Properties

Label 81.9.d.g.26.6
Level $81$
Weight $9$
Character 81.26
Analytic conductor $32.998$
Analytic rank $0$
Dimension $32$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,9,Mod(26,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.26");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 81.d (of order \(6\), degree \(2\), not 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: \(32.9976674150\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 26.6
Character \(\chi\) \(=\) 81.26
Dual form 81.9.d.g.53.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-8.67350 - 5.00765i) q^{2} +(-77.8470 - 134.835i) q^{4} +(-514.754 + 297.193i) q^{5} +(-2204.76 + 3818.75i) q^{7} +4123.23i q^{8} +5952.96 q^{10} +(3013.23 + 1739.69i) q^{11} +(9131.48 + 15816.2i) q^{13} +(38245.9 - 22081.3i) q^{14} +(718.880 - 1245.14i) q^{16} -86637.8i q^{17} +76109.5 q^{19} +(80144.1 + 46271.2i) q^{20} +(-17423.5 - 30178.4i) q^{22} +(-453885. + 262051. i) q^{23} +(-18664.8 + 32328.3i) q^{25} -182909. i q^{26} +686534. q^{28} +(-671532. - 387709. i) q^{29} +(462712. + 801441. i) q^{31} +(901661. - 520574. i) q^{32} +(-433851. + 751453. i) q^{34} -2.62095e6i q^{35} +237767. q^{37} +(-660136. - 381130. i) q^{38} +(-1.22540e6 - 2.12245e6i) q^{40} +(-446772. + 257944. i) q^{41} +(-1.97918e6 + 3.42804e6i) q^{43} -541718. i q^{44} +5.24903e6 q^{46} +(-4.61257e6 - 2.66307e6i) q^{47} +(-6.83949e6 - 1.18463e7i) q^{49} +(323777. - 186933. i) q^{50} +(1.42172e6 - 2.46248e6i) q^{52} -1.30260e7i q^{53} -2.06810e6 q^{55} +(-1.57456e7 - 9.09072e6i) q^{56} +(3.88302e6 + 6.72559e6i) q^{58} +(1.08626e7 - 6.27153e6i) q^{59} +(-5.94218e6 + 1.02922e7i) q^{61} -9.26840e6i q^{62} -1.07955e7 q^{64} +(-9.40093e6 - 5.42763e6i) q^{65} +(-6.76578e6 - 1.17187e7i) q^{67} +(-1.16818e7 + 6.74449e6i) q^{68} +(-1.31248e7 + 2.27328e7i) q^{70} +133345. i q^{71} +5.24749e7 q^{73} +(-2.06227e6 - 1.19065e6i) q^{74} +(-5.92489e6 - 1.02622e7i) q^{76} +(-1.32869e7 + 7.67118e6i) q^{77} +(2.39249e7 - 4.14392e7i) q^{79} +854585. i q^{80} +5.16676e6 q^{82} +(5.06857e7 + 2.92634e7i) q^{83} +(2.57482e7 + 4.45971e7i) q^{85} +(3.43328e7 - 1.98220e7i) q^{86} +(-7.17315e6 + 1.24243e7i) q^{88} -4.62606e7i q^{89} -8.05307e7 q^{91} +(7.06671e7 + 4.07997e7i) q^{92} +(2.66714e7 + 4.61962e7i) q^{94} +(-3.91777e7 + 2.26192e7i) q^{95} +(4.41196e7 - 7.64173e7i) q^{97} +1.36999e8i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2048 q^{4} - 3692 q^{7} + 21504 q^{10} - 63860 q^{13} - 95116 q^{16} + 370216 q^{19} + 691980 q^{22} + 541712 q^{25} - 1994264 q^{28} - 571136 q^{31} - 1027656 q^{34} + 8708536 q^{37} + 2973768 q^{40}+ \cdots + 133878688 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.67350 5.00765i −0.542094 0.312978i 0.203833 0.979006i \(-0.434660\pi\)
−0.745927 + 0.666028i \(0.767993\pi\)
\(3\) 0 0
\(4\) −77.8470 134.835i −0.304090 0.526699i
\(5\) −514.754 + 297.193i −0.823606 + 0.475509i −0.851658 0.524097i \(-0.824403\pi\)
0.0280522 + 0.999606i \(0.491070\pi\)
\(6\) 0 0
\(7\) −2204.76 + 3818.75i −0.918265 + 1.59048i −0.116217 + 0.993224i \(0.537077\pi\)
−0.802049 + 0.597258i \(0.796257\pi\)
\(8\) 4123.23i 1.00665i
\(9\) 0 0
\(10\) 5952.96 0.595296
\(11\) 3013.23 + 1739.69i 0.205808 + 0.118823i 0.599362 0.800478i \(-0.295421\pi\)
−0.393554 + 0.919302i \(0.628755\pi\)
\(12\) 0 0
\(13\) 9131.48 + 15816.2i 0.319718 + 0.553768i 0.980429 0.196872i \(-0.0630784\pi\)
−0.660711 + 0.750641i \(0.729745\pi\)
\(14\) 38245.9 22081.3i 0.995572 0.574794i
\(15\) 0 0
\(16\) 718.880 1245.14i 0.0109692 0.0189993i
\(17\) 86637.8i 1.03732i −0.854981 0.518659i \(-0.826432\pi\)
0.854981 0.518659i \(-0.173568\pi\)
\(18\) 0 0
\(19\) 76109.5 0.584016 0.292008 0.956416i \(-0.405677\pi\)
0.292008 + 0.956416i \(0.405677\pi\)
\(20\) 80144.1 + 46271.2i 0.500900 + 0.289195i
\(21\) 0 0
\(22\) −17423.5 30178.4i −0.0743780 0.128826i
\(23\) −453885. + 262051.i −1.62194 + 0.936427i −0.635538 + 0.772070i \(0.719222\pi\)
−0.986401 + 0.164357i \(0.947445\pi\)
\(24\) 0 0
\(25\) −18664.8 + 32328.3i −0.0477818 + 0.0827605i
\(26\) 182909.i 0.400259i
\(27\) 0 0
\(28\) 686534. 1.11694
\(29\) −671532. 387709.i −0.949455 0.548168i −0.0565435 0.998400i \(-0.518008\pi\)
−0.892912 + 0.450232i \(0.851341\pi\)
\(30\) 0 0
\(31\) 462712. + 801441.i 0.501031 + 0.867811i 0.999999 + 0.00119055i \(0.000378963\pi\)
−0.498969 + 0.866620i \(0.666288\pi\)
\(32\) 901661. 520574.i 0.859891 0.496458i
\(33\) 0 0
\(34\) −433851. + 751453.i −0.324657 + 0.562323i
\(35\) 2.62095e6i 1.74658i
\(36\) 0 0
\(37\) 237767. 0.126866 0.0634329 0.997986i \(-0.479795\pi\)
0.0634329 + 0.997986i \(0.479795\pi\)
\(38\) −660136. 381130.i −0.316591 0.182784i
\(39\) 0 0
\(40\) −1.22540e6 2.12245e6i −0.478671 0.829083i
\(41\) −446772. + 257944.i −0.158107 + 0.0912829i −0.576966 0.816768i \(-0.695763\pi\)
0.418859 + 0.908051i \(0.362430\pi\)
\(42\) 0 0
\(43\) −1.97918e6 + 3.42804e6i −0.578910 + 1.00270i 0.416695 + 0.909046i \(0.363188\pi\)
−0.995605 + 0.0936549i \(0.970145\pi\)
\(44\) 541718.i 0.144532i
\(45\) 0 0
\(46\) 5.24903e6 1.17232
\(47\) −4.61257e6 2.66307e6i −0.945260 0.545746i −0.0536550 0.998560i \(-0.517087\pi\)
−0.891605 + 0.452813i \(0.850420\pi\)
\(48\) 0 0
\(49\) −6.83949e6 1.18463e7i −1.18642 2.05494i
\(50\) 323777. 186933.i 0.0518044 0.0299093i
\(51\) 0 0
\(52\) 1.42172e6 2.46248e6i 0.194446 0.336791i
\(53\) 1.30260e7i 1.65085i −0.564514 0.825424i \(-0.690936\pi\)
0.564514 0.825424i \(-0.309064\pi\)
\(54\) 0 0
\(55\) −2.06810e6 −0.226006
\(56\) −1.57456e7 9.09072e6i −1.60106 0.924371i
\(57\) 0 0
\(58\) 3.88302e6 + 6.72559e6i 0.343129 + 0.594317i
\(59\) 1.08626e7 6.27153e6i 0.896450 0.517566i 0.0204032 0.999792i \(-0.493505\pi\)
0.876047 + 0.482226i \(0.160172\pi\)
\(60\) 0 0
\(61\) −5.94218e6 + 1.02922e7i −0.429167 + 0.743340i −0.996799 0.0799427i \(-0.974526\pi\)
0.567632 + 0.823282i \(0.307860\pi\)
\(62\) 9.26840e6i 0.627246i
\(63\) 0 0
\(64\) −1.07955e7 −0.643460
\(65\) −9.40093e6 5.42763e6i −0.526644 0.304058i
\(66\) 0 0
\(67\) −6.76578e6 1.17187e7i −0.335752 0.581540i 0.647877 0.761745i \(-0.275657\pi\)
−0.983629 + 0.180205i \(0.942324\pi\)
\(68\) −1.16818e7 + 6.74449e6i −0.546354 + 0.315438i
\(69\) 0 0
\(70\) −1.31248e7 + 2.27328e7i −0.546639 + 0.946807i
\(71\) 133345.i 0.00524738i 0.999997 + 0.00262369i \(0.000835147\pi\)
−0.999997 + 0.00262369i \(0.999165\pi\)
\(72\) 0 0
\(73\) 5.24749e7 1.84782 0.923910 0.382609i \(-0.124974\pi\)
0.923910 + 0.382609i \(0.124974\pi\)
\(74\) −2.06227e6 1.19065e6i −0.0687731 0.0397062i
\(75\) 0 0
\(76\) −5.92489e6 1.02622e7i −0.177593 0.307600i
\(77\) −1.32869e7 + 7.67118e6i −0.377972 + 0.218222i
\(78\) 0 0
\(79\) 2.39249e7 4.14392e7i 0.614246 1.06391i −0.376270 0.926510i \(-0.622794\pi\)
0.990516 0.137395i \(-0.0438731\pi\)
\(80\) 854585.i 0.0208639i
\(81\) 0 0
\(82\) 5.16676e6 0.114278
\(83\) 5.06857e7 + 2.92634e7i 1.06800 + 0.616612i 0.927635 0.373487i \(-0.121838\pi\)
0.140369 + 0.990099i \(0.455171\pi\)
\(84\) 0 0
\(85\) 2.57482e7 + 4.45971e7i 0.493254 + 0.854341i
\(86\) 3.43328e7 1.98220e7i 0.627647 0.362372i
\(87\) 0 0
\(88\) −7.17315e6 + 1.24243e7i −0.119613 + 0.207176i
\(89\) 4.62606e7i 0.737312i −0.929566 0.368656i \(-0.879818\pi\)
0.929566 0.368656i \(-0.120182\pi\)
\(90\) 0 0
\(91\) −8.05307e7 −1.17435
\(92\) 7.06671e7 + 4.07997e7i 0.986430 + 0.569515i
\(93\) 0 0
\(94\) 2.66714e7 + 4.61962e7i 0.341613 + 0.591691i
\(95\) −3.91777e7 + 2.26192e7i −0.480999 + 0.277705i
\(96\) 0 0
\(97\) 4.41196e7 7.64173e7i 0.498361 0.863187i −0.501637 0.865078i \(-0.667269\pi\)
0.999998 + 0.00189124i \(0.000602002\pi\)
\(98\) 1.36999e8i 1.48530i
\(99\) 0 0
\(100\) 5.81198e6 0.0581198
\(101\) −4.97112e7 2.87007e7i −0.477714 0.275809i 0.241749 0.970339i \(-0.422279\pi\)
−0.719464 + 0.694530i \(0.755612\pi\)
\(102\) 0 0
\(103\) 3.94562e7 + 6.83401e7i 0.350563 + 0.607193i 0.986348 0.164673i \(-0.0526569\pi\)
−0.635785 + 0.771866i \(0.719324\pi\)
\(104\) −6.52138e7 + 3.76512e7i −0.557450 + 0.321844i
\(105\) 0 0
\(106\) −6.52295e7 + 1.12981e8i −0.516679 + 0.894914i
\(107\) 2.50821e8i 1.91350i 0.290907 + 0.956751i \(0.406043\pi\)
−0.290907 + 0.956751i \(0.593957\pi\)
\(108\) 0 0
\(109\) −7.76440e7 −0.550050 −0.275025 0.961437i \(-0.588686\pi\)
−0.275025 + 0.961437i \(0.588686\pi\)
\(110\) 1.79376e7 + 1.03563e7i 0.122516 + 0.0707349i
\(111\) 0 0
\(112\) 3.16991e6 + 5.49044e6i 0.0201453 + 0.0348927i
\(113\) 5.33353e7 3.07931e7i 0.327115 0.188860i −0.327444 0.944870i \(-0.606187\pi\)
0.654560 + 0.756010i \(0.272854\pi\)
\(114\) 0 0
\(115\) 1.55759e8 2.69783e8i 0.890559 1.54249i
\(116\) 1.20728e8i 0.666769i
\(117\) 0 0
\(118\) −1.25622e8 −0.647946
\(119\) 3.30848e8 + 1.91015e8i 1.64983 + 0.952533i
\(120\) 0 0
\(121\) −1.01126e8 1.75156e8i −0.471762 0.817116i
\(122\) 1.03079e8 5.95127e7i 0.465298 0.268640i
\(123\) 0 0
\(124\) 7.20415e7 1.24780e8i 0.304717 0.527785i
\(125\) 2.54370e8i 1.04190i
\(126\) 0 0
\(127\) −3.58325e8 −1.37741 −0.688703 0.725044i \(-0.741819\pi\)
−0.688703 + 0.725044i \(0.741819\pi\)
\(128\) −1.37191e8 7.92071e7i −0.511075 0.295069i
\(129\) 0 0
\(130\) 5.43593e7 + 9.41530e7i 0.190327 + 0.329656i
\(131\) 1.62075e8 9.35739e7i 0.550339 0.317738i −0.198920 0.980016i \(-0.563743\pi\)
0.749259 + 0.662277i \(0.230410\pi\)
\(132\) 0 0
\(133\) −1.67803e8 + 2.90643e8i −0.536281 + 0.928867i
\(134\) 1.35523e8i 0.420332i
\(135\) 0 0
\(136\) 3.57228e8 1.04421
\(137\) 1.30060e8 + 7.50900e7i 0.369199 + 0.213157i 0.673108 0.739544i \(-0.264959\pi\)
−0.303909 + 0.952701i \(0.598292\pi\)
\(138\) 0 0
\(139\) −6.49820e7 1.12552e8i −0.174074 0.301505i 0.765766 0.643119i \(-0.222360\pi\)
−0.939840 + 0.341614i \(0.889027\pi\)
\(140\) −3.53396e8 + 2.04033e8i −0.919919 + 0.531115i
\(141\) 0 0
\(142\) 667743. 1.15656e6i 0.00164231 0.00284457i
\(143\) 6.35437e7i 0.151960i
\(144\) 0 0
\(145\) 4.60898e8 1.04264
\(146\) −4.55140e8 2.62775e8i −1.00169 0.578327i
\(147\) 0 0
\(148\) −1.85094e7 3.20593e7i −0.0385786 0.0668200i
\(149\) 1.30697e8 7.54578e7i 0.265167 0.153094i −0.361522 0.932363i \(-0.617743\pi\)
0.626689 + 0.779269i \(0.284410\pi\)
\(150\) 0 0
\(151\) −8.56221e7 + 1.48302e8i −0.164694 + 0.285258i −0.936547 0.350543i \(-0.885997\pi\)
0.771853 + 0.635802i \(0.219330\pi\)
\(152\) 3.13817e8i 0.587899i
\(153\) 0 0
\(154\) 1.53658e8 0.273195
\(155\) −4.76366e8 2.75030e8i −0.825304 0.476490i
\(156\) 0 0
\(157\) 3.60934e8 + 6.25156e8i 0.594059 + 1.02894i 0.993679 + 0.112259i \(0.0358087\pi\)
−0.399620 + 0.916681i \(0.630858\pi\)
\(158\) −4.15026e8 + 2.39615e8i −0.665958 + 0.384491i
\(159\) 0 0
\(160\) −3.09422e8 + 5.35935e8i −0.472141 + 0.817772i
\(161\) 2.31103e9i 3.43955i
\(162\) 0 0
\(163\) −1.90963e8 −0.270520 −0.135260 0.990810i \(-0.543187\pi\)
−0.135260 + 0.990810i \(0.543187\pi\)
\(164\) 6.95596e7 + 4.01603e7i 0.0961572 + 0.0555164i
\(165\) 0 0
\(166\) −2.93081e8 5.07632e8i −0.385972 0.668523i
\(167\) 4.84429e8 2.79685e8i 0.622822 0.359586i −0.155145 0.987892i \(-0.549584\pi\)
0.777967 + 0.628305i \(0.216251\pi\)
\(168\) 0 0
\(169\) 2.41098e8 4.17593e8i 0.295560 0.511926i
\(170\) 5.15751e8i 0.617510i
\(171\) 0 0
\(172\) 6.16292e8 0.704162
\(173\) −5.25797e8 3.03569e8i −0.586994 0.338901i 0.176914 0.984226i \(-0.443389\pi\)
−0.763908 + 0.645325i \(0.776722\pi\)
\(174\) 0 0
\(175\) −8.23024e7 1.42552e8i −0.0877527 0.151992i
\(176\) 4.33230e6 2.50125e6i 0.00451510 0.00260680i
\(177\) 0 0
\(178\) −2.31657e8 + 4.01241e8i −0.230762 + 0.399692i
\(179\) 4.18834e8i 0.407971i −0.978974 0.203986i \(-0.934610\pi\)
0.978974 0.203986i \(-0.0653896\pi\)
\(180\) 0 0
\(181\) 1.10216e9 1.02690 0.513451 0.858119i \(-0.328367\pi\)
0.513451 + 0.858119i \(0.328367\pi\)
\(182\) 6.98483e8 + 4.03269e8i 0.636605 + 0.367544i
\(183\) 0 0
\(184\) −1.08050e9 1.87147e9i −0.942653 1.63272i
\(185\) −1.22391e8 + 7.06627e7i −0.104487 + 0.0603258i
\(186\) 0 0
\(187\) 1.50723e8 2.61060e8i 0.123257 0.213488i
\(188\) 8.29247e8i 0.663823i
\(189\) 0 0
\(190\) 4.53077e8 0.347662
\(191\) −1.54781e9 8.93626e8i −1.16301 0.671463i −0.210985 0.977489i \(-0.567667\pi\)
−0.952023 + 0.306026i \(0.901001\pi\)
\(192\) 0 0
\(193\) 3.58643e8 + 6.21188e8i 0.258484 + 0.447707i 0.965836 0.259154i \(-0.0834438\pi\)
−0.707352 + 0.706861i \(0.750110\pi\)
\(194\) −7.65342e8 + 4.41870e8i −0.540317 + 0.311952i
\(195\) 0 0
\(196\) −1.06487e9 + 1.84440e9i −0.721558 + 1.24977i
\(197\) 1.81939e9i 1.20798i 0.796992 + 0.603990i \(0.206423\pi\)
−0.796992 + 0.603990i \(0.793577\pi\)
\(198\) 0 0
\(199\) −1.90300e9 −1.21346 −0.606730 0.794908i \(-0.707519\pi\)
−0.606730 + 0.794908i \(0.707519\pi\)
\(200\) −1.33297e8 7.69592e7i −0.0833108 0.0480995i
\(201\) 0 0
\(202\) 2.87446e8 + 4.97872e8i 0.172644 + 0.299028i
\(203\) 2.96113e9 1.70961e9i 1.74370 1.00673i
\(204\) 0 0
\(205\) 1.53318e8 2.65555e8i 0.0868118 0.150362i
\(206\) 7.90331e8i 0.438874i
\(207\) 0 0
\(208\) 2.62577e7 0.0140283
\(209\) 2.29335e8 + 1.32407e8i 0.120195 + 0.0693946i
\(210\) 0 0
\(211\) −7.99513e7 1.38480e8i −0.0403363 0.0698645i 0.845152 0.534525i \(-0.179510\pi\)
−0.885489 + 0.464661i \(0.846176\pi\)
\(212\) −1.75636e9 + 1.01403e9i −0.869499 + 0.502006i
\(213\) 0 0
\(214\) 1.25602e9 2.17550e9i 0.598884 1.03730i
\(215\) 2.35279e9i 1.10111i
\(216\) 0 0
\(217\) −4.08067e9 −1.84032
\(218\) 6.73445e8 + 3.88814e8i 0.298179 + 0.172153i
\(219\) 0 0
\(220\) 1.60995e8 + 2.78851e8i 0.0687261 + 0.119037i
\(221\) 1.37028e9 7.91131e8i 0.574434 0.331649i
\(222\) 0 0
\(223\) 3.06593e8 5.31035e8i 0.123977 0.214735i −0.797355 0.603510i \(-0.793768\pi\)
0.921333 + 0.388775i \(0.127102\pi\)
\(224\) 4.59096e9i 1.82352i
\(225\) 0 0
\(226\) −6.16805e8 −0.236436
\(227\) 2.56740e9 + 1.48229e9i 0.966919 + 0.558251i 0.898296 0.439392i \(-0.144806\pi\)
0.0686235 + 0.997643i \(0.478139\pi\)
\(228\) 0 0
\(229\) 1.89482e9 + 3.28193e9i 0.689013 + 1.19340i 0.972158 + 0.234328i \(0.0752889\pi\)
−0.283145 + 0.959077i \(0.591378\pi\)
\(230\) −2.70196e9 + 1.55998e9i −0.965533 + 0.557451i
\(231\) 0 0
\(232\) 1.59862e9 2.76888e9i 0.551813 0.955768i
\(233\) 3.76374e9i 1.27701i 0.769616 + 0.638507i \(0.220448\pi\)
−0.769616 + 0.638507i \(0.779552\pi\)
\(234\) 0 0
\(235\) 3.16578e9 1.03803
\(236\) −1.69124e9 9.76439e8i −0.545202 0.314773i
\(237\) 0 0
\(238\) −1.91307e9 3.31354e9i −0.596243 1.03272i
\(239\) −4.58786e8 + 2.64880e8i −0.140611 + 0.0811816i −0.568655 0.822576i \(-0.692536\pi\)
0.428044 + 0.903758i \(0.359203\pi\)
\(240\) 0 0
\(241\) 4.19453e8 7.26513e8i 0.124341 0.215365i −0.797134 0.603802i \(-0.793652\pi\)
0.921475 + 0.388437i \(0.126985\pi\)
\(242\) 2.02562e9i 0.590604i
\(243\) 0 0
\(244\) 1.85032e9 0.522021
\(245\) 7.04131e9 + 4.06530e9i 1.95429 + 1.12831i
\(246\) 0 0
\(247\) 6.94992e8 + 1.20376e9i 0.186721 + 0.323409i
\(248\) −3.30453e9 + 1.90787e9i −0.873581 + 0.504362i
\(249\) 0 0
\(250\) −1.27380e9 + 2.20628e9i −0.326092 + 0.564808i
\(251\) 2.40283e9i 0.605380i −0.953089 0.302690i \(-0.902115\pi\)
0.953089 0.302690i \(-0.0978847\pi\)
\(252\) 0 0
\(253\) −1.82355e9 −0.445076
\(254\) 3.10793e9 + 1.79436e9i 0.746683 + 0.431097i
\(255\) 0 0
\(256\) 2.17510e9 + 3.76739e9i 0.506431 + 0.877164i
\(257\) 4.15154e9 2.39689e9i 0.951648 0.549434i 0.0580555 0.998313i \(-0.481510\pi\)
0.893592 + 0.448879i \(0.148177\pi\)
\(258\) 0 0
\(259\) −5.24218e8 + 9.07972e8i −0.116496 + 0.201778i
\(260\) 1.69010e9i 0.369844i
\(261\) 0 0
\(262\) −1.87434e9 −0.397780
\(263\) −1.94790e9 1.12462e9i −0.407139 0.235062i 0.282421 0.959291i \(-0.408863\pi\)
−0.689560 + 0.724229i \(0.742196\pi\)
\(264\) 0 0
\(265\) 3.87123e9 + 6.70517e9i 0.784993 + 1.35965i
\(266\) 2.91088e9 1.68059e9i 0.581429 0.335688i
\(267\) 0 0
\(268\) −1.05339e9 + 1.82453e9i −0.204197 + 0.353680i
\(269\) 2.01512e9i 0.384851i −0.981312 0.192425i \(-0.938365\pi\)
0.981312 0.192425i \(-0.0616353\pi\)
\(270\) 0 0
\(271\) −5.85840e9 −1.08618 −0.543090 0.839675i \(-0.682746\pi\)
−0.543090 + 0.839675i \(0.682746\pi\)
\(272\) −1.07876e8 6.22821e7i −0.0197083 0.0113786i
\(273\) 0 0
\(274\) −7.52049e8 1.30259e9i −0.133427 0.231102i
\(275\) −1.12482e8 + 6.49417e7i −0.0196677 + 0.0113552i
\(276\) 0 0
\(277\) 3.40794e9 5.90273e9i 0.578859 1.00261i −0.416751 0.909021i \(-0.636831\pi\)
0.995611 0.0935933i \(-0.0298353\pi\)
\(278\) 1.30163e9i 0.217925i
\(279\) 0 0
\(280\) 1.08068e10 1.75819
\(281\) −1.79419e9 1.03588e9i −0.287768 0.166143i 0.349167 0.937061i \(-0.386465\pi\)
−0.636935 + 0.770918i \(0.719798\pi\)
\(282\) 0 0
\(283\) −4.80878e8 8.32906e8i −0.0749704 0.129852i 0.826103 0.563519i \(-0.190553\pi\)
−0.901073 + 0.433667i \(0.857220\pi\)
\(284\) 1.79795e7 1.03805e7i 0.00276379 0.00159567i
\(285\) 0 0
\(286\) 3.18204e8 5.51146e8i 0.0475600 0.0823764i
\(287\) 2.27481e9i 0.335288i
\(288\) 0 0
\(289\) −5.30347e8 −0.0760272
\(290\) −3.99760e9 2.30801e9i −0.565207 0.326322i
\(291\) 0 0
\(292\) −4.08501e9 7.07544e9i −0.561903 0.973245i
\(293\) −1.05291e10 + 6.07899e9i −1.42864 + 0.824823i −0.997013 0.0772309i \(-0.975392\pi\)
−0.431623 + 0.902054i \(0.642059\pi\)
\(294\) 0 0
\(295\) −3.72771e9 + 6.45659e9i −0.492215 + 0.852541i
\(296\) 9.80369e8i 0.127709i
\(297\) 0 0
\(298\) −1.51146e9 −0.191660
\(299\) −8.28928e9 4.78582e9i −1.03713 0.598786i
\(300\) 0 0
\(301\) −8.72720e9 1.51160e10i −1.06319 1.84149i
\(302\) 1.48529e9 8.57530e8i 0.178559 0.103091i
\(303\) 0 0
\(304\) 5.47136e7 9.47667e7i 0.00640620 0.0110959i
\(305\) 7.06391e9i 0.816292i
\(306\) 0 0
\(307\) 4.91035e9 0.552788 0.276394 0.961044i \(-0.410860\pi\)
0.276394 + 0.961044i \(0.410860\pi\)
\(308\) 2.06868e9 + 1.19436e9i 0.229875 + 0.132718i
\(309\) 0 0
\(310\) 2.75451e9 + 4.77094e9i 0.298261 + 0.516604i
\(311\) 2.32924e9 1.34479e9i 0.248984 0.143751i −0.370315 0.928906i \(-0.620750\pi\)
0.619299 + 0.785155i \(0.287417\pi\)
\(312\) 0 0
\(313\) 2.56653e9 4.44536e9i 0.267405 0.463158i −0.700786 0.713371i \(-0.747167\pi\)
0.968191 + 0.250213i \(0.0805007\pi\)
\(314\) 7.22972e9i 0.743709i
\(315\) 0 0
\(316\) −7.44993e9 −0.747144
\(317\) −1.33196e10 7.69006e9i −1.31903 0.761540i −0.335455 0.942056i \(-0.608890\pi\)
−0.983572 + 0.180516i \(0.942223\pi\)
\(318\) 0 0
\(319\) −1.34899e9 2.33651e9i −0.130270 0.225634i
\(320\) 5.55701e9 3.20834e9i 0.529958 0.305971i
\(321\) 0 0
\(322\) −1.15728e10 + 2.00447e10i −1.07650 + 1.86456i
\(323\) 6.59396e9i 0.605810i
\(324\) 0 0
\(325\) −6.81747e8 −0.0611068
\(326\) 1.65632e9 + 9.56278e8i 0.146647 + 0.0846669i
\(327\) 0 0
\(328\) −1.06356e9 1.84214e9i −0.0918899 0.159158i
\(329\) 2.03392e10 1.17428e10i 1.73600 1.00228i
\(330\) 0 0
\(331\) 3.70488e9 6.41704e9i 0.308647 0.534593i −0.669419 0.742885i \(-0.733457\pi\)
0.978067 + 0.208292i \(0.0667904\pi\)
\(332\) 9.11226e9i 0.750022i
\(333\) 0 0
\(334\) −5.60225e9 −0.450170
\(335\) 6.96542e9 + 4.02149e9i 0.553055 + 0.319306i
\(336\) 0 0
\(337\) −2.35250e9 4.07466e9i −0.182394 0.315916i 0.760301 0.649571i \(-0.225051\pi\)
−0.942695 + 0.333655i \(0.891718\pi\)
\(338\) −4.18232e9 + 2.41466e9i −0.320443 + 0.185008i
\(339\) 0 0
\(340\) 4.00883e9 6.94350e9i 0.299987 0.519593i
\(341\) 3.21990e9i 0.238136i
\(342\) 0 0
\(343\) 3.48977e10 2.52127
\(344\) −1.41346e10 8.16061e9i −1.00937 0.582759i
\(345\) 0 0
\(346\) 3.04033e9 + 5.26601e9i 0.212137 + 0.367432i
\(347\) −4.21934e9 + 2.43604e9i −0.291023 + 0.168022i −0.638403 0.769702i \(-0.720405\pi\)
0.347380 + 0.937724i \(0.387071\pi\)
\(348\) 0 0
\(349\) −1.18998e10 + 2.06110e10i −0.802117 + 1.38931i 0.116104 + 0.993237i \(0.462959\pi\)
−0.918221 + 0.396070i \(0.870374\pi\)
\(350\) 1.64857e9i 0.109859i
\(351\) 0 0
\(352\) 3.62255e9 0.235963
\(353\) −6.84869e9 3.95409e9i −0.441071 0.254652i 0.262981 0.964801i \(-0.415294\pi\)
−0.704052 + 0.710149i \(0.748628\pi\)
\(354\) 0 0
\(355\) −3.96291e7 6.86397e7i −0.00249518 0.00432177i
\(356\) −6.23754e9 + 3.60125e9i −0.388341 + 0.224209i
\(357\) 0 0
\(358\) −2.09737e9 + 3.63275e9i −0.127686 + 0.221158i
\(359\) 7.90247e9i 0.475757i 0.971295 + 0.237879i \(0.0764520\pi\)
−0.971295 + 0.237879i \(0.923548\pi\)
\(360\) 0 0
\(361\) −1.11909e10 −0.658926
\(362\) −9.55954e9 5.51920e9i −0.556676 0.321397i
\(363\) 0 0
\(364\) 6.26907e9 + 1.08583e10i 0.357106 + 0.618526i
\(365\) −2.70116e10 + 1.55952e10i −1.52188 + 0.878656i
\(366\) 0 0
\(367\) 6.94556e9 1.20301e10i 0.382863 0.663137i −0.608608 0.793471i \(-0.708272\pi\)
0.991470 + 0.130334i \(0.0416049\pi\)
\(368\) 7.53531e8i 0.0410875i
\(369\) 0 0
\(370\) 1.41542e9 0.0755226
\(371\) 4.97429e10 + 2.87191e10i 2.62564 + 1.51592i
\(372\) 0 0
\(373\) −1.08855e10 1.88542e10i −0.562356 0.974029i −0.997290 0.0735671i \(-0.976562\pi\)
0.434934 0.900462i \(-0.356772\pi\)
\(374\) −2.61459e9 + 1.50953e9i −0.133634 + 0.0771536i
\(375\) 0 0
\(376\) 1.09805e10 1.90187e10i 0.549375 0.951546i
\(377\) 1.41614e10i 0.701038i
\(378\) 0 0
\(379\) −1.86928e10 −0.905975 −0.452988 0.891517i \(-0.649642\pi\)
−0.452988 + 0.891517i \(0.649642\pi\)
\(380\) 6.09973e9 + 3.52168e9i 0.292534 + 0.168894i
\(381\) 0 0
\(382\) 8.94992e9 + 1.55017e10i 0.420306 + 0.727992i
\(383\) −1.29018e10 + 7.44885e9i −0.599590 + 0.346174i −0.768880 0.639393i \(-0.779186\pi\)
0.169290 + 0.985566i \(0.445852\pi\)
\(384\) 0 0
\(385\) 4.55965e9 7.89754e9i 0.207533 0.359459i
\(386\) 7.18383e9i 0.323599i
\(387\) 0 0
\(388\) −1.37383e10 −0.606186
\(389\) −1.45384e10 8.39374e9i −0.634918 0.366570i 0.147736 0.989027i \(-0.452801\pi\)
−0.782654 + 0.622457i \(0.786135\pi\)
\(390\) 0 0
\(391\) 2.27035e10 + 3.93236e10i 0.971372 + 1.68246i
\(392\) 4.88453e10 2.82008e10i 2.06861 1.19431i
\(393\) 0 0
\(394\) 9.11084e9 1.57804e10i 0.378071 0.654838i
\(395\) 2.84413e10i 1.16832i
\(396\) 0 0
\(397\) 3.63950e10 1.46514 0.732570 0.680692i \(-0.238321\pi\)
0.732570 + 0.680692i \(0.238321\pi\)
\(398\) 1.65056e10 + 9.52953e9i 0.657809 + 0.379786i
\(399\) 0 0
\(400\) 2.68354e7 + 4.64803e7i 0.00104826 + 0.00181564i
\(401\) −2.67932e9 + 1.54691e9i −0.103621 + 0.0598255i −0.550915 0.834561i \(-0.685721\pi\)
0.447294 + 0.894387i \(0.352388\pi\)
\(402\) 0 0
\(403\) −8.45049e9 + 1.46367e10i −0.320377 + 0.554910i
\(404\) 8.93706e9i 0.335482i
\(405\) 0 0
\(406\) −3.42444e10 −1.26033
\(407\) 7.16446e8 + 4.13640e8i 0.0261099 + 0.0150746i
\(408\) 0 0
\(409\) 2.89420e9 + 5.01291e9i 0.103427 + 0.179142i 0.913095 0.407748i \(-0.133686\pi\)
−0.809667 + 0.586889i \(0.800352\pi\)
\(410\) −2.65961e9 + 1.53553e9i −0.0941202 + 0.0543403i
\(411\) 0 0
\(412\) 6.14309e9 1.06401e10i 0.213205 0.369282i
\(413\) 5.53087e10i 1.90105i
\(414\) 0 0
\(415\) −3.47875e10 −1.17282
\(416\) 1.64670e10 + 9.50722e9i 0.549846 + 0.317454i
\(417\) 0 0
\(418\) −1.32609e9 2.29686e9i −0.0434379 0.0752367i
\(419\) −2.09245e10 + 1.20808e10i −0.678889 + 0.391957i −0.799436 0.600751i \(-0.794868\pi\)
0.120547 + 0.992708i \(0.461535\pi\)
\(420\) 0 0
\(421\) −5.83472e9 + 1.01060e10i −0.185734 + 0.321701i −0.943824 0.330450i \(-0.892800\pi\)
0.758090 + 0.652150i \(0.226133\pi\)
\(422\) 1.60147e9i 0.0504975i
\(423\) 0 0
\(424\) 5.37092e10 1.66182
\(425\) 2.80085e9 + 1.61707e9i 0.0858489 + 0.0495649i
\(426\) 0 0
\(427\) −2.62021e10 4.53834e10i −0.788179 1.36517i
\(428\) 3.38194e10 1.95257e10i 1.00784 0.581876i
\(429\) 0 0
\(430\) −1.17820e10 + 2.04069e10i −0.344622 + 0.596904i
\(431\) 6.44251e10i 1.86701i 0.358568 + 0.933504i \(0.383265\pi\)
−0.358568 + 0.933504i \(0.616735\pi\)
\(432\) 0 0
\(433\) −5.35776e10 −1.52416 −0.762082 0.647480i \(-0.775823\pi\)
−0.762082 + 0.647480i \(0.775823\pi\)
\(434\) 3.53937e10 + 2.04346e10i 0.997624 + 0.575978i
\(435\) 0 0
\(436\) 6.04435e9 + 1.04691e10i 0.167265 + 0.289711i
\(437\) −3.45450e10 + 1.99445e10i −0.947238 + 0.546888i
\(438\) 0 0
\(439\) 2.13976e9 3.70617e9i 0.0576111 0.0997854i −0.835781 0.549062i \(-0.814985\pi\)
0.893393 + 0.449277i \(0.148318\pi\)
\(440\) 8.52725e9i 0.227509i
\(441\) 0 0
\(442\) −1.58468e10 −0.415196
\(443\) −1.04572e10 6.03744e9i −0.271518 0.156761i 0.358059 0.933699i \(-0.383439\pi\)
−0.629577 + 0.776938i \(0.716772\pi\)
\(444\) 0 0
\(445\) 1.37483e10 + 2.38128e10i 0.350599 + 0.607255i
\(446\) −5.31847e9 + 3.07062e9i −0.134415 + 0.0776044i
\(447\) 0 0
\(448\) 2.38014e10 4.12252e10i 0.590867 1.02341i
\(449\) 3.17911e10i 0.782205i −0.920347 0.391103i \(-0.872094\pi\)
0.920347 0.391103i \(-0.127906\pi\)
\(450\) 0 0
\(451\) −1.79497e9 −0.0433861
\(452\) −8.30398e9 4.79431e9i −0.198945 0.114861i
\(453\) 0 0
\(454\) −1.48456e10 2.57133e10i −0.349440 0.605249i
\(455\) 4.14535e10 2.39332e10i 0.967198 0.558412i
\(456\) 0 0
\(457\) 4.15200e9 7.19148e9i 0.0951903 0.164874i −0.814498 0.580167i \(-0.802987\pi\)
0.909688 + 0.415292i \(0.136321\pi\)
\(458\) 3.79544e10i 0.862583i
\(459\) 0 0
\(460\) −4.85016e10 −1.08324
\(461\) −2.76292e10 1.59518e10i −0.611738 0.353187i 0.161908 0.986806i \(-0.448235\pi\)
−0.773645 + 0.633619i \(0.781569\pi\)
\(462\) 0 0
\(463\) −1.37770e10 2.38625e10i −0.299800 0.519269i 0.676290 0.736636i \(-0.263587\pi\)
−0.976090 + 0.217366i \(0.930253\pi\)
\(464\) −9.65501e8 + 5.57432e8i −0.0208296 + 0.0120260i
\(465\) 0 0
\(466\) 1.88475e10 3.26448e10i 0.399677 0.692261i
\(467\) 2.60699e10i 0.548114i −0.961713 0.274057i \(-0.911634\pi\)
0.961713 0.274057i \(-0.0883658\pi\)
\(468\) 0 0
\(469\) 5.96675e10 1.23324
\(470\) −2.74584e10 1.58531e10i −0.562709 0.324880i
\(471\) 0 0
\(472\) 2.58590e10 + 4.47891e10i 0.521007 + 0.902411i
\(473\) −1.19274e10 + 6.88631e9i −0.238288 + 0.137576i
\(474\) 0 0
\(475\) −1.42057e9 + 2.46049e9i −0.0279053 + 0.0483334i
\(476\) 5.94798e10i 1.15862i
\(477\) 0 0
\(478\) 5.30570e9 0.101632
\(479\) 1.92371e9 + 1.11066e9i 0.0365425 + 0.0210978i 0.518160 0.855284i \(-0.326617\pi\)
−0.481617 + 0.876382i \(0.659951\pi\)
\(480\) 0 0
\(481\) 2.17116e9 + 3.76056e9i 0.0405613 + 0.0702542i
\(482\) −7.27624e9 + 4.20094e9i −0.134809 + 0.0778321i
\(483\) 0 0
\(484\) −1.57448e10 + 2.72707e10i −0.286916 + 0.496953i
\(485\) 5.24482e10i 0.947902i
\(486\) 0 0
\(487\) 8.62519e10 1.53339 0.766696 0.642011i \(-0.221900\pi\)
0.766696 + 0.642011i \(0.221900\pi\)
\(488\) −4.24370e10 2.45010e10i −0.748282 0.432021i
\(489\) 0 0
\(490\) −4.07152e10 7.05208e10i −0.706272 1.22330i
\(491\) 3.81434e9 2.20221e9i 0.0656286 0.0378907i −0.466827 0.884349i \(-0.654603\pi\)
0.532455 + 0.846458i \(0.321269\pi\)
\(492\) 0 0
\(493\) −3.35902e10 + 5.81800e10i −0.568624 + 0.984886i
\(494\) 1.39211e10i 0.233758i
\(495\) 0 0
\(496\) 1.33054e9 0.0219837
\(497\) −5.09210e8 2.93992e8i −0.00834586 0.00481848i
\(498\) 0 0
\(499\) 1.38520e10 + 2.39924e10i 0.223414 + 0.386965i 0.955843 0.293879i \(-0.0949464\pi\)
−0.732428 + 0.680844i \(0.761613\pi\)
\(500\) −3.42980e10 + 1.98020e10i −0.548768 + 0.316831i
\(501\) 0 0
\(502\) −1.20325e10 + 2.08409e10i −0.189471 + 0.328173i
\(503\) 2.37306e10i 0.370712i −0.982671 0.185356i \(-0.940656\pi\)
0.982671 0.185356i \(-0.0593438\pi\)
\(504\) 0 0
\(505\) 3.41187e10 0.524598
\(506\) 1.58165e10 + 9.13167e9i 0.241273 + 0.139299i
\(507\) 0 0
\(508\) 2.78945e10 + 4.83147e10i 0.418855 + 0.725478i
\(509\) −3.31689e10 + 1.91501e10i −0.494152 + 0.285299i −0.726295 0.687383i \(-0.758759\pi\)
0.232143 + 0.972682i \(0.425426\pi\)
\(510\) 0 0
\(511\) −1.15694e11 + 2.00388e11i −1.69679 + 2.93893i
\(512\) 3.01455e9i 0.0438674i
\(513\) 0 0
\(514\) −4.80111e10 −0.687843
\(515\) −4.06205e10 2.34522e10i −0.577452 0.333392i
\(516\) 0 0
\(517\) −9.26582e9 1.60489e10i −0.129695 0.224638i
\(518\) 9.09360e9 5.25019e9i 0.126304 0.0729216i
\(519\) 0 0
\(520\) 2.23794e10 3.87622e10i 0.306080 0.530146i
\(521\) 1.29094e11i 1.75208i −0.482238 0.876040i \(-0.660176\pi\)
0.482238 0.876040i \(-0.339824\pi\)
\(522\) 0 0
\(523\) 1.37220e11 1.83405 0.917024 0.398831i \(-0.130584\pi\)
0.917024 + 0.398831i \(0.130584\pi\)
\(524\) −2.52341e10 1.45689e10i −0.334705 0.193242i
\(525\) 0 0
\(526\) 1.12634e10 + 1.95087e10i 0.147138 + 0.254851i
\(527\) 6.94351e10 4.00884e10i 0.900195 0.519728i
\(528\) 0 0
\(529\) 9.81855e10 1.70062e11i 1.25379 2.17163i
\(530\) 7.75431e10i 0.982742i
\(531\) 0 0
\(532\) 5.22518e10 0.652311
\(533\) −8.15937e9 4.71081e9i −0.101099 0.0583696i
\(534\) 0 0
\(535\) −7.45424e10 1.29111e11i −0.909888 1.57597i
\(536\) 4.83188e10 2.78969e10i 0.585406 0.337984i
\(537\) 0 0
\(538\) −1.00910e10 + 1.74782e10i −0.120450 + 0.208625i
\(539\) 4.75944e10i 0.563898i
\(540\) 0 0
\(541\) −7.71547e10 −0.900686 −0.450343 0.892856i \(-0.648698\pi\)
−0.450343 + 0.892856i \(0.648698\pi\)
\(542\) 5.08128e10 + 2.93368e10i 0.588811 + 0.339950i
\(543\) 0 0
\(544\) −4.51014e10 7.81179e10i −0.514985 0.891980i
\(545\) 3.99676e10 2.30753e10i 0.453025 0.261554i
\(546\) 0 0
\(547\) 2.66534e10 4.61651e10i 0.297717 0.515661i −0.677896 0.735157i \(-0.737108\pi\)
0.975613 + 0.219497i \(0.0704415\pi\)
\(548\) 2.33821e10i 0.259276i
\(549\) 0 0
\(550\) 1.30082e9 0.0142157
\(551\) −5.11099e10 2.95083e10i −0.554497 0.320139i
\(552\) 0 0
\(553\) 1.05497e11 + 1.82727e11i 1.12808 + 1.95390i
\(554\) −5.91175e10 + 3.41315e10i −0.627592 + 0.362340i
\(555\) 0 0
\(556\) −1.01173e10 + 1.75237e10i −0.105868 + 0.183369i
\(557\) 1.56229e11i 1.62309i 0.584291 + 0.811544i \(0.301373\pi\)
−0.584291 + 0.811544i \(0.698627\pi\)
\(558\) 0 0
\(559\) −7.22912e10 −0.740352
\(560\) −3.26344e9 1.88415e9i −0.0331836 0.0191586i
\(561\) 0 0
\(562\) 1.03746e10 + 1.79693e10i 0.103998 + 0.180130i
\(563\) −4.20078e10 + 2.42532e10i −0.418116 + 0.241399i −0.694271 0.719714i \(-0.744273\pi\)
0.276155 + 0.961113i \(0.410940\pi\)
\(564\) 0 0
\(565\) −1.83030e10 + 3.17018e10i −0.179609 + 0.311093i
\(566\) 9.63228e9i 0.0938563i
\(567\) 0 0
\(568\) −5.49811e8 −0.00528227
\(569\) −4.20475e10 2.42762e10i −0.401136 0.231596i 0.285838 0.958278i \(-0.407728\pi\)
−0.686974 + 0.726682i \(0.741061\pi\)
\(570\) 0 0
\(571\) −8.27408e10 1.43311e11i −0.778351 1.34814i −0.932892 0.360156i \(-0.882723\pi\)
0.154541 0.987986i \(-0.450610\pi\)
\(572\) 8.56791e9 4.94668e9i 0.0800370 0.0462094i
\(573\) 0 0
\(574\) −1.13914e10 + 1.97306e10i −0.104938 + 0.181757i
\(575\) 1.95644e10i 0.178977i
\(576\) 0 0
\(577\) −1.25738e11 −1.13439 −0.567194 0.823584i \(-0.691971\pi\)
−0.567194 + 0.823584i \(0.691971\pi\)
\(578\) 4.59997e9 + 2.65579e9i 0.0412139 + 0.0237948i
\(579\) 0 0
\(580\) −3.58795e10 6.21451e10i −0.317055 0.549155i
\(581\) −2.23499e11 + 1.29037e11i −1.96142 + 1.13243i
\(582\) 0 0
\(583\) 2.26612e10 3.92503e10i 0.196159 0.339757i
\(584\) 2.16366e11i 1.86011i
\(585\) 0 0
\(586\) 1.21766e11 1.03261
\(587\) 5.90985e10 + 3.41205e10i 0.497765 + 0.287385i 0.727790 0.685800i \(-0.240548\pi\)
−0.230025 + 0.973185i \(0.573881\pi\)
\(588\) 0 0
\(589\) 3.52168e10 + 6.09973e10i 0.292610 + 0.506815i
\(590\) 6.46646e10 3.73341e10i 0.533653 0.308105i
\(591\) 0 0
\(592\) 1.70926e8 2.96052e8i 0.00139162 0.00241036i
\(593\) 2.22279e10i 0.179755i 0.995953 + 0.0898774i \(0.0286475\pi\)
−0.995953 + 0.0898774i \(0.971352\pi\)
\(594\) 0 0
\(595\) −2.27074e11 −1.81175
\(596\) −2.03487e10 1.17483e10i −0.161269 0.0931088i
\(597\) 0 0
\(598\) 4.79314e10 + 8.30195e10i 0.374813 + 0.649196i
\(599\) 1.84741e11 1.06660e11i 1.43501 0.828503i 0.437513 0.899212i \(-0.355859\pi\)
0.997497 + 0.0707089i \(0.0225261\pi\)
\(600\) 0 0
\(601\) −1.74980e10 + 3.03074e10i −0.134119 + 0.232301i −0.925261 0.379332i \(-0.876154\pi\)
0.791142 + 0.611633i \(0.209487\pi\)
\(602\) 1.74811e11i 1.33101i
\(603\) 0 0
\(604\) 2.66617e10 0.200327
\(605\) 1.04110e11 + 6.01082e10i 0.777093 + 0.448655i
\(606\) 0 0
\(607\) 5.53846e10 + 9.59289e10i 0.407975 + 0.706634i 0.994663 0.103179i \(-0.0329015\pi\)
−0.586687 + 0.809814i \(0.699568\pi\)
\(608\) 6.86250e10 3.96207e10i 0.502190 0.289939i
\(609\) 0 0
\(610\) −3.53736e10 + 6.12688e10i −0.255481 + 0.442507i
\(611\) 9.72710e10i 0.697940i
\(612\) 0 0
\(613\) −4.84434e10 −0.343078 −0.171539 0.985177i \(-0.554874\pi\)
−0.171539 + 0.985177i \(0.554874\pi\)
\(614\) −4.25899e10 2.45893e10i −0.299663 0.173011i
\(615\) 0 0
\(616\) −3.16301e10 5.47849e10i −0.219673 0.380485i
\(617\) 6.64633e10 3.83726e10i 0.458607 0.264777i −0.252851 0.967505i \(-0.581368\pi\)
0.711459 + 0.702728i \(0.248035\pi\)
\(618\) 0 0
\(619\) 1.05958e11 1.83524e11i 0.721721 1.25006i −0.238589 0.971121i \(-0.576685\pi\)
0.960310 0.278936i \(-0.0899818\pi\)
\(620\) 8.56410e10i 0.579582i
\(621\) 0 0
\(622\) −2.69368e10 −0.179964
\(623\) 1.76658e11 + 1.01993e11i 1.17268 + 0.677048i
\(624\) 0 0
\(625\) 6.83063e10 + 1.18310e11i 0.447652 + 0.775356i
\(626\) −4.45216e10 + 2.57045e10i −0.289917 + 0.167383i
\(627\) 0 0
\(628\) 5.61953e10 9.73330e10i 0.361294 0.625780i
\(629\) 2.05996e10i 0.131600i
\(630\) 0 0
\(631\) −1.44761e10 −0.0913130 −0.0456565 0.998957i \(-0.514538\pi\)
−0.0456565 + 0.998957i \(0.514538\pi\)
\(632\) 1.70864e11 + 9.86481e10i 1.07098 + 0.618330i
\(633\) 0 0
\(634\) 7.70182e10 + 1.33400e11i 0.476691 + 0.825652i
\(635\) 1.84449e11 1.06492e11i 1.13444 0.654969i
\(636\) 0 0
\(637\) 1.24909e11 2.16349e11i 0.758642 1.31401i
\(638\) 2.70210e10i 0.163087i
\(639\) 0 0
\(640\) 9.41593e10 0.561233
\(641\) 2.06878e10 + 1.19441e10i 0.122541 + 0.0707494i 0.560018 0.828481i \(-0.310794\pi\)
−0.437476 + 0.899230i \(0.644128\pi\)
\(642\) 0 0
\(643\) −7.57675e10 1.31233e11i −0.443240 0.767714i 0.554688 0.832059i \(-0.312838\pi\)
−0.997928 + 0.0643445i \(0.979504\pi\)
\(644\) −3.11607e11 + 1.79907e11i −1.81161 + 1.04593i
\(645\) 0 0
\(646\) −3.30202e10 + 5.71927e10i −0.189605 + 0.328406i
\(647\) 1.51614e11i 0.865208i 0.901584 + 0.432604i \(0.142405\pi\)
−0.901584 + 0.432604i \(0.857595\pi\)
\(648\) 0 0
\(649\) 4.36420e10 0.245995
\(650\) 5.91313e9 + 3.41395e9i 0.0331256 + 0.0191251i
\(651\) 0 0
\(652\) 1.48659e10 + 2.57485e10i 0.0822624 + 0.142483i
\(653\) −1.58425e11 + 9.14665e10i −0.871305 + 0.503048i −0.867782 0.496946i \(-0.834455\pi\)
−0.00352329 + 0.999994i \(0.501122\pi\)
\(654\) 0 0
\(655\) −5.56191e10 + 9.63351e10i −0.302175 + 0.523383i
\(656\) 7.41722e8i 0.00400521i
\(657\) 0 0
\(658\) −2.35216e11 −1.25477
\(659\) 2.57869e11 + 1.48881e11i 1.36728 + 0.789398i 0.990580 0.136938i \(-0.0437260\pi\)
0.376698 + 0.926336i \(0.377059\pi\)
\(660\) 0 0
\(661\) −5.59595e10 9.69247e10i −0.293135 0.507725i 0.681414 0.731898i \(-0.261365\pi\)
−0.974549 + 0.224173i \(0.928032\pi\)
\(662\) −6.42686e10 + 3.71055e10i −0.334631 + 0.193199i
\(663\) 0 0
\(664\) −1.20660e11 + 2.08989e11i −0.620712 + 1.07511i
\(665\) 1.99480e11i 1.02003i
\(666\) 0 0
\(667\) 4.06397e11 2.05328
\(668\) −7.54226e10 4.35452e10i −0.378787 0.218693i
\(669\) 0 0
\(670\) −4.02764e10 6.97607e10i −0.199872 0.346188i
\(671\) −3.58103e10 + 2.06751e10i −0.176652 + 0.101990i
\(672\) 0 0
\(673\) 2.33548e10 4.04517e10i 0.113845 0.197186i −0.803472 0.595342i \(-0.797016\pi\)
0.917318 + 0.398156i \(0.130350\pi\)
\(674\) 4.71220e10i 0.228341i
\(675\) 0 0
\(676\) −7.50749e10 −0.359507
\(677\) −1.48801e11 8.59105e10i −0.708357 0.408970i 0.102095 0.994775i \(-0.467445\pi\)
−0.810452 + 0.585804i \(0.800779\pi\)
\(678\) 0 0
\(679\) 1.94546e11 + 3.36963e11i 0.915256 + 1.58527i
\(680\) −1.83884e11 + 1.06166e11i −0.860022 + 0.496534i
\(681\) 0 0
\(682\) 1.61241e10 2.79278e10i 0.0745313 0.129092i
\(683\) 6.74141e10i 0.309790i 0.987931 + 0.154895i \(0.0495040\pi\)
−0.987931 + 0.154895i \(0.950496\pi\)
\(684\) 0 0
\(685\) −8.92650e10 −0.405433
\(686\) −3.02685e11 1.74755e11i −1.36677 0.789103i
\(687\) 0 0
\(688\) 2.84558e9 + 4.92869e9i 0.0127004 + 0.0219977i
\(689\) 2.06021e11 1.18946e11i 0.914187 0.527806i
\(690\) 0 0
\(691\) −3.43078e10 + 5.94228e10i −0.150481 + 0.260640i −0.931404 0.363987i \(-0.881415\pi\)
0.780924 + 0.624626i \(0.214749\pi\)
\(692\) 9.45277e10i 0.412225i
\(693\) 0 0
\(694\) 4.87953e10 0.210349
\(695\) 6.68995e10 + 3.86244e10i 0.286737 + 0.165548i
\(696\) 0 0
\(697\) 2.23477e10 + 3.87073e10i 0.0946894 + 0.164007i
\(698\) 2.06426e11 1.19180e11i 0.869644 0.502089i
\(699\) 0 0
\(700\) −1.28140e10 + 2.21945e10i −0.0533694 + 0.0924385i
\(701\) 3.47803e11i 1.44033i −0.693804 0.720164i \(-0.744066\pi\)
0.693804 0.720164i \(-0.255934\pi\)
\(702\) 0 0
\(703\) 1.80963e10 0.0740916
\(704\) −3.25292e10 1.87808e10i −0.132429 0.0764580i
\(705\) 0 0
\(706\) 3.96014e10 + 6.85916e10i 0.159401 + 0.276091i
\(707\) 2.19202e11 1.26556e11i 0.877337 0.506531i
\(708\) 0 0
\(709\) 1.32405e11 2.29332e11i 0.523986 0.907570i −0.475624 0.879648i \(-0.657778\pi\)
0.999610 0.0279213i \(-0.00888879\pi\)
\(710\) 7.93795e8i 0.00312374i
\(711\) 0 0
\(712\) 1.90743e11 0.742215
\(713\) −4.20036e11 2.42508e11i −1.62528 0.938357i
\(714\) 0 0
\(715\) −1.88848e10 3.27094e10i −0.0722583 0.125155i
\(716\) −5.64734e10 + 3.26049e10i −0.214878 + 0.124060i
\(717\) 0 0
\(718\) 3.95728e10 6.85421e10i 0.148901 0.257905i
\(719\) 2.48269e11i 0.928981i −0.885578 0.464491i \(-0.846237\pi\)
0.885578 0.464491i \(-0.153763\pi\)
\(720\) 0 0
\(721\) −3.47965e11 −1.28764
\(722\) 9.70643e10 + 5.60401e10i 0.357199 + 0.206229i
\(723\) 0 0
\(724\) −8.57995e10 1.48609e11i −0.312270 0.540868i
\(725\) 2.50679e10 1.44730e10i 0.0907333 0.0523849i
\(726\) 0 0
\(727\) −1.47750e11 + 2.55911e11i −0.528921 + 0.916117i 0.470511 + 0.882394i \(0.344070\pi\)
−0.999431 + 0.0337230i \(0.989264\pi\)
\(728\) 3.32047e11i 1.18215i
\(729\) 0 0
\(730\) 3.12380e11 1.10000
\(731\) 2.96997e11 + 1.71472e11i 1.04012 + 0.600513i
\(732\) 0 0
\(733\) −2.13954e11 3.70578e11i −0.741146 1.28370i −0.951974 0.306179i \(-0.900949\pi\)
0.210828 0.977523i \(-0.432384\pi\)
\(734\) −1.20485e11 + 6.95618e10i −0.415095 + 0.239655i
\(735\) 0 0
\(736\) −2.72834e11 + 4.72562e11i −0.929794 + 1.61045i
\(737\) 4.70814e10i 0.159580i
\(738\) 0 0
\(739\) −1.19830e10 −0.0401781 −0.0200890 0.999798i \(-0.506395\pi\)
−0.0200890 + 0.999798i \(0.506395\pi\)
\(740\) 1.90556e10 + 1.10018e10i 0.0635471 + 0.0366889i
\(741\) 0 0
\(742\) −2.87630e11 4.98190e11i −0.948896 1.64354i
\(743\) 2.40378e11 1.38782e11i 0.788749 0.455384i −0.0507731 0.998710i \(-0.516169\pi\)
0.839522 + 0.543326i \(0.182835\pi\)
\(744\) 0 0
\(745\) −4.48511e10 + 7.76844e10i −0.145595 + 0.252179i
\(746\) 2.18042e11i 0.704020i
\(747\) 0 0
\(748\) −4.69332e10 −0.149925
\(749\) −9.57823e11 5.52999e11i −3.04339 1.75710i
\(750\) 0 0
\(751\) −7.24572e9 1.25499e10i −0.0227783 0.0394532i 0.854412 0.519597i \(-0.173918\pi\)
−0.877190 + 0.480144i \(0.840585\pi\)
\(752\) −6.63176e9 + 3.82885e9i −0.0207376 + 0.0119728i
\(753\) 0 0
\(754\) −7.09154e10 + 1.22829e11i −0.219409 + 0.380028i
\(755\) 1.01785e11i 0.313254i
\(756\) 0 0
\(757\) 1.94269e11 0.591590 0.295795 0.955251i \(-0.404415\pi\)
0.295795 + 0.955251i \(0.404415\pi\)
\(758\) 1.62132e11 + 9.36067e10i 0.491123 + 0.283550i
\(759\) 0 0
\(760\) −9.32644e10 1.61539e11i −0.279551 0.484197i
\(761\) −3.88024e11 + 2.24026e11i −1.15696 + 0.667974i −0.950575 0.310496i \(-0.899505\pi\)
−0.206390 + 0.978470i \(0.566172\pi\)
\(762\) 0 0
\(763\) 1.71186e11 2.96503e11i 0.505092 0.874845i
\(764\) 2.78264e11i 0.816740i
\(765\) 0 0
\(766\) 1.49205e11 0.433379
\(767\) 1.98383e11 + 1.14537e11i 0.573223 + 0.330950i
\(768\) 0 0
\(769\) −1.13694e11 1.96924e11i −0.325113 0.563111i 0.656423 0.754393i \(-0.272069\pi\)
−0.981535 + 0.191282i \(0.938736\pi\)
\(770\) −7.90961e10 + 4.56662e10i −0.225005 + 0.129907i
\(771\) 0 0
\(772\) 5.58386e10 9.67152e10i 0.157205 0.272286i
\(773\) 3.48003e11i 0.974686i −0.873211 0.487343i \(-0.837966\pi\)
0.873211 0.487343i \(-0.162034\pi\)
\(774\) 0 0
\(775\) −3.45457e10 −0.0957605
\(776\) 3.15087e11 + 1.81915e11i 0.868926 + 0.501675i
\(777\) 0 0
\(778\) 8.40657e10 + 1.45606e11i 0.229457 + 0.397431i
\(779\) −3.40036e10 + 1.96320e10i −0.0923368 + 0.0533107i
\(780\) 0 0
\(781\) −2.31978e8 + 4.01798e8i −0.000623509 + 0.00107995i
\(782\) 4.54764e11i 1.21607i
\(783\) 0 0
\(784\) −1.96671e10 −0.0520566
\(785\) −3.71585e11 2.14534e11i −0.978541 0.564961i
\(786\) 0 0
\(787\) −1.27120e11 2.20178e11i −0.331370 0.573950i 0.651411 0.758725i \(-0.274178\pi\)
−0.982781 + 0.184775i \(0.940844\pi\)
\(788\) 2.45317e11 1.41634e11i 0.636242 0.367334i
\(789\) 0 0
\(790\) 1.42424e11 2.46686e11i 0.365658 0.633338i
\(791\) 2.71565e11i 0.693695i
\(792\) 0 0
\(793\) −2.17044e11 −0.548851
\(794\) −3.15672e11 1.82253e11i −0.794243 0.458557i
\(795\) 0 0
\(796\) 1.48143e11 + 2.56590e11i 0.369001 + 0.639128i
\(797\) 4.79540e11 2.76863e11i 1.18848 0.686169i 0.230519 0.973068i \(-0.425958\pi\)
0.957961 + 0.286898i \(0.0926242\pi\)
\(798\) 0 0
\(799\) −2.30722e11 + 3.99623e11i −0.566112 + 0.980535i
\(800\) 3.88656e10i 0.0948866i
\(801\) 0 0
\(802\) 3.09854e10 0.0748962
\(803\) 1.58119e11 + 9.12899e10i 0.380296 + 0.219564i
\(804\) 0 0
\(805\) 6.86823e11 + 1.18961e12i 1.63554 + 2.83284i
\(806\) 1.46591e11 8.46342e10i 0.347349 0.200542i
\(807\) 0 0
\(808\) 1.18340e11 2.04971e11i 0.277642 0.480891i
\(809\) 1.00027e11i 0.233519i 0.993160 + 0.116759i \(0.0372506\pi\)
−0.993160 + 0.116759i \(0.962749\pi\)
\(810\) 0 0
\(811\) 9.06002e10 0.209433 0.104717 0.994502i \(-0.466606\pi\)
0.104717 + 0.994502i \(0.466606\pi\)
\(812\) −4.61029e11 2.66175e11i −1.06048 0.612271i
\(813\) 0 0
\(814\) −4.14273e9 7.17542e9i −0.00943602 0.0163437i
\(815\) 9.82992e10 5.67531e10i 0.222802 0.128635i
\(816\) 0 0
\(817\) −1.50634e11 + 2.60906e11i −0.338092 + 0.585593i
\(818\) 5.79726e10i 0.129482i
\(819\) 0 0
\(820\) −4.77415e10 −0.105594
\(821\) 5.36582e11 + 3.09796e11i 1.18104 + 0.681871i 0.956254 0.292538i \(-0.0944997\pi\)
0.224782 + 0.974409i \(0.427833\pi\)
\(822\) 0 0
\(823\) −1.81861e10 3.14993e10i −0.0396407 0.0686597i 0.845524 0.533937i \(-0.179288\pi\)
−0.885165 + 0.465277i \(0.845955\pi\)
\(824\) −2.81782e11 + 1.62687e11i −0.611231 + 0.352894i
\(825\) 0 0
\(826\) 2.76967e11 4.79720e11i 0.594987 1.03055i
\(827\) 6.85214e10i 0.146489i 0.997314 + 0.0732444i \(0.0233353\pi\)
−0.997314 + 0.0732444i \(0.976665\pi\)
\(828\) 0 0
\(829\) −6.13133e11 −1.29819 −0.649093 0.760709i \(-0.724851\pi\)
−0.649093 + 0.760709i \(0.724851\pi\)
\(830\) 3.01730e11 + 1.74204e11i 0.635778 + 0.367067i
\(831\) 0 0
\(832\) −9.85786e10 1.70743e11i −0.205726 0.356328i
\(833\) −1.02634e12 + 5.92558e11i −2.13163 + 1.23070i
\(834\) 0 0
\(835\) −1.66241e11 + 2.87938e11i −0.341973 + 0.592315i
\(836\) 4.12299e10i 0.0844087i
\(837\) 0 0
\(838\) 2.41985e11 0.490695
\(839\) 3.19993e11 + 1.84748e11i 0.645792 + 0.372848i 0.786842 0.617154i \(-0.211715\pi\)
−0.141050 + 0.990002i \(0.545048\pi\)
\(840\) 0 0
\(841\) 5.05133e10 + 8.74916e10i 0.100977 + 0.174897i
\(842\) 1.01215e11 5.84364e10i 0.201370 0.116261i
\(843\) 0 0
\(844\) −1.24479e10 + 2.15605e10i −0.0245317 + 0.0424901i
\(845\) 2.86610e11i 0.562167i
\(846\) 0 0
\(847\) 8.91836e11 1.73281
\(848\) −1.62191e10 9.36411e9i −0.0313649 0.0181085i
\(849\) 0 0
\(850\) −1.61955e10 2.80514e10i −0.0310254 0.0537376i
\(851\) −1.07919e11 + 6.23069e10i −0.205768 + 0.118800i
\(852\) 0 0
\(853\) −1.02690e11 + 1.77864e11i −0.193969 + 0.335963i −0.946562 0.322522i \(-0.895469\pi\)
0.752593 + 0.658486i \(0.228803\pi\)
\(854\) 5.24844e11i 0.986730i
\(855\) 0 0
\(856\) −1.03419e12 −1.92623
\(857\) 4.89607e11 + 2.82675e11i 0.907662 + 0.524039i 0.879678 0.475570i \(-0.157758\pi\)
0.0279838 + 0.999608i \(0.491091\pi\)
\(858\) 0 0
\(859\) −3.17033e10 5.49116e10i −0.0582279 0.100854i 0.835442 0.549579i \(-0.185212\pi\)
−0.893670 + 0.448725i \(0.851878\pi\)
\(860\) −3.17239e11 + 1.83158e11i −0.579952 + 0.334836i
\(861\) 0 0
\(862\) 3.22618e11 5.58791e11i 0.584332 1.01209i
\(863\) 7.20037e11i 1.29811i 0.760742 + 0.649055i \(0.224835\pi\)
−0.760742 + 0.649055i \(0.775165\pi\)
\(864\) 0 0
\(865\) 3.60875e11 0.644602
\(866\) 4.64705e11 + 2.68298e11i 0.826240 + 0.477030i
\(867\) 0 0
\(868\) 3.17668e11 + 5.50217e11i 0.559621 + 0.969293i
\(869\) 1.44183e11 8.32439e10i 0.252833 0.145973i
\(870\) 0 0
\(871\) 1.23563e11 2.14018e11i 0.214692 0.371858i
\(872\) 3.20145e11i 0.553707i
\(873\) 0 0
\(874\) 3.99501e11 0.684655
\(875\) 9.71377e11 + 5.60825e11i 1.65713 + 0.956742i
\(876\) 0 0
\(877\) −2.43477e11 4.21715e11i −0.411586 0.712887i 0.583478 0.812129i \(-0.301692\pi\)
−0.995063 + 0.0992421i \(0.968358\pi\)
\(878\) −3.71184e10 + 2.14303e10i −0.0624612 + 0.0360620i
\(879\) 0 0
\(880\) −1.48671e9 + 2.57506e9i −0.00247911 + 0.00429395i
\(881\) 1.10625e12i 1.83633i 0.396196 + 0.918166i \(0.370330\pi\)
−0.396196 + 0.918166i \(0.629670\pi\)
\(882\) 0 0
\(883\) 7.45262e10 0.122593 0.0612966 0.998120i \(-0.480476\pi\)
0.0612966 + 0.998120i \(0.480476\pi\)
\(884\) −2.13344e11 1.23174e11i −0.349359 0.201702i
\(885\) 0 0
\(886\) 6.04667e10 + 1.04731e11i 0.0981254 + 0.169958i
\(887\) 1.00427e12 5.79818e11i 1.62240 0.936692i 0.636123 0.771588i \(-0.280537\pi\)
0.986276 0.165105i \(-0.0527962\pi\)
\(888\) 0 0
\(889\) 7.90018e11 1.36835e12i 1.26482 2.19074i
\(890\) 2.75387e11i 0.438919i
\(891\) 0 0
\(892\) −9.54693e10 −0.150801
\(893\) −3.51060e11 2.02685e11i −0.552047 0.318724i
\(894\) 0 0
\(895\) 1.24475e11 + 2.15596e11i 0.193994 + 0.336008i
\(896\) 6.04944e11 3.49265e11i 0.938606 0.541904i
\(897\) 0 0
\(898\) −1.59199e11 + 2.75740e11i −0.244813 + 0.424028i
\(899\) 7.17591e11i 1.09860i
\(900\) 0 0
\(901\) −1.12854e12 −1.71245
\(902\) 1.55686e10 + 8.98856e9i 0.0235193 + 0.0135789i
\(903\) 0 0
\(904\) 1.26967e11 + 2.19914e11i 0.190116 + 0.329290i
\(905\) −5.67339e11 + 3.27553e11i −0.845762 + 0.488301i
\(906\) 0 0
\(907\) −6.30868e11 + 1.09270e12i −0.932201 + 1.61462i −0.152650 + 0.988280i \(0.548781\pi\)
−0.779551 + 0.626339i \(0.784553\pi\)
\(908\) 4.61567e11i 0.679034i
\(909\) 0 0
\(910\) −4.79396e11 −0.699083
\(911\) −6.43775e11 3.71684e11i −0.934675 0.539635i −0.0463878 0.998924i \(-0.514771\pi\)
−0.888287 + 0.459289i \(0.848104\pi\)
\(912\) 0 0
\(913\) 1.01818e11 + 1.76355e11i 0.146536 + 0.253807i
\(914\) −7.20248e10 + 4.15835e10i −0.103204 + 0.0595849i
\(915\) 0 0
\(916\) 2.95013e11 5.10977e11i 0.419043 0.725804i
\(917\) 8.25230e11i 1.16707i
\(918\) 0 0
\(919\) −8.99130e10 −0.126055 −0.0630276 0.998012i \(-0.520076\pi\)
−0.0630276 + 0.998012i \(0.520076\pi\)
\(920\) 1.11238e12 + 6.42232e11i 1.55275 + 0.896481i
\(921\) 0 0
\(922\) 1.59761e11 + 2.76715e11i 0.221079 + 0.382921i
\(923\) −2.10900e9 + 1.21763e9i −0.00290583 + 0.00167768i
\(924\) 0 0
\(925\) −4.43786e9 + 7.68660e9i −0.00606187 + 0.0104995i
\(926\) 2.75962e11i 0.375323i
\(927\) 0 0
\(928\) −8.07325e11 −1.08857
\(929\) −7.43680e11 4.29364e11i −0.998442 0.576451i −0.0906554 0.995882i \(-0.528896\pi\)
−0.907787 + 0.419431i \(0.862230\pi\)
\(930\) 0 0
\(931\) −5.20550e11 9.01620e11i −0.692890 1.20012i
\(932\) 5.07483e11 2.92995e11i 0.672602 0.388327i
\(933\) 0 0
\(934\) −1.30549e11 + 2.26117e11i −0.171548 + 0.297129i
\(935\) 1.79175e11i 0.234440i
\(936\) 0 0
\(937\) 1.25416e11 0.162702 0.0813512 0.996685i \(-0.474076\pi\)
0.0813512 + 0.996685i \(0.474076\pi\)
\(938\) −5.17526e11 2.98794e11i −0.668530 0.385976i
\(939\) 0 0
\(940\) −2.46447e11 4.26858e11i −0.315654 0.546729i
\(941\) −8.77244e11 + 5.06477e11i −1.11882 + 0.645954i −0.941101 0.338127i \(-0.890207\pi\)
−0.177724 + 0.984080i \(0.556873\pi\)
\(942\) 0 0
\(943\) 1.35189e11 2.34154e11i 0.170960 0.296111i
\(944\) 1.80339e10i 0.0227092i
\(945\) 0 0
\(946\) 1.37937e11 0.172233
\(947\) −2.58946e11 1.49503e11i −0.321966 0.185887i 0.330303 0.943875i \(-0.392849\pi\)
−0.652269 + 0.757988i \(0.726183\pi\)
\(948\) 0 0
\(949\) 4.79173e11 + 8.29952e11i 0.590782 + 1.02326i
\(950\) 2.46425e10 1.42274e10i 0.0302546 0.0174675i
\(951\) 0 0
\(952\) −7.87600e11 + 1.36416e12i −0.958866 + 1.66080i
\(953\) 9.57954e11i 1.16138i 0.814126 + 0.580688i \(0.197217\pi\)
−0.814126 + 0.580688i \(0.802783\pi\)
\(954\) 0 0
\(955\) 1.06232e12 1.27715
\(956\) 7.14301e10 + 4.12402e10i 0.0855165 + 0.0493730i
\(957\) 0 0
\(958\) −1.11235e10 1.92665e10i −0.0132063 0.0228740i
\(959\) −5.73500e11 + 3.31110e11i −0.678045 + 0.391470i
\(960\) 0 0
\(961\) −1.75995e9 + 3.04832e9i −0.00206351 + 0.00357410i
\(962\) 4.34896e10i 0.0507792i
\(963\) 0 0
\(964\) −1.30612e11 −0.151243
\(965\) −3.69226e11 2.13173e11i −0.425778 0.245823i
\(966\) 0 0
\(967\) −5.92952e11 1.02702e12i −0.678131 1.17456i −0.975543 0.219808i \(-0.929457\pi\)
0.297412 0.954749i \(-0.403876\pi\)
\(968\) 7.22210e11 4.16968e11i 0.822549 0.474899i
\(969\) 0 0
\(970\) 2.62642e11 4.54909e11i 0.296672 0.513851i
\(971\) 5.47759e10i 0.0616187i 0.999525 + 0.0308093i \(0.00980847\pi\)
−0.999525 + 0.0308093i \(0.990192\pi\)
\(972\) 0 0
\(973\) 5.73077e11 0.639384
\(974\) −7.48106e11 4.31919e11i −0.831242 0.479918i
\(975\) 0 0
\(976\) 8.54343e9 + 1.47977e10i 0.00941527 + 0.0163077i
\(977\) −8.01165e11 + 4.62553e11i −0.879313 + 0.507672i −0.870432 0.492289i \(-0.836160\pi\)
−0.00888112 + 0.999961i \(0.502827\pi\)
\(978\) 0 0
\(979\) 8.04791e10 1.39394e11i 0.0876097 0.151744i
\(980\) 1.26589e12i 1.37243i
\(981\) 0 0
\(982\) −4.41116e10 −0.0474358
\(983\) −5.00770e11 2.89120e11i −0.536321 0.309645i 0.207266 0.978285i \(-0.433543\pi\)
−0.743586 + 0.668640i \(0.766877\pi\)
\(984\) 0 0
\(985\) −5.40709e11 9.36536e11i −0.574406 0.994900i
\(986\) 5.82690e11 3.36416e11i 0.616495 0.355934i
\(987\) 0 0
\(988\) 1.08206e11 1.87418e11i 0.113560 0.196691i
\(989\) 2.07458e12i 2.16843i
\(990\) 0 0
\(991\) −1.41284e11 −0.146487 −0.0732435 0.997314i \(-0.523335\pi\)
−0.0732435 + 0.997314i \(0.523335\pi\)
\(992\) 8.34419e11 + 4.81752e11i 0.861664 + 0.497482i
\(993\) 0 0
\(994\) 2.94442e9 + 5.09988e9i 0.00301616 + 0.00522414i
\(995\) 9.79575e11 5.65558e11i 0.999414 0.577012i
\(996\) 0 0
\(997\) 6.20994e11 1.07559e12i 0.628502 1.08860i −0.359351 0.933203i \(-0.617002\pi\)
0.987852 0.155395i \(-0.0496649\pi\)
\(998\) 2.77464e11i 0.279695i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 81.9.d.g.26.6 32
3.2 odd 2 inner 81.9.d.g.26.11 32
9.2 odd 6 81.9.b.b.80.6 16
9.4 even 3 inner 81.9.d.g.53.11 32
9.5 odd 6 inner 81.9.d.g.53.6 32
9.7 even 3 81.9.b.b.80.11 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.9.b.b.80.6 16 9.2 odd 6
81.9.b.b.80.11 yes 16 9.7 even 3
81.9.d.g.26.6 32 1.1 even 1 trivial
81.9.d.g.26.11 32 3.2 odd 2 inner
81.9.d.g.53.6 32 9.5 odd 6 inner
81.9.d.g.53.11 32 9.4 even 3 inner