LMFDB - Embedded newform 81.10.e.a.10.2

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			10.2
Character	$\chi$	$=$	81.10
Dual form			81.10.e.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.66051 - 37.7736i) q^{2} +(-901.361 + 328.069i) q^{4} +(-1267.19 - 1063.30i) q^{5} +(-6241.55 - 2271.74i) q^{7} +(8576.64 + 14855.2i) q^{8} +(-31724.5 + 54948.4i) q^{10} +(37918.2 - 31817.2i) q^{11} +(-21165.8 + 120037. i) q^{13} +(-44239.9 + 250897. i) q^{14} +(127793. - 107231. i) q^{16} +(-276424. + 478780. i) q^{17} +(-125531. - 217426. i) q^{19} +(1.49103e6 + 542690. i) q^{20} +(-1.45440e6 - 1.22039e6i) q^{22} +(-1.39365e6 + 507246. i) q^{23} +(136009. + 771347. i) q^{25} +4.67521e6 q^{26} +6.37118e6 q^{28} +(-768276. - 4.35711e6i) q^{29} +(4.08737e6 - 1.48768e6i) q^{31} +(1.82609e6 + 1.53227e6i) q^{32} +(1.99264e7 + 7.25260e6i) q^{34} +(5.49369e6 + 9.51535e6i) q^{35} +(-2.07515e6 + 3.59427e6i) q^{37} +(-7.37687e6 + 6.18993e6i) q^{38} +(4.92725e6 - 2.79438e7i) q^{40} +(4.87410e6 - 2.76424e7i) q^{41} +(1.02503e7 - 8.60103e6i) q^{43} +(-2.37398e7 + 4.11185e7i) q^{44} +(2.84429e7 + 4.92645e7i) q^{46} +(-4.37834e7 - 1.59359e7i) q^{47} +(2.88352e6 + 2.41956e6i) q^{49} +(2.82307e7 - 1.02751e7i) q^{50} +(-2.03024e7 - 1.15141e8i) q^{52} +6.59519e7 q^{53} -8.18807e7 q^{55} +(-1.97845e7 - 1.12203e8i) q^{56} +(-1.59467e8 + 5.80411e7i) q^{58} +(-8.19525e7 - 6.87663e7i) q^{59} +(1.05647e8 + 3.84524e7i) q^{61} +(-8.34191e7 - 1.44486e8i) q^{62} +(8.84233e7 - 1.53154e8i) q^{64} +(1.54456e8 - 1.29604e8i) q^{65} +(-9.19132e6 + 5.21266e7i) q^{67} +(9.20849e7 - 5.22239e8i) q^{68} +(3.22839e8 - 2.70894e8i) q^{70} +(-1.13461e8 + 1.96520e8i) q^{71} +(-1.24677e8 - 2.15948e8i) q^{73} +(1.49590e8 + 5.44464e7i) q^{74} +(1.84479e8 + 1.54797e8i) q^{76} +(-3.08949e8 + 1.12448e8i) q^{77} +(3.72121e7 + 2.11041e8i) q^{79} -2.75957e8 q^{80} -1.07662e9 q^{82} +(1.45485e8 + 8.25085e8i) q^{83} +(8.59367e8 - 3.12784e8i) q^{85} +(-3.93164e8 - 3.29904e8i) q^{86} +(7.97860e8 + 2.90397e8i) q^{88} +(1.28696e8 + 2.22908e8i) q^{89} +(4.04800e8 - 7.01135e8i) q^{91} +(1.08977e9 - 9.14423e8i) q^{92} +(-3.10335e8 + 1.76000e9i) q^{94} +(-7.21172e7 + 4.08997e8i) q^{95} +(5.02984e6 - 4.22054e6i) q^{97} +(7.21899e7 - 1.25036e8i) 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−6.66051	−	37.7736i	−0.294356	−	1.66937i	−0.669810	−	0.742533i	$-0.733624\pi$
$2$	−6.66051	−	37.7736i	−0.294356	−	1.66937i	0.375454	−	0.926841i	$-0.377487\pi$
$3$		0			0
$3$		0			0
$4$	−901.361	+	328.069i	−1.76047	+	0.640759i
$5$	−1267.19	−	1063.30i	−0.906727	−	0.760834i	0.0647667	−	0.997900i	$-0.479370\pi$
$5$	−1267.19	−	1063.30i	−0.906727	−	0.760834i	−0.971493	+	0.237066i	$0.923814\pi$
$6$		0			0
$7$	−6241.55	−	2271.74i	−0.982543	−	0.357616i	−0.199714	−	0.979854i	$-0.564001\pi$
$7$	−6241.55	−	2271.74i	−0.982543	−	0.357616i	−0.782828	+	0.622238i	$0.786224\pi$
$8$	8576.64	+	14855.2i	0.740307	+	1.28225i
$9$		0			0
$10$	−31724.5	+	54948.4i	−1.00322	+	1.73762i
$11$	37918.2	−	31817.2i	0.780874	−	0.655231i	−0.162595	−	0.986693i	$-0.551986\pi$
$11$	37918.2	−	31817.2i	0.780874	−	0.655231i	0.943469	+	0.331462i	$0.107542\pi$
$12$		0			0
$13$	−21165.8	+	120037.i	−0.205537	+	1.16566i	0.691057	+	0.722801i	$0.257146\pi$
$13$	−21165.8	+	120037.i	−0.205537	+	1.16566i	−0.896593	+	0.442855i	$0.853966\pi$
$14$	−44239.9	+	250897.i	−0.307778	+	1.74550i
$15$		0			0
$16$	127793.	−	107231.i	0.487492	−	0.409054i
$17$	−276424.	+	478780.i	−0.802703	+	1.39032i	0.115127	+	0.993351i	$0.463272\pi$
$17$	−276424.	+	478780.i	−0.802703	+	1.39032i	−0.917831	+	0.396972i	$0.870061\pi$
$18$		0			0
$19$	−125531.	−	217426.i	−0.220984	−	0.382755i	0.734123	−	0.679016i	$-0.237593\pi$
$19$	−125531.	−	217426.i	−0.220984	−	0.382755i	−0.955107	+	0.296261i	$0.904260\pi$
$20$	1.49103e6	+	542690.i	2.08378	+	0.758433i
$21$		0			0
$22$	−1.45440e6	−	1.22039e6i	−1.32368	−	1.11070i
$23$	−1.39365e6	+	507246.i	−1.03843	+	0.377958i	−0.804285	−	0.594244i	$-0.797451\pi$
$23$	−1.39365e6	+	507246.i	−1.03843	+	0.377958i	−0.234145	+	0.972202i	$0.575229\pi$
$24$		0			0
$25$	136009.	+	771347.i	0.0696367	+	0.394930i
$26$	4.67521e6			2.00642
$27$		0			0
$28$	6.37118e6			1.95888
$29$	−768276.	−	4.35711e6i	−0.201709	−	1.14395i	−0.902534	−	0.430618i	$-0.858296\pi$
$29$	−768276.	−	4.35711e6i	−0.201709	−	1.14395i	0.700825	−	0.713333i	$-0.252815\pi$
$30$		0			0
$31$	4.08737e6	−	1.48768e6i	0.794907	−	0.289323i	0.0875328	−	0.996162i	$-0.472102\pi$
$31$	4.08737e6	−	1.48768e6i	0.794907	−	0.289323i	0.707374	+	0.706839i	$0.249880\pi$
$32$	1.82609e6	+	1.53227e6i	0.307856	+	0.258322i
$33$		0			0
$34$	1.99264e7	+	7.25260e6i	2.55725	+	0.930762i
$35$	5.49369e6	+	9.51535e6i	0.618811	+	1.07181i
$36$		0			0
$37$	−2.07515e6	+	3.59427e6i	−0.182030	+	0.315285i	−0.942572	−	0.334004i	$-0.891600\pi$
$37$	−2.07515e6	+	3.59427e6i	−0.182030	+	0.315285i	0.760542	+	0.649289i	$0.224933\pi$
$38$	−7.37687e6	+	6.18993e6i	−0.573913	+	0.481570i
$39$		0			0
$40$	4.92725e6	−	2.79438e7i	0.304323	−	1.72590i
$41$	4.87410e6	−	2.76424e7i	0.269381	−	1.52774i	−0.486881	−	0.873468i	$-0.661866\pi$
$41$	4.87410e6	−	2.76424e7i	0.269381	−	1.52774i	0.756263	−	0.654268i	$-0.227023\pi$
$42$		0			0
$43$	1.02503e7	−	8.60103e6i	0.457224	−	0.383656i	−0.384884	−	0.922965i	$-0.625759\pi$
$43$	1.02503e7	−	8.60103e6i	0.457224	−	0.383656i	0.842108	+	0.539308i	$0.181314\pi$
$44$	−2.37398e7	+	4.11185e7i	−0.954860	+	1.65387i
$45$		0			0
$46$	2.84429e7	+	4.92645e7i	0.936620	+	1.62227i
$47$	−4.37834e7	−	1.59359e7i	−1.30879	−	0.476360i	−0.408939	−	0.912562i	$-0.634101\pi$
$47$	−4.37834e7	−	1.59359e7i	−1.30879	−	0.476360i	−0.899849	+	0.436202i	$0.856323\pi$
$48$		0			0
$49$	2.88352e6	+	2.41956e6i	0.0714563	+	0.0599590i
$50$	2.82307e7	−	1.02751e7i	0.638787	−	0.232499i
$51$		0			0
$52$	−2.03024e7	−	1.15141e8i	−0.385063	−	2.18380i
$53$	6.59519e7			1.14812			0.574059	−	0.818814i	$-0.305368\pi$
$53$	6.59519e7			1.14812			0.574059	+	0.818814i	$0.305368\pi$
$54$		0			0
$55$	−8.18807e7			−1.20656
$56$	−1.97845e7	−	1.12203e8i	−0.268830	−	1.52461i
$57$		0			0
$58$	−1.59467e8	+	5.80411e7i	−1.85031	+	0.673457i
$59$	−8.19525e7	−	6.87663e7i	−0.880498	−	0.738825i	0.0857836	−	0.996314i	$-0.472661\pi$
$59$	−8.19525e7	−	6.87663e7i	−0.880498	−	0.738825i	−0.966281	+	0.257488i	$0.917105\pi$
$60$		0			0
$61$	1.05647e8	+	3.84524e7i	0.976953	+	0.355582i	0.780655	−	0.624963i	$-0.214886\pi$
$61$	1.05647e8	+	3.84524e7i	0.976953	+	0.355582i	0.196298	+	0.980544i	$0.437108\pi$
$62$	−8.34191e7	−	1.44486e8i	−0.716973	−	1.24183i
$63$		0			0
$64$	8.84233e7	−	1.53154e8i	0.658805	−	1.14108i
$65$	1.54456e8	−	1.29604e8i	1.07324	−	0.900552i
$66$		0			0
$67$	−9.19132e6	+	5.21266e7i	−0.0557239	+	0.316026i	−0.999910	−	0.0133854i	$-0.995739\pi$
$67$	−9.19132e6	+	5.21266e7i	−0.0557239	+	0.316026i	0.944187	+	0.329411i	$0.106850\pi$
$68$	9.20849e7	−	5.22239e8i	0.522274	−	2.96196i
$69$		0			0
$70$	3.22839e8	−	2.70894e8i	1.60710	−	1.34852i
$71$	−1.13461e8	+	1.96520e8i	−0.529888	+	0.917792i	0.469505	+	0.882930i	$0.344433\pi$
$71$	−1.13461e8	+	1.96520e8i	−0.529888	+	0.917792i	−0.999392	+	0.0348621i	$0.988901\pi$
$72$		0			0
$73$	−1.24677e8	−	2.15948e8i	−0.513848	−	0.890011i	−0.999871	−	0.0160648i	$-0.994886\pi$
$73$	−1.24677e8	−	2.15948e8i	−0.513848	−	0.890011i	0.486023	−	0.873946i	$-0.338447\pi$
$74$	1.49590e8	+	5.44464e7i	0.579910	+	0.211070i
$75$		0			0
$76$	1.84479e8	+	1.54797e8i	0.634288	+	0.532231i
$77$	−3.08949e8	+	1.12448e8i	−1.00156	+	0.364539i
$78$		0			0
$79$	3.72121e7	+	2.11041e8i	0.107489	+	0.609599i	0.990197	+	0.139677i	$0.0446066\pi$
$79$	3.72121e7	+	2.11041e8i	0.107489	+	0.609599i	−0.882708	+	0.469921i	$0.844282\pi$
$80$	−2.75957e8			−0.753244
$81$		0			0
$82$	−1.07662e9			−2.62966
$83$	1.45485e8	+	8.25085e8i	0.336485	+	1.90830i	0.412048	+	0.911162i	$0.364814\pi$
$83$	1.45485e8	+	8.25085e8i	0.336485	+	1.90830i	−0.0755624	+	0.997141i	$0.524075\pi$
$84$		0			0
$85$	8.59367e8	−	3.12784e8i	1.78564	−	0.649919i
$86$	−3.93164e8	−	3.29904e8i	−0.775052	−	0.650346i
$87$		0			0
$88$	7.97860e8	+	2.90397e8i	1.41826	+	0.516203i
$89$	1.28696e8	+	2.22908e8i	0.217425	+	0.376592i	0.954020	−	0.299743i	$-0.0969008\pi$
$89$	1.28696e8	+	2.22908e8i	0.217425	+	0.376592i	−0.736595	+	0.676334i	$0.763567\pi$
$90$		0			0
$91$	4.04800e8	−	7.01135e8i	0.618806	−	1.07180i
$92$	1.08977e9	−	9.14423e8i	1.58595	−	1.33077i
$93$		0			0
$94$	−3.10335e8	+	1.76000e9i	−0.409973	+	2.32507i
$95$	−7.21172e7	+	4.08997e8i	−0.0908411	+	0.515186i
$96$		0			0
$97$	5.02984e6	−	4.22054e6i	0.00576875	−	0.00484055i	−0.639899	−	0.768459i	$-0.721024\pi$
$97$	5.02984e6	−	4.22054e6i	0.00576875	−	0.00484055i	0.645667	+	0.763619i	$0.276579\pi$
$98$	7.21899e7	−	1.25036e8i	0.0790604	−	0.136937i
$99$		0			0
$100$	−3.75648e8	−	6.50642e8i	−0.375648	−	0.650642i
$101$	9.56729e8	+	3.48221e8i	0.914835	+	0.332973i	0.756182	−	0.654361i	$-0.227063\pi$
$101$	9.56729e8	+	3.48221e8i	0.914835	+	0.332973i	0.158653	+	0.987334i	$0.449285\pi$
$102$		0			0
$103$	8.84812e8	+	7.42445e8i	0.774610	+	0.649975i	0.941885	−	0.335935i	$-0.109052\pi$
$103$	8.84812e8	+	7.42445e8i	0.774610	+	0.649975i	−0.167275	+	0.985910i	$0.553497\pi$
$104$	−1.96470e9	+	7.15093e8i	−1.64682	+	0.599394i
$105$		0			0
$106$	−4.39273e8	−	2.49124e9i	−0.337955	−	1.91664i
$107$	−6.92477e8			−0.510714			−0.255357	−	0.966847i	$-0.582193\pi$
$107$	−6.92477e8			−0.510714			−0.255357	+	0.966847i	$0.582193\pi$
$108$		0			0
$109$	1.43630e9			0.974599			0.487300	−	0.873235i	$-0.337982\pi$
$109$	1.43630e9			0.974599			0.487300	+	0.873235i	$0.337982\pi$
$110$	5.45367e8	+	3.09293e9i	0.355158	+	2.01420i
$111$		0			0
$112$	−1.04123e9	+	3.78976e8i	−0.625266	+	0.227578i
$113$	3.02900e7	+	2.54163e7i	0.0174762	+	0.0146643i	0.651484	−	0.758662i	$-0.274147\pi$
$113$	3.02900e7	+	2.54163e7i	0.0174762	+	0.0146643i	−0.634008	+	0.773327i	$0.718591\pi$
$114$		0			0
$115$	2.30537e9	+	8.39085e8i	1.22914	+	0.447369i
$116$	2.12192e9	+	3.67528e9i	1.08810	+	1.88464i
$117$		0			0
$118$	−2.05171e9	+	3.55366e9i	−0.974196	+	1.68736i
$119$	2.81298e9	−	2.36037e9i	1.28589	−	1.07899i
$120$		0			0
$121$	1.60061e7	−	9.07752e7i	0.00678816	−	0.0384975i
$122$	7.48823e8	−	4.24679e9i	0.306027	−	1.73557i
$123$		0			0
$124$	−3.19614e9	+	2.68188e9i	−1.21402	+	1.01869i
$125$	−9.67606e8	+	1.67594e9i	−0.354490	+	0.613994i
$126$		0			0
$127$	−1.67167e9	−	2.89543e9i	−0.570210	−	0.987633i	−0.996544	−	0.0830672i	$-0.973528\pi$
$127$	−1.67167e9	−	2.89543e9i	−0.570210	−	0.987633i	0.426334	−	0.904566i	$-0.359805\pi$
$128$	−5.22721e9	−	1.90255e9i	−1.72118	−	0.626457i
$129$		0			0
$130$	−5.92437e9	−	4.97114e9i	−1.81927	−	1.52655i
$131$	1.75537e9	−	6.38902e8i	0.520772	−	0.189545i	−0.0682414	−	0.997669i	$-0.521739\pi$
$131$	1.75537e9	−	6.38902e8i	0.520772	−	0.189545i	0.589013	+	0.808123i	$0.299517\pi$
$132$		0			0
$133$	2.89573e8	+	1.64225e9i	0.0802464	+	0.455100i
$134$	2.03023e9			0.543968
$135$		0			0
$136$	−9.48314e9			−2.37699
$137$	1.11329e8	+	6.31377e8i	0.0270001	+	0.153125i	0.995327	−	0.0965601i	$-0.0307840\pi$
$137$	1.11329e8	+	6.31377e8i	0.0270001	+	0.153125i	−0.968327	+	0.249685i	$0.919673\pi$
$138$		0			0
$139$	−7.13598e9	+	2.59728e9i	−1.62139	+	0.590137i	−0.983646	−	0.180112i	$-0.942354\pi$
$139$	−7.13598e9	+	2.59728e9i	−1.62139	+	0.590137i	−0.637743	+	0.770250i	$0.720132\pi$
$140$	−8.07349e9	−	6.77446e9i	−1.77617	−	1.49039i
$141$		0			0
$142$	8.17898e9	+	2.97691e9i	1.68811	+	0.614423i
$143$	3.01667e9	+	5.22503e9i	0.603276	+	1.04490i
$144$		0			0
$145$	−3.65935e9	+	6.33819e9i	−0.687462	+	1.19072i
$146$	−7.32670e9	+	6.14783e9i	−1.33451	+	1.11978i
$147$		0			0
$148$	6.91295e8	−	3.92053e9i	0.118437	−	0.671687i
$149$	−1.00593e9	+	5.70488e9i	−0.167197	+	0.948219i	0.779574	+	0.626310i	$0.215436\pi$
$149$	−1.00593e9	+	5.70488e9i	−0.167197	+	0.948219i	−0.946771	+	0.321909i	$0.895676\pi$
$150$		0			0
$151$	6.91249e9	−	5.80027e9i	1.08203	−	0.907929i	0.0859401	−	0.996300i	$-0.472611\pi$
$151$	6.91249e9	−	5.80027e9i	1.08203	−	0.907929i	0.996088	+	0.0883713i	$0.0281662\pi$
$152$	2.15327e9	−	3.72957e9i	0.327191	−	0.566712i
$153$		0			0
$154$	6.30533e9	+	1.09212e10i	0.903368	+	1.56468i
$155$	−6.76132e9	−	2.46092e9i	−0.940890	−	0.342456i
$156$		0			0
$157$	−3.44722e9	−	2.89256e9i	−0.452814	−	0.379956i	0.387665	−	0.921800i	$-0.373282\pi$
$157$	−3.44722e9	−	2.89256e9i	−0.452814	−	0.379956i	−0.840479	+	0.541844i	$0.817726\pi$
$158$	7.72391e9	−	2.81127e9i	0.986008	−	0.358878i
$159$		0			0
$160$	−6.84742e8	−	3.88336e9i	−0.0826013	−	0.468455i
$161$	9.85084e9			1.15547
$162$		0			0
$163$	1.21094e10			1.34362			0.671810	−	0.740723i	$-0.265517\pi$
$163$	1.21094e10			1.34362			0.671810	+	0.740723i	$0.265517\pi$
$164$	4.67528e9	+	2.65148e10i	0.504673	+	2.86214i
$165$		0			0
$166$	3.01975e10	−	1.09910e10i	3.08663	−	1.12344i
$167$	6.62379e9	+	5.55802e9i	0.658995	+	0.552963i	0.909785	−	0.415079i	$-0.136246\pi$
$167$	6.62379e9	+	5.55802e9i	0.658995	+	0.552963i	−0.250790	+	0.968041i	$0.580690\pi$
$168$		0			0
$169$	−3.99594e9	−	1.45440e9i	−0.376815	−	0.137150i
$170$	−1.75388e10	−	3.03781e10i	−1.61057	−	2.78959i
$171$		0			0
$172$	−6.41750e9	+	1.11154e10i	−0.559098	+	0.968386i
$173$	7.87225e9	−	6.60560e9i	0.668176	−	0.560667i	−0.244349	−	0.969687i	$-0.578574\pi$
$173$	7.87225e9	−	6.60560e9i	0.668176	−	0.560667i	0.912525	+	0.409021i	$0.134130\pi$
$174$		0			0
$175$	9.03390e8	−	5.12338e9i	0.0728122	−	0.412938i
$176$	1.43390e9	−	8.13203e9i	0.112645	−	0.638840i
$177$		0			0
$178$	7.56286e9	−	6.34600e9i	0.564672	−	0.473816i
$179$	3.34166e9	−	5.78792e9i	0.243289	−	0.421389i	−0.718360	−	0.695672i	$-0.755107\pi$
$179$	3.34166e9	−	5.78792e9i	0.243289	−	0.421389i	0.961649	+	0.274282i	$0.0884402\pi$
$180$		0			0
$181$	−1.57438e9	−	2.72690e9i	−0.109032	−	0.188850i	0.806346	−	0.591444i	$-0.201442\pi$
$181$	−1.57438e9	−	2.72690e9i	−0.109032	−	0.188850i	−0.915379	+	0.402594i	$0.868109\pi$
$182$	−2.91806e10	−	1.06209e10i	−1.97139	−	0.717527i
$183$		0			0
$184$	−1.94880e10	−	1.63524e10i	−1.25339	−	1.05172i
$185$	6.45139e9	−	2.34812e9i	0.404931	−	0.147383i
$186$		0			0
$187$	4.75192e9	+	2.69495e10i	0.284173	+	1.61162i
$188$	4.46927e10			2.60931
$189$		0			0
$190$	1.59296e10			0.886777
$191$	3.92109e9	+	2.22376e10i	0.213185	+	1.20903i	0.884028	+	0.467434i	$0.154821\pi$
$191$	3.92109e9	+	2.22376e10i	0.213185	+	1.20903i	−0.670843	+	0.741599i	$0.734068\pi$
$192$		0			0
$193$	1.70499e9	−	6.20566e8i	0.0884533	−	0.0321944i	−0.297414	−	0.954748i	$-0.596124\pi$
$193$	1.70499e9	−	6.20566e8i	0.0884533	−	0.0321944i	0.385868	+	0.922554i	$0.373902\pi$
$194$	−1.92926e8	−	1.61884e8i	−0.00977875	−	0.00820535i
$195$		0			0
$196$	−3.39287e9	−	1.23491e9i	−0.164216	−	0.0597697i
$197$	1.01275e10	+	1.75413e10i	0.479074	+	0.829781i	0.999712	−	0.0239967i	$-0.00763912\pi$
$197$	1.01275e10	+	1.75413e10i	0.479074	+	0.829781i	−0.520638	+	0.853778i	$0.674306\pi$
$198$		0			0
$199$	1.39361e10	−	2.41380e10i	0.629945	−	1.09110i	−0.357618	−	0.933868i	$-0.616411\pi$
$199$	1.39361e10	−	2.41380e10i	0.629945	−	1.09110i	0.987562	−	0.157228i	$-0.0502557\pi$
$200$	−1.02920e10	+	8.63600e9i	−0.454846	+	0.381661i
$201$		0			0
$202$	6.78126e9	−	3.84585e10i	0.286569	−	1.62521i
$203$	−5.10298e9	+	2.89404e10i	−0.210907	+	1.19612i
$204$		0			0
$205$	−3.55685e10	+	2.98455e10i	−1.40661	+	1.18028i
$206$	2.21515e10	−	3.83676e10i	0.857041	−	1.48444i
$207$		0			0
$208$	1.01669e10	+	1.76095e10i	0.376619	+	0.652323i
$209$	−1.16778e10	−	4.25037e9i	−0.423353	−	0.154088i
$210$		0			0
$211$	−2.27641e10	−	1.91014e10i	−0.790643	−	0.663428i	0.155262	−	0.987873i	$-0.450378\pi$
$211$	−2.27641e10	−	1.91014e10i	−0.790643	−	0.663428i	−0.945904	+	0.324445i	$0.894822\pi$
$212$	−5.94465e10	+	2.16368e10i	−2.02123	+	0.735666i
$213$		0			0
$214$	4.61225e9	+	2.61573e10i	0.150332	+	0.852573i
$215$	−2.21345e10			−0.706476
$216$		0			0
$217$	−2.88912e10			−0.884497
$218$	−9.56649e9	−	5.42543e10i	−0.286879	−	1.62697i
$219$		0			0
$220$	7.38041e10	−	2.68625e10i	2.12412	−	0.773115i
$221$	−5.16206e10	−	4.33148e10i	−1.45565	−	1.22144i
$222$		0			0
$223$	−2.27683e10	−	8.28698e9i	−0.616536	−	0.224401i	0.0148246	−	0.999890i	$-0.495281\pi$
$223$	−2.27683e10	−	8.28698e9i	−0.616536	−	0.224401i	−0.631361	+	0.775489i	$0.717503\pi$
$224$	−7.91673e9	−	1.37122e10i	−0.210102	−	0.363907i
$225$		0			0
$226$	7.58320e8	−	1.31345e9i	0.0193359	−	0.0334908i
$227$	−2.46596e10	+	2.06918e10i	−0.616409	+	0.517229i	−0.896672	−	0.442695i	$-0.854023\pi$
$227$	−2.46596e10	+	2.06918e10i	−0.616409	+	0.517229i	0.280263	+	0.959923i	$0.409578\pi$
$228$		0			0
$229$	−1.21430e10	+	6.88665e10i	−0.291788	+	1.65481i	0.388192	+	0.921579i	$0.373100\pi$
$229$	−1.21430e10	+	6.88665e10i	−0.291788	+	1.65481i	−0.679979	+	0.733231i	$0.738011\pi$
$230$	1.63404e10	−	9.26708e10i	0.385023	−	2.18357i
$231$		0			0
$232$	5.81364e10	−	4.87822e10i	1.31750	−	1.10552i
$233$	3.99736e10	−	6.92363e10i	0.888529	−	1.53898i	0.0469149	−	0.998899i	$-0.485061\pi$
$233$	3.99736e10	−	6.92363e10i	0.888529	−	1.53898i	0.841614	−	0.540079i	$-0.181606\pi$
$234$		0			0
$235$	3.85373e10	+	6.67485e10i	0.824282	+	1.42770i
$236$	9.64289e10	+	3.50972e10i	2.02350	+	0.736494i
$237$		0			0
$238$	−1.07895e11	−	9.05350e10i	−2.17975	−	1.82903i
$239$	9.22270e9	−	3.35679e9i	0.182838	−	0.0665478i	−0.248979	−	0.968509i	$-0.580095\pi$
$239$	9.22270e9	−	3.35679e9i	0.182838	−	0.0665478i	0.431817	+	0.901961i	$0.357873\pi$
$240$		0			0
$241$	−1.34912e8	−	7.65126e8i	−0.00257617	−	0.0146102i	0.983493	−	0.180948i	$-0.0579167\pi$
$241$	−1.34912e8	−	7.65126e8i	−0.00257617	−	0.0146102i	−0.986069	+	0.166338i	$0.946806\pi$
$242$	−3.53552e9			−0.0662649
$243$		0			0
$244$	−1.07841e11			−1.94774
$245$	−1.08125e9	−	6.13208e9i	−0.0191725	−	0.108733i
$246$		0			0
$247$	2.87562e10	−	1.04664e10i	0.491580	−	0.178921i
$248$	5.71557e10	+	4.79593e10i	0.959459	+	0.805082i
$249$		0			0
$250$	6.97511e10	+	2.53873e10i	1.12933	+	0.411043i
$251$	9.77853e9	+	1.69369e10i	0.155504	+	0.269341i	0.933242	−	0.359247i	$-0.116967\pi$
$251$	9.77853e9	+	1.69369e10i	0.155504	+	0.269341i	−0.777738	+	0.628588i	$0.783633\pi$
$252$		0			0
$253$	−3.67055e10	+	6.35757e10i	−0.563233	+	0.975549i
$254$	−9.82365e10	+	8.24302e10i	−1.48088	+	1.24261i
$255$		0			0
$256$	−2.13272e10	+	1.20953e11i	−0.310352	+	1.76009i
$257$	−8.71450e9	+	4.94224e10i	−0.124607	+	0.706683i	0.856933	+	0.515428i	$0.172367\pi$
$257$	−8.71450e9	+	4.94224e10i	−0.124607	+	0.706683i	−0.981540	+	0.191255i	$0.938744\pi$
$258$		0			0
$259$	2.11174e10	−	1.77196e10i	0.291603	−	0.244684i
$260$	−9.67018e10	+	1.67492e11i	−1.31236	+	2.27308i
$261$		0			0
$262$	−3.58253e10	−	6.20512e10i	−0.469714	−	0.813569i
$263$	−1.49766e10	−	5.45104e9i	−0.193025	−	0.0702552i	0.243699	−	0.969851i	$-0.421639\pi$
$263$	−1.49766e10	−	5.45104e9i	−0.193025	−	0.0702552i	−0.436724	+	0.899596i	$0.643861\pi$
$264$		0			0
$265$	−8.35736e10	−	7.01266e10i	−1.04103	−	0.873527i
$266$	6.01050e10	−	2.18764e10i	0.736111	−	0.267923i
$267$		0			0
$268$	−8.81640e9	−	5.00003e10i	−0.104396	−	0.592060i
$269$	6.87430e10			0.800467			0.400233	−	0.916413i	$-0.368929\pi$
$269$	6.87430e10			0.800467			0.400233	+	0.916413i	$0.368929\pi$
$270$		0			0
$271$	−3.14947e10			−0.354711			−0.177356	−	0.984147i	$-0.556754\pi$
$271$	−3.14947e10			−0.354711			−0.177356	+	0.984147i	$0.556754\pi$
$272$	1.60151e10	+	9.08260e10i	0.177406	+	1.00612i
$273$		0			0
$274$	2.31079e10	−	8.41058e9i	0.247675	−	0.0901464i
$275$	2.96993e10	+	2.49207e10i	0.313148	+	0.262762i
$276$		0			0
$277$	5.24601e10	+	1.90939e10i	0.535389	+	0.194866i	0.595543	−	0.803323i	$-0.296937\pi$
$277$	5.24601e10	+	1.90939e10i	0.535389	+	0.194866i	−0.0601537	+	0.998189i	$0.519159\pi$
$278$	1.45638e11	+	2.52253e11i	1.46242	+	2.53299i
$279$		0			0
$280$	−9.42348e10	+	1.63219e11i	−0.916221	+	1.58694i
$281$	−6.77113e10	+	5.68165e10i	−0.647862	+	0.543621i	−0.906421	−	0.422374i	$-0.861197\pi$
$281$	−6.77113e10	+	5.68165e10i	−0.647862	+	0.543621i	0.258559	+	0.965995i	$0.416752\pi$
$282$		0			0
$283$	−2.70675e10	+	1.53507e11i	−0.250847	+	1.42262i	0.555666	+	0.831406i	$0.312463\pi$
$283$	−2.70675e10	+	1.53507e11i	−0.250847	+	1.42262i	−0.806512	+	0.591217i	$0.798648\pi$
$284$	3.77972e10	−	2.14358e11i	0.344768	−	1.95528i
$285$		0			0
$286$	1.77276e11	−	1.48752e11i	1.56676	−	1.31467i
$287$	−9.32183e10	+	1.61459e11i	−0.811022	+	1.40473i
$288$		0			0
$289$	−9.35261e10	−	1.61992e11i	−0.788665	−	1.36601i
$290$	2.63789e11	+	9.60115e10i	2.19011	+	0.797136i
$291$		0			0
$292$	1.83225e11	+	1.53744e11i	1.47490	+	1.23759i
$293$	1.41951e10	−	5.16660e9i	0.112521	−	0.0409544i	−0.285146	−	0.958484i	$-0.592042\pi$
$293$	1.41951e10	−	5.16660e9i	0.112521	−	0.0409544i	0.397667	+	0.917530i	$0.369820\pi$
$294$		0			0
$295$	3.07302e10	+	1.74280e11i	0.236247	+	1.33983i
$296$	−7.11914e10			−0.539032
$297$		0			0
$298$	2.22194e11			1.63215
$299$	−3.13907e10	−	1.78025e11i	−0.227133	−	1.28814i
$300$		0			0
$301$	−8.35172e10	+	3.03978e10i	−0.586444	+	0.213448i
$302$	−2.65138e11	−	2.22477e11i	−1.83417	−	1.53905i
$303$		0			0
$304$	−3.93568e10	−	1.43247e10i	−0.264295	−	0.0961955i
$305$	−9.29886e10	−	1.61061e11i	−0.615291	−	1.06571i
$306$		0			0
$307$	7.85491e10	−	1.36051e11i	0.504683	−	0.874136i	−0.495303	−	0.868720i	$-0.664943\pi$
$307$	7.85491e10	−	1.36051e11i	0.504683	−	0.874136i	0.999985	−	0.00541540i	$-0.00172378\pi$
$308$	2.41584e11	−	2.02713e11i	1.52964	−	1.28352i
$309$		0			0
$310$	−4.79240e10	+	2.71790e11i	−0.294731	+	1.67150i
$311$	−3.30446e10	+	1.87405e11i	−0.200299	+	1.13595i	0.704368	+	0.709835i	$0.251230\pi$
$311$	−3.30446e10	+	1.87405e11i	−0.200299	+	1.13595i	−0.904667	+	0.426118i	$0.859881\pi$
$312$		0			0
$313$	1.04760e9	−	8.79037e8i	0.00616942	−	0.00517676i	−0.639698	−	0.768627i	$-0.720940\pi$
$313$	1.04760e9	−	8.79037e8i	0.00616942	−	0.00517676i	0.645867	+	0.763450i	$0.276496\pi$
$314$	−8.63022e10	+	1.49480e11i	−0.501001	+	0.867759i
$315$		0			0
$316$	−1.02777e11	−	1.78016e11i	−0.579836	−	1.00431i
$317$	1.38987e10	+	5.05873e9i	0.0773052	+	0.0281368i	0.380383	−	0.924829i	$-0.375792\pi$
$317$	1.38987e10	+	5.05873e9i	0.0773052	+	0.0281368i	−0.303078	+	0.952966i	$0.598014\pi$
$318$		0			0
$319$	−1.67762e11	−	1.40769e11i	−0.907062	−	0.761115i
$320$	−2.74897e11	+	1.00054e11i	−1.46553	+	0.533410i
$321$		0			0
$322$	−6.56116e10	−	3.72102e11i	−0.340118	−	1.92890i
$323$	1.38799e11			0.709537
$324$		0			0
$325$	−9.54689e10			−0.474665
$326$	−8.06544e10	−	4.57414e11i	−0.395502	−	2.24301i
$327$		0			0
$328$	4.52436e11	−	1.64673e11i	2.15836	−	0.785580i
$329$	2.37074e11	+	1.98929e11i	1.11559	+	0.936088i
$330$		0			0
$331$	−2.28939e10	−	8.33270e9i	−0.104832	−	0.0381557i	0.289072	−	0.957307i	$-0.406653\pi$
$331$	−2.28939e10	−	8.33270e9i	−0.104832	−	0.0381557i	−0.393904	+	0.919152i	$0.628876\pi$
$332$	−4.01819e11	−	6.95971e11i	−1.81514	−	3.14391i
$333$		0			0
$334$	1.65829e11	−	2.87224e11i	0.729122	−	1.26288i
$335$	6.70732e10	−	5.62811e10i	0.290970	−	0.244153i
$336$		0			0
$337$	−1.72673e10	+	9.79279e10i	−0.0729274	+	0.413592i	0.926387	+	0.376572i	$0.122897\pi$
$337$	−1.72673e10	+	9.79279e10i	−0.0729274	+	0.413592i	−0.999315	+	0.0370193i	$0.988214\pi$
$338$	−2.83231e10	+	1.60628e11i	−0.118036	+	0.669417i
$339$		0			0
$340$	−6.71985e11	+	5.63862e11i	−2.72712	+	2.28833i
$341$	1.07652e11	−	1.86459e11i	0.431149	−	0.746772i
$342$		0			0
$343$	1.21516e11	+	2.10471e11i	0.474033	+	0.821050i
$344$	2.15683e11	+	7.85022e10i	0.830430	+	0.302252i
$345$		0			0
$346$	−3.01950e11	−	2.53367e11i	−1.13264	−	0.950401i
$347$	2.54080e10	−	9.24774e9i	0.0940778	−	0.0342415i	−0.294552	−	0.955635i	$-0.595171\pi$
$347$	2.54080e10	−	9.24774e9i	0.0940778	−	0.0342415i	0.388630	+	0.921394i	$0.372948\pi$
$348$		0			0
$349$	7.19556e9	+	4.08081e10i	0.0259627	+	0.147242i	0.995033	−	0.0995413i	$-0.0317375\pi$
$349$	7.19556e9	+	4.08081e10i	0.0259627	+	0.147242i	−0.969071	+	0.246783i	$0.920626\pi$
$350$	−1.99546e11			−0.710781
$351$		0			0
$352$	1.17995e11			0.409658
$353$	5.91040e10	+	3.35195e11i	0.202596	+	1.14898i	0.901178	+	0.433449i	$0.142703\pi$
$353$	5.91040e10	+	3.35195e11i	0.202596	+	1.14898i	−0.698582	+	0.715530i	$0.746185\pi$
$354$		0			0
$355$	3.52736e11	−	1.28385e11i	1.17875	−	0.429030i
$356$	−1.89131e11	−	1.58700e11i	−0.624075	−	0.523661i
$357$		0			0
$358$	−2.40888e11	−	8.76759e10i	−0.775070	−	0.282102i
$359$	−3.39530e10	−	5.88084e10i	−0.107883	−	0.186859i	0.807029	−	0.590511i	$-0.201074\pi$
$359$	−3.39530e10	−	5.88084e10i	−0.107883	−	0.186859i	−0.914912	+	0.403652i	$0.867741\pi$
$360$		0			0
$361$	1.29828e11	−	2.24868e11i	0.402333	−	0.696860i
$362$	−9.25189e10	+	7.76326e10i	−0.283166	+	0.237605i
$363$		0			0
$364$	−1.34851e11	+	7.64778e11i	−0.402622	+	2.28338i
$365$	−7.16268e10	+	4.06216e11i	−0.211231	+	1.19795i
$366$		0			0
$367$	−3.41197e11	+	2.86299e11i	−0.981767	+	0.823800i	−0.984355	−	0.176196i	$-0.943621\pi$
$367$	−3.41197e11	+	2.86299e11i	−0.981767	+	0.823800i	0.00258821	+	0.999997i	$0.499176\pi$
$368$	−1.23706e11	+	2.14265e11i	−0.351621	+	0.609025i
$369$		0			0
$370$	−1.31666e11	−	2.28053e11i	−0.365231	−	0.632598i
$371$	−4.11642e11	−	1.49826e11i	−1.12807	−	0.410585i
$372$		0			0
$373$	1.34299e11	+	1.12690e11i	0.359238	+	0.301436i	0.804487	−	0.593971i	$-0.202440\pi$
$373$	1.34299e11	+	1.12690e11i	0.359238	+	0.301436i	−0.445249	+	0.895407i	$0.646885\pi$
$374$	9.86329e11	−	3.58995e11i	2.60675	−	0.948780i
$375$		0			0
$376$	−1.38784e11	−	7.87086e11i	−0.358093	−	2.03085i
$377$	5.39276e11			1.37491
$378$		0			0
$379$	3.84776e10			0.0957924			0.0478962	−	0.998852i	$-0.484748\pi$
$379$	3.84776e10			0.0957924			0.0478962	+	0.998852i	$0.484748\pi$
$380$	−6.91754e10	−	3.92313e11i	−0.170187	−	0.965177i
$381$		0			0
$382$	8.13879e11	−	2.96228e11i	1.95558	−	0.711771i
$383$	2.32590e11	+	1.95166e11i	0.552326	+	0.463457i	0.875728	−	0.482805i	$-0.160382\pi$
$383$	2.32590e11	+	1.95166e11i	0.552326	+	0.463457i	−0.323401	+	0.946262i	$0.604826\pi$
$384$		0			0
$385$	5.11063e11	+	1.86012e11i	1.18550	+	0.431486i
$386$	−3.47971e10	−	6.02704e10i	−0.0797811	−	0.138185i
$387$		0			0
$388$	−3.14908e9	+	5.45436e9i	−0.00705408	+	0.0122180i
$389$	4.59316e11	−	3.85412e11i	1.01704	−	0.853398i	0.0277873	−	0.999614i	$-0.491154\pi$
$389$	4.59316e11	−	3.85412e11i	1.01704	−	0.853398i	0.989253	+	0.146216i	$0.0467094\pi$
$390$		0			0
$391$	1.42378e11	−	8.07464e11i	0.308068	−	1.74714i
$392$	−1.12121e10	+	6.35869e10i	−0.0239828	+	0.136013i
$393$		0			0
$394$	5.95144e11	−	4.99385e11i	1.24420	−	1.04400i
$395$	1.77244e11	−	3.06996e11i	0.366341	−	0.634520i
$396$		0			0
$397$	4.81387e11	+	8.33786e11i	0.972606	+	1.68460i	0.687620	+	0.726071i	$0.258656\pi$
$397$	4.81387e11	+	8.33786e11i	0.972606	+	1.68460i	0.284986	+	0.958532i	$0.408011\pi$
$398$	−1.00460e12	−	3.65645e11i	−2.00687	−	0.730443i
$399$		0			0
$400$	1.00093e11	+	8.39883e10i	0.195495	+	0.164040i
$401$	−4.21153e11	+	1.53287e11i	−0.813373	+	0.296044i	−0.715016	−	0.699108i	$-0.753581\pi$
$401$	−4.21153e11	+	1.53287e11i	−0.813373	+	0.296044i	−0.0983565	+	0.995151i	$0.531359\pi$
$402$		0			0
$403$	9.20645e10	+	5.22124e11i	0.173868	+	0.986054i
$404$	−9.76599e11			−1.82390
$405$		0			0
$406$	1.12717e12			2.05884
$407$	3.56734e10	+	2.02314e11i	0.0644421	+	0.365469i
$408$		0			0
$409$	−9.30266e11	+	3.38589e11i	−1.64381	+	0.598299i	−0.987699	−	0.156364i	$-0.950023\pi$
$409$	−9.30266e11	+	3.38589e11i	−1.64381	+	0.598299i	−0.656113	+	0.754663i	$0.727800\pi$
$410$	1.36428e12	+	1.14477e12i	2.38438	+	2.00073i
$411$		0			0
$412$	−1.04111e12	−	3.78932e11i	−1.78016	−	0.647924i
$413$	3.55292e11	+	6.15383e11i	0.600911	+	1.04081i
$414$		0			0
$415$	6.92955e11	−	1.20023e12i	1.14680	−	1.98632i
$416$	−2.22580e11	+	1.86767e11i	−0.364390	+	0.305760i
$417$		0			0
$418$	−8.27718e10	+	4.69422e11i	−0.132614	+	0.752091i
$419$	5.24542e10	−	2.97483e11i	0.0831414	−	0.471518i	−0.914601	−	0.404358i	$-0.867495\pi$
$419$	5.24542e10	−	2.97483e11i	0.0831414	−	0.471518i	0.997742	−	0.0671602i	$-0.0213939\pi$
$420$		0			0
$421$	1.32396e11	−	1.11094e11i	0.205403	−	0.172353i	−0.534283	−	0.845305i	$-0.679418\pi$
$421$	1.32396e11	−	1.11094e11i	0.205403	−	0.172353i	0.739686	+	0.672952i	$0.234974\pi$
$422$	−5.69908e11	+	9.87109e11i	−0.874779	+	1.51516i
$423$		0			0
$424$	5.65646e11	+	9.79727e11i	0.849960	+	1.47217i
$425$	−4.06901e11	−	1.48100e11i	−0.604977	−	0.220194i
$426$		0			0
$427$	−5.72048e11	−	4.80006e11i	−0.832736	−	0.698748i
$428$	6.24171e11	−	2.27180e11i	0.899098	−	0.327245i
$429$		0			0
$430$	1.47427e11	+	8.36102e11i	0.207955	+	1.17937i
$431$	7.96895e10			0.111238			0.0556190	−	0.998452i	$-0.482287\pi$
$431$	7.96895e10			0.111238			0.0556190	+	0.998452i	$0.482287\pi$
$432$		0			0
$433$	8.39928e10			0.114828			0.0574138	−	0.998350i	$-0.481715\pi$
$433$	8.39928e10			0.114828			0.0574138	+	0.998350i	$0.481715\pi$
$434$	1.92430e11	+	1.09132e12i	0.260357	+	1.47656i
$435$		0			0
$436$	−1.29463e12	+	4.71205e11i	−1.71575	+	0.624483i
$437$	2.85234e11	+	2.39340e11i	0.374141	+	0.313942i
$438$		0			0
$439$	−6.17433e10	−	2.24727e10i	−0.0793413	−	0.0288779i	0.302045	−	0.953294i	$-0.402331\pi$
$439$	−6.17433e10	−	2.24727e10i	−0.0793413	−	0.0288779i	−0.381386	+	0.924416i	$0.624553\pi$
$440$	−7.02261e11	−	1.21635e12i	−0.893226	−	1.54711i
$441$		0			0
$442$	−1.29234e12	+	2.23840e12i	−1.61056	+	2.78957i
$443$	−5.95235e11	+	4.99462e11i	−0.734297	+	0.616148i	−0.931299	−	0.364255i	$-0.881324\pi$
$443$	−5.95235e11	+	4.99462e11i	−0.734297	+	0.616148i	0.197002	+	0.980403i	$0.436879\pi$
$444$		0			0
$445$	7.39355e10	−	4.19309e11i	0.0893784	−	0.506890i
$446$	−1.61381e11	+	9.15236e11i	−0.193128	+	1.09528i
$447$		0			0
$448$	−8.99823e11	+	7.55041e11i	−1.05537	+	0.885564i
$449$	4.52852e11	−	7.84363e11i	0.525833	−	0.910769i	−0.473714	−	0.880679i	$-0.657087\pi$
$449$	4.52852e11	−	7.84363e11i	0.525833	−	0.910769i	0.999547	−	0.0300906i	$-0.00957960\pi$
$450$		0			0
$451$	−6.94686e11	−	1.20323e12i	−0.790667	−	1.36948i
$452$	−3.56406e10	−	1.29721e10i	−0.0401626	−	0.0146180i
$453$		0			0
$454$	9.45850e11	+	7.93663e11i	1.04489	+	0.876768i
$455$	−1.25847e12	+	4.58047e11i	−1.37655	+	0.501024i
$456$		0			0
$457$	−2.88192e9	−	1.63442e10i	−0.00309072	−	0.0175283i	0.983223	−	0.182405i	$-0.0583884\pi$
$457$	−2.88192e9	−	1.63442e10i	−0.00309072	−	0.0175283i	−0.986314	+	0.164877i	$0.947277\pi$
$458$	2.68221e12			2.84839
$459$		0			0
$460$	−2.35324e12			−2.45051
$461$	−1.11931e10	−	6.34793e10i	−0.0115424	−	0.0654603i	0.978493	−	0.206282i	$-0.0661366\pi$
$461$	−1.11931e10	−	6.34793e10i	−0.0115424	−	0.0654603i	−0.990035	+	0.140822i	$0.955025\pi$
$462$		0			0
$463$	6.27940e11	−	2.28552e11i	0.635044	−	0.231137i	−0.00438125	−	0.999990i	$-0.501395\pi$
$463$	6.27940e11	−	2.28552e11i	0.635044	−	0.231137i	0.639425	+	0.768853i	$0.279172\pi$
$464$	−5.65398e11	−	4.74425e11i	−0.566270	−	0.475157i
$465$		0			0
$466$	−2.88155e12	−	1.04880e12i	−2.83067	−	1.03028i
$467$	−4.30814e11	−	7.46191e11i	−0.419144	−	0.725979i	0.576709	−	0.816949i	$-0.304336\pi$
$467$	−4.30814e11	−	7.46191e11i	−0.419144	−	0.725979i	−0.995854	+	0.0909703i	$0.971003\pi$
$468$		0			0
$469$	1.75786e11	−	3.04471e11i	0.167767	−	0.290581i
$470$	2.26466e12	−	1.90027e12i	2.14073	−	1.79629i
$471$		0			0
$472$	3.18659e11	−	1.80720e12i	0.295520	−	1.67598i
$473$	1.15013e11	−	6.52272e11i	0.105651	−	0.599175i
$474$		0			0
$475$	1.50638e11	−	1.26400e11i	0.135773	−	0.113927i
$476$	−1.76114e12	+	3.05039e12i	−1.57240	+	2.72348i
$477$		0			0
$478$	−1.88226e11	−	3.26017e11i	−0.164913	−	0.285637i
$479$	−1.82421e12	−	6.63957e11i	−1.58330	−	0.576276i	−0.607385	−	0.794408i	$-0.707781\pi$
$479$	−1.82421e12	−	6.63957e11i	−1.58330	−	0.576276i	−0.975919	+	0.218132i	$0.930004\pi$
$480$		0			0
$481$	−3.87524e11	−	3.25171e11i	−0.330100	−	0.276987i
$482$	−2.80030e10	+	1.01922e10i	−0.0236316	+	0.00860119i
$483$		0			0
$484$	1.53532e10	+	8.70723e10i	0.0127173	+	0.0721234i
$485$	−1.08614e10			−0.00891353
$486$		0			0
$487$	5.72232e11			0.460991			0.230495	−	0.973073i	$-0.425965\pi$
$487$	5.72232e11			0.460991			0.230495	+	0.973073i	$0.425965\pi$
$488$	3.34880e11	+	1.89920e12i	0.267301	+	1.51594i
$489$		0			0
$490$	−2.24429e11	+	8.16856e10i	−0.175872	+	0.0640122i
$491$	−7.12809e11	−	5.98118e11i	−0.553486	−	0.464430i	0.322634	−	0.946524i	$-0.395432\pi$
$491$	−7.12809e11	−	5.98118e11i	−0.553486	−	0.464430i	−0.876119	+	0.482094i	$0.839876\pi$
$492$		0			0
$493$	2.29846e12	+	8.36573e11i	1.75237	+	0.637812i
$494$	−5.86884e11	−	1.01651e12i	−0.443385	−	0.767965i
$495$		0			0
$496$	3.62812e11	−	6.28409e11i	0.269162	−	0.466203i
$497$	1.15461e12	−	9.68837e11i	0.848855	−	0.712274i
$498$		0			0
$499$	−1.58542e11	+	8.99136e11i	−0.114470	+	0.649191i	0.872541	+	0.488540i	$0.162470\pi$
$499$	−1.58542e11	+	8.99136e11i	−0.114470	+	0.649191i	−0.987011	+	0.160651i	$0.948641\pi$
$500$	3.22338e11	−	1.82807e12i	0.230646	−	1.30806i
$501$		0			0
$502$	5.74638e11	−	4.82179e11i	0.403857	−	0.338876i
$503$	7.25687e11	−	1.25693e12i	0.505467	−	0.875495i	−0.494513	−	0.869170i	$-0.664653\pi$
$503$	7.25687e11	−	1.25693e12i	0.505467	−	0.875495i	0.999980	−	0.00632474i	$-0.00201324\pi$
$504$		0			0
$505$	−8.42094e11	−	1.45855e12i	−0.576169	−	0.997953i
$506$	2.64596e12	+	9.63051e11i	1.79435	+	0.653089i
$507$		0			0
$508$	2.45668e12	+	2.06140e12i	1.63667	+	1.37333i
$509$	−1.80985e12	+	6.58730e11i	−1.19512	+	0.434988i	−0.861519	−	0.507725i	$-0.830486\pi$
$509$	−1.80985e12	+	6.58730e11i	−1.19512	+	0.434988i	−0.333602	+	0.942714i	$0.608264\pi$
$510$		0			0
$511$	2.87604e11	+	1.63108e12i	0.186595	+	1.05823i
$512$	1.86278e12			1.19797
$513$		0			0
$514$	1.92490e12			1.21640
$515$	−3.31783e11	−	1.88164e12i	−0.207837	−	1.17870i
$516$		0			0
$517$	−2.16722e12	+	7.88804e11i	−1.33412	+	0.485581i
$518$	−8.09987e11	−	6.79660e11i	−0.494304	−	0.414770i
$519$		0			0
$520$	3.25001e12	+	1.18291e12i	1.94926	+	0.709472i
$521$	−4.58274e11	−	7.93754e11i	−0.272493	−	0.471972i	0.697007	−	0.717065i	$-0.254515\pi$
$521$	−4.58274e11	−	7.93754e11i	−0.272493	−	0.471972i	−0.969500	+	0.245093i	$0.921182\pi$
$522$		0			0
$523$	−1.67783e11	+	2.90608e11i	−0.0980594	+	0.169844i	−0.910881	−	0.412668i	$-0.864597\pi$
$523$	−1.67783e11	+	2.90608e11i	−0.0980594	+	0.169844i	0.812822	+	0.582512i	$0.197930\pi$
$524$	−1.37262e12	+	1.15176e12i	−0.795351	+	0.667378i
$525$		0			0
$526$	−1.06154e11	+	6.02027e11i	−0.0604643	+	0.342910i
$527$	−4.17574e11	+	2.36818e12i	−0.235823	+	1.33742i
$528$		0			0
$529$	3.05188e11	−	2.56083e11i	0.169440	−	0.142177i
$530$	−2.09229e12	+	3.62395e12i	−1.15181	+	1.99499i
$531$		0			0
$532$	−7.99781e11	−	1.38526e12i	−0.432881	−	0.749772i
$533$	3.21495e12	+	1.17015e12i	1.72545	+	0.628011i
$534$		0			0
$535$	8.77499e11	+	7.36309e11i	0.463078	+	0.388569i
$536$	−8.53180e11	+	3.10532e11i	−0.446477	+	0.162504i
$537$		0			0
$538$	−4.57863e11	−	2.59667e12i	−0.235622	−	1.33628i
$539$	1.86322e11			0.0950853
$540$		0			0
$541$	−2.23022e11			−0.111934			−0.0559668	−	0.998433i	$-0.517824\pi$
$541$	−2.23022e11			−0.111934			−0.0559668	+	0.998433i	$0.517824\pi$
$542$	2.09770e11	+	1.18967e12i	0.104411	+	0.592146i
$543$		0			0
$544$	−1.23840e12	+	4.50740e11i	−0.606268	+	0.220664i
$545$	−1.82006e12	−	1.52722e12i	−0.883695	−	0.741508i
$546$		0			0
$547$	−1.84968e12	−	6.73228e11i	−0.883392	−	0.321528i	−0.139814	−	0.990178i	$-0.544651\pi$
$547$	−1.84968e12	−	6.73228e11i	−0.883392	−	0.321528i	−0.743578	+	0.668649i	$0.766873\pi$
$548$	−3.07482e11	−	5.32575e11i	−0.145649	−	0.252271i
$549$		0			0
$550$	7.43531e11	−	1.28783e12i	0.346471	−	0.600106i
$551$	−8.50907e11	+	7.13995e11i	−0.393278	+	0.329999i
$552$		0			0
$553$	2.47168e11	−	1.40176e12i	0.112390	−	0.637396i
$554$	3.71835e11	−	2.10878e12i	0.167709	−	0.951125i
$555$		0			0
$556$	5.58001e12	−	4.68218e12i	2.47627	−	2.07784i
$557$	−2.02524e12	+	3.50782e12i	−0.891514	+	1.54415i	−0.0534524	+	0.998570i	$0.517023\pi$
$557$	−2.02524e12	+	3.50782e12i	−0.891514	+	1.54415i	−0.838061	+	0.545576i	$0.816311\pi$
$558$		0			0
$559$	8.15487e11	+	1.41246e12i	0.353235	+	0.611821i
$560$	1.72240e12	+	6.26902e11i	0.740095	+	0.269372i
$561$		0			0
$562$	2.59716e12	+	2.17927e12i	1.09821	+	0.921506i
$563$	3.48127e12	−	1.26708e12i	1.46033	−	0.531515i	0.514871	−	0.857268i	$-0.327840\pi$
$563$	3.48127e12	−	1.26708e12i	1.46033	−	0.531515i	0.945455	+	0.325753i	$0.105618\pi$
$564$		0			0
$565$	−1.13580e10	−	6.44146e10i	−0.00468906	−	0.0265930i
$566$	5.97881e12			2.44873
$567$		0			0
$568$	−3.89245e12			−1.56912
$569$	−7.46587e10	−	4.23411e11i	−0.0298590	−	0.169339i	0.966232	−	0.257675i	$-0.0829563\pi$
$569$	−7.46587e10	−	4.23411e11i	−0.0298590	−	0.169339i	−0.996091	+	0.0883358i	$0.971845\pi$
$570$		0			0
$571$	8.35234e11	−	3.04000e11i	0.328810	−	0.119677i	−0.172340	−	0.985038i	$-0.555133\pi$
$571$	8.35234e11	−	3.04000e11i	0.328810	−	0.119677i	0.501150	+	0.865360i	$0.332910\pi$
$572$	−4.43328e12	−	3.71996e12i	−1.73158	−	1.45297i
$573$		0			0
$574$	6.71976e12	+	2.44579e12i	2.58375	+	0.940408i
$575$	−5.80811e11	−	1.00599e12i	−0.221579	−	0.383787i
$576$		0			0
$577$	−1.70998e12	+	2.96177e12i	−0.642244	+	1.11240i	0.342686	+	0.939450i	$0.388663\pi$
$577$	−1.70998e12	+	2.96177e12i	−0.642244	+	1.11240i	−0.984931	+	0.172950i	$0.944670\pi$
$578$	−5.49609e12	+	4.61177e12i	−2.04823	+	1.71867i
$579$		0			0
$580$	1.21904e12	−	6.91351e12i	0.447292	−	2.53672i
$581$	9.66328e11	−	5.48032e12i	0.351829	−	1.99532i
$582$		0			0
$583$	2.50078e12	−	2.09840e12i	0.896535	−	0.752282i
$584$	2.13862e12	−	3.70421e12i	0.760811	−	1.31776i
$585$		0			0
$586$	−2.89708e11	−	5.01789e11i	−0.101489	−	0.175785i
$587$	5.87191e11	+	2.13720e11i	0.204131	+	0.0742975i	0.442062	−	0.896984i	$-0.354247\pi$
$587$	5.87191e11	+	2.13720e11i	0.204131	+	0.0742975i	−0.237931	+	0.971282i	$0.576469\pi$
$588$		0			0
$589$	−8.36553e11	−	7.01951e11i	−0.286401	−	0.240319i
$590$	6.37850e12	−	2.32159e12i	2.16713	−	0.788770i
$591$		0			0
$592$	1.20228e11	+	6.81844e11i	0.0402306	+	0.228159i
$593$	−4.28663e12			−1.42354			−0.711771	−	0.702412i	$-0.752107\pi$
$593$	−4.28663e12			−1.42354			−0.711771	+	0.702412i	$0.752107\pi$
$594$		0			0
$595$	−6.07434e12			−1.98689
$596$	−9.64892e11	−	5.47217e12i	−0.313235	−	1.77644i
$597$		0			0
$598$	−6.51559e12	+	2.37148e12i	−2.08352	+	0.758340i
$599$	2.17974e12	+	1.82902e12i	0.691805	+	0.580494i	0.919429	−	0.393255i	$-0.128651\pi$
$599$	2.17974e12	+	1.82902e12i	0.691805	+	0.580494i	−0.227624	+	0.973749i	$0.573096\pi$
$600$		0			0
$601$	−2.84017e12	−	1.03374e12i	−0.887992	−	0.323203i	−0.142562	−	0.989786i	$-0.545534\pi$
$601$	−2.84017e12	−	1.03374e12i	−0.887992	−	0.323203i	−0.745431	+	0.666583i	$0.767756\pi$
$602$	1.70450e12	+	2.95228e12i	0.528948	+	0.916164i
$603$		0			0
$604$	−4.32776e12	+	7.49591e12i	−1.32311	+	2.29170i
$605$	−1.16804e11	+	9.80101e10i	−0.0354452	+	0.0297421i
$606$		0			0
$607$	1.03064e12	−	5.84502e12i	0.308146	−	1.74758i	−0.300171	−	0.953886i	$-0.597044\pi$
$607$	1.03064e12	−	5.84502e12i	0.308146	−	1.74758i	0.608316	−	0.793695i	$-0.291845\pi$
$608$	1.03925e11	−	5.89388e11i	0.0308428	−	0.174918i
$609$		0			0
$610$	−5.46450e12	+	4.58526e12i	−1.59796	+	1.34085i
$611$	2.83960e12	−	4.91834e12i	0.824275	−	1.42769i
$612$		0			0
$613$	4.42844e11	+	7.67028e11i	0.126671	+	0.219401i	0.922385	−	0.386272i	$-0.126237\pi$
$613$	4.42844e11	+	7.67028e11i	0.126671	+	0.219401i	−0.795714	+	0.605673i	$0.792904\pi$
$614$	−5.66231e12	−	2.06091e12i	−1.60782	−	0.585197i
$615$		0			0
$616$	−4.32018e12	−	3.62506e12i	−1.20889	−	1.01438i
$617$	−5.20216e12	+	1.89343e12i	−1.44511	+	0.525977i	−0.941221	−	0.337792i	$-0.890320\pi$
$617$	−5.20216e12	+	1.89343e12i	−1.44511	+	0.525977i	−0.503889	+	0.863769i	$0.668098\pi$
$618$		0			0
$619$	4.67017e11	+	2.64859e12i	0.127857	+	0.725114i	0.979570	+	0.201105i	$0.0644532\pi$
$619$	4.67017e11	+	2.64859e12i	0.127857	+	0.725114i	−0.851713	+	0.524009i	$0.824436\pi$
$620$	6.90174e12			1.87584
$621$		0			0
$622$	7.29907e12			1.95529
$623$	−2.96874e11	−	1.68366e12i	−0.0789543	−	0.447772i
$624$		0			0
$625$	4.44569e12	−	1.61810e12i	1.16541	−	0.424175i
$626$	−4.01819e10	−	3.37166e10i	−0.0104579	−	0.00877526i
$627$		0			0
$628$	4.05614e12	+	1.47632e12i	1.04063	+	0.378757i
$629$	−1.14724e12	−	1.98708e12i	−0.292232	−	0.506160i
$630$		0			0
$631$	1.58541e12	−	2.74601e12i	0.398116	−	0.689557i	−0.595378	−	0.803446i	$-0.702998\pi$
$631$	1.58541e12	−	2.74601e12i	0.398116	−	0.689557i	0.993493	+	0.113889i	$0.0363309\pi$
$632$	−2.81589e12	+	2.36281e12i	−0.702083	+	0.589118i
$633$		0			0
$634$	9.85138e10	−	5.58699e11i	0.0242156	−	0.137334i
$635$	−9.60372e11	+	5.44654e12i	−0.234400	+	1.32935i
$636$		0			0
$637$	−3.51469e11	+	2.94917e11i	−0.0845784	+	0.0709697i
$638$	−4.19999e12	+	7.27459e12i	−1.00359	+	1.73826i
$639$		0			0
$640$	4.60089e12	+	7.96897e12i	1.08401	+	1.87755i
$641$	4.69733e12	+	1.70969e12i	1.09898	+	0.399996i	0.826940	−	0.562290i	$-0.190080\pi$
$641$	4.69733e12	+	1.70969e12i	1.09898	+	0.399996i	0.272040	+	0.962286i	$0.412302\pi$
$642$		0			0
$643$	5.48401e11	+	4.60163e11i	0.126517	+	0.106160i	0.703851	−	0.710348i	$-0.251462\pi$
$643$	5.48401e11	+	4.60163e11i	0.126517	+	0.106160i	−0.577334	+	0.816508i	$0.695907\pi$
$644$	−8.87917e12	+	3.23175e12i	−2.03416	+	0.740375i
$645$		0			0
$646$	−9.24472e11	−	5.24294e12i	−0.208856	−	1.18448i
$647$	2.81481e12			0.631509			0.315754	−	0.948841i	$-0.397742\pi$
$647$	2.81481e12			0.631509			0.315754	+	0.948841i	$0.397742\pi$
$648$		0			0
$649$	−5.29544e12			−1.17166
$650$	6.35872e11	+	3.60621e12i	0.139720	+	0.792393i
$651$		0			0
$652$	−1.09149e13	+	3.97270e12i	−2.36541	+	0.860937i
$653$	−1.28518e12	−	1.07839e12i	−0.276601	−	0.232096i	0.493925	−	0.869505i	$-0.335562\pi$
$653$	−1.28518e12	−	1.07839e12i	−0.276601	−	0.232096i	−0.770526	+	0.637409i	$0.780006\pi$
$654$		0			0
$655$	−2.90373e12	−	1.05687e12i	−0.616410	−	0.224355i
$656$	−2.34125e12	−	4.05516e12i	−0.493606	−	0.854951i
$657$		0			0
$658$	5.93523e12	−	1.02801e13i	1.23430	−	2.13787i
$659$	−3.55641e12	+	2.98419e12i	−0.734561	+	0.616370i	−0.931371	−	0.364072i	$-0.881386\pi$
$659$	−3.55641e12	+	2.98419e12i	−0.734561	+	0.616370i	0.196810	+	0.980442i	$0.436942\pi$
$660$		0			0
$661$	3.65973e10	−	2.07554e11i	0.00745664	−	0.0422887i	−0.980852	−	0.194752i	$-0.937610\pi$
$661$	3.65973e10	−	2.07554e11i	0.00745664	−	0.0422887i	0.988309	+	0.152464i	$0.0487207\pi$
$662$	−1.62271e11	+	9.20286e11i	−0.0328383	+	0.186235i
$663$		0			0
$664$	−1.10090e13	+	9.23766e12i	−2.19782	+	1.84419i
$665$	1.37926e12	−	2.38894e12i	0.273494	−	0.473706i
$666$		0			0
$667$	3.28083e12	+	5.68256e12i	0.641826	+	1.11168i
$668$	−7.79384e12	−	2.83672e12i	−1.51446	−	0.551218i
$669$		0			0
$670$	−2.57268e12	−	2.15874e12i	−0.493230	−	0.413869i
$671$	5.22940e12	−	1.90335e12i	0.995865	−	0.362465i
$672$		0			0
$673$	1.20305e11	+	6.82284e11i	0.0226056	+	0.128203i	0.994022	−	0.109179i	$-0.0348220\pi$
$673$	1.20305e11	+	6.82284e11i	0.0226056	+	0.128203i	−0.971417	+	0.237381i	$0.923711\pi$
$674$	3.81410e12			0.711906
$675$		0			0
$676$	4.07893e12			0.751252
$677$	1.35200e12	+	7.66757e12i	0.247359	+	1.40284i	0.814950	+	0.579531i	$0.196764\pi$
$677$	1.35200e12	+	7.66757e12i	0.247359	+	1.40284i	−0.567592	+	0.823310i	$0.692125\pi$
$678$		0			0
$679$	−4.09820e10	+	1.49162e10i	−0.00739910	+	0.00269305i
$680$	1.20169e13	+	1.00834e13i	2.15528	+	1.80849i
$681$		0			0
$682$	−7.76024e12	−	2.82450e12i	−1.37355	−	0.499932i
$683$	−1.68944e12	−	2.92620e12i	−0.297064	−	0.514530i	0.678399	−	0.734694i	$-0.262674\pi$
$683$	−1.68944e12	−	2.92620e12i	−0.297064	−	0.514530i	−0.975463	+	0.220164i	$0.929341\pi$
$684$		0			0
$685$	5.30267e11	−	9.18449e11i	0.0920210	−	0.159385i
$686$	7.14091e12	−	5.99194e12i	1.23110	−	1.03302i
$687$		0			0
$688$	3.87620e11	−	2.19830e12i	0.0659567	−	0.374059i
$689$	−1.39592e12	+	7.91668e12i	−0.235980	+	1.33831i
$690$		0			0
$691$	−3.19878e12	+	2.68409e12i	−0.533744	+	0.447864i	−0.869392	−	0.494123i	$-0.835489\pi$
$691$	−3.19878e12	+	2.68409e12i	−0.533744	+	0.447864i	0.335648	+	0.941987i	$0.391045\pi$
$692$	−4.92865e12	+	8.53667e12i	−0.817053	+	1.41518i
$693$		0			0
$694$	−5.18551e11	−	8.98156e11i	−0.0848542	−	0.146972i
$695$	1.18043e13	+	4.29642e12i	1.91915	+	0.698515i
$696$		0			0
$697$	1.18873e13	+	9.97463e12i	1.90781	+	1.60085i
$698$	1.49354e12	−	5.43605e11i	0.238160	−	0.0866830i
$699$		0			0
$700$	8.66539e11	+	4.91439e12i	0.136410	+	0.773621i
$701$	7.20180e12			1.12644			0.563222	−	0.826306i	$-0.309562\pi$
$701$	7.20180e12			1.12644			0.563222	+	0.826306i	$0.309562\pi$
$702$		0			0
$703$	1.04198e12			0.160902
$704$	−1.52006e12	−	8.62069e12i	−0.233230	−	1.32271i
$705$		0			0
$706$	1.22679e13	−	4.46514e12i	1.85844	−	0.676416i
$707$	−5.18041e12	−	4.34688e12i	−0.779788	−	0.654320i
$708$		0			0
$709$	7.73684e12	+	2.81598e12i	1.14989	+	0.418525i	0.845475	−	0.534015i	$-0.179317\pi$
$709$	7.73684e12	+	2.81598e12i	1.14989	+	0.418525i	0.304413	+	0.952540i	$0.401540\pi$
$710$	−7.19898e12	−	1.24690e13i	−1.06318	−	1.84149i
$711$		0			0
$712$	−2.20756e12	+	3.82360e12i	−0.321923	+	0.557587i
$713$	−4.94173e12	+	4.14660e12i	−0.716104	+	0.600882i
$714$		0			0
$715$	1.73307e12	−	9.82872e12i	0.247992	−	1.40643i
$716$	−1.11320e12	+	6.31330e12i	−0.158295	+	0.897734i
$717$		0			0
$718$	−1.99526e12	+	1.67422e12i	−0.280182	+	0.235100i
$719$	−7.23256e11	+	1.25272e12i	−0.100928	+	0.174813i	−0.912067	−	0.410041i	$-0.865515\pi$
$719$	−7.23256e11	+	1.25272e12i	−0.100928	+	0.174813i	0.811139	+	0.584853i	$0.198848\pi$
$720$		0			0
$721$	−3.83596e12	−	6.64407e12i	−0.528646	−	0.915642i
$722$	−9.35881e12	−	3.40633e12i	−1.28175	−	0.466519i
$723$		0			0
$724$	2.31370e12	+	1.94142e12i	0.312956	+	0.262601i
$725$	3.25635e12	−	1.18521e12i	0.437734	−	0.159322i
$726$		0			0
$727$	5.19680e11	+	2.94725e12i	0.0689972	+	0.391303i	0.999676	+	0.0254645i	$0.00810648\pi$
$727$	5.19680e11	+	2.94725e12i	0.0689972	+	0.391303i	−0.930679	+	0.365838i	$0.880782\pi$
$728$	1.38873e13			1.83243
$729$		0			0
$730$	1.58213e13			2.06200
$731$	1.28457e12	+	7.28517e12i	0.166391	+	0.943651i
$732$		0			0
$733$	7.93751e12	−	2.88902e12i	1.01558	−	0.369643i	0.220010	−	0.975498i	$-0.429391\pi$
$733$	7.93751e12	−	2.88902e12i	1.01558	−	0.369643i	0.795575	+	0.605855i	$0.207169\pi$
$734$	1.30871e13	+	1.09814e13i	1.66422	+	1.39645i
$735$		0			0
$736$	−3.32217e12	−	1.20917e12i	−0.417322	−	0.151893i
$737$	1.31000e12	+	2.26899e12i	0.163557	+	0.283288i
$738$		0			0
$739$	−7.61213e12	+	1.31846e13i	−0.938872	+	1.62617i	−0.171291	+	0.985220i	$0.554794\pi$
$739$	−7.61213e12	+	1.31846e13i	−0.938872	+	1.62617i	−0.767580	+	0.640953i	$0.778539\pi$
$740$	−5.04469e12	+	4.23300e12i	−0.618432	+	0.518926i
$741$		0			0
$742$	−2.91771e12	+	1.65471e13i	−0.353365	+	2.00404i
$743$	5.80875e11	−	3.29431e12i	0.0699251	−	0.396565i	−0.929677	−	0.368375i	$-0.879914\pi$
$743$	5.80875e11	−	3.29431e12i	0.0699251	−	0.396565i	0.999603	−	0.0281904i	$-0.00897449\pi$
$744$		0			0
$745$	7.34069e12	−	6.15957e12i	0.873039	−	0.732567i
$746$	3.36221e12	−	5.82352e12i	0.397466	−	0.688431i
$747$		0			0
$748$	−1.31245e13	−	2.27323e13i	−1.53294	−	2.65513i
$749$	4.32213e12	+	1.57313e12i	0.501799	+	0.182640i
$750$		0			0
$751$	−1.61433e12	−	1.35459e12i	−0.185188	−	0.155391i	0.545481	−	0.838123i	$-0.316347\pi$
$751$	−1.61433e12	−	1.35459e12i	−0.185188	−	0.155391i	−0.730669	+	0.682732i	$0.760792\pi$
$752$	−7.30404e12	+	2.65845e12i	−0.832880	+	0.303144i
$753$		0			0
$754$	−3.59185e12	−	2.03704e13i	−0.404713	−	2.29524i
$755$	−1.49268e13			−1.67189
$756$		0			0
$757$	−5.15114e12			−0.570127			−0.285064	−	0.958509i	$-0.592015\pi$
$757$	−5.15114e12			−0.570127			−0.285064	+	0.958509i	$0.592015\pi$
$758$	−2.56280e11	−	1.45344e12i	−0.0281970	−	0.159913i
$759$		0			0
$760$	−6.69424e12	+	2.43650e12i	−0.727847	+	0.264915i
$761$	5.68577e12	+	4.77093e12i	0.614551	+	0.515670i	0.896086	−	0.443881i	$-0.146399\pi$
$761$	5.68577e12	+	4.77093e12i	0.614551	+	0.515670i	−0.281534	+	0.959551i	$0.590843\pi$
$762$		0			0
$763$	−8.96474e12	−	3.26290e12i	−0.957585	−	0.348533i
$764$	−1.08298e13	−	1.87577e13i	−1.15000	−	1.99187i
$765$		0			0
$766$	5.82296e12	−	1.00857e13i	0.611102	−	1.05846i
$767$	9.98910e12	−	8.38185e12i	1.04219	−	0.874502i
$768$		0			0
$769$	−2.86125e12	+	1.62270e13i	−0.295045	+	1.67328i	0.371976	+	0.928242i	$0.378680\pi$
$769$	−2.86125e12	+	1.62270e13i	−0.295045	+	1.67328i	−0.667020	+	0.745039i	$0.732431\pi$
$770$	3.62239e12	−	2.05436e13i	0.371353	−	2.10605i
$771$		0			0
$772$	−1.33322e12	+	1.11871e12i	−0.135091	+	0.113354i
$773$	−7.87724e12	+	1.36438e13i	−0.793535	+	1.37444i	0.130230	+	0.991484i	$0.458429\pi$
$773$	−7.87724e12	+	1.36438e13i	−0.793535	+	1.37444i	−0.923765	+	0.382960i	$0.874905\pi$
$774$		0			0
$775$	1.70344e12	+	2.95044e12i	0.169617	+	0.293785i
$776$	1.05836e11	+	3.85211e10i	0.0104774	+	0.00381348i
$777$		0			0
$778$	−1.76177e13	−	1.47830e13i	−1.72401	−	1.44662i
$779$	−6.62203e12	+	2.41022e12i	−0.644277	+	0.234498i
$780$		0			0
$781$	1.95048e12	+	1.10617e13i	0.187590	+	1.06388i
$782$	−3.14491e13			−3.00731
$783$		0			0
$784$	6.27946e11			0.0593609
$785$	1.29262e12	+	7.33084e12i	0.121495	+	0.689033i
$786$		0			0
$787$	8.51859e12	−	3.10051e12i	0.791555	−	0.288103i	0.0855728	−	0.996332i	$-0.472728\pi$
$787$	8.51859e12	−	3.10051e12i	0.791555	−	0.288103i	0.705982	+	0.708229i	$0.250506\pi$
$788$	−1.48833e13	−	1.24885e13i	−1.37509	−	1.15383i
$789$		0			0
$790$	−1.27769e13	−	4.65040e12i	−1.16709	−	0.424785i
$791$	−1.31317e11	−	2.27448e11i	−0.0119269	−	0.0206580i
$792$		0			0
$793$	−6.85182e12	+	1.18677e13i	−0.615285	+	1.06571i
$794$	2.82888e13	−	2.37372e13i	2.52594	−	2.11951i
$795$		0			0
$796$	−4.64253e12	+	2.63291e13i	−0.409869	+	2.32449i
$797$	1.35062e12	−	7.65975e12i	0.118569	−	0.672438i	−0.866352	−	0.499434i	$-0.833541\pi$
$797$	1.35062e12	−	7.65975e12i	0.118569	−	0.672438i	0.984921	−	0.173004i	$-0.0553474\pi$
$798$		0			0
$799$	1.97325e13	−	1.65576e13i	1.71286	−	1.43726i
$800$	−9.33549e11	+	1.61695e12i	−0.0805809	+	0.139570i
$801$		0			0
$802$	8.59529e12	+	1.48875e13i	0.733628	+	1.27068i
$803$	−1.15984e13	−	4.22147e12i	−0.984413	−	0.358297i
$804$		0			0
$805$	−1.24829e13	−	1.04744e13i	−1.04769	−	0.879118i
$806$	1.91093e13	−	6.95522e12i	1.59491	−	0.580501i
$807$		0			0
$808$	3.03264e12	+	1.71989e13i	0.250305	+	1.41955i
$809$	9.31588e12			0.764637			0.382319	−	0.924031i	$-0.375126\pi$
$809$	9.31588e12			0.764637			0.382319	+	0.924031i	$0.375126\pi$
$810$		0			0
$811$	6.18994e12			0.502450			0.251225	−	0.967929i	$-0.419167\pi$
$811$	6.18994e12			0.502450			0.251225	+	0.967929i	$0.419167\pi$
$812$	−4.89482e12	−	2.77599e13i	−0.395125	−	2.24087i
$813$		0			0
$814$	7.40452e12	−	2.69503e12i	0.591136	−	0.215156i
$815$	−1.53448e13	−	1.28759e13i	−1.21830	−	1.02227i
$816$		0			0
$817$	−3.15682e12	−	1.14899e12i	−0.247885	−	0.0902229i
$818$	1.89858e13	+	3.28843e13i	1.48265	+	2.56802i
$819$		0			0
$820$	2.22687e13	−	3.85705e13i	1.72002	−	2.97915i
$821$	1.44318e13	−	1.21097e13i	1.10860	−	0.930227i	0.110628	−	0.993862i	$-0.464714\pi$
$821$	1.44318e13	−	1.21097e13i	1.10860	−	0.930227i	0.997973	+	0.0636350i	$0.0202694\pi$
$822$		0			0
$823$	1.98293e11	−	1.12458e12i	0.0150664	−	0.0854456i	−0.976347	−	0.216207i	$-0.930631\pi$
$823$	1.98293e11	−	1.12458e12i	0.0150664	−	0.0854456i	0.991414	+	0.130762i	$0.0417423\pi$
$824$	−3.44044e12	+	1.95117e13i	−0.259981	+	1.47443i
$825$		0			0
$826$	2.08788e13	−	1.75194e13i	1.56062	−	1.30951i
$827$	−1.49796e12	+	2.59454e12i	−0.111359	+	0.192879i	−0.916318	−	0.400451i	$-0.868854\pi$
$827$	−1.49796e12	+	2.59454e12i	−0.111359	+	0.192879i	0.804960	+	0.593330i	$0.202187\pi$
$828$		0			0
$829$	2.69478e11	+	4.66749e11i	0.0198165	+	0.0343232i	0.875764	−	0.482740i	$-0.160358\pi$
$829$	2.69478e11	+	4.66749e11i	0.0198165	+	0.0343232i	−0.855947	+	0.517063i	$0.827025\pi$
$830$	−4.99526e13	−	1.81812e13i	−3.65348	−	1.32976i
$831$		0			0
$832$	1.65126e13	+	1.38557e13i	1.19470	+	1.00247i
$833$	−1.95551e12	+	7.11747e11i	−0.140721	+	0.0512181i
$834$		0			0
$835$	−2.48376e12	−	1.40861e13i	−0.176816	−	1.00277i
$836$	1.19203e13			0.844034
$837$		0			0
$838$	−1.15864e13			−0.811613
$839$	2.60173e12	+	1.47551e13i	0.181273	+	1.02805i	0.930651	+	0.365907i	$0.119241\pi$
$839$	2.60173e12	+	1.47551e13i	0.181273	+	1.02805i	−0.749379	+	0.662142i	$0.769648\pi$
$840$		0			0
$841$	−4.76189e12	+	1.73319e12i	−0.328244	+	0.119471i
$842$	−5.07823e12	−	4.26114e12i	−0.348183	−	0.292161i
$843$		0			0
$844$	2.67853e13	+	9.74904e12i	1.81700	+	0.661334i
$845$	3.51715e12	+	6.09188e12i	0.237321	+	0.411051i
$846$		0			0
$847$	−3.06121e11	+	5.30216e11i	−0.0204370	+	0.0353979i
$848$	8.42820e12	−	7.07210e12i	0.559698	−	0.469642i
$849$		0			0
$850$	−2.88410e12	+	1.63566e13i	−0.189507	+	1.07475i
$851$	1.06885e12	−	6.06176e12i	0.0698609	−	0.396201i
$852$		0			0
$853$	−8.26456e12	+	6.93479e12i	−0.534502	+	0.448500i	−0.869653	−	0.493664i	$-0.835657\pi$
$853$	−8.26456e12	+	6.93479e12i	−0.534502	+	0.448500i	0.335151	+	0.942164i	$0.391213\pi$
$854$	−1.43214e13	+	2.48054e13i	−0.921352	+	1.59583i
$855$		0			0
$856$	−5.93912e12	−	1.02869e13i	−0.378086	−	0.654863i
$857$	1.84347e13	+	6.70967e12i	1.16741	+	0.424901i	0.851738	−	0.523969i	$-0.175549\pi$
$857$	1.84347e13	+	6.70967e12i	1.16741	+	0.424901i	0.315668	+	0.948870i	$0.397771\pi$
$858$		0			0
$859$	−1.85446e13	−	1.55608e13i	−1.16211	−	0.975130i	−0.162183	−	0.986761i	$-0.551853\pi$
$859$	−1.85446e13	−	1.55608e13i	−1.16211	−	0.975130i	−0.999932	+	0.0116305i	$0.996298\pi$
$860$	1.99512e13	−	7.26165e12i	1.24373	−	0.452681i
$861$		0			0
$862$	−5.30773e11	−	3.01016e12i	−0.0327436	−	0.185698i
$863$	−1.57285e13			−0.965245			−0.482623	−	0.875828i	$-0.660316\pi$
$863$	−1.57285e13			−0.965245			−0.482623	+	0.875828i	$0.660316\pi$
$864$		0			0
$865$	−1.69993e13			−1.03243
$866$	−5.59434e11	−	3.17271e12i	−0.0338002	−	0.191690i
$867$		0			0
$868$	2.60414e13	−	9.47828e12i	1.55713	−	0.566749i
$869$	8.12573e12	+	6.81830e12i	0.483363	+	0.405590i
$870$		0			0
$871$	−6.06258e12	−	2.20660e12i	−0.356924	−	0.129910i
$872$	1.23186e13	+	2.13365e13i	0.721503	+	1.24968i
$873$		0			0
$874$	7.14093e12	−	1.23685e13i	0.413955	−	0.716991i
$875$	9.84667e12	−	8.26233e12i	0.567875	−	0.476504i
$876$		0			0
$877$	−2.23500e12	+	1.26753e13i	−0.127579	+	0.723536i	0.852164	+	0.523275i	$0.175290\pi$
$877$	−2.23500e12	+	1.26753e13i	−0.127579	+	0.723536i	−0.979743	+	0.200261i	$0.935821\pi$
$878$	−4.37634e11	+	2.48195e12i	−0.0248534	+	0.140951i
$879$		0			0
$880$	−1.04638e13	+	8.78016e12i	−0.588189	+	0.493549i
$881$	4.22517e11	−	7.31821e11i	0.0236294	−	0.0409273i	−0.853969	−	0.520324i	$-0.825811\pi$
$881$	4.22517e11	−	7.31821e11i	0.0236294	−	0.0409273i	0.877598	+	0.479397i	$0.159144\pi$
$882$		0			0
$883$	−9.05578e12	−	1.56851e13i	−0.501306	−	0.868287i	−0.999999	−	0.00150840i	$-0.999520\pi$
$883$	−9.05578e12	−	1.56851e13i	−0.501306	−	0.868287i	0.498693	−	0.866779i	$-0.333813\pi$
$884$	6.07390e13	+	2.21072e13i	3.34528	+	1.21758i
$885$		0			0
$886$	2.28310e13	+	1.91575e13i	1.24473	+	1.04445i
$887$	−2.00565e13	+	7.29998e12i	−1.08793	+	0.395973i	−0.822852	−	0.568255i	$-0.807619\pi$
$887$	−2.00565e13	+	7.29998e12i	−1.08793	+	0.395973i	−0.265074	+	0.964228i	$0.585396\pi$
$888$		0			0
$889$	3.85619e12	+	2.18696e13i	0.207062	+	1.17431i
$890$	−1.63313e13			−0.872499
$891$		0			0
$892$	2.32411e13			1.22918
$893$	2.03130e12	+	1.15201e13i	0.106892	+	0.606212i
$894$		0			0
$895$	−1.03888e13	+	3.78121e12i	−0.541204	+	0.196982i
$896$	2.83038e13	+	2.37497e13i	1.46710	+	1.23104i
$897$		0			0
$898$	−3.26444e13	−	1.18816e13i	−1.67520	−	0.609721i
$899$	−9.62222e12	−	1.66662e13i	−0.491311	−	0.850976i
$900$		0			0
$901$	−1.82307e13	+	3.15765e13i	−0.921597	+	1.59625i
$902$	−4.08234e13	+	3.42549e13i	−2.05343	+	1.72303i
$903$		0			0
$904$	−1.17778e11	+	6.67950e11i	−0.00586550	+	0.0332649i
$905$	−9.04476e11	+	5.12954e12i	−0.0448207	+	0.254191i
$906$		0			0
$907$	−1.38458e13	+	1.16180e13i	−0.679337	+	0.570032i	−0.915813	−	0.401606i	$-0.868452\pi$
$907$	−1.38458e13	+	1.16180e13i	−0.679337	+	0.570032i	0.236475	+	0.971638i	$0.424008\pi$
$908$	1.54388e13	−	2.67408e13i	0.753751	−	1.30554i
$909$		0			0
$910$	2.56842e13	+	4.44863e13i	1.24159	+	2.15050i
$911$	1.36017e13	+	4.95060e12i	0.654273	+	0.238136i	0.647762	−	0.761843i	$-0.275705\pi$
$911$	1.36017e13	+	4.95060e12i	0.654273	+	0.238136i	0.00651124	+	0.999979i	$0.497927\pi$
$912$		0			0
$913$	3.17684e13	+	2.66568e13i	1.51313	+	1.26967i
$914$	−5.98185e11	+	2.17721e11i	−0.0283516	+	0.0103191i
$915$		0			0
$916$	−1.16477e13	−	6.60573e13i	−0.546651	−	3.10021i
$917$	−1.24076e13			−0.579465
$918$		0			0
$919$	−1.99628e13			−0.923212			−0.461606	−	0.887085i	$-0.652727\pi$
$919$	−1.99628e13			−0.923212			−0.461606	+	0.887085i	$0.652727\pi$
$920$	7.30754e12	+	4.14431e13i	0.336299	+	1.90725i
$921$		0			0
$922$	−2.32329e12	+	8.45609e11i	−0.105880	+	0.0385372i
$923$	−2.11882e13	−	1.77790e13i	−0.960918	−	0.806306i
$924$		0			0
$925$	−3.05467e12	−	1.11181e12i	−0.137191	−	0.0499335i
$926$	−1.28156e13	−	2.21973e13i	−0.572783	−	0.992089i
$927$		0			0
$928$	5.27334e12	−	9.13369e12i	0.233410	−	0.404278i
$929$	8.86612e12	−	7.43956e12i	0.390537	−	0.327700i	−0.426285	−	0.904589i	$-0.640178\pi$
$929$	8.86612e12	−	7.43956e12i	0.390537	−	0.327700i	0.816823	+	0.576889i	$0.195733\pi$
$930$		0			0
$931$	1.64104e11	−	9.30683e11i	0.00715891	−	0.0406002i
$932$	−1.33164e13	+	7.55210e13i	−0.578116	+	3.27866i
$933$		0			0
$934$	−2.53169e13	+	2.12434e13i	−1.08855	+	0.913404i
$935$	2.26338e13	−	3.92028e13i	0.968511	−	1.67751i
$936$		0			0
$937$	−2.27734e13	−	3.94446e13i	−0.965160	−	1.67171i	−0.709185	−	0.705022i	$-0.750937\pi$
$937$	−2.27734e13	−	3.94446e13i	−0.965160	−	1.67171i	−0.255974	−	0.966684i	$-0.582396\pi$
$938$	−1.26718e13	−	4.61215e12i	−0.534472	−	0.194532i
$939$		0			0
$940$	−5.66341e13	−	4.75217e13i	−2.36593	−	1.98526i
$941$	−8.42439e12	+	3.06623e12i	−0.350256	+	0.127483i	−0.511156	−	0.859488i	$-0.670782\pi$
$941$	−8.42439e12	+	3.06623e12i	−0.350256	+	0.127483i	0.160900	+	0.986971i	$0.448560\pi$
$942$		0			0
$943$	7.22872e12	+	4.09961e13i	0.297686	+	1.68826i
$944$	−1.78469e13			−0.731455
$945$		0			0
$946$	−2.54047e13			−1.03135
$947$	−5.05426e12	−	2.86642e13i	−0.204213	−	1.15815i	−0.898674	−	0.438618i	$-0.855468\pi$
$947$	−5.05426e12	−	2.86642e13i	−0.204213	−	1.15815i	0.694461	−	0.719531i	$-0.255643\pi$
$948$		0			0
$949$	2.85606e13	−	1.03952e13i	1.14306	−	0.416040i
$950$	−5.77790e12	−	4.84824e12i	−0.230152	−	0.193120i
$951$		0			0
$952$	5.91895e13	+	2.15432e13i	2.33549	+	0.850050i
$953$	−7.09458e12	−	1.22882e13i	−0.278618	−	0.482580i	0.692424	−	0.721491i	$-0.256543\pi$
$953$	−7.09458e12	−	1.22882e13i	−0.278618	−	0.482580i	−0.971041	+	0.238911i	$0.923210\pi$
$954$		0			0
$955$	1.86765e13	−	3.23486e13i	0.726573	−	1.25846i
$956$	−7.21173e12	+	6.05136e12i	−0.279241	+	0.234311i
$957$		0			0
$958$	−1.29299e13	+	7.33292e13i	−0.495965	+	2.81276i
$959$	7.39459e11	−	4.19368e12i	0.0282313	−	0.160107i
$960$		0			0
$961$	−5.76052e12	+	4.83365e12i	−0.217875	+	0.182818i
$962$	−9.70178e12	+	1.68040e13i	−0.365228	+	0.632593i
$963$		0			0
$964$	3.72618e11	+	6.45394e11i	0.0138969	+	0.0240701i
$965$	−2.82039e12	−	1.02654e12i	−0.104698	−	0.0381068i
$966$		0			0
$967$	−1.55505e13	−	1.30484e13i	−0.571906	−	0.479886i	0.310372	−	0.950615i	$-0.399546\pi$
$967$	−1.55505e13	−	1.30484e13i	−0.571906	−	0.479886i	−0.882278	+	0.470729i	$0.843991\pi$
$968$	1.48576e12	−	5.40772e11i	0.0543888	−	0.0197959i
$969$		0			0
$970$	7.23428e10	+	4.10276e11i	0.00262375	+	0.0148800i
$971$	3.75903e13			1.35703			0.678516	−	0.734586i	$-0.262624\pi$
$971$	3.75903e13			1.35703			0.678516	+	0.734586i	$0.262624\pi$
$972$		0			0
$973$	5.04400e13			1.80413
$974$	−3.81136e12	−	2.16153e13i	−0.135695	−	0.769565i
$975$		0			0
$976$	1.76243e13	−	6.41471e12i	0.621709	−	0.226283i
$977$	2.47308e13	+	2.07516e13i	0.868385	+	0.728662i	0.963757	−	0.266780i	$-0.0859597\pi$
$977$	2.47308e13	+	2.07516e13i	0.868385	+	0.728662i	−0.0953723	+	0.995442i	$0.530404\pi$
$978$		0			0
$979$	1.19722e13	+	4.35753e12i	0.416536	+	0.151607i
$980$	2.98634e12	+	5.17250e12i	0.103424	+	0.179136i
$981$		0			0
$982$	−1.78454e13	+	3.09091e13i	−0.612385	+	1.06068i
$983$	−3.07284e13	+	2.57842e13i	−1.04966	+	0.880772i	−0.993058	−	0.117625i	$-0.962472\pi$
$983$	−3.07284e13	+	2.57842e13i	−1.04966	+	0.880772i	−0.0566046	+	0.998397i	$0.518027\pi$
$984$		0			0
$985$	5.81820e12	−	3.29966e13i	0.196936	−	1.11688i
$986$	1.62914e13	−	9.23933e13i	0.548925	−	3.11311i
$987$		0			0
$988$	−2.24860e13	+	1.88680e13i	−0.750768	+	0.629969i
$989$	−9.92247e12	+	1.71862e13i	−0.329789	+	0.571212i
$990$		0			0
$991$	−1.25256e12	−	2.16950e12i	−0.0412542	−	0.0714543i	0.844661	−	0.535302i	$-0.179802\pi$
$991$	−1.25256e12	−	2.16950e12i	−0.0412542	−	0.0714543i	−0.885915	+	0.463847i	$0.846469\pi$
$992$	9.74346e12	+	3.54633e12i	0.319456	+	0.116272i
$993$		0			0
$994$	−4.42868e13	−	3.71610e13i	−1.43892	−	1.20739i
$995$	−4.33256e13	+	1.57692e13i	−1.40133	+	0.510043i
$996$		0			0
$997$	5.06613e12	+	2.87315e13i	0.162386	+	0.920936i	0.951719	+	0.306971i	$0.0993154\pi$
$997$	5.06613e12	+	2.87315e13i	0.162386	+	0.920936i	−0.789333	+	0.613965i	$0.789574\pi$
$998$	3.50196e13			1.11744
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.10.2		156
3.2	odd	2		27.10.e.a.13.25	✓	156
27.2	odd	18		27.10.e.a.25.25	yes	156
27.25	even	9	inner	81.10.e.a.73.2		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.13.25	✓	156	3.2	odd	2
27.10.e.a.25.25	yes	156	27.2	odd	18
81.10.e.a.10.2		156	1.1	even	1	trivial
81.10.e.a.73.2		156	27.25	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-6.66051 - 37.7736i) q^{2} +(-901.361 + 328.069i) q^{4} +(-1267.19 - 1063.30i) q^{5} +(-6241.55 - 2271.74i) q^{7} +(8576.64 + 14855.2i) q^{8} +(-31724.5 + 54948.4i) q^{10} +(37918.2 - 31817.2i) q^{11} +(-21165.8 + 120037. i) q^{13} +(-44239.9 + 250897. i) q^{14} +(127793. - 107231. i) q^{16} +(-276424. + 478780. i) q^{17} +(-125531. - 217426. i) q^{19} +(1.49103e6 + 542690. i) q^{20} +(-1.45440e6 - 1.22039e6i) q^{22} +(-1.39365e6 + 507246. i) q^{23} +(136009. + 771347. i) q^{25} +4.67521e6 q^{26} +6.37118e6 q^{28} +(-768276. - 4.35711e6i) q^{29} +(4.08737e6 - 1.48768e6i) q^{31} +(1.82609e6 + 1.53227e6i) q^{32} +(1.99264e7 + 7.25260e6i) q^{34} +(5.49369e6 + 9.51535e6i) q^{35} +(-2.07515e6 + 3.59427e6i) q^{37} +(-7.37687e6 + 6.18993e6i) q^{38} +(4.92725e6 - 2.79438e7i) q^{40} +(4.87410e6 - 2.76424e7i) q^{41} +(1.02503e7 - 8.60103e6i) q^{43} +(-2.37398e7 + 4.11185e7i) q^{44} +(2.84429e7 + 4.92645e7i) q^{46} +(-4.37834e7 - 1.59359e7i) q^{47} +(2.88352e6 + 2.41956e6i) q^{49} +(2.82307e7 - 1.02751e7i) q^{50} +(-2.03024e7 - 1.15141e8i) q^{52} +6.59519e7 q^{53} -8.18807e7 q^{55} +(-1.97845e7 - 1.12203e8i) q^{56} +(-1.59467e8 + 5.80411e7i) q^{58} +(-8.19525e7 - 6.87663e7i) q^{59} +(1.05647e8 + 3.84524e7i) q^{61} +(-8.34191e7 - 1.44486e8i) q^{62} +(8.84233e7 - 1.53154e8i) q^{64} +(1.54456e8 - 1.29604e8i) q^{65} +(-9.19132e6 + 5.21266e7i) q^{67} +(9.20849e7 - 5.22239e8i) q^{68} +(3.22839e8 - 2.70894e8i) q^{70} +(-1.13461e8 + 1.96520e8i) q^{71} +(-1.24677e8 - 2.15948e8i) q^{73} +(1.49590e8 + 5.44464e7i) q^{74} +(1.84479e8 + 1.54797e8i) q^{76} +(-3.08949e8 + 1.12448e8i) q^{77} +(3.72121e7 + 2.11041e8i) q^{79} -2.75957e8 q^{80} -1.07662e9 q^{82} +(1.45485e8 + 8.25085e8i) q^{83} +(8.59367e8 - 3.12784e8i) q^{85} +(-3.93164e8 - 3.29904e8i) q^{86} +(7.97860e8 + 2.90397e8i) q^{88} +(1.28696e8 + 2.22908e8i) q^{89} +(4.04800e8 - 7.01135e8i) q^{91} +(1.08977e9 - 9.14423e8i) q^{92} +(-3.10335e8 + 1.76000e9i) q^{94} +(-7.21172e7 + 4.08997e8i) q^{95} +(5.02984e6 - 4.22054e6i) q^{97} +(7.21899e7 - 1.25036e8i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more