LMFDB - Embedded newform 81.10.e.a.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,10,Mod(10,81)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, 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:	$41.7179027293$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	81.19
Dual form			81.10.e.a.64.12

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.82322 + 1.75551i) q^{2} +(-372.033 + 312.173i) q^{4} +(-203.603 - 1154.69i) q^{5} +(-440.948 - 369.999i) q^{7} +(2560.36 - 4434.68i) q^{8} +(3009.09 + 5211.90i) q^{10} +(-12328.1 + 69916.4i) q^{11} +(-143827. - 52348.7i) q^{13} +(2776.32 + 1010.50i) q^{14} +(38614.5 - 218993. i) q^{16} +(-164482. - 284892. i) q^{17} +(140625. - 243570. i) q^{19} +(436210. + 366024. i) q^{20} +(-63277.4 - 358864. i) q^{22} +(-821687. + 689477. i) q^{23} +(543480. - 197811. i) q^{25} +785607. q^{26} +279551. q^{28} +(-1.62591e6 + 591785. i) q^{29} +(4.00947e6 - 3.36434e6i) q^{31} +(653471. + 3.70602e6i) q^{32} +(1.29346e6 + 1.08535e6i) q^{34} +(-337456. + 584492. i) q^{35} +(3.24063e6 + 5.61294e6i) q^{37} +(-250677. + 1.42166e6i) q^{38} +(-5.64198e6 - 2.05351e6i) q^{40} +(1.80717e7 + 6.57754e6i) q^{41} +(-5.74575e6 + 3.25858e7i) q^{43} +(-1.72395e7 - 2.98597e7i) q^{44} +(2.75279e6 - 4.76797e6i) q^{46} +(2.17446e7 + 1.82459e7i) q^{47} +(-6.94979e6 - 3.94142e7i) q^{49} +(-2.27407e6 + 1.90817e6i) q^{50} +(6.98503e7 - 2.54234e7i) q^{52} +5.03334e7 q^{53} +8.32418e7 q^{55} +(-2.76981e6 + 1.00813e6i) q^{56} +(6.80326e6 - 5.70861e6i) q^{58} +(1.89454e7 + 1.07445e8i) q^{59} +(-3.81453e7 - 3.20077e7i) q^{61} +(-1.34324e7 + 2.32656e7i) q^{62} +(4.72694e7 + 8.18730e7i) q^{64} +(-3.11630e7 + 1.76734e8i) q^{65} +(1.99585e8 + 7.26431e7i) q^{67} +(1.50128e8 + 5.46423e7i) q^{68} +(601546. - 3.41154e6i) q^{70} +(1.75242e8 + 3.03528e8i) q^{71} +(1.92455e8 - 3.33341e8i) q^{73} +(-2.54838e7 - 2.13835e7i) q^{74} +(2.37187e7 + 1.34516e8i) q^{76} +(3.13051e7 - 2.62681e7i) q^{77} +(4.56193e7 - 1.66041e7i) q^{79} -2.60732e8 q^{80} -9.87104e7 q^{82} +(1.67411e8 - 6.09326e7i) q^{83} +(-2.95473e8 + 2.47931e8i) q^{85} +(-2.94916e7 - 1.67255e8i) q^{86} +(2.78492e8 + 2.33682e8i) q^{88} +(3.40131e8 - 5.89124e8i) q^{89} +(4.40512e7 + 7.62990e7i) q^{91} +(9.04587e7 - 5.13017e8i) q^{92} +(-1.36910e8 - 4.98311e7i) q^{94} +(-3.09880e8 - 1.12787e8i) q^{95} +(2.16877e8 - 1.22997e9i) q^{97} +(1.02712e8 + 1.77903e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) $ 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−4.82322	+	1.75551i	−0.213158	+	0.0775832i	−0.446392	−	0.894837i	$-0.647291\pi$
$2$	−4.82322	+	1.75551i	−0.213158	+	0.0775832i	0.233234	+	0.972421i	$0.425069\pi$
$3$		0			0
$3$		0			0
$4$	−372.033	+	312.173i	−0.726627	+	0.609713i
$5$	−203.603	−	1154.69i	−0.145687	−	0.826230i	−0.966813	−	0.255484i	$-0.917765\pi$
$5$	−203.603	−	1154.69i	−0.145687	−	0.826230i	0.821127	−	0.570746i	$-0.193346\pi$
$6$		0			0
$7$	−440.948	−	369.999i	−0.0694139	−	0.0582452i	0.607421	−	0.794380i	$-0.292204\pi$
$7$	−440.948	−	369.999i	−0.0694139	−	0.0582452i	−0.676834	+	0.736135i	$0.736649\pi$
$8$	2560.36	−	4434.68i	0.221002	−	0.382787i
$9$		0			0
$10$	3009.09	+	5211.90i	0.0951558	+	0.164815i
$11$	−12328.1	+	69916.4i	−0.253881	+	1.43983i	0.545047	+	0.838405i	$0.316512\pi$
$11$	−12328.1	+	69916.4i	−0.253881	+	1.43983i	−0.798928	+	0.601426i	$0.794599\pi$
$12$		0			0
$13$	−143827.	−	52348.7i	−1.39667	−	0.508348i	−0.469485	−	0.882940i	$-0.655560\pi$
$13$	−143827.	−	52348.7i	−1.39667	−	0.508348i	−0.927190	+	0.374592i	$0.877783\pi$
$14$	2776.32	+	1010.50i	0.0193150	+	0.00703008i
$15$		0			0
$16$	38614.5	−	218993.i	0.147302	−	0.835394i
$17$	−164482.	−	284892.i	−0.477639	−	0.827294i	0.522033	−	0.852925i	$-0.325174\pi$
$17$	−164482.	−	284892.i	−0.477639	−	0.827294i	−0.999671	+	0.0256311i	$0.991840\pi$
$18$		0			0
$19$	140625.	−	243570.i	0.247555	−	0.428779i	−0.715292	−	0.698826i	$-0.753706\pi$
$19$	140625.	−	243570.i	0.247555	−	0.428779i	0.962847	+	0.270048i	$0.0870394\pi$
$20$	436210.	+	366024.i	0.609622	+	0.511534i
$21$		0			0
$22$	−63277.4	−	358864.i	−0.0575899	−	0.326609i
$23$	−821687.	+	689477.i	−0.612253	+	0.513741i	−0.895358	−	0.445348i	$-0.853080\pi$
$23$	−821687.	+	689477.i	−0.612253	+	0.513741i	0.283105	+	0.959089i	$0.408636\pi$
$24$		0			0
$25$	543480.	−	197811.i	0.278262	−	0.101279i
$26$	785607.			0.337152
$27$		0			0
$28$	279551.			0.0859508
$29$	−1.62591e6	+	591785.i	−0.426881	+	0.155372i	−0.546521	−	0.837445i	$-0.684048\pi$
$29$	−1.62591e6	+	591785.i	−0.426881	+	0.155372i	0.119640	+	0.992817i	$0.461826\pi$
$30$		0			0
$31$	4.00947e6	−	3.36434e6i	0.779756	−	0.654293i	−0.163431	−	0.986555i	$-0.552256\pi$
$31$	4.00947e6	−	3.36434e6i	0.779756	−	0.654293i	0.943187	+	0.332262i	$0.107812\pi$
$32$	653471.	+	3.70602e6i	0.110167	+	0.624788i
$33$		0			0
$34$	1.29346e6	+	1.08535e6i	0.165997	+	0.139288i
$35$	−337456.	+	584492.i	−0.0380112	+	0.0658373i
$36$		0			0
$37$	3.24063e6	+	5.61294e6i	0.284264	+	0.492360i	0.972430	−	0.233193i	$-0.0749175\pi$
$37$	3.24063e6	+	5.61294e6i	0.284264	+	0.492360i	−0.688167	+	0.725553i	$0.741584\pi$
$38$	−250677.	+	1.42166e6i	−0.0195024	+	0.110604i
$39$		0			0
$40$	−5.64198e6	−	2.05351e6i	−0.348467	−	0.126832i
$41$	1.80717e7	+	6.57754e6i	0.998781	+	0.363527i	0.789114	−	0.614246i	$-0.210540\pi$
$41$	1.80717e7	+	6.57754e6i	0.998781	+	0.363527i	0.209667	+	0.977773i	$0.432762\pi$
$42$		0			0
$43$	−5.74575e6	+	3.25858e7i	−0.256294	+	1.45352i	0.536434	+	0.843942i	$0.319771\pi$
$43$	−5.74575e6	+	3.25858e7i	−0.256294	+	1.45352i	−0.792728	+	0.609575i	$0.791340\pi$
$44$	−1.72395e7	−	2.98597e7i	−0.693407	−	1.20102i
$45$		0			0
$46$	2.75279e6	−	4.76797e6i	0.0906490	−	0.157009i
$47$	2.17446e7	+	1.82459e7i	0.649996	+	0.545412i	0.907070	−	0.420980i	$-0.138314\pi$
$47$	2.17446e7	+	1.82459e7i	0.649996	+	0.545412i	−0.257073	+	0.966392i	$0.582758\pi$
$48$		0			0
$49$	−6.94979e6	−	3.94142e7i	−0.172222	−	0.976722i
$50$	−2.27407e6	+	1.90817e6i	−0.0514562	+	0.0431769i
$51$		0			0
$52$	6.98503e7	−	2.54234e7i	1.32481	−	0.482191i
$53$	5.03334e7			0.876223			0.438112	−	0.898921i	$-0.355647\pi$
$53$	5.03334e7			0.876223			0.438112	+	0.898921i	$0.355647\pi$
$54$		0			0
$55$	8.32418e7			1.22662
$56$	−2.76981e6	+	1.00813e6i	−0.0376361	+	0.0136984i
$57$		0			0
$58$	6.80326e6	−	5.70861e6i	0.0789389	−	0.0662376i
$59$	1.89454e7	+	1.07445e8i	0.203549	+	1.15438i	0.899707	+	0.436495i	$0.143780\pi$
$59$	1.89454e7	+	1.07445e8i	0.203549	+	1.15438i	−0.696158	+	0.717889i	$0.745109\pi$
$60$		0			0
$61$	−3.81453e7	−	3.20077e7i	−0.352742	−	0.295985i	0.449148	−	0.893457i	$-0.351728\pi$
$61$	−3.81453e7	−	3.20077e7i	−0.352742	−	0.295985i	−0.801890	+	0.597472i	$0.796172\pi$
$62$	−1.34324e7	+	2.32656e7i	−0.115449	+	0.199964i
$63$		0			0
$64$	4.72694e7	+	8.18730e7i	0.352184	+	0.610001i
$65$	−3.11630e7	+	1.76734e8i	−0.216535	+	1.22803i
$66$		0			0
$67$	1.99585e8	+	7.26431e7i	1.21002	+	0.440411i	0.866710	−	0.498812i	$-0.166230\pi$
$67$	1.99585e8	+	7.26431e7i	1.21002	+	0.440411i	0.343308	+	0.939223i	$0.388453\pi$
$68$	1.50128e8	+	5.46423e7i	0.851477	+	0.309912i
$69$		0			0
$70$	601546.	−	3.41154e6i	0.00299452	−	0.0169828i
$71$	1.75242e8	+	3.03528e8i	0.818419	+	1.41754i	0.906847	+	0.421461i	$0.138482\pi$
$71$	1.75242e8	+	3.03528e8i	0.818419	+	1.41754i	−0.0884276	+	0.996083i	$0.528184\pi$
$72$		0			0
$73$	1.92455e8	−	3.33341e8i	0.793186	−	1.37384i	−0.130798	−	0.991409i	$-0.541754\pi$
$73$	1.92455e8	−	3.33341e8i	0.793186	−	1.37384i	0.923984	−	0.382430i	$-0.124913\pi$
$74$	−2.54838e7	−	2.13835e7i	−0.0987920	−	0.0828963i
$75$		0			0
$76$	2.37187e7	+	1.34516e8i	0.0815512	+	0.462500i
$77$	3.13051e7	−	2.62681e7i	0.101486	−	0.0851569i
$78$		0			0
$79$	4.56193e7	−	1.66041e7i	0.131773	−	0.0479615i	−0.275292	−	0.961361i	$-0.588774\pi$
$79$	4.56193e7	−	1.66041e7i	0.131773	−	0.0479615i	0.407065	+	0.913399i	$0.366552\pi$
$80$	−2.60732e8			−0.711687
$81$		0			0
$82$	−9.87104e7			−0.241102
$83$	1.67411e8	−	6.09326e7i	0.387197	−	0.140928i	−0.141084	−	0.989998i	$-0.545059\pi$
$83$	1.67411e8	−	6.09326e7i	0.387197	−	0.140928i	0.528281	+	0.849069i	$0.322837\pi$
$84$		0			0
$85$	−2.95473e8	+	2.47931e8i	−0.613949	+	0.515165i
$86$	−2.94916e7	−	1.67255e8i	−0.0581373	−	0.329713i
$87$		0			0
$88$	2.78492e8	+	2.33682e8i	0.495040	+	0.415388i
$89$	3.40131e8	−	5.89124e8i	0.574634	−	0.995295i	−0.421448	−	0.906853i	$-0.638478\pi$
$89$	3.40131e8	−	5.89124e8i	0.574634	−	0.995295i	0.996081	−	0.0884419i	$-0.0281887\pi$
$90$		0			0
$91$	4.40512e7	+	7.62990e7i	0.0673398	+	0.116636i
$92$	9.04587e7	−	5.13017e8i	0.131645	−	0.746597i
$93$		0			0
$94$	−1.36910e8	−	4.98311e7i	−0.180867	−	0.0658301i
$95$	−3.09880e8	−	1.12787e8i	−0.390335	−	0.142070i
$96$		0			0
$97$	2.16877e8	−	1.22997e9i	0.248737	−	1.41066i	−0.562913	−	0.826516i	$-0.690319\pi$
$97$	2.16877e8	−	1.22997e9i	0.248737	−	1.41066i	0.811650	−	0.584144i	$-0.198569\pi$
$98$	1.02712e8	+	1.77903e8i	0.112488	+	0.194835i
$99$		0			0
$100$	−1.40442e8	+	2.43252e8i	−0.140442	+	0.243252i
$101$	1.70877e8	+	1.43383e8i	0.163395	+	0.137104i	0.720819	−	0.693123i	$-0.243766\pi$
$101$	1.70877e8	+	1.43383e8i	0.163395	+	0.137104i	−0.557424	+	0.830228i	$0.688210\pi$
$102$		0			0
$103$	1.03428e8	+	5.86567e8i	0.0905460	+	0.513512i	0.996021	+	0.0891133i	$0.0284033\pi$
$103$	1.03428e8	+	5.86567e8i	0.0905460	+	0.513512i	−0.905476	+	0.424399i	$0.860486\pi$
$104$	−6.00399e8	+	5.03794e8i	−0.503257	+	0.422283i
$105$		0			0
$106$	−2.42769e8	+	8.83606e7i	−0.186774	+	0.0679802i
$107$	−1.08574e9			−0.800754			−0.400377	−	0.916351i	$-0.631121\pi$
$107$	−1.08574e9			−0.800754			−0.400377	+	0.916351i	$0.631121\pi$
$108$		0			0
$109$	−1.86453e9			−1.26517			−0.632587	−	0.774489i	$-0.718007\pi$
$109$	−1.86453e9			−1.26517			−0.632587	+	0.774489i	$0.718007\pi$
$110$	−4.01493e8	+	1.46132e8i	−0.261464	+	0.0951650i
$111$		0			0
$112$	−9.80544e7	+	8.22774e7i	−0.0588825	+	0.0494083i
$113$	2.47881e8	+	1.40580e9i	0.143018	+	0.811095i	0.968937	+	0.247307i	$0.0795455\pi$
$113$	2.47881e8	+	1.40580e9i	0.143018	+	0.811095i	−0.825919	+	0.563788i	$0.809343\pi$
$114$		0			0
$115$	9.63431e8	+	8.08414e8i	0.513665	+	0.431016i
$116$	4.20155e8	−	7.27730e8i	0.215451	−	0.373172i
$117$		0			0
$118$	−2.79997e8	−	4.84970e8i	−0.132949	−	0.230274i
$119$	−3.28816e7	+	1.86481e8i	−0.0150311	+	0.0852458i
$120$		0			0
$121$	−2.52057e9	−	9.17412e8i	−1.06897	−	0.389072i
$122$	2.40173e8	+	8.74158e7i	0.0981532	+	0.0357249i
$123$		0			0
$124$	−4.41398e8	+	2.50329e9i	−0.167661	+	0.950855i
$125$	−1.48409e9	−	2.57052e9i	−0.543707	−	0.941727i
$126$		0			0
$127$	2.21753e9	−	3.84088e9i	0.756402	−	1.31013i	−0.188272	−	0.982117i	$-0.560289\pi$
$127$	2.21753e9	−	3.84088e9i	0.756402	−	1.31013i	0.944674	−	0.328010i	$-0.106378\pi$
$128$	−1.84770e9	−	1.55040e9i	−0.608396	−	0.510505i
$129$		0			0
$130$	−1.59952e8	−	9.07134e8i	−0.0491185	−	0.278565i
$131$	1.64912e9	−	1.38378e9i	0.489251	−	0.410530i	−0.364507	−	0.931201i	$-0.618763\pi$
$131$	1.64912e9	−	1.38378e9i	0.489251	−	0.410530i	0.853758	+	0.520671i	$0.174318\pi$
$132$		0			0
$133$	−1.52129e8	+	5.53705e7i	−0.0421580	+	0.0153443i
$134$	−1.09017e9			−0.292094
$135$		0			0
$136$	−1.68454e9			−0.422236
$137$	−3.56983e9	+	1.29931e9i	−0.865775	+	0.315116i	−0.736455	−	0.676487i	$-0.763502\pi$
$137$	−3.56983e9	+	1.29931e9i	−0.865775	+	0.315116i	−0.129320	+	0.991603i	$0.541279\pi$
$138$		0			0
$139$	−4.78102e9	+	4.01175e9i	−1.08631	+	0.911523i	−0.996429	−	0.0844297i	$-0.973093\pi$
$139$	−4.78102e9	+	4.01175e9i	−1.08631	+	0.911523i	−0.0898811	+	0.995953i	$0.528649\pi$
$140$	−5.69175e7	−	3.22795e8i	−0.0125219	−	0.0710151i
$141$		0			0
$142$	−1.37808e9	−	1.15634e9i	−0.284430	−	0.238665i
$143$	5.43315e9	−	9.41050e9i	1.08653	−	1.88192i
$144$		0			0
$145$	1.01437e9	+	1.75694e9i	0.190564	+	0.330066i
$146$	−3.43067e8	+	1.94563e9i	−0.0624873	+	0.354383i
$147$		0			0
$148$	−2.95783e9	−	1.07656e9i	−0.506752	−	0.184443i
$149$	4.70352e9	+	1.71194e9i	0.781780	+	0.284545i	0.701915	−	0.712261i	$-0.252329\pi$
$149$	4.70352e9	+	1.71194e9i	0.781780	+	0.284545i	0.0798651	+	0.996806i	$0.474551\pi$
$150$		0			0
$151$	−5.60010e8	+	3.17597e9i	−0.0876595	+	0.497142i	0.909091	+	0.416597i	$0.136777\pi$
$151$	−5.60010e8	+	3.17597e9i	−0.0876595	+	0.497142i	−0.996751	+	0.0805453i	$0.974334\pi$
$152$	−7.20103e8	−	1.24726e9i	−0.109421	−	0.189522i
$153$		0			0
$154$	−1.04877e8	+	1.81653e8i	−0.0150258	+	0.0260255i
$155$	−4.70111e9	−	3.94470e9i	−0.654196	−	0.548936i
$156$		0			0
$157$	8.02176e8	+	4.54936e9i	0.105371	+	0.597589i	0.991071	+	0.133332i	$0.0425675\pi$
$157$	8.02176e8	+	4.54936e9i	0.105371	+	0.597589i	−0.885701	+	0.464257i	$0.846321\pi$
$158$	−1.90883e8	+	1.60170e8i	−0.0243675	+	0.0204468i
$159$		0			0
$160$	4.14626e9	−	1.50911e9i	0.500169	−	0.182047i
$161$	6.17427e8			0.0724218
$162$		0			0
$163$	4.02954e9			0.447107			0.223553	−	0.974692i	$-0.428234\pi$
$163$	4.02954e9			0.447107			0.223553	+	0.974692i	$0.428234\pi$
$164$	−8.77658e9	+	3.19442e9i	−0.947389	+	0.344821i
$165$		0			0
$166$	−7.00491e8	+	5.87782e8i	−0.0716006	+	0.0600800i
$167$	1.78494e9	+	1.01229e10i	0.177583	+	1.00712i	0.935120	+	0.354330i	$0.115291\pi$
$167$	1.78494e9	+	1.01229e10i	0.177583	+	1.00712i	−0.757538	+	0.652791i	$0.773598\pi$
$168$		0			0
$169$	9.82229e9	+	8.24188e9i	0.926238	+	0.777206i
$170$	9.89885e8	−	1.71453e9i	0.0909002	−	0.157444i
$171$		0			0
$172$	−8.03479e9	−	1.39167e10i	−0.699997	−	1.21243i
$173$	−1.57684e9	+	8.94273e9i	−0.133839	+	0.759037i	0.841823	+	0.539754i	$0.181483\pi$
$173$	−1.57684e9	+	8.94273e9i	−0.133839	+	0.759037i	−0.975661	+	0.219283i	$0.929628\pi$
$174$		0			0
$175$	−3.12836e8	−	1.13863e8i	−0.0252143	−	0.00917724i
$176$	1.48352e10	+	5.39956e9i	1.16543	+	0.424182i
$177$		0			0
$178$	−6.06314e8	+	3.43857e9i	−0.0452697	+	0.256737i
$179$	9.77182e9	+	1.69253e10i	0.711438	+	1.23225i	0.964318	+	0.264748i	$0.0852889\pi$
$179$	9.77182e9	+	1.69253e10i	0.711438	+	1.23225i	−0.252880	+	0.967498i	$0.581378\pi$
$180$		0			0
$181$	1.29853e10	−	2.24912e10i	0.899289	−	1.55761i	0.0708832	−	0.997485i	$-0.477418\pi$
$181$	1.29853e10	−	2.24912e10i	0.899289	−	1.55761i	0.828405	−	0.560129i	$-0.189248\pi$
$182$	−3.46412e8	−	2.90674e8i	−0.0234030	−	0.0196375i
$183$		0			0
$184$	9.53792e8	+	5.40922e9i	0.0613442	+	0.347900i
$185$	5.82140e9	−	4.88474e9i	0.365389	−	0.306597i
$186$		0			0
$187$	2.19464e10	−	7.98783e9i	1.31243	−	0.477685i
$188$	−1.37856e10			−0.804850
$189$		0			0
$190$	1.69262e9			0.0942253
$191$	−1.30602e10	+	4.75351e9i	−0.710065	+	0.258443i	−0.671702	−	0.740821i	$-0.734437\pi$
$191$	−1.30602e10	+	4.75351e9i	−0.710065	+	0.258443i	−0.0383631	+	0.999264i	$0.512214\pi$
$192$		0			0
$193$	−3.44582e8	+	2.89139e8i	−0.0178766	+	0.0150002i	−0.651682	−	0.758492i	$-0.725936\pi$
$193$	−3.44582e8	+	2.89139e8i	−0.0178766	+	0.0150002i	0.633806	+	0.773492i	$0.281492\pi$
$194$	1.11318e9	+	6.31315e9i	0.0564231	+	0.319991i
$195$		0			0
$196$	1.48896e10	+	1.24939e10i	0.720661	+	0.604706i
$197$	1.48978e10	−	2.58038e10i	0.704734	−	1.22063i	−0.262054	−	0.965053i	$-0.584400\pi$
$197$	1.48978e10	−	2.58038e10i	0.704734	−	1.22063i	0.966788	−	0.255581i	$-0.0822668\pi$
$198$		0			0
$199$	−1.10366e10	−	1.91160e10i	−0.498881	−	0.864086i	0.501119	−	0.865379i	$-0.332922\pi$
$199$	−1.10366e10	−	1.91160e10i	−0.498881	−	0.864086i	−0.999999	+	0.00129214i	$0.999589\pi$
$200$	5.14280e8	−	2.91663e9i	0.0227282	−	0.128898i
$201$		0			0
$202$	−1.07589e9	−	3.91591e8i	−0.0454659	−	0.0165482i
$203$	9.35904e8	+	3.40641e8i	0.0386811	+	0.0140788i
$204$		0			0
$205$	3.91558e9	−	2.22064e10i	0.154847	−	0.878184i
$206$	−1.52858e9	−	2.64757e9i	−0.0591405	−	0.102434i
$207$		0			0
$208$	−1.70178e10	+	2.94758e10i	−0.630404	+	1.09189i
$209$	1.52959e10	+	1.28348e10i	0.554519	+	0.465297i
$210$		0			0
$211$	1.04654e9	+	5.93525e9i	0.0363485	+	0.206143i	0.997573	−	0.0696232i	$-0.0221797\pi$
$211$	1.04654e9	+	5.93525e9i	0.0363485	+	0.206143i	−0.961225	+	0.275766i	$0.911069\pi$
$212$	−1.87257e10	+	1.57127e10i	−0.636688	+	0.534244i
$213$		0			0
$214$	5.23676e9	−	1.90602e9i	0.170687	−	0.0621250i
$215$	3.87964e10			1.23828
$216$		0			0
$217$	−3.01277e9			−0.0922353
$218$	8.99303e9	−	3.27320e9i	0.269682	−	0.0981562i
$219$		0			0
$220$	−3.09687e10	+	2.59858e10i	−0.891294	+	0.747885i
$221$	8.74328e9	+	4.95856e10i	0.246552	+	1.39827i
$222$		0			0
$223$	4.79845e10	+	4.02638e10i	1.29936	+	1.09029i	0.990255	+	0.139264i	$0.0444736\pi$
$223$	4.79845e10	+	4.02638e10i	1.29936	+	1.09029i	0.309104	+	0.951028i	$0.399971\pi$
$224$	1.08308e9	−	1.87595e9i	0.0287438	−	0.0497857i
$225$		0			0
$226$	−3.66348e9	−	6.34534e9i	−0.0934128	−	0.161796i
$227$	−2.56021e9	+	1.45197e10i	−0.0639969	+	0.362944i	0.935945	+	0.352147i	$0.114548\pi$
$227$	−2.56021e9	+	1.45197e10i	−0.0639969	+	0.362944i	−0.999942	+	0.0107977i	$0.996563\pi$
$228$		0			0
$229$	4.91315e9	+	1.78824e9i	0.118059	+	0.0429701i	0.400374	−	0.916352i	$-0.368880\pi$
$229$	4.91315e9	+	1.78824e9i	0.118059	+	0.0429701i	−0.282315	+	0.959322i	$0.591102\pi$
$230$	−6.06601e9	−	2.20785e9i	−0.142932	−	0.0520228i
$231$		0			0
$232$	−1.53856e9	+	8.72559e9i	−0.0348672	+	0.197742i
$233$	−3.50624e10	−	6.07298e10i	−0.779363	−	1.34990i	−0.932310	−	0.361661i	$-0.882210\pi$
$233$	−3.50624e10	−	6.07298e10i	−0.779363	−	1.34990i	0.152947	−	0.988234i	$-0.451124\pi$
$234$		0			0
$235$	1.66411e10	−	2.88232e10i	0.355940	−	0.616505i
$236$	−4.05896e10	−	3.40587e10i	−0.851747	−	0.714700i
$237$		0			0
$238$	−1.68774e8	−	9.57162e8i	−0.00340964	−	0.0193370i
$239$	4.76010e10	−	3.99420e10i	0.943681	−	0.791842i	−0.0345410	−	0.999403i	$-0.510997\pi$
$239$	4.76010e10	−	3.99420e10i	0.943681	−	0.791842i	0.978222	+	0.207561i	$0.0665525\pi$
$240$		0			0
$241$	−1.98105e10	+	7.21044e9i	−0.378285	+	0.137684i	−0.524163	−	0.851618i	$-0.675622\pi$
$241$	−1.98105e10	+	7.21044e9i	−0.378285	+	0.137684i	0.145878	+	0.989303i	$0.453399\pi$
$242$	1.37678e10			0.258045
$243$		0			0
$244$	2.41832e10			0.436778
$245$	−4.40963e10	+	1.60497e10i	−0.781906	+	0.284590i
$246$		0			0
$247$	−3.29763e10	+	2.76704e10i	−0.563723	+	0.473020i
$248$	−4.65408e9	−	2.63946e10i	−0.0781271	−	0.443081i
$249$		0			0
$250$	1.16706e10	+	9.79283e9i	0.188958	+	0.158554i
$251$	−2.25558e10	+	3.90679e10i	−0.358697	+	0.621281i	−0.987743	−	0.156087i	$-0.950112\pi$
$251$	−2.25558e10	+	3.90679e10i	−0.358697	+	0.621281i	0.629047	+	0.777368i	$0.283445\pi$
$252$		0			0
$253$	−3.80758e10	−	6.59493e10i	−0.584261	−	1.01197i
$254$	−3.95295e9	+	2.24183e10i	−0.0595894	+	0.337948i
$255$		0			0
$256$	−3.38512e10	−	1.23208e10i	−0.492599	−	0.179291i
$257$	7.93532e10	+	2.88822e10i	1.13466	+	0.412982i	0.839982	−	0.542614i	$-0.182565\pi$
$257$	7.93532e10	+	2.88822e10i	1.13466	+	0.412982i	0.294678	+	0.955597i	$0.404788\pi$
$258$		0			0
$259$	6.47833e8	−	3.67404e9i	0.00894570	−	0.0507336i
$260$	−4.35779e10	−	7.54792e10i	−0.591407	−	1.02435i
$261$		0			0
$262$	−5.52483e9	+	9.56929e9i	−0.0724375	+	0.125465i
$263$	−4.66786e10	−	3.91680e10i	−0.601612	−	0.504812i	0.290351	−	0.956920i	$-0.406228\pi$
$263$	−4.66786e10	−	3.91680e10i	−0.601612	−	0.504812i	−0.891963	+	0.452108i	$0.850672\pi$
$264$		0			0
$265$	−1.02480e10	−	5.81195e10i	−0.127654	−	0.723961i
$266$	6.36549e8	−	5.34128e8i	0.00779587	−	0.00654151i
$267$		0			0
$268$	−9.69295e10	+	3.52795e10i	−1.14776	+	0.417749i
$269$	1.46201e10			0.170242			0.0851209	−	0.996371i	$-0.472872\pi$
$269$	1.46201e10			0.170242			0.0851209	+	0.996371i	$0.472872\pi$
$270$		0			0
$271$	2.22347e10			0.250420			0.125210	−	0.992130i	$-0.460039\pi$
$271$	2.22347e10			0.250420			0.125210	+	0.992130i	$0.460039\pi$
$272$	−6.87409e10	+	2.50196e10i	−0.761474	+	0.277154i
$273$		0			0
$274$	1.49371e10	−	1.25337e10i	0.160099	−	0.134339i
$275$	7.13010e9	+	4.04368e10i	0.0751794	+	0.426363i
$276$		0			0
$277$	−1.16713e11	−	9.79335e10i	−1.19113	−	0.999476i	−0.999839	−	0.0179427i	$-0.994288\pi$
$277$	−1.16713e11	−	9.79335e10i	−1.19113	−	0.999476i	−0.191290	−	0.981534i	$-0.561267\pi$
$278$	1.60172e10	−	2.77427e10i	0.160837	−	0.278578i
$279$		0			0
$280$	1.72802e9	+	2.99302e9i	0.0168011	+	0.0291004i
$281$	8.09146e9	−	4.58890e10i	0.0774192	−	0.439066i	−0.921317	−	0.388812i	$-0.872886\pi$
$281$	8.09146e9	−	4.58890e10i	0.0774192	−	0.439066i	0.998736	−	0.0502543i	$-0.0160032\pi$
$282$		0			0
$283$	−1.08318e11	−	3.94245e10i	−1.00383	−	0.365365i	−0.212771	−	0.977102i	$-0.568249\pi$
$283$	−1.08318e11	−	3.94245e10i	−1.00383	−	0.365365i	−0.791061	+	0.611737i	$0.790471\pi$
$284$	−1.59949e11	−	5.82167e10i	−1.45898	−	0.531025i
$285$		0			0
$286$	−9.68508e9	+	5.49268e10i	−0.0855965	+	0.485442i
$287$	−5.53497e9	−	9.58685e9i	−0.0481556	−	0.0834080i
$288$		0			0
$289$	5.18499e9	−	8.98066e9i	0.0437227	−	0.0757300i
$290$	−7.97685e9	−	6.69337e9i	−0.0662278	−	0.0555717i
$291$		0			0
$292$	3.24606e10	+	1.84093e11i	0.261296	+	1.48188i
$293$	−1.29042e10	+	1.08279e10i	−0.102288	+	0.0858299i	−0.692497	−	0.721420i	$-0.743490\pi$
$293$	−1.29042e10	+	1.08279e10i	−0.102288	+	0.0858299i	0.590209	+	0.807250i	$0.299045\pi$
$294$		0			0
$295$	1.20208e11	−	4.37521e10i	0.924132	−	0.336356i
$296$	3.31887e10			0.251292
$297$		0			0
$298$	−2.56914e10			−0.188719
$299$	1.54274e11	−	5.61511e10i	1.11628	−	0.406292i
$300$		0			0
$301$	1.45903e10	−	1.22427e10i	0.102451	−	0.0859664i
$302$	−2.87440e9	−	1.63015e10i	−0.0198845	−	0.112771i
$303$		0			0
$304$	−4.79101e10	−	4.02014e10i	−0.321733	−	0.269966i
$305$	−2.91925e10	+	5.05629e10i	−0.193162	+	0.334567i
$306$		0			0
$307$	1.28073e11	+	2.21829e11i	0.822878	+	1.42527i	0.903531	+	0.428524i	$0.140966\pi$
$307$	1.28073e11	+	2.21829e11i	0.822878	+	1.42527i	−0.0806528	+	0.996742i	$0.525701\pi$
$308$	−3.44634e9	+	1.95452e10i	−0.0218213	+	0.123755i
$309$		0			0
$310$	2.95995e10	+	1.07733e10i	0.182035	+	0.0662555i
$311$	−6.65416e10	−	2.42192e10i	−0.403340	−	0.146804i	0.132381	−	0.991199i	$-0.457738\pi$
$311$	−6.65416e10	−	2.42192e10i	−0.403340	−	0.146804i	−0.535721	+	0.844395i	$0.679960\pi$
$312$		0			0
$313$	3.00272e9	−	1.70293e10i	0.0176834	−	0.100287i	−0.974689	−	0.223567i	$-0.928230\pi$
$313$	3.00272e9	−	1.70293e10i	0.0176834	−	0.100287i	0.992372	+	0.123279i	$0.0393411\pi$
$314$	−1.18555e10	−	2.05343e10i	−0.0688235	−	0.119206i
$315$		0			0
$316$	−1.17886e10	+	2.04184e10i	−0.0665072	+	0.115194i
$317$	1.80799e11	+	1.51709e11i	1.00561	+	0.843807i	0.987752	−	0.156033i	$-0.0498706\pi$
$317$	1.80799e11	+	1.51709e11i	1.00561	+	0.843807i	0.0178587	+	0.999841i	$0.494315\pi$
$318$		0			0
$319$	−2.13309e10	−	1.20974e11i	−0.115332	−	0.654083i
$320$	8.49138e10	−	7.12511e10i	0.452693	−	0.379854i
$321$		0			0
$322$	−2.97799e9	+	1.08390e9i	−0.0154373	+	0.00561871i
$323$	−9.25216e10			−0.472968
$324$		0			0
$325$	−8.85223e10			−0.440127
$326$	−1.94353e10	+	7.07389e9i	−0.0953044	+	0.0346880i
$327$		0			0
$328$	7.54392e10	−	6.33010e10i	0.359886	−	0.301980i
$329$	−2.83727e9	−	1.60910e10i	−0.0133512	−	0.0757183i
$330$		0			0
$331$	1.82248e11	+	1.52924e11i	0.834519	+	0.700244i	0.956324	−	0.292310i	$-0.0944238\pi$
$331$	1.82248e11	+	1.52924e11i	0.834519	+	0.700244i	−0.121805	+	0.992554i	$0.538868\pi$
$332$	−4.32609e10	+	7.49301e10i	−0.195422	+	0.338481i
$333$		0			0
$334$	−2.63800e10	−	4.56916e10i	−0.115989	−	0.200899i
$335$	4.32441e10	−	2.45250e11i	0.187597	−	1.06391i
$336$		0			0
$337$	3.87477e11	+	1.41030e11i	1.63648	+	0.595631i	0.986419	−	0.164248i	$-0.0525197\pi$
$337$	3.87477e11	+	1.41030e11i	1.63648	+	0.595631i	0.650064	+	0.759879i	$0.274742\pi$
$338$	−6.18437e10	−	2.25093e10i	−0.257733	−	0.0938072i
$339$		0			0
$340$	3.25283e10	−	1.84477e11i	0.132010	−	0.748665i
$341$	1.85793e11	+	3.21803e11i	0.744107	+	1.28883i
$342$		0			0
$343$	−2.31329e10	+	4.00673e10i	−0.0902414	+	0.156303i
$344$	1.29796e11	+	1.08912e11i	0.499746	+	0.419336i
$345$		0			0
$346$	−8.09357e9	−	4.59009e10i	−0.0303597	−	0.172178i
$347$	8.58760e8	−	7.20585e8i	0.00317972	−	0.00266810i	−0.641196	−	0.767377i	$-0.721562\pi$
$347$	8.58760e8	−	7.20585e8i	0.00317972	−	0.00266810i	0.644376	+	0.764709i	$0.277117\pi$
$348$		0			0
$349$	−2.74997e11	+	1.00091e11i	−0.992231	+	0.361143i	−0.786584	−	0.617484i	$-0.788152\pi$
$349$	−2.74997e11	+	1.00091e11i	−0.992231	+	0.361143i	−0.205647	+	0.978626i	$0.565930\pi$
$350$	1.70877e9			0.00608662
$351$		0			0
$352$	−2.67168e11			−0.927559
$353$	4.45541e11	−	1.62164e11i	1.52722	−	0.555862i	0.564281	−	0.825583i	$-0.309154\pi$
$353$	4.45541e11	−	1.62164e11i	1.52722	−	0.555862i	0.962939	+	0.269721i	$0.0869314\pi$
$354$		0			0
$355$	3.14801e11	−	2.64150e11i	1.05198	−	0.882719i
$356$	5.73686e10	+	3.25353e11i	0.189299	+	1.07357i
$357$		0			0
$358$	−7.68441e10	−	6.44798e10i	−0.247250	−	0.207468i
$359$	−2.51241e11	+	4.35163e11i	−0.798300	+	1.38270i	0.122422	+	0.992478i	$0.460934\pi$
$359$	−2.51241e11	+	4.35163e11i	−0.798300	+	1.38270i	−0.920722	+	0.390218i	$0.872400\pi$
$360$		0			0
$361$	1.21793e11	+	2.10951e11i	0.377433	+	0.653733i
$362$	−2.31475e10	+	1.31276e11i	−0.0708460	+	0.401788i
$363$		0			0
$364$	−4.02070e10	−	1.46341e10i	−0.120045	−	0.0436929i
$365$	−4.24090e11	−	1.54356e11i	−1.25066	−	0.455204i
$366$		0			0
$367$	8.92505e10	−	5.06165e11i	0.256811	−	1.45645i	−0.534571	−	0.845124i	$-0.679527\pi$
$367$	8.92505e10	−	5.06165e11i	0.256811	−	1.45645i	0.791382	−	0.611323i	$-0.209362\pi$
$368$	1.19262e11	+	2.06568e11i	0.338990	+	0.587148i
$369$		0			0
$370$	−1.95027e10	+	3.37797e10i	−0.0540987	+	0.0937017i
$371$	−2.21944e10	−	1.86233e10i	−0.0608220	−	0.0510357i
$372$		0			0
$373$	−3.61006e10	−	2.04737e11i	−0.0965661	−	0.547653i	−0.994256	−	0.107026i	$-0.965867\pi$
$373$	−3.61006e10	−	2.04737e11i	−0.0965661	−	0.547653i	0.897690	−	0.440627i	$-0.145244\pi$
$374$	−9.18294e10	+	7.70540e10i	−0.242694	+	0.203645i
$375$		0			0
$376$	1.36589e11	−	4.97142e10i	0.352427	−	0.128273i
$377$	2.64830e11			0.675197
$378$		0			0
$379$	5.11931e11			1.27449			0.637243	−	0.770663i	$-0.280075\pi$
$379$	5.11931e11			1.27449			0.637243	+	0.770663i	$0.280075\pi$
$380$	1.50495e11	−	5.47756e10i	0.370250	−	0.134760i
$381$		0			0
$382$	5.46472e10	−	4.58544e10i	0.131305	−	0.110178i
$383$	−6.18978e10	−	3.51040e11i	−0.146988	−	0.833608i	−0.965750	−	0.259475i	$-0.916450\pi$
$383$	−6.18978e10	−	3.51040e11i	−0.146988	−	0.833608i	0.818762	−	0.574133i	$-0.194661\pi$
$384$		0			0
$385$	−3.67053e10	−	3.07994e10i	−0.0851443	−	0.0714446i
$386$	1.15441e9	−	1.99950e9i	0.00264677	−	0.00458435i
$387$		0			0
$388$	3.03278e11	+	5.25293e11i	0.679358	+	1.17668i
$389$	−6.84736e10	+	3.88333e11i	−0.151618	+	0.859866i	0.810196	+	0.586160i	$0.199361\pi$
$389$	−6.84736e10	+	3.88333e11i	−0.151618	+	0.859866i	−0.961813	+	0.273707i	$0.911750\pi$
$390$		0			0
$391$	3.31579e11	+	1.20685e11i	0.717451	+	0.261131i
$392$	−1.92583e11	−	7.00946e10i	−0.411938	−	0.149933i
$393$		0			0
$394$	−2.65567e10	+	1.50611e11i	−0.0555190	+	0.314864i
$395$	−2.84608e10	−	4.92955e10i	−0.0588248	−	0.101887i
$396$		0			0
$397$	−6.50349e10	+	1.12644e11i	−0.131398	+	0.227588i	−0.924216	−	0.381871i	$-0.875280\pi$
$397$	−6.50349e10	+	1.12644e11i	−0.131398	+	0.227588i	0.792818	+	0.609459i	$0.208613\pi$
$398$	8.67901e10	+	7.28256e10i	0.173379	+	0.145482i
$399$		0			0
$400$	−2.23331e10	−	1.26657e11i	−0.0436192	−	0.247377i
$401$	7.62899e11	−	6.40148e11i	1.47339	−	1.23632i	0.560471	−	0.828174i	$-0.310620\pi$
$401$	7.62899e11	−	6.40148e11i	1.47339	−	1.23632i	0.912917	−	0.408145i	$-0.133824\pi$
$402$		0			0
$403$	−7.52788e11	+	2.73993e11i	−1.42167	+	0.517447i
$404$	−1.08332e11			−0.202321
$405$		0			0
$406$	−5.11207e9			−0.00933747
$407$	−4.32387e11	+	1.57376e11i	−0.781084	+	0.284291i
$408$		0			0
$409$	−1.81185e11	+	1.52032e11i	−0.320160	+	0.268646i	−0.788676	−	0.614809i	$-0.789233\pi$
$409$	−1.81185e11	+	1.52032e11i	−0.320160	+	0.268646i	0.468516	+	0.883455i	$0.344789\pi$
$410$	2.00978e10	+	1.13980e11i	0.0351253	+	0.199206i
$411$		0			0
$412$	−2.21589e11	−	1.85935e11i	−0.378888	−	0.317925i
$413$	3.14005e10	−	5.43872e10i	0.0531081	−	0.0919860i
$414$		0			0
$415$	−1.04444e11	−	1.80902e11i	−0.172849	−	0.299382i
$416$	1.00019e11	−	5.67234e11i	0.163742	−	0.928629i
$417$		0			0
$418$	−9.63070e10	−	3.50529e10i	−0.154300	−	0.0561604i
$419$	−5.69703e11	−	2.07355e11i	−0.902995	−	0.328663i	−0.151543	−	0.988451i	$-0.548424\pi$
$419$	−5.69703e11	−	2.07355e11i	−0.902995	−	0.328663i	−0.751452	+	0.659787i	$0.770646\pi$
$420$		0			0
$421$	−1.59940e11	+	9.07063e11i	−0.248134	+	1.40724i	0.564966	+	0.825114i	$0.308889\pi$
$421$	−1.59940e11	+	9.07063e11i	−0.248134	+	1.40724i	−0.813100	+	0.582124i	$0.802222\pi$
$422$	−1.54671e10	−	2.67898e10i	−0.0237412	−	0.0411209i
$423$		0			0
$424$	1.28872e11	−	2.23212e11i	0.193647	−	0.335407i
$425$	−1.45748e11	−	1.22297e11i	−0.216696	−	0.181830i
$426$		0			0
$427$	4.97726e9	+	2.82275e10i	0.00724545	+	0.0410910i
$428$	4.03931e11	−	3.38939e11i	0.581849	−	0.488230i
$429$		0			0
$430$	−1.87123e11	+	6.81073e10i	−0.263949	+	0.0960695i
$431$	−1.12321e12			−1.56788			−0.783941	−	0.620836i	$-0.786793\pi$
$431$	−1.12321e12			−1.56788			−0.783941	+	0.620836i	$0.786793\pi$
$432$		0			0
$433$	−2.33971e11			−0.319864			−0.159932	−	0.987128i	$-0.551128\pi$
$433$	−2.33971e11			−0.319864			−0.159932	+	0.987128i	$0.551128\pi$
$434$	1.45312e10	−	5.28894e9i	0.0196607	−	0.00715591i
$435$		0			0
$436$	6.93667e11	−	5.82056e11i	0.919310	−	0.771392i
$437$	5.23861e10	+	2.97096e11i	0.0687147	+	0.389700i
$438$		0			0
$439$	−9.14258e11	−	7.67153e11i	−1.17484	−	0.985807i	−0.999999	−	0.00120975i	$-0.999615\pi$
$439$	−9.14258e11	−	7.67153e11i	−1.17484	−	0.985807i	−0.174839	−	0.984597i	$-0.555941\pi$
$440$	2.13129e11	−	3.69151e11i	0.271085	−	0.469533i
$441$		0			0
$442$	−1.29219e11	−	2.23813e11i	−0.161037	−	0.278924i
$443$	6.46091e10	−	3.66417e11i	0.0797035	−	0.452021i	−0.918671	−	0.395024i	$-0.870736\pi$
$443$	6.46091e10	−	3.66417e11i	0.0797035	−	0.452021i	0.998374	−	0.0569970i	$-0.0181525\pi$
$444$		0			0
$445$	−7.49508e11	−	2.72798e11i	−0.906058	−	0.329778i
$446$	−3.02123e11	−	1.09964e11i	−0.361557	−	0.131596i
$447$		0			0
$448$	9.44961e9	−	5.35914e10i	0.0110831	−	0.0628556i
$449$	5.94911e11	+	1.03042e12i	0.690786	+	1.19648i	0.971581	+	0.236709i	$0.0760689\pi$
$449$	5.94911e11	+	1.03042e12i	0.690786	+	1.19648i	−0.280794	+	0.959768i	$0.590598\pi$
$450$		0			0
$451$	−6.82668e11	+	1.18242e12i	−0.776989	+	1.34578i
$452$	−5.31074e11	−	4.45624e11i	−0.598456	−	0.502164i
$453$		0			0
$454$	−1.31409e10	−	7.45260e10i	−0.0145169	−	0.0823296i
$455$	7.91327e10	−	6.64003e10i	0.0865575	−	0.0726304i
$456$		0			0
$457$	4.38390e11	−	1.59561e11i	0.470151	−	0.171121i	−0.0960696	−	0.995375i	$-0.530627\pi$
$457$	4.38390e11	−	1.59561e11i	0.470151	−	0.171121i	0.566221	+	0.824254i	$0.308405\pi$
$458$	−2.68365e10			−0.0284991
$459$		0			0
$460$	−6.10793e11			−0.636039
$461$	4.28880e11	−	1.56100e11i	0.442264	−	0.160971i	−0.111283	−	0.993789i	$-0.535496\pi$
$461$	4.28880e11	−	1.56100e11i	0.442264	−	0.160971i	0.553547	+	0.832818i	$0.313274\pi$
$462$		0			0
$463$	−6.66831e11	+	5.59538e11i	−0.674375	+	0.565868i	−0.914357	−	0.404909i	$-0.867303\pi$
$463$	−6.66831e11	+	5.59538e11i	−0.674375	+	0.565868i	0.239982	+	0.970777i	$0.422859\pi$
$464$	6.68131e10	+	3.78916e11i	0.0669161	+	0.379500i
$465$		0			0
$466$	2.75725e11	+	2.31361e11i	0.270857	+	0.227276i
$467$	6.42551e11	−	1.11293e12i	0.625146	−	1.08279i	−0.363366	−	0.931646i	$-0.618373\pi$
$467$	6.42551e11	−	1.11293e12i	0.625146	−	1.08279i	0.988513	−	0.151139i	$-0.0482940\pi$
$468$		0			0
$469$	−6.11288e10	−	1.05878e11i	−0.0583403	−	0.101048i
$470$	−2.96642e10	+	1.68234e11i	−0.0280409	+	0.159028i
$471$		0			0
$472$	5.24989e11	+	1.91080e11i	0.486868	+	0.177205i
$473$	−2.20745e12	−	8.03444e11i	−2.02775	−	0.738041i
$474$		0			0
$475$	2.82463e10	−	1.60193e11i	0.0254590	−	0.144385i
$476$	−4.59812e10	−	7.96418e10i	−0.0410534	−	0.0711066i
$477$		0			0
$478$	−1.59471e11	+	2.76213e11i	−0.139720	+	0.242001i
$479$	9.49325e11	+	7.96578e11i	0.823958	+	0.691383i	0.953895	−	0.300139i	$-0.0970332\pi$
$479$	9.49325e11	+	7.96578e11i	0.823958	+	0.691383i	−0.129937	+	0.991522i	$0.541478\pi$
$480$		0			0
$481$	−1.72260e11	−	9.76935e11i	−0.146734	−	0.832171i
$482$	8.28924e10	−	6.95550e10i	0.0699525	−	0.0586971i
$483$		0			0
$484$	1.22413e12	−	4.45546e11i	1.01396	−	0.369052i
$485$	−1.46439e12			−1.20177
$486$		0			0
$487$	1.32515e12			1.06754			0.533769	−	0.845630i	$-0.320775\pi$
$487$	1.32515e12			1.06754			0.533769	+	0.845630i	$0.320775\pi$
$488$	−2.39610e11	+	8.72107e10i	−0.191256	+	0.0696115i
$489$		0			0
$490$	1.84510e11	−	1.54823e11i	0.144590	−	0.121326i
$491$	3.50397e11	+	1.98720e12i	0.272078	+	1.54303i	0.748093	+	0.663594i	$0.230970\pi$
$491$	3.50397e11	+	1.98720e12i	0.272078	+	1.54303i	−0.476015	+	0.879437i	$0.657919\pi$
$492$		0			0
$493$	4.36029e11	+	3.65872e11i	0.332433	+	0.278945i
$494$	1.10476e11	−	1.91351e11i	0.0834637	−	0.144563i
$495$		0			0
$496$	−5.81945e11	−	1.00796e12i	−0.431732	−	0.747783i
$497$	3.50326e10	−	1.98680e11i	0.0257554	−	0.146066i
$498$		0			0
$499$	−4.82759e11	−	1.75710e11i	−0.348560	−	0.126865i	0.161806	−	0.986823i	$-0.448268\pi$
$499$	−4.82759e11	−	1.75710e11i	−0.348560	−	0.126865i	−0.510366	+	0.859957i	$0.670490\pi$
$500$	1.35458e12	+	4.93025e11i	0.969255	+	0.352780i
$501$		0			0
$502$	4.02078e10	−	2.28030e11i	0.0282581	−	0.160260i
$503$	−7.16695e11	−	1.24135e12i	−0.499204	−	0.864647i	0.500795	−	0.865566i	$-0.333041\pi$
$503$	−7.16695e11	−	1.24135e12i	−0.499204	−	0.864647i	−1.00000		0.000918437i	$0.999708\pi$
$504$		0			0
$505$	1.30772e11	−	2.26503e11i	0.0894753	−	0.154976i
$506$	2.99423e11	+	2.51245e11i	0.203052	+	0.170381i
$507$		0			0
$508$	3.74022e11	+	2.12119e12i	0.249179	+	1.41316i
$509$	7.35298e11	−	6.16988e11i	0.485549	−	0.407424i	−0.366879	−	0.930269i	$-0.619574\pi$
$509$	7.35298e11	−	6.16988e11i	0.485549	−	0.407424i	0.852428	+	0.522845i	$0.175129\pi$
$510$		0			0
$511$	−2.08198e11	+	7.57780e10i	−0.135078	+	0.0491642i
$512$	1.41984e12			0.913116
$513$		0			0
$514$	−4.33441e11			−0.273902
$515$	6.56246e11	−	2.38854e11i	0.411087	−	0.149624i
$516$		0			0
$517$	−1.54376e12	+	1.29537e12i	−0.950323	+	0.797416i
$518$	3.32517e9	+	1.88580e10i	0.00202923	+	0.0115083i
$519$		0			0
$520$	7.03970e11	+	5.90701e11i	0.422220	+	0.354285i
$521$	−1.14586e12	+	1.98469e12i	−0.681336	+	1.18011i	0.293238	+	0.956040i	$0.405267\pi$
$521$	−1.14586e12	+	1.98469e12i	−0.681336	+	1.18011i	−0.974573	+	0.224069i	$0.928066\pi$
$522$		0			0
$523$	−4.98633e11	−	8.63657e11i	−0.291422	−	0.504759i	0.682724	−	0.730677i	$-0.260795\pi$
$523$	−4.98633e11	−	8.63657e11i	−0.291422	−	0.504759i	−0.974146	+	0.225918i	$0.927462\pi$
$524$	−1.81550e11	+	1.02962e12i	−0.105197	+	0.596604i
$525$		0			0
$526$	2.93900e11	+	1.06971e11i	0.167403	+	0.0609299i
$527$	−1.61796e12	−	5.88889e11i	−0.913735	−	0.332572i
$528$		0			0
$529$	−1.12976e11	+	6.40721e11i	−0.0627245	+	0.355728i
$530$	1.51458e11	+	2.62332e11i	0.0833777	+	0.144414i
$531$		0			0
$532$	3.93120e10	−	6.80903e10i	0.0212776	−	0.0368539i
$533$	−2.25486e12	−	1.89206e12i	−1.21017	−	1.01546i
$534$		0			0
$535$	2.21060e11	+	1.25369e12i	0.116659	+	0.661606i
$536$	8.33159e11	−	6.99103e11i	0.436000	−	0.365847i
$537$		0			0
$538$	−7.05161e10	+	2.56658e10i	−0.0362884	+	0.0132079i
$539$	2.84138e12			1.45004
$540$		0			0
$541$	2.03546e11			0.102159			0.0510794	−	0.998695i	$-0.483734\pi$
$541$	2.03546e11			0.102159			0.0510794	+	0.998695i	$0.483734\pi$
$542$	−1.07243e11	+	3.90332e10i	−0.0533791	+	0.0194284i
$543$		0			0
$544$	9.48331e11	−	7.95744e11i	0.464264	−	0.389564i
$545$	3.79624e11	+	2.15296e12i	0.184319	+	1.04532i
$546$		0			0
$547$	5.09924e11	+	4.27877e11i	0.243536	+	0.204351i	0.756383	−	0.654129i	$-0.226965\pi$
$547$	5.09924e11	+	4.27877e11i	0.243536	+	0.204351i	−0.512847	+	0.858480i	$0.671409\pi$
$548$	9.22485e11	−	1.59779e12i	0.436965	−	0.756846i
$549$		0			0
$550$	−1.05377e11	−	1.82519e11i	−0.0491037	−	0.0850501i
$551$	−8.45037e10	+	4.79244e11i	−0.0390565	+	0.221501i
$552$		0			0
$553$	−2.62592e10	−	9.55758e9i	−0.0119404	−	0.00434595i
$554$	7.34853e11	+	2.67465e11i	0.331441	+	0.120635i
$555$		0			0
$556$	5.26338e11	−	2.98501e12i	0.233576	−	1.32467i
$557$	−4.51240e11	−	7.81571e11i	−0.198637	−	0.344049i	0.749450	−	0.662061i	$-0.230318\pi$
$557$	−4.51240e11	−	7.81571e11i	−0.198637	−	0.344049i	−0.948087	+	0.318012i	$0.896985\pi$
$558$		0			0
$559$	2.53222e12	−	4.38593e12i	1.09685	−	1.89980i
$560$	1.14969e11	+	9.64706e10i	0.0494009	+	0.0414523i
$561$		0			0
$562$	4.15315e10	+	2.35537e11i	0.0175616	+	0.0995969i
$563$	3.00202e12	−	2.51899e12i	1.25929	−	1.05667i	0.263532	−	0.964651i	$-0.415113\pi$
$563$	3.00202e12	−	2.51899e12i	1.25929	−	1.05667i	0.995757	−	0.0920186i	$-0.0293319\pi$
$564$		0			0
$565$	1.57280e12	−	5.72452e11i	0.649315	−	0.236331i
$566$	5.91651e11			0.242321
$567$		0			0
$568$	1.79473e12			0.723489
$569$	−3.73460e12	+	1.35928e12i	−1.49361	+	0.543631i	−0.954398	−	0.298536i	$-0.903502\pi$
$569$	−3.73460e12	+	1.35928e12i	−1.49361	+	0.543631i	−0.539216	+	0.842168i	$0.681279\pi$
$570$		0			0
$571$	−7.88821e11	+	6.61899e11i	−0.310539	+	0.260573i	−0.784715	−	0.619857i	$-0.787191\pi$
$571$	−7.88821e11	+	6.61899e11i	−0.310539	+	0.260573i	0.474176	+	0.880430i	$0.342746\pi$
$572$	9.16389e11	+	5.19710e12i	0.357930	+	2.02992i
$573$		0			0
$574$	4.35262e10	+	3.65228e10i	0.0167358	+	0.0140430i
$575$	−3.10185e11	+	5.37256e11i	−0.118335	+	0.204963i
$576$		0			0
$577$	8.29829e11	+	1.43731e12i	0.311672	+	0.539832i	0.978724	−	0.205179i	$-0.0657777\pi$
$577$	8.29829e11	+	1.43731e12i	0.311672	+	0.539832i	−0.667053	+	0.745011i	$0.732444\pi$
$578$	−9.24270e9	+	5.24180e10i	−0.00344448	+	0.0195346i
$579$		0			0
$580$	−9.25848e11	−	3.36981e11i	−0.339714	−	0.123646i
$581$	−9.63645e10	−	3.50738e10i	−0.0350852	−	0.0127700i
$582$		0			0
$583$	−6.20517e11	+	3.51913e12i	−0.222457	+	1.26161i
$584$	−9.85506e11	−	1.70695e12i	−0.350592	−	0.607243i
$585$		0			0
$586$	4.32311e10	−	7.48785e10i	0.0151446	−	0.0262312i
$587$	2.56726e12	+	2.15418e12i	0.892478	+	0.748878i	0.968706	−	0.248212i	$-0.0798430\pi$
$587$	2.56726e12	+	2.15418e12i	0.892478	+	0.748878i	−0.0762274	+	0.997090i	$0.524287\pi$
$588$		0			0
$589$	−2.55621e11	−	1.44970e12i	−0.0875140	−	0.496317i
$590$	−5.02982e11	+	4.22052e11i	−0.170891	+	0.143394i
$591$		0			0
$592$	1.35433e12	−	4.92936e11i	0.453187	−	0.164947i
$593$	−1.51807e11			−0.0504135			−0.0252067	−	0.999682i	$-0.508024\pi$
$593$	−1.51807e11			−0.0504135			−0.0252067	+	0.999682i	$0.508024\pi$
$594$		0			0
$595$	2.22023e11			0.0726225
$596$	−2.28428e12	+	8.31412e11i	−0.741553	+	0.269903i
$597$		0			0
$598$	−6.45523e11	+	5.41658e11i	−0.206422	+	0.173209i
$599$	9.76595e11	+	5.53854e12i	0.309951	+	1.75782i	0.599230	+	0.800577i	$0.295474\pi$
$599$	9.76595e11	+	5.53854e12i	0.309951	+	1.75782i	−0.289278	+	0.957245i	$0.593415\pi$
$600$		0			0
$601$	3.63412e12	+	3.04939e12i	1.13622	+	0.953405i	0.999309	−	0.0371781i	$-0.0118369\pi$
$601$	3.63412e12	+	3.04939e12i	1.13622	+	0.953405i	0.136915	+	0.990583i	$0.456281\pi$
$602$	−4.88800e10	+	8.46627e10i	−0.0151687	+	0.0262729i
$603$		0			0
$604$	−7.83110e11	−	1.35639e12i	−0.239418	−	0.414684i
$605$	−5.46131e11	+	3.09727e12i	−0.165729	+	0.939895i
$606$		0			0
$607$	−1.67977e12	−	6.11388e11i	−0.502229	−	0.182796i	0.0784673	−	0.996917i	$-0.474997\pi$
$607$	−1.67977e12	−	6.11388e11i	−0.502229	−	0.182796i	−0.580696	+	0.814120i	$0.697220\pi$
$608$	9.94571e11	+	3.61994e11i	0.295168	+	0.107432i
$609$		0			0
$610$	5.20382e10	−	2.95123e11i	0.0152173	−	0.0863017i
$611$	−2.17231e12	−	3.76255e12i	−0.630575	−	1.09219i
$612$		0			0
$613$	8.97771e11	−	1.55498e12i	0.256799	−	0.444789i	−0.708584	−	0.705627i	$-0.750665\pi$
$613$	8.97771e11	−	1.55498e12i	0.256799	−	0.444789i	0.965383	+	0.260838i	$0.0839988\pi$
$614$	−1.00715e12	−	8.45097e11i	−0.285980	−	0.239966i
$615$		0			0
$616$	−3.63381e10	−	2.06084e11i	−0.0101683	−	0.0576674i
$617$	4.09727e12	−	3.43802e12i	1.13818	−	0.955048i	0.138804	−	0.990320i	$-0.455674\pi$
$617$	4.09727e12	−	3.43802e12i	1.13818	−	0.955048i	0.999378	+	0.0352723i	$0.0112298\pi$
$618$		0			0
$619$	4.64841e11	−	1.69188e11i	0.127261	−	0.0463193i	−0.277604	−	0.960695i	$-0.589540\pi$
$619$	4.64841e11	−	1.69188e11i	0.127261	−	0.0463193i	0.404866	+	0.914376i	$0.367318\pi$
$620$	2.98040e12			0.810050
$621$		0			0
$622$	3.63461e11			0.0973647
$623$	−3.67955e11	+	1.33925e11i	−0.0978586	+	0.0356176i
$624$		0			0
$625$	−1.80065e12	+	1.51093e12i	−0.472031	+	0.396081i
$626$	1.54122e10	+	8.74072e10i	0.00401126	+	0.0227490i
$627$		0			0
$628$	−1.71862e12	−	1.44210e12i	−0.440923	−	0.369978i
$629$	1.06605e12	−	1.84646e12i	0.271551	−	0.470340i
$630$		0			0
$631$	−6.83547e11	−	1.18394e12i	−0.171647	−	0.297301i	0.767349	−	0.641230i	$-0.221575\pi$
$631$	−6.83547e11	−	1.18394e12i	−0.171647	−	0.297301i	−0.938996	+	0.343929i	$0.888242\pi$
$632$	4.31682e10	−	2.44819e11i	0.0107631	−	0.0610406i
$633$		0			0
$634$	−1.13836e12	−	4.14329e11i	−0.279819	−	0.101846i
$635$	−4.88652e12	−	1.77855e12i	−1.19266	−	0.434094i
$636$		0			0
$637$	−1.06372e12	+	6.03264e12i	−0.255976	+	1.45171i
$638$	3.15254e11	+	5.46036e11i	0.0753299	+	0.130475i
$639$		0			0
$640$	−1.41404e12	+	2.44919e12i	−0.333159	+	0.577048i
$641$	−3.06971e12	−	2.57580e12i	−0.718186	−	0.602630i	0.208697	−	0.977980i	$-0.433078\pi$
$641$	−3.06971e12	−	2.57580e12i	−0.718186	−	0.602630i	−0.926883	+	0.375351i	$0.877522\pi$
$642$		0			0
$643$	−1.68695e11	−	9.56716e11i	−0.0389182	−	0.220716i	0.959146	−	0.282912i	$-0.0913006\pi$
$643$	−1.68695e11	−	9.56716e11i	−0.0389182	−	0.220716i	−0.998064	+	0.0621965i	$0.980189\pi$
$644$	−2.29703e11	+	1.92744e11i	−0.0526236	+	0.0441565i
$645$		0			0
$646$	4.46252e11	−	1.62422e11i	0.100817	−	0.0366944i
$647$	−2.07885e12			−0.466395			−0.233198	−	0.972429i	$-0.574919\pi$
$647$	−2.07885e12			−0.466395			−0.233198	+	0.972429i	$0.574919\pi$
$648$		0			0
$649$	−7.74569e12			−1.71380
$650$	4.26962e11	−	1.55402e11i	0.0938165	−	0.0341464i
$651$		0			0
$652$	−1.49912e12	+	1.25791e12i	−0.324880	+	0.272607i
$653$	−3.38608e11	−	1.92034e12i	−0.0728766	−	0.413304i	−0.999320	−	0.0368699i	$-0.988261\pi$
$653$	−3.38608e11	−	1.92034e12i	−0.0728766	−	0.413304i	0.926443	−	0.376434i	$-0.122850\pi$
$654$		0			0
$655$	−1.93360e12	−	1.62248e12i	−0.410469	−	0.344425i
$656$	2.13827e12	−	3.70359e12i	0.450811	−	0.780827i
$657$		0			0
$658$	4.19326e10	+	7.26294e10i	0.00872038	+	0.0151041i
$659$	1.07304e12	−	6.08551e12i	0.221631	−	1.25693i	−0.647390	−	0.762159i	$-0.724139\pi$
$659$	1.07304e12	−	6.08551e12i	0.221631	−	1.25693i	0.869021	−	0.494775i	$-0.164750\pi$
$660$		0			0
$661$	1.19594e12	+	4.35288e11i	0.243671	+	0.0886891i	0.460969	−	0.887416i	$-0.347502\pi$
$661$	1.19594e12	+	4.35288e11i	0.243671	+	0.0886891i	−0.217298	+	0.976105i	$0.569724\pi$
$662$	−1.14748e12	−	4.17648e11i	−0.232212	−	0.0845181i
$663$		0			0
$664$	1.58416e11	−	8.98422e11i	0.0316259	−	0.179359i
$665$	9.49099e10	+	1.64389e11i	0.0188198	+	0.0325968i
$666$		0			0
$667$	9.27970e11	−	1.60729e12i	0.181538	−	0.314433i
$668$	−3.82416e12	−	3.20885e12i	−0.743091	−	0.623527i
$669$		0			0
$670$	2.21962e11	+	1.25881e12i	0.0425541	+	0.241336i
$671$	2.70812e12	−	2.27238e12i	0.515724	−	0.432743i
$672$		0			0
$673$	2.80815e11	−	1.02208e11i	0.0527658	−	0.0192052i	−0.315502	−	0.948925i	$-0.602173\pi$
$673$	2.80815e11	−	1.02208e11i	0.0527658	−	0.0192052i	0.368268	+	0.929720i	$0.379951\pi$
$674$	−2.11647e12			−0.395041
$675$		0			0
$676$	−6.22711e12			−1.14690
$677$	4.73930e12	−	1.72497e12i	0.867093	−	0.315596i	0.130103	−	0.991500i	$-0.458469\pi$
$677$	4.73930e12	−	1.72497e12i	0.867093	−	0.315596i	0.736989	+	0.675905i	$0.236247\pi$
$678$		0			0
$679$	−5.50720e11	+	4.62109e11i	−0.0994299	+	0.0834316i
$680$	3.42977e11	+	1.94512e12i	0.0615142	+	0.348864i
$681$		0			0
$682$	−1.46105e12	−	1.22597e12i	−0.258604	−	0.216995i
$683$	−1.13832e12	+	1.97163e12i	−0.200158	+	0.346683i	−0.948579	−	0.316540i	$-0.897479\pi$
$683$	−1.13832e12	+	1.97163e12i	−0.200158	+	0.346683i	0.748422	+	0.663223i	$0.230812\pi$
$684$		0			0
$685$	2.22713e12	+	3.85751e12i	0.386490	+	0.669421i
$686$	4.12364e10	−	2.33863e11i	0.00710922	−	0.0403184i
$687$		0			0
$688$	6.91421e12	+	2.51656e12i	1.17651	+	0.428213i
$689$	−7.23930e12	−	2.63489e12i	−1.22380	−	0.445426i
$690$		0			0
$691$	2.12817e11	−	1.20695e12i	0.0355104	−	0.201389i	−0.961891	−	0.273433i	$-0.911841\pi$
$691$	2.12817e11	−	1.20695e12i	0.0355104	−	0.201389i	0.997401	+	0.0720434i	$0.0229520\pi$
$692$	−2.20504e12	−	3.81924e12i	−0.365543	−	0.633140i
$693$		0			0
$694$	−2.87699e9	+	4.98310e9i	−0.000470783	+	0.000815421i
$695$	5.60576e12	+	4.70379e12i	0.911388	+	0.764745i
$696$		0			0
$697$	−1.09858e12	−	6.23036e12i	−0.176313	−	0.999921i
$698$	1.15066e12	−	9.65517e11i	0.183484	−	0.153961i
$699$		0			0
$700$	1.51931e11	−	5.52982e10i	0.0239168	−	0.00870502i
$701$	−1.15369e12			−0.180450			−0.0902252	−	0.995921i	$-0.528759\pi$
$701$	−1.15369e12			−0.180450			−0.0902252	+	0.995921i	$0.528759\pi$
$702$		0			0
$703$	1.82286e12			0.281484
$704$	−6.30701e12	+	2.29556e12i	−0.967712	+	0.352218i
$705$		0			0
$706$	−1.86426e12	+	1.56430e12i	−0.282414	+	0.236973i
$707$	−2.22963e10	−	1.26449e11i	−0.00335619	−	0.0190339i
$708$		0			0
$709$	4.61341e11	+	3.87111e11i	0.0685669	+	0.0575344i	0.676427	−	0.736510i	$-0.263527\pi$
$709$	4.61341e11	+	3.87111e11i	0.0685669	+	0.0575344i	−0.607860	+	0.794044i	$0.707972\pi$
$710$	−1.05464e12	+	1.82669e12i	−0.155755	+	0.269775i
$711$		0			0
$712$	−1.74172e12	−	3.01674e12i	−0.253990	−	0.439924i
$713$	−9.74889e11	+	5.52887e12i	−0.141271	+	0.801186i
$714$		0			0
$715$	−1.19724e13	−	4.35760e12i	−1.71319	−	0.623549i
$716$	−8.91906e12	−	3.24627e12i	−1.26827	−	0.461611i
$717$		0			0
$718$	4.47860e11	−	2.53994e12i	0.0628901	−	0.356668i
$719$	6.43613e12	+	1.11477e13i	0.898141	+	1.55563i	0.829868	+	0.557959i	$0.188415\pi$
$719$	6.43613e12	+	1.11477e13i	0.898141	+	1.55563i	0.0682726	+	0.997667i	$0.478251\pi$
$720$		0			0
$721$	1.71423e11	−	2.96914e11i	0.0236244	−	0.0409187i
$722$	−9.57760e11	−	8.03656e11i	−0.131172	−	0.110066i
$723$		0			0
$724$	2.19018e12	+	1.24211e13i	0.296249	+	1.68011i
$725$	−7.66592e11	+	6.43247e11i	−0.103049	+	0.0864682i
$726$		0			0
$727$	−1.65453e11	+	6.02198e10i	−0.0219669	+	0.00799530i	−0.352980	−	0.935631i	$-0.614832\pi$
$727$	−1.65453e11	+	6.02198e10i	−0.0219669	+	0.00799530i	0.331013	+	0.943626i	$0.392609\pi$
$728$	4.51148e11			0.0595289
$729$		0			0
$730$	2.31645e12			0.301905
$731$	1.02285e13	−	3.72287e12i	1.32490	−	0.482225i
$732$		0			0
$733$	1.10709e13	−	9.28958e12i	1.41649	−	1.18858i	0.463306	−	0.886198i	$-0.346663\pi$
$733$	1.10709e13	−	9.28958e12i	1.41649	−	1.18858i	0.953187	−	0.302381i	$-0.0977814\pi$
$734$	4.58101e11	+	2.59802e12i	0.0582545	+	0.330378i
$735$		0			0
$736$	−3.09216e12	−	2.59463e12i	−0.388430	−	0.325931i
$737$	−7.53946e12	+	1.30587e13i	−0.941318	+	1.63041i
$738$		0			0
$739$	−3.65737e11	−	6.33476e11i	−0.0451096	−	0.0781322i	0.842589	−	0.538557i	$-0.181030\pi$
$739$	−3.65737e11	−	6.33476e11i	−0.0451096	−	0.0781322i	−0.887699	+	0.460425i	$0.847697\pi$
$740$	−6.40872e11	+	3.63457e12i	−0.0785650	+	0.445564i
$741$		0			0
$742$	1.39742e11	+	5.08619e10i	0.0169242	+	0.00615991i
$743$	3.62672e12	+	1.32002e12i	0.436581	+	0.158902i	0.550954	−	0.834535i	$-0.314264\pi$
$743$	3.62672e12	+	1.32002e12i	0.436581	+	0.158902i	−0.114374	+	0.993438i	$0.536486\pi$
$744$		0			0
$745$	1.01911e12	−	5.77966e12i	0.121204	−	0.687384i
$746$	5.33538e11	+	9.24114e11i	0.0630725	+	0.109245i
$747$		0			0
$748$	−5.67120e12	+	9.82280e12i	−0.662396	+	1.14730i
$749$	4.78755e11	+	4.01723e11i	0.0555834	+	0.0466400i
$750$		0			0
$751$	−4.82128e11	−	2.73429e12i	−0.0553074	−	0.313664i	0.944586	−	0.328264i	$-0.106464\pi$
$751$	−4.82128e11	−	2.73429e12i	−0.0553074	−	0.313664i	−0.999893	+	0.0146003i	$0.995352\pi$
$752$	4.83538e12	−	4.05737e12i	0.551380	−	0.462662i
$753$		0			0
$754$	−1.27733e12	+	4.64910e11i	−0.143924	+	0.0523839i
$755$	3.78129e12			0.423524
$756$		0			0
$757$	1.43220e13			1.58516			0.792581	−	0.609767i	$-0.208737\pi$
$757$	1.43220e13			1.58516			0.792581	+	0.609767i	$0.208737\pi$
$758$	−2.46916e12	+	8.98699e11i	−0.271667	+	0.0988787i
$759$		0			0
$760$	−1.29358e12	+	1.08544e12i	−0.140647	+	0.118017i
$761$	−1.37154e12	−	7.77841e12i	−0.148244	−	0.840736i	−0.964705	−	0.263334i	$-0.915178\pi$
$761$	−1.37154e12	−	7.77841e12i	−0.148244	−	0.840736i	0.816460	−	0.577402i	$-0.195933\pi$
$762$		0			0
$763$	8.22161e11	+	6.89875e11i	0.0878206	+	0.0736902i
$764$	3.37490e12	−	5.84549e12i	0.358377	−	0.620727i
$765$		0			0
$766$	9.14800e11	+	1.58448e12i	0.0960056	+	0.166287i
$767$	2.89973e12	−	1.64452e13i	0.302537	−	1.71577i
$768$		0			0
$769$	1.36410e13	+	4.96493e12i	1.40663	+	0.511970i	0.930138	−	0.367210i	$-0.119687\pi$
$769$	1.36410e13	+	4.96493e12i	1.40663	+	0.511970i	0.476489	+	0.879180i	$0.341909\pi$
$770$	2.31106e11	+	8.41158e10i	0.0236921	+	0.00862322i
$771$		0			0
$772$	3.79347e10	−	2.15138e11i	0.00384378	−	0.0217992i
$773$	1.96630e12	+	3.40574e12i	0.198081	+	0.343086i	0.947906	−	0.318550i	$-0.103196\pi$
$773$	1.96630e12	+	3.40574e12i	0.198081	+	0.343086i	−0.749825	+	0.661636i	$0.769862\pi$
$774$		0			0
$775$	1.51356e12	−	2.62157e12i	0.150710	−	0.261038i
$776$	−4.89924e12	−	4.11095e12i	−0.485010	−	0.406972i
$777$		0			0
$778$	−3.51458e11	−	1.99322e12i	−0.0343927	−	0.195050i
$779$	4.14343e12	−	3.47675e12i	0.403126	−	0.338263i
$780$		0			0
$781$	−2.33820e13	+	8.51035e12i	−2.24881	+	0.818498i
$782$	−1.81114e12			−0.173190
$783$		0			0
$784$	−8.89982e12			−0.841316
$785$	5.08978e12	−	1.85253e12i	0.478394	−	0.174121i
$786$		0			0
$787$	1.19610e13	−	1.00364e13i	1.11143	−	0.932596i	0.113285	−	0.993562i	$-0.463863\pi$
$787$	1.19610e13	−	1.00364e13i	1.11143	−	0.932596i	0.998140	+	0.0609660i	$0.0194181\pi$
$788$	2.51276e12	+	1.42506e13i	0.232158	+	1.31663i
$789$		0			0
$790$	2.23811e11	+	1.87800e11i	0.0204437	+	0.0171543i
$791$	4.10844e11	−	7.11602e11i	0.0373149	−	0.0646313i
$792$		0			0
$793$	3.81076e12	+	6.60043e12i	0.342202	+	0.592711i
$794$	1.15931e11	−	6.57475e11i	0.0103516	−	0.0587066i
$795$		0			0
$796$	1.00735e13	+	3.66644e12i	0.889345	+	0.323695i
$797$	−6.32997e12	−	2.30392e12i	−0.555698	−	0.202258i	0.0488781	−	0.998805i	$-0.484435\pi$
$797$	−6.32997e12	−	2.30392e12i	−0.555698	−	0.202258i	−0.604576	+	0.796547i	$0.706658\pi$
$798$		0			0
$799$	1.62150e12	−	9.19599e12i	0.140753	−	0.798248i
$800$	1.08824e12	+	1.88489e12i	0.0939333	+	0.162697i
$801$		0			0
$802$	−2.55584e12	+	4.42685e12i	−0.218147	+	0.377842i
$803$	2.09334e13	+	1.75652e13i	1.77672	+	1.49085i
$804$		0			0
$805$	−1.25710e11	−	7.12937e11i	−0.0105509	−	0.0598370i
$806$	3.14987e12	−	2.64305e12i	0.262896	−	0.220596i
$807$		0			0
$808$	1.07336e12	−	3.90673e11i	0.0885923	−	0.0322450i
$809$	−8.17110e12			−0.670675			−0.335338	−	0.942098i	$-0.608850\pi$
$809$	−8.17110e12			−0.670675			−0.335338	+	0.942098i	$0.608850\pi$
$810$		0			0
$811$	2.07621e13			1.68530			0.842651	−	0.538460i	$-0.180994\pi$
$811$	2.07621e13			1.68530			0.842651	+	0.538460i	$0.180994\pi$
$812$	−4.54526e11	+	1.65434e11i	−0.0366908	+	0.0133543i
$813$		0			0
$814$	1.80922e12	−	1.51812e12i	0.144438	−	0.121198i
$815$	−8.20427e11	−	4.65287e12i	−0.0651375	−	0.369413i
$816$		0			0
$817$	7.12893e12	+	5.98188e12i	0.559790	+	0.469719i
$818$	6.07001e11	−	1.05136e12i	0.0474023	−	0.0821032i
$819$		0			0
$820$	5.47550e12	+	9.48385e12i	0.422923	+	0.732525i
$821$	−3.56272e12	+	2.02052e13i	−0.273676	+	1.55210i	0.469458	+	0.882955i	$0.344449\pi$
$821$	−3.56272e12	+	2.02052e13i	−0.273676	+	1.55210i	−0.743135	+	0.669142i	$0.766662\pi$
$822$		0			0
$823$	−1.30605e13	−	4.75362e12i	−0.992336	−	0.361181i	−0.205712	−	0.978613i	$-0.565951\pi$
$823$	−1.30605e13	−	4.75362e12i	−0.992336	−	0.361181i	−0.786625	+	0.617432i	$0.788173\pi$
$824$	2.86605e12	+	1.04316e12i	0.216576	+	0.0788274i
$825$		0			0
$826$	−5.59742e10	+	3.17445e11i	−0.00418386	+	0.0237279i
$827$	7.13700e12	+	1.23617e13i	0.530568	+	0.918971i	0.999364	+	0.0356643i	$0.0113547\pi$
$827$	7.13700e12	+	1.23617e13i	0.530568	+	0.918971i	−0.468796	+	0.883307i	$0.655312\pi$
$828$		0			0
$829$	−3.70442e12	+	6.41625e12i	−0.272411	+	0.471830i	−0.969479	−	0.245175i	$-0.921154\pi$
$829$	−3.70442e12	+	6.41625e12i	−0.272411	+	0.471830i	0.697067	+	0.717006i	$0.254488\pi$
$830$	8.21329e11	+	6.89177e11i	0.0600711	+	0.0504056i
$831$		0			0
$832$	−2.51267e12	−	1.42500e13i	−0.181794	−	1.03101i
$833$	−1.00857e13	+	8.46289e12i	−0.725776	+	0.608999i
$834$		0			0
$835$	1.13254e13	−	4.12212e12i	0.806242	−	0.293448i
$836$	−9.69725e12			−0.686626
$837$		0			0
$838$	3.11181e12			0.217979
$839$	1.28307e13	−	4.67001e12i	0.893970	−	0.325378i	0.146136	−	0.989264i	$-0.453316\pi$
$839$	1.28307e13	−	4.67001e12i	0.893970	−	0.325378i	0.747834	+	0.663886i	$0.231094\pi$
$840$		0			0
$841$	−8.81973e12	+	7.40063e12i	−0.607958	+	0.510137i
$842$	−8.20932e11	−	4.65573e12i	−0.0562863	−	0.319215i
$843$		0			0
$844$	−2.24217e12	−	1.88141e12i	−0.152100	−	0.127627i
$845$	7.51697e12	−	1.30198e13i	0.507210	−	0.878514i
$846$		0			0
$847$	7.71998e11	+	1.33714e12i	0.0515396	+	0.0892692i
$848$	1.94360e12	−	1.10227e13i	0.129070	−	0.731991i
$849$		0			0
$850$	9.17666e11	+	3.34003e11i	0.0602975	+	0.0219465i
$851$	−6.53277e12	−	2.37773e12i	−0.426987	−	0.155410i
$852$		0			0
$853$	−3.48320e12	+	1.97542e13i	−0.225272	+	1.27758i	0.636892	+	0.770953i	$0.280220\pi$
$853$	−3.48320e12	+	1.97542e13i	−0.225272	+	1.27758i	−0.862164	+	0.506628i	$0.830892\pi$
$854$	−7.35600e10	−	1.27410e11i	−0.00473240	−	0.00819675i
$855$		0			0
$856$	−2.77989e12	+	4.81491e12i	−0.176968	+	0.306518i
$857$	1.19917e13	+	1.00623e13i	0.759396	+	0.637209i	0.937970	−	0.346718i	$-0.112704\pi$
$857$	1.19917e13	+	1.00623e13i	0.759396	+	0.637209i	−0.178574	+	0.983927i	$0.557148\pi$
$858$		0			0
$859$	−1.80369e12	−	1.02293e13i	−0.113030	−	0.641025i	−0.987707	−	0.156318i	$-0.950037\pi$
$859$	−1.80369e12	−	1.02293e13i	−0.113030	−	0.641025i	0.874677	−	0.484707i	$-0.161074\pi$
$860$	−1.44335e13	+	1.21112e13i	−0.899766	+	0.754993i
$861$		0			0
$862$	5.41749e12	−	1.97180e12i	0.334207	−	0.121641i
$863$	−1.57454e13			−0.966288			−0.483144	−	0.875541i	$-0.660505\pi$
$863$	−1.57454e13			−0.966288			−0.483144	+	0.875541i	$0.660505\pi$
$864$		0			0
$865$	1.06471e13			0.646637
$866$	1.12849e12	−	4.10737e11i	0.0681817	−	0.0248161i
$867$		0			0
$868$	1.12085e12	−	9.40505e11i	0.0670207	−	0.0562370i
$869$	5.98495e11	+	3.39423e12i	0.0356018	+	0.201908i
$870$		0			0
$871$	−2.49030e13	−	2.08961e13i	−1.46612	−	1.23022i
$872$	−4.77387e12	+	8.26859e12i	−0.279606	+	0.484292i
$873$		0			0
$874$	−7.74224e11	−	1.34100e12i	−0.0448813	−	0.0777367i
$875$	−2.96683e11	+	1.68258e12i	−0.0171103	+	0.0970372i
$876$		0			0
$877$	1.03678e13	+	3.77357e12i	0.591818	+	0.215404i	0.620529	−	0.784184i	$-0.286918\pi$
$877$	1.03678e13	+	3.77357e12i	0.591818	+	0.215404i	−0.0287108	+	0.999588i	$0.509140\pi$
$878$	5.75641e12	+	2.09516e12i	0.326908	+	0.118985i
$879$		0			0
$880$	3.21434e12	−	1.82294e13i	0.180684	−	1.02471i
$881$	6.34675e12	+	1.09929e13i	0.354944	+	0.614781i	0.987108	−	0.160053i	$-0.0511665\pi$
$881$	6.34675e12	+	1.09929e13i	0.354944	+	0.614781i	−0.632164	+	0.774834i	$0.717833\pi$
$882$		0			0
$883$	−6.78125e11	+	1.17455e12i	−0.0375394	+	0.0650201i	−0.884185	−	0.467138i	$-0.845285\pi$
$883$	−6.78125e11	+	1.17455e12i	−0.0375394	+	0.0650201i	0.846645	+	0.532158i	$0.178619\pi$
$884$	−1.87321e13	−	1.57181e13i	−1.03169	−	0.865693i
$885$		0			0
$886$	3.31623e11	+	1.88073e12i	0.0180798	+	0.102536i
$887$	1.03849e13	−	8.71394e12i	0.563306	−	0.472670i	−0.316111	−	0.948722i	$-0.602377\pi$
$887$	1.03849e13	−	8.71394e12i	0.563306	−	0.472670i	0.879417	+	0.476052i	$0.157933\pi$
$888$		0			0
$889$	−2.39894e12	+	8.73142e11i	−0.128813	+	0.0468842i
$890$	4.09394e12			0.218719
$891$		0			0
$892$	−3.04211e13			−1.60891
$893$	7.50199e12	−	2.73050e12i	0.394771	−	0.143685i
$894$		0			0
$895$	1.75539e13	−	1.47295e13i	0.914471	−	0.767332i
$896$	2.41091e11	+	1.36729e12i	0.0124967	+	0.0708722i
$897$		0			0
$898$	−4.67829e12	−	3.92555e12i	−0.240073	−	0.201445i
$899$	−4.52808e12	+	7.84287e12i	−0.231204	+	0.400458i
$900$		0			0
$901$	−8.27896e12	−	1.43396e13i	−0.418518	−	0.724894i
$902$	1.21692e12	−	6.90147e12i	0.0612112	−	0.347146i
$903$		0			0
$904$	6.86895e12	+	2.50009e12i	0.342084	+	0.124508i
$905$	−2.86143e13	−	1.04147e13i	−1.41796	−	0.516095i
$906$		0			0
$907$	−4.77134e11	+	2.70596e12i	−0.0234103	+	0.132766i	−0.994273	−	0.106870i	$-0.965917\pi$
$907$	−4.77134e11	+	2.70596e12i	−0.0234103	+	0.132766i	0.970863	+	0.239636i	$0.0770282\pi$
$908$	−3.58016e12	−	6.20102e12i	−0.174790	−	0.302745i
$909$		0			0
$910$	−2.65108e11	+	4.59181e11i	−0.0128155	+	0.0221972i
$911$	−1.61221e13	−	1.35280e13i	−0.775512	−	0.650732i	0.166602	−	0.986024i	$-0.446720\pi$
$911$	−1.61221e13	−	1.35280e13i	−0.775512	−	0.650732i	−0.942114	+	0.335292i	$0.891165\pi$
$912$		0			0
$913$	2.19632e12	+	1.24559e13i	0.104611	+	0.593278i
$914$	−1.83434e12	+	1.53919e12i	−0.0869404	+	0.0729517i
$915$		0			0
$916$	−2.38610e12	+	8.68468e11i	−0.111985	+	0.0407590i
$917$	−1.23917e12			−0.0578721
$918$		0			0
$919$	−2.55574e13			−1.18194			−0.590972	−	0.806692i	$-0.701256\pi$
$919$	−2.55574e13			−1.18194			−0.590972	+	0.806692i	$0.701256\pi$
$920$	6.05179e12	−	2.20267e12i	0.278508	−	0.101369i
$921$		0			0
$922$	−1.79455e12	+	1.50581e12i	−0.0817836	+	0.0686246i
$923$	−9.31522e12	−	5.28292e13i	−0.422460	−	2.39589i
$924$		0			0
$925$	2.87152e12	+	2.40949e12i	0.128966	+	0.108215i
$926$	2.23400e12	−	3.86940e12i	0.0998467	−	0.172940i
$927$		0			0
$928$	−3.25565e12	−	5.63896e12i	−0.144103	−	0.249593i
$929$	6.29727e12	−	3.57136e13i	0.277384	−	1.57312i	−0.453901	−	0.891052i	$-0.649968\pi$
$929$	6.29727e12	−	3.57136e13i	0.277384	−	1.57312i	0.731285	−	0.682072i	$-0.238921\pi$
$930$		0			0
$931$	−1.05775e13	−	3.84988e12i	−0.461432	−	0.167947i
$932$	3.20026e13	+	1.16480e13i	1.38935	+	0.505684i
$933$		0			0
$934$	−1.14540e12	+	6.49591e12i	−0.0492491	+	0.279305i
$935$	−1.36918e13	−	2.37149e13i	−0.585880	−	1.01477i
$936$		0			0
$937$	−2.55461e12	+	4.42471e12i	−0.108267	+	0.187524i	−0.915068	−	0.403299i	$-0.867863\pi$
$937$	−2.55461e12	+	4.42471e12i	−0.108267	+	0.187524i	0.806801	+	0.590823i	$0.201197\pi$
$938$	4.80708e11	+	4.03362e11i	0.0202753	+	0.0170130i
$939$		0			0
$940$	2.80679e12	+	1.59181e13i	0.117256	+	0.664990i
$941$	3.82223e12	−	3.20723e12i	0.158914	−	0.133345i	−0.559863	−	0.828585i	$-0.689146\pi$
$941$	3.82223e12	−	3.20723e12i	0.158914	−	0.133345i	0.718778	+	0.695240i	$0.244702\pi$
$942$		0			0
$943$	−1.93843e13	+	7.05531e12i	−0.798266	+	0.290545i
$944$	2.42612e13			0.994348
$945$		0			0
$946$	1.20574e13			0.489491
$947$	−2.70313e13	+	9.83859e12i	−1.09217	+	0.397519i	−0.824426	−	0.565970i	$-0.808502\pi$
$947$	−2.70313e13	+	9.83859e12i	−1.09217	+	0.397519i	−0.267749	+	0.963489i	$0.586280\pi$
$948$		0			0
$949$	−4.51301e13	+	3.78687e13i	−1.80621	+	1.51559i
$950$	1.44982e11	+	8.22232e11i	0.00577506	+	0.0327520i
$951$		0			0
$952$	7.42794e11	+	6.23278e11i	0.0293091	+	0.0245932i
$953$	−2.07896e13	+	3.60087e13i	−0.816448	+	1.41413i	0.0918357	+	0.995774i	$0.470727\pi$
$953$	−2.07896e13	+	3.60087e13i	−0.816448	+	1.41413i	−0.908284	+	0.418355i	$0.862607\pi$
$954$		0			0
$955$	8.14792e12	+	1.41126e13i	0.316980	+	0.549025i
$956$	−5.24034e12	+	2.97195e13i	−0.202908	+	1.15075i
$957$		0			0
$958$	−5.97720e12	−	2.17552e12i	−0.229273	−	0.0834486i
$959$	2.05485e12	+	7.47906e11i	0.0784508	+	0.0285537i
$960$		0			0
$961$	1.65832e11	−	9.40478e11i	0.00627209	−	0.0355708i
$962$	2.54586e12	+	4.40956e12i	0.0958401	+	0.166000i
$963$		0			0
$964$	5.11926e12	−	8.86683e12i	0.190924	−	0.330690i
$965$	4.04024e11	+	3.39016e11i	0.0149980	+	0.0125848i
$966$		0			0
$967$	3.55453e12	+	2.01588e13i	0.130726	+	0.741386i	0.977741	+	0.209816i	$0.0672866\pi$
$967$	3.55453e12	+	2.01588e13i	0.130726	+	0.741386i	−0.847014	+	0.531570i	$0.821602\pi$
$968$	−1.05220e13	+	8.82900e12i	−0.385176	+	0.323201i
$969$		0			0
$970$	7.06309e12	−	2.57075e12i	0.256166	−	0.0932369i
$971$	2.70481e13			0.976451			0.488225	−	0.872718i	$-0.337644\pi$
$971$	2.70481e13			0.976451			0.488225	+	0.872718i	$0.337644\pi$
$972$		0			0
$973$	3.59253e12			0.128497
$974$	−6.39147e12	+	2.32630e12i	−0.227554	+	0.0828230i
$975$		0			0
$976$	−8.48244e12	+	7.11761e12i	−0.299224	+	0.251079i
$977$	8.79943e11	+	4.99040e12i	0.0308979	+	0.175231i	0.996352	−	0.0853443i	$-0.0271990\pi$
$977$	8.79943e11	+	4.99040e12i	0.0308979	+	0.175231i	−0.965454	+	0.260575i	$0.916088\pi$
$978$		0			0
$979$	3.69962e13	+	3.10435e13i	1.28717	+	1.08006i
$980$	1.13950e13	−	1.97367e13i	0.394636	−	0.683529i
$981$		0			0
$982$	−5.17858e12	−	8.96957e12i	−0.177709	−	0.307801i
$983$	−1.60186e12	+	9.08461e12i	−0.0547185	+	0.310324i	−0.999867	−	0.0163173i	$-0.994806\pi$
$983$	−1.60186e12	+	9.08461e12i	−0.0547185	+	0.310324i	0.945148	+	0.326641i	$0.105917\pi$
$984$		0			0
$985$	−3.28287e13	−	1.19487e13i	−1.11119	−	0.404442i
$986$	−2.74535e12	−	9.99227e11i	−0.0925022	−	0.0336681i
$987$		0			0
$988$	3.63033e12	−	2.05886e13i	0.121210	−	0.687418i
$989$	−1.77459e13	−	3.07369e13i	−0.589815	−	1.02159i
$990$		0			0
$991$	2.01024e13	−	3.48184e13i	0.662090	−	1.14677i	−0.317975	−	0.948099i	$-0.603003\pi$
$991$	2.01024e13	−	3.48184e13i	0.662090	−	1.14677i	0.980065	−	0.198675i	$-0.0636638\pi$
$992$	1.50884e13	+	1.26607e13i	0.494698	+	0.415101i
$993$		0			0
$994$	1.79814e11	+	1.01977e12i	0.00584231	+	0.0331334i
$995$	−1.98259e13	+	1.66359e13i	−0.641254	+	0.538076i
$996$		0			0
$997$	−1.53940e13	+	5.60295e12i	−0.493427	+	0.179593i	−0.576735	−	0.816931i	$-0.695674\pi$
$997$	−1.53940e13	+	5.60295e12i	−0.493427	+	0.179593i	0.0833084	+	0.996524i	$0.473451\pi$
$998$	2.63691e12			0.0841410
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.19.12		156
3.2	odd	2		27.10.e.a.7.15	yes	156
27.4	even	9	inner	81.10.e.a.64.12		156
27.23	odd	18		27.10.e.a.4.15	✓	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.4.15	✓	156	27.23	odd	18
27.10.e.a.7.15	yes	156	3.2	odd	2
81.10.e.a.19.12		156	1.1	even	1	trivial
81.10.e.a.64.12		156	27.4	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.82322 + 1.75551i) q^{2} +(-372.033 + 312.173i) q^{4} +(-203.603 - 1154.69i) q^{5} +(-440.948 - 369.999i) q^{7} +(2560.36 - 4434.68i) q^{8} +(3009.09 + 5211.90i) q^{10} +(-12328.1 + 69916.4i) q^{11} +(-143827. - 52348.7i) q^{13} +(2776.32 + 1010.50i) q^{14} +(38614.5 - 218993. i) q^{16} +(-164482. - 284892. i) q^{17} +(140625. - 243570. i) q^{19} +(436210. + 366024. i) q^{20} +(-63277.4 - 358864. i) q^{22} +(-821687. + 689477. i) q^{23} +(543480. - 197811. i) q^{25} +785607. q^{26} +279551. q^{28} +(-1.62591e6 + 591785. i) q^{29} +(4.00947e6 - 3.36434e6i) q^{31} +(653471. + 3.70602e6i) q^{32} +(1.29346e6 + 1.08535e6i) q^{34} +(-337456. + 584492. i) q^{35} +(3.24063e6 + 5.61294e6i) q^{37} +(-250677. + 1.42166e6i) q^{38} +(-5.64198e6 - 2.05351e6i) q^{40} +(1.80717e7 + 6.57754e6i) q^{41} +(-5.74575e6 + 3.25858e7i) q^{43} +(-1.72395e7 - 2.98597e7i) q^{44} +(2.75279e6 - 4.76797e6i) q^{46} +(2.17446e7 + 1.82459e7i) q^{47} +(-6.94979e6 - 3.94142e7i) q^{49} +(-2.27407e6 + 1.90817e6i) q^{50} +(6.98503e7 - 2.54234e7i) q^{52} +5.03334e7 q^{53} +8.32418e7 q^{55} +(-2.76981e6 + 1.00813e6i) q^{56} +(6.80326e6 - 5.70861e6i) q^{58} +(1.89454e7 + 1.07445e8i) q^{59} +(-3.81453e7 - 3.20077e7i) q^{61} +(-1.34324e7 + 2.32656e7i) q^{62} +(4.72694e7 + 8.18730e7i) q^{64} +(-3.11630e7 + 1.76734e8i) q^{65} +(1.99585e8 + 7.26431e7i) q^{67} +(1.50128e8 + 5.46423e7i) q^{68} +(601546. - 3.41154e6i) q^{70} +(1.75242e8 + 3.03528e8i) q^{71} +(1.92455e8 - 3.33341e8i) q^{73} +(-2.54838e7 - 2.13835e7i) q^{74} +(2.37187e7 + 1.34516e8i) q^{76} +(3.13051e7 - 2.62681e7i) q^{77} +(4.56193e7 - 1.66041e7i) q^{79} -2.60732e8 q^{80} -9.87104e7 q^{82} +(1.67411e8 - 6.09326e7i) q^{83} +(-2.95473e8 + 2.47931e8i) q^{85} +(-2.94916e7 - 1.67255e8i) q^{86} +(2.78492e8 + 2.33682e8i) q^{88} +(3.40131e8 - 5.89124e8i) q^{89} +(4.40512e7 + 7.62990e7i) q^{91} +(9.04587e7 - 5.13017e8i) q^{92} +(-1.36910e8 - 4.98311e7i) q^{94} +(-3.09880e8 - 1.12787e8i) q^{95} +(2.16877e8 - 1.22997e9i) q^{97} +(1.02712e8 + 1.77903e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) \) 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Introduction

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