LMFDB - Embedded newform 390.2.s.b.77.4

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			77.4
Character	$\chi$	$=$	390.77
Dual form			390.2.s.b.233.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.128848 + 1.72725i) q^{3} +1.00000i q^{4} +(-1.56114 - 1.60089i) q^{5} +(1.31246 - 1.13024i) q^{6} +(0.236462 - 0.236462i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.96680 - 0.445105i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.128848 + 1.72725i) 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} +(-1.72725 - 0.128848i) q^{12} +(-0.965701 + 3.47382i) q^{13} -0.334408 q^{14} +(2.96628 - 2.49021i) q^{15} -1.00000 q^{16} +(2.69197 - 2.69197i) q^{17} +(1.78311 + 2.41258i) 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} +(1.15107 - 5.06705i) q^{27} +(0.236462 + 0.236462i) q^{28} -4.55580 q^{29} +(-3.85833 - 0.336634i) q^{30} -7.05293i q^{31} +(0.707107 + 0.707107i) q^{32} +(0.259274 - 3.47567i) 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} +(0.0430876 - 0.577606i) q^{42} +(2.76440 - 2.76440i) q^{43} -2.01226i q^{44} +(3.91902 + 5.44438i) q^{45} +8.81099i q^{46} +(2.04369 + 2.04369i) q^{47} +(0.128848 - 1.72725i) 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} +(1.03284 - 13.8457i) q^{57} +(3.22144 + 3.22144i) q^{58} +12.3272i q^{59} +(2.49021 + 2.96628i) q^{60} +5.48892 q^{61} +(-4.98717 + 4.98717i) q^{62} +(-0.806784 + 0.596284i) 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} +(-2.41258 + 1.78311i) q^{72} +(2.59128 + 2.59128i) q^{73} -1.69340 q^{74} +(-8.61734 - 0.861115i) q^{75} -8.01600i q^{76} +(-0.475822 + 0.475822i) q^{77} +(2.65881 + 5.65073i) 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} +(0.587005 - 7.86902i) q^{87} +(-1.42288 + 1.42288i) q^{88} +1.02859i q^{89} +(1.07859 - 6.62093i) q^{90} +(0.593074 + 1.04978i) q^{91} +(6.23031 - 6.23031i) q^{92} +(12.1822 + 0.908753i) 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 - 8 q^{3} - 12 q^{9}+O(q^{10}) $ 24 * q - 8 * q^3 - 12 * q^9	$ 24 q - 8 q^{3} - 12 q^{9} + 4 q^{10} + 4 q^{12} - 8 q^{13} - 16 q^{14} - 24 q^{16} + 52 q^{17} + 16 q^{22} - 16 q^{23} + 16 q^{25} + 40 q^{27} - 80 q^{29} + 20 q^{35} - 16 q^{38} - 32 q^{39} - 4 q^{42} + 28 q^{43} + 8 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} - 104 q^{75} + 32 q^{77} + 44 q^{78} + 12 q^{81} + 32 q^{82} - 32 q^{87} - 16 q^{88} + 64 q^{90} + 64 q^{91} + 16 q^{92} + 96 q^{95}+O(q^{100}) $ 24 * q - 8 * q^3 - 12 * q^9 + 4 * q^10 + 4 * q^12 - 8 * q^13 - 16 * q^14 - 24 * q^16 + 52 * q^17 + 16 * q^22 - 16 * q^23 + 16 * q^25 + 40 * q^27 - 80 * q^29 + 20 * q^35 - 16 * q^38 - 32 * q^39 - 4 * q^42 + 28 * q^43 + 8 * 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 - 104 * q^75 + 32 * q^77 + 44 * q^78 + 12 * q^81 + 32 * q^82 - 32 * q^87 - 16 * q^88 + 64 * 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
$3$	−0.128848	+	1.72725i	−0.0743902	+	0.997229i
$3$	−0.128848	+	1.72725i	−0.0743902	+	0.997229i
$4$			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	$-0.598108\pi$
$11$	−2.01226			−0.606718			−0.303359	+	0.952876i	$0.598108\pi$
$12$	−1.72725	−	0.128848i	−0.498615	−	0.0371951i
$13$	−0.965701	+	3.47382i	−0.267837	+	0.963464i
$13$	−0.965701	+	3.47382i	−0.267837	+	0.963464i
$14$	−0.334408			−0.0893742
$15$	2.96628	−	2.49021i	0.765891	−	0.642970i
$16$	−1.00000			−0.250000
$17$	2.69197	−	2.69197i	0.652900	−	0.652900i	−0.300791	−	0.953690i	$-0.597251\pi$
$17$	2.69197	−	2.69197i	0.652900	−	0.652900i	0.953690	+	0.300791i	$0.0972505\pi$
$18$	1.78311	+	2.41258i	0.420282	+	0.568650i
$19$	−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	$-0.879314\pi$
$23$	−6.23031	−	6.23031i	−1.29911	−	1.29911i	−0.370128	−	0.928981i	$-0.620686\pi$
$24$	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
$27$	1.15107	−	5.06705i	0.221524	−	0.975155i
$28$	0.236462	+	0.236462i	0.0446871	+	0.0446871i
$29$	−4.55580			−0.845991			−0.422996	−	0.906132i	$-0.639021\pi$
$29$	−4.55580			−0.845991			−0.422996	+	0.906132i	$0.639021\pi$
$30$	−3.85833	−	0.336634i	−0.704431	−	0.0614607i
$31$		−	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
$33$	0.259274	−	3.47567i	0.0451339	−	0.605037i
$34$	−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
$39$	−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	$0.711663\pi$
$42$	0.0430876	−	0.577606i	0.00664857	−	0.0891265i
$43$	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
$45$	3.91902	+	5.44438i	0.584214	+	0.811600i
$46$			8.81099i			1.29911i
$47$	2.04369	+	2.04369i	0.298102	+	0.298102i	0.840270	−	0.542168i	$-0.182396\pi$
$47$	2.04369	+	2.04369i	0.298102	+	0.298102i	−0.542168	+	0.840270i	$0.682396\pi$
$48$	0.128848	−	1.72725i	0.0185976	−	0.249307i
$49$			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	0.998198	−	0.0600063i	$-0.0191121\pi$
$53$	6.83014	+	6.83014i	0.938192	+	0.938192i	−0.0600063	+	0.998198i	$0.519112\pi$
$54$	−4.39688	+	2.76902i	−0.598339	+	0.376815i
$55$	3.14141	+	3.22139i	0.423588	+	0.434373i
$56$		−	0.334408i		−	0.0446871i
$57$	1.03284	−	13.8457i	0.136803	−	1.83390i
$58$	3.22144	+	3.22144i	0.422996	+	0.422996i
$59$			12.3272i			1.60487i	0.596742	+	0.802433i	$0.296461\pi$
$59$			12.3272i			1.60487i	−0.596742	+	0.802433i	$0.703539\pi$
$60$	2.49021	+	2.96628i	0.321485	+	0.382946i
$61$	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
$63$	−0.806784	+	0.596284i	−0.101645	+	0.0751247i
$64$		−	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	$-0.699623\pi$
$71$	−9.88936			−1.17365			−0.586826	+	0.809713i	$0.699623\pi$
$72$	−2.41258	+	1.78311i	−0.284325	+	0.210141i
$73$	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
$75$	−8.61734	−	0.861115i	−0.995044	−	0.0994331i
$76$		−	8.01600i		−	0.919499i
$77$	−0.475822	+	0.475822i	−0.0542249	+	0.0542249i
$78$	2.65881	+	5.65073i	0.301051	+	0.639819i
$79$		−	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	−0.851661	−	0.524093i	$-0.824404\pi$
$83$	−2.98429	+	2.98429i	−0.327568	+	0.327568i	0.524093	+	0.851661i	$0.324404\pi$
$84$	−0.438897	+	0.377962i	−0.0478876	+	0.0412390i
$85$	−8.51210	−	0.106997i	−0.923267	−	0.0116054i
$86$	−3.90946			−0.421568
$87$	0.587005	−	7.86902i	0.0629335	−	0.843647i
$88$	−1.42288	+	1.42288i	−0.151679	+	0.151679i
$89$			1.02859i			0.109030i	0.998513	+	0.0545151i	$0.0173613\pi$
$89$			1.02859i			0.109030i	−0.998513	+	0.0545151i	$0.982639\pi$
$90$	1.07859	−	6.62093i	0.113693	−	0.697907i
$91$	0.593074	+	1.04978i	0.0621711	+	0.110047i
$92$	6.23031	−	6.23031i	0.649554	−	0.649554i
$93$	12.1822	+	0.908753i	1.26323	+	0.0942333i
$94$		−	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	$0.0556170\pi$
$101$			3.49411i			0.347677i	−0.984774	+	0.173838i	$0.944383\pi$
$102$	0.490527	−	6.57569i	0.0485694	−	0.651091i
$103$	−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
$105$	0.112573	−	1.29025i	0.0109860	−	0.125916i
$106$		−	9.65927i		−	0.938192i
$107$	−0.993509	+	0.993509i	−0.0960462	+	0.0960462i	−0.753497	−	0.657451i	$-0.771635\pi$
$107$	−0.993509	+	0.993509i	−0.0960462	+	0.0960462i	0.657451	+	0.753497i	$0.271635\pi$
$108$	5.06705	+	1.15107i	0.487577	+	0.110762i
$109$	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	0.256129	−	0.966643i	$-0.417553\pi$
$113$	−7.55286	−	7.55286i	−0.710513	−	0.710513i	−0.966643	+	0.256129i	$0.917553\pi$
$114$	−10.5207	+	9.06002i	−0.985352	+	0.848549i
$115$	−0.247633	+	19.7004i	−0.0230919	+	1.83707i
$116$		−	4.55580i		−	0.422996i
$117$	4.41125	−	9.87628i	0.407820	−	0.913062i
$118$	8.71665	−	8.71665i	0.802433	−	0.802433i
$119$		−	1.27310i		−	0.116705i
$120$	0.336634	−	3.85833i	0.0307303	−	0.352215i
$121$	−6.95083			−0.631893
$122$	−3.88125	−	3.88125i	−0.351392	−	0.351392i
$123$	1.01813	−	13.6484i	0.0918017	−	1.23064i
$124$	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	$-0.804826\pi$
$131$		−	13.1727i		−	1.15091i	0.817835	−	0.575453i	$-0.195174\pi$
$132$	3.47567	+	0.259274i	0.302518	+	0.0225669i
$133$	−1.89548	+	1.89548i	−0.164359	+	0.164359i
$134$	6.03328			0.521196
$135$	−9.90877	+	6.06765i	−0.852811	+	0.522220i
$136$		−	3.80703i		−	0.326450i
$137$	4.54541	+	4.54541i	0.388340	+	0.388340i	0.874095	−	0.485755i	$-0.161455\pi$
$137$	4.54541	+	4.54541i	0.388340	+	0.388340i	−0.485755	+	0.874095i	$0.661455\pi$
$138$	−15.2188	−	1.13528i	−1.29551	−	0.0966410i
$139$			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
$147$	−11.8976	−	0.887525i	−0.981298	−	0.0732018i
$148$	1.19742	+	1.19742i	0.0984270	+	0.0984270i
$149$			3.81004i			0.312130i	0.987747	+	0.156065i	$0.0498810\pi$
$149$			3.81004i			0.312130i	−0.987747	+	0.156065i	$0.950119\pi$
$150$	5.48448	+	6.70228i	0.447806	+	0.547239i
$151$			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
$153$	−9.18475	+	6.78833i	−0.742543	+	0.548804i
$154$	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	0.108131	−	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
$162$	−4.21626	−	7.95130i	−0.331261	−	0.624713i
$163$	−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
$165$	−5.96892	+	5.01094i	−0.464680	+	0.390101i
$166$	4.22042			0.327568
$167$	9.30685	+	9.30685i	0.720185	+	0.720185i	0.968643	−	0.248457i	$-0.0799236\pi$
$167$	9.30685	+	9.30685i	0.720185	+	0.720185i	−0.248457	+	0.968643i	$0.579924\pi$
$168$	0.577606	+	0.0430876i	0.0445633	+	0.00332428i
$169$	−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	$-0.257819\pi$
$173$	−0.456884	−	0.456884i	−0.0347362	−	0.0347362i	−0.724262	+	0.689525i	$0.757819\pi$
$174$	−5.97931	+	5.14916i	−0.453290	+	0.390357i
$175$	1.15222	+	1.21165i	0.0870994	+	0.0915924i
$176$	2.01226			0.151679
$177$	−21.2922	−	1.58833i	−1.60042	−	0.119386i
$178$	0.727322	−	0.727322i	0.0545151	−	0.0545151i
$179$	−12.2071			−0.912401			−0.456201	−	0.889877i	$-0.650790\pi$
$179$	−12.2071			−0.912401			−0.456201	+	0.889877i	$0.650790\pi$
$180$	−5.44438	+	3.91902i	−0.405800	+	0.292107i
$181$	−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
$183$	−0.707235	+	9.48075i	−0.0522803	+	0.700837i
$184$	−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	$0.940562\pi$
$192$	1.72725	+	0.128848i	0.124654	+	0.00929878i
$193$	−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
$195$	5.78600	+	12.7091i	0.414344	+	0.910120i
$196$	−6.88817			−0.492012
$197$	5.66495	+	5.66495i	0.403611	+	0.403611i	0.879504	−	0.475892i	$-0.157875\pi$
$197$	5.66495	+	5.66495i	0.403611	+	0.403611i	−0.475892	+	0.879504i	$0.657875\pi$
$198$	−3.58806	−	4.85472i	−0.254993	−	0.345010i
$199$		−	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
$207$	15.7109	+	21.2572i	1.09198	+	1.47748i
$208$	0.965701	−	3.47382i	0.0669593	−	0.240866i
$209$	16.1302			1.11575
$210$	−0.991948	+	0.832746i	−0.0684509	+	0.0574649i
$211$	−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
$213$	1.27422	−	17.0814i	0.0873082	−	1.17040i
$214$	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
$222$	0.218191	−	2.92493i	0.0146440	−	0.196308i
$223$	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
$225$	2.59769	−	14.7734i	0.173179	−	0.984890i
$226$			10.6814i			0.710513i
$227$	−3.35070	−	3.35070i	−0.222393	−	0.222393i	0.587112	−	0.809506i	$-0.300265\pi$
$227$	−3.35070	−	3.35070i	−0.222393	−	0.222393i	−0.809506	+	0.587112i	$0.800265\pi$
$228$	13.8457	+	1.03284i	0.916951	+	0.0684017i
$229$	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	0.413050	−	0.910708i	$-0.364463\pi$
$233$	−7.59642	−	7.59642i	−0.497658	−	0.497658i	−0.910708	+	0.413050i	$0.864463\pi$
$234$	−10.1028	+	3.86436i	−0.660441	+	0.252621i
$235$	0.0812295	−	6.46219i	0.00529883	−	0.421547i
$236$	−12.3272			−0.802433
$237$	18.4255	+	1.37449i	1.19686	+	0.0892824i
$238$	−0.900217	+	0.900217i	−0.0583524	+	0.0583524i
$239$		−	2.60829i		−	0.168716i	−0.996436	−	0.0843581i	$-0.973116\pi$
$239$		−	2.60829i		−	0.168716i	0.996436	−	0.0843581i	$-0.0268840\pi$
$240$	−2.96628	+	2.49021i	−0.191473	+	0.160743i
$241$			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
$243$	−5.67037	+	14.5206i	−0.363754	+	0.931495i
$244$			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	$-0.635131\pi$
$251$		−	28.8733i		−	1.82247i	0.411891	−	0.911233i	$-0.364869\pi$
$252$	−0.596284	−	0.806784i	−0.0375624	−	0.0508226i
$253$	12.5370	+	12.5370i	0.788193	+	0.788193i
$254$		−	16.1885i		−	1.01575i
$255$	1.28157	−	14.6887i	0.0802553	−	0.919845i
$256$	1.00000			0.0625000
$257$	−18.2476	+	18.2476i	−1.13825	+	1.13825i	−0.149490	+	0.988763i	$0.547763\pi$
$257$	−18.2476	+	18.2476i	−1.13825	+	1.13825i	−0.988763	+	0.149490i	$0.952237\pi$
$258$	0.503725	−	6.75262i	0.0313605	−	0.420400i
$259$		−	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	0.554852	−	0.831949i	$-0.312775\pi$
$263$	−4.49375	−	4.49375i	−0.277096	−	0.277096i	−0.831949	+	0.554852i	$0.812775\pi$
$264$	−2.27434	−	2.64101i	−0.139976	−	0.162543i
$265$	0.271475	−	21.5971i	0.0166766	−	1.32670i
$266$	2.68061			0.164359
$267$	−1.77663	−	0.132531i	−0.108728	−	0.00811078i
$268$	−4.26617	−	4.26617i	−0.260598	−	0.260598i
$269$	15.5655			0.949047			0.474523	−	0.880243i	$-0.342620\pi$
$269$	15.5655			0.949047			0.474523	+	0.880243i	$0.342620\pi$
$270$	11.2970	+	2.71608i	0.687515	+	0.165296i
$271$		−	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
$273$	−1.88965	+	0.889127i	−0.114367	+	0.0538124i
$274$		−	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	$-0.494778\pi$
$281$	0.549953			0.0328074			0.0164037	+	0.999865i	$0.494778\pi$
$282$	4.99212	+	0.372397i	0.297276	+	0.0221759i
$283$	−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
$285$	−23.7777	+	19.9615i	−1.40847	+	1.18242i
$286$	−6.31690	+	3.56875i	−0.373526	+	0.211025i
$287$	−1.86848	+	1.86848i	−0.110293	+	0.110293i
$288$	−1.78311	−	2.41258i	−0.105070	−	0.142163i
$289$			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	−0.913809	−	0.406145i	$-0.866873\pi$
$293$	−8.68980	+	8.68980i	−0.507664	+	0.507664i	0.406145	+	0.913809i	$0.366873\pi$
$294$	7.78530	+	9.04045i	0.454048	+	0.527250i
$295$	19.7345	−	19.2445i	1.14899	−	1.12046i
$296$		−	1.69340i		−	0.0984270i
$297$	−2.31625	+	10.1962i	−0.134403	+	0.591644i
$298$	2.69410	−	2.69410i	0.156065	−	0.156065i
$299$	27.6596	−	15.6263i	1.59959	−	0.903695i
$300$	0.861115	−	8.61734i	0.0497165	−	0.497522i
$301$		−	1.30735i		−	0.0753545i
$302$	2.72810	−	2.72810i	0.156985	−	0.156985i
$303$	−6.03520	−	0.450208i	−0.346713	−	0.0258638i
$304$	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	$-0.920151\pi$
$311$		−	8.75515i		−	0.496459i	0.968701	−	0.248229i	$-0.0798487\pi$
$312$	−5.65073	+	2.65881i	−0.319909	+	0.150526i
$313$	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
$315$	2.21409	+	0.360688i	0.124750	+	0.0203225i
$316$	10.6675			0.600095
$317$	−5.00531	−	5.00531i	−0.281126	−	0.281126i	0.552432	−	0.833558i	$-0.313700\pi$
$317$	−5.00531	−	5.00531i	−0.281126	−	0.281126i	−0.833558	+	0.552432i	$0.813700\pi$
$318$	16.6840	+	1.24458i	0.935592	+	0.0697923i
$319$	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
$327$	−0.693113	+	9.29145i	−0.0383293	+	0.513818i
$328$	−5.58743	+	5.58743i	−0.308514	+	0.308514i
$329$	0.966508			0.0532853
$330$	7.76394	+	0.677394i	0.427391	+	0.0372893i
$331$		−	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
$333$	−4.08546	+	3.01951i	−0.223882	+	0.165468i
$334$		−	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
$342$	−14.2934	−	19.3392i	−0.772897	−	1.04575i
$343$	3.28402	+	3.28402i	0.177321	+	0.177321i
$344$		−	3.90946i		−	0.210784i
$345$	−33.9957	−	2.96608i	−1.83026	−	0.159688i
$346$			0.646131i			0.0347362i
$347$	4.80078	−	4.80078i	0.257719	−	0.257719i	−0.566407	−	0.824126i	$-0.691667\pi$
$347$	4.80078	−	4.80078i	0.257719	−	0.257719i	0.824126	+	0.566407i	$0.191667\pi$
$348$	7.86902	+	0.587005i	0.421824	+	0.0314667i
$349$	−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
$351$	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	−0.724537	−	0.689236i	$-0.757946\pi$
$353$	−0.663250	+	0.663250i	−0.0353012	+	0.0353012i	0.689236	+	0.724537i	$0.257946\pi$
$354$	13.9327	+	16.1790i	0.740516	+	0.859903i
$355$	15.4387	+	15.8318i	0.819400	+	0.840262i
$356$	−1.02859			−0.0545151
$357$	2.19896	+	0.164036i	0.116381	+	0.00868169i
$358$	8.63172	+	8.63172i	0.456201	+	0.456201i
$359$		−	25.4249i		−	1.34188i	−0.741513	−	0.670939i	$-0.765891\pi$
$359$		−	25.4249i		−	1.34188i	0.741513	−	0.670939i	$-0.234109\pi$
$360$	6.62093	+	1.07859i	0.348953	+	0.0568466i
$361$	45.2563			2.38191
$362$	4.27956	+	4.27956i	0.224929	+	0.224929i
$363$	0.895598	−	12.0058i	0.0470067	−	0.630143i
$364$	−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
$372$	−0.908753	+	12.1822i	−0.0471167	+	0.631617i
$373$	−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
$375$	12.0743	+	15.1397i	0.623515	+	0.781811i
$376$	2.89021			0.149051
$377$	4.39954	−	15.8260i	0.226588	−	0.815082i
$378$	−0.384927	+	1.69446i	−0.0197985	+	0.0871537i
$379$	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	−0.580340	−	0.814375i	$-0.697080\pi$
$383$	4.58015	−	4.58015i	0.234035	−	0.234035i	0.814375	+	0.580340i	$0.197080\pi$
$384$	−1.13024	−	1.31246i	−0.0576774	−	0.0669762i
$385$	1.50456	+	0.0189123i	0.0766796	+	0.000963859i
$386$			16.4519i			0.837377i
$387$	−9.43188	+	6.97098i	−0.479449	+	0.354355i
$388$	10.9826	+	10.9826i	0.557559	+	0.557559i
$389$	−3.69834			−0.187513			−0.0937566	−	0.995595i	$-0.529888\pi$
$389$	−3.69834			−0.187513			−0.0937566	+	0.995595i	$0.529888\pi$
$390$	4.89540	−	13.0780i	0.247888	−	0.662232i
$391$	−33.5437			−1.69638
$392$	4.87067	+	4.87067i	0.246006	+	0.246006i
$393$	22.7526	+	1.69727i	1.14772	+	0.0856162i
$394$		−	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	$-0.759699\pi$
$401$	−29.1692			−1.45664			−0.728321	+	0.685236i	$0.759699\pi$
$402$	−0.777374	+	10.4210i	−0.0387719	+	0.519752i
$403$	24.5006	+	6.81102i	1.22046	+	0.339281i
$404$	−3.49411			−0.173838
$405$	−9.20363	−	17.8967i	−0.457332	−	0.889296i
$406$	1.52349			0.0756098
$407$	−2.40951	+	2.40951i	−0.119435	+	0.119435i
$408$	6.57569	+	0.490527i	0.325545	+	0.0242847i
$409$	−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
$417$	−1.22560	−	0.0914263i	−0.0600181	−	0.00447717i
$418$	−11.4058	−	11.4058i	−0.557876	−	0.557876i
$419$	−1.04983			−0.0512874			−0.0256437	−	0.999671i	$-0.508164\pi$
$419$	−1.04983			−0.0512874			−0.0256437	+	0.999671i	$0.508164\pi$
$420$	1.29025	+	0.112573i	0.0629579	+	0.00549300i
$421$			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
$423$	−5.15355	−	6.97286i	−0.250574	−	0.339032i
$424$	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	$0.682992\pi$
$432$	−1.15107	+	5.06705i	−0.0553810	+	0.243789i
$433$	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
$435$	−13.5138	+	11.3449i	−0.647937	+	0.543947i
$436$			5.37932i			0.257623i
$437$	49.9422	+	49.9422i	2.38906	+	2.38906i
$438$	6.32972	+	0.472178i	0.302446	+	0.0225615i
$439$			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	0.787654	−	0.616118i	$-0.211296\pi$
$443$	3.61041	+	3.61041i	0.171536	+	0.171536i	−0.616118	+	0.787654i	$0.711296\pi$
$444$	−2.22252	+	1.91395i	−0.105476	+	0.0908322i
$445$	1.64665	−	1.60577i	0.0780589	−	0.0761209i
$446$		−	9.28761i		−	0.439781i
$447$	−6.58089	−	0.490914i	−0.311266	−	0.0232195i
$448$	−0.236462	−	0.236462i	−0.0111718	−	0.0111718i
$449$			20.7104i			0.977386i	0.872456	+	0.488693i	$0.162526\pi$
$449$			20.7104i			0.977386i	−0.872456	+	0.488693i	$0.837474\pi$
$450$	−12.2832	+	8.60950i	−0.579035	+	0.405856i
$451$	15.9005			0.748724
$452$	7.55286	−	7.55286i	0.355257	−	0.355257i
$453$	−6.66395	−	0.497110i	−0.313100	−	0.0233563i
$454$			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	$-0.0818216\pi$
$461$	41.5309			1.93429			0.967144	+	0.254229i	$0.0818216\pi$
$462$	−0.0867033	+	1.16229i	−0.00403380	+	0.0540747i
$463$	−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
$465$	−17.5633	−	20.9210i	−0.814478	−	0.970188i
$466$			10.7430i			0.497658i
$467$	−11.4427	+	11.4427i	−0.529507	+	0.529507i	−0.920425	−	0.390918i	$-0.872157\pi$
$467$	−11.4427	+	11.4427i	−0.529507	+	0.529507i	0.390918	+	0.920425i	$0.372157\pi$
$468$	9.87628	+	4.41125i	0.456531	+	0.203910i
$469$			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
$477$	−17.2235	−	23.3038i	−0.788610	−	1.06701i
$478$	−1.84434	+	1.84434i	−0.0843581	+	0.0843581i
$479$		−	21.8587i		−	0.998752i	−0.866385	−	0.499376i	$-0.833563\pi$
$479$		−	21.8587i		−	0.998752i	0.866385	−	0.499376i	$-0.166437\pi$
$480$	3.85833	+	0.336634i	0.176108	+	0.0153652i
$481$	3.00326	+	5.31595i	0.136937	+	0.242387i
$482$	1.71933	−	1.71933i	0.0783132	−	0.0783132i
$483$	0.379645	−	5.08928i	0.0172744	−	0.231570i
$484$		−	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	$0.102405\pi$
$491$			14.0128i			0.632390i	−0.948694	+	0.316195i	$0.897595\pi$
$492$	13.6484	+	1.01813i	0.615318	+	0.0459009i
$493$	−12.2641	+	12.2641i	−0.552347	+	0.552347i
$494$	−25.1640	+	14.2164i	−1.13218	+	0.639628i
$495$	−7.88608	−	10.9555i	−0.354453	−	0.492412i
$496$			7.05293i			0.316686i
$497$	−2.33846	+	2.33846i	−0.104894	+	0.104894i
$498$	−0.543792	+	7.28973i	−0.0243679	+	0.326661i
$499$	−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	0.798609	−	0.601850i	$-0.205569\pi$
$503$	4.41285	+	4.41285i	0.196759	+	0.196759i	−0.601850	+	0.798609i	$0.705569\pi$
$504$	−0.148846	+	0.992119i	−0.00663015	+	0.0441925i
$505$	5.59367	−	5.45479i	0.248915	−	0.242735i
$506$		−	17.7300i		−	0.788193i
$507$	13.0234	−	18.3682i	0.578391	−	0.815760i
$508$	−11.4470	+	11.4470i	−0.507877	+	0.507877i
$509$		−	36.2523i		−	1.60686i	−0.595402	−	0.803428i	$-0.703007\pi$
$509$		−	36.2523i		−	1.60686i	0.595402	−	0.803428i	$-0.296993\pi$
$510$	−11.2927	+	9.48030i	−0.500050	+	0.419795i
$511$	1.22548			0.0542119
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−9.22700	+	40.6175i	−0.407382	+	1.79331i
$514$	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	$-0.940046\pi$
$521$		−	8.54770i		−	0.374482i	0.982314	−	0.187241i	$-0.0599545\pi$
$522$	−8.12347	−	10.9912i	−0.355555	−	0.481073i
$523$	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
$525$	−2.24129	+	1.83405i	−0.0978180	+	0.0800445i
$526$			6.35512i			0.277096i
$527$	−18.9863	−	18.9863i	−0.827056	−	0.827056i
$528$	−0.259274	+	3.47567i	−0.0112835	+	0.151259i
$529$			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
$537$	1.57286	−	21.0847i	0.0678738	−	0.909873i
$538$	−11.0065	−	11.0065i	−0.474523	−	0.474523i
$539$		−	13.8608i		−	0.597025i
$540$	−6.06765	−	9.90877i	−0.261110	−	0.426405i
$541$			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
$543$	0.779813	−	10.4537i	0.0334650	−	0.448611i
$544$	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	0.996829	−	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
$552$	1.13528	−	15.2188i	0.0483205	−	0.647755i
$553$	−2.52246	−	2.52246i	−0.107266	−	0.107266i
$554$		−	3.19261i		−	0.135641i
$555$	0.570056	−	6.53369i	0.0241975	−	0.277340i
$556$	−0.709569			−0.0300924
$557$	0.846759	+	0.846759i	0.0358783	+	0.0358783i	0.724818	−	0.688940i	$-0.241924\pi$
$557$	0.846759	+	0.846759i	0.0358783	+	0.0358783i	−0.688940	+	0.724818i	$0.741924\pi$
$558$	17.0157	−	12.5761i	0.720334	−	0.532389i
$559$	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	$-0.223568\pi$
$563$	2.78320	+	2.78320i	0.117298	+	0.117298i	−0.646021	+	0.763319i	$0.723568\pi$
$564$	−3.26664	−	3.79329i	−0.137550	−	0.159726i
$565$	−0.300200	+	23.8824i	−0.0126295	+	1.00474i
$566$	16.9310			0.711665
$567$	2.65897	−	1.40995i	0.111666	−	0.0592123i
$568$	−6.99284	+	6.99284i	−0.293413	+	0.293413i
$569$	−1.33774			−0.0560812			−0.0280406	−	0.999607i	$-0.508927\pi$
$569$	−1.33774			−0.0560812			−0.0280406	+	0.999607i	$0.508927\pi$
$570$	30.9283	+	2.69846i	1.29545	+	0.113026i
$571$	−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
$573$	−8.86317	−	0.661165i	−0.370264	−	0.0276206i
$574$	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
$582$	2.00124	−	26.8273i	0.0829540	−	1.11203i
$583$	−13.7440	−	13.7440i	−0.569218	−	0.569218i
$584$	3.66462			0.151643
$585$	−22.6974	+	8.35634i	−0.938422	+	0.345492i
$586$	12.2892			0.507664
$587$	−1.02834	−	1.02834i	−0.0424440	−	0.0424440i	0.685566	−	0.728010i	$-0.259555\pi$
$587$	−1.02834	−	1.02834i	−0.0424440	−	0.0424440i	−0.728010	+	0.685566i	$0.759555\pi$
$588$	0.887525	−	11.8976i	0.0366009	−	0.490649i
$589$			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	−0.446368	−	0.894850i	$-0.647283\pi$
$593$	10.9212	−	10.9212i	0.448482	−	0.448482i	0.894850	+	0.446368i	$0.147283\pi$
$594$	8.84765	−	5.57197i	0.363023	−	0.228621i
$595$	−2.03809	+	1.98749i	−0.0835534	+	0.0814790i
$596$	−3.81004			−0.156065
$597$	17.0991	+	1.27554i	0.699821	+	0.0522045i
$598$	−30.6078	−	8.50878i	−1.25164	−	0.347950i
$599$	−4.08722			−0.166999			−0.0834996	−	0.996508i	$-0.526610\pi$
$599$	−4.08722			−0.166999			−0.0834996	+	0.996508i	$0.526610\pi$
$600$	−6.70228	+	5.48448i	−0.273619	+	0.223903i
$601$	−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
$603$	14.5558	−	10.7580i	0.592757	−	0.438099i
$604$	−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
$612$	−6.78833	−	9.18475i	−0.274402	−	0.371272i
$613$	−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
$615$	−23.4390	+	19.6772i	−0.945153	+	0.793461i
$616$			0.672913i			0.0271125i
$617$	16.1485	+	16.1485i	0.650116	+	0.650116i	0.953021	−	0.302905i	$-0.0979564\pi$
$617$	16.1485	+	16.1485i	0.650116	+	0.650116i	−0.302905	+	0.953021i	$0.597956\pi$
$618$	−0.470586	+	6.30839i	−0.0189298	+	0.253761i
$619$	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
$624$	5.87573	+	2.11560i	0.235218	+	0.0846919i
$625$	−24.9684	−	1.25640i	−0.998736	−	0.0502560i
$626$	−27.2765			−1.09019
$627$	−2.07834	+	27.8610i	−0.0830011	+	1.11266i
$628$	11.1016	−	11.1016i	0.443003	−	0.443003i
$629$		−	6.44683i		−	0.257052i
$630$	−1.31055	−	1.82064i	−0.0522136	−	0.0725361i
$631$			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
$633$	2.97047	−	39.8202i	0.118065	−	1.58271i
$634$			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	$0.196291\pi$
$641$			29.2838i			1.15664i	−0.815810	+	0.578319i	$0.803709\pi$
$642$	−0.181035	+	2.42685i	−0.00714490	+	0.0957800i
$643$	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
$645$	1.31606	−	15.0840i	0.0518197	−	0.593931i
$646$	30.5171			1.20068
$647$	18.2201	−	18.2201i	0.716306	−	0.716306i	−0.251540	−	0.967847i	$-0.580937\pi$
$647$	18.2201	−	18.2201i	0.716306	−	0.716306i	0.967847	+	0.251540i	$0.0809371\pi$
$648$	7.95130	−	4.21626i	0.312357	−	0.165630i
$649$		−	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	0.998002	−	0.0631814i	$-0.0201247\pi$
$653$	23.8883	+	23.8883i	0.934821	+	0.934821i	−0.0631814	+	0.998002i	$0.520125\pi$
$654$	7.06015	−	6.07994i	0.276074	−	0.237744i
$655$	−21.0880	+	20.5645i	−0.823978	+	0.803520i
$656$	7.90181			0.308514
$657$	−6.53441	−	8.84119i	−0.254931	−	0.344928i
$658$	−0.683424	−	0.683424i	−0.0266427	−	0.0266427i
$659$	−39.4014			−1.53486			−0.767431	−	0.641132i	$-0.778465\pi$
$659$	−39.4014			−1.53486			−0.767431	+	0.641132i	$0.778465\pi$
$660$	−5.01094	−	5.96892i	−0.195051	−	0.232340i
$661$		−	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
$663$	−21.5125	+	10.1222i	−0.835475	+	0.393113i
$664$			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
$672$	−0.0430876	+	0.577606i	−0.00166214	+	0.0222816i
$673$	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
$675$	25.1826	+	6.39037i	0.969279	+	0.245966i
$676$	6.70934	−	11.1348i	0.258052	−	0.428263i
$677$	−18.8046	+	18.8046i	−0.722721	+	0.722721i	−0.969159	−	0.246438i	$-0.920740\pi$
$677$	−18.8046	+	18.8046i	−0.722721	+	0.722721i	0.246438	+	0.969159i	$0.420740\pi$
$678$	−18.4494	−	1.37627i	−0.708545	−	0.0528553i
$679$		−	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	−0.860311	−	0.509770i	$-0.829730\pi$
$683$	−9.16112	+	9.16112i	−0.350540	+	0.350540i	0.509770	+	0.860311i	$0.329730\pi$
$684$	−3.56796	+	23.7818i	−0.136424	+	0.909322i
$685$	0.180664	−	14.3727i	0.00690283	−	0.549153i
$686$		−	4.64431i		−	0.177321i
$687$	−3.13303	+	41.9994i	−0.119532	+	1.60238i
$688$	−2.76440	+	2.76440i	−0.105392	+	0.105392i
$689$	−30.3225	+	17.1308i	−1.15520	+	0.652631i
$690$	21.9412	+	26.1359i	0.835288	+	0.994976i
$691$			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
$693$	1.62346	−	1.19988i	0.0616700	−	0.0455795i
$694$	−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	$0.874064\pi$
$702$	−5.37299	−	17.9480i	−0.202790	−	0.677404i
$703$	−9.59849	+	9.59849i	−0.362014	+	0.362014i
$704$			2.01226i			0.0758397i
$705$	11.1514	+	0.972943i	0.419985	+	0.0366431i
$706$	0.937977			0.0353012
$707$	0.826223	+	0.826223i	0.0310733	+	0.0310733i
$708$	1.58833	−	21.2922i	0.0596932	−	0.800209i
$709$	−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
$717$	4.50517	+	0.336072i	0.168249	+	0.0125508i
$718$	−17.9782	+	17.9782i	−0.670939	+	0.670939i
$719$	22.3663			0.834123			0.417061	−	0.908878i	$-0.363060\pi$
$719$	22.3663			0.834123			0.417061	+	0.908878i	$0.363060\pi$
$720$	−3.91902	−	5.44438i	−0.146053	−	0.202900i
$721$			1.22135i			0.0454853i
$722$	−32.0010	−	32.0010i	−1.19096	−	1.19096i
$723$	−4.19981	−	0.313293i	−0.156192	−	0.0116515i
$724$		−	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
$732$	−9.48075	−	0.707235i	−0.350419	−	0.0261402i
$733$	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
$735$	17.1530	+	20.4323i	0.632698	+	0.753656i
$736$		−	8.81099i		−	0.324777i
$737$	8.58463	−	8.58463i	0.316219	−	0.316219i
$738$	−14.0898	−	19.0637i	−0.518651	−	0.701746i
$739$	−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
$741$	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	0.273836	−	0.961776i	$-0.411708\pi$
$743$	33.6803	−	33.6803i	1.23561	−	1.23561i	0.961776	−	0.273836i	$-0.0882924\pi$
$744$	9.25669	−	7.97152i	0.339367	−	0.292250i
$745$	6.09944	−	5.94800i	0.223466	−	0.217918i
$746$	10.6136			0.388593
$747$	10.1821	−	7.52546i	0.372544	−	0.275342i
$748$	−5.41694	−	5.41694i	−0.198063	−	0.198063i
$749$			0.469854i			0.0171681i
$750$	2.16755	−	19.2432i	0.0791478	−	0.702663i
$751$	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
$753$	49.8715	+	3.72026i	1.81742	+	0.135574i
$754$	−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	$-0.328740\pi$
$761$	28.2729			1.02489			0.512446	+	0.858720i	$0.328740\pi$
$762$	27.9615	+	2.08585i	1.01294	+	0.0755622i
$763$	1.27200	−	1.27200i	0.0460497	−	0.0460497i
$764$	−5.13137			−0.185647
$765$	25.2060	+	4.10621i	0.911326	+	0.148460i
$766$	−6.47732			−0.234035
$767$	−42.8225	−	11.9044i	−1.54623	−	0.429843i
$768$	−0.128848	+	1.72725i	−0.00464939	+	0.0623268i
$769$	−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	−0.214025	−	0.976828i	$-0.568657\pi$
$773$	21.2081	−	21.2081i	0.762803	−	0.762803i	0.976828	+	0.214025i	$0.0686574\pi$
$774$	11.5986	+	1.74012i	0.416902	+	0.0625473i
$775$	35.2535	+	0.886410i	1.26634	+	0.0318408i
$776$		−	15.5318i		−	0.557559i
$777$	0.978119	+	0.0729647i	0.0350898	+	0.00261759i
$778$	2.61512	+	2.61512i	0.0937566	+	0.0937566i
$779$	63.3410			2.26943
$780$	−12.7091	+	5.78600i	−0.455060	+	0.207172i
$781$	19.8999			0.712075
$782$	23.7189	+	23.7189i	0.848188	+	0.848188i
$783$	−5.24406	+	23.0845i	−0.187407	+	0.824972i
$784$		−	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
$792$	4.85472	−	3.58806i	0.172505	−	0.127496i
$793$	−5.30066	+	19.0675i	−0.188232	+	0.677108i
$794$	13.5948			0.482461
$795$	37.2686	+	3.25164i	1.32178	+	0.115324i
$796$	9.89963			0.350883
$797$	13.6728	−	13.6728i	0.484316	−	0.484316i	−0.422191	−	0.906507i	$-0.638739\pi$
$797$	13.6728	−	13.6728i	0.484316	−	0.484316i	0.906507	+	0.422191i	$0.138739\pi$
$798$	−0.345391	+	4.63009i	−0.0122267	+	0.163903i
$799$	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
$807$	−2.00558	+	26.8856i	−0.0705998	+	0.946417i
$808$	2.47071	+	2.47071i	0.0869192	+	0.0869192i
$809$	−32.5723			−1.14518			−0.572590	−	0.819842i	$-0.694061\pi$
$809$	−32.5723			−1.14518			−0.572590	+	0.819842i	$0.694061\pi$
$810$	−6.14696	+	19.1629i	−0.215982	+	0.673314i
$811$			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
$813$	15.2000	+	1.13387i	0.533086	+	0.0397666i
$814$	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	$0.517893\pi$
$822$	11.1031	+	0.828255i	0.387264	+	0.0288887i
$823$	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
$825$	17.3403	+	1.73278i	0.603711	+	0.0603278i
$826$		−	4.12231i		−	0.143434i
$827$	−17.4931	−	17.4931i	−0.608295	−	0.608295i	0.334205	−	0.942500i	$-0.391532\pi$
$827$	−17.4931	−	17.4931i	−0.608295	−	0.608295i	−0.942500	+	0.334205i	$0.891532\pi$
$828$	−21.2572	+	15.7109i	−0.738739	+	0.545992i
$829$		−	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
$837$	−35.7376	−	8.11843i	−1.23527	−	0.280614i
$838$	0.742340	+	0.742340i	0.0256437	+	0.0256437i
$839$			30.7292i			1.06089i	0.847719	+	0.530445i	$0.177975\pi$
$839$			30.7292i			1.06089i	−0.847719	+	0.530445i	$0.822025\pi$
$840$	−0.832746	−	0.991948i	−0.0287325	−	0.0342255i
$841$	−8.24467			−0.284299
$842$	19.4657	−	19.4657i	0.670834	−	0.670834i
$843$	−0.0708602	+	0.949907i	−0.00244055	+	0.0327165i
$844$		−	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
$852$	17.0814	+	1.27422i	0.585200	+	0.0436541i
$853$	−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
$855$	−31.4149	−	43.6421i	−1.07437	−	1.49253i
$856$			1.40503i			0.0480231i
$857$	24.8921	−	24.8921i	0.850299	−	0.850299i	−0.139871	−	0.990170i	$-0.544669\pi$
$857$	24.8921	−	24.8921i	0.850299	−	0.850299i	0.990170	+	0.139871i	$0.0446688\pi$
$858$	−5.35021	−	11.3707i	−0.182653	−	0.388190i
$859$			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	−0.0710755	−	0.997471i	$-0.522643\pi$
$863$	27.2146	−	27.2146i	0.926395	−	0.926395i	0.997471	+	0.0710755i	$0.0226431\pi$
$864$	4.39688	−	2.76902i	0.149585	−	0.0942039i
$865$	−0.0181596	+	1.44468i	−0.000617444	+	0.0491206i
$866$	−23.3774			−0.794395
$867$	−4.32944	−	0.322963i	−0.147035	−	0.0109684i
$868$	1.66775	−	1.66775i	0.0566071	−	0.0566071i
$869$			21.4658i			0.728177i
$870$	17.5778	+	1.53364i	0.595942	+	0.0519952i
$871$	−10.7001	−	18.9398i	−0.362558	−	0.641750i
$872$	3.80376	−	3.80376i	0.128811	−	0.128811i
$873$	−37.4717	+	27.6948i	−1.26823	+	0.937329i
$874$		−	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	$-0.899500\pi$
$881$		−	18.4330i		−	0.621023i	0.950570	−	0.310511i	$-0.100500\pi$
$882$	−16.6183	+	12.2823i	−0.559566	+	0.413568i
$883$	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
$885$	30.6974	+	36.5660i	1.03188	+	1.22915i
$886$		−	5.10590i		−	0.171536i
$887$	−21.3790	+	21.3790i	−0.717838	+	0.717838i	−0.968162	−	0.250324i	$-0.919463\pi$
$887$	−21.3790	+	21.3790i	−0.717838	+	0.717838i	0.250324	+	0.968162i	$0.419463\pi$
$888$	2.92493	+	0.218191i	0.0981542	+	0.00732201i
$889$	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
$897$	23.4268	+	49.7885i	0.782197	+	1.66239i
$898$	14.6445	−	14.6445i	0.488693	−	0.488693i
$899$			32.1317i			1.07165i
$900$	14.7734	+	2.59769i	0.492445	+	0.0865896i
$901$	36.7731			1.22509
$902$	−11.2433	−	11.2433i	−0.374362	−	0.374362i
$903$	2.25813	+	0.168449i	0.0751457	+	0.00560564i
$904$	−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	$0.0339284\pi$
$911$			6.42215i			0.212775i	−0.994325	+	0.106388i	$0.966072\pi$
$912$	−1.03284	+	13.8457i	−0.0342009	+	0.458475i
$913$	6.00515	−	6.00515i	0.198742	−	0.198742i
$914$	−16.0220			−0.529960
$915$	16.2817	−	13.6686i	0.538256	−	0.451869i
$916$			24.3157i			0.803415i
$917$	−3.11485	−	3.11485i	−0.102861	−	0.102861i
$918$	−4.38216	+	19.2904i	−0.144633	+	0.636678i
$919$			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
$927$	8.81139	−	6.51238i	0.289404	−	0.213895i
$928$	−3.22144	−	3.22144i	−0.105749	−	0.105749i
$929$		−	7.75923i		−	0.254572i	−0.991866	−	0.127286i	$-0.959373\pi$
$929$		−	7.75923i		−	0.254572i	0.991866	−	0.127286i	$-0.0406266\pi$
$930$	−2.37426	+	27.2125i	−0.0778549	+	0.892333i
$931$		−	55.2156i		−	1.80962i
$932$	7.59642	−	7.59642i	0.248829	−	0.248829i
$933$	15.1223	+	1.12808i	0.495083	+	0.0369317i
$934$	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	0.952176	−	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	$-0.570443\pi$
$941$	−13.4668			−0.439006			−0.219503	+	0.975612i	$0.570443\pi$
$942$	−27.1180	−	2.02292i	−0.883551	−	0.0659102i
$943$	49.2307	+	49.2307i	1.60317	+	1.60317i
$944$		−	12.3272i		−	0.401216i
$945$	−0.908279	+	3.77781i	−0.0295463	+	0.122892i
$946$	7.86683			0.255773
$947$	13.4019	+	13.4019i	0.435504	+	0.435504i	0.890496	−	0.454991i	$-0.150358\pi$
$947$	13.4019	+	13.4019i	0.435504	+	0.435504i	−0.454991	+	0.890496i	$0.650358\pi$
$948$	−1.37449	+	18.4255i	−0.0446412	+	0.598432i
$949$	−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	$0.0214085\pi$
$953$	32.8756	+	32.8756i	1.06495	+	1.06495i	0.0672062	+	0.997739i	$0.478591\pi$
$954$	−4.29939	+	28.6571i	−0.139198	+	0.927808i
$955$	8.21475	−	8.01079i	0.265823	−	0.259223i
$956$	2.60829			0.0843581
$957$	−1.18120	+	15.8345i	−0.0381829	+	0.511856i
$958$	−15.4565	+	15.4565i	−0.499376	+	0.499376i
$959$	2.14963			0.0694152
$960$	−2.49021	−	2.96628i	−0.0803713	−	0.0957364i
$961$	−18.7438			−0.604639
$962$	1.63532	−	5.88257i	0.0527248	−	0.189662i
$963$	3.38976	−	2.50532i	0.109233	−	0.0807329i
$964$	−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	$-0.836790\pi$
$971$		−	30.5730i		−	0.981133i	0.871404	−	0.490566i	$-0.163210\pi$
$972$	−14.5206	−	5.67037i	−0.465747	−	0.181877i
$973$	0.167786	+	0.167786i	0.00537897	+	0.00537897i
$974$	25.7689			0.825687
$975$	11.3131	−	29.1035i	0.362310	−	0.932058i
$976$	−5.48892			−0.175696
$977$	−16.1846	−	16.1846i	−0.517792	−	0.517792i	0.399111	−	0.916903i	$-0.369319\pi$
$977$	−16.1846	−	16.1846i	−0.517792	−	0.517792i	−0.916903	+	0.399111i	$0.869319\pi$
$978$	−18.8934	−	1.40939i	−0.604144	−	0.0450673i
$979$		−	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	$0.502751\pi$
$983$	−31.6227	+	31.6227i	−1.00861	+	1.00861i	−0.999963	+	0.00864329i	$0.997249\pi$
$984$	−8.93096	−	10.3708i	−0.284709	−	0.330610i
$985$	0.225163	−	17.9127i	0.00717427	−	0.570747i
$986$	17.3441			0.552347
$987$	−0.124532	+	1.66940i	−0.00396391	+	0.0531377i
$988$	27.8461	+	7.74106i	0.885904	+	0.246276i
$989$	−34.4462			−1.09532
$990$	−2.17039	+	13.3230i	−0.0689797	+	0.423433i
$991$	−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
$993$	35.7979	+	2.67041i	1.13601	+	0.0847430i
$994$	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.b.77.4	✓	24
3.2	odd	2		390.2.s.c.77.7	yes	24
5.3	odd	4		390.2.s.c.233.1	yes	24
13.12	even	2	inner	390.2.s.b.77.10	yes	24
15.8	even	4	inner	390.2.s.b.233.10	yes	24
39.38	odd	2		390.2.s.c.77.1	yes	24
65.38	odd	4		390.2.s.c.233.7	yes	24
195.38	even	4	inner	390.2.s.b.233.4	yes	24

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

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.128848 + 1.72725i) q^{3} +1.00000i q^{4} +(-1.56114 - 1.60089i) q^{5} +(1.31246 - 1.13024i) q^{6} +(0.236462 - 0.236462i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.96680 - 0.445105i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.128848 + 1.72725i) 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} +(-1.72725 - 0.128848i) q^{12} +(-0.965701 + 3.47382i) q^{13} -0.334408 q^{14} +(2.96628 - 2.49021i) q^{15} -1.00000 q^{16} +(2.69197 - 2.69197i) q^{17} +(1.78311 + 2.41258i) 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} +(1.15107 - 5.06705i) q^{27} +(0.236462 + 0.236462i) q^{28} -4.55580 q^{29} +(-3.85833 - 0.336634i) q^{30} -7.05293i q^{31} +(0.707107 + 0.707107i) q^{32} +(0.259274 - 3.47567i) 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} +(0.0430876 - 0.577606i) q^{42} +(2.76440 - 2.76440i) q^{43} -2.01226i q^{44} +(3.91902 + 5.44438i) q^{45} +8.81099i q^{46} +(2.04369 + 2.04369i) q^{47} +(0.128848 - 1.72725i) 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} +(1.03284 - 13.8457i) q^{57} +(3.22144 + 3.22144i) q^{58} +12.3272i q^{59} +(2.49021 + 2.96628i) q^{60} +5.48892 q^{61} +(-4.98717 + 4.98717i) q^{62} +(-0.806784 + 0.596284i) 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} +(-2.41258 + 1.78311i) q^{72} +(2.59128 + 2.59128i) q^{73} -1.69340 q^{74} +(-8.61734 - 0.861115i) q^{75} -8.01600i q^{76} +(-0.475822 + 0.475822i) q^{77} +(2.65881 + 5.65073i) 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} +(0.587005 - 7.86902i) q^{87} +(-1.42288 + 1.42288i) q^{88} +1.02859i q^{89} +(1.07859 - 6.62093i) q^{90} +(0.593074 + 1.04978i) q^{91} +(6.23031 - 6.23031i) q^{92} +(12.1822 + 0.908753i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{3} - 12 q^{9}+O(q^{10}) \) 24 * q - 8 * q^3 - 12 * q^9	\( 24 q - 8 q^{3} - 12 q^{9} + 4 q^{10} + 4 q^{12} - 8 q^{13} - 16 q^{14} - 24 q^{16} + 52 q^{17} + 16 q^{22} - 16 q^{23} + 16 q^{25} + 40 q^{27} - 80 q^{29} + 20 q^{35} - 16 q^{38} - 32 q^{39} - 4 q^{42} + 28 q^{43} + 8 q^{48} - 20 q^{51} - 8 q^{52} + 72 q^{53} + 24 q^{55} - 64 q^{61} - 32 q^{62} - 12 q^{65} + 8 q^{66} + 52 q^{68} - 16 q^{69} - 120 q^{74} - 104 q^{75} + 32 q^{77} + 44 q^{78} + 12 q^{81} + 32 q^{82} - 32 q^{87} - 16 q^{88} + 64 q^{90} + 64 q^{91} + 16 q^{92} + 96 q^{95}+O(q^{100}) \) 24 * q - 8 * q^3 - 12 * q^9 + 4 * q^10 + 4 * q^12 - 8 * q^13 - 16 * q^14 - 24 * q^16 + 52 * q^17 + 16 * q^22 - 16 * q^23 + 16 * q^25 + 40 * q^27 - 80 * q^29 + 20 * q^35 - 16 * q^38 - 32 * q^39 - 4 * q^42 + 28 * q^43 + 8 * 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 - 104 * q^75 + 32 * q^77 + 44 * q^78 + 12 * q^81 + 32 * q^82 - 32 * q^87 - 16 * q^88 + 64 * q^90 + 64 * q^91 + 16 * q^92 + 96 * q^95

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