i | ||||||
\(405\) | 3.63991e16 | − | 2.85303e18i | 5.02864e−5 | − | 0.00394154i | ||||
\(406\) | −7.98510e20 | −1.08161 | ||||||||
\(407\) | 9.19207e20i | 1.22084i | ||||||||
\(408\) | 4.65097e18 | − | 4.62139e18i | 0.00605706 | − | 0.00601855i | ||||
\(409\) | −8.16315e20 | −1.04249 | −0.521244 | − | 0.853407i | \(-0.674532\pi\) | ||||
−0.521244 | + | 0.853407i | \(0.674532\pi\) | |||||||
\(410\) | − | 3.75236e18i | − | 0.00469931i | ||||||
\(411\) | 2.72028e20 | + | 2.73769e20i | 0.334102 | + | 0.336240i | ||||
\(412\) | −3.20605e20 | −0.386182 | ||||||||
\(413\) | 9.65702e20i | 1.14089i | ||||||||
\(414\) | 4.96937e18 | − | 7.79047e20i | 0.00575836 | − | 0.902737i | ||||
\(415\) | −1.01449e18 | −0.00115309 | ||||||||
\(416\) | − | 2.81046e20i | − | 0.313351i | ||||||
\(417\) | −1.52830e20 | + | 1.51858e20i | −0.167156 | + | 0.166093i | ||||
\(418\) | −1.80299e20 | −0.193456 | ||||||||
\(419\) | − | 9.99098e20i | − | 1.05171i | −0.850574 | − | 0.525855i | \(-0.823746\pi\) | ||
0.850574 | − | 0.525855i | \(-0.176254\pi\) | |||||||
\(420\) | 1.38165e18 | + | 1.39049e18i | 0.00142694 | + | 0.00143607i | ||||
\(421\) | 8.93599e20 | 0.905494 | 0.452747 | − | 0.891639i | \(-0.350444\pi\) | ||||
0.452747 | + | 0.891639i | \(0.350444\pi\) | |||||||
\(422\) | − | 5.76894e20i | − | 0.573583i | ||||||
\(423\) | −1.24517e21 | − | 7.94268e18i | −1.21480 | − | 0.00774897i | ||||
\(424\) | −4.76668e20 | −0.456341 | ||||||||
\(425\) | 2.57067e19i | 0.0241510i | ||||||||
\(426\) | −2.69488e20 | + | 2.67774e20i | −0.248463 | + | 0.246883i | ||||
\(427\) | 5.06738e20 | 0.458522 | ||||||||
\(428\) | − | 8.07803e20i | − | 0.717390i | ||||||
\(429\) | 1.54077e21 | + | 1.55063e21i | 1.34301 | + | 1.35161i | ||||
\(430\) | 2.69367e18 | 0.00230460 | ||||||||
\(431\) | − | 1.38442e21i | − | 1.16265i | −0.813670 | − | 0.581327i | \(-0.802534\pi\) | ||
0.813670 | − | 0.581327i | \(-0.197466\pi\) | |||||||
\(432\) | 2.12373e20 | + | 2.16477e20i | 0.175077 | + | 0.178460i | ||||
\(433\) | 1.26892e21 | 1.02690 | 0.513452 | − | 0.858118i | \(-0.328366\pi\) | ||||
0.513452 | + | 0.858118i | \(0.328366\pi\) | |||||||
\(434\) | − | 2.13721e20i | − | 0.169796i | ||||||
\(435\) | −5.33863e18 | + | 5.30468e18i | −0.00416404 | + | 0.00413757i | ||||
\(436\) | 1.05122e21 | 0.805012 | ||||||||
\(437\) | 4.32170e20i | 0.324940i | ||||||||
\(438\) | 2.33609e19 | + | 2.35104e19i | 0.0172463 | + | 0.0173567i | ||||
\(439\) | 7.85494e20 | 0.569412 | 0.284706 | − | 0.958615i | \(-0.408104\pi\) | ||||
0.284706 | + | 0.958615i | \(0.408104\pi\) | |||||||
\(440\) | 2.10453e18i | 0.00149808i | ||||||||
\(441\) | 5.02406e17 | − | 7.87621e19i | 0.000351193 | − | 0.0550565i | ||||
\(442\) | 4.40971e19 | 0.0302714 | ||||||||
\(443\) | − | 1.76848e21i | − | 1.19225i | −0.802890 | − | 0.596127i | \(-0.796705\pi\) | ||
0.802890 | − | 0.596127i | \(-0.203295\pi\) | |||||||
\(444\) | −6.08385e20 | + | 6.04517e20i | −0.402824 | + | 0.400262i | ||||
\(445\) | 6.46259e18 | 0.00420268 | ||||||||
\(446\) | 1.29108e20i | 0.0824657i | ||||||||
\(447\) | −8.08195e19 | − | 8.13367e19i | −0.0507056 | − | 0.0510301i | ||||
\(448\) | −2.08340e20 | −0.128395 | ||||||||
\(449\) | − | 1.12071e20i | − | 0.0678456i | −0.999424 | − | 0.0339228i | \(-0.989200\pi\) | ||
0.999424 | − | 0.0339228i | \(-0.0108000\pi\) | |||||||
\(450\) | −1.18897e21 | − | 7.58415e18i | −0.707081 | − | 0.00451032i | ||||
\(451\) | −3.10198e21 | −1.81229 | ||||||||
\(452\) | 8.61164e20i | 0.494286i | ||||||||
\(453\) | −1.62192e20 | + | 1.61160e20i | −0.0914625 | + | 0.0908810i | ||||
\(454\) | 1.80596e21 | 1.00060 | ||||||||
\(455\) | 1.31837e19i | 0.00717703i | ||||||||
\(456\) | −1.18573e20 | − | 1.19332e20i | −0.0634262 | − | 0.0638321i | ||||
\(457\) | −2.74111e21 | −1.44078 | −0.720389 | − | 0.693571i | \(-0.756037\pi\) | ||||
−0.720389 | + | 0.693571i | \(0.756037\pi\) | |||||||
\(458\) | 1.43594e21i | 0.741672i | ||||||||
\(459\) | −3.39659e19 | + | 3.33221e19i | −0.0172402 | + | 0.0169134i | ||||
\(460\) | 5.04450e18 | 0.00251626 | ||||||||
\(461\) | 1.29478e21i | 0.634728i | 0.948304 | + | 0.317364i | \(0.102798\pi\) | ||||
−0.948304 | + | 0.317364i | \(0.897202\pi\) | |||||||
\(462\) | 1.14949e21 | − | 1.14218e21i | 0.553819 | − | 0.550297i | ||||
\(463\) | −1.59724e21 | −0.756351 | −0.378176 | − | 0.925734i | \(-0.623448\pi\) | ||||
−0.378176 | + | 0.925734i | \(0.623448\pi\) | |||||||
\(464\) | − | 7.99895e20i | − | 0.372296i | ||||||
\(465\) | −1.41979e18 | − | 1.42888e18i | −0.000649533 | − | 0.000653690i | ||||
\(466\) | 1.62421e19 | 0.00730391 | ||||||||
\(467\) | 3.21129e21i | 1.41953i | 0.704439 | + | 0.709765i | \(0.251199\pi\) | ||||
−0.704439 | + | 0.709765i | \(0.748801\pi\) | |||||||
\(468\) | −1.30098e19 | + | 2.03955e21i | −0.00565333 | + | 0.886272i | ||||
\(469\) | 3.04079e21 | 1.29898 | ||||||||
\(470\) | − | 8.06276e18i | − | 0.00338611i | ||||||
\(471\) | 8.64421e20 | − | 8.58925e20i | 0.356909 | − | 0.354640i | ||||
\(472\) | −9.67377e20 | −0.392699 | ||||||||
\(473\) | − | 2.22679e21i | − | 0.888770i | ||||||
\(474\) | −3.54383e20 | − | 3.56651e20i | −0.139074 | − | 0.139964i | ||||
\(475\) | 6.59569e20 | 0.254514 | ||||||||
\(476\) | − | 3.26892e19i | − | 0.0124036i | ||||||
\(477\) | 3.45917e21 | + | 2.20653e19i | 1.29070 | + | 0.00823309i | ||||
\(478\) | 3.19134e21 | 1.17098 | ||||||||
\(479\) | − | 9.37816e20i | − | 0.338403i | −0.985582 | − | 0.169201i | \(-0.945881\pi\) | ||
0.985582 | − | 0.169201i | \(-0.0541188\pi\) | |||||||
\(480\) | −1.39290e18 | + | 1.38405e18i | −0.000494301 | + | 0.000491158i | ||||
\(481\) | −5.76827e21 | −2.01319 | ||||||||
\(482\) | 1.37982e21i | 0.473638i | ||||||||
\(483\) | −2.73776e21 | − | 2.75528e21i | −0.924312 | − | 0.930226i | ||||
\(484\) | 2.34084e20 | 0.0777334 | ||||||||
\(485\) | − | 5.87955e18i | − | 0.00192048i | ||||||
\(486\) | −1.53117e21 | − | 1.58080e21i | −0.491963 | − | 0.507909i | ||||
\(487\) | 2.10022e21 | 0.663793 | 0.331896 | − | 0.943316i | \(-0.392312\pi\) | ||||
0.331896 | + | 0.943316i | \(0.392312\pi\) | |||||||
\(488\) | 5.07617e20i | 0.157826i | ||||||||
\(489\) | 3.79039e21 | − | 3.76629e21i | 1.15935 | − | 1.15197i | ||||
\(490\) | 5.10002e17 | 0.000153463 | ||||||||
\(491\) | 1.84865e21i | 0.547271i | 0.961833 | + | 0.273636i | \(0.0882262\pi\) | ||||
−0.961833 | + | 0.273636i | \(0.911774\pi\) | |||||||
\(492\) | −2.04002e21 | − | 2.05307e21i | −0.594174 | − | 0.597976i | ||||
\(493\) | 1.25506e20 | 0.0359658 | ||||||||
\(494\) | − | 1.13142e21i | − | 0.319013i | ||||||
\(495\) | 9.74204e16 | − | 1.52726e19i | 2.70277e−5 | − | 0.00423712i | ||||
\(496\) | 2.14091e20 | 0.0584447 | ||||||||
\(497\) | 1.89409e21i | 0.508803i | ||||||||
\(498\) | −5.55072e20 | + | 5.51542e20i | −0.146728 | + | 0.145795i | ||||
\(499\) | 7.18549e21 | 1.86918 | 0.934591 | − | 0.355723i | \(-0.115765\pi\) | ||||
0.934591 | + | 0.355723i | \(0.115765\pi\) | |||||||
\(500\) | − | 1.53978e19i | − | 0.00394183i | ||||||
\(501\) | 7.01751e20 | + | 7.06242e20i | 0.176800 | + | 0.177931i | ||||
\(502\) | −2.72802e21 | −0.676423 | ||||||||
\(503\) | − | 1.44507e21i | − | 0.352652i | −0.984332 | − | 0.176326i | \(-0.943579\pi\) | ||
0.984332 | − | 0.176326i | \(-0.0564212\pi\) | |||||||
\(504\) | 1.51192e21 | + | 9.64420e18i | 0.363149 | + | 0.00231644i | ||||
\(505\) | −6.08822e18 | −0.00143933 | ||||||||
\(506\) | − | 4.17016e21i | − | 0.970395i | ||||||
\(507\) | −6.63371e21 | + | 6.59153e21i | −1.51947 | + | 1.50981i | ||||
\(508\) | 1.67495e21 | 0.377652 | ||||||||
\(509\) | 7.91565e21i | 1.75689i | 0.477845 | + | 0.878444i | \(0.341418\pi\) | ||||
−0.477845 | + | 0.878444i | \(0.658582\pi\) | |||||||
\(510\) | −2.17162e17 | − | 2.18552e17i | −4.74485e−5 | − | 4.77521e-5i | ||||
\(511\) | 1.65243e20 | 0.0355430 | ||||||||
\(512\) | − | 2.08701e20i | − | 0.0441942i | ||||||
\(513\) | 8.54962e20 | + | 8.71481e20i | 0.178241 | + | 0.181685i | ||||
\(514\) | −6.58907e21 | −1.35244 | ||||||||
\(515\) | 1.50654e19i | 0.00304455i | ||||||||
\(516\) | 1.47382e21 | − | 1.46445e21i | 0.293256 | − | 0.291391i | ||||
\(517\) | −6.66528e21 | −1.30585 | ||||||||
\(518\) | 4.27603e21i | 0.824902i | ||||||||
\(519\) | −1.92943e21 | − | 1.94178e21i | −0.366514 | − | 0.368859i | ||||
\(520\) | −1.32065e19 | −0.00247037 | ||||||||
\(521\) | − | 4.02768e21i | − | 0.741914i | −0.928650 | − | 0.370957i | \(-0.879030\pi\) | ||
0.928650 | − | 0.370957i | \(-0.120970\pi\) | |||||||
\(522\) | −3.70277e19 | + | 5.80482e21i | −0.00671680 | + | 1.05299i | ||||
\(523\) | 7.03477e21 | 1.25671 | 0.628357 | − | 0.777925i | \(-0.283728\pi\) | ||||
0.628357 | + | 0.777925i | \(0.283728\pi\) | |||||||
\(524\) | − | 3.52129e21i | − | 0.619515i | ||||||
\(525\) | −4.20505e21 | + | 4.17832e21i | −0.728613 | + | 0.723980i | ||||
\(526\) | 1.09709e21 | 0.187222 | ||||||||
\(527\) | 3.35917e19i | 0.00564607i | ||||||||
\(528\) | 1.14416e21 | + | 1.15148e21i | 0.189415 | + | 0.190627i | ||||
\(529\) | −3.86313e21 | −0.629933 | ||||||||
\(530\) | 2.23989e19i | 0.00359766i | ||||||||
\(531\) | 7.02024e21 | + | 4.47806e19i | 1.11070 | + | 0.00708489i | ||||
\(532\) | −8.38724e20 | −0.130715 | ||||||||
\(533\) | − | 1.94658e22i | − | 2.98850i | ||||||
\(534\) | 3.53595e21 | − | 3.51347e21i | 0.534781 | − | 0.531381i | ||||
\(535\) | −3.79592e19 | −0.00565570 | ||||||||
\(536\) | 3.04607e21i | 0.447117i | ||||||||
\(537\) | −6.41079e20 | − | 6.45181e20i | −0.0927080 | − | 0.0933012i | ||||
\(538\) | 4.69559e21 | 0.669009 | ||||||||
\(539\) | − | 4.21606e20i | − | 0.0591829i | ||||||
\(540\) | 1.01724e19 | − | 9.97954e18i | 0.00140693 | − | 0.00138026i | ||||
\(541\) | 4.29480e21 | 0.585281 | 0.292641 | − | 0.956222i | \(-0.405466\pi\) | ||||
0.292641 | + | 0.956222i | \(0.405466\pi\) | |||||||
\(542\) | 2.54983e21i | 0.342387i | ||||||||
\(543\) | −3.01260e21 | + | 2.99344e21i | −0.398605 | + | 0.396070i | ||||
\(544\) | 3.27459e19 | 0.00426939 | ||||||||
\(545\) | − | 4.93975e19i | − | 0.00634648i | ||||||
\(546\) | 7.16746e21 | + | 7.21333e21i | 0.907453 | + | 0.913260i | ||||
\(547\) | −3.57218e21 | −0.445692 | −0.222846 | − | 0.974854i | \(-0.571535\pi\) | ||||
−0.222846 | + | 0.974854i | \(0.571535\pi\) | |||||||
\(548\) | 1.92752e21i | 0.237003i | ||||||||
\(549\) | 2.34979e19 | − | 3.68377e21i | 0.00284742 | − | 0.446389i | ||||
\(550\) | −6.36442e21 | −0.760076 | ||||||||
\(551\) | − | 3.22018e21i | − | 0.379024i | ||||||
\(552\) | 2.76006e21 | − | 2.74251e21i | 0.320188 | − | 0.318153i | ||||
\(553\) | −2.50671e21 | −0.286618 | ||||||||
\(554\) | − | 1.11690e22i | − | 1.25874i | ||||||
\(555\) | 2.84066e19 | + | 2.85884e19i | 0.00315555 | + | 0.00317575i | ||||
\(556\) | −1.07603e21 | −0.117822 | ||||||||
\(557\) | 9.60998e21i | 1.03724i | 0.855004 | + | 0.518622i | \(0.173555\pi\) | ||||
−0.855004 | + | 0.518622i | \(0.826445\pi\) | |||||||
\(558\) | −1.55366e21 | − | 9.91043e18i | −0.165303 | − | 0.00105443i | ||||
\(559\) | 1.39737e22 | 1.46560 | ||||||||
\(560\) | 9.79001e18i | 0.00101223i | ||||||||
\(561\) | −1.80671e20 | + | 1.79522e20i | −0.0184156 | + | 0.0182985i | ||||
\(562\) | 6.97957e21 | 0.701355 | ||||||||
\(563\) | 1.05802e22i | 1.04816i | 0.851669 | + | 0.524079i | \(0.175590\pi\) | ||||
−0.851669 | + | 0.524079i | \(0.824410\pi\) | |||||||
\(564\) | −4.38342e21 | − | 4.41147e21i | −0.428135 | − | 0.430875i | ||||
\(565\) | 4.04666e19 | 0.00389681 | ||||||||
\(566\) | 5.58641e21i | 0.530398i | ||||||||
\(567\) | −1.09715e22 | − | 1.39976e20i | −1.02708 | − | 0.0131035i | ||||
\(568\) | −1.89737e21 | −0.175132 | ||||||||
\(569\) | − | 9.33207e21i | − | 0.849336i | −0.905349 | − | 0.424668i | \(-0.860391\pi\) | ||
0.905349 | − | 0.424668i | \(-0.139609\pi\) | |||||||
\(570\) | −5.60749e18 | + | 5.57183e18i | −0.000503234 | + | 0.000500034i | ||||
\(571\) | −9.20209e21 | −0.814324 | −0.407162 | − | 0.913356i | \(-0.633482\pi\) | ||||
−0.407162 | + | 0.913356i | \(0.633482\pi\) | |||||||
\(572\) | 1.09175e22i | 0.952696i | ||||||||
\(573\) | −3.45186e21 | − | 3.47395e21i | −0.297041 | − | 0.298942i | ||||
\(574\) | −1.44300e22 | −1.22453 | ||||||||
\(575\) | 1.52553e22i | 1.27667i | ||||||||
\(576\) | −9.66092e18 | + | 1.51454e21i | −0.000797331 | + | 0.124997i | ||||
\(577\) | −7.92579e21 | −0.645113 | −0.322557 | − | 0.946550i | \(-0.604542\pi\) | ||||
−0.322557 | + | 0.946550i | \(0.604542\pi\) | |||||||
\(578\) | − | 8.80348e21i | − | 0.706694i | ||||||
\(579\) | 1.02983e21 | − | 1.02328e21i | 0.0815337 | − | 0.0810153i | ||||
\(580\) | −3.75875e19 | −0.00293508 | ||||||||
\(581\) | 3.90131e21i | 0.300470i | ||||||||
\(582\) | −3.19649e21 | − | 3.21695e21i | −0.242823 | − | 0.244377i | ||||
\(583\) | 1.85166e22 | 1.38744 | ||||||||
\(584\) | 1.65529e20i | 0.0122341i | ||||||||
\(585\) | 9.58395e19 | + | 6.11339e17i | 0.00698711 | + | 4.45692e-5i | ||||
\(586\) | 1.71202e21 | 0.123120 | ||||||||
\(587\) | − | 8.82724e21i | − | 0.626210i | −0.949719 | − | 0.313105i | \(-0.898631\pi\) | ||
0.949719 | − | 0.313105i | \(-0.101369\pi\) | |||||||
\(588\) | 2.79043e20 | − | 2.77269e20i | 0.0195278 | − | 0.0194036i | ||||
\(589\) | 8.61878e20 | 0.0595009 | ||||||||
\(590\) | 4.54576e19i | 0.00309592i | ||||||||
\(591\) | 5.61283e21 | + | 5.64875e21i | 0.377122 | + | 0.379536i | ||||
\(592\) | −4.28344e21 | −0.283935 | ||||||||
\(593\) | 2.25118e22i | 1.47222i | 0.676863 | + | 0.736109i | \(0.263339\pi\) | ||||
−0.676863 | + | 0.736109i | \(0.736661\pi\) | |||||||
\(594\) | −8.24983e21 | − | 8.40923e21i | −0.532296 | − | 0.542581i | ||||
\(595\) | −1.53609e18 | −9.77868e−5 | ||||||||
\(596\) | − | 5.72665e20i | − | 0.0359692i | ||||||
\(597\) | 2.14005e22 | − | 2.12644e22i | 1.32626 | − | 1.31783i | ||||
\(598\) | 2.61689e22 | 1.60020 | ||||||||
\(599\) | 1.26203e22i | 0.761472i | 0.924684 | + | 0.380736i | \(0.124329\pi\) | ||||
−0.924684 | + | 0.380736i | \(0.875671\pi\) | |||||||
\(600\) | −4.18556e21 | − | 4.21235e21i | −0.249198 | − | 0.250792i | ||||
\(601\) | 2.45052e22 | 1.43967 | 0.719834 | − | 0.694146i | \(-0.244218\pi\) | ||||
0.719834 | + | 0.694146i | \(0.244218\pi\) | |||||||
\(602\) | − | 1.03587e22i | − | 0.600529i | ||||||
\(603\) | 1.41005e20 | − | 2.21053e22i | 0.00806668 | − | 1.26461i | ||||
\(604\) | −1.14194e21 | −0.0644685 | ||||||||
\(605\) | − | 1.09997e19i | − | 0.000612828i | ||||||
\(606\) | −3.33112e21 | + | 3.30994e21i | −0.183151 | + | 0.181987i | ||||
\(607\) | −3.45572e22 | −1.87512 | −0.937561 | − | 0.347820i | \(-0.886922\pi\) | ||||
−0.937561 | + | 0.347820i | \(0.886922\pi\) | |||||||
\(608\) | − | 8.40179e20i | − | 0.0449928i | ||||||
\(609\) | 2.03996e22 | + | 2.05301e22i | 1.07816 | + | 1.08506i | ||||
\(610\) | 2.38532e19 | 0.00124425 | ||||||||
\(611\) | − | 4.18264e22i | − | 2.15338i | ||||||
\(612\) | −2.37637e20 | − | 1.51583e18i | −0.0120754 | − | 7.70265e-5i | ||||
\(613\) | −3.57279e22 | −1.79194 | −0.895971 | − | 0.444113i | \(-0.853519\pi\) | ||||
−0.895971 | + | 0.444113i | \(0.853519\pi\) | |||||||
\(614\) | 5.78223e21i | 0.286252i | ||||||||
\(615\) | −9.64751e19 | + | 9.58617e19i | −0.00471427 | + | 0.00468429i | ||||
\(616\) | 8.09315e21 | 0.390366 | ||||||||
\(617\) | 6.54663e21i | 0.311700i | 0.987781 | + | 0.155850i | \(0.0498116\pi\) | ||||
−0.987781 | + | 0.155850i | \(0.950188\pi\) | |||||||
\(618\) | 8.19051e21 | + | 8.24292e21i | 0.384949 | + | 0.387412i | ||||
\(619\) | −6.20428e21 | −0.287850 | −0.143925 | − | 0.989589i | \(-0.545972\pi\) | ||||
−0.143925 | + | 0.989589i | \(0.545972\pi\) | |||||||
\(620\) | − | 1.00603e19i | − | 0.000460761i | ||||||
\(621\) | −2.01567e22 | + | 1.97746e22i | −0.911351 | + | 0.894076i | ||||
\(622\) | −9.13914e21 | −0.407927 | ||||||||
\(623\) | − | 2.48524e22i | − | 1.09513i | ||||||
\(624\) | −7.22584e21 | + | 7.17989e21i | −0.314349 | + | 0.312350i | ||||
\(625\) | 2.32820e22 | 0.999953 | ||||||||
\(626\) | 1.73974e22i | 0.737718i | ||||||||
\(627\) | 4.60609e21 | + | 4.63557e21i | 0.192838 | + | 0.194072i | ||||
\(628\) | 6.08611e21 | 0.251572 | ||||||||
\(629\) | − | 6.72087e20i | − | 0.0274297i | ||||||
\(630\) | 4.53187e17 | − | 7.10460e19i | 1.82622e−5 | − | 0.00286296i | ||||
\(631\) | −1.70005e22 | −0.676436 | −0.338218 | − | 0.941068i | \(-0.609824\pi\) | ||||
−0.338218 | + | 0.941068i | \(0.609824\pi\) | |||||||
\(632\) | − | 2.51106e21i | − | 0.0986554i | ||||||
\(633\) | −1.48322e22 | + | 1.47379e22i | −0.575410 | + | 0.571751i | ||||
\(634\) | 1.95600e22 | 0.749299 | ||||||||
\(635\) | − | 7.87067e19i | − | 0.00297730i | ||||||
\(636\) | 1.21775e22 | + | 1.22554e22i | 0.454883 | + | 0.457794i | ||||
\(637\) | 2.64569e21 | 0.0975940 | ||||||||
\(638\) | 3.10726e22i | 1.13191i | ||||||||
\(639\) | 1.37692e22 | + | 8.78309e19i | 0.495339 | + | 0.00315966i | ||||
\(640\) | −9.80699e18 | −0.000348414 | ||||||||
\(641\) | 7.96286e21i | 0.279386i | 0.990195 | + | 0.139693i | \(0.0446116\pi\) | ||||
−0.990195 | + | 0.139693i | \(0.955388\pi\) | |||||||
\(642\) | −2.07690e22 | + | 2.06370e22i | −0.719675 | + | 0.715099i | ||||
\(643\) | −4.33342e22 | −1.48301 | −0.741503 | − | 0.670950i | \(-0.765887\pi\) | ||||
−0.741503 | + | 0.670950i | \(0.765887\pi\) | |||||||
\(644\) | − | 1.93990e22i | − | 0.655682i | ||||||
\(645\) | −6.88152e19 | − | 6.92556e19i | −0.00229724 | − | 0.00231194i | ||||
\(646\) | 1.31827e20 | 0.00434655 | ||||||||
\(647\) | 9.44823e21i | 0.307692i | 0.988095 | + | 0.153846i | \(0.0491660\pi\) | ||||
−0.988095 | + | 0.153846i | \(0.950834\pi\) | |||||||
\(648\) | 1.40218e20 | − | 1.09906e22i | 0.00451030 | − | 0.353525i | ||||
\(649\) | 3.75786e22 | 1.19394 | ||||||||
\(650\) | − | 3.99384e22i | − | 1.25338i | ||||||
\(651\) | −5.49486e21 | + | 5.45993e21i | −0.170337 | + | 0.169254i | ||||
\(652\) | 2.66869e22 | 0.817180 | ||||||||
\(653\) | − | 3.94924e22i | − | 1.19456i | −0.802032 | − | 0.597281i | \(-0.796248\pi\) | ||
0.802032 | − | 0.597281i | \(-0.203752\pi\) | |||||||
\(654\) | −2.68556e22 | − | 2.70275e22i | −0.802441 | − | 0.807575i | ||||
\(655\) | −1.65467e20 | −0.00488407 | ||||||||
\(656\) | − | 1.44550e22i | − | 0.421491i | ||||||
\(657\) | 7.66246e18 | − | 1.20124e21i | 0.000220722 | − | 0.0346025i | ||||
\(658\) | −3.10060e22 | −0.882345 | ||||||||
\(659\) | 1.45144e22i | 0.408054i | 0.978965 | + | 0.204027i | \(0.0654030\pi\) | ||||
−0.978965 | + | 0.204027i | \(0.934597\pi\) | |||||||
\(660\) | 5.41086e19 | − | 5.37646e19i | 0.00150285 | − | 0.00149329i | ||||
\(661\) | −2.68605e21 | −0.0737061 | −0.0368530 | − | 0.999321i | \(-0.511733\pi\) | ||||
−0.0368530 | + | 0.999321i | \(0.511733\pi\) | |||||||
\(662\) | 9.24907e21i | 0.250746i | ||||||||
\(663\) | −1.12655e21 | − | 1.13376e21i | −0.0301747 | − | 0.0303677i | ||||
\(664\) | −3.90808e21 | −0.103423 | ||||||||
\(665\) | 3.94121e19i | 0.00103052i | ||||||||
\(666\) | 3.10849e22 | + | 1.98284e20i | 0.803074 | + | 0.00512263i | ||||
\(667\) | 7.44801e22 | 1.90123 | ||||||||
\(668\) | 4.97242e21i | 0.125417i | ||||||||
\(669\) | 3.31943e21 | − | 3.29832e21i | 0.0827283 | − | 0.0822023i | ||||
\(670\) | 1.43136e20 | 0.00352494 | ||||||||
\(671\) | − | 1.97188e22i | − | 0.479845i | ||||||
\(672\) | 5.32246e21 | + | 5.35652e21i | 0.127985 | + | 0.128804i | ||||
\(673\) | 4.46588e22 | 1.06117 | 0.530587 | − | 0.847630i | \(-0.321971\pi\) | ||||
0.530587 | + | 0.847630i | \(0.321971\pi\) | |||||||
\(674\) | − | 9.50819e21i | − | 0.223264i | ||||||
\(675\) | 3.01796e22 | + | 3.07627e22i | 0.700298 | + | 0.713829i | ||||
\(676\) | −4.67058e22 | −1.07102 | ||||||||
\(677\) | − | 1.65298e22i | − | 0.374592i | −0.982304 | − | 0.187296i | \(-0.940028\pi\) | ||
0.982304 | − | 0.187296i | \(-0.0599723\pi\) | |||||||
\(678\) | 2.21410e22 | − | 2.20002e22i | 0.495860 | − | 0.492707i | ||||
\(679\) | −2.26103e22 | −0.500435 | ||||||||
\(680\) | − | 1.53875e18i | − | 3.36587e-5i | ||||||
\(681\) | −4.61370e22 | − | 4.64323e22i | −0.997407 | − | 1.00379i | ||||
\(682\) | −8.31657e21 | −0.177692 | ||||||||
\(683\) | 6.32799e22i | 1.33629i | 0.744032 | + | 0.668144i | \(0.232911\pi\) | ||||
−0.744032 | + | 0.668144i | \(0.767089\pi\) | |||||||
\(684\) | −3.88925e19 | + | 6.09717e21i | −0.000811740 | + | 0.127256i | ||||
\(685\) | 9.05751e19 | 0.00186846 | ||||||||
\(686\) | 3.36606e22i | 0.686323i | ||||||||
\(687\) | 3.69187e22 | − | 3.66840e22i | 0.744034 | − | 0.739303i | ||||
\(688\) | 1.03767e22 | 0.206705 | ||||||||
\(689\) | 1.16197e23i | 2.28792i | ||||||||
\(690\) | −1.28872e20 | − | 1.29697e20i | −0.00250822 | − | 0.00252427i | ||||
\(691\) | −6.70574e22 | −1.29010 | −0.645049 | − | 0.764141i | \(-0.723163\pi\) | ||||
−0.645049 | + | 0.764141i | \(0.723163\pi\) | |||||||
\(692\) | − | 1.36714e22i | − | 0.259995i | ||||||
\(693\) | −5.87319e22 | − | 3.74638e20i | −1.10410 | − | 0.00704280i | ||||
\(694\) | −5.75148e22 | −1.06882 | ||||||||
\(695\) | 5.05632e19i | 0.000928872i | ||||||||
\(696\) | −2.05657e22 | + | 2.04349e22i | −0.373482 | + | 0.371107i | ||||
\(697\) | 2.26804e21 | 0.0407183 | ||||||||
\(698\) | 1.42029e22i | 0.252077i | ||||||||
\(699\) | −4.14938e20 | − | 4.17593e20i | −0.00728058 | − | 0.00732717i | ||||
\(700\) | −2.96064e22 | −0.513572 | ||||||||
\(701\) | − | 5.60289e22i | − | 0.960877i | −0.877028 | − | 0.480439i | \(-0.840478\pi\) | ||
0.877028 | − | 0.480439i | \(-0.159522\pi\) | |||||||
\(702\) | 5.27702e22 | − | 5.17699e22i | 0.894729 | − | 0.877769i | ||||
\(703\) | −1.72441e22 | −0.289066 | ||||||||
\(704\) | 8.10718e21i | 0.134366i | ||||||||
\(705\) | −2.07298e20 | + | 2.05980e20i | −0.00339689 | + | 0.00337529i | ||||
\(706\) | 4.42982e22 | 0.717709 | ||||||||
\(707\) | 2.34127e22i | 0.375057i | ||||||||
\(708\) | 2.47136e22 | + | 2.48718e22i | 0.391444 | + | 0.393949i | ||||
\(709\) | 6.28170e21 | 0.0983801 | 0.0491900 | − | 0.998789i | \(-0.484336\pi\) | ||||
0.0491900 | + | 0.998789i | \(0.484336\pi\) | |||||||
\(710\) | 8.91588e19i | 0.00138069i | ||||||||
\(711\) | −1.16239e20 | + | 1.82227e22i | −0.00177990 | + | 0.279034i | ||||
\(712\) | 2.48955e22 | 0.376947 | ||||||||
\(713\) | 1.99345e22i | 0.298463i | ||||||||
\(714\) | −8.40457e20 | + | 8.35113e20i | −0.0124431 | + | 0.0123640i | ||||
\(715\) | 5.13019e20 | 0.00751078 | ||||||||
\(716\) | − | 4.54251e21i | − | 0.0657645i | ||||||
\(717\) | −8.15292e22 | − | 8.20510e22i | −1.16724 | − | 1.17471i | ||||
\(718\) | 3.20698e22 | 0.454047 | ||||||||
\(719\) | 7.38151e21i | 0.103351i | 0.998664 | + | 0.0516755i | \(0.0164561\pi\) | ||||
−0.998664 | + | 0.0516755i | \(0.983544\pi\) | |||||||
\(720\) | 7.11692e19 | + | 4.53972e17i | 0.000985444 | + | 6.28593e-6i | ||||
\(721\) | 5.79352e22 | 0.793342 | ||||||||
\(722\) | 4.88311e22i | 0.661301i | ||||||||
\(723\) | 3.54759e22 | − | 3.52503e22i | 0.475146 | − | 0.472125i | ||||
\(724\) | −2.12107e22 | −0.280961 | ||||||||
\(725\) | − | 1.13670e23i | − | 1.48916i | ||||||
\(726\) | −5.98014e21 | − | 6.01841e21i | −0.0774851 | − | 0.0779810i | ||||
\(727\) | 1.20780e23 | 1.54782 | 0.773909 | − | 0.633296i | \(-0.218299\pi\) | ||||
0.773909 | + | 0.633296i | \(0.218299\pi\) | |||||||
\(728\) | 5.07867e22i | 0.643723i | ||||||||
\(729\) | −1.52632e21 | + | 7.97518e22i | −0.0191349 | + | 0.999817i | ||||
\(730\) | 7.77831e18 | 9.64500e−5 | ||||||||
\(731\) | 1.62814e21i | 0.0199688i | ||||||||
\(732\) | 1.30511e22 | − | 1.29681e22i | 0.158328 | − | 0.157321i | ||||
\(733\) | −1.21835e23 | −1.46198 | −0.730989 | − | 0.682389i | \(-0.760941\pi\) | ||||
−0.730989 | + | 0.682389i | \(0.760941\pi\) | |||||||
\(734\) | − | 6.17627e22i | − | 0.733091i | ||||||
\(735\) | −1.30290e19 | − | 1.31124e19i | −0.000152973 | − | 0.000153952i | ||||
\(736\) | 1.94327e22 | 0.225689 | ||||||||
\(737\) | − | 1.18327e23i | − | 1.35939i | ||||||
\(738\) | −6.69133e20 | + | 1.04900e23i | −0.00760434 | + | 1.19213i | ||||
\(739\) | 4.92047e22 | 0.553161 | 0.276580 | − | 0.960991i | \(-0.410799\pi\) | ||||
0.276580 | + | 0.960991i | \(0.410799\pi\) | |||||||
\(740\) | 2.01281e20i | 0.00223846i | ||||||||
\(741\) | −2.90894e22 | + | 2.89045e22i | −0.320029 | + | 0.317994i | ||||
\(742\) | 8.61368e22 | 0.937470 | ||||||||
\(743\) | − | 1.09751e23i | − | 1.18168i | −0.806790 | − | 0.590838i | \(-0.798797\pi\) | ||
0.806790 | − | 0.590838i | \(-0.201203\pi\) | |||||||
\(744\) | −5.46939e21 | − | 5.50439e21i | −0.0582580 | − | 0.0586308i | ||||
\(745\) | −2.69099e19 | −0.000283571 | ||||||||
\(746\) | − | 7.80552e22i | − | 0.813751i | ||||||
\(747\) | 2.83609e22 | + | 1.80908e20i | 0.292519 | + | 0.00186592i | ||||
\(748\) | −1.27205e21 | −0.0129805 | ||||||||
\(749\) | 1.45975e23i | 1.47375i | ||||||||
\(750\) | −3.95884e20 | + | 3.93367e20i | −0.00395438 | + | 0.00392923i | ||||
\(751\) | −1.90969e22 | −0.188731 | −0.0943656 | − | 0.995538i | \(-0.530082\pi\) | ||||
−0.0943656 | + | 0.995538i | \(0.530082\pi\) | |||||||
\(752\) | − | 3.10598e22i | − | 0.303707i | ||||||
\(753\) | 6.96929e22 | + | 7.01389e22i | 0.674262 | + | 0.678577i | ||||
\(754\) | −1.94989e23 | −1.86655 | ||||||||
\(755\) | 5.36604e19i | 0.000508251i | ||||||||
\(756\) | −3.83771e22 | − | 3.91186e22i | −0.359665 | − | 0.366614i | ||||
\(757\) | 8.80933e22 | 0.816913 | 0.408456 | − | 0.912778i | \(-0.366067\pi\) | ||||
0.408456 | + | 0.912778i | \(0.366067\pi\) | |||||||
\(758\) | 1.71294e22i | 0.157177i | ||||||||
\(759\) | −1.07217e23 | + | 1.06535e23i | −0.973485 | + | 0.967295i | ||||
\(760\) | −3.94805e19 | −0.000354710 | ||||||||
\(761\) | − | 3.94699e22i | − | 0.350904i | −0.984488 | − | 0.175452i | \(-0.943861\pi\) | ||
0.984488 | − | 0.175452i | \(-0.0561387\pi\) | |||||||
\(762\) | −4.27899e22 | − | 4.30638e22i | −0.376445 | − | 0.378854i | ||||
\(763\) | −1.89962e23 | −1.65375 | ||||||||
\(764\) | − | 2.44590e22i | − | 0.210713i | ||||||
\(765\) | −7.12299e16 | + | 1.11667e19i | −6.07255e−7 | + | 9.51992e-5i | ||||
\(766\) | 2.95275e22 | 0.249113 | ||||||||
\(767\) | 2.35816e23i | 1.96884i | ||||||||
\(768\) | −5.36581e21 | + | 5.33169e21i | −0.0443349 | + | 0.0440530i | ||||
\(769\) | −1.37597e23 | −1.12512 | −0.562561 | − | 0.826756i | \(-0.690184\pi\) | ||||
−0.562561 | + | 0.826756i | \(0.690184\pi\) | |||||||
\(770\) | − | 3.80302e20i | − | 0.00307753i | ||||||
\(771\) | 1.68331e23 | + | 1.69408e23i | 1.34812 | + | 1.35675i | ||||
\(772\) | 7.25070e21 | 0.0574700 | ||||||||
\(773\) | 1.68912e21i | 0.0132503i | 0.999978 | + | 0.00662514i | \(0.00210886\pi\) | ||||
−0.999978 | + | 0.00662514i | \(0.997891\pi\) | |||||||
\(774\) | −7.53034e22 | − | 4.80344e20i | −0.584638 | − | 0.00372928i | ||||
\(775\) | 3.04237e22 | 0.233775 | ||||||||
\(776\) | − | 2.26495e22i | − | 0.172252i | ||||||
\(777\) | 1.09939e23 | − | 1.09240e23i | 0.827529 | − | 0.822267i | ||||
\(778\) | 1.28082e23 | 0.954228 | ||||||||
\(779\) | − | 5.81923e22i | − | 0.429107i | ||||||
\(780\) | 3.37387e20 | + | 3.39546e20i | 0.00246248 | + | 0.00247823i | ||||
\(781\) | 7.37053e22 | 0.532464 | ||||||||
\(782\) | 3.04905e21i | 0.0218027i | ||||||||
\(783\) | 1.50191e23 | − | 1.47344e23i | 1.06304 | − | 1.04289i | ||||
\(784\) | 1.96465e21 | 0.0137644 | ||||||||
\(785\) | − | 2.85990e20i | − | 0.00198332i | ||||||
\(786\) | −9.05342e22 | + | 8.99585e22i | −0.621487 | + | 0.617536i | ||||
\(787\) | −1.14982e23 | −0.781325 | −0.390662 | − | 0.920534i | \(-0.627754\pi\) | ||||
−0.390662 | + | 0.920534i | \(0.627754\pi\) | |||||||
\(788\) | 3.97710e22i | 0.267520i | ||||||||
\(789\) | −2.80274e22 | − | 2.82068e22i | −0.186624 | − | 0.187818i | ||||
\(790\) | −1.17996e20 | −0.000777770 | ||||||||
\(791\) | − | 1.55617e23i | − | 1.01542i | ||||||
\(792\) | 3.75287e20 | − | 5.88337e22i | 0.00242417 | − | 0.380036i | ||||
\(793\) | 1.23741e23 | 0.791276 | ||||||||
\(794\) | 1.36530e22i | 0.0864299i | ||||||||
\(795\) | 5.75888e20 | − | 5.72226e20i | 0.00360911 | − | 0.00358617i | ||||
\(796\) | 1.50674e23 | 0.934832 | ||||||||
\(797\) | − | 1.29946e23i | − | 0.798172i | −0.916913 | − | 0.399086i | \(-0.869327\pi\) | ||
0.916913 | − | 0.399086i | \(-0.130673\pi\) | |||||||
\(798\) | 2.14269e22 | + | 2.15640e22i | 0.130298 | + | 0.131131i | ||||
\(799\) | 4.87338e21 | 0.0293398 | ||||||||
\(800\) | − | 2.96577e22i | − | 0.176774i | ||||||
\(801\) | −1.80666e23 | − | 1.15243e21i | −1.06615 | − | 0.00680071i | ||||
\(802\) | −1.03814e23 | −0.606540 | ||||||||
\(803\) | − | 6.43013e21i | − | 0.0371959i | ||||||
\(804\) | 7.83159e22 | − | 7.78179e22i | 0.448540 | − | 0.445688i | ||||
\(805\) | −9.11572e20 | −0.00516920 | ||||||||
\(806\) | − | 5.21887e22i | − | 0.293019i | ||||||
\(807\) | −1.19958e23 | − | 1.20726e23i | −0.666872 | − | 0.671140i | ||||
\(808\) | −2.34533e22 | −0.129096 | ||||||||
\(809\) | 2.22849e23i | 1.21457i | 0.794484 | + | 0.607286i | \(0.207742\pi\) | ||||
−0.794484 | + | 0.607286i | \(0.792258\pi\) | |||||||
\(810\) | −5.16453e20 | − | 6.58894e18i | −0.00278709 | − | 3.55579e-5i | ||||
\(811\) | −1.26998e22 | −0.0678626 | −0.0339313 | − | 0.999424i | \(-0.510803\pi\) | ||||
−0.0339313 | + | 0.999424i | \(0.510803\pi\) | |||||||
\(812\) | 1.44546e23i | 0.764816i | ||||||||
\(813\) | 6.55575e22 | − | 6.51407e22i | 0.343477 | − | 0.341293i | ||||
\(814\) | 1.66394e23 | 0.863263 | ||||||||
\(815\) | − | 1.25403e21i | − | 0.00644241i | ||||||
\(816\) | −8.36562e20 | − | 8.41915e20i | −0.00425576 | − | 0.00428299i | ||||
\(817\) | 4.17739e22 | 0.210440 | ||||||||
\(818\) | 1.47769e23i | 0.737151i | ||||||||
\(819\) | 2.35095e21 | − | 3.68558e23i | 0.0116138 | − | 1.82069i | ||||
\(820\) | −6.79250e20 | −0.00332291 | ||||||||
\(821\) | 3.11342e23i | 1.50832i | 0.656694 | + | 0.754158i | \(0.271955\pi\) | ||||
−0.656694 | + | 0.754158i | \(0.728045\pi\) | |||||||
\(822\) | 4.95574e22 | − | 4.92423e22i | 0.237758 | − | 0.236246i | ||||
\(823\) | −1.82111e23 | −0.865240 | −0.432620 | − | 0.901576i | \(-0.642411\pi\) | ||||
−0.432620 | + | 0.901576i | \(0.642411\pi\) | |||||||
\(824\) | 5.80357e22i | 0.273072i | ||||||||
\(825\) | 1.62592e23 | + | 1.63632e23i | 0.757648 | + | 0.762496i | ||||
\(826\) | 1.74811e23 | 0.806729 | ||||||||
\(827\) | 2.11001e22i | 0.0964365i | 0.998837 | + | 0.0482182i | \(0.0153543\pi\) | ||||
−0.998837 | + | 0.0482182i | \(0.984646\pi\) | |||||||
\(828\) | −1.41023e23 | − | 8.99552e20i | −0.638331 | − | 0.00407177i | ||||
\(829\) | 9.46833e22 | 0.424460 | 0.212230 | − | 0.977220i | \(-0.431927\pi\) | ||||
0.212230 | + | 0.977220i | \(0.431927\pi\) | |||||||
\(830\) | 1.83643e20i | 0.000815360i | ||||||||
\(831\) | −2.87160e23 | + | 2.85334e23i | −1.26275 | + | 1.25472i | ||||
\(832\) | −5.08748e22 | −0.221572 | ||||||||
\(833\) | 3.08261e20i | 0.00132972i | ||||||||
\(834\) | 2.74893e22 | + | 2.76652e22i | 0.117445 | + | 0.118197i | ||||
\(835\) | 2.33657e20 | 0.000988750 | ||||||||
\(836\) | 3.26375e22i | 0.136794i | ||||||||
\(837\) | 3.94365e22 | + | 4.01985e22i | 0.163717 | + | 0.166881i | ||||
\(838\) | −1.80856e23 | −0.743671 | ||||||||
\(839\) | 8.89724e21i | 0.0362376i | 0.999836 | + | 0.0181188i | \(0.00576771\pi\) | ||||
−0.999836 | + | 0.0181188i | \(0.994232\pi\) | |||||||
\(840\) | 2.51706e20 | − | 2.50106e20i | 0.00101545 | − | 0.00100900i | ||||
\(841\) | −3.04719e23 | −1.21767 | ||||||||
\(842\) | − | 1.61759e23i | − | 0.640281i | ||||||
\(843\) | −1.78307e23 | − | 1.79448e23i | −0.699115 | − | 0.703589i | ||||
\(844\) | −1.04429e23 | −0.405585 | ||||||||
\(845\) | 2.19473e21i | 0.00844360i | ||||||||
\(846\) | −1.43778e21 | + | 2.25400e23i | −0.00547935 | + | 0.858997i | ||||
\(847\) | −4.23003e22 | −0.159689 | ||||||||
\(848\) | 8.62861e22i | 0.322682i | ||||||||
\(849\) | 1.43630e23 | − | 1.42716e23i | 0.532087 | − | 0.528703i | ||||
\(850\) | 4.65341e21 | 0.0170773 | ||||||||
\(851\) | − | 3.98842e23i | − | 1.44999i | ||||||
\(852\) | 4.84723e22 | + | 4.87825e22i | 0.174573 | + | 0.175690i | ||||
\(853\) | −1.10686e22 | −0.0394912 | −0.0197456 | − | 0.999805i | \(-0.506286\pi\) | ||||
−0.0197456 | + | 0.999805i | \(0.506286\pi\) | |||||||
\(854\) | − | 9.17294e22i | − | 0.324224i | ||||||
\(855\) | 2.86509e20 | + | 1.82758e18i | 0.00100325 | + | 6.39952e-6i | ||||
\(856\) | −1.46228e23 | −0.507272 | ||||||||
\(857\) | 7.48244e21i | 0.0257156i | 0.999917 | + | 0.0128578i | \(0.00409288\pi\) | ||||
−0.999917 | + | 0.0128578i | \(0.995907\pi\) | |||||||
\(858\) | 2.80694e23 | − | 2.78909e23i | 0.955730 | − | 0.949653i | ||||
\(859\) | 5.10699e23 | 1.72274 | 0.861369 | − | 0.507979i | \(-0.169607\pi\) | ||||
0.861369 | + | 0.507979i | \(0.169607\pi\) | |||||||
\(860\) | − | 4.87606e20i | − | 0.00162960i | ||||||
\(861\) | 3.68644e23 | + | 3.71003e23i | 1.22062 | + | 1.22843i | ||||
\(862\) | −2.50607e23 | −0.822121 | ||||||||
\(863\) | − | 3.74423e22i | − | 0.121696i | −0.998147 | − | 0.0608479i | \(-0.980620\pi\) | ||
0.998147 | − | 0.0608479i | \(-0.0193805\pi\) | |||||||
\(864\) | 3.91864e22 | − | 3.84436e22i | 0.126190 | − | 0.123798i | ||||
\(865\) | −6.42429e20 | −0.00204973 | ||||||||
\(866\) | − | 2.29698e23i | − | 0.726131i | ||||||
\(867\) | −2.26342e23 | + | 2.24903e23i | −0.708945 | + | 0.704437i | ||||
\(868\) | −3.86875e22 | −0.120064 | ||||||||
\(869\) | 9.75445e22i | 0.299947i | ||||||||
\(870\) | 9.60250e20 | + | 9.66394e20i | 0.00292570 | + | 0.00294442i | ||||
\(871\) | 7.42535e23 | 2.24167 | ||||||||
\(872\) | − | 1.90291e23i | − | 0.569230i | ||||||
\(873\) | −1.04846e21 | + | 1.64367e23i | −0.00310769 | + | 0.487192i | ||||
\(874\) | 7.82311e22 | 0.229767 | ||||||||
\(875\) | 2.78247e21i | 0.00809777i | ||||||||
\(876\) | 4.25584e21 | − | 4.22878e21i | 0.0122730 | − | 0.0121950i | ||||
\(877\) | 1.19013e23 | 0.340093 | 0.170046 | − | 0.985436i | \(-0.445608\pi\) | ||||
0.170046 | + | 0.985436i | \(0.445608\pi\) | |||||||
\(878\) | − | 1.42190e23i | − | 0.402635i | ||||||
\(879\) | −4.37369e22 | − | 4.40168e22i | −0.122726 | − | 0.123512i | ||||
\(880\) | 3.80961e20 | 0.00105930 | ||||||||
\(881\) | − | 6.62213e23i | − | 1.82469i | −0.409417 | − | 0.912347i | \(-0.634268\pi\) | ||
0.409417 | − | 0.912347i | \(-0.365732\pi\) | |||||||
\(882\) | −1.42575e22 | − | 9.09452e19i | −0.0389308 | − | 0.000248331i | ||||
\(883\) | −2.22463e23 | −0.601967 | −0.300984 | − | 0.953629i | \(-0.597315\pi\) | ||||
−0.300984 | + | 0.953629i | \(0.597315\pi\) | |||||||
\(884\) | − | 7.98243e21i | − | 0.0214051i | ||||||
\(885\) | 1.16874e21 | − | 1.16131e21i | 0.00310578 | − | 0.00308603i | ||||
\(886\) | −3.20128e23 | −0.843052 | ||||||||
\(887\) | 6.12511e23i | 1.59855i | 0.600969 | + | 0.799273i | \(0.294782\pi\) | ||||
−0.600969 | + | 0.799273i | \(0.705218\pi\) | |||||||
\(888\) | 1.09429e23 | + | 1.10130e23i | 0.283028 | + | 0.284839i | ||||
\(889\) | −3.02673e23 | −0.775817 | ||||||||
\(890\) | − | 1.16985e21i | − | 0.00297174i | ||||||
\(891\) | −5.44691e21 | + | 4.26938e23i | −0.0137129 | + | 1.07484i | ||||
\(892\) | 2.33710e22 | 0.0583121 | ||||||||
\(893\) | − | 1.25039e23i | − | 0.309196i | ||||||
\(894\) | −1.47235e22 | + | 1.46299e22i | −0.0360837 | + | 0.0358543i | ||||
\(895\) | −2.13455e20 | −0.000518469 | ||||||||
\(896\) | 3.77135e22i | 0.0907890i | ||||||||
\(897\) | −6.68537e23 | − | 6.72815e23i | −1.59509 | − | 1.60530i | ||||
\(898\) | −2.02870e22 | −0.0479741 | ||||||||
\(899\) | − | 1.48536e23i | − | 0.348140i | ||||||
\(900\) | −1.37288e21 | + | 2.15226e23i | −0.00318928 | + | 0.499982i | ||||
\(901\) | −1.35386e22 | −0.0311728 | ||||||||
\(902\) | 5.61518e23i | 1.28148i | ||||||||
\(903\) | −2.66328e23 | + | 2.64634e23i | −0.602441 | + | 0.598610i | ||||
\(904\) | 1.55887e23 | 0.349513 | ||||||||
\(905\) | 9.96704e20i | 0.00221502i | ||||||||
\(906\) | 2.91732e22 | + | 2.93598e22i | 0.0642625 | + | 0.0646738i | ||||
\(907\) | −1.43848e23 | −0.314085 | −0.157042 | − | 0.987592i | \(-0.550196\pi\) | ||||
−0.157042 | + | 0.987592i | \(0.550196\pi\) | |||||||
\(908\) | − | 3.26914e23i | − | 0.707534i | ||||||
\(909\) | 1.70201e23 | + | 1.08567e21i | 0.365132 | + | 0.00232910i | ||||
\(910\) | 2.38650e21 | 0.00507492 | ||||||||
\(911\) | − | 3.11935e23i | − | 0.657532i | −0.944411 | − | 0.328766i | \(-0.893367\pi\) | ||
0.944411 | − | 0.328766i | \(-0.106633\pi\) | |||||||
\(912\) | −2.16014e22 | + | 2.14641e22i | −0.0451361 | + | 0.0448491i | ||||
\(913\) | 1.51813e23 | 0.314443 | ||||||||
\(914\) | 4.96194e23i | 1.01878i | ||||||||
\(915\) | −6.09379e20 | − | 6.13278e20i | −0.00124028 | − | 0.00124821i | ||||
\(916\) | 2.59933e23 | 0.524441 | ||||||||
\(917\) | 6.36318e23i | 1.27268i | ||||||||
\(918\) | 6.03194e21 | + | 6.14849e21i | 0.0119596 | + | 0.0121907i | ||||
\(919\) | 1.01950e23 | 0.200384 | 0.100192 | − | 0.994968i | \(-0.468054\pi\) | ||||
0.100192 | + | 0.994968i | \(0.468054\pi\) | |||||||
\(920\) | − | 9.13152e20i | − | 0.00177927i | ||||||
\(921\) | 1.48664e23 | − | 1.47719e23i | 0.287163 | − | 0.285337i | ||||
\(922\) | 2.34380e23 | 0.448821 | ||||||||
\(923\) | 4.62520e23i | 0.878046i | ||||||||
\(924\) | −2.06756e23 | − | 2.08079e23i | −0.389119 | − | 0.391609i | ||||
\(925\) | −6.08704e23 | −1.13572 | ||||||||
\(926\) | 2.89132e23i | 0.534821i | ||||||||
\(927\) | 2.68651e21 | − | 4.21164e23i | 0.00492664 | − | 0.772349i | ||||
\(928\) | −1.44796e23 | −0.263253 | ||||||||
\(929\) | − | 7.21030e23i | − | 1.29965i | −0.760082 | − | 0.649827i | \(-0.774841\pi\) | ||
0.760082 | − | 0.649827i | \(-0.225159\pi\) | |||||||
\(930\) | −2.58655e20 | + | 2.57010e20i | −0.000462229 | + | 0.000459289i | ||||
\(931\) | 7.90921e21 | 0.0140131 | ||||||||
\(932\) | − | 2.94014e21i | − | 0.00516465i | ||||||
\(933\) | 2.33478e23 | + | 2.34972e23i | 0.406624 | + | 0.409226i | ||||
\(934\) | 5.81305e23 | 1.00376 | ||||||||
\(935\) | 5.97742e19i | 0.000102334i | ||||||||
\(936\) | 3.69197e23 | + | 2.35503e21i | 0.626689 | + | 0.00399751i | ||||
\(937\) | −8.54104e23 | −1.43745 | −0.718727 | − | 0.695292i | \(-0.755275\pi\) | ||||
−0.718727 | + | 0.695292i | \(0.755275\pi\) | |||||||
\(938\) | − | 5.50442e23i | − | 0.918521i | ||||||
\(939\) | 4.47297e23 | − | 4.44452e23i | 0.740067 | − | 0.735361i | ||||
\(940\) | −1.45952e21 | −0.00239434 | ||||||||
\(941\) | − | 5.41229e23i | − | 0.880368i | −0.897908 | − | 0.440184i | \(-0.854913\pi\) | ||
0.897908 | − | 0.440184i | \(-0.145087\pi\) | |||||||
\(942\) | −1.55482e23 | − | 1.56477e23i | −0.250768 | − | 0.252373i | ||||
\(943\) | 1.34594e24 | 2.15245 | ||||||||
\(944\) | 1.75114e23i | 0.277680i | ||||||||
\(945\) | −1.83821e21 | + | 1.80336e21i | −0.00289028 | + | 0.00283549i | ||||
\(946\) | −4.03091e23 | −0.628455 | ||||||||
\(947\) | 1.14023e24i | 1.76276i | 0.472411 | + | 0.881378i | \(0.343384\pi\) | ||||
−0.472411 | + | 0.881378i | \(0.656616\pi\) | |||||||
\(948\) | −6.45607e22 | + | 6.41502e22i | −0.0989695 | + | 0.0983402i | ||||
\(949\) | 4.03508e22 | 0.0613370 | ||||||||
\(950\) | − | 1.19395e23i | − | 0.179968i | ||||||
\(951\) | −4.99700e23 | − | 5.02898e23i | −0.746905 | − | 0.751685i | ||||
\(952\) | −5.91739e21 | −0.00877070 | ||||||||
\(953\) | 5.58622e23i | 0.821060i | 0.911847 | + | 0.410530i | \(0.134656\pi\) | ||||
−0.911847 | + | 0.410530i | \(0.865344\pi\) | |||||||
\(954\) | 3.99425e21 | − | 6.26177e23i | 0.00582168 | − | 0.912663i | ||||
\(955\) | −1.14934e21 | −0.00166120 | ||||||||
\(956\) | − | 5.77694e23i | − | 0.828008i | ||||||
\(957\) | 7.98893e23 | − | 7.93814e23i | 1.13552 | − | 1.12830i | ||||
\(958\) | −1.69763e23 | −0.239287 | ||||||||
\(959\) | − | 3.48314e23i | − | 0.486880i | ||||||
\(960\) | 2.50539e20 | + | 2.52143e20i | 0.000347301 | + | 0.000349524i | ||||
\(961\) | −6.87668e23 | −0.945347 | ||||||||
\(962\) | 1.04417e24i | 1.42354i | ||||||||
\(963\) | 1.06117e24 | + | 6.76900e21i | 1.43475 | + | 0.00915196i | ||||
\(964\) | 2.49774e23 | 0.334912 | ||||||||
\(965\) | − | 3.40715e20i | − | 0.000453077i | ||||||
\(966\) | −4.98759e23 | + | 4.95588e23i | −0.657769 | + | 0.653587i | ||||
\(967\) | −3.89856e23 | −0.509908 | −0.254954 | − | 0.966953i | \(-0.582060\pi\) | ||||
−0.254954 | + | 0.966953i | \(0.582060\pi\) | |||||||
\(968\) | − | 4.23736e22i | − | 0.0549658i | ||||||
\(969\) | −3.36779e21 | − | 3.38934e21i | −0.00433266 | − | 0.00436039i | ||||
\(970\) | −1.06431e21 | −0.00135799 | ||||||||
\(971\) | 1.74385e23i | 0.220676i | 0.993894 | + | 0.110338i | \(0.0351934\pi\) | ||||
−0.993894 | + | 0.110338i | \(0.964807\pi\) | |||||||
\(972\) | −2.86155e23 | + | 2.77171e23i | −0.359146 | + | 0.347871i | ||||
\(973\) | 1.94445e23 | 0.242043 | ||||||||
\(974\) | − | 3.80180e23i | − | 0.469372i | ||||||
\(975\) | −1.02684e24 | + | 1.02031e24i | −1.25737 | + | 1.24938i | ||||
\(976\) | 9.18884e22 | 0.111600 | ||||||||
\(977\) | 8.37409e23i | 1.00874i | 0.863486 | + | 0.504372i | \(0.168276\pi\) | ||||
−0.863486 | + | 0.504372i | \(0.831724\pi\) | |||||||
\(978\) | −6.81771e23 | − | 6.86134e23i | −0.814569 | − | 0.819782i | ||||
\(979\) | −9.67088e23 | −1.14605 | ||||||||
\(980\) | − | 9.23202e19i | − | 0.000108515i | ||||||
\(981\) | −8.80873e21 | + | 1.38094e24i | −0.0102698 | + | 1.60999i | ||||
\(982\) | 3.34641e23 | 0.386979 | ||||||||
\(983\) | − | 1.05513e24i | − | 1.21026i | −0.796126 | − | 0.605131i | \(-0.793121\pi\) | ||
0.796126 | − | 0.605131i | \(-0.206879\pi\) | |||||||
\(984\) | −3.71646e23 | + | 3.69283e23i | −0.422833 | + | 0.420144i | ||||
\(985\) | 1.86886e21 | 0.00210905 | ||||||||
\(986\) | − | 2.27191e22i | − | 0.0254317i | ||||||
\(987\) | 7.92111e23 | + | 7.97180e23i | 0.879526 | + | 0.885154i | ||||
\(988\) | −2.04809e23 | −0.225576 | ||||||||
\(989\) | 9.66197e23i | 1.05559i | ||||||||
\(990\) | −2.76463e21 | − | 1.76350e19i | −0.00299610 | − | 1.91114e-5i | ||||
\(991\) | 6.82404e23 | 0.733588 | 0.366794 | − | 0.930302i | \(-0.380455\pi\) | ||||
0.366794 | + | 0.930302i | \(0.380455\pi\) | |||||||
\(992\) | − | 3.87546e22i | − | 0.0413267i | ||||||
\(993\) | 2.37798e23 | − | 2.36286e23i | 0.251544 | − | 0.249945i | ||||
\(994\) | 3.42867e23 | 0.359778 | ||||||||
\(995\) | − | 7.08026e21i | − | 0.00736995i | ||||||
\(996\) | 9.98398e22 | + | 1.00479e23i | 0.103093 | + | 0.103753i | ||||
\(997\) | 7.77833e23 | 0.796756 | 0.398378 | − | 0.917221i | \(-0.369573\pi\) | ||||
0.398378 | + | 0.917221i | \(0.369573\pi\) | |||||||
\(998\) | − | 1.30071e24i | − | 1.32171i | ||||||
\(999\) | −7.89029e23 | − | 8.04274e23i | −0.795370 | − | 0.810737i |
(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 | 6.17.b.a.5.1 | ✓ | 6 | |
3.2 | odd | 2 | inner | 6.17.b.a.5.4 | yes | 6 | |
4.3 | odd | 2 | 48.17.e.d.17.5 | 6 | |||
12.11 | even | 2 | 48.17.e.d.17.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.17.b.a.5.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
6.17.b.a.5.4 | yes | 6 | 3.2 | odd | 2 | inner | |
48.17.e.d.17.5 | 6 | 4.3 | odd | 2 | |||
48.17.e.d.17.6 | 6 | 12.11 | even | 2 |