Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,11,Mod(3,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.3");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.c (of order \(4\), degree \(2\), 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: | \(6.35357252674\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 1148x^{3} + 68121x^{2} - 299628x + 658952 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8}\cdot 5^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.3 | ||
Root | \(-12.3957 + 12.3957i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.3 |
Dual form | 10.11.c.c.7.3 |
$q$-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 \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.0000 | + | 16.0000i | −0.500000 | + | 0.500000i | ||||
\(3\) | 326.149 | + | 326.149i | 1.34218 | + | 1.34218i | 0.893891 | + | 0.448284i | \(0.147965\pi\) |
0.448284 | + | 0.893891i | \(0.352035\pi\) | |||||||
\(4\) | − | 512.000i | − | 0.500000i | ||||||
\(5\) | 3124.94 | − | 19.4459i | 0.999981 | − | 0.00622269i | ||||
\(6\) | −10436.8 | −1.34218 | ||||||||
\(7\) | −1507.13 | + | 1507.13i | −0.0896728 | + | 0.0896728i | −0.750520 | − | 0.660847i | \(-0.770197\pi\) |
0.660847 | + | 0.750520i | \(0.270197\pi\) | |||||||
\(8\) | 8192.00 | + | 8192.00i | 0.250000 | + | 0.250000i | ||||
\(9\) | 153697.i | 2.60287i | ||||||||
\(10\) | −49687.9 | + | 50310.2i | −0.496879 | + | 0.503102i | ||||
\(11\) | −71462.1 | −0.443723 | −0.221862 | − | 0.975078i | \(-0.571213\pi\) | ||||
−0.221862 | + | 0.975078i | \(0.571213\pi\) | |||||||
\(12\) | 166988. | − | 166988.i | 0.671088 | − | 0.671088i | ||||
\(13\) | −300816. | − | 300816.i | −0.810186 | − | 0.810186i | 0.174475 | − | 0.984662i | \(-0.444177\pi\) |
−0.984662 | + | 0.174475i | \(0.944177\pi\) | |||||||
\(14\) | − | 48228.2i | − | 0.0896728i | ||||||
\(15\) | 1.02554e6 | + | 1.01285e6i | 1.35050 | + | 1.33380i | ||||
\(16\) | −262144. | −0.250000 | ||||||||
\(17\) | 1.11637e6 | − | 1.11637e6i | 0.786252 | − | 0.786252i | −0.194626 | − | 0.980878i | \(-0.562349\pi\) |
0.980878 | + | 0.194626i | \(0.0623492\pi\) | |||||||
\(18\) | −2.45915e6 | − | 2.45915e6i | −1.30143 | − | 1.30143i | ||||
\(19\) | 684142.i | 0.276299i | 0.990411 | + | 0.138149i | \(0.0441154\pi\) | ||||
−0.990411 | + | 0.138149i | \(0.955885\pi\) | |||||||
\(20\) | −9956.30 | − | 1.59997e6i | −0.00311134 | − | 0.499990i | ||||
\(21\) | −983097. | −0.240713 | ||||||||
\(22\) | 1.14339e6 | − | 1.14339e6i | 0.221862 | − | 0.221862i | ||||
\(23\) | 1.52597e6 | + | 1.52597e6i | 0.237087 | + | 0.237087i | 0.815643 | − | 0.578556i | \(-0.196384\pi\) |
−0.578556 | + | 0.815643i | \(0.696384\pi\) | |||||||
\(24\) | 5.34362e6i | 0.671088i | ||||||||
\(25\) | 9.76487e6 | − | 121534.i | 0.999923 | − | 0.0124451i | ||||
\(26\) | 9.62613e6 | 0.810186 | ||||||||
\(27\) | −3.08693e7 | + | 3.08693e7i | −2.15133 | + | 2.15133i | ||||
\(28\) | 771651. | + | 771651.i | 0.0448364 | + | 0.0448364i | ||||
\(29\) | − | 2.47039e7i | − | 1.20441i | −0.798340 | − | 0.602207i | \(-0.794288\pi\) | ||
0.798340 | − | 0.602207i | \(-0.205712\pi\) | |||||||
\(30\) | −3.26142e7 | + | 202952.i | −1.34215 | + | 0.00835194i | ||||
\(31\) | 4.13378e7 | 1.44390 | 0.721952 | − | 0.691943i | \(-0.243245\pi\) | ||||
0.721952 | + | 0.691943i | \(0.243245\pi\) | |||||||
\(32\) | 4.19430e6 | − | 4.19430e6i | 0.125000 | − | 0.125000i | ||||
\(33\) | −2.33073e7 | − | 2.33073e7i | −0.595555 | − | 0.595555i | ||||
\(34\) | 3.57237e7i | 0.786252i | ||||||||
\(35\) | −4.68038e6 | + | 4.73900e6i | −0.0891130 | + | 0.0902290i | ||||
\(36\) | 7.86928e7 | 1.30143 | ||||||||
\(37\) | 2.53176e7 | − | 2.53176e7i | 0.365102 | − | 0.365102i | −0.500586 | − | 0.865687i | \(-0.666882\pi\) |
0.865687 | + | 0.500586i | \(0.166882\pi\) | |||||||
\(38\) | −1.09463e7 | − | 1.09463e7i | −0.138149 | − | 0.138149i | ||||
\(39\) | − | 1.96222e8i | − | 2.17482i | ||||||
\(40\) | 2.57588e7 | + | 2.54402e7i | 0.251551 | + | 0.248439i | ||||
\(41\) | −1.32462e8 | −1.14333 | −0.571664 | − | 0.820488i | \(-0.693702\pi\) | ||||
−0.571664 | + | 0.820488i | \(0.693702\pi\) | |||||||
\(42\) | 1.57296e7 | − | 1.57296e7i | 0.120357 | − | 0.120357i | ||||
\(43\) | −2.46531e7 | − | 2.46531e7i | −0.167699 | − | 0.167699i | 0.618268 | − | 0.785967i | \(-0.287835\pi\) |
−0.785967 | + | 0.618268i | \(0.787835\pi\) | |||||||
\(44\) | 3.65886e7i | 0.221862i | ||||||||
\(45\) | 2.98877e6 | + | 4.80293e8i | 0.0161968 | + | 2.60282i | ||||
\(46\) | −4.88310e7 | −0.237087 | ||||||||
\(47\) | 5.19304e7 | − | 5.19304e7i | 0.226429 | − | 0.226429i | −0.584770 | − | 0.811199i | \(-0.698815\pi\) |
0.811199 | + | 0.584770i | \(0.198815\pi\) | |||||||
\(48\) | −8.54979e7 | − | 8.54979e7i | −0.335544 | − | 0.335544i | ||||
\(49\) | 2.77932e8i | 0.983918i | ||||||||
\(50\) | −1.54293e8 | + | 1.58182e8i | −0.493739 | + | 0.506184i | ||||
\(51\) | 7.28202e8 | 2.11058 | ||||||||
\(52\) | −1.54018e8 | + | 1.54018e8i | −0.405093 | + | 0.405093i | ||||
\(53\) | −3.03473e8 | − | 3.03473e8i | −0.725672 | − | 0.725672i | 0.244083 | − | 0.969754i | \(-0.421513\pi\) |
−0.969754 | + | 0.244083i | \(0.921513\pi\) | |||||||
\(54\) | − | 9.87817e8i | − | 2.15133i | ||||||
\(55\) | −2.23315e8 | + | 1.38964e6i | −0.443715 | + | 0.00276115i | ||||
\(56\) | −2.46928e7 | −0.0448364 | ||||||||
\(57\) | −2.23132e8 | + | 2.23132e8i | −0.370841 | + | 0.370841i | ||||
\(58\) | 3.95262e8 | + | 3.95262e8i | 0.602207 | + | 0.602207i | ||||
\(59\) | − | 6.92655e7i | − | 0.0968851i | −0.998826 | − | 0.0484426i | \(-0.984574\pi\) | ||
0.998826 | − | 0.0484426i | \(-0.0154258\pi\) | |||||||
\(60\) | 5.18580e8 | − | 5.25075e8i | 0.666899 | − | 0.675251i | ||||
\(61\) | 6.38536e8 | 0.756025 | 0.378012 | − | 0.925801i | \(-0.376608\pi\) | ||||
0.378012 | + | 0.925801i | \(0.376608\pi\) | |||||||
\(62\) | −6.61404e8 | + | 6.61404e8i | −0.721952 | + | 0.721952i | ||||
\(63\) | −2.31641e8 | − | 2.31641e8i | −0.233407 | − | 0.233407i | ||||
\(64\) | 1.34218e8i | 0.125000i | ||||||||
\(65\) | −9.45883e8 | − | 9.34184e8i | −0.815212 | − | 0.805129i | ||||
\(66\) | 7.45832e8 | 0.595555 | ||||||||
\(67\) | 7.98844e8 | − | 7.98844e8i | 0.591682 | − | 0.591682i | −0.346404 | − | 0.938085i | \(-0.612597\pi\) |
0.938085 | + | 0.346404i | \(0.112597\pi\) | |||||||
\(68\) | −5.71579e8 | − | 5.71579e8i | −0.393126 | − | 0.393126i | ||||
\(69\) | 9.95386e8i | 0.636423i | ||||||||
\(70\) | −937840. | − | 1.50710e8i | −0.000558005 | − | 0.0896710i | ||||
\(71\) | −4.06392e8 | −0.225244 | −0.112622 | − | 0.993638i | \(-0.535925\pi\) | ||||
−0.112622 | + | 0.993638i | \(0.535925\pi\) | |||||||
\(72\) | −1.25908e9 | + | 1.25908e9i | −0.650717 | + | 0.650717i | ||||
\(73\) | −5.91419e8 | − | 5.91419e8i | −0.285286 | − | 0.285286i | 0.549927 | − | 0.835213i | \(-0.314656\pi\) |
−0.835213 | + | 0.549927i | \(0.814656\pi\) | |||||||
\(74\) | 8.10163e8i | 0.365102i | ||||||||
\(75\) | 3.22444e9 | + | 3.14516e9i | 1.35878 | + | 1.32537i | ||||
\(76\) | 3.50281e8 | 0.138149 | ||||||||
\(77\) | 1.07703e8 | − | 1.07703e8i | 0.0397899 | − | 0.0397899i | ||||
\(78\) | 3.13955e9 | + | 3.13955e9i | 1.08741 | + | 1.08741i | ||||
\(79\) | 6.97925e8i | 0.226816i | 0.993549 | + | 0.113408i | \(0.0361767\pi\) | ||||
−0.993549 | + | 0.113408i | \(0.963823\pi\) | |||||||
\(80\) | −8.19184e8 | + | 5.09762e6i | −0.249995 | + | 0.00155567i | ||||
\(81\) | −1.10603e10 | −3.17206 | ||||||||
\(82\) | 2.11939e9 | − | 2.11939e9i | 0.571664 | − | 0.571664i | ||||
\(83\) | −2.76663e9 | − | 2.76663e9i | −0.702362 | − | 0.702362i | 0.262555 | − | 0.964917i | \(-0.415435\pi\) |
−0.964917 | + | 0.262555i | \(0.915435\pi\) | |||||||
\(84\) | 5.03346e8i | 0.120357i | ||||||||
\(85\) | 3.46687e9 | − | 3.51028e9i | 0.781344 | − | 0.791129i | ||||
\(86\) | 7.88901e8 | 0.167699 | ||||||||
\(87\) | 8.05714e9 | − | 8.05714e9i | 1.61653 | − | 1.61653i | ||||
\(88\) | −5.85417e8 | − | 5.85417e8i | −0.110931 | − | 0.110931i | ||||
\(89\) | 3.28276e9i | 0.587880i | 0.955824 | + | 0.293940i | \(0.0949667\pi\) | ||||
−0.955824 | + | 0.293940i | \(0.905033\pi\) | |||||||
\(90\) | −7.73251e9 | − | 7.63687e9i | −1.30951 | − | 1.29331i | ||||
\(91\) | 9.06739e8 | 0.145303 | ||||||||
\(92\) | 7.81297e8 | − | 7.81297e8i | 0.118543 | − | 0.118543i | ||||
\(93\) | 1.34823e10 | + | 1.34823e10i | 1.93797 | + | 1.93797i | ||||
\(94\) | 1.66177e9i | 0.226429i | ||||||||
\(95\) | 1.33038e7 | + | 2.13790e9i | 0.00171932 | + | 0.276293i | ||||
\(96\) | 2.73593e9 | 0.335544 | ||||||||
\(97\) | −3.71980e9 | + | 3.71980e9i | −0.433172 | + | 0.433172i | −0.889706 | − | 0.456534i | \(-0.849091\pi\) |
0.456534 | + | 0.889706i | \(0.349091\pi\) | |||||||
\(98\) | −4.44692e9 | − | 4.44692e9i | −0.491959 | − | 0.491959i | ||||
\(99\) | − | 1.09835e10i | − | 1.15495i | ||||||
\(100\) | −6.22257e7 | − | 4.99961e9i | −0.00622257 | − | 0.499961i | ||||
\(101\) | −1.25605e10 | −1.19509 | −0.597546 | − | 0.801834i | \(-0.703858\pi\) | ||||
−0.597546 | + | 0.801834i | \(0.703858\pi\) | |||||||
\(102\) | −1.16512e10 | + | 1.16512e10i | −1.05529 | + | 1.05529i | ||||
\(103\) | 2.20101e9 | + | 2.20101e9i | 0.189861 | + | 0.189861i | 0.795636 | − | 0.605775i | \(-0.207137\pi\) |
−0.605775 | + | 0.795636i | \(0.707137\pi\) | |||||||
\(104\) | − | 4.92858e9i | − | 0.405093i | ||||||
\(105\) | −3.07212e9 | + | 1.91172e7i | −0.240709 | + | 0.00149788i | ||||
\(106\) | 9.71112e9 | 0.725672 | ||||||||
\(107\) | −1.14498e10 | + | 1.14498e10i | −0.816358 | + | 0.816358i | −0.985578 | − | 0.169220i | \(-0.945875\pi\) |
0.169220 | + | 0.985578i | \(0.445875\pi\) | |||||||
\(108\) | 1.58051e10 | + | 1.58051e10i | 1.07567 | + | 1.07567i | ||||
\(109\) | 2.68242e10i | 1.74339i | 0.490052 | + | 0.871693i | \(0.336978\pi\) | ||||
−0.490052 | + | 0.871693i | \(0.663022\pi\) | |||||||
\(110\) | 3.55080e9 | − | 3.59527e9i | 0.220477 | − | 0.223238i | ||||
\(111\) | 1.65146e10 | 0.980061 | ||||||||
\(112\) | 3.95085e8 | − | 3.95085e8i | 0.0224182 | − | 0.0224182i | ||||
\(113\) | −2.19648e10 | − | 2.19648e10i | −1.19216 | − | 1.19216i | −0.976459 | − | 0.215702i | \(-0.930796\pi\) |
−0.215702 | − | 0.976459i | \(-0.569204\pi\) | |||||||
\(114\) | − | 7.14023e9i | − | 0.370841i | ||||||
\(115\) | 4.79824e9 | + | 4.73889e9i | 0.238557 | + | 0.235607i | ||||
\(116\) | −1.26484e10 | −0.602207 | ||||||||
\(117\) | 4.62345e10 | − | 4.62345e10i | 2.10881 | − | 2.10881i | ||||
\(118\) | 1.10825e9 | + | 1.10825e9i | 0.0484426 | + | 0.0484426i | ||||
\(119\) | 3.36502e9i | 0.141011i | ||||||||
\(120\) | 1.03911e8 | + | 1.66985e10i | 0.00417597 | + | 0.671075i | ||||
\(121\) | −2.08306e10 | −0.803110 | ||||||||
\(122\) | −1.02166e10 | + | 1.02166e10i | −0.378012 | + | 0.378012i | ||||
\(123\) | −4.32022e10 | − | 4.32022e10i | −1.53455 | − | 1.53455i | ||||
\(124\) | − | 2.11649e10i | − | 0.721952i | ||||||
\(125\) | 3.05123e10 | − | 5.69674e8i | 0.999826 | − | 0.0186671i | ||||
\(126\) | 7.41252e9 | 0.233407 | ||||||||
\(127\) | −2.16505e10 | + | 2.16505e10i | −0.655313 | + | 0.655313i | −0.954268 | − | 0.298954i | \(-0.903362\pi\) |
0.298954 | + | 0.954268i | \(0.403362\pi\) | |||||||
\(128\) | −2.14748e9 | − | 2.14748e9i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | − | 1.60812e10i | − | 0.450163i | ||||||
\(130\) | 3.00811e10 | − | 1.87189e8i | 0.810170 | − | 0.00504153i | ||||
\(131\) | 6.24374e10 | 1.61841 | 0.809204 | − | 0.587528i | \(-0.199899\pi\) | ||||
0.809204 | + | 0.587528i | \(0.199899\pi\) | |||||||
\(132\) | −1.19333e10 | + | 1.19333e10i | −0.297777 | + | 0.297777i | ||||
\(133\) | −1.03109e9 | − | 1.03109e9i | −0.0247765 | − | 0.0247765i | ||||
\(134\) | 2.55630e10i | 0.591682i | ||||||||
\(135\) | −9.58643e10 | + | 9.70649e10i | −2.13790 | + | 2.16468i | ||||
\(136\) | 1.82905e10 | 0.393126 | ||||||||
\(137\) | 1.70085e10 | − | 1.70085e10i | 0.352423 | − | 0.352423i | −0.508588 | − | 0.861010i | \(-0.669832\pi\) |
0.861010 | + | 0.508588i | \(0.169832\pi\) | |||||||
\(138\) | −1.59262e10 | − | 1.59262e10i | −0.318212 | − | 0.318212i | ||||
\(139\) | 1.11583e9i | 0.0215043i | 0.999942 | + | 0.0107522i | \(0.00342259\pi\) | ||||
−0.999942 | + | 0.0107522i | \(0.996577\pi\) | |||||||
\(140\) | 2.42637e9 | + | 2.39636e9i | 0.0451145 | + | 0.0445565i | ||||
\(141\) | 3.38740e10 | 0.607815 | ||||||||
\(142\) | 6.50228e9 | − | 6.50228e9i | 0.112622 | − | 0.112622i | ||||
\(143\) | 2.14970e10 | + | 2.14970e10i | 0.359499 | + | 0.359499i | ||||
\(144\) | − | 4.02907e10i | − | 0.650717i | ||||||
\(145\) | −4.80389e8 | − | 7.71982e10i | −0.00749469 | − | 1.20439i | ||||
\(146\) | 1.89254e10 | 0.285286 | ||||||||
\(147\) | −9.06473e10 | + | 9.06473e10i | −1.32059 | + | 1.32059i | ||||
\(148\) | −1.29626e10 | − | 1.29626e10i | −0.182551 | − | 0.182551i | ||||
\(149\) | − | 2.71583e10i | − | 0.369804i | −0.982757 | − | 0.184902i | \(-0.940803\pi\) | ||
0.982757 | − | 0.184902i | \(-0.0591968\pi\) | |||||||
\(150\) | −1.01914e11 | + | 1.26843e9i | −1.34207 | + | 0.0167035i | ||||
\(151\) | 4.49613e9 | 0.0572735 | 0.0286368 | − | 0.999590i | \(-0.490883\pi\) | ||||
0.0286368 | + | 0.999590i | \(0.490883\pi\) | |||||||
\(152\) | −5.60450e9 | + | 5.60450e9i | −0.0690746 | + | 0.0690746i | ||||
\(153\) | 1.71582e11 | + | 1.71582e11i | 2.04651 | + | 2.04651i | ||||
\(154\) | 3.44649e9i | 0.0397899i | ||||||||
\(155\) | 1.29178e11 | − | 8.03850e8i | 1.44388 | − | 0.00898497i | ||||
\(156\) | −1.00466e11 | −1.08741 | ||||||||
\(157\) | −8.17410e10 | + | 8.17410e10i | −0.856922 | + | 0.856922i | −0.990974 | − | 0.134052i | \(-0.957201\pi\) |
0.134052 | + | 0.990974i | \(0.457201\pi\) | |||||||
\(158\) | −1.11668e10 | − | 1.11668e10i | −0.113408 | − | 0.113408i | ||||
\(159\) | − | 1.97954e11i | − | 1.94796i | ||||||
\(160\) | 1.30254e10 | − | 1.31885e10i | 0.124220 | − | 0.125775i | ||||
\(161\) | −4.59967e9 | −0.0425204 | ||||||||
\(162\) | 1.76965e11 | − | 1.76965e11i | 1.58603 | − | 1.58603i | ||||
\(163\) | −1.47684e11 | − | 1.47684e11i | −1.28350 | − | 1.28350i | −0.938664 | − | 0.344834i | \(-0.887935\pi\) |
−0.344834 | − | 0.938664i | \(-0.612065\pi\) | |||||||
\(164\) | 6.78203e10i | 0.571664i | ||||||||
\(165\) | −7.32870e10 | − | 7.23806e10i | −0.599249 | − | 0.591837i | ||||
\(166\) | 8.85323e10 | 0.702362 | ||||||||
\(167\) | 1.23605e11 | − | 1.23605e11i | 0.951596 | − | 0.951596i | −0.0472858 | − | 0.998881i | \(-0.515057\pi\) |
0.998881 | + | 0.0472858i | \(0.0150572\pi\) | |||||||
\(168\) | −8.05353e9 | − | 8.05353e9i | −0.0601783 | − | 0.0601783i | ||||
\(169\) | 4.31226e10i | 0.312803i | ||||||||
\(170\) | 6.94679e8 | + | 1.11634e11i | 0.00489260 | + | 0.786237i | ||||
\(171\) | −1.05151e11 | −0.719169 | ||||||||
\(172\) | −1.26224e10 | + | 1.26224e10i | −0.0838494 | + | 0.0838494i | ||||
\(173\) | −1.80164e10 | − | 1.80164e10i | −0.116262 | − | 0.116262i | 0.646582 | − | 0.762844i | \(-0.276198\pi\) |
−0.762844 | + | 0.646582i | \(0.776198\pi\) | |||||||
\(174\) | 2.57829e11i | 1.61653i | ||||||||
\(175\) | −1.45338e10 | + | 1.49001e10i | −0.0885498 | + | 0.0907818i | ||||
\(176\) | 1.87334e10 | 0.110931 | ||||||||
\(177\) | 2.25909e10 | − | 2.25909e10i | 0.130037 | − | 0.130037i | ||||
\(178\) | −5.25241e10 | − | 5.25241e10i | −0.293940 | − | 0.293940i | ||||
\(179\) | 3.15130e11i | 1.71485i | 0.514613 | + | 0.857423i | \(0.327936\pi\) | ||||
−0.514613 | + | 0.857423i | \(0.672064\pi\) | |||||||
\(180\) | 2.45910e11 | − | 1.53025e9i | 1.30141 | − | 0.00809842i | ||||
\(181\) | −2.08416e11 | −1.07285 | −0.536425 | − | 0.843948i | \(-0.680226\pi\) | ||||
−0.536425 | + | 0.843948i | \(0.680226\pi\) | |||||||
\(182\) | −1.45078e10 | + | 1.45078e10i | −0.0726516 | + | 0.0726516i | ||||
\(183\) | 2.08258e11 | + | 2.08258e11i | 1.01472 | + | 1.01472i | ||||
\(184\) | 2.50015e10i | 0.118543i | ||||||||
\(185\) | 7.86236e10 | − | 7.96083e10i | 0.362823 | − | 0.367366i | ||||
\(186\) | −4.31432e11 | −1.93797 | ||||||||
\(187\) | −7.97778e10 | + | 7.97778e10i | −0.348878 | + | 0.348878i | ||||
\(188\) | −2.65883e10 | − | 2.65883e10i | −0.113215 | − | 0.113215i | ||||
\(189\) | − | 9.30480e10i | − | 0.385832i | ||||||
\(190\) | −3.44193e10 | − | 3.39936e10i | −0.139006 | − | 0.137287i | ||||
\(191\) | −3.00305e10 | −0.118140 | −0.0590699 | − | 0.998254i | \(-0.518813\pi\) | ||||
−0.0590699 | + | 0.998254i | \(0.518813\pi\) | |||||||
\(192\) | −4.37749e10 | + | 4.37749e10i | −0.167772 | + | 0.167772i | ||||
\(193\) | −3.12278e10 | − | 3.12278e10i | −0.116615 | − | 0.116615i | 0.646391 | − | 0.763006i | \(-0.276277\pi\) |
−0.763006 | + | 0.646391i | \(0.776277\pi\) | |||||||
\(194\) | − | 1.19034e11i | − | 0.433172i | ||||||
\(195\) | −3.81571e9 | − | 6.13181e11i | −0.0135332 | − | 2.17478i | ||||
\(196\) | 1.42301e11 | 0.491959 | ||||||||
\(197\) | 7.34355e9 | − | 7.34355e9i | 0.0247500 | − | 0.0247500i | −0.694623 | − | 0.719373i | \(-0.744429\pi\) |
0.719373 | + | 0.694623i | \(0.244429\pi\) | |||||||
\(198\) | 1.75736e11 | + | 1.75736e11i | 0.577477 | + | 0.577477i | ||||
\(199\) | 2.55725e11i | 0.819423i | 0.912215 | + | 0.409712i | \(0.134371\pi\) | ||||
−0.912215 | + | 0.409712i | \(0.865629\pi\) | |||||||
\(200\) | 8.09894e10 | + | 7.89982e10i | 0.253092 | + | 0.246869i | ||||
\(201\) | 5.21084e11 | 1.58828 | ||||||||
\(202\) | 2.00969e11 | − | 2.00969e11i | 0.597546 | − | 0.597546i | ||||
\(203\) | 3.72320e10 | + | 3.72320e10i | 0.108003 | + | 0.108003i | ||||
\(204\) | − | 3.72839e11i | − | 1.05529i | ||||||
\(205\) | −4.13934e11 | + | 2.57583e9i | −1.14331 | + | 0.00711457i | ||||
\(206\) | −7.04325e10 | −0.189861 | ||||||||
\(207\) | −2.34537e11 | + | 2.34537e11i | −0.617105 | + | 0.617105i | ||||
\(208\) | 7.88572e10 | + | 7.88572e10i | 0.202547 | + | 0.202547i | ||||
\(209\) | − | 4.88903e10i | − | 0.122600i | ||||||
\(210\) | 4.88480e10 | − | 4.94598e10i | 0.119605 | − | 0.121103i | ||||
\(211\) | 5.52308e11 | 1.32059 | 0.660297 | − | 0.751005i | \(-0.270430\pi\) | ||||
0.660297 | + | 0.751005i | \(0.270430\pi\) | |||||||
\(212\) | −1.55378e11 | + | 1.55378e11i | −0.362836 | + | 0.362836i | ||||
\(213\) | −1.32544e11 | − | 1.32544e11i | −0.302317 | − | 0.302317i | ||||
\(214\) | − | 3.66395e11i | − | 0.816358i | ||||||
\(215\) | −7.75190e10 | − | 7.65602e10i | −0.168739 | − | 0.166652i | ||||
\(216\) | −5.05762e11 | −1.07567 | ||||||||
\(217\) | −6.23014e10 | + | 6.23014e10i | −0.129479 | + | 0.129479i | ||||
\(218\) | −4.29186e11 | − | 4.29186e11i | −0.871693 | − | 0.871693i | ||||
\(219\) | − | 3.85781e11i | − | 0.765809i | ||||||
\(220\) | 7.11498e8 | + | 1.14337e11i | 0.00138058 | + | 0.221857i | ||||
\(221\) | −6.71642e11 | −1.27402 | ||||||||
\(222\) | −2.64233e11 | + | 2.64233e11i | −0.490030 | + | 0.490030i | ||||
\(223\) | 7.13397e11 | + | 7.13397e11i | 1.29362 | + | 1.29362i | 0.932531 | + | 0.361090i | \(0.117595\pi\) |
0.361090 | + | 0.932531i | \(0.382405\pi\) | |||||||
\(224\) | 1.26427e10i | 0.0224182i | ||||||||
\(225\) | 1.86795e10 | + | 1.50083e12i | 0.0323931 | + | 2.60267i | ||||
\(226\) | 7.02874e11 | 1.19216 | ||||||||
\(227\) | 7.15956e11 | − | 7.15956e11i | 1.18784 | − | 1.18784i | 0.210173 | − | 0.977664i | \(-0.432597\pi\) |
0.977664 | − | 0.210173i | \(-0.0674026\pi\) | |||||||
\(228\) | 1.14244e11 | + | 1.14244e11i | 0.185421 | + | 0.185421i | ||||
\(229\) | 2.72580e11i | 0.432829i | 0.976302 | + | 0.216415i | \(0.0694363\pi\) | ||||
−0.976302 | + | 0.216415i | \(0.930564\pi\) | |||||||
\(230\) | −1.52594e11 | + | 9.49563e8i | −0.237082 | + | 0.00147531i | ||||
\(231\) | 7.02542e10 | 0.106810 | ||||||||
\(232\) | 2.02374e11 | − | 2.02374e11i | 0.301103 | − | 0.301103i | ||||
\(233\) | −3.08559e11 | − | 3.08559e11i | −0.449323 | − | 0.449323i | 0.445806 | − | 0.895130i | \(-0.352917\pi\) |
−0.895130 | + | 0.445806i | \(0.852917\pi\) | |||||||
\(234\) | 1.47951e12i | 2.10881i | ||||||||
\(235\) | 1.61269e11 | − | 1.63289e11i | 0.225016 | − | 0.227834i | ||||
\(236\) | −3.54640e10 | −0.0484426 | ||||||||
\(237\) | −2.27627e11 | + | 2.27627e11i | −0.304426 | + | 0.304426i | ||||
\(238\) | −5.38403e10 | − | 5.38403e10i | −0.0705054 | − | 0.0705054i | ||||
\(239\) | − | 1.51966e11i | − | 0.194875i | −0.995242 | − | 0.0974375i | \(-0.968935\pi\) | ||
0.995242 | − | 0.0974375i | \(-0.0310646\pi\) | |||||||
\(240\) | −2.68838e11 | − | 2.65513e11i | −0.337625 | − | 0.333449i | ||||
\(241\) | −1.68383e11 | −0.207116 | −0.103558 | − | 0.994623i | \(-0.533023\pi\) | ||||
−0.103558 | + | 0.994623i | \(0.533023\pi\) | |||||||
\(242\) | 3.33290e11 | − | 3.33290e11i | 0.401555 | − | 0.401555i | ||||
\(243\) | −1.78450e12 | − | 1.78450e12i | −2.10613 | − | 2.10613i | ||||
\(244\) | − | 3.26930e11i | − | 0.378012i | ||||||
\(245\) | 5.40464e9 | + | 8.68522e11i | 0.00612261 | + | 0.983899i | ||||
\(246\) | 1.38247e12 | 1.53455 | ||||||||
\(247\) | 2.05801e11 | − | 2.05801e11i | 0.223853 | − | 0.223853i | ||||
\(248\) | 3.38639e11 | + | 3.38639e11i | 0.360976 | + | 0.360976i | ||||
\(249\) | − | 1.80467e12i | − | 1.88539i | ||||||
\(250\) | −4.79081e11 | + | 4.97311e11i | −0.490579 | + | 0.509246i | ||||
\(251\) | −1.52960e12 | −1.53535 | −0.767676 | − | 0.640838i | \(-0.778587\pi\) | ||||
−0.767676 | + | 0.640838i | \(0.778587\pi\) | |||||||
\(252\) | −1.18600e11 | + | 1.18600e11i | −0.116703 | + | 0.116703i | ||||
\(253\) | −1.09049e11 | − | 1.09049e11i | −0.105201 | − | 0.105201i | ||||
\(254\) | − | 6.92816e11i | − | 0.655313i | ||||||
\(255\) | 2.27559e12 | − | 1.41605e10i | 2.11054 | − | 0.0131335i | ||||
\(256\) | 6.87195e10 | 0.0625000 | ||||||||
\(257\) | −8.15308e11 | + | 8.15308e11i | −0.727203 | + | 0.727203i | −0.970062 | − | 0.242858i | \(-0.921915\pi\) |
0.242858 | + | 0.970062i | \(0.421915\pi\) | |||||||
\(258\) | 2.57299e11 | + | 2.57299e11i | 0.225081 | + | 0.225081i | ||||
\(259\) | 7.63138e10i | 0.0654793i | ||||||||
\(260\) | −4.78302e11 | + | 4.84292e11i | −0.402564 | + | 0.407606i | ||||
\(261\) | 3.79691e12 | 3.13493 | ||||||||
\(262\) | −9.98998e11 | + | 9.98998e11i | −0.809204 | + | 0.809204i | ||||
\(263\) | 4.93450e11 | + | 4.93450e11i | 0.392161 | + | 0.392161i | 0.875457 | − | 0.483296i | \(-0.160561\pi\) |
−0.483296 | + | 0.875457i | \(0.660561\pi\) | |||||||
\(264\) | − | 3.81866e11i | − | 0.297777i | ||||||
\(265\) | −9.54235e11 | − | 9.42432e11i | −0.730173 | − | 0.721142i | ||||
\(266\) | 3.29949e10 | 0.0247765 | ||||||||
\(267\) | −1.07067e12 | + | 1.07067e12i | −0.789039 | + | 0.789039i | ||||
\(268\) | −4.09008e11 | − | 4.09008e11i | −0.295841 | − | 0.295841i | ||||
\(269\) | − | 9.86681e11i | − | 0.700512i | −0.936654 | − | 0.350256i | \(-0.886095\pi\) | ||
0.936654 | − | 0.350256i | \(-0.113905\pi\) | |||||||
\(270\) | −1.92090e10 | − | 3.08687e12i | −0.0133871 | − | 2.15129i | ||||
\(271\) | −8.14097e11 | −0.556967 | −0.278484 | − | 0.960441i | \(-0.589832\pi\) | ||||
−0.278484 | + | 0.960441i | \(0.589832\pi\) | |||||||
\(272\) | −2.92648e11 | + | 2.92648e11i | −0.196563 | + | 0.196563i | ||||
\(273\) | 2.95732e11 | + | 2.95732e11i | 0.195022 | + | 0.195022i | ||||
\(274\) | 5.44273e11i | 0.352423i | ||||||||
\(275\) | −6.97818e11 | + | 8.68511e9i | −0.443689 | + | 0.00552219i | ||||
\(276\) | 5.09638e11 | 0.318212 | ||||||||
\(277\) | 1.79975e12 | − | 1.79975e12i | 1.10360 | − | 1.10360i | 0.109630 | − | 0.993972i | \(-0.465033\pi\) |
0.993972 | − | 0.109630i | \(-0.0349666\pi\) | |||||||
\(278\) | −1.78534e10 | − | 1.78534e10i | −0.0107522 | − | 0.0107522i | ||||
\(279\) | 6.35349e12i | 3.75830i | ||||||||
\(280\) | −7.71636e10 | + | 4.80174e8i | −0.0448355 | + | 0.000279003i | ||||
\(281\) | −2.26906e12 | −1.29514 | −0.647568 | − | 0.762008i | \(-0.724214\pi\) | ||||
−0.647568 | + | 0.762008i | \(0.724214\pi\) | |||||||
\(282\) | −5.41985e11 | + | 5.41985e11i | −0.303907 | + | 0.303907i | ||||
\(283\) | 8.09303e11 | + | 8.09303e11i | 0.445840 | + | 0.445840i | 0.893969 | − | 0.448129i | \(-0.147909\pi\) |
−0.448129 | + | 0.893969i | \(0.647909\pi\) | |||||||
\(284\) | 2.08073e11i | 0.112622i | ||||||||
\(285\) | −6.92935e11 | + | 7.01613e11i | −0.368526 | + | 0.373142i | ||||
\(286\) | −6.87903e11 | −0.359499 | ||||||||
\(287\) | 1.99637e11 | − | 1.99637e11i | 0.102525 | − | 0.102525i | ||||
\(288\) | 6.44651e11 | + | 6.44651e11i | 0.325359 | + | 0.325359i | ||||
\(289\) | − | 4.76549e11i | − | 0.236384i | ||||||
\(290\) | 1.24286e12 | + | 1.22748e12i | 0.605942 | + | 0.598448i | ||||
\(291\) | −2.42641e12 | −1.16279 | ||||||||
\(292\) | −3.02807e11 | + | 3.02807e11i | −0.142643 | + | 0.142643i | ||||
\(293\) | 1.68288e12 | + | 1.68288e12i | 0.779318 | + | 0.779318i | 0.979715 | − | 0.200397i | \(-0.0642231\pi\) |
−0.200397 | + | 0.979715i | \(0.564223\pi\) | |||||||
\(294\) | − | 2.90071e12i | − | 1.32059i | ||||||
\(295\) | −1.34693e9 | − | 2.16451e11i | −0.000602886 | − | 0.0968833i | ||||
\(296\) | 4.14803e11 | 0.182551 | ||||||||
\(297\) | 2.20598e12 | − | 2.20598e12i | 0.954596 | − | 0.954596i | ||||
\(298\) | 4.34533e11 | + | 4.34533e11i | 0.184902 | + | 0.184902i | ||||
\(299\) | − | 9.18074e11i | − | 0.384168i | ||||||
\(300\) | 1.61032e12 | − | 1.65091e12i | 0.662684 | − | 0.679388i | ||||
\(301\) | 7.43110e10 | 0.0300760 | ||||||||
\(302\) | −7.19381e10 | + | 7.19381e10i | −0.0286368 | + | 0.0286368i | ||||
\(303\) | −4.09661e12 | − | 4.09661e12i | −1.60402 | − | 1.60402i | ||||
\(304\) | − | 1.79344e11i | − | 0.0690746i | ||||||
\(305\) | 1.99539e12 | − | 1.24169e10i | 0.756010 | − | 0.00470450i | ||||
\(306\) | −5.49062e12 | −2.04651 | ||||||||
\(307\) | 2.99054e12 | − | 2.99054e12i | 1.09662 | − | 1.09662i | 0.101820 | − | 0.994803i | \(-0.467533\pi\) |
0.994803 | − | 0.101820i | \(-0.0324667\pi\) | |||||||
\(308\) | −5.51438e10 | − | 5.51438e10i | −0.0198950 | − | 0.0198950i | ||||
\(309\) | 1.43572e12i | 0.509655i | ||||||||
\(310\) | −2.05399e12 | + | 2.07971e12i | −0.717446 | + | 0.726431i | ||||
\(311\) | 3.03633e12 | 1.04363 | 0.521815 | − | 0.853058i | \(-0.325255\pi\) | ||||
0.521815 | + | 0.853058i | \(0.325255\pi\) | |||||||
\(312\) | 1.60745e12 | − | 1.60745e12i | 0.543706 | − | 0.543706i | ||||
\(313\) | 8.96455e11 | + | 8.96455e11i | 0.298405 | + | 0.298405i | 0.840389 | − | 0.541984i | \(-0.182327\pi\) |
−0.541984 | + | 0.840389i | \(0.682327\pi\) | |||||||
\(314\) | − | 2.61571e12i | − | 0.856922i | ||||||
\(315\) | −7.28369e11 | − | 7.19360e11i | −0.234854 | − | 0.231950i | ||||
\(316\) | 3.57337e11 | 0.113408 | ||||||||
\(317\) | 3.27607e12 | − | 3.27607e12i | 1.02343 | − | 1.02343i | 0.0237088 | − | 0.999719i | \(-0.492453\pi\) |
0.999719 | − | 0.0237088i | \(-0.00754744\pi\) | |||||||
\(318\) | 3.16727e12 | + | 3.16727e12i | 0.973979 | + | 0.973979i | ||||
\(319\) | 1.76539e12i | 0.534426i | ||||||||
\(320\) | 2.60998e9 | + | 4.19422e11i | 0.000777836 | + | 0.124998i | ||||
\(321\) | −7.46870e12 | −2.19139 | ||||||||
\(322\) | 7.35947e10 | − | 7.35947e10i | 0.0212602 | − | 0.0212602i | ||||
\(323\) | 7.63753e11 | + | 7.63753e11i | 0.217240 | + | 0.217240i | ||||
\(324\) | 5.66287e12i | 1.58603i | ||||||||
\(325\) | −2.97399e12 | − | 2.90087e12i | −0.820206 | − | 0.800041i | ||||
\(326\) | 4.72588e12 | 1.28350 | ||||||||
\(327\) | −8.74866e12 | + | 8.74866e12i | −2.33993 | + | 2.33993i | ||||
\(328\) | −1.08513e12 | − | 1.08513e12i | −0.285832 | − | 0.285832i | ||||
\(329\) | 1.56532e11i | 0.0406090i | ||||||||
\(330\) | 2.33068e12 | − | 1.45034e10i | 0.595543 | − | 0.00370595i | ||||
\(331\) | 6.48540e11 | 0.163229 | 0.0816144 | − | 0.996664i | \(-0.473992\pi\) | ||||
0.0816144 | + | 0.996664i | \(0.473992\pi\) | |||||||
\(332\) | −1.41652e12 | + | 1.41652e12i | −0.351181 | + | 0.351181i | ||||
\(333\) | 3.89123e12 | + | 3.89123e12i | 0.950312 | + | 0.950312i | ||||
\(334\) | 3.95535e12i | 0.951596i | ||||||||
\(335\) | 2.48081e12 | − | 2.51187e12i | 0.587988 | − | 0.595352i | ||||
\(336\) | 2.57713e11 | 0.0601783 | ||||||||
\(337\) | −6.16866e11 | + | 6.16866e11i | −0.141919 | + | 0.141919i | −0.774497 | − | 0.632578i | \(-0.781997\pi\) |
0.632578 | + | 0.774497i | \(0.281997\pi\) | |||||||
\(338\) | −6.89961e11 | − | 6.89961e11i | −0.156402 | − | 0.156402i | ||||
\(339\) | − | 1.43276e13i | − | 3.20018i | ||||||
\(340\) | −1.79726e12 | − | 1.77503e12i | −0.395565 | − | 0.390672i | ||||
\(341\) | −2.95408e12 | −0.640694 | ||||||||
\(342\) | 1.68241e12 | − | 1.68241e12i | 0.359585 | − | 0.359585i | ||||
\(343\) | −8.44607e11 | − | 8.44607e11i | −0.177903 | − | 0.177903i | ||||
\(344\) | − | 4.03917e11i | − | 0.0838494i | ||||||
\(345\) | 1.93562e10 | + | 3.11052e12i | 0.00396026 | + | 0.636411i | ||||
\(346\) | 5.76526e11 | 0.116262 | ||||||||
\(347\) | −5.59961e12 | + | 5.59961e12i | −1.11304 | + | 1.11304i | −0.120302 | + | 0.992737i | \(0.538386\pi\) |
−0.992737 | + | 0.120302i | \(0.961614\pi\) | |||||||
\(348\) | −4.12526e12 | − | 4.12526e12i | −0.808267 | − | 0.808267i | ||||
\(349\) | 6.66328e12i | 1.28695i | 0.765468 | + | 0.643474i | \(0.222507\pi\) | ||||
−0.765468 | + | 0.643474i | \(0.777493\pi\) | |||||||
\(350\) | −5.86139e9 | − | 4.70942e11i | −0.00111599 | − | 0.0896658i | ||||
\(351\) | 1.85720e13 | 3.48596 | ||||||||
\(352\) | −2.99734e11 | + | 2.99734e11i | −0.0554654 | + | 0.0554654i | ||||
\(353\) | 4.34264e12 | + | 4.34264e12i | 0.792284 | + | 0.792284i | 0.981865 | − | 0.189581i | \(-0.0607130\pi\) |
−0.189581 | + | 0.981865i | \(0.560713\pi\) | |||||||
\(354\) | 7.22908e11i | 0.130037i | ||||||||
\(355\) | −1.26995e12 | + | 7.90266e9i | −0.225240 | + | 0.00140162i | ||||
\(356\) | 1.68077e12 | 0.293940 | ||||||||
\(357\) | −1.09750e12 | + | 1.09750e12i | −0.189261 | + | 0.189261i | ||||
\(358\) | −5.04208e12 | − | 5.04208e12i | −0.857423 | − | 0.857423i | ||||
\(359\) | 4.49607e12i | 0.753982i | 0.926217 | + | 0.376991i | \(0.123041\pi\) | ||||
−0.926217 | + | 0.376991i | \(0.876959\pi\) | |||||||
\(360\) | −3.91008e12 | + | 3.95905e12i | −0.646656 | + | 0.654754i | ||||
\(361\) | 5.66302e12 | 0.923659 | ||||||||
\(362\) | 3.33466e12 | − | 3.33466e12i | 0.536425 | − | 0.536425i | ||||
\(363\) | −6.79387e12 | − | 6.79387e12i | −1.07791 | − | 1.07791i | ||||
\(364\) | − | 4.64250e11i | − | 0.0726516i | ||||||
\(365\) | −1.85965e12 | − | 1.83665e12i | −0.287056 | − | 0.283506i | ||||
\(366\) | −6.66424e12 | −1.01472 | ||||||||
\(367\) | 2.25425e12 | − | 2.25425e12i | 0.338587 | − | 0.338587i | −0.517248 | − | 0.855836i | \(-0.673044\pi\) |
0.855836 | + | 0.517248i | \(0.173044\pi\) | |||||||
\(368\) | −4.00024e11 | − | 4.00024e11i | −0.0592716 | − | 0.0592716i | ||||
\(369\) | − | 2.03589e13i | − | 2.97593i | ||||||
\(370\) | 1.57543e10 | + | 2.53171e12i | 0.00227191 | + | 0.365095i | ||||
\(371\) | 9.14746e11 | 0.130146 | ||||||||
\(372\) | 6.90292e12 | − | 6.90292e12i | 0.968987 | − | 0.968987i | ||||
\(373\) | −6.84615e12 | − | 6.84615e12i | −0.948205 | − | 0.948205i | 0.0505184 | − | 0.998723i | \(-0.483913\pi\) |
−0.998723 | + | 0.0505184i | \(0.983913\pi\) | |||||||
\(374\) | − | 2.55289e12i | − | 0.348878i | ||||||
\(375\) | 1.01373e13 | + | 9.76573e12i | 1.36700 | + | 1.31689i | ||||
\(376\) | 8.50827e11 | 0.113215 | ||||||||
\(377\) | −7.43134e12 | + | 7.43134e12i | −0.975799 | + | 0.975799i | ||||
\(378\) | 1.48877e12 | + | 1.48877e12i | 0.192916 | + | 0.192916i | ||||
\(379\) | 1.40526e13i | 1.79705i | 0.438927 | + | 0.898523i | \(0.355359\pi\) | ||||
−0.438927 | + | 0.898523i | \(0.644641\pi\) | |||||||
\(380\) | 1.09461e12 | − | 6.81153e9i | 0.138147 | − | 0.000859659i | ||||
\(381\) | −1.41226e13 | −1.75909 | ||||||||
\(382\) | 4.80489e11 | − | 4.80489e11i | 0.0590699 | − | 0.0590699i | ||||
\(383\) | −2.81487e12 | − | 2.81487e12i | −0.341558 | − | 0.341558i | 0.515395 | − | 0.856953i | \(-0.327645\pi\) |
−0.856953 | + | 0.515395i | \(0.827645\pi\) | |||||||
\(384\) | − | 1.40080e12i | − | 0.167772i | ||||||
\(385\) | 3.34470e11 | − | 3.38659e11i | 0.0395415 | − | 0.0400367i | ||||
\(386\) | 9.99290e11 | 0.116615 | ||||||||
\(387\) | 3.78911e12 | − | 3.78911e12i | 0.436498 | − | 0.436498i | ||||
\(388\) | 1.90454e12 | + | 1.90454e12i | 0.216586 | + | 0.216586i | ||||
\(389\) | − | 1.40114e12i | − | 0.157302i | −0.996902 | − | 0.0786509i | \(-0.974939\pi\) | ||
0.996902 | − | 0.0786509i | \(-0.0250613\pi\) | |||||||
\(390\) | 9.87195e12 | + | 9.74985e12i | 1.09416 | + | 1.08062i | ||||
\(391\) | 3.40708e12 | 0.372819 | ||||||||
\(392\) | −2.27682e12 | + | 2.27682e12i | −0.245979 | + | 0.245979i | ||||
\(393\) | 2.03639e13 | + | 2.03639e13i | 2.17219 | + | 2.17219i | ||||
\(394\) | 2.34994e11i | 0.0247500i | ||||||||
\(395\) | 1.35718e10 | + | 2.18097e12i | 0.00141140 | + | 0.226811i | ||||
\(396\) | −5.62355e12 | −0.577477 | ||||||||
\(397\) | 7.93928e12 | − | 7.93928e12i | 0.805061 | − | 0.805061i | −0.178821 | − | 0.983882i | \(-0.557228\pi\) |
0.983882 | + | 0.178821i | \(0.0572282\pi\) | |||||||
\(398\) | −4.09161e12 | − | 4.09161e12i | −0.409712 | − | 0.409712i | ||||
\(399\) | − | 6.72578e11i | − | 0.0665087i | ||||||
\(400\) | −2.55980e12 | + | 3.18595e10i | −0.249981 | + | 0.00311128i | ||||
\(401\) | 3.42032e12 | 0.329871 | 0.164936 | − | 0.986304i | \(-0.447258\pi\) | ||||
0.164936 | + | 0.986304i | \(0.447258\pi\) | |||||||
\(402\) | −8.33734e12 | + | 8.33734e12i | −0.794141 | + | 0.794141i | ||||
\(403\) | −1.24351e13 | − | 1.24351e13i | −1.16983 | − | 1.16983i | ||||
\(404\) | 6.43100e12i | 0.597546i | ||||||||
\(405\) | −3.45628e13 | + | 2.15077e11i | −3.17200 | + | 0.0197387i | ||||
\(406\) | −1.19142e12 | −0.108003 | ||||||||
\(407\) | −1.80925e12 | + | 1.80925e12i | −0.162004 | + | 0.162004i | ||||
\(408\) | 5.96543e12 | + | 5.96543e12i | 0.527644 | + | 0.527644i | ||||
\(409\) | 6.67262e12i | 0.583016i | 0.956568 | + | 0.291508i | \(0.0941569\pi\) | ||||
−0.956568 | + | 0.291508i | \(0.905843\pi\) | |||||||
\(410\) | 6.58174e12 | − | 6.66416e12i | 0.568095 | − | 0.575210i | ||||
\(411\) | 1.10946e13 | 0.946026 | ||||||||
\(412\) | 1.12692e12 | − | 1.12692e12i | 0.0949307 | − | 0.0949307i | ||||
\(413\) | 1.04392e11 | + | 1.04392e11i | 0.00868796 | + | 0.00868796i | ||||
\(414\) | − | 7.50518e12i | − | 0.617105i | ||||||
\(415\) | −8.69936e12 | − | 8.59176e12i | −0.706719 | − | 0.697978i | ||||
\(416\) | −2.52343e12 | −0.202547 | ||||||||
\(417\) | −3.63928e11 | + | 3.63928e11i | −0.0288626 | + | 0.0288626i | ||||
\(418\) | 7.82244e11 | + | 7.82244e11i | 0.0613001 | + | 0.0613001i | ||||
\(419\) | − | 2.04512e13i | − | 1.58361i | −0.610775 | − | 0.791804i | \(-0.709142\pi\) | ||
0.610775 | − | 0.791804i | \(-0.290858\pi\) | |||||||
\(420\) | 9.78801e9 | + | 1.57292e12i | 0.000748941 | + | 0.120354i | ||||
\(421\) | 1.53655e13 | 1.16181 | 0.580906 | − | 0.813971i | \(-0.302698\pi\) | ||||
0.580906 | + | 0.813971i | \(0.302698\pi\) | |||||||
\(422\) | −8.83693e12 | + | 8.83693e12i | −0.660297 | + | 0.660297i | ||||
\(423\) | 7.98153e12 | + | 7.98153e12i | 0.589365 | + | 0.589365i | ||||
\(424\) | − | 4.97210e12i | − | 0.362836i | ||||||
\(425\) | 1.07655e13 | − | 1.10368e13i | 0.776406 | − | 0.795976i | ||||
\(426\) | 4.24142e12 | 0.302317 | ||||||||
\(427\) | −9.62356e11 | + | 9.62356e11i | −0.0677948 | + | 0.0677948i | ||||
\(428\) | 5.86232e12 | + | 5.86232e12i | 0.408179 | + | 0.408179i | ||||
\(429\) | 1.40224e13i | 0.965020i | ||||||||
\(430\) | 2.46527e12 | − | 1.53409e10i | 0.167696 | − | 0.00104354i | ||||
\(431\) | −1.77529e13 | −1.19367 | −0.596834 | − | 0.802365i | \(-0.703575\pi\) | ||||
−0.596834 | + | 0.802365i | \(0.703575\pi\) | |||||||
\(432\) | 8.09219e12 | − | 8.09219e12i | 0.537833 | − | 0.537833i | ||||
\(433\) | −4.48900e11 | − | 4.48900e11i | −0.0294924 | − | 0.0294924i | 0.692207 | − | 0.721699i | \(-0.256639\pi\) |
−0.721699 | + | 0.692207i | \(0.756639\pi\) | |||||||
\(434\) | − | 1.99365e12i | − | 0.129479i | ||||||
\(435\) | 2.50214e13 | − | 2.53348e13i | 1.60644 | − | 1.62656i | ||||
\(436\) | 1.37340e13 | 0.871693 | ||||||||
\(437\) | −1.04398e12 | + | 1.04398e12i | −0.0655067 | + | 0.0655067i | ||||
\(438\) | 6.17250e12 | + | 6.17250e12i | 0.382904 | + | 0.382904i | ||||
\(439\) | 9.39701e12i | 0.576325i | 0.957582 | + | 0.288162i | \(0.0930443\pi\) | ||||
−0.957582 | + | 0.288162i | \(0.906956\pi\) | |||||||
\(440\) | −1.84078e12 | − | 1.81801e12i | −0.111619 | − | 0.110238i | ||||
\(441\) | −4.27173e13 | −2.56101 | ||||||||
\(442\) | 1.07463e13 | − | 1.07463e13i | 0.637010 | − | 0.637010i | ||||
\(443\) | −4.16887e12 | − | 4.16887e12i | −0.244343 | − | 0.244343i | 0.574301 | − | 0.818644i | \(-0.305274\pi\) |
−0.818644 | + | 0.574301i | \(0.805274\pi\) | |||||||
\(444\) | − | 8.45547e12i | − | 0.490030i | ||||||
\(445\) | 6.38362e10 | + | 1.02584e13i | 0.00365819 | + | 0.587869i | ||||
\(446\) | −2.28287e13 | −1.29362 | ||||||||
\(447\) | 8.85765e12 | − | 8.85765e12i | 0.496342 | − | 0.496342i | ||||
\(448\) | −2.02284e11 | − | 2.02284e11i | −0.0112091 | − | 0.0112091i | ||||
\(449\) | − | 8.98571e12i | − | 0.492403i | −0.969219 | − | 0.246201i | \(-0.920818\pi\) | ||
0.969219 | − | 0.246201i | \(-0.0791825\pi\) | |||||||
\(450\) | −2.43121e13 | − | 2.37144e13i | −1.31753 | − | 1.28514i | ||||
\(451\) | 9.46598e12 | 0.507321 | ||||||||
\(452\) | −1.12460e13 | + | 1.12460e13i | −0.596081 | + | 0.596081i | ||||
\(453\) | 1.46641e12 | + | 1.46641e12i | 0.0768711 | + | 0.0768711i | ||||
\(454\) | 2.29106e13i | 1.18784i | ||||||||
\(455\) | 2.83351e12 | − | 1.76324e10i | 0.145300 | − | 0.000904177i | ||||
\(456\) | −3.65580e12 | −0.185421 | ||||||||
\(457\) | 5.53018e12 | − | 5.53018e12i | 0.277433 | − | 0.277433i | −0.554650 | − | 0.832084i | \(-0.687148\pi\) |
0.832084 | + | 0.554650i | \(0.187148\pi\) | |||||||
\(458\) | −4.36128e12 | − | 4.36128e12i | −0.216415 | − | 0.216415i | ||||
\(459\) | 6.89228e13i | 3.38298i | ||||||||
\(460\) | 2.42631e12 | − | 2.45670e12i | 0.117803 | − | 0.119279i | ||||
\(461\) | 1.62906e13 | 0.782406 | 0.391203 | − | 0.920304i | \(-0.372059\pi\) | ||||
0.391203 | + | 0.920304i | \(0.372059\pi\) | |||||||
\(462\) | −1.12407e12 | + | 1.12407e12i | −0.0534050 | + | 0.0534050i | ||||
\(463\) | 7.68718e12 | + | 7.68718e12i | 0.361295 | + | 0.361295i | 0.864290 | − | 0.502994i | \(-0.167768\pi\) |
−0.502994 | + | 0.864290i | \(0.667768\pi\) | |||||||
\(464\) | 6.47598e12i | 0.301103i | ||||||||
\(465\) | 4.23934e13 | + | 4.18691e13i | 1.95000 | + | 1.92588i | ||||
\(466\) | 9.87390e12 | 0.449323 | ||||||||
\(467\) | −1.94981e13 | + | 1.94981e13i | −0.877826 | + | 0.877826i | −0.993309 | − | 0.115484i | \(-0.963158\pi\) |
0.115484 | + | 0.993309i | \(0.463158\pi\) | |||||||
\(468\) | −2.36721e13 | − | 2.36721e13i | −1.05440 | − | 1.05440i | ||||
\(469\) | 2.40792e12i | 0.106115i | ||||||||
\(470\) | 3.23146e10 | + | 5.19294e12i | 0.00140900 | + | 0.226425i | ||||
\(471\) | −5.33194e13 | −2.30028 | ||||||||
\(472\) | 5.67423e11 | − | 5.67423e11i | 0.0242213 | − | 0.0242213i | ||||
\(473\) | 1.76177e12 | + | 1.76177e12i | 0.0744119 | + | 0.0744119i | ||||
\(474\) | − | 7.28407e12i | − | 0.304426i | ||||||
\(475\) | 8.31469e10 | + | 6.68056e12i | 0.00343857 | + | 0.276277i | ||||
\(476\) | 1.72289e12 | 0.0705054 | ||||||||
\(477\) | 4.66428e13 | − | 4.66428e13i | 1.88883 | − | 1.88883i | ||||
\(478\) | 2.43145e12 | + | 2.43145e12i | 0.0974375 | + | 0.0974375i | ||||
\(479\) | − | 3.68363e13i | − | 1.46083i | −0.683006 | − | 0.730413i | \(-0.739328\pi\) | ||
0.683006 | − | 0.730413i | \(-0.260672\pi\) | |||||||
\(480\) | 8.54963e12 | − | 5.32027e10i | 0.335537 | − | 0.00208798i | ||||
\(481\) | −1.52319e13 | −0.591600 | ||||||||
\(482\) | 2.69413e12 | − | 2.69413e12i | 0.103558 | − | 0.103558i | ||||
\(483\) | −1.50018e12 | − | 1.50018e12i | −0.0570699 | − | 0.0570699i | ||||
\(484\) | 1.06653e13i | 0.401555i | ||||||||
\(485\) | −1.15518e13 | + | 1.16965e13i | −0.430469 | + | 0.435860i | ||||
\(486\) | 5.71040e13 | 2.10613 | ||||||||
\(487\) | −1.50421e13 | + | 1.50421e13i | −0.549116 | + | 0.549116i | −0.926185 | − | 0.377069i | \(-0.876932\pi\) |
0.377069 | + | 0.926185i | \(0.376932\pi\) | |||||||
\(488\) | 5.23088e12 | + | 5.23088e12i | 0.189006 | + | 0.189006i | ||||
\(489\) | − | 9.63338e13i | − | 3.44536i | ||||||
\(490\) | −1.39828e13 | − | 1.38099e13i | −0.495011 | − | 0.488888i | ||||
\(491\) | −2.16133e13 | −0.757380 | −0.378690 | − | 0.925524i | \(-0.623625\pi\) | ||||
−0.378690 | + | 0.925524i | \(0.623625\pi\) | |||||||
\(492\) | −2.21195e13 | + | 2.21195e13i | −0.767273 | + | 0.767273i | ||||
\(493\) | −2.75786e13 | − | 2.75786e13i | −0.946972 | − | 0.946972i | ||||
\(494\) | 6.58564e12i | 0.223853i | ||||||||
\(495\) | −2.13584e11 | − | 3.43228e13i | −0.00718692 | − | 1.15493i | ||||
\(496\) | −1.08364e13 | −0.360976 | ||||||||
\(497\) | 6.12486e11 | − | 6.12486e11i | 0.0201983 | − | 0.0201983i | ||||
\(498\) | 2.88747e13 | + | 2.88747e13i | 0.942693 | + | 0.942693i | ||||
\(499\) | 5.41692e13i | 1.75085i | 0.483350 | + | 0.875427i | \(0.339420\pi\) | ||||
−0.483350 | + | 0.875427i | \(0.660580\pi\) | |||||||
\(500\) | −2.91673e11 | − | 1.56223e13i | −0.00933355 | − | 0.499913i | ||||
\(501\) | 8.06270e13 | 2.55442 | ||||||||
\(502\) | 2.44735e13 | − | 2.44735e13i | 0.767676 | − | 0.767676i | ||||
\(503\) | 1.09238e13 | + | 1.09238e13i | 0.339262 | + | 0.339262i | 0.856090 | − | 0.516827i | \(-0.172887\pi\) |
−0.516827 | + | 0.856090i | \(0.672887\pi\) | |||||||
\(504\) | − | 3.79521e12i | − | 0.116703i | ||||||
\(505\) | −3.92510e13 | + | 2.44251e11i | −1.19507 | + | 0.00743669i | ||||
\(506\) | 3.48957e12 | 0.105201 | ||||||||
\(507\) | −1.40644e13 | + | 1.40644e13i | −0.419837 | + | 0.419837i | ||||
\(508\) | 1.10850e13 | + | 1.10850e13i | 0.327657 | + | 0.327657i | ||||
\(509\) | 2.14613e13i | 0.628155i | 0.949397 | + | 0.314078i | \(0.101695\pi\) | ||||
−0.949397 | + | 0.314078i | \(0.898305\pi\) | |||||||
\(510\) | −3.61828e13 | + | 3.66360e13i | −1.04870 | + | 1.06183i | ||||
\(511\) | 1.78269e12 | 0.0511648 | ||||||||
\(512\) | −1.09951e12 | + | 1.09951e12i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −2.11190e13 | − | 2.11190e13i | −0.594410 | − | 0.594410i | ||||
\(514\) | − | 2.60898e13i | − | 0.727203i | ||||||
\(515\) | 6.92084e12 | + | 6.83524e12i | 0.191039 | + | 0.188676i | ||||
\(516\) | −8.23357e12 | −0.225081 | ||||||||
\(517\) | −3.71105e12 | + | 3.71105e12i | −0.100472 | + | 0.100472i | ||||
\(518\) | −1.22102e12 | − | 1.22102e12i | −0.0327397 | − | 0.0327397i | ||||
\(519\) | − | 1.17521e13i | − | 0.312088i | ||||||
\(520\) | −9.58406e10 | − | 1.54015e13i | −0.00252077 | − | 0.405085i | ||||
\(521\) | 3.08056e13 | 0.802493 | 0.401246 | − | 0.915970i | \(-0.368577\pi\) | ||||
0.401246 | + | 0.915970i | \(0.368577\pi\) | |||||||
\(522\) | −6.07506e13 | + | 6.07506e13i | −1.56747 | + | 1.56747i | ||||
\(523\) | −5.30765e11 | − | 5.30765e11i | −0.0135642 | − | 0.0135642i | 0.700292 | − | 0.713856i | \(-0.253053\pi\) |
−0.713856 | + | 0.700292i | \(0.753053\pi\) | |||||||
\(524\) | − | 3.19679e13i | − | 0.809204i | ||||||
\(525\) | −9.59981e12 | + | 1.19480e11i | −0.240695 | + | 0.00299571i | ||||
\(526\) | −1.57904e13 | −0.392161 | ||||||||
\(527\) | 4.61481e13 | − | 4.61481e13i | 1.13527 | − | 1.13527i | ||||
\(528\) | 6.10986e12 | + | 6.10986e12i | 0.148889 | + | 0.148889i | ||||
\(529\) | − | 3.67693e13i | − | 0.887580i | ||||||
\(530\) | 3.03467e13 | − | 1.88841e11i | 0.725658 | − | 0.00451563i | ||||
\(531\) | 1.06459e13 | 0.252179 | ||||||||
\(532\) | −5.27919e11 | + | 5.27919e11i | −0.0123882 | + | 0.0123882i | ||||
\(533\) | 3.98466e13 | + | 3.98466e13i | 0.926308 | + | 0.926308i | ||||
\(534\) | − | 3.42614e13i | − | 0.789039i | ||||||
\(535\) | −3.55574e13 | + | 3.60027e13i | −0.811262 | + | 0.821422i | ||||
\(536\) | 1.30883e13 | 0.295841 | ||||||||
\(537\) | −1.02779e14 | + | 1.02779e14i | −2.30162 | + | 2.30162i | ||||
\(538\) | 1.57869e13 | + | 1.57869e13i | 0.350256 | + | 0.350256i | ||||
\(539\) | − | 1.98616e13i | − | 0.436587i | ||||||
\(540\) | 4.96972e13 | + | 4.90825e13i | 1.08234 | + | 1.06895i | ||||
\(541\) | 1.52125e13 | 0.328258 | 0.164129 | − | 0.986439i | \(-0.447519\pi\) | ||||
0.164129 | + | 0.986439i | \(0.447519\pi\) | |||||||
\(542\) | 1.30256e13 | − | 1.30256e13i | 0.278484 | − | 0.278484i | ||||
\(543\) | −6.79747e13 | − | 6.79747e13i | −1.43995 | − | 1.43995i | ||||
\(544\) | − | 9.36475e12i | − | 0.196563i | ||||||
\(545\) | 5.21620e11 | + | 8.38239e13i | 0.0108485 | + | 1.74335i | ||||
\(546\) | −9.46342e12 | −0.195022 | ||||||||
\(547\) | 4.79703e13 | − | 4.79703e13i | 0.979571 | − | 0.979571i | −0.0202243 | − | 0.999795i | \(-0.506438\pi\) |
0.999795 | + | 0.0202243i | \(0.00643804\pi\) | |||||||
\(548\) | −8.70836e12 | − | 8.70836e12i | −0.176211 | − | 0.176211i | ||||
\(549\) | 9.81409e13i | 1.96783i | ||||||||
\(550\) | 1.10261e13 | − | 1.13040e13i | 0.219083 | − | 0.224606i | ||||
\(551\) | 1.69010e13 | 0.332778 | ||||||||
\(552\) | −8.15420e12 | + | 8.15420e12i | −0.159106 | + | 0.159106i | ||||
\(553\) | −1.05186e12 | − | 1.05186e12i | −0.0203392 | − | 0.0203392i | ||||
\(554\) | 5.75919e13i | 1.10360i | ||||||||
\(555\) | 5.16071e13 | − | 3.21141e11i | 0.980042 | − | 0.00609861i | ||||
\(556\) | 5.71307e11 | 0.0107522 | ||||||||
\(557\) | 4.65821e13 | − | 4.65821e13i | 0.868846 | − | 0.868846i | −0.123498 | − | 0.992345i | \(-0.539411\pi\) |
0.992345 | + | 0.123498i | \(0.0394114\pi\) | |||||||
\(558\) | −1.01656e14 | − | 1.01656e14i | −1.87915 | − | 1.87915i | ||||
\(559\) | 1.48321e13i | 0.271735i | ||||||||
\(560\) | 1.22693e12 | − | 1.24230e12i | 0.0222783 | − | 0.0225573i | ||||
\(561\) | −5.20388e13 | −0.936512 | ||||||||
\(562\) | 3.63050e13 | − | 3.63050e13i | 0.647568 | − | 0.647568i | ||||
\(563\) | 8.88206e12 | + | 8.88206e12i | 0.157026 | + | 0.157026i | 0.781247 | − | 0.624221i | \(-0.214584\pi\) |
−0.624221 | + | 0.781247i | \(0.714584\pi\) | |||||||
\(564\) | − | 1.73435e13i | − | 0.303907i | ||||||
\(565\) | −6.90658e13 | − | 6.82116e13i | −1.19956 | − | 1.18472i | ||||
\(566\) | −2.58977e13 | −0.445840 | ||||||||
\(567\) | 1.66693e13 | − | 1.66693e13i | 0.284448 | − | 0.284448i | ||||
\(568\) | −3.32917e12 | − | 3.32917e12i | −0.0563111 | − | 0.0563111i | ||||
\(569\) | − | 2.03394e12i | − | 0.0341018i | −0.999855 | − | 0.0170509i | \(-0.994572\pi\) | ||
0.999855 | − | 0.0170509i | \(-0.00542773\pi\) | |||||||
\(570\) | −1.38848e11 | − | 2.23128e13i | −0.00230763 | − | 0.370834i | ||||
\(571\) | 4.37466e13 | 0.720716 | 0.360358 | − | 0.932814i | \(-0.382655\pi\) | ||||
0.360358 | + | 0.932814i | \(0.382655\pi\) | |||||||
\(572\) | 1.10064e13 | − | 1.10064e13i | 0.179749 | − | 0.179749i | ||||
\(573\) | −9.79442e12 | − | 9.79442e12i | −0.158564 | − | 0.158564i | ||||
\(574\) | 6.38838e12i | 0.102525i | ||||||||
\(575\) | 1.50864e13 | + | 1.47154e13i | 0.240019 | + | 0.234118i | ||||
\(576\) | −2.06288e13 | −0.325359 | ||||||||
\(577\) | 6.55899e12 | − | 6.55899e12i | 0.102555 | − | 0.102555i | −0.653967 | − | 0.756523i | \(-0.726897\pi\) |
0.756523 | + | 0.653967i | \(0.226897\pi\) | |||||||
\(578\) | 7.62478e12 | + | 7.62478e12i | 0.118192 | + | 0.118192i | ||||
\(579\) | − | 2.03698e13i | − | 0.313036i | ||||||
\(580\) | −3.95255e13 | + | 2.45959e11i | −0.602195 | + | 0.00374734i | ||||
\(581\) | 8.33936e12 | 0.125966 | ||||||||
\(582\) | 3.88226e13 | − | 3.88226e13i | 0.581393 | − | 0.581393i | ||||
\(583\) | 2.16868e13 | + | 2.16868e13i | 0.321997 | + | 0.321997i | ||||
\(584\) | − | 9.68981e12i | − | 0.142643i | ||||||
\(585\) | 1.43581e14 | − | 1.45379e14i | 2.09565 | − | 2.12189i | ||||
\(586\) | −5.38521e13 | −0.779318 | ||||||||
\(587\) | −3.54072e13 | + | 3.54072e13i | −0.508044 | + | 0.508044i | −0.913925 | − | 0.405882i | \(-0.866964\pi\) |
0.405882 | + | 0.913925i | \(0.366964\pi\) | |||||||
\(588\) | 4.64114e13 | + | 4.64114e13i | 0.660295 | + | 0.660295i | ||||
\(589\) | 2.82809e13i | 0.398949i | ||||||||
\(590\) | 3.48476e12 | + | 3.44166e12i | 0.0487431 | + | 0.0481402i | ||||
\(591\) | 4.79018e12 | 0.0664376 | ||||||||
\(592\) | −6.63685e12 | + | 6.63685e12i | −0.0912754 | + | 0.0912754i | ||||
\(593\) | 1.82645e13 | + | 1.82645e13i | 0.249077 | + | 0.249077i | 0.820592 | − | 0.571515i | \(-0.193644\pi\) |
−0.571515 | + | 0.820592i | \(0.693644\pi\) | |||||||
\(594\) | 7.05914e13i | 0.954596i | ||||||||
\(595\) | 6.54357e10 | + | 1.05155e13i | 0.000877466 | + | 0.141008i | ||||
\(596\) | −1.39051e13 | −0.184902 | ||||||||
\(597\) | −8.34045e13 | + | 8.34045e13i | −1.09981 | + | 1.09981i | ||||
\(598\) | 1.46892e13 | + | 1.46892e13i | 0.192084 | + | 0.192084i | ||||
\(599\) | − | 7.75562e13i | − | 1.00573i | −0.864364 | − | 0.502866i | \(-0.832279\pi\) | ||
0.864364 | − | 0.502866i | \(-0.167721\pi\) | |||||||
\(600\) | 6.49434e11 | + | 5.21797e13i | 0.00835177 | + | 0.671036i | ||||
\(601\) | −6.85036e13 | −0.873657 | −0.436829 | − | 0.899545i | \(-0.643898\pi\) | ||||
−0.436829 | + | 0.899545i | \(0.643898\pi\) | |||||||
\(602\) | −1.18898e12 | + | 1.18898e12i | −0.0150380 | + | 0.0150380i | ||||
\(603\) | 1.22780e14 | + | 1.22780e14i | 1.54007 | + | 1.54007i | ||||
\(604\) | − | 2.30202e12i | − | 0.0286368i | ||||||
\(605\) | −6.50943e13 | + | 4.05070e11i | −0.803094 | + | 0.00499750i | ||||
\(606\) | 1.31091e14 | 1.60402 | ||||||||
\(607\) | −1.16409e14 | + | 1.16409e14i | −1.41268 | + | 1.41268i | −0.673414 | + | 0.739265i | \(0.735173\pi\) |
−0.739265 | + | 0.673414i | \(0.764827\pi\) | |||||||
\(608\) | 2.86950e12 | + | 2.86950e12i | 0.0345373 | + | 0.0345373i | ||||
\(609\) | 2.42863e13i | 0.289918i | ||||||||
\(610\) | −3.17275e13 | + | 3.21248e13i | −0.375653 | + | 0.380357i | ||||
\(611\) | −3.12430e13 | −0.366899 | ||||||||
\(612\) | 8.78499e13 | − | 8.78499e13i | 1.02326 | − | 1.02326i | ||||
\(613\) | −7.77875e13 | − | 7.77875e13i | −0.898685 | − | 0.898685i | 0.0966345 | − | 0.995320i | \(-0.469192\pi\) |
−0.995320 | + | 0.0966345i | \(0.969192\pi\) | |||||||
\(614\) | 9.56972e13i | 1.09662i | ||||||||
\(615\) | −1.35844e14 | − | 1.34164e14i | −1.54407 | − | 1.52497i | ||||
\(616\) | 1.76460e12 | 0.0198950 | ||||||||
\(617\) | −6.34760e12 | + | 6.34760e12i | −0.0709878 | + | 0.0709878i | −0.741709 | − | 0.670722i | \(-0.765985\pi\) |
0.670722 | + | 0.741709i | \(0.265985\pi\) | |||||||
\(618\) | −2.29714e13 | − | 2.29714e13i | −0.254827 | − | 0.254827i | ||||
\(619\) | − | 8.98265e13i | − | 0.988443i | −0.869336 | − | 0.494221i | \(-0.835453\pi\) | ||
0.869336 | − | 0.494221i | \(-0.164547\pi\) | |||||||
\(620\) | −4.11571e11 | − | 6.61392e13i | −0.00449248 | − | 0.721939i | ||||
\(621\) | −9.42112e13 | −1.02010 | ||||||||
\(622\) | −4.85813e13 | + | 4.85813e13i | −0.521815 | + | 0.521815i | ||||
\(623\) | −4.94755e12 | − | 4.94755e12i | −0.0527169 | − | 0.0527169i | ||||
\(624\) | 5.14384e13i | 0.543706i | ||||||||
\(625\) | 9.53379e13 | − | 2.37354e12i | 0.999690 | − | 0.0248883i | ||||
\(626\) | −2.86866e13 | −0.298405 | ||||||||
\(627\) | 1.59455e13 | − | 1.59455e13i | 0.164551 | − | 0.164551i | ||||
\(628\) | 4.18514e13 | + | 4.18514e13i | 0.428461 | + | 0.428461i | ||||
\(629\) | − | 5.65274e13i | − | 0.574124i | ||||||
\(630\) | 2.31637e13 | − | 1.44143e11i | 0.233402 | − | 0.00145242i | ||||
\(631\) | 1.81926e14 | 1.81865 | 0.909324 | − | 0.416089i | \(-0.136599\pi\) | ||||
0.909324 | + | 0.416089i | \(0.136599\pi\) | |||||||
\(632\) | −5.71740e12 | + | 5.71740e12i | −0.0567039 | + | 0.0567039i | ||||
\(633\) | 1.80135e14 | + | 1.80135e14i | 1.77247 | + | 1.77247i | ||||
\(634\) | 1.04834e14i | 1.02343i | ||||||||
\(635\) | −6.72354e13 | + | 6.80775e13i | −0.651223 | + | 0.659379i | ||||
\(636\) | −1.01353e14 | −0.973979 | ||||||||
\(637\) | 8.36066e13 | − | 8.36066e13i | 0.797156 | − | 0.797156i | ||||
\(638\) | −2.82463e13 | − | 2.82463e13i | −0.267213 | − | 0.267213i | ||||
\(639\) | − | 6.24612e13i | − | 0.586281i | ||||||
\(640\) | −6.75252e12 | − | 6.66900e12i | −0.0628877 | − | 0.0621099i | ||||
\(641\) | −1.99408e14 | −1.84269 | −0.921344 | − | 0.388748i | \(-0.872908\pi\) | ||||
−0.921344 | + | 0.388748i | \(0.872908\pi\) | |||||||
\(642\) | 1.19499e14 | − | 1.19499e14i | 1.09570 | − | 1.09570i | ||||
\(643\) | 1.52095e14 | + | 1.52095e14i | 1.38376 | + | 1.38376i | 0.837841 | + | 0.545914i | \(0.183818\pi\) |
0.545914 | + | 0.837841i | \(0.316182\pi\) | |||||||
\(644\) | 2.35503e12i | 0.0212602i | ||||||||
\(645\) | −3.12713e11 | − | 5.02527e13i | −0.00280122 | − | 0.450154i | ||||
\(646\) | −2.44401e13 | −0.217240 | ||||||||
\(647\) | 8.79654e13 | − | 8.79654e13i | 0.775873 | − | 0.775873i | −0.203253 | − | 0.979126i | \(-0.565151\pi\) |
0.979126 | + | 0.203253i | \(0.0651515\pi\) | |||||||
\(648\) | −9.06059e13 | − | 9.06059e13i | −0.793015 | − | 0.793015i | ||||
\(649\) | 4.94986e12i | 0.0429902i | ||||||||
\(650\) | 9.39979e13 | − | 1.16991e12i | 0.810123 | − | 0.0100829i | ||||
\(651\) | −4.06390e13 | −0.347567 | ||||||||
\(652\) | −7.56142e13 | + | 7.56142e13i | −0.641749 | + | 0.641749i | ||||
\(653\) | −1.01299e14 | − | 1.01299e14i | −0.853173 | − | 0.853173i | 0.137349 | − | 0.990523i | \(-0.456142\pi\) |
−0.990523 | + | 0.137349i | \(0.956142\pi\) | |||||||
\(654\) | − | 2.79957e14i | − | 2.33993i | ||||||
\(655\) | 1.95113e14 | − | 1.21415e12i | 1.61838 | − | 0.0100708i | ||||
\(656\) | 3.47240e13 | 0.285832 | ||||||||
\(657\) | 9.08993e13 | − | 9.08993e13i | 0.742563 | − | 0.742563i | ||||
\(658\) | −2.50451e12 | − | 2.50451e12i | −0.0203045 | − | 0.0203045i | ||||
\(659\) | 4.67893e11i | 0.00376461i | 0.999998 | + | 0.00188230i | \(0.000599156\pi\) | ||||
−0.999998 | + | 0.00188230i | \(0.999401\pi\) | |||||||
\(660\) | −3.70588e13 | + | 3.75230e13i | −0.295919 | + | 0.299624i | ||||
\(661\) | −1.34088e13 | −0.106263 | −0.0531317 | − | 0.998588i | \(-0.516920\pi\) | ||||
−0.0531317 | + | 0.998588i | \(0.516920\pi\) | |||||||
\(662\) | −1.03766e13 | + | 1.03766e13i | −0.0816144 | + | 0.0816144i | ||||
\(663\) | −2.19055e14 | − | 2.19055e14i | −1.70996 | − | 1.70996i | ||||
\(664\) | − | 4.53285e13i | − | 0.351181i | ||||||
\(665\) | −3.24215e12 | − | 3.20205e12i | −0.0249302 | − | 0.0246218i | ||||
\(666\) | −1.24519e14 | −0.950312 | ||||||||
\(667\) | 3.76974e13 | − | 3.76974e13i | 0.285550 | − | 0.285550i | ||||
\(668\) | −6.32856e13 | − | 6.32856e13i | −0.475798 | − | 0.475798i | ||||
\(669\) | 4.65347e14i | 3.47253i | ||||||||
\(670\) | 4.97096e11 | + | 7.98829e13i | 0.00368185 | + | 0.591670i | ||||
\(671\) | −4.56311e13 | −0.335466 | ||||||||
\(672\) | −4.12341e12 | + | 4.12341e12i | −0.0300891 | + | 0.0300891i | ||||
\(673\) | −1.01893e14 | − | 1.01893e14i | −0.738024 | − | 0.738024i | 0.234171 | − | 0.972195i | \(-0.424762\pi\) |
−0.972195 | + | 0.234171i | \(0.924762\pi\) | |||||||
\(674\) | − | 1.97397e13i | − | 0.141919i | ||||||
\(675\) | −2.97683e14 | + | 3.05186e14i | −2.12439 | + | 2.17794i | ||||
\(676\) | 2.20788e13 | 0.156402 | ||||||||
\(677\) | −5.83118e13 | + | 5.83118e13i | −0.410028 | + | 0.410028i | −0.881748 | − | 0.471720i | \(-0.843633\pi\) |
0.471720 | + | 0.881748i | \(0.343633\pi\) | |||||||
\(678\) | 2.29241e14 | + | 2.29241e14i | 1.60009 | + | 1.60009i | ||||
\(679\) | − | 1.12124e13i | − | 0.0776875i | ||||||
\(680\) | 5.71568e13 | − | 3.55676e11i | 0.393118 | − | 0.00244630i | ||||
\(681\) | 4.67016e14 | 3.18857 | ||||||||
\(682\) | 4.72653e13 | − | 4.72653e13i | 0.320347 | − | 0.320347i | ||||
\(683\) | −6.32645e13 | − | 6.32645e13i | −0.425654 | − | 0.425654i | 0.461491 | − | 0.887145i | \(-0.347315\pi\) |
−0.887145 | + | 0.461491i | \(0.847315\pi\) | |||||||
\(684\) | 5.38371e13i | 0.359585i | ||||||||
\(685\) | 5.28199e13 | − | 5.34813e13i | 0.350223 | − | 0.354609i | ||||
\(686\) | 2.70274e13 | 0.177903 | ||||||||
\(687\) | −8.89016e13 | + | 8.89016e13i | −0.580933 | + | 0.580933i | ||||
\(688\) | 6.46268e12 | + | 6.46268e12i | 0.0419247 | + | 0.0419247i | ||||
\(689\) | 1.82579e14i | 1.17586i | ||||||||
\(690\) | −5.00780e13 | − | 4.94586e13i | −0.320186 | − | 0.316225i | ||||
\(691\) | 1.47937e14 | 0.939047 | 0.469524 | − | 0.882920i | \(-0.344426\pi\) | ||||
0.469524 | + | 0.882920i | \(0.344426\pi\) | |||||||
\(692\) | −9.22441e12 | + | 9.22441e12i | −0.0581311 | + | 0.0581311i | ||||
\(693\) | 1.65536e13 | + | 1.65536e13i | 0.103568 | + | 0.103568i | ||||
\(694\) | − | 1.79188e14i | − | 1.11304i | ||||||
\(695\) | 2.16984e10 | + | 3.48692e12i | 0.000133815 | + | 0.0215039i | ||||
\(696\) | 1.32008e14 | 0.808267 | ||||||||
\(697\) | −1.47875e14 | + | 1.47875e14i | −0.898943 | + | 0.898943i | ||||
\(698\) | −1.06612e14 | − | 1.06612e14i | −0.643474 | − | 0.643474i | ||||
\(699\) | − | 2.01272e14i | − | 1.20614i | ||||||
\(700\) | 7.62885e12 | + | 7.44129e12i | 0.0453909 | + | 0.0442749i | ||||
\(701\) | 1.82732e13 | 0.107951 | 0.0539753 | − | 0.998542i | \(-0.482811\pi\) | ||||
0.0539753 | + | 0.998542i | \(0.482811\pi\) | |||||||
\(702\) | −2.97151e14 | + | 2.97151e14i | −1.74298 | + | 1.74298i | ||||
\(703\) | 1.73208e13 | + | 1.73208e13i | 0.100877 | + | 0.100877i | ||||
\(704\) | − | 9.59148e12i | − | 0.0554654i | ||||||
\(705\) | 1.05854e14 | − | 6.58711e11i | 0.607803 | − | 0.00378224i | ||||
\(706\) | −1.38965e14 | −0.792284 | ||||||||
\(707\) | 1.89304e13 | − | 1.89304e13i | 0.107167 | − | 0.107167i | ||||
\(708\) | −1.15665e13 | − | 1.15665e13i | −0.0650184 | − | 0.0650184i | ||||
\(709\) | − | 3.45145e14i | − | 1.92650i | −0.268598 | − | 0.963252i | \(-0.586560\pi\) | ||
0.268598 | − | 0.963252i | \(-0.413440\pi\) | |||||||
\(710\) | 2.01928e13 | − | 2.04457e13i | 0.111919 | − | 0.113321i | ||||
\(711\) | −1.07269e14 | −0.590372 | ||||||||
\(712\) | −2.68924e13 | + | 2.68924e13i | −0.146970 | + | 0.146970i | ||||
\(713\) | 6.30802e13 | + | 6.30802e13i | 0.342330 | + | 0.342330i | ||||
\(714\) | − | 3.51199e13i | − | 0.189261i | ||||||
\(715\) | 6.75948e13 | + | 6.67587e13i | 0.361729 | + | 0.357254i | ||||
\(716\) | 1.61347e14 | 0.857423 | ||||||||
\(717\) | 4.95634e13 | − | 4.95634e13i | 0.261556 | − | 0.261556i | ||||
\(718\) | −7.19372e13 | − | 7.19372e13i | −0.376991 | − | 0.376991i | ||||
\(719\) | 1.61283e14i | 0.839354i | 0.907673 | + | 0.419677i | \(0.137857\pi\) | ||||
−0.907673 | + | 0.419677i | \(0.862143\pi\) | |||||||
\(720\) | −7.83489e11 | − | 1.25906e14i | −0.00404921 | − | 0.650705i | ||||
\(721\) | −6.63443e12 | −0.0340508 | ||||||||
\(722\) | −9.06082e13 | + | 9.06082e13i | −0.461830 | + | 0.461830i | ||||
\(723\) | −5.49178e13 | − | 5.49178e13i | −0.277985 | − | 0.277985i | ||||
\(724\) | 1.06709e14i | 0.536425i | ||||||||
\(725\) | −3.00238e12 | − | 2.41230e14i | −0.0149891 | − | 1.20432i | ||||
\(726\) | 2.17404e14 | 1.07791 | ||||||||
\(727\) | −4.18604e13 | + | 4.18604e13i | −0.206125 | + | 0.206125i | −0.802618 | − | 0.596493i | \(-0.796560\pi\) |
0.596493 | + | 0.802618i | \(0.296560\pi\) | |||||||
\(728\) | 7.42801e12 | + | 7.42801e12i | 0.0363258 | + | 0.0363258i | ||||
\(729\) | − | 5.10925e14i | − | 2.48153i | ||||||
\(730\) | 5.91408e13 | − | 3.68022e11i | 0.285281 | − | 0.00177525i | ||||
\(731\) | −5.50438e13 | −0.263707 | ||||||||
\(732\) | 1.06628e14 | − | 1.06628e14i | 0.507359 | − | 0.507359i | ||||
\(733\) | −6.68708e13 | − | 6.68708e13i | −0.316022 | − | 0.316022i | 0.531215 | − | 0.847237i | \(-0.321736\pi\) |
−0.847237 | + | 0.531215i | \(0.821736\pi\) | |||||||
\(734\) | 7.21359e13i | 0.338587i | ||||||||
\(735\) | −2.81504e14 | + | 2.85030e14i | −1.31235 | + | 1.32878i | ||||
\(736\) | 1.28008e13 | 0.0592716 | ||||||||
\(737\) | −5.70871e13 | + | 5.70871e13i | −0.262543 | + | 0.262543i | ||||
\(738\) | 3.25743e14 | + | 3.25743e14i | 1.48797 | + | 1.48797i | ||||
\(739\) | 2.11418e14i | 0.959223i | 0.877481 | + | 0.479612i | \(0.159222\pi\) | ||||
−0.877481 | + | 0.479612i | \(0.840778\pi\) | |||||||
\(740\) | −4.07594e13 | − | 4.02553e13i | −0.183683 | − | 0.181411i | ||||
\(741\) | 1.34244e14 | 0.600901 | ||||||||
\(742\) | −1.46359e13 | + | 1.46359e13i | −0.0650730 | + | 0.0650730i | ||||
\(743\) | 1.26357e14 | + | 1.26357e14i | 0.558028 | + | 0.558028i | 0.928746 | − | 0.370717i | \(-0.120888\pi\) |
−0.370717 | + | 0.928746i | \(0.620888\pi\) | |||||||
\(744\) | 2.20893e14i | 0.968987i | ||||||||
\(745\) | −5.28118e11 | − | 8.48681e13i | −0.00230117 | − | 0.369797i | ||||
\(746\) | 2.19077e14 | 0.948205 | ||||||||
\(747\) | 4.25223e14 | − | 4.25223e14i | 1.82816 | − | 1.82816i | ||||
\(748\) | 4.08462e13 | + | 4.08462e13i | 0.174439 | + | 0.174439i | ||||
\(749\) | − | 3.45128e13i | − | 0.146410i | ||||||
\(750\) | −3.18449e14 | + | 5.94555e12i | −1.34194 | + | 0.0250545i | ||||
\(751\) | −4.63669e14 | −1.94092 | −0.970461 | − | 0.241258i | \(-0.922440\pi\) | ||||
−0.970461 | + | 0.241258i | \(0.922440\pi\) | |||||||
\(752\) | −1.36132e13 | + | 1.36132e13i | −0.0566073 | + | 0.0566073i | ||||
\(753\) | −4.98876e14 | − | 4.98876e14i | −2.06071 | − | 2.06071i | ||||
\(754\) | − | 2.37803e14i | − | 0.975799i | ||||||
\(755\) | 1.40501e13 | − | 8.74312e10i | 0.0572724 | − | 0.000356395i | ||||
\(756\) | −4.76406e13 | −0.192916 | ||||||||
\(757\) | 6.74662e12 | − | 6.74662e12i | 0.0271398 | − | 0.0271398i | −0.693407 | − | 0.720546i | \(-0.743891\pi\) |
0.720546 | + | 0.693407i | \(0.243891\pi\) | |||||||
\(758\) | −2.24841e14 | − | 2.24841e14i | −0.898523 | − | 0.898523i | ||||
\(759\) | − | 7.11324e13i | − | 0.282396i | ||||||
\(760\) | −1.74047e13 | + | 1.76227e13i | −0.0686435 | + | 0.0695031i | ||||
\(761\) | 1.52599e14 | 0.597900 | 0.298950 | − | 0.954269i | \(-0.403364\pi\) | ||||
0.298950 | + | 0.954269i | \(0.403364\pi\) | |||||||
\(762\) | 2.25961e14 | − | 2.25961e14i | 0.879546 | − | 0.879546i | ||||
\(763\) | −4.04275e13 | − | 4.04275e13i | −0.156334 | − | 0.156334i | ||||
\(764\) | 1.53756e13i | 0.0590699i | ||||||||
\(765\) | 5.39519e14 | + | 5.32846e14i | 2.05921 | + | 2.03374i | ||||
\(766\) | 9.00759e13 | 0.341558 | ||||||||
\(767\) | −2.08362e13 | + | 2.08362e13i | −0.0784950 | + | 0.0784950i | ||||
\(768\) | 2.24128e13 | + | 2.24128e13i | 0.0838860 | + | 0.0838860i | ||||
\(769\) | 3.85474e14i | 1.43338i | 0.697389 | + | 0.716692i | \(0.254345\pi\) | ||||
−0.697389 | + | 0.716692i | \(0.745655\pi\) | |||||||
\(770\) | 6.70200e10 | + | 1.07701e13i | 0.000247600 | + | 0.0397891i | ||||
\(771\) | −5.31823e14 | −1.95207 | ||||||||
\(772\) | −1.59886e13 | + | 1.59886e13i | −0.0583076 | + | 0.0583076i | ||||
\(773\) | 2.19032e14 | + | 2.19032e14i | 0.793616 | + | 0.793616i | 0.982080 | − | 0.188464i | \(-0.0603510\pi\) |
−0.188464 | + | 0.982080i | \(0.560351\pi\) | |||||||
\(774\) | 1.21252e14i | 0.436498i | ||||||||
\(775\) | 4.03658e14 | − | 5.02396e12i | 1.44379 | − | 0.0179696i | ||||
\(776\) | −6.09452e13 | −0.216586 | ||||||||
\(777\) | −2.48896e13 | + | 2.48896e13i | −0.0878848 | + | 0.0878848i | ||||
\(778\) | 2.24183e13 | + | 2.24183e13i | 0.0786509 | + | 0.0786509i | ||||
\(779\) | − | 9.06226e13i | − | 0.315900i | ||||||
\(780\) | −3.13949e14 | + | 1.95364e12i | −1.08739 | + | 0.00676662i | ||||
\(781\) | 2.90416e13 | 0.0999461 | ||||||||
\(782\) | −5.45133e13 | + | 5.45133e13i | −0.186410 | + | 0.186410i | ||||
\(783\) | 7.62591e14 | + | 7.62591e14i | 2.59109 | + | 2.59109i | ||||
\(784\) | − | 7.28583e13i | − | 0.245979i | ||||||
\(785\) | −2.53846e14 | + | 2.57025e14i | −0.851574 | + | 0.862238i | ||||
\(786\) | −6.51643e14 | −2.17219 | ||||||||
\(787\) | −3.33654e14 | + | 3.33654e14i | −1.10515 | + | 1.10515i | −0.111375 | + | 0.993778i | \(0.535525\pi\) |
−0.993778 | + | 0.111375i | \(0.964475\pi\) | |||||||
\(788\) | −3.75990e12 | − | 3.75990e12i | −0.0123750 | − | 0.0123750i | ||||
\(789\) | 3.21876e14i | 1.05270i | ||||||||
\(790\) | −3.51127e13 | − | 3.46784e13i | −0.114111 | − | 0.112700i | ||||
\(791\) | 6.62076e13 | 0.213809 | ||||||||
\(792\) | 8.99768e13 | − | 8.99768e13i | 0.288739 | − | 0.288739i | ||||
\(793\) | −1.92082e14 | − | 1.92082e14i | −0.612521 | − | 0.612521i | ||||
\(794\) | 2.54057e14i | 0.805061i | ||||||||
\(795\) | −3.84940e12 | − | 6.18595e14i | −0.0121215 | − | 1.94792i | ||||
\(796\) | 1.30931e14 | 0.409712 | ||||||||
\(797\) | 3.59536e14 | − | 3.59536e14i | 1.11802 | − | 1.11802i | 0.125993 | − | 0.992031i | \(-0.459788\pi\) |
0.992031 | − | 0.125993i | \(-0.0402118\pi\) | |||||||
\(798\) | 1.07613e13 | + | 1.07613e13i | 0.0332543 | + | 0.0332543i | ||||
\(799\) | − | 1.15947e14i | − | 0.356061i | ||||||
\(800\) | 4.04471e13 | − | 4.14666e13i | 0.123435 | − | 0.126546i | ||||
\(801\) | −5.04550e14 | −1.53018 | ||||||||
\(802\) | −5.47250e13 | + | 5.47250e13i | −0.164936 | + | 0.164936i | ||||
\(803\) | 4.22640e13 | + | 4.22640e13i | 0.126588 | + | 0.126588i | ||||
\(804\) | − | 2.66795e14i | − | 0.794141i | ||||||
\(805\) | −1.43737e13 | + | 8.94447e10i | −0.0425196 | + | 0.000264591i | ||||
\(806\) | 3.97923e14 | 1.16983 | ||||||||
\(807\) | 3.21805e14 | − | 3.21805e14i | 0.940210 | − | 0.940210i | ||||
\(808\) | −1.02896e14 | − | 1.02896e14i | −0.298773 | − | 0.298773i | ||||
\(809\) | 3.41953e14i | 0.986789i | 0.869806 | + | 0.493394i | \(0.164244\pi\) | ||||
−0.869806 | + | 0.493394i | \(0.835756\pi\) | |||||||
\(810\) | 5.49563e14 | − | 5.56445e14i | 1.57613 | − | 1.59587i | ||||
\(811\) | −4.43760e14 | −1.26486 | −0.632431 | − | 0.774616i | \(-0.717943\pi\) | ||||
−0.632431 | + | 0.774616i | \(0.717943\pi\) | |||||||
\(812\) | 1.90628e13 | − | 1.90628e13i | 0.0540015 | − | 0.0540015i | ||||
\(813\) | −2.65517e14 | − | 2.65517e14i | −0.747548 | − | 0.747548i | ||||
\(814\) | − | 5.78959e13i | − | 0.162004i | ||||||
\(815\) | −4.64375e14 | − | 4.58631e14i | −1.29146 | − | 1.27549i | ||||
\(816\) | −1.90894e14 | −0.527644 | ||||||||
\(817\) | 1.68663e13 | − | 1.68663e13i | 0.0463349 | − | 0.0463349i | ||||
\(818\) | −1.06762e14 | − | 1.06762e14i | −0.291508 | − | 0.291508i | ||||
\(819\) | 1.39363e14i | 0.378206i | ||||||||
\(820\) | 1.31883e12 | + | 2.11934e14i | 0.00355728 | + | 0.571653i | ||||
\(821\) | 4.33407e14 | 1.16193 | 0.580965 | − | 0.813929i | \(-0.302675\pi\) | ||||
0.580965 | + | 0.813929i | \(0.302675\pi\) | |||||||
\(822\) | −1.77514e14 | + | 1.77514e14i | −0.473013 | + | 0.473013i | ||||
\(823\) | 3.52407e14 | + | 3.52407e14i | 0.933352 | + | 0.933352i | 0.997914 | − | 0.0645613i | \(-0.0205648\pi\) |
−0.0645613 | + | 0.997914i | \(0.520565\pi\) | |||||||
\(824\) | 3.60614e13i | 0.0949307i | ||||||||
\(825\) | −2.30425e14 | − | 2.24760e14i | −0.602920 | − | 0.588097i | ||||
\(826\) | −3.34055e12 | −0.00868796 | ||||||||
\(827\) | 2.80216e14 | − | 2.80216e14i | 0.724379 | − | 0.724379i | −0.245115 | − | 0.969494i | \(-0.578826\pi\) |
0.969494 | + | 0.245115i | \(0.0788258\pi\) | |||||||
\(828\) | 1.20083e14 | + | 1.20083e14i | 0.308553 | + | 0.308553i | ||||
\(829\) | − | 5.19271e14i | − | 1.32624i | −0.748514 | − | 0.663119i | \(-0.769232\pi\) | ||
0.748514 | − | 0.663119i | \(-0.230768\pi\) | |||||||
\(830\) | 2.76658e14 | − | 1.72159e12i | 0.702349 | − | 0.00437058i | ||||
\(831\) | 1.17397e15 | 2.96246 | ||||||||
\(832\) | 4.03749e13 | − | 4.03749e13i | 0.101273 | − | 0.101273i | ||||
\(833\) | 3.10274e14 | + | 3.10274e14i | 0.773607 | + | 0.773607i | ||||
\(834\) | − | 1.16457e13i | − | 0.0288626i | ||||||
\(835\) | 3.83853e14 | − | 3.88661e14i | 0.945656 | − | 0.957499i | ||||
\(836\) | −2.50318e13 | −0.0613001 | ||||||||
\(837\) | −1.27607e15 | + | 1.27607e15i | −3.10632 | + | 3.10632i | ||||
\(838\) | 3.27219e14 | + | 3.27219e14i | 0.791804 | + | 0.791804i | ||||
\(839\) | − | 4.00090e14i | − | 0.962384i | −0.876615 | − | 0.481192i | \(-0.840204\pi\) | ||
0.876615 | − | 0.481192i | \(-0.159796\pi\) | |||||||
\(840\) | −2.53234e13 | − | 2.50102e13i | −0.0605516 | − | 0.0598027i | ||||
\(841\) | −1.89575e14 | −0.450611 | ||||||||
\(842\) | −2.45848e14 | + | 2.45848e14i | −0.580906 | + | 0.580906i | ||||
\(843\) | −7.40052e14 | − | 7.40052e14i | −1.73830 | − | 1.73830i | ||||
\(844\) | − | 2.82782e14i | − | 0.660297i | ||||||
\(845\) | 8.38557e11 | + | 1.34755e14i | 0.00194648 | + | 0.312797i | ||||
\(846\) | −2.55409e14 | −0.589365 | ||||||||
\(847\) | 3.13944e13 | − | 3.13944e13i | 0.0720171 | − | 0.0720171i | ||||
\(848\) | 7.95535e13 | + | 7.95535e13i | 0.181418 | + | 0.181418i | ||||
\(849\) | 5.27906e14i | 1.19679i | ||||||||
\(850\) | 4.34166e12 | + | 3.48837e14i | 0.00978501 | + | 0.786191i | ||||
\(851\) | 7.72678e13 | 0.173121 | ||||||||
\(852\) | −6.78627e13 | + | 6.78627e13i | −0.151159 | + | 0.151159i | ||||
\(853\) | 2.04891e13 | + | 2.04891e13i | 0.0453709 | + | 0.0453709i | 0.729428 | − | 0.684057i | \(-0.239786\pi\) |
−0.684057 | + | 0.729428i | \(0.739786\pi\) | |||||||
\(854\) | − | 3.07954e13i | − | 0.0677948i | ||||||
\(855\) | −3.28589e14 | + | 2.04475e12i | −0.719155 | + | 0.00447516i | ||||
\(856\) | −1.87594e14 | −0.408179 | ||||||||
\(857\) | 2.95150e14 | − | 2.95150e14i | 0.638467 | − | 0.638467i | −0.311711 | − | 0.950177i | \(-0.600902\pi\) |
0.950177 | + | 0.311711i | \(0.100902\pi\) | |||||||
\(858\) | −2.24359e14 | − | 2.24359e14i | −0.482510 | − | 0.482510i | ||||
\(859\) | 3.11199e14i | 0.665384i | 0.943036 | + | 0.332692i | \(0.107957\pi\) | ||||
−0.943036 | + | 0.332692i | \(0.892043\pi\) | |||||||
\(860\) | −3.91988e13 | + | 3.96897e13i | −0.0833260 | + | 0.0843696i | ||||
\(861\) | 1.30223e14 | 0.275214 | ||||||||
\(862\) | 2.84047e14 | − | 2.84047e14i | 0.596834 | − | 0.596834i | ||||
\(863\) | 1.34806e14 | + | 1.34806e14i | 0.281614 | + | 0.281614i | 0.833752 | − | 0.552138i | \(-0.186188\pi\) |
−0.552138 | + | 0.833752i | \(0.686188\pi\) | |||||||
\(864\) | 2.58950e14i | 0.537833i | ||||||||
\(865\) | −5.66506e13 | − | 5.59499e13i | −0.116983 | − | 0.115536i | ||||
\(866\) | 1.43648e13 | 0.0294924 | ||||||||
\(867\) | 1.55426e14 | − | 1.55426e14i | 0.317269 | − | 0.317269i | ||||
\(868\) | 3.18983e13 | + | 3.18983e13i | 0.0647395 | + | 0.0647395i | ||||
\(869\) | − | 4.98752e13i | − | 0.100643i | ||||||
\(870\) | 5.01371e12 | + | 8.05699e14i | 0.0100592 | + | 1.61650i | ||||
\(871\) | −4.80611e14 | −0.958745 | ||||||||
\(872\) | −2.19743e14 | + | 2.19743e14i | −0.435847 | + | 0.435847i | ||||
\(873\) | −5.71721e14 | − | 5.71721e14i | −1.12749 | − | 1.12749i | ||||
\(874\) | − | 3.34074e13i | − | 0.0655067i | ||||||
\(875\) | −4.51274e13 | + | 4.68445e13i | −0.0879832 | + | 0.0913311i | ||||
\(876\) | −1.97520e14 | −0.382904 | ||||||||
\(877\) | 8.27935e13 | − | 8.27935e13i | 0.159587 | − | 0.159587i | −0.622797 | − | 0.782384i | \(-0.714004\pi\) |
0.782384 | + | 0.622797i | \(0.214004\pi\) | |||||||
\(878\) | −1.50352e14 | − | 1.50352e14i | −0.288162 | − | 0.288162i | ||||
\(879\) | 1.09774e15i | 2.09196i | ||||||||
\(880\) | 5.85406e13 | − | 3.64287e11i | 0.110929 | − | 0.000690288i | ||||
\(881\) | 2.97854e14 | 0.561208 | 0.280604 | − | 0.959824i | \(-0.409465\pi\) | ||||
0.280604 | + | 0.959824i | \(0.409465\pi\) | |||||||
\(882\) | 6.83477e14 | − | 6.83477e14i | 1.28050 | − | 1.28050i | ||||
\(883\) | 1.59243e14 | + | 1.59243e14i | 0.296658 | + | 0.296658i | 0.839704 | − | 0.543045i | \(-0.182729\pi\) |
−0.543045 | + | 0.839704i | \(0.682729\pi\) | |||||||
\(884\) | 3.43881e14i | 0.637010i | ||||||||
\(885\) | 7.01558e13 | − | 7.10344e13i | 0.129225 | − | 0.130844i | ||||
\(886\) | 1.33404e14 | 0.244343 | ||||||||
\(887\) | −1.95156e14 | + | 1.95156e14i | −0.355437 | + | 0.355437i | −0.862128 | − | 0.506691i | \(-0.830869\pi\) |
0.506691 | + | 0.862128i | \(0.330869\pi\) | |||||||
\(888\) | 1.35288e14 | + | 1.35288e14i | 0.245015 | + | 0.245015i | ||||
\(889\) | − | 6.52602e13i | − | 0.117528i | ||||||
\(890\) | −1.65156e14 | − | 1.63113e14i | −0.295764 | − | 0.292105i | ||||
\(891\) | 7.90392e14 | 1.40752 | ||||||||
\(892\) | 3.65259e14 | − | 3.65259e14i | 0.646811 | − | 0.646811i | ||||
\(893\) | 3.55278e13 | + | 3.55278e13i | 0.0625620 | + | 0.0625620i | ||||
\(894\) | 2.83445e14i | 0.496342i | ||||||||
\(895\) | 6.12799e12 | + | 9.84763e14i | 0.0106709 | + | 1.71481i | ||||
\(896\) | 6.47308e12 | 0.0112091 | ||||||||
\(897\) | 2.99429e14 | − | 2.99429e14i | 0.515621 | − | 0.515621i | ||||
\(898\) | 1.43771e14 | + | 1.43771e14i | 0.246201 | + | 0.246201i | ||||
\(899\) | − | 1.02120e15i | − | 1.73906i | ||||||
\(900\) | 7.68425e14 | − | 9.56389e12i | 1.30133 | − | 0.0161965i | ||||
\(901\) | −6.77573e14 | −1.14112 | ||||||||
\(902\) | −1.51456e14 | + | 1.51456e14i | −0.253661 | + | 0.253661i | ||||
\(903\) | 2.42364e13 | + | 2.42364e13i | 0.0403673 | + | 0.0403673i | ||||
\(904\) | − | 3.59871e14i | − | 0.596081i | ||||||
\(905\) | −6.51289e14 | + | 4.05284e12i | −1.07283 | + | 0.00667601i | ||||
\(906\) | −4.69250e13 | −0.0768711 | ||||||||
\(907\) | −2.14673e14 | + | 2.14673e14i | −0.349737 | + | 0.349737i | −0.860011 | − | 0.510275i | \(-0.829544\pi\) |
0.510275 | + | 0.860011i | \(0.329544\pi\) | |||||||
\(908\) | −3.66569e14 | − | 3.66569e14i | −0.593918 | − | 0.593918i | ||||
\(909\) | − | 1.93052e15i | − | 3.11067i | ||||||
\(910\) | −4.50540e13 | + | 4.56182e13i | −0.0721981 | + | 0.0731023i | ||||
\(911\) | −1.02617e15 | −1.63542 | −0.817709 | − | 0.575631i | \(-0.804756\pi\) | ||||
−0.817709 | + | 0.575631i | \(0.804756\pi\) | |||||||
\(912\) | 5.84927e13 | − | 5.84927e13i | 0.0927103 | − | 0.0927103i | ||||
\(913\) | 1.97709e14 | + | 1.97709e14i | 0.311655 | + | 0.311655i | ||||
\(914\) | 1.76966e14i | 0.277433i | ||||||||
\(915\) | 6.54842e14 | + | 6.46742e14i | 1.02101 | + | 1.00838i | ||||
\(916\) | 1.39561e14 | 0.216415 | ||||||||
\(917\) | −9.41012e13 | + | 9.41012e13i | −0.145127 | + | 0.145127i | ||||
\(918\) | −1.10276e15 | − | 1.10276e15i | −1.69149 | − | 1.69149i | ||||
\(919\) | − | 1.06960e15i | − | 1.63172i | −0.578250 | − | 0.815859i | \(-0.696264\pi\) | ||
0.578250 | − | 0.815859i | \(-0.303736\pi\) | |||||||
\(920\) | 4.86176e11 | + | 7.81282e13i | 0.000737657 | + | 0.118541i | ||||
\(921\) | 1.95072e15 | 2.94372 | ||||||||
\(922\) | −2.60650e14 | + | 2.60650e14i | −0.391203 | + | 0.391203i | ||||
\(923\) | 1.22249e14 | + | 1.22249e14i | 0.182490 | + | 0.182490i | ||||
\(924\) | − | 3.59701e13i | − | 0.0534050i | ||||||
\(925\) | 2.44146e14 | − | 2.50300e14i | 0.360530 | − | 0.369617i | ||||
\(926\) | −2.45990e14 | −0.361295 | ||||||||
\(927\) | −3.38289e14 | + | 3.38289e14i | −0.494185 | + | 0.494185i | ||||
\(928\) | −1.03616e14 | − | 1.03616e14i | −0.150552 | − | 0.150552i | ||||
\(929\) | 1.65091e14i | 0.238585i | 0.992859 | + | 0.119293i | \(0.0380627\pi\) | ||||
−0.992859 | + | 0.119293i | \(0.961937\pi\) | |||||||
\(930\) | −1.34820e15 | + | 8.38959e12i | −1.93794 | + | 0.0120594i | ||||
\(931\) | −1.90145e14 | −0.271855 | ||||||||
\(932\) | −1.57982e14 | + | 1.57982e14i | −0.224662 | + | 0.224662i | ||||
\(933\) | 9.90295e14 | + | 9.90295e14i | 1.40074 | + | 1.40074i | ||||
\(934\) | − | 6.23940e14i | − | 0.877826i | ||||||
\(935\) | −2.47749e14 | + | 2.50852e14i | −0.346701 | + | 0.351043i | ||||
\(936\) | 7.57507e14 | 1.05440 | ||||||||
\(937\) | −4.68468e14 | + | 4.68468e14i | −0.648608 | + | 0.648608i | −0.952657 | − | 0.304049i | \(-0.901662\pi\) |
0.304049 | + | 0.952657i | \(0.401662\pi\) | |||||||
\(938\) | −3.85268e13 | − | 3.85268e13i | −0.0530577 | − | 0.0530577i | ||||
\(939\) | 5.84755e14i | 0.801025i | ||||||||
\(940\) | −8.36040e13 | − | 8.25699e13i | −0.113917 | − | 0.112508i | ||||
\(941\) | −4.34456e14 | −0.588840 | −0.294420 | − | 0.955676i | \(-0.595126\pi\) | ||||
−0.294420 | + | 0.955676i | \(0.595126\pi\) | |||||||
\(942\) | 8.53111e14 | − | 8.53111e14i | 1.15014 | − | 1.15014i | ||||
\(943\) | −2.02132e14 | − | 2.02132e14i | −0.271068 | − | 0.271068i | ||||
\(944\) | 1.81575e13i | 0.0242213i | ||||||||
\(945\) | −1.80940e12 | − | 2.90769e14i | −0.00240091 | − | 0.385824i | ||||
\(946\) | −5.63765e13 | −0.0744119 | ||||||||
\(947\) | −3.62573e14 | + | 3.62573e14i | −0.476043 | + | 0.476043i | −0.903864 | − | 0.427821i | \(-0.859281\pi\) |
0.427821 | + | 0.903864i | \(0.359281\pi\) | |||||||
\(948\) | 1.16545e14 | + | 1.16545e14i | 0.152213 | + | 0.152213i | ||||
\(949\) | 3.55817e14i | 0.462270i | ||||||||
\(950\) | −1.08219e14 | − | 1.05559e14i | −0.139858 | − | 0.136419i | ||||
\(951\) | 2.13697e15 | 2.74724 | ||||||||
\(952\) | −2.75662e13 | + | 2.75662e13i | −0.0352527 | + | 0.0352527i | ||||
\(953\) | 7.02985e14 | + | 7.02985e14i | 0.894297 | + | 0.894297i | 0.994924 | − | 0.100627i | \(-0.0320849\pi\) |
−0.100627 | + | 0.994924i | \(0.532085\pi\) | |||||||
\(954\) | 1.49257e15i | 1.88883i | ||||||||
\(955\) | −9.38436e13 | + | 5.83971e11i | −0.118138 | + | 0.000735147i | ||||
\(956\) | −7.78064e13 | −0.0974375 | ||||||||
\(957\) | −5.75780e14 | + | 5.75780e14i | −0.717294 | + | 0.717294i | ||||
\(958\) | 5.89381e14 | + | 5.89381e14i | 0.730413 | + | 0.730413i | ||||
\(959\) | 5.12681e13i | 0.0632054i | ||||||||
\(960\) | −1.35943e14 | + | 1.37645e14i | −0.166725 | + | 0.168813i | ||||
\(961\) | 8.89183e14 | 1.08486 | ||||||||
\(962\) | 2.43710e14 | − | 2.43710e14i | 0.295800 | − | 0.295800i | ||||
\(963\) | −1.75980e15 | − | 1.75980e15i | −2.12487 | − | 2.12487i | ||||
\(964\) | 8.62120e13i | 0.103558i | ||||||||
\(965\) | −9.81923e13 | − | 9.69778e13i | −0.117339 | − | 0.115887i | ||||
\(966\) | 4.80057e13 | 0.0570699 | ||||||||
\(967\) | −4.96692e14 | + | 4.96692e14i | −0.587428 | + | 0.587428i | −0.936934 | − | 0.349506i | \(-0.886349\pi\) |
0.349506 | + | 0.936934i | \(0.386349\pi\) | |||||||
\(968\) | −1.70644e14 | − | 1.70644e14i | −0.200777 | − | 0.200777i | ||||
\(969\) | 4.98194e14i | 0.583149i | ||||||||
\(970\) | −2.31471e12 | − | 3.71973e14i | −0.00269550 | − | 0.433164i | ||||
\(971\) | −8.90045e14 | −1.03114 | −0.515568 | − | 0.856849i | \(-0.672419\pi\) | ||||
−0.515568 | + | 0.856849i | \(0.672419\pi\) | |||||||
\(972\) | −9.13664e14 | + | 9.13664e14i | −1.05307 | + | 1.05307i | ||||
\(973\) | −1.68171e12 | − | 1.68171e12i | −0.00192835 | − | 0.00192835i | ||||
\(974\) | − | 4.81348e14i | − | 0.549116i | ||||||
\(975\) | −2.38477e13 | − | 1.91608e15i | −0.0270660 | − | 2.17466i | ||||
\(976\) | −1.67388e14 | −0.189006 | ||||||||
\(977\) | 5.13225e14 | − | 5.13225e14i | 0.576548 | − | 0.576548i | −0.357403 | − | 0.933950i | \(-0.616338\pi\) |
0.933950 | + | 0.357403i | \(0.116338\pi\) | |||||||
\(978\) | 1.54134e15 | + | 1.54134e15i | 1.72268 | + | 1.72268i | ||||
\(979\) | − | 2.34593e14i | − | 0.260856i | ||||||
\(980\) | 4.44683e14 | − | 2.76718e12i | 0.491949 | − | 0.00306130i | ||||
\(981\) | −4.12279e15 | −4.53781 | ||||||||
\(982\) | 3.45813e14 | − | 3.45813e14i | 0.378690 | − | 0.378690i | ||||
\(983\) | 3.69731e14 | + | 3.69731e14i | 0.402827 | + | 0.402827i | 0.879228 | − | 0.476401i | \(-0.158059\pi\) |
−0.476401 | + | 0.879228i | \(0.658059\pi\) | |||||||
\(984\) | − | 7.07824e14i | − | 0.767273i | ||||||
\(985\) | 2.28053e13 | − | 2.30909e13i | 0.0245955 | − | 0.0249035i | ||||
\(986\) | 8.82514e14 | 0.946972 | ||||||||
\(987\) | −5.10526e13 | + | 5.10526e13i | −0.0545045 | + | 0.0545045i | ||||
\(988\) | −1.05370e14 | − | 1.05370e14i | −0.111927 | − | 0.111927i | ||||
\(989\) | − | 7.52399e13i | − | 0.0795183i | ||||||
\(990\) | 5.52582e14 | + | 5.45747e14i | 0.581059 | + | 0.573872i | ||||
\(991\) | 1.22959e15 | 1.28645 | 0.643224 | − | 0.765678i | \(-0.277597\pi\) | ||||
0.643224 | + | 0.765678i | \(0.277597\pi\) | |||||||
\(992\) | 1.73383e14 | − | 1.73383e14i | 0.180488 | − | 0.180488i | ||||
\(993\) | 2.11520e14 | + | 2.11520e14i | 0.219082 | + | 0.219082i | ||||
\(994\) | 1.95996e13i | 0.0201983i | ||||||||
\(995\) | 4.97281e12 | + | 7.99126e14i | 0.00509901 | + | 0.819408i | ||||
\(996\) | −9.23990e14 | −0.942693 | ||||||||
\(997\) | 1.01829e15 | − | 1.01829e15i | 1.03370 | − | 1.03370i | 0.0342927 | − | 0.999412i | \(-0.489082\pi\) |
0.999412 | − | 0.0342927i | \(-0.0109179\pi\) | |||||||
\(998\) | −8.66708e14 | − | 8.66708e14i | −0.875427 | − | 0.875427i | ||||
\(999\) | 1.56307e15i | 1.57091i |
(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 | 10.11.c.c.3.3 | ✓ | 6 | |
3.2 | odd | 2 | 90.11.g.c.73.1 | 6 | |||
4.3 | odd | 2 | 80.11.p.c.33.1 | 6 | |||
5.2 | odd | 4 | inner | 10.11.c.c.7.3 | yes | 6 | |
5.3 | odd | 4 | 50.11.c.e.7.1 | 6 | |||
5.4 | even | 2 | 50.11.c.e.43.1 | 6 | |||
15.2 | even | 4 | 90.11.g.c.37.1 | 6 | |||
20.7 | even | 4 | 80.11.p.c.17.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.11.c.c.3.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
10.11.c.c.7.3 | yes | 6 | 5.2 | odd | 4 | inner | |
50.11.c.e.7.1 | 6 | 5.3 | odd | 4 | |||
50.11.c.e.43.1 | 6 | 5.4 | even | 2 | |||
80.11.p.c.17.1 | 6 | 20.7 | even | 4 | |||
80.11.p.c.33.1 | 6 | 4.3 | odd | 2 | |||
90.11.g.c.37.1 | 6 | 15.2 | even | 4 | |||
90.11.g.c.73.1 | 6 | 3.2 | odd | 2 |