LMFDB - Embedded newform 81.10.e.a.10.3

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			10.3
Character	$\chi$	$=$	81.10
Dual form			81.10.e.a.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.61278 - 37.5029i) q^{2} +(-881.618 + 320.883i) q^{4} +(-1241.60 - 1041.82i) q^{5} +(9160.78 + 3334.25i) q^{7} +(8115.13 + 14055.8i) q^{8} +(-30861.0 + 53452.8i) q^{10} +(51265.0 - 43016.4i) q^{11} +(23395.9 - 132685. i) q^{13} +(64465.9 - 365605. i) q^{14} +(105495. - 88521.1i) q^{16} +(211869. - 366968. i) q^{17} +(357829. + 619778. i) q^{19} +(1.42892e6 + 520083. i) q^{20} +(-1.95224e6 - 1.63813e6i) q^{22} +(841310. - 306212. i) q^{23} +(117010. + 663595. i) q^{25} -5.13079e6 q^{26} -9.14621e6 q^{28} +(-518380. - 2.93988e6i) q^{29} +(3.67352e6 - 1.33705e6i) q^{31} +(2.34833e6 + 1.97048e6i) q^{32} +(-1.51634e7 - 5.51903e6i) q^{34} +(-7.90029e6 - 1.36837e7i) q^{35} +(265173. - 459292. i) q^{37} +(2.08772e7 - 1.75181e7i) q^{38} +(4.56796e6 - 2.59062e7i) q^{40} +(-2.21098e6 + 1.25391e7i) q^{41} +(4.03280e6 - 3.38392e6i) q^{43} +(-3.13929e7 + 5.43741e7i) q^{44} +(-1.70472e7 - 2.95267e7i) q^{46} +(-2.97072e7 - 1.08125e7i) q^{47} +(4.18899e7 + 3.51498e7i) q^{49} +(2.41130e7 - 8.77641e6i) q^{50} +(2.19500e7 + 1.24485e8i) q^{52} -4.09188e6 q^{53} -1.08466e8 q^{55} +(2.74753e7 + 1.55820e8i) q^{56} +(-1.06826e8 + 3.88815e7i) q^{58} +(2.89699e7 + 2.43087e7i) q^{59} +(7.67470e7 + 2.79336e7i) q^{61} +(-7.44355e7 - 1.28926e8i) q^{62} +(9.36247e7 - 1.62163e8i) q^{64} +(-1.67283e8 + 1.40367e8i) q^{65} +(2.22923e7 - 1.26426e8i) q^{67} +(-6.90338e7 + 3.91510e8i) q^{68} +(-4.60936e8 + 3.86771e8i) q^{70} +(-1.48576e8 + 2.57342e8i) q^{71} +(1.19955e8 + 2.07769e8i) q^{73} +(-1.89783e7 - 6.90755e6i) q^{74} +(-5.14344e8 - 4.31586e8i) q^{76} +(6.13054e8 - 2.23133e8i) q^{77} +(-5.26889e7 - 2.98814e8i) q^{79} -2.23206e8 q^{80} +4.84873e8 q^{82} +(4.68884e7 + 2.65917e8i) q^{83} +(-6.45371e8 + 2.34896e8i) q^{85} +(-1.53575e8 - 1.28865e8i) q^{86} +(1.02065e9 + 3.71487e8i) q^{88} +(-2.90441e8 - 5.03059e8i) q^{89} +(6.56730e8 - 1.13749e9i) q^{91} +(-6.43456e8 + 5.39923e8i) q^{92} +(-2.09055e8 + 1.18561e9i) q^{94} +(2.01420e8 - 1.14231e9i) q^{95} +(-2.71680e8 + 2.27966e8i) q^{97} +(1.04121e9 - 1.80343e9i) 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 $

$2$	−6.61278	−	37.5029i	−0.292246	−	1.65741i	−0.678189	−	0.734888i	$-0.737235\pi$
$2$	−6.61278	−	37.5029i	−0.292246	−	1.65741i	0.385942	−	0.922523i	$-0.373876\pi$
$3$		0			0
$3$		0			0
$4$	−881.618	+	320.883i	−1.72191	+	0.626724i
$5$	−1241.60	−	1041.82i	−0.888414	−	0.745468i	0.0794773	−	0.996837i	$-0.474675\pi$
$5$	−1241.60	−	1041.82i	−0.888414	−	0.745468i	−0.967891	+	0.251369i	$0.919119\pi$
$6$		0			0
$7$	9160.78	+	3334.25i	1.44209	+	0.524876i	0.940369	−	0.340156i	$-0.110480\pi$
$7$	9160.78	+	3334.25i	1.44209	+	0.524876i	0.501717	+	0.865032i	$0.332702\pi$
$8$	8115.13	+	14055.8i	0.700471	+	1.21325i
$9$		0			0
$10$	−30861.0	+	53452.8i	−0.975911	+	1.69033i
$11$	51265.0	−	43016.4i	1.05573	−	0.885864i	0.0620469	−	0.998073i	$-0.480237\pi$
$11$	51265.0	−	43016.4i	1.05573	−	0.885864i	0.993685	+	0.112209i	$0.0357927\pi$
$12$		0			0
$13$	23395.9	−	132685.i	0.227193	−	1.28848i	−0.631254	−	0.775576i	$-0.717460\pi$
$13$	23395.9	−	132685.i	0.227193	−	1.28848i	0.858448	−	0.512901i	$-0.171429\pi$
$14$	64465.9	−	365605.i	0.448492	−	2.54352i
$15$		0			0
$16$	105495.	−	88521.1i	0.402433	−	0.337681i
$17$	211869.	−	366968.i	0.615243	−	1.06563i	−0.375098	−	0.926985i	$-0.622391\pi$
$17$	211869.	−	366968.i	0.615243	−	1.06563i	0.990342	−	0.138648i	$-0.0442756\pi$
$18$		0			0
$19$	357829.	+	619778.i	0.629918	+	1.09105i	0.987568	+	0.157194i	$0.0502448\pi$
$19$	357829.	+	619778.i	0.629918	+	1.09105i	−0.357650	+	0.933856i	$0.616422\pi$
$20$	1.42892e6	+	520083.i	1.99697	+	0.726838i
$21$		0			0
$22$	−1.95224e6	−	1.63813e6i	−1.77677	−	1.49089i
$23$	841310.	−	306212.i	0.626875	−	0.228164i	−0.00899585	−	0.999960i	$-0.502864\pi$
$23$	841310.	−	306212.i	0.626875	−	0.228164i	0.635870	+	0.771796i	$0.280641\pi$
$24$		0			0
$25$	117010.	+	663595.i	0.0599090	+	0.339761i
$26$	−5.13079e6			−2.20193
$27$		0			0
$28$	−9.14621e6			−2.81209
$29$	−518380.	−	2.93988e6i	−0.136100	−	0.771860i	−0.974088	−	0.226171i	$-0.927379\pi$
$29$	−518380.	−	2.93988e6i	−0.136100	−	0.771860i	0.837988	−	0.545689i	$-0.183732\pi$
$30$		0			0
$31$	3.67352e6	−	1.33705e6i	0.714421	−	0.260028i	0.0408657	−	0.999165i	$-0.486988\pi$
$31$	3.67352e6	−	1.33705e6i	0.714421	−	0.260028i	0.673556	+	0.739137i	$0.264766\pi$
$32$	2.34833e6	+	1.97048e6i	0.395898	+	0.332198i
$33$		0			0
$34$	−1.51634e7	−	5.51903e6i	−1.94599	−	0.708284i
$35$	−7.90029e6	−	1.36837e7i	−0.889891	−	1.54134i
$36$		0			0
$37$	265173.	−	459292.i	0.0232606	−	0.0402885i	−0.854161	−	0.520009i	$-0.825929\pi$
$37$	265173.	−	459292.i	0.0232606	−	0.0402885i	0.877421	+	0.479720i	$0.159262\pi$
$38$	2.08772e7	−	1.75181e7i	1.62423	−	1.36289i
$39$		0			0
$40$	4.56796e6	−	2.59062e7i	0.282132	−	1.60005i
$41$	−2.21098e6	+	1.25391e7i	−0.122196	+	0.693008i	0.860738	+	0.509049i	$0.170003\pi$
$41$	−2.21098e6	+	1.25391e7i	−0.122196	+	0.693008i	−0.982934	+	0.183959i	$0.941108\pi$
$42$		0			0
$43$	4.03280e6	−	3.38392e6i	0.179887	−	0.150943i	−0.548398	−	0.836217i	$-0.684762\pi$
$43$	4.03280e6	−	3.38392e6i	0.179887	−	0.150943i	0.728285	+	0.685274i	$0.240318\pi$
$44$	−3.13929e7	+	5.43741e7i	−1.26268	+	2.18703i
$45$		0			0
$46$	−1.70472e7	−	2.95267e7i	−0.561363	−	0.972309i
$47$	−2.97072e7	−	1.08125e7i	−0.888018	−	0.323212i	−0.142577	−	0.989784i	$-0.545539\pi$
$47$	−2.97072e7	−	1.08125e7i	−0.888018	−	0.323212i	−0.745441	+	0.666572i	$0.767761\pi$
$48$		0			0
$49$	4.18899e7	+	3.51498e7i	1.03807	+	0.871046i
$50$	2.41130e7	−	8.77641e6i	0.545615	−	0.198588i
$51$		0			0
$52$	2.19500e7	+	1.24485e8i	0.416313	+	2.36103i
$53$	−4.09188e6			−0.0712330			−0.0356165	−	0.999366i	$-0.511339\pi$
$53$	−4.09188e6			−0.0712330			−0.0356165	+	0.999366i	$0.511339\pi$
$54$		0			0
$55$	−1.08466e8			−1.59831
$56$	2.74753e7	+	1.55820e8i	0.373333	+	2.11727i
$57$		0			0
$58$	−1.06826e8	+	3.88815e7i	−1.23951	+	0.451146i
$59$	2.89699e7	+	2.43087e7i	0.311253	+	0.261172i	0.785010	−	0.619484i	$-0.212658\pi$
$59$	2.89699e7	+	2.43087e7i	0.311253	+	0.261172i	−0.473757	+	0.880656i	$0.657102\pi$
$60$		0			0
$61$	7.67470e7	+	2.79336e7i	0.709704	+	0.258311i	0.671548	−	0.740961i	$-0.265630\pi$
$61$	7.67470e7	+	2.79336e7i	0.709704	+	0.258311i	0.0381555	+	0.999272i	$0.487852\pi$
$62$	−7.44355e7	−	1.28926e8i	−0.639760	−	1.10810i
$63$		0			0
$64$	9.36247e7	−	1.62163e8i	0.697558	−	1.20821i
$65$	−1.67283e8	+	1.40367e8i	−1.16236	+	0.975336i
$66$		0			0
$67$	2.22923e7	−	1.26426e8i	0.135151	−	0.766478i	−0.839604	−	0.543199i	$-0.817213\pi$
$67$	2.22923e7	−	1.26426e8i	0.135151	−	0.766478i	0.974755	−	0.223279i	$-0.0716760\pi$
$68$	−6.90338e7	+	3.91510e8i	−0.391536	+	2.22051i
$69$		0			0
$70$	−4.60936e8	+	3.86771e8i	−2.29456	+	1.92536i
$71$	−1.48576e8	+	2.57342e8i	−0.693884	+	1.20184i	0.276672	+	0.960964i	$0.410769\pi$
$71$	−1.48576e8	+	2.57342e8i	−0.693884	+	1.20184i	−0.970556	+	0.240877i	$0.922565\pi$
$72$		0			0
$73$	1.19955e8	+	2.07769e8i	0.494386	+	0.856303i	0.999979	−	0.00646983i	$-0.00205943\pi$
$73$	1.19955e8	+	2.07769e8i	0.494386	+	0.856303i	−0.505593	+	0.862772i	$0.668726\pi$
$74$	−1.89783e7	−	6.90755e6i	−0.0735725	−	0.0267782i
$75$		0			0
$76$	−5.14344e8	−	4.31586e8i	−1.76845	−	1.48391i
$77$	6.13054e8	−	2.23133e8i	1.98742	−	0.723363i
$78$		0			0
$79$	−5.26889e7	−	2.98814e8i	−0.152194	−	0.863135i	−0.961306	−	0.275481i	$-0.911163\pi$
$79$	−5.26889e7	−	2.98814e8i	−0.152194	−	0.863135i	0.809113	−	0.587654i	$-0.199948\pi$
$80$	−2.23206e8			−0.609257
$81$		0			0
$82$	4.84873e8			1.18431
$83$	4.68884e7	+	2.65917e8i	0.108446	+	0.615029i	0.989788	+	0.142549i	$0.0455299\pi$
$83$	4.68884e7	+	2.65917e8i	0.108446	+	0.615029i	−0.881342	+	0.472480i	$0.843359\pi$
$84$		0			0
$85$	−6.45371e8	+	2.34896e8i	−1.34099	+	0.488079i
$86$	−1.53575e8	−	1.28865e8i	−0.302746	−	0.254034i
$87$		0			0
$88$	1.02065e9	+	3.71487e8i	1.81429	+	0.660346i
$89$	−2.90441e8	−	5.03059e8i	−0.490685	−	0.849892i	0.509257	−	0.860614i	$-0.329920\pi$
$89$	−2.90441e8	−	5.03059e8i	−0.490685	−	0.849892i	−0.999943	+	0.0107223i	$0.996587\pi$
$90$		0			0
$91$	6.56730e8	−	1.13749e9i	1.00392	−	1.73885i
$92$	−6.43456e8	+	5.39923e8i	−0.936426	+	0.785755i
$93$		0			0
$94$	−2.09055e8	+	1.18561e9i	−0.276175	+	1.56627i
$95$	2.01420e8	−	1.14231e9i	0.253715	−	1.43889i
$96$		0			0
$97$	−2.71680e8	+	2.27966e8i	−0.311590	+	0.261455i	−0.785149	−	0.619307i	$-0.787414\pi$
$97$	−2.71680e8	+	2.27966e8i	−0.311590	+	0.261455i	0.473559	+	0.880762i	$0.342969\pi$
$98$	1.04121e9	−	1.80343e9i	1.14031	−	1.97507i
$99$		0			0
$100$	−3.16094e8	−	5.47491e8i	−0.316094	−	0.547491i
$101$	−1.17167e9	−	4.26451e8i	−1.12036	−	0.407778i	−0.285576	−	0.958356i	$-0.592185\pi$
$101$	−1.17167e9	−	4.26451e8i	−1.12036	−	0.407778i	−0.834784	+	0.550578i	$0.814407\pi$
$102$		0			0
$103$	−1.64034e9	−	1.37641e9i	−1.43604	−	1.20498i	−0.942030	−	0.335529i	$-0.891085\pi$
$103$	−1.64034e9	−	1.37641e9i	−1.43604	−	1.20498i	−0.494014	−	0.869454i	$-0.664471\pi$
$104$	2.05486e9	−	7.47907e8i	1.72239	−	0.626899i
$105$		0			0
$106$	2.70587e7	+	1.53457e8i	0.0208176	+	0.118062i
$107$	−1.07082e9			−0.789750			−0.394875	−	0.918735i	$-0.629212\pi$
$107$	−1.07082e9			−0.789750			−0.394875	+	0.918735i	$0.629212\pi$
$108$		0			0
$109$	1.22729e8			0.0832778			0.0416389	−	0.999133i	$-0.486742\pi$
$109$	1.22729e8			0.0832778			0.0416389	+	0.999133i	$0.486742\pi$
$110$	7.17261e8	+	4.06779e9i	0.467100	+	2.64906i
$111$		0			0
$112$	1.26157e9	−	4.59174e8i	0.757583	−	0.275738i
$113$	−1.15062e9	−	9.65488e8i	−0.663866	−	0.557050i	0.247377	−	0.968919i	$-0.420431\pi$
$113$	−1.15062e9	−	9.65488e8i	−0.663866	−	0.557050i	−0.911243	+	0.411870i	$0.864876\pi$
$114$		0			0
$115$	−1.36359e9	−	4.96305e8i	−0.727013	−	0.264611i
$116$	1.40037e9	+	2.42551e9i	0.718094	+	1.24378i
$117$		0			0
$118$	7.20074e8	−	1.24720e9i	0.341907	−	0.592201i
$119$	3.16444e9	−	2.65528e9i	1.44656	−	1.21381i
$120$		0			0
$121$	3.68231e8	−	2.08834e9i	0.156166	−	0.885661i
$122$	5.40082e8	−	3.06296e9i	0.220719	−	1.25176i
$123$		0			0
$124$	−2.80960e9	+	2.35754e9i	−1.06720	+	0.895490i
$125$	−1.03673e9	+	1.79567e9i	−0.379814	+	0.657858i
$126$		0			0
$127$	4.63931e8	+	8.03551e8i	0.158247	+	0.274092i	0.934237	−	0.356654i	$-0.116082\pi$
$127$	4.63931e8	+	8.03551e8i	0.158247	+	0.274092i	−0.775989	+	0.630746i	$0.782749\pi$
$128$	−5.22580e9	−	1.90204e9i	−1.72071	−	0.626288i
$129$		0			0
$130$	6.37037e9	+	5.34537e9i	1.95623	+	1.64147i
$131$	4.24209e9	−	1.54399e9i	1.25852	−	0.458063i	0.375246	−	0.926925i	$-0.377558\pi$
$131$	4.24209e9	−	1.54399e9i	1.25852	−	0.458063i	0.883271	+	0.468863i	$0.155336\pi$
$132$		0			0
$133$	1.21150e9	+	6.87073e9i	0.335730	+	1.90402i
$134$	−4.88876e9			−1.30987
$135$		0			0
$136$	6.87737e9			1.72384
$137$	7.47967e7	+	4.24193e8i	0.0181401	+	0.102878i	0.992534	−	0.121972i	$-0.0389219\pi$
$137$	7.47967e7	+	4.24193e8i	0.0181401	+	0.102878i	−0.974393	+	0.224850i	$0.927811\pi$
$138$		0			0
$139$	7.57071e9	−	2.75551e9i	1.72016	−	0.626089i	0.722310	−	0.691569i	$-0.243080\pi$
$139$	7.57071e9	−	2.75551e9i	1.72016	−	0.626089i	0.997854	+	0.0654804i	$0.0208580\pi$
$140$	1.13559e10	+	9.52873e9i	2.49830	+	2.09633i
$141$		0			0
$142$	1.06336e10	+	3.87030e9i	2.19473	+	0.798817i
$143$	−4.50824e9	−	7.80850e9i	−0.901561	−	1.56155i
$144$		0			0
$145$	−2.41921e9	+	4.19020e9i	−0.454484	+	0.787189i
$146$	6.99870e9	−	5.87260e9i	1.27476	−	1.06965i
$147$		0			0
$148$	−8.64019e7	+	4.90010e8i	−0.0148029	+	0.0839512i
$149$	−8.54017e8	+	4.84337e9i	−0.141948	+	0.805026i	0.827820	+	0.560994i	$0.189581\pi$
$149$	−8.54017e8	+	4.84337e9i	−0.141948	+	0.805026i	−0.969767	+	0.244031i	$0.921530\pi$
$150$		0			0
$151$	−1.20881e9	+	1.01431e9i	−0.189218	+	0.158773i	−0.732476	−	0.680793i	$-0.761635\pi$
$151$	−1.20881e9	+	1.01431e9i	−0.189218	+	0.158773i	0.543257	+	0.839566i	$0.317191\pi$
$152$	−5.80765e9	+	1.00591e10i	−0.882479	+	1.52850i
$153$		0			0
$154$	−1.24221e10	−	2.15158e10i	−1.77973	−	3.08258i
$155$	−5.95400e9	−	2.16708e9i	−0.828544	−	0.301566i
$156$		0			0
$157$	−7.61749e9	−	6.39183e9i	−1.00061	−	0.839608i	−0.0135378	−	0.999908i	$-0.504309\pi$
$157$	−7.61749e9	−	6.39183e9i	−1.00061	−	0.839608i	−0.987068	+	0.160300i	$0.948754\pi$
$158$	−1.08580e10	+	3.95198e9i	−1.38609	+	0.504496i
$159$		0			0
$160$	−8.62783e8	−	4.89308e9i	−0.104079	−	0.590259i
$161$	8.72804e9			1.02376
$162$		0			0
$163$	−1.51960e10			−1.68611			−0.843056	−	0.537826i	$-0.819246\pi$
$163$	−1.51960e10			−1.68611			−0.843056	+	0.537826i	$0.819246\pi$
$164$	−2.07434e9	−	1.17641e10i	−0.223914	−	1.26988i
$165$		0			0
$166$	9.66262e9	−	3.51691e9i	0.987662	−	0.359480i
$167$	−7.30584e9	−	6.13032e9i	−0.726852	−	0.609901i	0.202420	−	0.979299i	$-0.435120\pi$
$167$	−7.30584e9	−	6.13032e9i	−0.726852	−	0.609901i	−0.929271	+	0.369398i	$0.879564\pi$
$168$		0			0
$169$	−7.09298e9	−	2.58163e9i	−0.668865	−	0.243447i
$170$	1.30770e10	+	2.26500e10i	1.20085	+	2.07993i
$171$		0			0
$172$	−2.46955e9	+	4.27739e9i	−0.215149	+	0.372649i
$173$	9.30068e9	−	7.80420e9i	0.789418	−	0.662401i	−0.156183	−	0.987728i	$-0.549919\pi$
$173$	9.30068e9	−	7.80420e9i	0.789418	−	0.662401i	0.945601	+	0.325328i	$0.105475\pi$
$174$		0			0
$175$	−1.14069e9	+	6.46919e9i	−0.0919384	+	0.521409i
$176$	1.60035e9	−	9.07606e9i	0.125721	−	0.713001i
$177$		0			0
$178$	−1.69456e10	+	1.42190e10i	−1.26522	+	1.06165i
$179$	2.95892e9	−	5.12500e9i	0.215424	−	0.373126i	−0.737979	−	0.674823i	$-0.764220\pi$
$179$	2.95892e9	−	5.12500e9i	0.215424	−	0.373126i	0.953404	+	0.301697i	$0.0975532\pi$
$180$		0			0
$181$	9.54730e9	+	1.65364e10i	0.661191	+	1.14522i	0.980303	+	0.197500i	$0.0632822\pi$
$181$	9.54730e9	+	1.65364e10i	0.661191	+	1.14522i	−0.319112	+	0.947717i	$0.603385\pi$
$182$	−4.70020e10	−	1.71073e10i	−3.17538	−	1.15574i
$183$		0			0
$184$	1.11314e10	+	9.34034e9i	0.715928	+	0.600735i
$185$	−8.07739e8	+	2.93993e8i	−0.0506989	+	0.0184529i
$186$		0			0
$187$	−4.92418e9	−	2.79264e10i	−0.294474	−	1.67004i
$188$	2.96600e10			1.73165
$189$		0			0
$190$	−4.41718e10			−2.45898
$191$	2.35641e8	+	1.33639e9i	0.0128115	+	0.0726577i	0.990543	−	0.137201i	$-0.0438107\pi$
$191$	2.35641e8	+	1.33639e9i	0.0128115	+	0.0726577i	−0.977732	+	0.209859i	$0.932700\pi$
$192$		0			0
$193$	1.38564e10	−	5.04331e9i	0.718856	−	0.261642i	0.0434159	−	0.999057i	$-0.486176\pi$
$193$	1.38564e10	−	5.04331e9i	0.718856	−	0.261642i	0.675440	+	0.737415i	$0.263954\pi$
$194$	1.03460e10	+	8.68129e9i	0.524400	+	0.440024i
$195$		0			0
$196$	−4.82099e10	−	1.75470e10i	−2.33337	−	0.849278i
$197$	7.75260e9	+	1.34279e10i	0.366732	+	0.635199i	0.989053	−	0.147564i	$-0.0471431\pi$
$197$	7.75260e9	+	1.34279e10i	0.366732	+	0.635199i	−0.622320	+	0.782763i	$0.713810\pi$
$198$		0			0
$199$	1.59656e10	−	2.76532e10i	0.721681	−	1.24999i	−0.238644	−	0.971107i	$-0.576703\pi$
$199$	1.59656e10	−	2.76532e10i	0.721681	−	1.24999i	0.960325	−	0.278882i	$-0.0899638\pi$
$200$	−8.37782e9	+	7.02982e9i	−0.370251	+	0.310677i
$201$		0			0
$202$	−8.24521e9	+	4.67609e10i	−0.348434	+	1.97607i
$203$	5.05353e9	−	2.86600e10i	0.208863	−	1.18452i
$204$		0			0
$205$	1.58086e10	−	1.32650e10i	0.625176	−	0.524585i
$206$	−4.07723e10	+	7.06196e10i	−1.57747	+	2.73227i
$207$		0			0
$208$	−9.27726e9	−	1.60687e10i	−0.343665	−	0.595244i
$209$	4.50047e10	+	1.63804e10i	1.63155	+	0.593834i
$210$		0			0
$211$	2.27993e10	+	1.91309e10i	0.791865	+	0.664454i	0.946206	−	0.323564i	$-0.104881\pi$
$211$	2.27993e10	+	1.91309e10i	0.791865	+	0.664454i	−0.154341	+	0.988018i	$0.549325\pi$
$212$	3.60747e9	−	1.31301e9i	0.122657	−	0.0446435i
$213$		0			0
$214$	7.08110e9	+	4.01589e10i	0.230802	+	1.30894i
$215$	−8.53257e9			−0.272337
$216$		0			0
$217$	3.81103e10			1.16674
$218$	−8.11582e8	−	4.60271e9i	−0.0243376	−	0.138025i
$219$		0			0
$220$	9.56255e10	−	3.48048e10i	2.75215	−	1.00170i
$221$	−4.37342e10	−	3.66974e10i	−1.23326	−	1.03483i
$222$		0			0
$223$	−3.60170e10	−	1.31091e10i	−0.975294	−	0.354978i	−0.195285	−	0.980746i	$-0.562563\pi$
$223$	−3.60170e10	−	1.31091e10i	−0.975294	−	0.354978i	−0.780009	+	0.625768i	$0.784786\pi$
$224$	1.49424e10	+	2.58810e10i	0.396557	+	0.686856i
$225$		0			0
$226$	−2.85998e10	+	4.95363e10i	−0.729248	+	1.26309i
$227$	−3.27814e10	+	2.75068e10i	−0.819428	+	0.687582i	−0.952838	−	0.303479i	$-0.901852\pi$
$227$	−3.27814e10	+	2.75068e10i	−0.819428	+	0.687582i	0.133410	+	0.991061i	$0.457407\pi$
$228$		0			0
$229$	−4.33114e9	+	2.45631e10i	−0.104074	+	0.590233i	0.887512	+	0.460784i	$0.152432\pi$
$229$	−4.33114e9	+	2.45631e10i	−0.104074	+	0.590233i	−0.991586	+	0.129449i	$0.958679\pi$
$230$	−9.59578e9	+	5.44204e10i	−0.226102	+	1.28229i
$231$		0			0
$232$	3.71157e10	−	3.11437e10i	0.841126	−	0.705789i
$233$	−1.73450e9	+	3.00424e9i	−0.0385543	+	0.0667779i	−0.884659	−	0.466239i	$-0.845609\pi$
$233$	−1.73450e9	+	3.00424e9i	−0.0385543	+	0.0667779i	0.846104	+	0.533017i	$0.178942\pi$
$234$		0			0
$235$	2.56196e10	+	4.43745e10i	0.547984	+	0.949135i
$236$	−3.33406e10	−	1.21350e10i	−0.699632	−	0.254645i
$237$		0			0
$238$	−1.20507e11	−	1.01117e11i	−2.43453	−	2.04281i
$239$	2.59096e10	−	9.43032e9i	0.513653	−	0.186955i	−0.0721714	−	0.997392i	$-0.522993\pi$
$239$	2.59096e10	−	9.43032e9i	0.513653	−	0.186955i	0.585825	+	0.810438i	$0.300771\pi$
$240$		0			0
$241$	1.53696e10	+	8.71652e10i	0.293485	+	1.66443i	0.673299	+	0.739371i	$0.264877\pi$
$241$	1.53696e10	+	8.71652e10i	0.293485	+	1.66443i	−0.379814	+	0.925063i	$0.624012\pi$
$242$	−8.07540e10			−1.51354
$243$		0			0
$244$	−7.66249e10			−1.38394
$245$	−1.53905e10	−	8.72838e10i	−0.272901	−	1.54770i
$246$		0			0
$247$	9.06069e10	−	3.29782e10i	1.54891	−	0.563756i
$248$	4.86044e10	+	4.07839e10i	0.815911	+	0.684631i
$249$		0			0
$250$	7.41986e10	+	2.70061e10i	1.20134	+	0.437252i
$251$	2.97826e10	+	5.15849e10i	0.473620	+	0.820335i	0.999544	−	0.0301972i	$-0.00961352\pi$
$251$	2.97826e10	+	5.15849e10i	0.473620	+	0.820335i	−0.525924	+	0.850532i	$0.676280\pi$
$252$		0			0
$253$	2.99576e10	−	5.18880e10i	0.459689	−	0.796205i
$254$	2.70677e10	−	2.27125e10i	0.408036	−	0.342383i
$255$		0			0
$256$	−2.01269e10	+	1.14145e11i	−0.292885	+	1.66104i
$257$	−1.77025e10	+	1.00396e11i	−0.253126	+	1.43555i	0.547712	+	0.836667i	$0.315499\pi$
$257$	−1.77025e10	+	1.00396e11i	−0.253126	+	1.43555i	−0.800838	+	0.598881i	$0.795612\pi$
$258$		0			0
$259$	3.96058e9	−	3.32332e9i	0.0546903	−	0.0458906i
$260$	1.02438e11	−	1.77428e11i	1.39021	−	2.40792i
$261$		0			0
$262$	−8.59563e10	−	1.48881e11i	−1.12699	−	1.95201i
$263$	2.15781e9	+	7.85380e8i	0.0278108	+	0.0101223i	0.355888	−	0.934529i	$-0.384178\pi$
$263$	2.15781e9	+	7.85380e8i	0.0278108	+	0.0101223i	−0.328077	+	0.944651i	$0.606401\pi$
$264$		0			0
$265$	5.08046e9	+	4.26301e9i	0.0632844	+	0.0531019i
$266$	2.49661e11	−	9.08693e10i	3.05762	−	1.11288i
$267$		0			0
$268$	2.09146e10	+	1.18613e11i	0.247653	+	1.40451i
$269$	−1.85141e9			−0.0215584			−0.0107792	−	0.999942i	$-0.503431\pi$
$269$	−1.85141e9			−0.0215584			−0.0107792	+	0.999942i	$0.503431\pi$
$270$		0			0
$271$	9.38886e10			1.05743			0.528714	−	0.848800i	$-0.322674\pi$
$271$	9.38886e10			1.05743			0.528714	+	0.848800i	$0.322674\pi$
$272$	−1.01332e10	−	5.74682e10i	−0.112250	−	0.636602i
$273$		0			0
$274$	1.54139e10	−	5.61019e9i	0.165209	−	0.0601312i
$275$	3.45440e10	+	2.89858e10i	0.364229	+	0.305625i
$276$		0			0
$277$	4.17222e10	+	1.51856e10i	0.425803	+	0.154979i	0.546028	−	0.837767i	$-0.316139\pi$
$277$	4.17222e10	+	1.51856e10i	0.425803	+	0.154979i	−0.120225	+	0.992747i	$0.538362\pi$
$278$	−1.53403e11	−	2.65702e11i	−1.54040	−	2.66805i
$279$		0			0
$280$	1.28224e11	−	2.22090e11i	1.24669	−	2.15932i
$281$	2.73934e10	−	2.29858e10i	0.262100	−	0.219928i	−0.502262	−	0.864716i	$-0.667499\pi$
$281$	2.73934e10	−	2.29858e10i	0.262100	−	0.219928i	0.764362	+	0.644788i	$0.223054\pi$
$282$		0			0
$283$	2.13889e10	−	1.21302e11i	0.198221	−	1.12417i	−0.709536	−	0.704669i	$-0.751095\pi$
$283$	2.13889e10	−	1.21302e11i	0.198221	−	1.12417i	0.907757	−	0.419497i	$-0.137794\pi$
$284$	4.84110e10	−	2.74552e11i	0.441582	−	2.50434i
$285$		0			0
$286$	−2.63030e11	+	2.20708e11i	−2.32465	+	1.95061i
$287$	−6.20627e10	+	1.07496e11i	−0.539961	+	0.935239i
$288$		0			0
$289$	−3.04829e10	−	5.27979e10i	−0.257049	−	0.445221i
$290$	1.73143e11	+	6.30187e10i	1.43752	+	0.523213i
$291$		0			0
$292$	−1.72424e11	−	1.44681e11i	−1.38795	−	1.16463i
$293$	−3.38752e10	+	1.23296e10i	−0.268521	+	0.0977335i	−0.472771	−	0.881185i	$-0.656746\pi$
$293$	−3.38752e10	+	1.23296e10i	−0.268521	+	0.0977335i	0.204251	+	0.978919i	$0.434524\pi$
$294$		0			0
$295$	−1.06436e10	−	6.03631e10i	−0.0818260	−	0.464058i
$296$	8.60764e9			0.0651735
$297$		0			0
$298$	1.87288e11			1.37574
$299$	−2.09465e10	−	1.18793e11i	−0.151562	−	0.859551i
$300$		0			0
$301$	4.82265e10	−	1.75530e10i	0.338638	−	0.123254i
$302$	4.60334e10	+	3.86266e10i	0.318450	+	0.267211i
$303$		0			0
$304$	9.26126e10	+	3.37082e10i	0.621927	+	0.226363i
$305$	−6.61869e10	−	1.14639e11i	−0.437948	−	0.758549i
$306$		0			0
$307$	−9.24670e10	+	1.60158e11i	−0.594106	+	1.02902i	0.399566	+	0.916704i	$0.369161\pi$
$307$	−9.24670e10	+	1.60158e11i	−0.594106	+	1.02902i	−0.993672	+	0.112318i	$0.964173\pi$
$308$	−4.68880e11	+	3.93437e11i	−2.96882	+	2.49113i
$309$		0			0
$310$	−4.18993e10	+	2.37623e11i	−0.257679	+	1.46137i
$311$	7.36847e9	−	4.17887e10i	0.0446638	−	0.253301i	−0.954298	−	0.298857i	$-0.903395\pi$
$311$	7.36847e9	−	4.17887e10i	0.0446638	−	0.253301i	0.998962	+	0.0455558i	$0.0145059\pi$
$312$		0			0
$313$	5.57703e10	−	4.67968e10i	0.328438	−	0.275592i	−0.463625	−	0.886031i	$-0.653452\pi$
$313$	5.57703e10	−	4.67968e10i	0.328438	−	0.275592i	0.792063	+	0.610439i	$0.209007\pi$
$314$	−1.89340e11	+	3.27946e11i	−1.09915	+	1.90379i
$315$		0			0
$316$	1.42336e11	+	2.46533e11i	0.803012	+	1.39086i
$317$	2.84222e11	+	1.03448e11i	1.58085	+	0.575382i	0.975389	−	0.220492i	$-0.0707664\pi$
$317$	2.84222e11	+	1.03448e11i	1.58085	+	0.575382i	0.605461	+	0.795875i	$0.292989\pi$
$318$		0			0
$319$	−1.53038e11	−	1.28414e11i	−0.827447	−	0.694311i
$320$	−2.85189e11	+	1.03800e11i	−1.52040	+	0.553380i
$321$		0			0
$322$	−5.77166e10	−	3.27327e11i	−0.299191	−	1.69680i
$323$	3.03251e11			1.55021
$324$		0			0
$325$	9.07867e10			0.451385
$326$	1.00488e11	+	5.69896e11i	0.492760	+	2.79458i
$327$		0			0
$328$	−1.94189e11	+	7.06791e10i	−0.926388	+	0.337178i
$329$	−2.36090e11	−	1.98103e11i	−1.11095	−	0.932199i
$330$		0			0
$331$	1.62610e11	+	5.91853e10i	0.744598	+	0.271011i	0.686331	−	0.727290i	$-0.259220\pi$
$331$	1.62610e11	+	5.91853e10i	0.744598	+	0.271011i	0.0582670	+	0.998301i	$0.481443\pi$
$332$	−1.26666e11	−	2.19392e11i	−0.572188	−	0.991058i
$333$		0			0
$334$	−1.81593e11	+	3.14529e11i	−0.798437	+	1.38293i
$335$	−1.59392e11	+	1.33745e11i	−0.691455	+	0.580199i
$336$		0			0
$337$	−2.94939e10	+	1.67268e11i	−0.124565	+	0.706445i	0.857000	+	0.515317i	$0.172326\pi$
$337$	−2.94939e10	+	1.67268e11i	−0.124565	+	0.706445i	−0.981565	+	0.191128i	$0.938785\pi$
$338$	−4.99145e10	+	2.83079e11i	−0.208018	+	1.17973i
$339$		0			0
$340$	4.93597e11	−	4.14177e11i	2.00317	−	1.68086i
$341$	1.30808e11	−	2.26565e11i	0.523888	−	0.907400i
$342$		0			0
$343$	6.98486e10	+	1.20981e11i	0.272480	+	0.471949i
$344$	8.02905e10	+	2.92234e10i	0.309137	+	0.112517i
$345$		0			0
$346$	−3.54184e11	−	2.97195e11i	−1.32857	−	1.11481i
$347$	−1.02685e11	+	3.73742e10i	−0.380210	+	0.138385i	−0.525053	−	0.851070i	$-0.675954\pi$
$347$	−1.02685e11	+	3.73742e10i	−0.380210	+	0.138385i	0.144843	+	0.989455i	$0.453732\pi$
$348$		0			0
$349$	2.67405e9	+	1.51653e10i	0.00964840	+	0.0547188i	0.989252	−	0.146222i	$-0.0467113\pi$
$349$	2.67405e9	+	1.51653e10i	0.00964840	+	0.0547188i	−0.979603	+	0.200941i	$0.935600\pi$
$350$	2.50156e11			0.891057
$351$		0			0
$352$	2.05150e11			0.712245
$353$	−9.60340e10	−	5.44636e11i	−0.329184	−	1.86690i	−0.478472	−	0.878103i	$-0.658809\pi$
$353$	−9.60340e10	−	5.44636e11i	−0.329184	−	1.86690i	0.149288	−	0.988794i	$-0.452302\pi$
$354$		0			0
$355$	4.52576e11	−	1.64724e11i	1.51239	−	0.550465i
$356$	4.17481e11	+	3.50308e11i	1.37756	+	1.15591i
$357$		0			0
$358$	−2.11769e11	−	7.70777e10i	−0.681380	−	0.248002i
$359$	2.42280e11	+	4.19641e11i	0.769825	+	1.33338i	0.937658	+	0.347560i	$0.112990\pi$
$359$	2.42280e11	+	4.19641e11i	0.769825	+	1.33338i	−0.167833	+	0.985815i	$0.553677\pi$
$360$		0			0
$361$	−9.47390e10	+	1.64093e11i	−0.293593	+	0.508519i
$362$	5.57030e11	−	4.67403e11i	1.70486	−	1.43055i
$363$		0			0
$364$	−2.13984e11	+	1.21356e12i	−0.638889	+	3.62332i
$365$	6.75221e10	−	3.82937e11i	0.199126	−	1.12930i
$366$		0			0
$367$	−3.42857e11	+	2.87691e11i	−0.986541	+	0.827806i	−0.985063	−	0.172193i	$-0.944915\pi$
$367$	−3.42857e11	+	2.87691e11i	−0.986541	+	0.827806i	−0.00147785	+	0.999999i	$0.500470\pi$
$368$	6.16480e10	−	1.06778e11i	0.175228	−	0.303504i
$369$		0			0
$370$	1.63670e10	+	2.83485e10i	0.0454006	+	0.0786361i
$371$	−3.74848e10	−	1.36434e10i	−0.102724	−	0.0373885i
$372$		0			0
$373$	−3.38603e11	−	2.84122e11i	−0.905735	−	0.760002i	0.0655675	−	0.997848i	$-0.479114\pi$
$373$	−3.38603e11	−	2.84122e11i	−0.905735	−	0.760002i	−0.971303	+	0.237846i	$0.923559\pi$
$374$	−1.01476e12	+	3.69342e11i	−2.68189	+	0.976128i
$375$		0			0
$376$	−8.90988e10	−	5.05304e11i	−0.229893	−	1.30379i
$377$	−4.02206e11			−1.02544
$378$		0			0
$379$	−6.65757e11			−1.65745			−0.828723	−	0.559659i	$-0.810932\pi$
$379$	−6.65757e11			−1.65745			−0.828723	+	0.559659i	$0.810932\pi$
$380$	1.88972e11	+	1.07171e12i	0.464912	+	2.63664i
$381$		0			0
$382$	4.85601e10	−	1.76744e10i	0.116680	−	0.0424679i
$383$	−4.17637e11	−	3.50439e11i	−0.991755	−	0.832182i	−0.00593455	−	0.999982i	$-0.501889\pi$
$383$	−4.17637e11	−	3.50439e11i	−0.991755	−	0.832182i	−0.985821	+	0.167801i	$0.946333\pi$
$384$		0			0
$385$	−9.93632e11	−	3.61652e11i	−2.30490	−	0.838915i
$386$	−2.80768e11	−	4.86304e11i	−0.643732	−	1.11498i
$387$		0			0
$388$	1.66367e11	−	2.88156e11i	0.372670	−	0.645484i
$389$	6.16350e11	−	5.17179e11i	1.36475	−	1.14516i	0.390272	−	0.920699i	$-0.372381\pi$
$389$	6.16350e11	−	5.17179e11i	1.36475	−	1.14516i	0.974482	−	0.224465i	$-0.0720636\pi$
$390$		0			0
$391$	6.58775e10	−	3.73610e11i	0.142542	−	0.808394i
$392$	−1.54117e11	+	8.74043e11i	−0.329658	+	1.86959i
$393$		0			0
$394$	4.52319e11	−	3.79541e11i	0.945610	−	0.793461i
$395$	−2.45893e11	+	4.25899e11i	−0.508228	+	0.880277i
$396$		0			0
$397$	2.32548e11	+	4.02784e11i	0.469845	+	0.813795i	0.999405	−	0.0344768i	$-0.0109765\pi$
$397$	2.32548e11	+	4.02784e11i	0.469845	+	0.813795i	−0.529561	+	0.848272i	$0.677643\pi$
$398$	−1.14265e12	−	4.15891e11i	−2.28265	−	0.830818i
$399$		0			0
$400$	7.10861e10	+	5.96483e10i	0.138840	+	0.116501i
$401$	4.37962e10	−	1.59405e10i	0.0845837	−	0.0307859i	−0.299382	−	0.954133i	$-0.596780\pi$
$401$	4.37962e10	−	1.59405e10i	0.0845837	−	0.0307859i	0.383965	+	0.923347i	$0.374558\pi$
$402$		0			0
$403$	−9.14612e10	−	5.18702e11i	−0.172729	−	0.979592i
$404$	1.16980e12			2.18472
$405$		0			0
$406$	−1.10825e12			−2.02428
$407$	−6.16305e9	−	3.49524e10i	−0.0111332	−	0.0631396i
$408$		0			0
$409$	−1.88046e10	+	6.84430e9i	−0.0332283	+	0.0120941i	−0.358581	−	0.933499i	$-0.616739\pi$
$409$	−1.88046e10	+	6.84430e9i	−0.0332283	+	0.0120941i	0.325353	+	0.945593i	$0.394517\pi$
$410$	−6.02016e11	−	5.05152e11i	−1.05216	−	0.882865i
$411$		0			0
$412$	1.88782e12	+	6.87112e11i	3.22793	+	1.17487i
$413$	1.84336e11	+	3.19279e11i	0.311770	+	0.540002i
$414$		0			0
$415$	2.18822e11	−	3.79012e11i	0.362139	−	0.627243i
$416$	3.16395e11	−	2.65487e11i	0.517975	−	0.434633i
$417$		0			0
$418$	3.16706e11	−	1.79613e12i	0.507414	−	2.87769i
$419$	4.09285e10	−	2.32117e11i	0.0648728	−	0.367912i	−0.935038	−	0.354548i	$-0.884635\pi$
$419$	4.09285e10	−	2.32117e11i	0.0648728	−	0.367912i	0.999911	−	0.0133641i	$-0.00425404\pi$
$420$		0			0
$421$	−6.24091e11	+	5.23674e11i	−0.968229	+	0.812441i	−0.982272	−	0.187461i	$-0.939974\pi$
$421$	−6.24091e11	+	5.23674e11i	−0.968229	+	0.812441i	0.0140430	+	0.999901i	$0.495530\pi$
$422$	5.66699e11	−	9.81551e11i	0.869853	−	1.50663i
$423$		0			0
$424$	−3.32061e10	−	5.75147e10i	−0.0498967	−	0.0864236i
$425$	2.68309e11	+	9.76563e10i	0.398919	+	0.145195i
$426$		0			0
$427$	6.09924e11	+	5.11787e11i	0.887872	+	0.745013i
$428$	9.44055e11	−	3.43608e11i	1.35988	−	0.494955i
$429$		0			0
$430$	5.64240e10	+	3.19996e11i	0.0795895	+	0.451374i
$431$	−1.48147e11			−0.206798			−0.103399	−	0.994640i	$-0.532972\pi$
$431$	−1.48147e11			−0.206798			−0.103399	+	0.994640i	$0.532972\pi$
$432$		0			0
$433$	7.08214e11			0.968209			0.484104	−	0.875010i	$-0.339146\pi$
$433$	7.08214e11			0.968209			0.484104	+	0.875010i	$0.339146\pi$
$434$	−2.52015e11	−	1.42925e12i	−0.340975	−	1.93377i
$435$		0			0
$436$	−1.08200e11	+	3.93817e10i	−0.143397	+	0.0521922i
$437$	4.90828e11	+	4.11854e11i	0.643818	+	0.540227i
$438$		0			0
$439$	−3.82071e11	−	1.39062e11i	−0.490968	−	0.178698i	0.0846591	−	0.996410i	$-0.473020\pi$
$439$	−3.82071e11	−	1.39062e11i	−0.490968	−	0.178698i	−0.575627	+	0.817712i	$0.695242\pi$
$440$	−8.80214e11	−	1.52458e12i	−1.11957	−	1.93915i
$441$		0			0
$442$	−1.08705e12	+	1.88283e12i	−1.35472	+	2.34645i
$443$	4.48333e11	−	3.76196e11i	0.553074	−	0.464085i	−0.322906	−	0.946431i	$-0.604660\pi$
$443$	4.48333e11	−	3.76196e11i	0.553074	−	0.464085i	0.875981	+	0.482346i	$0.160215\pi$
$444$		0			0
$445$	−1.63488e11	+	9.27184e11i	−0.197635	+	1.12085i
$446$	−2.53458e11	+	1.43743e12i	−0.303318	+	1.72020i
$447$		0			0
$448$	1.39837e12	−	1.17337e12i	1.64010	−	1.37621i
$449$	−1.15769e11	+	2.00518e11i	−0.134426	+	0.232833i	−0.925378	−	0.379045i	$-0.876252\pi$
$449$	−1.15769e11	+	2.00518e11i	−0.134426	+	0.232833i	0.790952	+	0.611878i	$0.209586\pi$
$450$		0			0
$451$	4.26040e11	+	7.37924e11i	0.484905	+	0.839879i
$452$	1.32422e12	+	4.81976e11i	1.49223	+	0.543129i
$453$		0			0
$454$	1.24836e12	+	1.04750e12i	1.37908	+	1.15719i
$455$	−2.00046e12	+	7.28107e11i	−2.18815	+	0.796423i
$456$		0			0
$457$	−1.43209e11	−	8.12180e11i	−0.153585	−	0.871023i	−0.960068	−	0.279766i	$-0.909743\pi$
$457$	−1.43209e11	−	8.12180e11i	−0.153585	−	0.871023i	0.806483	−	0.591257i	$-0.201368\pi$
$458$	9.49829e11			1.00867
$459$		0			0
$460$	1.36142e12			1.41769
$461$	1.92138e11	+	1.08967e12i	0.198134	+	1.12367i	0.907885	+	0.419219i	$0.137696\pi$
$461$	1.92138e11	+	1.08967e12i	0.198134	+	1.12367i	−0.709751	+	0.704452i	$0.751193\pi$
$462$		0			0
$463$	9.19311e11	−	3.34602e11i	0.929711	−	0.338387i	0.167616	−	0.985852i	$-0.446393\pi$
$463$	9.19311e11	−	3.34602e11i	0.929711	−	0.338387i	0.762095	+	0.647465i	$0.224171\pi$
$464$	−3.14928e11	−	2.64256e11i	−0.315413	−	0.264663i
$465$		0			0
$466$	1.24138e11	+	4.51824e10i	0.121946	+	0.0443846i
$467$	6.79708e11	+	1.17729e12i	0.661297	+	1.14540i	0.980275	+	0.197637i	$0.0633268\pi$
$467$	6.79708e11	+	1.17729e12i	0.661297	+	1.14540i	−0.318979	+	0.947762i	$0.603340\pi$
$468$		0			0
$469$	6.25751e11	−	1.08383e12i	0.597205	−	1.03439i
$470$	1.49476e12	−	1.25425e12i	1.41296	−	1.18562i
$471$		0			0
$472$	−1.06583e11	+	6.04464e11i	−0.0988439	+	0.560572i
$473$	6.11773e10	−	3.46954e11i	0.0561972	−	0.318710i
$474$		0			0
$475$	−3.69412e11	+	3.09973e11i	−0.332958	+	0.279385i
$476$	−1.93780e12	+	3.35636e12i	−1.73012	+	2.99666i
$477$		0			0
$478$	−5.24999e11	−	9.09325e11i	−0.459974	−	0.796698i
$479$	−1.07486e12	−	3.91217e11i	−0.932914	−	0.339553i	−0.169550	−	0.985522i	$-0.554231\pi$
$479$	−1.07486e12	−	3.91217e11i	−0.932914	−	0.339553i	−0.763364	+	0.645969i	$0.776454\pi$
$480$		0			0
$481$	−5.47373e10	−	4.59300e10i	−0.0466262	−	0.0391241i
$482$	3.16731e12	−	1.15281e12i	2.67288	−	0.972849i
$483$		0			0
$484$	3.45474e11	+	1.95928e12i	0.286161	+	1.62290i
$485$	5.74817e11			0.471728
$486$		0			0
$487$	−1.29566e12			−1.04379			−0.521894	−	0.853010i	$-0.674774\pi$
$487$	−1.29566e12			−1.04379			−0.521894	+	0.853010i	$0.674774\pi$
$488$	2.30182e11	+	1.30543e12i	0.183731	+	1.04199i
$489$		0			0
$490$	−3.17162e12	+	1.15438e12i	−2.48542	+	0.904618i
$491$	−4.71619e11	−	3.95736e11i	−0.366206	−	0.307283i	0.441053	−	0.897481i	$-0.354605\pi$
$491$	−4.71619e11	−	3.95736e11i	−0.366206	−	0.307283i	−0.807258	+	0.590198i	$0.799050\pi$
$492$		0			0
$493$	−1.18867e12	−	4.32640e11i	−0.906253	−	0.329849i
$494$	−1.83594e12	−	3.17995e12i	−1.38704	−	2.40242i
$495$		0			0
$496$	2.69182e11	−	4.66236e11i	0.199700	−	0.345890i
$497$	−2.21911e12	+	1.86206e12i	−1.63146	+	1.36896i
$498$		0			0
$499$	4.37285e11	−	2.47997e12i	0.315727	−	1.79058i	−0.252383	−	0.967627i	$-0.581214\pi$
$499$	4.37285e11	−	2.47997e12i	0.315727	−	1.79058i	0.568111	−	0.822952i	$-0.307675\pi$
$500$	3.37801e11	−	1.91577e12i	0.241711	−	1.37081i
$501$		0			0
$502$	1.73764e12	−	1.45805e12i	1.22122	−	1.02472i
$503$	−2.59221e11	+	4.48984e11i	−0.180557	+	0.312734i	−0.942070	−	0.335415i	$-0.891123\pi$
$503$	−2.59221e11	+	4.48984e11i	−0.180557	+	0.312734i	0.761513	+	0.648149i	$0.224457\pi$
$504$		0			0
$505$	1.01045e12	+	1.75015e12i	0.691358	+	1.19747i
$506$	−2.14406e12	−	7.80373e11i	−1.45398	−	0.529206i
$507$		0			0
$508$	−6.66855e11	−	5.59558e11i	−0.444268	−	0.372785i
$509$	5.21676e11	−	1.89875e11i	0.344486	−	0.125383i	−0.163983	−	0.986463i	$-0.552434\pi$
$509$	5.21676e11	−	1.89875e11i	0.344486	−	0.125383i	0.508468	+	0.861081i	$0.330212\pi$
$510$		0			0
$511$	4.06131e11	+	2.30328e12i	0.263495	+	1.49435i
$512$	1.56656e12			1.00747
$513$		0			0
$514$	3.88221e12			2.45327
$515$	6.02668e11	+	3.41790e12i	0.377525	+	2.14105i
$516$		0			0
$517$	−1.98806e12	+	7.23594e11i	−1.22383	+	0.445438i
$518$	−1.50825e11	−	1.26557e11i	−0.0920426	−	0.0772329i
$519$		0			0
$520$	−3.33049e12	−	1.21220e12i	−1.99753	−	0.727041i
$521$	−8.51875e11	−	1.47549e12i	−0.506531	−	0.877338i	−0.999971	−	0.00755790i	$-0.997594\pi$
$521$	−8.51875e11	−	1.47549e12i	−0.506531	−	0.877338i	0.493440	−	0.869780i	$-0.335739\pi$
$522$		0			0
$523$	−9.46454e10	+	1.63931e11i	−0.0553149	+	0.0958082i	−0.892357	−	0.451330i	$-0.850950\pi$
$523$	−9.46454e10	+	1.63931e11i	−0.0553149	+	0.0958082i	0.837042	+	0.547139i	$0.184283\pi$
$524$	−3.24446e12	+	2.72243e12i	−1.87997	+	1.57749i
$525$		0			0
$526$	1.51849e10	−	8.61179e10i	0.00864921	−	0.0490521i
$527$	2.87649e11	−	1.63134e12i	0.162448	−	0.921291i
$528$		0			0
$529$	−7.65727e11	+	6.42521e11i	−0.425131	+	0.356728i
$530$	1.26280e11	−	2.18723e11i	0.0695171	−	0.120407i
$531$		0			0
$532$	−3.27278e12	−	5.66861e12i	−1.77139	−	3.06814i
$533$	1.61202e12	+	5.86727e11i	0.865163	+	0.314894i
$534$		0			0
$535$	1.32953e12	+	1.11561e12i	0.701625	+	0.588733i
$536$	1.95792e12	−	7.12626e11i	1.02460	−	0.372924i
$537$		0			0
$538$	1.22429e10	+	6.94332e10i	0.00630036	+	0.0357311i
$539$	3.65951e12			1.86755
$540$		0			0
$541$	1.71246e12			0.859474			0.429737	−	0.902954i	$-0.358606\pi$
$541$	1.71246e12			0.859474			0.429737	+	0.902954i	$0.358606\pi$
$542$	−6.20864e11	−	3.52110e12i	−0.309029	−	1.75259i
$543$		0			0
$544$	1.22064e12	−	4.44277e11i	0.597575	−	0.217500i
$545$	−1.52380e11	−	1.27862e11i	−0.0739851	−	0.0620809i
$546$		0			0
$547$	6.72612e11	+	2.44811e11i	0.321234	+	0.116920i	0.497604	−	0.867404i	$-0.334213\pi$
$547$	6.72612e11	+	2.44811e11i	0.321234	+	0.116920i	−0.176370	+	0.984324i	$0.556436\pi$
$548$	−2.02058e11	−	3.49975e11i	−0.0957115	−	0.165777i
$549$		0			0
$550$	8.58622e11	−	1.48718e12i	0.400101	−	0.692996i
$551$	1.63658e12	−	1.37325e12i	0.756406	−	0.634700i
$552$		0			0
$553$	5.13648e11	−	2.91304e12i	0.233562	−	1.32460i
$554$	2.93606e11	−	1.66512e12i	0.132425	−	0.751022i
$555$		0			0
$556$	−5.79028e12	+	4.85862e12i	−2.56958	+	2.15614i
$557$	−1.16608e12	+	2.01971e12i	−0.513312	+	0.889082i	0.486569	+	0.873642i	$0.338248\pi$
$557$	−1.16608e12	+	2.01971e12i	−0.513312	+	0.889082i	−0.999881	+	0.0154397i	$0.995085\pi$
$558$		0			0
$559$	−3.54645e11	−	6.14263e11i	−0.153617	−	0.266073i
$560$	−2.04474e12	−	7.44224e11i	−0.878601	−	0.319785i
$561$		0			0
$562$	−1.04318e12	−	8.75331e11i	−0.441108	−	0.370134i
$563$	−1.04738e12	+	3.81214e11i	−0.439355	+	0.159912i	−0.552220	−	0.833698i	$-0.686219\pi$
$563$	−1.04738e12	+	3.81214e11i	−0.439355	+	0.159912i	0.112866	+	0.993610i	$0.463997\pi$
$564$		0			0
$565$	4.22743e11	+	2.39749e12i	0.174525	+	0.989782i
$566$	−4.69064e12			−1.92114
$567$		0			0
$568$	−4.82286e12			−1.94418
$569$	−3.67748e11	−	2.08560e12i	−0.147077	−	0.834116i	−0.965676	−	0.259750i	$-0.916360\pi$
$569$	−3.67748e11	−	2.08560e12i	−0.147077	−	0.834116i	0.818599	−	0.574366i	$-0.194751\pi$
$570$		0			0
$571$	−2.80930e12	+	1.02250e12i	−1.10595	+	0.402533i	−0.829506	−	0.558497i	$-0.811378\pi$
$571$	−2.80930e12	+	1.02250e12i	−1.10595	+	0.402533i	−0.276444	+	0.961030i	$0.589156\pi$
$572$	6.48016e12	+	5.43750e12i	2.53107	+	2.12382i
$573$		0			0
$574$	4.44181e12	+	1.61669e12i	1.70788	+	0.621616i
$575$	3.01642e11	+	5.22459e11i	0.115076	+	0.199318i
$576$		0			0
$577$	1.49735e12	−	2.59348e12i	0.562382	−	0.974074i	−0.434906	−	0.900476i	$-0.643218\pi$
$577$	1.49735e12	−	2.59348e12i	0.562382	−	0.974074i	0.997288	−	0.0735985i	$-0.0234483\pi$
$578$	−1.77850e12	+	1.49234e12i	−0.662793	+	0.556149i
$579$		0			0
$580$	7.88259e11	−	4.47044e12i	0.289230	−	1.64030i
$581$	−4.57101e11	+	2.59235e12i	−0.166425	+	0.943845i
$582$		0			0
$583$	−2.09770e11	+	1.76018e11i	−0.0752030	+	0.0631028i
$584$	−1.94690e12	+	3.37214e12i	−0.692607	+	1.19963i
$585$		0			0
$586$	6.86404e11	+	1.18889e12i	0.240459	+	0.416487i
$587$	8.38843e11	+	3.05314e11i	0.291615	+	0.106139i	0.483685	−	0.875242i	$-0.339298\pi$
$587$	8.38843e11	+	3.05314e11i	0.291615	+	0.106139i	−0.192070	+	0.981381i	$0.561520\pi$
$588$		0			0
$589$	2.14316e12	+	1.79833e12i	0.733730	+	0.615673i
$590$	−2.19341e12	+	7.98335e11i	−0.745222	+	0.271238i
$591$		0			0
$592$	−1.26826e10	−	7.19266e10i	−0.00424385	−	0.0240681i
$593$	−3.77700e12			−1.25430			−0.627149	−	0.778900i	$-0.715778\pi$
$593$	−3.77700e12			−1.25430			−0.627149	+	0.778900i	$0.715778\pi$
$594$		0			0
$595$	−6.69530e12			−2.19000
$596$	−8.01238e11	−	4.54404e12i	−0.260108	−	1.47514i
$597$		0			0
$598$	−4.31658e12	+	1.57111e12i	−1.38034	+	0.502401i
$599$	3.36683e12	+	2.82510e12i	1.06856	+	0.896631i	0.994921	−	0.100654i	$-0.0320935\pi$
$599$	3.36683e12	+	2.82510e12i	1.06856	+	0.896631i	0.0736415	+	0.997285i	$0.476538\pi$
$600$		0			0
$601$	−2.19366e11	−	7.98426e10i	−0.0685857	−	0.0249631i	0.307499	−	0.951548i	$-0.400508\pi$
$601$	−2.19366e11	−	7.98426e10i	−0.0685857	−	0.0249631i	−0.376085	+	0.926585i	$0.622730\pi$
$602$	−9.77200e11	−	1.69256e12i	−0.303249	−	0.525242i
$603$		0			0
$604$	7.40235e11	−	1.28212e12i	0.226310	−	0.391980i
$605$	−2.63288e12	+	2.20925e12i	−0.798972	+	0.670417i
$606$		0			0
$607$	−1.00818e12	+	5.71768e12i	−0.301432	+	1.70951i	0.338409	+	0.940999i	$0.390111\pi$
$607$	−1.00818e12	+	5.71768e12i	−0.301432	+	1.70951i	−0.639841	+	0.768508i	$0.721000\pi$
$608$	−3.80961e11	+	2.16054e12i	−0.113061	+	0.641203i
$609$		0			0
$610$	−3.86162e12	+	3.24029e12i	−1.12924	+	0.947543i
$611$	−2.12969e12	+	3.68874e12i	−0.618203	+	1.07076i
$612$		0			0
$613$	−1.53253e12	−	2.65443e12i	−0.438367	−	0.759274i	0.559197	−	0.829035i	$-0.311110\pi$
$613$	−1.53253e12	−	2.65443e12i	−0.438367	−	0.759274i	−0.997564	+	0.0697610i	$0.977776\pi$
$614$	6.61784e12	+	2.40870e12i	1.87914	+	0.683950i
$615$		0			0
$616$	8.11133e12	+	6.80622e12i	2.26976	+	1.90455i
$617$	4.79504e12	−	1.74525e12i	1.33202	−	0.484814i	0.424726	−	0.905322i	$-0.360370\pi$
$617$	4.79504e12	−	1.74525e12i	1.33202	−	0.484814i	0.907289	+	0.420508i	$0.138148\pi$
$618$		0			0
$619$	1.02333e11	+	5.80361e11i	0.0280162	+	0.158888i	0.995606	−	0.0936384i	$-0.0298498\pi$
$619$	1.02333e11	+	5.80361e11i	0.0280162	+	0.158888i	−0.967590	+	0.252526i	$0.918739\pi$
$620$	5.94453e12			1.61568
$621$		0			0
$622$	−1.61592e12			−0.432876
$623$	−9.83343e11	−	5.57681e12i	−0.261522	−	1.48317i
$624$		0			0
$625$	4.39468e12	−	1.59953e12i	1.15204	−	0.419308i
$626$	−2.12381e12	−	1.78209e12i	−0.552754	−	0.463816i
$627$		0			0
$628$	8.76674e12	+	3.19083e12i	2.24916	+	0.818626i
$629$	−1.12364e11	−	1.94620e11i	−0.0286219	−	0.0495745i
$630$		0			0
$631$	5.61187e10	−	9.72005e10i	0.0140921	−	0.0244082i	−0.858893	−	0.512154i	$-0.828848\pi$
$631$	5.61187e10	−	9.72005e10i	0.0140921	−	0.0244082i	0.872985	+	0.487746i	$0.162181\pi$
$632$	3.77249e12	−	3.16550e12i	0.940593	−	0.789251i
$633$		0			0
$634$	2.00012e12	−	1.13432e13i	0.491647	−	2.78827i
$635$	2.61144e11	−	1.48102e12i	0.0637379	−	0.361476i
$636$		0			0
$637$	5.64391e12	−	4.73580e12i	1.35817	−	1.13964i
$638$	−3.80389e12	+	6.58853e12i	−0.908940	+	1.57433i
$639$		0			0
$640$	4.50675e12	+	7.80593e12i	1.06183	+	1.83914i
$641$	−4.20138e12	−	1.52918e12i	−0.982949	−	0.357764i	−0.199963	−	0.979803i	$-0.564082\pi$
$641$	−4.20138e12	−	1.52918e12i	−0.982949	−	0.357764i	−0.782986	+	0.622039i	$0.786304\pi$
$642$		0			0
$643$	1.33757e12	+	1.12235e12i	0.308578	+	0.258928i	0.783904	−	0.620882i	$-0.213225\pi$
$643$	1.33757e12	+	1.12235e12i	0.308578	+	0.258928i	−0.475326	+	0.879810i	$0.657670\pi$
$644$	−7.69479e12	+	2.80068e12i	−1.76283	+	0.641618i
$645$		0			0
$646$	−2.00533e12	−	1.13728e13i	−0.453043	−	2.56934i
$647$	4.93576e12			1.10735			0.553675	−	0.832733i	$-0.313225\pi$
$647$	4.93576e12			1.10735			0.553675	+	0.832733i	$0.313225\pi$
$648$		0			0
$649$	2.53081e12			0.559963
$650$	−6.00352e11	−	3.40477e12i	−0.131916	−	0.748130i
$651$		0			0
$652$	1.33971e13	−	4.87615e12i	2.90333	−	1.05673i
$653$	−4.12280e12	−	3.45944e12i	−0.887326	−	0.744555i	0.0803456	−	0.996767i	$-0.474398\pi$
$653$	−4.12280e12	−	3.45944e12i	−0.887326	−	0.744555i	−0.967672	+	0.252212i	$0.918842\pi$
$654$		0			0
$655$	−6.87553e12	−	2.50249e12i	−1.45955	−	0.531234i
$656$	8.76725e11	+	1.51853e12i	0.184840	+	0.320152i
$657$		0			0
$658$	−5.86822e12	+	1.01641e13i	−1.22037	+	2.11374i
$659$	−3.70769e12	+	3.11112e12i	−0.765807	+	0.642588i	−0.939631	−	0.342188i	$-0.888832\pi$
$659$	−3.70769e12	+	3.11112e12i	−0.765807	+	0.642588i	0.173824	+	0.984777i	$0.444387\pi$
$660$		0			0
$661$	−9.37173e10	+	5.31497e11i	−0.0190947	+	0.108292i	−0.992865	−	0.119240i	$-0.961954\pi$
$661$	−9.37173e10	+	5.31497e11i	−0.0190947	+	0.108292i	0.973771	+	0.227531i	$0.0730654\pi$
$662$	1.14432e12	−	6.48974e12i	0.231571	−	1.31331i
$663$		0			0
$664$	−3.35718e12	+	2.81701e12i	−0.670221	+	0.562382i
$665$	5.65390e12	−	9.79284e12i	1.12112	−	1.94183i
$666$		0			0
$667$	−1.33634e12	−	2.31461e12i	−0.261428	−	0.452806i
$668$	8.40807e12	+	3.06029e12i	1.63381	+	0.594659i
$669$		0			0
$670$	6.06986e12	+	5.09322e12i	1.16370	+	0.976463i
$671$	5.13604e12	−	1.86936e12i	0.978085	−	0.355994i
$672$		0			0
$673$	6.83923e11	+	3.87872e12i	0.128511	+	0.728821i	0.979160	+	0.203088i	$0.0650977\pi$
$673$	6.83923e11	+	3.87872e12i	0.128511	+	0.728821i	−0.850650	+	0.525733i	$0.823791\pi$
$674$	6.46808e12			1.20727
$675$		0			0
$676$	7.08169e12			1.30430
$677$	1.40415e12	+	7.96332e12i	0.256900	+	1.45695i	0.791148	+	0.611625i	$0.209484\pi$
$677$	1.40415e12	+	7.96332e12i	0.256900	+	1.45695i	−0.534248	+	0.845328i	$0.679405\pi$
$678$		0			0
$679$	−3.24889e12	+	1.18250e12i	−0.586572	+	0.213495i
$680$	−8.53892e12	−	7.16500e12i	−1.53148	−	1.28507i
$681$		0			0
$682$	−9.36186e12	−	3.40744e12i	−1.65704	−	0.603113i
$683$	4.43784e12	+	7.68656e12i	0.780330	+	1.35157i	0.931750	+	0.363101i	$0.118282\pi$
$683$	4.43784e12	+	7.68656e12i	0.780330	+	1.35157i	−0.151420	+	0.988469i	$0.548385\pi$
$684$		0			0
$685$	3.49067e11	−	6.04601e11i	0.0605760	−	0.104921i
$686$	4.07526e12	−	3.41955e12i	0.702582	−	0.589536i
$687$		0			0
$688$	1.25893e11	−	7.13977e11i	0.0214217	−	0.121489i
$689$	−9.57334e10	+	5.42931e11i	−0.0161837	+	0.0917822i
$690$		0			0
$691$	3.04573e11	−	2.55567e11i	0.0508207	−	0.0426436i	−0.617024	−	0.786945i	$-0.711662\pi$
$691$	3.04573e11	−	2.55567e11i	0.0508207	−	0.0426436i	0.667844	+	0.744301i	$0.267217\pi$
$692$	−5.69541e12	+	9.86475e12i	−0.944165	+	1.63534i
$693$		0			0
$694$	2.08067e12	+	3.60383e12i	0.340476	+	0.589721i
$695$	−1.22705e13	−	4.46610e12i	−1.99495	−	0.726101i
$696$		0			0
$697$	4.13300e12	+	3.46800e12i	0.663312	+	0.556585i
$698$	5.51060e11	−	2.00570e11i	0.0878719	−	0.0319827i
$699$		0			0
$700$	−1.07020e12	−	6.06938e12i	−0.168470	−	0.955439i
$701$	5.09147e12			0.796365			0.398183	−	0.917306i	$-0.369641\pi$
$701$	5.09147e12			0.796365			0.398183	+	0.917306i	$0.369641\pi$
$702$		0			0
$703$	3.79546e11			0.0586091
$704$	−2.17599e12	−	1.23407e13i	−0.333872	−	1.89348i
$705$		0			0
$706$	−1.97904e13	+	7.20311e12i	−2.99801	+	1.09119i
$707$	−9.31147e12	−	7.81325e12i	−1.40162	−	1.17610i
$708$		0			0
$709$	−5.93257e11	−	2.15928e11i	−0.0881729	−	0.0320923i	0.297557	−	0.954704i	$-0.403828\pi$
$709$	−5.93257e11	−	2.15928e11i	−0.0881729	−	0.0320923i	−0.385730	+	0.922612i	$0.626050\pi$
$710$	−9.17043e12	−	1.58836e13i	−1.35434	−	2.34578i
$711$		0			0
$712$	4.71393e12	−	8.16477e12i	0.687422	−	1.19065i
$713$	2.68114e12	−	2.24975e12i	0.388524	−	0.326010i
$714$		0			0
$715$	−2.53766e12	+	1.43918e13i	−0.363125	+	2.05939i
$716$	−9.64113e11	+	5.46776e12i	−0.137094	+	0.777500i
$717$		0			0
$718$	1.41356e13	−	1.18612e13i	1.98497	−	1.66559i
$719$	5.27092e12	−	9.12950e12i	0.735540	−	1.27399i	−0.218946	−	0.975737i	$-0.570262\pi$
$719$	5.27092e12	−	9.12950e12i	0.735540	−	1.27399i	0.954486	−	0.298256i	$-0.0964048\pi$
$720$		0			0
$721$	−1.04375e13	−	1.80783e13i	−1.43843	−	2.49143i
$722$	6.78044e12	+	2.46788e12i	0.928626	+	0.337992i
$723$		0			0
$724$	−1.37233e13	−	1.15152e13i	−1.85625	−	1.55758i
$725$	1.89023e12	−	6.87989e11i	0.254094	−	0.0924826i
$726$		0			0
$727$	−2.25862e12	−	1.28093e13i	−0.299874	−	1.70067i	−0.646702	−	0.762743i	$-0.723852\pi$
$727$	−2.25862e12	−	1.28093e13i	−0.299874	−	1.70067i	0.346828	−	0.937929i	$-0.387259\pi$
$728$	2.13178e13			2.81288
$729$		0			0
$730$	−1.48078e13			−1.92991
$731$	−3.87365e11	−	2.19686e12i	−0.0501756	−	0.284560i
$732$		0			0
$733$	−4.84063e12	+	1.76184e12i	−0.619346	+	0.225424i	−0.632588	−	0.774489i	$-0.718007\pi$
$733$	−4.84063e12	+	1.76184e12i	−0.619346	+	0.225424i	0.0132414	+	0.999912i	$0.495785\pi$
$734$	1.30565e13	+	1.09557e13i	1.66033	+	1.39318i
$735$		0			0
$736$	2.57906e12	+	9.38699e11i	0.323974	+	0.117917i
$737$	−4.29558e12	−	7.44016e12i	−0.536312	−	0.928920i
$738$		0			0
$739$	−6.80061e11	+	1.17790e12i	−0.0838780	+	0.145281i	−0.904913	−	0.425598i	$-0.860064\pi$
$739$	−6.80061e11	+	1.17790e12i	−0.0838780	+	0.145281i	0.821035	+	0.570878i	$0.193397\pi$
$740$	6.17780e11	−	5.18379e11i	0.0757340	−	0.0635484i
$741$		0			0
$742$	−2.63787e11	+	1.49601e12i	−0.0319474	+	0.181183i
$743$	−2.14481e10	+	1.21638e11i	−0.00258190	+	0.0146427i	−0.986071	−	0.166322i	$-0.946811\pi$
$743$	−2.14481e10	+	1.21638e11i	−0.00258190	+	0.0146427i	0.983490	+	0.180965i	$0.0579220\pi$
$744$		0			0
$745$	6.10628e12	−	5.12378e12i	0.726229	−	0.609379i
$746$	−8.41629e12	+	1.45774e13i	−0.994938	+	1.72328i
$747$		0			0
$748$	1.33023e13	+	2.30403e13i	1.55371	+	2.69111i
$749$	−9.80955e12	−	3.57038e12i	−1.13889	−	0.414521i
$750$		0			0
$751$	1.95666e11	+	1.64183e11i	0.0224458	+	0.0188343i	0.653942	−	0.756545i	$-0.273114\pi$
$751$	1.95666e11	+	1.64183e11i	0.0224458	+	0.0188343i	−0.631496	+	0.775379i	$0.717559\pi$
$752$	−4.09111e12	+	1.48904e12i	−0.466510	+	0.169796i
$753$		0			0
$754$	2.65970e12	+	1.50839e13i	0.299682	+	1.69958i
$755$	2.55759e12			0.286464
$756$		0			0
$757$	1.34688e13			1.49072			0.745360	−	0.666662i	$-0.232277\pi$
$757$	1.34688e13			1.49072			0.745360	+	0.666662i	$0.232277\pi$
$758$	4.40250e12	+	2.49678e13i	0.484382	+	2.74707i
$759$		0			0
$760$	1.76906e13	−	6.43886e12i	1.92345	−	0.700080i
$761$	−8.76212e11	−	7.35229e11i	−0.0947061	−	0.0794679i	0.594205	−	0.804313i	$-0.297467\pi$
$761$	−8.76212e11	−	7.35229e11i	−0.0947061	−	0.0794679i	−0.688911	+	0.724846i	$0.741911\pi$
$762$		0			0
$763$	1.12430e12	+	4.09210e11i	0.120094	+	0.0437105i
$764$	−6.36568e11	−	1.10257e12i	−0.0675966	−	0.117081i
$765$		0			0
$766$	−1.03808e13	+	1.79800e13i	−1.08943	+	1.88695i
$767$	3.90317e12	−	3.27515e12i	0.407229	−	0.341706i
$768$		0			0
$769$	1.58478e12	−	8.98772e12i	0.163418	−	0.926790i	−0.787263	−	0.616618i	$-0.788502\pi$
$769$	1.58478e12	−	8.98772e12i	0.163418	−	0.926790i	0.950681	−	0.310172i	$-0.100387\pi$
$770$	−6.99235e12	+	3.96556e13i	−0.716828	+	4.06534i
$771$		0			0
$772$	−1.05977e13	+	8.89254e12i	−1.07383	+	0.901049i
$773$	2.26657e12	−	3.92582e12i	0.228329	−	0.395478i	−0.728984	−	0.684531i	$-0.760007\pi$
$773$	2.26657e12	−	3.92582e12i	0.228329	−	0.395478i	0.957313	+	0.289053i	$0.0933404\pi$
$774$		0			0
$775$	1.31710e12	+	2.28128e12i	0.131148	+	0.227154i
$776$	−5.40896e12	−	1.96870e12i	−0.535471	−	0.194896i
$777$		0			0
$778$	−2.34715e13	−	1.96950e13i	−2.29685	−	1.92729i
$779$	−8.56259e12	+	3.11653e12i	−0.833080	+	0.303216i
$780$		0			0
$781$	3.45316e12	+	1.95838e13i	0.332113	+	1.88351i
$782$	−1.44471e13			−1.38150
$783$		0			0
$784$	7.53070e12			0.711890
$785$	2.79869e12	+	1.58721e13i	0.263052	+	1.49184i
$786$		0			0
$787$	1.46649e13	−	5.33760e12i	1.36268	−	0.495975i	0.445799	−	0.895133i	$-0.352920\pi$
$787$	1.46649e13	−	5.33760e12i	1.36268	−	0.495975i	0.916882	+	0.399158i	$0.130697\pi$
$788$	−1.11436e13	−	9.35060e12i	−1.02957	−	0.863916i
$789$		0			0
$790$	1.75985e13	+	6.40532e12i	1.60751	+	0.585085i
$791$	−7.32143e12	−	1.26811e13i	−0.664970	−	1.15176i
$792$		0			0
$793$	5.50194e12	−	9.52964e12i	0.494068	−	0.855751i
$794$	1.35678e13	−	1.13847e13i	1.21148	−	1.01655i
$795$		0			0
$796$	−5.20211e12	+	2.95026e13i	−0.459272	+	2.60466i
$797$	2.66540e12	−	1.51162e13i	0.233991	−	1.32703i	−0.610736	−	0.791834i	$-0.709126\pi$
$797$	2.66540e12	−	1.51162e13i	0.233991	−	1.32703i	0.844727	−	0.535197i	$-0.179763\pi$
$798$		0			0
$799$	−1.02619e13	+	8.61075e12i	−0.890773	+	0.747447i
$800$	−1.03282e12	+	1.78890e12i	−0.0891500	+	0.154412i
$801$		0			0
$802$	−8.87430e11	−	1.53707e12i	−0.0757442	−	0.131193i
$803$	1.50870e13	+	5.49121e12i	1.28051	+	0.466066i
$804$		0			0
$805$	−1.08367e13	−	9.09307e12i	−0.909527	−	0.763184i
$806$	−1.88480e13	+	6.86012e12i	−1.57311	+	0.572564i
$807$		0			0
$808$	−3.51409e12	−	1.99294e13i	−0.290043	−	1.64492i
$809$	−1.59419e13			−1.30849			−0.654246	−	0.756282i	$-0.727014\pi$
$809$	−1.59419e13			−1.30849			−0.654246	+	0.756282i	$0.727014\pi$
$810$		0			0
$811$	1.43124e13			1.16177			0.580883	−	0.813987i	$-0.302707\pi$
$811$	1.43124e13			1.16177			0.580883	+	0.813987i	$0.302707\pi$
$812$	4.74121e12	+	2.68887e13i	0.382725	+	2.17054i
$813$		0			0
$814$	−1.27006e12	+	4.62265e11i	−0.101395	+	0.0369046i
$815$	1.88674e13	+	1.58316e13i	1.49797	+	1.25694i
$816$		0			0
$817$	3.54033e12	+	1.28858e12i	0.278000	+	0.101184i
$818$	3.81032e11	+	6.59966e11i	0.0297558	+	0.0515385i
$819$		0			0
$820$	−9.68066e12	+	1.67674e13i	−0.747727	+	1.29510i
$821$	−1.15994e13	+	9.73305e12i	−0.891028	+	0.747661i	−0.968416	−	0.249340i	$-0.919786\pi$
$821$	−1.15994e13	+	9.73305e12i	−0.891028	+	0.747661i	0.0773880	+	0.997001i	$0.475342\pi$
$822$		0			0
$823$	−3.25956e11	+	1.84859e12i	−0.0247662	+	0.140456i	−0.994684	−	0.102978i	$-0.967163\pi$
$823$	−3.25956e11	+	1.84859e12i	−0.0247662	+	0.140456i	0.969917	+	0.243434i	$0.0782740\pi$
$824$	6.03499e12	−	3.42261e13i	0.456041	−	2.58634i
$825$		0			0
$826$	1.07549e13	−	9.02446e12i	0.803891	−	0.674545i
$827$	9.18022e11	−	1.59006e12i	0.0682462	−	0.118206i	−0.829883	−	0.557937i	$-0.811593\pi$
$827$	9.18022e11	−	1.59006e12i	0.0682462	−	0.118206i	0.898129	+	0.439731i	$0.144926\pi$
$828$		0			0
$829$	−8.03155e12	−	1.39111e13i	−0.590614	−	1.02297i	−0.994150	−	0.108010i	$-0.965552\pi$
$829$	−8.03155e12	−	1.39111e13i	−0.590614	−	1.02297i	0.403535	−	0.914964i	$-0.367781\pi$
$830$	−1.56611e13	−	5.70016e12i	−1.14543	−	0.416904i
$831$		0			0
$832$	−1.93261e13	−	1.62165e13i	−1.39827	−	1.17328i
$833$	2.17740e13	−	7.92510e12i	1.56688	−	0.570298i
$834$		0			0
$835$	2.68419e12	+	1.52228e13i	0.191084	+	1.08369i
$836$	−4.49331e13			−3.18155
$837$		0			0
$838$	−8.97571e12			−0.628740
$839$	4.19598e12	+	2.37966e13i	0.292351	+	1.65801i	0.677778	+	0.735267i	$0.262943\pi$
$839$	4.19598e12	+	2.37966e13i	0.292351	+	1.65801i	−0.385427	+	0.922738i	$0.625946\pi$
$840$		0			0
$841$	5.25809e12	−	1.91379e12i	0.362448	−	0.131920i
$842$	2.37663e13	+	1.99423e13i	1.62951	+	1.36732i
$843$		0			0
$844$	−2.62391e13	−	9.55025e12i	−1.77995	−	0.647849i
$845$	6.11701e12	+	1.05950e13i	0.412747	+	0.714899i
$846$		0			0
$847$	1.03363e13	−	1.79031e13i	0.690067	−	1.19523i
$848$	−4.31674e11	+	3.62218e11i	−0.0286665	+	0.0240541i
$849$		0			0
$850$	1.88813e12	−	1.07081e13i	0.124064	−	0.703605i
$851$	8.24516e10	−	4.67606e11i	0.00538910	−	0.0305631i
$852$		0			0
$853$	2.64964e12	−	2.22331e12i	0.171362	−	0.143790i	−0.553073	−	0.833133i	$-0.686545\pi$
$853$	2.64964e12	−	2.22331e12i	0.171362	−	0.143790i	0.724435	+	0.689343i	$0.242101\pi$
$854$	1.51602e13	−	2.62583e13i	0.975316	−	1.68930i
$855$		0			0
$856$	−8.68985e12	−	1.50513e13i	−0.553197	−	0.958166i
$857$	−7.62208e11	−	2.77421e11i	−0.0482681	−	0.0175681i	0.317773	−	0.948167i	$-0.397065\pi$
$857$	−7.62208e11	−	2.77421e11i	−0.0482681	−	0.0175681i	−0.366041	+	0.930599i	$0.619287\pi$
$858$		0			0
$859$	1.35901e13	+	1.14035e13i	0.851637	+	0.714608i	0.960149	−	0.279487i	$-0.0901644\pi$
$859$	1.35901e13	+	1.14035e13i	0.851637	+	0.714608i	−0.108513	+	0.994095i	$0.534609\pi$
$860$	7.52246e12	−	2.73795e12i	0.468940	−	0.170680i
$861$		0			0
$862$	9.79666e11	+	5.55596e12i	0.0604359	+	0.342749i
$863$	−5.67923e12			−0.348531			−0.174265	−	0.984699i	$-0.555755\pi$
$863$	−5.67923e12			−0.348531			−0.174265	+	0.984699i	$0.555755\pi$
$864$		0			0
$865$	−1.96783e13			−1.19513
$866$	−4.68326e12	−	2.65601e13i	−0.282955	−	1.60472i
$867$		0			0
$868$	−3.35987e13	+	1.22289e13i	−2.00902	+	0.731224i
$869$	−1.55550e13	−	1.30522e13i	−0.925296	−	0.776416i
$870$		0			0
$871$	−1.62533e13	−	5.91571e12i	−0.956884	−	0.348277i
$872$	9.95964e11	+	1.72506e12i	0.0583337	+	0.101037i
$873$		0			0
$874$	1.22000e13	−	2.11310e13i	0.707225	−	1.22495i
$875$	−1.54845e13	+	1.29930e13i	−0.893019	+	0.749332i
$876$		0			0
$877$	−3.68175e12	+	2.08803e13i	−0.210163	+	1.19189i	0.678942	+	0.734192i	$0.262439\pi$
$877$	−3.68175e12	+	2.08803e13i	−0.210163	+	1.19189i	−0.889105	+	0.457702i	$0.848673\pi$
$878$	−2.68870e12	+	1.52484e13i	−0.152692	+	0.865960i
$879$		0			0
$880$	−1.14426e13	+	9.60152e12i	−0.643212	+	0.539719i
$881$	4.49342e12	−	7.78283e12i	0.251296	−	0.435257i	−0.712587	−	0.701584i	$-0.752477\pi$
$881$	4.49342e12	−	7.78283e12i	0.251296	−	0.435257i	0.963883	+	0.266327i	$0.0858100\pi$
$882$		0			0
$883$	8.76115e12	+	1.51748e13i	0.484996	+	0.840037i	0.999851	−	0.0172398i	$-0.00548788\pi$
$883$	8.76115e12	+	1.51748e13i	0.484996	+	0.840037i	−0.514856	+	0.857277i	$0.672155\pi$
$884$	5.03324e13	+	1.83195e13i	2.77212	+	1.00897i
$885$		0			0
$886$	−1.70732e13	−	1.43261e13i	−0.930813	−	0.781045i
$887$	−1.50480e11	+	5.47702e10i	−0.00816248	+	0.00297090i	−0.346098	−	0.938198i	$-0.612494\pi$
$887$	−1.50480e11	+	5.47702e10i	−0.00816248	+	0.00297090i	0.337936	+	0.941169i	$0.390271\pi$
$888$		0			0
$889$	1.57072e12	+	8.90801e12i	0.0843416	+	0.478325i
$890$	3.58532e13			1.91546
$891$		0			0
$892$	3.59597e13			1.90184
$893$	−3.92873e12	−	2.22809e13i	−0.206738	−	1.17247i
$894$		0			0
$895$	−9.01313e12	+	3.28051e12i	−0.469539	+	0.170898i
$896$	−4.15306e13	−	3.48483e13i	−2.15269	−	1.80632i
$897$		0			0
$898$	8.28555e12	+	3.01569e12i	0.425185	+	0.154755i
$899$	−5.83504e12	−	1.01066e13i	−0.297938	−	0.516043i
$900$		0			0
$901$	−8.66942e11	+	1.50159e12i	−0.0438256	+	0.0759083i
$902$	2.48570e13	−	2.08575e13i	1.25031	−	1.04914i
$903$		0			0
$904$	4.23326e12	−	2.40080e13i	0.210823	−	1.19563i
$905$	5.37412e12	−	3.04782e13i	0.266311	−	1.51032i
$906$		0			0
$907$	2.90354e13	−	2.43636e13i	1.42461	−	1.19539i	0.475789	−	0.879559i	$-0.342163\pi$
$907$	2.90354e13	−	2.43636e13i	1.42461	−	1.19539i	0.948817	−	0.315827i	$-0.102282\pi$
$908$	2.00742e13	−	3.47695e13i	0.980057	−	1.69751i
$909$		0			0
$910$	4.05347e13	+	7.02082e13i	1.95948	+	3.39392i
$911$	−1.68656e12	−	6.13857e11i	−0.0811276	−	0.0295280i	0.301138	−	0.953581i	$-0.402634\pi$
$911$	−1.68656e12	−	6.13857e11i	−0.0811276	−	0.0295280i	−0.382265	+	0.924053i	$0.624856\pi$
$912$		0			0
$913$	1.38425e13	+	1.16153e13i	0.659322	+	0.553237i
$914$	−2.95121e13	+	1.07415e13i	−1.39876	+	0.509106i
$915$		0			0
$916$	−4.06347e12	−	2.30451e13i	−0.190707	−	1.08155i
$917$	4.40089e13			2.05532
$918$		0			0
$919$	−3.29913e13			−1.52574			−0.762869	−	0.646553i	$-0.776210\pi$
$919$	−3.29913e13			−1.52574			−0.762869	+	0.646553i	$0.776210\pi$
$920$	−4.08971e12	−	2.31939e13i	−0.188212	−	1.06740i
$921$		0			0
$922$	3.95951e13	−	1.44114e13i	1.80448	−	0.656777i
$923$	3.06693e13	+	2.57346e13i	1.39090	+	1.16710i
$924$		0			0
$925$	3.35812e11	+	1.22226e11i	0.0150820	+	0.00548939i
$926$	−1.86277e13	−	3.22642e13i	−0.832551	−	1.44202i
$927$		0			0
$928$	4.57565e12	−	7.92525e12i	0.202529	−	0.350790i
$929$	−6.60168e12	+	5.53946e12i	−0.290793	+	0.244004i	−0.776500	−	0.630118i	$-0.783007\pi$
$929$	−6.60168e12	+	5.53946e12i	−0.290793	+	0.244004i	0.485707	+	0.874122i	$0.338562\pi$
$930$		0			0
$931$	−6.79565e12	+	3.85401e13i	−0.296454	+	1.68128i
$932$	5.65157e11	−	3.20516e12i	0.0245356	−	0.139148i
$933$		0			0
$934$	3.96570e13	−	3.32762e13i	1.70514	−	1.43078i
$935$	−2.29805e13	+	3.98035e13i	−0.983349	+	1.70321i
$936$		0			0
$937$	6.35838e12	+	1.10130e13i	0.269475	+	0.466744i	0.968726	−	0.248132i	$-0.0798166\pi$
$937$	6.35838e12	+	1.10130e13i	0.269475	+	0.466744i	−0.699251	+	0.714876i	$0.746483\pi$
$938$	−4.47848e13	−	1.63003e13i	−1.88894	−	0.687518i
$939$		0			0
$940$	−3.68257e13	−	3.09005e13i	−1.53842	−	1.29089i
$941$	−2.37799e12	+	8.65519e11i	−0.0988684	+	0.0359851i	−0.390981	−	0.920399i	$-0.627864\pi$
$941$	−2.37799e12	+	8.65519e11i	−0.0988684	+	0.0359851i	0.292112	+	0.956384i	$0.405642\pi$
$942$		0			0
$943$	1.97949e12	+	1.12263e13i	0.0815177	+	0.462310i
$944$	5.20802e12			0.213451
$945$		0			0
$946$	−1.34163e13			−0.544657
$947$	3.16316e12	+	1.79391e13i	0.127804	+	0.724815i	0.979603	+	0.200945i	$0.0644011\pi$
$947$	3.16316e12	+	1.79391e13i	0.127804	+	0.724815i	−0.851798	+	0.523870i	$0.824488\pi$
$948$		0			0
$949$	3.03743e13	−	1.10553e13i	1.21565	−	0.442460i
$950$	1.40677e13	+	1.18042e13i	0.560361	+	0.470199i
$951$		0			0
$952$	6.30020e13	+	2.29309e13i	2.48593	+	0.904803i
$953$	1.37479e13	+	2.38121e13i	0.539907	+	0.935147i	0.998908	+	0.0467114i	$0.0148741\pi$
$953$	1.37479e13	+	2.38121e13i	0.539907	+	0.935147i	−0.459001	+	0.888436i	$0.651793\pi$
$954$		0			0
$955$	1.09971e12	−	1.90475e12i	0.0427821	−	0.0741007i
$956$	−1.98163e13	+	1.66279e13i	−0.767296	+	0.643838i
$957$		0			0
$958$	−7.56397e12	+	4.28974e13i	−0.290138	+	1.64545i
$959$	−7.29170e11	+	4.13533e12i	−0.0278384	+	0.157880i
$960$		0			0
$961$	−8.54691e12	+	7.17171e12i	−0.323261	+	0.271248i
$962$	−1.36054e12	+	2.35653e12i	−0.0512183	+	0.0887127i
$963$		0			0
$964$	−4.15199e13	−	7.19146e13i	−1.54849	−	2.68207i
$965$	−2.24583e13	−	8.17414e12i	−0.833688	−	0.303437i
$966$		0			0
$967$	−2.67535e13	−	2.24489e13i	−0.983924	−	0.825611i	0.000752475	−	1.00000i	$-0.499760\pi$
$967$	−2.67535e13	−	2.24489e13i	−0.983924	−	0.825611i	−0.984677	+	0.174389i	$0.944205\pi$
$968$	3.23416e13	−	1.17714e13i	1.18392	−	0.430912i
$969$		0			0
$970$	−3.80114e12	−	2.15573e13i	−0.137861	−	0.781847i
$971$	1.90619e13			0.688144			0.344072	−	0.938943i	$-0.388194\pi$
$971$	1.90619e13			0.688144			0.344072	+	0.938943i	$0.388194\pi$
$972$		0			0
$973$	7.85411e13			2.80924
$974$	8.56794e12	+	4.85912e13i	0.305043	+	1.72999i
$975$		0			0
$976$	1.05692e13	−	3.84686e12i	0.372835	−	0.135701i
$977$	−7.65075e12	−	6.41974e12i	−0.268645	−	0.225420i	0.498507	−	0.866886i	$-0.333882\pi$
$977$	−7.65075e12	−	6.41974e12i	−0.268645	−	0.225420i	−0.767151	+	0.641466i	$0.778326\pi$
$978$		0			0
$979$	−3.65292e13	−	1.32956e13i	−1.27092	−	0.462577i
$980$	4.15764e13	+	7.20124e13i	1.43989	+	2.49396i
$981$		0			0
$982$	−1.17225e13	+	2.03040e13i	−0.402272	+	0.696755i
$983$	−3.03891e13	+	2.54995e13i	−1.03807	+	0.871044i	−0.991789	−	0.127884i	$-0.959181\pi$
$983$	−3.03891e13	+	2.54995e13i	−1.03807	+	0.871044i	−0.0462808	+	0.998928i	$0.514737\pi$
$984$		0			0
$985$	4.36389e12	−	2.47489e13i	0.147710	−	0.837707i
$986$	−8.36486e12	+	4.74395e13i	−0.281847	+	1.59843i
$987$		0			0
$988$	−6.92986e13	+	5.81484e13i	−2.31376	+	1.94147i
$989$	2.35664e12	−	4.08182e12i	0.0783267	−	0.135666i
$990$		0			0
$991$	1.08584e13	+	1.88074e13i	0.357632	+	0.619437i	0.987565	−	0.157213i	$-0.0502509\pi$
$991$	1.08584e13	+	1.88074e13i	0.357632	+	0.619437i	−0.629933	+	0.776650i	$0.716918\pi$
$992$	1.12613e13	+	4.09876e12i	0.369219	+	0.134385i
$993$		0			0
$994$	8.45071e13	+	7.09099e13i	2.74571	+	2.30392i
$995$	−4.86325e13	+	1.77008e13i	−1.57298	+	0.572517i
$996$		0			0
$997$	−9.72994e12	−	5.51812e13i	−0.311876	−	1.76874i	−0.589227	−	0.807968i	$-0.700568\pi$
$997$	−9.72994e12	−	5.51812e13i	−0.311876	−	1.76874i	0.277351	−	0.960769i	$-0.410544\pi$
$998$	−9.58977e13			−3.06000
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.10.3		156
3.2	odd	2		27.10.e.a.13.24	✓	156
27.2	odd	18		27.10.e.a.25.24	yes	156
27.25	even	9	inner	81.10.e.a.73.3		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.13.24	✓	156	3.2	odd	2
27.10.e.a.25.24	yes	156	27.2	odd	18
81.10.e.a.10.3		156	1.1	even	1	trivial
81.10.e.a.73.3		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+(-6.61278 - 37.5029i) q^{2} +(-881.618 + 320.883i) q^{4} +(-1241.60 - 1041.82i) q^{5} +(9160.78 + 3334.25i) q^{7} +(8115.13 + 14055.8i) q^{8} +(-30861.0 + 53452.8i) q^{10} +(51265.0 - 43016.4i) q^{11} +(23395.9 - 132685. i) q^{13} +(64465.9 - 365605. i) q^{14} +(105495. - 88521.1i) q^{16} +(211869. - 366968. i) q^{17} +(357829. + 619778. i) q^{19} +(1.42892e6 + 520083. i) q^{20} +(-1.95224e6 - 1.63813e6i) q^{22} +(841310. - 306212. i) q^{23} +(117010. + 663595. i) q^{25} -5.13079e6 q^{26} -9.14621e6 q^{28} +(-518380. - 2.93988e6i) q^{29} +(3.67352e6 - 1.33705e6i) q^{31} +(2.34833e6 + 1.97048e6i) q^{32} +(-1.51634e7 - 5.51903e6i) q^{34} +(-7.90029e6 - 1.36837e7i) q^{35} +(265173. - 459292. i) q^{37} +(2.08772e7 - 1.75181e7i) q^{38} +(4.56796e6 - 2.59062e7i) q^{40} +(-2.21098e6 + 1.25391e7i) q^{41} +(4.03280e6 - 3.38392e6i) q^{43} +(-3.13929e7 + 5.43741e7i) q^{44} +(-1.70472e7 - 2.95267e7i) q^{46} +(-2.97072e7 - 1.08125e7i) q^{47} +(4.18899e7 + 3.51498e7i) q^{49} +(2.41130e7 - 8.77641e6i) q^{50} +(2.19500e7 + 1.24485e8i) q^{52} -4.09188e6 q^{53} -1.08466e8 q^{55} +(2.74753e7 + 1.55820e8i) q^{56} +(-1.06826e8 + 3.88815e7i) q^{58} +(2.89699e7 + 2.43087e7i) q^{59} +(7.67470e7 + 2.79336e7i) q^{61} +(-7.44355e7 - 1.28926e8i) q^{62} +(9.36247e7 - 1.62163e8i) q^{64} +(-1.67283e8 + 1.40367e8i) q^{65} +(2.22923e7 - 1.26426e8i) q^{67} +(-6.90338e7 + 3.91510e8i) q^{68} +(-4.60936e8 + 3.86771e8i) q^{70} +(-1.48576e8 + 2.57342e8i) q^{71} +(1.19955e8 + 2.07769e8i) q^{73} +(-1.89783e7 - 6.90755e6i) q^{74} +(-5.14344e8 - 4.31586e8i) q^{76} +(6.13054e8 - 2.23133e8i) q^{77} +(-5.26889e7 - 2.98814e8i) q^{79} -2.23206e8 q^{80} +4.84873e8 q^{82} +(4.68884e7 + 2.65917e8i) q^{83} +(-6.45371e8 + 2.34896e8i) q^{85} +(-1.53575e8 - 1.28865e8i) q^{86} +(1.02065e9 + 3.71487e8i) q^{88} +(-2.90441e8 - 5.03059e8i) q^{89} +(6.56730e8 - 1.13749e9i) q^{91} +(-6.43456e8 + 5.39923e8i) q^{92} +(-2.09055e8 + 1.18561e9i) q^{94} +(2.01420e8 - 1.14231e9i) q^{95} +(-2.71680e8 + 2.27966e8i) q^{97} +(1.04121e9 - 1.80343e9i) 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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