LMFDB - Embedded newform 690.2.x.a.77.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(77,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 11, 12]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("690.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.x (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$48$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			77.3
Character	$\chi$	$=$	690.77
Dual form			690.2.x.a.233.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599278 - 0.800541i) q^{2} +(-1.71709 - 0.227188i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.19043 - 1.89285i) q^{5} +(0.847138 + 1.51075i) q^{6} +(-0.982544 - 4.51668i) q^{7} +(0.936950 - 0.349464i) q^{8} +(2.89677 + 0.780204i) q^{9} +O(q^{10})$	\(q+(-0.599278 - 0.800541i) q^{2} +(-1.71709 - 0.227188i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.19043 - 1.89285i) q^{5} +(0.847138 + 1.51075i) q^{6} +(-0.982544 - 4.51668i) q^{7} +(0.936950 - 0.349464i) q^{8} +(2.89677 + 0.780204i) q^{9} +(-0.801902 + 2.08733i) q^{10} +(2.29560 - 0.330057i) q^{11} +(0.701745 - 1.58353i) q^{12} +(1.32630 - 6.09690i) q^{13} +(-3.02697 + 3.49331i) q^{14} +(1.61404 + 3.52063i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(-0.741286 + 1.35756i) q^{17} +(-1.11138 - 2.78654i) q^{18} +(0.143225 - 0.487778i) q^{19} +(2.15156 - 0.608936i) q^{20} +(0.660975 + 7.97875i) q^{21} +(-1.63992 - 1.63992i) q^{22} +(4.63358 - 1.23690i) q^{23} +(-1.68822 + 0.387196i) q^{24} +(-2.16574 + 4.50662i) q^{25} +(-5.67564 + 2.59198i) q^{26} +(-4.79675 - 1.99779i) q^{27} +(4.61054 + 0.329752i) q^{28} +(-9.49339 + 2.78751i) q^{29} +(1.85115 - 3.40195i) q^{30} +(4.07885 - 8.93143i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(-4.01672 + 0.0452037i) q^{33} +(1.53102 - 0.220128i) q^{34} +(-7.37973 + 7.23661i) q^{35} +(-1.56471 + 2.55962i) q^{36} +(0.560536 - 0.0400903i) q^{37} +(-0.476318 + 0.177657i) q^{38} +(-3.66251 + 10.1676i) q^{39} +(-1.77686 - 1.35749i) q^{40} +(-1.84982 + 1.60288i) q^{41} +(5.99121 - 5.31063i) q^{42} +(-3.45100 - 1.28716i) q^{43} +(-0.330057 + 2.29560i) q^{44} +(-1.97161 - 6.41192i) q^{45} +(-3.76699 - 2.96813i) q^{46} +(-5.95683 + 5.95683i) q^{47} +(1.32168 + 1.11945i) q^{48} +(-13.0676 + 5.96776i) q^{49} +(4.90561 - 0.966952i) q^{50} +(1.58128 - 2.16264i) q^{51} +(5.47627 + 2.99027i) q^{52} +(1.55455 + 7.14614i) q^{53} +(1.27527 + 5.03723i) q^{54} +(-3.35750 - 3.95230i) q^{55} +(-2.49901 - 3.88854i) q^{56} +(-0.356746 + 0.805018i) q^{57} +(7.92070 + 5.92936i) q^{58} +(8.07982 - 5.19258i) q^{59} +(-3.83275 + 0.556787i) q^{60} +(0.830120 - 1.81771i) q^{61} +(-9.59434 + 2.08712i) q^{62} +(0.677727 - 13.8504i) q^{63} +(0.755750 - 0.654861i) q^{64} +(-13.1194 + 4.74747i) q^{65} +(2.44332 + 3.18846i) q^{66} +(-1.19147 + 0.891924i) q^{67} +(-1.09373 - 1.09373i) q^{68} +(-8.23727 + 1.07117i) q^{69} +(10.2157 + 1.57104i) q^{70} +(5.86721 + 0.843577i) q^{71} +(2.98678 - 0.281306i) q^{72} +(4.23704 - 2.31360i) q^{73} +(-0.368011 - 0.424707i) q^{74} +(4.74261 - 7.24622i) q^{75} +(0.427669 + 0.274846i) q^{76} +(-3.74629 - 10.0442i) q^{77} +(10.3344 - 3.16121i) q^{78} +(4.57951 + 7.12586i) q^{79} +(-0.0218939 + 2.23596i) q^{80} +(7.78256 + 4.52014i) q^{81} +(2.39173 + 0.520289i) q^{82} +(-3.74852 + 0.268100i) q^{83} +(-7.84177 - 1.61367i) q^{84} +(3.45211 - 0.212949i) q^{85} +(1.03768 + 3.53403i) q^{86} +(16.9343 - 2.62961i) q^{87} +(2.03552 - 1.11148i) q^{88} +(-2.26057 - 4.94995i) q^{89} +(-3.95147 + 5.42088i) q^{90} -28.8409 q^{91} +(-0.118633 + 4.79436i) q^{92} +(-9.03285 + 14.4094i) q^{93} +(8.33848 + 1.19889i) q^{94} +(-1.09379 + 0.309565i) q^{95} +(0.104114 - 1.72892i) q^{96} +(-1.23231 + 17.2300i) q^{97} +(12.6086 + 6.88479i) q^{98} +(6.90733 + 0.834934i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) $ 960 * q + 8 * q^3 + 8 * q^6	$ 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) $ 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$3$	−1.71709	−	0.227188i	−0.991360	−	0.131167i
$3$	−1.71709	−	0.227188i	−0.991360	−	0.131167i
$4$	−0.281733	+	0.959493i	−0.140866	+	0.479746i
$5$	−1.19043	−	1.89285i	−0.532378	−	0.846507i
$5$	−1.19043	−	1.89285i	−0.532378	−	0.846507i
$6$	0.847138	+	1.51075i	0.345843	+	0.616760i
$7$	−0.982544	−	4.51668i	−0.371367	−	1.70714i	−0.661320	−	0.750104i	$-0.730003\pi$
$7$	−0.982544	−	4.51668i	−0.371367	−	1.70714i	0.289954	−	0.957041i	$-0.406360\pi$
$8$	0.936950	−	0.349464i	0.331262	−	0.123554i
$9$	2.89677	+	0.780204i	0.965590	+	0.260068i
$10$	−0.801902	+	2.08733i	−0.253584	+	0.660072i
$11$	2.29560	−	0.330057i	0.692149	−	0.0995159i	0.212741	−	0.977109i	$-0.431761\pi$
$11$	2.29560	−	0.330057i	0.692149	−	0.0995159i	0.479407	+	0.877593i	$0.340852\pi$
$12$	0.701745	−	1.58353i	0.202576	−	0.457125i
$13$	1.32630	−	6.09690i	0.367849	−	1.69098i	−0.305939	−	0.952051i	$-0.598971\pi$
$13$	1.32630	−	6.09690i	0.367849	−	1.69098i	0.673789	−	0.738924i	$-0.264666\pi$
$14$	−3.02697	+	3.49331i	−0.808992	+	0.933627i
$15$	1.61404	+	3.52063i	0.416744	+	0.909024i
$16$	−0.841254	−	0.540641i	−0.210313	−	0.135160i
$17$	−0.741286	+	1.35756i	−0.179788	+	0.329258i	−0.951995	−	0.306114i	$-0.900971\pi$
$17$	−0.741286	+	1.35756i	−0.179788	+	0.329258i	0.772207	+	0.635372i	$0.219153\pi$
$18$	−1.11138	−	2.78654i	−0.261956	−	0.656795i
$19$	0.143225	−	0.487778i	0.0328580	−	0.111904i	−0.941431	−	0.337205i	$-0.890518\pi$
$19$	0.143225	−	0.487778i	0.0328580	−	0.111904i	0.974289	+	0.225301i	$0.0723366\pi$
$20$	2.15156	−	0.608936i	0.481103	−	0.136162i
$21$	0.660975	+	7.97875i	0.144237	+	1.74111i
$22$	−1.63992	−	1.63992i	−0.349633	−	0.349633i
$23$	4.63358	−	1.23690i	0.966169	−	0.257912i
$23$	4.63358	−	1.23690i	0.966169	−	0.257912i
$24$	−1.68822	+	0.387196i	−0.344606	+	0.0790361i
$25$	−2.16574	+	4.50662i	−0.433147	+	0.901323i
$26$	−5.67564	+	2.59198i	−1.11308	+	0.508329i
$27$	−4.79675	−	1.99779i	−0.923135	−	0.384475i
$28$	4.61054	+	0.329752i	0.871310	+	0.0623173i
$29$	−9.49339	+	2.78751i	−1.76288	+	0.517628i	−0.992743	−	0.120253i	$-0.961629\pi$
$29$	−9.49339	+	2.78751i	−1.76288	+	0.517628i	−0.770135	+	0.637881i	$0.779811\pi$
$30$	1.85115	−	3.40195i	0.337973	−	0.621108i
$31$	4.07885	−	8.93143i	0.732583	−	1.60413i	−0.0628014	−	0.998026i	$-0.520003\pi$
$31$	4.07885	−	8.93143i	0.732583	−	1.60413i	0.795384	−	0.606106i	$-0.207269\pi$
$32$	0.0713392	+	0.997452i	0.0126111	+	0.176326i
$33$	−4.01672	+	0.0452037i	−0.699222	+	0.00786895i
$34$	1.53102	−	0.220128i	0.262568	−	0.0377516i
$35$	−7.37973	+	7.23661i	−1.24740	+	1.22321i
$36$	−1.56471	+	2.55962i	−0.260786	+	0.426604i
$37$	0.560536	−	0.0400903i	0.0921516	−	0.00659081i	−0.0251872	−	0.999683i	$-0.508018\pi$
$37$	0.560536	−	0.0400903i	0.0921516	−	0.00659081i	0.117339	+	0.993092i	$0.462564\pi$
$38$	−0.476318	+	0.177657i	−0.0772690	+	0.0288198i
$39$	−3.66251	+	10.1676i	−0.586472	+	1.62812i
$40$	−1.77686	−	1.35749i	−0.280946	−	0.214638i
$41$	−1.84982	+	1.60288i	−0.288894	+	0.250328i	−0.787235	−	0.616653i	$-0.788488\pi$
$41$	−1.84982	+	1.60288i	−0.288894	+	0.250328i	0.498341	+	0.866981i	$0.333943\pi$
$42$	5.99121	−	5.31063i	0.924464	−	0.819447i
$43$	−3.45100	−	1.28716i	−0.526272	−	0.196289i	0.0722635	−	0.997386i	$-0.476978\pi$
$43$	−3.45100	−	1.28716i	−0.526272	−	0.196289i	−0.598536	+	0.801096i	$0.704250\pi$
$44$	−0.330057	+	2.29560i	−0.0497580	+	0.346074i
$45$	−1.97161	−	6.41192i	−0.293910	−	0.955833i
$46$	−3.76699	−	2.96813i	−0.555413	−	0.437626i
$47$	−5.95683	+	5.95683i	−0.868893	+	0.868893i	−0.992350	−	0.123457i	$-0.960602\pi$
$47$	−5.95683	+	5.95683i	−0.868893	+	0.868893i	0.123457	+	0.992350i	$0.460602\pi$
$48$	1.32168	+	1.11945i	0.190768	+	0.161579i
$49$	−13.0676	+	5.96776i	−1.86680	+	0.852538i
$50$	4.90561	−	0.966952i	0.693758	−	0.136748i
$51$	1.58128	−	2.16264i	0.221423	−	0.302831i
$52$	5.47627	+	2.99027i	0.759422	+	0.414676i
$53$	1.55455	+	7.14614i	0.213534	+	0.981598i	0.951712	+	0.306993i	$0.0993227\pi$
$53$	1.55455	+	7.14614i	0.213534	+	0.981598i	−0.738178	+	0.674606i	$0.764314\pi$
$54$	1.27527	+	5.03723i	0.173543	+	0.685480i
$55$	−3.35750	−	3.95230i	−0.452726	−	0.532928i
$56$	−2.49901	−	3.88854i	−0.333944	−	0.519628i
$57$	−0.356746	+	0.805018i	−0.0472522	+	0.106627i
$58$	7.92070	+	5.92936i	1.04004	+	0.778563i
$59$	8.07982	−	5.19258i	1.05190	−	0.676017i	0.104000	−	0.994577i	$-0.466836\pi$
$59$	8.07982	−	5.19258i	1.05190	−	0.676017i	0.947903	+	0.318561i	$0.103199\pi$
$60$	−3.83275	+	0.556787i	−0.494806	+	0.0718809i
$61$	0.830120	−	1.81771i	0.106286	−	0.232734i	−0.849015	−	0.528369i	$-0.822804\pi$
$61$	0.830120	−	1.81771i	0.106286	−	0.232734i	0.955301	+	0.295635i	$0.0955312\pi$
$62$	−9.59434	+	2.08712i	−1.21848	+	0.265065i
$63$	0.677727	−	13.8504i	0.0853856	−	1.74498i
$64$	0.755750	−	0.654861i	0.0944687	−	0.0818576i
$65$	−13.1194	+	4.74747i	−1.62726	+	0.588851i
$66$	2.44332	+	3.18846i	0.300752	+	0.392473i
$67$	−1.19147	+	0.891924i	−0.145561	+	0.108966i	−0.669577	−	0.742743i	$-0.733524\pi$
$67$	−1.19147	+	0.891924i	−0.145561	+	0.108966i	0.524015	+	0.851709i	$0.324433\pi$
$68$	−1.09373	−	1.09373i	−0.132634	−	0.132634i
$69$	−8.23727	+	1.07117i	−0.991651	+	0.128954i
$70$	10.2157	+	1.57104i	1.22101	+	0.187775i
$71$	5.86721	+	0.843577i	0.696309	+	0.100114i	0.481375	−	0.876514i	$-0.340137\pi$
$71$	5.86721	+	0.843577i	0.696309	+	0.100114i	0.214934	+	0.976629i	$0.431046\pi$
$72$	2.98678	−	0.281306i	0.351996	−	0.0331522i
$73$	4.23704	−	2.31360i	0.495908	−	0.270786i	−0.211773	−	0.977319i	$-0.567924\pi$
$73$	4.23704	−	2.31360i	0.495908	−	0.270786i	0.707680	+	0.706533i	$0.249742\pi$
$74$	−0.368011	−	0.424707i	−0.0427804	−	0.0493712i
$75$	4.74261	−	7.24622i	0.547629	−	0.836721i
$76$	0.427669	+	0.274846i	0.0490570	+	0.0315270i
$77$	−3.74629	−	10.0442i	−0.426929	−	1.14464i
$78$	10.3344	−	3.16121i	1.17014	−	0.357937i
$79$	4.57951	+	7.12586i	0.515236	+	0.801722i	0.997224	−	0.0744553i	$-0.0237218\pi$
$79$	4.57951	+	7.12586i	0.515236	+	0.801722i	−0.481989	+	0.876177i	$0.660085\pi$
$80$	−0.0218939	+	2.23596i	−0.00244781	+	0.249988i
$81$	7.78256	+	4.52014i	0.864729	+	0.502238i
$82$	2.39173	+	0.520289i	0.264123	+	0.0574564i
$83$	−3.74852	+	0.268100i	−0.411454	+	0.0294278i	−0.275532	−	0.961292i	$-0.588854\pi$
$83$	−3.74852	+	0.268100i	−0.411454	+	0.0294278i	−0.135922	+	0.990720i	$0.543400\pi$
$84$	−7.84177	−	1.61367i	−0.855608	−	0.176066i
$85$	3.45211	−	0.212949i	0.374434	−	0.0230975i
$86$	1.03768	+	3.53403i	0.111896	+	0.381084i
$87$	16.9343	−	2.62961i	1.81554	−	0.281924i
$88$	2.03552	−	1.11148i	0.216987	−	0.118484i
$89$	−2.26057	−	4.94995i	−0.239620	−	0.524694i	0.751169	−	0.660110i	$-0.229490\pi$
$89$	−2.26057	−	4.94995i	−0.239620	−	0.524694i	−0.990789	+	0.135416i	$0.956763\pi$
$90$	−3.95147	+	5.42088i	−0.416521	+	0.571410i
$91$	−28.8409			−3.02335
$92$	−0.118633	+	4.79436i	−0.0123684	+	0.499847i
$93$	−9.03285	+	14.4094i	−0.936663	+	1.49418i
$94$	8.33848	+	1.19889i	0.860049	+	0.123656i
$95$	−1.09379	+	0.309565i	−0.112220	+	0.0317607i
$96$	0.104114	−	1.72892i	0.0106261	−	0.176457i
$97$	−1.23231	+	17.2300i	−0.125122	+	1.74944i	0.416790	+	0.909003i	$0.363155\pi$
$97$	−1.23231	+	17.2300i	−0.125122	+	1.74944i	−0.541912	+	0.840435i	$0.682299\pi$
$98$	12.6086	+	6.88479i	1.27366	+	0.695469i
$99$	6.90733	+	0.834934i	0.694213	+	0.0839140i
$100$	−3.71391	−	3.34767i	−0.371391	−	0.334767i
$101$	7.75699	+	6.72147i	0.771850	+	0.668812i	0.948966	−	0.315378i	$-0.102131\pi$
$101$	7.75699	+	6.72147i	0.771850	+	0.668812i	−0.177116	+	0.984190i	$0.556677\pi$
$102$	−2.67891	+	0.0301481i	−0.265252	+	0.00298511i
$103$	3.74585	+	2.80411i	0.369090	+	0.276297i	0.767682	−	0.640831i	$-0.221410\pi$
$103$	3.74585	+	2.80411i	0.369090	+	0.276297i	−0.398592	+	0.917128i	$0.630501\pi$
$104$	−0.887972	−	6.17598i	−0.0870728	−	0.605605i
$105$	14.3157	−	10.7493i	1.39707	−	1.04902i
$106$	4.78918	−	5.52700i	0.465166	−	0.536830i
$107$	−4.15694	−	11.1452i	−0.401866	−	1.07745i	−0.967518	−	0.252801i	$-0.918648\pi$
$107$	−4.15694	−	11.1452i	−0.401866	−	1.07745i	0.565652	−	0.824644i	$-0.308625\pi$
$108$	3.26827	−	4.03961i	0.314489	−	0.388711i
$109$	−0.0157254	−	0.0535556i	−0.00150622	−	0.00512970i	0.958736	−	0.284296i	$-0.0917600\pi$
$109$	−0.0157254	−	0.0535556i	−0.00150622	−	0.00512970i	−0.960243	+	0.279167i	$0.909942\pi$
$110$	−1.15190	+	5.05635i	−0.109830	+	0.482104i
$111$	−0.971597	−	0.0585087i	−0.0922199	−	0.00555340i
$112$	−1.61533	+	4.33088i	−0.152635	+	0.409229i
$113$	−2.02921	+	1.51905i	−0.190892	+	0.142900i	−0.690449	−	0.723381i	$-0.742587\pi$
$113$	−2.02921	+	1.51905i	−0.190892	+	0.142900i	0.499557	+	0.866281i	$0.333496\pi$
$114$	0.858240	−	0.196839i	0.0803816	−	0.0184357i
$115$	−7.85723	−	7.29821i	−0.732691	−	0.680562i
$116$		−	9.89418i		−	0.918651i
$117$	8.59881	−	16.6265i	0.794960	−	1.53712i
$118$	−8.99893	−	3.35643i	−0.828419	−	0.308984i
$119$	6.86003	+	2.01429i	0.628858	+	0.184649i
$120$	2.74261	+	2.73461i	0.250365	+	0.249634i
$121$	−5.39359	+	1.58370i	−0.490327	+	0.143973i
$122$	−1.95262	+	0.424767i	−0.176782	+	0.0384566i
$123$	3.54047	−	2.33203i	0.319233	−	0.210272i
$124$	7.42050	+	6.42990i	0.666381	+	0.577422i
$125$	11.1085	−	1.26542i	0.993574	−	0.113182i
$126$	−11.4939	+	7.75767i	−1.02396	+	0.691108i
$127$	0.887369	−	1.18539i	0.0787413	−	0.105186i	−0.759441	−	0.650576i	$-0.774528\pi$
$127$	0.887369	−	1.18539i	0.0787413	−	0.105186i	0.838182	+	0.545390i	$0.183618\pi$
$128$	−0.977147	−	0.212565i	−0.0863684	−	0.0187883i
$129$	5.63323	+	2.99418i	0.495978	+	0.263623i
$130$	11.6627	+	7.65754i	1.02289	+	0.671611i
$131$	3.78222	−	5.88526i	0.330454	−	0.514197i	−0.635777	−	0.771873i	$-0.719320\pi$
$131$	3.78222	−	5.88526i	0.330454	−	0.514197i	0.966231	+	0.257676i	$0.0829566\pi$
$132$	1.08827	−	3.86675i	0.0947217	−	0.336558i
$133$	−2.34386	−	0.167636i	−0.203239	−	0.0145359i
$134$	1.42804	+	0.419311i	0.123364	+	0.0362230i
$135$	1.92871	+	11.4578i	0.165997	+	0.986126i
$136$	−0.220128	+	1.53102i	−0.0188758	+	0.131284i
$137$	9.84239	−	9.84239i	0.840892	−	0.840892i	−0.148083	−	0.988975i	$-0.547310\pi$
$137$	9.84239	−	9.84239i	0.840892	−	0.840892i	0.988975	+	0.148083i	$0.0473102\pi$
$138$	5.79393	+	5.95235i	0.493212	+	0.506697i
$139$		−	1.87424i		−	0.158971i	−0.996836	−	0.0794856i	$-0.974672\pi$
$139$		−	1.87424i		−	0.158971i	0.996836	−	0.0794856i	$-0.0253278\pi$
$140$	−4.86437	−	9.11959i	−0.411114	−	0.770746i
$141$	11.5817	−	8.87507i	0.975356	−	0.747415i
$142$	−2.84077	−	5.20248i	−0.238392	−	0.436582i
$143$	1.03232	−	14.4338i	0.0863273	−	1.20701i
$144$	−2.01511	−	2.22246i	−0.167926	−	0.185205i
$145$	16.5776	+	14.6512i	1.37669	+	1.21671i
$146$	−4.39129	−	2.00544i	−0.363426	−	0.165971i
$147$	23.7940	−	7.27837i	1.96249	−	0.600309i
$148$	−0.119455	+	0.549125i	−0.00981913	+	0.0451378i
$149$	1.23475	+	8.58790i	0.101155	+	0.703548i	0.975781	+	0.218750i	$0.0701979\pi$
$149$	1.23475	+	8.58790i	0.101155	+	0.703548i	−0.874626	+	0.484798i	$0.838893\pi$
$150$	−8.64304	+	0.545844i	−0.705701	+	0.0445680i
$151$	4.23151	−	2.71943i	0.344355	−	0.221304i	−0.357019	−	0.934097i	$-0.616207\pi$
$151$	4.23151	−	2.71943i	0.344355	−	0.221304i	0.701374	+	0.712794i	$0.252570\pi$
$152$	−0.0362668	−	0.507075i	−0.00294162	−	0.0411293i
$153$	−3.20651	+	3.35420i	−0.259231	+	0.271171i
$154$	−5.79572	+	9.01831i	−0.467032	+	0.726716i
$155$	−21.7614	+	2.91164i	−1.74792	+	0.233868i
$156$	−8.72387	−	6.37869i	−0.698469	−	0.510704i
$157$	−9.58012	−	17.5447i	−0.764577	−	1.40022i	−0.911597	−	0.411084i	$-0.865150\pi$
$157$	−9.58012	−	17.5447i	−0.764577	−	1.40022i	0.147020	−	0.989133i	$-0.453032\pi$
$158$	2.96015	−	7.93646i	0.235497	−	0.631391i
$159$	−1.04577	−	12.6237i	−0.0829353	−	1.00113i
$160$	1.80310	−	1.32243i	0.142548	−	0.104548i
$161$	−10.1394	−	19.7131i	−0.799095	−	1.55361i
$162$	−1.04536	−	8.93908i	−0.0821309	−	0.702321i
$163$	−0.340815	−	0.455276i	−0.0266947	−	0.0356600i	0.786995	−	0.616959i	$-0.211636\pi$
$163$	−0.340815	−	0.455276i	−0.0266947	−	0.0356600i	−0.813690	+	0.581299i	$0.802545\pi$
$164$	−1.01680	−	2.22648i	−0.0793986	−	0.173859i
$165$	4.86721	+	7.54923i	0.378911	+	0.587707i
$166$	2.46103	+	2.84018i	0.191013	+	0.220441i
$167$	9.83994	−	18.0205i	0.761438	−	1.39447i	−0.152371	−	0.988323i	$-0.548691\pi$
$167$	9.83994	−	18.0205i	0.761438	−	1.39447i	0.913808	−	0.406145i	$-0.133127\pi$
$168$	3.40759	+	7.24470i	0.262901	+	0.558941i
$169$	−23.5879	−	10.7722i	−1.81445	−	0.828633i
$170$	−2.23925	−	2.63594i	−0.171743	−	0.202168i
$171$	0.795455	−	1.30124i	0.0608300	−	0.0995081i
$172$	2.20727	−	2.94857i	0.168303	−	0.224827i
$173$	−6.96631	+	9.30590i	−0.529639	+	0.707515i	−0.982957	−	0.183834i	$-0.941149\pi$
$173$	−6.96631	+	9.30590i	−0.529639	+	0.707515i	0.453318	+	0.891349i	$0.350240\pi$
$174$	−12.2534	−	11.9807i	−0.928931	−	0.908255i
$175$	22.4829	+	5.35399i	1.69955	+	0.404724i
$176$	−2.10962	−	0.963432i	−0.159019	−	0.0726214i
$177$	−15.0534	+	7.08047i	−1.13149	+	0.532201i
$178$	−2.60793	+	4.77607i	−0.195473	+	0.357982i
$179$	−9.93485	−	11.4654i	−0.742565	−	0.856966i	0.251260	−	0.967920i	$-0.419155\pi$
$179$	−9.93485	−	11.4654i	−0.742565	−	0.856966i	−0.993826	+	0.110954i	$0.964610\pi$
$180$	6.70766	−	0.0852951i	0.499960	−	0.00635752i
$181$	−5.37542	−	11.7705i	−0.399552	−	0.874897i	−0.997316	−	0.0732243i	$-0.976671\pi$
$181$	−5.37542	−	11.7705i	−0.399552	−	0.874897i	0.597764	−	0.801672i	$-0.296056\pi$
$182$	17.2837	+	23.0883i	1.28115	+	1.71142i
$183$	−1.83835	+	2.93257i	−0.135895	+	0.216782i
$184$	3.90918	−	2.77818i	0.288189	−	0.204810i
$185$	−0.743166	−	1.01328i	−0.0546387	−	0.0744982i
$186$	16.9485	−	1.40405i	1.24272	−	0.102950i
$187$	−1.25362	+	3.36109i	−0.0916739	+	0.245787i
$188$	−4.03730	−	7.39377i	−0.294451	−	0.539246i
$189$	−4.31036	+	23.6283i	−0.313532	+	1.71871i
$190$	0.903303	+	0.690107i	0.0655325	+	0.0500656i
$191$	−7.09179	+	11.0350i	−0.513144	+	0.798467i	−0.997058	−	0.0766479i	$-0.975578\pi$
$191$	−7.09179	+	11.0350i	−0.513144	+	0.798467i	0.483914	+	0.875115i	$0.339215\pi$
$192$	−1.44646	+	0.952755i	−0.104390	+	0.0687592i
$193$	−0.584025	−	8.16574i	−0.0420391	−	0.587783i	−0.974192	−	0.225719i	$-0.927527\pi$
$193$	−0.584025	−	8.16574i	−0.0420391	−	0.587783i	0.932153	−	0.362064i	$-0.117928\pi$
$194$	14.5318	−	9.33902i	1.04332	−	0.670503i
$195$	23.6056	−	5.17125i	1.69044	−	0.370321i
$196$	−2.04446	−	14.2196i	−0.146033	−	1.01568i
$197$	1.49321	−	6.86416i	0.106387	−	0.489051i	−0.892863	−	0.450328i	$-0.851307\pi$
$197$	1.49321	−	6.86416i	0.106387	−	0.489051i	0.999250	−	0.0387236i	$-0.0123292\pi$
$198$	−3.47101	−	6.02996i	−0.246674	−	0.428531i
$199$	21.5702	+	9.85080i	1.52907	+	0.698305i	0.989620	−	0.143710i	$-0.0459032\pi$
$199$	21.5702	+	9.85080i	1.52907	+	0.698305i	0.539454	+	0.842015i	$0.318631\pi$
$200$	−0.454286	+	4.97932i	−0.0321229	+	0.352091i
$201$	2.24849	−	1.26082i	0.158596	−	0.0889315i
$202$	0.732223	−	10.2378i	0.0515191	−	0.720331i
$203$	21.9180	+	40.1398i	1.53834	+	2.81726i
$204$	1.62955	+	2.12651i	0.114091	+	0.148885i
$205$	5.23610	+	1.59331i	0.365705	+	0.111282i
$206$		−	4.67915i		−	0.326012i
$207$	14.3875	+	0.0321196i	0.999998	+	0.00223246i
$208$	−4.41199	+	4.41199i	−0.305916	+	0.305916i
$209$	0.167791	−	1.16701i	0.0116064	−	0.0807241i
$210$	−17.1843	−	5.01850i	−1.18583	−	0.346309i
$211$	5.66420	+	1.66316i	0.389940	+	0.114497i	0.470825	−	0.882227i	$-0.343956\pi$
$211$	5.66420	+	1.66316i	0.389940	+	0.114497i	−0.0808850	+	0.996723i	$0.525775\pi$
$212$	−7.29464	−	0.521723i	−0.500998	−	0.0358321i
$213$	−9.88285	−	2.78145i	−0.677162	−	0.190582i
$214$	−6.43102	+	10.0069i	−0.439615	+	0.684055i
$215$	1.67179	+	8.06448i	0.114015	+	0.549993i
$216$	−5.19247	−	0.195535i	−0.353303	−	0.0133045i
$217$	−44.3480	−	9.64733i	−3.01054	−	0.654903i
$218$	−0.0334496	+	0.0446835i	−0.00226550	+	0.00302635i
$219$	−7.80098	+	3.01004i	−0.527141	+	0.203400i
$220$	4.73812	−	2.10801i	0.319444	−	0.142122i
$221$	7.29377	+	6.32008i	0.490632	+	0.425135i
$222$	0.535418	+	0.812867i	0.0359349	+	0.0545560i
$223$	21.1888	−	4.60933i	1.41890	−	0.308664i	0.563282	−	0.826265i	$-0.309539\pi$
$223$	21.1888	−	4.60933i	1.41890	−	0.308664i	0.855622	+	0.517601i	$0.173175\pi$
$224$	4.43508	−	1.30226i	0.296331	−	0.0870107i
$225$	−9.78972	+	11.3649i	−0.652648	+	0.757661i
$226$	2.43212	+	0.714136i	0.161782	+	0.0475036i
$227$	−8.61226	−	3.21221i	−0.571616	−	0.213202i	0.0470006	−	0.998895i	$-0.485034\pi$
$227$	−8.61226	−	3.21221i	−0.571616	−	0.213202i	−0.618616	+	0.785693i	$0.712306\pi$
$228$	−0.671902	−	0.569096i	−0.0444978	−	0.0376893i
$229$			10.2005i			0.674071i	0.941492	+	0.337035i	$0.109424\pi$
$229$			10.2005i			0.674071i	−0.941492	+	0.337035i	$0.890576\pi$
$230$	−1.13385	+	10.6637i	−0.0747642	+	0.703143i
$231$	4.15078	+	18.0978i	0.273101	+	1.19075i
$232$	−7.92070	+	5.92936i	−0.520019	+	0.389281i
$233$	−0.732921	+	1.96504i	−0.0480152	+	0.128734i	−0.958744	−	0.284272i	$-0.908248\pi$
$233$	−0.732921	+	1.96504i	−0.0480152	+	0.128734i	0.910729	+	0.413005i	$0.135521\pi$
$234$	−18.4633	+	3.08021i	−1.20698	+	0.201360i
$235$	18.3666	+	4.18416i	1.19810	+	0.272944i
$236$	2.70590	+	9.21545i	0.176139	+	0.599875i
$237$	−6.24451	−	13.2761i	−0.405624	−	0.862377i
$238$	−2.49854	−	6.69886i	−0.161957	−	0.434222i
$239$	−1.68500	+	1.94459i	−0.108993	+	0.125785i	−0.807625	−	0.589697i	$-0.799247\pi$
$239$	−1.68500	+	1.94459i	−0.108993	+	0.125785i	0.698631	+	0.715482i	$0.253793\pi$
$240$	0.545578	−	3.83436i	0.0352169	−	0.247507i
$241$	0.647107	+	4.50073i	0.0416838	+	0.289917i	0.999991	+	0.00417821i	$0.00132997\pi$
$241$	0.647107	+	4.50073i	0.0416838	+	0.289917i	−0.958307	+	0.285739i	$0.907761\pi$
$242$	4.50008	+	3.36872i	0.289276	+	0.216549i
$243$	−12.3364	−	9.52958i	−0.791381	−	0.611323i
$244$	1.51021	+	1.30860i	0.0966811	+	0.0837747i
$245$	26.8521	+	17.6307i	1.71552	+	1.12638i
$246$	−3.98861	−	1.43676i	−0.254304	−	0.0916042i
$247$	−2.78397	−	1.52017i	−0.177140	−	0.0967258i
$248$	0.700460	−	9.79371i	0.0444793	−	0.621901i
$249$	6.49745	+	0.391270i	0.411759	+	0.0247958i
$250$	−7.67009	−	8.13447i	−0.485099	−	0.514469i
$251$	−13.6440	−	1.96171i	−0.861200	−	0.123822i	−0.302457	−	0.953163i	$-0.597807\pi$
$251$	−13.6440	−	1.96171i	−0.861200	−	0.123822i	−0.558743	+	0.829341i	$0.688716\pi$
$252$	13.0984	+	4.55237i	0.825121	+	0.286773i
$253$	10.2286	−	4.36877i	0.643066	−	0.274662i
$254$	−1.48073			−0.0929094
$255$	−5.97596	−	0.418628i	−0.374229	−	0.0262155i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−6.98140	+	3.81213i	−0.435488	+	0.237794i	−0.682010	−	0.731343i	$-0.738894\pi$
$257$	−6.98140	+	3.81213i	−0.435488	+	0.237794i	0.246522	+	0.969137i	$0.420712\pi$
$258$	−0.978904	−	6.30398i	−0.0609439	−	0.392469i
$259$	−0.731827	−	2.49237i	−0.0454735	−	0.154868i
$260$	−0.859012	−	13.9255i	−0.0532737	−	0.863620i
$261$	−29.6750	+	0.668002i	−1.83684	+	0.0413483i
$262$	−6.97799	+	0.499076i	−0.431102	+	0.0308330i
$263$	−21.4216	−	4.65999i	−1.32092	−	0.287348i	−0.503799	−	0.863821i	$-0.668065\pi$
$263$	−21.4216	−	4.65999i	−1.32092	−	0.287348i	−0.817116	+	0.576473i	$0.804428\pi$
$264$	−3.74767	+	1.44605i	−0.230653	+	0.0889985i
$265$	11.6760	−	11.4495i	0.717249	−	0.703339i
$266$	1.27042	+	1.97682i	0.0778947	+	0.121207i
$267$	2.75702	+	9.01307i	0.168727	+	0.551591i
$268$	−0.520118	−	1.39449i	−0.0317713	−	0.0851821i
$269$	10.1801	+	6.54237i	0.620694	+	0.398896i	0.812854	−	0.582468i	$-0.197913\pi$
$269$	10.1801	+	6.54237i	0.620694	+	0.398896i	−0.192160	+	0.981364i	$0.561549\pi$
$270$	8.01657	−	8.41038i	0.487873	−	0.511840i
$271$	−0.397128	−	0.458310i	−0.0241238	−	0.0278404i	0.743559	−	0.668670i	$-0.233136\pi$
$271$	−0.397128	−	0.458310i	−0.0241238	−	0.0278404i	−0.767683	+	0.640829i	$0.778591\pi$
$272$	1.35756	−	0.741286i	0.0823145	−	0.0449471i
$273$	49.5223	+	6.55231i	2.99722	+	0.396564i
$274$	−13.7776	−	1.98091i	−0.832333	−	0.119671i
$275$	−3.48422	+	11.0602i	−0.210106	+	0.666955i
$276$	1.29293	−	8.20538i	0.0778250	−	0.493906i
$277$	−0.759785	−	0.759785i	−0.0456511	−	0.0456511i	0.683913	−	0.729564i	$-0.260277\pi$
$277$	−0.759785	−	0.759785i	−0.0456511	−	0.0456511i	−0.729564	+	0.683913i	$0.760277\pi$
$278$	−1.50041	+	1.12319i	−0.0899885	+	0.0673645i
$279$	18.7838	−	22.6900i	1.12456	−	1.35841i
$280$	−4.38550	+	9.35929i	−0.262084	+	0.559325i
$281$	−13.5411	+	11.7334i	−0.807794	+	0.699957i	−0.957393	−	0.288790i	$-0.906747\pi$
$281$	−13.5411	+	11.7334i	−0.807794	+	0.699957i	0.149599	+	0.988747i	$0.452202\pi$
$282$	−14.0455	−	3.95301i	−0.836398	−	0.235398i
$283$	−18.8945	+	4.11024i	−1.12316	+	0.244328i	−0.735533	−	0.677489i	$-0.763068\pi$
$283$	−18.8945	+	4.11024i	−1.12316	+	0.244328i	−0.387626	+	0.921817i	$0.626705\pi$
$284$	−2.46239	+	5.39188i	−0.146116	+	0.319949i
$285$	1.94846	−	0.283054i	0.115417	−	0.0167667i
$286$	−12.1735	+	7.82342i	−0.719833	+	0.462609i
$287$	9.05724	+	6.78017i	0.534632	+	0.400220i
$288$	−0.571563	+	2.94505i	−0.0336796	+	0.173539i
$289$	7.89742	+	12.2886i	0.464554	+	0.722860i
$290$	1.79431	−	22.0512i	0.105365	−	1.29489i
$291$	6.03043	−	29.3054i	0.353510	−	1.71791i
$292$	1.02617	+	4.71722i	0.0600520	+	0.276055i
$293$	−7.18076	−	3.92099i	−0.419505	−	0.229067i	0.255610	−	0.966780i	$-0.417724\pi$
$293$	−7.18076	−	3.92099i	−0.419505	−	0.229067i	−0.675114	+	0.737713i	$0.735906\pi$
$294$	−20.0858	−	14.6863i	−1.17143	−	0.856522i
$295$	−19.4472	−	9.11243i	−1.13226	−	0.530546i
$296$	0.511184	−	0.233450i	0.0297120	−	0.0135690i
$297$	−11.6708	−	3.00292i	−0.677208	−	0.174247i
$298$	6.13501	−	6.13501i	0.355392	−	0.355392i
$299$	−1.39574	−	29.8910i	−0.0807179	−	1.72864i
$300$	5.61655	+	6.59199i	0.324272	+	0.380589i
$301$	−2.42291	+	16.8517i	−0.139654	+	0.971318i
$302$	−4.71286	−	1.75781i	−0.271195	−	0.101150i
$303$	−11.7924	−	13.3036i	−0.677455	−	0.764275i
$304$	−0.384201	+	0.332912i	−0.0220354	+	0.0190938i
$305$	−4.42885	+	0.592572i	−0.253595	+	0.0339306i
$306$	4.60677	+	0.556850i	0.263351	+	0.0318330i
$307$	−7.28552	+	2.71736i	−0.415806	+	0.155088i	−0.548656	−	0.836048i	$-0.684860\pi$
$307$	−7.28552	+	2.71736i	−0.415806	+	0.155088i	0.132849	+	0.991136i	$0.457587\pi$
$308$	10.6928	−	0.764762i	0.609277	−	0.0435764i
$309$	−5.79489	−	5.66592i	−0.329660	−	0.322323i
$310$	15.3720	+	15.6760i	0.873072	+	0.890339i
$311$	17.6911	−	2.54360i	1.00317	−	0.144234i	0.378896	−	0.925439i	$-0.376304\pi$
$311$	17.6911	−	2.54360i	1.00317	−	0.144234i	0.624275	+	0.781205i	$0.285395\pi$
$312$	0.121614	+	10.8064i	0.00688505	+	0.611794i
$313$	0.541230	+	7.56739i	0.0305921	+	0.427734i	0.989550	+	0.144187i	$0.0460567\pi$
$313$	0.541230	+	7.56739i	0.0305921	+	0.427734i	−0.958958	+	0.283547i	$0.908489\pi$
$314$	−8.30409	+	18.1834i	−0.468627	+	1.02615i
$315$	−27.0234	+	15.2051i	−1.52260	+	0.856711i
$316$	−8.12741	+	2.38642i	−0.457203	+	0.134247i
$317$	−2.37073	−	0.169558i	−0.133154	−	0.00952334i	0.00460322	−	0.999989i	$-0.498535\pi$
$317$	−2.37073	−	0.169558i	−0.133154	−	0.00952334i	−0.137757	+	0.990466i	$0.543989\pi$
$318$	−9.47910	+	8.40230i	−0.531562	+	0.471178i
$319$	−20.8730	+	9.53236i	−1.16866	+	0.533710i
$320$	−2.13922	−	0.650950i	−0.119586	−	0.0363892i
$321$	4.60577	+	20.0816i	0.257069	+	1.12085i
$322$	−9.70484	+	19.9306i	−0.540830	+	1.11069i
$323$	0.556020	+	0.556020i	0.0309378	+	0.0309378i
$324$	−6.52965	+	6.19384i	−0.362758	+	0.344102i
$325$	24.6040	+	19.1814i	1.36478	+	1.06399i
$326$	−0.160224	+	0.545673i	−0.00887400	+	0.0302221i
$327$	0.0148346	+	0.0955323i	0.000820354	+	0.00528295i
$328$	−1.17304	+	2.14827i	−0.0647705	+	0.118618i
$329$	32.7579	+	21.0522i	1.80600	+	1.16065i
$330$	3.12666	−	8.42048i	0.172117	−	0.463532i
$331$	21.2430	−	24.5157i	1.16762	−	1.34750i	0.241441	−	0.970416i	$-0.422380\pi$
$331$	21.2430	−	24.5157i	1.16762	−	1.34750i	0.926178	−	0.377088i	$-0.123074\pi$
$332$	0.798842	−	3.67222i	0.0438421	−	0.201539i
$333$	1.65502	+	0.321200i	0.0906948	+	0.0176017i
$334$	−20.3230	+	2.92201i	−1.11203	+	0.159885i
$335$	3.10664	+	1.19350i	0.169734	+	0.0652076i
$336$	3.75759	−	7.06950i	0.204993	−	0.385673i
$337$	29.4835	−	10.9968i	1.60607	−	0.599033i	0.622992	−	0.782228i	$-0.285917\pi$
$337$	29.4835	−	10.9968i	1.60607	−	0.599033i	0.983076	+	0.183196i	$0.0586442\pi$
$338$	5.51208	+	25.3386i	0.299818	+	1.37824i
$339$	3.82944	−	2.14733i	0.207987	−	0.116627i
$340$	−0.768250	+	3.37227i	−0.0416642	+	0.182887i
$341$	6.41551	−	21.8492i	0.347419	−	1.18320i
$342$	−1.51839	+	0.143008i	−0.0821053	+	0.00773297i
$343$	20.4036	+	27.2560i	1.10169	+	1.47169i
$344$	−3.68322			−0.198586
$345$	11.8335	+	14.3167i	0.637093	+	0.770787i
$346$	11.6245			0.624938
$347$	7.69146	+	10.2746i	0.412899	+	0.551569i	0.957987	−	0.286810i	$-0.0925948\pi$
$347$	7.69146	+	10.2746i	0.412899	+	0.551569i	−0.545088	+	0.838379i	$0.683504\pi$
$348$	−2.24784	+	16.9892i	−0.120497	+	0.910714i
$349$	4.65322	−	15.8474i	0.249081	−	0.848292i	−0.736115	−	0.676857i	$-0.763342\pi$
$349$	4.65322	−	15.8474i	0.249081	−	0.848292i	0.985195	−	0.171435i	$-0.0548403\pi$
$350$	−9.18739	−	21.2070i	−0.491087	−	1.13356i
$351$	−18.5422	+	26.5956i	−0.989712	+	1.41957i
$352$	0.492982	+	2.26620i	0.0262760	+	0.120789i
$353$	−29.8670	+	11.1398i	−1.58966	+	0.592912i	−0.979867	−	0.199650i	$-0.936020\pi$
$353$	−29.8670	+	11.1398i	−1.58966	+	0.592912i	−0.609791	+	0.792562i	$0.708747\pi$
$354$	14.6894	+	7.80773i	0.780733	+	0.414976i
$355$	−5.38776	−	12.1099i	−0.285952	−	0.642729i
$356$	5.38632	−	0.774436i	0.285474	−	0.0410450i
$357$	−11.3216	−	5.01722i	−0.599205	−	0.265540i
$358$	−3.22481	+	14.8242i	−0.170437	+	0.783485i
$359$	−21.0701	+	24.3162i	−1.11204	+	1.28336i	−0.156761	+	0.987637i	$0.550105\pi$
$359$	−21.0701	+	24.3162i	−1.11204	+	1.28336i	−0.955274	+	0.295721i	$0.904440\pi$
$360$	−4.08803	−	5.31864i	−0.215458	−	0.280317i
$361$	15.7664	+	10.1325i	0.829811	+	0.533287i
$362$	−6.20143	+	11.3571i	−0.325940	+	0.596914i
$363$	9.62106	−	1.49399i	0.504975	−	0.0784142i
$364$	8.12542	−	27.6726i	0.425887	−	1.45044i
$365$	−9.42320	−	5.26588i	−0.493233	−	0.275629i
$366$	3.44932	−	0.285749i	0.180299	−	0.0149363i
$367$	−0.156895	−	0.156895i	−0.00818987	−	0.00818987i	0.703000	−	0.711190i	$-0.251843\pi$
$367$	−0.156895	−	0.156895i	−0.00818987	−	0.00818987i	−0.711190	+	0.703000i	$0.751843\pi$
$368$	−4.56674	−	1.46456i	−0.238058	−	0.0763453i
$369$	−6.60909	+	3.19994i	−0.344056	+	0.166582i
$370$	−0.365813	+	1.20217i	−0.0190177	+	0.0624980i
$371$	30.7494	−	14.0428i	1.59643	−	0.729066i
$372$	−11.2808	−	12.7265i	−0.584884	−	0.659840i
$373$	−22.9785	−	1.64346i	−1.18978	−	0.0850949i	−0.537629	−	0.843182i	$-0.680680\pi$
$373$	−22.9785	−	1.64346i	−1.18978	−	0.0850949i	−0.652154	+	0.758087i	$0.726134\pi$
$374$	3.44196	−	1.01065i	0.177979	−	0.0522595i
$375$	−19.3617	−	0.350889i	−0.999836	−	0.0181198i
$376$	−3.49955	+	7.66295i	−0.180476	+	0.395186i
$377$	4.40410	+	61.5773i	0.226822	+	3.17139i
$378$	21.4985	−	10.7093i	1.10577	−	0.550827i
$379$	6.67020	−	0.959030i	0.342625	−	0.0492621i	0.0311454	−	0.999515i	$-0.490085\pi$
$379$	6.67020	−	0.959030i	0.342625	−	0.0492621i	0.311480	+	0.950253i	$0.399175\pi$
$380$	0.0111302	−	1.13670i	0.000570968	−	0.0583113i
$381$	−1.79300	+	1.83381i	−0.0918580	+	0.0939490i
$382$	13.0840	−	0.935783i	0.669433	−	0.0478788i
$383$	21.3798	−	7.97424i	1.09246	−	0.407465i	0.262294	−	0.964988i	$-0.415521\pi$
$383$	21.3798	−	7.97424i	1.09246	−	0.407465i	0.830161	+	0.557523i	$0.188248\pi$
$384$	1.62955	+	0.586989i	0.0831578	+	0.0299547i
$385$	−14.5524	+	19.0481i	−0.741659	+	0.970780i
$386$	−6.18702	+	5.36108i	−0.314911	+	0.272872i
$387$	−8.99250	−	6.42107i	−0.457115	−	0.326402i
$388$	−16.1849	−	6.03664i	−0.821661	−	0.306464i
$389$	4.18288	−	29.0926i	0.212080	−	1.47505i	−0.554113	−	0.832442i	$-0.686942\pi$
$389$	4.18288	−	29.0926i	0.212080	−	1.47505i	0.766193	−	0.642610i	$-0.222149\pi$
$390$	−18.2861	−	15.7983i	−0.925955	−	0.799977i
$391$	−1.75564	+	7.20728i	−0.0887864	+	0.364488i
$392$	−10.1581	+	10.1581i	−0.513064	+	0.513064i
$393$	−7.83147	+	9.24621i	−0.395045	+	0.466410i
$394$	−6.38989	+	2.91817i	−0.321918	+	0.147015i
$395$	8.03656	−	17.1512i	0.404363	−	0.862970i
$396$	−2.74713	+	6.39231i	−0.138049	+	0.321226i
$397$	2.90562	+	1.58659i	0.145829	+	0.0796286i	0.550507	−	0.834831i	$-0.314435\pi$
$397$	2.90562	+	1.58659i	0.145829	+	0.0796286i	−0.404678	+	0.914459i	$0.632616\pi$
$398$	−5.04059	−	23.1712i	−0.252662	−	1.16147i
$399$	3.98653	+	0.820344i	0.199576	+	0.0410686i
$400$	4.25839	−	2.62032i	0.212920	−	0.131016i
$401$	15.5289	+	24.1635i	0.775477	+	1.20667i	0.973995	+	0.226569i	$0.0727508\pi$
$401$	15.5289	+	24.1635i	0.775477	+	1.20667i	−0.198518	+	0.980097i	$0.563613\pi$
$402$	−2.35681	−	1.04443i	−0.117547	−	0.0520914i
$403$	−49.0442	−	36.7141i	−2.44307	−	1.82886i
$404$	−8.63460	+	5.54912i	−0.429588	+	0.276079i
$405$	−0.708686	−	20.1121i	−0.0352149	−	0.999380i
$406$	18.9986	−	41.6011i	0.942884	−	2.06463i
$407$	1.27353	−	0.277040i	0.0631267	−	0.0137324i
$408$	0.725809	−	2.57889i	0.0359329	−	0.127674i
$409$	20.7766	−	18.0030i	1.02733	−	0.890191i	0.0333208	−	0.999445i	$-0.489392\pi$
$409$	20.7766	−	18.0030i	1.02733	−	0.890191i	0.994014	+	0.109254i	$0.0348462\pi$
$410$	−1.86237	−	5.14655i	−0.0919759	−	0.254170i
$411$	−19.1363	+	14.6642i	−0.943925	+	0.723330i
$412$	−3.74585	+	2.80411i	−0.184545	+	0.138149i
$413$	−31.3920	−	31.3920i	−1.54470	−	1.54470i
$414$	−8.59637	−	11.5370i	−0.422489	−	0.567013i
$415$	4.96984	+	6.77623i	0.243960	+	0.332632i
$416$	6.17598	+	0.887972i	0.302802	+	0.0435364i
$417$	−0.425806	+	3.21824i	−0.0208518	+	0.157598i
$418$	−1.03480	+	0.565042i	−0.0506136	+	0.0276371i
$419$	−15.0791	−	17.4022i	−0.736663	−	0.850154i	0.256542	−	0.966533i	$-0.417417\pi$
$419$	−15.0791	−	17.4022i	−0.736663	−	0.850154i	−0.993205	+	0.116379i	$0.962871\pi$
$420$	6.28067	+	16.7642i	0.306466	+	0.818011i
$421$	6.66741	+	4.28488i	0.324950	+	0.208832i	0.692937	−	0.720999i	$-0.256317\pi$
$421$	6.66741	+	4.28488i	0.324950	+	0.208832i	−0.367987	+	0.929831i	$0.619953\pi$
$422$	−2.06300	−	5.53112i	−0.100425	−	0.269251i
$423$	−21.9031	+	12.6080i	−1.06497	+	0.613023i
$424$	3.95385	+	6.15232i	0.192016	+	0.298783i
$425$	−4.51259	−	6.28082i	−0.218893	−	0.304665i
$426$	3.69590	+	9.57849i	0.179067	+	0.464079i
$427$	−9.02564	−	1.96341i	−0.436781	−	0.0950159i
$428$	11.8649	−	0.848592i	0.573510	−	0.0410182i
$429$	−5.05177	+	24.5495i	−0.243902	+	1.18526i
$430$	5.45408	−	6.17120i	0.263019	−	0.297602i
$431$	−10.3331	−	35.1912i	−0.497726	−	1.69510i	−0.698625	−	0.715488i	$-0.746205\pi$
$431$	−10.3331	−	35.1912i	−0.497726	−	1.69510i	0.200899	−	0.979612i	$-0.435614\pi$
$432$	2.95520	+	4.27397i	0.142182	+	0.205631i
$433$	4.20749	−	2.29746i	0.202199	−	0.110409i	−0.374959	−	0.927041i	$-0.622343\pi$
$433$	4.20749	−	2.29746i	0.202199	−	0.110409i	0.577158	+	0.816632i	$0.304162\pi$
$434$	18.8537	+	41.2839i	0.905007	+	1.98169i
$435$	−25.1366	−	28.9236i	−1.20521	−	1.38678i
$436$	0.0558166			0.00267313
$437$	0.0603097	−	2.43731i	0.00288500	−	0.116593i
$438$	7.08462	+	4.44116i	0.338516	+	0.212207i
$439$	5.59744	+	0.804790i	0.267151	+	0.0384105i	0.274589	−	0.961562i	$-0.411458\pi$
$439$	5.59744	+	0.804790i	0.267151	+	0.0384105i	−0.00743743	+	0.999972i	$0.502367\pi$
$440$	−4.52700	−	2.52978i	−0.215816	−	0.120603i
$441$	−42.5099	+	7.09187i	−2.02428	+	0.337708i
$442$	0.688497	−	9.62645i	0.0327485	−	0.457883i
$443$	12.7612	+	6.96816i	0.606304	+	0.331067i	0.752906	−	0.658128i	$-0.228652\pi$
$443$	12.7612	+	6.96816i	0.606304	+	0.331067i	−0.146601	+	0.989196i	$0.546833\pi$
$444$	0.329869	−	0.915757i	0.0156549	−	0.0434599i
$445$	−6.67844	+	10.1715i	−0.316589	+	0.482175i
$446$	−16.3879	−	14.2002i	−0.775990	−	0.672399i
$447$	−0.169108	−	15.0267i	−0.00799856	−	0.710738i
$448$	−3.70035	−	2.77005i	−0.174825	−	0.130873i
$449$	−4.13336	−	28.7482i	−0.195065	−	1.35671i	−0.818353	−	0.574716i	$-0.805112\pi$
$449$	−4.13336	−	28.7482i	−0.195065	−	1.35671i	0.623287	−	0.781993i	$-0.285797\pi$
$450$	14.9648	+	1.02634i	0.705450	+	0.0483819i
$451$	−3.71741	+	4.29012i	−0.175046	+	0.202014i
$452$	−0.885822	−	2.37498i	−0.0416656	−	0.111710i
$453$	−7.88369	+	3.70814i	−0.370408	+	0.174224i
$454$	2.58963	+	8.81947i	0.121537	+	0.413918i
$455$	34.3331	+	54.5914i	1.60956	+	2.55928i
$456$	−0.0529285	+	0.878932i	−0.00247860	+	0.0411597i
$457$	−11.3874	+	30.5307i	−0.532678	+	1.42816i	0.340259	+	0.940332i	$0.389485\pi$
$457$	−11.3874	+	30.5307i	−0.532678	+	1.42816i	−0.872937	+	0.487833i	$0.837788\pi$
$458$	8.16596	−	6.11296i	0.381570	−	0.285640i
$459$	6.26790	−	5.03097i	0.292560	−	0.234825i
$460$	9.21622	−	5.48282i	0.429709	−	0.255638i
$461$		−	34.0241i		−	1.58466i	−0.610093	−	0.792330i	$-0.708868\pi$
$461$		−	34.0241i		−	1.58466i	0.610093	−	0.792330i	$-0.291132\pi$
$462$	12.0006	−	14.1685i	0.558318	−	0.659178i
$463$	−33.1002	−	12.3457i	−1.53830	−	0.573755i	−0.569582	−	0.821935i	$-0.692895\pi$
$463$	−33.1002	−	12.3457i	−1.53830	−	0.573755i	−0.968714	+	0.248180i	$0.920168\pi$
$464$	9.49339	+	2.78751i	0.440720	+	0.129407i
$465$	38.0277	−	0.0555963i	1.76349	−	0.00257822i
$466$	2.01232	−	0.590869i	0.0932188	−	0.0273715i
$467$	10.3995	−	2.26226i	0.481229	−	0.104685i	0.0345946	−	0.999401i	$-0.488986\pi$
$467$	10.3995	−	2.26226i	0.481229	−	0.104685i	0.446635	+	0.894716i	$0.352622\pi$
$468$	13.5305	+	12.9347i	0.625447	+	0.597908i
$469$	5.19921	+	4.50514i	0.240077	+	0.208028i
$470$	−7.65709	−	17.2107i	−0.353195	−	0.793869i
$471$	12.4639	+	32.3022i	0.574308	+	1.48841i
$472$	5.75576	−	7.68880i	0.264930	−	0.353906i
$473$	−8.34693	−	1.81576i	−0.383792	−	0.0834889i
$474$	−6.88590	+	12.9551i	−0.316280	+	0.595046i
$475$	1.88804	+	1.70186i	0.0866293	+	0.0780866i
$476$	−3.86539	+	6.01466i	−0.177170	+	0.275682i
$477$	−1.07228	+	21.9136i	−0.0490962	+	1.00336i
$478$	2.56650	+	0.183560i	0.117389	+	0.00839584i
$479$	−25.2008	−	7.39962i	−1.15145	−	0.338097i	−0.350347	−	0.936620i	$-0.613936\pi$
$479$	−25.2008	−	7.39962i	−1.15145	−	0.338097i	−0.801106	+	0.598523i	$0.795755\pi$
$480$	−3.39652	+	1.86109i	−0.155029	+	0.0849468i
$481$	0.499012	−	3.47070i	0.0227530	−	0.158250i
$482$	3.21522	−	3.21522i	0.146449	−	0.146449i
$483$	12.9316	+	36.1526i	0.588408	+	1.64500i
$484$		−	5.62130i		−	0.255513i
$485$	34.0807	−	18.1786i	1.54752	−	0.825446i
$486$	−0.235889	+	15.5867i	−0.0107001	+	0.707026i
$487$	3.45724	+	6.33145i	0.156662	+	0.286906i	0.944207	−	0.329351i	$-0.106830\pi$
$487$	3.45724	+	6.33145i	0.156662	+	0.286906i	−0.787545	+	0.616257i	$0.788648\pi$
$488$	0.142556	−	1.99320i	0.00645323	−	0.0902279i
$489$	0.481776	+	0.859177i	0.0217867	+	0.0388533i
$490$	−1.97779	−	32.0619i	−0.0893474	−	1.44841i
$491$	−13.9425	−	6.36734i	−0.629218	−	0.287354i	0.0751687	−	0.997171i	$-0.476050\pi$
$491$	−13.9425	−	6.36734i	−0.629218	−	0.287354i	−0.704386	+	0.709817i	$0.748778\pi$
$492$	1.24010	+	4.05406i	0.0559081	+	0.182771i
$493$	3.25310	−	14.9542i	0.146512	−	0.673505i
$494$	0.451419	+	3.13969i	0.0203103	+	0.141261i
$495$	−6.64232	−	14.0685i	−0.298550	−	0.632330i
$496$	−8.26004	+	5.30840i	−0.370887	+	0.238354i
$497$	−1.95462	−	27.3291i	−0.0876766	−	1.22588i
$498$	−3.58055	−	5.43596i	−0.160448	−	0.243591i
$499$	8.75969	−	13.6303i	0.392137	−	0.610178i	−0.587914	−	0.808924i	$-0.700050\pi$
$499$	8.75969	−	13.6303i	0.392137	−	0.610178i	0.980051	+	0.198746i	$0.0636869\pi$
$500$	−1.91547	+	11.0150i	−0.0856622	+	0.492607i
$501$	−20.9901	+	28.7072i	−0.937767	+	1.28255i
$502$	6.60610	+	12.0982i	0.294845	+	0.539968i
$503$	7.47479	−	20.0407i	0.333285	−	0.893570i	−0.656922	−	0.753959i	$-0.728142\pi$
$503$	7.47479	−	20.0407i	0.333285	−	0.893570i	0.990206	−	0.139612i	$-0.0445854\pi$
$504$	−4.20521	−	13.2139i	−0.187315	−	0.588596i
$505$	3.48853	−	22.6843i	0.155238	−	1.00944i
$506$	−9.62715	−	5.57030i	−0.427979	−	0.247630i
$507$	38.0551	+	23.8557i	1.69009	+	1.05947i
$508$	0.887369	+	1.18539i	0.0393707	+	0.0525930i
$509$	2.94248	+	6.44314i	0.130423	+	0.285587i	0.963566	−	0.267471i	$-0.0861880\pi$
$509$	2.94248	+	6.44314i	0.130423	+	0.285587i	−0.833143	+	0.553058i	$0.813461\pi$
$510$	3.24613	+	5.03487i	0.143741	+	0.222948i
$511$	−14.6129	−	16.8641i	−0.646435	−	0.746025i
$512$	0.479249	−	0.877679i	0.0211800	−	0.0387883i
$513$	−1.66149	+	2.05362i	−0.0733566	+	0.0906695i
$514$	7.23556	+	3.30437i	0.319147	+	0.145750i
$515$	0.848563	−	10.4284i	0.0373922	−	0.459532i
$516$	−4.45996	+	4.56149i	−0.196339	+	0.200808i
$517$	−11.7084	+	15.6406i	−0.514934	+	0.687872i
$518$	−1.55668	+	2.07948i	−0.0683966	+	0.0913671i
$519$	14.0759	−	14.3964i	0.617866	−	0.631931i
$520$	−10.6331	+	9.03289i	−0.466293	+	0.396118i
$521$	−29.3441	−	13.4010i	−1.28559	−	0.587108i	−0.348862	−	0.937174i	$-0.613432\pi$
$521$	−29.3441	−	13.4010i	−1.28559	−	0.587108i	−0.936725	+	0.350066i	$0.886159\pi$
$522$	18.3183	+	23.3557i	0.801772	+	1.02225i
$523$	−6.18241	+	11.3222i	−0.270338	+	0.495087i	−0.977216	−	0.212249i	$-0.931921\pi$
$523$	−6.18241	+	11.3222i	−0.270338	+	0.495087i	0.706878	+	0.707336i	$0.250103\pi$
$524$	4.58129	+	5.28709i	0.200134	+	0.230967i
$525$	−37.3887	−	14.3011i	−1.63178	−	0.624152i
$526$	9.10700	+	19.9415i	0.397084	+	0.869493i
$527$	9.10140	+	12.1580i	0.396463	+	0.529613i
$528$	3.40352	+	2.13358i	0.148119	+	0.0928520i
$529$	19.9402	−	11.4626i	0.866963	−	0.498372i
$530$	−16.1630	−	2.48565i	−0.702074	−	0.107970i
$531$	27.4567	−	8.73782i	1.19152	−	0.379189i
$532$	0.821188	−	2.20169i	0.0356030	−	0.0954554i
$533$	7.31919	+	13.4041i	0.317029	+	0.580596i
$534$	5.56311	−	7.60844i	0.240739	−	0.329249i
$535$	−16.1476	+	21.1360i	−0.698120	+	0.913791i
$536$	−0.804653	+	1.25206i	−0.0347557	+	0.0540809i
$537$	14.4542	+	21.9442i	0.623744	+	0.946962i
$538$	−0.863286	−	12.0703i	−0.0372189	−	0.520388i
$539$	−28.0282	+	18.0126i	−1.20726	+	0.775859i
$540$	−11.5370	−	1.37744i	−0.496474	−	0.0592757i
$541$	−6.05157	−	42.0896i	−0.260177	−	1.80957i	−0.531470	−	0.847077i	$-0.678360\pi$
$541$	−6.05157	−	42.0896i	−0.260177	−	1.80957i	0.271293	−	0.962497i	$-0.412549\pi$
$542$	−0.128906	+	0.592572i	−0.00553700	+	0.0254532i
$543$	6.55594	+	21.4323i	0.281342	+	0.919746i
$544$	−1.40699	−	0.642550i	−0.0603241	−	0.0275491i
$545$	−0.0826526	+	0.0935201i	−0.00354045	+	0.00400596i
$546$	−24.4322	−	43.5713i	−1.04560	−	1.86468i
$547$	0.591505	−	8.27032i	0.0252909	−	0.353613i	−0.969011	−	0.247016i	$-0.920550\pi$
$547$	0.591505	−	8.27032i	0.0252909	−	0.353613i	0.994302	−	0.106597i	$-0.0339956\pi$
$548$	6.67078	+	12.2166i	0.284962	+	0.521868i
$549$	3.82285	−	4.61782i	0.163155	−	0.197084i
$550$	10.9422	−	3.83886i	0.466575	−	0.163690i
$551$			5.02991i			0.214281i
$552$	−7.34357	+	3.88226i	−0.312563	+	0.165240i
$553$	27.6857	−	27.6857i	1.17731	−	1.17731i
$554$	−0.152917	+	1.06356i	−0.00649682	+	0.0451864i
$555$	1.04587	+	1.90874i	0.0443949	+	0.0810213i
$556$	1.79832	+	0.528035i	0.0762658	+	0.0223937i
$557$	17.8612	+	1.27746i	0.756803	+	0.0541276i	0.444408	−	0.895825i	$-0.353414\pi$
$557$	17.8612	+	1.27746i	0.756803	+	0.0541276i	0.312395	+	0.949952i	$0.398869\pi$
$558$	−29.4210	−	1.43963i	−1.24549	−	0.0609443i
$559$	−12.4247	+	19.3332i	−0.525509	+	0.817708i
$560$	10.1206	−	2.09804i	0.427675	−	0.0886584i
$561$	2.91618	−	5.48647i	0.123121	−	0.231639i
$562$	17.5080	+	3.80862i	0.738529	+	0.160657i
$563$	4.76880	−	6.37037i	0.200981	−	0.268479i	−0.688715	−	0.725032i	$-0.741825\pi$
$563$	4.76880	−	6.37037i	0.200981	−	0.268479i	0.889696	+	0.456553i	$0.150916\pi$
$564$	5.25262	+	13.6130i	0.221175	+	0.573209i
$565$	5.29097	+	2.03266i	0.222593	+	0.0855147i
$566$	14.6134	+	12.6626i	0.614249	+	0.532250i
$567$	12.7693	−	39.5926i	0.536262	−	1.66273i
$568$	5.79208	−	1.25999i	0.243030	−	0.0528680i
$569$	39.0263	−	11.4592i	1.63607	−	0.480393i	0.670796	−	0.741642i	$-0.265953\pi$
$569$	39.0263	−	11.4592i	1.63607	−	0.480393i	0.965271	+	0.261249i	$0.0841345\pi$
$570$	−1.39426	−	1.39019i	−0.0583993	−	0.0582288i
$571$	−1.81887	−	0.534068i	−0.0761173	−	0.0223500i	0.243452	−	0.969913i	$-0.421720\pi$
$571$	−1.81887	−	0.534068i	−0.0761173	−	0.0223500i	−0.319569	+	0.947563i	$0.603538\pi$
$572$	13.5583	+	5.05697i	0.566900	+	0.211443i
$573$	14.6842	−	17.3369i	0.613443	−	0.724261i
$574$		−	11.3139i		−	0.472233i
$575$	−4.46088	+	23.5606i	−0.186032	+	0.982544i
$576$	2.70016	−	1.30734i	0.112507	−	0.0544726i
$577$	22.6704	−	16.9708i	0.943781	−	0.706505i	−0.0122028	−	0.999926i	$-0.503884\pi$
$577$	22.6704	−	16.9708i	0.943781	−	0.706505i	0.955984	+	0.293420i	$0.0947935\pi$
$578$	5.10480	−	13.6865i	0.212332	−	0.569284i
$579$	−0.852338	+	14.1540i	−0.0354220	+	0.588219i
$580$	−18.7282	+	11.7784i	−0.777644	+	0.489070i
$581$	4.89401	+	16.6675i	0.203038	+	0.691483i
$582$	−27.0741	+	12.7344i	−1.12226	+	0.527860i
$583$	5.92725	+	15.8916i	0.245482	+	0.658162i
$584$	3.16137	−	3.64842i	0.130818	−	0.150973i
$585$	−41.7078	+	3.51656i	−1.72440	+	0.145392i
$586$	1.16435	+	8.09826i	0.0480990	+	0.334536i
$587$	25.9781	+	19.4470i	1.07223	+	0.802663i	0.981163	−	0.193182i	$-0.0618807\pi$
$587$	25.9781	+	19.4470i	1.07223	+	0.802663i	0.0910689	+	0.995845i	$0.470972\pi$
$588$	0.280004	+	24.8807i	0.0115472	+	1.02606i
$589$	−3.77236	−	3.26877i	−0.155438	−	0.134687i
$590$	4.35942	+	21.0292i	0.179475	+	0.865758i
$591$	−4.12342	+	11.4471i	−0.169615	+	0.470872i
$592$	−0.493228	−	0.269323i	−0.0202715	−	0.0110691i
$593$	−0.0403940	+	0.564782i	−0.00165878	+	0.0231928i	−0.998214	−	0.0597380i	$-0.980973\pi$
$593$	−0.0403940	+	0.564782i	−0.00165878	+	0.0231928i	0.996555	+	0.0829308i	$0.0264280\pi$
$594$	4.59009	+	11.1425i	0.188334	+	0.457184i
$595$	−4.35367	−	15.3829i	−0.178483	−	0.630636i
$596$	−8.58790	−	1.23475i	−0.351774	−	0.0505775i
$597$	−34.8000	−	21.8152i	−1.42427	−	0.892836i
$598$	−23.0925	+	19.0303i	−0.944323	+	0.778209i
$599$	−3.48181			−0.142263			−0.0711315	−	0.997467i	$-0.522661\pi$
$599$	−3.48181			−0.142263			−0.0711315	+	0.997467i	$0.522661\pi$
$600$	1.91129	−	8.44671i	0.0780281	−	0.344836i
$601$	8.76187	+	19.1858i	0.357404	+	0.782606i	0.999867	+	0.0162895i	$0.00518533\pi$
$601$	8.76187	+	19.1858i	0.357404	+	0.782606i	−0.642463	+	0.766317i	$0.722087\pi$
$602$	14.9425	−	8.15922i	0.609011	−	0.332545i
$603$	−4.14730	+	1.65411i	−0.168891	+	0.0673605i
$604$	1.41712	+	4.82625i	0.0576616	+	0.196377i
$605$	9.41842	+	8.32395i	0.382913	+	0.338417i
$606$	−3.58320	+	17.4129i	−0.145558	+	0.707350i
$607$	15.7357	−	1.12544i	0.638690	−	0.0456800i	0.251761	−	0.967789i	$-0.418990\pi$
$607$	15.7357	−	1.12544i	0.638690	−	0.0456800i	0.386929	+	0.922109i	$0.373536\pi$
$608$	0.496753	+	0.108062i	0.0201460	+	0.00438249i
$609$	−28.5158	−	73.9029i	−1.15552	−	2.99470i
$610$	3.12849	+	3.19036i	0.126669	+	0.129174i
$611$	28.4176	+	44.2187i	1.14965	+	1.78890i
$612$	−2.31495	−	4.02162i	−0.0935764	−	0.162564i
$613$	−9.42065	−	25.2577i	−0.380496	−	1.02015i	−0.976186	−	0.216936i	$-0.930394\pi$
$613$	−9.42065	−	25.2577i	−0.380496	−	1.02015i	0.595690	−	0.803215i	$-0.296879\pi$
$614$	6.54140	+	4.20391i	0.263990	+	0.169656i
$615$	−8.62886	−	3.92543i	−0.347949	−	0.158289i
$616$	−7.02016	−	8.10170i	−0.282850	−	0.326427i
$617$	10.0507	−	5.48808i	0.404624	−	0.220942i	−0.264031	−	0.964514i	$-0.585052\pi$
$617$	10.0507	−	5.48808i	0.404624	−	0.220942i	0.668655	+	0.743573i	$0.266870\pi$
$618$	−1.06305	+	8.03451i	−0.0427621	+	0.323195i
$619$	−29.0164	−	4.17192i	−1.16627	−	0.167684i	−0.468137	−	0.883656i	$-0.655075\pi$
$619$	−29.0164	−	4.17192i	−1.16627	−	0.167684i	−0.698129	+	0.715972i	$0.745984\pi$
$620$	3.33720	−	21.7002i	0.134025	−	0.871502i
$621$	−24.6972	−	3.32381i	−0.991065	−	0.133380i
$622$	−12.6381	−	12.6381i	−0.506744	−	0.506744i
$623$	−20.1362	+	15.0738i	−0.806741	+	0.603919i
$624$	8.57811	−	6.57341i	0.343399	−	0.263147i
$625$	−15.6192	−	19.5203i	−0.624767	−	0.780811i
$626$	5.73366	−	4.96824i	0.229163	−	0.198571i
$627$	−0.553244	+	1.96574i	−0.0220944	+	0.0785043i
$628$	19.5330	−	4.24915i	0.779453	−	0.169560i
$629$	−0.361093	+	0.790683i	−0.0143977	+	0.0315266i
$630$	28.3668	+	12.5213i	1.13016	+	0.498860i
$631$	0.0427439	−	0.0274699i	0.00170161	−	0.00109356i	−0.539790	−	0.841800i	$-0.681496\pi$
$631$	0.0427439	−	0.0274699i	0.00170161	−	0.00109356i	0.541491	+	0.840706i	$0.317860\pi$
$632$	6.78101	+	5.07620i	0.269734	+	0.201920i
$633$	−9.34807	−	4.14263i	−0.371552	−	0.164655i
$634$	1.28499	+	1.99948i	0.0510335	+	0.0794096i
$635$	−3.30011	−	0.268530i	−0.130961	−	0.0106563i
$636$	12.4070	+	2.55310i	0.491970	+	0.101237i
$637$	19.0533	+	87.5867i	0.754920	+	3.47031i
$638$	20.1398	+	10.9971i	0.797340	+	0.435381i
$639$	16.3378	+	7.02127i	0.646313	+	0.277757i
$640$	0.760875	+	2.10263i	0.0300762	+	0.0831139i
$641$	18.9322	−	8.64604i	0.747776	−	0.341498i	−0.00481289	−	0.999988i	$-0.501532\pi$
$641$	18.9322	−	8.64604i	0.747776	−	0.341498i	0.752589	+	0.658490i	$0.228805\pi$
$642$	13.3160	−	15.7216i	0.525543	−	0.620481i
$643$	19.4072	−	19.4072i	0.765347	−	0.765347i	−0.211937	−	0.977283i	$-0.567977\pi$
$643$	19.4072	−	19.4072i	0.765347	−	0.765347i	0.977283	+	0.211937i	$0.0679771\pi$
$644$	21.7712	−	4.17484i	0.857904	−	0.164512i
$645$	−1.03846	−	14.2272i	−0.0408893	−	0.560196i
$646$	0.111907	−	0.778327i	0.00440291	−	0.0306229i
$647$	−29.5746	−	11.0308i	−1.16270	−	0.433664i	−0.307288	−	0.951616i	$-0.599422\pi$
$647$	−29.5746	−	11.0308i	−1.16270	−	0.433664i	−0.855409	+	0.517953i	$0.826694\pi$
$648$	8.87150	+	1.51542i	0.348505	+	0.0595313i
$649$	16.8342	−	14.5869i	0.660799	−	0.572585i
$650$	0.610895	−	31.1915i	0.0239613	−	1.22343i
$651$	73.9577	+	26.6407i	2.89863	+	1.04413i
$652$	0.532853	−	0.198744i	0.0208681	−	0.00778341i
$653$	18.2504	−	1.30529i	0.714192	−	0.0510800i	0.290485	−	0.956880i	$-0.406183\pi$
$653$	18.2504	−	1.30529i	0.714192	−	0.0510800i	0.423707	+	0.905800i	$0.360729\pi$
$654$	0.0675875	−	0.0691261i	0.00264288	−	0.00270304i
$655$	−15.6424	−	0.153166i	−0.611198	−	0.00598468i
$656$	2.42276	−	0.348340i	0.0945927	−	0.0136004i
$657$	14.0788	−	3.39621i	0.549266	−	0.132499i
$658$	−2.77791	−	38.8402i	−0.108294	−	1.51415i
$659$	9.61744	−	21.0592i	0.374642	−	0.820352i	−0.624582	−	0.780959i	$-0.714731\pi$
$659$	9.61744	−	21.0592i	0.374642	−	0.820352i	0.999224	−	0.0393923i	$-0.0125422\pi$
$660$	−8.61468	+	2.54319i	−0.335326	+	0.0989934i
$661$	5.38824	−	1.58213i	0.209578	−	0.0615377i	−0.175258	−	0.984522i	$-0.556076\pi$
$661$	5.38824	−	1.58213i	0.209578	−	0.0615377i	0.384836	+	0.922985i	$0.374258\pi$
$662$	−32.3562	−	2.31416i	−1.25756	−	0.0899425i
$663$	−11.0882	−	12.5092i	−0.430629	−	0.485817i
$664$	−3.41849	+	1.56117i	−0.132663	+	0.0605852i
$665$	2.47290	+	4.63613i	0.0958950	+	0.179781i
$666$	−0.734685	−	1.51740i	−0.0284685	−	0.0587982i
$667$	−40.5405	+	24.6585i	−1.56974	+	0.954783i
$668$	14.5183	+	14.5183i	0.561731	+	0.561731i
$669$	−37.4301	+	3.10078i	−1.44713	+	0.119883i
$670$	−0.906298	−	3.20223i	−0.0350134	−	0.123713i
$671$	1.30567	−	4.44671i	0.0504050	−	0.171664i
$672$	−7.91127	+	1.22849i	−0.305184	+	0.0473900i
$673$	−5.99142	+	10.9725i	−0.230952	+	0.422958i	−0.967296	−	0.253650i	$-0.918369\pi$
$673$	−5.99142	+	10.9725i	−0.230952	+	0.422958i	0.736344	+	0.676608i	$0.236551\pi$
$674$	−26.4722	−	17.0126i	−1.01967	−	0.655302i
$675$	19.3918	−	17.2904i	0.746390	−	0.665509i
$676$	16.9813	−	19.5975i	0.653129	−	0.753751i
$677$	2.52437	−	11.6044i	0.0970196	−	0.445992i	−0.902852	−	0.429952i	$-0.858530\pi$
$677$	2.52437	−	11.6044i	0.0970196	−	0.445992i	0.999871	−	0.0160399i	$-0.00510588\pi$
$678$	−4.01392	−	1.77878i	−0.154154	−	0.0683137i
$679$	79.0331	−	11.3632i	3.03301	−	0.436081i
$680$	3.16004	−	1.40591i	0.121182	−	0.0539143i
$681$	14.0582	+	7.47224i	0.538712	+	0.286337i
$682$	−21.3359	+	7.95787i	−0.816993	+	0.304723i
$683$	6.06946	+	27.9009i	0.232241	+	1.06760i	0.934580	+	0.355753i	$0.115776\pi$
$683$	6.06946	+	27.9009i	0.232241	+	1.06760i	−0.702339	+	0.711843i	$0.747861\pi$
$684$	1.02442	+	1.12983i	0.0391698	+	0.0432003i
$685$	−30.3468	−	6.91343i	−1.15949	−	0.264148i
$686$	9.59215	−	32.6678i	0.366230	−	1.24726i
$687$	2.31744	−	17.5152i	0.0884160	−	0.668247i
$688$	2.20727	+	2.94857i	0.0841515	+	0.112413i
$689$	45.6311			1.73841
$690$	4.36959	−	18.0529i	0.166348	−	0.687262i
$691$	4.14058			0.157515			0.0787575	−	0.996894i	$-0.474905\pi$
$691$	4.14058			0.157515			0.0787575	+	0.996894i	$0.474905\pi$
$692$	−6.96631	−	9.30590i	−0.264819	−	0.353757i
$693$	−3.01562	−	32.0186i	−0.114554	−	1.21628i
$694$	3.61591	−	12.3147i	0.137258	−	0.467458i
$695$	−3.54765	+	2.23116i	−0.134570	+	0.0846327i
$696$	14.9476	−	8.38173i	0.566587	−	0.317709i
$697$	−0.804767	−	3.69945i	−0.0304827	−	0.140127i
$698$	−15.4751	+	5.77190i	−0.585740	+	0.218470i
$699$	1.70492	−	3.20763i	0.0644861	−	0.121324i
$700$	−11.4713	+	20.0638i	−0.433573	+	0.758339i
$701$	−48.3255	+	6.94816i	−1.82523	+	0.262429i	−0.967718	−	0.252035i	$-0.918900\pi$
$701$	−48.3255	+	6.94816i	−1.82523	+	0.262429i	−0.857512	+	0.514463i	$0.827991\pi$
$702$	32.4029	−	1.09434i	1.22297	−	0.0413033i
$703$	0.0607274	−	0.279159i	0.00229038	−	0.0105287i
$704$	1.51876	−	1.75274i	0.0572402	−	0.0660588i
$705$	−30.5864	−	11.3572i	−1.15195	−	0.427738i
$706$	26.8165	+	17.2339i	1.00925	+	0.648607i
$707$	22.7372	−	41.6400i	0.855119	−	1.56603i
$708$	−2.55262	−	16.4385i	−0.0959334	−	0.617795i
$709$	−4.13419	+	14.0798i	−0.155263	+	0.528776i	−0.999979	−	0.00643758i	$-0.997951\pi$
$709$	−4.13419	+	14.0798i	−0.155263	+	0.528776i	0.844717	+	0.535214i	$0.179769\pi$
$710$	−6.46575	+	11.5703i	−0.242655	+	0.434227i
$711$	7.70618	+	24.2149i	0.289004	+	0.908131i
$712$	−3.84787	−	3.84787i	−0.144205	−	0.144205i
$713$	7.85238	−	46.4296i	0.294074	−	1.73880i
$714$	2.76831	+	12.0702i	0.103602	+	0.451714i
$715$	−28.5498	+	15.2284i	−1.06770	+	0.569511i
$716$	13.8000	−	6.30223i	0.515729	−	0.235525i
$717$	3.33507	−	2.95621i	0.124550	−	0.110402i
$718$	32.0929	+	2.29533i	1.19770	+	0.0856609i
$719$	28.0821	−	8.24565i	1.04729	−	0.307511i	0.287566	−	0.957761i	$-0.407154\pi$
$719$	28.0821	−	8.24565i	1.04729	−	0.307511i	0.759720	+	0.650250i	$0.225336\pi$
$720$	−1.80793	+	6.45998i	−0.0673774	+	0.240749i
$721$	8.98481	−	19.6740i	0.334612	−	0.732698i
$722$	−1.33701	−	18.6938i	−0.0497583	−	0.695711i
$723$	−0.0886259	−	7.87515i	−0.00329603	−	0.292880i
$724$	12.8082	−	1.84154i	0.476012	−	0.0684402i
$725$	7.99795	−	48.8201i	0.297036	−	1.81313i
$726$	−6.96169	−	6.80674i	−0.258373	−	0.252622i
$727$	16.7803	−	1.20015i	0.622346	−	0.0445111i	0.243394	−	0.969927i	$-0.421739\pi$
$727$	16.7803	−	1.20015i	0.622346	−	0.0445111i	0.378952	+	0.925416i	$0.376285\pi$
$728$	−27.0225	+	10.0789i	−1.00152	+	0.373547i
$729$	19.0177	+	19.1658i	0.704358	+	0.709845i
$730$	1.43156	+	10.6994i	0.0529843	+	0.396002i
$731$	4.30557	−	3.73080i	0.159247	−	0.137989i
$732$	−2.29586	−	2.59008i	−0.0848573	−	0.0957323i
$733$	−19.8011	−	7.38541i	−0.731369	−	0.272786i	−0.0439358	−	0.999034i	$-0.513990\pi$
$733$	−19.8011	−	7.38541i	−0.731369	−	0.272786i	−0.687433	+	0.726248i	$0.741262\pi$
$734$	−0.0315773	+	0.219625i	−0.00116554	+	0.00810650i
$735$	−42.1020	−	36.3739i	−1.55295	−	1.34167i
$736$	1.56431	+	4.53354i	0.0576611	+	0.167108i
$737$	−2.44075	+	2.44075i	−0.0899062	+	0.0899062i
$738$	6.52237	+	3.37320i	0.240092	+	0.124169i
$739$	22.5252	−	10.2869i	0.828601	−	0.378409i	0.0444746	−	0.999011i	$-0.485839\pi$
$739$	22.5252	−	10.2869i	0.828601	−	0.378409i	0.784126	+	0.620601i	$0.213111\pi$
$740$	1.18161	−	0.427587i	0.0434370	−	0.0157184i
$741$	4.43496	+	3.24274i	0.162922	+	0.119125i
$742$	−29.6693	−	16.2007i	−1.08919	−	0.594745i
$743$	4.45738	+	20.4903i	0.163526	+	0.751715i	0.983731	+	0.179646i	$0.0574952\pi$
$743$	4.45738	+	20.4903i	0.163526	+	0.751715i	−0.820206	+	0.572069i	$0.806141\pi$
$744$	−3.42777	+	16.6575i	−0.125668	+	0.610694i
$745$	14.7857	−	12.5605i	0.541706	−	0.460182i
$746$	12.4549	+	19.3801i	0.456005	+	0.709557i
$747$	−11.0678	−	2.14799i	−0.404949	−	0.0785908i
$748$	−2.87176	−	2.14977i	−0.105002	−	0.0786033i
$749$	−46.2548	+	29.7262i	−1.69011	+	1.08617i
$750$	11.3222	+	15.7101i	0.413427	+	0.573654i
$751$	−7.95713	+	17.4237i	−0.290360	+	0.635800i	−0.997453	−	0.0713205i	$-0.977279\pi$
$751$	−7.95713	+	17.4237i	−0.290360	+	0.635800i	0.707094	+	0.707120i	$0.250006\pi$
$752$	8.23171	−	1.79070i	0.300179	−	0.0653001i
$753$	22.9822	+	6.46817i	0.837518	+	0.235713i
$754$	46.6559	−	40.4276i	1.69911	−	1.47229i
$755$	−10.1848	−	4.77230i	−0.370662	−	0.173682i
$756$	−21.4568	−	10.7926i	−0.780377	−	0.392524i
$757$	2.64779	−	1.98211i	0.0962356	−	0.0720411i	−0.550076	−	0.835114i	$-0.685401\pi$
$757$	2.64779	−	1.98211i	0.0962356	−	0.0720411i	0.646312	+	0.763073i	$0.276310\pi$
$758$	−4.76504	−	4.76504i	−0.173074	−	0.173074i
$759$	−18.5559	+	5.17774i	−0.673537	+	0.187940i
$760$	−0.916643	+	0.672287i	−0.0332501	+	0.0243864i
$761$	−32.6088	−	4.68843i	−1.18207	−	0.169956i	−0.476874	−	0.878972i	$-0.658230\pi$
$761$	−32.6088	−	4.68843i	−1.18207	−	0.169956i	−0.705192	+	0.709016i	$0.749139\pi$
$762$	2.54254	+	0.336405i	0.0921067	+	0.0121867i
$763$	−0.226443	+	0.123647i	−0.00819778	+	0.00447633i
$764$	−8.59006	−	9.91345i	−0.310777	−	0.358656i
$765$	10.1661	+	2.07649i	0.367557	+	0.0750756i
$766$	−19.1961	−	12.3366i	−0.693584	−	0.445740i
$767$	−20.9424	−	56.1487i	−0.756186	−	2.02741i
$768$	−0.506646	−	1.65629i	−0.0182820	−	0.0597664i
$769$	12.7910	+	19.9032i	0.461255	+	0.717727i	0.991498	−	0.130118i	$-0.0415357\pi$
$769$	12.7910	+	19.9032i	0.461255	+	0.717727i	−0.530243	+	0.847846i	$0.677899\pi$
$770$	23.9697	+	0.234704i	0.863808	+	0.00845816i
$771$	12.8537	−	4.95967i	0.462916	−	0.178618i
$772$	7.99951	+	1.74019i	0.287909	+	0.0626307i
$773$	−0.527127	+	0.0377008i	−0.0189594	+	0.00135601i	−0.0808157	−	0.996729i	$-0.525753\pi$
$773$	−0.527127	+	0.0377008i	−0.0189594	+	0.00135601i	0.0618562	+	0.998085i	$0.480298\pi$
$774$	0.248672	+	11.0469i	0.00893832	+	0.397072i
$775$	31.4168	+	37.7249i	1.12853	+	1.35512i
$776$	4.86664	+	16.5743i	0.174702	+	0.594981i
$777$	0.690372	+	4.44588i	0.0247669	+	0.159495i
$778$	−25.7965	+	14.0860i	−0.924850	+	0.505006i
$779$	0.516911	+	1.13188i	0.0185202	+	0.0405537i
$780$	−1.68870	+	24.1064i	−0.0604652	+	0.863146i
$781$	13.7472			0.491912
$782$	6.82184	−	2.91370i	0.243949	−	0.104194i
$783$	51.1063	+	5.59480i	1.82639	+	0.199942i
$784$	14.2196	+	2.04446i	0.507842	+	0.0730166i
$785$	−21.8049	+	39.0195i	−0.778250	+	1.39266i
$786$	12.0952	+	0.728362i	0.431421	+	0.0259798i
$787$	−2.26908	+	31.7259i	−0.0808839	+	1.13090i	0.781248	+	0.624221i	$0.214583\pi$
$787$	−2.26908	+	31.7259i	−0.0808839	+	1.13090i	−0.862132	+	0.506684i	$0.830871\pi$
$788$	6.16543	+	3.36658i	0.219634	+	0.119929i
$789$	35.7241	+	12.8684i	1.27181	+	0.458126i
$790$	−18.5464	+	3.84472i	−0.659850	+	0.136789i
$791$	8.85485	+	7.67277i	0.314842	+	0.272812i
$792$	6.76360	−	1.63157i	0.240334	−	0.0579755i
$793$	−9.98140	−	7.47198i	−0.354450	−	0.265338i
$794$	−0.471143	−	3.27687i	−0.0167203	−	0.116292i
$795$	−22.6498	+	17.0072i	−0.803307	+	0.603183i
$796$	−15.5288	+	17.9212i	−0.550404	+	0.635200i
$797$	−4.36563	−	11.7047i	−0.154639	−	0.414602i	0.836410	−	0.548105i	$-0.184650\pi$
$797$	−4.36563	−	11.7047i	−0.154639	−	0.414602i	−0.991049	+	0.133502i	$0.957378\pi$
$798$	−1.73232	−	3.68299i	−0.0613234	−	0.130377i
$799$	−3.67106	−	12.5025i	−0.129873	−	0.442307i
$800$	−4.64964	−	1.83872i	−0.164389	−	0.0650086i
$801$	−2.68637	−	16.1026i	−0.0949184	−	0.568957i
$802$	10.0377	−	26.9122i	0.354444	−	0.950302i
$803$	8.96291	−	6.70955i	0.316294	−	0.236775i
$804$	0.576276	+	2.51263i	0.0203237	+	0.0886135i
$805$	−25.2436	+	42.6594i	−0.889720	+	1.50355i
$806$			61.2638i			2.15793i
$807$	−15.9938	−	13.5466i	−0.563009	−	0.476864i
$808$	9.61683	+	3.58689i	0.338319	+	0.126186i
$809$	−14.4360	−	4.23880i	−0.507544	−	0.149028i	0.0179281	−	0.999839i	$-0.494293\pi$
$809$	−14.4360	−	4.23880i	−0.507544	−	0.149028i	−0.525472	+	0.850811i	$0.676111\pi$
$810$	−15.6759	+	12.6201i	−0.550795	+	0.443425i
$811$	−41.9129	+	12.3067i	−1.47176	+	0.432148i	−0.916671	−	0.399644i	$-0.869134\pi$
$811$	−41.9129	+	12.3067i	−1.47176	+	0.432148i	−0.555089	+	0.831791i	$0.687316\pi$
$812$	−44.6888	+	9.72146i	−1.56827	+	0.341156i
$813$	0.577780	+	0.877181i	0.0202636	+	0.0307641i
$814$	−0.984982	−	0.853492i	−0.0345236	−	0.0299149i
$815$	−0.456050	+	1.18709i	−0.0159747	+	0.0415818i
$816$	−2.49947	+	0.964430i	−0.0874989	+	0.0337618i
$817$	−1.12211	+	1.49897i	−0.0392578	+	0.0524423i
$818$	−26.8631	−	5.84370i	−0.939245	−	0.204320i
$819$	−83.5454	−	22.5018i	−2.91931	−	0.786275i
$820$	−3.00395	+	4.57512i	−0.104903	+	0.159770i
$821$	5.57317	−	8.67202i	0.194505	−	0.302656i	−0.730278	−	0.683150i	$-0.760610\pi$
$821$	5.57317	−	8.67202i	0.194505	−	0.302656i	0.924783	+	0.380494i	$0.124246\pi$
$822$	23.2072	+	6.53150i	0.809445	+	0.227812i
$823$	−11.1949	−	0.800672i	−0.390228	−	0.0279097i	−0.125153	−	0.992137i	$-0.539942\pi$
$823$	−11.1949	−	0.800672i	−0.390228	−	0.0279097i	−0.265075	+	0.964228i	$0.585397\pi$
$824$	4.48961	+	1.31827i	0.156403	+	0.0459241i
$825$	8.49545	−	18.1997i	0.295774	−	0.633633i
$826$	−6.31807	+	43.9431i	−0.219834	+	1.52898i
$827$	−17.3033	+	17.3033i	−0.601696	+	0.601696i	−0.940763	−	0.339066i	$-0.889889\pi$
$827$	−17.3033	+	17.3033i	−0.601696	+	0.601696i	0.339066	+	0.940763i	$0.389889\pi$
$828$	−4.08423	+	13.7956i	−0.141937	+	0.479431i
$829$			24.0295i			0.834579i	0.908774	+	0.417290i	$0.137020\pi$
$829$			24.0295i			0.834579i	−0.908774	+	0.417290i	$0.862980\pi$
$830$	2.44634	−	8.03940i	0.0849135	−	0.279052i
$831$	1.13200	+	1.47723i	0.0392687	+	0.0512446i
$832$	−2.99027	−	5.47627i	−0.103669	−	0.189855i
$833$	1.58519	−	22.1639i	0.0549237	−	0.767934i
$834$	2.83151	−	1.58774i	0.0980470	−	0.0549790i
$835$	−45.8239	+	2.82671i	−1.58580	+	0.0978224i
$836$	1.07247	+	0.489781i	0.0370921	+	0.0169394i
$837$	−37.4083	+	34.6932i	−1.29302	+	1.19917i
$838$	−4.89462	+	22.5002i	−0.169082	+	0.777257i
$839$	0.958127	+	6.66392i	0.0330782	+	0.230064i	0.999654	−	0.0263185i	$-0.00837842\pi$
$839$	0.958127	+	6.66392i	0.0330782	+	0.230064i	−0.966575	+	0.256383i	$0.917469\pi$
$840$	9.65660	−	15.0744i	0.333184	−	0.520115i
$841$	57.9579	−	37.2473i	1.99855	−	1.28439i
$842$	−0.565403	−	7.90537i	−0.0194851	−	0.272437i
$843$	25.9169	−	17.0709i	0.892626	−	0.587954i
$844$	−3.19158	+	4.96619i	−0.109859	+	0.170943i
$845$	7.68963	+	57.4718i	0.264531	+	1.97709i
$846$	23.2193	+	9.97863i	0.798296	+	0.343072i
$847$	12.4525	+	22.8051i	0.427873	+	0.783592i
$848$	2.55573	−	6.85217i	0.0877640	−	0.235305i
$849$	33.3772	−	2.76503i	1.14550	−	0.0948957i
$850$	−2.32376	+	7.37647i	−0.0797044	+	0.253011i
$851$	2.54770	−	0.879090i	0.0873341	−	0.0301348i
$852$	5.45311	−	8.69890i	0.186820	−	0.298019i
$853$	16.3511	+	21.8426i	0.559852	+	0.747875i	0.987766	−	0.155944i	$-0.0498421\pi$
$853$	16.3511	+	21.8426i	0.559852	+	0.747875i	−0.427913	+	0.903820i	$0.640751\pi$
$854$	3.83707	+	8.40202i	0.131302	+	0.287511i
$855$	−3.40998	+	0.0433616i	−0.116619	+	0.00148293i
$856$	−7.78968	−	8.98977i	−0.266246	−	0.307264i
$857$	−16.9668	+	31.0724i	−0.579575	+	1.06141i	0.409263	+	0.912416i	$0.365786\pi$
$857$	−16.9668	+	31.0724i	−0.579575	+	1.06141i	−0.988838	+	0.148995i	$0.952396\pi$
$858$	22.6803	−	10.6678i	0.774293	−	0.364193i
$859$	−1.42289	−	0.649813i	−0.0485484	−	0.0221713i	0.390993	−	0.920394i	$-0.372132\pi$
$859$	−1.42289	−	0.649813i	−0.0485484	−	0.0221713i	−0.439541	+	0.898222i	$0.644859\pi$
$860$	−8.20881	−	0.667952i	−0.279918	−	0.0227770i
$861$	−14.0117	−	13.6998i	−0.477517	−	0.466889i
$862$	−21.9796	+	29.3613i	−0.748629	+	1.00005i
$863$	−19.1290	+	25.5533i	−0.651158	+	0.869845i	−0.997672	−	0.0681998i	$-0.978274\pi$
$863$	−19.1290	+	25.5533i	−0.651158	+	0.869845i	0.346514	+	0.938045i	$0.387365\pi$
$864$	1.65050	−	4.92705i	0.0561513	−	0.167622i
$865$	25.9076	+	2.10810i	0.880884	+	0.0716776i
$866$	−4.36067	−	1.99145i	−0.148181	−	0.0676722i
$867$	−10.7687	−	22.8948i	−0.365725	−	0.777549i
$868$	21.7508	−	39.8337i	0.738271	−	1.35204i
$869$	12.8647	+	14.8466i	0.436404	+	0.503637i
$870$	−8.09074	+	37.4561i	−0.274302	+	1.26988i
$871$	3.85772	+	8.44723i	0.130714	+	0.286224i
$872$	−0.0334496	−	0.0446835i	−0.00113275	−	0.00151317i
$873$	−17.0126	+	48.9498i	−0.575790	+	1.65670i
$874$	−1.98731	+	1.41235i	−0.0672219	+	0.0477734i
$875$	−16.6301	−	48.9302i	−0.562199	−	1.65414i
$876$	−0.690323	−	8.33301i	−0.0233239	−	0.281546i
$877$	5.13405	−	13.7649i	0.173365	−	0.464808i	−0.820987	−	0.570947i	$-0.806576\pi$
$877$	5.13405	−	13.7649i	0.173365	−	0.464808i	0.994351	+	0.106139i	$0.0338488\pi$
$878$	−2.71015	−	4.96327i	−0.0914632	−	0.167502i
$879$	11.4392	+	8.36407i	0.385834	+	0.282113i
$880$	0.687735	+	5.14009i	0.0231835	+	0.173272i
$881$	25.8702	−	40.2548i	0.871588	−	1.35622i	−0.0620772	−	0.998071i	$-0.519772\pi$
$881$	25.8702	−	40.2548i	0.871588	−	1.35622i	0.933665	−	0.358146i	$-0.116591\pi$
$882$	31.1525	+	29.7809i	1.04896	+	1.00278i
$883$	1.92485	+	26.9130i	0.0647765	+	0.905694i	0.921118	+	0.389284i	$0.127277\pi$
$883$	1.92485	+	26.9130i	0.0647765	+	0.905694i	−0.856341	+	0.516410i	$0.827268\pi$
$884$	−8.11897	+	5.21774i	−0.273070	+	0.175492i
$885$	31.3224	+	20.0650i	1.05289	+	0.674478i
$886$	−2.06922	−	14.3918i	−0.0695169	−	0.483501i
$887$	0.443176	−	2.03725i	0.0148804	−	0.0684040i	−0.969108	−	0.246637i	$-0.920674\pi$
$887$	0.443176	−	2.03725i	0.0148804	−	0.0684040i	0.983988	+	0.178233i	$0.0570381\pi$
$888$	−0.930785	+	0.284719i	−0.0312351	+	0.00955454i
$889$	−6.22589	−	2.84327i	−0.208810	−	0.0953602i
$890$	12.1449	−	0.749179i	0.407099	−	0.0251125i
$891$	19.3575	+	7.80774i	0.648502	+	0.261569i
$892$	−1.54694	+	21.6291i	−0.0517954	+	0.724194i
$893$	2.05245	+	3.75878i	0.0686825	+	0.125783i
$894$	−11.9281	+	9.14054i	−0.398937	+	0.305705i
$895$	−9.87552	+	32.4540i	−0.330102	+	1.08482i
$896$			4.62231i			0.154421i
$897$	−4.39427	+	51.6425i	−0.146720	+	1.72429i
$898$	−20.5371	+	20.5371i	−0.685330	+	0.685330i
$899$	−13.8256	+	96.1594i	−0.461111	+	3.20709i
$900$	−8.14647	−	12.5950i	−0.271549	−	0.419835i
$901$	−10.8537	−	3.18694i	−0.361590	−	0.106172i
$902$	5.66218	+	0.404967i	0.188530	+	0.0134839i
$903$	7.98887	−	28.3854i	0.265853	−	0.944608i
$904$	−1.37042	+	2.13241i	−0.0455794	+	0.0709229i
$905$	−15.8807	+	24.1869i	−0.527893	+	0.803999i
$906$	7.69304	+	4.08901i	0.255584	+	0.135848i
$907$	−48.8169	−	10.6195i	−1.62094	−	0.352614i	−0.691727	−	0.722159i	$-0.743150\pi$
$907$	−48.8169	−	10.6195i	−1.62094	−	0.352614i	−0.929213	+	0.369545i	$0.879513\pi$
$908$	5.50844	−	7.35842i	0.182804	−	0.244198i
$909$	17.2261	+	25.5226i	0.571354	+	0.846531i
$910$	23.1276	−	60.2005i	0.766671	−	1.99563i
$911$	33.8840	+	29.3607i	1.12263	+	0.972762i	0.999807	−	0.0196668i	$-0.00626052\pi$
$911$	33.8840	+	29.3607i	1.12263	+	0.972762i	0.122821	+	0.992429i	$0.460806\pi$
$912$	0.735340	−	0.484353i	0.0243495	−	0.0160385i
$913$	−8.51662	+	1.85268i	−0.281859	+	0.0613146i
$914$	31.2652	−	9.18030i	1.03416	−	0.303657i
$915$	7.73934	−	0.0113149i	0.255855	−	0.000374058i
$916$	−9.78735	−	2.87383i	−0.323383	−	0.0949539i
$917$	−30.2980	−	11.3006i	−1.00053	−	0.373178i
$918$	−7.78371	−	2.00276i	−0.256901	−	0.0661010i
$919$		−	17.3596i		−	0.572640i	−0.958134	−	0.286320i	$-0.907568\pi$
$919$		−	17.3596i		−	0.572640i	0.958134	−	0.286320i	$-0.0924321\pi$
$920$	−9.91230	−	4.09224i	−0.326799	−	0.134917i
$921$	13.1272	−	3.01075i	0.432556	−	0.0992077i
$922$	−27.2377	+	20.3899i	−0.897025	+	0.671504i
$923$	12.9249	−	34.6529i	0.425427	−	1.14061i
$924$	−18.5342	−	1.11611i	−0.609729	−	0.0367173i
$925$	−1.03330	+	2.61295i	−0.0339748	+	0.0859132i
$926$	9.95293	+	33.8966i	0.327074	+	1.11391i
$927$	8.66310	+	11.0454i	0.284534	+	0.362778i
$928$	−3.45766	−	9.27034i	−0.113503	−	0.304314i
$929$	−12.3573	+	14.2611i	−0.405430	+	0.467891i	−0.921344	−	0.388749i	$-0.872907\pi$
$929$	−12.3573	+	14.2611i	−0.405430	+	0.467891i	0.515913	+	0.856641i	$0.327453\pi$
$930$	−22.8337	−	30.4094i	−0.748746	−	0.997165i
$931$	1.03935	+	7.22881i	0.0340632	+	0.236915i
$932$	−1.67895	−	1.25685i	−0.0549959	−	0.0411694i
$933$	−30.9551	+	0.348364i	−1.01342	+	0.0114049i
$934$	−8.04320	−	6.96947i	−0.263181	−	0.228048i
$935$	7.85438	−	1.62824i	0.256866	−	0.0532491i
$936$	2.24627	−	18.5832i	0.0734217	−	0.607411i
$937$	−7.11549	−	3.88535i	−0.232453	−	0.126929i	0.358802	−	0.933414i	$-0.383185\pi$
$937$	−7.11549	−	3.88535i	−0.232453	−	0.126929i	−0.591255	+	0.806485i	$0.701367\pi$
$938$	0.490780	−	6.86201i	0.0160245	−	0.224052i
$939$	0.789883	−	13.1168i	0.0257769	−	0.428051i
$940$	−9.18913	+	16.4438i	−0.299716	+	0.536337i
$941$	−8.64752	−	1.24333i	−0.281901	−	0.0405313i	−8.60867e−5	−	1.00000i	$-0.500027\pi$
$941$	−8.64752	−	1.24333i	−0.281901	−	0.0405313i	−0.281815	+	0.959469i	$0.590936\pi$
$942$	18.3899	−	29.3359i	0.599175	−	0.955815i
$943$	−6.58871	+	9.71514i	−0.214558	+	0.316368i
$944$	−9.60450			−0.312600
$945$	49.8560	−	19.9691i	1.62181	−	0.649594i
$946$	3.54854	+	7.77021i	0.115373	+	0.252631i
$947$	17.7750	−	9.70586i	0.577609	−	0.315398i	−0.163756	−	0.986501i	$-0.552361\pi$
$947$	17.7750	−	9.70586i	0.577609	−	0.315398i	0.741364	+	0.671103i	$0.234179\pi$
$948$	14.4976	−	2.25124i	0.470861	−	0.0731170i
$949$	−8.48619	−	28.9013i	−0.275473	−	0.938176i
$950$	0.230946	−	2.53134i	0.00749287	−	0.0821275i
$951$	4.03223	+	0.829749i	0.130754	+	0.0269065i
$952$	7.13143	−	0.510050i	0.231131	−	0.0165308i
$953$	−11.5197	−	2.50595i	−0.373158	−	0.0811756i	0.0220753	−	0.999756i	$-0.492973\pi$
$953$	−11.5197	−	2.50595i	−0.373158	−	0.0811756i	−0.395233	+	0.918581i	$0.629336\pi$
$954$	18.1853	−	12.2739i	0.588772	−	0.397383i
$955$	29.3299	+	0.287190i	0.949095	+	0.00929327i
$956$	−1.39110	−	2.16459i	−0.0449914	−	0.0700080i
$957$	38.0063	−	11.6258i	1.22857	−	0.375809i
$958$	9.17857	+	24.6087i	0.296546	+	0.795071i
$959$	−54.1255	−	34.7843i	−1.74780	−	1.12325i
$960$	3.52534	+	1.60374i	0.113780	+	0.0517606i
$961$	−42.8327	−	49.4316i	−1.38170	−	1.59457i
$962$	−3.07749	+	1.68044i	−0.0992222	+	0.0541794i
$963$	−3.34618	−	35.5283i	−0.107829	−	1.14488i
$964$	−4.50073	−	0.647107i	−0.144959	−	0.0208419i
$965$	−14.7612	+	10.8262i	−0.475181	+	0.348509i
$966$	21.1921	−	32.0178i	0.681843	−	1.03015i
$967$	−17.1862	−	17.1862i	−0.552671	−	0.552671i	0.374540	−	0.927211i	$-0.377801\pi$
$967$	−17.1862	−	17.1862i	−0.552671	−	0.552671i	−0.927211	+	0.374540i	$0.877801\pi$
$968$	−4.50008	+	3.36872i	−0.144638	+	0.108275i
$969$	−0.828413	−	1.08106i	−0.0266125	−	0.0347285i
$970$	−34.9765	−	16.3890i	−1.12303	−	0.526219i
$971$	−30.3073	+	26.2614i	−0.972607	+	0.842769i	−0.987580	−	0.157119i	$-0.949779\pi$
$971$	−30.3073	+	26.2614i	−0.972607	+	0.842769i	0.0149728	+	0.999888i	$0.495234\pi$
$972$	12.6191	−	9.15191i	0.404759	−	0.293548i
$973$	−8.46535	+	1.84152i	−0.271387	+	0.0590366i
$974$	2.99675	−	6.56196i	0.0960219	−	0.210259i
$975$	−37.8893	−	38.5258i	−1.21343	−	1.23381i
$976$	−1.68107	+	1.08036i	−0.0538097	+	0.0345814i
$977$	19.9769	+	14.9545i	0.639118	+	0.478438i	0.869021	−	0.494776i	$-0.164750\pi$
$977$	19.9769	+	14.9545i	0.639118	+	0.478438i	−0.229903	+	0.973214i	$0.573841\pi$
$978$	0.399089	−	0.900567i	0.0127615	−	0.0287970i
$979$	−6.82312	−	10.6170i	−0.218068	−	0.339320i
$980$	−24.4817	+	20.7973i	−0.782038	+	0.664346i
$981$	−0.00376844	−	0.167407i	−0.000120317	−	0.00534491i
$982$	3.25813	+	14.9774i	0.103971	+	0.477947i
$983$	−22.3212	−	12.1883i	−0.711937	−	0.388747i	0.0820938	−	0.996625i	$-0.473839\pi$
$983$	−22.3212	−	12.1883i	−0.711937	−	0.388747i	−0.794031	+	0.607878i	$0.792021\pi$
$984$	2.50228	−	3.42226i	0.0797697	−	0.109098i
$985$	−14.7704	+	5.34492i	−0.470623	+	0.170303i
$986$	−13.9210	+	6.35750i	−0.443335	+	0.202464i
$987$	−51.4654	−	43.5907i	−1.63816	−	1.38751i
$988$	2.24292	−	2.24292i	0.0713569	−	0.0713569i
$989$	−17.5826	−	1.69560i	−0.559093	−	0.0539169i
$990$	−7.28178	+	13.7484i	−0.231430	+	0.436951i
$991$	0.964875	−	6.71086i	0.0306503	−	0.213177i	−0.968741	−	0.248076i	$-0.920202\pi$
$991$	0.964875	−	6.71086i	0.0306503	−	0.213177i	0.999391	+	0.0348986i	$0.0111108\pi$
$992$	9.19965	+	3.43129i	0.292089	+	0.108944i
$993$	−42.0457	+	37.2694i	−1.33428	+	1.18271i
$994$	−20.7067	+	17.9425i	−0.656778	+	0.569101i
$995$	−7.03188	−	52.5559i	−0.222926	−	1.66613i
$996$	−2.20596	+	6.12402i	−0.0698987	+	0.194047i
$997$	32.6305	−	12.1705i	1.03342	−	0.385445i	0.225190	−	0.974315i	$-0.427700\pi$
$997$	32.6305	−	12.1705i	1.03342	−	0.385445i	0.808228	+	0.588870i	$0.200427\pi$
$998$	−16.1611	+	1.15587i	−0.511572	+	0.0365883i
$999$	−2.76885	−	0.927530i	−0.0876024	−	0.0293458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.x.a.77.3	✓	960
3.2	odd	2	inner	690.2.x.a.77.29	yes	960
5.3	odd	4	inner	690.2.x.a.353.14	yes	960
15.8	even	4	inner	690.2.x.a.353.41	yes	960
23.3	even	11	inner	690.2.x.a.647.41	yes	960
69.26	odd	22	inner	690.2.x.a.647.14	yes	960
115.3	odd	44	inner	690.2.x.a.233.29	yes	960
345.233	even	44	inner	690.2.x.a.233.3	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.x.a.77.3	✓	960	1.1	even	1	trivial
690.2.x.a.77.29	yes	960	3.2	odd	2	inner
690.2.x.a.233.3	yes	960	345.233	even	44	inner
690.2.x.a.233.29	yes	960	115.3	odd	44	inner
690.2.x.a.353.14	yes	960	5.3	odd	4	inner
690.2.x.a.353.41	yes	960	15.8	even	4	inner
690.2.x.a.647.14	yes	960	69.26	odd	22	inner
690.2.x.a.647.41	yes	960	23.3	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.599278 - 0.800541i) q^{2} +(-1.71709 - 0.227188i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.19043 - 1.89285i) q^{5} +(0.847138 + 1.51075i) q^{6} +(-0.982544 - 4.51668i) q^{7} +(0.936950 - 0.349464i) q^{8} +(2.89677 + 0.780204i) q^{9} +O(q^{10})\)	\(q+(-0.599278 - 0.800541i) q^{2} +(-1.71709 - 0.227188i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.19043 - 1.89285i) q^{5} +(0.847138 + 1.51075i) q^{6} +(-0.982544 - 4.51668i) q^{7} +(0.936950 - 0.349464i) q^{8} +(2.89677 + 0.780204i) q^{9} +(-0.801902 + 2.08733i) q^{10} +(2.29560 - 0.330057i) q^{11} +(0.701745 - 1.58353i) q^{12} +(1.32630 - 6.09690i) q^{13} +(-3.02697 + 3.49331i) q^{14} +(1.61404 + 3.52063i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(-0.741286 + 1.35756i) q^{17} +(-1.11138 - 2.78654i) q^{18} +(0.143225 - 0.487778i) q^{19} +(2.15156 - 0.608936i) q^{20} +(0.660975 + 7.97875i) q^{21} +(-1.63992 - 1.63992i) q^{22} +(4.63358 - 1.23690i) q^{23} +(-1.68822 + 0.387196i) q^{24} +(-2.16574 + 4.50662i) q^{25} +(-5.67564 + 2.59198i) q^{26} +(-4.79675 - 1.99779i) q^{27} +(4.61054 + 0.329752i) q^{28} +(-9.49339 + 2.78751i) q^{29} +(1.85115 - 3.40195i) q^{30} +(4.07885 - 8.93143i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(-4.01672 + 0.0452037i) q^{33} +(1.53102 - 0.220128i) q^{34} +(-7.37973 + 7.23661i) q^{35} +(-1.56471 + 2.55962i) q^{36} +(0.560536 - 0.0400903i) q^{37} +(-0.476318 + 0.177657i) q^{38} +(-3.66251 + 10.1676i) q^{39} +(-1.77686 - 1.35749i) q^{40} +(-1.84982 + 1.60288i) q^{41} +(5.99121 - 5.31063i) q^{42} +(-3.45100 - 1.28716i) q^{43} +(-0.330057 + 2.29560i) q^{44} +(-1.97161 - 6.41192i) q^{45} +(-3.76699 - 2.96813i) q^{46} +(-5.95683 + 5.95683i) q^{47} +(1.32168 + 1.11945i) q^{48} +(-13.0676 + 5.96776i) q^{49} +(4.90561 - 0.966952i) q^{50} +(1.58128 - 2.16264i) q^{51} +(5.47627 + 2.99027i) q^{52} +(1.55455 + 7.14614i) q^{53} +(1.27527 + 5.03723i) q^{54} +(-3.35750 - 3.95230i) q^{55} +(-2.49901 - 3.88854i) q^{56} +(-0.356746 + 0.805018i) q^{57} +(7.92070 + 5.92936i) q^{58} +(8.07982 - 5.19258i) q^{59} +(-3.83275 + 0.556787i) q^{60} +(0.830120 - 1.81771i) q^{61} +(-9.59434 + 2.08712i) q^{62} +(0.677727 - 13.8504i) q^{63} +(0.755750 - 0.654861i) q^{64} +(-13.1194 + 4.74747i) q^{65} +(2.44332 + 3.18846i) q^{66} +(-1.19147 + 0.891924i) q^{67} +(-1.09373 - 1.09373i) q^{68} +(-8.23727 + 1.07117i) q^{69} +(10.2157 + 1.57104i) q^{70} +(5.86721 + 0.843577i) q^{71} +(2.98678 - 0.281306i) q^{72} +(4.23704 - 2.31360i) q^{73} +(-0.368011 - 0.424707i) q^{74} +(4.74261 - 7.24622i) q^{75} +(0.427669 + 0.274846i) q^{76} +(-3.74629 - 10.0442i) q^{77} +(10.3344 - 3.16121i) q^{78} +(4.57951 + 7.12586i) q^{79} +(-0.0218939 + 2.23596i) q^{80} +(7.78256 + 4.52014i) q^{81} +(2.39173 + 0.520289i) q^{82} +(-3.74852 + 0.268100i) q^{83} +(-7.84177 - 1.61367i) q^{84} +(3.45211 - 0.212949i) q^{85} +(1.03768 + 3.53403i) q^{86} +(16.9343 - 2.62961i) q^{87} +(2.03552 - 1.11148i) q^{88} +(-2.26057 - 4.94995i) q^{89} +(-3.95147 + 5.42088i) q^{90} -28.8409 q^{91} +(-0.118633 + 4.79436i) q^{92} +(-9.03285 + 14.4094i) q^{93} +(8.33848 + 1.19889i) q^{94} +(-1.09379 + 0.309565i) q^{95} +(0.104114 - 1.72892i) q^{96} +(-1.23231 + 17.2300i) q^{97} +(12.6086 + 6.88479i) q^{98} +(6.90733 + 0.834934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) \) 960 * q + 8 * q^3 + 8 * q^6	\( 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) \) 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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