LMFDB - Embedded newform 390.2.s.c.77.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(77,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("390.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.s (of order $4$, degree $2$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.7
Character	$\chi$	$=$	390.77
Dual form			390.2.s.c.233.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.72725 + 0.128848i) q^{3} +1.00000i q^{4} +(1.56114 + 1.60089i) q^{5} +(-1.31246 - 1.13024i) q^{6} +(0.236462 - 0.236462i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.96680 - 0.445105i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.72725 + 0.128848i) q^{3} +1.00000i q^{4} +(1.56114 + 1.60089i) q^{5} +(-1.31246 - 1.13024i) q^{6} +(0.236462 - 0.236462i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.96680 - 0.445105i) q^{9} +(-0.0281051 + 2.23589i) q^{10} +2.01226 q^{11} +(-0.128848 - 1.72725i) q^{12} +(-0.965701 + 3.47382i) q^{13} +0.334408 q^{14} +(-2.90275 - 2.56399i) q^{15} -1.00000 q^{16} +(-2.69197 + 2.69197i) q^{17} +(2.41258 + 1.78311i) q^{18} -8.01600 q^{19} +(-1.60089 + 1.56114i) q^{20} +(-0.377962 + 0.438897i) q^{21} +(1.42288 + 1.42288i) q^{22} +(6.23031 + 6.23031i) q^{23} +(1.13024 - 1.31246i) q^{24} +(-0.125680 + 4.99842i) q^{25} +(-3.13922 + 1.77351i) q^{26} +(-5.06705 + 1.15107i) q^{27} +(0.236462 + 0.236462i) q^{28} +4.55580 q^{29} +(-0.239545 - 3.86557i) q^{30} -7.05293i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.47567 + 0.259274i) q^{33} -3.80703 q^{34} +(0.747699 + 0.00939855i) q^{35} +(0.445105 + 2.96680i) q^{36} +(1.19742 - 1.19742i) q^{37} +(-5.66817 - 5.66817i) q^{38} +(1.22042 - 6.12459i) q^{39} +(-2.23589 - 0.0281051i) q^{40} +7.90181 q^{41} +(-0.577606 + 0.0430876i) q^{42} +(2.76440 - 2.76440i) q^{43} +2.01226i q^{44} +(5.34415 + 4.05464i) q^{45} +8.81099i q^{46} +(-2.04369 - 2.04369i) q^{47} +(1.72725 - 0.128848i) q^{48} +6.88817i q^{49} +(-3.62329 + 3.44555i) q^{50} +(4.30286 - 4.99657i) q^{51} +(-3.47382 - 0.965701i) q^{52} +(-6.83014 - 6.83014i) q^{53} +(-4.39688 - 2.76902i) q^{54} +(3.14141 + 3.22139i) q^{55} +0.334408i q^{56} +(13.8457 - 1.03284i) q^{57} +(3.22144 + 3.22144i) q^{58} -12.3272i q^{59} +(2.56399 - 2.90275i) q^{60} +5.48892 q^{61} +(4.98717 - 4.98717i) q^{62} +(0.596284 - 0.806784i) q^{63} -1.00000i q^{64} +(-7.06879 + 3.87714i) q^{65} +(-2.64101 - 2.27434i) q^{66} +(-4.26617 + 4.26617i) q^{67} +(-2.69197 - 2.69197i) q^{68} +(-11.5641 - 9.95855i) q^{69} +(0.522057 + 0.535349i) q^{70} +9.88936 q^{71} +(-1.78311 + 2.41258i) q^{72} +(2.59128 + 2.59128i) q^{73} +1.69340 q^{74} +(-0.426954 - 8.64972i) q^{75} -8.01600i q^{76} +(0.475822 - 0.475822i) q^{77} +(5.19370 - 3.46777i) q^{78} -10.6675i q^{79} +(-1.56114 - 1.60089i) q^{80} +(8.60376 - 2.64107i) q^{81} +(5.58743 + 5.58743i) q^{82} +(2.98429 - 2.98429i) q^{83} +(-0.438897 - 0.377962i) q^{84} +(-8.51210 - 0.106997i) q^{85} +3.90946 q^{86} +(-7.86902 + 0.587005i) q^{87} +(-1.42288 + 1.42288i) q^{88} -1.02859i q^{89} +(0.911824 + 6.64594i) q^{90} +(0.593074 + 1.04978i) q^{91} +(-6.23031 + 6.23031i) q^{92} +(0.908753 + 12.1822i) q^{93} -2.89021i q^{94} +(-12.5141 - 12.8327i) q^{95} +(1.31246 + 1.13024i) q^{96} +(10.9826 - 10.9826i) q^{97} +(-4.87067 + 4.87067i) q^{98} +(5.96995 - 0.895665i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} + 12 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 + 12 * q^9	$ 24 q + 4 q^{3} + 12 q^{9} + 4 q^{10} - 8 q^{12} - 8 q^{13} + 16 q^{14} - 24 q^{16} - 52 q^{17} + 16 q^{22} + 16 q^{23} + 16 q^{25} - 56 q^{27} + 80 q^{29} + 8 q^{30} - 20 q^{35} + 16 q^{38} + 32 q^{39} - 48 q^{42} + 28 q^{43} - 4 q^{48} - 20 q^{51} - 8 q^{52} - 72 q^{53} + 24 q^{55} - 64 q^{61} + 32 q^{62} + 12 q^{65} + 8 q^{66} - 52 q^{68} + 16 q^{69} + 120 q^{74} + 24 q^{75} - 32 q^{77} - 64 q^{78} + 12 q^{81} + 32 q^{82} - 16 q^{88} - 44 q^{90} + 64 q^{91} - 16 q^{92} - 96 q^{95}+O(q^{100}) $ 24 * q + 4 * q^3 + 12 * q^9 + 4 * q^10 - 8 * q^12 - 8 * q^13 + 16 * q^14 - 24 * q^16 - 52 * q^17 + 16 * q^22 + 16 * q^23 + 16 * q^25 - 56 * q^27 + 80 * q^29 + 8 * q^30 - 20 * q^35 + 16 * q^38 + 32 * q^39 - 48 * q^42 + 28 * q^43 - 4 * q^48 - 20 * q^51 - 8 * q^52 - 72 * q^53 + 24 * q^55 - 64 * q^61 + 32 * q^62 + 12 * q^65 + 8 * q^66 - 52 * q^68 + 16 * q^69 + 120 * q^74 + 24 * q^75 - 32 * q^77 - 64 * q^78 + 12 * q^81 + 32 * q^82 - 16 * q^88 - 44 * q^90 + 64 * q^91 - 16 * q^92 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.72725	+	0.128848i	−0.997229	+	0.0743902i
$3$	−1.72725	+	0.128848i	−0.997229	+	0.0743902i
$4$			1.00000i			0.500000i
$5$	1.56114	+	1.60089i	0.698163	+	0.715939i
$5$	1.56114	+	1.60089i	0.698163	+	0.715939i
$6$	−1.31246	−	1.13024i	−0.535810	−	0.461419i
$7$	0.236462	−	0.236462i	0.0893742	−	0.0893742i	−0.661006	−	0.750380i	$-0.729870\pi$
$7$	0.236462	−	0.236462i	0.0893742	−	0.0893742i	0.750380	+	0.661006i	$0.229870\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.96680	−	0.445105i	0.988932	−	0.148368i
$10$	−0.0281051	+	2.23589i	−0.00888760	+	0.707051i
$11$	2.01226			0.606718			0.303359	−	0.952876i	$-0.401892\pi$
$11$	2.01226			0.606718			0.303359	+	0.952876i	$0.401892\pi$
$12$	−0.128848	−	1.72725i	−0.0371951	−	0.498615i
$13$	−0.965701	+	3.47382i	−0.267837	+	0.963464i
$13$	−0.965701	+	3.47382i	−0.267837	+	0.963464i
$14$	0.334408			0.0893742
$15$	−2.90275	−	2.56399i	−0.749488	−	0.662018i
$16$	−1.00000			−0.250000
$17$	−2.69197	+	2.69197i	−0.652900	+	0.652900i	−0.953690	−	0.300791i	$-0.902749\pi$
$17$	−2.69197	+	2.69197i	−0.652900	+	0.652900i	0.300791	+	0.953690i	$0.402749\pi$
$18$	2.41258	+	1.78311i	0.568650	+	0.420282i
$19$	−8.01600			−1.83900			−0.919499	−	0.393093i	$-0.871405\pi$
$19$	−8.01600			−1.83900			−0.919499	+	0.393093i	$0.871405\pi$
$20$	−1.60089	+	1.56114i	−0.357969	+	0.349082i
$21$	−0.377962	+	0.438897i	−0.0824780	+	0.0957751i
$22$	1.42288	+	1.42288i	0.303359	+	0.303359i
$23$	6.23031	+	6.23031i	1.29911	+	1.29911i	0.928981	+	0.370128i	$0.120686\pi$
$23$	6.23031	+	6.23031i	1.29911	+	1.29911i	0.370128	+	0.928981i	$0.379314\pi$
$24$	1.13024	−	1.31246i	0.230710	−	0.267905i
$25$	−0.125680	+	4.99842i	−0.0251360	+	0.999684i
$26$	−3.13922	+	1.77351i	−0.615651	+	0.347813i
$27$	−5.06705	+	1.15107i	−0.975155	+	0.221524i
$28$	0.236462	+	0.236462i	0.0446871	+	0.0446871i
$29$	4.55580			0.845991			0.422996	−	0.906132i	$-0.360979\pi$
$29$	4.55580			0.845991			0.422996	+	0.906132i	$0.360979\pi$
$30$	−0.239545	−	3.86557i	−0.0437347	−	0.705753i
$31$		−	7.05293i		−	1.26674i	−0.773848	−	0.633372i	$-0.781670\pi$
$31$		−	7.05293i		−	1.26674i	0.773848	−	0.633372i	$-0.218330\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−3.47567	+	0.259274i	−0.605037	+	0.0451339i
$34$	−3.80703			−0.652900
$35$	0.747699	+	0.00939855i	0.126384	+	0.00158864i
$36$	0.445105	+	2.96680i	0.0741841	+	0.494466i
$37$	1.19742	−	1.19742i	0.196854	−	0.196854i	−0.601796	−	0.798650i	$-0.705548\pi$
$37$	1.19742	−	1.19742i	0.196854	−	0.196854i	0.798650	+	0.601796i	$0.205548\pi$
$38$	−5.66817	−	5.66817i	−0.919499	−	0.919499i
$39$	1.22042	−	6.12459i	0.195423	−	0.980719i
$40$	−2.23589	−	0.0281051i	−0.353525	−	0.00444380i
$41$	7.90181			1.23406			0.617028	−	0.786941i	$-0.288337\pi$
$41$	7.90181			1.23406			0.617028	+	0.786941i	$0.288337\pi$
$42$	−0.577606	+	0.0430876i	−0.0891265	+	0.00664857i
$43$	2.76440	−	2.76440i	0.421568	−	0.421568i	−0.464176	−	0.885743i	$-0.653649\pi$
$43$	2.76440	−	2.76440i	0.421568	−	0.421568i	0.885743	+	0.464176i	$0.153649\pi$
$44$			2.01226i			0.303359i
$45$	5.34415	+	4.05464i	0.796659	+	0.604429i
$46$			8.81099i			1.29911i
$47$	−2.04369	−	2.04369i	−0.298102	−	0.298102i	0.542168	−	0.840270i	$-0.317604\pi$
$47$	−2.04369	−	2.04369i	−0.298102	−	0.298102i	−0.840270	+	0.542168i	$0.817604\pi$
$48$	1.72725	−	0.128848i	0.249307	−	0.0185976i
$49$			6.88817i			0.984025i
$50$	−3.62329	+	3.44555i	−0.512410	+	0.487274i
$51$	4.30286	−	4.99657i	0.602521	−	0.699660i
$52$	−3.47382	−	0.965701i	−0.481732	−	0.133919i
$53$	−6.83014	−	6.83014i	−0.938192	−	0.938192i	0.0600063	−	0.998198i	$-0.480888\pi$
$53$	−6.83014	−	6.83014i	−0.938192	−	0.938192i	−0.998198	+	0.0600063i	$0.980888\pi$
$54$	−4.39688	−	2.76902i	−0.598339	−	0.376815i
$55$	3.14141	+	3.22139i	0.423588	+	0.434373i
$56$			0.334408i			0.0446871i
$57$	13.8457	−	1.03284i	1.83390	−	0.136803i
$58$	3.22144	+	3.22144i	0.422996	+	0.422996i
$59$		−	12.3272i		−	1.60487i	−0.596742	−	0.802433i	$-0.703539\pi$
$59$		−	12.3272i		−	1.60487i	0.596742	−	0.802433i	$-0.296461\pi$
$60$	2.56399	−	2.90275i	0.331009	−	0.374744i
$61$	5.48892			0.702784			0.351392	−	0.936228i	$-0.385708\pi$
$61$	5.48892			0.702784			0.351392	+	0.936228i	$0.385708\pi$
$62$	4.98717	−	4.98717i	0.633372	−	0.633372i
$63$	0.596284	−	0.806784i	0.0751247	−	0.101645i
$64$		−	1.00000i		−	0.125000i
$65$	−7.06879	+	3.87714i	−0.876775	+	0.480900i
$66$	−2.64101	−	2.27434i	−0.325085	−	0.279951i
$67$	−4.26617	+	4.26617i	−0.521196	+	0.521196i	−0.917933	−	0.396736i	$-0.870143\pi$
$67$	−4.26617	+	4.26617i	−0.521196	+	0.521196i	0.396736	+	0.917933i	$0.370143\pi$
$68$	−2.69197	−	2.69197i	−0.326450	−	0.326450i
$69$	−11.5641	−	9.95855i	−1.39215	−	1.19887i
$70$	0.522057	+	0.535349i	0.0623978	+	0.0639864i
$71$	9.88936			1.17365			0.586826	−	0.809713i	$-0.300377\pi$
$71$	9.88936			1.17365			0.586826	+	0.809713i	$0.300377\pi$
$72$	−1.78311	+	2.41258i	−0.210141	+	0.284325i
$73$	2.59128	+	2.59128i	0.303286	+	0.303286i	0.842298	−	0.539012i	$-0.181202\pi$
$73$	2.59128	+	2.59128i	0.303286	+	0.303286i	−0.539012	+	0.842298i	$0.681202\pi$
$74$	1.69340			0.196854
$75$	−0.426954	−	8.64972i	−0.0493004	−	0.998784i
$76$		−	8.01600i		−	0.919499i
$77$	0.475822	−	0.475822i	0.0542249	−	0.0542249i
$78$	5.19370	−	3.46777i	0.588071	−	0.392648i
$79$		−	10.6675i		−	1.20019i	−0.799929	−	0.600095i	$-0.795129\pi$
$79$		−	10.6675i		−	1.20019i	0.799929	−	0.600095i	$-0.204871\pi$
$80$	−1.56114	−	1.60089i	−0.174541	−	0.178985i
$81$	8.60376	−	2.64107i	0.955974	−	0.293452i
$82$	5.58743	+	5.58743i	0.617028	+	0.617028i
$83$	2.98429	−	2.98429i	0.327568	−	0.327568i	−0.524093	−	0.851661i	$-0.675596\pi$
$83$	2.98429	−	2.98429i	0.327568	−	0.327568i	0.851661	+	0.524093i	$0.175596\pi$
$84$	−0.438897	−	0.377962i	−0.0478876	−	0.0412390i
$85$	−8.51210	−	0.106997i	−0.923267	−	0.0116054i
$86$	3.90946			0.421568
$87$	−7.86902	+	0.587005i	−0.843647	+	0.0629335i
$88$	−1.42288	+	1.42288i	−0.151679	+	0.151679i
$89$		−	1.02859i		−	0.109030i	−0.998513	−	0.0545151i	$-0.982639\pi$
$89$		−	1.02859i		−	0.109030i	0.998513	−	0.0545151i	$-0.0173613\pi$
$90$	0.911824	+	6.64594i	0.0961147	+	0.700544i
$91$	0.593074	+	1.04978i	0.0621711	+	0.110047i
$92$	−6.23031	+	6.23031i	−0.649554	+	0.649554i
$93$	0.908753	+	12.1822i	0.0942333	+	1.26323i
$94$		−	2.89021i		−	0.298102i
$95$	−12.5141	−	12.8327i	−1.28392	−	1.31661i
$96$	1.31246	+	1.13024i	0.133952	+	0.115355i
$97$	10.9826	−	10.9826i	1.11512	−	1.11512i	0.122671	−	0.992447i	$-0.460854\pi$
$97$	10.9826	−	10.9826i	1.11512	−	1.11512i	0.992447	−	0.122671i	$-0.0391461\pi$
$98$	−4.87067	+	4.87067i	−0.492012	+	0.492012i
$99$	5.96995	−	0.895665i	0.600003	−	0.0900177i
$100$	−4.99842	−	0.125680i	−0.499842	−	0.0125680i
$101$		−	3.49411i		−	0.347677i	−0.984774	−	0.173838i	$-0.944383\pi$
$101$		−	3.49411i		−	0.347677i	0.984774	−	0.173838i	$-0.0556170\pi$
$102$	6.57569	−	0.490527i	0.651091	−	0.0485694i
$103$	−2.58254	+	2.58254i	−0.254466	+	0.254466i	−0.822799	−	0.568333i	$-0.807589\pi$
$103$	−2.58254	+	2.58254i	−0.254466	+	0.254466i	0.568333	+	0.822799i	$0.307589\pi$
$104$	−1.77351	−	3.13922i	−0.173907	−	0.307825i
$105$	−1.29268	+	0.0801056i	−0.126152	+	0.00781751i
$106$		−	9.65927i		−	0.938192i
$107$	0.993509	−	0.993509i	0.0960462	−	0.0960462i	−0.657451	−	0.753497i	$-0.728365\pi$
$107$	0.993509	−	0.993509i	0.0960462	−	0.0960462i	0.753497	+	0.657451i	$0.228365\pi$
$108$	−1.15107	−	5.06705i	−0.110762	−	0.487577i
$109$	5.37932			0.515246			0.257623	−	0.966246i	$-0.417061\pi$
$109$	5.37932			0.515246			0.257623	+	0.966246i	$0.417061\pi$
$110$	−0.0565546	+	4.49919i	−0.00539227	+	0.428980i
$111$	−1.91395	+	2.22252i	−0.181664	+	0.210953i
$112$	−0.236462	+	0.236462i	−0.0223435	+	0.0223435i
$113$	7.55286	+	7.55286i	0.710513	+	0.710513i	0.966643	−	0.256129i	$-0.0824473\pi$
$113$	7.55286	+	7.55286i	0.710513	+	0.710513i	−0.256129	+	0.966643i	$0.582447\pi$
$114$	10.5207	+	9.06002i	0.985352	+	0.848549i
$115$	−0.247633	+	19.7004i	−0.0230919	+	1.83707i
$116$			4.55580i			0.422996i
$117$	−1.31883	+	10.7360i	−0.121926	+	0.992539i
$118$	8.71665	−	8.71665i	0.802433	−	0.802433i
$119$			1.27310i			0.116705i
$120$	3.86557	−	0.239545i	0.352876	−	0.0218674i
$121$	−6.95083			−0.631893
$122$	3.88125	+	3.88125i	0.351392	+	0.351392i
$123$	−13.6484	+	1.01813i	−1.23064	+	0.0918017i
$124$	7.05293			0.633372
$125$	−8.19811	+	7.60204i	−0.733261	+	0.679947i
$126$	0.992119	−	0.148846i	0.0883850	−	0.0132603i
$127$	11.4470	+	11.4470i	1.01575	+	1.01575i	0.999874	+	0.0158806i	$0.00505516\pi$
$127$	11.4470	+	11.4470i	1.01575	+	1.01575i	0.0158806	+	0.999874i	$0.494945\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−4.41864	+	5.13101i	−0.389039	+	0.451760i
$130$	−7.73994	−	2.25684i	−0.678838	−	0.197938i
$131$			13.1727i			1.15091i	0.817835	+	0.575453i	$0.195174\pi$
$131$			13.1727i			1.15091i	−0.817835	+	0.575453i	$0.804826\pi$
$132$	−0.259274	−	3.47567i	−0.0225669	−	0.302518i
$133$	−1.89548	+	1.89548i	−0.164359	+	0.164359i
$134$	−6.03328			−0.521196
$135$	−9.75312	−	6.31479i	−0.839415	−	0.543491i
$136$		−	3.80703i		−	0.326450i
$137$	−4.54541	−	4.54541i	−0.388340	−	0.388340i	0.485755	−	0.874095i	$-0.338545\pi$
$137$	−4.54541	−	4.54541i	−0.388340	−	0.388340i	−0.874095	+	0.485755i	$0.838545\pi$
$138$	−1.13528	−	15.2188i	−0.0966410	−	1.29551i
$139$			0.709569i			0.0601848i	0.999547	+	0.0300924i	$0.00958016\pi$
$139$			0.709569i			0.0601848i	−0.999547	+	0.0300924i	$0.990420\pi$
$140$	−0.00939855	+	0.747699i	−0.000794322	+	0.0631921i
$141$	3.79329	+	3.26664i	0.319452	+	0.275100i
$142$	6.99284	+	6.99284i	0.586826	+	0.586826i
$143$	−1.94324	+	6.99021i	−0.162502	+	0.584551i
$144$	−2.96680	+	0.445105i	−0.247233	+	0.0370921i
$145$	7.11225	+	7.29333i	0.590640	+	0.605678i
$146$			3.66462i			0.303286i
$147$	−0.887525	−	11.8976i	−0.0732018	−	0.981298i
$148$	1.19742	+	1.19742i	0.0984270	+	0.0984270i
$149$		−	3.81004i		−	0.312130i	−0.987747	−	0.156065i	$-0.950119\pi$
$149$		−	3.81004i		−	0.312130i	0.987747	−	0.156065i	$-0.0498810\pi$
$150$	5.81438	−	6.41818i	0.474742	−	0.524042i
$151$			3.85812i			0.313969i	0.987601	+	0.156985i	$0.0501773\pi$
$151$			3.85812i			0.313969i	−0.987601	+	0.156985i	$0.949823\pi$
$152$	5.66817	−	5.66817i	0.459749	−	0.459749i
$153$	−6.78833	+	9.18475i	−0.548804	+	0.742543i
$154$	0.672913			0.0542249
$155$	11.2909	−	11.0106i	0.906910	−	0.884394i
$156$	6.12459	+	1.22042i	0.490360	+	0.0977115i
$157$	−11.1016	−	11.1016i	−0.886006	−	0.886006i	0.108131	−	0.994137i	$-0.465513\pi$
$157$	−11.1016	−	11.1016i	−0.886006	−	0.886006i	−0.994137	+	0.108131i	$0.965513\pi$
$158$	7.54308	−	7.54308i	0.600095	−	0.600095i
$159$	12.6774	+	10.9173i	1.00538	+	0.865800i
$160$	0.0281051	−	2.23589i	0.00222190	−	0.176763i
$161$	2.94646			0.232214
$162$	7.95130	+	4.21626i	0.624713	+	0.331261i
$163$	−7.73462	−	7.73462i	−0.605823	−	0.605823i	0.336029	−	0.941852i	$-0.390916\pi$
$163$	−7.73462	−	7.73462i	−0.605823	−	0.605823i	−0.941852	+	0.336029i	$0.890916\pi$
$164$			7.90181i			0.617028i
$165$	−5.84108	−	5.15939i	−0.454728	−	0.401658i
$166$	4.22042			0.327568
$167$	−9.30685	−	9.30685i	−0.720185	−	0.720185i	0.248457	−	0.968643i	$-0.420076\pi$
$167$	−9.30685	−	9.30685i	−0.720185	−	0.720185i	−0.968643	+	0.248457i	$0.920076\pi$
$168$	−0.0430876	−	0.577606i	−0.00332428	−	0.0445633i
$169$	−11.1348	−	6.70934i	−0.856526	−	0.516103i
$170$	−5.94330	−	6.09462i	−0.455831	−	0.467436i
$171$	−23.7818	+	3.56796i	−1.81864	+	0.272849i
$172$	2.76440	+	2.76440i	0.210784	+	0.210784i
$173$	0.456884	+	0.456884i	0.0347362	+	0.0347362i	0.724262	−	0.689525i	$-0.242181\pi$
$173$	0.456884	+	0.456884i	0.0347362	+	0.0347362i	−0.689525	+	0.724262i	$0.742181\pi$
$174$	−5.97931	−	5.14916i	−0.453290	−	0.390357i
$175$	1.15222	+	1.21165i	0.0870994	+	0.0915924i
$176$	−2.01226			−0.151679
$177$	1.58833	+	21.2922i	0.119386	+	1.60042i
$178$	0.727322	−	0.727322i	0.0545151	−	0.0545151i
$179$	12.2071			0.912401			0.456201	−	0.889877i	$-0.349210\pi$
$179$	12.2071			0.912401			0.456201	+	0.889877i	$0.349210\pi$
$180$	−4.05464	+	5.34415i	−0.302215	+	0.398329i
$181$	−6.05221			−0.449857			−0.224929	−	0.974375i	$-0.572215\pi$
$181$	−6.05221			−0.449857			−0.224929	+	0.974375i	$0.572215\pi$
$182$	−0.322938	+	1.16167i	−0.0239377	+	0.0861088i
$183$	−9.48075	+	0.707235i	−0.700837	+	0.0522803i
$184$	−8.81099			−0.649554
$185$	3.78626	+	0.0475932i	0.278372	+	0.00349912i
$186$	−7.97152	+	9.25669i	−0.584500	+	0.678733i
$187$	−5.41694	+	5.41694i	−0.396126	+	0.396126i
$188$	2.04369	−	2.04369i	0.149051	−	0.149051i
$189$	−0.925980	+	1.47035i	−0.0673551	+	0.106952i
$190$	0.225290	−	17.9229i	0.0163443	−	1.30026i
$191$		−	5.13137i		−	0.371293i	−0.982617	−	0.185647i	$-0.940562\pi$
$191$		−	5.13137i		−	0.371293i	0.982617	−	0.185647i	$-0.0594379\pi$
$192$	0.128848	+	1.72725i	0.00929878	+	0.124654i
$193$	−11.6332	−	11.6332i	−0.837377	−	0.837377i	0.151136	−	0.988513i	$-0.451707\pi$
$193$	−11.6332	−	11.6332i	−0.837377	−	0.837377i	−0.988513	+	0.151136i	$0.951707\pi$
$194$	15.5318			1.11512
$195$	11.7100	−	7.60760i	0.838572	−	0.544791i
$196$	−6.88817			−0.492012
$197$	−5.66495	−	5.66495i	−0.403611	−	0.403611i	0.475892	−	0.879504i	$-0.342125\pi$
$197$	−5.66495	−	5.66495i	−0.403611	−	0.403611i	−0.879504	+	0.475892i	$0.842125\pi$
$198$	4.85472	+	3.58806i	0.345010	+	0.254993i
$199$		−	9.89963i		−	0.701766i	−0.936419	−	0.350883i	$-0.885882\pi$
$199$		−	9.89963i		−	0.701766i	0.936419	−	0.350883i	$-0.114118\pi$
$200$	−3.44555	−	3.62329i	−0.243637	−	0.256205i
$201$	6.81907	−	7.91844i	0.480980	−	0.558524i
$202$	2.47071	−	2.47071i	0.173838	−	0.173838i
$203$	1.07727	−	1.07727i	0.0756098	−	0.0756098i
$204$	4.99657	+	4.30286i	0.349830	+	0.301261i
$205$	12.3358	+	12.6499i	0.861573	+	0.883508i
$206$	−3.65227			−0.254466
$207$	21.2572	+	15.7109i	1.47748	+	1.09198i
$208$	0.965701	−	3.47382i	0.0669593	−	0.240866i
$209$	−16.1302			−1.11575
$210$	−0.970703	−	0.857416i	−0.0669848	−	0.0591673i
$211$	−23.0541			−1.58711			−0.793555	−	0.608499i	$-0.791772\pi$
$211$	−23.0541			−1.58711			−0.793555	+	0.608499i	$0.791772\pi$
$212$	6.83014	−	6.83014i	0.469096	−	0.469096i
$213$	−17.0814	+	1.27422i	−1.17040	+	0.0873082i
$214$	1.40503			0.0960462
$215$	8.74112	+	0.109876i	0.596140	+	0.00749345i
$216$	2.76902	−	4.39688i	0.188408	−	0.299170i
$217$	−1.66775	−	1.66775i	−0.113214	−	0.113214i
$218$	3.80376	+	3.80376i	0.257623	+	0.257623i
$219$	−4.80967	−	4.14191i	−0.325007	−	0.279884i
$220$	−3.22139	+	3.14141i	−0.217186	+	0.211794i
$221$	−6.75179	−	11.9511i	−0.454175	−	0.803916i
$222$	−2.92493	+	0.218191i	−0.196308	+	0.0146440i
$223$	6.56733	+	6.56733i	0.439781	+	0.439781i	0.891938	−	0.452157i	$-0.149345\pi$
$223$	6.56733	+	6.56733i	0.439781	+	0.439781i	−0.452157	+	0.891938i	$0.649345\pi$
$224$	−0.334408			−0.0223435
$225$	1.85195	+	14.8852i	0.123464	+	0.992349i
$226$			10.6814i			0.710513i
$227$	3.35070	+	3.35070i	0.222393	+	0.222393i	0.809506	−	0.587112i	$-0.199735\pi$
$227$	3.35070	+	3.35070i	0.222393	+	0.222393i	−0.587112	+	0.809506i	$0.699735\pi$
$228$	1.03284	+	13.8457i	0.0684017	+	0.916951i
$229$	24.3157			1.60683			0.803415	−	0.595420i	$-0.203014\pi$
$229$	24.3157			1.60683			0.803415	+	0.595420i	$0.203014\pi$
$230$	−14.1054	+	13.7552i	−0.930082	+	0.906990i
$231$	−0.760555	+	0.883172i	−0.0500409	+	0.0581085i
$232$	−3.22144	+	3.22144i	−0.211498	+	0.211498i
$233$	7.59642	+	7.59642i	0.497658	+	0.497658i	0.910708	−	0.413050i	$-0.135537\pi$
$233$	7.59642	+	7.59642i	0.497658	+	0.497658i	−0.413050	+	0.910708i	$0.635537\pi$
$234$	−8.52402	+	6.65891i	−0.557232	+	0.435307i
$235$	0.0812295	−	6.46219i	0.00529883	−	0.421547i
$236$	12.3272			0.802433
$237$	1.37449	+	18.4255i	0.0892824	+	1.19686i
$238$	−0.900217	+	0.900217i	−0.0583524	+	0.0583524i
$239$			2.60829i			0.168716i	0.996436	+	0.0843581i	$0.0268840\pi$
$239$			2.60829i			0.168716i	−0.996436	+	0.0843581i	$0.973116\pi$
$240$	2.90275	+	2.56399i	0.187372	+	0.165505i
$241$			2.43150i			0.156626i	0.996929	+	0.0783132i	$0.0249534\pi$
$241$			2.43150i			0.156626i	−0.996929	+	0.0783132i	$0.975047\pi$
$242$	−4.91498	−	4.91498i	−0.315947	−	0.315947i
$243$	−14.5206	+	5.67037i	−0.931495	+	0.363754i
$244$			5.48892i			0.351392i
$245$	−11.0272	+	10.7534i	−0.704501	+	0.687010i
$246$	−10.3708	−	8.93096i	−0.661219	−	0.569417i
$247$	7.74106	−	27.8461i	0.492552	−	1.77181i
$248$	4.98717	+	4.98717i	0.316686	+	0.316686i
$249$	−4.77010	+	5.53914i	−0.302293	+	0.351029i
$250$	−11.1724	−	0.421487i	−0.706604	−	0.0266572i
$251$			28.8733i			1.82247i	0.411891	+	0.911233i	$0.364869\pi$
$251$			28.8733i			1.82247i	−0.411891	+	0.911233i	$0.635131\pi$
$252$	0.806784	+	0.596284i	0.0508226	+	0.0375624i
$253$	12.5370	+	12.5370i	0.788193	+	0.788193i
$254$			16.1885i			1.01575i
$255$	14.7163	−	0.911954i	0.921572	−	0.0571088i
$256$	1.00000			0.0625000
$257$	18.2476	−	18.2476i	1.13825	−	1.13825i	0.149490	−	0.988763i	$-0.452237\pi$
$257$	18.2476	−	18.2476i	1.13825	−	1.13825i	0.988763	−	0.149490i	$-0.0477632\pi$
$258$	−6.75262	+	0.503725i	−0.420400	+	0.0313605i
$259$		−	0.566286i		−	0.0351873i
$260$	−3.87714	−	7.06879i	−0.240450	−	0.438388i
$261$	13.5161	−	2.02781i	0.836628	−	0.125518i
$262$	−9.31452	+	9.31452i	−0.575453	+	0.575453i
$263$	4.49375	+	4.49375i	0.277096	+	0.277096i	0.831949	−	0.554852i	$-0.187225\pi$
$263$	4.49375	+	4.49375i	0.277096	+	0.277096i	−0.554852	+	0.831949i	$0.687225\pi$
$264$	2.27434	−	2.64101i	0.139976	−	0.162543i
$265$	0.271475	−	21.5971i	0.0166766	−	1.32670i
$266$	−2.68061			−0.164359
$267$	0.132531	+	1.77663i	0.00811078	+	0.108728i
$268$	−4.26617	−	4.26617i	−0.260598	−	0.260598i
$269$	−15.5655			−0.949047			−0.474523	−	0.880243i	$-0.657380\pi$
$269$	−15.5655			−0.949047			−0.474523	+	0.880243i	$0.657380\pi$
$270$	−2.43126	−	11.3617i	−0.147962	−	0.691453i
$271$		−	8.80009i		−	0.534567i	−0.963618	−	0.267284i	$-0.913874\pi$
$271$		−	8.80009i		−	0.534567i	0.963618	−	0.267284i	$-0.0861261\pi$
$272$	2.69197	−	2.69197i	0.163225	−	0.163225i
$273$	−1.15965	−	1.73681i	−0.0701852	−	0.105117i
$274$		−	6.42817i		−	0.388340i
$275$	−0.252900	+	10.0581i	−0.0152504	+	0.606526i
$276$	9.95855	−	11.5641i	0.599434	−	0.696075i
$277$	2.25752	+	2.25752i	0.135641	+	0.135641i	0.771667	−	0.636026i	$-0.219423\pi$
$277$	2.25752	+	2.25752i	0.135641	+	0.135641i	−0.636026	+	0.771667i	$0.719423\pi$
$278$	−0.501741	+	0.501741i	−0.0300924	+	0.0300924i
$279$	−3.13929	−	20.9246i	−0.187944	−	1.25272i
$280$	−0.535349	+	0.522057i	−0.0319932	+	0.0311989i
$281$	−0.549953			−0.0328074			−0.0164037	−	0.999865i	$-0.505222\pi$
$281$	−0.549953			−0.0328074			−0.0164037	+	0.999865i	$0.505222\pi$
$282$	0.372397	+	4.99212i	0.0221759	+	0.297276i
$283$	−11.9721	+	11.9721i	−0.711665	+	0.711665i	−0.966883	−	0.255219i	$-0.917852\pi$
$283$	−11.9721	+	11.9721i	−0.711665	+	0.711665i	0.255219	+	0.966883i	$0.417852\pi$
$284$			9.88936i			0.586826i
$285$	23.2685	+	20.5529i	1.37831	+	1.21745i
$286$	−6.31690	+	3.56875i	−0.373526	+	0.211025i
$287$	1.86848	−	1.86848i	0.110293	−	0.110293i
$288$	−2.41258	−	1.78311i	−0.142163	−	0.105070i
$289$			2.50655i			0.147444i
$290$	−0.128041	+	10.1863i	−0.00751883	+	0.598159i
$291$	−17.5547	+	20.3849i	−1.02908	+	1.19498i
$292$	−2.59128	+	2.59128i	−0.151643	+	0.151643i
$293$	8.68980	−	8.68980i	0.507664	−	0.507664i	−0.406145	−	0.913809i	$-0.633127\pi$
$293$	8.68980	−	8.68980i	0.507664	−	0.507664i	0.913809	+	0.406145i	$0.133127\pi$
$294$	7.78530	−	9.04045i	0.454048	−	0.527250i
$295$	19.7345	−	19.2445i	1.14899	−	1.12046i
$296$			1.69340i			0.0984270i
$297$	−10.1962	+	2.31625i	−0.591644	+	0.134403i
$298$	2.69410	−	2.69410i	0.156065	−	0.156065i
$299$	−27.6596	+	15.6263i	−1.59959	+	0.903695i
$300$	8.64972	−	0.426954i	0.499392	−	0.0246502i
$301$		−	1.30735i		−	0.0753545i
$302$	−2.72810	+	2.72810i	−0.156985	+	0.156985i
$303$	0.450208	+	6.03520i	0.0258638	+	0.346713i
$304$	8.01600			0.459749
$305$	8.56898	+	8.78714i	0.490658	+	0.503150i
$306$	−11.2947	+	1.69453i	−0.645674	+	0.0968696i
$307$	−14.0154	+	14.0154i	−0.799902	+	0.799902i	−0.983080	−	0.183178i	$-0.941362\pi$
$307$	−14.0154	+	14.0154i	−0.799902	+	0.799902i	0.183178	+	0.983080i	$0.441362\pi$
$308$	0.475822	+	0.475822i	0.0271125	+	0.0271125i
$309$	4.12795	−	4.79346i	0.234831	−	0.272690i
$310$	15.7696	+	0.198223i	0.895652	+	0.0112583i
$311$			8.75515i			0.496459i	0.968701	+	0.248229i	$0.0798487\pi$
$311$			8.75515i			0.496459i	−0.968701	+	0.248229i	$0.920151\pi$
$312$	3.46777	+	5.19370i	0.196324	+	0.294035i
$313$	19.2874	−	19.2874i	1.09019	−	1.09019i	0.0946807	−	0.995508i	$-0.469817\pi$
$313$	19.2874	−	19.2874i	1.09019	−	1.09019i	0.995508	−	0.0946807i	$-0.0301830\pi$
$314$		−	15.7001i		−	0.886006i
$315$	2.22245	−	0.304921i	0.125221	−	0.0171803i
$316$	10.6675			0.600095
$317$	5.00531	+	5.00531i	0.281126	+	0.281126i	0.833558	−	0.552432i	$-0.186300\pi$
$317$	5.00531	+	5.00531i	0.281126	+	0.281126i	−0.552432	+	0.833558i	$0.686300\pi$
$318$	1.24458	+	16.6840i	0.0697923	+	0.935592i
$319$	9.16744			0.513278
$320$	1.60089	−	1.56114i	0.0894923	−	0.0872704i
$321$	−1.58803	+	1.84405i	−0.0886351	+	0.102925i
$322$	2.08346	+	2.08346i	0.116107	+	0.116107i
$323$	21.5789	−	21.5789i	1.20068	−	1.20068i
$324$	2.64107	+	8.60376i	0.146726	+	0.477987i
$325$	−17.2422	−	5.26357i	−0.956427	−	0.291970i
$326$		−	10.9384i		−	0.605823i
$327$	−9.29145	+	0.693113i	−0.513818	+	0.0383293i
$328$	−5.58743	+	5.58743i	−0.308514	+	0.308514i
$329$	−0.966508			−0.0532853
$330$	−0.482026	−	7.77851i	−0.0265346	−	0.428193i
$331$		−	20.7254i		−	1.13917i	−0.821933	−	0.569584i	$-0.807104\pi$
$331$		−	20.7254i		−	1.13917i	0.821933	−	0.569584i	$-0.192896\pi$
$332$	2.98429	+	2.98429i	0.163784	+	0.163784i
$333$	3.01951	−	4.08546i	0.165468	−	0.223882i
$334$		−	13.1619i		−	0.720185i
$335$	−13.4898	−	0.169566i	−0.737025	−	0.00926437i
$336$	0.377962	−	0.438897i	0.0206195	−	0.0239438i
$337$	−12.8983	−	12.8983i	−0.702616	−	0.702616i	0.262355	−	0.964971i	$-0.415501\pi$
$337$	−12.8983	−	12.8983i	−0.702616	−	0.702616i	−0.964971	+	0.262355i	$0.915501\pi$
$338$	−3.12930	−	12.6177i	−0.170211	−	0.686315i
$339$	−14.0189	−	12.0725i	−0.761400	−	0.655689i
$340$	0.106997	−	8.51210i	0.00580271	−	0.461633i
$341$		−	14.1923i		−	0.768556i
$342$	−19.3392	−	14.2934i	−1.04575	−	0.772897i
$343$	3.28402	+	3.28402i	0.177321	+	0.177321i
$344$			3.90946i			0.210784i
$345$	−2.11063	−	34.0595i	−0.113632	−	1.83370i
$346$			0.646131i			0.0347362i
$347$	−4.80078	+	4.80078i	−0.257719	+	0.257719i	−0.824126	−	0.566407i	$-0.808333\pi$
$347$	−4.80078	+	4.80078i	−0.257719	+	0.257719i	0.566407	+	0.824126i	$0.308333\pi$
$348$	−0.587005	−	7.86902i	−0.0314667	−	0.421824i
$349$	−2.35848			−0.126246			−0.0631232	−	0.998006i	$-0.520106\pi$
$349$	−2.35848			−0.126246			−0.0631232	+	0.998006i	$0.520106\pi$
$350$	−0.0420283	+	1.67151i	−0.00224651	+	0.0893459i
$351$	0.894642	−	18.7136i	0.0477524	−	0.998859i
$352$	−1.42288	−	1.42288i	−0.0758397	−	0.0758397i
$353$	0.663250	−	0.663250i	0.0353012	−	0.0353012i	−0.689236	−	0.724537i	$-0.742054\pi$
$353$	0.663250	−	0.663250i	0.0353012	−	0.0353012i	0.724537	+	0.689236i	$0.242054\pi$
$354$	−13.9327	+	16.1790i	−0.740516	+	0.859903i
$355$	15.4387	+	15.8318i	0.819400	+	0.840262i
$356$	1.02859			0.0545151
$357$	−0.164036	−	2.19896i	−0.00868169	−	0.116381i
$358$	8.63172	+	8.63172i	0.456201	+	0.456201i
$359$			25.4249i			1.34188i	0.741513	+	0.670939i	$0.234109\pi$
$359$			25.4249i			1.34188i	−0.741513	+	0.670939i	$0.765891\pi$
$360$	−6.64594	+	0.911824i	−0.350272	+	0.0480573i
$361$	45.2563			2.38191
$362$	−4.27956	−	4.27956i	−0.224929	−	0.224929i
$363$	12.0058	−	0.895598i	0.630143	−	0.0470067i
$364$	−1.04978	+	0.593074i	−0.0550233	+	0.0310855i
$365$	−0.102994	+	8.19369i	−0.00539098	+	0.428878i
$366$	−7.20399	−	6.20381i	−0.376559	−	0.324278i
$367$	−16.7964	−	16.7964i	−0.876763	−	0.876763i	0.116435	−	0.993198i	$-0.462853\pi$
$367$	−16.7964	−	16.7964i	−0.876763	−	0.876763i	−0.993198	+	0.116435i	$0.962853\pi$
$368$	−6.23031	−	6.23031i	−0.324777	−	0.324777i
$369$	23.4431	−	3.51713i	1.22040	−	0.183095i
$370$	2.64364	+	2.71094i	0.137436	+	0.140935i
$371$	−3.23013			−0.167700
$372$	−12.1822	+	0.908753i	−0.631617	+	0.0471167i
$373$	−7.50497	+	7.50497i	−0.388593	+	0.388593i	−0.874185	−	0.485593i	$-0.838604\pi$
$373$	−7.50497	+	7.50497i	−0.388593	+	0.388593i	0.485593	+	0.874185i	$0.338604\pi$
$374$	−7.66071			−0.396126
$375$	13.1807	−	14.1869i	0.680648	−	0.732610i
$376$	2.89021			0.149051
$377$	−4.39954	+	15.8260i	−0.226588	+	0.815082i
$378$	−1.69446	+	0.384927i	−0.0871537	+	0.0197985i
$379$	18.8907			0.970350			0.485175	−	0.874417i	$-0.338756\pi$
$379$	18.8907			0.970350			0.485175	+	0.874417i	$0.338756\pi$
$380$	12.8327	−	12.5141i	0.658304	−	0.641960i
$381$	−21.2467	−	18.2969i	−1.08850	−	0.937378i
$382$	3.62843	−	3.62843i	0.185647	−	0.185647i
$383$	−4.58015	+	4.58015i	−0.234035	+	0.234035i	−0.814375	−	0.580340i	$-0.802920\pi$
$383$	−4.58015	+	4.58015i	−0.234035	+	0.234035i	0.580340	+	0.814375i	$0.302920\pi$
$384$	−1.13024	+	1.31246i	−0.0576774	+	0.0669762i
$385$	1.50456	+	0.0189123i	0.0766796	+	0.000963859i
$386$		−	16.4519i		−	0.837377i
$387$	6.97098	−	9.43188i	0.354355	−	0.479449i
$388$	10.9826	+	10.9826i	0.557559	+	0.557559i
$389$	3.69834			0.187513			0.0937566	−	0.995595i	$-0.470112\pi$
$389$	3.69834			0.187513			0.0937566	+	0.995595i	$0.470112\pi$
$390$	13.6596	+	2.90085i	0.691681	+	0.146890i
$391$	−33.5437			−1.69638
$392$	−4.87067	−	4.87067i	−0.246006	−	0.246006i
$393$	−1.69727	−	22.7526i	−0.0856162	−	1.14772i
$394$		−	8.01145i		−	0.403611i
$395$	17.0775	−	16.6535i	0.859262	−	0.837929i
$396$	0.895665	+	5.96995i	0.0450088	+	0.300001i
$397$	−9.61297	+	9.61297i	−0.482461	+	0.482461i	−0.905917	−	0.423456i	$-0.860817\pi$
$397$	−9.61297	+	9.61297i	−0.482461	+	0.482461i	0.423456	+	0.905917i	$0.360817\pi$
$398$	7.00009	−	7.00009i	0.350883	−	0.350883i
$399$	3.02974	−	3.51820i	0.151677	−	0.176130i
$400$	0.125680	−	4.99842i	0.00628399	−	0.249921i
$401$	29.1692			1.45664			0.728321	−	0.685236i	$-0.240301\pi$
$401$	29.1692			1.45664			0.728321	+	0.685236i	$0.240301\pi$
$402$	10.4210	−	0.777374i	0.519752	−	0.0387719i
$403$	24.5006	+	6.81102i	1.22046	+	0.339281i
$404$	3.49411			0.173838
$405$	17.6597	+	9.65057i	0.877520	+	0.479541i
$406$	1.52349			0.0756098
$407$	2.40951	−	2.40951i	0.119435	−	0.119435i
$408$	0.490527	+	6.57569i	0.0242847	+	0.325545i
$409$	−34.3528			−1.69864			−0.849318	−	0.527882i	$-0.822986\pi$
$409$	−34.3528			−1.69864			−0.849318	+	0.527882i	$0.822986\pi$
$410$	−0.222081	+	17.6676i	−0.0109678	+	0.872540i
$411$	8.43672	+	7.26539i	0.416153	+	0.358375i
$412$	−2.58254	−	2.58254i	−0.127233	−	0.127233i
$413$	−2.91491	−	2.91491i	−0.143434	−	0.143434i
$414$	3.92181	+	26.1404i	0.192747	+	1.28473i
$415$	9.43641	+	0.118615i	0.463215	+	0.00582260i
$416$	3.13922	−	1.77351i	0.153913	−	0.0869533i
$417$	−0.0914263	−	1.22560i	−0.00447717	−	0.0600181i
$418$	−11.4058	−	11.4058i	−0.557876	−	0.557876i
$419$	1.04983			0.0512874			0.0256437	−	0.999671i	$-0.491836\pi$
$419$	1.04983			0.0512874			0.0256437	+	0.999671i	$0.491836\pi$
$420$	−0.0801056	−	1.29268i	−0.00390875	−	0.0630761i
$421$			27.5287i			1.34167i	0.741608	+	0.670834i	$0.234064\pi$
$421$			27.5287i			1.34167i	−0.741608	+	0.670834i	$0.765936\pi$
$422$	−16.3017	−	16.3017i	−0.793555	−	0.793555i
$423$	−6.97286	−	5.15355i	−0.339032	−	0.250574i
$424$	9.65927			0.469096
$425$	−13.1173	−	13.7939i	−0.636282	−	0.669105i
$426$	−12.9794	−	11.1774i	−0.628854	−	0.541546i
$427$	1.29792	−	1.29792i	0.0628108	−	0.0628108i
$428$	0.993509	+	0.993509i	0.0480231	+	0.0480231i
$429$	2.45579	−	12.3242i	0.118567	−	0.595020i
$430$	6.10321	+	6.25860i	0.294323	+	0.301817i
$431$	22.5766			1.08748			0.543739	−	0.839254i	$-0.317008\pi$
$431$	22.5766			1.08748			0.543739	+	0.839254i	$0.317008\pi$
$432$	5.06705	−	1.15107i	0.243789	−	0.0553810i
$433$	16.5303	−	16.5303i	0.794395	−	0.794395i	−0.187810	−	0.982205i	$-0.560139\pi$
$433$	16.5303	−	16.5303i	0.794395	−	0.794395i	0.982205	+	0.187810i	$0.0601390\pi$
$434$		−	2.35855i		−	0.113214i
$435$	−13.2244	−	11.6810i	−0.634060	−	0.560062i
$436$			5.37932i			0.257623i
$437$	−49.9422	−	49.9422i	−2.38906	−	2.38906i
$438$	−0.472178	−	6.32972i	−0.0225615	−	0.302446i
$439$			28.1244i			1.34230i	0.741319	+	0.671152i	$0.234200\pi$
$439$			28.1244i			1.34230i	−0.741319	+	0.671152i	$0.765800\pi$
$440$	−4.49919	−	0.0565546i	−0.214490	−	0.00269613i
$441$	3.06596	+	20.4358i	0.145998	+	0.973134i
$442$	3.67645	−	13.2249i	0.174871	−	0.629045i
$443$	−3.61041	−	3.61041i	−0.171536	−	0.171536i	0.616118	−	0.787654i	$-0.288704\pi$
$443$	−3.61041	−	3.61041i	−0.171536	−	0.171536i	−0.787654	+	0.616118i	$0.788704\pi$
$444$	−2.22252	−	1.91395i	−0.105476	−	0.0908322i
$445$	1.64665	−	1.60577i	0.0780589	−	0.0761209i
$446$			9.28761i			0.439781i
$447$	0.490914	+	6.58089i	0.0232195	+	0.311266i
$448$	−0.236462	−	0.236462i	−0.0111718	−	0.0111718i
$449$		−	20.7104i		−	0.977386i	−0.872456	−	0.488693i	$-0.837474\pi$
$449$		−	20.7104i		−	0.977386i	0.872456	−	0.488693i	$-0.162526\pi$
$450$	−9.21592	+	11.8350i	−0.434443	+	0.557906i
$451$	15.9005			0.748724
$452$	−7.55286	+	7.55286i	−0.355257	+	0.355257i
$453$	−0.497110	−	6.66395i	−0.0233563	−	0.313100i
$454$			4.73860i			0.222393i
$455$	−0.754703	+	2.58829i	−0.0353810	+	0.121341i
$456$	−9.06002	+	10.5207i	−0.424275	+	0.492676i
$457$	11.3293	−	11.3293i	0.529960	−	0.529960i	−0.390600	−	0.920560i	$-0.627732\pi$
$457$	11.3293	−	11.3293i	0.529960	−	0.529960i	0.920560	+	0.390600i	$0.127732\pi$
$458$	17.1938	+	17.1938i	0.803415	+	0.803415i
$459$	10.5417	−	16.7390i	0.492045	−	0.781311i
$460$	−19.7004	−	0.247633i	−0.918536	−	0.0115460i
$461$	−41.5309			−1.93429			−0.967144	−	0.254229i	$-0.918178\pi$
$461$	−41.5309			−1.93429			−0.967144	+	0.254229i	$0.918178\pi$
$462$	−1.16229	+	0.0867033i	−0.0540747	+	0.00403380i
$463$	−24.1073	−	24.1073i	−1.12036	−	1.12036i	−0.991687	−	0.128676i	$-0.958927\pi$
$463$	−24.1073	−	24.1073i	−1.12036	−	1.12036i	−0.128676	−	0.991687i	$-0.541073\pi$
$464$	−4.55580			−0.211498
$465$	−18.0836	+	20.4729i	−0.838607	+	0.949409i
$466$			10.7430i			0.497658i
$467$	11.4427	−	11.4427i	0.529507	−	0.529507i	−0.390918	−	0.920425i	$-0.627843\pi$
$467$	11.4427	−	11.4427i	0.529507	−	0.529507i	0.920425	+	0.390918i	$0.127843\pi$
$468$	−10.7360	−	1.31883i	−0.496270	−	0.0609628i
$469$			2.01758i			0.0931630i
$470$	4.62690	−	4.51202i	0.213423	−	0.208124i
$471$	20.6057	+	17.7449i	0.949461	+	0.817641i
$472$	8.71665	+	8.71665i	0.401216	+	0.401216i
$473$	5.56269	−	5.56269i	0.255773	−	0.255773i
$474$	−12.0569	+	14.0007i	−0.553791	+	0.643074i
$475$	1.00745	−	40.0673i	0.0462249	−	1.83842i
$476$	−1.27310			−0.0583524
$477$	−23.3038	−	17.2235i	−1.06701	−	0.788610i
$478$	−1.84434	+	1.84434i	−0.0843581	+	0.0843581i
$479$			21.8587i			0.998752i	0.866385	+	0.499376i	$0.166437\pi$
$479$			21.8587i			0.998752i	−0.866385	+	0.499376i	$0.833563\pi$
$480$	0.239545	+	3.86557i	0.0109337	+	0.176438i
$481$	3.00326	+	5.31595i	0.136937	+	0.242387i
$482$	−1.71933	+	1.71933i	−0.0783132	+	0.0783132i
$483$	−5.08928	+	0.379645i	−0.231570	+	0.0172744i
$484$		−	6.95083i		−	0.315947i
$485$	34.7274	+	0.436523i	1.57689	+	0.0198215i
$486$	−14.2771	−	6.25804i	−0.647625	−	0.283870i
$487$	−18.2213	+	18.2213i	−0.825687	+	0.825687i	−0.986917	−	0.161229i	$-0.948454\pi$
$487$	−18.2213	+	18.2213i	−0.825687	+	0.825687i	0.161229	+	0.986917i	$0.448454\pi$
$488$	−3.88125	+	3.88125i	−0.175696	+	0.175696i
$489$	14.3562	+	12.3631i	0.649211	+	0.559077i
$490$	−15.4012	−	0.193593i	−0.695755	−	0.00874562i
$491$		−	14.0128i		−	0.632390i	−0.948694	−	0.316195i	$-0.897595\pi$
$491$		−	14.0128i		−	0.632390i	0.948694	−	0.316195i	$-0.102405\pi$
$492$	−1.01813	−	13.6484i	−0.0459009	−	0.615318i
$493$	−12.2641	+	12.2641i	−0.552347	+	0.552347i
$494$	25.1640	−	14.2164i	1.13218	−	0.639628i
$495$	10.7538	+	8.15896i	0.483347	+	0.366718i
$496$			7.05293i			0.316686i
$497$	2.33846	−	2.33846i	0.104894	−	0.104894i
$498$	−7.28973	+	0.543792i	−0.326661	+	0.0243679i
$499$	−28.6558			−1.28281			−0.641405	−	0.767202i	$-0.721648\pi$
$499$	−28.6558			−1.28281			−0.641405	+	0.767202i	$0.721648\pi$
$500$	−7.60204	−	8.19811i	−0.339973	−	0.366631i
$501$	17.2744	+	14.8761i	0.771765	+	0.664615i
$502$	−20.4165	+	20.4165i	−0.911233	+	0.911233i
$503$	−4.41285	−	4.41285i	−0.196759	−	0.196759i	0.601850	−	0.798609i	$-0.294431\pi$
$503$	−4.41285	−	4.41285i	−0.196759	−	0.196759i	−0.798609	+	0.601850i	$0.794431\pi$
$504$	0.148846	+	0.992119i	0.00663015	+	0.0441925i
$505$	5.59367	−	5.45479i	0.248915	−	0.242735i
$506$			17.7300i			0.788193i
$507$	20.0972	+	10.1540i	0.892546	+	0.450956i
$508$	−11.4470	+	11.4470i	−0.507877	+	0.507877i
$509$			36.2523i			1.60686i	0.595402	+	0.803428i	$0.296993\pi$
$509$			36.2523i			1.60686i	−0.595402	+	0.803428i	$0.703007\pi$
$510$	11.0509	+	9.76116i	0.489340	+	0.432232i
$511$	1.22548			0.0542119
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	40.6175	−	9.22700i	1.79331	−	0.407382i
$514$	25.8060			1.13825
$515$	−8.16608	−	0.102647i	−0.359840	−	0.00452318i
$516$	−5.13101	−	4.41864i	−0.225880	−	0.194520i
$517$	−4.11242	−	4.11242i	−0.180864	−	0.180864i
$518$	0.400425	−	0.400425i	0.0175937	−	0.0175937i
$519$	−0.848022	−	0.730285i	−0.0372240	−	0.0320559i
$520$	2.25684	−	7.73994i	0.0989688	−	0.339419i
$521$			8.54770i			0.374482i	0.982314	+	0.187241i	$0.0599545\pi$
$521$			8.54770i			0.374482i	−0.982314	+	0.187241i	$0.940046\pi$
$522$	10.9912	+	8.12347i	0.481073	+	0.355555i
$523$	0.832709	−	0.832709i	0.0364118	−	0.0364118i	−0.688666	−	0.725078i	$-0.741804\pi$
$523$	0.832709	−	0.832709i	0.0364118	−	0.0364118i	0.725078	+	0.688666i	$0.241804\pi$
$524$	−13.1727			−0.575453
$525$	−2.14629	−	1.94437i	−0.0936717	−	0.0848593i
$526$			6.35512i			0.277096i
$527$	18.9863	+	18.9863i	0.827056	+	0.827056i
$528$	3.47567	−	0.259274i	0.151259	−	0.0112835i
$529$			54.6335i			2.37537i
$530$	15.4634	−	15.0795i	0.671688	−	0.655011i
$531$	−5.48690	−	36.5723i	−0.238111	−	1.58710i
$532$	−1.89548	−	1.89548i	−0.0821794	−	0.0821794i
$533$	−7.63079	+	27.4495i	−0.330526	+	1.18897i
$534$	−1.16255	+	1.34998i	−0.0503087	+	0.0584194i
$535$	3.14150	+	0.0394886i	0.135819	+	0.00170724i
$536$		−	6.03328i		−	0.260598i
$537$	−21.0847	+	1.57286i	−0.909873	+	0.0678738i
$538$	−11.0065	−	11.0065i	−0.474523	−	0.474523i
$539$			13.8608i			0.597025i
$540$	6.31479	−	9.75312i	0.271745	−	0.419707i
$541$			13.5211i			0.581316i	0.956827	+	0.290658i	$0.0938742\pi$
$541$			13.5211i			0.581316i	−0.956827	+	0.290658i	$0.906126\pi$
$542$	6.22260	−	6.22260i	0.267284	−	0.267284i
$543$	10.4537	−	0.779813i	0.448611	−	0.0334650i
$544$	3.80703			0.163225
$545$	8.39788	+	8.61169i	0.359726	+	0.368884i
$546$	0.408116	−	2.04811i	0.0174658	−	0.0876510i
$547$	21.4527	+	21.4527i	0.917252	+	0.917252i	0.996829	−	0.0795767i	$-0.0253569\pi$
$547$	21.4527	+	21.4527i	0.917252	+	0.917252i	−0.0795767	+	0.996829i	$0.525357\pi$
$548$	4.54541	−	4.54541i	0.194170	−	0.194170i
$549$	16.2845	−	2.44314i	0.695006	−	0.104271i
$550$	−7.29098	+	6.93332i	−0.310888	+	0.295638i
$551$	−36.5193			−1.55578
$552$	15.2188	−	1.13528i	0.647755	−	0.0483205i
$553$	−2.52246	−	2.52246i	−0.107266	−	0.107266i
$554$			3.19261i			0.135641i
$555$	−6.54596	+	0.405646i	−0.277861	+	0.0172187i
$556$	−0.709569			−0.0300924
$557$	−0.846759	−	0.846759i	−0.0358783	−	0.0358783i	0.688940	−	0.724818i	$-0.258076\pi$
$557$	−0.846759	−	0.846759i	−0.0358783	−	0.0358783i	−0.724818	+	0.688940i	$0.758076\pi$
$558$	12.5761	−	17.0157i	0.532389	−	0.720334i
$559$	6.93345	+	12.2726i	0.293254	+	0.519077i
$560$	−0.747699	−	0.00939855i	−0.0315960	−	0.000397161i
$561$	8.65846	−	10.0544i	0.365560	−	0.424496i
$562$	−0.388876	−	0.388876i	−0.0164037	−	0.0164037i
$563$	−2.78320	−	2.78320i	−0.117298	−	0.117298i	0.646021	−	0.763319i	$-0.276432\pi$
$563$	−2.78320	−	2.78320i	−0.117298	−	0.117298i	−0.763319	+	0.646021i	$0.776432\pi$
$564$	−3.26664	+	3.79329i	−0.137550	+	0.159726i
$565$	−0.300200	+	23.8824i	−0.0126295	+	1.00474i
$566$	−16.9310			−0.711665
$567$	1.40995	−	2.65897i	0.0592123	−	0.111666i
$568$	−6.99284	+	6.99284i	−0.293413	+	0.293413i
$569$	1.33774			0.0560812			0.0280406	−	0.999607i	$-0.491073\pi$
$569$	1.33774			0.0560812			0.0280406	+	0.999607i	$0.491073\pi$
$570$	1.92019	+	30.9864i	0.0804280	+	1.29788i
$571$	−30.9261			−1.29422			−0.647108	−	0.762398i	$-0.724022\pi$
$571$	−30.9261			−1.29422			−0.647108	+	0.762398i	$0.724022\pi$
$572$	−6.99021	−	1.94324i	−0.292275	−	0.0812509i
$573$	0.661165	+	8.86317i	0.0276206	+	0.370264i
$574$	2.64243			0.110293
$575$	−31.9247	+	30.3587i	−1.33135	+	1.26604i
$576$	−0.445105	−	2.96680i	−0.0185460	−	0.123617i
$577$	32.6325	−	32.6325i	1.35851	−	1.35851i	0.482754	−	0.875756i	$-0.339636\pi$
$577$	32.6325	−	32.6325i	1.35851	−	1.35851i	0.875756	−	0.482754i	$-0.160364\pi$
$578$	−1.77240	+	1.77240i	−0.0737220	+	0.0737220i
$579$	21.5924	+	18.5946i	0.897350	+	0.772764i
$580$	−7.29333	+	7.11225i	−0.302839	+	0.295320i
$581$		−	1.41134i		−	0.0585523i
$582$	−26.8273	+	2.00124i	−1.11203	+	0.0829540i
$583$	−13.7440	−	13.7440i	−0.569218	−	0.569218i
$584$	−3.66462			−0.151643
$585$	−19.2459	+	14.6490i	−0.795721	+	0.605663i
$586$	12.2892			0.507664
$587$	1.02834	+	1.02834i	0.0424440	+	0.0424440i	0.728010	−	0.685566i	$-0.240445\pi$
$587$	1.02834	+	1.02834i	0.0424440	+	0.0424440i	−0.685566	+	0.728010i	$0.740445\pi$
$588$	11.8976	−	0.887525i	0.490649	−	0.0366009i
$589$			56.5363i			2.32954i
$590$	27.5623	+	0.346457i	1.13472	+	0.0142634i
$591$	10.5147	+	9.05488i	0.432518	+	0.372468i
$592$	−1.19742	+	1.19742i	−0.0492135	+	0.0492135i
$593$	−10.9212	+	10.9212i	−0.448482	+	0.448482i	−0.894850	−	0.446368i	$-0.852717\pi$
$593$	−10.9212	+	10.9212i	−0.448482	+	0.448482i	0.446368	+	0.894850i	$0.352717\pi$
$594$	−8.84765	−	5.57197i	−0.363023	−	0.228621i
$595$	−2.03809	+	1.98749i	−0.0835534	+	0.0814790i
$596$	3.81004			0.156065
$597$	1.27554	+	17.0991i	0.0522045	+	0.699821i
$598$	−30.6078	−	8.50878i	−1.25164	−	0.347950i
$599$	4.08722			0.166999			0.0834996	−	0.996508i	$-0.473390\pi$
$599$	4.08722			0.166999			0.0834996	+	0.996508i	$0.473390\pi$
$600$	6.41818	+	5.81438i	0.262021	+	0.237371i
$601$	−6.82276			−0.278306			−0.139153	−	0.990271i	$-0.544438\pi$
$601$	−6.82276			−0.278306			−0.139153	+	0.990271i	$0.544438\pi$
$602$	0.924438	−	0.924438i	0.0376773	−	0.0376773i
$603$	−10.7580	+	14.5558i	−0.438099	+	0.592757i
$604$	−3.85812			−0.156985
$605$	−10.8512	−	11.1275i	−0.441165	−	0.452397i
$606$	−3.94919	+	4.58588i	−0.160425	+	0.186289i
$607$	11.7904	+	11.7904i	0.478559	+	0.478559i	0.904671	−	0.426111i	$-0.140117\pi$
$607$	11.7904	+	11.7904i	0.478559	+	0.478559i	−0.426111	+	0.904671i	$0.640117\pi$
$608$	5.66817	+	5.66817i	0.229875	+	0.229875i
$609$	−1.72192	+	1.99953i	−0.0697756	+	0.0810249i
$610$	−0.154267	+	12.2726i	−0.00624607	+	0.496904i
$611$	9.07299	−	5.12581i	0.367054	−	0.207368i
$612$	−9.18475	−	6.78833i	−0.371272	−	0.274402i
$613$	−17.6058	−	17.6058i	−0.711093	−	0.711093i	0.255671	−	0.966764i	$-0.417704\pi$
$613$	−17.6058	−	17.6058i	−0.711093	−	0.711093i	−0.966764	+	0.255671i	$0.917704\pi$
$614$	−19.8208			−0.799902
$615$	−22.9370	−	20.2601i	−0.924910	−	0.816968i
$616$			0.672913i			0.0271125i
$617$	−16.1485	−	16.1485i	−0.650116	−	0.650116i	0.302905	−	0.953021i	$-0.402044\pi$
$617$	−16.1485	−	16.1485i	−0.650116	−	0.650116i	−0.953021	+	0.302905i	$0.902044\pi$
$618$	6.30839	−	0.470586i	0.253761	−	0.0189298i
$619$	34.9009			1.40279			0.701393	−	0.712775i	$-0.252562\pi$
$619$	34.9009			1.40279			0.701393	+	0.712775i	$0.252562\pi$
$620$	11.0106	+	11.2909i	0.442197	+	0.453455i
$621$	−38.7408	−	24.3978i	−1.55462	−	0.979049i
$622$	−6.19082	+	6.19082i	−0.248229	+	0.248229i
$623$	−0.243222	−	0.243222i	−0.00974448	−	0.00974448i
$624$	−1.22042	+	6.12459i	−0.0488557	+	0.245180i
$625$	−24.9684	−	1.25640i	−0.998736	−	0.0502560i
$626$	27.2765			1.09019
$627$	27.8610	−	2.07834i	1.11266	−	0.0830011i
$628$	11.1016	−	11.1016i	0.443003	−	0.443003i
$629$			6.44683i			0.257052i
$630$	1.78712	+	1.35590i	0.0712007	+	0.0540204i
$631$			11.3113i			0.450297i	0.974324	+	0.225149i	$0.0722868\pi$
$631$			11.3113i			0.450297i	−0.974324	+	0.225149i	$0.927713\pi$
$632$	7.54308	+	7.54308i	0.300048	+	0.300048i
$633$	39.8202	−	2.97047i	1.58271	−	0.118065i
$634$			7.07857i			0.281126i
$635$	−0.454978	+	36.1956i	−0.0180552	+	1.43638i
$636$	−10.9173	+	12.6774i	−0.432900	+	0.502692i
$637$	−23.9283	−	6.65192i	−0.948072	−	0.263559i
$638$	6.48236	+	6.48236i	0.256639	+	0.256639i
$639$	29.3397	−	4.40180i	1.16066	−	0.174133i
$640$	2.23589	+	0.0281051i	0.0883814	+	0.00111095i
$641$		−	29.2838i		−	1.15664i	−0.815810	−	0.578319i	$-0.803709\pi$
$641$		−	29.2838i		−	1.15664i	0.815810	−	0.578319i	$-0.196291\pi$
$642$	−2.42685	+	0.181035i	−0.0957800	+	0.00714490i
$643$	0.691053	+	0.691053i	0.0272525	+	0.0272525i	0.720602	−	0.693349i	$-0.243866\pi$
$643$	0.691053	+	0.691053i	0.0272525	+	0.0272525i	−0.693349	+	0.720602i	$0.743866\pi$
$644$			2.94646i			0.116107i
$645$	−15.1123	+	0.936491i	−0.595045	+	0.0368743i
$646$	30.5171			1.20068
$647$	−18.2201	+	18.2201i	−0.716306	+	0.716306i	−0.967847	−	0.251540i	$-0.919063\pi$
$647$	−18.2201	+	18.2201i	−0.716306	+	0.716306i	0.251540	+	0.967847i	$0.419063\pi$
$648$	−4.21626	+	7.95130i	−0.165630	+	0.312357i
$649$		−	24.8055i		−	0.973701i
$650$	−8.47020	−	15.9140i	−0.332229	−	0.624199i
$651$	3.09551	+	2.66574i	0.121322	+	0.104478i
$652$	7.73462	−	7.73462i	0.302911	−	0.302911i
$653$	−23.8883	−	23.8883i	−0.934821	−	0.934821i	0.0631814	−	0.998002i	$-0.479875\pi$
$653$	−23.8883	−	23.8883i	−0.934821	−	0.934821i	−0.998002	+	0.0631814i	$0.979875\pi$
$654$	−7.06015	−	6.07994i	−0.276074	−	0.237744i
$655$	−21.0880	+	20.5645i	−0.823978	+	0.803520i
$656$	−7.90181			−0.308514
$657$	8.84119	+	6.53441i	0.344928	+	0.254931i
$658$	−0.683424	−	0.683424i	−0.0266427	−	0.0266427i
$659$	39.4014			1.53486			0.767431	−	0.641132i	$-0.221535\pi$
$659$	39.4014			1.53486			0.767431	+	0.641132i	$0.221535\pi$
$660$	5.15939	−	5.84108i	0.200829	−	0.227364i
$661$		−	24.8182i		−	0.965317i	−0.875809	−	0.482659i	$-0.839671\pi$
$661$		−	24.8182i		−	0.965317i	0.875809	−	0.482659i	$-0.160329\pi$
$662$	14.6550	−	14.6550i	0.569584	−	0.569584i
$663$	13.2019	+	19.7726i	0.512720	+	0.767903i
$664$			4.22042i			0.163784i
$665$	−5.99356	−	0.0753388i	−0.232420	−	0.00292151i
$666$	5.02398	−	0.753741i	0.194675	−	0.0292069i
$667$	28.3840	+	28.3840i	1.09903	+	1.09903i
$668$	9.30685	−	9.30685i	0.360093	−	0.360093i
$669$	−12.1896	−	10.4973i	−0.471278	−	0.405847i
$670$	−9.41880	−	9.65860i	−0.363880	−	0.373144i
$671$	11.0451			0.426392
$672$	0.577606	−	0.0430876i	0.0222816	−	0.00166214i
$673$	2.37353	−	2.37353i	0.0914927	−	0.0914927i	−0.659879	−	0.751372i	$-0.729393\pi$
$673$	2.37353	−	2.37353i	0.0914927	−	0.0914927i	0.751372	+	0.659879i	$0.229393\pi$
$674$		−	18.2410i		−	0.702616i
$675$	−5.11672	−	25.4719i	−0.196943	−	0.980415i
$676$	6.70934	−	11.1348i	0.258052	−	0.428263i
$677$	18.8046	−	18.8046i	0.722721	−	0.722721i	−0.246438	−	0.969159i	$-0.579260\pi$
$677$	18.8046	−	18.8046i	0.722721	−	0.722721i	0.969159	+	0.246438i	$0.0792602\pi$
$678$	−1.37627	−	18.4494i	−0.0528553	−	0.708545i
$679$		−	5.19395i		−	0.199326i
$680$	6.09462	−	5.94330i	0.233718	−	0.227915i
$681$	−6.21922	−	5.35576i	−0.238321	−	0.205233i
$682$	10.0355	−	10.0355i	0.384278	−	0.384278i
$683$	9.16112	−	9.16112i	0.350540	−	0.350540i	−0.509770	−	0.860311i	$-0.670270\pi$
$683$	9.16112	−	9.16112i	0.350540	−	0.350540i	0.860311	+	0.509770i	$0.170270\pi$
$684$	−3.56796	−	23.7818i	−0.136424	−	0.909322i
$685$	0.180664	−	14.3727i	0.00690283	−	0.549153i
$686$			4.64431i			0.177321i
$687$	−41.9994	+	3.13303i	−1.60238	+	0.119532i
$688$	−2.76440	+	2.76440i	−0.105392	+	0.105392i
$689$	30.3225	−	17.1308i	1.15520	−	0.652631i
$690$	22.5912	−	25.5761i	0.860034	−	0.973666i
$691$			10.3308i			0.393002i	0.980504	+	0.196501i	$0.0629579\pi$
$691$			10.3308i			0.393002i	−0.980504	+	0.196501i	$0.937042\pi$
$692$	−0.456884	+	0.456884i	−0.0173681	+	0.0173681i
$693$	1.19988	−	1.62346i	0.0455795	−	0.0616700i
$694$	−6.78932			−0.257719
$695$	−1.13594	+	1.10774i	−0.0430887	+	0.0420189i
$696$	5.14916	−	5.97931i	0.195178	−	0.226645i
$697$	−21.2715	+	21.2715i	−0.805715	+	0.805715i
$698$	−1.66770	−	1.66770i	−0.0631232	−	0.0631232i
$699$	−14.0997	−	12.1421i	−0.533300	−	0.459258i
$700$	−1.21165	+	1.15222i	−0.0457962	+	0.0435497i
$701$		−	20.4079i		−	0.770795i	−0.922751	−	0.385397i	$-0.874064\pi$
$701$		−	20.4079i		−	0.770795i	0.922751	−	0.385397i	$-0.125936\pi$
$702$	13.8651	−	12.5999i	0.523306	−	0.475553i
$703$	−9.59849	+	9.59849i	−0.362014	+	0.362014i
$704$		−	2.01226i		−	0.0758397i
$705$	0.692335	+	11.1723i	0.0260748	+	0.420773i
$706$	0.937977			0.0353012
$707$	−0.826223	−	0.826223i	−0.0310733	−	0.0310733i
$708$	−21.2922	+	1.58833i	−0.800209	+	0.0596932i
$709$	−51.7409			−1.94317			−0.971586	−	0.236687i	$-0.923938\pi$
$709$	−51.7409			−1.94317			−0.971586	+	0.236687i	$0.923938\pi$
$710$	−0.277941	+	22.1115i	−0.0104310	+	0.829831i
$711$	−4.74817	−	31.6484i	−0.178070	−	1.18691i
$712$	0.727322	+	0.727322i	0.0272575	+	0.0272575i
$713$	43.9419	−	43.9419i	1.64564	−	1.64564i
$714$	1.43891	−	1.67089i	0.0538498	−	0.0625315i
$715$	−14.2242	+	7.80180i	−0.531955	+	0.291771i
$716$			12.2071i			0.456201i
$717$	−0.336072	−	4.50517i	−0.0125508	−	0.168249i
$718$	−17.9782	+	17.9782i	−0.670939	+	0.670939i
$719$	−22.3663			−0.834123			−0.417061	−	0.908878i	$-0.636940\pi$
$719$	−22.3663			−0.834123			−0.417061	+	0.908878i	$0.636940\pi$
$720$	−5.34415	−	4.05464i	−0.199165	−	0.151107i
$721$			1.22135i			0.0454853i
$722$	32.0010	+	32.0010i	1.19096	+	1.19096i
$723$	−0.313293	−	4.19981i	−0.0116515	−	0.156192i
$724$		−	6.05221i		−	0.224929i
$725$	−0.572572	+	22.7718i	−0.0212648	+	0.845724i
$726$	9.12269	+	7.85612i	0.338575	+	0.291568i
$727$	−6.91747	−	6.91747i	−0.256555	−	0.256555i	0.567097	−	0.823651i	$-0.308067\pi$
$727$	−6.91747	−	6.91747i	−0.256555	−	0.256555i	−0.823651	+	0.567097i	$0.808067\pi$
$728$	−1.16167	−	0.322938i	−0.0430544	−	0.0119689i
$729$	24.3501	−	11.6651i	0.901854	−	0.432041i
$730$	−5.86665	+	5.72099i	−0.217134	+	0.211743i
$731$			14.8834i			0.550483i
$732$	−0.707235	−	9.48075i	−0.0261402	−	0.350419i
$733$	36.6546	+	36.6546i	1.35387	+	1.35387i	0.881285	+	0.472585i	$0.156679\pi$
$733$	36.6546	+	36.6546i	1.35387	+	1.35387i	0.472585	+	0.881285i	$0.343321\pi$
$734$		−	23.7536i		−	0.876763i
$735$	17.6612	−	19.9947i	0.651442	−	0.737514i
$736$		−	8.81099i		−	0.324777i
$737$	−8.58463	+	8.58463i	−0.316219	+	0.316219i
$738$	19.0637	+	14.0898i	0.701746	+	0.518651i
$739$	−13.6336			−0.501519			−0.250760	−	0.968049i	$-0.580680\pi$
$739$	−13.6336			−0.501519			−0.250760	+	0.968049i	$0.580680\pi$
$740$	−0.0475932	+	3.78626i	−0.00174956	+	0.139186i
$741$	−9.78286	+	49.0947i	−0.359382	+	1.80354i
$742$	−2.28405	−	2.28405i	−0.0838501	−	0.0838501i
$743$	−33.6803	+	33.6803i	−1.23561	+	1.23561i	−0.273836	+	0.961776i	$0.588292\pi$
$743$	−33.6803	+	33.6803i	−1.23561	+	1.23561i	−0.961776	+	0.273836i	$0.911708\pi$
$744$	−9.25669	−	7.97152i	−0.339367	−	0.292250i
$745$	6.09944	−	5.94800i	0.223466	−	0.217918i
$746$	−10.6136			−0.388593
$747$	7.52546	−	10.1821i	0.275342	−	0.372544i
$748$	−5.41694	−	5.41694i	−0.198063	−	0.198063i
$749$		−	0.469854i		−	0.0171681i
$750$	19.3518	−	0.711522i	0.706629	−	0.0259811i
$751$	13.7857			0.503048			0.251524	−	0.967851i	$-0.419068\pi$
$751$	13.7857			0.503048			0.251524	+	0.967851i	$0.419068\pi$
$752$	2.04369	+	2.04369i	0.0745256	+	0.0745256i
$753$	−3.72026	−	49.8715i	−0.135574	−	1.81742i
$754$	−14.3016	+	8.07975i	−0.520835	+	0.294247i
$755$	−6.17642	+	6.02307i	−0.224783	+	0.219202i
$756$	−1.47035	−	0.925980i	−0.0534761	−	0.0336776i
$757$	−27.1169	−	27.1169i	−0.985579	−	0.985579i	0.0143184	−	0.999897i	$-0.495442\pi$
$757$	−27.1169	−	27.1169i	−0.985579	−	0.985579i	−0.999897	+	0.0143184i	$0.995442\pi$
$758$	13.3577	+	13.3577i	0.485175	+	0.485175i
$759$	−23.2699	−	20.0391i	−0.844643	−	0.727375i
$760$	17.9229	+	0.225290i	0.650132	+	0.00817214i
$761$	−28.2729			−1.02489			−0.512446	−	0.858720i	$-0.671260\pi$
$761$	−28.2729			−1.02489			−0.512446	+	0.858720i	$0.671260\pi$
$762$	−2.08585	−	27.9615i	−0.0755622	−	1.01294i
$763$	1.27200	−	1.27200i	0.0460497	−	0.0460497i
$764$	5.13137			0.185647
$765$	−25.3013	+	3.47134i	−0.914770	+	0.125506i
$766$	−6.47732			−0.234035
$767$	42.8225	+	11.9044i	1.54623	+	0.429843i
$768$	−1.72725	+	0.128848i	−0.0623268	+	0.00464939i
$769$	−8.13103			−0.293212			−0.146606	−	0.989195i	$-0.546835\pi$
$769$	−8.13103			−0.293212			−0.146606	+	0.989195i	$0.546835\pi$
$770$	1.05051	+	1.07726i	0.0378578	+	0.0388217i
$771$	−29.1670	+	33.8693i	−1.05042	+	1.21977i
$772$	11.6332	−	11.6332i	0.418689	−	0.418689i
$773$	−21.2081	+	21.2081i	−0.762803	+	0.762803i	−0.976828	−	0.214025i	$-0.931343\pi$
$773$	−21.2081	+	21.2081i	−0.762803	+	0.762803i	0.214025	+	0.976828i	$0.431343\pi$
$774$	11.5986	−	1.74012i	0.416902	−	0.0625473i
$775$	35.2535	+	0.886410i	1.26634	+	0.0318408i
$776$			15.5318i			0.557559i
$777$	0.0729647	+	0.978119i	0.00261759	+	0.0350898i
$778$	2.61512	+	2.61512i	0.0937566	+	0.0937566i
$779$	−63.3410			−2.26943
$780$	7.60760	+	11.7100i	0.272396	+	0.419286i
$781$	19.8999			0.712075
$782$	−23.7189	−	23.7189i	−0.848188	−	0.848188i
$783$	−23.0845	+	5.24406i	−0.824972	+	0.187407i
$784$		−	6.88817i		−	0.246006i
$785$	0.441251	−	35.1036i	0.0157489	−	1.25290i
$786$	14.8884	−	17.2887i	0.531050	−	0.616667i
$787$	21.8538	−	21.8538i	0.779005	−	0.779005i	−0.200657	−	0.979662i	$-0.564308\pi$
$787$	21.8538	−	21.8538i	0.779005	−	0.779005i	0.979662	+	0.200657i	$0.0643075\pi$
$788$	5.66495	−	5.66495i	0.201806	−	0.201806i
$789$	−8.34084	−	7.18282i	−0.296942	−	0.255715i
$790$	23.8514	+	0.299812i	0.848596	+	0.0106668i
$791$	3.57193			0.127003
$792$	−3.58806	+	4.85472i	−0.127496	+	0.172505i
$793$	−5.30066	+	19.0675i	−0.188232	+	0.677108i
$794$	−13.5948			−0.482461
$795$	2.31383	+	37.3386i	0.0820631	+	1.32426i
$796$	9.89963			0.350883
$797$	−13.6728	+	13.6728i	−0.484316	+	0.484316i	−0.906507	−	0.422191i	$-0.861261\pi$
$797$	−13.6728	+	13.6728i	−0.484316	+	0.484316i	0.422191	+	0.906507i	$0.361261\pi$
$798$	4.63009	−	0.345391i	0.163903	−	0.0122267i
$799$	11.0031			0.389262
$800$	3.62329	−	3.44555i	0.128102	−	0.121819i
$801$	−0.457830	−	3.05161i	−0.0161766	−	0.107823i
$802$	20.6258	+	20.6258i	0.728321	+	0.728321i
$803$	5.21431	+	5.21431i	0.184009	+	0.184009i
$804$	7.91844	+	6.81907i	0.279262	+	0.240490i
$805$	4.59984	+	4.71695i	0.162123	+	0.166251i
$806$	12.5084	+	22.1407i	0.440590	+	0.779871i
$807$	26.8856	−	2.00558i	0.946417	−	0.0705998i
$808$	2.47071	+	2.47071i	0.0869192	+	0.0869192i
$809$	32.5723			1.14518			0.572590	−	0.819842i	$-0.305939\pi$
$809$	32.5723			1.14518			0.572590	+	0.819842i	$0.305939\pi$
$810$	5.66334	+	19.3113i	0.198989	+	0.678530i
$811$			43.4132i			1.52444i	0.647316	+	0.762222i	$0.275892\pi$
$811$			43.4132i			1.52444i	−0.647316	+	0.762222i	$0.724108\pi$
$812$	1.07727	+	1.07727i	0.0378049	+	0.0378049i
$813$	1.13387	+	15.2000i	0.0397666	+	0.533086i
$814$	3.40756			0.119435
$815$	0.307425	−	24.4571i	0.0107686	−	0.856695i
$816$	−4.30286	+	4.99657i	−0.150630	+	0.174915i
$817$	−22.1595	+	22.1595i	−0.775262	+	0.775262i
$818$	−24.2911	−	24.2911i	−0.849318	−	0.849318i
$819$	2.22679	+	2.85050i	0.0778104	+	0.0996044i
$820$	−12.6499	+	12.3358i	−0.441754	+	0.430786i
$821$	3.21969			0.112368			0.0561841	−	0.998420i	$-0.482107\pi$
$821$	3.21969			0.112368			0.0561841	+	0.998420i	$0.482107\pi$
$822$	0.828255	+	11.1031i	0.0288887	+	0.387264i
$823$	23.3869	−	23.3869i	0.815215	−	0.815215i	−0.170195	−	0.985410i	$-0.554440\pi$
$823$	23.3869	−	23.3869i	0.815215	−	0.815215i	0.985410	+	0.170195i	$0.0544399\pi$
$824$		−	3.65227i		−	0.127233i
$825$	−0.859141	−	17.4055i	−0.0299115	−	0.605980i
$826$		−	4.12231i		−	0.143434i
$827$	17.4931	+	17.4931i	0.608295	+	0.608295i	0.942500	−	0.334205i	$-0.108468\pi$
$827$	17.4931	+	17.4931i	0.608295	+	0.608295i	−0.334205	+	0.942500i	$0.608468\pi$
$828$	−15.7109	+	21.2572i	−0.545992	+	0.738739i
$829$		−	46.9837i		−	1.63181i	−0.578186	−	0.815905i	$-0.696239\pi$
$829$		−	46.9837i		−	1.63181i	0.578186	−	0.815905i	$-0.303761\pi$
$830$	6.58867	+	6.75642i	0.228696	+	0.234519i
$831$	−4.19018	−	3.60842i	−0.145356	−	0.125175i
$832$	3.47382	+	0.965701i	0.120433	+	0.0334797i
$833$	−18.5428	−	18.5428i	−0.642469	−	0.642469i
$834$	0.801985	−	0.931281i	0.0277705	−	0.0322476i
$835$	0.369915	−	29.4285i	0.0128014	−	1.01842i
$836$		−	16.1302i		−	0.557876i
$837$	8.11843	+	35.7376i	0.280614	+	1.23527i
$838$	0.742340	+	0.742340i	0.0256437	+	0.0256437i
$839$		−	30.7292i		−	1.06089i	−0.847719	−	0.530445i	$-0.822025\pi$
$839$		−	30.7292i		−	1.06089i	0.847719	−	0.530445i	$-0.177975\pi$
$840$	0.857416	−	0.970703i	0.0295837	−	0.0334924i
$841$	−8.24467			−0.284299
$842$	−19.4657	+	19.4657i	−0.670834	+	0.670834i
$843$	0.949907	−	0.0708602i	0.0327165	−	0.00244055i
$844$		−	23.0541i		−	0.793555i
$845$	−6.64215	−	28.2999i	−0.228497	−	0.973545i
$846$	−1.28645	−	8.57466i	−0.0442289	−	0.294803i
$847$	−1.64361	+	1.64361i	−0.0564749	+	0.0564749i
$848$	6.83014	+	6.83014i	0.234548	+	0.234548i
$849$	19.1362	−	22.2213i	0.656752	−	0.762634i
$850$	0.478466	−	19.0291i	0.0164113	−	0.652693i
$851$	14.9205			0.511469
$852$	−1.27422	−	17.0814i	−0.0436541	−	0.585200i
$853$	−14.1733	−	14.1733i	−0.485285	−	0.485285i	0.421529	−	0.906815i	$-0.361493\pi$
$853$	−14.1733	−	14.1733i	−0.485285	−	0.485285i	−0.906815	+	0.421529i	$0.861493\pi$
$854$	1.83554			0.0628108
$855$	−42.8387	−	32.5020i	−1.46505	−	1.11154i
$856$			1.40503i			0.0480231i
$857$	−24.8921	+	24.8921i	−0.850299	+	0.850299i	−0.990170	−	0.139871i	$-0.955331\pi$
$857$	−24.8921	+	24.8921i	−0.850299	+	0.850299i	0.139871	+	0.990170i	$0.455331\pi$
$858$	10.4511	−	6.97805i	0.356793	−	0.238227i
$859$			22.3349i			0.762056i	0.924564	+	0.381028i	$0.124430\pi$
$859$			22.3349i			0.762056i	−0.924564	+	0.381028i	$0.875570\pi$
$860$	−0.109876	+	8.74112i	−0.00374673	+	0.298070i
$861$	−2.98658	+	3.46808i	−0.101782	+	0.118192i
$862$	15.9641	+	15.9641i	0.543739	+	0.543739i
$863$	−27.2146	+	27.2146i	−0.926395	+	0.926395i	−0.997471	−	0.0710755i	$-0.977357\pi$
$863$	−27.2146	+	27.2146i	−0.926395	+	0.926395i	0.0710755	+	0.997471i	$0.477357\pi$
$864$	4.39688	+	2.76902i	0.149585	+	0.0942039i
$865$	−0.0181596	+	1.44468i	−0.000617444	+	0.0491206i
$866$	23.3774			0.794395
$867$	−0.322963	−	4.32944i	−0.0109684	−	0.147035i
$868$	1.66775	−	1.66775i	0.0566071	−	0.0566071i
$869$		−	21.4658i		−	0.728177i
$870$	−1.09132	−	17.6108i	−0.0369992	−	0.597061i
$871$	−10.7001	−	18.9398i	−0.362558	−	0.641750i
$872$	−3.80376	+	3.80376i	−0.128811	+	0.128811i
$873$	27.6948	−	37.4717i	0.937329	−	1.26823i
$874$		−	70.6289i		−	2.38906i
$875$	−0.140949	+	3.73613i	−0.00476493	+	0.126304i
$876$	4.14191	−	4.80967i	0.139942	−	0.162504i
$877$	25.8361	−	25.8361i	0.872421	−	0.872421i	−0.120314	−	0.992736i	$-0.538390\pi$
$877$	25.8361	−	25.8361i	0.872421	−	0.872421i	0.992736	+	0.120314i	$0.0383903\pi$
$878$	−19.8870	+	19.8870i	−0.671152	+	0.671152i
$879$	−13.8898	+	16.1291i	−0.468492	+	0.544022i
$880$	−3.14141	−	3.22139i	−0.105897	−	0.108593i
$881$			18.4330i			0.621023i	0.950570	+	0.310511i	$0.100500\pi$
$881$			18.4330i			0.621023i	−0.950570	+	0.310511i	$0.899500\pi$
$882$	−12.2823	+	16.6183i	−0.413568	+	0.559566i
$883$	5.81874	−	5.81874i	0.195816	−	0.195816i	−0.602388	−	0.798204i	$-0.705784\pi$
$883$	5.81874	−	5.81874i	0.195816	−	0.195816i	0.798204	+	0.602388i	$0.205784\pi$
$884$	11.9511	−	6.75179i	0.401958	−	0.227087i
$885$	−31.6068	+	35.7828i	−1.06245	+	1.20283i
$886$		−	5.10590i		−	0.171536i
$887$	21.3790	−	21.3790i	0.717838	−	0.717838i	−0.250324	−	0.968162i	$-0.580537\pi$
$887$	21.3790	−	21.3790i	0.717838	−	0.717838i	0.968162	+	0.250324i	$0.0805372\pi$
$888$	−0.218191	−	2.92493i	−0.00732201	−	0.0981542i
$889$	5.41354			0.181564
$890$	2.29981	+	0.0289086i	0.0770899	+	0.000969017i
$891$	17.3130	−	5.31451i	0.580006	−	0.178043i
$892$	−6.56733	+	6.56733i	−0.219891	+	0.219891i
$893$	16.3822	+	16.3822i	0.548209	+	0.548209i
$894$	−4.30626	+	5.00052i	−0.144023	+	0.167242i
$895$	19.0570	+	19.5422i	0.637005	+	0.653223i
$896$		−	0.334408i		−	0.0111718i
$897$	45.7616	−	30.5545i	1.52794	−	1.02019i
$898$	14.6445	−	14.6445i	0.488693	−	0.488693i
$899$		−	32.1317i		−	1.07165i
$900$	−14.8852	+	1.85195i	−0.496175	+	0.0617318i
$901$	36.7731			1.22509
$902$	11.2433	+	11.2433i	0.374362	+	0.374362i
$903$	0.168449	+	2.25813i	0.00560564	+	0.0751457i
$904$	−10.6814			−0.355257
$905$	−9.44835	−	9.68890i	−0.314074	−	0.322070i
$906$	4.36061	−	5.06363i	0.144872	−	0.168228i
$907$	0.553858	+	0.553858i	0.0183906	+	0.0183906i	0.716242	−	0.697852i	$-0.245861\pi$
$907$	0.553858	+	0.553858i	0.0183906	+	0.0183906i	−0.697852	+	0.716242i	$0.745861\pi$
$908$	−3.35070	+	3.35070i	−0.111197	+	0.111197i
$909$	−1.55524	−	10.3663i	−0.0515842	−	0.343829i
$910$	−2.36386	+	1.29655i	−0.0783611	+	0.0429801i
$911$		−	6.42215i		−	0.212775i	−0.994325	−	0.106388i	$-0.966072\pi$
$911$		−	6.42215i		−	0.212775i	0.994325	−	0.106388i	$-0.0339284\pi$
$912$	−13.8457	+	1.03284i	−0.458475	+	0.0342009i
$913$	6.00515	−	6.00515i	0.198742	−	0.198742i
$914$	16.0220			0.529960
$915$	−15.9330	−	14.0735i	−0.526728	−	0.465256i
$916$			24.3157i			0.803415i
$917$	3.11485	+	3.11485i	0.102861	+	0.102861i
$918$	19.2904	−	4.38216i	0.636678	−	0.144633i
$919$			6.94188i			0.228992i	0.993424	+	0.114496i	$0.0365252\pi$
$919$			6.94188i			0.228992i	−0.993424	+	0.114496i	$0.963475\pi$
$920$	−13.7552	−	14.1054i	−0.453495	−	0.465041i
$921$	22.4023	−	26.0140i	0.738181	−	0.857191i
$922$	−29.3668	−	29.3668i	−0.967144	−	0.967144i
$923$	−9.55017	+	34.3539i	−0.314348	+	1.13077i
$924$	−0.883172	−	0.760555i	−0.0290542	−	0.0250204i
$925$	5.83470	+	6.13568i	0.191844	+	0.201740i
$926$		−	34.0929i		−	1.12036i
$927$	−6.51238	+	8.81139i	−0.213895	+	0.289404i
$928$	−3.22144	−	3.22144i	−0.105749	−	0.105749i
$929$			7.75923i			0.254572i	0.991866	+	0.127286i	$0.0406266\pi$
$929$			7.75923i			0.254572i	−0.991866	+	0.127286i	$0.959373\pi$
$930$	−27.2636	+	1.68949i	−0.894008	+	0.0554007i
$931$		−	55.2156i		−	1.80962i
$932$	−7.59642	+	7.59642i	−0.248829	+	0.248829i
$933$	−1.12808	−	15.1223i	−0.0369317	−	0.495083i
$934$	16.1825			0.529507
$935$	−17.1285	−	0.215305i	−0.560162	−	0.00704122i
$936$	−6.65891	−	8.52402i	−0.217653	−	0.278616i
$937$	19.7935	+	19.7935i	0.646624	+	0.646624i	0.952176	−	0.305551i	$-0.0988408\pi$
$937$	19.7935	+	19.7935i	0.646624	+	0.646624i	−0.305551	+	0.952176i	$0.598841\pi$
$938$	−1.42664	+	1.42664i	−0.0465815	+	0.0465815i
$939$	−30.8291	+	35.7993i	−1.00607	+	1.16827i
$940$	6.46219	+	0.0812295i	0.210774	+	0.00264942i
$941$	13.4668			0.439006			0.219503	−	0.975612i	$-0.429557\pi$
$941$	13.4668			0.439006			0.219503	+	0.975612i	$0.429557\pi$
$942$	2.02292	+	27.1180i	0.0659102	+	0.883551i
$943$	49.2307	+	49.2307i	1.60317	+	1.60317i
$944$			12.3272i			0.401216i
$945$	−3.79945	+	0.813033i	−0.123596	+	0.0264480i
$946$	7.86683			0.255773
$947$	−13.4019	−	13.4019i	−0.435504	−	0.435504i	0.454991	−	0.890496i	$-0.349642\pi$
$947$	−13.4019	−	13.4019i	−0.435504	−	0.435504i	−0.890496	+	0.454991i	$0.849642\pi$
$948$	−18.4255	+	1.37449i	−0.598432	+	0.0446412i
$949$	−11.5040	+	6.49923i	−0.373437	+	0.210974i
$950$	29.0443	−	27.6195i	0.942320	−	0.896096i
$951$	−9.29035	−	8.00050i	−0.301260	−	0.259434i
$952$	−0.900217	−	0.900217i	−0.0291762	−	0.0291762i
$953$	−32.8756	−	32.8756i	−1.06495	−	1.06495i	−0.997739	−	0.0672062i	$-0.978591\pi$
$953$	−32.8756	−	32.8756i	−1.06495	−	1.06495i	−0.0672062	−	0.997739i	$-0.521409\pi$
$954$	−4.29939	−	28.6571i	−0.139198	−	0.927808i
$955$	8.21475	−	8.01079i	0.265823	−	0.259223i
$956$	−2.60829			−0.0843581
$957$	−15.8345	+	1.18120i	−0.511856	+	0.0381829i
$958$	−15.4565	+	15.4565i	−0.499376	+	0.499376i
$959$	−2.14963			−0.0694152
$960$	−2.56399	+	2.90275i	−0.0827523	+	0.0936860i
$961$	−18.7438			−0.604639
$962$	−1.63532	+	5.88257i	−0.0527248	+	0.189662i
$963$	2.50532	−	3.38976i	0.0807329	−	0.109233i
$964$	−2.43150			−0.0783132
$965$	0.462381	−	36.7846i	0.0148846	−	1.18414i
$966$	−3.86711	−	3.33021i	−0.124422	−	0.107148i
$967$	−16.0743	+	16.0743i	−0.516915	+	0.516915i	−0.916637	−	0.399722i	$-0.869107\pi$
$967$	−16.0743	+	16.0743i	−0.516915	+	0.516915i	0.399722	+	0.916637i	$0.369107\pi$
$968$	4.91498	−	4.91498i	0.157973	−	0.157973i
$969$	−34.4918	+	40.0525i	−1.10803	+	1.28667i
$970$	24.2473	+	24.8647i	0.778535	+	0.798357i
$971$			30.5730i			0.981133i	0.871404	+	0.490566i	$0.163210\pi$
$971$			30.5730i			0.981133i	−0.871404	+	0.490566i	$0.836790\pi$
$972$	−5.67037	−	14.5206i	−0.181877	−	0.465747i
$973$	0.167786	+	0.167786i	0.00537897	+	0.00537897i
$974$	−25.7689			−0.825687
$975$	30.4599	+	6.86989i	0.975497	+	0.220012i
$976$	−5.48892			−0.175696
$977$	16.1846	+	16.1846i	0.517792	+	0.517792i	0.916903	−	0.399111i	$-0.130681\pi$
$977$	16.1846	+	16.1846i	0.517792	+	0.517792i	−0.399111	+	0.916903i	$0.630681\pi$
$978$	1.40939	+	18.8934i	0.0450673	+	0.604144i
$979$		−	2.06978i		−	0.0661506i
$980$	−10.7534	−	11.0272i	−0.343505	−	0.352251i
$981$	15.9594	−	2.39436i	0.509543	−	0.0764461i
$982$	9.90856	−	9.90856i	0.316195	−	0.316195i
$983$	31.6227	−	31.6227i	1.00861	−	1.00861i	0.00864329	−	0.999963i	$-0.497249\pi$
$983$	31.6227	−	31.6227i	1.00861	−	1.00861i	0.999963	−	0.00864329i	$-0.00275128\pi$
$984$	8.93096	−	10.3708i	0.284709	−	0.330610i
$985$	0.225163	−	17.9127i	0.00717427	−	0.570747i
$986$	−17.3441			−0.552347
$987$	1.66940	−	0.124532i	0.0531377	−	0.00396391i
$988$	27.8461	+	7.74106i	0.885904	+	0.246276i
$989$	34.4462			1.09532
$990$	1.83482	+	13.3733i	0.0583145	+	0.425033i
$991$	−17.3473			−0.551055			−0.275527	−	0.961293i	$-0.588852\pi$
$991$	−17.3473			−0.551055			−0.275527	+	0.961293i	$0.588852\pi$
$992$	−4.98717	+	4.98717i	−0.158343	+	0.158343i
$993$	2.67041	+	35.7979i	0.0847430	+	1.13601i
$994$	3.30708			0.104894
$995$	15.8482	−	15.4547i	0.502421	−	0.489947i
$996$	−5.53914	−	4.77010i	−0.175514	−	0.151146i
$997$	−19.9335	−	19.9335i	−0.631300	−	0.631300i	0.317094	−	0.948394i	$-0.397293\pi$
$997$	−19.9335	−	19.9335i	−0.631300	−	0.631300i	−0.948394	+	0.317094i	$0.897293\pi$
$998$	−20.2627	−	20.2627i	−0.641405	−	0.641405i
$999$	−4.68906	+	7.44568i	−0.148355	+	0.235571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.s.c.77.7	yes	24
3.2	odd	2		390.2.s.b.77.4	✓	24
5.3	odd	4		390.2.s.b.233.10	yes	24
13.12	even	2	inner	390.2.s.c.77.1	yes	24
15.8	even	4	inner	390.2.s.c.233.1	yes	24
39.38	odd	2		390.2.s.b.77.10	yes	24
65.38	odd	4		390.2.s.b.233.4	yes	24
195.38	even	4	inner	390.2.s.c.233.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.s.b.77.4	✓	24	3.2	odd	2
390.2.s.b.77.10	yes	24	39.38	odd	2
390.2.s.b.233.4	yes	24	65.38	odd	4
390.2.s.b.233.10	yes	24	5.3	odd	4
390.2.s.c.77.1	yes	24	13.12	even	2	inner
390.2.s.c.77.7	yes	24	1.1	even	1	trivial
390.2.s.c.233.1	yes	24	15.8	even	4	inner
390.2.s.c.233.7	yes	24	195.38	even	4	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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.72725 + 0.128848i) q^{3} +1.00000i q^{4} +(1.56114 + 1.60089i) q^{5} +(-1.31246 - 1.13024i) q^{6} +(0.236462 - 0.236462i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.96680 - 0.445105i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.72725 + 0.128848i) q^{3} +1.00000i q^{4} +(1.56114 + 1.60089i) q^{5} +(-1.31246 - 1.13024i) q^{6} +(0.236462 - 0.236462i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.96680 - 0.445105i) q^{9} +(-0.0281051 + 2.23589i) q^{10} +2.01226 q^{11} +(-0.128848 - 1.72725i) q^{12} +(-0.965701 + 3.47382i) q^{13} +0.334408 q^{14} +(-2.90275 - 2.56399i) q^{15} -1.00000 q^{16} +(-2.69197 + 2.69197i) q^{17} +(2.41258 + 1.78311i) q^{18} -8.01600 q^{19} +(-1.60089 + 1.56114i) q^{20} +(-0.377962 + 0.438897i) q^{21} +(1.42288 + 1.42288i) q^{22} +(6.23031 + 6.23031i) q^{23} +(1.13024 - 1.31246i) q^{24} +(-0.125680 + 4.99842i) q^{25} +(-3.13922 + 1.77351i) q^{26} +(-5.06705 + 1.15107i) q^{27} +(0.236462 + 0.236462i) q^{28} +4.55580 q^{29} +(-0.239545 - 3.86557i) q^{30} -7.05293i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.47567 + 0.259274i) q^{33} -3.80703 q^{34} +(0.747699 + 0.00939855i) q^{35} +(0.445105 + 2.96680i) q^{36} +(1.19742 - 1.19742i) q^{37} +(-5.66817 - 5.66817i) q^{38} +(1.22042 - 6.12459i) q^{39} +(-2.23589 - 0.0281051i) q^{40} +7.90181 q^{41} +(-0.577606 + 0.0430876i) q^{42} +(2.76440 - 2.76440i) q^{43} +2.01226i q^{44} +(5.34415 + 4.05464i) q^{45} +8.81099i q^{46} +(-2.04369 - 2.04369i) q^{47} +(1.72725 - 0.128848i) q^{48} +6.88817i q^{49} +(-3.62329 + 3.44555i) q^{50} +(4.30286 - 4.99657i) q^{51} +(-3.47382 - 0.965701i) q^{52} +(-6.83014 - 6.83014i) q^{53} +(-4.39688 - 2.76902i) q^{54} +(3.14141 + 3.22139i) q^{55} +0.334408i q^{56} +(13.8457 - 1.03284i) q^{57} +(3.22144 + 3.22144i) q^{58} -12.3272i q^{59} +(2.56399 - 2.90275i) q^{60} +5.48892 q^{61} +(4.98717 - 4.98717i) q^{62} +(0.596284 - 0.806784i) q^{63} -1.00000i q^{64} +(-7.06879 + 3.87714i) q^{65} +(-2.64101 - 2.27434i) q^{66} +(-4.26617 + 4.26617i) q^{67} +(-2.69197 - 2.69197i) q^{68} +(-11.5641 - 9.95855i) q^{69} +(0.522057 + 0.535349i) q^{70} +9.88936 q^{71} +(-1.78311 + 2.41258i) q^{72} +(2.59128 + 2.59128i) q^{73} +1.69340 q^{74} +(-0.426954 - 8.64972i) q^{75} -8.01600i q^{76} +(0.475822 - 0.475822i) q^{77} +(5.19370 - 3.46777i) q^{78} -10.6675i q^{79} +(-1.56114 - 1.60089i) q^{80} +(8.60376 - 2.64107i) q^{81} +(5.58743 + 5.58743i) q^{82} +(2.98429 - 2.98429i) q^{83} +(-0.438897 - 0.377962i) q^{84} +(-8.51210 - 0.106997i) q^{85} +3.90946 q^{86} +(-7.86902 + 0.587005i) q^{87} +(-1.42288 + 1.42288i) q^{88} -1.02859i q^{89} +(0.911824 + 6.64594i) q^{90} +(0.593074 + 1.04978i) q^{91} +(-6.23031 + 6.23031i) q^{92} +(0.908753 + 12.1822i) q^{93} -2.89021i q^{94} +(-12.5141 - 12.8327i) q^{95} +(1.31246 + 1.13024i) q^{96} +(10.9826 - 10.9826i) q^{97} +(-4.87067 + 4.87067i) q^{98} +(5.96995 - 0.895665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} + 12 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 + 12 * q^9	\( 24 q + 4 q^{3} + 12 q^{9} + 4 q^{10} - 8 q^{12} - 8 q^{13} + 16 q^{14} - 24 q^{16} - 52 q^{17} + 16 q^{22} + 16 q^{23} + 16 q^{25} - 56 q^{27} + 80 q^{29} + 8 q^{30} - 20 q^{35} + 16 q^{38} + 32 q^{39} - 48 q^{42} + 28 q^{43} - 4 q^{48} - 20 q^{51} - 8 q^{52} - 72 q^{53} + 24 q^{55} - 64 q^{61} + 32 q^{62} + 12 q^{65} + 8 q^{66} - 52 q^{68} + 16 q^{69} + 120 q^{74} + 24 q^{75} - 32 q^{77} - 64 q^{78} + 12 q^{81} + 32 q^{82} - 16 q^{88} - 44 q^{90} + 64 q^{91} - 16 q^{92} - 96 q^{95}+O(q^{100}) \) 24 * q + 4 * q^3 + 12 * q^9 + 4 * q^10 - 8 * q^12 - 8 * q^13 + 16 * q^14 - 24 * q^16 - 52 * q^17 + 16 * q^22 + 16 * q^23 + 16 * q^25 - 56 * q^27 + 80 * q^29 + 8 * q^30 - 20 * q^35 + 16 * q^38 + 32 * q^39 - 48 * q^42 + 28 * q^43 - 4 * q^48 - 20 * q^51 - 8 * q^52 - 72 * q^53 + 24 * q^55 - 64 * q^61 + 32 * q^62 + 12 * q^65 + 8 * q^66 - 52 * q^68 + 16 * q^69 + 120 * q^74 + 24 * q^75 - 32 * q^77 - 64 * q^78 + 12 * q^81 + 32 * q^82 - 16 * q^88 - 44 * q^90 + 64 * q^91 - 16 * q^92 - 96 * q^95

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