Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,15,Mod(7,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.7");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.9194761782\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} + 9158 x^{12} + 65217 x^{11} + 61148515 x^{10} + 439019974 x^{9} + 189458968156 x^{8} + 1788546506656 x^{7} + 430738312102192 x^{6} + \cdots + 89\!\cdots\!84 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{81}\cdot 3^{41} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 7.9 | ||
Root | \(-30.4205 + 52.6899i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.7 |
Dual form | 12.15.d.a.7.10 |
$q$-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 \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 67.3573 | − | 108.844i | 0.526229 | − | 0.850343i | ||||
\(3\) | 1262.67i | 0.577350i | ||||||||
\(4\) | −7309.99 | − | 14662.9i | −0.446167 | − | 0.894950i | ||||
\(5\) | 30766.3 | 0.393809 | 0.196905 | − | 0.980423i | \(-0.436911\pi\) | ||||
0.196905 | + | 0.980423i | \(0.436911\pi\) | |||||||
\(6\) | 137433. | + | 85049.7i | 0.490946 | + | 0.303818i | ||||
\(7\) | − | 368697.i | − | 0.447696i | −0.974624 | − | 0.223848i | \(-0.928138\pi\) | ||
0.974624 | − | 0.223848i | \(-0.0718620\pi\) | |||||||
\(8\) | −2.08834e6 | − | 192002.i | −0.995800 | − | 0.0915537i | ||||
\(9\) | −1.59432e6 | −0.333333 | ||||||||
\(10\) | 2.07234e6 | − | 3.34873e6i | 0.207234 | − | 0.334873i | ||||
\(11\) | − | 3.40375e7i | − | 1.74666i | −0.487129 | − | 0.873330i | \(-0.661956\pi\) | ||
0.487129 | − | 0.873330i | \(-0.338044\pi\) | |||||||
\(12\) | 1.85143e7 | − | 9.23007e6i | 0.516700 | − | 0.257594i | ||||
\(13\) | −3.66786e7 | −0.584534 | −0.292267 | − | 0.956337i | \(-0.594410\pi\) | ||||
−0.292267 | + | 0.956337i | \(0.594410\pi\) | |||||||
\(14\) | −4.01305e7 | − | 2.48344e7i | −0.380696 | − | 0.235591i | ||||
\(15\) | 3.88476e7i | 0.227366i | ||||||||
\(16\) | −1.61563e8 | + | 2.14371e8i | −0.601871 | + | 0.798594i | ||||
\(17\) | −4.79329e8 | −1.16813 | −0.584065 | − | 0.811707i | \(-0.698539\pi\) | ||||
−0.584065 | + | 0.811707i | \(0.698539\pi\) | |||||||
\(18\) | −1.07389e8 | + | 1.73532e8i | −0.175410 | + | 0.283448i | ||||
\(19\) | − | 3.76963e8i | − | 0.421719i | −0.977516 | − | 0.210860i | \(-0.932374\pi\) | ||
0.977516 | − | 0.210860i | \(-0.0676263\pi\) | |||||||
\(20\) | −2.24902e8 | − | 4.51122e8i | −0.175704 | − | 0.352439i | ||||
\(21\) | 4.65541e8 | 0.258478 | ||||||||
\(22\) | −3.70477e9 | − | 2.29267e9i | −1.48526 | − | 0.919143i | ||||
\(23\) | − | 1.93464e9i | − | 0.568206i | −0.958794 | − | 0.284103i | \(-0.908304\pi\) | ||
0.958794 | − | 0.284103i | \(-0.0916958\pi\) | |||||||
\(24\) | 2.42434e8 | − | 2.63688e9i | 0.0528586 | − | 0.574925i | ||||
\(25\) | −5.15695e9 | −0.844914 | ||||||||
\(26\) | −2.47057e9 | + | 3.99225e9i | −0.307599 | + | 0.497054i | ||||
\(27\) | − | 2.01310e9i | − | 0.192450i | ||||||
\(28\) | −5.40616e9 | + | 2.69517e9i | −0.400666 | + | 0.199747i | ||||
\(29\) | 2.43110e10 | 1.40934 | 0.704671 | − | 0.709534i | \(-0.251095\pi\) | ||||
0.704671 | + | 0.709534i | \(0.251095\pi\) | |||||||
\(30\) | 4.22832e9 | + | 2.61667e9i | 0.193339 | + | 0.119646i | ||||
\(31\) | − | 5.84660e9i | − | 0.212506i | −0.994339 | − | 0.106253i | \(-0.966115\pi\) | ||
0.994339 | − | 0.106253i | \(-0.0338854\pi\) | |||||||
\(32\) | 1.24505e10 | + | 3.20246e10i | 0.362357 | + | 0.932039i | ||||
\(33\) | 4.29779e10 | 1.00843 | ||||||||
\(34\) | −3.22863e10 | + | 5.21720e10i | −0.614703 | + | 0.993311i | ||||
\(35\) | − | 1.13435e10i | − | 0.176307i | ||||||
\(36\) | 1.16545e10 | + | 2.33773e10i | 0.148722 | + | 0.298317i | ||||
\(37\) | 1.15754e11 | 1.21933 | 0.609667 | − | 0.792658i | \(-0.291303\pi\) | ||||
0.609667 | + | 0.792658i | \(0.291303\pi\) | |||||||
\(38\) | −4.10301e10 | − | 2.53912e10i | −0.358606 | − | 0.221921i | ||||
\(39\) | − | 4.63128e10i | − | 0.337481i | ||||||
\(40\) | −6.42507e10 | − | 5.90720e9i | −0.392155 | − | 0.0360547i | ||||
\(41\) | 2.02030e11 | 1.03736 | 0.518678 | − | 0.854970i | \(-0.326424\pi\) | ||||
0.518678 | + | 0.854970i | \(0.326424\pi\) | |||||||
\(42\) | 3.13576e10 | − | 5.06713e10i | 0.136018 | − | 0.219795i | ||||
\(43\) | − | 3.29553e11i | − | 1.21240i | −0.795312 | − | 0.606201i | \(-0.792693\pi\) | ||
0.795312 | − | 0.606201i | \(-0.207307\pi\) | |||||||
\(44\) | −4.99086e11 | + | 2.48814e11i | −1.56317 | + | 0.779301i | ||||
\(45\) | −4.90515e10 | −0.131270 | ||||||||
\(46\) | −2.10574e11 | − | 1.30312e11i | −0.483170 | − | 0.299006i | ||||
\(47\) | 2.44877e11i | 0.483351i | 0.970357 | + | 0.241676i | \(0.0776970\pi\) | ||||
−0.970357 | + | 0.241676i | \(0.922303\pi\) | |||||||
\(48\) | −2.70679e11 | − | 2.04001e11i | −0.461068 | − | 0.347490i | ||||
\(49\) | 5.42285e11 | 0.799568 | ||||||||
\(50\) | −3.47358e11 | + | 5.61302e11i | −0.444618 | + | 0.718467i | ||||
\(51\) | − | 6.05231e11i | − | 0.674420i | ||||||
\(52\) | 2.68121e11 | + | 5.37814e11i | 0.260800 | + | 0.523129i | ||||
\(53\) | −1.47142e12 | −1.25258 | −0.626288 | − | 0.779591i | \(-0.715427\pi\) | ||||
−0.626288 | + | 0.779591i | \(0.715427\pi\) | |||||||
\(54\) | −2.19113e11 | − | 1.35597e11i | −0.163649 | − | 0.101273i | ||||
\(55\) | − | 1.04721e12i | − | 0.687850i | ||||||
\(56\) | −7.07906e10 | + | 7.69967e11i | −0.0409883 | + | 0.445816i | ||||
\(57\) | 4.75978e11 | 0.243480 | ||||||||
\(58\) | 1.63752e12 | − | 2.64610e12i | 0.741636 | − | 1.19842i | ||||
\(59\) | 2.31401e12i | 0.929826i | 0.885356 | + | 0.464913i | \(0.153914\pi\) | ||||
−0.885356 | + | 0.464913i | \(0.846086\pi\) | |||||||
\(60\) | 5.69617e11 | − | 2.83976e11i | 0.203481 | − | 0.101443i | ||||
\(61\) | 7.16981e11 | 0.228139 | 0.114069 | − | 0.993473i | \(-0.463611\pi\) | ||||
0.114069 | + | 0.993473i | \(0.463611\pi\) | |||||||
\(62\) | −6.36367e11 | − | 3.93811e11i | −0.180703 | − | 0.111827i | ||||
\(63\) | 5.87823e11i | 0.149232i | ||||||||
\(64\) | 4.32432e12 | + | 8.01933e11i | 0.983236 | + | 0.182338i | ||||
\(65\) | −1.12847e12 | −0.230195 | ||||||||
\(66\) | 2.89487e12 | − | 4.67788e12i | 0.530667 | − | 0.857515i | ||||
\(67\) | 2.62990e12i | 0.433926i | 0.976180 | + | 0.216963i | \(0.0696151\pi\) | ||||
−0.976180 | + | 0.216963i | \(0.930385\pi\) | |||||||
\(68\) | 3.50389e12 | + | 7.02833e12i | 0.521180 | + | 1.04542i | ||||
\(69\) | 2.44280e12 | 0.328054 | ||||||||
\(70\) | −1.23467e12 | − | 7.64065e11i | −0.149921 | − | 0.0927778i | ||||
\(71\) | 1.80292e13i | 1.98229i | 0.132771 | + | 0.991147i | \(0.457613\pi\) | ||||
−0.132771 | + | 0.991147i | \(0.542387\pi\) | |||||||
\(72\) | 3.32950e12 | + | 3.06113e11i | 0.331933 | + | 0.0305179i | ||||
\(73\) | −1.82099e13 | −1.64834 | −0.824172 | − | 0.566339i | \(-0.808359\pi\) | ||||
−0.824172 | + | 0.566339i | \(0.808359\pi\) | |||||||
\(74\) | 7.79685e12 | − | 1.25991e13i | 0.641648 | − | 1.03685i | ||||
\(75\) | − | 6.51150e12i | − | 0.487812i | ||||||
\(76\) | −5.52735e12 | + | 2.75560e12i | −0.377417 | + | 0.188157i | ||||
\(77\) | −1.25495e13 | −0.781973 | ||||||||
\(78\) | −5.04087e12 | − | 3.11951e12i | −0.286975 | − | 0.177592i | ||||
\(79\) | − | 2.69258e13i | − | 1.40210i | −0.713113 | − | 0.701049i | \(-0.752715\pi\) | ||
0.713113 | − | 0.701049i | \(-0.247285\pi\) | |||||||
\(80\) | −4.97071e12 | + | 6.59540e12i | −0.237022 | + | 0.314493i | ||||
\(81\) | 2.54187e12 | 0.111111 | ||||||||
\(82\) | 1.36082e13 | − | 2.19897e13i | 0.545887 | − | 0.882109i | ||||
\(83\) | − | 1.90822e13i | − | 0.703205i | −0.936149 | − | 0.351602i | \(-0.885637\pi\) | ||
0.936149 | − | 0.351602i | \(-0.114363\pi\) | |||||||
\(84\) | −3.40310e12 | − | 6.82616e12i | −0.115324 | − | 0.231325i | ||||
\(85\) | −1.47472e13 | −0.460020 | ||||||||
\(86\) | −3.58699e13 | − | 2.21978e13i | −1.03096 | − | 0.638001i | ||||
\(87\) | 3.06966e13i | 0.813684i | ||||||||
\(88\) | −6.53526e12 | + | 7.10819e13i | −0.159913 | + | 1.73932i | ||||
\(89\) | 4.60407e13 | 1.04091 | 0.520453 | − | 0.853890i | \(-0.325763\pi\) | ||||
0.520453 | + | 0.853890i | \(0.325763\pi\) | |||||||
\(90\) | −3.30397e12 | + | 5.33895e12i | −0.0690779 | + | 0.111624i | ||||
\(91\) | 1.35233e13i | 0.261694i | ||||||||
\(92\) | −2.83674e13 | + | 1.41422e13i | −0.508516 | + | 0.253515i | ||||
\(93\) | 7.38230e12 | 0.122691 | ||||||||
\(94\) | 2.66533e13 | + | 1.64942e13i | 0.411014 | + | 0.254353i | ||||
\(95\) | − | 1.15978e13i | − | 0.166077i | ||||||
\(96\) | −4.04364e13 | + | 1.57208e13i | −0.538113 | + | 0.209207i | ||||
\(97\) | 1.38373e14 | 1.71257 | 0.856286 | − | 0.516501i | \(-0.172766\pi\) | ||||
0.856286 | + | 0.516501i | \(0.172766\pi\) | |||||||
\(98\) | 3.65269e13 | − | 5.90245e13i | 0.420756 | − | 0.679907i | ||||
\(99\) | 5.42667e13i | 0.582220i | ||||||||
\(100\) | 3.76973e13 | + | 7.56156e13i | 0.376973 | + | 0.756156i | ||||
\(101\) | 1.10297e14 | 1.02876 | 0.514382 | − | 0.857561i | \(-0.328021\pi\) | ||||
0.514382 | + | 0.857561i | \(0.328021\pi\) | |||||||
\(102\) | −6.58758e13 | − | 4.07667e13i | −0.573488 | − | 0.354899i | ||||
\(103\) | − | 2.02040e14i | − | 1.64277i | −0.570372 | − | 0.821386i | \(-0.693201\pi\) | ||
0.570372 | − | 0.821386i | \(-0.306799\pi\) | |||||||
\(104\) | 7.65976e13 | + | 7.04237e12i | 0.582079 | + | 0.0535163i | ||||
\(105\) | 1.43230e13 | 0.101791 | ||||||||
\(106\) | −9.91106e13 | + | 1.60155e14i | −0.659142 | + | 1.06512i | ||||
\(107\) | − | 8.40010e13i | − | 0.523116i | −0.965188 | − | 0.261558i | \(-0.915764\pi\) | ||
0.965188 | − | 0.261558i | \(-0.0842363\pi\) | |||||||
\(108\) | −2.95177e13 | + | 1.47157e13i | −0.172233 | + | 0.0858648i | ||||
\(109\) | −2.83963e14 | −1.55337 | −0.776687 | − | 0.629887i | \(-0.783101\pi\) | ||||
−0.776687 | + | 0.629887i | \(0.783101\pi\) | |||||||
\(110\) | −1.13982e14 | − | 7.05371e13i | −0.584909 | − | 0.361967i | ||||
\(111\) | 1.46158e14i | 0.703982i | ||||||||
\(112\) | 7.90379e13 | + | 5.95680e13i | 0.357527 | + | 0.269455i | ||||
\(113\) | 1.45379e14 | 0.617951 | 0.308975 | − | 0.951070i | \(-0.400014\pi\) | ||||
0.308975 | + | 0.951070i | \(0.400014\pi\) | |||||||
\(114\) | 3.20606e13 | − | 5.18073e13i | 0.128126 | − | 0.207041i | ||||
\(115\) | − | 5.95218e13i | − | 0.223765i | ||||||
\(116\) | −1.77713e14 | − | 3.56468e14i | −0.628801 | − | 1.26129i | ||||
\(117\) | 5.84776e13 | 0.194845 | ||||||||
\(118\) | 2.51866e14 | + | 1.55866e14i | 0.790671 | + | 0.489301i | ||||
\(119\) | 1.76727e14i | 0.522967i | ||||||||
\(120\) | 7.45881e12 | − | 8.11271e13i | 0.0208162 | − | 0.226411i | ||||
\(121\) | −7.78799e14 | −2.05082 | ||||||||
\(122\) | 4.82939e13 | − | 7.80390e13i | 0.120053 | − | 0.193996i | ||||
\(123\) | 2.55096e14i | 0.598918i | ||||||||
\(124\) | −8.57279e13 | + | 4.27386e13i | −0.190182 | + | 0.0948132i | ||||
\(125\) | −3.46443e14 | −0.726544 | ||||||||
\(126\) | 6.39809e13 | + | 3.95941e13i | 0.126899 | + | 0.0785302i | ||||
\(127\) | − | 2.92861e14i | − | 0.549586i | −0.961503 | − | 0.274793i | \(-0.911391\pi\) | ||
0.961503 | − | 0.274793i | \(-0.0886094\pi\) | |||||||
\(128\) | 3.78560e14 | − | 4.16660e14i | 0.672457 | − | 0.740136i | ||||
\(129\) | 4.16116e14 | 0.699981 | ||||||||
\(130\) | −7.60105e13 | + | 1.22827e14i | −0.121135 | + | 0.195745i | ||||
\(131\) | 8.92594e14i | 1.34820i | 0.738639 | + | 0.674101i | \(0.235469\pi\) | ||||
−0.738639 | + | 0.674101i | \(0.764531\pi\) | |||||||
\(132\) | −3.14168e14 | − | 6.30179e14i | −0.449930 | − | 0.902498i | ||||
\(133\) | −1.38985e14 | −0.188802 | ||||||||
\(134\) | 2.86249e14 | + | 1.77143e14i | 0.368986 | + | 0.228344i | ||||
\(135\) | − | 6.19356e13i | − | 0.0757886i | ||||||
\(136\) | 1.00100e15 | + | 9.20321e13i | 1.16322 | + | 0.106947i | ||||
\(137\) | 1.11799e14 | 0.123423 | 0.0617115 | − | 0.998094i | \(-0.480344\pi\) | ||||
0.0617115 | + | 0.998094i | \(0.480344\pi\) | |||||||
\(138\) | 1.64541e14 | − | 2.65884e14i | 0.172631 | − | 0.278958i | ||||
\(139\) | − | 1.36899e15i | − | 1.36552i | −0.730645 | − | 0.682758i | \(-0.760781\pi\) | ||
0.730645 | − | 0.682758i | \(-0.239219\pi\) | |||||||
\(140\) | −1.66328e14 | + | 8.29206e13i | −0.157786 | + | 0.0786623i | ||||
\(141\) | −3.09197e14 | −0.279063 | ||||||||
\(142\) | 1.96237e15 | + | 1.21440e15i | 1.68563 | + | 1.04314i | ||||
\(143\) | 1.24845e15i | 1.02098i | ||||||||
\(144\) | 2.57584e14 | − | 3.41776e14i | 0.200624 | − | 0.266198i | ||||
\(145\) | 7.47959e14 | 0.555011 | ||||||||
\(146\) | −1.22657e15 | + | 1.98204e15i | −0.867406 | + | 1.40166i | ||||
\(147\) | 6.84725e14i | 0.461631i | ||||||||
\(148\) | −8.46158e14 | − | 1.69728e15i | −0.544026 | − | 1.09124i | ||||
\(149\) | 4.24688e13 | 0.0260475 | 0.0130237 | − | 0.999915i | \(-0.495854\pi\) | ||||
0.0130237 | + | 0.999915i | \(0.495854\pi\) | |||||||
\(150\) | −7.08737e14 | − | 4.38597e14i | −0.414807 | − | 0.256700i | ||||
\(151\) | − | 4.14395e14i | − | 0.231513i | −0.993278 | − | 0.115757i | \(-0.963071\pi\) | ||
0.993278 | − | 0.115757i | \(-0.0369292\pi\) | |||||||
\(152\) | −7.23776e13 | + | 7.87228e14i | −0.0386099 | + | 0.419948i | ||||
\(153\) | 7.64205e14 | 0.389376 | ||||||||
\(154\) | −8.45301e14 | + | 1.36594e15i | −0.411497 | + | 0.664946i | ||||
\(155\) | − | 1.79878e14i | − | 0.0836869i | ||||||
\(156\) | −6.79079e14 | + | 3.38547e14i | −0.302028 | + | 0.150573i | ||||
\(157\) | 1.48358e15 | 0.630977 | 0.315488 | − | 0.948929i | \(-0.397832\pi\) | ||||
0.315488 | + | 0.948929i | \(0.397832\pi\) | |||||||
\(158\) | −2.93071e15 | − | 1.81365e15i | −1.19226 | − | 0.737825i | ||||
\(159\) | − | 1.85791e15i | − | 0.723176i | ||||||
\(160\) | 3.83056e14 | + | 9.85281e14i | 0.142699 | + | 0.367046i | ||||
\(161\) | −7.13297e14 | −0.254384 | ||||||||
\(162\) | 1.71213e14 | − | 2.76667e14i | 0.0584699 | − | 0.0944826i | ||||
\(163\) | − | 2.98948e15i | − | 0.977873i | −0.872319 | − | 0.488937i | \(-0.837385\pi\) | ||
0.872319 | − | 0.488937i | \(-0.162615\pi\) | |||||||
\(164\) | −1.47683e15 | − | 2.96233e15i | −0.462834 | − | 0.928382i | ||||
\(165\) | 1.32227e15 | 0.397131 | ||||||||
\(166\) | −2.07698e15 | − | 1.28533e15i | −0.597965 | − | 0.370047i | ||||
\(167\) | − | 1.80982e15i | − | 0.499598i | −0.968298 | − | 0.249799i | \(-0.919635\pi\) | ||
0.968298 | − | 0.249799i | \(-0.0803646\pi\) | |||||||
\(168\) | −9.72210e14 | − | 8.93848e13i | −0.257392 | − | 0.0236646i | ||||
\(169\) | −2.59205e15 | −0.658320 | ||||||||
\(170\) | −9.93330e14 | + | 1.60514e15i | −0.242076 | + | 0.391175i | ||||
\(171\) | 6.01000e14i | 0.140573i | ||||||||
\(172\) | −4.83220e15 | + | 2.40903e15i | −1.08504 | + | 0.540933i | ||||
\(173\) | 4.35216e15 | 0.938387 | 0.469194 | − | 0.883095i | \(-0.344545\pi\) | ||||
0.469194 | + | 0.883095i | \(0.344545\pi\) | |||||||
\(174\) | 3.34114e15 | + | 2.06764e15i | 0.691910 | + | 0.428184i | ||||
\(175\) | 1.90135e15i | 0.378265i | ||||||||
\(176\) | 7.29664e15 | + | 5.49921e15i | 1.39487 | + | 1.05126i | ||||
\(177\) | −2.92182e15 | −0.536835 | ||||||||
\(178\) | 3.10118e15 | − | 5.01125e15i | 0.547755 | − | 0.885128i | ||||
\(179\) | − | 5.79613e14i | − | 0.0984390i | −0.998788 | − | 0.0492195i | \(-0.984327\pi\) | ||
0.998788 | − | 0.0492195i | \(-0.0156734\pi\) | |||||||
\(180\) | 3.58566e14 | + | 7.19235e14i | 0.0585682 | + | 0.117480i | ||||
\(181\) | 1.66845e15 | 0.262158 | 0.131079 | − | 0.991372i | \(-0.458156\pi\) | ||||
0.131079 | + | 0.991372i | \(0.458156\pi\) | |||||||
\(182\) | 1.47193e15 | + | 9.10894e14i | 0.222530 | + | 0.137711i | ||||
\(183\) | 9.05307e14i | 0.131716i | ||||||||
\(184\) | −3.71455e14 | + | 4.04020e15i | −0.0520214 | + | 0.565820i | ||||
\(185\) | 3.56131e15 | 0.480185 | ||||||||
\(186\) | 4.97252e14 | − | 8.03518e14i | 0.0645633 | − | 0.104329i | ||||
\(187\) | 1.63151e16i | 2.04032i | ||||||||
\(188\) | 3.59059e15 | − | 1.79005e15i | 0.432575 | − | 0.215655i | ||||
\(189\) | −7.42223e14 | −0.0861592 | ||||||||
\(190\) | −1.26235e15 | − | 7.81194e14i | −0.141222 | − | 0.0873944i | ||||
\(191\) | − | 7.74538e15i | − | 0.835235i | −0.908623 | − | 0.417618i | \(-0.862865\pi\) | ||
0.908623 | − | 0.417618i | \(-0.137135\pi\) | |||||||
\(192\) | −1.01257e15 | + | 5.46016e15i | −0.105273 | + | 0.567671i | ||||
\(193\) | −4.19241e14 | −0.0420303 | −0.0210152 | − | 0.999779i | \(-0.506690\pi\) | ||||
−0.0210152 | + | 0.999779i | \(0.506690\pi\) | |||||||
\(194\) | 9.32042e15 | − | 1.50611e16i | 0.901205 | − | 1.45627i | ||||
\(195\) | − | 1.42488e15i | − | 0.132903i | ||||||
\(196\) | −3.96410e15 | − | 7.95145e15i | −0.356740 | − | 0.715573i | ||||
\(197\) | −1.76103e16 | −1.52934 | −0.764669 | − | 0.644424i | \(-0.777097\pi\) | ||||
−0.764669 | + | 0.644424i | \(0.777097\pi\) | |||||||
\(198\) | 5.90660e15 | + | 3.65526e15i | 0.495087 | + | 0.306381i | ||||
\(199\) | 5.65746e15i | 0.457772i | 0.973453 | + | 0.228886i | \(0.0735084\pi\) | ||||
−0.973453 | + | 0.228886i | \(0.926492\pi\) | |||||||
\(200\) | 1.07695e16 | + | 9.90145e14i | 0.841366 | + | 0.0773550i | ||||
\(201\) | −3.32069e15 | −0.250527 | ||||||||
\(202\) | 7.42933e15 | − | 1.20052e16i | 0.541365 | − | 0.874802i | ||||
\(203\) | − | 8.96339e15i | − | 0.630957i | ||||||
\(204\) | −8.87442e15 | + | 4.42424e15i | −0.603572 | + | 0.300904i | ||||
\(205\) | 6.21571e15 | 0.408520 | ||||||||
\(206\) | −2.19909e16 | − | 1.36089e16i | −1.39692 | − | 0.864474i | ||||
\(207\) | 3.08444e15i | 0.189402i | ||||||||
\(208\) | 5.92593e15 | − | 7.86283e15i | 0.351814 | − | 0.466805i | ||||
\(209\) | −1.28309e16 | −0.736600 | ||||||||
\(210\) | 9.64758e14 | − | 1.55897e15i | 0.0535653 | − | 0.0865571i | ||||
\(211\) | 2.83607e16i | 1.52314i | 0.648082 | + | 0.761571i | \(0.275572\pi\) | ||||
−0.648082 | + | 0.761571i | \(0.724428\pi\) | |||||||
\(212\) | 1.07560e16 | + | 2.15752e16i | 0.558858 | + | 1.12099i | ||||
\(213\) | −2.27648e16 | −1.14448 | ||||||||
\(214\) | −9.14300e15 | − | 5.65808e15i | −0.444828 | − | 0.275279i | ||||
\(215\) | − | 1.01391e16i | − | 0.477455i | ||||||
\(216\) | −3.86519e14 | + | 4.20404e15i | −0.0176195 | + | 0.191642i | ||||
\(217\) | −2.15563e15 | −0.0951383 | ||||||||
\(218\) | −1.91270e16 | + | 3.09076e16i | −0.817430 | + | 1.32090i | ||||
\(219\) | − | 2.29930e16i | − | 0.951672i | ||||||
\(220\) | −1.53551e16 | + | 7.65508e15i | −0.615592 | + | 0.306896i | ||||
\(221\) | 1.75811e16 | 0.682811 | ||||||||
\(222\) | 1.59084e16 | + | 9.84481e15i | 0.598627 | + | 0.370456i | ||||
\(223\) | − | 3.08803e16i | − | 1.12602i | −0.826449 | − | 0.563011i | \(-0.809643\pi\) | ||
0.826449 | − | 0.563011i | \(-0.190357\pi\) | |||||||
\(224\) | 1.18074e16 | − | 4.59046e15i | 0.417271 | − | 0.162226i | ||||
\(225\) | 8.22184e15 | 0.281638 | ||||||||
\(226\) | 9.79237e15 | − | 1.58237e16i | 0.325184 | − | 0.525470i | ||||
\(227\) | 2.50452e16i | 0.806386i | 0.915115 | + | 0.403193i | \(0.132100\pi\) | ||||
−0.915115 | + | 0.403193i | \(0.867900\pi\) | |||||||
\(228\) | −3.47939e15 | − | 6.97919e15i | −0.108632 | − | 0.217902i | ||||
\(229\) | 4.62302e16 | 1.39984 | 0.699919 | − | 0.714223i | \(-0.253220\pi\) | ||||
0.699919 | + | 0.714223i | \(0.253220\pi\) | |||||||
\(230\) | −6.47859e15 | − | 4.00923e15i | −0.190277 | − | 0.117751i | ||||
\(231\) | − | 1.58458e16i | − | 0.451473i | ||||||
\(232\) | −5.07697e16 | − | 4.66775e15i | −1.40342 | − | 0.129030i | ||||
\(233\) | 2.49166e15 | 0.0668340 | 0.0334170 | − | 0.999441i | \(-0.489361\pi\) | ||||
0.0334170 | + | 0.999441i | \(0.489361\pi\) | |||||||
\(234\) | 3.93889e15 | − | 6.36493e15i | 0.102533 | − | 0.165685i | ||||
\(235\) | 7.53396e15i | 0.190348i | ||||||||
\(236\) | 3.39301e16 | − | 1.69154e16i | 0.832148 | − | 0.414857i | ||||
\(237\) | 3.39982e16 | 0.809502 | ||||||||
\(238\) | 1.92357e16 | + | 1.19039e16i | 0.444702 | + | 0.275200i | ||||
\(239\) | − | 1.31724e16i | − | 0.295718i | −0.989008 | − | 0.147859i | \(-0.952762\pi\) | ||
0.989008 | − | 0.147859i | \(-0.0472382\pi\) | |||||||
\(240\) | −8.32779e15 | − | 6.27635e15i | −0.181573 | − | 0.136845i | ||||
\(241\) | 3.30650e16 | 0.700245 | 0.350122 | − | 0.936704i | \(-0.386140\pi\) | ||||
0.350122 | + | 0.936704i | \(0.386140\pi\) | |||||||
\(242\) | −5.24578e16 | + | 8.47675e16i | −1.07920 | + | 1.74390i | ||||
\(243\) | 3.20953e15i | 0.0641500i | ||||||||
\(244\) | −5.24113e15 | − | 1.05130e16i | −0.101788 | − | 0.204173i | ||||
\(245\) | 1.66841e16 | 0.314877 | ||||||||
\(246\) | 2.77656e16 | + | 1.71826e16i | 0.509286 | + | 0.315168i | ||||
\(247\) | 1.38265e16i | 0.246509i | ||||||||
\(248\) | −1.12256e15 | + | 1.22097e16i | −0.0194557 | + | 0.211614i | ||||
\(249\) | 2.40944e16 | 0.405995 | ||||||||
\(250\) | −2.33355e16 | + | 3.77082e16i | −0.382328 | + | 0.617812i | ||||
\(251\) | 3.75727e16i | 0.598628i | 0.954155 | + | 0.299314i | \(0.0967577\pi\) | ||||
−0.954155 | + | 0.299314i | \(0.903242\pi\) | |||||||
\(252\) | 8.61916e15 | − | 4.29698e15i | 0.133555 | − | 0.0665824i | ||||
\(253\) | −6.58503e16 | −0.992462 | ||||||||
\(254\) | −3.18762e16 | − | 1.97263e16i | −0.467337 | − | 0.289208i | ||||
\(255\) | − | 1.86208e16i | − | 0.265593i | ||||||
\(256\) | −1.98521e16 | − | 6.92690e16i | −0.275503 | − | 0.961300i | ||||
\(257\) | 3.46414e16 | 0.467804 | 0.233902 | − | 0.972260i | \(-0.424851\pi\) | ||||
0.233902 | + | 0.972260i | \(0.424851\pi\) | |||||||
\(258\) | 2.80284e16 | − | 4.52916e16i | 0.368350 | − | 0.595224i | ||||
\(259\) | − | 4.26780e16i | − | 0.545891i | ||||||
\(260\) | 8.24909e15 | + | 1.65466e16i | 0.102705 | + | 0.206013i | ||||
\(261\) | −3.87595e16 | −0.469780 | ||||||||
\(262\) | 9.71534e16 | + | 6.01227e16i | 1.14643 | + | 0.709462i | ||||
\(263\) | − | 4.51324e16i | − | 0.518558i | −0.965802 | − | 0.259279i | \(-0.916515\pi\) | ||
0.965802 | − | 0.259279i | \(-0.0834850\pi\) | |||||||
\(264\) | −8.97527e16 | − | 8.25185e15i | −1.00420 | − | 0.0923259i | ||||
\(265\) | −4.52701e16 | −0.493276 | ||||||||
\(266\) | −9.36166e15 | + | 1.51277e16i | −0.0993531 | + | 0.160547i | ||||
\(267\) | 5.81340e16i | 0.600968i | ||||||||
\(268\) | 3.85619e16 | − | 1.92246e16i | 0.388342 | − | 0.193603i | ||||
\(269\) | −1.92854e17 | −1.89218 | −0.946088 | − | 0.323909i | \(-0.895003\pi\) | ||||
−0.946088 | + | 0.323909i | \(0.895003\pi\) | |||||||
\(270\) | −6.74131e15 | − | 4.17181e15i | −0.0644463 | − | 0.0398821i | ||||
\(271\) | − | 1.21122e17i | − | 1.12833i | −0.825660 | − | 0.564167i | \(-0.809197\pi\) | ||
0.825660 | − | 0.564167i | \(-0.190803\pi\) | |||||||
\(272\) | 7.74420e16 | − | 1.02754e17i | 0.703063 | − | 0.932860i | ||||
\(273\) | −1.70754e16 | −0.151089 | ||||||||
\(274\) | 7.53051e15 | − | 1.21687e16i | 0.0649487 | − | 0.104952i | ||||
\(275\) | 1.75529e17i | 1.47578i | ||||||||
\(276\) | −1.78569e16 | − | 3.58185e16i | −0.146367 | − | 0.293592i | ||||
\(277\) | −9.92031e16 | −0.792806 | −0.396403 | − | 0.918077i | \(-0.629742\pi\) | ||||
−0.396403 | + | 0.918077i | \(0.629742\pi\) | |||||||
\(278\) | −1.49006e17 | − | 9.22114e16i | −1.16116 | − | 0.718573i | ||||
\(279\) | 9.32137e15i | 0.0708354i | ||||||||
\(280\) | −2.17797e15 | + | 2.36891e16i | −0.0161416 | + | 0.175566i | ||||
\(281\) | 1.87290e16 | 0.135385 | 0.0676925 | − | 0.997706i | \(-0.478436\pi\) | ||||
0.0676925 | + | 0.997706i | \(0.478436\pi\) | |||||||
\(282\) | −2.08267e16 | + | 3.36543e16i | −0.146851 | + | 0.237299i | ||||
\(283\) | 4.34201e16i | 0.298666i | 0.988787 | + | 0.149333i | \(0.0477126\pi\) | ||||
−0.988787 | + | 0.149333i | \(0.952287\pi\) | |||||||
\(284\) | 2.64360e17 | − | 1.31793e17i | 1.77405 | − | 0.884433i | ||||
\(285\) | 1.46441e16 | 0.0958845 | ||||||||
\(286\) | 1.35886e17 | + | 8.40920e16i | 0.868185 | + | 0.537270i | ||||
\(287\) | − | 7.44878e16i | − | 0.464421i | ||||||
\(288\) | −1.98501e16 | − | 5.10576e16i | −0.120786 | − | 0.310680i | ||||
\(289\) | 6.13781e16 | 0.364526 | ||||||||
\(290\) | 5.03805e16 | − | 8.14108e16i | 0.292063 | − | 0.471950i | ||||
\(291\) | 1.74719e17i | 0.988754i | ||||||||
\(292\) | 1.33114e17 | + | 2.67009e17i | 0.735436 | + | 1.47519i | ||||
\(293\) | 3.03810e17 | 1.63881 | 0.819405 | − | 0.573215i | \(-0.194304\pi\) | ||||
0.819405 | + | 0.573215i | \(0.194304\pi\) | |||||||
\(294\) | 7.45281e16 | + | 4.61212e16i | 0.392544 | + | 0.242923i | ||||
\(295\) | 7.11937e16i | 0.366174i | ||||||||
\(296\) | −2.41733e17 | − | 2.22249e16i | −1.21421 | − | 0.111634i | ||||
\(297\) | −6.85207e16 | −0.336145 | ||||||||
\(298\) | 2.86058e15 | − | 4.62247e15i | 0.0137069 | − | 0.0221493i | ||||
\(299\) | 7.09600e16i | 0.332136i | ||||||||
\(300\) | −9.54772e16 | + | 4.75990e16i | −0.436567 | + | 0.217645i | ||||
\(301\) | −1.21505e17 | −0.542788 | ||||||||
\(302\) | −4.51043e16 | − | 2.79125e16i | −0.196865 | − | 0.121829i | ||||
\(303\) | 1.39269e17i | 0.593957i | ||||||||
\(304\) | 8.08098e16 | + | 6.09034e16i | 0.336782 | + | 0.253820i | ||||
\(305\) | 2.20589e16 | 0.0898430 | ||||||||
\(306\) | 5.14747e16 | − | 8.31790e16i | 0.204901 | − | 0.331104i | ||||
\(307\) | − | 6.06880e16i | − | 0.236121i | −0.993006 | − | 0.118060i | \(-0.962332\pi\) | ||
0.993006 | − | 0.118060i | \(-0.0376676\pi\) | |||||||
\(308\) | 9.17369e16 | + | 1.84012e17i | 0.348890 | + | 0.699827i | ||||
\(309\) | 2.55109e17 | 0.948455 | ||||||||
\(310\) | −1.95787e16 | − | 1.21161e16i | −0.0711625 | − | 0.0440384i | ||||
\(311\) | − | 4.00103e17i | − | 1.42183i | −0.703276 | − | 0.710917i | \(-0.748280\pi\) | ||
0.703276 | − | 0.710917i | \(-0.251720\pi\) | |||||||
\(312\) | −8.89216e15 | + | 9.67172e16i | −0.0308976 | + | 0.336064i | ||||
\(313\) | −2.92916e17 | −0.995250 | −0.497625 | − | 0.867392i | \(-0.665794\pi\) | ||||
−0.497625 | + | 0.867392i | \(0.665794\pi\) | |||||||
\(314\) | 9.99299e16 | − | 1.61479e17i | 0.332038 | − | 0.536547i | ||||
\(315\) | 1.80851e16i | 0.0587690i | ||||||||
\(316\) | −3.94809e17 | + | 1.96827e17i | −1.25481 | + | 0.625570i | ||||
\(317\) | 1.65545e17 | 0.514636 | 0.257318 | − | 0.966327i | \(-0.417161\pi\) | ||||
0.257318 | + | 0.966327i | \(0.417161\pi\) | |||||||
\(318\) | −2.02222e17 | − | 1.25143e17i | −0.614947 | − | 0.380556i | ||||
\(319\) | − | 8.27483e17i | − | 2.46164i | ||||||
\(320\) | 1.33043e17 | + | 2.46725e16i | 0.387207 | + | 0.0718065i | ||||
\(321\) | 1.06065e17 | 0.302021 | ||||||||
\(322\) | −4.80458e16 | + | 7.76381e16i | −0.133864 | + | 0.216313i | ||||
\(323\) | 1.80689e17i | 0.492622i | ||||||||
\(324\) | −1.85810e16 | − | 3.72710e16i | −0.0495741 | − | 0.0994389i | ||||
\(325\) | 1.89150e17 | 0.493881 | ||||||||
\(326\) | −3.25387e17 | − | 2.01363e17i | −0.831528 | − | 0.514585i | ||||
\(327\) | − | 3.58550e17i | − | 0.896841i | ||||||
\(328\) | −4.21907e17 | − | 3.87901e16i | −1.03300 | − | 0.0949738i | ||||
\(329\) | 9.02854e16 | 0.216395 | ||||||||
\(330\) | 8.90647e16 | − | 1.43921e17i | 0.208982 | − | 0.337697i | ||||
\(331\) | 7.06800e17i | 1.62368i | 0.583880 | + | 0.811840i | \(0.301534\pi\) | ||||
−0.583880 | + | 0.811840i | \(0.698466\pi\) | |||||||
\(332\) | −2.79800e17 | + | 1.39491e17i | −0.629333 | + | 0.313746i | ||||
\(333\) | −1.84549e17 | −0.406444 | ||||||||
\(334\) | −1.96988e17 | − | 1.21905e17i | −0.424830 | − | 0.262903i | ||||
\(335\) | 8.09124e16i | 0.170884i | ||||||||
\(336\) | −7.52144e16 | + | 9.97984e16i | −0.155570 | + | 0.206419i | ||||
\(337\) | 1.03081e17 | 0.208819 | 0.104409 | − | 0.994534i | \(-0.466705\pi\) | ||||
0.104409 | + | 0.994534i | \(0.466705\pi\) | |||||||
\(338\) | −1.74594e17 | + | 2.82129e17i | −0.346427 | + | 0.559798i | ||||
\(339\) | 1.83566e17i | 0.356774i | ||||||||
\(340\) | 1.07802e17 | + | 2.16236e17i | 0.205246 | + | 0.411695i | ||||
\(341\) | −1.99003e17 | −0.371176 | ||||||||
\(342\) | 6.54152e16 | + | 4.04818e16i | 0.119535 | + | 0.0739736i | ||||
\(343\) | − | 4.49998e17i | − | 0.805660i | ||||||
\(344\) | −6.32749e16 | + | 6.88221e17i | −0.111000 | + | 1.20731i | ||||
\(345\) | 7.51561e16 | 0.129191 | ||||||||
\(346\) | 2.93150e17 | − | 4.73706e17i | 0.493806 | − | 0.797951i | ||||
\(347\) | 2.48415e17i | 0.410083i | 0.978753 | + | 0.205041i | \(0.0657329\pi\) | ||||
−0.978753 | + | 0.205041i | \(0.934267\pi\) | |||||||
\(348\) | 4.50100e17 | − | 2.24392e17i | 0.728206 | − | 0.363038i | ||||
\(349\) | 5.13504e17 | 0.814265 | 0.407133 | − | 0.913369i | \(-0.366529\pi\) | ||||
0.407133 | + | 0.913369i | \(0.366529\pi\) | |||||||
\(350\) | 2.06951e17 | + | 1.28070e17i | 0.321655 | + | 0.199054i | ||||
\(351\) | 7.38376e16i | 0.112494i | ||||||||
\(352\) | 1.09004e18 | − | 4.23783e17i | 1.62796 | − | 0.632914i | ||||
\(353\) | −4.41600e17 | −0.646557 | −0.323278 | − | 0.946304i | \(-0.604785\pi\) | ||||
−0.323278 | + | 0.946304i | \(0.604785\pi\) | |||||||
\(354\) | −1.96806e17 | + | 3.18023e17i | −0.282498 | + | 0.456494i | ||||
\(355\) | 5.54692e17i | 0.780645i | ||||||||
\(356\) | −3.36557e17 | − | 6.75088e17i | −0.464418 | − | 0.931559i | ||||
\(357\) | −2.23147e17 | −0.301935 | ||||||||
\(358\) | −6.30874e16 | − | 3.90412e16i | −0.0837069 | − | 0.0518014i | ||||
\(359\) | 2.62499e17i | 0.341559i | 0.985309 | + | 0.170780i | \(0.0546286\pi\) | ||||
−0.985309 | + | 0.170780i | \(0.945371\pi\) | |||||||
\(360\) | 1.02436e17 | + | 9.41798e15i | 0.130718 | + | 0.0120182i | ||||
\(361\) | 6.56906e17 | 0.822153 | ||||||||
\(362\) | 1.12382e17 | − | 1.81601e17i | 0.137955 | − | 0.222924i | ||||
\(363\) | − | 9.83362e17i | − | 1.18404i | ||||||
\(364\) | 1.98290e17 | − | 9.88554e16i | 0.234203 | − | 0.116759i | ||||
\(365\) | −5.60252e17 | −0.649133 | ||||||||
\(366\) | 9.85371e16 | + | 6.09790e16i | 0.112004 | + | 0.0693127i | ||||
\(367\) | − | 2.42222e16i | − | 0.0270116i | −0.999909 | − | 0.0135058i | \(-0.995701\pi\) | ||
0.999909 | − | 0.0135058i | \(-0.00429917\pi\) | |||||||
\(368\) | 4.14731e17 | + | 3.12567e17i | 0.453766 | + | 0.341987i | ||||
\(369\) | −3.22100e17 | −0.345785 | ||||||||
\(370\) | 2.39880e17 | − | 3.87627e17i | 0.252687 | − | 0.408322i | ||||
\(371\) | 5.42507e17i | 0.560774i | ||||||||
\(372\) | −5.39646e16 | − | 1.08246e17i | −0.0547404 | − | 0.109802i | ||||
\(373\) | −4.64802e17 | −0.462707 | −0.231354 | − | 0.972870i | \(-0.574315\pi\) | ||||
−0.231354 | + | 0.972870i | \(0.574315\pi\) | |||||||
\(374\) | 1.77580e18 | + | 1.09894e18i | 1.73498 | + | 1.07368i | ||||
\(375\) | − | 4.37442e17i | − | 0.419470i | ||||||
\(376\) | 4.70168e16 | − | 5.11387e17i | 0.0442526 | − | 0.481321i | ||||
\(377\) | −8.91693e17 | −0.823808 | ||||||||
\(378\) | −4.99941e16 | + | 8.07864e16i | −0.0453395 | + | 0.0732649i | ||||
\(379\) | 1.66809e18i | 1.48506i | 0.669811 | + | 0.742532i | \(0.266375\pi\) | ||||
−0.669811 | + | 0.742532i | \(0.733625\pi\) | |||||||
\(380\) | −1.70056e17 | + | 8.47796e16i | −0.148630 | + | 0.0740979i | ||||
\(381\) | 3.69786e17 | 0.317304 | ||||||||
\(382\) | −8.43037e17 | − | 5.21707e17i | −0.710237 | − | 0.439525i | ||||
\(383\) | − | 3.29986e17i | − | 0.272963i | −0.990643 | − | 0.136482i | \(-0.956420\pi\) | ||
0.990643 | − | 0.136482i | \(-0.0435795\pi\) | |||||||
\(384\) | 5.26101e17 | + | 4.77994e17i | 0.427318 | + | 0.388243i | ||||
\(385\) | −3.86103e17 | −0.307948 | ||||||||
\(386\) | −2.82389e16 | + | 4.56318e16i | −0.0221176 | + | 0.0357402i | ||||
\(387\) | 5.25415e17i | 0.404134i | ||||||||
\(388\) | −1.01151e18 | − | 2.02894e18i | −0.764093 | − | 1.53267i | ||||
\(389\) | 4.56208e17 | 0.338466 | 0.169233 | − | 0.985576i | \(-0.445871\pi\) | ||||
0.169233 | + | 0.985576i | \(0.445871\pi\) | |||||||
\(390\) | −1.55089e17 | − | 9.59758e16i | −0.113013 | − | 0.0699374i | ||||
\(391\) | 9.27329e17i | 0.663738i | ||||||||
\(392\) | −1.13248e18 | − | 1.04120e17i | −0.796210 | − | 0.0732034i | ||||
\(393\) | −1.12705e18 | −0.778385 | ||||||||
\(394\) | −1.18618e18 | + | 1.91677e18i | −0.804781 | + | 1.30046i | ||||
\(395\) | − | 8.28407e17i | − | 0.552159i | ||||||
\(396\) | 7.95705e17 | − | 3.96689e17i | 0.521058 | − | 0.259767i | ||||
\(397\) | −7.12062e17 | −0.458125 | −0.229063 | − | 0.973412i | \(-0.573566\pi\) | ||||
−0.229063 | + | 0.973412i | \(0.573566\pi\) | |||||||
\(398\) | 6.15780e17 | + | 3.81071e17i | 0.389264 | + | 0.240893i | ||||
\(399\) | − | 1.75492e17i | − | 0.109005i | ||||||
\(400\) | 8.33174e17 | − | 1.10550e18i | 0.508529 | − | 0.674743i | ||||
\(401\) | 1.12281e17 | 0.0673436 | 0.0336718 | − | 0.999433i | \(-0.489280\pi\) | ||||
0.0336718 | + | 0.999433i | \(0.489280\pi\) | |||||||
\(402\) | −2.23672e17 | + | 3.61436e17i | −0.131835 | + | 0.213034i | ||||
\(403\) | 2.14445e17i | 0.124217i | ||||||||
\(404\) | −8.06274e17 | − | 1.61728e18i | −0.459000 | − | 0.920692i | ||||
\(405\) | 7.82039e16 | 0.0437566 | ||||||||
\(406\) | −9.75610e17 | − | 6.03749e17i | −0.536530 | − | 0.332028i | ||||
\(407\) | − | 3.93996e18i | − | 2.12976i | ||||||
\(408\) | −1.16206e17 | + | 1.26393e18i | −0.0617456 | + | 0.671587i | ||||
\(409\) | 1.36519e18 | 0.713065 | 0.356532 | − | 0.934283i | \(-0.383959\pi\) | ||||
0.356532 | + | 0.934283i | \(0.383959\pi\) | |||||||
\(410\) | 4.18673e17 | − | 6.76542e17i | 0.214975 | − | 0.347382i | ||||
\(411\) | 1.41165e17i | 0.0712583i | ||||||||
\(412\) | −2.96249e18 | + | 1.47691e18i | −1.47020 | + | 0.732950i | ||||
\(413\) | 8.53170e17 | 0.416280 | ||||||||
\(414\) | 3.35723e17 | + | 2.07760e17i | 0.161057 | + | 0.0996688i | ||||
\(415\) | − | 5.87089e17i | − | 0.276928i | ||||||
\(416\) | −4.56667e17 | − | 1.17462e18i | −0.211810 | − | 0.544809i | ||||
\(417\) | 1.72858e18 | 0.788381 | ||||||||
\(418\) | −8.64251e17 | + | 1.39656e18i | −0.387620 | + | 0.626362i | ||||
\(419\) | 2.54171e17i | 0.112106i | 0.998428 | + | 0.0560528i | \(0.0178515\pi\) | ||||
−0.998428 | + | 0.0560528i | \(0.982148\pi\) | |||||||
\(420\) | −1.04701e17 | − | 2.10016e17i | −0.0454157 | − | 0.0910977i | ||||
\(421\) | 1.38924e18 | 0.592655 | 0.296328 | − | 0.955086i | \(-0.404238\pi\) | ||||
0.296328 | + | 0.955086i | \(0.404238\pi\) | |||||||
\(422\) | 3.08689e18 | + | 1.91030e18i | 1.29519 | + | 0.801521i | ||||
\(423\) | − | 3.90413e17i | − | 0.161117i | ||||||
\(424\) | 3.07282e18 | + | 2.82515e17i | 1.24732 | + | 0.114678i | ||||
\(425\) | 2.47187e18 | 0.986969 | ||||||||
\(426\) | −1.53338e18 | + | 2.47781e18i | −0.602257 | + | 0.973199i | ||||
\(427\) | − | 2.64349e17i | − | 0.102137i | ||||||
\(428\) | −1.23169e18 | + | 6.14047e17i | −0.468163 | + | 0.233397i | ||||
\(429\) | −1.57637e18 | −0.589464 | ||||||||
\(430\) | −1.10358e18 | − | 6.82946e17i | −0.406000 | − | 0.251250i | ||||
\(431\) | − | 6.88298e17i | − | 0.249136i | −0.992211 | − | 0.124568i | \(-0.960246\pi\) | ||
0.992211 | − | 0.124568i | \(-0.0397544\pi\) | |||||||
\(432\) | 4.31549e17 | + | 3.25243e17i | 0.153689 | + | 0.115830i | ||||
\(433\) | 1.64319e18 | 0.575800 | 0.287900 | − | 0.957661i | \(-0.407043\pi\) | ||||
0.287900 | + | 0.957661i | \(0.407043\pi\) | |||||||
\(434\) | −1.45197e17 | + | 2.34627e17i | −0.0500645 | + | 0.0809002i | ||||
\(435\) | 9.44422e17i | 0.320436i | ||||||||
\(436\) | 2.07577e18 | + | 4.16371e18i | 0.693063 | + | 1.39019i | ||||
\(437\) | −7.29288e17 | −0.239623 | ||||||||
\(438\) | −2.50265e18 | − | 1.54875e18i | −0.809248 | − | 0.500797i | ||||
\(439\) | 3.97715e18i | 1.26567i | 0.774287 | + | 0.632835i | \(0.218109\pi\) | ||||
−0.774287 | + | 0.632835i | \(0.781891\pi\) | |||||||
\(440\) | −2.01066e17 | + | 2.18693e18i | −0.0629753 | + | 0.684962i | ||||
\(441\) | −8.64578e17 | −0.266523 | ||||||||
\(442\) | 1.18422e18 | − | 1.91360e18i | 0.359315 | − | 0.580624i | ||||
\(443\) | 3.21465e18i | 0.960079i | 0.877247 | + | 0.480040i | \(0.159378\pi\) | ||||
−0.877247 | + | 0.480040i | \(0.840622\pi\) | |||||||
\(444\) | 2.14309e18 | − | 1.06841e18i | 0.630029 | − | 0.314093i | ||||
\(445\) | 1.41650e18 | 0.409919 | ||||||||
\(446\) | −3.36113e18 | − | 2.08001e18i | −0.957506 | − | 0.592546i | ||||
\(447\) | 5.36238e16i | 0.0150385i | ||||||||
\(448\) | 2.95670e17 | − | 1.59436e18i | 0.0816322 | − | 0.440191i | ||||
\(449\) | 6.29446e18 | 1.71094 | 0.855469 | − | 0.517855i | \(-0.173269\pi\) | ||||
0.855469 | + | 0.517855i | \(0.173269\pi\) | |||||||
\(450\) | 5.53801e17 | − | 8.94897e17i | 0.148206 | − | 0.239489i | ||||
\(451\) | − | 6.87657e18i | − | 1.81191i | ||||||
\(452\) | −1.06272e18 | − | 2.13168e18i | −0.275709 | − | 0.553035i | ||||
\(453\) | 5.23242e17 | 0.133664 | ||||||||
\(454\) | 2.72601e18 | + | 1.68697e18i | 0.685705 | + | 0.424344i | ||||
\(455\) | 4.16063e17i | 0.103057i | ||||||||
\(456\) | −9.94005e17 | − | 9.13887e16i | −0.242457 | − | 0.0222915i | ||||
\(457\) | −7.34945e18 | −1.76539 | −0.882697 | − | 0.469942i | \(-0.844275\pi\) | ||||
−0.882697 | + | 0.469942i | \(0.844275\pi\) | |||||||
\(458\) | 3.11394e18 | − | 5.03188e18i | 0.736634 | − | 1.19034i | ||||
\(459\) | 9.64934e17i | 0.224807i | ||||||||
\(460\) | −8.72760e17 | + | 4.35104e17i | −0.200258 | + | 0.0998363i | ||||
\(461\) | −8.27064e18 | −1.86910 | −0.934550 | − | 0.355832i | \(-0.884197\pi\) | ||||
−0.934550 | + | 0.355832i | \(0.884197\pi\) | |||||||
\(462\) | −1.72472e18 | − | 1.06733e18i | −0.383907 | − | 0.237578i | ||||
\(463\) | − | 2.96915e18i | − | 0.650976i | −0.945546 | − | 0.325488i | \(-0.894471\pi\) | ||
0.945546 | − | 0.325488i | \(-0.105529\pi\) | |||||||
\(464\) | −3.92776e18 | + | 5.21156e18i | −0.848241 | + | 1.12549i | ||||
\(465\) | 2.27126e17 | 0.0483166 | ||||||||
\(466\) | 1.67831e17 | − | 2.71202e17i | 0.0351700 | − | 0.0568318i | ||||
\(467\) | − | 1.84642e17i | − | 0.0381164i | −0.999818 | − | 0.0190582i | \(-0.993933\pi\) | ||
0.999818 | − | 0.0190582i | \(-0.00606678\pi\) | |||||||
\(468\) | −4.27471e17 | − | 8.57449e17i | −0.0869332 | − | 0.174376i | ||||
\(469\) | 9.69638e17 | 0.194267 | ||||||||
\(470\) | 8.20026e17 | + | 5.07467e17i | 0.161861 | + | 0.100167i | ||||
\(471\) | 1.87326e18i | 0.364294i | ||||||||
\(472\) | 4.44295e17 | − | 4.83246e18i | 0.0851290 | − | 0.925921i | ||||
\(473\) | −1.12172e19 | −2.11765 | ||||||||
\(474\) | 2.29003e18 | − | 3.70050e18i | 0.425983 | − | 0.688354i | ||||
\(475\) | 1.94398e18i | 0.356317i | ||||||||
\(476\) | 2.59133e18 | − | 1.29187e18i | 0.468030 | − | 0.233331i | ||||
\(477\) | 2.34591e18 | 0.417526 | ||||||||
\(478\) | −1.43373e18 | − | 8.87254e17i | −0.251462 | − | 0.155615i | ||||
\(479\) | 9.34485e18i | 1.61519i | 0.589737 | + | 0.807596i | \(0.299232\pi\) | ||||
−0.589737 | + | 0.807596i | \(0.700768\pi\) | |||||||
\(480\) | −1.24408e18 | + | 4.83671e17i | −0.211914 | + | 0.0823875i | ||||
\(481\) | −4.24569e18 | −0.712742 | ||||||||
\(482\) | 2.22717e18 | − | 3.59893e18i | 0.368489 | − | 0.595448i | ||||
\(483\) | − | 9.00655e17i | − | 0.146869i | ||||||
\(484\) | 5.69301e18 | + | 1.14194e19i | 0.915007 | + | 1.83538i | ||||
\(485\) | 4.25723e18 | 0.674427 | ||||||||
\(486\) | 3.49337e17 | + | 2.16185e17i | 0.0545495 | + | 0.0337576i | ||||
\(487\) | − | 7.97764e18i | − | 1.22792i | −0.789336 | − | 0.613962i | \(-0.789575\pi\) | ||
0.789336 | − | 0.613962i | \(-0.210425\pi\) | |||||||
\(488\) | −1.49730e18 | − | 1.37662e17i | −0.227180 | − | 0.0208869i | ||||
\(489\) | 3.77471e18 | 0.564575 | ||||||||
\(490\) | 1.12380e18 | − | 1.81597e18i | 0.165697 | − | 0.267754i | ||||
\(491\) | 6.36977e17i | 0.0925876i | 0.998928 | + | 0.0462938i | \(0.0147410\pi\) | ||||
−0.998928 | + | 0.0462938i | \(0.985259\pi\) | |||||||
\(492\) | 3.74043e18 | − | 1.86475e18i | 0.536002 | − | 0.267217i | ||||
\(493\) | −1.16529e19 | −1.64629 | ||||||||
\(494\) | 1.50493e18 | + | 9.31314e17i | 0.209617 | + | 0.129720i | ||||
\(495\) | 1.66959e18i | 0.229283i | ||||||||
\(496\) | 1.25334e18 | + | 9.44597e17i | 0.169706 | + | 0.127901i | ||||
\(497\) | 6.64732e18 | 0.887466 | ||||||||
\(498\) | 1.62294e18 | − | 2.62253e18i | 0.213646 | − | 0.345235i | ||||
\(499\) | − | 1.24967e18i | − | 0.162215i | −0.996705 | − | 0.0811075i | \(-0.974154\pi\) | ||
0.996705 | − | 0.0811075i | \(-0.0258457\pi\) | |||||||
\(500\) | 2.53250e18 | + | 5.07985e18i | 0.324160 | + | 0.650221i | ||||
\(501\) | 2.28520e18 | 0.288443 | ||||||||
\(502\) | 4.08956e18 | + | 2.53080e18i | 0.509039 | + | 0.315015i | ||||
\(503\) | 1.01888e19i | 1.25069i | 0.780349 | + | 0.625344i | \(0.215041\pi\) | ||||
−0.780349 | + | 0.625344i | \(0.784959\pi\) | |||||||
\(504\) | 1.12863e17 | − | 1.22758e18i | 0.0136628 | − | 0.148605i | ||||
\(505\) | 3.39345e18 | 0.405137 | ||||||||
\(506\) | −4.43550e18 | + | 7.16740e18i | −0.522262 | + | 0.843934i | ||||
\(507\) | − | 3.27290e18i | − | 0.380081i | ||||||
\(508\) | −4.29418e18 | + | 2.14081e18i | −0.491852 | + | 0.245207i | ||||
\(509\) | 1.16612e19 | 1.31741 | 0.658704 | − | 0.752402i | \(-0.271105\pi\) | ||||
0.658704 | + | 0.752402i | \(0.271105\pi\) | |||||||
\(510\) | −2.02676e18 | − | 1.25424e18i | −0.225845 | − | 0.139762i | ||||
\(511\) | 6.71395e18i | 0.737958i | ||||||||
\(512\) | −8.87669e18 | − | 2.50499e18i | −0.962413 | − | 0.271591i | ||||
\(513\) | −7.58862e17 | −0.0811599 | ||||||||
\(514\) | 2.33335e18 | − | 3.77051e18i | 0.246172 | − | 0.397794i | ||||
\(515\) | − | 6.21604e18i | − | 0.646939i | ||||||
\(516\) | −3.04180e18 | − | 6.10144e18i | −0.312308 | − | 0.626448i | ||||
\(517\) | 8.33498e18 | 0.844250 | ||||||||
\(518\) | −4.64524e18 | − | 2.87468e18i | −0.464195 | − | 0.287264i | ||||
\(519\) | 5.49532e18i | 0.541778i | ||||||||
\(520\) | 2.35663e18 | + | 2.16668e17i | 0.229228 | + | 0.0210752i | ||||
\(521\) | 2.34671e18 | 0.225214 | 0.112607 | − | 0.993640i | \(-0.464080\pi\) | ||||
0.112607 | + | 0.993640i | \(0.464080\pi\) | |||||||
\(522\) | −2.61074e18 | + | 4.21874e18i | −0.247212 | + | 0.399475i | ||||
\(523\) | − | 1.95230e19i | − | 1.82404i | −0.410147 | − | 0.912020i | \(-0.634523\pi\) | ||
0.410147 | − | 0.912020i | \(-0.365477\pi\) | |||||||
\(524\) | 1.30880e19 | − | 6.52486e18i | 1.20657 | − | 0.601523i | ||||
\(525\) | −2.40077e18 | −0.218392 | ||||||||
\(526\) | −4.91238e18 | − | 3.03999e18i | −0.440953 | − | 0.272880i | ||||
\(527\) | 2.80244e18i | 0.248235i | ||||||||
\(528\) | −6.94366e18 | + | 9.21321e18i | −0.606947 | + | 0.805329i | ||||
\(529\) | 7.85000e18 | 0.677142 | ||||||||
\(530\) | −3.04927e18 | + | 4.92737e18i | −0.259576 | + | 0.419454i | ||||
\(531\) | − | 3.68928e18i | − | 0.309942i | ||||||
\(532\) | 1.01598e18 | + | 2.03792e18i | 0.0842372 | + | 0.168968i | ||||
\(533\) | −7.41017e18 | −0.606370 | ||||||||
\(534\) | 6.32753e18 | + | 3.91575e18i | 0.511029 | + | 0.316247i | ||||
\(535\) | − | 2.58440e18i | − | 0.206008i | ||||||
\(536\) | 5.04947e17 | − | 5.49214e18i | 0.0397276 | − | 0.432104i | ||||
\(537\) | 7.31857e17 | 0.0568338 | ||||||||
\(538\) | −1.29901e19 | + | 2.09909e19i | −0.995718 | + | 1.60900i | ||||
\(539\) | − | 1.84580e19i | − | 1.39657i | ||||||
\(540\) | −9.08153e17 | + | 4.52749e17i | −0.0678270 | + | 0.0338143i | ||||
\(541\) | 1.02621e19 | 0.756583 | 0.378291 | − | 0.925687i | \(-0.376512\pi\) | ||||
0.378291 | + | 0.925687i | \(0.376512\pi\) | |||||||
\(542\) | −1.31834e19 | − | 8.15845e18i | −0.959472 | − | 0.593762i | ||||
\(543\) | 2.10670e18i | 0.151357i | ||||||||
\(544\) | −5.96787e18 | − | 1.53503e19i | −0.423280 | − | 1.08874i | ||||
\(545\) | −8.73649e18 | −0.611733 | ||||||||
\(546\) | −1.15015e18 | + | 1.85856e18i | −0.0795074 | + | 0.128477i | ||||
\(547\) | 2.17511e19i | 1.48447i | 0.670141 | + | 0.742233i | \(0.266233\pi\) | ||||
−0.670141 | + | 0.742233i | \(0.733767\pi\) | |||||||
\(548\) | −8.17253e17 | − | 1.63930e18i | −0.0550672 | − | 0.110457i | ||||
\(549\) | −1.14310e18 | −0.0760462 | ||||||||
\(550\) | 1.91053e19 | + | 1.18232e19i | 1.25492 | + | 0.776597i | ||||
\(551\) | − | 9.16433e18i | − | 0.594346i | ||||||
\(552\) | −5.10142e18 | − | 4.69024e17i | −0.326676 | − | 0.0300345i | ||||
\(553\) | −9.92746e18 | −0.627715 | ||||||||
\(554\) | −6.68205e18 | + | 1.07976e19i | −0.417197 | + | 0.674157i | ||||
\(555\) | 4.49675e18i | 0.277235i | ||||||||
\(556\) | −2.00733e19 | + | 1.00073e19i | −1.22207 | + | 0.609247i | ||||
\(557\) | 5.10549e17 | 0.0306938 | 0.0153469 | − | 0.999882i | \(-0.495115\pi\) | ||||
0.0153469 | + | 0.999882i | \(0.495115\pi\) | |||||||
\(558\) | 1.01457e18 | + | 6.27862e17i | 0.0602344 | + | 0.0372756i | ||||
\(559\) | 1.20876e19i | 0.708690i | ||||||||
\(560\) | 2.43171e18 | + | 1.83269e18i | 0.140798 | + | 0.106114i | ||||
\(561\) | −2.06005e19 | −1.17798 | ||||||||
\(562\) | 1.26154e18 | − | 2.03854e18i | 0.0712435 | − | 0.115124i | ||||
\(563\) | − | 2.78917e19i | − | 1.55566i | −0.628472 | − | 0.777832i | \(-0.716319\pi\) | ||
0.628472 | − | 0.777832i | \(-0.283681\pi\) | |||||||
\(564\) | 2.26023e18 | + | 4.53372e18i | 0.124509 | + | 0.249747i | ||||
\(565\) | 4.47279e18 | 0.243355 | ||||||||
\(566\) | 4.72601e18 | + | 2.92466e18i | 0.253969 | + | 0.157167i | ||||
\(567\) | − | 9.37179e17i | − | 0.0497440i | ||||||
\(568\) | 3.46164e18 | − | 3.76512e19i | 0.181486 | − | 1.97397i | ||||
\(569\) | 2.07494e19 | 1.07453 | 0.537266 | − | 0.843413i | \(-0.319457\pi\) | ||||
0.537266 | + | 0.843413i | \(0.319457\pi\) | |||||||
\(570\) | 9.86386e17 | − | 1.59392e18i | 0.0504572 | − | 0.0815347i | ||||
\(571\) | − | 1.24535e19i | − | 0.629274i | −0.949212 | − | 0.314637i | \(-0.898117\pi\) | ||
0.949212 | − | 0.314637i | \(-0.101883\pi\) | |||||||
\(572\) | 1.83058e19 | − | 9.12615e18i | 0.913728 | − | 0.455528i | ||||
\(573\) | 9.77981e18 | 0.482223 | ||||||||
\(574\) | −8.10754e18 | − | 5.01729e18i | −0.394917 | − | 0.244392i | ||||
\(575\) | 9.97685e18i | 0.480085i | ||||||||
\(576\) | −6.89436e18 | − | 1.27854e18i | −0.327745 | − | 0.0607795i | ||||
\(577\) | −9.37091e18 | −0.440099 | −0.220050 | − | 0.975489i | \(-0.570622\pi\) | ||||
−0.220050 | + | 0.975489i | \(0.570622\pi\) | |||||||
\(578\) | 4.13426e18 | − | 6.68063e18i | 0.191824 | − | 0.309972i | ||||
\(579\) | − | 5.29361e17i | − | 0.0242662i | ||||||
\(580\) | −5.46758e18 | − | 1.09672e19i | −0.247628 | − | 0.496707i | ||||
\(581\) | −7.03556e18 | −0.314822 | ||||||||
\(582\) | 1.90171e19 | + | 1.17686e19i | 0.840780 | + | 0.520311i | ||||
\(583\) | 5.00833e19i | 2.18783i | ||||||||
\(584\) | 3.80286e19 | + | 3.49634e18i | 1.64142 | + | 0.150912i | ||||
\(585\) | 1.79914e18 | 0.0767316 | ||||||||
\(586\) | 2.04638e19 | − | 3.30679e19i | 0.862389 | − | 1.39355i | ||||
\(587\) | 2.05232e19i | 0.854631i | 0.904103 | + | 0.427315i | \(0.140541\pi\) | ||||
−0.904103 | + | 0.427315i | \(0.859459\pi\) | |||||||
\(588\) | 1.00400e19 | − | 5.00533e18i | 0.413136 | − | 0.205964i | ||||
\(589\) | −2.20395e18 | −0.0896179 | ||||||||
\(590\) | 7.74900e18 | + | 4.79541e18i | 0.311374 | + | 0.192691i | ||||
\(591\) | − | 2.22359e19i | − | 0.882963i | ||||||
\(592\) | −1.87016e19 | + | 2.48142e19i | −0.733881 | + | 0.973752i | ||||
\(593\) | −1.53306e19 | −0.594535 | −0.297268 | − | 0.954794i | \(-0.596075\pi\) | ||||
−0.297268 | + | 0.954794i | \(0.596075\pi\) | |||||||
\(594\) | −4.61537e18 | + | 7.45806e18i | −0.176889 | + | 0.285838i | ||||
\(595\) | 5.43725e18i | 0.205949i | ||||||||
\(596\) | −3.10446e17 | − | 6.22714e17i | −0.0116215 | − | 0.0233112i | ||||
\(597\) | −7.14347e18 | −0.264295 | ||||||||
\(598\) | 7.72357e18 | + | 4.77968e18i | 0.282429 | + | 0.174779i | ||||
\(599\) | 1.55665e19i | 0.562605i | 0.959619 | + | 0.281302i | \(0.0907664\pi\) | ||||
−0.959619 | + | 0.281302i | \(0.909234\pi\) | |||||||
\(600\) | −1.25022e18 | + | 1.35983e19i | −0.0446610 | + | 0.485763i | ||||
\(601\) | 6.07039e18 | 0.214336 | 0.107168 | − | 0.994241i | \(-0.465822\pi\) | ||||
0.107168 | + | 0.994241i | \(0.465822\pi\) | |||||||
\(602\) | −8.18428e18 | + | 1.32251e19i | −0.285631 | + | 0.461556i | ||||
\(603\) | − | 4.19291e18i | − | 0.144642i | ||||||
\(604\) | −6.07621e18 | + | 3.02922e18i | −0.207193 | + | 0.103293i | ||||
\(605\) | −2.39608e19 | −0.807632 | ||||||||
\(606\) | 1.51586e19 | + | 9.38076e18i | 0.505067 | + | 0.312557i | ||||
\(607\) | 3.31096e19i | 1.09052i | 0.838267 | + | 0.545260i | \(0.183569\pi\) | ||||
−0.838267 | + | 0.545260i | \(0.816431\pi\) | |||||||
\(608\) | 1.20721e19 | − | 4.69337e18i | 0.393059 | − | 0.152813i | ||||
\(609\) | 1.13178e19 | 0.364283 | ||||||||
\(610\) | 1.48583e18 | − | 2.40097e18i | 0.0472780 | − | 0.0763974i | ||||
\(611\) | − | 8.98175e18i | − | 0.282535i | ||||||
\(612\) | −5.58633e18 | − | 1.12054e19i | −0.173727 | − | 0.348472i | ||||
\(613\) | −2.86054e18 | −0.0879479 | −0.0439739 | − | 0.999033i | \(-0.514002\pi\) | ||||
−0.0439739 | + | 0.999033i | \(0.514002\pi\) | |||||||
\(614\) | −6.60552e18 | − | 4.08778e18i | −0.200784 | − | 0.124253i | ||||
\(615\) | 7.84836e18i | 0.235859i | ||||||||
\(616\) | 2.62077e19 | + | 2.40953e18i | 0.778689 | + | 0.0715926i | ||||
\(617\) | 1.58813e19 | 0.466541 | 0.233271 | − | 0.972412i | \(-0.425057\pi\) | ||||
0.233271 | + | 0.972412i | \(0.425057\pi\) | |||||||
\(618\) | 1.71835e19 | − | 2.77671e19i | 0.499104 | − | 0.806512i | ||||
\(619\) | − | 2.38745e19i | − | 0.685646i | −0.939400 | − | 0.342823i | \(-0.888617\pi\) | ||
0.939400 | − | 0.342823i | \(-0.111383\pi\) | |||||||
\(620\) | −2.63753e18 | + | 1.31491e18i | −0.0748955 | + | 0.0373383i | ||||
\(621\) | −3.89462e18 | −0.109351 | ||||||||
\(622\) | −4.35488e19 | − | 2.69499e19i | −1.20905 | − | 0.748210i | ||||
\(623\) | − | 1.69751e19i | − | 0.466010i | ||||||
\(624\) | 9.92812e18 | + | 7.48246e18i | 0.269510 | + | 0.203120i | ||||
\(625\) | 2.08167e19 | 0.558795 | ||||||||
\(626\) | −1.97300e19 | + | 3.18821e19i | −0.523729 | + | 0.846304i | ||||
\(627\) | − | 1.62011e19i | − | 0.425276i | ||||||
\(628\) | −1.08450e19 | − | 2.17535e19i | −0.281521 | − | 0.564692i | ||||
\(629\) | −5.54840e19 | −1.42434 | ||||||||
\(630\) | 1.96846e18 | + | 1.21817e18i | 0.0499738 | + | 0.0309259i | ||||
\(631\) | − | 5.06382e19i | − | 1.27137i | −0.771948 | − | 0.635686i | \(-0.780717\pi\) | ||
0.771948 | − | 0.635686i | \(-0.219283\pi\) | |||||||
\(632\) | −5.16980e18 | + | 5.62303e19i | −0.128367 | + | 1.39621i | ||||
\(633\) | −3.58101e19 | −0.879386 | ||||||||
\(634\) | 1.11506e19 | − | 1.80185e19i | 0.270816 | − | 0.437617i | ||||
\(635\) | − | 9.01027e18i | − | 0.216432i | ||||||
\(636\) | −2.72422e19 | + | 1.35813e19i | −0.647206 | + | 0.322657i | ||||
\(637\) | −1.98903e19 | −0.467375 | ||||||||
\(638\) | −9.00665e19 | − | 5.57370e19i | −2.09324 | − | 1.29539i | ||||
\(639\) | − | 2.87444e19i | − | 0.660765i | ||||||
\(640\) | 1.16469e19 | − | 1.28191e19i | 0.264820 | − | 0.291472i | ||||
\(641\) | 2.72200e19 | 0.612183 | 0.306092 | − | 0.952002i | \(-0.400979\pi\) | ||||
0.306092 | + | 0.952002i | \(0.400979\pi\) | |||||||
\(642\) | 7.14426e18 | − | 1.15445e19i | 0.158932 | − | 0.256822i | ||||
\(643\) | − | 4.50961e18i | − | 0.0992343i | −0.998768 | − | 0.0496172i | \(-0.984200\pi\) | ||
0.998768 | − | 0.0496172i | \(-0.0158001\pi\) | |||||||
\(644\) | 5.21420e18 | + | 1.04590e19i | 0.113498 | + | 0.227661i | ||||
\(645\) | 1.28023e19 | 0.275659 | ||||||||
\(646\) | 1.96669e19 | + | 1.21707e19i | 0.418898 | + | 0.259232i | ||||
\(647\) | 2.95245e19i | 0.622089i | 0.950395 | + | 0.311045i | \(0.100679\pi\) | ||||
−0.950395 | + | 0.311045i | \(0.899321\pi\) | |||||||
\(648\) | −5.30829e18 | − | 4.88043e17i | −0.110644 | − | 0.0101726i | ||||
\(649\) | 7.87631e19 | 1.62409 | ||||||||
\(650\) | 1.27406e19 | − | 2.05878e19i | 0.259895 | − | 0.419968i | ||||
\(651\) | − | 2.72183e18i | − | 0.0549281i | ||||||
\(652\) | −4.38343e19 | + | 2.18531e19i | −0.875147 | + | 0.436294i | ||||
\(653\) | 1.20764e19 | 0.238531 | 0.119266 | − | 0.992862i | \(-0.461946\pi\) | ||||
0.119266 | + | 0.992862i | \(0.461946\pi\) | |||||||
\(654\) | −3.90260e19 | − | 2.41509e19i | −0.762622 | − | 0.471943i | ||||
\(655\) | 2.74618e19i | 0.530934i | ||||||||
\(656\) | −3.26406e19 | + | 4.33092e19i | −0.624354 | + | 0.828426i | ||||
\(657\) | 2.90325e19 | 0.549448 | ||||||||
\(658\) | 6.08138e18 | − | 9.82702e18i | 0.113873 | − | 0.184010i | ||||
\(659\) | 4.66830e19i | 0.864890i | 0.901660 | + | 0.432445i | \(0.142349\pi\) | ||||
−0.901660 | + | 0.432445i | \(0.857651\pi\) | |||||||
\(660\) | −9.66580e18 | − | 1.93883e19i | −0.177186 | − | 0.355412i | ||||
\(661\) | 6.58636e19 | 1.19464 | 0.597318 | − | 0.802005i | \(-0.296233\pi\) | ||||
0.597318 | + | 0.802005i | \(0.296233\pi\) | |||||||
\(662\) | 7.69308e19 | + | 4.76081e19i | 1.38068 | + | 0.854427i | ||||
\(663\) | 2.21991e19i | 0.394221i | ||||||||
\(664\) | −3.66382e18 | + | 3.98502e19i | −0.0643810 | + | 0.700251i | ||||
\(665\) | −4.27606e18 | −0.0743520 | ||||||||
\(666\) | −1.24307e19 | + | 2.00870e19i | −0.213883 | + | 0.345617i | ||||
\(667\) | − | 4.70330e19i | − | 0.800796i | ||||||
\(668\) | −2.65372e19 | + | 1.32298e19i | −0.447115 | + | 0.222904i | ||||
\(669\) | 3.89915e19 | 0.650110 | ||||||||
\(670\) | 8.80683e18 | + | 5.45004e18i | 0.145310 | + | 0.0899241i | ||||
\(671\) | − | 2.44042e19i | − | 0.398480i | ||||||
\(672\) | 5.79621e18 | + | 1.49088e19i | 0.0936611 | + | 0.240911i | ||||
\(673\) | −8.37485e19 | −1.33928 | −0.669640 | − | 0.742686i | \(-0.733552\pi\) | ||||
−0.669640 | + | 0.742686i | \(0.733552\pi\) | |||||||
\(674\) | 6.94325e18 | − | 1.12197e19i | 0.109886 | − | 0.177567i | ||||
\(675\) | 1.03814e19i | 0.162604i | ||||||||
\(676\) | 1.89479e19 | + | 3.80069e19i | 0.293720 | + | 0.589163i | ||||
\(677\) | 7.84417e19 | 1.20344 | 0.601722 | − | 0.798705i | \(-0.294481\pi\) | ||||
0.601722 | + | 0.798705i | \(0.294481\pi\) | |||||||
\(678\) | 1.99800e19 | + | 1.23645e19i | 0.303380 | + | 0.187745i | ||||
\(679\) | − | 5.10177e19i | − | 0.766713i | ||||||
\(680\) | 3.07972e19 | + | 2.83149e18i | 0.458088 | + | 0.0421165i | ||||
\(681\) | −3.16237e19 | −0.465567 | ||||||||
\(682\) | −1.34043e19 | + | 2.16603e19i | −0.195323 | + | 0.315627i | ||||
\(683\) | − | 6.47022e18i | − | 0.0933198i | −0.998911 | − | 0.0466599i | \(-0.985142\pi\) | ||
0.998911 | − | 0.0466599i | \(-0.0148577\pi\) | |||||||
\(684\) | 8.81238e18 | − | 4.39331e18i | 0.125806 | − | 0.0627190i | ||||
\(685\) | 3.43966e18 | 0.0486051 | ||||||||
\(686\) | −4.89796e19 | − | 3.03107e19i | −0.685087 | − | 0.423962i | ||||
\(687\) | 5.83733e19i | 0.808196i | ||||||||
\(688\) | 7.06466e19 | + | 5.32438e19i | 0.968216 | + | 0.729709i | ||||
\(689\) | 5.39695e19 | 0.732174 | ||||||||
\(690\) | 5.06231e18 | − | 8.18029e18i | 0.0679838 | − | 0.109856i | ||||
\(691\) | 4.17252e19i | 0.554692i | 0.960770 | + | 0.277346i | \(0.0894548\pi\) | ||||
−0.960770 | + | 0.277346i | \(0.910545\pi\) | |||||||
\(692\) | −3.18143e19 | − | 6.38151e19i | −0.418677 | − | 0.839810i | ||||
\(693\) | 2.00080e19 | 0.260658 | ||||||||
\(694\) | 2.70385e19 | + | 1.67326e19i | 0.348711 | + | 0.215797i | ||||
\(695\) | − | 4.21188e19i | − | 0.537752i | ||||||
\(696\) | 5.89381e18 | − | 6.41051e19i | 0.0744958 | − | 0.810266i | ||||
\(697\) | −9.68386e19 | −1.21177 | ||||||||
\(698\) | 3.45882e19 | − | 5.58918e19i | 0.428490 | − | 0.692405i | ||||
\(699\) | 3.14613e18i | 0.0385866i | ||||||||
\(700\) | 2.78793e19 | − | 1.38989e19i | 0.338528 | − | 0.168769i | ||||
\(701\) | −2.45302e19 | −0.294900 | −0.147450 | − | 0.989069i | \(-0.547107\pi\) | ||||
−0.147450 | + | 0.989069i | \(0.547107\pi\) | |||||||
\(702\) | 8.03678e18 | + | 4.97350e18i | 0.0956582 | + | 0.0591974i | ||||
\(703\) | − | 4.36348e19i | − | 0.514216i | ||||||
\(704\) | 2.72957e19 | − | 1.47189e20i | 0.318483 | − | 1.71738i | ||||
\(705\) | −9.51287e18 | −0.109897 | ||||||||
\(706\) | −2.97450e19 | + | 4.80655e19i | −0.340237 | + | 0.549795i | ||||
\(707\) | − | 4.06664e19i | − | 0.460574i | ||||||
\(708\) | 2.13585e19 | + | 4.28423e19i | 0.239518 | + | 0.480441i | ||||
\(709\) | −1.36131e20 | −1.51158 | −0.755792 | − | 0.654812i | \(-0.772748\pi\) | ||||
−0.755792 | + | 0.654812i | \(0.772748\pi\) | |||||||
\(710\) | 6.03749e19 | + | 3.73626e19i | 0.663816 | + | 0.410798i | ||||
\(711\) | 4.29284e19i | 0.467366i | ||||||||
\(712\) | −9.61488e19 | − | 8.83991e18i | −1.03654 | − | 0.0952989i | ||||
\(713\) | −1.13111e19 | −0.120747 | ||||||||
\(714\) | −1.50306e19 | + | 2.42882e19i | −0.158887 | + | 0.256749i | ||||
\(715\) | 3.84102e19i | 0.402072i | ||||||||
\(716\) | −8.49879e18 | + | 4.23697e18i | −0.0880979 | + | 0.0439202i | ||||
\(717\) | 1.66323e19 | 0.170733 | ||||||||
\(718\) | 2.85714e19 | + | 1.76812e19i | 0.290443 | + | 0.179738i | ||||
\(719\) | 7.37506e19i | 0.742443i | 0.928544 | + | 0.371221i | \(0.121061\pi\) | ||||
−0.928544 | + | 0.371221i | \(0.878939\pi\) | |||||||
\(720\) | 7.92492e18 | − | 1.05152e19i | 0.0790074 | − | 0.104831i | ||||
\(721\) | −7.44917e19 | −0.735464 | ||||||||
\(722\) | 4.42474e19 | − | 7.15002e19i | 0.432641 | − | 0.699112i | ||||
\(723\) | 4.17501e19i | 0.404286i | ||||||||
\(724\) | −1.21964e19 | − | 2.44643e19i | −0.116966 | − | 0.234619i | ||||
\(725\) | −1.25370e20 | −1.19077 | ||||||||
\(726\) | −1.07033e20 | − | 6.62366e19i | −1.00684 | − | 0.623077i | ||||
\(727\) | − | 1.10896e20i | − | 1.03318i | −0.856234 | − | 0.516589i | \(-0.827202\pi\) | ||
0.856234 | − | 0.516589i | \(-0.172798\pi\) | |||||||
\(728\) | 2.59650e18 | − | 2.82413e19i | 0.0239590 | − | 0.260595i | ||||
\(729\) | −4.05256e18 | −0.0370370 | ||||||||
\(730\) | −3.77371e19 | + | 6.09801e19i | −0.341592 | + | 0.551986i | ||||
\(731\) | 1.57964e20i | 1.41624i | ||||||||
\(732\) | 1.32744e19 | − | 6.61779e18i | 0.117879 | − | 0.0587672i | ||||
\(733\) | −8.60133e18 | −0.0756550 | −0.0378275 | − | 0.999284i | \(-0.512044\pi\) | ||||
−0.0378275 | + | 0.999284i | \(0.512044\pi\) | |||||||
\(734\) | −2.63644e18 | − | 1.63154e18i | −0.0229692 | − | 0.0142143i | ||||
\(735\) | 2.10665e19i | 0.181794i | ||||||||
\(736\) | 6.19562e19 | − | 2.40872e19i | 0.529590 | − | 0.205893i | ||||
\(737\) | 8.95152e19 | 0.757922 | ||||||||
\(738\) | −2.16958e19 | + | 3.50587e19i | −0.181962 | + | 0.294036i | ||||
\(739\) | 9.08303e19i | 0.754605i | 0.926090 | + | 0.377302i | \(0.123148\pi\) | ||||
−0.926090 | + | 0.377302i | \(0.876852\pi\) | |||||||
\(740\) | −2.60332e19 | − | 5.22190e19i | −0.214242 | − | 0.429741i | ||||
\(741\) | −1.74582e19 | −0.142322 | ||||||||
\(742\) | 5.90486e19 | + | 3.65418e19i | 0.476850 | + | 0.295095i | ||||
\(743\) | − | 9.43891e19i | − | 0.755093i | −0.925991 | − | 0.377546i | \(-0.876768\pi\) | ||
0.925991 | − | 0.377546i | \(-0.123232\pi\) | |||||||
\(744\) | −1.54168e19 | − | 1.41742e18i | −0.122175 | − | 0.0112328i | ||||
\(745\) | 1.30661e18 | 0.0102577 | ||||||||
\(746\) | −3.13078e19 | + | 5.05909e19i | −0.243490 | + | 0.393460i | ||||
\(747\) | 3.04232e19i | 0.234402i | ||||||||
\(748\) | 2.39226e20 | − | 1.19263e20i | 1.82599 | − | 0.910325i | ||||
\(749\) | −3.09709e19 | −0.234197 | ||||||||
\(750\) | −4.76129e19 | − | 2.94649e19i | −0.356694 | − | 0.220737i | ||||
\(751\) | − | 1.32469e20i | − | 0.983182i | −0.870826 | − | 0.491591i | \(-0.836415\pi\) | ||
0.870826 | − | 0.491591i | \(-0.163585\pi\) | |||||||
\(752\) | −5.24944e19 | − | 3.95631e19i | −0.386001 | − | 0.290915i | ||||
\(753\) | −4.74418e19 | −0.345618 | ||||||||
\(754\) | −6.00620e19 | + | 9.70554e19i | −0.433511 | + | 0.700519i | ||||
\(755\) | − | 1.27494e19i | − | 0.0911719i | ||||||
\(756\) | 5.42565e18 | + | 1.08831e19i | 0.0384414 | + | 0.0771082i | ||||
\(757\) | 9.32107e19 | 0.654327 | 0.327163 | − | 0.944968i | \(-0.393907\pi\) | ||||
0.327163 | + | 0.944968i | \(0.393907\pi\) | |||||||
\(758\) | 1.81562e20 | + | 1.12358e20i | 1.26281 | + | 0.781483i | ||||
\(759\) | − | 8.31469e19i | − | 0.572998i | ||||||
\(760\) | −2.22679e18 | + | 2.42201e19i | −0.0152049 | + | 0.165379i | ||||
\(761\) | 1.19531e20 | 0.808702 | 0.404351 | − | 0.914604i | \(-0.367497\pi\) | ||||
0.404351 | + | 0.914604i | \(0.367497\pi\) | |||||||
\(762\) | 2.49078e19 | − | 4.02489e19i | 0.166974 | − | 0.269817i | ||||
\(763\) | 1.04696e20i | 0.695440i | ||||||||
\(764\) | −1.13569e20 | + | 5.66186e19i | −0.747494 | + | 0.372654i | ||||
\(765\) | 2.35118e19 | 0.153340 | ||||||||
\(766\) | −3.59170e19 | − | 2.22270e19i | −0.232113 | − | 0.143641i | ||||
\(767\) | − | 8.48749e19i | − | 0.543515i | ||||||
\(768\) | 8.74635e19 | − | 2.50666e19i | 0.555007 | − | 0.159062i | ||||
\(769\) | −8.80481e19 | −0.553651 | −0.276825 | − | 0.960920i | \(-0.589282\pi\) | ||||
−0.276825 | + | 0.960920i | \(0.589282\pi\) | |||||||
\(770\) | −2.60068e19 | + | 4.20249e19i | −0.162051 | + | 0.261862i | ||||
\(771\) | 4.37405e19i | 0.270087i | ||||||||
\(772\) | 3.06465e18 | + | 6.14727e18i | 0.0187525 | + | 0.0376150i | ||||
\(773\) | −7.84083e19 | −0.475451 | −0.237725 | − | 0.971332i | \(-0.576402\pi\) | ||||
−0.237725 | + | 0.971332i | \(0.576402\pi\) | |||||||
\(774\) | 5.71882e19 | + | 3.53905e19i | 0.343652 | + | 0.212667i | ||||
\(775\) | 3.01506e19i | 0.179550i | ||||||||
\(776\) | −2.88970e20 | − | 2.65679e19i | −1.70538 | − | 0.156792i | ||||
\(777\) | 5.38881e19 | 0.315170 | ||||||||
\(778\) | 3.07289e19 | − | 4.96554e19i | 0.178111 | − | 0.287813i | ||||
\(779\) | − | 7.61576e19i | − | 0.437473i | ||||||
\(780\) | −2.08928e19 | + | 1.04158e19i | −0.118942 | + | 0.0592969i | ||||
\(781\) | 6.13668e20 | 3.46239 | ||||||||
\(782\) | 1.00934e20 | + | 6.24624e19i | 0.564405 | + | 0.349278i | ||||
\(783\) | − | 4.89403e19i | − | 0.271228i | ||||||
\(784\) | −8.76135e19 | + | 1.16250e20i | −0.481237 | + | 0.638530i | ||||
\(785\) | 4.56443e19 | 0.248484 | ||||||||
\(786\) | −7.59148e19 | + | 1.22672e20i | −0.409608 | + | 0.661894i | ||||
\(787\) | − | 1.07032e20i | − | 0.572390i | −0.958171 | − | 0.286195i | \(-0.907610\pi\) | ||
0.958171 | − | 0.286195i | \(-0.0923905\pi\) | |||||||
\(788\) | 1.28731e20 | + | 2.58217e20i | 0.682339 | + | 1.36868i | ||||
\(789\) | 5.69870e19 | 0.299390 | ||||||||
\(790\) | −9.01671e19 | − | 5.57993e19i | −0.469525 | − | 0.290562i | ||||
\(791\) | − | 5.36010e19i | − | 0.276654i | ||||||
\(792\) | 1.04193e19 | − | 1.13328e20i | 0.0533044 | − | 0.579775i | ||||
\(793\) | −2.62979e19 | −0.133355 | ||||||||
\(794\) | −4.79626e19 | + | 7.75036e19i | −0.241079 | + | 0.389564i | ||||
\(795\) | − | 5.71609e19i | − | 0.284793i | ||||||
\(796\) | 8.29545e19 | − | 4.13560e19i | 0.409683 | − | 0.204243i | ||||
\(797\) | −1.83071e20 | −0.896213 | −0.448106 | − | 0.893980i | \(-0.647901\pi\) | ||||
−0.448106 | + | 0.893980i | \(0.647901\pi\) | |||||||
\(798\) | −1.91012e19 | − | 1.18206e19i | −0.0926916 | − | 0.0573615i | ||||
\(799\) | − | 1.17376e20i | − | 0.564616i | ||||||
\(800\) | −6.42065e19 | − | 1.65149e20i | −0.306160 | − | 0.787494i | ||||
\(801\) | −7.34037e19 | −0.346969 | ||||||||
\(802\) | 7.56295e18 | − | 1.22211e19i | 0.0354381 | − | 0.0572651i | ||||
\(803\) | 6.19819e20i | 2.87910i | ||||||||
\(804\) | 2.42742e19 | + | 4.86907e19i | 0.111777 | + | 0.224210i | ||||
\(805\) | −2.19455e19 | −0.100179 | ||||||||
\(806\) | 2.33411e19 | + | 1.44445e19i | 0.105627 | + | 0.0653666i | ||||
\(807\) | − | 2.43509e20i | − | 1.09245i | ||||||
\(808\) | −2.30339e20 | − | 2.11773e19i | −1.02444 | − | 0.0941872i | ||||
\(809\) | 2.61524e20 | 1.15311 | 0.576557 | − | 0.817057i | \(-0.304396\pi\) | ||||
0.576557 | + | 0.817057i | \(0.304396\pi\) | |||||||
\(810\) | 5.26760e18 | − | 8.51202e18i | 0.0230260 | − | 0.0372081i | ||||
\(811\) | 8.41939e19i | 0.364867i | 0.983218 | + | 0.182434i | \(0.0583974\pi\) | ||||
−0.983218 | + | 0.182434i | \(0.941603\pi\) | |||||||
\(812\) | −1.31429e20 | + | 6.55223e19i | −0.564675 | + | 0.281512i | ||||
\(813\) | 1.52937e20 | 0.651444 | ||||||||
\(814\) | −4.28840e20 | − | 2.65385e20i | −1.81103 | − | 1.12074i | ||||
\(815\) | − | 9.19754e19i | − | 0.385095i | ||||||
\(816\) | 1.29744e20 | + | 9.77833e19i | 0.538587 | + | 0.405913i | ||||
\(817\) | −1.24229e20 | −0.511293 | ||||||||
\(818\) | 9.19553e19 | − | 1.48592e20i | 0.375235 | − | 0.606350i | ||||
\(819\) | − | 2.15605e19i | − | 0.0872313i | ||||||
\(820\) | −4.54368e19 | − | 9.11401e19i | −0.182268 | − | 0.365605i | ||||
\(821\) | −6.50000e19 | −0.258530 | −0.129265 | − | 0.991610i | \(-0.541262\pi\) | ||||
−0.129265 | + | 0.991610i | \(0.541262\pi\) | |||||||
\(822\) | 1.53650e19 | + | 9.50851e18i | 0.0605940 | + | 0.0374981i | ||||
\(823\) | 2.68219e20i | 1.04880i | 0.851473 | + | 0.524398i | \(0.175710\pi\) | ||||
−0.851473 | + | 0.524398i | \(0.824290\pi\) | |||||||
\(824\) | −3.87922e19 | + | 4.21930e20i | −0.150402 | + | 1.63587i | ||||
\(825\) | −2.21635e20 | −0.852041 | ||||||||
\(826\) | 5.74672e19 | − | 9.28624e19i | 0.219058 | − | 0.353981i | ||||
\(827\) | − | 3.15873e20i | − | 1.19392i | −0.802272 | − | 0.596958i | \(-0.796376\pi\) | ||
0.802272 | − | 0.596958i | \(-0.203624\pi\) | |||||||
\(828\) | 4.52268e19 | − | 2.25473e19i | 0.169505 | − | 0.0845048i | ||||
\(829\) | −4.92038e20 | −1.82859 | −0.914296 | − | 0.405047i | \(-0.867255\pi\) | ||||
−0.914296 | + | 0.405047i | \(0.867255\pi\) | |||||||
\(830\) | −6.39011e19 | − | 3.95447e19i | −0.235484 | − | 0.145728i | ||||
\(831\) | − | 1.25260e20i | − | 0.457726i | ||||||
\(832\) | −1.58610e20 | − | 2.94138e19i | −0.574735 | − | 0.106583i | ||||
\(833\) | −2.59933e20 | −0.933999 | ||||||||
\(834\) | 1.16432e20 | − | 1.88145e20i | 0.414868 | − | 0.670394i | ||||
\(835\) | − | 5.56816e19i | − | 0.196746i | ||||||
\(836\) | 9.37935e19 | + | 1.88137e20i | 0.328646 | + | 0.659220i | ||||
\(837\) | −1.17698e19 | −0.0408968 | ||||||||
\(838\) | 2.76650e19 | + | 1.71203e19i | 0.0953283 | + | 0.0589932i | ||||
\(839\) | − | 3.72904e20i | − | 1.27428i | −0.770750 | − | 0.637138i | \(-0.780118\pi\) | ||
0.770750 | − | 0.637138i | \(-0.219882\pi\) | |||||||
\(840\) | −2.99113e19 | − | 2.75004e18i | −0.101363 | − | 0.00931933i | ||||
\(841\) | 2.93465e20 | 0.986243 | ||||||||
\(842\) | 9.35753e19 | − | 1.51210e20i | 0.311872 | − | 0.503960i | ||||
\(843\) | 2.36485e19i | 0.0781646i | ||||||||
\(844\) | 4.15849e20 | − | 2.07317e20i | 1.36314 | − | 0.679575i | ||||
\(845\) | −7.97480e19 | −0.259252 | ||||||||
\(846\) | −4.24940e19 | − | 2.62971e19i | −0.137005 | − | 0.0847844i | ||||
\(847\) | 2.87141e20i | 0.918145i | ||||||||
\(848\) | 2.37727e20 | − | 3.15429e20i | 0.753889 | − | 1.00030i | ||||
\(849\) | −5.48251e19 | −0.172435 | ||||||||
\(850\) | 1.66499e20 | − | 2.69048e20i | 0.519372 | − | 0.839262i | ||||
\(851\) | − | 2.23942e20i | − | 0.692832i | ||||||
\(852\) | 1.66411e20 | + | 3.33798e20i | 0.510628 | + | 1.02425i | ||||
\(853\) | 9.24649e19 | 0.281406 | 0.140703 | − | 0.990052i | \(-0.455064\pi\) | ||||
0.140703 | + | 0.990052i | \(0.455064\pi\) | |||||||
\(854\) | −2.87728e19 | − | 1.78058e19i | −0.0868513 | − | 0.0537473i | ||||
\(855\) | 1.84906e19i | 0.0553589i | ||||||||
\(856\) | −1.61284e19 | + | 1.75423e20i | −0.0478932 | + | 0.520919i | ||||
\(857\) | 2.60110e20 | 0.766110 | 0.383055 | − | 0.923726i | \(-0.374872\pi\) | ||||
0.383055 | + | 0.923726i | \(0.374872\pi\) | |||||||
\(858\) | −1.06180e20 | + | 1.71578e20i | −0.310193 | + | 0.501247i | ||||
\(859\) | 4.50661e20i | 1.30586i | 0.757417 | + | 0.652931i | \(0.226461\pi\) | ||||
−0.757417 | + | 0.652931i | \(0.773539\pi\) | |||||||
\(860\) | −1.48669e20 | + | 7.41171e19i | −0.427298 | + | 0.213024i | ||||
\(861\) | 9.40531e19 | 0.268133 | ||||||||
\(862\) | −7.49171e19 | − | 4.63619e19i | −0.211851 | − | 0.131102i | ||||
\(863\) | 5.88823e20i | 1.65162i | 0.563952 | + | 0.825808i | \(0.309280\pi\) | ||||
−0.563952 | + | 0.825808i | \(0.690720\pi\) | |||||||
\(864\) | 6.44687e19 | − | 2.50640e19i | 0.179371 | − | 0.0697356i | ||||
\(865\) | 1.33900e20 | 0.369545 | ||||||||
\(866\) | 1.10681e20 | − | 1.78851e20i | 0.303002 | − | 0.489627i | ||||
\(867\) | 7.74999e19i | 0.210459i | ||||||||
\(868\) | 1.57576e19 | + | 3.16076e19i | 0.0424475 | + | 0.0851440i | ||||
\(869\) | −9.16485e20 | −2.44899 | ||||||||
\(870\) | 1.02795e20 | + | 6.36137e19i | 0.272481 | + | 0.168623i | ||||
\(871\) | − | 9.64612e19i | − | 0.253645i | ||||||
\(872\) | 5.93012e20 | + | 5.45214e19i | 1.54685 | + | 0.142217i | ||||
\(873\) | −2.20611e20 | −0.570858 | ||||||||
\(874\) | −4.91229e19 | + | 7.93786e19i | −0.126097 | + | 0.203762i | ||||
\(875\) | 1.27733e20i | 0.325271i | ||||||||
\(876\) | −3.37144e20 | + | 1.68079e20i | −0.851699 | + | 0.424604i | ||||
\(877\) | 1.50279e20 | 0.376618 | 0.188309 | − | 0.982110i | \(-0.439699\pi\) | ||||
0.188309 | + | 0.982110i | \(0.439699\pi\) | |||||||
\(878\) | 4.32889e20 | + | 2.67890e20i | 1.07625 | + | 0.666032i | ||||
\(879\) | 3.83610e20i | 0.946168i | ||||||||
\(880\) | 2.24491e20 | + | 1.69190e20i | 0.549313 | + | 0.413997i | ||||
\(881\) | 5.39574e20 | 1.30984 | 0.654922 | − | 0.755697i | \(-0.272701\pi\) | ||||
0.654922 | + | 0.755697i | \(0.272701\pi\) | |||||||
\(882\) | −5.82356e19 | + | 9.41041e19i | −0.140252 | + | 0.226636i | ||||
\(883\) | 5.23695e20i | 1.25128i | 0.780113 | + | 0.625639i | \(0.215162\pi\) | ||||
−0.780113 | + | 0.625639i | \(0.784838\pi\) | |||||||
\(884\) | −1.28518e20 | − | 2.57790e20i | −0.304648 | − | 0.611082i | ||||
\(885\) | −8.98938e19 | −0.211411 | ||||||||
\(886\) | 3.49895e20 | + | 2.16530e20i | 0.816397 | + | 0.505221i | ||||
\(887\) | − | 5.41727e20i | − | 1.25405i | −0.778998 | − | 0.627026i | \(-0.784272\pi\) | ||
0.778998 | − | 0.627026i | \(-0.215728\pi\) | |||||||
\(888\) | 2.80626e19 | − | 3.05228e20i | 0.0644522 | − | 0.701026i | ||||
\(889\) | −1.07977e20 | −0.246048 | ||||||||
\(890\) | 9.54118e19 | − | 1.54178e20i | 0.215711 | − | 0.348571i | ||||
\(891\) | − | 8.65186e19i | − | 0.194073i | ||||||
\(892\) | −4.52793e20 | + | 2.25735e20i | −1.00773 | + | 0.502394i | ||||
\(893\) | 9.23094e19 | 0.203838 | ||||||||
\(894\) | 5.83663e18 | + | 3.61195e18i | 0.0127879 | + | 0.00791370i | ||||
\(895\) | − | 1.78326e19i | − | 0.0387662i | ||||||
\(896\) | −1.53621e20 | − | 1.39574e20i | −0.331356 | − | 0.301057i | ||||
\(897\) | −8.95988e19 | −0.191759 | ||||||||
\(898\) | 4.23978e20 | − | 6.85114e20i | 0.900344 | − | 1.45488i | ||||
\(899\) | − | 1.42137e20i | − | 0.299494i | ||||||
\(900\) | −6.01016e19 | − | 1.20556e20i | −0.125658 | − | 0.252052i | ||||
\(901\) | 7.05292e20 | 1.46317 | ||||||||
\(902\) | −7.48473e20 | − | 4.63187e20i | −1.54074 | − | 0.953478i | ||||
\(903\) | − | 1.53421e20i | − | 0.313379i | ||||||
\(904\) | −3.03602e20 | − | 2.79132e19i | −0.615356 | − | 0.0565757i | ||||
\(905\) | 5.13321e19 | 0.103240 | ||||||||
\(906\) | 3.52441e19 | − | 5.69517e19i | 0.0703379 | − | 0.113660i | ||||
\(907\) | − | 4.02735e20i | − | 0.797570i | −0.917045 | − | 0.398785i | \(-0.869432\pi\) | ||
0.917045 | − | 0.398785i | \(-0.130568\pi\) | |||||||
\(908\) | 3.67234e20 | − | 1.83080e20i | 0.721675 | − | 0.359783i | ||||
\(909\) | −1.75850e20 | −0.342921 | ||||||||
\(910\) | 4.52859e19 | + | 2.80249e19i | 0.0876341 | + | 0.0542318i | ||||
\(911\) | − | 4.59442e19i | − | 0.0882271i | −0.999027 | − | 0.0441135i | \(-0.985954\pi\) | ||
0.999027 | − | 0.0441135i | \(-0.0140463\pi\) | |||||||
\(912\) | −7.69006e19 | + | 1.02036e20i | −0.146543 | + | 0.194441i | ||||
\(913\) | −6.49510e20 | −1.22826 | ||||||||
\(914\) | −4.95039e20 | + | 7.99943e20i | −0.929001 | + | 1.50119i | ||||
\(915\) | 2.78530e19i | 0.0518709i | ||||||||
\(916\) | −3.37943e20 | − | 6.77867e20i | −0.624561 | − | 1.25278i | ||||
\(917\) | 3.29097e20 | 0.603585 | ||||||||
\(918\) | 1.05027e20 | + | 6.49954e19i | 0.191163 | + | 0.118300i | ||||
\(919\) | − | 6.77369e20i | − | 1.22354i | −0.791037 | − | 0.611768i | \(-0.790459\pi\) | ||
0.791037 | − | 0.611768i | \(-0.209541\pi\) | |||||||
\(920\) | −1.14283e19 | + | 1.24302e20i | −0.0204865 | + | 0.222825i | ||||
\(921\) | 7.66286e19 | 0.136324 | ||||||||
\(922\) | −5.57088e20 | + | 9.00208e20i | −0.983574 | + | 1.58938i | ||||
\(923\) | − | 6.61287e20i | − | 1.15872i | ||||||
\(924\) | −2.32345e20 | + | 1.15833e20i | −0.404045 | + | 0.201432i | ||||
\(925\) | −5.96935e20 | −1.03023 | ||||||||
\(926\) | −3.23174e20 | − | 1.99994e20i | −0.553553 | − | 0.342562i | ||||
\(927\) | 3.22118e20i | 0.547591i | ||||||||
\(928\) | 3.02683e20 | + | 7.78550e20i | 0.510684 | + | 1.31356i | ||||
\(929\) | 7.95494e20 | 1.33207 | 0.666035 | − | 0.745921i | \(-0.267990\pi\) | ||||
0.666035 | + | 0.745921i | \(0.267990\pi\) | |||||||
\(930\) | 1.52986e19 | − | 2.47213e19i | 0.0254256 | − | 0.0410857i | ||||
\(931\) | − | 2.04421e20i | − | 0.337193i | ||||||
\(932\) | −1.82140e19 | − | 3.65349e19i | −0.0298191 | − | 0.0598131i | ||||
\(933\) | 5.05196e20 | 0.820897 | ||||||||
\(934\) | −2.00971e19 | − | 1.24370e19i | −0.0324120 | − | 0.0200579i | ||||
\(935\) | 5.01957e20i | 0.803498i | ||||||||
\(936\) | −1.22121e20 | − | 1.12278e19i | −0.194026 | − | 0.0178388i | ||||
\(937\) | −7.01109e20 | −1.10563 | −0.552814 | − | 0.833305i | \(-0.686446\pi\) | ||||
−0.552814 | + | 0.833305i | \(0.686446\pi\) | |||||||
\(938\) | 6.53122e19 | − | 1.05539e20i | 0.102229 | − | 0.165194i | ||||
\(939\) | − | 3.69854e20i | − | 0.574608i | ||||||
\(940\) | 1.10469e20 | − | 5.50732e19i | 0.170352 | − | 0.0849269i | ||||
\(941\) | −5.22508e20 | −0.799771 | −0.399885 | − | 0.916565i | \(-0.630950\pi\) | ||||
−0.399885 | + | 0.916565i | \(0.630950\pi\) | |||||||
\(942\) | 2.03893e20 | + | 1.26178e20i | 0.309775 | + | 0.191702i | ||||
\(943\) | − | 3.90855e20i | − | 0.589432i | ||||||
\(944\) | −4.96057e20 | − | 3.73860e20i | −0.742553 | − | 0.559635i | ||||
\(945\) | −2.28355e19 | −0.0339303 | ||||||||
\(946\) | −7.55557e20 | + | 1.22092e21i | −1.11437 | + | 1.80073i | ||||
\(947\) | 8.65791e20i | 1.26755i | 0.773519 | + | 0.633773i | \(0.218494\pi\) | ||||
−0.773519 | + | 0.633773i | \(0.781506\pi\) | |||||||
\(948\) | −2.48527e20 | − | 4.98511e20i | −0.361173 | − | 0.724464i | ||||
\(949\) | 6.67915e20 | 0.963514 | ||||||||
\(950\) | 2.11590e20 | + | 1.30941e20i | 0.302991 | + | 0.187504i | ||||
\(951\) | 2.09027e20i | 0.297125i | ||||||||
\(952\) | 3.39320e19 | − | 3.69067e20i | 0.0478796 | − | 0.520771i | ||||
\(953\) | −9.85667e19 | −0.138064 | −0.0690319 | − | 0.997614i | \(-0.521991\pi\) | ||||
−0.0690319 | + | 0.997614i | \(0.521991\pi\) | |||||||
\(954\) | 1.58014e20 | − | 2.55338e20i | 0.219714 | − | 0.355040i | ||||
\(955\) | − | 2.38297e20i | − | 0.328923i | ||||||
\(956\) | −1.93144e20 | + | 9.62899e19i | −0.264653 | + | 0.131940i | ||||
\(957\) | 1.04483e21 | 1.42123 | ||||||||
\(958\) | 1.01713e21 | + | 6.29444e20i | 1.37347 | + | 0.849960i | ||||
\(959\) | − | 4.12202e19i | − | 0.0552560i | ||||||
\(960\) | −3.11531e19 | + | 1.67989e20i | −0.0414575 | + | 0.223554i | ||||
\(961\) | 7.22761e20 | 0.954841 | ||||||||
\(962\) | −2.85978e20 | + | 4.62117e20i | −0.375065 | + | 0.606075i | ||||
\(963\) | 1.33925e20i | 0.174372i | ||||||||
\(964\) | −2.41705e20 | − | 4.84828e20i | −0.312426 | − | 0.626684i | ||||
\(965\) | −1.28985e19 | −0.0165519 | ||||||||
\(966\) | −9.80309e19 | − | 6.06657e19i | −0.124889 | − | 0.0772864i | ||||
\(967\) | 1.44990e20i | 0.183380i | 0.995788 | + | 0.0916902i | \(0.0292269\pi\) | ||||
−0.995788 | + | 0.0916902i | \(0.970773\pi\) | |||||||
\(968\) | 1.62640e21 | + | 1.49531e20i | 2.04221 | + | 0.187760i | ||||
\(969\) | −2.28150e20 | −0.284416 | ||||||||
\(970\) | 2.86755e20 | − | 4.63373e20i | 0.354903 | − | 0.573494i | ||||
\(971\) | − | 4.14638e20i | − | 0.509489i | −0.967008 | − | 0.254745i | \(-0.918009\pi\) | ||
0.967008 | − | 0.254745i | \(-0.0819914\pi\) | |||||||
\(972\) | 4.70608e19 | − | 2.34616e19i | 0.0574111 | − | 0.0286216i | ||||
\(973\) | −5.04743e20 | −0.611336 | ||||||||
\(974\) | −8.68317e20 | − | 5.37352e20i | −1.04416 | − | 0.646169i | ||||
\(975\) | 2.38833e20i | 0.285142i | ||||||||
\(976\) | −1.15838e20 | + | 1.53700e20i | −0.137310 | + | 0.182190i | ||||
\(977\) | 1.07505e21 | 1.26522 | 0.632610 | − | 0.774470i | \(-0.281983\pi\) | ||||
0.632610 | + | 0.774470i | \(0.281983\pi\) | |||||||
\(978\) | 2.54254e20 | − | 4.10854e20i | 0.297096 | − | 0.480083i | ||||
\(979\) | − | 1.56711e21i | − | 1.81811i | ||||||
\(980\) | −1.21961e20 | − | 2.44637e20i | −0.140488 | − | 0.281799i | ||||
\(981\) | 4.52728e20 | 0.517791 | ||||||||
\(982\) | 6.93310e19 | + | 4.29050e19i | 0.0787313 | + | 0.0487223i | ||||
\(983\) | 1.75429e21i | 1.97800i | 0.147904 | + | 0.989002i | \(0.452747\pi\) | ||||
−0.147904 | + | 0.989002i | \(0.547253\pi\) | |||||||
\(984\) | 4.89789e19 | − | 5.32728e20i | 0.0548332 | − | 0.596403i | ||||
\(985\) | −5.41805e20 | −0.602267 | ||||||||
\(986\) | −7.84910e20 | + | 1.26835e21i | −0.866327 | + | 1.39991i | ||||
\(987\) | 1.14000e20i | 0.124935i | ||||||||
\(988\) | 2.02736e20 | − | 1.01072e20i | 0.220613 | − | 0.109984i | ||||
\(989\) | −6.37568e20 | −0.688894 | ||||||||
\(990\) | 1.81724e20 | + | 1.12459e20i | 0.194970 | + | 0.120656i | ||||
\(991\) | 1.15921e21i | 1.23494i | 0.786595 | + | 0.617469i | \(0.211842\pi\) | ||||
−0.786595 | + | 0.617469i | \(0.788158\pi\) | |||||||
\(992\) | 1.87235e20 | − | 7.27930e19i | 0.198064 | − | 0.0770031i | ||||
\(993\) | −8.92451e20 | −0.937432 | ||||||||
\(994\) | 4.47745e20 | − | 7.23520e20i | 0.467010 | − | 0.754650i | ||||
\(995\) | 1.74059e20i | 0.180275i | ||||||||
\(996\) | −1.76130e20 | − | 3.53293e20i | −0.181142 | − | 0.363346i | ||||
\(997\) | 6.04030e20 | 0.616869 | 0.308434 | − | 0.951246i | \(-0.400195\pi\) | ||||
0.308434 | + | 0.951246i | \(0.400195\pi\) | |||||||
\(998\) | −1.36019e20 | − | 8.41742e19i | −0.137938 | − | 0.0853622i | ||||
\(999\) | − | 2.33023e20i | − | 0.234661i |
(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 | 12.15.d.a.7.9 | ✓ | 14 | |
3.2 | odd | 2 | 36.15.d.e.19.6 | 14 | |||
4.3 | odd | 2 | inner | 12.15.d.a.7.10 | yes | 14 | |
12.11 | even | 2 | 36.15.d.e.19.5 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.15.d.a.7.9 | ✓ | 14 | 1.1 | even | 1 | trivial | |
12.15.d.a.7.10 | yes | 14 | 4.3 | odd | 2 | inner | |
36.15.d.e.19.5 | 14 | 12.11 | even | 2 | |||
36.15.d.e.19.6 | 14 | 3.2 | odd | 2 |