Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,9,Mod(23,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.23");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.4434941320\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 23.9 | ||
Character | \(\chi\) | \(=\) | 33.23 |
Dual form | 33.9.b.a.23.18 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 12.0893i | − | 0.755581i | −0.925891 | − | 0.377791i | \(-0.876684\pi\) | ||
0.925891 | − | 0.377791i | \(-0.123316\pi\) | |||||||
\(3\) | −77.6992 | − | 22.8875i | −0.959249 | − | 0.282562i | ||||
\(4\) | 109.849 | 0.429097 | ||||||||
\(5\) | 288.931i | 0.462289i | 0.972919 | + | 0.231145i | \(0.0742471\pi\) | ||||
−0.972919 | + | 0.231145i | \(0.925753\pi\) | |||||||
\(6\) | −276.694 | + | 939.329i | −0.213498 | + | 0.724791i | ||||
\(7\) | 3024.09 | 1.25951 | 0.629757 | − | 0.776792i | \(-0.283154\pi\) | ||||
0.629757 | + | 0.776792i | \(0.283154\pi\) | |||||||
\(8\) | − | 4422.86i | − | 1.07980i | ||||||
\(9\) | 5513.32 | + | 3556.68i | 0.840318 | + | 0.542094i | ||||
\(10\) | 3492.97 | 0.349297 | ||||||||
\(11\) | − | 4414.43i | − | 0.301511i | ||||||
\(12\) | −8535.16 | − | 2514.17i | −0.411611 | − | 0.121246i | ||||
\(13\) | −9096.59 | −0.318497 | −0.159248 | − | 0.987239i | \(-0.550907\pi\) | ||||
−0.159248 | + | 0.987239i | \(0.550907\pi\) | |||||||
\(14\) | − | 36559.2i | − | 0.951666i | ||||||
\(15\) | 6612.91 | − | 22449.7i | 0.130625 | − | 0.443451i | ||||
\(16\) | −25347.9 | −0.386779 | ||||||||
\(17\) | − | 107300.i | − | 1.28470i | −0.766411 | − | 0.642351i | \(-0.777959\pi\) | ||
0.766411 | − | 0.642351i | \(-0.222041\pi\) | |||||||
\(18\) | 42997.8 | − | 66652.2i | 0.409596 | − | 0.634928i | ||||
\(19\) | −55815.2 | −0.428290 | −0.214145 | − | 0.976802i | \(-0.568697\pi\) | ||||
−0.214145 | + | 0.976802i | \(0.568697\pi\) | |||||||
\(20\) | 31738.7i | 0.198367i | ||||||||
\(21\) | −234970. | − | 69214.0i | −1.20819 | − | 0.355891i | ||||
\(22\) | −53367.3 | −0.227816 | ||||||||
\(23\) | − | 145256.i | − | 0.519068i | −0.965734 | − | 0.259534i | \(-0.916431\pi\) | ||
0.965734 | − | 0.259534i | \(-0.0835689\pi\) | |||||||
\(24\) | −101228. | + | 343652.i | −0.305110 | + | 1.03580i | ||||
\(25\) | 307144. | 0.786288 | ||||||||
\(26\) | 109971.i | 0.240650i | ||||||||
\(27\) | −346977. | − | 402537.i | −0.652899 | − | 0.757445i | ||||
\(28\) | 332193. | 0.540454 | ||||||||
\(29\) | − | 1.02612e6i | − | 1.45079i | −0.688331 | − | 0.725396i | \(-0.741657\pi\) | ||
0.688331 | − | 0.725396i | \(-0.258343\pi\) | |||||||
\(30\) | −271401. | − | 79945.4i | −0.335063 | − | 0.0986981i | ||||
\(31\) | 304251. | 0.329447 | 0.164723 | − | 0.986340i | \(-0.447327\pi\) | ||||
0.164723 | + | 0.986340i | \(0.447327\pi\) | |||||||
\(32\) | − | 825812.i | − | 0.787556i | ||||||
\(33\) | −101035. | + | 342997.i | −0.0851956 | + | 0.289224i | ||||
\(34\) | −1.29718e6 | −0.970697 | ||||||||
\(35\) | 873754.i | 0.582260i | ||||||||
\(36\) | 605632. | + | 390697.i | 0.360578 | + | 0.232611i | ||||
\(37\) | 2.96195e6 | 1.58041 | 0.790207 | − | 0.612840i | \(-0.209973\pi\) | ||||
0.790207 | + | 0.612840i | \(0.209973\pi\) | |||||||
\(38\) | 674767.i | 0.323608i | ||||||||
\(39\) | 706798. | + | 208198.i | 0.305518 | + | 0.0899951i | ||||
\(40\) | 1.27790e6 | 0.499180 | ||||||||
\(41\) | 2.62933e6i | 0.930487i | 0.885183 | + | 0.465244i | \(0.154033\pi\) | ||||
−0.885183 | + | 0.465244i | \(0.845967\pi\) | |||||||
\(42\) | −836749. | + | 2.84062e6i | −0.268904 | + | 0.912884i | ||||
\(43\) | −1.66848e6 | −0.488030 | −0.244015 | − | 0.969771i | \(-0.578465\pi\) | ||||
−0.244015 | + | 0.969771i | \(0.578465\pi\) | |||||||
\(44\) | − | 484920.i | − | 0.129378i | ||||||
\(45\) | −1.02763e6 | + | 1.59297e6i | −0.250604 | + | 0.388470i | ||||
\(46\) | −1.75605e6 | −0.392198 | ||||||||
\(47\) | 4.65098e6i | 0.953132i | 0.879139 | + | 0.476566i | \(0.158119\pi\) | ||||
−0.879139 | + | 0.476566i | \(0.841881\pi\) | |||||||
\(48\) | 1.96951e6 | + | 580151.i | 0.371017 | + | 0.109289i | ||||
\(49\) | 3.38035e6 | 0.586377 | ||||||||
\(50\) | − | 3.71316e6i | − | 0.594105i | ||||||
\(51\) | −2.45582e6 | + | 8.33709e6i | −0.363008 | + | 1.23235i | ||||
\(52\) | −999250. | −0.136666 | ||||||||
\(53\) | − | 4.33867e6i | − | 0.549861i | −0.961464 | − | 0.274930i | \(-0.911345\pi\) | ||
0.961464 | − | 0.274930i | \(-0.0886548\pi\) | |||||||
\(54\) | −4.86640e6 | + | 4.19471e6i | −0.572311 | + | 0.493318i | ||||
\(55\) | 1.27546e6 | 0.139386 | ||||||||
\(56\) | − | 1.33751e7i | − | 1.36002i | ||||||
\(57\) | 4.33680e6 | + | 1.27747e6i | 0.410837 | + | 0.121018i | ||||
\(58\) | −1.24050e7 | −1.09619 | ||||||||
\(59\) | − | 1.79174e7i | − | 1.47866i | −0.673344 | − | 0.739329i | \(-0.735143\pi\) | ||
0.673344 | − | 0.739329i | \(-0.264857\pi\) | |||||||
\(60\) | 726420. | − | 2.46607e6i | 0.0560509 | − | 0.190283i | ||||
\(61\) | 1.96177e6 | 0.141687 | 0.0708434 | − | 0.997487i | \(-0.477431\pi\) | ||||
0.0708434 | + | 0.997487i | \(0.477431\pi\) | |||||||
\(62\) | − | 3.67818e6i | − | 0.248924i | ||||||
\(63\) | 1.66728e7 | + | 1.07557e7i | 1.05839 | + | 0.682776i | ||||
\(64\) | −1.64726e7 | −0.981841 | ||||||||
\(65\) | − | 2.62829e6i | − | 0.147238i | ||||||
\(66\) | 4.14660e6 | + | 1.22145e6i | 0.218533 | + | 0.0643722i | ||||
\(67\) | 2.34416e7 | 1.16329 | 0.581646 | − | 0.813442i | \(-0.302409\pi\) | ||||
0.581646 | + | 0.813442i | \(0.302409\pi\) | |||||||
\(68\) | − | 1.17867e7i | − | 0.551262i | ||||||
\(69\) | −3.32456e6 | + | 1.12863e7i | −0.146669 | + | 0.497915i | ||||
\(70\) | 1.05631e7 | 0.439945 | ||||||||
\(71\) | 2.05631e7i | 0.809199i | 0.914494 | + | 0.404600i | \(0.132589\pi\) | ||||
−0.914494 | + | 0.404600i | \(0.867411\pi\) | |||||||
\(72\) | 1.57307e7 | − | 2.43846e7i | 0.585353 | − | 0.907374i | ||||
\(73\) | −1.67837e7 | −0.591011 | −0.295506 | − | 0.955341i | \(-0.595488\pi\) | ||||
−0.295506 | + | 0.955341i | \(0.595488\pi\) | |||||||
\(74\) | − | 3.58079e7i | − | 1.19413i | ||||||
\(75\) | −2.38648e7 | − | 7.02976e6i | −0.754247 | − | 0.222175i | ||||
\(76\) | −6.13124e6 | −0.183778 | ||||||||
\(77\) | − | 1.33496e7i | − | 0.379758i | ||||||
\(78\) | 2.51697e6 | − | 8.54469e6i | 0.0679986 | − | 0.230844i | ||||
\(79\) | −7.34684e7 | −1.88622 | −0.943110 | − | 0.332482i | \(-0.892114\pi\) | ||||
−0.943110 | + | 0.332482i | \(0.892114\pi\) | |||||||
\(80\) | − | 7.32380e6i | − | 0.178804i | ||||||
\(81\) | 1.77468e7 | + | 3.92183e7i | 0.412268 | + | 0.911063i | ||||
\(82\) | 3.17868e7 | 0.703059 | ||||||||
\(83\) | − | 5.71837e7i | − | 1.20493i | −0.798147 | − | 0.602463i | \(-0.794186\pi\) | ||
0.798147 | − | 0.602463i | \(-0.205814\pi\) | |||||||
\(84\) | −2.58111e7 | − | 7.60307e6i | −0.518430 | − | 0.152712i | ||||
\(85\) | 3.10022e7 | 0.593904 | ||||||||
\(86\) | 2.01707e7i | 0.368746i | ||||||||
\(87\) | −2.34853e7 | + | 7.97285e7i | −0.409939 | + | 1.39167i | ||||
\(88\) | −1.95244e7 | −0.325572 | ||||||||
\(89\) | 8.04561e7i | 1.28233i | 0.767404 | + | 0.641164i | \(0.221548\pi\) | ||||
−0.767404 | + | 0.641164i | \(0.778452\pi\) | |||||||
\(90\) | 1.92579e7 | + | 1.24234e7i | 0.293521 | + | 0.189352i | ||||
\(91\) | −2.75089e7 | −0.401151 | ||||||||
\(92\) | − | 1.59563e7i | − | 0.222730i | ||||||
\(93\) | −2.36401e7 | − | 6.96355e6i | −0.316022 | − | 0.0930891i | ||||
\(94\) | 5.62271e7 | 0.720169 | ||||||||
\(95\) | − | 1.61267e7i | − | 0.197994i | ||||||
\(96\) | −1.89008e7 | + | 6.41649e7i | −0.222533 | + | 0.755462i | ||||
\(97\) | 3.68114e7 | 0.415811 | 0.207905 | − | 0.978149i | \(-0.433335\pi\) | ||||
0.207905 | + | 0.978149i | \(0.433335\pi\) | |||||||
\(98\) | − | 4.08660e7i | − | 0.443055i | ||||||
\(99\) | 1.57007e7 | − | 2.43382e7i | 0.163448 | − | 0.253365i | ||||
\(100\) | 3.37394e7 | 0.337394 | ||||||||
\(101\) | 1.65981e8i | 1.59504i | 0.603292 | + | 0.797520i | \(0.293855\pi\) | ||||
−0.603292 | + | 0.797520i | \(0.706145\pi\) | |||||||
\(102\) | 1.00790e8 | + | 2.96891e7i | 0.931140 | + | 0.274282i | ||||
\(103\) | 1.54289e8 | 1.37084 | 0.685421 | − | 0.728147i | \(-0.259618\pi\) | ||||
0.685421 | + | 0.728147i | \(0.259618\pi\) | |||||||
\(104\) | 4.02329e7i | 0.343913i | ||||||||
\(105\) | 1.99981e7 | − | 6.78900e7i | 0.164525 | − | 0.558533i | ||||
\(106\) | −5.24514e7 | −0.415464 | ||||||||
\(107\) | 7.37016e7i | 0.562266i | 0.959669 | + | 0.281133i | \(0.0907102\pi\) | ||||
−0.959669 | + | 0.281133i | \(0.909290\pi\) | |||||||
\(108\) | −3.81150e7 | − | 4.42183e7i | −0.280157 | − | 0.325017i | ||||
\(109\) | 1.70291e8 | 1.20638 | 0.603192 | − | 0.797596i | \(-0.293895\pi\) | ||||
0.603192 | + | 0.797596i | \(0.293895\pi\) | |||||||
\(110\) | − | 1.54195e7i | − | 0.105317i | ||||||
\(111\) | −2.30141e8 | − | 6.77917e7i | −1.51601 | − | 0.446565i | ||||
\(112\) | −7.66545e7 | −0.487153 | ||||||||
\(113\) | 2.65009e8i | 1.62535i | 0.582719 | + | 0.812673i | \(0.301989\pi\) | ||||
−0.582719 | + | 0.812673i | \(0.698011\pi\) | |||||||
\(114\) | 1.54437e7 | − | 5.24288e7i | 0.0914393 | − | 0.310421i | ||||
\(115\) | 4.19691e7 | 0.239960 | ||||||||
\(116\) | − | 1.12718e8i | − | 0.622531i | ||||||
\(117\) | −5.01524e7 | − | 3.23537e7i | −0.267639 | − | 0.172655i | ||||
\(118\) | −2.16609e8 | −1.11725 | ||||||||
\(119\) | − | 3.24484e8i | − | 1.61810i | ||||||
\(120\) | −9.92918e7 | − | 2.92479e7i | −0.478838 | − | 0.141049i | ||||
\(121\) | −1.94872e7 | −0.0909091 | ||||||||
\(122\) | − | 2.37165e7i | − | 0.107056i | ||||||
\(123\) | 6.01789e7 | − | 2.04297e8i | 0.262920 | − | 0.892569i | ||||
\(124\) | 3.34216e7 | 0.141365 | ||||||||
\(125\) | 2.01607e8i | 0.825782i | ||||||||
\(126\) | 1.30029e8 | − | 2.01563e8i | 0.515892 | − | 0.799701i | ||||
\(127\) | −1.11160e8 | −0.427299 | −0.213650 | − | 0.976910i | \(-0.568535\pi\) | ||||
−0.213650 | + | 0.976910i | \(0.568535\pi\) | |||||||
\(128\) | − | 1.22662e7i | − | 0.0456952i | ||||||
\(129\) | 1.29639e8 | + | 3.81873e7i | 0.468143 | + | 0.137899i | ||||
\(130\) | −3.17741e7 | −0.111250 | ||||||||
\(131\) | − | 2.78342e7i | − | 0.0945135i | −0.998883 | − | 0.0472567i | \(-0.984952\pi\) | ||
0.998883 | − | 0.0472567i | \(-0.0150479\pi\) | |||||||
\(132\) | −1.10986e7 | + | 3.76779e7i | −0.0365572 | + | 0.124105i | ||||
\(133\) | −1.68790e8 | −0.539438 | ||||||||
\(134\) | − | 2.83393e8i | − | 0.878961i | ||||||
\(135\) | 1.16305e8 | − | 1.00252e8i | 0.350159 | − | 0.301828i | ||||
\(136\) | −4.74571e8 | −1.38722 | ||||||||
\(137\) | 4.61369e8i | 1.30968i | 0.755766 | + | 0.654841i | \(0.227265\pi\) | ||||
−0.755766 | + | 0.654841i | \(0.772735\pi\) | |||||||
\(138\) | 1.36444e8 | + | 4.01916e7i | 0.376216 | + | 0.110820i | ||||
\(139\) | −3.23476e8 | −0.866528 | −0.433264 | − | 0.901267i | \(-0.642638\pi\) | ||||
−0.433264 | + | 0.901267i | \(0.642638\pi\) | |||||||
\(140\) | 9.59809e7i | 0.249846i | ||||||||
\(141\) | 1.06449e8 | − | 3.61377e8i | 0.269319 | − | 0.914291i | ||||
\(142\) | 2.48594e8 | 0.611416 | ||||||||
\(143\) | 4.01562e7i | 0.0960304i | ||||||||
\(144\) | −1.39751e8 | − | 9.01545e7i | −0.325017 | − | 0.209671i | ||||
\(145\) | 2.96477e8 | 0.670686 | ||||||||
\(146\) | 2.02903e8i | 0.446557i | ||||||||
\(147\) | −2.62650e8 | − | 7.73677e7i | −0.562482 | − | 0.165688i | ||||
\(148\) | 3.25367e8 | 0.678151 | ||||||||
\(149\) | − | 4.91992e8i | − | 0.998188i | −0.866548 | − | 0.499094i | \(-0.833666\pi\) | ||
0.866548 | − | 0.499094i | \(-0.166334\pi\) | |||||||
\(150\) | −8.49849e7 | + | 2.88509e8i | −0.167871 | + | 0.569895i | ||||
\(151\) | 9.97334e8 | 1.91837 | 0.959186 | − | 0.282775i | \(-0.0912549\pi\) | ||||
0.959186 | + | 0.282775i | \(0.0912549\pi\) | |||||||
\(152\) | 2.46863e8i | 0.462467i | ||||||||
\(153\) | 3.81630e8 | − | 5.91577e8i | 0.696430 | − | 1.07956i | ||||
\(154\) | −1.61388e8 | −0.286938 | ||||||||
\(155\) | 8.79075e7i | 0.152300i | ||||||||
\(156\) | 7.76409e7 | + | 2.28703e7i | 0.131097 | + | 0.0386166i | ||||
\(157\) | −5.11837e8 | −0.842429 | −0.421214 | − | 0.906961i | \(-0.638396\pi\) | ||||
−0.421214 | + | 0.906961i | \(0.638396\pi\) | |||||||
\(158\) | 8.88181e8i | 1.42519i | ||||||||
\(159\) | −9.93012e7 | + | 3.37111e8i | −0.155370 | + | 0.527453i | ||||
\(160\) | 2.38603e8 | 0.364079 | ||||||||
\(161\) | − | 4.39269e8i | − | 0.653774i | ||||||
\(162\) | 4.74121e8 | − | 2.14546e8i | 0.688382 | − | 0.311502i | ||||
\(163\) | −2.20655e8 | −0.312581 | −0.156291 | − | 0.987711i | \(-0.549954\pi\) | ||||
−0.156291 | + | 0.987711i | \(0.549954\pi\) | |||||||
\(164\) | 2.88829e8i | 0.399269i | ||||||||
\(165\) | −9.91025e7 | − | 2.91922e7i | −0.133705 | − | 0.0393850i | ||||
\(166\) | −6.91311e8 | −0.910419 | ||||||||
\(167\) | 4.76017e8i | 0.612007i | 0.952030 | + | 0.306004i | \(0.0989920\pi\) | ||||
−0.952030 | + | 0.306004i | \(0.901008\pi\) | |||||||
\(168\) | −3.06123e8 | + | 1.03924e9i | −0.384290 | + | 1.30460i | ||||
\(169\) | −7.32983e8 | −0.898560 | ||||||||
\(170\) | − | 3.74794e8i | − | 0.448743i | ||||||
\(171\) | −3.07727e8 | − | 1.98517e8i | −0.359900 | − | 0.232174i | ||||
\(172\) | −1.83280e8 | −0.209412 | ||||||||
\(173\) | 1.15611e8i | 0.129067i | 0.997916 | + | 0.0645335i | \(0.0205559\pi\) | ||||
−0.997916 | + | 0.0645335i | \(0.979444\pi\) | |||||||
\(174\) | 9.63862e8 | + | 2.83921e8i | 1.05152 | + | 0.309742i | ||||
\(175\) | 9.28832e8 | 0.990342 | ||||||||
\(176\) | 1.11897e8i | 0.116618i | ||||||||
\(177\) | −4.10085e8 | + | 1.39217e9i | −0.417812 | + | 1.41840i | ||||
\(178\) | 9.72658e8 | 0.968902 | ||||||||
\(179\) | − | 1.21391e9i | − | 1.18242i | −0.806516 | − | 0.591212i | \(-0.798650\pi\) | ||
0.806516 | − | 0.591212i | \(-0.201350\pi\) | |||||||
\(180\) | −1.12885e8 | + | 1.74986e8i | −0.107534 | + | 0.166691i | ||||
\(181\) | 8.96371e7 | 0.0835168 | 0.0417584 | − | 0.999128i | \(-0.486704\pi\) | ||||
0.0417584 | + | 0.999128i | \(0.486704\pi\) | |||||||
\(182\) | 3.32564e8i | 0.303103i | ||||||||
\(183\) | −1.52428e8 | − | 4.49001e7i | −0.135913 | − | 0.0400353i | ||||
\(184\) | −6.42449e8 | −0.560489 | ||||||||
\(185\) | 8.55799e8i | 0.730609i | ||||||||
\(186\) | −8.41844e7 | + | 2.85792e8i | −0.0703364 | + | 0.238780i | ||||
\(187\) | −4.73666e8 | −0.387352 | ||||||||
\(188\) | 5.10905e8i | 0.408986i | ||||||||
\(189\) | −1.04929e9 | − | 1.21731e9i | −0.822336 | − | 0.954013i | ||||
\(190\) | −1.94961e8 | −0.149601 | ||||||||
\(191\) | 5.21981e6i | 0.00392212i | 0.999998 | + | 0.00196106i | \(0.000624226\pi\) | ||||
−0.999998 | + | 0.00196106i | \(0.999376\pi\) | |||||||
\(192\) | 1.27990e9 | + | 3.77016e8i | 0.941830 | + | 0.277431i | ||||
\(193\) | 2.36333e9 | 1.70332 | 0.851660 | − | 0.524095i | \(-0.175597\pi\) | ||||
0.851660 | + | 0.524095i | \(0.175597\pi\) | |||||||
\(194\) | − | 4.45024e8i | − | 0.314179i | ||||||
\(195\) | −6.01549e7 | + | 2.04216e8i | −0.0416038 | + | 0.141238i | ||||
\(196\) | 3.71327e8 | 0.251613 | ||||||||
\(197\) | − | 8.07745e8i | − | 0.536302i | −0.963377 | − | 0.268151i | \(-0.913587\pi\) | ||
0.963377 | − | 0.268151i | \(-0.0864126\pi\) | |||||||
\(198\) | −2.94231e8 | − | 1.89811e8i | −0.191438 | − | 0.123498i | ||||
\(199\) | −2.92861e9 | −1.86745 | −0.933725 | − | 0.357992i | \(-0.883462\pi\) | ||||
−0.933725 | + | 0.357992i | \(0.883462\pi\) | |||||||
\(200\) | − | 1.35845e9i | − | 0.849033i | ||||||
\(201\) | −1.82139e9 | − | 5.36520e8i | −1.11589 | − | 0.328702i | ||||
\(202\) | 2.00659e9 | 1.20518 | ||||||||
\(203\) | − | 3.10308e9i | − | 1.82729i | ||||||
\(204\) | −2.69769e8 | + | 9.15820e8i | −0.155766 | + | 0.528797i | ||||
\(205\) | −7.59696e8 | −0.430154 | ||||||||
\(206\) | − | 1.86525e9i | − | 1.03578i | ||||||
\(207\) | 5.16631e8 | − | 8.00846e8i | 0.281384 | − | 0.436182i | ||||
\(208\) | 2.30580e8 | 0.123188 | ||||||||
\(209\) | 2.46392e8i | 0.129134i | ||||||||
\(210\) | −8.20742e8 | − | 2.41763e8i | −0.422017 | − | 0.124312i | ||||
\(211\) | 3.16998e8 | 0.159929 | 0.0799645 | − | 0.996798i | \(-0.474519\pi\) | ||||
0.0799645 | + | 0.996798i | \(0.474519\pi\) | |||||||
\(212\) | − | 4.76597e8i | − | 0.235944i | ||||||
\(213\) | 4.70638e8 | − | 1.59774e9i | 0.228649 | − | 0.776224i | ||||
\(214\) | 8.91000e8 | 0.424837 | ||||||||
\(215\) | − | 4.82075e8i | − | 0.225611i | ||||||
\(216\) | −1.78037e9 | + | 1.53463e9i | −0.817888 | + | 0.704999i | ||||
\(217\) | 9.20084e8 | 0.414943 | ||||||||
\(218\) | − | 2.05870e9i | − | 0.911521i | ||||||
\(219\) | 1.30408e9 | + | 3.84136e8i | 0.566927 | + | 0.166997i | ||||
\(220\) | 1.40108e8 | 0.0598099 | ||||||||
\(221\) | 9.76060e8i | 0.409174i | ||||||||
\(222\) | −8.19554e8 | + | 2.78225e9i | −0.337416 | + | 1.14547i | ||||
\(223\) | −8.14859e7 | −0.0329506 | −0.0164753 | − | 0.999864i | \(-0.505244\pi\) | ||||
−0.0164753 | + | 0.999864i | \(0.505244\pi\) | |||||||
\(224\) | − | 2.49733e9i | − | 0.991938i | ||||||
\(225\) | 1.69338e9 | + | 1.09241e9i | 0.660732 | + | 0.426243i | ||||
\(226\) | 3.20377e9 | 1.22808 | ||||||||
\(227\) | 3.08538e9i | 1.16200i | 0.813904 | + | 0.580999i | \(0.197338\pi\) | ||||
−0.813904 | + | 0.580999i | \(0.802662\pi\) | |||||||
\(228\) | 4.76392e8 | + | 1.40329e8i | 0.176289 | + | 0.0519287i | ||||
\(229\) | −1.94204e9 | −0.706182 | −0.353091 | − | 0.935589i | \(-0.614869\pi\) | ||||
−0.353091 | + | 0.935589i | \(0.614869\pi\) | |||||||
\(230\) | − | 5.07377e8i | − | 0.181309i | ||||||
\(231\) | −3.05540e8 | + | 1.03726e9i | −0.107305 | + | 0.364282i | ||||
\(232\) | −4.53837e9 | −1.56656 | ||||||||
\(233\) | 3.68647e9i | 1.25080i | 0.780305 | + | 0.625399i | \(0.215064\pi\) | ||||
−0.780305 | + | 0.625399i | \(0.784936\pi\) | |||||||
\(234\) | −3.91133e8 | + | 6.06308e8i | −0.130455 | + | 0.202223i | ||||
\(235\) | −1.34381e9 | −0.440623 | ||||||||
\(236\) | − | 1.96821e9i | − | 0.634488i | ||||||
\(237\) | 5.70843e9 | + | 1.68151e9i | 1.80935 | + | 0.532974i | ||||
\(238\) | −3.92279e9 | −1.22261 | ||||||||
\(239\) | − | 1.77521e9i | − | 0.544075i | −0.962287 | − | 0.272038i | \(-0.912302\pi\) | ||
0.962287 | − | 0.272038i | \(-0.0876975\pi\) | |||||||
\(240\) | −1.67624e8 | + | 5.69053e8i | −0.0505231 | + | 0.171517i | ||||
\(241\) | −2.17160e8 | −0.0643743 | −0.0321871 | − | 0.999482i | \(-0.510247\pi\) | ||||
−0.0321871 | + | 0.999482i | \(0.510247\pi\) | |||||||
\(242\) | 2.35586e8i | 0.0686892i | ||||||||
\(243\) | −4.81301e8 | − | 3.45341e9i | −0.138036 | − | 0.990427i | ||||
\(244\) | 2.15499e8 | 0.0607974 | ||||||||
\(245\) | 9.76687e8i | 0.271076i | ||||||||
\(246\) | −2.46981e9 | − | 7.27521e8i | −0.674408 | − | 0.198658i | ||||
\(247\) | 5.07728e8 | 0.136409 | ||||||||
\(248\) | − | 1.34566e9i | − | 0.355736i | ||||||
\(249\) | −1.30879e9 | + | 4.44313e9i | −0.340466 | + | 1.15582i | ||||
\(250\) | 2.43729e9 | 0.623946 | ||||||||
\(251\) | 7.62141e9i | 1.92017i | 0.279703 | + | 0.960087i | \(0.409764\pi\) | ||||
−0.279703 | + | 0.960087i | \(0.590236\pi\) | |||||||
\(252\) | 1.83149e9 | + | 1.18151e9i | 0.454153 | + | 0.292977i | ||||
\(253\) | −6.41224e8 | −0.156505 | ||||||||
\(254\) | 1.34384e9i | 0.322859i | ||||||||
\(255\) | −2.40884e9 | − | 7.09562e8i | −0.569702 | − | 0.167815i | ||||
\(256\) | −4.36527e9 | −1.01637 | ||||||||
\(257\) | 1.71391e9i | 0.392876i | 0.980516 | + | 0.196438i | \(0.0629374\pi\) | ||||
−0.980516 | + | 0.196438i | \(0.937063\pi\) | |||||||
\(258\) | 4.61658e8 | − | 1.56725e9i | 0.104194 | − | 0.353720i | ||||
\(259\) | 8.95722e9 | 1.99056 | ||||||||
\(260\) | − | 2.88714e8i | − | 0.0631793i | ||||||
\(261\) | 3.64957e9 | − | 5.65732e9i | 0.786466 | − | 1.21913i | ||||
\(262\) | −3.36496e8 | −0.0714126 | ||||||||
\(263\) | − | 1.42000e9i | − | 0.296802i | −0.988927 | − | 0.148401i | \(-0.952587\pi\) | ||
0.988927 | − | 0.148401i | \(-0.0474126\pi\) | |||||||
\(264\) | 1.51703e9 | + | 4.46864e8i | 0.312304 | + | 0.0919941i | ||||
\(265\) | 1.25357e9 | 0.254195 | ||||||||
\(266\) | 2.04056e9i | 0.407589i | ||||||||
\(267\) | 1.84144e9 | − | 6.25137e9i | 0.362337 | − | 1.23007i | ||||
\(268\) | 2.57503e9 | 0.499165 | ||||||||
\(269\) | 2.37499e9i | 0.453580i | 0.973944 | + | 0.226790i | \(0.0728230\pi\) | ||||
−0.973944 | + | 0.226790i | \(0.927177\pi\) | |||||||
\(270\) | −1.21198e9 | − | 1.40605e9i | −0.228056 | − | 0.264573i | ||||
\(271\) | −8.98873e9 | −1.66656 | −0.833281 | − | 0.552850i | \(-0.813540\pi\) | ||||
−0.833281 | + | 0.552850i | \(0.813540\pi\) | |||||||
\(272\) | 2.71982e9i | 0.496895i | ||||||||
\(273\) | 2.13742e9 | + | 6.29611e8i | 0.384804 | + | 0.113350i | ||||
\(274\) | 5.57763e9 | 0.989572 | ||||||||
\(275\) | − | 1.35586e9i | − | 0.237075i | ||||||
\(276\) | −3.65199e8 | + | 1.23979e9i | −0.0629351 | + | 0.213654i | ||||
\(277\) | −5.42150e9 | −0.920875 | −0.460437 | − | 0.887692i | \(-0.652307\pi\) | ||||
−0.460437 | + | 0.887692i | \(0.652307\pi\) | |||||||
\(278\) | 3.91059e9i | 0.654732i | ||||||||
\(279\) | 1.67743e9 | + | 1.08212e9i | 0.276840 | + | 0.178591i | ||||
\(280\) | 3.86449e9 | 0.628724 | ||||||||
\(281\) | 3.12144e9i | 0.500646i | 0.968162 | + | 0.250323i | \(0.0805367\pi\) | ||||
−0.968162 | + | 0.250323i | \(0.919463\pi\) | |||||||
\(282\) | −4.36880e9 | − | 1.28690e9i | −0.690821 | − | 0.203492i | ||||
\(283\) | 6.08486e9 | 0.948648 | 0.474324 | − | 0.880350i | \(-0.342693\pi\) | ||||
0.474324 | + | 0.880350i | \(0.342693\pi\) | |||||||
\(284\) | 2.25883e9i | 0.347225i | ||||||||
\(285\) | −3.69101e8 | + | 1.25303e9i | −0.0559456 | + | 0.189926i | ||||
\(286\) | 4.85461e8 | 0.0725588 | ||||||||
\(287\) | 7.95136e9i | 1.17196i | ||||||||
\(288\) | 2.93715e9 | − | 4.55297e9i | 0.426930 | − | 0.661797i | ||||
\(289\) | −4.53744e9 | −0.650459 | ||||||||
\(290\) | − | 3.58420e9i | − | 0.506758i | ||||||
\(291\) | −2.86022e9 | − | 8.42522e8i | −0.398866 | − | 0.117492i | ||||
\(292\) | −1.84367e9 | −0.253601 | ||||||||
\(293\) | − | 4.12562e9i | − | 0.559781i | −0.960032 | − | 0.279891i | \(-0.909702\pi\) | ||
0.960032 | − | 0.279891i | \(-0.0902982\pi\) | |||||||
\(294\) | −9.35321e8 | + | 3.17526e9i | −0.125191 | + | 0.425001i | ||||
\(295\) | 5.17690e9 | 0.683568 | ||||||||
\(296\) | − | 1.31003e10i | − | 1.70653i | ||||||
\(297\) | −1.77697e9 | + | 1.53171e9i | −0.228378 | + | 0.196856i | ||||
\(298\) | −5.94783e9 | −0.754212 | ||||||||
\(299\) | 1.32134e9i | 0.165322i | ||||||||
\(300\) | −2.62152e9 | − | 7.72211e8i | −0.323645 | − | 0.0953347i | ||||
\(301\) | −5.04564e9 | −0.614681 | ||||||||
\(302\) | − | 1.20571e10i | − | 1.44949i | ||||||
\(303\) | 3.79888e9 | − | 1.28966e10i | 0.450697 | − | 1.53004i | ||||
\(304\) | 1.41480e9 | 0.165654 | ||||||||
\(305\) | 5.66817e8i | 0.0655003i | ||||||||
\(306\) | −7.15176e9 | − | 4.61364e9i | −0.815693 | − | 0.526209i | ||||
\(307\) | −1.44676e9 | −0.162870 | −0.0814351 | − | 0.996679i | \(-0.525950\pi\) | ||||
−0.0814351 | + | 0.996679i | \(0.525950\pi\) | |||||||
\(308\) | − | 1.46644e9i | − | 0.162953i | ||||||
\(309\) | −1.19882e10 | − | 3.53130e9i | −1.31498 | − | 0.387347i | ||||
\(310\) | 1.06274e9 | 0.115075 | ||||||||
\(311\) | − | 6.21238e9i | − | 0.664074i | −0.943266 | − | 0.332037i | \(-0.892264\pi\) | ||
0.943266 | − | 0.332037i | \(-0.107736\pi\) | |||||||
\(312\) | 9.20831e8 | − | 3.12606e9i | 0.0971766 | − | 0.329898i | ||||
\(313\) | 1.17712e10 | 1.22643 | 0.613215 | − | 0.789916i | \(-0.289876\pi\) | ||||
0.613215 | + | 0.789916i | \(0.289876\pi\) | |||||||
\(314\) | 6.18775e9i | 0.636523i | ||||||||
\(315\) | −3.10767e9 | + | 4.81729e9i | −0.315640 | + | 0.489284i | ||||
\(316\) | −8.07042e9 | −0.809371 | ||||||||
\(317\) | 8.94887e9i | 0.886198i | 0.896473 | + | 0.443099i | \(0.146121\pi\) | ||||
−0.896473 | + | 0.443099i | \(0.853879\pi\) | |||||||
\(318\) | 4.07543e9 | + | 1.20048e9i | 0.398534 | + | 0.117394i | ||||
\(319\) | −4.52972e9 | −0.437430 | ||||||||
\(320\) | − | 4.75943e9i | − | 0.453895i | ||||||
\(321\) | 1.68685e9 | − | 5.72655e9i | 0.158875 | − | 0.539353i | ||||
\(322\) | −5.31046e9 | −0.493979 | ||||||||
\(323\) | 5.98895e9i | 0.550225i | ||||||||
\(324\) | 1.94946e9 | + | 4.30808e9i | 0.176903 | + | 0.390934i | ||||
\(325\) | −2.79396e9 | −0.250430 | ||||||||
\(326\) | 2.66756e9i | 0.236180i | ||||||||
\(327\) | −1.32315e10 | − | 3.89754e9i | −1.15722 | − | 0.340878i | ||||
\(328\) | 1.16292e10 | 1.00474 | ||||||||
\(329\) | 1.40650e10i | 1.20048i | ||||||||
\(330\) | −3.52913e8 | + | 1.19808e9i | −0.0297586 | + | 0.101025i | ||||
\(331\) | −1.45508e9 | −0.121220 | −0.0606100 | − | 0.998162i | \(-0.519305\pi\) | ||||
−0.0606100 | + | 0.998162i | \(0.519305\pi\) | |||||||
\(332\) | − | 6.28157e9i | − | 0.517030i | ||||||
\(333\) | 1.63302e10 | + | 1.05347e10i | 1.32805 | + | 0.856734i | ||||
\(334\) | 5.75471e9 | 0.462421 | ||||||||
\(335\) | 6.77301e9i | 0.537777i | ||||||||
\(336\) | 5.95600e9 | + | 1.75443e9i | 0.467302 | + | 0.137651i | ||||
\(337\) | 1.82980e10 | 1.41868 | 0.709340 | − | 0.704866i | \(-0.248993\pi\) | ||||
0.709340 | + | 0.704866i | \(0.248993\pi\) | |||||||
\(338\) | 8.86125e9i | 0.678935i | ||||||||
\(339\) | 6.06538e9 | − | 2.05909e10i | 0.459261 | − | 1.55911i | ||||
\(340\) | 3.40555e9 | 0.254842 | ||||||||
\(341\) | − | 1.34309e9i | − | 0.0993320i | ||||||
\(342\) | −2.39993e9 | + | 3.72021e9i | −0.175426 | + | 0.271934i | ||||
\(343\) | −7.21082e9 | −0.520964 | ||||||||
\(344\) | 7.37944e9i | 0.526974i | ||||||||
\(345\) | −3.26096e9 | − | 9.60568e8i | −0.230181 | − | 0.0678034i | ||||
\(346\) | 1.39766e9 | 0.0975205 | ||||||||
\(347\) | − | 1.17905e10i | − | 0.813234i | −0.913599 | − | 0.406617i | \(-0.866708\pi\) | ||
0.913599 | − | 0.406617i | \(-0.133292\pi\) | |||||||
\(348\) | −2.57983e9 | + | 8.75809e9i | −0.175903 | + | 0.597162i | ||||
\(349\) | 1.93748e10 | 1.30598 | 0.652988 | − | 0.757368i | \(-0.273515\pi\) | ||||
0.652988 | + | 0.757368i | \(0.273515\pi\) | |||||||
\(350\) | − | 1.12289e10i | − | 0.748284i | ||||||
\(351\) | 3.15631e9 | + | 3.66172e9i | 0.207946 | + | 0.241244i | ||||
\(352\) | −3.64549e9 | −0.237457 | ||||||||
\(353\) | 2.55809e10i | 1.64747i | 0.566977 | + | 0.823733i | \(0.308113\pi\) | ||||
−0.566977 | + | 0.823733i | \(0.691887\pi\) | |||||||
\(354\) | 1.68304e10 | + | 4.95764e9i | 1.07172 | + | 0.315691i | ||||
\(355\) | −5.94132e9 | −0.374084 | ||||||||
\(356\) | 8.83801e9i | 0.550243i | ||||||||
\(357\) | −7.42663e9 | + | 2.52121e10i | −0.457213 | + | 1.55216i | ||||
\(358\) | −1.46753e10 | −0.893417 | ||||||||
\(359\) | − | 2.66400e10i | − | 1.60382i | −0.597445 | − | 0.801910i | \(-0.703817\pi\) | ||
0.597445 | − | 0.801910i | \(-0.296183\pi\) | |||||||
\(360\) | 7.04548e9 | + | 4.54508e9i | 0.419469 | + | 0.270602i | ||||
\(361\) | −1.38682e10 | −0.816568 | ||||||||
\(362\) | − | 1.08365e9i | − | 0.0631037i | ||||||
\(363\) | 1.51414e9 | + | 4.46013e8i | 0.0872045 | + | 0.0256874i | ||||
\(364\) | −3.02183e9 | −0.172133 | ||||||||
\(365\) | − | 4.84932e9i | − | 0.273218i | ||||||
\(366\) | −5.42811e8 | + | 1.84275e9i | −0.0302499 | + | 0.102693i | ||||
\(367\) | −9.22091e9 | −0.508288 | −0.254144 | − | 0.967166i | \(-0.581794\pi\) | ||||
−0.254144 | + | 0.967166i | \(0.581794\pi\) | |||||||
\(368\) | 3.68195e9i | 0.200764i | ||||||||
\(369\) | −9.35170e9 | + | 1.44964e10i | −0.504412 | + | 0.781905i | ||||
\(370\) | 1.03460e10 | 0.552034 | ||||||||
\(371\) | − | 1.31205e10i | − | 0.692558i | ||||||
\(372\) | −2.59683e9 | − | 7.64938e8i | −0.135604 | − | 0.0399443i | ||||
\(373\) | −4.35860e9 | −0.225171 | −0.112585 | − | 0.993642i | \(-0.535913\pi\) | ||||
−0.112585 | + | 0.993642i | \(0.535913\pi\) | |||||||
\(374\) | 5.72629e9i | 0.292676i | ||||||||
\(375\) | 4.61428e9 | − | 1.56647e10i | 0.233335 | − | 0.792131i | ||||
\(376\) | 2.05706e10 | 1.02919 | ||||||||
\(377\) | 9.33417e9i | 0.462073i | ||||||||
\(378\) | −1.47164e10 | + | 1.26852e10i | −0.720834 | + | 0.621341i | ||||
\(379\) | −2.44788e10 | −1.18640 | −0.593202 | − | 0.805053i | \(-0.702137\pi\) | ||||
−0.593202 | + | 0.805053i | \(0.702137\pi\) | |||||||
\(380\) | − | 1.77150e9i | − | 0.0849586i | ||||||
\(381\) | 8.63701e9 | + | 2.54416e9i | 0.409886 | + | 0.120738i | ||||
\(382\) | 6.31039e7 | 0.00296348 | ||||||||
\(383\) | − | 2.29388e10i | − | 1.06604i | −0.846102 | − | 0.533022i | \(-0.821056\pi\) | ||
0.846102 | − | 0.533022i | \(-0.178944\pi\) | |||||||
\(384\) | −2.80743e8 | + | 9.53074e8i | −0.0129117 | + | 0.0438331i | ||||
\(385\) | 3.85713e9 | 0.175558 | ||||||||
\(386\) | − | 2.85711e10i | − | 1.28700i | ||||||
\(387\) | −9.19886e9 | − | 5.93424e9i | −0.410100 | − | 0.264558i | ||||
\(388\) | 4.04369e9 | 0.178423 | ||||||||
\(389\) | 3.63015e10i | 1.58536i | 0.609641 | + | 0.792678i | \(0.291314\pi\) | ||||
−0.609641 | + | 0.792678i | \(0.708686\pi\) | |||||||
\(390\) | 2.46882e9 | + | 7.27231e8i | 0.106717 | + | 0.0314350i | ||||
\(391\) | −1.55860e10 | −0.666847 | ||||||||
\(392\) | − | 1.49508e10i | − | 0.633169i | ||||||
\(393\) | −6.37056e8 | + | 2.16270e9i | −0.0267059 | + | 0.0906620i | ||||
\(394\) | −9.76507e9 | −0.405220 | ||||||||
\(395\) | − | 2.12273e10i | − | 0.871979i | ||||||
\(396\) | 1.72470e9 | − | 2.67352e9i | 0.0701349 | − | 0.108718i | ||||
\(397\) | 1.69733e10 | 0.683290 | 0.341645 | − | 0.939829i | \(-0.389016\pi\) | ||||
0.341645 | + | 0.939829i | \(0.389016\pi\) | |||||||
\(398\) | 3.54048e10i | 1.41101i | ||||||||
\(399\) | 1.31149e10 | + | 3.86319e9i | 0.517455 | + | 0.152425i | ||||
\(400\) | −7.78546e9 | −0.304120 | ||||||||
\(401\) | − | 3.89763e10i | − | 1.50738i | −0.657230 | − | 0.753690i | \(-0.728272\pi\) | ||
0.657230 | − | 0.753690i | \(-0.271728\pi\) | |||||||
\(402\) | −6.48615e9 | + | 2.20194e10i | −0.248361 | + | 0.843142i | ||||
\(403\) | −2.76765e9 | −0.104928 | ||||||||
\(404\) | 1.82328e10i | 0.684427i | ||||||||
\(405\) | −1.13314e10 | + | 5.12759e9i | −0.421175 | + | 0.190587i | ||||
\(406\) | −3.75140e10 | −1.38067 | ||||||||
\(407\) | − | 1.30753e10i | − | 0.476513i | ||||||
\(408\) | 3.68737e10 | + | 1.08617e10i | 1.33069 | + | 0.391975i | ||||
\(409\) | 1.22202e10 | 0.436702 | 0.218351 | − | 0.975870i | \(-0.429932\pi\) | ||||
0.218351 | + | 0.975870i | \(0.429932\pi\) | |||||||
\(410\) | 9.18419e9i | 0.325017i | ||||||||
\(411\) | 1.05596e10 | − | 3.58480e10i | 0.370066 | − | 1.25631i | ||||
\(412\) | 1.69485e10 | 0.588224 | ||||||||
\(413\) | − | 5.41840e10i | − | 1.86239i | ||||||
\(414\) | −9.68167e9 | − | 6.24571e9i | −0.329571 | − | 0.212608i | ||||
\(415\) | 1.65222e10 | 0.557024 | ||||||||
\(416\) | 7.51208e9i | 0.250834i | ||||||||
\(417\) | 2.51338e10 | + | 7.40355e9i | 0.831216 | + | 0.244848i | ||||
\(418\) | 2.97871e9 | 0.0975715 | ||||||||
\(419\) | − | 1.98327e10i | − | 0.643467i | −0.946830 | − | 0.321734i | \(-0.895734\pi\) | ||
0.946830 | − | 0.321734i | \(-0.104266\pi\) | |||||||
\(420\) | 2.19676e9 | − | 7.45764e9i | 0.0705970 | − | 0.239665i | ||||
\(421\) | −8.40602e9 | −0.267585 | −0.133793 | − | 0.991009i | \(-0.542716\pi\) | ||||
−0.133793 | + | 0.991009i | \(0.542716\pi\) | |||||||
\(422\) | − | 3.83229e9i | − | 0.120839i | ||||||
\(423\) | −1.65420e10 | + | 2.56424e10i | −0.516687 | + | 0.800934i | ||||
\(424\) | −1.91893e10 | −0.593739 | ||||||||
\(425\) | − | 3.29564e10i | − | 1.01015i | ||||||
\(426\) | −1.93155e10 | − | 5.68969e9i | −0.586500 | − | 0.172763i | ||||
\(427\) | 5.93259e9 | 0.178457 | ||||||||
\(428\) | 8.09603e9i | 0.241267i | ||||||||
\(429\) | 9.19076e8 | − | 3.12011e9i | 0.0271345 | − | 0.0921171i | ||||
\(430\) | −5.82795e9 | −0.170468 | ||||||||
\(431\) | − | 3.38236e10i | − | 0.980192i | −0.871668 | − | 0.490096i | \(-0.836962\pi\) | ||
0.871668 | − | 0.490096i | \(-0.163038\pi\) | |||||||
\(432\) | 8.79515e9 | + | 1.02035e10i | 0.252527 | + | 0.292964i | ||||
\(433\) | 4.38280e10 | 1.24681 | 0.623405 | − | 0.781899i | \(-0.285749\pi\) | ||||
0.623405 | + | 0.781899i | \(0.285749\pi\) | |||||||
\(434\) | − | 1.11232e10i | − | 0.313523i | ||||||
\(435\) | −2.30360e10 | − | 6.78562e9i | −0.643355 | − | 0.189510i | ||||
\(436\) | 1.87063e10 | 0.517656 | ||||||||
\(437\) | 8.10752e9i | 0.222312i | ||||||||
\(438\) | 4.64394e9 | − | 1.57654e10i | 0.126180 | − | 0.428359i | ||||
\(439\) | −2.04097e10 | −0.549513 | −0.274757 | − | 0.961514i | \(-0.588597\pi\) | ||||
−0.274757 | + | 0.961514i | \(0.588597\pi\) | |||||||
\(440\) | − | 5.64120e9i | − | 0.150508i | ||||||
\(441\) | 1.86369e10 | + | 1.20228e10i | 0.492743 | + | 0.317872i | ||||
\(442\) | 1.17999e10 | 0.309164 | ||||||||
\(443\) | − | 2.67296e10i | − | 0.694030i | −0.937860 | − | 0.347015i | \(-0.887195\pi\) | ||
0.937860 | − | 0.347015i | \(-0.112805\pi\) | |||||||
\(444\) | −2.52807e10 | − | 7.44684e9i | −0.650516 | − | 0.191620i | ||||
\(445\) | −2.32463e10 | −0.592806 | ||||||||
\(446\) | 9.85107e8i | 0.0248968i | ||||||||
\(447\) | −1.12605e10 | + | 3.82273e10i | −0.282050 | + | 0.957511i | ||||
\(448\) | −4.98146e10 | −1.23664 | ||||||||
\(449\) | 6.99604e10i | 1.72134i | 0.509163 | + | 0.860670i | \(0.329955\pi\) | ||||
−0.509163 | + | 0.860670i | \(0.670045\pi\) | |||||||
\(450\) | 1.32065e10 | − | 2.04718e10i | 0.322061 | − | 0.499237i | ||||
\(451\) | 1.16070e10 | 0.280552 | ||||||||
\(452\) | 2.91109e10i | 0.697432i | ||||||||
\(453\) | −7.74921e10 | − | 2.28265e10i | −1.84020 | − | 0.542059i | ||||
\(454\) | 3.73001e10 | 0.877984 | ||||||||
\(455\) | − | 7.94818e9i | − | 0.185448i | ||||||
\(456\) | 5.65007e9 | − | 1.91810e10i | 0.130676 | − | 0.443621i | ||||
\(457\) | −7.59737e8 | −0.0174180 | −0.00870900 | − | 0.999962i | \(-0.502772\pi\) | ||||
−0.00870900 | + | 0.999962i | \(0.502772\pi\) | |||||||
\(458\) | 2.34779e10i | 0.533578i | ||||||||
\(459\) | −4.31921e10 | + | 3.72305e10i | −0.973091 | + | 0.838780i | ||||
\(460\) | 4.61025e9 | 0.102966 | ||||||||
\(461\) | 4.80756e10i | 1.06444i | 0.846607 | + | 0.532219i | \(0.178642\pi\) | ||||
−0.846607 | + | 0.532219i | \(0.821358\pi\) | |||||||
\(462\) | 1.25397e10 | + | 3.69377e9i | 0.275245 | + | 0.0810777i | ||||
\(463\) | 7.87575e10 | 1.71383 | 0.856916 | − | 0.515456i | \(-0.172378\pi\) | ||||
0.856916 | + | 0.515456i | \(0.172378\pi\) | |||||||
\(464\) | 2.60100e10i | 0.561136i | ||||||||
\(465\) | 2.01198e9 | − | 6.83034e9i | 0.0430341 | − | 0.146093i | ||||
\(466\) | 4.45668e10 | 0.945079 | ||||||||
\(467\) | 7.63344e10i | 1.60492i | 0.596708 | + | 0.802458i | \(0.296475\pi\) | ||||
−0.596708 | + | 0.802458i | \(0.703525\pi\) | |||||||
\(468\) | −5.50919e9 | − | 3.55401e9i | −0.114843 | − | 0.0740859i | ||||
\(469\) | 7.08897e10 | 1.46518 | ||||||||
\(470\) | 1.62457e10i | 0.332926i | ||||||||
\(471\) | 3.97693e10 | + | 1.17147e10i | 0.808099 | + | 0.238038i | ||||
\(472\) | −7.92462e10 | −1.59665 | ||||||||
\(473\) | 7.36538e9i | 0.147147i | ||||||||
\(474\) | 2.03283e10 | − | 6.90110e10i | 0.402705 | − | 1.36711i | ||||
\(475\) | −1.71433e10 | −0.336760 | ||||||||
\(476\) | − | 3.56442e10i | − | 0.694322i | ||||||
\(477\) | 1.54312e10 | − | 2.39205e10i | 0.298076 | − | 0.462058i | ||||
\(478\) | −2.14611e10 | −0.411093 | ||||||||
\(479\) | 8.37315e10i | 1.59055i | 0.606250 | + | 0.795274i | \(0.292673\pi\) | ||||
−0.606250 | + | 0.795274i | \(0.707327\pi\) | |||||||
\(480\) | −1.85392e10 | − | 5.46102e9i | −0.349242 | − | 0.102875i | ||||
\(481\) | −2.69437e10 | −0.503357 | ||||||||
\(482\) | 2.62532e9i | 0.0486400i | ||||||||
\(483\) | −1.00538e10 | + | 3.41309e10i | −0.184731 | + | 0.627132i | ||||
\(484\) | −2.14064e9 | −0.0390088 | ||||||||
\(485\) | 1.06360e10i | 0.192225i | ||||||||
\(486\) | −4.17493e10 | + | 5.81859e9i | −0.748348 | + | 0.104297i | ||||
\(487\) | 9.25576e9 | 0.164549 | 0.0822747 | − | 0.996610i | \(-0.473782\pi\) | ||||
0.0822747 | + | 0.996610i | \(0.473782\pi\) | |||||||
\(488\) | − | 8.67664e9i | − | 0.152993i | ||||||
\(489\) | 1.71447e10 | + | 5.05024e9i | 0.299843 | + | 0.0883235i | ||||
\(490\) | 1.18075e10 | 0.204820 | ||||||||
\(491\) | 4.12896e9i | 0.0710420i | 0.999369 | + | 0.0355210i | \(0.0113091\pi\) | ||||
−0.999369 | + | 0.0355210i | \(0.988691\pi\) | |||||||
\(492\) | 6.61058e9 | − | 2.24418e10i | 0.112818 | − | 0.382999i | ||||
\(493\) | −1.10102e11 | −1.86384 | ||||||||
\(494\) | − | 6.13808e9i | − | 0.103068i | ||||||
\(495\) | 7.03205e9 | + | 4.53642e9i | 0.117128 | + | 0.0755601i | ||||
\(496\) | −7.71214e9 | −0.127423 | ||||||||
\(497\) | 6.21848e10i | 1.01920i | ||||||||
\(498\) | 5.37143e10 | + | 1.58224e10i | 0.873319 | + | 0.257250i | ||||
\(499\) | 5.86503e10 | 0.945950 | 0.472975 | − | 0.881076i | \(-0.343180\pi\) | ||||
0.472975 | + | 0.881076i | \(0.343180\pi\) | |||||||
\(500\) | 2.21463e10i | 0.354341i | ||||||||
\(501\) | 1.08948e10 | − | 3.69861e10i | 0.172930 | − | 0.587067i | ||||
\(502\) | 9.21375e10 | 1.45085 | ||||||||
\(503\) | − | 1.14732e10i | − | 0.179230i | −0.995976 | − | 0.0896152i | \(-0.971436\pi\) | ||
0.995976 | − | 0.0896152i | \(-0.0285637\pi\) | |||||||
\(504\) | 4.75711e10 | − | 7.37415e10i | 0.737260 | − | 1.14285i | ||||
\(505\) | −4.79569e10 | −0.737370 | ||||||||
\(506\) | 7.75195e9i | 0.118252i | ||||||||
\(507\) | 5.69522e10 | + | 1.67761e10i | 0.861943 | + | 0.253899i | ||||
\(508\) | −1.22107e10 | −0.183353 | ||||||||
\(509\) | − | 5.97986e10i | − | 0.890881i | −0.895312 | − | 0.445440i | \(-0.853047\pi\) | ||
0.895312 | − | 0.445440i | \(-0.146953\pi\) | |||||||
\(510\) | −8.57811e9 | + | 2.91212e10i | −0.126798 | + | 0.430456i | ||||
\(511\) | −5.07554e10 | −0.744387 | ||||||||
\(512\) | 4.96329e10i | 0.722253i | ||||||||
\(513\) | 1.93666e10 | + | 2.24677e10i | 0.279630 | + | 0.324406i | ||||
\(514\) | 2.07200e10 | 0.296850 | ||||||||
\(515\) | 4.45790e10i | 0.633725i | ||||||||
\(516\) | 1.42407e10 | + | 4.19483e9i | 0.200879 | + | 0.0591719i | ||||
\(517\) | 2.05314e10 | 0.287380 | ||||||||
\(518\) | − | 1.08287e11i | − | 1.50403i | ||||||
\(519\) | 2.64605e9 | − | 8.98288e9i | 0.0364694 | − | 0.123807i | ||||
\(520\) | −1.16245e10 | −0.158987 | ||||||||
\(521\) | − | 1.25170e11i | − | 1.69882i | −0.527730 | − | 0.849412i | \(-0.676957\pi\) | ||
0.527730 | − | 0.849412i | \(-0.323043\pi\) | |||||||
\(522\) | −6.83931e10 | − | 4.41208e10i | −0.921149 | − | 0.594239i | ||||
\(523\) | −4.60203e10 | −0.615095 | −0.307548 | − | 0.951533i | \(-0.599508\pi\) | ||||
−0.307548 | + | 0.951533i | \(0.599508\pi\) | |||||||
\(524\) | − | 3.05756e9i | − | 0.0405554i | ||||||
\(525\) | −7.21695e10 | − | 2.12587e10i | −0.949984 | − | 0.279833i | ||||
\(526\) | −1.71669e10 | −0.224258 | ||||||||
\(527\) | − | 3.26460e10i | − | 0.423241i | ||||||
\(528\) | 2.56103e9 | − | 8.69427e9i | 0.0329518 | − | 0.111866i | ||||
\(529\) | 5.72115e10 | 0.730569 | ||||||||
\(530\) | − | 1.51548e10i | − | 0.192065i | ||||||
\(531\) | 6.37266e10 | − | 9.87846e10i | 0.801572 | − | 1.24254i | ||||
\(532\) | −1.85414e10 | −0.231471 | ||||||||
\(533\) | − | 2.39180e10i | − | 0.296357i | ||||||
\(534\) | −7.55747e10 | − | 2.22617e10i | −0.929419 | − | 0.273775i | ||||
\(535\) | −2.12947e10 | −0.259930 | ||||||||
\(536\) | − | 1.03679e11i | − | 1.25612i | ||||||
\(537\) | −2.77833e10 | + | 9.43195e10i | −0.334108 | + | 1.13424i | ||||
\(538\) | 2.87120e10 | 0.342716 | ||||||||
\(539\) | − | 1.49223e10i | − | 0.176799i | ||||||
\(540\) | 1.27760e10 | − | 1.10126e10i | 0.150252 | − | 0.129514i | ||||
\(541\) | 7.62294e10 | 0.889884 | 0.444942 | − | 0.895559i | \(-0.353224\pi\) | ||||
0.444942 | + | 0.895559i | \(0.353224\pi\) | |||||||
\(542\) | 1.08667e11i | 1.25922i | ||||||||
\(543\) | −6.96473e9 | − | 2.05157e9i | −0.0801134 | − | 0.0235986i | ||||
\(544\) | −8.86093e10 | −1.01177 | ||||||||
\(545\) | 4.92023e10i | 0.557699i | ||||||||
\(546\) | 7.61156e9 | − | 2.58399e10i | 0.0856452 | − | 0.290751i | ||||
\(547\) | 5.83750e10 | 0.652045 | 0.326022 | − | 0.945362i | \(-0.394292\pi\) | ||||
0.326022 | + | 0.945362i | \(0.394292\pi\) | |||||||
\(548\) | 5.06808e10i | 0.561981i | ||||||||
\(549\) | 1.08159e10 | + | 6.97740e9i | 0.119062 | + | 0.0768076i | ||||
\(550\) | −1.63915e10 | −0.179129 | ||||||||
\(551\) | 5.72730e10i | 0.621360i | ||||||||
\(552\) | 4.99177e10 | + | 1.47040e10i | 0.537648 | + | 0.158373i | ||||
\(553\) | −2.22175e11 | −2.37572 | ||||||||
\(554\) | 6.55422e10i | 0.695796i | ||||||||
\(555\) | 1.95871e10 | − | 6.64949e10i | 0.206442 | − | 0.700836i | ||||
\(556\) | −3.55334e10 | −0.371824 | ||||||||
\(557\) | − | 9.65542e9i | − | 0.100311i | −0.998741 | − | 0.0501557i | \(-0.984028\pi\) | ||
0.998741 | − | 0.0501557i | \(-0.0159718\pi\) | |||||||
\(558\) | 1.30821e10 | − | 2.02790e10i | 0.134940 | − | 0.209175i | ||||
\(559\) | 1.51775e10 | 0.155436 | ||||||||
\(560\) | − | 2.21479e10i | − | 0.225206i | ||||||
\(561\) | 3.68035e10 | + | 1.08410e10i | 0.371567 | + | 0.109451i | ||||
\(562\) | 3.77361e10 | 0.378278 | ||||||||
\(563\) | 4.32026e10i | 0.430007i | 0.976613 | + | 0.215004i | \(0.0689764\pi\) | ||||
−0.976613 | + | 0.215004i | \(0.931024\pi\) | |||||||
\(564\) | 1.16933e10 | − | 3.96969e10i | 0.115564 | − | 0.392319i | ||||
\(565\) | −7.65692e10 | −0.751381 | ||||||||
\(566\) | − | 7.35617e10i | − | 0.716780i | ||||||
\(567\) | 5.36679e10 | + | 1.18600e11i | 0.519257 | + | 1.14750i | ||||
\(568\) | 9.09477e10 | 0.873773 | ||||||||
\(569\) | 2.03534e10i | 0.194173i | 0.995276 | + | 0.0970865i | \(0.0309523\pi\) | ||||
−0.995276 | + | 0.0970865i | \(0.969048\pi\) | |||||||
\(570\) | 1.51483e10 | + | 4.46217e9i | 0.143504 | + | 0.0422714i | ||||
\(571\) | −1.64922e11 | −1.55144 | −0.775718 | − | 0.631079i | \(-0.782612\pi\) | ||||
−0.775718 | + | 0.631079i | \(0.782612\pi\) | |||||||
\(572\) | 4.41112e9i | 0.0412064i | ||||||||
\(573\) | 1.19468e8 | − | 4.05575e8i | 0.00110824 | − | 0.00376229i | ||||
\(574\) | 9.61263e10 | 0.885513 | ||||||||
\(575\) | − | 4.46146e10i | − | 0.408137i | ||||||
\(576\) | −9.08186e10 | − | 5.85877e10i | −0.825059 | − | 0.532251i | ||||
\(577\) | 1.34081e11 | 1.20966 | 0.604830 | − | 0.796355i | \(-0.293241\pi\) | ||||
0.604830 | + | 0.796355i | \(0.293241\pi\) | |||||||
\(578\) | 5.48545e10i | 0.491474i | ||||||||
\(579\) | −1.83629e11 | − | 5.40908e10i | −1.63391 | − | 0.481293i | ||||
\(580\) | 3.25677e10 | 0.287789 | ||||||||
\(581\) | − | 1.72929e11i | − | 1.51762i | ||||||
\(582\) | −1.01855e10 | + | 3.45780e10i | −0.0887750 | + | 0.301376i | ||||
\(583\) | −1.91527e10 | −0.165789 | ||||||||
\(584\) | 7.42318e10i | 0.638173i | ||||||||
\(585\) | 9.34797e9 | − | 1.44906e10i | 0.0798167 | − | 0.123726i | ||||
\(586\) | −4.98758e10 | −0.422960 | ||||||||
\(587\) | 4.99106e10i | 0.420378i | 0.977661 | + | 0.210189i | \(0.0674080\pi\) | ||||
−0.977661 | + | 0.210189i | \(0.932592\pi\) | |||||||
\(588\) | −2.88518e10 | − | 8.49875e9i | −0.241359 | − | 0.0710961i | ||||
\(589\) | −1.69818e10 | −0.141099 | ||||||||
\(590\) | − | 6.25851e10i | − | 0.516491i | ||||||
\(591\) | −1.84873e10 | + | 6.27611e10i | −0.151538 | + | 0.514447i | ||||
\(592\) | −7.50793e10 | −0.611271 | ||||||||
\(593\) | − | 1.06852e10i | − | 0.0864098i | −0.999066 | − | 0.0432049i | \(-0.986243\pi\) | ||
0.999066 | − | 0.0432049i | \(-0.0137568\pi\) | |||||||
\(594\) | 1.85172e10 | + | 2.14823e10i | 0.148741 | + | 0.172558i | ||||
\(595\) | 9.37535e10 | 0.748031 | ||||||||
\(596\) | − | 5.40447e10i | − | 0.428320i | ||||||
\(597\) | 2.27550e11 | + | 6.70285e10i | 1.79135 | + | 0.527670i | ||||
\(598\) | 1.59741e10 | 0.124914 | ||||||||
\(599\) | − | 1.03233e11i | − | 0.801884i | −0.916103 | − | 0.400942i | \(-0.868683\pi\) | ||
0.916103 | − | 0.400942i | \(-0.131317\pi\) | |||||||
\(600\) | −3.10916e10 | + | 1.05551e11i | −0.239904 | + | 0.814435i | ||||
\(601\) | 2.03937e11 | 1.56314 | 0.781571 | − | 0.623817i | \(-0.214419\pi\) | ||||
0.781571 | + | 0.623817i | \(0.214419\pi\) | |||||||
\(602\) | 6.09982e10i | 0.464442i | ||||||||
\(603\) | 1.29241e11 | + | 8.33744e10i | 0.977534 | + | 0.630613i | ||||
\(604\) | 1.09556e11 | 0.823168 | ||||||||
\(605\) | − | 5.63045e9i | − | 0.0420263i | ||||||
\(606\) | −1.55910e11 | − | 4.59258e10i | −1.15607 | − | 0.340539i | ||||
\(607\) | 1.07455e11 | 0.791536 | 0.395768 | − | 0.918351i | \(-0.370478\pi\) | ||||
0.395768 | + | 0.918351i | \(0.370478\pi\) | |||||||
\(608\) | 4.60929e10i | 0.337303i | ||||||||
\(609\) | −7.10217e10 | + | 2.41107e11i | −0.516324 | + | 1.75283i | ||||
\(610\) | 6.85242e9 | 0.0494908 | ||||||||
\(611\) | − | 4.23081e10i | − | 0.303570i | ||||||
\(612\) | 4.19216e10 | − | 6.49841e10i | 0.298836 | − | 0.463235i | ||||
\(613\) | −8.14120e10 | −0.576563 | −0.288281 | − | 0.957546i | \(-0.593084\pi\) | ||||
−0.288281 | + | 0.957546i | \(0.593084\pi\) | |||||||
\(614\) | 1.74903e10i | 0.123062i | ||||||||
\(615\) | 5.90278e10 | + | 1.73875e10i | 0.412625 | + | 0.121545i | ||||
\(616\) | −5.90436e10 | −0.410062 | ||||||||
\(617\) | − | 2.64218e10i | − | 0.182315i | −0.995836 | − | 0.0911574i | \(-0.970943\pi\) | ||
0.995836 | − | 0.0911574i | \(-0.0290566\pi\) | |||||||
\(618\) | −4.26909e10 | + | 1.44928e11i | −0.292672 | + | 0.993573i | ||||
\(619\) | −1.19674e11 | −0.815152 | −0.407576 | − | 0.913171i | \(-0.633626\pi\) | ||||
−0.407576 | + | 0.913171i | \(0.633626\pi\) | |||||||
\(620\) | 9.65654e9i | 0.0653514i | ||||||||
\(621\) | −5.84712e10 | + | 5.04007e10i | −0.393165 | + | 0.338899i | ||||
\(622\) | −7.51034e10 | −0.501762 | ||||||||
\(623\) | 2.43307e11i | 1.61511i | ||||||||
\(624\) | −1.79159e10 | − | 5.27740e9i | −0.118168 | − | 0.0348082i | ||||
\(625\) | 6.17276e10 | 0.404538 | ||||||||
\(626\) | − | 1.42305e11i | − | 0.926667i | ||||||
\(627\) | 5.63930e9 | − | 1.91445e10i | 0.0364884 | − | 0.123872i | ||||
\(628\) | −5.62247e10 | −0.361484 | ||||||||
\(629\) | − | 3.17816e11i | − | 2.03036i | ||||||
\(630\) | 5.82377e10 | + | 3.75695e10i | 0.369694 | + | 0.238492i | ||||
\(631\) | 2.68955e11 | 1.69653 | 0.848265 | − | 0.529572i | \(-0.177648\pi\) | ||||
0.848265 | + | 0.529572i | \(0.177648\pi\) | |||||||
\(632\) | 3.24940e11i | 2.03674i | ||||||||
\(633\) | −2.46305e10 | − | 7.25530e9i | −0.153412 | − | 0.0451898i | ||||
\(634\) | 1.08186e11 | 0.669595 | ||||||||
\(635\) | − | 3.21174e10i | − | 0.197536i | ||||||
\(636\) | −1.09081e10 | + | 3.70312e10i | −0.0666687 | + | 0.226329i | ||||
\(637\) | −3.07496e10 | −0.186759 | ||||||||
\(638\) | 5.47612e10i | 0.330514i | ||||||||
\(639\) | −7.31364e10 | + | 1.13371e11i | −0.438662 | + | 0.679985i | ||||
\(640\) | 3.54409e9 | 0.0211244 | ||||||||
\(641\) | − | 7.90714e10i | − | 0.468368i | −0.972192 | − | 0.234184i | \(-0.924758\pi\) | ||
0.972192 | − | 0.234184i | \(-0.0752418\pi\) | |||||||
\(642\) | −6.92300e10 | − | 2.03928e10i | −0.407525 | − | 0.120043i | ||||
\(643\) | 9.87009e10 | 0.577401 | 0.288700 | − | 0.957420i | \(-0.406777\pi\) | ||||
0.288700 | + | 0.957420i | \(0.406777\pi\) | |||||||
\(644\) | − | 4.82532e10i | − | 0.280532i | ||||||
\(645\) | −1.10335e10 | + | 3.74568e10i | −0.0637491 | + | 0.216417i | ||||
\(646\) | 7.24022e10 | 0.415740 | ||||||||
\(647\) | − | 1.09583e11i | − | 0.625353i | −0.949860 | − | 0.312677i | \(-0.898774\pi\) | ||
0.949860 | − | 0.312677i | \(-0.101226\pi\) | |||||||
\(648\) | 1.73457e11 | − | 7.84914e10i | 0.983765 | − | 0.445166i | ||||
\(649\) | −7.90952e10 | −0.445832 | ||||||||
\(650\) | 3.37770e10i | 0.189221i | ||||||||
\(651\) | −7.14898e10 | − | 2.10584e10i | −0.398034 | − | 0.117247i | ||||
\(652\) | −2.42387e10 | −0.134128 | ||||||||
\(653\) | − | 2.25362e11i | − | 1.23944i | −0.784821 | − | 0.619722i | \(-0.787245\pi\) | ||
0.784821 | − | 0.619722i | \(-0.212755\pi\) | |||||||
\(654\) | −4.71185e10 | + | 1.59959e11i | −0.257561 | + | 0.874376i | ||||
\(655\) | 8.04216e9 | 0.0436926 | ||||||||
\(656\) | − | 6.66482e10i | − | 0.359893i | ||||||
\(657\) | −9.25338e10 | − | 5.96942e10i | −0.496637 | − | 0.320384i | ||||
\(658\) | 1.70036e11 | 0.907063 | ||||||||
\(659\) | 3.65202e11i | 1.93639i | 0.250206 | + | 0.968193i | \(0.419502\pi\) | ||||
−0.250206 | + | 0.968193i | \(0.580498\pi\) | |||||||
\(660\) | −1.08863e10 | − | 3.20673e9i | −0.0573726 | − | 0.0169000i | ||||
\(661\) | −2.13153e11 | −1.11657 | −0.558285 | − | 0.829649i | \(-0.688540\pi\) | ||||
−0.558285 | + | 0.829649i | \(0.688540\pi\) | |||||||
\(662\) | 1.75909e10i | 0.0915916i | ||||||||
\(663\) | 2.23396e10 | − | 7.58391e10i | 0.115617 | − | 0.392499i | ||||
\(664\) | −2.52915e11 | −1.30108 | ||||||||
\(665\) | − | 4.87688e10i | − | 0.249376i | ||||||
\(666\) | 1.27357e11 | − | 1.97421e11i | 0.647332 | − | 1.00345i | ||||
\(667\) | −1.49050e11 | −0.753060 | ||||||||
\(668\) | 5.22899e10i | 0.262610i | ||||||||
\(669\) | 6.33139e9 | + | 1.86501e9i | 0.0316078 | + | 0.00931057i | ||||
\(670\) | 8.18809e10 | 0.406334 | ||||||||
\(671\) | − | 8.66011e9i | − | 0.0427202i | ||||||
\(672\) | −5.71578e10 | + | 1.94041e11i | −0.280284 | + | 0.951516i | ||||
\(673\) | −3.78188e11 | −1.84352 | −0.921759 | − | 0.387763i | \(-0.873248\pi\) | ||||
−0.921759 | + | 0.387763i | \(0.873248\pi\) | |||||||
\(674\) | − | 2.21210e11i | − | 1.07193i | ||||||
\(675\) | −1.06572e11 | − | 1.23637e11i | −0.513367 | − | 0.595570i | ||||
\(676\) | −8.05173e10 | −0.385569 | ||||||||
\(677\) | − | 2.71560e11i | − | 1.29274i | −0.763024 | − | 0.646371i | \(-0.776286\pi\) | ||
0.763024 | − | 0.646371i | \(-0.223714\pi\) | |||||||
\(678\) | −2.48930e11 | − | 7.33263e10i | −1.17804 | − | 0.347009i | ||||
\(679\) | 1.11321e11 | 0.523720 | ||||||||
\(680\) | − | 1.37118e11i | − | 0.641297i | ||||||
\(681\) | 7.06167e10 | − | 2.39732e11i | 0.328336 | − | 1.11465i | ||||
\(682\) | −1.62371e10 | −0.0750534 | ||||||||
\(683\) | − | 2.43241e11i | − | 1.11778i | −0.829243 | − | 0.558888i | \(-0.811228\pi\) | ||
0.829243 | − | 0.558888i | \(-0.188772\pi\) | |||||||
\(684\) | −3.38035e10 | − | 2.18068e10i | −0.154432 | − | 0.0996250i | ||||
\(685\) | −1.33304e11 | −0.605453 | ||||||||
\(686\) | 8.71737e10i | 0.393631i | ||||||||
\(687\) | 1.50895e11 | + | 4.44485e10i | 0.677405 | + | 0.199540i | ||||
\(688\) | 4.22925e10 | 0.188760 | ||||||||
\(689\) | 3.94671e10i | 0.175129i | ||||||||
\(690\) | −1.16126e10 | + | 3.94228e10i | −0.0512310 | + | 0.173920i | ||||
\(691\) | −1.99275e11 | −0.874061 | −0.437030 | − | 0.899447i | \(-0.643970\pi\) | ||||
−0.437030 | + | 0.899447i | \(0.643970\pi\) | |||||||
\(692\) | 1.26997e10i | 0.0553822i | ||||||||
\(693\) | 4.74804e10 | − | 7.36009e10i | 0.205865 | − | 0.319117i | ||||
\(694\) | −1.42539e11 | −0.614464 | ||||||||
\(695\) | − | 9.34621e10i | − | 0.400587i | ||||||
\(696\) | 3.52628e11 | + | 1.03872e11i | 1.50273 | + | 0.442651i | ||||
\(697\) | 2.82126e11 | 1.19540 | ||||||||
\(698\) | − | 2.34228e11i | − | 0.986771i | ||||||
\(699\) | 8.43741e10 | − | 2.86436e11i | 0.353427 | − | 1.19983i | ||||
\(700\) | 1.02031e11 | 0.424953 | ||||||||
\(701\) | 5.28783e10i | 0.218980i | 0.993988 | + | 0.109490i | \(0.0349218\pi\) | ||||
−0.993988 | + | 0.109490i | \(0.965078\pi\) | |||||||
\(702\) | 4.42676e10 | − | 3.81576e10i | 0.182279 | − | 0.157120i | ||||
\(703\) | −1.65322e11 | −0.676876 | ||||||||
\(704\) | 7.27169e10i | 0.296036i | ||||||||
\(705\) | 1.04413e11 | + | 3.07565e10i | 0.422667 | + | 0.124503i | ||||
\(706\) | 3.09255e11 | 1.24480 | ||||||||
\(707\) | 5.01941e11i | 2.00898i | ||||||||
\(708\) | −4.50474e10 | + | 1.52928e11i | −0.179282 | + | 0.608632i | ||||
\(709\) | 4.08782e11 | 1.61773 | 0.808866 | − | 0.587993i | \(-0.200082\pi\) | ||||
0.808866 | + | 0.587993i | \(0.200082\pi\) | |||||||
\(710\) | 7.18264e10i | 0.282651i | ||||||||
\(711\) | −4.05055e11 | − | 2.61304e11i | −1.58502 | − | 1.02251i | ||||
\(712\) | 3.55846e11 | 1.38466 | ||||||||
\(713\) | − | 4.41944e10i | − | 0.171005i | ||||||
\(714\) | 3.04797e11 | + | 8.97828e10i | 1.17278 | + | 0.345462i | ||||
\(715\) | −1.16024e10 | −0.0443939 | ||||||||
\(716\) | − | 1.33346e11i | − | 0.507374i | ||||||
\(717\) | −4.06302e10 | + | 1.37933e11i | −0.153735 | + | 0.521904i | ||||
\(718\) | −3.22058e11 | −1.21182 | ||||||||
\(719\) | 3.15768e11i | 1.18155i | 0.806835 | + | 0.590776i | \(0.201178\pi\) | ||||
−0.806835 | + | 0.590776i | \(0.798822\pi\) | |||||||
\(720\) | 2.60484e10 | − | 4.03785e10i | 0.0969285 | − | 0.150252i | ||||
\(721\) | 4.66586e11 | 1.72659 | ||||||||
\(722\) | 1.67657e11i | 0.616983i | ||||||||
\(723\) | 1.68732e10 | + | 4.97026e9i | 0.0617510 | + | 0.0181897i | ||||
\(724\) | 9.84653e9 | 0.0358368 | ||||||||
\(725\) | − | 3.15166e11i | − | 1.14074i | ||||||
\(726\) | 5.39198e9 | − | 1.83049e10i | 0.0194089 | − | 0.0658901i | ||||
\(727\) | −4.33193e11 | −1.55076 | −0.775378 | − | 0.631497i | \(-0.782441\pi\) | ||||
−0.775378 | + | 0.631497i | \(0.782441\pi\) | |||||||
\(728\) | 1.21668e11i | 0.433163i | ||||||||
\(729\) | −4.16432e10 | + | 2.79343e11i | −0.147446 | + | 0.989070i | ||||
\(730\) | −5.86249e10 | −0.206439 | ||||||||
\(731\) | 1.79027e11i | 0.626973i | ||||||||
\(732\) | −1.67441e10 | − | 4.93222e9i | −0.0583198 | − | 0.0171790i | ||||
\(733\) | −3.83767e11 | −1.32939 | −0.664695 | − | 0.747115i | \(-0.731438\pi\) | ||||
−0.664695 | + | 0.747115i | \(0.731438\pi\) | |||||||
\(734\) | 1.11474e11i | 0.384053i | ||||||||
\(735\) | 2.23539e10 | − | 7.58877e10i | 0.0765957 | − | 0.260029i | ||||
\(736\) | −1.19955e11 | −0.408795 | ||||||||
\(737\) | − | 1.03481e11i | − | 0.350745i | ||||||
\(738\) | 1.75251e11 | + | 1.13056e11i | 0.590793 | + | 0.381124i | ||||
\(739\) | 1.24082e11 | 0.416036 | 0.208018 | − | 0.978125i | \(-0.433299\pi\) | ||||
0.208018 | + | 0.978125i | \(0.433299\pi\) | |||||||
\(740\) | 9.40086e10i | 0.313502i | ||||||||
\(741\) | −3.94500e10 | − | 1.16206e10i | −0.130850 | − | 0.0385440i | ||||
\(742\) | −1.58618e11 | −0.523284 | ||||||||
\(743\) | 1.57217e10i | 0.0515875i | 0.999667 | + | 0.0257937i | \(0.00821131\pi\) | ||||
−0.999667 | + | 0.0257937i | \(0.991789\pi\) | |||||||
\(744\) | −3.07988e10 | + | 1.04557e11i | −0.100518 | + | 0.341240i | ||||
\(745\) | 1.42152e11 | 0.461452 | ||||||||
\(746\) | 5.26924e10i | 0.170135i | ||||||||
\(747\) | 2.03384e11 | − | 3.15273e11i | 0.653183 | − | 1.01252i | ||||
\(748\) | −5.20317e10 | −0.166212 | ||||||||
\(749\) | 2.22881e11i | 0.708182i | ||||||||
\(750\) | −1.89375e11 | − | 5.57834e10i | −0.598519 | − | 0.176303i | ||||
\(751\) | −2.53140e11 | −0.795793 | −0.397897 | − | 0.917430i | \(-0.630260\pi\) | ||||
−0.397897 | + | 0.917430i | \(0.630260\pi\) | |||||||
\(752\) | − | 1.17893e11i | − | 0.368651i | ||||||
\(753\) | 1.74435e11 | − | 5.92177e11i | 0.542568 | − | 1.84192i | ||||
\(754\) | 1.12844e11 | 0.349134 | ||||||||
\(755\) | 2.88161e11i | 0.886843i | ||||||||
\(756\) | −1.15263e11 | − | 1.33720e11i | −0.352862 | − | 0.409364i | ||||
\(757\) | −5.52233e11 | −1.68166 | −0.840831 | − | 0.541298i | \(-0.817933\pi\) | ||||
−0.840831 | + | 0.541298i | \(0.817933\pi\) | |||||||
\(758\) | 2.95931e11i | 0.896425i | ||||||||
\(759\) | 4.98226e10 | + | 1.46760e10i | 0.150127 | + | 0.0442223i | ||||
\(760\) | −7.13262e10 | −0.213794 | ||||||||
\(761\) | 3.94928e11i | 1.17755i | 0.808297 | + | 0.588776i | \(0.200390\pi\) | ||||
−0.808297 | + | 0.588776i | \(0.799610\pi\) | |||||||
\(762\) | 3.07572e10 | − | 1.04415e11i | 0.0912277 | − | 0.309702i | ||||
\(763\) | 5.14976e11 | 1.51946 | ||||||||
\(764\) | 5.73390e8i | 0.00168297i | ||||||||
\(765\) | 1.70925e11 | + | 1.10265e11i | 0.499068 | + | 0.321952i | ||||
\(766\) | −2.77314e11 | −0.805482 | ||||||||
\(767\) | 1.62988e11i | 0.470948i | ||||||||
\(768\) | 3.39178e11 | + | 9.99101e10i | 0.974950 | + | 0.287187i | ||||
\(769\) | −6.77887e10 | −0.193844 | −0.0969219 | − | 0.995292i | \(-0.530900\pi\) | ||||
−0.0969219 | + | 0.995292i | \(0.530900\pi\) | |||||||
\(770\) | − | 4.66299e10i | − | 0.132648i | ||||||
\(771\) | 3.92271e10 | − | 1.33169e11i | 0.111012 | − | 0.376866i | ||||
\(772\) | 2.59610e11 | 0.730889 | ||||||||
\(773\) | 1.08276e11i | 0.303258i | 0.988437 | + | 0.151629i | \(0.0484519\pi\) | ||||
−0.988437 | + | 0.151629i | \(0.951548\pi\) | |||||||
\(774\) | −7.17409e10 | + | 1.11208e11i | −0.199895 | + | 0.309864i | ||||
\(775\) | 9.34489e10 | 0.259040 | ||||||||
\(776\) | − | 1.62812e11i | − | 0.448992i | ||||||
\(777\) | −6.95969e11 | − | 2.05008e11i | −1.90944 | − | 0.562455i | ||||
\(778\) | 4.38860e11 | 1.19786 | ||||||||
\(779\) | − | 1.46757e11i | − | 0.398519i | ||||||
\(780\) | −6.60795e9 | + | 2.24328e10i | −0.0178520 | + | 0.0606047i | ||||
\(781\) | 9.07744e10 | 0.243983 | ||||||||
\(782\) | 1.88423e11i | 0.503857i | ||||||||
\(783\) | −4.13051e11 | + | 3.56040e11i | −1.09890 | + | 0.947221i | ||||
\(784\) | −8.56848e10 | −0.226798 | ||||||||
\(785\) | − | 1.47886e11i | − | 0.389446i | ||||||
\(786\) | 2.61455e10 | + | 7.70156e9i | 0.0685025 | + | 0.0201785i | ||||
\(787\) | 4.20493e11 | 1.09612 | 0.548062 | − | 0.836438i | \(-0.315366\pi\) | ||||
0.548062 | + | 0.836438i | \(0.315366\pi\) | |||||||
\(788\) | − | 8.87299e10i | − | 0.230126i | ||||||
\(789\) | −3.25004e10 | + | 1.10333e11i | −0.0838649 | + | 0.284707i | ||||
\(790\) | −2.56623e11 | −0.658851 | ||||||||
\(791\) | 8.01411e11i | 2.04715i | ||||||||
\(792\) | −1.07644e11 | − | 6.94420e10i | −0.273584 | − | 0.176491i | ||||
\(793\) | −1.78454e10 | −0.0451268 | ||||||||
\(794\) | − | 2.05196e11i | − | 0.516281i | ||||||
\(795\) | −9.74017e10 | − | 2.86912e10i | −0.243836 | − | 0.0718257i | ||||
\(796\) | −3.21704e11 | −0.801317 | ||||||||
\(797\) | 5.60638e11i | 1.38947i | 0.719265 | + | 0.694736i | \(0.244479\pi\) | ||||
−0.719265 | + | 0.694736i | \(0.755521\pi\) | |||||||
\(798\) | 4.67033e10 | − | 1.58550e11i | 0.115169 | − | 0.390979i | ||||
\(799\) | 4.99048e11 | 1.22449 | ||||||||
\(800\) | − | 2.53643e11i | − | 0.619246i | ||||||
\(801\) | −2.86157e11 | + | 4.43581e11i | −0.695142 | + | 1.07756i | ||||
\(802\) | −4.71196e11 | −1.13895 | ||||||||
\(803\) | 7.40903e10i | 0.178197i | ||||||||
\(804\) | −2.00078e11 | − | 5.89361e10i | −0.478823 | − | 0.141045i | ||||
\(805\) | 1.26918e11 | 0.302233 | ||||||||
\(806\) | 3.34589e10i | 0.0792815i | ||||||||
\(807\) | 5.43577e10 | − | 1.84535e11i | 0.128164 | − | 0.435096i | ||||
\(808\) | 7.34108e11 | 1.72232 | ||||||||
\(809\) | − | 5.67646e11i | − | 1.32521i | −0.748970 | − | 0.662603i | \(-0.769452\pi\) | ||
0.748970 | − | 0.662603i | \(-0.230548\pi\) | |||||||
\(810\) | 6.19890e10 | + | 1.36988e11i | 0.144004 | + | 0.318232i | ||||
\(811\) | 3.88871e11 | 0.898923 | 0.449462 | − | 0.893300i | \(-0.351616\pi\) | ||||
0.449462 | + | 0.893300i | \(0.351616\pi\) | |||||||
\(812\) | − | 3.40869e11i | − | 0.784087i | ||||||
\(813\) | 6.98417e11 | + | 2.05730e11i | 1.59865 | + | 0.470907i | ||||
\(814\) | −1.58071e11 | −0.360044 | ||||||||
\(815\) | − | 6.37540e10i | − | 0.144503i | ||||||
\(816\) | 6.22500e10 | − | 2.11328e11i | 0.140404 | − | 0.476646i | ||||
\(817\) | 9.31265e10 | 0.209019 | ||||||||
\(818\) | − | 1.47734e11i | − | 0.329964i | ||||||
\(819\) | −1.51666e11 | − | 9.78405e10i | −0.337095 | − | 0.217462i | ||||
\(820\) | −8.34517e10 | −0.184578 | ||||||||
\(821\) | 4.86132e11i | 1.06999i | 0.844854 | + | 0.534997i | \(0.179687\pi\) | ||||
−0.844854 | + | 0.534997i | \(0.820313\pi\) | |||||||
\(822\) | −4.33377e11 | − | 1.27658e11i | −0.949246 | − | 0.279615i | ||||
\(823\) | 3.59285e11 | 0.783140 | 0.391570 | − | 0.920148i | \(-0.371932\pi\) | ||||
0.391570 | + | 0.920148i | \(0.371932\pi\) | |||||||
\(824\) | − | 6.82400e11i | − | 1.48023i | ||||||
\(825\) | −3.10324e10 | + | 1.05350e11i | −0.0669883 | + | 0.227414i | ||||
\(826\) | −6.55047e11 | −1.40719 | ||||||||
\(827\) | 2.32417e10i | 0.0496874i | 0.999691 | + | 0.0248437i | \(0.00790881\pi\) | ||||
−0.999691 | + | 0.0248437i | \(0.992091\pi\) | |||||||
\(828\) | 5.67513e10 | − | 8.79720e10i | 0.120741 | − | 0.187164i | ||||
\(829\) | 7.31109e11 | 1.54798 | 0.773988 | − | 0.633200i | \(-0.218259\pi\) | ||||
0.773988 | + | 0.633200i | \(0.218259\pi\) | |||||||
\(830\) | − | 1.99741e11i | − | 0.420877i | ||||||
\(831\) | 4.21246e11 | + | 1.24085e11i | 0.883348 | + | 0.260204i | ||||
\(832\) | 1.49844e11 | 0.312713 | ||||||||
\(833\) | − | 3.62710e11i | − | 0.753320i | ||||||
\(834\) | 8.95038e10 | − | 3.03850e11i | 0.185002 | − | 0.628051i | ||||
\(835\) | −1.37536e11 | −0.282924 | ||||||||
\(836\) | 2.70659e10i | 0.0554112i | ||||||||
\(837\) | −1.05568e11 | − | 1.22472e11i | −0.215095 | − | 0.249538i | ||||
\(838\) | −2.39764e11 | −0.486192 | ||||||||
\(839\) | 2.00560e11i | 0.404760i | 0.979307 | + | 0.202380i | \(0.0648675\pi\) | ||||
−0.979307 | + | 0.202380i | \(0.935132\pi\) | |||||||
\(840\) | −3.00268e11 | − | 8.84485e10i | −0.603103 | − | 0.177653i | ||||
\(841\) | −5.52672e11 | −1.10480 | ||||||||
\(842\) | 1.01623e11i | 0.202182i | ||||||||
\(843\) | 7.14421e10 | − | 2.42534e11i | 0.141463 | − | 0.480244i | ||||
\(844\) | 3.48219e10 | 0.0686250 | ||||||||
\(845\) | − | 2.11781e11i | − | 0.415395i | ||||||
\(846\) | 3.09998e11 | + | 1.99982e11i | 0.605170 | + | 0.390399i | ||||
\(847\) | −5.89310e10 | −0.114501 | ||||||||
\(848\) | 1.09976e11i | 0.212674i | ||||||||
\(849\) | −4.72789e11 | − | 1.39267e11i | −0.909989 | − | 0.268052i | ||||
\(850\) | −3.98420e11 | −0.763248 | ||||||||
\(851\) | − | 4.30243e11i | − | 0.820342i | ||||||
\(852\) | 5.16991e10 | − | 1.75510e11i | 0.0981125 | − | 0.333075i | ||||
\(853\) | 3.67449e11 | 0.694066 | 0.347033 | − | 0.937853i | \(-0.387189\pi\) | ||||
0.347033 | + | 0.937853i | \(0.387189\pi\) | |||||||
\(854\) | − | 7.17208e10i | − | 0.134838i | ||||||
\(855\) | 5.73577e10 | − | 8.89119e10i | 0.107331 | − | 0.166378i | ||||
\(856\) | 3.25971e11 | 0.607134 | ||||||||
\(857\) | − | 9.09693e11i | − | 1.68644i | −0.537567 | − | 0.843221i | \(-0.680656\pi\) | ||
0.537567 | − | 0.843221i | \(-0.319344\pi\) | |||||||
\(858\) | −3.77199e10 | − | 1.11110e10i | −0.0696019 | − | 0.0205023i | ||||
\(859\) | −5.49492e11 | −1.00923 | −0.504614 | − | 0.863345i | \(-0.668365\pi\) | ||||
−0.504614 | + | 0.863345i | \(0.668365\pi\) | |||||||
\(860\) | − | 5.29554e10i | − | 0.0968091i | ||||||
\(861\) | 1.81987e11 | − | 6.17814e11i | 0.331152 | − | 1.12420i | ||||
\(862\) | −4.08904e11 | −0.740615 | ||||||||
\(863\) | 3.87633e11i | 0.698840i | 0.936966 | + | 0.349420i | \(0.113621\pi\) | ||||
−0.936966 | + | 0.349420i | \(0.886379\pi\) | |||||||
\(864\) | −3.32420e11 | + | 2.86538e11i | −0.596531 | + | 0.514194i | ||||
\(865\) | −3.34036e10 | −0.0596663 | ||||||||
\(866\) | − | 5.29850e11i | − | 0.942067i | ||||||
\(867\) | 3.52556e11 | + | 1.03851e11i | 0.623952 | + | 0.183795i | ||||
\(868\) | 1.01070e11 | 0.178051 | ||||||||
\(869\) | 3.24321e11i | 0.568717i | ||||||||
\(870\) | −8.20334e10 | + | 2.78490e11i | −0.143190 | + | 0.486107i | ||||
\(871\) | −2.13239e11 | −0.370505 | ||||||||
\(872\) | − | 7.53172e11i | − | 1.30265i | ||||||
\(873\) | 2.02953e11 | + | 1.30927e11i | 0.349413 | + | 0.225409i | ||||
\(874\) | 9.80142e10 | 0.167975 | ||||||||
\(875\) | 6.09679e11i | 1.04008i | ||||||||
\(876\) | 1.43251e11 | + | 4.21969e10i | 0.243267 | + | 0.0716580i | ||||
\(877\) | −2.30189e11 | −0.389122 | −0.194561 | − | 0.980890i | \(-0.562328\pi\) | ||||
−0.194561 | + | 0.980890i | \(0.562328\pi\) | |||||||
\(878\) | 2.46739e11i | 0.415202i | ||||||||
\(879\) | −9.44251e10 | + | 3.20557e11i | −0.158173 | + | 0.536970i | ||||
\(880\) | −3.23304e10 | −0.0539114 | ||||||||
\(881\) | 1.72949e11i | 0.287088i | 0.989644 | + | 0.143544i | \(0.0458499\pi\) | ||||
−0.989644 | + | 0.143544i | \(0.954150\pi\) | |||||||
\(882\) | 1.45347e11 | − | 2.25308e11i | 0.240178 | − | 0.372307i | ||||
\(883\) | −9.66785e11 | −1.59033 | −0.795165 | − | 0.606393i | \(-0.792616\pi\) | ||||
−0.795165 | + | 0.606393i | \(0.792616\pi\) | |||||||
\(884\) | 1.07219e11i | 0.175575i | ||||||||
\(885\) | −4.02241e11 | − | 1.18486e11i | −0.655712 | − | 0.193150i | ||||
\(886\) | −3.23143e11 | −0.524396 | ||||||||
\(887\) | − | 2.15715e11i | − | 0.348486i | −0.984703 | − | 0.174243i | \(-0.944252\pi\) | ||
0.984703 | − | 0.174243i | \(-0.0557478\pi\) | |||||||
\(888\) | −2.99833e11 | + | 1.01788e12i | −0.482200 | + | 1.63699i | ||||
\(889\) | −3.36157e11 | −0.538189 | ||||||||
\(890\) | 2.81031e11i | 0.447913i | ||||||||
\(891\) | 1.73126e11 | − | 7.83418e10i | 0.274696 | − | 0.124303i | ||||
\(892\) | −8.95113e9 | −0.0141390 | ||||||||
\(893\) | − | 2.59595e11i | − | 0.408217i | ||||||
\(894\) | 4.62142e11 | + | 1.36131e11i | 0.723478 | + | 0.213112i | ||||
\(895\) | 3.50735e11 | 0.546622 | ||||||||
\(896\) | − | 3.70942e10i | − | 0.0575537i | ||||||
\(897\) | 3.02421e10 | − | 1.02667e11i | 0.0467135 | − | 0.158585i | ||||
\(898\) | 8.45772e11 | 1.30061 | ||||||||
\(899\) | − | 3.12198e11i | − | 0.477959i | ||||||
\(900\) | 1.86016e11 | + | 1.20000e11i | 0.283518 | + | 0.182899i | ||||
\(901\) | −4.65537e11 | −0.706407 | ||||||||
\(902\) | − | 1.40321e11i | − | 0.211980i | ||||||
\(903\) | 3.92042e11 | + | 1.15482e11i | 0.589632 | + | 0.173685i | ||||
\(904\) | 1.17209e12 | 1.75505 | ||||||||
\(905\) | 2.58989e10i | 0.0386089i | ||||||||
\(906\) | −2.75956e11 | + | 9.36825e11i | −0.409569 | + | 1.39042i | ||||
\(907\) | 3.25292e11 | 0.480667 | 0.240333 | − | 0.970690i | \(-0.422743\pi\) | ||||
0.240333 | + | 0.970690i | \(0.422743\pi\) | |||||||
\(908\) | 3.38926e11i | 0.498610i | ||||||||
\(909\) | −5.90340e11 | + | 9.15105e11i | −0.864662 | + | 1.34034i | ||||
\(910\) | −9.60880e10 | −0.140121 | ||||||||
\(911\) | 1.03719e12i | 1.50585i | 0.658104 | + | 0.752927i | \(0.271359\pi\) | ||||
−0.658104 | + | 0.752927i | \(0.728641\pi\) | |||||||
\(912\) | −1.09929e11 | − | 3.23812e10i | −0.158903 | − | 0.0468074i | ||||
\(913\) | −2.52434e11 | −0.363299 | ||||||||
\(914\) | 9.18469e9i | 0.0131607i | ||||||||
\(915\) | 1.29730e10 | − | 4.40412e10i | 0.0185079 | − | 0.0628311i | ||||
\(916\) | −2.13331e11 | −0.303021 | ||||||||
\(917\) | − | 8.41733e10i | − | 0.119041i | ||||||
\(918\) | 4.50091e11 | + | 5.22162e11i | 0.633767 | + | 0.735249i | ||||
\(919\) | −2.16984e11 | −0.304205 | −0.152103 | − | 0.988365i | \(-0.548604\pi\) | ||||
−0.152103 | + | 0.988365i | \(0.548604\pi\) | |||||||
\(920\) | − | 1.85623e11i | − | 0.259108i | ||||||
\(921\) | 1.12412e11 | + | 3.31126e10i | 0.156233 | + | 0.0460209i | ||||
\(922\) | 5.81200e11 | 0.804270 | ||||||||
\(923\) | − | 1.87054e11i | − | 0.257727i | ||||||
\(924\) | −3.35632e10 | + | 1.13941e11i | −0.0460443 | + | 0.156313i | ||||
\(925\) | 9.09745e11 | 1.24266 | ||||||||
\(926\) | − | 9.52123e11i | − | 1.29494i | ||||||
\(927\) | 8.50647e11 | + | 5.48758e11i | 1.15194 | + | 0.743125i | ||||
\(928\) | −8.47381e11 | −1.14258 | ||||||||
\(929\) | − | 9.82796e11i | − | 1.31947i | −0.751497 | − | 0.659736i | \(-0.770668\pi\) | ||
0.751497 | − | 0.659736i | \(-0.229332\pi\) | |||||||
\(930\) | −8.25741e10 | − | 2.43235e10i | −0.110385 | − | 0.0325158i | ||||
\(931\) | −1.88675e11 | −0.251140 | ||||||||
\(932\) | 4.04954e11i | 0.536713i | ||||||||
\(933\) | −1.42186e11 | + | 4.82697e11i | −0.187642 | + | 0.637013i | ||||
\(934\) | 9.22829e11 | 1.21265 | ||||||||
\(935\) | − | 1.36857e11i | − | 0.179069i | ||||||
\(936\) | −1.43096e11 | + | 2.21817e11i | −0.186433 | + | 0.288996i | ||||
\(937\) | 1.41312e11 | 0.183324 | 0.0916621 | − | 0.995790i | \(-0.470782\pi\) | ||||
0.0916621 | + | 0.995790i | \(0.470782\pi\) | |||||||
\(938\) | − | 8.57006e11i | − | 1.10706i | ||||||
\(939\) | −9.14611e11 | − | 2.69413e11i | −1.17645 | − | 0.346542i | ||||
\(940\) | −1.47616e11 | −0.189070 | ||||||||
\(941\) | 1.01179e12i | 1.29042i | 0.764006 | + | 0.645210i | \(0.223230\pi\) | ||||
−0.764006 | + | 0.645210i | \(0.776770\pi\) | |||||||
\(942\) | 1.41622e11 | − | 4.80783e11i | 0.179857 | − | 0.610584i | ||||
\(943\) | 3.81928e11 | 0.482986 | ||||||||
\(944\) | 4.54170e11i | 0.571914i | ||||||||
\(945\) | 3.51719e11 | − | 3.03173e11i | 0.441030 | − | 0.380157i | ||||
\(946\) | 8.90422e10 | 0.111181 | ||||||||
\(947\) | − | 1.81833e11i | − | 0.226086i | −0.993590 | − | 0.113043i | \(-0.963940\pi\) | ||
0.993590 | − | 0.113043i | \(-0.0360597\pi\) | |||||||
\(948\) | 6.27065e11 | + | 1.84712e11i | 0.776388 | + | 0.228697i | ||||
\(949\) | 1.52674e11 | 0.188235 | ||||||||
\(950\) | 2.07251e11i | 0.254449i | ||||||||
\(951\) | 2.04817e11 | − | 6.95320e11i | 0.250406 | − | 0.850085i | ||||
\(952\) | −1.43515e12 | −1.74722 | ||||||||
\(953\) | − | 8.23641e11i | − | 0.998542i | −0.866446 | − | 0.499271i | \(-0.833601\pi\) | ||
0.866446 | − | 0.499271i | \(-0.166399\pi\) | |||||||
\(954\) | −2.89182e11 | − | 1.86553e11i | −0.349122 | − | 0.225221i | ||||
\(955\) | −1.50816e9 | −0.00181316 | ||||||||
\(956\) | − | 1.95005e11i | − | 0.233461i | ||||||
\(957\) | 3.51956e11 | + | 1.03674e11i | 0.419605 | + | 0.123601i | ||||
\(958\) | 1.01226e12 | 1.20179 | ||||||||
\(959\) | 1.39522e12i | 1.64956i | ||||||||
\(960\) | −1.08932e11 | + | 3.69804e11i | −0.128253 | + | 0.435398i | ||||
\(961\) | −7.60322e11 | −0.891465 | ||||||||
\(962\) | 3.25730e11i | 0.380327i | ||||||||
\(963\) | −2.62133e11 | + | 4.06341e11i | −0.304801 | + | 0.472482i | ||||
\(964\) | −2.38548e10 | −0.0276228 | ||||||||
\(965\) | 6.82840e11i | 0.787426i | ||||||||
\(966\) | 4.12618e11 | + | 1.21543e11i | 0.473849 | + | 0.139580i | ||||
\(967\) | −1.10952e12 | −1.26890 | −0.634451 | − | 0.772963i | \(-0.718774\pi\) | ||||
−0.634451 | + | 0.772963i | \(0.718774\pi\) | |||||||
\(968\) | 8.61890e10i | 0.0981635i | ||||||||
\(969\) | 1.37072e11 | − | 4.65336e11i | 0.155473 | − | 0.527803i | ||||
\(970\) | 1.28581e11 | 0.145242 | ||||||||
\(971\) | − | 5.41910e11i | − | 0.609608i | −0.952415 | − | 0.304804i | \(-0.901409\pi\) | ||
0.952415 | − | 0.304804i | \(-0.0985909\pi\) | |||||||
\(972\) | −5.28703e10 | − | 3.79353e11i | −0.0592307 | − | 0.424989i | ||||
\(973\) | −9.78221e11 | −1.09140 | ||||||||
\(974\) | − | 1.11896e11i | − | 0.124330i | ||||||
\(975\) | 2.17089e11 | + | 6.39468e10i | 0.240225 | + | 0.0707621i | ||||
\(976\) | −4.97269e10 | −0.0548015 | ||||||||
\(977\) | − | 6.42355e11i | − | 0.705013i | −0.935809 | − | 0.352506i | \(-0.885329\pi\) | ||
0.935809 | − | 0.352506i | \(-0.114671\pi\) | |||||||
\(978\) | 6.10538e10 | − | 2.07267e11i | 0.0667356 | − | 0.226556i | ||||
\(979\) | 3.55168e11 | 0.386636 | ||||||||
\(980\) | 1.07288e11i | 0.116318i | ||||||||
\(981\) | 9.38869e11 | + | 6.05671e11i | 1.01375 | + | 0.653974i | ||||
\(982\) | 4.99163e10 | 0.0536780 | ||||||||
\(983\) | 1.02977e11i | 0.110287i | 0.998478 | + | 0.0551436i | \(0.0175617\pi\) | ||||
−0.998478 | + | 0.0551436i | \(0.982438\pi\) | |||||||
\(984\) | −9.03577e11 | − | 2.66163e11i | −0.963795 | − | 0.283901i | ||||
\(985\) | 2.33383e11 | 0.247927 | ||||||||
\(986\) | 1.33106e12i | 1.40828i | ||||||||
\(987\) | 3.21913e11 | − | 1.09284e12i | 0.339211 | − | 1.15156i | ||||
\(988\) | 5.57733e10 | 0.0585327 | ||||||||
\(989\) | 2.42357e11i | 0.253321i | ||||||||
\(990\) | 5.48421e10 | − | 8.50126e10i | 0.0570918 | − | 0.0884998i | ||||
\(991\) | 3.42425e11 | 0.355034 | 0.177517 | − | 0.984118i | \(-0.443193\pi\) | ||||
0.177517 | + | 0.984118i | \(0.443193\pi\) | |||||||
\(992\) | − | 2.51254e11i | − | 0.259458i | ||||||
\(993\) | 1.13058e11 | + | 3.33031e10i | 0.116280 | + | 0.0342521i | ||||
\(994\) | 7.51771e11 | 0.770087 | ||||||||
\(995\) | − | 8.46165e11i | − | 0.863302i | ||||||
\(996\) | −1.43769e11 | + | 4.88073e11i | −0.146093 | + | 0.495961i | ||||
\(997\) | 1.26844e12 | 1.28378 | 0.641889 | − | 0.766797i | \(-0.278151\pi\) | ||||
0.641889 | + | 0.766797i | \(0.278151\pi\) | |||||||
\(998\) | − | 7.09041e11i | − | 0.714742i | ||||||
\(999\) | −1.02773e12 | − | 1.19230e12i | −1.03185 | − | 1.19708i |
(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 | 33.9.b.a.23.9 | ✓ | 26 | |
3.2 | odd | 2 | inner | 33.9.b.a.23.18 | yes | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.9.b.a.23.9 | ✓ | 26 | 1.1 | even | 1 | trivial | |
33.9.b.a.23.18 | yes | 26 | 3.2 | odd | 2 | inner |