LMFDB - Embedded newform 656.2.n.g.493.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [656,2,Mod(165,656)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("656.165"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(656, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.n (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [80,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.25
Character	$\chi$	$=$	656.493
Dual form			656.2.n.g.165.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.448028 - 1.34137i) q^{2} +(1.35244 + 1.35244i) q^{3} +(-1.59854 - 1.20194i) q^{4} +(-1.01984 + 1.01984i) q^{5} +(2.42005 - 1.20819i) q^{6} +1.02501i q^{7} +(-2.32844 + 1.60573i) q^{8} +0.658196i q^{9} +(0.911065 + 1.82490i) q^{10} +(-3.45580 + 3.45580i) q^{11} +(-0.536381 - 3.78749i) q^{12} +(4.74217 + 4.74217i) q^{13} +(1.37491 + 0.459232i) q^{14} -2.75855 q^{15} +(1.11068 + 3.84271i) q^{16} +1.03515 q^{17} +(0.882884 + 0.294890i) q^{18} +(4.00658 + 4.00658i) q^{19} +(2.85604 - 0.404470i) q^{20} +(-1.38626 + 1.38626i) q^{21} +(3.08721 + 6.18379i) q^{22} -7.29883i q^{23} +(-5.32074 - 0.977415i) q^{24} +2.91986i q^{25} +(8.48563 - 4.23638i) q^{26} +(3.16715 - 3.16715i) q^{27} +(1.23200 - 1.63852i) q^{28} +(-0.0824890 - 0.0824890i) q^{29} +(-1.23590 + 3.70023i) q^{30} -7.42872 q^{31} +(5.65210 + 0.231811i) q^{32} -9.34753 q^{33} +(0.463775 - 1.38852i) q^{34} +(-1.04534 - 1.04534i) q^{35} +(0.791113 - 1.05216i) q^{36} +(-5.94518 + 5.94518i) q^{37} +(7.16937 - 3.57925i) q^{38} +12.8270i q^{39} +(0.737042 - 4.01222i) q^{40} +1.00000i q^{41} +(1.23841 + 2.48057i) q^{42} +(2.12772 - 2.12772i) q^{43} +(9.67790 - 1.37058i) q^{44} +(-0.671255 - 0.671255i) q^{45} +(-9.79043 - 3.27008i) q^{46} +3.96220 q^{47} +(-3.69491 + 6.69916i) q^{48} +5.94936 q^{49} +(3.91661 + 1.30818i) q^{50} +(1.39998 + 1.39998i) q^{51} +(-1.88075 - 13.2804i) q^{52} +(3.16372 - 3.16372i) q^{53} +(-2.82935 - 5.66729i) q^{54} -7.04871i q^{55} +(-1.64589 - 2.38667i) q^{56} +10.8373i q^{57} +(-0.147606 + 0.0736909i) q^{58} +(-1.21040 + 1.21040i) q^{59} +(4.40965 + 3.31561i) q^{60} +(-5.94068 - 5.94068i) q^{61} +(-3.32827 + 9.96465i) q^{62} -0.674656 q^{63} +(2.84324 - 7.47770i) q^{64} -9.67251 q^{65} +(-4.18795 + 12.5385i) q^{66} +(5.63874 + 5.63874i) q^{67} +(-1.65473 - 1.24419i) q^{68} +(9.87124 - 9.87124i) q^{69} +(-1.87053 + 0.933848i) q^{70} -3.72306i q^{71} +(-1.05689 - 1.53257i) q^{72} -0.818434i q^{73} +(5.31108 + 10.6383i) q^{74} +(-3.94893 + 3.94893i) q^{75} +(-1.58902 - 11.2204i) q^{76} +(-3.54222 - 3.54222i) q^{77} +(17.2058 + 5.74686i) q^{78} -16.8179 q^{79} +(-5.05165 - 2.78623i) q^{80} +10.5414 q^{81} +(1.34137 + 0.448028i) q^{82} +(-10.2774 - 10.2774i) q^{83} +(3.88221 - 0.549794i) q^{84} +(-1.05568 + 1.05568i) q^{85} +(-1.90078 - 3.80734i) q^{86} -0.223123i q^{87} +(2.49752 - 13.5957i) q^{88} +5.40600i q^{89} +(-1.20114 + 0.599660i) q^{90} +(-4.86076 + 4.86076i) q^{91} +(-8.77276 + 11.6675i) q^{92} +(-10.0469 - 10.0469i) q^{93} +(1.77518 - 5.31478i) q^{94} -8.17214 q^{95} +(7.33063 + 7.95765i) q^{96} +14.3892 q^{97} +(2.66548 - 7.98029i) q^{98} +(-2.27459 - 2.27459i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{4} + 4 q^{10} - 4 q^{11} + 14 q^{12} + 6 q^{14} - 48 q^{15} + 6 q^{16} + 40 q^{18} - 8 q^{19} - 42 q^{20} + 2 q^{22} - 2 q^{24} - 48 q^{26} + 42 q^{28} - 8 q^{29} - 14 q^{30} + 80 q^{31} - 20 q^{32}+ \cdots + 12 q^{99}+O(q^{100}) $ 80 * q - 2 * q^4 + 4 * q^10 - 4 * q^11 + 14 * q^12 + 6 * q^14 - 48 * q^15 + 6 * q^16 + 40 * q^18 - 8 * q^19 - 42 * q^20 + 2 * q^22 - 2 * q^24 - 48 * q^26 + 42 * q^28 - 8 * q^29 - 14 * q^30 + 80 * q^31 - 20 * q^32 + 12 * q^34 - 60 * q^36 - 8 * q^37 + 26 * q^40 - 46 * q^42 + 4 * q^43 + 82 * q^44 - 56 * q^47 + 10 * q^48 - 80 * q^49 + 70 * q^50 - 12 * q^51 - 28 * q^52 + 8 * q^53 + 38 * q^54 + 14 * q^56 - 60 * q^58 + 16 * q^59 + 144 * q^60 + 16 * q^61 - 40 * q^62 + 104 * q^63 - 14 * q^64 + 58 * q^66 + 20 * q^67 - 84 * q^68 - 40 * q^69 + 34 * q^70 + 6 * q^72 - 48 * q^74 - 28 * q^75 + 50 * q^76 + 8 * q^77 - 12 * q^78 - 144 * q^79 - 14 * q^80 - 80 * q^81 + 2 * q^82 - 112 * q^84 - 16 * q^85 + 2 * q^86 - 10 * q^88 - 116 * q^90 - 16 * q^91 + 64 * q^92 + 24 * q^94 + 96 * q^95 - 6 * q^96 + 178 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.448028	−	1.34137i	0.316803	−	0.948491i
$2$	0.448028	−	1.34137i	0.316803	−	0.948491i
$3$	1.35244	+	1.35244i	0.780833	+	0.780833i	0.979971	−	0.199139i	$-0.0638145\pi$
$3$	1.35244	+	1.35244i	0.780833	+	0.780833i	−0.199139	+	0.979971i	$0.563814\pi$
$4$	−1.59854	−	1.20194i	−0.799271	−	0.600970i
$5$	−1.01984	+	1.01984i	−0.456086	+	0.456086i	−0.897368	−	0.441282i	$-0.854524\pi$
$5$	−1.01984	+	1.01984i	−0.456086	+	0.456086i	0.441282	+	0.897368i	$0.354524\pi$
$6$	2.42005	−	1.20819i	0.987983	−	0.493242i
$7$			1.02501i			0.387416i	0.981059	+	0.193708i	$0.0620515\pi$
$7$			1.02501i			0.387416i	−0.981059	+	0.193708i	$0.937948\pi$
$8$	−2.32844	+	1.60573i	−0.823227	+	0.567712i
$9$			0.658196i			0.219399i
$10$	0.911065	+	1.82490i	0.288104	+	0.577083i
$11$	−3.45580	+	3.45580i	−1.04196	+	1.04196i	−0.0428817	+	0.999080i	$0.513654\pi$
$11$	−3.45580	+	3.45580i	−1.04196	+	1.04196i	−0.999080	+	0.0428817i	$0.986346\pi$
$12$	−0.536381	−	3.78749i	−0.154840	−	1.09335i
$13$	4.74217	+	4.74217i	1.31524	+	1.31524i	0.917495	+	0.397747i	$0.130208\pi$
$13$	4.74217	+	4.74217i	1.31524	+	1.31524i	0.397747	+	0.917495i	$0.369792\pi$
$14$	1.37491	+	0.459232i	0.367461	+	0.122735i
$15$	−2.75855			−0.712253
$16$	1.11068	+	3.84271i	0.277669	+	0.960677i
$17$	1.03515			0.251060			0.125530	−	0.992090i	$-0.459937\pi$
$17$	1.03515			0.251060			0.125530	+	0.992090i	$0.459937\pi$
$18$	0.882884	+	0.294890i	0.208098	+	0.0695063i
$19$	4.00658	+	4.00658i	0.919173	+	0.919173i	0.996969	−	0.0777959i	$-0.0247883\pi$
$19$	4.00658	+	4.00658i	0.919173	+	0.919173i	−0.0777959	+	0.996969i	$0.524788\pi$
$20$	2.85604	−	0.404470i	0.638631	−	0.0904423i
$21$	−1.38626	+	1.38626i	−0.302507	+	0.302507i
$22$	3.08721	+	6.18379i	0.658195	+	1.31839i
$23$		−	7.29883i		−	1.52191i	−0.648804	−	0.760956i	$-0.724730\pi$
$23$		−	7.29883i		−	1.52191i	0.648804	−	0.760956i	$-0.275270\pi$
$24$	−5.32074	−	0.977415i	−1.08609	−	0.199514i
$25$			2.91986i			0.583971i
$26$	8.48563	−	4.23638i	1.66417	−	0.830823i
$27$	3.16715	−	3.16715i	0.609519	−	0.609519i
$28$	1.23200	−	1.63852i	0.232826	−	0.309651i
$29$	−0.0824890	−	0.0824890i	−0.0153178	−	0.0153178i	0.699406	−	0.714724i	$-0.253448\pi$
$29$	−0.0824890	−	0.0824890i	−0.0153178	−	0.0153178i	−0.714724	+	0.699406i	$0.753448\pi$
$30$	−1.23590	+	3.70023i	−0.225644	+	0.675566i
$31$	−7.42872			−1.33424			−0.667119	−	0.744951i	$-0.732473\pi$
$31$	−7.42872			−1.33424			−0.667119	+	0.744951i	$0.732473\pi$
$32$	5.65210	+	0.231811i	0.999160	+	0.0409788i
$33$	−9.34753			−1.62720
$34$	0.463775	−	1.38852i	0.0795367	−	0.238128i
$35$	−1.04534	−	1.04534i	−0.176695	−	0.176695i
$36$	0.791113	−	1.05216i	0.131852	−	0.175359i
$37$	−5.94518	+	5.94518i	−0.977382	+	0.977382i	−0.999750	−	0.0223681i	$-0.992879\pi$
$37$	−5.94518	+	5.94518i	−0.977382	+	0.977382i	0.0223681	+	0.999750i	$0.492879\pi$
$38$	7.16937	−	3.57925i	1.16303	−	0.580631i
$39$			12.8270i			2.05397i
$40$	0.737042	−	4.01222i	0.116537	−	0.634388i
$41$			1.00000i			0.156174i
$41$			1.00000i			0.156174i
$42$	1.23841	+	2.48057i	0.191090	+	0.382761i
$43$	2.12772	−	2.12772i	0.324475	−	0.324475i	−0.526006	−	0.850481i	$-0.676311\pi$
$43$	2.12772	−	2.12772i	0.324475	−	0.324475i	0.850481	+	0.526006i	$0.176311\pi$
$44$	9.67790	−	1.37058i	1.45900	−	0.206622i
$45$	−0.671255	−	0.671255i	−0.100065	−	0.100065i
$46$	−9.79043	−	3.27008i	−1.44352	−	0.482147i
$47$	3.96220			0.577947			0.288973	−	0.957337i	$-0.406686\pi$
$47$	3.96220			0.577947			0.288973	+	0.957337i	$0.406686\pi$
$48$	−3.69491	+	6.69916i	−0.533315	+	0.966941i
$49$	5.94936			0.849908
$50$	3.91661	+	1.30818i	0.553892	+	0.185004i
$51$	1.39998	+	1.39998i	0.196036	+	0.196036i
$52$	−1.88075	−	13.2804i	−0.260814	−	1.84166i
$53$	3.16372	−	3.16372i	0.434570	−	0.434570i	−0.455610	−	0.890180i	$-0.650579\pi$
$53$	3.16372	−	3.16372i	0.434570	−	0.434570i	0.890180	+	0.455610i	$0.150579\pi$
$54$	−2.82935	−	5.66729i	−0.385026	−	0.771221i
$55$		−	7.04871i		−	0.950448i
$56$	−1.64589	−	2.38667i	−0.219941	−	0.318932i
$57$			10.8373i			1.43544i
$58$	−0.147606	+	0.0736909i	−0.0193816	+	0.00967609i
$59$	−1.21040	+	1.21040i	−0.157581	+	0.157581i	−0.781494	−	0.623913i	$-0.785542\pi$
$59$	−1.21040	+	1.21040i	−0.157581	+	0.157581i	0.623913	+	0.781494i	$0.285542\pi$
$60$	4.40965	+	3.31561i	0.569284	+	0.428043i
$61$	−5.94068	−	5.94068i	−0.760627	−	0.760627i	0.215809	−	0.976436i	$-0.430761\pi$
$61$	−5.94068	−	5.94068i	−0.760627	−	0.760627i	−0.976436	+	0.215809i	$0.930761\pi$
$62$	−3.32827	+	9.96465i	−0.422691	+	1.26551i
$63$	−0.674656			−0.0849987
$64$	2.84324	−	7.47770i	0.355405	−	0.934712i
$65$	−9.67251			−1.19973
$66$	−4.18795	+	12.5385i	−0.515501	+	1.54338i
$67$	5.63874	+	5.63874i	0.688882	+	0.688882i	0.961985	−	0.273103i	$-0.0880499\pi$
$67$	5.63874	+	5.63874i	0.688882	+	0.688882i	−0.273103	+	0.961985i	$0.588050\pi$
$68$	−1.65473	−	1.24419i	−0.200665	−	0.150880i
$69$	9.87124	−	9.87124i	1.18836	−	1.18836i
$70$	−1.87053	+	0.933848i	−0.223571	+	0.111616i
$71$		−	3.72306i		−	0.441846i	−0.975291	−	0.220923i	$-0.929093\pi$
$71$		−	3.72306i		−	0.441846i	0.975291	−	0.220923i	$-0.0709070\pi$
$72$	−1.05689	−	1.53257i	−0.124555	−	0.180615i
$73$		−	0.818434i		−	0.0957904i	−0.998852	−	0.0478952i	$-0.984749\pi$
$73$		−	0.818434i		−	0.0957904i	0.998852	−	0.0478952i	$-0.0152514\pi$
$74$	5.31108	+	10.6383i	0.617400	+	1.23668i
$75$	−3.94893	+	3.94893i	−0.455984	+	0.455984i
$76$	−1.58902	−	11.2204i	−0.182273	−	1.28706i
$77$	−3.54222	−	3.54222i	−0.403673	−	0.403673i
$78$	17.2058	+	5.74686i	1.94817	+	0.650704i
$79$	−16.8179			−1.89216			−0.946081	−	0.323932i	$-0.894995\pi$
$79$	−16.8179			−1.89216			−0.946081	+	0.323932i	$0.894995\pi$
$80$	−5.05165	−	2.78623i	−0.564792	−	0.311510i
$81$	10.5414			1.17126
$82$	1.34137	+	0.448028i	0.148129	+	0.0494764i
$83$	−10.2774	−	10.2774i	−1.12809	−	1.12809i	−0.990487	−	0.137603i	$-0.956060\pi$
$83$	−10.2774	−	10.2774i	−1.12809	−	1.12809i	−0.137603	−	0.990487i	$-0.543940\pi$
$84$	3.88221	−	0.549794i	0.423583	−	0.0599875i
$85$	−1.05568	+	1.05568i	−0.114505	+	0.114505i
$86$	−1.90078	−	3.80734i	−0.204967	−	0.410556i
$87$		−	0.223123i		−	0.0239213i
$88$	2.49752	−	13.5957i	0.266236	−	1.44931i
$89$			5.40600i			0.573035i	0.958075	+	0.286517i	$0.0924976\pi$
$89$			5.40600i			0.573035i	−0.958075	+	0.286517i	$0.907502\pi$
$90$	−1.20114	+	0.599660i	−0.126611	+	0.0632097i
$91$	−4.86076	+	4.86076i	−0.509546	+	0.509546i
$92$	−8.77276	+	11.6675i	−0.914624	+	1.21642i
$93$	−10.0469	−	10.0469i	−1.04182	−	1.04182i
$94$	1.77518	−	5.31478i	0.183095	−	0.548177i
$95$	−8.17214			−0.838444
$96$	7.33063	+	7.95765i	0.748179	+	0.812174i
$97$	14.3892			1.46101			0.730503	−	0.682909i	$-0.239286\pi$
$97$	14.3892			1.46101			0.730503	+	0.682909i	$0.239286\pi$
$98$	2.66548	−	7.98029i	0.269254	−	0.806131i
$99$	−2.27459	−	2.27459i	−0.228605	−	0.228605i
$100$	3.50949	−	4.66751i	0.350949	−	0.466751i
$101$	6.34907	−	6.34907i	0.631756	−	0.631756i	−0.316752	−	0.948508i	$-0.602592\pi$
$101$	6.34907	−	6.34907i	0.631756	−	0.631756i	0.948508	+	0.316752i	$0.102592\pi$
$102$	2.50511	−	1.25066i	0.248043	−	0.123834i
$103$		−	17.0715i		−	1.68210i	−0.540954	−	0.841052i	$-0.681937\pi$
$103$		−	17.0715i		−	1.68210i	0.540954	−	0.841052i	$-0.318063\pi$
$104$	−18.6565	−	3.42719i	−1.82942	−	0.336064i
$105$		−	2.82753i		−	0.275939i
$106$	−2.82628	−	5.66114i	−0.274512	−	0.549859i
$107$	5.04780	−	5.04780i	0.487989	−	0.487989i	−0.419682	−	0.907671i	$-0.637858\pi$
$107$	5.04780	−	5.04780i	0.487989	−	0.487989i	0.907671	+	0.419682i	$0.137858\pi$
$108$	−8.86956	+	1.25610i	−0.853474	+	0.120868i
$109$	10.8358	+	10.8358i	1.03788	+	1.03788i	0.999254	+	0.0386246i	$0.0122976\pi$
$109$	10.8358	+	10.8358i	1.03788	+	1.03788i	0.0386246	+	0.999254i	$0.487702\pi$
$110$	−9.45493	−	3.15802i	−0.901492	−	0.301105i
$111$	−16.0810			−1.52634
$112$	−3.93880	+	1.13845i	−0.372182	+	0.107574i
$113$	18.5040			1.74071			0.870355	−	0.492425i	$-0.163889\pi$
$113$	18.5040			1.74071			0.870355	+	0.492425i	$0.163889\pi$
$114$	14.5369	+	4.85543i	1.36150	+	0.454752i
$115$	7.44364	+	7.44364i	0.694123	+	0.694123i
$116$	0.0327153	+	0.231009i	0.00303754	+	0.0214487i
$117$	−3.12128	+	3.12128i	−0.288563	+	0.288563i
$118$	1.08130	+	2.16589i	0.0995418	+	0.199386i
$119$			1.06103i			0.0972649i
$120$	6.42310	−	4.42949i	0.586346	−	0.404355i
$121$		−	12.8851i		−	1.17137i
$122$	−10.6302	+	5.30706i	−0.962417	+	0.480479i
$123$	−1.35244	+	1.35244i	−0.121946	+	0.121946i
$124$	11.8751	+	8.92888i	1.06642	+	0.801837i
$125$	−8.07698	−	8.07698i	−0.722427	−	0.722427i
$126$	−0.302265	+	0.904963i	−0.0269279	+	0.0806205i
$127$	−6.62865			−0.588197			−0.294099	−	0.955775i	$-0.595019\pi$
$127$	−6.62865			−0.588197			−0.294099	+	0.955775i	$0.595019\pi$
$128$	−8.75650	−	7.16405i	−0.773973	−	0.633219i
$129$	5.75524			0.506721
$130$	−4.33355	+	12.9744i	−0.380078	+	1.13793i
$131$	4.35337	+	4.35337i	0.380356	+	0.380356i	0.871230	−	0.490875i	$-0.163323\pi$
$131$	4.35337	+	4.35337i	0.380356	+	0.380356i	−0.490875	+	0.871230i	$0.663323\pi$
$132$	14.9424	+	11.2352i	1.30057	+	0.977896i
$133$	−4.10678	+	4.10678i	−0.356103	+	0.356103i
$134$	10.0899	−	5.03732i	0.871639	−	0.435159i
$135$			6.45997i			0.555986i
$136$	−2.41028	+	1.66217i	−0.206680	+	0.142530i
$137$		−	12.2685i		−	1.04817i	−0.851666	−	0.524085i	$-0.824407\pi$
$137$		−	12.2685i		−	1.04817i	0.851666	−	0.524085i	$-0.175593\pi$
$138$	−8.81839	−	17.6636i	−0.750671	−	1.50362i
$139$	−6.13710	+	6.13710i	−0.520542	+	0.520542i	−0.917735	−	0.397193i	$-0.869984\pi$
$139$	−6.13710	+	6.13710i	−0.520542	+	0.520542i	0.397193	+	0.917735i	$0.369984\pi$
$140$	0.414585	+	2.92747i	0.0350388	+	0.247416i
$141$	5.35865	+	5.35865i	0.451280	+	0.451280i
$142$	−4.99400	−	1.66804i	−0.419087	−	0.139978i
$143$	−32.7760			−2.74086
$144$	−2.52926	+	0.731044i	−0.210771	+	0.0609203i
$145$	0.168251			0.0139725
$146$	−1.09782	−	0.366681i	−0.0908564	−	0.0303467i
$147$	8.04616	+	8.04616i	0.663636	+	0.663636i
$148$	16.6494	−	2.35787i	1.36857	−	0.193816i
$149$	5.72132	−	5.72132i	0.468709	−	0.468709i	−0.432787	−	0.901496i	$-0.642470\pi$
$149$	5.72132	−	5.72132i	0.468709	−	0.468709i	0.901496	+	0.432787i	$0.142470\pi$
$150$	3.52775	+	7.06621i	0.288039	+	0.576954i
$151$			3.63183i			0.295554i	0.989021	+	0.147777i	$0.0472119\pi$
$151$			3.63183i			0.295554i	−0.989021	+	0.147777i	$0.952788\pi$
$152$	−15.7626	−	2.89558i	−1.27851	−	0.234862i
$153$			0.681331i			0.0550823i
$154$	−6.33843	+	3.16441i	−0.510765	+	0.254995i
$155$	7.57610	−	7.57610i	0.608527	−	0.608527i
$156$	15.4173	−	20.5045i	1.23437	−	1.64168i
$157$	−2.00607	−	2.00607i	−0.160102	−	0.160102i	0.622510	−	0.782612i	$-0.286113\pi$
$157$	−2.00607	−	2.00607i	−0.160102	−	0.160102i	−0.782612	+	0.622510i	$0.786113\pi$
$158$	−7.53488	+	22.5590i	−0.599443	+	1.79470i
$159$	8.55748			0.678652
$160$	−6.00065	+	5.52783i	−0.474393	+	0.437013i
$161$	7.48136			0.589614
$162$	4.72282	−	14.1399i	0.371060	−	1.11093i
$163$	2.48464	+	2.48464i	0.194612	+	0.194612i	0.797686	−	0.603074i	$-0.206057\pi$
$163$	2.48464	+	2.48464i	0.194612	+	0.194612i	−0.603074	+	0.797686i	$0.706057\pi$
$164$	1.20194	−	1.59854i	0.0938558	−	0.124825i
$165$	9.53297	−	9.53297i	0.742141	−	0.742141i
$166$	−18.3903	+	9.18123i	−1.42737	+	0.712601i
$167$			22.6196i			1.75036i	0.483802	+	0.875178i	$0.339256\pi$
$167$			22.6196i			1.75036i	−0.483802	+	0.875178i	$0.660744\pi$
$168$	1.00186	−	5.45379i	0.0772950	−	0.420769i
$169$			31.9764i			2.45972i
$170$	0.943087	+	1.88904i	0.0723314	+	0.144883i
$171$	−2.63712	+	2.63712i	−0.201666	+	0.201666i
$172$	−5.95866	+	0.843859i	−0.454343	+	0.0643437i
$173$	0.391368	+	0.391368i	0.0297551	+	0.0297551i	0.721828	−	0.692073i	$-0.243302\pi$
$173$	0.391368	+	0.391368i	0.0297551	+	0.0297551i	−0.692073	+	0.721828i	$0.743302\pi$
$174$	−0.299291	−	0.0999653i	−0.0226892	−	0.00757835i
$175$	−2.99287			−0.226240
$176$	−17.1179	−	9.44134i	−1.29031	−	0.711668i
$177$	−3.27399			−0.246088
$178$	7.25144	+	2.42204i	0.543519	+	0.181539i
$179$	8.20394	+	8.20394i	0.613191	+	0.613191i	0.943776	−	0.330585i	$-0.107246\pi$
$179$	8.20394	+	8.20394i	0.613191	+	0.613191i	−0.330585	+	0.943776i	$0.607246\pi$
$180$	0.266221	+	1.87984i	0.0198429	+	0.140115i
$181$	7.23493	−	7.23493i	0.537768	−	0.537768i	−0.385104	−	0.922873i	$-0.625835\pi$
$181$	7.23493	−	7.23493i	0.537768	−	0.537768i	0.922873	+	0.385104i	$0.125835\pi$
$182$	4.34232	+	8.69783i	0.321874	+	0.644726i
$183$		−	16.0689i		−	1.18784i
$184$	11.7200	+	16.9949i	0.864008	+	1.25288i
$185$		−	12.1263i		−	0.891540i
$186$	−17.9779	+	8.97532i	−1.31820	+	0.658102i
$187$	−3.57726	+	3.57726i	−0.261595	+	0.261595i
$188$	−6.33375	−	4.76233i	−0.461936	−	0.347329i
$189$	3.24636	+	3.24636i	0.236138	+	0.236138i
$190$	−3.66135	+	10.9619i	−0.265622	+	0.795257i
$191$	13.4440			0.972773			0.486386	−	0.873744i	$-0.338315\pi$
$191$	13.4440			0.972773			0.486386	+	0.873744i	$0.338315\pi$
$192$	13.9585	−	6.26783i	1.00737	−	0.452342i
$193$	−20.5846			−1.48171			−0.740856	−	0.671664i	$-0.765580\pi$
$193$	−20.5846			−1.48171			−0.740856	+	0.671664i	$0.765580\pi$
$194$	6.44678	−	19.3013i	0.462852	−	1.38575i
$195$	−13.0815	−	13.0815i	−0.936786	−	0.936786i
$196$	−9.51030	−	7.15078i	−0.679307	−	0.510770i
$197$	−9.76672	+	9.76672i	−0.695850	+	0.695850i	−0.963513	−	0.267662i	$-0.913749\pi$
$197$	−9.76672	+	9.76672i	−0.695850	+	0.695850i	0.267662	+	0.963513i	$0.413749\pi$
$198$	−4.07015	+	2.03199i	−0.289253	+	0.144407i
$199$		−	18.0458i		−	1.27923i	−0.768695	−	0.639616i	$-0.779094\pi$
$199$		−	18.0458i		−	1.27923i	0.768695	−	0.639616i	$-0.220906\pi$
$200$	−4.68851	−	6.79870i	−0.331528	−	0.480741i
$201$			15.2521i			1.07580i
$202$	−5.67189	−	11.3610i	−0.399073	−	0.799358i
$203$	0.0845519	−	0.0845519i	0.00593438	−	0.00593438i
$204$	−0.555233	−	3.92061i	−0.0388741	−	0.274498i
$205$	−1.01984	−	1.01984i	−0.0712287	−	0.0712287i
$206$	−22.8992	−	7.64850i	−1.59546	−	0.532896i
$207$	4.80407			0.333906
$208$	−12.9558	+	23.4898i	−0.898320	+	1.62872i
$209$	−27.6919			−1.91549
$210$	−3.79276	−	1.26681i	−0.261725	−	0.0874183i
$211$	7.07525	+	7.07525i	0.487080	+	0.487080i	0.907384	−	0.420303i	$-0.138076\pi$
$211$	7.07525	+	7.07525i	0.487080	+	0.487080i	−0.420303	+	0.907384i	$0.638076\pi$
$212$	−8.85993	+	1.25474i	−0.608503	+	0.0861756i
$213$	5.03523	−	5.03523i	0.345008	−	0.345008i
$214$	−4.50941	−	9.03252i	−0.308257	−	0.617450i
$215$			4.33987i			0.295977i
$216$	−2.28891	+	12.4601i	−0.155741	+	0.847804i
$217$		−	7.61449i		−	0.516905i
$218$	19.3895	−	9.68004i	1.31322	−	0.655615i
$219$	1.10688	−	1.10688i	0.0747963	−	0.0747963i
$220$	−8.47214	+	11.2677i	−0.571191	+	0.759666i
$221$	4.90885	+	4.90885i	0.330205	+	0.330205i
$222$	−7.20474	+	21.5706i	−0.483550	+	1.44772i
$223$	1.07505			0.0719908			0.0359954	−	0.999352i	$-0.488540\pi$
$223$	1.07505			0.0719908			0.0359954	+	0.999352i	$0.488540\pi$
$224$	−0.237608	+	5.79345i	−0.0158759	+	0.387091i
$225$	−1.92184			−0.128123
$226$	8.29030	−	24.8207i	0.551463	−	1.65105i
$227$	−16.8155	−	16.8155i	−1.11609	−	1.11609i	−0.992310	−	0.123777i	$-0.960499\pi$
$227$	−16.8155	−	16.8155i	−1.11609	−	1.11609i	−0.123777	−	0.992310i	$-0.539501\pi$
$228$	13.0258	−	17.3240i	0.862657	−	1.14731i
$229$	8.05862	−	8.05862i	0.532529	−	0.532529i	−0.388795	−	0.921324i	$-0.627109\pi$
$229$	8.05862	−	8.05862i	0.532529	−	0.532529i	0.921324	+	0.388795i	$0.127109\pi$
$230$	13.3196	−	6.64971i	0.878270	−	0.438469i
$231$		−	9.58128i		−	0.630402i
$232$	0.324526	+	0.0596152i	0.0213062	+	0.00391393i
$233$		−	0.135059i		−	0.00884799i	−0.999990	−	0.00442399i	$-0.998592\pi$
$233$		−	0.135059i		−	0.00884799i	0.999990	−	0.00442399i	$-0.00140821\pi$
$234$	2.78837	+	5.58521i	0.182282	+	0.365117i
$235$	−4.04081	+	4.04081i	−0.263593	+	0.263593i
$236$	3.38971	−	0.480047i	0.220651	−	0.0312484i
$237$	−22.7452	−	22.7452i	−1.47746	−	1.47746i
$238$	1.42324	+	0.475373i	0.0922549	+	0.0308138i
$239$	12.2825			0.794492			0.397246	−	0.917712i	$-0.369966\pi$
$239$	12.2825			0.794492			0.397246	+	0.917712i	$0.369966\pi$
$240$	−3.06385	−	10.6003i	−0.197771	−	0.684245i
$241$	19.0933			1.22991			0.614955	−	0.788562i	$-0.289174\pi$
$241$	19.0933			1.22991			0.614955	+	0.788562i	$0.289174\pi$
$242$	−17.2836	−	5.77286i	−1.11103	−	0.371094i
$243$	4.75513	+	4.75513i	0.305041	+	0.305041i
$244$	2.35609	+	16.6368i	0.150833	+	1.06506i
$245$	−6.06739	+	6.06739i	−0.387631	+	0.387631i
$246$	1.20819	+	2.42005i	0.0770315	+	0.154297i
$247$			37.9998i			2.41787i
$248$	17.2973	−	11.9285i	1.09838	−	0.757463i
$249$		−	27.7992i		−	1.76170i
$250$	−14.4529	+	7.21550i	−0.914083	+	0.456348i
$251$	−8.63346	+	8.63346i	−0.544939	+	0.544939i	−0.924973	−	0.380034i	$-0.875912\pi$
$251$	−8.63346	+	8.63346i	−0.544939	+	0.544939i	0.380034	+	0.924973i	$0.375912\pi$
$252$	1.07847	+	0.810897i	0.0679370	+	0.0510817i
$253$	25.2233	+	25.2233i	1.58577	+	1.58577i
$254$	−2.96982	+	8.89146i	−0.186343	+	0.557900i
$255$	−2.85550			−0.178819
$256$	−13.5328	+	8.53601i	−0.845800	+	0.533501i
$257$	25.1829			1.57087			0.785435	−	0.618945i	$-0.212439\pi$
$257$	25.1829			1.57087			0.785435	+	0.618945i	$0.212439\pi$
$258$	2.57851	−	7.71991i	0.160531	−	0.480620i
$259$	−6.09386	−	6.09386i	−0.378654	−	0.378654i
$260$	15.4619	+	11.6258i	0.958907	+	0.721000i
$261$	0.0542940	−	0.0542940i	0.00336071	−	0.00336071i
$262$	7.78990	−	3.88905i	0.481262	−	0.240266i
$263$			14.1488i			0.872454i	0.899837	+	0.436227i	$0.143685\pi$
$263$			14.1488i			0.872454i	−0.899837	+	0.436227i	$0.856315\pi$
$264$	21.7651	−	15.0096i	1.33955	−	0.923779i
$265$			6.45296i			0.396402i
$266$	3.66876	+	7.34866i	0.224946	+	0.450575i
$267$	−7.31130	+	7.31130i	−0.447444	+	0.447444i
$268$	−2.23634	−	15.7912i	−0.136606	−	0.964601i
$269$	0.601271	+	0.601271i	0.0366601	+	0.0366601i	0.725199	−	0.688539i	$-0.241748\pi$
$269$	0.601271	+	0.601271i	0.0366601	+	0.0366601i	−0.688539	+	0.725199i	$0.741748\pi$
$270$	8.66521	+	2.89425i	0.527348	+	0.176138i
$271$	−21.9854			−1.33552			−0.667760	−	0.744376i	$-0.732747\pi$
$271$	−21.9854			−1.33552			−0.667760	+	0.744376i	$0.732747\pi$
$272$	1.14971	+	3.97777i	0.0697117	+	0.241188i
$273$	−13.1478			−0.795741
$274$	−16.4566	−	5.49664i	−0.994181	−	0.332064i
$275$	−10.0904	−	10.0904i	−0.608476	−	0.608476i
$276$	−27.6443	+	3.91495i	−1.66399	+	0.235653i
$277$	0.618961	−	0.618961i	0.0371898	−	0.0371898i	−0.688267	−	0.725457i	$-0.741628\pi$
$277$	0.618961	−	0.618961i	0.0371898	−	0.0371898i	0.725457	+	0.688267i	$0.241628\pi$
$278$	5.48253	+	10.9817i	0.328820	+	0.658639i
$279$		−	4.88956i		−	0.292730i
$280$	4.11256	+	0.755474i	0.245772	+	0.0451482i
$281$		−	8.84493i		−	0.527644i	−0.964571	−	0.263822i	$-0.915017\pi$
$281$		−	8.84493i		−	0.527644i	0.964571	−	0.263822i	$-0.0849832\pi$
$282$	9.58875	−	4.78710i	0.571002	−	0.285068i
$283$	22.9316	−	22.9316i	1.36314	−	1.36314i	0.493265	−	0.869879i	$-0.335803\pi$
$283$	22.9316	−	22.9316i	1.36314	−	1.36314i	0.869879	−	0.493265i	$-0.164197\pi$
$284$	−4.47490	+	5.95148i	−0.265537	+	0.353155i
$285$	−11.0523	−	11.0523i	−0.654684	−	0.654684i
$286$	−14.6845	+	43.9647i	−0.868315	+	2.59969i
$287$	−1.02501			−0.0605043
$288$	−0.152577	+	3.72019i	−0.00899070	+	0.219215i
$289$	−15.9285			−0.936969
$290$	0.0753811	−	0.225687i	0.00442653	−	0.0132528i
$291$	19.4606	+	19.4606i	1.14080	+	1.14080i
$292$	−0.983709	+	1.30830i	−0.0575672	+	0.0765626i
$293$	21.7652	−	21.7652i	1.27154	−	1.27154i	0.326256	−	0.945281i	$-0.394213\pi$
$293$	21.7652	−	21.7652i	1.27154	−	1.27154i	0.945281	−	0.326256i	$-0.105787\pi$
$294$	14.3978	−	7.18797i	0.839695	−	0.419211i
$295$		−	2.46883i		−	0.143741i
$296$	4.29661	−	23.3894i	0.249735	−	1.35948i
$297$			21.8901i			1.27019i
$298$	−5.11109	−	10.2377i	−0.296078	−	0.593055i
$299$	34.6123	−	34.6123i	2.00168	−	2.00168i
$300$	11.0589	−	1.56615i	0.638487	−	0.0904220i
$301$	2.18093	+	2.18093i	0.125707	+	0.125707i
$302$	4.87163	+	1.62716i	0.280331	+	0.0936326i
$303$	17.1735			0.986592
$304$	−10.9461	+	19.8461i	−0.627802	+	1.13825i
$305$	12.1171			0.693822
$306$	0.913916	+	0.305255i	0.0522451	+	0.0174503i
$307$	−3.25725	−	3.25725i	−0.185901	−	0.185901i	0.608020	−	0.793921i	$-0.291964\pi$
$307$	−3.25725	−	3.25725i	−0.185901	−	0.185901i	−0.793921	+	0.608020i	$0.791964\pi$
$308$	1.40485	+	9.91992i	0.0800487	+	0.565240i
$309$	23.0882	−	23.0882i	1.31344	−	1.31344i
$310$	−6.76804	−	13.5566i	−0.384399	−	0.769966i
$311$			21.3514i			1.21073i	0.795948	+	0.605365i	$0.206973\pi$
$311$			21.3514i			1.21073i	−0.795948	+	0.605365i	$0.793027\pi$
$312$	−20.5968	−	29.8669i	−1.16606	−	1.69088i
$313$			1.09572i			0.0619336i	0.999520	+	0.0309668i	$0.00985861\pi$
$313$			1.09572i			0.0619336i	−0.999520	+	0.0309668i	$0.990141\pi$
$314$	−3.58966	+	1.79211i	−0.202576	+	0.101134i
$315$	0.688041	−	0.688041i	0.0387667	−	0.0387667i
$316$	26.8841	+	20.2141i	1.51235	+	1.13713i
$317$	−6.87612	−	6.87612i	−0.386202	−	0.386202i	0.487129	−	0.873330i	$-0.338044\pi$
$317$	−6.87612	−	6.87612i	−0.386202	−	0.386202i	−0.873330	+	0.487129i	$0.838044\pi$
$318$	3.83399	−	11.4787i	0.214999	−	0.643696i
$319$	0.570130			0.0319212
$320$	4.72640	+	10.5257i	0.264214	+	0.588404i
$321$	13.6537			0.762076
$322$	3.35185	−	10.0353i	0.186792	−	0.559243i
$323$	4.14741	+	4.14741i	0.230768	+	0.230768i
$324$	−16.8508	−	12.6701i	−0.936157	−	0.703894i
$325$	−13.8465	+	13.8465i	−0.768064	+	0.768064i
$326$	4.44601	−	2.21963i	0.246241	−	0.122934i
$327$			29.3095i			1.62082i
$328$	−1.60573	−	2.32844i	−0.0886618	−	0.128566i
$329$			4.06129i			0.223906i
$330$	−8.51620	−	17.0583i	−0.468801	−	0.939027i
$331$	4.93683	−	4.93683i	0.271352	−	0.271352i	−0.558292	−	0.829645i	$-0.688543\pi$
$331$	4.93683	−	4.93683i	0.271352	−	0.271352i	0.829645	+	0.558292i	$0.188543\pi$
$332$	4.07603	+	28.7817i	0.223701	+	1.57960i
$333$	−3.91310	−	3.91310i	−0.214436	−	0.214436i
$334$	30.3412	+	10.1342i	1.66020	+	0.554518i
$335$	−11.5012			−0.628379
$336$	−6.86669	−	3.78731i	−0.374609	−	0.206615i
$337$	27.3817			1.49158			0.745788	−	0.666184i	$-0.232073\pi$
$337$	27.3817			1.49158			0.745788	+	0.666184i	$0.232073\pi$
$338$	42.8922	+	14.3263i	2.33303	+	0.779249i
$339$	25.0256	+	25.0256i	1.35920	+	1.35920i
$340$	2.95643	−	0.418686i	0.160335	−	0.0227065i
$341$	25.6721	−	25.6721i	1.39022	−	1.39022i
$342$	2.35585	+	4.71885i	0.127390	+	0.255166i
$343$			13.2732i			0.716685i
$344$	−1.53772	+	8.37083i	−0.0829080	+	0.451325i
$345$			20.1342i			1.08399i
$346$	0.700312	−	0.349625i	0.0376490	−	0.0187960i
$347$	−10.5013	+	10.5013i	−0.563741	+	0.563741i	−0.930368	−	0.366627i	$-0.880512\pi$
$347$	−10.5013	+	10.5013i	−0.563741	+	0.563741i	0.366627	+	0.930368i	$0.380512\pi$
$348$	−0.268181	+	0.356672i	−0.0143760	+	0.0191196i
$349$	14.1648	+	14.1648i	0.758226	+	0.758226i	0.975999	−	0.217773i	$-0.0698792\pi$
$349$	14.1648	+	14.1648i	0.758226	+	0.758226i	−0.217773	+	0.975999i	$0.569879\pi$
$350$	−1.34089	+	4.01455i	−0.0716736	+	0.214587i
$351$	30.0384			1.60333
$352$	−20.3336	+	18.7314i	−1.08378	+	0.998388i
$353$	−23.9136			−1.27279			−0.636397	−	0.771362i	$-0.719576\pi$
$353$	−23.9136			−1.27279			−0.636397	+	0.771362i	$0.719576\pi$
$354$	−1.46684	+	4.39163i	−0.0779616	+	0.233413i
$355$	3.79693	+	3.79693i	0.201520	+	0.201520i
$356$	6.49769	−	8.64172i	0.344377	−	0.458010i
$357$	−1.43499	+	1.43499i	−0.0759476	+	0.0759476i
$358$	14.6801	−	7.32892i	0.775867	−	0.387345i
$359$		−	25.5088i		−	1.34630i	−0.739504	−	0.673152i	$-0.764940\pi$
$359$		−	25.5088i		−	1.34630i	0.739504	−	0.673152i	$-0.235060\pi$
$360$	2.64083	+	0.485119i	0.139184	+	0.0255680i
$361$			13.1054i			0.689759i
$362$	−6.46327	−	12.9462i	−0.339702	−	0.680436i
$363$	17.4263	−	17.4263i	0.914643	−	0.914643i
$364$	13.6125	−	1.92779i	0.713488	−	0.101044i
$365$	0.834671	+	0.834671i	0.0436887	+	0.0436887i
$366$	−21.5543	−	7.19929i	−1.12666	−	0.376313i
$367$	20.8960			1.09076			0.545381	−	0.838188i	$-0.316385\pi$
$367$	20.8960			1.09076			0.545381	+	0.838188i	$0.316385\pi$
$368$	28.0473	−	8.10664i	1.46207	−	0.422588i
$369$	−0.658196			−0.0342643
$370$	−16.2658	−	5.43290i	−0.845618	−	0.282443i
$371$	3.24283	+	3.24283i	0.168359	+	0.168359i
$372$	3.98462	+	28.1362i	0.206593	+	1.45879i
$373$	4.25718	−	4.25718i	0.220428	−	0.220428i	−0.588251	−	0.808679i	$-0.700183\pi$
$373$	4.25718	−	4.25718i	0.220428	−	0.220428i	0.808679	+	0.588251i	$0.200183\pi$
$374$	3.19572	+	6.40114i	0.165247	+	0.330995i
$375$		−	21.8473i		−	1.12819i
$376$	−9.22574	+	6.36224i	−0.475781	+	0.328108i
$377$		−	0.782354i		−	0.0402933i
$378$	5.80902	−	2.90010i	0.298784	−	0.149165i
$379$	16.3955	−	16.3955i	0.842183	−	0.842183i	−0.146960	−	0.989142i	$-0.546949\pi$
$379$	16.3955	−	16.3955i	0.842183	−	0.842183i	0.989142	+	0.146960i	$0.0469488\pi$
$380$	13.0635	+	9.82243i	0.670144	+	0.503880i
$381$	−8.96486	−	8.96486i	−0.459284	−	0.459284i
$382$	6.02328	−	18.0333i	0.308178	−	0.922666i
$383$	−1.16329			−0.0594411			−0.0297206	−	0.999558i	$-0.509462\pi$
$383$	−1.16329			−0.0594411			−0.0297206	+	0.999558i	$0.509462\pi$
$384$	−2.15370	−	21.5316i	−0.109905	−	1.09878i
$385$	7.22498			0.368219
$386$	−9.22247	+	27.6115i	−0.469411	+	1.40539i
$387$	1.40046	+	1.40046i	0.0711894	+	0.0711894i
$388$	−23.0018	−	17.2950i	−1.16774	−	0.878022i
$389$	2.45051	−	2.45051i	0.124246	−	0.124246i	−0.642250	−	0.766496i	$-0.721999\pi$
$389$	2.45051	−	2.45051i	0.124246	−	0.124246i	0.766496	+	0.642250i	$0.221999\pi$
$390$	−23.4080	+	11.6862i	−1.18531	+	0.591756i
$391$		−	7.55537i		−	0.382091i
$392$	−13.8527	+	9.55308i	−0.699668	+	0.482504i
$393$			11.7754i			0.593988i
$394$	8.72502	+	17.4765i	0.439560	+	0.880456i
$395$	17.1515	−	17.1515i	0.862988	−	0.862988i
$396$	0.902108	+	6.36996i	0.0453326	+	0.320103i
$397$	4.77808	+	4.77808i	0.239805	+	0.239805i	0.816769	−	0.576964i	$-0.195763\pi$
$397$	4.77808	+	4.77808i	0.239805	+	0.239805i	−0.576964	+	0.816769i	$0.695763\pi$
$398$	−24.2060	−	8.08501i	−1.21334	−	0.405265i
$399$	−11.1084			−0.556113
$400$	−11.2202	+	3.24302i	−0.561008	+	0.162151i
$401$	−8.25428			−0.412199			−0.206100	−	0.978531i	$-0.566077\pi$
$401$	−8.25428			−0.412199			−0.206100	+	0.978531i	$0.566077\pi$
$402$	20.4588	+	6.83338i	1.02039	+	0.340818i
$403$	−35.2283	−	35.2283i	−1.75485	−	1.75485i
$404$	−17.7805	+	2.51805i	−0.884612	+	0.125278i
$405$	−10.7505	+	10.7505i	−0.534197	+	0.534197i
$406$	−0.0755337	−	0.151297i	−0.00374867	−	0.00750874i
$407$		−	41.0907i		−	2.03679i
$408$	−5.50775	−	1.01177i	−0.272674	−	0.0500900i
$409$			21.4397i			1.06012i	0.847959	+	0.530062i	$0.177831\pi$
$409$			21.4397i			1.06012i	−0.847959	+	0.530062i	$0.822169\pi$
$410$	−1.82490	+	0.911065i	−0.0901252	+	0.0449943i
$411$	16.5925	−	16.5925i	0.818446	−	0.818446i
$412$	−20.5189	+	27.2895i	−1.01089	+	1.34446i
$413$	−1.24067	−	1.24067i	−0.0610494	−	0.0610494i
$414$	2.15235	−	6.44403i	0.105782	−	0.316707i
$415$	20.9626			1.02901
$416$	25.7040	+	27.9025i	1.26024	+	1.36803i
$417$	−16.6001			−0.812913
$418$	−12.4067	+	37.1450i	−0.606833	+	1.81682i
$419$	−8.02160	−	8.02160i	−0.391881	−	0.391881i	0.483476	−	0.875357i	$-0.339374\pi$
$419$	−8.02160	−	8.02160i	−0.391881	−	0.391881i	−0.875357	+	0.483476i	$0.839374\pi$
$420$	−3.39852	+	4.51993i	−0.165831	+	0.220550i
$421$	−13.3486	+	13.3486i	−0.650572	+	0.650572i	−0.953131	−	0.302559i	$-0.902159\pi$
$421$	−13.3486	+	13.3486i	−0.650572	+	0.650572i	0.302559	+	0.953131i	$0.402159\pi$
$422$	12.6604	−	6.32061i	0.616300	−	0.307683i
$423$			2.60791i			0.126801i
$424$	−2.28643	+	12.4466i	−0.111039	+	0.604460i
$425$			3.02248i			0.146612i
$426$	−4.49818	−	9.01002i	−0.217937	−	0.436537i
$427$	6.08925	−	6.08925i	0.294679	−	0.294679i
$428$	−14.1363	+	2.00197i	−0.683303	+	0.0967687i
$429$	−44.3276	−	44.3276i	−2.14016	−	2.14016i
$430$	5.82137	+	1.94438i	0.280731	+	0.0937664i
$431$	−17.1326			−0.825249			−0.412624	−	0.910901i	$-0.635388\pi$
$431$	−17.1326			−0.825249			−0.412624	+	0.910901i	$0.635388\pi$
$432$	15.6881	+	8.65276i	0.754795	+	0.416306i
$433$	−4.97273			−0.238974			−0.119487	−	0.992836i	$-0.538125\pi$
$433$	−4.97273			−0.238974			−0.119487	+	0.992836i	$0.538125\pi$
$434$	−10.2138	−	3.41150i	−0.490280	−	0.163757i
$435$	0.227550	+	0.227550i	0.0109102	+	0.0109102i
$436$	−4.29749	−	30.3454i	−0.205812	−	1.45328i
$437$	29.2434	−	29.2434i	1.39890	−	1.39890i
$438$	−0.988826	−	1.98065i	−0.0472479	−	0.0946393i
$439$		−	1.83690i		−	0.0876705i	−0.999039	−	0.0438353i	$-0.986042\pi$
$439$		−	1.83690i		−	0.0876705i	0.999039	−	0.0438353i	$-0.0139577\pi$
$440$	11.3184	+	16.4125i	0.539581	+	0.782435i
$441$			3.91585i			0.186469i
$442$	8.78388	−	4.38528i	0.417807	−	0.208586i
$443$	−7.69365	+	7.69365i	−0.365537	+	0.365537i	−0.865846	−	0.500310i	$-0.833219\pi$
$443$	−7.69365	+	7.69365i	−0.365537	+	0.365537i	0.500310	+	0.865846i	$0.333219\pi$
$444$	25.7062	+	19.3284i	1.21996	+	0.917287i
$445$	−5.51325	−	5.51325i	−0.261353	−	0.261353i
$446$	0.481653	−	1.44204i	0.0228069	−	0.0682827i
$447$	15.4755			0.731966
$448$	7.66470	+	2.91434i	0.362123	+	0.137690i
$449$	−21.4195			−1.01085			−0.505424	−	0.862871i	$-0.668664\pi$
$449$	−21.4195			−1.01085			−0.505424	+	0.862871i	$0.668664\pi$
$450$	−0.861037	+	2.57790i	−0.0405897	+	0.121523i
$451$	−3.45580	−	3.45580i	−0.162727	−	0.162727i
$452$	−29.5794	−	22.2407i	−1.39130	−	1.04612i
$453$	−4.91184	+	4.91184i	−0.230779	+	0.230779i
$454$	−30.0897	+	15.0220i	−1.41218	+	0.705018i
$455$		−	9.91439i		−	0.464794i
$456$	−17.4019	−	25.2341i	−0.814918	−	1.18169i
$457$			41.0438i			1.91995i	0.280088	+	0.959974i	$0.409637\pi$
$457$			41.0438i			1.91995i	−0.280088	+	0.959974i	$0.590363\pi$
$458$	−7.19910	−	14.4201i	−0.336392	−	0.673806i
$459$	3.27847	−	3.27847i	0.153026	−	0.153026i
$460$	−2.95216	−	20.8458i	−0.137645	−	0.971939i
$461$	5.88141	+	5.88141i	0.273925	+	0.273925i	0.830678	−	0.556753i	$-0.187953\pi$
$461$	5.88141	+	5.88141i	0.273925	+	0.273925i	−0.556753	+	0.830678i	$0.687953\pi$
$462$	−12.8520	−	4.29268i	−0.597931	−	0.199714i
$463$	13.7885			0.640807			0.320404	−	0.947281i	$-0.396182\pi$
$463$	13.7885			0.640807			0.320404	+	0.947281i	$0.396182\pi$
$464$	0.225362	−	0.408600i	0.0104622	−	0.0189688i
$465$	20.4925			0.950315
$466$	−0.181164	−	0.0605100i	−0.00839224	−	0.00280307i
$467$	−3.75052	−	3.75052i	−0.173553	−	0.173553i	0.614985	−	0.788539i	$-0.289162\pi$
$467$	−3.75052	−	3.75052i	−0.173553	−	0.173553i	−0.788539	+	0.614985i	$0.789162\pi$
$468$	8.74110	−	1.23791i	0.404057	−	0.0572222i
$469$	−5.77975	+	5.77975i	−0.266884	+	0.266884i
$470$	3.60982	+	7.23061i	0.166509	+	0.333523i
$471$		−	5.42619i		−	0.250025i
$472$	0.874762	−	4.76192i	0.0402642	−	0.219185i
$473$			14.7060i			0.676181i
$474$	−40.7002	+	20.3193i	−1.86942	+	0.933294i
$475$	−11.6986	+	11.6986i	−0.536771	+	0.536771i
$476$	1.27530	−	1.69611i	0.0584533	−	0.0777410i
$477$	2.08235	+	2.08235i	0.0953441	+	0.0953441i
$478$	5.50292	−	16.4754i	0.251698	−	0.753568i
$479$	−19.2105			−0.877749			−0.438875	−	0.898548i	$-0.644623\pi$
$479$	−19.2105			−0.877749			−0.438875	+	0.898548i	$0.644623\pi$
$480$	−15.5916	−	0.639462i	−0.711655	−	0.0291873i
$481$	−56.3862			−2.57099
$482$	8.55434	−	25.6112i	0.389640	−	1.16656i
$483$	10.1181	+	10.1181i	0.460390	+	0.460390i
$484$	−15.4871	+	20.5973i	−0.703958	+	0.936242i
$485$	−14.6747	+	14.6747i	−0.666345	+	0.666345i
$486$	8.50881	−	4.24795i	0.385967	−	0.192691i
$487$		−	24.9255i		−	1.12948i	−0.825268	−	0.564741i	$-0.808976\pi$
$487$		−	24.9255i		−	1.12948i	0.825268	−	0.564741i	$-0.191024\pi$
$488$	23.3717	+	4.29336i	1.05799	+	0.194351i
$489$			6.72066i			0.303919i
$490$	5.42025	+	10.8570i	0.244862	+	0.490468i
$491$	−12.2312	+	12.2312i	−0.551987	+	0.551987i	−0.927014	−	0.375027i	$-0.877633\pi$
$491$	−12.2312	+	12.2312i	−0.551987	+	0.551987i	0.375027	+	0.927014i	$0.377633\pi$
$492$	3.78749	−	0.536381i	0.170753	−	0.0241819i
$493$	−0.0853883	−	0.0853883i	−0.00384570	−	0.00384570i
$494$	50.9718	+	17.0250i	2.29333	+	0.765990i
$495$	4.63944			0.208527
$496$	−8.25091	−	28.5464i	−0.370477	−	1.28177i
$497$	3.81617			0.171179
$498$	−37.2889	−	12.4548i	−1.67096	−	0.558112i
$499$	8.07305	+	8.07305i	0.361399	+	0.361399i	0.864328	−	0.502929i	$-0.167744\pi$
$499$	8.07305	+	8.07305i	0.361399	+	0.361399i	−0.502929	+	0.864328i	$0.667744\pi$
$500$	3.20334	+	22.6194i	0.143258	+	1.01157i
$501$	−30.5917	+	30.5917i	−1.36673	+	1.36673i
$502$	7.71263	+	15.4487i	0.344231	+	0.689508i
$503$			19.6275i			0.875146i	0.899183	+	0.437573i	$0.144162\pi$
$503$			19.6275i			0.875146i	−0.899183	+	0.437573i	$0.855838\pi$
$504$	1.57090	−	1.08332i	0.0699732	−	0.0482548i
$505$			12.9501i			0.576270i
$506$	45.1345	−	22.5330i	2.00647	−	1.00171i
$507$	−43.2462	+	43.2462i	−1.92063	+	1.92063i
$508$	10.5962	+	7.96724i	0.470129	+	0.353489i
$509$	15.7954	+	15.7954i	0.700117	+	0.700117i	0.964435	−	0.264319i	$-0.0851471\pi$
$509$	15.7954	+	15.7954i	0.700117	+	0.700117i	−0.264319	+	0.964435i	$0.585147\pi$
$510$	−1.27934	+	3.83028i	−0.0566503	+	0.169608i
$511$	0.838901			0.0371108
$512$	5.38688	+	21.9768i	0.238069	+	0.971248i
$513$	25.3789			1.12051
$514$	11.2827	−	33.7796i	0.497657	−	1.48996i
$515$	17.4102	+	17.4102i	0.767184	+	0.767184i
$516$	−9.20000	−	6.91746i	−0.405008	−	0.304524i
$517$	−13.6926	+	13.6926i	−0.602198	+	0.602198i
$518$	−10.9043	+	5.44389i	−0.479109	+	0.239191i
$519$			1.05860i			0.0464676i
$520$	22.5218	−	15.5315i	0.987648	−	0.681100i
$521$		−	26.5179i		−	1.16177i	−0.813986	−	0.580885i	$-0.802707\pi$
$521$		−	26.5179i		−	1.16177i	0.813986	−	0.580885i	$-0.197293\pi$
$522$	−0.0485031	−	0.0971535i	−0.00212292	−	0.00425229i
$523$	−0.752863	+	0.752863i	−0.0329204	+	0.0329204i	−0.723375	−	0.690455i	$-0.757410\pi$
$523$	−0.752863	+	0.752863i	−0.0329204	+	0.0329204i	0.690455	+	0.723375i	$0.257410\pi$
$524$	−1.72655	−	12.1915i	−0.0754249	−	0.532590i
$525$	−4.04769	−	4.04769i	−0.176656	−	0.176656i
$526$	18.9788	+	6.33906i	0.827515	+	0.276396i
$527$	−7.68982			−0.334974
$528$	−10.3821	−	35.9198i	−0.451822	−	1.56321i
$529$	−30.2730			−1.31622
$530$	8.65581	+	2.89111i	0.375984	+	0.125582i
$531$	−0.796681	−	0.796681i	−0.0345730	−	0.0345730i
$532$	11.5010	−	1.62876i	0.498630	−	0.0706155i
$533$	−4.74217	+	4.74217i	−0.205406	+	0.205406i
$534$	6.53149	+	13.0828i	0.282645	+	0.566149i
$535$			10.2959i			0.445130i
$536$	−22.1838	−	4.07514i	−0.958193	−	0.176019i
$537$			22.1907i			0.957599i
$538$	1.07591	−	0.537140i	0.0463859	−	0.0231578i
$539$	−20.5598	+	20.5598i	−0.885572	+	0.885572i
$540$	7.76450	−	10.3265i	0.334131	−	0.444384i
$541$	−11.0816	−	11.0816i	−0.476437	−	0.476437i	0.427553	−	0.903990i	$-0.359376\pi$
$541$	−11.0816	−	11.0816i	−0.476437	−	0.476437i	−0.903990	+	0.427553i	$0.859376\pi$
$542$	−9.85009	+	29.4906i	−0.423097	+	1.26673i
$543$	19.5697			0.839814
$544$	5.85076	+	0.239959i	0.250849	+	0.0102881i
$545$	−22.1015			−0.946723
$546$	−5.89058	+	17.6360i	−0.252093	+	0.754753i
$547$	7.87345	+	7.87345i	0.336644	+	0.336644i	0.855103	−	0.518458i	$-0.173494\pi$
$547$	7.87345	+	7.87345i	0.336644	+	0.336644i	−0.518458	+	0.855103i	$0.673494\pi$
$548$	−14.7460	+	19.6118i	−0.629920	+	0.837773i
$549$	3.91014	−	3.91014i	0.166881	−	0.166881i
$550$	−18.0558	+	9.01420i	−0.769901	+	0.384367i
$551$		−	0.660998i		−	0.0281595i
$552$	−7.13399	+	38.8352i	−0.303643	+	1.65293i
$553$		−	17.2385i		−	0.733054i
$554$	−0.552944	−	1.10757i	−0.0234923	−	0.0470560i
$555$	16.4001	−	16.4001i	0.696143	−	0.696143i
$556$	17.1869	−	2.43399i	0.728885	−	0.103224i
$557$	−3.11365	−	3.11365i	−0.131930	−	0.131930i	0.638058	−	0.769988i	$-0.279738\pi$
$557$	−3.11365	−	3.11365i	−0.131930	−	0.131930i	−0.769988	+	0.638058i	$0.779738\pi$
$558$	−6.55870	−	2.19066i	−0.277652	−	0.0927379i
$559$	20.1801			0.853526
$560$	2.85591	−	5.17798i	0.120684	−	0.218810i
$561$	−9.67607			−0.408524
$562$	−11.8643	−	3.96277i	−0.500466	−	0.167159i
$563$	0.644740	+	0.644740i	0.0271726	+	0.0271726i	0.720563	−	0.693390i	$-0.243884\pi$
$563$	0.644740	+	0.644740i	0.0271726	+	0.0271726i	−0.693390	+	0.720563i	$0.743884\pi$
$564$	−2.12525	−	15.0068i	−0.0894891	−	0.631900i
$565$	−18.8711	+	18.8711i	−0.793913	+	0.793913i
$566$	−20.4858	−	41.0338i	−0.861082	−	1.72478i
$567$			10.8050i			0.453767i
$568$	5.97825	+	8.66892i	0.250842	+	0.363740i
$569$		−	14.9176i		−	0.625378i	−0.949856	−	0.312689i	$-0.898770\pi$
$569$		−	14.9176i		−	0.625378i	0.949856	−	0.312689i	$-0.101230\pi$
$570$	−19.7770	+	9.87352i	−0.828369	+	0.413556i
$571$	3.66426	−	3.66426i	0.153344	−	0.153344i	−0.626266	−	0.779610i	$-0.715417\pi$
$571$	3.66426	−	3.66426i	0.153344	−	0.153344i	0.779610	+	0.626266i	$0.215417\pi$
$572$	52.3938	+	39.3948i	2.19069	+	1.64718i
$573$	18.1822	+	18.1822i	0.759573	+	0.759573i
$574$	−0.459232	+	1.37491i	−0.0191680	+	0.0573878i
$575$	21.3115			0.888753
$576$	4.92179	+	1.87141i	0.205075	+	0.0779755i
$577$	17.6076			0.733016			0.366508	−	0.930415i	$-0.380553\pi$
$577$	17.6076			0.733016			0.366508	+	0.930415i	$0.380553\pi$
$578$	−7.13639	+	21.3660i	−0.296835	+	0.888707i
$579$	−27.8395	−	27.8395i	−1.15697	−	1.15697i
$580$	−0.268956	−	0.202228i	−0.0111678	−	0.00839705i
$581$	10.5344	−	10.5344i	0.437041	−	0.437041i
$582$	34.8228	−	17.3850i	1.44345	−	0.720631i
$583$			21.8663i			0.905610i
$584$	1.31419	+	1.90567i	0.0543814	+	0.0788573i
$585$		−	6.36641i		−	0.263219i
$586$	−19.4438	−	38.9466i	−0.803215	−	1.60887i
$587$	2.82562	−	2.82562i	0.116626	−	0.116626i	−0.646385	−	0.763011i	$-0.723720\pi$
$587$	2.82562	−	2.82562i	0.116626	−	0.116626i	0.763011	+	0.646385i	$0.223720\pi$
$588$	−3.19112	−	22.5331i	−0.131600	−	0.929251i
$589$	−29.7638	−	29.7638i	−1.22640	−	1.22640i
$590$	−3.31161	−	1.10610i	−0.136337	−	0.0455375i
$591$	−26.4178			−1.08669
$592$	−29.4488	−	16.2424i	−1.21034	−	0.667559i
$593$	−34.7694			−1.42781			−0.713905	−	0.700243i	$-0.753075\pi$
$593$	−34.7694			−1.42781			−0.713905	+	0.700243i	$0.753075\pi$
$594$	29.3627	+	9.80735i	1.20476	+	0.402401i
$595$	−1.08208	−	1.08208i	−0.0443611	−	0.0443611i
$596$	−16.0225	+	2.26909i	−0.656306	+	0.0929454i
$597$	24.4059	−	24.4059i	0.998865	−	0.998865i
$598$	−30.9206	−	61.9352i	−1.26444	−	2.53272i
$599$		−	0.0528874i		−	0.00216092i	−0.999999	−	0.00108046i	$-0.999656\pi$
$599$		−	0.0528874i		−	0.00216092i	0.999999	−	0.00108046i	$-0.000343921\pi$
$600$	2.85391	−	15.5358i	0.116510	−	0.634246i
$601$			1.75258i			0.0714893i	0.999361	+	0.0357446i	$0.0113803\pi$
$601$			1.75258i			0.0714893i	−0.999361	+	0.0357446i	$0.988620\pi$
$602$	3.90255	−	1.94832i	0.159056	−	0.0794075i
$603$	−3.71140	+	3.71140i	−0.151140	+	0.151140i
$604$	4.36525	−	5.80564i	0.177619	−	0.236228i
$605$	13.1407	+	13.1407i	0.534245	+	0.534245i
$606$	7.69420	−	23.0360i	0.312556	−	0.935774i
$607$	−16.1912			−0.657181			−0.328591	−	0.944472i	$-0.606574\pi$
$607$	−16.1912			−0.657181			−0.328591	+	0.944472i	$0.606574\pi$
$608$	21.7169	+	23.5744i	0.880735	+	0.956068i
$609$	0.228703			0.00926751
$610$	5.42879	−	16.2535i	0.219805	−	0.658084i
$611$	18.7895	+	18.7895i	0.760140	+	0.760140i
$612$	0.818919	−	1.08914i	0.0331028	−	0.0440257i
$613$	5.64511	−	5.64511i	0.228004	−	0.228004i	−0.583855	−	0.811858i	$-0.698456\pi$
$613$	5.64511	−	5.64511i	0.228004	−	0.228004i	0.811858	+	0.583855i	$0.198456\pi$
$614$	−5.82851	+	2.90983i	−0.235219	+	0.117431i
$615$		−	2.75855i		−	0.111235i
$616$	13.9357	+	2.55998i	0.561485	+	0.103144i
$617$		−	25.8661i		−	1.04133i	−0.853761	−	0.520664i	$-0.825684\pi$
$617$		−	25.8661i		−	1.04133i	0.853761	−	0.520664i	$-0.174316\pi$
$618$	−20.6256	−	41.3139i	−0.829685	−	1.66189i
$619$	−2.35822	+	2.35822i	−0.0947849	+	0.0947849i	−0.752909	−	0.658124i	$-0.771350\pi$
$619$	−2.35822	+	2.35822i	−0.0947849	+	0.0947849i	0.658124	+	0.752909i	$0.271350\pi$
$620$	−21.2167	+	3.00469i	−0.852085	+	0.120671i
$621$	−23.1165	−	23.1165i	−0.927634	−	0.927634i
$622$	28.6402	+	9.56604i	1.14837	+	0.383563i
$623$	−5.54119			−0.222003
$624$	−49.2905	+	14.2467i	−1.97320	+	0.570324i
$625$	1.87516			0.0750064
$626$	1.46976	+	0.490911i	0.0587434	+	0.0196208i
$627$	−37.4516	−	37.4516i	−1.49567	−	1.49567i
$628$	0.795611	+	5.61797i	0.0317483	+	0.224181i
$629$	−6.15414	+	6.15414i	−0.245382	+	0.245382i
$630$	−0.614656	−	1.23118i	−0.0244885	−	0.0490513i
$631$		−	41.7505i		−	1.66206i	−0.556226	−	0.831031i	$-0.687751\pi$
$631$		−	41.7505i		−	1.66206i	0.556226	−	0.831031i	$-0.312249\pi$
$632$	39.1594	−	27.0051i	1.55768	−	1.07420i
$633$			19.1377i			0.760656i
$634$	−12.3041	+	6.14273i	−0.488659	+	0.243959i
$635$	6.76015	−	6.76015i	0.268268	−	0.268268i
$636$	−13.6795	−	10.2856i	−0.542427	−	0.407850i
$637$	28.2129	+	28.2129i	1.11784	+	1.11784i
$638$	0.255434	−	0.764755i	0.0101127	−	0.0302770i
$639$	2.45051			0.0969406
$640$	16.2364	−	1.62404i	0.641800	−	0.0641960i
$641$	−28.2480			−1.11573			−0.557864	−	0.829933i	$-0.688379\pi$
$641$	−28.2480			−1.11573			−0.557864	+	0.829933i	$0.688379\pi$
$642$	6.11724	−	18.3147i	0.241428	−	0.722822i
$643$	6.67869	+	6.67869i	0.263382	+	0.263382i	0.826427	−	0.563045i	$-0.190370\pi$
$643$	6.67869	+	6.67869i	0.263382	+	0.263382i	−0.563045	+	0.826427i	$0.690370\pi$
$644$	−11.9593	−	8.99215i	−0.471261	−	0.354340i
$645$	−5.86942	+	5.86942i	−0.231108	+	0.231108i
$646$	7.42136	−	3.70505i	0.291989	−	0.145773i
$647$		−	28.1133i		−	1.10525i	−0.833431	−	0.552623i	$-0.813627\pi$
$647$		−	28.1133i		−	1.10525i	0.833431	−	0.552623i	$-0.186373\pi$
$648$	−24.5449	+	16.9266i	−0.964215	+	0.664941i
$649$		−	8.36580i		−	0.328386i
$650$	12.3696	+	24.7768i	0.485176	+	0.971827i
$651$	10.2982	−	10.2982i	0.403617	−	0.403617i
$652$	−0.985412	−	6.95819i	−0.0385917	−	0.272504i
$653$	10.8798	+	10.8798i	0.425758	+	0.425758i	0.887181	−	0.461422i	$-0.152661\pi$
$653$	10.8798	+	10.8798i	0.425758	+	0.425758i	−0.461422	+	0.887181i	$0.652661\pi$
$654$	39.3148	+	13.1315i	1.53733	+	0.513481i
$655$	−8.87947			−0.346950
$656$	−3.84271	+	1.11068i	−0.150033	+	0.0433646i
$657$	0.538690			0.0210163
$658$	5.44769	+	1.81957i	0.212373	+	0.0709342i
$659$	14.7632	+	14.7632i	0.575091	+	0.575091i	0.933547	−	0.358456i	$-0.116697\pi$
$659$	14.7632	+	14.7632i	0.575091	+	0.575091i	−0.358456	+	0.933547i	$0.616697\pi$
$660$	−26.6969	+	3.78079i	−1.03918	+	0.147167i
$661$	7.35906	−	7.35906i	0.286234	−	0.286234i	−0.549355	−	0.835589i	$-0.685127\pi$
$661$	7.35906	−	7.35906i	0.286234	−	0.286234i	0.835589	+	0.549355i	$0.185127\pi$
$662$	−4.41027	−	8.83394i	−0.171410	−	0.343341i
$663$			13.2779i			0.515670i
$664$	40.4330	+	7.42752i	1.56911	+	0.288244i
$665$		−	8.37651i		−	0.324827i
$666$	−7.00208	+	3.49573i	−0.271325	+	0.135457i
$667$	−0.602073	+	0.602073i	−0.0233124	+	0.0233124i
$668$	27.1874	−	36.1584i	1.05191	−	1.39901i
$669$	1.45395	+	1.45395i	0.0562128	+	0.0562128i
$670$	−5.15286	+	15.4274i	−0.199073	+	0.596012i
$671$	41.0596			1.58509
$672$	−8.15665	+	7.51395i	−0.314650	+	0.289857i
$673$	−22.1721			−0.854670			−0.427335	−	0.904093i	$-0.640548\pi$
$673$	−22.1721			−0.854670			−0.427335	+	0.904093i	$0.640548\pi$
$674$	12.2677	−	36.7289i	0.472536	−	1.41475i
$675$	9.24763	+	9.24763i	0.355941	+	0.355941i
$676$	38.4338	−	51.1157i	1.47822	−	1.96599i
$677$	−13.8053	+	13.8053i	−0.530579	+	0.530579i	−0.920745	−	0.390166i	$-0.872418\pi$
$677$	−13.8053	+	13.8053i	−0.530579	+	0.530579i	0.390166	+	0.920745i	$0.372418\pi$
$678$	44.7807	−	22.3564i	1.71979	−	0.858592i
$679$			14.7491i			0.566018i
$680$	0.762948	−	4.15324i	0.0292577	−	0.159270i
$681$		−	45.4841i		−	1.74295i
$682$	−22.9340	−	45.9376i	−0.878188	−	1.75904i
$683$	−8.69592	+	8.69592i	−0.332740	+	0.332740i	−0.853626	−	0.520886i	$-0.825602\pi$
$683$	−8.69592	+	8.69592i	−0.332740	+	0.332740i	0.520886	+	0.853626i	$0.325602\pi$
$684$	7.38521	−	1.04589i	0.282381	−	0.0399905i
$685$	12.5119	+	12.5119i	0.478056	+	0.478056i
$686$	17.8042	+	5.94676i	0.679769	+	0.227048i
$687$	21.7976			0.831632
$688$	10.5394	+	5.81301i	0.401812	+	0.221619i
$689$	30.0058			1.14313
$690$	27.0073	+	9.02066i	1.02815	+	0.343411i
$691$	−18.0189	−	18.0189i	−0.685470	−	0.685470i	0.275757	−	0.961227i	$-0.411071\pi$
$691$	−18.0189	−	18.0189i	−0.685470	−	0.685470i	−0.961227	+	0.275757i	$0.911071\pi$
$692$	−0.155217	−	1.09602i	−0.00590047	−	0.0416644i
$693$	2.33148	−	2.33148i	0.0885654	−	0.0885654i
$694$	9.38127	+	18.7910i	0.356108	+	0.713298i
$695$		−	12.5177i		−	0.474824i
$696$	0.358276	+	0.519528i	0.0135804	+	0.0196927i
$697$			1.03515i			0.0392090i
$698$	25.3465	−	12.6540i	0.959380	−	0.478962i
$699$	0.182659	−	0.182659i	0.00690880	−	0.00690880i
$700$	4.78424	+	3.59726i	0.180827	+	0.135964i
$701$	−1.02598	−	1.02598i	−0.0387506	−	0.0387506i	0.687466	−	0.726217i	$-0.258723\pi$
$701$	−1.02598	−	1.02598i	−0.0387506	−	0.0387506i	−0.726217	+	0.687466i	$0.758723\pi$
$702$	13.4580	−	40.2925i	0.507940	−	1.52074i
$703$	−47.6397			−1.79677
$704$	16.0157	+	35.6671i	0.603616	+	1.34425i
$705$	−10.9299			−0.411645
$706$	−10.7140	+	32.0770i	−0.403225	+	1.20723i
$707$	6.50785	+	6.50785i	0.244753	+	0.244753i
$708$	5.23362	+	3.93514i	0.196691	+	0.147892i
$709$	−11.2843	+	11.2843i	−0.423790	+	0.423790i	−0.886506	−	0.462716i	$-0.846875\pi$
$709$	−11.2843	+	11.2843i	−0.423790	+	0.423790i	0.462716	+	0.886506i	$0.346875\pi$
$710$	6.79421	−	3.39195i	0.254982	−	0.127298i
$711$		−	11.0695i		−	0.415138i
$712$	−8.68059	−	12.5875i	−0.325319	−	0.471738i
$713$			54.2210i			2.03059i
$714$	1.28193	+	2.56776i	0.0479752	+	0.0960960i
$715$	33.4262	−	33.4262i	1.25007	−	1.25007i
$716$	−3.25370	−	22.9750i	−0.121596	−	0.858616i
$717$	16.6114	+	16.6114i	0.620365	+	0.620365i
$718$	−34.2167	−	11.4287i	−1.27696	−	0.426514i
$719$	−49.4501			−1.84418			−0.922088	−	0.386979i	$-0.873518\pi$
$719$	−49.4501			−1.84418			−0.922088	+	0.386979i	$0.873518\pi$
$720$	1.83389	−	3.32498i	0.0683450	−	0.123915i
$721$	17.4984			0.651675
$722$	17.5792	+	5.87159i	0.654231	+	0.218518i
$723$	25.8226	+	25.8226i	0.960354	+	0.960354i
$724$	−20.2613	+	2.86939i	−0.753006	+	0.106640i
$725$	0.240856	−	0.240856i	0.00894517	−	0.00894517i
$726$	−15.5676	−	31.1825i	−0.577769	−	1.15729i
$727$			43.3450i			1.60758i	0.594915	+	0.803789i	$0.297186\pi$
$727$			43.3450i			1.60758i	−0.594915	+	0.803789i	$0.702814\pi$
$728$	3.51289	−	19.1231i	0.130197	−	0.708748i
$729$		−	18.7620i		−	0.694890i
$730$	1.49356	−	0.745646i	0.0552790	−	0.0275976i
$731$	2.20251	−	2.20251i	0.0814627	−	0.0814627i
$732$	−19.3138	+	25.6868i	−0.713859	+	0.949410i
$733$	21.5250	+	21.5250i	0.795042	+	0.795042i	0.982309	−	0.187267i	$-0.0599629\pi$
$733$	21.5250	+	21.5250i	0.795042	+	0.795042i	−0.187267	+	0.982309i	$0.559963\pi$
$734$	9.36198	−	28.0292i	0.345557	−	1.03458i
$735$	−16.4116			−0.605350
$736$	1.69195	−	41.2537i	0.0623661	−	1.52063i
$737$	−38.9727			−1.43558
$738$	−0.294890	+	0.882884i	−0.0108551	+	0.0324994i
$739$	−33.1711	−	33.1711i	−1.22022	−	1.22022i	−0.967553	−	0.252666i	$-0.918693\pi$
$739$	−33.1711	−	33.1711i	−1.22022	−	1.22022i	−0.252666	−	0.967553i	$-0.581307\pi$
$740$	−14.5750	+	19.3843i	−0.535789	+	0.712582i
$741$	−51.3925	+	51.3925i	−1.88795	+	1.88795i
$742$	5.80271	−	2.89696i	0.213024	−	0.106351i
$743$		−	24.2892i		−	0.891084i	−0.895261	−	0.445542i	$-0.853011\pi$
$743$		−	24.2892i		−	0.891084i	0.895261	−	0.445542i	$-0.146989\pi$
$744$	39.5263	+	7.26094i	1.44910	+	0.266199i
$745$			11.6697i			0.427543i
$746$	−3.80311	−	7.61778i	−0.139242	−	0.278907i
$747$	6.76455	−	6.76455i	0.247502	−	0.247502i
$748$	10.0181	−	1.41875i	0.366296	−	0.0518746i
$749$	5.17403	+	5.17403i	0.189055	+	0.189055i
$750$	−29.3053	−	9.78819i	−1.07008	−	0.357414i
$751$	13.2483			0.483439			0.241719	−	0.970346i	$-0.422289\pi$
$751$	13.2483			0.483439			0.241719	+	0.970346i	$0.422289\pi$
$752$	4.40073	+	15.2256i	0.160478	+	0.555220i
$753$	−23.3525			−0.851012
$754$	−1.04943	−	0.350516i	−0.0382178	−	0.0127651i
$755$	−3.70389	−	3.70389i	−0.134798	−	0.134798i
$756$	−1.28751	−	9.09136i	−0.0468263	−	0.330650i
$757$	−3.95467	+	3.95467i	−0.143735	+	0.143735i	−0.775313	−	0.631578i	$-0.782408\pi$
$757$	−3.95467	+	3.95467i	−0.143735	+	0.143735i	0.631578	+	0.775313i	$0.282408\pi$
$758$	−14.6468	−	29.3381i	−0.531997	−	1.06561i
$759$			68.2260i			2.47645i
$760$	19.0283	−	13.1223i	0.690230	−	0.475995i
$761$		−	32.0200i		−	1.16072i	−0.814358	−	0.580362i	$-0.802911\pi$
$761$		−	32.0200i		−	1.16072i	0.814358	−	0.580362i	$-0.197089\pi$
$762$	−16.0417	+	8.00868i	−0.581129	+	0.290124i
$763$	−11.1067	+	11.1067i	−0.402091	+	0.402091i
$764$	−21.4908	−	16.1589i	−0.777509	−	0.584608i
$765$	−0.694848	−	0.694848i	−0.0251223	−	0.0251223i
$766$	−0.521184	+	1.56040i	−0.0188311	+	0.0563794i
$767$	−11.4799			−0.414514
$768$	−29.8468	−	6.75786i	−1.07700	−	0.243853i
$769$	−3.60337			−0.129941			−0.0649705	−	0.997887i	$-0.520695\pi$
$769$	−3.60337			−0.129941			−0.0649705	+	0.997887i	$0.520695\pi$
$770$	3.23699	−	9.69137i	0.116653	−	0.349253i
$771$	34.0585	+	34.0585i	1.22659	+	1.22659i
$772$	32.9054	+	24.7415i	1.18429	+	0.890465i
$773$	−20.5006	+	20.5006i	−0.737354	+	0.737354i	−0.972065	−	0.234711i	$-0.924586\pi$
$773$	−20.5006	+	20.5006i	−0.737354	+	0.737354i	0.234711	+	0.972065i	$0.424586\pi$
$774$	2.50598	−	1.25109i	0.0900756	−	0.0449695i
$775$		−	21.6908i		−	0.779156i
$776$	−33.5045	+	23.1053i	−1.20274	+	0.829432i
$777$		−	16.4832i		−	0.591330i
$778$	−2.18915	−	4.38494i	−0.0784847	−	0.157208i
$779$	−4.00658	+	4.00658i	−0.143551	+	0.143551i
$780$	5.18815	+	36.6345i	0.185765	+	1.31173i
$781$	12.8661	+	12.8661i	0.460387	+	0.460387i
$782$	−10.1345	−	3.38501i	−0.362410	−	0.121048i
$783$	−0.522511			−0.0186730
$784$	6.60782	+	22.8616i	0.235993	+	0.816487i
$785$	4.09174			0.146040
$786$	15.7951	+	5.27568i	0.563392	+	0.188177i
$787$	25.9659	+	25.9659i	0.925584	+	0.925584i	0.997417	−	0.0718329i	$-0.0228848\pi$
$787$	25.9659	+	25.9659i	0.925584	+	0.925584i	−0.0718329	+	0.997417i	$0.522885\pi$
$788$	27.3515	−	3.87350i	0.974359	−	0.137988i
$789$	−19.1355	+	19.1355i	−0.681240	+	0.681240i
$790$	−15.3222	−	30.6909i	−0.545139	−	1.09193i
$791$			18.9667i			0.674380i
$792$	8.94864	+	1.64386i	0.317976	+	0.0584120i
$793$		−	56.3435i		−	2.00082i
$794$	8.54988	−	4.26846i	0.303424	−	0.151482i
$795$	−8.72726	+	8.72726i	−0.309524	+	0.309524i
$796$	−21.6900	+	28.8469i	−0.768780	+	1.02245i
$797$	−3.40842	−	3.40842i	−0.120733	−	0.120733i	0.644159	−	0.764892i	$-0.277207\pi$
$797$	−3.40842	−	3.40842i	−0.120733	−	0.120733i	−0.764892	+	0.644159i	$0.777207\pi$
$798$	−4.97685	+	14.9004i	−0.176179	+	0.527469i
$799$	4.10147			0.145099
$800$	−0.676855	+	16.5033i	−0.0239304	+	0.583481i
$801$	−3.55821			−0.125723
$802$	−3.69814	+	11.0720i	−0.130586	+	0.390967i
$803$	2.82834	+	2.82834i	0.0998100	+	0.0998100i
$804$	18.3322	−	24.3812i	0.646526	−	0.859859i
$805$	−7.62978	+	7.62978i	−0.268914	+	0.268914i
$806$	−63.0374	+	31.4709i	−2.22040	+	1.10851i
$807$			1.62637i			0.0572509i
$808$	−4.58850	+	24.9783i	−0.161423	+	0.878735i
$809$		−	28.9861i		−	1.01910i	−0.860442	−	0.509549i	$-0.829812\pi$
$809$		−	28.9861i		−	1.01910i	0.860442	−	0.509549i	$-0.170188\pi$
$810$	9.60387	+	19.2369i	0.337446	+	0.675916i
$811$	−23.9577	+	23.9577i	−0.841269	+	0.841269i	−0.989024	−	0.147755i	$-0.952795\pi$
$811$	−23.9577	+	23.9577i	−0.841269	+	0.841269i	0.147755	+	0.989024i	$0.452795\pi$
$812$	−0.236786	+	0.0335334i	−0.00830956	+	0.00117679i
$813$	−29.7340	−	29.7340i	−1.04282	−	1.04282i
$814$	−55.1178	−	18.4098i	−1.93188	−	0.645261i
$815$	−5.06787			−0.177520
$816$	−3.82478	+	6.93462i	−0.133894	+	0.242760i
$817$	17.0498			0.596497
$818$	28.7585	+	9.60557i	1.00552	+	0.335851i
$819$	−3.19934	−	3.19934i	−0.111794	−	0.111794i
$820$	0.404470	+	2.85604i	0.0141247	+	0.0997373i
$821$	−9.91704	+	9.91704i	−0.346107	+	0.346107i	−0.858657	−	0.512550i	$-0.828701\pi$
$821$	−9.91704	+	9.91704i	−0.346107	+	0.346107i	0.512550	+	0.858657i	$0.328701\pi$
$822$	−14.8227	−	29.6905i	−0.517002	−	1.03558i
$823$		−	8.92649i		−	0.311158i	−0.987823	−	0.155579i	$-0.950276\pi$
$823$		−	8.92649i		−	0.311158i	0.987823	−	0.155579i	$-0.0497243\pi$
$824$	27.4123	+	39.7499i	0.954951	+	1.38475i
$825$		−	27.2934i		−	0.950235i
$826$	−2.22005	+	1.10834i	−0.0772454	+	0.0385641i
$827$	−26.0358	+	26.0358i	−0.905353	+	0.905353i	−0.995893	−	0.0905400i	$-0.971141\pi$
$827$	−26.0358	+	26.0358i	−0.905353	+	0.905353i	0.0905400	+	0.995893i	$0.471141\pi$
$828$	−7.67950	−	5.77420i	−0.266881	−	0.200667i
$829$	−26.1870	−	26.1870i	−0.909511	−	0.909511i	0.0867213	−	0.996233i	$-0.472361\pi$
$829$	−26.1870	−	26.1870i	−0.909511	−	0.909511i	−0.996233	+	0.0867213i	$0.972361\pi$
$830$	9.39182	−	28.1186i	0.325995	−	0.976010i
$831$	1.67422			0.0580780
$832$	48.9437	−	21.9774i	1.69682	−	0.761929i
$833$	6.15847			0.213378
$834$	−7.43732	+	22.2669i	−0.257533	+	0.771041i
$835$	−23.0683	−	23.0683i	−0.798312	−	0.798312i
$836$	44.2666	+	33.2840i	1.53099	+	1.15115i
$837$	−23.5279	+	23.5279i	−0.813243	+	0.813243i
$838$	−14.3538	+	7.16603i	−0.495845	+	0.247546i
$839$		−	37.5159i		−	1.29519i	−0.761983	−	0.647597i	$-0.775774\pi$
$839$		−	37.5159i		−	1.29519i	0.761983	−	0.647597i	$-0.224226\pi$
$840$	4.54026	+	6.58373i	0.156654	+	0.227160i
$841$		−	28.9864i		−	0.999531i
$842$	11.9249	+	23.8860i	0.410958	+	0.823165i
$843$	11.9622	−	11.9622i	0.412002	−	0.412002i
$844$	−2.80606	−	19.8141i	−0.0965884	−	0.682030i
$845$	−32.6108	−	32.6108i	−1.12185	−	1.12185i
$846$	3.49817	+	1.16841i	0.120269	+	0.0401709i
$847$	13.2073			0.453808
$848$	15.6711	+	8.64337i	0.538148	+	0.296814i
$849$	62.0274			2.12877
$850$	4.05427	+	1.35416i	0.139060	+	0.0464472i
$851$	43.3929	+	43.3929i	1.48749	+	1.48749i
$852$	−14.1011	+	1.99698i	−0.483095	+	0.0684154i
$853$	11.9777	−	11.9777i	0.410107	−	0.410107i	−0.471669	−	0.881776i	$-0.656348\pi$
$853$	11.9777	−	11.9777i	0.410107	−	0.410107i	0.881776	+	0.471669i	$0.156348\pi$
$854$	−5.43978	−	10.8961i	−0.186145	−	0.372856i
$855$		−	5.37888i		−	0.183954i
$856$	−3.64807	+	19.8589i	−0.124688	+	0.678764i
$857$			4.88221i			0.166773i	0.996517	+	0.0833866i	$0.0265736\pi$
$857$			4.88221i			0.166773i	−0.996517	+	0.0833866i	$0.973426\pi$
$858$	−79.3196	+	39.5997i	−2.70793	+	1.35191i
$859$	5.74849	−	5.74849i	0.196136	−	0.196136i	−0.602205	−	0.798341i	$-0.705711\pi$
$859$	5.74849	−	5.74849i	0.196136	−	0.196136i	0.798341	+	0.602205i	$0.205711\pi$
$860$	5.21627	−	6.93747i	0.177873	−	0.236566i
$861$	−1.38626	−	1.38626i	−0.0472437	−	0.0472437i
$862$	−7.67588	+	22.9812i	−0.261442	+	0.782741i
$863$	−31.5811			−1.07503			−0.537517	−	0.843253i	$-0.680637\pi$
$863$	−31.5811			−1.07503			−0.537517	+	0.843253i	$0.680637\pi$
$864$	18.6353	−	17.1669i	0.633984	−	0.584029i
$865$	−0.798265			−0.0271418
$866$	−2.22792	+	6.67026i	−0.0757077	+	0.226665i
$867$	−21.5423	−	21.5423i	−0.731616	−	0.731616i
$868$	−9.15217	+	12.1721i	−0.310645	+	0.413148i
$869$	58.1192	−	58.1192i	1.97156	−	1.97156i
$870$	0.407177	−	0.203280i	0.0138046	−	0.00689183i
$871$			53.4798i			1.81209i
$872$	−42.6298	−	7.83106i	−1.44363	−	0.265193i
$873$			9.47095i			0.320543i
$874$	−26.1243	−	52.3280i	−0.883669	−	1.77002i
$875$	8.27897	−	8.27897i	0.279880	−	0.279880i
$876$	−3.09981	+	0.438992i	−0.104733	+	0.0148322i
$877$	17.9321	+	17.9321i	0.605525	+	0.605525i	0.941773	−	0.336248i	$-0.109158\pi$
$877$	17.9321	+	17.9321i	0.605525	+	0.605525i	−0.336248	+	0.941773i	$0.609158\pi$
$878$	−2.46396	−	0.822982i	−0.0831547	−	0.0277743i
$879$	58.8724			1.98572
$880$	27.0861	−	7.82884i	0.913074	−	0.263910i
$881$	−53.2910			−1.79542			−0.897709	−	0.440588i	$-0.854770\pi$
$881$	−53.2910			−1.79542			−0.897709	+	0.440588i	$0.854770\pi$
$882$	5.25260	+	1.75441i	0.176864	+	0.0590740i
$883$	−29.2144	−	29.2144i	−0.983143	−	0.983143i	0.0167168	−	0.999860i	$-0.494679\pi$
$883$	−29.2144	−	29.2144i	−0.983143	−	0.983143i	−0.999860	+	0.0167168i	$0.994679\pi$
$884$	−1.94686	−	13.7472i	−0.0654799	−	0.462367i
$885$	3.33895	−	3.33895i	0.112237	−	0.112237i
$886$	6.87306	+	13.7670i	0.230905	+	0.462511i
$887$			44.3931i			1.49057i	0.666744	+	0.745287i	$0.267687\pi$
$887$			44.3931i			1.49057i	−0.666744	+	0.745287i	$0.732313\pi$
$888$	37.4436	−	25.8218i	1.25653	−	0.866524i
$889$		−	6.79441i		−	0.227877i
$890$	−9.86539	+	4.92522i	−0.330689	+	0.165094i
$891$	−36.4288	+	36.4288i	−1.22041	+	1.22041i
$892$	−1.71852	−	1.29215i	−0.0575402	−	0.0432643i
$893$	15.8749	+	15.8749i	0.531233	+	0.531233i
$894$	6.93345	−	20.7584i	0.231889	−	0.694264i
$895$	−16.7334			−0.559336
$896$	7.34321	−	8.97548i	0.245319	−	0.299850i
$897$	93.6223			3.12596
$898$	−9.59652	+	28.7314i	−0.320240	+	0.958780i
$899$	0.612788	+	0.612788i	0.0204376	+	0.0204376i
$900$	3.07214	+	2.30994i	0.102405	+	0.0769979i
$901$	3.27491	−	3.27491i	0.109103	−	0.109103i
$902$	−6.18379	+	3.08721i	−0.205898	+	0.102793i
$903$			5.89917i			0.196312i
$904$	−43.0854	+	29.7125i	−1.43300	+	0.988223i
$905$			14.7569i			0.490537i
$906$	4.38795	+	8.78924i	0.145780	+	0.292003i
$907$	3.29645	−	3.29645i	0.109457	−	0.109457i	−0.650257	−	0.759714i	$-0.725339\pi$
$907$	3.29645	−	3.29645i	0.109457	−	0.109457i	0.759714	+	0.650257i	$0.225339\pi$
$908$	6.66907	+	47.0916i	0.221321	+	1.56279i
$909$	4.17894	+	4.17894i	0.138607	+	0.138607i
$910$	−13.2989	−	4.44192i	−0.440853	−	0.147248i
$911$	41.8953			1.38805			0.694026	−	0.719950i	$-0.255835\pi$
$911$	41.8953			1.38805			0.694026	+	0.719950i	$0.255835\pi$
$912$	−41.6447	+	12.0368i	−1.37899	+	0.398578i
$913$	71.0332			2.35086
$914$	55.0549	+	18.3888i	1.82105	+	0.608246i
$915$	16.3876	+	16.3876i	0.541759	+	0.541759i
$916$	−22.5680	+	3.19606i	−0.745669	+	0.105601i
$917$	−4.46224	+	4.46224i	−0.147356	+	0.147356i
$918$	−2.92879	−	5.86649i	−0.0966646	−	0.193623i
$919$		−	33.9736i		−	1.12068i	−0.828261	−	0.560342i	$-0.810670\pi$
$919$		−	33.9736i		−	1.12068i	0.828261	−	0.560342i	$-0.189330\pi$
$920$	−29.2845	−	5.37955i	−0.965482	−	0.177358i
$921$		−	8.81047i		−	0.290315i
$922$	10.5242	−	5.25411i	0.346595	−	0.173035i
$923$	17.6554	−	17.6554i	0.581135	−	0.581135i
$924$	−11.5161	+	15.3161i	−0.378853	+	0.503862i
$925$	−17.3591	−	17.3591i	−0.570763	−	0.570763i
$926$	6.17764	−	18.4955i	0.203010	−	0.607800i
$927$	11.2364			0.369052
$928$	−0.447115	−	0.485358i	−0.0146773	−	0.0159327i
$929$	20.4003			0.669313			0.334656	−	0.942340i	$-0.391380\pi$
$929$	20.4003			0.669313			0.334656	+	0.942340i	$0.391380\pi$
$930$	9.18119	−	27.4880i	0.301063	−	0.901366i
$931$	23.8366	+	23.8366i	0.781213	+	0.781213i
$932$	−0.162333	+	0.215897i	−0.00531738	+	0.00707194i
$933$	−28.8766	+	28.8766i	−0.945377	+	0.945377i
$934$	−6.71117	+	3.35050i	−0.219596	+	0.109632i
$935$		−	7.29646i		−	0.238620i
$936$	2.25576	−	12.2797i	0.0737319	−	0.401373i
$937$			27.2949i			0.891685i	0.895111	+	0.445842i	$0.147096\pi$
$937$			27.2949i			0.891685i	−0.895111	+	0.445842i	$0.852904\pi$
$938$	5.16330	+	10.3423i	0.168588	+	0.337687i
$939$	−1.48189	+	1.48189i	−0.0483597	+	0.0483597i
$940$	11.3162	−	1.60259i	0.369094	−	0.0522708i
$941$	−13.5322	−	13.5322i	−0.441138	−	0.441138i	0.451256	−	0.892394i	$-0.350976\pi$
$941$	−13.5322	−	13.5322i	−0.441138	−	0.441138i	−0.892394	+	0.451256i	$0.850976\pi$
$942$	−7.27852	−	2.43108i	−0.237147	−	0.0792089i
$943$	7.29883			0.237683
$944$	−5.99558	−	3.30685i	−0.195139	−	0.107629i
$945$	−6.62152			−0.215398
$946$	19.7261	+	6.58868i	0.641352	+	0.214216i
$947$	−16.9133	−	16.9133i	−0.549609	−	0.549609i	0.376719	−	0.926328i	$-0.377052\pi$
$947$	−16.9133	−	16.9133i	−0.549609	−	0.549609i	−0.926328	+	0.376719i	$0.877052\pi$
$948$	9.02080	+	63.6976i	0.292982	+	2.06880i
$949$	3.88116	−	3.88116i	0.125988	−	0.125988i
$950$	10.4509	+	20.9335i	0.339072	+	0.679173i
$951$		−	18.5991i		−	0.603118i
$952$	−1.70374	−	2.47055i	−0.0552185	−	0.0800711i
$953$			32.2461i			1.04455i	0.852776	+	0.522277i	$0.174917\pi$
$953$			32.2461i			1.04455i	−0.852776	+	0.522277i	$0.825083\pi$
$954$	3.72614	−	1.86025i	0.120638	−	0.0602277i
$955$	−13.7107	+	13.7107i	−0.443668	+	0.443668i
$956$	−19.6342	−	14.7629i	−0.635014	−	0.477466i
$957$	0.771068	+	0.771068i	0.0249251	+	0.0249251i
$958$	−8.60683	+	25.7684i	−0.278074	+	0.832538i
$959$	12.5753			0.406079
$960$	−7.84321	+	20.6276i	−0.253139	+	0.665752i
$961$	24.1859			0.780189
$962$	−25.2626	+	75.6346i	−0.814497	+	2.43856i
$963$	3.32244	+	3.32244i	0.107064	+	0.107064i
$964$	−30.5215	−	22.9491i	−0.983032	−	0.739140i
$965$	20.9930	−	20.9930i	0.675788	−	0.675788i
$966$	18.1053	−	9.03892i	0.582528	−	0.290822i
$967$		−	31.0841i		−	0.999598i	−0.866142	−	0.499799i	$-0.833407\pi$
$967$		−	31.0841i		−	0.999598i	0.866142	−	0.499799i	$-0.166593\pi$
$968$	20.6900	+	30.0021i	0.665001	+	0.964302i
$969$			11.2182i			0.360382i
$970$	13.1095	+	26.2589i	0.420922	+	0.843122i
$971$	6.64842	−	6.64842i	0.213358	−	0.213358i	−0.592334	−	0.805692i	$-0.701794\pi$
$971$	6.64842	−	6.64842i	0.213358	−	0.213358i	0.805692	+	0.592334i	$0.201794\pi$
$972$	−1.88589	−	13.3166i	−0.0604900	−	0.427132i
$973$	−6.29058	−	6.29058i	−0.201667	−	0.201667i
$974$	−33.4343	−	11.1673i	−1.07130	−	0.357824i
$975$	−37.4531			−1.19946
$976$	16.2301	−	29.4265i	0.519514	−	0.941919i
$977$	−20.9573			−0.670484			−0.335242	−	0.942132i	$-0.608818\pi$
$977$	−20.9573			−0.670484			−0.335242	+	0.942132i	$0.608818\pi$
$978$	9.01489	+	3.01104i	0.288264	+	0.0962825i
$979$	−18.6820	−	18.6820i	−0.597081	−	0.597081i
$980$	16.9916	−	2.40634i	0.542778	−	0.0768676i
$981$	−7.13206	+	7.13206i	−0.227709	+	0.227709i
$982$	10.9267	+	21.8865i	0.348684	+	0.698426i
$983$			30.7515i			0.980820i	0.871492	+	0.490410i	$0.163153\pi$
$983$			30.7515i			0.980820i	−0.871492	+	0.490410i	$0.836847\pi$
$984$	0.977415	−	5.32074i	0.0311589	−	0.169619i
$985$		−	19.9210i		−	0.634735i
$986$	−0.152794	+	0.0762809i	−0.00486594	+	0.00242928i
$987$	−5.49265	+	5.49265i	−0.174833	+	0.174833i
$988$	45.6735	−	60.7443i	1.45307	−	1.93254i
$989$	−15.5299	−	15.5299i	−0.493822	−	0.493822i
$990$	2.07860	−	6.22320i	0.0660621	−	0.197786i
$991$	2.16821			0.0688755			0.0344378	−	0.999407i	$-0.489036\pi$
$991$	2.16821			0.0688755			0.0344378	+	0.999407i	$0.489036\pi$
$992$	−41.9879	−	1.72206i	−1.33312	−	0.0546755i
$993$	13.3535			0.423762
$994$	1.70975	−	5.11889i	0.0542299	−	0.162361i
$995$	18.4038	+	18.4038i	0.583439	+	0.583439i
$996$	−33.4129	+	44.4381i	−1.05873	+	1.40808i
$997$	−10.0902	+	10.0902i	−0.319559	+	0.319559i	−0.848598	−	0.529038i	$-0.822553\pi$
$997$	−10.0902	+	10.0902i	−0.319559	+	0.319559i	0.529038	+	0.848598i	$0.322553\pi$
$998$	14.4459	−	7.21199i	0.457277	−	0.228292i
$999$			37.6586i			1.19146i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.n.g.493.25	yes	80
16.5	even	4	inner	656.2.n.g.165.25	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
656.2.n.g.165.25	✓	80	16.5	even	4	inner
656.2.n.g.493.25	yes	80	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.448028 - 1.34137i) q^{2} +(1.35244 + 1.35244i) q^{3} +(-1.59854 - 1.20194i) q^{4} +(-1.01984 + 1.01984i) q^{5} +(2.42005 - 1.20819i) q^{6} +1.02501i q^{7} +(-2.32844 + 1.60573i) q^{8} +0.658196i q^{9} +(0.911065 + 1.82490i) q^{10} +(-3.45580 + 3.45580i) q^{11} +(-0.536381 - 3.78749i) q^{12} +(4.74217 + 4.74217i) q^{13} +(1.37491 + 0.459232i) q^{14} -2.75855 q^{15} +(1.11068 + 3.84271i) q^{16} +1.03515 q^{17} +(0.882884 + 0.294890i) q^{18} +(4.00658 + 4.00658i) q^{19} +(2.85604 - 0.404470i) q^{20} +(-1.38626 + 1.38626i) q^{21} +(3.08721 + 6.18379i) q^{22} -7.29883i q^{23} +(-5.32074 - 0.977415i) q^{24} +2.91986i q^{25} +(8.48563 - 4.23638i) q^{26} +(3.16715 - 3.16715i) q^{27} +(1.23200 - 1.63852i) q^{28} +(-0.0824890 - 0.0824890i) q^{29} +(-1.23590 + 3.70023i) q^{30} -7.42872 q^{31} +(5.65210 + 0.231811i) q^{32} -9.34753 q^{33} +(0.463775 - 1.38852i) q^{34} +(-1.04534 - 1.04534i) q^{35} +(0.791113 - 1.05216i) q^{36} +(-5.94518 + 5.94518i) q^{37} +(7.16937 - 3.57925i) q^{38} +12.8270i q^{39} +(0.737042 - 4.01222i) q^{40} +1.00000i q^{41} +(1.23841 + 2.48057i) q^{42} +(2.12772 - 2.12772i) q^{43} +(9.67790 - 1.37058i) q^{44} +(-0.671255 - 0.671255i) q^{45} +(-9.79043 - 3.27008i) q^{46} +3.96220 q^{47} +(-3.69491 + 6.69916i) q^{48} +5.94936 q^{49} +(3.91661 + 1.30818i) q^{50} +(1.39998 + 1.39998i) q^{51} +(-1.88075 - 13.2804i) q^{52} +(3.16372 - 3.16372i) q^{53} +(-2.82935 - 5.66729i) q^{54} -7.04871i q^{55} +(-1.64589 - 2.38667i) q^{56} +10.8373i q^{57} +(-0.147606 + 0.0736909i) q^{58} +(-1.21040 + 1.21040i) q^{59} +(4.40965 + 3.31561i) q^{60} +(-5.94068 - 5.94068i) q^{61} +(-3.32827 + 9.96465i) q^{62} -0.674656 q^{63} +(2.84324 - 7.47770i) q^{64} -9.67251 q^{65} +(-4.18795 + 12.5385i) q^{66} +(5.63874 + 5.63874i) q^{67} +(-1.65473 - 1.24419i) q^{68} +(9.87124 - 9.87124i) q^{69} +(-1.87053 + 0.933848i) q^{70} -3.72306i q^{71} +(-1.05689 - 1.53257i) q^{72} -0.818434i q^{73} +(5.31108 + 10.6383i) q^{74} +(-3.94893 + 3.94893i) q^{75} +(-1.58902 - 11.2204i) q^{76} +(-3.54222 - 3.54222i) q^{77} +(17.2058 + 5.74686i) q^{78} -16.8179 q^{79} +(-5.05165 - 2.78623i) q^{80} +10.5414 q^{81} +(1.34137 + 0.448028i) q^{82} +(-10.2774 - 10.2774i) q^{83} +(3.88221 - 0.549794i) q^{84} +(-1.05568 + 1.05568i) q^{85} +(-1.90078 - 3.80734i) q^{86} -0.223123i q^{87} +(2.49752 - 13.5957i) q^{88} +5.40600i q^{89} +(-1.20114 + 0.599660i) q^{90} +(-4.86076 + 4.86076i) q^{91} +(-8.77276 + 11.6675i) q^{92} +(-10.0469 - 10.0469i) q^{93} +(1.77518 - 5.31478i) q^{94} -8.17214 q^{95} +(7.33063 + 7.95765i) q^{96} +14.3892 q^{97} +(2.66548 - 7.98029i) q^{98} +(-2.27459 - 2.27459i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{4} + 4 q^{10} - 4 q^{11} + 14 q^{12} + 6 q^{14} - 48 q^{15} + 6 q^{16} + 40 q^{18} - 8 q^{19} - 42 q^{20} + 2 q^{22} - 2 q^{24} - 48 q^{26} + 42 q^{28} - 8 q^{29} - 14 q^{30} + 80 q^{31} - 20 q^{32}+ \cdots + 12 q^{99}+O(q^{100}) \) 80 * q - 2 * q^4 + 4 * q^10 - 4 * q^11 + 14 * q^12 + 6 * q^14 - 48 * q^15 + 6 * q^16 + 40 * q^18 - 8 * q^19 - 42 * q^20 + 2 * q^22 - 2 * q^24 - 48 * q^26 + 42 * q^28 - 8 * q^29 - 14 * q^30 + 80 * q^31 - 20 * q^32 + 12 * q^34 - 60 * q^36 - 8 * q^37 + 26 * q^40 - 46 * q^42 + 4 * q^43 + 82 * q^44 - 56 * q^47 + 10 * q^48 - 80 * q^49 + 70 * q^50 - 12 * q^51 - 28 * q^52 + 8 * q^53 + 38 * q^54 + 14 * q^56 - 60 * q^58 + 16 * q^59 + 144 * q^60 + 16 * q^61 - 40 * q^62 + 104 * q^63 - 14 * q^64 + 58 * q^66 + 20 * q^67 - 84 * q^68 - 40 * q^69 + 34 * q^70 + 6 * q^72 - 48 * q^74 - 28 * q^75 + 50 * q^76 + 8 * q^77 - 12 * q^78 - 144 * q^79 - 14 * q^80 - 80 * q^81 + 2 * q^82 - 112 * q^84 - 16 * q^85 + 2 * q^86 - 10 * q^88 - 116 * q^90 - 16 * q^91 + 64 * q^92 + 24 * q^94 + 96 * q^95 - 6 * q^96 + 178 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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