LMFDB - Embedded newform 390.2.s.c.233.1

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			233.1
Character	$\chi$	$=$	390.233
Dual form			390.2.s.c.77.1

$q$-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} +(-3.47382 - 0.965701i) 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} +(5.87573 + 2.11560i) 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} +(-0.965701 + 3.47382i) 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} +(6.96910 - 4.05360i) 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} +(-5.65073 + 2.65881i) 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 $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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	$-0.270130\pi$
$7$	−0.236462	−	0.236462i	−0.0893742	−	0.0893742i	−0.750380	+	0.661006i	$0.770130\pi$
$8$	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	$-0.598108\pi$
$11$	−2.01226			−0.606718			−0.303359	+	0.952876i	$0.598108\pi$
$12$	−0.128848	+	1.72725i	−0.0371951	+	0.498615i
$13$	−3.47382	−	0.965701i	−0.963464	−	0.267837i
$13$	−3.47382	−	0.965701i	−0.963464	−	0.267837i
$14$	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	0.300791	−	0.953690i	$-0.402749\pi$
$17$	−2.69197	−	2.69197i	−0.652900	−	0.652900i	−0.953690	+	0.300791i	$0.902749\pi$
$18$	−2.41258	+	1.78311i	−0.568650	+	0.420282i
$19$	8.01600			1.83900			0.919499	−	0.393093i	$-0.128595\pi$
$19$	8.01600			1.83900			0.919499	+	0.393093i	$0.128595\pi$
$20$	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	0.370128	−	0.928981i	$-0.379314\pi$
$23$	6.23031	−	6.23031i	1.29911	−	1.29911i	0.928981	−	0.370128i	$-0.120686\pi$
$24$	−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	$-0.294452\pi$
$37$	−1.19742	−	1.19742i	−0.196854	−	0.196854i	−0.798650	+	0.601796i	$0.794452\pi$
$38$	−5.66817	+	5.66817i	−0.919499	+	0.919499i
$39$	5.87573	+	2.11560i	0.940870	+	0.338768i
$40$	−2.23589	+	0.0281051i	−0.353525	+	0.00444380i
$41$	−7.90181			−1.23406			−0.617028	−	0.786941i	$-0.711663\pi$
$41$	−7.90181			−1.23406			−0.617028	+	0.786941i	$0.711663\pi$
$42$	−0.577606	−	0.0430876i	−0.0891265	−	0.00664857i
$43$	2.76440	+	2.76440i	0.421568	+	0.421568i	0.885743	−	0.464176i	$-0.153649\pi$
$43$	2.76440	+	2.76440i	0.421568	+	0.421568i	−0.464176	+	0.885743i	$0.653649\pi$
$44$			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	$-0.682396\pi$
$47$	2.04369	−	2.04369i	0.298102	−	0.298102i	0.840270	+	0.542168i	$0.182396\pi$
$48$	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
$52$	−0.965701	+	3.47382i	−0.133919	+	0.481732i
$53$	−6.83014	+	6.83014i	−0.938192	+	0.938192i	−0.998198	−	0.0600063i	$-0.980888\pi$
$53$	−6.83014	+	6.83014i	−0.938192	+	0.938192i	0.0600063	+	0.998198i	$0.480888\pi$
$54$	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
$65$	6.96910	−	4.05360i	0.864410	−	0.502787i
$66$	−2.64101	+	2.27434i	−0.325085	+	0.279951i
$67$	4.26617	+	4.26617i	0.521196	+	0.521196i	0.917933	−	0.396736i	$-0.129857\pi$
$67$	4.26617	+	4.26617i	0.521196	+	0.521196i	−0.396736	+	0.917933i	$0.629857\pi$
$68$	−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	$-0.699623\pi$
$71$	−9.88936			−1.17365			−0.586826	+	0.809713i	$0.699623\pi$
$72$	1.78311	+	2.41258i	0.210141	+	0.284325i
$73$	−2.59128	+	2.59128i	−0.303286	+	0.303286i	−0.842298	−	0.539012i	$-0.818798\pi$
$73$	−2.59128	+	2.59128i	−0.303286	+	0.303286i	0.539012	+	0.842298i	$0.318798\pi$
$74$	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
$78$	−5.65073	+	2.65881i	−0.639819	+	0.301051i
$79$			10.6675i			1.20019i	0.799929	+	0.600095i	$0.204871\pi$
$79$			10.6675i			1.20019i	−0.799929	+	0.600095i	$0.795129\pi$
$80$	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	$-0.324404\pi$
$83$	−2.98429	−	2.98429i	−0.327568	−	0.327568i	−0.851661	+	0.524093i	$0.824404\pi$
$84$	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	−0.992447	−	0.122671i	$-0.960854\pi$
$97$	−10.9826	−	10.9826i	−1.11512	−	1.11512i	−0.122671	−	0.992447i	$-0.539146\pi$
$98$	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	$0.0556170\pi$
$101$			3.49411i			0.347677i	−0.984774	+	0.173838i	$0.944383\pi$
$102$	−6.57569	−	0.490527i	−0.651091	−	0.0485694i
$103$	−2.58254	−	2.58254i	−0.254466	−	0.254466i	0.568333	−	0.822799i	$-0.307589\pi$
$103$	−2.58254	−	2.58254i	−0.254466	−	0.254466i	−0.822799	+	0.568333i	$0.807589\pi$
$104$	−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	0.753497	−	0.657451i	$-0.228365\pi$
$107$	0.993509	+	0.993509i	0.0960462	+	0.0960462i	−0.657451	+	0.753497i	$0.728365\pi$
$108$	−1.15107	+	5.06705i	−0.110762	+	0.487577i
$109$	−5.37932			−0.515246			−0.257623	−	0.966246i	$-0.582939\pi$
$109$	−5.37932			−0.515246			−0.257623	+	0.966246i	$0.582939\pi$
$110$	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	−0.256129	−	0.966643i	$-0.582447\pi$
$113$	7.55286	−	7.55286i	0.710513	−	0.710513i	0.966643	+	0.256129i	$0.0824473\pi$
$114$	10.5207	−	9.06002i	0.985352	−	0.848549i
$115$	0.247633	+	19.7004i	0.0230919	+	1.83707i
$116$		−	4.55580i		−	0.422996i
$117$	−9.87628	−	4.41125i	−0.913062	−	0.407820i
$118$	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	0.0158806	−	0.999874i	$-0.494945\pi$
$127$	11.4470	−	11.4470i	1.01575	−	1.01575i	0.999874	−	0.0158806i	$-0.00505516\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−4.41864	−	5.13101i	−0.389039	−	0.451760i
$130$	−2.06157	+	7.79422i	−0.180812	+	0.683599i
$131$		−	13.1727i		−	1.15091i	−0.817835	−	0.575453i	$-0.804826\pi$
$131$		−	13.1727i		−	1.15091i	0.817835	−	0.575453i	$-0.195174\pi$
$132$	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	$-0.661455\pi$
$137$	4.54541	−	4.54541i	0.388340	−	0.388340i	0.874095	+	0.485755i	$0.161455\pi$
$138$	1.13528	−	15.2188i	0.0966410	−	1.29551i
$139$		−	0.709569i		−	0.0601848i	−0.999547	−	0.0300924i	$-0.990420\pi$
$139$		−	0.709569i		−	0.0601848i	0.999547	−	0.0300924i	$-0.00958016\pi$
$140$	−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
$143$	6.99021	+	1.94324i	0.584551	+	0.162502i
$144$	−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
$156$	2.11560	−	5.87573i	0.169384	−	0.470435i
$157$	−11.1016	+	11.1016i	−0.886006	+	0.886006i	−0.994137	−	0.108131i	$-0.965513\pi$
$157$	−11.1016	+	11.1016i	−0.886006	+	0.886006i	0.108131	+	0.994137i	$0.465513\pi$
$158$	−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	$-0.609084\pi$
$163$	7.73462	−	7.73462i	0.605823	−	0.605823i	0.941852	+	0.336029i	$0.109084\pi$
$164$			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	$-0.579924\pi$
$167$	9.30685	−	9.30685i	0.720185	−	0.720185i	0.968643	+	0.248457i	$0.0799236\pi$
$168$	−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	−0.689525	−	0.724262i	$-0.742181\pi$
$173$	0.456884	−	0.456884i	0.0347362	−	0.0347362i	0.724262	+	0.689525i	$0.242181\pi$
$174$	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	$0.572215\pi$
$182$	−1.16167	−	0.322938i	−0.0861088	−	0.0239377i
$183$	−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	$0.0594379\pi$
$191$			5.13137i			0.371293i	−0.982617	+	0.185647i	$0.940562\pi$
$192$	0.128848	−	1.72725i	0.00929878	−	0.124654i
$193$	11.6332	−	11.6332i	0.837377	−	0.837377i	−0.151136	−	0.988513i	$-0.548293\pi$
$193$	11.6332	−	11.6332i	0.837377	−	0.837377i	0.988513	+	0.151136i	$0.0482931\pi$
$194$	15.5318			1.11512
$195$	−12.5597	+	6.10363i	−0.899418	+	0.437090i
$196$	−6.88817			−0.492012
$197$	5.66495	−	5.66495i	0.403611	−	0.403611i	−0.475892	−	0.879504i	$-0.657875\pi$
$197$	5.66495	−	5.66495i	0.403611	−	0.403611i	0.879504	+	0.475892i	$0.157875\pi$
$198$	4.85472	−	3.58806i	0.345010	−	0.254993i
$199$			9.89963i			0.701766i	0.936419	+	0.350883i	$0.114118\pi$
$199$			9.89963i			0.701766i	−0.936419	+	0.350883i	$0.885882\pi$
$200$	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
$208$	3.47382	+	0.965701i	0.240866	+	0.0669593i
$209$	−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	$-0.850655\pi$
$223$	−6.56733	+	6.56733i	−0.439781	+	0.439781i	0.452157	+	0.891938i	$0.350655\pi$
$224$	−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	$-0.800265\pi$
$227$	−3.35070	+	3.35070i	−0.222393	+	0.222393i	0.587112	+	0.809506i	$0.300265\pi$
$228$	−1.03284	+	13.8457i	−0.0684017	+	0.916951i
$229$	−24.3157			−1.60683			−0.803415	−	0.595420i	$-0.796986\pi$
$229$	−24.3157			−1.60683			−0.803415	+	0.595420i	$0.796986\pi$
$230$	−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	−0.413050	−	0.910708i	$-0.635537\pi$
$233$	7.59642	−	7.59642i	0.497658	−	0.497658i	0.910708	+	0.413050i	$0.135537\pi$
$234$	10.1028	−	3.86436i	0.660441	−	0.252621i
$235$	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
$247$	−27.8461	−	7.74106i	−1.77181	−	0.492552i
$248$	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	$-0.635131\pi$
$251$		−	28.8733i		−	1.82247i	0.411891	−	0.911233i	$-0.364869\pi$
$252$	−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	0.988763	+	0.149490i	$0.0477632\pi$
$257$	18.2476	+	18.2476i	1.13825	+	1.13825i	0.149490	+	0.988763i	$0.452237\pi$
$258$	6.75262	+	0.503725i	0.420400	+	0.0313605i
$259$			0.566286i			0.0351873i
$260$	−4.05360	−	6.96910i	−0.251393	−	0.432205i
$261$	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	−0.554852	−	0.831949i	$-0.687225\pi$
$263$	4.49375	−	4.49375i	0.277096	−	0.277096i	0.831949	+	0.554852i	$0.187225\pi$
$264$	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
$273$	−0.889127	−	1.88965i	−0.0538124	−	0.114367i
$274$			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	−0.636026	−	0.771667i	$-0.719423\pi$
$277$	2.25752	−	2.25752i	0.135641	−	0.135641i	0.771667	+	0.636026i	$0.219423\pi$
$278$	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	$-0.494778\pi$
$281$	0.549953			0.0328074			0.0164037	+	0.999865i	$0.494778\pi$
$282$	0.372397	−	4.99212i	0.0221759	−	0.297276i
$283$	−11.9721	−	11.9721i	−0.711665	−	0.711665i	0.255219	−	0.966883i	$-0.417852\pi$
$283$	−11.9721	−	11.9721i	−0.711665	−	0.711665i	−0.966883	+	0.255219i	$0.917852\pi$
$284$			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	$-0.366873\pi$
$293$	−8.68980	−	8.68980i	−0.507664	−	0.507664i	−0.913809	+	0.406145i	$0.866873\pi$
$294$	−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	$-0.0586383\pi$
$307$	14.0154	+	14.0154i	0.799902	+	0.799902i	−0.183178	+	0.983080i	$0.558638\pi$
$308$	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	$-0.920151\pi$
$311$		−	8.75515i		−	0.496459i	0.968701	−	0.248229i	$-0.0798487\pi$
$312$	2.65881	+	5.65073i	0.150526	+	0.319909i
$313$	19.2874	+	19.2874i	1.09019	+	1.09019i	0.995508	+	0.0946807i	$0.0301830\pi$
$313$	19.2874	+	19.2874i	1.09019	+	1.09019i	0.0946807	+	0.995508i	$0.469817\pi$
$314$		−	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	$-0.813700\pi$
$317$	−5.00531	+	5.00531i	−0.281126	+	0.281126i	0.552432	+	0.833558i	$0.313700\pi$
$318$	−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
$325$	−4.39039	+	17.4850i	−0.243535	+	0.969892i
$326$			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	−0.964971	−	0.262355i	$-0.915501\pi$
$337$	−12.8983	+	12.8983i	−0.702616	+	0.702616i	0.262355	+	0.964971i	$0.415501\pi$
$338$	−12.6177	+	3.12930i	−0.686315	+	0.170211i
$339$	−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	0.566407	−	0.824126i	$-0.308333\pi$
$347$	−4.80078	−	4.80078i	−0.257719	−	0.257719i	−0.824126	+	0.566407i	$0.808333\pi$
$348$	−0.587005	+	7.86902i	−0.0314667	+	0.421824i
$349$	2.35848			0.126246			0.0631232	−	0.998006i	$-0.479894\pi$
$349$	2.35848			0.126246			0.0631232	+	0.998006i	$0.479894\pi$
$350$	−0.0420283	−	1.67151i	−0.00224651	−	0.0893459i
$351$	16.4904	+	8.89188i	0.880194	+	0.474613i
$352$	−1.42288	+	1.42288i	−0.0758397	+	0.0758397i
$353$	−0.663250	−	0.663250i	−0.0353012	−	0.0353012i	0.689236	−	0.724537i	$-0.257946\pi$
$353$	−0.663250	−	0.663250i	−0.0353012	−	0.0353012i	−0.724537	+	0.689236i	$0.757946\pi$
$354$	−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	−0.993198	−	0.116435i	$-0.962853\pi$
$367$	−16.7964	+	16.7964i	−0.876763	+	0.876763i	0.116435	+	0.993198i	$0.462853\pi$
$368$	−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	0.485593	−	0.874185i	$-0.338604\pi$
$373$	−7.50497	−	7.50497i	−0.388593	−	0.388593i	−0.874185	+	0.485593i	$0.838604\pi$
$374$	−7.66071			−0.396126
$375$	−13.1807	−	14.1869i	−0.680648	−	0.732610i
$376$	2.89021			0.149051
$377$	−15.8260	−	4.39954i	−0.815082	−	0.226588i
$378$	−1.69446	−	0.384927i	−0.0871537	−	0.0197985i
$379$	−18.8907			−0.970350			−0.485175	−	0.874417i	$-0.661244\pi$
$379$	−18.8907			−0.970350			−0.485175	+	0.874417i	$0.661244\pi$
$380$	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	$-0.197080\pi$
$383$	4.58015	+	4.58015i	0.234035	+	0.234035i	−0.580340	+	0.814375i	$0.697080\pi$
$384$	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	$0.470112\pi$
$390$	4.56512	−	13.1970i	0.231164	−	0.668254i
$391$	−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	$-0.139183\pi$
$397$	9.61297	+	9.61297i	0.482461	+	0.482461i	−0.423456	+	0.905917i	$0.639183\pi$
$398$	−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	$-0.759699\pi$
$401$	−29.1692			−1.45664			−0.728321	+	0.685236i	$0.759699\pi$
$402$	10.4210	+	0.777374i	0.519752	+	0.0387719i
$403$	−6.81102	+	24.5006i	−0.339281	+	1.22046i
$404$	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	$-0.177014\pi$
$409$	34.3528			1.69864			0.849318	+	0.527882i	$0.177014\pi$
$410$	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
$429$	−11.8235	−	4.25713i	−0.570843	−	0.205536i
$430$	6.10321	−	6.25860i	0.294323	−	0.301817i
$431$	−22.5766			−1.08748			−0.543739	−	0.839254i	$-0.682992\pi$
$431$	−22.5766			−1.08748			−0.543739	+	0.839254i	$0.682992\pi$
$432$	5.06705	+	1.15107i	0.243789	+	0.0553810i
$433$	16.5303	+	16.5303i	0.794395	+	0.794395i	0.982205	−	0.187810i	$-0.0601390\pi$
$433$	16.5303	+	16.5303i	0.794395	+	0.794395i	−0.187810	+	0.982205i	$0.560139\pi$
$434$		−	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	$-0.765800\pi$
$439$		−	28.1244i		−	1.34230i	0.741319	−	0.671152i	$-0.234200\pi$
$440$	4.49919	−	0.0565546i	0.214490	−	0.00269613i
$441$	3.06596	−	20.4358i	0.145998	−	0.973134i
$442$	−13.2249	−	3.67645i	−0.629045	−	0.174871i
$443$	−3.61041	+	3.61041i	−0.171536	+	0.171536i	−0.787654	−	0.616118i	$-0.788704\pi$
$443$	−3.61041	+	3.61041i	−0.171536	+	0.171536i	0.616118	+	0.787654i	$0.288704\pi$
$444$	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
$455$	−2.60645	−	0.689405i	−0.122192	−	0.0323198i
$456$	−9.06002	−	10.5207i	−0.424275	−	0.492676i
$457$	−11.3293	−	11.3293i	−0.529960	−	0.529960i	0.390600	−	0.920560i	$-0.372268\pi$
$457$	−11.3293	−	11.3293i	−0.529960	−	0.529960i	−0.920560	+	0.390600i	$0.872268\pi$
$458$	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	$-0.0818216\pi$
$461$	41.5309			1.93429			0.967144	+	0.254229i	$0.0818216\pi$
$462$	1.16229	+	0.0867033i	0.0540747	+	0.00403380i
$463$	24.1073	−	24.1073i	1.12036	−	1.12036i	0.128676	−	0.991687i	$-0.458927\pi$
$463$	24.1073	−	24.1073i	1.12036	−	1.12036i	0.991687	−	0.128676i	$-0.0410726\pi$
$464$	−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	0.920425	−	0.390918i	$-0.127843\pi$
$467$	11.4427	+	11.4427i	0.529507	+	0.529507i	−0.390918	+	0.920425i	$0.627843\pi$
$468$	−4.41125	+	9.87628i	−0.203910	+	0.456531i
$469$		−	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	$-0.0515459\pi$
$487$	18.2213	+	18.2213i	0.825687	+	0.825687i	−0.161229	+	0.986917i	$0.551546\pi$
$488$	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	$0.102405\pi$
$491$			14.0128i			0.632390i	−0.948694	+	0.316195i	$0.897595\pi$
$492$	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	$-0.278352\pi$
$499$	28.6558			1.28281			0.641405	+	0.767202i	$0.278352\pi$
$500$	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	−0.798609	−	0.601850i	$-0.794431\pi$
$503$	−4.41285	+	4.41285i	−0.196759	+	0.196759i	0.601850	+	0.798609i	$0.294431\pi$
$504$	0.148846	−	0.992119i	0.00663015	−	0.0441925i
$505$	−5.59367	−	5.45479i	−0.248915	−	0.242735i
$506$		−	17.7300i		−	0.788193i
$507$	−18.3682	−	13.0234i	−0.815760	−	0.578391i
$508$	−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
$520$	7.79422	+	2.06157i	0.341799	+	0.0904059i
$521$		−	8.54770i		−	0.374482i	−0.982314	−	0.187241i	$-0.940046\pi$
$521$		−	8.54770i		−	0.374482i	0.982314	−	0.187241i	$-0.0599545\pi$
$522$	−10.9912	+	8.12347i	−0.481073	+	0.355555i
$523$	0.832709	+	0.832709i	0.0364118	+	0.0364118i	0.725078	−	0.688666i	$-0.241804\pi$
$523$	0.832709	+	0.832709i	0.0364118	+	0.0364118i	−0.688666	+	0.725078i	$0.741804\pi$
$524$	−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
$533$	27.4495	+	7.63079i	1.18897	+	0.330526i
$534$	−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
$546$	1.96489	+	0.707474i	0.0840895	+	0.0302771i
$547$	21.4527	−	21.4527i	0.917252	−	0.917252i	−0.0795767	−	0.996829i	$-0.525357\pi$
$547$	21.4527	−	21.4527i	0.917252	−	0.917252i	0.996829	+	0.0795767i	$0.0253569\pi$
$548$	−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	$-0.741924\pi$
$557$	0.846759	−	0.846759i	0.0358783	−	0.0358783i	0.724818	+	0.688940i	$0.241924\pi$
$558$	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	−0.763319	−	0.646021i	$-0.776432\pi$
$563$	−2.78320	+	2.78320i	−0.117298	+	0.117298i	0.646021	+	0.763319i	$0.276432\pi$
$564$	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	$0.724022\pi$
$572$	1.94324	−	6.99021i	0.0812509	−	0.292275i
$573$	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	−0.875756	−	0.482754i	$-0.839636\pi$
$577$	−32.6325	−	32.6325i	−1.35851	−	1.35851i	−0.482754	−	0.875756i	$-0.660364\pi$
$578$	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
$585$	22.4802	−	8.92422i	0.929441	−	0.368971i
$586$	12.2892			0.507664
$587$	−1.02834	+	1.02834i	−0.0424440	+	0.0424440i	−0.728010	−	0.685566i	$-0.759555\pi$
$587$	−1.02834	+	1.02834i	−0.0424440	+	0.0424440i	0.685566	+	0.728010i	$0.259555\pi$
$588$	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	$-0.147283\pi$
$593$	10.9212	+	10.9212i	0.448482	+	0.448482i	−0.446368	+	0.894850i	$0.647283\pi$
$594$	−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
$598$	8.50878	−	30.6078i	0.347950	−	1.25164i
$599$	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	−0.426111	−	0.904671i	$-0.640117\pi$
$607$	11.7904	−	11.7904i	0.478559	−	0.478559i	0.904671	+	0.426111i	$0.140117\pi$
$608$	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	$-0.582296\pi$
$613$	17.6058	−	17.6058i	0.711093	−	0.711093i	0.966764	+	0.255671i	$0.0822963\pi$
$614$	−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	$-0.597956\pi$
$617$	16.1485	−	16.1485i	0.650116	−	0.650116i	0.953021	+	0.302905i	$0.0979564\pi$
$618$	−6.30839	−	0.470586i	−0.253761	−	0.0189298i
$619$	−34.9009			−1.40279			−0.701393	−	0.712775i	$-0.747438\pi$
$619$	−34.9009			−1.40279			−0.701393	+	0.712775i	$0.747438\pi$
$620$	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
$624$	−5.87573	−	2.11560i	−0.235218	−	0.0846919i
$625$	−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
$637$	−6.65192	+	23.9283i	−0.263559	+	0.948072i
$638$	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	$0.196291\pi$
$641$			29.2838i			1.15664i	−0.815810	+	0.578319i	$0.803709\pi$
$642$	2.42685	+	0.181035i	0.0957800	+	0.00714490i
$643$	−0.691053	+	0.691053i	−0.0272525	+	0.0272525i	−0.720602	−	0.693349i	$-0.756134\pi$
$643$	−0.691053	+	0.691053i	−0.0272525	+	0.0272525i	0.693349	+	0.720602i	$0.256134\pi$
$644$			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	0.251540	−	0.967847i	$-0.419063\pi$
$647$	−18.2201	−	18.2201i	−0.716306	−	0.716306i	−0.967847	+	0.251540i	$0.919063\pi$
$648$	4.21626	+	7.95130i	0.165630	+	0.312357i
$649$			24.8055i			0.973701i
$650$	−9.25927	−	15.4682i	−0.363178	−	0.606714i
$651$	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	−0.998002	−	0.0631814i	$-0.979875\pi$
$653$	−23.8883	+	23.8883i	−0.934821	+	0.934821i	0.0631814	+	0.998002i	$0.479875\pi$
$654$	−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
$663$	−10.1222	−	21.5125i	−0.393113	−	0.835475i
$664$		−	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	0.751372	−	0.659879i	$-0.229393\pi$
$673$	2.37353	+	2.37353i	0.0914927	+	0.0914927i	−0.659879	+	0.751372i	$0.729393\pi$
$674$		−	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	0.969159	−	0.246438i	$-0.0792602\pi$
$677$	18.8046	+	18.8046i	0.722721	+	0.722721i	−0.246438	+	0.969159i	$0.579260\pi$
$678$	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	$-0.329730\pi$
$683$	−9.16112	−	9.16112i	−0.350540	−	0.350540i	−0.860311	+	0.509770i	$0.829730\pi$
$684$	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	$0.125936\pi$
$701$			20.4079i			0.770795i	−0.922751	+	0.385397i	$0.874064\pi$
$702$	−17.9480	+	5.37299i	−0.677404	+	0.202790i
$703$	−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	$-0.0760617\pi$
$709$	51.7409			1.94317			0.971586	+	0.236687i	$0.0760617\pi$
$710$	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
$715$	−14.0236	+	8.15687i	−0.524453	+	0.305050i
$716$		−	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	−0.823651	−	0.567097i	$-0.808067\pi$
$727$	−6.91747	+	6.91747i	−0.256555	+	0.256555i	0.567097	+	0.823651i	$0.308067\pi$
$728$	−0.322938	+	1.16167i	−0.0119689	+	0.0430544i
$729$	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	−0.472585	+	0.881285i	$0.656679\pi$
$733$	−36.6546	+	36.6546i	−1.35387	+	1.35387i	−0.881285	+	0.472585i	$0.843321\pi$
$734$		−	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	$-0.419320\pi$
$739$	13.6336			0.501519			0.250760	+	0.968049i	$0.419320\pi$
$740$	−0.0475932	−	3.78626i	−0.00174956	−	0.139186i
$741$	47.0999	+	16.9587i	1.73026	+	0.622993i
$742$	−2.28405	+	2.28405i	−0.0838501	+	0.0838501i
$743$	33.6803	+	33.6803i	1.23561	+	1.23561i	0.961776	+	0.273836i	$0.0882924\pi$
$743$	33.6803	+	33.6803i	1.23561	+	1.23561i	0.273836	+	0.961776i	$0.411708\pi$
$744$	−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	−0.999897	−	0.0143184i	$-0.995442\pi$
$757$	−27.1169	+	27.1169i	−0.985579	+	0.985579i	0.0143184	+	0.999897i	$0.495442\pi$
$758$	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	$-0.328740\pi$
$761$	28.2729			1.02489			0.512446	+	0.858720i	$0.328740\pi$
$762$	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
$767$	−11.9044	+	42.8225i	−0.429843	+	1.54623i
$768$	−1.72725	−	0.128848i	−0.0623268	−	0.00464939i
$769$	8.13103			0.293212			0.146606	−	0.989195i	$-0.453165\pi$
$769$	8.13103			0.293212			0.146606	+	0.989195i	$0.453165\pi$
$770$	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	$-0.0686574\pi$
$773$	21.2081	+	21.2081i	0.762803	+	0.762803i	−0.214025	+	0.976828i	$0.568657\pi$
$774$	−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
$780$	6.10363	+	12.5597i	0.218545	+	0.449709i
$781$	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	$-0.435692\pi$
$787$	−21.8538	−	21.8538i	−0.779005	−	0.779005i	−0.979662	+	0.200657i	$0.935692\pi$
$788$	−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
$793$	−19.0675	−	5.30066i	−0.677108	−	0.188232i
$794$	−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	0.422191	−	0.906507i	$-0.361261\pi$
$797$	−13.6728	−	13.6728i	−0.484316	−	0.484316i	−0.906507	+	0.422191i	$0.861261\pi$
$798$	−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
$819$	1.29227	+	3.37846i	0.0451556	+	0.118053i
$820$	−12.6499	−	12.3358i	−0.441754	−	0.430786i
$821$	−3.21969			−0.112368			−0.0561841	−	0.998420i	$-0.517893\pi$
$821$	−3.21969			−0.112368			−0.0561841	+	0.998420i	$0.517893\pi$
$822$	0.828255	−	11.1031i	0.0288887	−	0.387264i
$823$	23.3869	+	23.3869i	0.815215	+	0.815215i	0.985410	−	0.170195i	$-0.0544399\pi$
$823$	23.3869	+	23.3869i	0.815215	+	0.815215i	−0.170195	+	0.985410i	$0.554440\pi$
$824$		−	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	$-0.891532\pi$
$827$	−17.4931	+	17.4931i	−0.608295	+	0.608295i	0.334205	+	0.942500i	$0.391532\pi$
$828$	−15.7109	−	21.2572i	−0.545992	−	0.738739i
$829$			46.9837i			1.63181i	0.578186	+	0.815905i	$0.303761\pi$
$829$			46.9837i			1.63181i	−0.578186	+	0.815905i	$0.696239\pi$
$830$	−6.58867	+	6.75642i	−0.228696	+	0.234519i
$831$	−4.19018	+	3.60842i	−0.145356	+	0.125175i
$832$	0.965701	−	3.47382i	0.0334797	−	0.120433i
$833$	−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
$845$	−28.1240	+	7.35140i	−0.967494	+	0.252896i
$846$	−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	$-0.638507\pi$
$853$	14.1733	−	14.1733i	0.485285	−	0.485285i	0.906815	+	0.421529i	$0.138507\pi$
$854$	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	0.139871	−	0.990170i	$-0.455331\pi$
$857$	−24.8921	−	24.8921i	−0.850299	−	0.850299i	−0.990170	+	0.139871i	$0.955331\pi$
$858$	11.3707	−	5.35021i	0.388190	−	0.182653i
$859$		−	22.3349i		−	0.762056i	−0.924564	−	0.381028i	$-0.875570\pi$
$859$		−	22.3349i		−	0.762056i	0.924564	−	0.381028i	$-0.124430\pi$
$860$	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	$-0.0226431\pi$
$863$	27.2146	+	27.2146i	0.926395	+	0.926395i	−0.0710755	+	0.997471i	$0.522643\pi$
$864$	−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	$-0.461610\pi$
$877$	−25.8361	−	25.8361i	−0.872421	−	0.872421i	−0.992736	+	0.120314i	$0.961610\pi$
$878$	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	$-0.899500\pi$
$881$		−	18.4330i		−	0.621023i	0.950570	−	0.310511i	$-0.100500\pi$
$882$	12.2823	+	16.6183i	0.413568	+	0.559566i
$883$	5.81874	+	5.81874i	0.195816	+	0.195816i	0.798204	−	0.602388i	$-0.205784\pi$
$883$	5.81874	+	5.81874i	0.195816	+	0.195816i	−0.602388	+	0.798204i	$0.705784\pi$
$884$	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	0.968162	−	0.250324i	$-0.0805372\pi$
$887$	21.3790	+	21.3790i	0.717838	+	0.717838i	−0.250324	+	0.968162i	$0.580537\pi$
$888$	−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
$897$	49.7885	−	23.4268i	1.66239	−	0.782197i
$898$	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	−0.697852	−	0.716242i	$-0.745861\pi$
$907$	0.553858	−	0.553858i	0.0183906	−	0.0183906i	0.716242	+	0.697852i	$0.245861\pi$
$908$	3.35070	+	3.35070i	0.111197	+	0.111197i
$909$	−1.55524	+	10.3663i	−0.0515842	+	0.343829i
$910$	2.33052	−	1.35555i	0.0772560	−	0.0449362i
$911$			6.42215i			0.212775i	0.994325	+	0.106388i	$0.0339284\pi$
$911$			6.42215i			0.212775i	−0.994325	+	0.106388i	$0.966072\pi$
$912$	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	$-0.963475\pi$
$919$		−	6.94188i		−	0.228992i	0.993424	−	0.114496i	$-0.0365252\pi$
$920$	−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
$923$	34.3539	+	9.55017i	1.13077	+	0.314348i
$924$	−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
$936$	−3.86436	−	10.1028i	−0.126310	−	0.330221i
$937$	19.7935	−	19.7935i	0.646624	−	0.646624i	−0.305551	−	0.952176i	$-0.598841\pi$
$937$	19.7935	−	19.7935i	0.646624	−	0.646624i	0.952176	+	0.305551i	$0.0988408\pi$
$938$	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	$-0.570443\pi$
$941$	−13.4668			−0.439006			−0.219503	+	0.975612i	$0.570443\pi$
$942$	−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	$-0.650358\pi$
$947$	13.4019	−	13.4019i	0.435504	−	0.435504i	0.890496	+	0.454991i	$0.150358\pi$
$948$	−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	−0.0672062	+	0.997739i	$0.521409\pi$
$953$	−32.8756	+	32.8756i	−1.06495	+	1.06495i	−0.997739	+	0.0672062i	$0.978591\pi$
$954$	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
$962$	−5.88257	−	1.63532i	−0.189662	−	0.0527248i
$963$	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	$-0.130893\pi$
$967$	16.0743	+	16.0743i	0.516915	+	0.516915i	−0.399722	+	0.916637i	$0.630893\pi$
$968$	−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	$-0.836790\pi$
$971$		−	30.5730i		−	0.981133i	0.871404	−	0.490566i	$-0.163210\pi$
$972$	−5.67037	+	14.5206i	−0.181877	+	0.465747i
$973$	−0.167786	+	0.167786i	−0.00537897	+	0.00537897i
$974$	−25.7689			−0.825687
$975$	9.83621	−	29.6353i	0.315011	−	0.949088i
$976$	−5.48892			−0.175696
$977$	−16.1846	+	16.1846i	−0.517792	+	0.517792i	−0.916903	−	0.399111i	$-0.869319\pi$
$977$	−16.1846	+	16.1846i	−0.517792	+	0.517792i	0.399111	+	0.916903i	$0.369319\pi$
$978$	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	−0.999963	−	0.00864329i	$-0.997249\pi$
$983$	−31.6227	−	31.6227i	−1.00861	−	1.00861i	−0.00864329	−	0.999963i	$-0.502751\pi$
$984$	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
$988$	−7.74106	+	27.8461i	−0.246276	+	0.885904i
$989$	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	−0.948394	−	0.317094i	$-0.897293\pi$
$997$	−19.9335	+	19.9335i	−0.631300	+	0.631300i	0.317094	+	0.948394i	$0.397293\pi$
$998$	−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.233.1	yes	24
3.2	odd	2		390.2.s.b.233.10	yes	24
5.2	odd	4		390.2.s.b.77.4	✓	24
13.12	even	2	inner	390.2.s.c.233.7	yes	24
15.2	even	4	inner	390.2.s.c.77.7	yes	24
39.38	odd	2		390.2.s.b.233.4	yes	24
65.12	odd	4		390.2.s.b.77.10	yes	24
195.77	even	4	inner	390.2.s.c.77.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.s.b.77.4	✓	24	5.2	odd	4
390.2.s.b.77.10	yes	24	65.12	odd	4
390.2.s.b.233.4	yes	24	39.38	odd	2
390.2.s.b.233.10	yes	24	3.2	odd	2
390.2.s.c.77.1	yes	24	195.77	even	4	inner
390.2.s.c.77.7	yes	24	15.2	even	4	inner
390.2.s.c.233.1	yes	24	1.1	even	1	trivial
390.2.s.c.233.7	yes	24	13.12	even	2	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} +(-3.47382 - 0.965701i) 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} +(5.87573 + 2.11560i) 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} +(-0.965701 + 3.47382i) 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} +(6.96910 - 4.05360i) 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} +(-5.65073 + 2.65881i) 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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