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 | 7.7 | ||
Root | \(37.1678 + 64.3766i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.7 |
Dual form | 12.15.d.a.7.8 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 26.2042 | − | 125.289i | 0.204721 | − | 0.978820i | ||||
\(3\) | − | 1262.67i | − | 0.577350i | ||||||
\(4\) | −15010.7 | − | 6566.21i | −0.916179 | − | 0.400769i | ||||
\(5\) | −40325.1 | −0.516161 | −0.258081 | − | 0.966123i | \(-0.583090\pi\) | ||||
−0.258081 | + | 0.966123i | \(0.583090\pi\) | |||||||
\(6\) | −158198. | − | 33087.2i | −0.565122 | − | 0.118195i | ||||
\(7\) | 421333.i | 0.511610i | 0.966728 | + | 0.255805i | \(0.0823404\pi\) | ||||
−0.966728 | + | 0.255805i | \(0.917660\pi\) | |||||||
\(8\) | −1.21602e6 | + | 1.70861e6i | −0.579842 | + | 0.814729i | ||||
\(9\) | −1.59432e6 | −0.333333 | ||||||||
\(10\) | −1.05669e6 | + | 5.05229e6i | −0.105669 | + | 0.505229i | ||||
\(11\) | − | 1.42281e6i | − | 0.0730125i | −0.999333 | − | 0.0365063i | \(-0.988377\pi\) | ||
0.999333 | − | 0.0365063i | \(-0.0116229\pi\) | |||||||
\(12\) | −8.29092e6 | + | 1.89535e7i | −0.231384 | + | 0.528956i | ||||
\(13\) | −2.76240e7 | −0.440234 | −0.220117 | − | 0.975474i | \(-0.570644\pi\) | ||||
−0.220117 | + | 0.975474i | \(0.570644\pi\) | |||||||
\(14\) | 5.27883e7 | + | 1.10407e7i | 0.500774 | + | 0.104737i | ||||
\(15\) | 5.09171e7i | 0.298006i | ||||||||
\(16\) | 1.82205e8 | + | 1.97126e8i | 0.678768 | + | 0.734353i | ||||
\(17\) | 3.56692e8 | 0.869263 | 0.434632 | − | 0.900608i | \(-0.356879\pi\) | ||||
0.434632 | + | 0.900608i | \(0.356879\pi\) | |||||||
\(18\) | −4.17780e7 | + | 1.99751e8i | −0.0682402 | + | 0.326273i | ||||
\(19\) | 3.85490e8i | 0.431259i | 0.976475 | + | 0.215629i | \(0.0691803\pi\) | ||||
−0.976475 | + | 0.215629i | \(0.930820\pi\) | |||||||
\(20\) | 6.05307e8 | + | 2.64783e8i | 0.472896 | + | 0.206862i | ||||
\(21\) | 5.32002e8 | 0.295378 | ||||||||
\(22\) | −1.78262e8 | − | 3.72836e7i | −0.0714661 | − | 0.0149472i | ||||
\(23\) | 6.03923e9i | 1.77373i | 0.462033 | + | 0.886863i | \(0.347120\pi\) | ||||
−0.462033 | + | 0.886863i | \(0.652880\pi\) | |||||||
\(24\) | 2.15740e9 | + | 1.53542e9i | 0.470384 | + | 0.334772i | ||||
\(25\) | −4.47740e9 | −0.733578 | ||||||||
\(26\) | −7.23866e8 | + | 3.46098e9i | −0.0901249 | + | 0.430910i | ||||
\(27\) | 2.01310e9i | 0.192450i | ||||||||
\(28\) | 2.76656e9 | − | 6.32449e9i | 0.205037 | − | 0.468726i | ||||
\(29\) | −1.53493e10 | −0.889820 | −0.444910 | − | 0.895575i | \(-0.646764\pi\) | ||||
−0.444910 | + | 0.895575i | \(0.646764\pi\) | |||||||
\(30\) | 6.37935e9 | + | 1.33424e9i | 0.291694 | + | 0.0610079i | ||||
\(31\) | − | 3.72252e10i | − | 1.35302i | −0.736433 | − | 0.676511i | \(-0.763491\pi\) | ||
0.736433 | − | 0.676511i | \(-0.236509\pi\) | |||||||
\(32\) | 2.94723e10 | − | 1.76628e10i | 0.857757 | − | 0.514055i | ||||
\(33\) | −1.79653e9 | −0.0421538 | ||||||||
\(34\) | 9.34685e9 | − | 4.46896e10i | 0.177956 | − | 0.850853i | ||||
\(35\) | − | 1.69903e10i | − | 0.264073i | ||||||
\(36\) | 2.39319e10 | + | 1.04687e10i | 0.305393 | + | 0.133590i | ||||
\(37\) | −1.69904e11 | −1.78975 | −0.894874 | − | 0.446319i | \(-0.852735\pi\) | ||||
−0.894874 | + | 0.446319i | \(0.852735\pi\) | |||||||
\(38\) | 4.82976e10 | + | 1.01015e10i | 0.422125 | + | 0.0882875i | ||||
\(39\) | 3.48799e10i | 0.254169i | ||||||||
\(40\) | 4.90360e10 | − | 6.88999e10i | 0.299292 | − | 0.420531i | ||||
\(41\) | −3.36802e11 | −1.72937 | −0.864685 | − | 0.502315i | \(-0.832482\pi\) | ||||
−0.864685 | + | 0.502315i | \(0.832482\pi\) | |||||||
\(42\) | 1.39407e10 | − | 6.66540e10i | 0.0604700 | − | 0.289122i | ||||
\(43\) | 2.13791e11i | 0.786521i | 0.919427 | + | 0.393261i | \(0.128653\pi\) | ||||
−0.919427 | + | 0.393261i | \(0.871347\pi\) | |||||||
\(44\) | −9.34245e9 | + | 2.13573e10i | −0.0292612 | + | 0.0668925i | ||||
\(45\) | 6.42912e10 | 0.172054 | ||||||||
\(46\) | 7.56649e11 | + | 1.58253e11i | 1.73616 | + | 0.363118i | ||||
\(47\) | 4.76171e11i | 0.939892i | 0.882695 | + | 0.469946i | \(0.155727\pi\) | ||||
−0.882695 | + | 0.469946i | \(0.844273\pi\) | |||||||
\(48\) | 2.48905e11 | − | 2.30064e11i | 0.423979 | − | 0.391887i | ||||
\(49\) | 5.00702e11 | 0.738256 | ||||||||
\(50\) | −1.17327e11 | + | 5.60969e11i | −0.150178 | + | 0.718041i | ||||
\(51\) | − | 4.50383e11i | − | 0.501869i | ||||||
\(52\) | 4.14655e11 | + | 1.81385e11i | 0.403333 | + | 0.176432i | ||||
\(53\) | −1.64539e12 | −1.40067 | −0.700337 | − | 0.713812i | \(-0.746967\pi\) | ||||
−0.700337 | + | 0.713812i | \(0.746967\pi\) | |||||||
\(54\) | 2.52219e11 | + | 5.27516e10i | 0.188374 | + | 0.0393985i | ||||
\(55\) | 5.73748e10i | 0.0376862i | ||||||||
\(56\) | −7.19893e11 | − | 5.12347e11i | −0.416823 | − | 0.296653i | ||||
\(57\) | 4.86745e11 | 0.248987 | ||||||||
\(58\) | −4.02216e11 | + | 1.92310e12i | −0.182164 | + | 0.870974i | ||||
\(59\) | 9.85223e10i | 0.0395886i | 0.999804 | + | 0.0197943i | \(0.00630114\pi\) | ||||
−0.999804 | + | 0.0197943i | \(0.993699\pi\) | |||||||
\(60\) | 3.34332e11 | − | 7.64300e11i | 0.119432 | − | 0.273027i | ||||
\(61\) | 2.21058e12 | 0.703392 | 0.351696 | − | 0.936114i | \(-0.385605\pi\) | ||||
0.351696 | + | 0.936114i | \(0.385605\pi\) | |||||||
\(62\) | −4.66390e12 | − | 9.75457e11i | −1.32436 | − | 0.276991i | ||||
\(63\) | − | 6.71740e11i | − | 0.170537i | ||||||
\(64\) | −1.44065e12 | − | 4.15540e12i | −0.327567 | − | 0.944828i | ||||
\(65\) | 1.11394e12 | 0.227231 | ||||||||
\(66\) | −4.70767e10 | + | 2.25085e11i | −0.00862975 | + | 0.0412610i | ||||
\(67\) | − | 9.25057e12i | − | 1.52632i | −0.646211 | − | 0.763159i | \(-0.723648\pi\) | ||
0.646211 | − | 0.763159i | \(-0.276352\pi\) | |||||||
\(68\) | −5.35419e12 | − | 2.34211e12i | −0.796401 | − | 0.348374i | ||||
\(69\) | 7.62552e12 | 1.02406 | ||||||||
\(70\) | −2.12869e12 | − | 4.45217e11i | −0.258480 | − | 0.0540612i | ||||
\(71\) | 4.91016e12i | 0.539867i | 0.962879 | + | 0.269934i | \(0.0870018\pi\) | ||||
−0.962879 | + | 0.269934i | \(0.912998\pi\) | |||||||
\(72\) | 1.93872e12 | − | 2.72408e12i | 0.193281 | − | 0.271576i | ||||
\(73\) | 8.74284e12 | 0.791394 | 0.395697 | − | 0.918381i | \(-0.370503\pi\) | ||||
0.395697 | + | 0.918381i | \(0.370503\pi\) | |||||||
\(74\) | −4.45221e12 | + | 2.12871e13i | −0.366398 | + | 1.75184i | ||||
\(75\) | 5.65346e12i | 0.423531i | ||||||||
\(76\) | 2.53121e12 | − | 5.78646e12i | 0.172835 | − | 0.395110i | ||||
\(77\) | 5.99475e11 | 0.0373539 | ||||||||
\(78\) | 4.37006e12 | + | 9.14000e11i | 0.248786 | + | 0.0520336i | ||||
\(79\) | − | 5.31538e12i | − | 0.276787i | −0.990377 | − | 0.138393i | \(-0.955806\pi\) | ||
0.990377 | − | 0.138393i | \(-0.0441938\pi\) | |||||||
\(80\) | −7.34745e12 | − | 7.94914e12i | −0.350353 | − | 0.379044i | ||||
\(81\) | 2.54187e12 | 0.111111 | ||||||||
\(82\) | −8.82564e12 | + | 4.21976e13i | −0.354038 | + | 1.69274i | ||||
\(83\) | 1.43700e13i | 0.529555i | 0.964310 | + | 0.264777i | \(0.0852984\pi\) | ||||
−0.964310 | + | 0.264777i | \(0.914702\pi\) | |||||||
\(84\) | −7.98571e12 | − | 3.49323e12i | −0.270619 | − | 0.118378i | ||||
\(85\) | −1.43836e13 | −0.448680 | ||||||||
\(86\) | 2.67857e13 | + | 5.60223e12i | 0.769863 | + | 0.161017i | ||||
\(87\) | 1.93810e13i | 0.513738i | ||||||||
\(88\) | 2.43102e12 | + | 1.73016e12i | 0.0594854 | + | 0.0423357i | ||||
\(89\) | 1.13769e13 | 0.257214 | 0.128607 | − | 0.991696i | \(-0.458949\pi\) | ||||
0.128607 | + | 0.991696i | \(0.458949\pi\) | |||||||
\(90\) | 1.68470e12 | − | 8.05498e12i | 0.0352229 | − | 0.168410i | ||||
\(91\) | − | 1.16389e13i | − | 0.225228i | ||||||
\(92\) | 3.96548e13 | − | 9.06529e13i | 0.710855 | − | 1.62505i | ||||
\(93\) | −4.70029e13 | −0.781167 | ||||||||
\(94\) | 5.96590e13 | + | 1.24777e13i | 0.919986 | + | 0.192415i | ||||
\(95\) | − | 1.55449e13i | − | 0.222599i | ||||||
\(96\) | −2.23022e13 | − | 3.72137e13i | −0.296790 | − | 0.495227i | ||||
\(97\) | −8.88449e13 | −1.09959 | −0.549795 | − | 0.835300i | \(-0.685294\pi\) | ||||
−0.549795 | + | 0.835300i | \(0.685294\pi\) | |||||||
\(98\) | 1.31205e13 | − | 6.27325e13i | 0.151136 | − | 0.722620i | ||||
\(99\) | 2.26841e12i | 0.0243375i | ||||||||
\(100\) | 6.72089e13 | + | 2.93996e13i | 0.672089 | + | 0.293996i | ||||
\(101\) | −5.95274e13 | −0.555223 | −0.277611 | − | 0.960693i | \(-0.589543\pi\) | ||||
−0.277611 | + | 0.960693i | \(0.589543\pi\) | |||||||
\(102\) | −5.64280e13 | − | 1.18019e13i | −0.491240 | − | 0.102743i | ||||
\(103\) | − | 1.33826e14i | − | 1.08813i | −0.839044 | − | 0.544063i | \(-0.816885\pi\) | ||
0.839044 | − | 0.544063i | \(-0.183115\pi\) | |||||||
\(104\) | 3.35912e13 | − | 4.71987e13i | 0.255266 | − | 0.358671i | ||||
\(105\) | −2.14530e13 | −0.152463 | ||||||||
\(106\) | −4.31161e13 | + | 2.06149e14i | −0.286747 | + | 1.37101i | ||||
\(107\) | 8.37947e13i | 0.521831i | 0.965362 | + | 0.260916i | \(0.0840244\pi\) | ||||
−0.965362 | + | 0.260916i | \(0.915976\pi\) | |||||||
\(108\) | 1.32184e13 | − | 3.02179e13i | 0.0771281 | − | 0.176319i | ||||
\(109\) | −2.00753e14 | −1.09819 | −0.549095 | − | 0.835760i | \(-0.685028\pi\) | ||||
−0.549095 | + | 0.835760i | \(0.685028\pi\) | |||||||
\(110\) | 7.18844e12 | + | 1.50346e12i | 0.0368880 | + | 0.00771515i | ||||
\(111\) | 2.14532e14i | 1.03331i | ||||||||
\(112\) | −8.30558e13 | + | 7.67690e13i | −0.375702 | + | 0.347264i | ||||
\(113\) | 3.27875e14 | 1.39367 | 0.696833 | − | 0.717233i | \(-0.254592\pi\) | ||||
0.696833 | + | 0.717233i | \(0.254592\pi\) | |||||||
\(114\) | 1.27548e13 | − | 6.09837e13i | 0.0509728 | − | 0.243714i | ||||
\(115\) | − | 2.43532e14i | − | 0.915528i | ||||||
\(116\) | 2.30403e14 | + | 1.00787e14i | 0.815234 | + | 0.356613i | ||||
\(117\) | 4.40416e13 | 0.146745 | ||||||||
\(118\) | 1.23438e13 | + | 2.58170e12i | 0.0387502 | + | 0.00810461i | ||||
\(119\) | 1.50286e14i | 0.444723i | ||||||||
\(120\) | −8.69974e13 | − | 6.19160e13i | −0.242794 | − | 0.172796i | ||||
\(121\) | 3.77725e14 | 0.994669 | ||||||||
\(122\) | 5.79266e13 | − | 2.76962e14i | 0.143999 | − | 0.688495i | ||||
\(123\) | 4.25268e14i | 0.998452i | ||||||||
\(124\) | −2.44428e14 | + | 5.58775e14i | −0.542250 | + | 1.23961i | ||||
\(125\) | 4.26676e14 | 0.894805 | ||||||||
\(126\) | −8.41617e13 | − | 1.76024e13i | −0.166925 | − | 0.0349123i | ||||
\(127\) | − | 6.21176e14i | − | 1.16570i | −0.812578 | − | 0.582852i | \(-0.801937\pi\) | ||
0.812578 | − | 0.582852i | \(-0.198063\pi\) | |||||||
\(128\) | −5.58377e14 | + | 7.16090e13i | −0.991877 | + | 0.127203i | ||||
\(129\) | 2.69947e14 | 0.454098 | ||||||||
\(130\) | 2.91899e13 | − | 1.39564e14i | 0.0465189 | − | 0.222419i | ||||
\(131\) | 5.33781e14i | 0.806240i | 0.915147 | + | 0.403120i | \(0.132074\pi\) | ||||
−0.915147 | + | 0.403120i | \(0.867926\pi\) | |||||||
\(132\) | 2.69671e13 | + | 1.17964e13i | 0.0386204 | + | 0.0168940i | ||||
\(133\) | −1.62419e14 | −0.220636 | ||||||||
\(134\) | −1.15899e15 | − | 2.42404e14i | −1.49399 | − | 0.312469i | ||||
\(135\) | − | 8.11783e13i | − | 0.0993352i | ||||||
\(136\) | −4.33744e14 | + | 6.09448e14i | −0.504035 | + | 0.708214i | ||||
\(137\) | −7.49540e14 | −0.827467 | −0.413734 | − | 0.910398i | \(-0.635775\pi\) | ||||
−0.413734 | + | 0.910398i | \(0.635775\pi\) | |||||||
\(138\) | 1.99821e14 | − | 9.55394e14i | 0.209646 | − | 1.00237i | ||||
\(139\) | − | 1.89011e15i | − | 1.88531i | −0.333765 | − | 0.942656i | \(-0.608319\pi\) | ||
0.333765 | − | 0.942656i | \(-0.391681\pi\) | |||||||
\(140\) | −1.11562e14 | + | 2.55035e14i | −0.105832 | + | 0.241938i | ||||
\(141\) | 6.01245e14 | 0.542647 | ||||||||
\(142\) | 6.15189e14 | + | 1.28667e14i | 0.528433 | + | 0.110522i | ||||
\(143\) | 3.93036e13i | 0.0321426i | ||||||||
\(144\) | −2.90494e14 | − | 3.14283e14i | −0.226256 | − | 0.244784i | ||||
\(145\) | 6.18961e14 | 0.459290 | ||||||||
\(146\) | 2.29100e14 | − | 1.09538e15i | 0.162015 | − | 0.774633i | ||||
\(147\) | − | 6.32219e14i | − | 0.426232i | ||||||
\(148\) | 2.55038e15 | + | 1.11563e15i | 1.63973 | + | 0.717276i | ||||
\(149\) | −1.16262e15 | −0.713071 | −0.356536 | − | 0.934282i | \(-0.616042\pi\) | ||||
−0.356536 | + | 0.934282i | \(0.616042\pi\) | |||||||
\(150\) | 7.08317e14 | + | 1.48145e14i | 0.414561 | + | 0.0867056i | ||||
\(151\) | 1.08753e15i | 0.607581i | 0.952739 | + | 0.303791i | \(0.0982523\pi\) | ||||
−0.952739 | + | 0.303791i | \(0.901748\pi\) | |||||||
\(152\) | −6.58652e14 | − | 4.68762e14i | −0.351359 | − | 0.250062i | ||||
\(153\) | −5.68683e14 | −0.289754 | ||||||||
\(154\) | 1.57088e13 | − | 7.51076e13i | 0.00764711 | − | 0.0365628i | ||||
\(155\) | 1.50111e15i | 0.698377i | ||||||||
\(156\) | 2.29028e14 | − | 5.23570e14i | 0.101863 | − | 0.232864i | ||||
\(157\) | −3.10158e14 | −0.131912 | −0.0659562 | − | 0.997823i | \(-0.521010\pi\) | ||||
−0.0659562 | + | 0.997823i | \(0.521010\pi\) | |||||||
\(158\) | −6.65959e14 | − | 1.39286e14i | −0.270924 | − | 0.0566639i | ||||
\(159\) | 2.07757e15i | 0.808679i | ||||||||
\(160\) | −1.18847e15 | + | 7.12253e14i | −0.442741 | + | 0.265335i | ||||
\(161\) | −2.54452e15 | −0.907455 | ||||||||
\(162\) | 6.66077e13 | − | 3.18468e14i | 0.0227467 | − | 0.108758i | ||||
\(163\) | 1.56606e15i | 0.512266i | 0.966642 | + | 0.256133i | \(0.0824486\pi\) | ||||
−0.966642 | + | 0.256133i | \(0.917551\pi\) | |||||||
\(164\) | 5.05563e15 | + | 2.21151e15i | 1.58441 | + | 0.693078i | ||||
\(165\) | 7.24452e13 | 0.0217581 | ||||||||
\(166\) | 1.80041e15 | + | 3.76555e14i | 0.518339 | + | 0.108411i | ||||
\(167\) | 1.49948e15i | 0.413928i | 0.978349 | + | 0.206964i | \(0.0663582\pi\) | ||||
−0.978349 | + | 0.206964i | \(0.933642\pi\) | |||||||
\(168\) | −6.46923e14 | + | 9.08984e14i | −0.171273 | + | 0.240653i | ||||
\(169\) | −3.17429e15 | −0.806194 | ||||||||
\(170\) | −3.76912e14 | + | 1.80211e15i | −0.0918540 | + | 0.439177i | ||||
\(171\) | − | 6.14595e14i | − | 0.143753i | ||||||
\(172\) | 1.40380e15 | − | 3.20915e15i | 0.315214 | − | 0.720594i | ||||
\(173\) | 1.19192e15 | 0.256994 | 0.128497 | − | 0.991710i | \(-0.458985\pi\) | ||||
0.128497 | + | 0.991710i | \(0.458985\pi\) | |||||||
\(174\) | 2.42823e15 | + | 5.07864e14i | 0.502857 | + | 0.105173i | ||||
\(175\) | − | 1.88648e15i | − | 0.375305i | ||||||
\(176\) | 2.80473e14 | − | 2.59243e14i | 0.0536170 | − | 0.0495585i | ||||
\(177\) | 1.24401e14 | 0.0228565 | ||||||||
\(178\) | 2.98123e14 | − | 1.42540e15i | 0.0526569 | − | 0.251766i | ||||
\(179\) | − | 6.42994e15i | − | 1.09203i | −0.837774 | − | 0.546016i | \(-0.816144\pi\) | ||
0.837774 | − | 0.546016i | \(-0.183856\pi\) | |||||||
\(180\) | −9.65054e14 | − | 4.22149e14i | −0.157632 | − | 0.0689539i | ||||
\(181\) | −1.60145e15 | −0.251631 | −0.125816 | − | 0.992054i | \(-0.540155\pi\) | ||||
−0.125816 | + | 0.992054i | \(0.540155\pi\) | |||||||
\(182\) | −1.45823e15 | − | 3.04988e14i | −0.220457 | − | 0.0461088i | ||||
\(183\) | − | 2.79122e15i | − | 0.406104i | ||||||
\(184\) | −1.03187e16 | − | 7.34380e15i | −1.44511 | − | 1.02848i | ||||
\(185\) | 6.85140e15 | 0.923798 | ||||||||
\(186\) | −1.23168e15 | + | 5.88895e15i | −0.159921 | + | 0.764622i | ||||
\(187\) | − | 5.07504e14i | − | 0.0634671i | ||||||
\(188\) | 3.12664e15 | − | 7.14765e15i | 0.376680 | − | 0.861109i | ||||
\(189\) | −8.48183e14 | −0.0984593 | ||||||||
\(190\) | −1.94761e15 | − | 4.07342e14i | −0.217884 | − | 0.0455706i | ||||
\(191\) | − | 4.83572e15i | − | 0.521468i | −0.965411 | − | 0.260734i | \(-0.916035\pi\) | ||
0.965411 | − | 0.260734i | \(-0.0839645\pi\) | |||||||
\(192\) | −5.24688e15 | + | 1.81906e15i | −0.545497 | + | 0.189121i | ||||
\(193\) | 5.13392e15 | 0.514692 | 0.257346 | − | 0.966319i | \(-0.417152\pi\) | ||||
0.257346 | + | 0.966319i | \(0.417152\pi\) | |||||||
\(194\) | −2.32811e15 | + | 1.11313e16i | −0.225109 | + | 1.07630i | ||||
\(195\) | − | 1.40653e15i | − | 0.131192i | ||||||
\(196\) | −7.51587e15 | − | 3.28771e15i | −0.676374 | − | 0.295870i | ||||
\(197\) | 1.29818e16 | 1.12738 | 0.563692 | − | 0.825985i | \(-0.309380\pi\) | ||||
0.563692 | + | 0.825985i | \(0.309380\pi\) | |||||||
\(198\) | 2.84207e14 | + | 5.94421e13i | 0.0238220 | + | 0.00498239i | ||||
\(199\) | 2.28758e16i | 1.85100i | 0.378753 | + | 0.925498i | \(0.376353\pi\) | ||||
−0.378753 | + | 0.925498i | \(0.623647\pi\) | |||||||
\(200\) | 5.44460e15 | − | 7.65014e15i | 0.425359 | − | 0.597667i | ||||
\(201\) | −1.16804e16 | −0.881220 | ||||||||
\(202\) | −1.55987e15 | + | 7.45813e15i | −0.113666 | + | 0.543464i | ||||
\(203\) | − | 6.46715e15i | − | 0.455240i | ||||||
\(204\) | −2.95731e15 | + | 6.76055e15i | −0.201134 | + | 0.459802i | ||||
\(205\) | 1.35816e16 | 0.892633 | ||||||||
\(206\) | −1.67669e16 | − | 3.50680e15i | −1.06508 | − | 0.222762i | ||||
\(207\) | − | 9.62848e15i | − | 0.591242i | ||||||
\(208\) | −5.03324e15 | − | 5.44542e15i | −0.298816 | − | 0.323287i | ||||
\(209\) | 5.48478e14 | 0.0314873 | ||||||||
\(210\) | −5.62160e14 | + | 2.68783e15i | −0.0312122 | + | 0.149234i | ||||
\(211\) | 2.20180e16i | 1.18250i | 0.806488 | + | 0.591250i | \(0.201366\pi\) | ||||
−0.806488 | + | 0.591250i | \(0.798634\pi\) | |||||||
\(212\) | 2.46984e16 | + | 1.08040e16i | 1.28327 | + | 0.561347i | ||||
\(213\) | 6.19989e15 | 0.311693 | ||||||||
\(214\) | 1.04986e16 | + | 2.19578e15i | 0.510779 | + | 0.106830i | ||||
\(215\) | − | 8.62114e15i | − | 0.405972i | ||||||
\(216\) | −3.43960e15 | − | 2.44796e15i | −0.156795 | − | 0.111591i | ||||
\(217\) | 1.56842e16 | 0.692219 | ||||||||
\(218\) | −5.26059e15 | + | 2.51522e16i | −0.224822 | + | 1.07493i | ||||
\(219\) | − | 1.10393e16i | − | 0.456911i | ||||||
\(220\) | 3.76735e14 | − | 8.61235e14i | 0.0151035 | − | 0.0345273i | ||||
\(221\) | −9.85327e15 | −0.382679 | ||||||||
\(222\) | 2.68785e16 | + | 5.62165e15i | 1.01143 | + | 0.211540i | ||||
\(223\) | 1.34954e16i | 0.492097i | 0.969258 | + | 0.246048i | \(0.0791322\pi\) | ||||
−0.969258 | + | 0.246048i | \(0.920868\pi\) | |||||||
\(224\) | 7.44190e15 | + | 1.24176e16i | 0.262995 | + | 0.438837i | ||||
\(225\) | 7.13843e15 | 0.244526 | ||||||||
\(226\) | 8.59171e15 | − | 4.10791e16i | 0.285312 | − | 1.36415i | ||||
\(227\) | − | 1.75395e16i | − | 0.564724i | −0.959308 | − | 0.282362i | \(-0.908882\pi\) | ||
0.959308 | − | 0.282362i | \(-0.0911179\pi\) | |||||||
\(228\) | −7.30636e15 | − | 3.19607e15i | −0.228117 | − | 0.0997865i | ||||
\(229\) | −4.49532e16 | −1.36117 | −0.680585 | − | 0.732669i | \(-0.738275\pi\) | ||||
−0.680585 | + | 0.732669i | \(0.738275\pi\) | |||||||
\(230\) | −3.05119e16 | − | 6.38158e15i | −0.896138 | − | 0.187427i | ||||
\(231\) | − | 7.56936e14i | − | 0.0215663i | ||||||
\(232\) | 1.86650e16 | − | 2.62259e16i | 0.515955 | − | 0.724962i | ||||
\(233\) | −7.20644e16 | −1.93299 | −0.966494 | − | 0.256690i | \(-0.917368\pi\) | ||||
−0.966494 | + | 0.256690i | \(0.917368\pi\) | |||||||
\(234\) | 1.15408e15 | − | 5.51793e15i | 0.0300416 | − | 0.143637i | ||||
\(235\) | − | 1.92016e16i | − | 0.485136i | ||||||
\(236\) | 6.46918e14 | − | 1.47889e15i | 0.0158659 | − | 0.0362703i | ||||
\(237\) | −6.71155e15 | −0.159803 | ||||||||
\(238\) | 1.88292e16 | + | 3.93813e15i | 0.435304 | + | 0.0910440i | ||||
\(239\) | 6.29661e16i | 1.41358i | 0.707421 | + | 0.706792i | \(0.249858\pi\) | ||||
−0.707421 | + | 0.706792i | \(0.750142\pi\) | |||||||
\(240\) | −1.00371e16 | + | 9.27736e15i | −0.218841 | + | 0.202277i | ||||
\(241\) | −8.13249e15 | −0.172228 | −0.0861141 | − | 0.996285i | \(-0.527445\pi\) | ||||
−0.0861141 | + | 0.996285i | \(0.527445\pi\) | |||||||
\(242\) | 9.89801e15 | − | 4.73249e16i | 0.203629 | − | 0.973603i | ||||
\(243\) | − | 3.20953e15i | − | 0.0641500i | ||||||
\(244\) | −3.31823e16 | − | 1.45151e16i | −0.644433 | − | 0.281898i | ||||
\(245\) | −2.01908e16 | −0.381059 | ||||||||
\(246\) | 5.32814e16 | + | 1.11438e16i | 0.977305 | + | 0.204404i | ||||
\(247\) | − | 1.06488e16i | − | 0.189854i | ||||||
\(248\) | 6.36033e16 | + | 4.52664e16i | 1.10235 | + | 0.784539i | ||||
\(249\) | 1.81445e16 | 0.305738 | ||||||||
\(250\) | 1.11807e16 | − | 5.34579e16i | 0.183185 | − | 0.875854i | ||||
\(251\) | − | 6.32148e16i | − | 1.00717i | −0.863946 | − | 0.503585i | \(-0.832014\pi\) | ||
0.863946 | − | 0.503585i | \(-0.167986\pi\) | |||||||
\(252\) | −4.41078e15 | + | 1.00833e16i | −0.0683458 | + | 0.156242i | ||||
\(253\) | 8.59266e15 | 0.129504 | ||||||||
\(254\) | −7.78265e16 | − | 1.62774e16i | −1.14102 | − | 0.238644i | ||||
\(255\) | 1.81617e16i | 0.259045i | ||||||||
\(256\) | −5.66003e15 | + | 7.18350e16i | −0.0785486 | + | 0.996910i | ||||
\(257\) | 6.39849e16 | 0.864063 | 0.432032 | − | 0.901858i | \(-0.357797\pi\) | ||||
0.432032 | + | 0.901858i | \(0.357797\pi\) | |||||||
\(258\) | 7.07374e15 | − | 3.38213e16i | 0.0929633 | − | 0.444481i | ||||
\(259\) | − | 7.15861e16i | − | 0.915652i | ||||||
\(260\) | −1.67210e16 | − | 7.31436e15i | −0.208185 | − | 0.0910674i | ||||
\(261\) | 2.44717e16 | 0.296607 | ||||||||
\(262\) | 6.68769e16 | + | 1.39873e16i | 0.789164 | + | 0.165054i | ||||
\(263\) | 1.32846e17i | 1.52636i | 0.646187 | + | 0.763180i | \(0.276363\pi\) | ||||
−0.646187 | + | 0.763180i | \(0.723637\pi\) | |||||||
\(264\) | 2.18461e15 | − | 3.06957e15i | 0.0244425 | − | 0.0343439i | ||||
\(265\) | 6.63504e16 | 0.722973 | ||||||||
\(266\) | −4.25608e15 | + | 2.03494e16i | −0.0451687 | + | 0.215963i | ||||
\(267\) | − | 1.43652e16i | − | 0.148502i | ||||||
\(268\) | −6.07411e16 | + | 1.38857e17i | −0.611701 | + | 1.39838i | ||||
\(269\) | −5.81633e16 | −0.570668 | −0.285334 | − | 0.958428i | \(-0.592104\pi\) | ||||
−0.285334 | + | 0.958428i | \(0.592104\pi\) | |||||||
\(270\) | −1.01707e16 | − | 2.12721e15i | −0.0972314 | − | 0.0203360i | ||||
\(271\) | 7.87355e16i | 0.733476i | 0.930324 | + | 0.366738i | \(0.119525\pi\) | ||||
−0.930324 | + | 0.366738i | \(0.880475\pi\) | |||||||
\(272\) | 6.49912e16 | + | 7.03135e16i | 0.590028 | + | 0.638346i | ||||
\(273\) | −1.46960e16 | −0.130035 | ||||||||
\(274\) | −1.96411e16 | + | 9.39091e16i | −0.169400 | + | 0.809942i | ||||
\(275\) | 6.37048e15i | 0.0535604i | ||||||||
\(276\) | −1.14464e17 | − | 5.00707e16i | −0.938223 | − | 0.410412i | ||||
\(277\) | 4.58065e16 | 0.366074 | 0.183037 | − | 0.983106i | \(-0.441407\pi\) | ||||
0.183037 | + | 0.983106i | \(0.441407\pi\) | |||||||
\(278\) | −2.36810e17 | − | 4.95289e16i | −1.84538 | − | 0.385962i | ||||
\(279\) | 5.93489e16i | 0.451007i | ||||||||
\(280\) | 2.90298e16 | + | 2.06605e16i | 0.215148 | + | 0.153121i | ||||
\(281\) | 2.01962e17 | 1.45991 | 0.729954 | − | 0.683496i | \(-0.239541\pi\) | ||||
0.729954 | + | 0.683496i | \(0.239541\pi\) | |||||||
\(282\) | 1.57552e16 | − | 7.53293e16i | 0.111091 | − | 0.531154i | ||||
\(283\) | − | 1.73138e17i | − | 1.19093i | −0.803381 | − | 0.595465i | \(-0.796968\pi\) | ||
0.803381 | − | 0.595465i | \(-0.203032\pi\) | |||||||
\(284\) | 3.22411e16 | − | 7.37048e16i | 0.216362 | − | 0.494615i | ||||
\(285\) | −1.96280e16 | −0.128518 | ||||||||
\(286\) | 4.92431e15 | + | 1.02992e15i | 0.0314618 | + | 0.00658024i | ||||
\(287\) | − | 1.41906e17i | − | 0.884762i | ||||||
\(288\) | −4.69884e16 | + | 2.81602e16i | −0.285919 | + | 0.171352i | ||||
\(289\) | −4.11484e16 | −0.244382 | ||||||||
\(290\) | 1.62194e16 | − | 7.75490e16i | 0.0940262 | − | 0.449563i | ||||
\(291\) | 1.12181e17i | 0.634848i | ||||||||
\(292\) | −1.31236e17 | − | 5.74073e16i | −0.725058 | − | 0.317166i | ||||
\(293\) | 2.01914e17 | 1.08916 | 0.544582 | − | 0.838707i | \(-0.316688\pi\) | ||||
0.544582 | + | 0.838707i | \(0.316688\pi\) | |||||||
\(294\) | −7.92101e16 | − | 1.65668e16i | −0.417205 | − | 0.0872585i | ||||
\(295\) | − | 3.97292e15i | − | 0.0204341i | ||||||
\(296\) | 2.06606e17 | − | 2.90300e17i | 1.03777 | − | 1.45816i | ||||
\(297\) | 2.86425e15 | 0.0140513 | ||||||||
\(298\) | −3.04655e16 | + | 1.45663e17i | −0.145980 | + | 0.697969i | ||||
\(299\) | − | 1.66828e17i | − | 0.780853i | ||||||
\(300\) | 3.71218e16 | − | 8.48623e16i | 0.169738 | − | 0.388030i | ||||
\(301\) | −9.00771e16 | −0.402392 | ||||||||
\(302\) | 1.36256e17 | + | 2.84980e16i | 0.594713 | + | 0.124384i | ||||
\(303\) | 7.51632e16i | 0.320558i | ||||||||
\(304\) | −7.59902e16 | + | 7.02383e16i | −0.316696 | + | 0.292724i | ||||
\(305\) | −8.91419e16 | −0.363064 | ||||||||
\(306\) | −1.49019e16 | + | 7.12497e16i | −0.0593187 | + | 0.283618i | ||||
\(307\) | − | 4.51709e17i | − | 1.75748i | −0.477301 | − | 0.878740i | \(-0.658385\pi\) | ||
0.477301 | − | 0.878740i | \(-0.341615\pi\) | |||||||
\(308\) | −8.99853e15 | − | 3.93628e15i | −0.0342229 | − | 0.0149703i | ||||
\(309\) | −1.68977e17 | −0.628230 | ||||||||
\(310\) | 1.88072e17 | + | 3.93354e16i | 0.683586 | + | 0.142972i | ||||
\(311\) | 4.92127e17i | 1.74886i | 0.485152 | + | 0.874430i | \(0.338764\pi\) | ||||
−0.485152 | + | 0.874430i | \(0.661236\pi\) | |||||||
\(312\) | −5.95961e16 | − | 4.24145e16i | −0.207079 | − | 0.147378i | ||||
\(313\) | −5.06792e17 | −1.72194 | −0.860972 | − | 0.508652i | \(-0.830144\pi\) | ||||
−0.860972 | + | 0.508652i | \(0.830144\pi\) | |||||||
\(314\) | −8.12746e15 | + | 3.88594e16i | −0.0270052 | + | 0.129119i | ||||
\(315\) | 2.70880e16i | 0.0880243i | ||||||||
\(316\) | −3.49019e16 | + | 7.97875e16i | −0.110928 | + | 0.253586i | ||||
\(317\) | −1.35753e17 | −0.422022 | −0.211011 | − | 0.977484i | \(-0.567676\pi\) | ||||
−0.211011 | + | 0.977484i | \(0.567676\pi\) | |||||||
\(318\) | 2.60297e17 | + | 5.44412e16i | 0.791552 | + | 0.165553i | ||||
\(319\) | 2.18391e16i | 0.0649680i | ||||||||
\(320\) | 5.80944e16 | + | 1.67567e17i | 0.169077 | + | 0.487683i | ||||
\(321\) | 1.05805e17 | 0.301279 | ||||||||
\(322\) | −6.66773e16 | + | 3.18801e17i | −0.185775 | + | 0.888236i | ||||
\(323\) | 1.37501e17i | 0.374877i | ||||||||
\(324\) | −3.81551e16 | − | 1.66904e16i | −0.101798 | − | 0.0445299i | ||||
\(325\) | 1.23684e17 | 0.322946 | ||||||||
\(326\) | 1.96210e17 | + | 4.10375e16i | 0.501417 | + | 0.104871i | ||||
\(327\) | 2.53484e17i | 0.634040i | ||||||||
\(328\) | 4.09557e17 | − | 5.75464e17i | 1.00276 | − | 1.40897i | ||||
\(329\) | −2.00626e17 | −0.480858 | ||||||||
\(330\) | 1.89837e15 | − | 9.07659e15i | 0.00445434 | − | 0.0212973i | ||||
\(331\) | 1.13631e17i | 0.261036i | 0.991446 | + | 0.130518i | \(0.0416640\pi\) | ||||
−0.991446 | + | 0.130518i | \(0.958336\pi\) | |||||||
\(332\) | 9.43565e16 | − | 2.15704e17i | 0.212229 | − | 0.485167i | ||||
\(333\) | 2.70882e17 | 0.596583 | ||||||||
\(334\) | 1.87868e17 | + | 3.92926e16i | 0.405161 | + | 0.0847395i | ||||
\(335\) | 3.73030e17i | 0.787825i | ||||||||
\(336\) | 9.69336e16 | + | 1.04872e17i | 0.200493 | + | 0.216912i | ||||
\(337\) | 1.63714e17 | 0.331647 | 0.165824 | − | 0.986155i | \(-0.446972\pi\) | ||||
0.165824 | + | 0.986155i | \(0.446972\pi\) | |||||||
\(338\) | −8.31799e16 | + | 3.97704e17i | −0.165045 | + | 0.789120i | ||||
\(339\) | − | 4.13996e17i | − | 0.804634i | ||||||
\(340\) | 2.15908e17 | + | 9.44460e16i | 0.411071 | + | 0.179817i | ||||
\(341\) | −5.29642e16 | −0.0987875 | ||||||||
\(342\) | −7.70020e16 | − | 1.61050e16i | −0.140708 | − | 0.0294292i | ||||
\(343\) | 4.96719e17i | 0.889308i | ||||||||
\(344\) | −3.65286e17 | − | 2.59974e17i | −0.640802 | − | 0.456058i | ||||
\(345\) | −3.07500e17 | −0.528580 | ||||||||
\(346\) | 3.12333e16 | − | 1.49334e17i | 0.0526120 | − | 0.251551i | ||||
\(347\) | − | 6.87073e17i | − | 1.13422i | −0.823643 | − | 0.567109i | \(-0.808062\pi\) | ||
0.823643 | − | 0.567109i | \(-0.191938\pi\) | |||||||
\(348\) | 1.27260e17 | − | 2.90922e17i | 0.205890 | − | 0.470676i | ||||
\(349\) | 3.05107e16 | 0.0483810 | 0.0241905 | − | 0.999707i | \(-0.492299\pi\) | ||||
0.0241905 | + | 0.999707i | \(0.492299\pi\) | |||||||
\(350\) | −2.36355e17 | − | 4.94337e16i | −0.367357 | − | 0.0768328i | ||||
\(351\) | − | 5.56098e16i | − | 0.0847230i | ||||||
\(352\) | −2.51307e16 | − | 4.19334e16i | −0.0375324 | − | 0.0626270i | ||||
\(353\) | −3.83405e17 | −0.561352 | −0.280676 | − | 0.959803i | \(-0.590559\pi\) | ||||
−0.280676 | + | 0.959803i | \(0.590559\pi\) | |||||||
\(354\) | 3.25983e15 | − | 1.55860e16i | 0.00467920 | − | 0.0223724i | ||||
\(355\) | − | 1.98003e17i | − | 0.278659i | ||||||
\(356\) | −1.70775e17 | − | 7.47031e16i | −0.235654 | − | 0.103083i | ||||
\(357\) | 1.89761e17 | 0.256761 | ||||||||
\(358\) | −8.05601e17 | − | 1.68492e17i | −1.06890 | − | 0.223562i | ||||
\(359\) | − | 6.14785e17i | − | 0.799948i | −0.916526 | − | 0.399974i | \(-0.869019\pi\) | ||
0.916526 | − | 0.399974i | \(-0.130981\pi\) | |||||||
\(360\) | −7.81792e16 | + | 1.09849e17i | −0.0997640 | + | 0.140177i | ||||
\(361\) | 6.50404e17 | 0.814016 | ||||||||
\(362\) | −4.19649e16 | + | 2.00645e17i | −0.0515141 | + | 0.246302i | ||||
\(363\) | − | 4.76941e17i | − | 0.574273i | ||||||
\(364\) | −7.64234e16 | + | 1.74708e17i | −0.0902644 | + | 0.206349i | ||||
\(365\) | −3.52556e17 | −0.408487 | ||||||||
\(366\) | −3.49710e17 | − | 7.31419e16i | −0.397503 | − | 0.0831378i | ||||
\(367\) | 1.08652e18i | 1.21165i | 0.795599 | + | 0.605824i | \(0.207156\pi\) | ||||
−0.795599 | + | 0.605824i | \(0.792844\pi\) | |||||||
\(368\) | −1.19049e18 | + | 1.10038e18i | −1.30254 | + | 1.20395i | ||||
\(369\) | 5.36971e17 | 0.576457 | ||||||||
\(370\) | 1.79536e17 | − | 8.58405e17i | 0.189121 | − | 0.904233i | ||||
\(371\) | − | 6.93255e17i | − | 0.716598i | ||||||
\(372\) | 7.05545e17 | + | 3.08631e17i | 0.715689 | + | 0.313068i | ||||
\(373\) | 1.51836e18 | 1.51152 | 0.755760 | − | 0.654848i | \(-0.227268\pi\) | ||||
0.755760 | + | 0.654848i | \(0.227268\pi\) | |||||||
\(374\) | −6.35847e16 | − | 1.32988e16i | −0.0621229 | − | 0.0129930i | ||||
\(375\) | − | 5.38749e17i | − | 0.516616i | ||||||
\(376\) | −8.13591e17 | − | 5.79032e17i | −0.765757 | − | 0.544989i | ||||
\(377\) | 4.24009e17 | 0.391728 | ||||||||
\(378\) | −2.22260e16 | + | 1.06268e17i | −0.0201567 | + | 0.0963740i | ||||
\(379\) | − | 8.49805e17i | − | 0.756563i | −0.925691 | − | 0.378281i | \(-0.876515\pi\) | ||
0.925691 | − | 0.378281i | \(-0.123485\pi\) | |||||||
\(380\) | −1.02071e17 | + | 2.33340e17i | −0.0892108 | + | 0.203940i | ||||
\(381\) | −7.84337e17 | −0.673020 | ||||||||
\(382\) | −6.05863e17 | − | 1.26716e17i | −0.510423 | − | 0.106755i | ||||
\(383\) | 1.02544e18i | 0.848244i | 0.905605 | + | 0.424122i | \(0.139417\pi\) | ||||
−0.905605 | + | 0.424122i | \(0.860583\pi\) | |||||||
\(384\) | 9.04181e16 | + | 7.05043e17i | 0.0734407 | + | 0.572660i | ||||
\(385\) | −2.41739e16 | −0.0192806 | ||||||||
\(386\) | 1.34530e17 | − | 6.43223e17i | 0.105368 | − | 0.503791i | ||||
\(387\) | − | 3.40852e17i | − | 0.262174i | ||||||
\(388\) | 1.33362e18 | + | 5.83374e17i | 1.00742 | + | 0.440682i | ||||
\(389\) | 6.00365e17 | 0.445419 | 0.222709 | − | 0.974885i | \(-0.428510\pi\) | ||||
0.222709 | + | 0.974885i | \(0.428510\pi\) | |||||||
\(390\) | −1.76223e17 | − | 3.68571e16i | −0.128414 | − | 0.0268577i | ||||
\(391\) | 2.15415e18i | 1.54183i | ||||||||
\(392\) | −6.08862e17 | + | 8.55505e17i | −0.428072 | + | 0.601478i | ||||
\(393\) | 6.73987e17 | 0.465483 | ||||||||
\(394\) | 3.40179e17 | − | 1.62648e18i | 0.230799 | − | 1.10351i | ||||
\(395\) | 2.14343e17i | 0.142866i | ||||||||
\(396\) | 1.48949e16 | − | 3.40504e16i | 0.00975373 | − | 0.0222975i | ||||
\(397\) | −6.36458e17 | −0.409483 | −0.204742 | − | 0.978816i | \(-0.565635\pi\) | ||||
−0.204742 | + | 0.978816i | \(0.565635\pi\) | |||||||
\(398\) | 2.86609e18 | + | 5.99444e17i | 1.81179 | + | 0.378937i | ||||
\(399\) | 2.05081e17i | 0.127384i | ||||||||
\(400\) | −8.15807e17 | − | 8.82614e17i | −0.497929 | − | 0.538705i | ||||
\(401\) | 1.25198e18 | 0.750907 | 0.375454 | − | 0.926841i | \(-0.377487\pi\) | ||||
0.375454 | + | 0.926841i | \(0.377487\pi\) | |||||||
\(402\) | −3.06075e17 | + | 1.46342e18i | −0.180404 | + | 0.862556i | ||||
\(403\) | 1.02831e18i | 0.595645i | ||||||||
\(404\) | 8.93547e17 | + | 3.90869e17i | 0.508684 | + | 0.222516i | ||||
\(405\) | −1.02501e17 | −0.0573512 | ||||||||
\(406\) | −8.10263e17 | − | 1.69467e17i | −0.445599 | − | 0.0931971i | ||||
\(407\) | 2.41741e17i | 0.130674i | ||||||||
\(408\) | 7.69529e17 | + | 5.47673e17i | 0.408887 | + | 0.291005i | ||||
\(409\) | −2.66842e18 | −1.39377 | −0.696885 | − | 0.717183i | \(-0.745431\pi\) | ||||
−0.696885 | + | 0.717183i | \(0.745431\pi\) | |||||||
\(410\) | 3.55895e17 | − | 1.70162e18i | 0.182740 | − | 0.873728i | ||||
\(411\) | 9.46418e17i | 0.477738i | ||||||||
\(412\) | −8.78728e17 | + | 2.00882e18i | −0.436088 | + | 0.996919i | ||||
\(413\) | −4.15107e16 | −0.0202539 | ||||||||
\(414\) | −1.20634e18 | − | 2.52307e17i | −0.578720 | − | 0.121039i | ||||
\(415\) | − | 5.79472e17i | − | 0.273335i | ||||||
\(416\) | −8.14143e17 | + | 4.87917e17i | −0.377614 | + | 0.226304i | ||||
\(417\) | −2.38658e18 | −1.08849 | ||||||||
\(418\) | 1.43724e16 | − | 6.87183e16i | 0.00644609 | − | 0.0308204i | ||||
\(419\) | − | 3.95429e18i | − | 1.74410i | −0.489420 | − | 0.872048i | \(-0.662791\pi\) | ||
0.489420 | − | 0.872048i | \(-0.337209\pi\) | |||||||
\(420\) | 3.22024e17 | + | 1.40865e17i | 0.139683 | + | 0.0611023i | ||||
\(421\) | −2.93875e18 | −1.25368 | −0.626842 | − | 0.779146i | \(-0.715653\pi\) | ||||
−0.626842 | + | 0.779146i | \(0.715653\pi\) | |||||||
\(422\) | 2.75862e18 | + | 5.76966e17i | 1.15746 | + | 0.242082i | ||||
\(423\) | − | 7.59171e17i | − | 0.313297i | ||||||
\(424\) | 2.00082e18 | − | 2.81133e18i | 0.812170 | − | 1.14117i | ||||
\(425\) | −1.59706e18 | −0.637672 | ||||||||
\(426\) | 1.62463e17 | − | 7.76778e17i | 0.0638099 | − | 0.305091i | ||||
\(427\) | 9.31390e17i | 0.359862i | ||||||||
\(428\) | 5.50213e17 | − | 1.25781e18i | 0.209134 | − | 0.478091i | ||||
\(429\) | 4.96273e16 | 0.0185575 | ||||||||
\(430\) | −1.08013e18 | − | 2.25910e17i | −0.397373 | − | 0.0831107i | ||||
\(431\) | 6.89902e16i | 0.0249716i | 0.999922 | + | 0.0124858i | \(0.00397446\pi\) | ||||
−0.999922 | + | 0.0124858i | \(0.996026\pi\) | |||||||
\(432\) | −3.96834e17 | + | 3.66797e17i | −0.141326 | + | 0.130629i | ||||
\(433\) | 4.13265e18 | 1.44815 | 0.724076 | − | 0.689721i | \(-0.242267\pi\) | ||||
0.724076 | + | 0.689721i | \(0.242267\pi\) | |||||||
\(434\) | 4.10992e17 | − | 1.96505e18i | 0.141711 | − | 0.677558i | ||||
\(435\) | − | 7.81540e17i | − | 0.265171i | ||||||
\(436\) | 3.01345e18 | + | 1.31819e18i | 1.00614 | + | 0.440121i | ||||
\(437\) | −2.32806e18 | −0.764934 | ||||||||
\(438\) | −1.38310e18 | − | 2.89276e17i | −0.447234 | − | 0.0935392i | ||||
\(439\) | − | 1.68057e18i | − | 0.534815i | −0.963584 | − | 0.267408i | \(-0.913833\pi\) | ||
0.963584 | − | 0.267408i | \(-0.0861670\pi\) | |||||||
\(440\) | −9.80312e16 | − | 6.97688e16i | −0.0307041 | − | 0.0218521i | ||||
\(441\) | −7.98281e17 | −0.246085 | ||||||||
\(442\) | −2.58197e17 | + | 1.23451e18i | −0.0783422 | + | 0.374574i | ||||
\(443\) | 8.49726e17i | 0.253777i | 0.991917 | + | 0.126889i | \(0.0404991\pi\) | ||||
−0.991917 | + | 0.126889i | \(0.959501\pi\) | |||||||
\(444\) | 1.40866e18 | − | 3.22027e18i | 0.414120 | − | 0.946698i | ||||
\(445\) | −4.58775e17 | −0.132764 | ||||||||
\(446\) | 1.69082e18 | + | 3.53636e17i | 0.481674 | + | 0.100742i | ||||
\(447\) | 1.46800e18i | 0.411692i | ||||||||
\(448\) | 1.75080e18 | − | 6.06994e17i | 0.483383 | − | 0.167586i | ||||
\(449\) | 2.54692e18 | 0.692294 | 0.346147 | − | 0.938180i | \(-0.387490\pi\) | ||||
0.346147 | + | 0.938180i | \(0.387490\pi\) | |||||||
\(450\) | 1.87057e17 | − | 8.94367e17i | 0.0500595 | − | 0.239347i | ||||
\(451\) | 4.79205e17i | 0.126266i | ||||||||
\(452\) | −4.92162e18 | − | 2.15289e18i | −1.27685 | − | 0.558539i | ||||
\(453\) | 1.37319e18 | 0.350787 | ||||||||
\(454\) | −2.19751e18 | − | 4.59609e17i | −0.552763 | − | 0.115611i | ||||
\(455\) | 4.69339e17i | 0.116254i | ||||||||
\(456\) | −5.91890e17 | + | 8.31657e17i | −0.144373 | + | 0.202857i | ||||
\(457\) | −1.34598e18 | −0.323316 | −0.161658 | − | 0.986847i | \(-0.551684\pi\) | ||||
−0.161658 | + | 0.986847i | \(0.551684\pi\) | |||||||
\(458\) | −1.17797e18 | + | 5.63215e18i | −0.278660 | + | 1.33234i | ||||
\(459\) | 7.18056e17i | 0.167290i | ||||||||
\(460\) | −1.59908e18 | + | 3.65558e18i | −0.366916 | + | 0.838788i | ||||
\(461\) | 1.46325e18 | 0.330683 | 0.165341 | − | 0.986236i | \(-0.447127\pi\) | ||||
0.165341 | + | 0.986236i | \(0.447127\pi\) | |||||||
\(462\) | −9.48358e16 | − | 1.98349e16i | −0.0211095 | − | 0.00441506i | ||||
\(463\) | − | 1.76338e18i | − | 0.386615i | −0.981138 | − | 0.193308i | \(-0.938078\pi\) | ||
0.981138 | − | 0.193308i | \(-0.0619216\pi\) | |||||||
\(464\) | −2.79672e18 | − | 3.02575e18i | −0.603981 | − | 0.653442i | ||||
\(465\) | 1.89540e18 | 0.403208 | ||||||||
\(466\) | −1.88839e18 | + | 9.02887e18i | −0.395722 | + | 1.89205i | ||||
\(467\) | 8.72993e18i | 1.80216i | 0.433656 | + | 0.901078i | \(0.357223\pi\) | ||||
−0.433656 | + | 0.901078i | \(0.642777\pi\) | |||||||
\(468\) | −6.61094e17 | − | 2.89186e17i | −0.134444 | − | 0.0588107i | ||||
\(469\) | 3.89757e18 | 0.780879 | ||||||||
\(470\) | −2.40575e18 | − | 5.03164e17i | −0.474861 | − | 0.0993173i | ||||
\(471\) | 3.91626e17i | 0.0761597i | ||||||||
\(472\) | −1.68336e17 | − | 1.19805e17i | −0.0322540 | − | 0.0229552i | ||||
\(473\) | 3.04184e17 | 0.0574259 | ||||||||
\(474\) | −1.75871e17 | + | 8.40883e17i | −0.0327149 | + | 0.156418i | ||||
\(475\) | − | 1.72599e18i | − | 0.316362i | ||||||
\(476\) | 9.86809e17 | − | 2.25590e18i | 0.178232 | − | 0.407446i | ||||
\(477\) | 2.62328e18 | 0.466891 | ||||||||
\(478\) | 7.88896e18 | + | 1.64998e18i | 1.38365 | + | 0.289390i | ||||
\(479\) | − | 1.82595e18i | − | 0.315603i | −0.987471 | − | 0.157801i | \(-0.949559\pi\) | ||
0.987471 | − | 0.157801i | \(-0.0504406\pi\) | |||||||
\(480\) | 8.99337e17 | + | 1.50064e18i | 0.153191 | + | 0.255617i | ||||
\(481\) | 4.69343e18 | 0.787907 | ||||||||
\(482\) | −2.13106e17 | + | 1.01891e18i | −0.0352587 | + | 0.168581i | ||||
\(483\) | 3.21288e18i | 0.523920i | ||||||||
\(484\) | −5.66991e18 | − | 2.48022e18i | −0.911295 | − | 0.398633i | ||||
\(485\) | 3.58268e18 | 0.567565 | ||||||||
\(486\) | −4.02118e17 | − | 8.41032e16i | −0.0627914 | − | 0.0131328i | ||||
\(487\) | − | 1.22367e19i | − | 1.88349i | −0.336329 | − | 0.941745i | \(-0.609185\pi\) | ||
0.336329 | − | 0.941745i | \(-0.390815\pi\) | |||||||
\(488\) | −2.68810e18 | + | 3.77702e18i | −0.407856 | + | 0.573074i | ||||
\(489\) | 1.97741e18 | 0.295757 | ||||||||
\(490\) | −5.29086e17 | + | 2.52969e18i | −0.0780106 | + | 0.372988i | ||||
\(491\) | 2.33384e17i | 0.0339235i | 0.999856 | + | 0.0169617i | \(0.00539935\pi\) | ||||
−0.999856 | + | 0.0169617i | \(0.994601\pi\) | |||||||
\(492\) | 2.79240e18 | − | 6.38356e18i | 0.400149 | − | 0.914761i | ||||
\(493\) | −5.47497e18 | −0.773488 | ||||||||
\(494\) | −1.33417e18 | − | 2.79043e17i | −0.185833 | − | 0.0388671i | ||||
\(495\) | − | 9.14740e16i | − | 0.0125621i | ||||||
\(496\) | 7.33806e18 | − | 6.78262e18i | 0.993595 | − | 0.918387i | ||||
\(497\) | −2.06881e18 | −0.276201 | ||||||||
\(498\) | 4.75463e17 | − | 2.27331e18i | 0.0625910 | − | 0.299263i | ||||
\(499\) | − | 1.34709e19i | − | 1.74860i | −0.485382 | − | 0.874302i | \(-0.661320\pi\) | ||
0.485382 | − | 0.874302i | \(-0.338680\pi\) | |||||||
\(500\) | −6.40470e18 | − | 2.80165e18i | −0.819802 | − | 0.358611i | ||||
\(501\) | 1.89334e18 | 0.238981 | ||||||||
\(502\) | −7.92012e18 | − | 1.65650e18i | −0.985839 | − | 0.206188i | ||||
\(503\) | 5.59052e18i | 0.686240i | 0.939292 | + | 0.343120i | \(0.111484\pi\) | ||||
−0.939292 | + | 0.343120i | \(0.888516\pi\) | |||||||
\(504\) | 1.14774e18 | + | 8.16847e17i | 0.138941 | + | 0.0988843i | ||||
\(505\) | 2.40045e18 | 0.286584 | ||||||||
\(506\) | 2.25164e17 | − | 1.07657e18i | 0.0265122 | − | 0.126761i | ||||
\(507\) | 4.00807e18i | 0.465457i | ||||||||
\(508\) | −4.07877e18 | + | 9.32427e18i | −0.467179 | + | 1.06799i | ||||
\(509\) | −1.05635e19 | −1.19339 | −0.596697 | − | 0.802466i | \(-0.703521\pi\) | ||||
−0.596697 | + | 0.802466i | \(0.703521\pi\) | |||||||
\(510\) | 2.27546e18 | + | 4.75914e17i | 0.253559 | + | 0.0530319i | ||||
\(511\) | 3.68364e18i | 0.404885i | ||||||||
\(512\) | 8.85181e18 | + | 2.59152e18i | 0.959716 | + | 0.280973i | ||||
\(513\) | −7.76028e17 | −0.0829958 | ||||||||
\(514\) | 1.67668e18 | − | 8.01661e18i | 0.176892 | − | 0.845763i | ||||
\(515\) | 5.39654e18i | 0.561649i | ||||||||
\(516\) | −4.05208e18 | − | 1.77252e18i | −0.416035 | − | 0.181989i | ||||
\(517\) | 6.77500e17 | 0.0686239 | ||||||||
\(518\) | −8.96896e18 | − | 1.87586e18i | −0.896259 | − | 0.187453i | ||||
\(519\) | − | 1.50499e18i | − | 0.148376i | ||||||
\(520\) | −1.35457e18 | + | 1.90329e18i | −0.131758 | + | 0.185132i | ||||
\(521\) | −8.20022e18 | −0.786976 | −0.393488 | − | 0.919330i | \(-0.628732\pi\) | ||||
−0.393488 | + | 0.919330i | \(0.628732\pi\) | |||||||
\(522\) | 6.41263e17 | − | 3.06604e18i | 0.0607215 | − | 0.290325i | ||||
\(523\) | 1.36598e19i | 1.27624i | 0.769936 | + | 0.638121i | \(0.220288\pi\) | ||||
−0.769936 | + | 0.638121i | \(0.779712\pi\) | |||||||
\(524\) | 3.50492e18 | − | 8.01242e18i | 0.323116 | − | 0.738660i | ||||
\(525\) | −2.38199e18 | −0.216683 | ||||||||
\(526\) | 1.66441e19 | + | 3.48112e18i | 1.49403 | + | 0.312477i | ||||
\(527\) | − | 1.32779e19i | − | 1.17613i | ||||||
\(528\) | −3.27337e17 | − | 3.54143e17i | −0.0286126 | − | 0.0309558i | ||||
\(529\) | −2.48794e19 | −2.14610 | ||||||||
\(530\) | 1.73866e18 | − | 8.31297e18i | 0.148008 | − | 0.707661i | ||||
\(531\) | − | 1.57076e17i | − | 0.0131962i | ||||||
\(532\) | 2.43803e18 | + | 1.06648e18i | 0.202142 | + | 0.0884242i | ||||
\(533\) | 9.30382e18 | 0.761326 | ||||||||
\(534\) | −1.79980e18 | − | 3.76430e17i | −0.145357 | − | 0.0304015i | ||||
\(535\) | − | 3.37903e18i | − | 0.269349i | ||||||
\(536\) | 1.58056e19 | + | 1.12488e19i | 1.24353 | + | 0.885023i | ||||
\(537\) | −8.11886e18 | −0.630485 | ||||||||
\(538\) | −1.52413e18 | + | 7.28722e18i | −0.116827 | + | 0.558581i | ||||
\(539\) | − | 7.12402e17i | − | 0.0539019i | ||||||
\(540\) | −5.33033e17 | + | 1.21854e18i | −0.0398105 | + | 0.0910089i | ||||
\(541\) | 1.34807e19 | 0.993876 | 0.496938 | − | 0.867786i | \(-0.334458\pi\) | ||||
0.496938 | + | 0.867786i | \(0.334458\pi\) | |||||||
\(542\) | 9.86470e18 | + | 2.06320e18i | 0.717941 | + | 0.150158i | ||||
\(543\) | 2.02210e18i | 0.145279i | ||||||||
\(544\) | 1.05125e19 | − | 6.30018e18i | 0.745617 | − | 0.446849i | ||||
\(545\) | 8.09540e18 | 0.566843 | ||||||||
\(546\) | −3.85098e17 | + | 1.84125e18i | −0.0266209 | + | 0.127281i | ||||
\(547\) | 2.44729e19i | 1.67022i | 0.550080 | + | 0.835112i | \(0.314597\pi\) | ||||
−0.550080 | + | 0.835112i | \(0.685403\pi\) | |||||||
\(548\) | 1.12511e19 | + | 4.92163e18i | 0.758108 | + | 0.331623i | ||||
\(549\) | −3.52438e18 | −0.234464 | ||||||||
\(550\) | 7.98152e17 | + | 1.66934e17i | 0.0524260 | + | 0.0109649i | ||||
\(551\) | − | 5.91699e18i | − | 0.383742i | ||||||
\(552\) | −9.27276e18 | + | 1.30290e19i | −0.593794 | + | 0.834332i | ||||
\(553\) | 2.23954e18 | 0.141607 | ||||||||
\(554\) | 1.20032e18 | − | 5.73905e18i | 0.0749428 | − | 0.358320i | ||||
\(555\) | − | 8.65102e18i | − | 0.533355i | ||||||
\(556\) | −1.24108e19 | + | 2.83718e19i | −0.755576 | + | 1.72728i | ||||
\(557\) | 3.42126e18 | 0.205683 | 0.102842 | − | 0.994698i | \(-0.467206\pi\) | ||||
0.102842 | + | 0.994698i | \(0.467206\pi\) | |||||||
\(558\) | 7.43577e18 | + | 1.55519e18i | 0.441455 | + | 0.0923304i | ||||
\(559\) | − | 5.90577e18i | − | 0.346253i | ||||||
\(560\) | 3.34923e18 | − | 3.09572e18i | 0.193923 | − | 0.179244i | ||||
\(561\) | −6.40808e17 | −0.0366427 | ||||||||
\(562\) | 5.29226e18 | − | 2.53036e19i | 0.298873 | − | 1.42899i | ||||
\(563\) | 1.43757e19i | 0.801808i | 0.916120 | + | 0.400904i | \(0.131304\pi\) | ||||
−0.916120 | + | 0.400904i | \(0.868696\pi\) | |||||||
\(564\) | −9.02509e18 | − | 3.94790e18i | −0.497162 | − | 0.217476i | ||||
\(565\) | −1.32216e19 | −0.719356 | ||||||||
\(566\) | −2.16922e19 | − | 4.53694e18i | −1.16571 | − | 0.243808i | ||||
\(567\) | 1.07097e18i | 0.0568455i | ||||||||
\(568\) | −8.38955e18 | − | 5.97084e18i | −0.439846 | − | 0.313038i | ||||
\(569\) | 8.31630e18 | 0.430670 | 0.215335 | − | 0.976540i | \(-0.430916\pi\) | ||||
0.215335 | + | 0.976540i | \(0.430916\pi\) | |||||||
\(570\) | −5.14337e17 | + | 2.45917e18i | −0.0263102 | + | 0.125796i | ||||
\(571\) | 1.44832e19i | 0.731834i | 0.930647 | + | 0.365917i | \(0.119245\pi\) | ||||
−0.930647 | + | 0.365917i | \(0.880755\pi\) | |||||||
\(572\) | 2.58076e17 | − | 5.89974e17i | 0.0128818 | − | 0.0294483i | ||||
\(573\) | −6.10589e18 | −0.301070 | ||||||||
\(574\) | −1.77792e19 | − | 3.71853e18i | −0.866023 | − | 0.181129i | ||||
\(575\) | − | 2.70401e19i | − | 1.30117i | ||||||
\(576\) | 2.29687e18 | + | 6.62505e18i | 0.109189 | + | 0.314943i | ||||
\(577\) | 1.78526e19 | 0.838435 | 0.419218 | − | 0.907886i | \(-0.362304\pi\) | ||||
0.419218 | + | 0.907886i | \(0.362304\pi\) | |||||||
\(578\) | −1.07826e18 | + | 5.15545e18i | −0.0500299 | + | 0.239206i | ||||
\(579\) | − | 6.48242e18i | − | 0.297158i | ||||||
\(580\) | −9.29102e18 | − | 4.06423e18i | −0.420792 | − | 0.184070i | ||||
\(581\) | −6.05456e18 | −0.270925 | ||||||||
\(582\) | 1.40551e19 | + | 2.93963e18i | 0.621402 | + | 0.129967i | ||||
\(583\) | 2.34107e18i | 0.102267i | ||||||||
\(584\) | −1.06314e19 | + | 1.49381e19i | −0.458883 | + | 0.644771i | ||||
\(585\) | −1.77598e18 | −0.0757438 | ||||||||
\(586\) | 5.29101e18 | − | 2.52976e19i | 0.222974 | − | 1.06610i | ||||
\(587\) | 8.73511e18i | 0.363749i | 0.983322 | + | 0.181874i | \(0.0582165\pi\) | ||||
−0.983322 | + | 0.181874i | \(0.941784\pi\) | |||||||
\(588\) | −4.15128e18 | + | 9.49003e18i | −0.170821 | + | 0.390505i | ||||
\(589\) | 1.43499e19 | 0.583502 | ||||||||
\(590\) | −4.97763e17 | − | 1.04107e17i | −0.0200013 | − | 0.00418328i | ||||
\(591\) | − | 1.63917e19i | − | 0.650896i | ||||||
\(592\) | −3.09574e19 | − | 3.34926e19i | −1.21482 | − | 1.31431i | ||||
\(593\) | 2.36193e19 | 0.915974 | 0.457987 | − | 0.888959i | \(-0.348571\pi\) | ||||
0.457987 | + | 0.888959i | \(0.348571\pi\) | |||||||
\(594\) | 7.50554e16 | − | 3.58859e17i | 0.00287658 | − | 0.0137537i | ||||
\(595\) | − | 6.06030e18i | − | 0.229549i | ||||||
\(596\) | 1.74517e19 | + | 7.63399e18i | 0.653301 | + | 0.285777i | ||||
\(597\) | 2.88845e19 | 1.06867 | ||||||||
\(598\) | −2.09017e19 | − | 4.37159e18i | −0.764315 | − | 0.159857i | ||||
\(599\) | − | 2.83926e19i | − | 1.02616i | −0.858340 | − | 0.513082i | \(-0.828504\pi\) | ||
0.858340 | − | 0.513082i | \(-0.171496\pi\) | |||||||
\(600\) | −9.65956e18 | − | 6.87470e18i | −0.345063 | − | 0.245581i | ||||
\(601\) | −1.27318e19 | −0.449542 | −0.224771 | − | 0.974412i | \(-0.572163\pi\) | ||||
−0.224771 | + | 0.974412i | \(0.572163\pi\) | |||||||
\(602\) | −2.36040e18 | + | 1.12857e19i | −0.0823779 | + | 0.393869i | ||||
\(603\) | 1.47484e19i | 0.508772i | ||||||||
\(604\) | 7.14097e18 | − | 1.63246e19i | 0.243500 | − | 0.556653i | ||||
\(605\) | −1.52318e19 | −0.513409 | ||||||||
\(606\) | 9.41712e18 | + | 1.96959e18i | 0.313769 | + | 0.0656248i | ||||
\(607\) | − | 5.47340e18i | − | 0.180275i | −0.995929 | − | 0.0901377i | \(-0.971269\pi\) | ||
0.995929 | − | 0.0901377i | \(-0.0287307\pi\) | |||||||
\(608\) | 6.80882e18 | + | 1.13613e19i | 0.221690 | + | 0.369915i | ||||
\(609\) | −8.16585e18 | −0.262833 | ||||||||
\(610\) | −2.33590e18 | + | 1.11685e19i | −0.0743266 | + | 0.355374i | ||||
\(611\) | − | 1.31537e19i | − | 0.413772i | ||||||
\(612\) | 8.53631e18 | + | 3.73409e18i | 0.265467 | + | 0.116125i | ||||
\(613\) | 2.99704e19 | 0.921445 | 0.460722 | − | 0.887544i | \(-0.347590\pi\) | ||||
0.460722 | + | 0.887544i | \(0.347590\pi\) | |||||||
\(614\) | −5.65942e19 | − | 1.18367e19i | −1.72026 | − | 0.359792i | ||||
\(615\) | − | 1.71490e19i | − | 0.515362i | ||||||
\(616\) | −7.28972e17 | + | 1.02427e18i | −0.0216594 | + | 0.0304333i | ||||
\(617\) | 3.07296e19 | 0.902736 | 0.451368 | − | 0.892338i | \(-0.350936\pi\) | ||||
0.451368 | + | 0.892338i | \(0.350936\pi\) | |||||||
\(618\) | −4.42792e18 | + | 2.11710e19i | −0.128612 | + | 0.614925i | ||||
\(619\) | 2.87760e19i | 0.826411i | 0.910638 | + | 0.413205i | \(0.135591\pi\) | ||||
−0.910638 | + | 0.413205i | \(0.864409\pi\) | |||||||
\(620\) | 9.85658e18 | − | 2.25326e19i | 0.279888 | − | 0.639838i | ||||
\(621\) | −1.21575e19 | −0.341354 | ||||||||
\(622\) | 6.16582e19 | + | 1.28958e19i | 1.71182 | + | 0.358027i | ||||
\(623\) | 4.79346e18i | 0.131593i | ||||||||
\(624\) | −6.87574e18 | + | 6.35530e18i | −0.186650 | + | 0.172522i | ||||
\(625\) | 1.01221e19 | 0.271714 | ||||||||
\(626\) | −1.32801e19 | + | 6.34954e19i | −0.352517 | + | 1.68547i | ||||
\(627\) | − | 6.92544e17i | − | 0.0181792i | ||||||
\(628\) | 4.65568e18 | + | 2.03656e18i | 0.120855 | + | 0.0528665i | ||||
\(629\) | −6.06035e19 | −1.55576 | ||||||||
\(630\) | 3.39383e18 | + | 7.09820e17i | 0.0861600 | + | 0.0180204i | ||||
\(631\) | 3.32565e19i | 0.834969i | 0.908684 | + | 0.417485i | \(0.137088\pi\) | ||||
−0.908684 | + | 0.417485i | \(0.862912\pi\) | |||||||
\(632\) | 9.08192e18 | + | 6.46360e18i | 0.225506 | + | 0.160492i | ||||
\(633\) | 2.78014e19 | 0.682717 | ||||||||
\(634\) | −3.55731e18 | + | 1.70084e19i | −0.0863966 | + | 0.413084i | ||||
\(635\) | 2.50490e19i | 0.601691i | ||||||||
\(636\) | 1.36418e19 | − | 3.11858e19i | 0.324094 | − | 0.740895i | ||||
\(637\) | −1.38314e19 | −0.325005 | ||||||||
\(638\) | 2.73620e18 | + | 5.72276e17i | 0.0635920 | + | 0.0133003i | ||||
\(639\) | − | 7.82838e18i | − | 0.179956i | ||||||
\(640\) | 2.25166e19 | − | 2.88764e18i | 0.511968 | − | 0.0656573i | ||||
\(641\) | −5.79342e19 | −1.30295 | −0.651477 | − | 0.758668i | \(-0.725850\pi\) | ||||
−0.651477 | + | 0.758668i | \(0.725850\pi\) | |||||||
\(642\) | 2.77253e18 | − | 1.32562e19i | 0.0616781 | − | 0.294898i | ||||
\(643\) | 4.06293e19i | 0.894052i | 0.894521 | + | 0.447026i | \(0.147517\pi\) | ||||
−0.894521 | + | 0.447026i | \(0.852483\pi\) | |||||||
\(644\) | 3.81950e19 | + | 1.67079e19i | 0.831391 | + | 0.363680i | ||||
\(645\) | −1.08856e19 | −0.234388 | ||||||||
\(646\) | 1.72274e19 | + | 3.60312e18i | 0.366937 | + | 0.0767451i | ||||
\(647\) | 4.19383e19i | 0.883651i | 0.897101 | + | 0.441825i | \(0.145669\pi\) | ||||
−0.897101 | + | 0.441825i | \(0.854331\pi\) | |||||||
\(648\) | −3.09095e18 | + | 4.34306e18i | −0.0644269 | + | 0.0905254i | ||||
\(649\) | 1.40178e17 | 0.00289047 | ||||||||
\(650\) | 3.24104e18 | − | 1.54962e19i | 0.0661136 | − | 0.316106i | ||||
\(651\) | − | 1.98039e19i | − | 0.399653i | ||||||
\(652\) | 1.02831e19 | − | 2.35077e19i | 0.205301 | − | 0.469328i | ||||
\(653\) | −2.43906e19 | −0.481760 | −0.240880 | − | 0.970555i | \(-0.577436\pi\) | ||||
−0.240880 | + | 0.970555i | \(0.577436\pi\) | |||||||
\(654\) | 3.17588e19 | + | 6.64236e18i | 0.620612 | + | 0.129801i | ||||
\(655\) | − | 2.15248e19i | − | 0.416150i | ||||||
\(656\) | −6.13671e19 | − | 6.63926e19i | −1.17384 | − | 1.26997i | ||||
\(657\) | −1.39389e19 | −0.263798 | ||||||||
\(658\) | −5.25726e18 | + | 2.51363e19i | −0.0984415 | + | 0.470674i | ||||
\(659\) | 2.47690e19i | 0.458891i | 0.973321 | + | 0.229446i | \(0.0736913\pi\) | ||||
−0.973321 | + | 0.229446i | \(0.926309\pi\) | |||||||
\(660\) | −1.08745e18 | − | 4.75690e17i | −0.0199344 | − | 0.00872000i | ||||
\(661\) | −1.08965e19 | −0.197642 | −0.0988208 | − | 0.995105i | \(-0.531507\pi\) | ||||
−0.0988208 | + | 0.995105i | \(0.531507\pi\) | |||||||
\(662\) | 1.42367e19 | + | 2.97761e18i | 0.255507 | + | 0.0534394i | ||||
\(663\) | 1.24414e19i | 0.220940i | ||||||||
\(664\) | −2.45528e19 | − | 1.74742e19i | −0.431443 | − | 0.307058i | ||||
\(665\) | 6.54958e18 | 0.113884 | ||||||||
\(666\) | 7.09826e18 | − | 3.39385e19i | 0.122133 | − | 0.583947i | ||||
\(667\) | − | 9.26978e19i | − | 1.57830i | ||||||
\(668\) | 9.84587e18 | − | 2.25082e19i | 0.165890 | − | 0.379232i | ||||
\(669\) | 1.70401e19 | 0.284112 | ||||||||
\(670\) | 4.67366e19 | + | 9.77496e18i | 0.771140 | + | 0.161284i | ||||
\(671\) | − | 3.14523e18i | − | 0.0513565i | ||||||
\(672\) | 1.56793e19 | − | 9.39663e18i | 0.253363 | − | 0.151840i | ||||
\(673\) | −3.49979e19 | −0.559675 | −0.279838 | − | 0.960047i | \(-0.590281\pi\) | ||||
−0.279838 | + | 0.960047i | \(0.590281\pi\) | |||||||
\(674\) | 4.29000e18 | − | 2.05116e19i | 0.0678950 | − | 0.324623i | ||||
\(675\) | − | 9.01344e18i | − | 0.141177i | ||||||
\(676\) | 4.76483e19 | + | 2.08430e19i | 0.738618 | + | 0.323098i | ||||
\(677\) | 2.72380e18 | 0.0417882 | 0.0208941 | − | 0.999782i | \(-0.493349\pi\) | ||||
0.0208941 | + | 0.999782i | \(0.493349\pi\) | |||||||
\(678\) | −5.18691e19 | − | 1.08484e19i | −0.787592 | − | 0.164725i | ||||
\(679\) | − | 3.74333e19i | − | 0.562561i | ||||||
\(680\) | 1.74908e19 | − | 2.45760e19i | 0.260163 | − | 0.365552i | ||||
\(681\) | −2.21465e19 | −0.326043 | ||||||||
\(682\) | −1.38789e18 | + | 6.63584e18i | −0.0202238 | + | 0.0966952i | ||||
\(683\) | − | 1.07215e20i | − | 1.54636i | −0.634188 | − | 0.773179i | \(-0.718665\pi\) | ||
0.634188 | − | 0.773179i | \(-0.281335\pi\) | |||||||
\(684\) | −4.03556e18 | + | 9.22549e18i | −0.0576117 | + | 0.131703i | ||||
\(685\) | 3.02253e19 | 0.427106 | ||||||||
\(686\) | 6.22335e19 | + | 1.30162e19i | 0.870473 | + | 0.182060i | ||||
\(687\) | 5.67609e19i | 0.785872i | ||||||||
\(688\) | −4.21439e19 | + | 3.89539e19i | −0.577584 | + | 0.533865i | ||||
\(689\) | 4.54522e19 | 0.616624 | ||||||||
\(690\) | −8.05780e18 | + | 3.85263e19i | −0.108211 | + | 0.517385i | ||||
\(691\) | − | 3.15507e19i | − | 0.419434i | −0.977762 | − | 0.209717i | \(-0.932746\pi\) | ||
0.977762 | − | 0.209717i | \(-0.0672542\pi\) | |||||||
\(692\) | −1.78915e19 | − | 7.82638e18i | −0.235453 | − | 0.102995i | ||||
\(693\) | −9.55757e17 | −0.0124513 | ||||||||
\(694\) | −8.60827e19 | − | 1.80042e19i | −1.11020 | − | 0.232198i | ||||
\(695\) | 7.62188e19i | 0.973125i | ||||||||
\(696\) | −3.31146e19 | − | 2.35676e19i | −0.418557 | − | 0.297887i | ||||
\(697\) | −1.20135e20 | −1.50328 | ||||||||
\(698\) | 7.99510e17 | − | 3.82266e18i | 0.00990458 | − | 0.0473563i | ||||
\(699\) | 9.09931e19i | 1.11601i | ||||||||
\(700\) | −1.23870e19 | + | 2.83173e19i | −0.150411 | + | 0.343847i | ||||
\(701\) | 1.08018e19 | 0.129859 | 0.0649295 | − | 0.997890i | \(-0.479318\pi\) | ||||
0.0649295 | + | 0.997890i | \(0.479318\pi\) | |||||||
\(702\) | −6.96729e18 | − | 1.45721e18i | −0.0829286 | − | 0.0173445i | ||||
\(703\) | − | 6.54963e19i | − | 0.771844i | ||||||
\(704\) | −5.91233e18 | + | 2.04977e18i | −0.0689843 | + | 0.0239165i | ||||
\(705\) | −2.42452e19 | −0.280093 | ||||||||
\(706\) | −1.00468e19 | + | 4.80365e19i | −0.114920 | + | 0.549463i | ||||
\(707\) | − | 2.50808e19i | − | 0.284057i | ||||||
\(708\) | −1.86734e18 | − | 8.16841e17i | −0.0209407 | − | 0.00916019i | ||||
\(709\) | −2.65544e19 | −0.294857 | −0.147429 | − | 0.989073i | \(-0.547100\pi\) | ||||
−0.147429 | + | 0.989073i | \(0.547100\pi\) | |||||||
\(710\) | −2.48075e19 | − | 5.18851e18i | −0.272757 | − | 0.0570471i | ||||
\(711\) | 8.47444e18i | 0.0922622i | ||||||||
\(712\) | −1.38345e19 | + | 1.94387e19i | −0.149143 | + | 0.209559i | ||||
\(713\) | 2.24811e20 | 2.39989 | ||||||||
\(714\) | 4.97254e18 | − | 2.37750e19i | 0.0525643 | − | 0.251323i | ||||
\(715\) | − | 1.58492e18i | − | 0.0165907i | ||||||
\(716\) | −4.22203e19 | + | 9.65177e19i | −0.437653 | + | 1.00050i | ||||
\(717\) | 7.95051e19 | 0.816133 | ||||||||
\(718\) | −7.70258e19 | − | 1.61100e19i | −0.783006 | − | 0.163766i | ||||
\(719\) | 7.59497e19i | 0.764581i | 0.924042 | + | 0.382291i | \(0.124865\pi\) | ||||
−0.924042 | + | 0.382291i | \(0.875135\pi\) | |||||||
\(720\) | 1.17142e19 | + | 1.26735e19i | 0.116784 | + | 0.126348i | ||||
\(721\) | 5.63852e19 | 0.556696 | ||||||||
\(722\) | 1.70433e19 | − | 8.14885e19i | 0.166646 | − | 0.796776i | ||||
\(723\) | 1.02686e19i | 0.0994360i | ||||||||
\(724\) | 2.40389e19 | + | 1.05155e19i | 0.230539 | + | 0.100846i | ||||
\(725\) | 6.87249e19 | 0.652752 | ||||||||
\(726\) | −5.97554e19 | − | 1.24979e19i | −0.562110 | − | 0.117565i | ||||
\(727\) | 2.39540e19i | 0.223171i | 0.993755 | + | 0.111586i | \(0.0355929\pi\) | ||||
−0.993755 | + | 0.111586i | \(0.964407\pi\) | |||||||
\(728\) | 1.98863e19 | + | 1.41531e19i | 0.183500 | + | 0.130596i | ||||
\(729\) | −4.05256e18 | −0.0370370 | ||||||||
\(730\) | −9.23846e18 | + | 4.41714e19i | −0.0836256 | + | 0.399835i | ||||
\(731\) | 7.62576e19i | 0.683694i | ||||||||
\(732\) | −1.83278e19 | + | 4.18982e19i | −0.162754 | + | 0.372064i | ||||
\(733\) | 1.74351e20 | 1.53355 | 0.766774 | − | 0.641918i | \(-0.221861\pi\) | ||||
0.766774 | + | 0.641918i | \(0.221861\pi\) | |||||||
\(734\) | 1.36129e20 | + | 2.84715e19i | 1.18599 | + | 0.248049i | ||||
\(735\) | 2.54943e19i | 0.220004i | ||||||||
\(736\) | 1.06670e20 | + | 1.77990e20i | 0.911792 | + | 1.52143i | ||||
\(737\) | −1.31618e19 | −0.111440 | ||||||||
\(738\) | 1.40709e19 | − | 6.72766e19i | 0.118013 | − | 0.564247i | ||||
\(739\) | − | 1.29448e20i | − | 1.07544i | −0.843124 | − | 0.537719i | \(-0.819286\pi\) | ||
0.843124 | − | 0.537719i | \(-0.180714\pi\) | |||||||
\(740\) | −1.02844e20 | − | 4.49877e19i | −0.846364 | − | 0.370230i | ||||
\(741\) | −1.34458e19 | −0.109613 | ||||||||
\(742\) | −8.68573e19 | − | 1.81662e19i | −0.701421 | − | 0.146702i | ||||
\(743\) | − | 4.21533e19i | − | 0.337217i | −0.985683 | − | 0.168609i | \(-0.946073\pi\) | ||
0.985683 | − | 0.168609i | \(-0.0539274\pi\) | |||||||
\(744\) | 5.71563e19 | − | 8.03096e19i | 0.452954 | − | 0.636440i | ||||
\(745\) | 4.68826e19 | 0.368060 | ||||||||
\(746\) | 3.97876e19 | − | 1.90234e20i | 0.309439 | − | 1.47951i | ||||
\(747\) | − | 2.29105e19i | − | 0.176518i | ||||||
\(748\) | −3.33238e18 | + | 7.61799e18i | −0.0254357 | + | 0.0581472i | ||||
\(749\) | −3.53054e19 | −0.266974 | ||||||||
\(750\) | −6.74994e19 | − | 1.41175e19i | −0.505674 | − | 0.105762i | ||||
\(751\) | 9.37893e19i | 0.696103i | 0.937475 | + | 0.348052i | \(0.113157\pi\) | ||||
−0.937475 | + | 0.348052i | \(0.886843\pi\) | |||||||
\(752\) | −9.38659e19 | + | 8.67609e19i | −0.690213 | + | 0.637968i | ||||
\(753\) | −7.98192e19 | −0.581490 | ||||||||
\(754\) | 1.11108e19 | − | 5.31236e19i | 0.0801949 | − | 0.383432i | ||||
\(755\) | − | 4.38549e19i | − | 0.313610i | ||||||
\(756\) | 1.27318e19 | + | 5.56934e18i | 0.0902064 | + | 0.0394595i | ||||
\(757\) | −1.92048e20 | −1.34815 | −0.674075 | − | 0.738663i | \(-0.735457\pi\) | ||||
−0.674075 | + | 0.738663i | \(0.735457\pi\) | |||||||
\(758\) | −1.06471e20 | − | 2.22685e19i | −0.740539 | − | 0.154884i | ||||
\(759\) | − | 1.08496e19i | − | 0.0747693i | ||||||
\(760\) | 2.65602e19 | + | 1.89029e19i | 0.181358 | + | 0.129072i | ||||
\(761\) | −1.72126e20 | −1.16454 | −0.582269 | − | 0.812996i | \(-0.697835\pi\) | ||||
−0.582269 | + | 0.812996i | \(0.697835\pi\) | |||||||
\(762\) | −2.05530e19 | + | 9.82688e19i | −0.137781 | + | 0.658766i | ||||
\(763\) | − | 8.45840e19i | − | 0.561845i | ||||||
\(764\) | −3.17523e19 | + | 7.25874e19i | −0.208988 | + | 0.477758i | ||||
\(765\) | 2.29322e19 | 0.149560 | ||||||||
\(766\) | 1.28477e20 | + | 2.68710e19i | 0.830278 | + | 0.173653i | ||||
\(767\) | − | 2.72158e18i | − | 0.0174282i | ||||||
\(768\) | 9.07035e19 | + | 7.14672e18i | 0.575566 | + | 0.0453501i | ||||
\(769\) | −2.90260e19 | −0.182517 | −0.0912585 | − | 0.995827i | \(-0.529089\pi\) | ||||
−0.0912585 | + | 0.995827i | \(0.529089\pi\) | |||||||
\(770\) | −6.33458e17 | + | 3.02872e18i | −0.00394714 | + | 0.0188723i | ||||
\(771\) | − | 8.07915e19i | − | 0.498867i | ||||||
\(772\) | −7.70636e19 | − | 3.37104e19i | −0.471550 | − | 0.206273i | ||||
\(773\) | −1.24192e20 | −0.753072 | −0.376536 | − | 0.926402i | \(-0.622885\pi\) | ||||
−0.376536 | + | 0.926402i | \(0.622885\pi\) | |||||||
\(774\) | −4.27050e19 | − | 8.93177e18i | −0.256621 | − | 0.0536724i | ||||
\(775\) | 1.66672e20i | 0.992546i | ||||||||
\(776\) | 1.08037e20 | − | 1.51801e20i | 0.637588 | − | 0.895867i | ||||
\(777\) | −9.03893e19 | −0.528652 | ||||||||
\(778\) | 1.57321e19 | − | 7.52192e19i | 0.0911863 | − | 0.435985i | ||||
\(779\) | − | 1.29834e20i | − | 0.745805i | ||||||
\(780\) | −9.23559e18 | + | 2.11130e19i | −0.0525778 | + | 0.120195i | ||||
\(781\) | 6.98621e18 | 0.0394171 | ||||||||
\(782\) | 2.69891e20 | + | 5.64477e19i | 1.50918 | + | 0.315645i | ||||
\(783\) | − | 3.08996e19i | − | 0.171246i | ||||||
\(784\) | 9.12306e19 | + | 9.87016e19i | 0.501104 | + | 0.542140i | ||||
\(785\) | 1.25072e19 | 0.0680881 | ||||||||
\(786\) | 1.76613e19 | − | 8.44432e19i | 0.0952939 | − | 0.455624i | ||||
\(787\) | − | 1.78948e20i | − | 0.956982i | −0.878092 | − | 0.478491i | \(-0.841184\pi\) | ||
0.878092 | − | 0.478491i | \(-0.158816\pi\) | |||||||
\(788\) | −1.94866e20 | − | 8.52413e19i | −1.03289 | − | 0.451821i | ||||
\(789\) | 1.67739e20 | 0.881244 | ||||||||
\(790\) | 2.68549e19 | + | 5.61670e18i | 0.139841 | + | 0.0292477i | ||||
\(791\) | 1.38144e20i | 0.713013i | ||||||||
\(792\) | −3.87584e18 | − | 2.75843e18i | −0.0198285 | − | 0.0141119i | ||||
\(793\) | −6.10651e19 | −0.309657 | ||||||||
\(794\) | −1.66779e19 | + | 7.97412e19i | −0.0838297 | + | 0.400811i | ||||
\(795\) | − | 8.37783e19i | − | 0.417409i | ||||||
\(796\) | 1.50207e20 | − | 3.43382e20i | 0.741822 | − | 1.69584i | ||||
\(797\) | −2.76149e20 | −1.35187 | −0.675936 | − | 0.736961i | \(-0.736260\pi\) | ||||
−0.675936 | + | 0.736961i | \(0.736260\pi\) | |||||||
\(798\) | 2.56944e19 | + | 5.37400e18i | 0.124686 | + | 0.0260782i | ||||
\(799\) | 1.69847e20i | 0.817014i | ||||||||
\(800\) | −1.31959e20 | + | 7.90834e19i | −0.629232 | + | 0.377099i | ||||
\(801\) | −1.81385e19 | −0.0857379 | ||||||||
\(802\) | 3.28071e19 | − | 1.56859e20i | 0.153726 | − | 0.735003i | ||||
\(803\) | − | 1.24394e19i | − | 0.0577817i | ||||||
\(804\) | 1.75330e20 | + | 7.66957e19i | 0.807355 | + | 0.353166i | ||||
\(805\) | 1.02608e20 | 0.468393 | ||||||||
\(806\) | 1.28836e20 | + | 2.69460e19i | 0.583030 | + | 0.121941i | ||||
\(807\) | 7.34408e19i | 0.329475i | ||||||||
\(808\) | 7.23863e19 | − | 1.01709e20i | 0.321942 | − | 0.452356i | ||||
\(809\) | 1.62231e20 | 0.715308 | 0.357654 | − | 0.933854i | \(-0.383577\pi\) | ||||
0.357654 | + | 0.933854i | \(0.383577\pi\) | |||||||
\(810\) | −2.68596e18 | + | 1.28422e19i | −0.0117410 | + | 0.0561366i | ||||
\(811\) | 3.71751e20i | 1.61104i | 0.592568 | + | 0.805521i | \(0.298114\pi\) | ||||
−0.592568 | + | 0.805521i | \(0.701886\pi\) | |||||||
\(812\) | −4.24647e19 | + | 9.70763e19i | −0.182446 | + | 0.417082i | ||||
\(813\) | 9.94166e19 | 0.423472 | ||||||||
\(814\) | 3.02875e19 | + | 6.33463e18i | 0.127906 | + | 0.0267517i | ||||
\(815\) | − | 6.31516e19i | − | 0.264412i | ||||||
\(816\) | 8.87823e19 | − | 8.20622e19i | 0.368549 | − | 0.340653i | ||||
\(817\) | −8.24143e19 | −0.339194 | ||||||||
\(818\) | −6.99239e19 | + | 3.34324e20i | −0.285334 | + | 1.36425i | ||||
\(819\) | 1.85562e19i | 0.0750759i | ||||||||
\(820\) | −2.03869e20 | − | 8.91794e19i | −0.817812 | − | 0.357740i | ||||
\(821\) | −3.82848e20 | −1.52274 | −0.761368 | − | 0.648320i | \(-0.775472\pi\) | ||||
−0.761368 | + | 0.648320i | \(0.775472\pi\) | |||||||
\(822\) | 1.18576e20 | + | 2.48002e19i | 0.467620 | + | 0.0978029i | ||||
\(823\) | − | 2.71424e19i | − | 0.106133i | −0.998591 | − | 0.0530663i | \(-0.983101\pi\) | ||
0.998591 | − | 0.0530663i | \(-0.0168995\pi\) | |||||||
\(824\) | 2.28656e20 | + | 1.62735e20i | 0.886528 | + | 0.630942i | ||||
\(825\) | 8.04379e18 | 0.0309231 | ||||||||
\(826\) | −1.08776e18 | + | 5.20083e18i | −0.00414640 | + | 0.0198250i | ||||
\(827\) | 2.43731e20i | 0.921240i | 0.887597 | + | 0.460620i | \(0.152373\pi\) | ||||
−0.887597 | + | 0.460620i | \(0.847627\pi\) | |||||||
\(828\) | −6.32226e19 | + | 1.44530e20i | −0.236952 | + | 0.541683i | ||||
\(829\) | 1.75101e20 | 0.650740 | 0.325370 | − | 0.945587i | \(-0.394511\pi\) | ||||
0.325370 | + | 0.945587i | \(0.394511\pi\) | |||||||
\(830\) | −7.26015e19 | − | 1.51846e19i | −0.267546 | − | 0.0559574i | ||||
\(831\) | − | 5.78382e19i | − | 0.211353i | ||||||
\(832\) | 3.97966e19 | + | 1.14789e20i | 0.144206 | + | 0.415945i | ||||
\(833\) | 1.78597e20 | 0.641738 | ||||||||
\(834\) | −6.25384e19 | + | 2.99012e20i | −0.222835 | + | 1.06543i | ||||
\(835\) | − | 6.04665e19i | − | 0.213653i | ||||||
\(836\) | −8.23302e18 | − | 3.60142e18i | −0.0288480 | − | 0.0126191i | ||||
\(837\) | 7.49378e19 | 0.260389 | ||||||||
\(838\) | −4.95429e20 | − | 1.03619e20i | −1.70716 | − | 0.357052i | ||||
\(839\) | 3.16749e20i | 1.08238i | 0.840899 | + | 0.541192i | \(0.182027\pi\) | ||||
−0.840899 | + | 0.541192i | \(0.817973\pi\) | |||||||
\(840\) | 2.60872e19 | − | 3.66549e19i | 0.0884042 | − | 0.124216i | ||||
\(841\) | −6.19578e19 | −0.208221 | ||||||||
\(842\) | −7.70078e19 | + | 3.68193e20i | −0.256655 | + | 1.22713i | ||||
\(843\) | − | 2.55011e20i | − | 0.842879i | ||||||
\(844\) | 1.44575e20 | − | 3.30506e20i | 0.473910 | − | 1.08338i | ||||
\(845\) | 1.28004e20 | 0.416126 | ||||||||
\(846\) | −9.51157e19 | − | 1.98935e19i | −0.306662 | − | 0.0641384i | ||||
\(847\) | 1.59148e20i | 0.508882i | ||||||||
\(848\) | −2.99798e20 | − | 3.24349e20i | −0.950732 | − | 1.02859i | ||||
\(849\) | −2.18615e20 | −0.687584 | ||||||||
\(850\) | −4.18496e19 | + | 2.00093e20i | −0.130545 | + | 0.624167i | ||||
\(851\) | − | 1.02609e21i | − | 3.17452i | ||||||
\(852\) | −9.30645e19 | − | 4.07097e19i | −0.285566 | − | 0.124917i | ||||
\(853\) | 5.23738e20 | 1.59394 | 0.796968 | − | 0.604021i | \(-0.206436\pi\) | ||||
0.796968 | + | 0.604021i | \(0.206436\pi\) | |||||||
\(854\) | 1.16693e20 | + | 2.44064e19i | 0.352241 | + | 0.0736712i | ||||
\(855\) | 2.47836e19i | 0.0741996i | ||||||||
\(856\) | −1.43172e20 | − | 1.01896e20i | −0.425151 | − | 0.302580i | ||||
\(857\) | 5.14937e20 | 1.51666 | 0.758330 | − | 0.651871i | \(-0.226016\pi\) | ||||
0.758330 | + | 0.651871i | \(0.226016\pi\) | |||||||
\(858\) | 1.30045e18 | − | 6.21776e18i | 0.00379911 | − | 0.0181645i | ||||
\(859\) | 1.34780e19i | 0.0390546i | 0.999809 | + | 0.0195273i | \(0.00621612\pi\) | ||||
−0.999809 | + | 0.0195273i | \(0.993784\pi\) | |||||||
\(860\) | −5.66082e19 | + | 1.29409e20i | −0.162701 | + | 0.371943i | ||||
\(861\) | −1.79179e20 | −0.510818 | ||||||||
\(862\) | 8.64372e18 | + | 1.80784e18i | 0.0244427 | + | 0.00511220i | ||||
\(863\) | − | 1.69934e20i | − | 0.476655i | −0.971185 | − | 0.238327i | \(-0.923401\pi\) | ||
0.971185 | − | 0.238327i | \(-0.0765991\pi\) | |||||||
\(864\) | 3.55569e19 | + | 5.93306e19i | 0.0989299 | + | 0.165076i | ||||
\(865\) | −4.80642e19 | −0.132650 | ||||||||
\(866\) | 1.08293e20 | − | 5.17776e20i | 0.296466 | − | 1.41748i | ||||
\(867\) | 5.19567e19i | 0.141094i | ||||||||
\(868\) | −2.35430e20 | − | 1.02985e20i | −0.634196 | − | 0.277420i | ||||
\(869\) | −7.56277e18 | −0.0202089 | ||||||||
\(870\) | −9.79184e19 | − | 2.04797e19i | −0.259555 | − | 0.0542860i | ||||
\(871\) | 2.55538e20i | 0.671936i | ||||||||
\(872\) | 2.44120e20 | − | 3.43009e20i | 0.636777 | − | 0.894727i | ||||
\(873\) | 1.41648e20 | 0.366530 | ||||||||
\(874\) | −6.10050e19 | + | 2.91680e20i | −0.156598 | + | 0.748733i | ||||
\(875\) | 1.79773e20i | 0.457791i | ||||||||
\(876\) | −7.24862e19 | + | 1.65707e20i | −0.183116 | + | 0.418613i | ||||
\(877\) | −2.95602e20 | −0.740815 | −0.370408 | − | 0.928869i | \(-0.620782\pi\) | ||||
−0.370408 | + | 0.928869i | \(0.620782\pi\) | |||||||
\(878\) | −2.10556e20 | − | 4.40379e19i | −0.523488 | − | 0.109488i | ||||
\(879\) | − | 2.54950e20i | − | 0.628829i | ||||||
\(880\) | −1.13101e19 | + | 1.04540e19i | −0.0276750 | + | 0.0255802i | ||||
\(881\) | 3.77738e20 | 0.916980 | 0.458490 | − | 0.888700i | \(-0.348391\pi\) | ||||
0.458490 | + | 0.888700i | \(0.348391\pi\) | |||||||
\(882\) | −2.09183e19 | + | 1.00016e20i | −0.0503787 | + | 0.240873i | ||||
\(883\) | − | 9.48860e19i | − | 0.226713i | −0.993554 | − | 0.113357i | \(-0.963840\pi\) | ||
0.993554 | − | 0.113357i | \(-0.0361603\pi\) | |||||||
\(884\) | 1.47904e20 | + | 6.46986e19i | 0.350602 | + | 0.153366i | ||||
\(885\) | −5.01647e18 | −0.0117976 | ||||||||
\(886\) | 1.06461e20 | + | 2.22664e19i | 0.248403 | + | 0.0519535i | ||||
\(887\) | − | 5.81775e20i | − | 1.34676i | −0.739297 | − | 0.673379i | \(-0.764842\pi\) | ||
0.739297 | − | 0.673379i | \(-0.235158\pi\) | |||||||
\(888\) | −3.66552e20 | − | 2.60875e20i | −0.841869 | − | 0.599157i | ||||
\(889\) | 2.61722e20 | 0.596386 | ||||||||
\(890\) | −1.20218e19 | + | 5.74794e19i | −0.0271795 | + | 0.129952i | ||||
\(891\) | − | 3.61659e18i | − | 0.00811250i | ||||||
\(892\) | 8.86133e19 | − | 2.02574e20i | 0.197217 | − | 0.450849i | ||||
\(893\) | −1.83559e20 | −0.405337 | ||||||||
\(894\) | 1.83924e20 | + | 3.84677e19i | 0.402972 | + | 0.0842818i | ||||
\(895\) | 2.59288e20i | 0.563665i | ||||||||
\(896\) | −3.01712e19 | − | 2.35262e20i | −0.0650783 | − | 0.507454i | ||||
\(897\) | −2.10647e20 | −0.450826 | ||||||||
\(898\) | 6.67401e19 | − | 3.19101e20i | 0.141727 | − | 0.677632i | ||||
\(899\) | 5.71379e20i | 1.20395i | ||||||||
\(900\) | −1.07153e20 | − | 4.68724e19i | −0.224030 | − | 0.0979985i | ||||
\(901\) | −5.86897e20 | −1.21755 | ||||||||
\(902\) | 6.00391e19 | + | 1.25572e19i | 0.123591 | + | 0.0258492i | ||||
\(903\) | 1.13737e20i | 0.232321i | ||||||||
\(904\) | −3.98701e20 | + | 5.60210e20i | −0.808106 | + | 1.13546i | ||||
\(905\) | 6.45788e19 | 0.129882 | ||||||||
\(906\) | 3.59834e19 | − | 1.72046e20i | 0.0718134 | − | 0.343358i | ||||
\(907\) | − | 1.49722e20i | − | 0.296506i | −0.988949 | − | 0.148253i | \(-0.952635\pi\) | ||
0.988949 | − | 0.148253i | \(-0.0473650\pi\) | |||||||
\(908\) | −1.15168e20 | + | 2.63280e20i | −0.226324 | + | 0.517388i | ||||
\(909\) | 9.49059e19 | 0.185074 | ||||||||
\(910\) | 5.88030e19 | + | 1.22987e19i | 0.113792 | + | 0.0237995i | ||||
\(911\) | 3.99678e20i | 0.767506i | 0.923436 | + | 0.383753i | \(0.125369\pi\) | ||||
−0.923436 | + | 0.383753i | \(0.874631\pi\) | |||||||
\(912\) | 8.86875e19 | + | 9.59502e19i | 0.169005 | + | 0.182845i | ||||
\(913\) | 2.04458e19 | 0.0386641 | ||||||||
\(914\) | −3.52705e19 | + | 1.68637e20i | −0.0661894 | + | 0.316468i | ||||
\(915\) | 1.12556e20i | 0.209615i | ||||||||
\(916\) | 6.74779e20 | + | 2.95172e20i | 1.24708 | + | 0.545516i | ||||
\(917\) | −2.24899e20 | −0.412480 | ||||||||
\(918\) | 8.99645e19 | + | 1.88161e19i | 0.163747 | + | 0.0342477i | ||||
\(919\) | 2.96913e20i | 0.536315i | 0.963375 | + | 0.268158i | \(0.0864148\pi\) | ||||
−0.963375 | + | 0.268158i | \(0.913585\pi\) | |||||||
\(920\) | 4.16102e20 | + | 2.96139e20i | 0.745907 | + | 0.530862i | ||||
\(921\) | −5.70357e20 | −1.01468 | ||||||||
\(922\) | 3.83433e19 | − | 1.83329e20i | 0.0676975 | − | 0.323679i | ||||
\(923\) | − | 1.35638e20i | − | 0.237668i | ||||||
\(924\) | −4.97020e18 | + | 1.13621e19i | −0.00864311 | + | 0.0197586i | ||||
\(925\) | 7.60729e20 | 1.31292 | ||||||||
\(926\) | −2.20932e20 | − | 4.62080e19i | −0.378427 | − | 0.0791481i | ||||
\(927\) | 2.13362e20i | 0.362709i | ||||||||
\(928\) | −4.52379e20 | + | 2.71111e20i | −0.763250 | + | 0.457416i | ||||
\(929\) | 1.18672e20 | 0.198719 | 0.0993595 | − | 0.995052i | \(-0.468321\pi\) | ||||
0.0993595 | + | 0.995052i | \(0.468321\pi\) | |||||||
\(930\) | 4.96674e19 | − | 2.37472e20i | 0.0825450 | − | 0.394668i | ||||
\(931\) | 1.93016e20i | 0.318379i | ||||||||
\(932\) | 1.08173e21 | + | 4.73189e20i | 1.77096 | + | 0.774682i | ||||
\(933\) | 6.21392e20 | 1.00970 | ||||||||
\(934\) | 1.09376e21 | + | 2.28761e20i | 1.76399 | + | 0.368939i | ||||
\(935\) | 2.04652e19i | 0.0327592i | ||||||||
\(936\) | −5.35553e19 | + | 7.52499e19i | −0.0850886 | + | 0.119557i | ||||
\(937\) | −1.25633e21 | −1.98119 | −0.990597 | − | 0.136816i | \(-0.956313\pi\) | ||||
−0.990597 | + | 0.136816i | \(0.956313\pi\) | |||||||
\(938\) | 1.02133e20 | − | 4.88322e20i | 0.159862 | − | 0.764340i | ||||
\(939\) | 6.39908e20i | 0.994165i | ||||||||
\(940\) | −1.26082e20 | + | 2.88230e20i | −0.194428 | + | 0.444471i | ||||
\(941\) | −1.12598e21 | −1.72346 | −0.861731 | − | 0.507365i | \(-0.830620\pi\) | ||||
−0.861731 | + | 0.507365i | \(0.830620\pi\) | |||||||
\(942\) | 4.90664e19 | + | 1.02623e19i | 0.0745467 | + | 0.0155915i | ||||
\(943\) | − | 2.03402e21i | − | 3.06743i | ||||||
\(944\) | −1.94214e19 | + | 1.79513e19i | −0.0290720 | + | 0.0268715i | ||||
\(945\) | 3.42030e19 | 0.0508209 | ||||||||
\(946\) | 7.97090e18 | − | 3.81109e19i | 0.0117563 | − | 0.0562096i | ||||
\(947\) | 5.36078e20i | 0.784835i | 0.919787 | + | 0.392417i | \(0.128361\pi\) | ||||
−0.919787 | + | 0.392417i | \(0.871639\pi\) | |||||||
\(948\) | 1.00745e20 | + | 4.40694e19i | 0.146408 | + | 0.0640441i | ||||
\(949\) | −2.41512e20 | −0.348398 | ||||||||
\(950\) | −2.16248e20 | − | 4.52283e19i | −0.309661 | − | 0.0647658i | ||||
\(951\) | 1.71411e20i | 0.243655i | ||||||||
\(952\) | −2.56780e20 | − | 1.82750e20i | −0.362329 | − | 0.257869i | ||||
\(953\) | 7.55090e20 | 1.05767 | 0.528833 | − | 0.848726i | \(-0.322630\pi\) | ||||
0.528833 | + | 0.848726i | \(0.322630\pi\) | |||||||
\(954\) | 6.87410e19 | − | 3.28668e20i | 0.0955823 | − | 0.457003i | ||||
\(955\) | 1.95001e20i | 0.269161i | ||||||||
\(956\) | 4.13449e20 | − | 9.45164e20i | 0.566521 | − | 1.29510i | ||||
\(957\) | 2.75754e19 | 0.0375093 | ||||||||
\(958\) | −2.28772e20 | − | 4.78477e19i | −0.308919 | − | 0.0646104i | ||||
\(959\) | − | 3.15806e20i | − | 0.423340i | ||||||
\(960\) | 2.11581e20 | − | 7.33538e19i | 0.281564 | − | 0.0976167i | ||||
\(961\) | −6.28768e20 | −0.830667 | ||||||||
\(962\) | 1.22988e20 | − | 5.88035e20i | 0.161301 | − | 0.771219i | ||||
\(963\) | − | 1.33596e20i | − | 0.173944i | ||||||
\(964\) | 1.22074e20 | + | 5.33996e19i | 0.157792 | + | 0.0690238i | ||||
\(965\) | −2.07026e20 | −0.265664 | ||||||||
\(966\) | 4.02539e20 | + | 8.41911e19i | 0.512823 | + | 0.107257i | ||||
\(967\) | − | 5.17850e20i | − | 0.654966i | −0.944857 | − | 0.327483i | \(-0.893800\pi\) | ||
0.944857 | − | 0.327483i | \(-0.106200\pi\) | |||||||
\(968\) | −4.59320e20 | + | 6.45386e20i | −0.576751 | + | 0.810386i | ||||
\(969\) | 1.73618e20 | 0.216435 | ||||||||
\(970\) | 9.38814e19 | − | 4.48870e20i | 0.116192 | − | 0.555544i | ||||
\(971\) | 7.83883e20i | 0.963201i | 0.876391 | + | 0.481600i | \(0.159944\pi\) | ||||
−0.876391 | + | 0.481600i | \(0.840056\pi\) | |||||||
\(972\) | −2.10744e19 | + | 4.81771e19i | −0.0257094 | + | 0.0587729i | ||||
\(973\) | 7.96365e20 | 0.964544 | ||||||||
\(974\) | −1.53313e21 | − | 3.20655e20i | −1.84360 | − | 0.385589i | ||||
\(975\) | − | 1.56171e20i | − | 0.186453i | ||||||
\(976\) | 4.02780e20 | + | 4.35764e20i | 0.477440 | + | 0.516538i | ||||
\(977\) | 1.40271e20 | 0.165084 | 0.0825420 | − | 0.996588i | \(-0.473696\pi\) | ||||
0.0825420 | + | 0.996588i | \(0.473696\pi\) | |||||||
\(978\) | 5.18166e19 | − | 2.47748e20i | 0.0605476 | − | 0.289493i | ||||
\(979\) | − | 1.61871e19i | − | 0.0187798i | ||||||
\(980\) | 3.03078e20 | + | 1.32577e20i | 0.349118 | + | 0.152717i | ||||
\(981\) | 3.20066e20 | 0.366063 | ||||||||
\(982\) | 2.92404e19 | + | 6.11565e18i | 0.0332050 | + | 0.00694483i | ||||
\(983\) | 1.18991e21i | 1.34165i | 0.741615 | + | 0.670826i | \(0.234060\pi\) | ||||
−0.741615 | + | 0.670826i | \(0.765940\pi\) | |||||||
\(984\) | −7.26618e20 | − | 5.17133e20i | −0.813468 | − | 0.578944i | ||||
\(985\) | −5.23493e20 | −0.581912 | ||||||||
\(986\) | −1.43467e20 | + | 6.85954e20i | −0.158349 | + | 0.757105i | ||||
\(987\) | 2.53324e20i | 0.277623i | ||||||||
\(988\) | −6.99220e19 | + | 1.59845e20i | −0.0760879 | + | 0.173941i | ||||
\(989\) | −1.29113e21 | −1.39507 | ||||||||
\(990\) | −1.14607e19 | − | 2.39701e18i | −0.0122960 | − | 0.00257172i | ||||
\(991\) | − | 1.35364e21i | − | 1.44208i | −0.692895 | − | 0.721039i | \(-0.743665\pi\) | ||
0.692895 | − | 0.721039i | \(-0.256335\pi\) | |||||||
\(992\) | −6.57500e20 | − | 1.09711e21i | −0.695527 | − | 1.16056i | ||||
\(993\) | 1.43478e20 | 0.150709 | ||||||||
\(994\) | −5.42116e19 | + | 2.59199e20i | −0.0565441 | + | 0.270352i | ||||
\(995\) | − | 9.22470e20i | − | 0.955412i | ||||||
\(996\) | −2.72362e20 | − | 1.19141e20i | −0.280111 | − | 0.122531i | ||||
\(997\) | 1.79645e21 | 1.83463 | 0.917315 | − | 0.398162i | \(-0.130352\pi\) | ||||
0.917315 | + | 0.398162i | \(0.130352\pi\) | |||||||
\(998\) | −1.68775e21 | − | 3.52994e20i | −1.71157 | − | 0.357975i | ||||
\(999\) | − | 3.42033e20i | − | 0.344437i |
(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.7.7 | ✓ | 14 | |
3.2 | odd | 2 | 36.15.d.e.19.8 | 14 | |||
4.3 | odd | 2 | inner | 12.15.d.a.7.8 | yes | 14 | |
12.11 | even | 2 | 36.15.d.e.19.7 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.15.d.a.7.7 | ✓ | 14 | 1.1 | even | 1 | trivial | |
12.15.d.a.7.8 | yes | 14 | 4.3 | odd | 2 | inner | |
36.15.d.e.19.7 | 14 | 12.11 | even | 2 | |||
36.15.d.e.19.8 | 14 | 3.2 | odd | 2 |