LMFDB - Embedded newform 731.2.f.c.259.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(259,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("731.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.f (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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			259.16
Character	$\chi$	$=$	731.259
Dual form			731.2.f.c.302.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.265604i q^{2} +(0.626669 - 0.626669i) q^{3} +1.92945 q^{4} +(-0.906788 + 0.906788i) q^{5} +(0.166446 + 0.166446i) q^{6} +(-0.565427 - 0.565427i) q^{7} +1.04368i q^{8} +2.21457i q^{9} +O(q^{10})$	\(q+0.265604i q^{2} +(0.626669 - 0.626669i) q^{3} +1.92945 q^{4} +(-0.906788 + 0.906788i) q^{5} +(0.166446 + 0.166446i) q^{6} +(-0.565427 - 0.565427i) q^{7} +1.04368i q^{8} +2.21457i q^{9} +(-0.240847 - 0.240847i) q^{10} +(-0.293775 - 0.293775i) q^{11} +(1.20913 - 1.20913i) q^{12} +2.06835 q^{13} +(0.150180 - 0.150180i) q^{14} +1.13651i q^{15} +3.58170 q^{16} +(4.07748 + 0.611664i) q^{17} -0.588200 q^{18} +0.741114i q^{19} +(-1.74961 + 1.74961i) q^{20} -0.708671 q^{21} +(0.0780280 - 0.0780280i) q^{22} +(0.987551 + 0.987551i) q^{23} +(0.654042 + 0.654042i) q^{24} +3.35547i q^{25} +0.549362i q^{26} +(3.26781 + 3.26781i) q^{27} +(-1.09097 - 1.09097i) q^{28} +(1.94682 - 1.94682i) q^{29} -0.301862 q^{30} +(-0.117581 + 0.117581i) q^{31} +3.03868i q^{32} -0.368200 q^{33} +(-0.162461 + 1.08300i) q^{34} +1.02544 q^{35} +4.27292i q^{36} +(6.90645 - 6.90645i) q^{37} -0.196843 q^{38} +(1.29617 - 1.29617i) q^{39} +(-0.946397 - 0.946397i) q^{40} +(-3.76516 - 3.76516i) q^{41} -0.188226i q^{42} +1.00000i q^{43} +(-0.566826 - 0.566826i) q^{44} +(-2.00815 - 2.00815i) q^{45} +(-0.262298 + 0.262298i) q^{46} -13.3103 q^{47} +(2.24454 - 2.24454i) q^{48} -6.36059i q^{49} -0.891228 q^{50} +(2.93854 - 2.17192i) q^{51} +3.99078 q^{52} +6.63470i q^{53} +(-0.867945 + 0.867945i) q^{54} +0.532784 q^{55} +(0.590125 - 0.590125i) q^{56} +(0.464433 + 0.464433i) q^{57} +(0.517084 + 0.517084i) q^{58} -4.51651i q^{59} +2.19285i q^{60} +(0.233168 + 0.233168i) q^{61} +(-0.0312302 - 0.0312302i) q^{62} +(1.25218 - 1.25218i) q^{63} +6.35632 q^{64} +(-1.87555 + 1.87555i) q^{65} -0.0977954i q^{66} -7.32571 q^{67} +(7.86732 + 1.18018i) q^{68} +1.23773 q^{69} +0.272363i q^{70} +(-3.39207 + 3.39207i) q^{71} -2.31131 q^{72} +(7.82642 - 7.82642i) q^{73} +(1.83438 + 1.83438i) q^{74} +(2.10277 + 2.10277i) q^{75} +1.42994i q^{76} +0.332217i q^{77} +(0.344268 + 0.344268i) q^{78} +(-0.237981 - 0.237981i) q^{79} +(-3.24784 + 3.24784i) q^{80} -2.54805 q^{81} +(1.00004 - 1.00004i) q^{82} +11.2205i q^{83} -1.36735 q^{84} +(-4.25206 + 3.14276i) q^{85} -0.265604 q^{86} -2.44002i q^{87} +(0.306607 - 0.306607i) q^{88} -3.63274 q^{89} +(0.533373 - 0.533373i) q^{90} +(-1.16950 - 1.16950i) q^{91} +(1.90543 + 1.90543i) q^{92} +0.147369i q^{93} -3.53526i q^{94} +(-0.672033 - 0.672033i) q^{95} +(1.90424 + 1.90424i) q^{96} +(11.6837 - 11.6837i) q^{97} +1.68940 q^{98} +(0.650586 - 0.650586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) $ 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7	$ 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) $ 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7 + 4 * q^10 - 6 * q^11 - 14 * q^12 + 16 * q^13 + 6 * q^14 + 44 * q^16 + 8 * q^17 - 16 * q^18 + 12 * q^20 + 28 * q^21 + 14 * q^22 + 6 * q^23 + 62 * q^24 - 4 * q^27 + 34 * q^28 - 12 * q^29 - 96 * q^30 + 14 * q^31 - 44 * q^33 + 6 * q^34 - 32 * q^35 + 8 * q^37 + 72 * q^38 - 32 * q^39 - 84 * q^40 + 24 * q^41 + 4 * q^44 + 48 * q^45 - 4 * q^46 - 8 * q^47 + 38 * q^48 - 64 * q^50 + 28 * q^51 - 48 * q^52 + 34 * q^54 + 56 * q^55 - 26 * q^56 - 102 * q^57 + 76 * q^58 - 40 * q^61 + 34 * q^62 + 4 * q^63 - 204 * q^64 + 18 * q^65 - 20 * q^67 + 30 * q^68 - 16 * q^69 - 26 * q^71 + 144 * q^72 + 8 * q^73 - 80 * q^74 + 142 * q^75 - 32 * q^78 - 22 * q^79 - 32 * q^80 - 32 * q^81 + 100 * q^82 - 20 * q^84 - 2 * q^85 + 12 * q^86 + 34 * q^88 + 68 * q^89 - 10 * q^90 - 28 * q^91 + 68 * q^92 - 62 * q^95 + 62 * q^96 - 2 * q^97 - 32 * q^98 + 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$			0.265604i			0.187811i	0.995581	+	0.0939054i	$0.0299351\pi$
$2$			0.265604i			0.187811i	−0.995581	+	0.0939054i	$0.970065\pi$
$3$	0.626669	−	0.626669i	0.361807	−	0.361807i	−0.502671	−	0.864478i	$-0.667649\pi$
$3$	0.626669	−	0.626669i	0.361807	−	0.361807i	0.864478	+	0.502671i	$0.167649\pi$
$4$	1.92945			0.964727
$5$	−0.906788	+	0.906788i	−0.405528	+	0.405528i	−0.880176	−	0.474648i	$-0.842575\pi$
$5$	−0.906788	+	0.906788i	−0.405528	+	0.405528i	0.474648	+	0.880176i	$0.342575\pi$
$6$	0.166446	+	0.166446i	0.0679513	+	0.0679513i
$7$	−0.565427	−	0.565427i	−0.213711	−	0.213711i	0.592131	−	0.805842i	$-0.298287\pi$
$7$	−0.565427	−	0.565427i	−0.213711	−	0.213711i	−0.805842	+	0.592131i	$0.798287\pi$
$8$			1.04368i			0.368997i
$9$			2.21457i			0.738191i
$10$	−0.240847	−	0.240847i	−0.0761625	−	0.0761625i
$11$	−0.293775	−	0.293775i	−0.0885766	−	0.0885766i	0.661430	−	0.750007i	$-0.269950\pi$
$11$	−0.293775	−	0.293775i	−0.0885766	−	0.0885766i	−0.750007	+	0.661430i	$0.769950\pi$
$12$	1.20913	−	1.20913i	0.349045	−	0.349045i
$13$	2.06835			0.573656			0.286828	−	0.957982i	$-0.407399\pi$
$13$	2.06835			0.573656			0.286828	+	0.957982i	$0.407399\pi$
$14$	0.150180	−	0.150180i	0.0401373	−	0.0401373i
$15$			1.13651i			0.293446i
$16$	3.58170			0.895426
$17$	4.07748	+	0.611664i	0.988935	+	0.148350i
$17$	4.07748	+	0.611664i	0.988935	+	0.148350i
$18$	−0.588200			−0.138640
$19$			0.741114i			0.170023i	0.996380	+	0.0850116i	$0.0270927\pi$
$19$			0.741114i			0.170023i	−0.996380	+	0.0850116i	$0.972907\pi$
$20$	−1.74961	+	1.74961i	−0.391224	+	0.391224i
$21$	−0.708671			−0.154645
$22$	0.0780280	−	0.0780280i	0.0166356	−	0.0166356i
$23$	0.987551	+	0.987551i	0.205919	+	0.205919i	0.802530	−	0.596612i	$-0.203487\pi$
$23$	0.987551	+	0.987551i	0.205919	+	0.205919i	−0.596612	+	0.802530i	$0.703487\pi$
$24$	0.654042	+	0.654042i	0.133506	+	0.133506i
$25$			3.35547i			0.671094i
$26$			0.549362i			0.107739i
$27$	3.26781	+	3.26781i	0.628890	+	0.628890i
$28$	−1.09097	−	1.09097i	−0.206173	−	0.206173i
$29$	1.94682	−	1.94682i	0.361515	−	0.361515i	−0.502855	−	0.864371i	$-0.667717\pi$
$29$	1.94682	−	1.94682i	0.361515	−	0.361515i	0.864371	+	0.502855i	$0.167717\pi$
$30$	−0.301862			−0.0551123
$31$	−0.117581	+	0.117581i	−0.0211183	+	0.0211183i	−0.717587	−	0.696469i	$-0.754753\pi$
$31$	−0.117581	+	0.117581i	−0.0211183	+	0.0211183i	0.696469	+	0.717587i	$0.254753\pi$
$32$			3.03868i			0.537167i
$33$	−0.368200			−0.0640953
$34$	−0.162461	+	1.08300i	−0.0278618	+	0.185733i
$35$	1.02544			0.173332
$36$			4.27292i			0.712153i
$37$	6.90645	−	6.90645i	1.13541	−	1.13541i	0.146151	−	0.989262i	$-0.453311\pi$
$37$	6.90645	−	6.90645i	1.13541	−	1.13541i	0.989262	−	0.146151i	$-0.0466887\pi$
$38$	−0.196843			−0.0319322
$39$	1.29617	−	1.29617i	0.207553	−	0.207553i
$40$	−0.946397	−	0.946397i	−0.149638	−	0.149638i
$41$	−3.76516	−	3.76516i	−0.588020	−	0.588020i	0.349075	−	0.937095i	$-0.386496\pi$
$41$	−3.76516	−	3.76516i	−0.588020	−	0.588020i	−0.937095	+	0.349075i	$0.886496\pi$
$42$		−	0.188226i		−	0.0290439i
$43$			1.00000i			0.152499i
$43$			1.00000i			0.152499i
$44$	−0.566826	−	0.566826i	−0.0854522	−	0.0854522i
$45$	−2.00815	−	2.00815i	−0.299357	−	0.299357i
$46$	−0.262298	+	0.262298i	−0.0386737	+	0.0386737i
$47$	−13.3103			−1.94150			−0.970750	−	0.240094i	$-0.922822\pi$
$47$	−13.3103			−1.94150			−0.970750	+	0.240094i	$0.922822\pi$
$48$	2.24454	−	2.24454i	0.323972	−	0.323972i
$49$		−	6.36059i		−	0.908655i
$50$	−0.891228			−0.126039
$51$	2.93854	−	2.17192i	0.411478	−	0.304130i
$52$	3.99078			0.553422
$53$			6.63470i			0.911346i	0.890147	+	0.455673i	$0.150601\pi$
$53$			6.63470i			0.911346i	−0.890147	+	0.455673i	$0.849399\pi$
$54$	−0.867945	+	0.867945i	−0.118112	+	0.118112i
$55$	0.532784			0.0718405
$56$	0.590125	−	0.590125i	0.0788588	−	0.0788588i
$57$	0.464433	+	0.464433i	0.0615156	+	0.0615156i
$58$	0.517084	+	0.517084i	0.0678965	+	0.0678965i
$59$		−	4.51651i		−	0.587999i	−0.955806	−	0.294000i	$-0.905014\pi$
$59$		−	4.51651i		−	0.587999i	0.955806	−	0.294000i	$-0.0949864\pi$
$60$			2.19285i			0.283095i
$61$	0.233168	+	0.233168i	0.0298541	+	0.0298541i	0.721876	−	0.692022i	$-0.243280\pi$
$61$	0.233168	+	0.233168i	0.0298541	+	0.0298541i	−0.692022	+	0.721876i	$0.743280\pi$
$62$	−0.0312302	−	0.0312302i	−0.00396623	−	0.00396623i
$63$	1.25218	−	1.25218i	0.157760	−	0.157760i
$64$	6.35632			0.794540
$65$	−1.87555	+	1.87555i	−0.232634	+	0.232634i
$66$		−	0.0977954i		−	0.0120378i
$67$	−7.32571			−0.894978			−0.447489	−	0.894289i	$-0.647682\pi$
$67$	−7.32571			−0.894978			−0.447489	+	0.894289i	$0.647682\pi$
$68$	7.86732	+	1.18018i	0.954052	+	0.143118i
$69$	1.23773			0.149006
$70$			0.272363i			0.0325536i
$71$	−3.39207	+	3.39207i	−0.402565	+	0.402565i	−0.879136	−	0.476571i	$-0.841879\pi$
$71$	−3.39207	+	3.39207i	−0.402565	+	0.402565i	0.476571	+	0.879136i	$0.341879\pi$
$72$	−2.31131			−0.272390
$73$	7.82642	−	7.82642i	0.916013	−	0.916013i	−0.0807234	−	0.996737i	$-0.525723\pi$
$73$	7.82642	−	7.82642i	0.916013	−	0.916013i	0.996737	+	0.0807234i	$0.0257230\pi$
$74$	1.83438	+	1.83438i	0.213243	+	0.213243i
$75$	2.10277	+	2.10277i	0.242807	+	0.242807i
$76$			1.42994i			0.164026i
$77$			0.332217i			0.0378596i
$78$	0.344268	+	0.344268i	0.0389807	+	0.0389807i
$79$	−0.237981	−	0.237981i	−0.0267749	−	0.0267749i	0.693593	−	0.720368i	$-0.256027\pi$
$79$	−0.237981	−	0.237981i	−0.0267749	−	0.0267749i	−0.720368	+	0.693593i	$0.756027\pi$
$80$	−3.24784	+	3.24784i	−0.363120	+	0.363120i
$81$	−2.54805			−0.283116
$82$	1.00004	−	1.00004i	0.110436	−	0.110436i
$83$			11.2205i			1.23161i	0.787900	+	0.615803i	$0.211168\pi$
$83$			11.2205i			1.23161i	−0.787900	+	0.615803i	$0.788832\pi$
$84$	−1.36735			−0.149190
$85$	−4.25206	+	3.14276i	−0.461201	+	0.340881i
$86$	−0.265604			−0.0286409
$87$		−	2.44002i		−	0.261598i
$88$	0.306607	−	0.306607i	0.0326845	−	0.0326845i
$89$	−3.63274			−0.385070			−0.192535	−	0.981290i	$-0.561671\pi$
$89$	−3.63274			−0.385070			−0.192535	+	0.981290i	$0.561671\pi$
$90$	0.533373	−	0.533373i	0.0562224	−	0.0562224i
$91$	−1.16950	−	1.16950i	−0.122597	−	0.122597i
$92$	1.90543	+	1.90543i	0.198655	+	0.198655i
$93$			0.147369i			0.0152815i
$94$		−	3.53526i		−	0.364634i
$95$	−0.672033	−	0.672033i	−0.0689491	−	0.0689491i
$96$	1.90424	+	1.90424i	0.194351	+	0.194351i
$97$	11.6837	−	11.6837i	1.18630	−	1.18630i	0.208223	−	0.978081i	$-0.433232\pi$
$97$	11.6837	−	11.6837i	1.18630	−	1.18630i	0.978081	−	0.208223i	$-0.0667679\pi$
$98$	1.68940			0.170655
$99$	0.650586	−	0.650586i	0.0653864	−	0.0653864i
$100$			6.47423i			0.647423i
$101$	−3.57197			−0.355424			−0.177712	−	0.984083i	$-0.556870\pi$
$101$	−3.57197			−0.355424			−0.177712	+	0.984083i	$0.556870\pi$
$102$	0.576872	+	0.780490i	0.0571188	+	0.0772800i
$103$	−4.92865			−0.485634			−0.242817	−	0.970072i	$-0.578071\pi$
$103$	−4.92865			−0.485634			−0.242817	+	0.970072i	$0.578071\pi$
$104$			2.15869i			0.211677i
$105$	0.642614	−	0.642614i	0.0627127	−	0.0627127i
$106$	−1.76221			−0.171161
$107$	−11.6790	+	11.6790i	−1.12905	+	1.12905i	−0.138718	+	0.990332i	$0.544298\pi$
$107$	−11.6790	+	11.6790i	−1.12905	+	1.12905i	−0.990332	+	0.138718i	$0.955702\pi$
$108$	6.30509	+	6.30509i	0.606708	+	0.606708i
$109$	3.65860	+	3.65860i	0.350430	+	0.350430i	0.860270	−	0.509839i	$-0.170295\pi$
$109$	3.65860	+	3.65860i	0.350430	+	0.350430i	−0.509839	+	0.860270i	$0.670295\pi$
$110$			0.141510i			0.0134924i
$111$		−	8.65612i		−	0.821602i
$112$	−2.02519	−	2.02519i	−0.191363	−	0.191363i
$113$	−12.9203	−	12.9203i	−1.21544	−	1.21544i	−0.969211	−	0.246233i	$-0.920807\pi$
$113$	−12.9203	−	12.9203i	−1.21544	−	1.21544i	−0.246233	−	0.969211i	$-0.579193\pi$
$114$	−0.123355	+	0.123355i	−0.0115533	+	0.0115533i
$115$	−1.79100			−0.167011
$116$	3.75630	−	3.75630i	0.348764	−	0.348764i
$117$			4.58051i			0.423468i
$118$	1.19960			0.110433
$119$	−1.95967	−	2.65137i	−0.179642	−	0.243051i
$120$	−1.18615			−0.108281
$121$		−	10.8274i		−	0.984308i
$122$	−0.0619304	+	0.0619304i	−0.00560692	+	0.00560692i
$123$	−4.71902			−0.425500
$124$	−0.226868	+	0.226868i	−0.0203734	+	0.0203734i
$125$	−7.57664	−	7.57664i	−0.677675	−	0.677675i
$126$	0.332584	+	0.332584i	0.0296290	+	0.0296290i
$127$			14.3300i			1.27158i	0.771861	+	0.635792i	$0.219326\pi$
$127$			14.3300i			1.27158i	−0.771861	+	0.635792i	$0.780674\pi$
$128$			7.76562i			0.686390i
$129$	0.626669	+	0.626669i	0.0551751	+	0.0551751i
$130$	−0.498155	−	0.498155i	−0.0436911	−	0.0436911i
$131$	13.8689	−	13.8689i	1.21173	−	1.21173i	0.241271	−	0.970458i	$-0.422436\pi$
$131$	13.8689	−	13.8689i	1.21173	−	1.21173i	0.970458	−	0.241271i	$-0.0775643\pi$
$132$	−0.710424			−0.0618345
$133$	0.419045	−	0.419045i	0.0363358	−	0.0363358i
$134$		−	1.94574i		−	0.168086i
$135$	−5.92642			−0.510065
$136$	−0.638382	+	4.25559i	−0.0547408	+	0.364914i
$137$	20.2419			1.72938			0.864692	−	0.502302i	$-0.167514\pi$
$137$	20.2419			1.72938			0.864692	+	0.502302i	$0.167514\pi$
$138$			0.328748i			0.0279849i
$139$	−7.47378	+	7.47378i	−0.633918	+	0.633918i	−0.949048	−	0.315131i	$-0.897952\pi$
$139$	−7.47378	+	7.47378i	−0.633918	+	0.633918i	0.315131	+	0.949048i	$0.397952\pi$
$140$	1.97855			0.167218
$141$	−8.34112	+	8.34112i	−0.702449	+	0.702449i
$142$	−0.900949	−	0.900949i	−0.0756060	−	0.0756060i
$143$	−0.607629	−	0.607629i	−0.0508125	−	0.0508125i
$144$			7.93194i			0.660995i
$145$			3.53071i			0.293209i
$146$	2.07873	+	2.07873i	0.172037	+	0.172037i
$147$	−3.98598	−	3.98598i	−0.328758	−	0.328758i
$148$	13.3257	−	13.3257i	1.09536	−	1.09536i
$149$	−9.16916			−0.751167			−0.375583	−	0.926789i	$-0.622558\pi$
$149$	−9.16916			−0.751167			−0.375583	+	0.926789i	$0.622558\pi$
$150$	−0.558505	+	0.558505i	−0.0456017	+	0.0456017i
$151$		−	24.4491i		−	1.98964i	−0.101661	−	0.994819i	$-0.532416\pi$
$151$		−	24.4491i		−	1.98964i	0.101661	−	0.994819i	$-0.467584\pi$
$152$	−0.773486			−0.0627380
$153$	−1.35457	+	9.02988i	−0.109511	+	0.730023i
$154$	−0.0882382			−0.00711044
$155$		−	0.213243i		−	0.0171281i
$156$	2.50090	−	2.50090i	0.200232	−	0.200232i
$157$	−15.7373			−1.25597			−0.627985	−	0.778225i	$-0.716120\pi$
$157$	−15.7373			−1.25597			−0.627985	+	0.778225i	$0.716120\pi$
$158$	0.0632088	−	0.0632088i	0.00502862	−	0.00502862i
$159$	4.15776	+	4.15776i	0.329732	+	0.329732i
$160$	−2.75544	−	2.75544i	−0.217836	−	0.217836i
$161$		−	1.11678i		−	0.0880142i
$162$		−	0.676773i		−	0.0531723i
$163$	−9.82048	−	9.82048i	−0.769200	−	0.769200i	0.208766	−	0.977966i	$-0.433055\pi$
$163$	−9.82048	−	9.82048i	−0.769200	−	0.769200i	−0.977966	+	0.208766i	$0.933055\pi$
$164$	−7.26471	−	7.26471i	−0.567279	−	0.567279i
$165$	0.333879	−	0.333879i	0.0259924	−	0.0259924i
$166$	−2.98021			−0.231309
$167$	−14.7703	+	14.7703i	−1.14296	+	1.14296i	−0.155054	+	0.987906i	$0.549555\pi$
$167$	−14.7703	+	14.7703i	−1.14296	+	1.14296i	−0.987906	+	0.155054i	$0.950445\pi$
$168$		−	0.739626i		−	0.0570634i
$169$	−8.72194			−0.670918
$170$	−0.834732	−	1.12937i	−0.0640210	−	0.0866185i
$171$	−1.64125			−0.125509
$172$			1.92945i			0.147120i
$173$	−2.02835	+	2.02835i	−0.154212	+	0.154212i	−0.779996	−	0.625784i	$-0.784779\pi$
$173$	−2.02835	+	2.02835i	−0.154212	+	0.154212i	0.625784	+	0.779996i	$0.284779\pi$
$174$	0.648081			0.0491309
$175$	1.89727	−	1.89727i	0.143420	−	0.143420i
$176$	−1.05222	−	1.05222i	−0.0793137	−	0.0793137i
$177$	−2.83035	−	2.83035i	−0.212742	−	0.212742i
$178$		−	0.964873i		−	0.0723203i
$179$			0.398610i			0.0297935i	0.999889	+	0.0148967i	$0.00474196\pi$
$179$			0.398610i			0.0297935i	−0.999889	+	0.0148967i	$0.995258\pi$
$180$	−3.87463	−	3.87463i	−0.288798	−	0.288798i
$181$	−11.8696	−	11.8696i	−0.882258	−	0.882258i	0.111506	−	0.993764i	$-0.464433\pi$
$181$	−11.8696	−	11.8696i	−0.882258	−	0.882258i	−0.993764	+	0.111506i	$0.964433\pi$
$182$	0.310624	−	0.310624i	0.0230250	−	0.0230250i
$183$	0.292238			0.0216029
$184$	−1.03069	+	1.03069i	−0.0759833	+	0.0759833i
$185$			12.5254i			0.920884i
$186$	−0.0391419			−0.00287003
$187$	−1.01817	−	1.37756i	−0.0744561	−	0.100737i
$188$	−25.6815			−1.87302
$189$		−	3.69541i		−	0.268802i
$190$	0.178495	−	0.178495i	0.0129494	−	0.0129494i
$191$	16.5388			1.19671			0.598353	−	0.801232i	$-0.295822\pi$
$191$	16.5388			1.19671			0.598353	+	0.801232i	$0.295822\pi$
$192$	3.98331	−	3.98331i	0.287470	−	0.287470i
$193$	9.01243	+	9.01243i	0.648729	+	0.648729i	0.952686	−	0.303957i	$-0.0983079\pi$
$193$	9.01243	+	9.01243i	0.648729	+	0.648729i	−0.303957	+	0.952686i	$0.598308\pi$
$194$	3.10325	+	3.10325i	0.222801	+	0.222801i
$195$			2.35070i			0.168337i
$196$		−	12.2725i		−	0.876604i
$197$	−14.4718	−	14.4718i	−1.03107	−	1.03107i	−0.999502	−	0.0315680i	$-0.989950\pi$
$197$	−14.4718	−	14.4718i	−1.03107	−	1.03107i	−0.0315680	−	0.999502i	$-0.510050\pi$
$198$	0.172799	+	0.172799i	0.0122803	+	0.0122803i
$199$	2.93391	−	2.93391i	0.207979	−	0.207979i	−0.595429	−	0.803408i	$-0.703018\pi$
$199$	2.93391	−	2.93391i	0.207979	−	0.207979i	0.803408	+	0.595429i	$0.203018\pi$
$200$	−3.50204			−0.247632
$201$	−4.59079	+	4.59079i	−0.323810	+	0.323810i
$202$		−	0.948731i		−	0.0667524i
$203$	−2.20157			−0.154520
$204$	5.66978	−	4.19062i	0.396964	−	0.293402i
$205$	6.82841			0.476917
$206$		−	1.30907i		−	0.0912073i
$207$	−2.18700	+	2.18700i	−0.152007	+	0.152007i
$208$	7.40821			0.513667
$209$	0.217721	−	0.217721i	0.0150601	−	0.0150601i
$210$	0.170681	+	0.170681i	0.0117781	+	0.0117781i
$211$	5.25401	+	5.25401i	0.361701	+	0.361701i	0.864439	−	0.502738i	$-0.167674\pi$
$211$	5.25401	+	5.25401i	0.361701	+	0.361701i	−0.502738	+	0.864439i	$0.667674\pi$
$212$			12.8014i			0.879200i
$213$			4.25141i			0.291302i
$214$	−3.10199	−	3.10199i	−0.212048	−	0.212048i
$215$	−0.906788	−	0.906788i	−0.0618424	−	0.0618424i
$216$	−3.41055	+	3.41055i	−0.232059	+	0.232059i
$217$	0.132967			0.00902642
$218$	−0.971740	+	0.971740i	−0.0658146	+	0.0658146i
$219$		−	9.80915i		−	0.662841i
$220$	1.02798			0.0693065
$221$	8.43365	+	1.26513i	0.567309	+	0.0851021i
$222$	2.29910			0.154306
$223$		−	15.0100i		−	1.00514i	−0.864536	−	0.502571i	$-0.832388\pi$
$223$		−	15.0100i		−	1.00514i	0.864536	−	0.502571i	$-0.167612\pi$
$224$	1.71815	−	1.71815i	0.114799	−	0.114799i
$225$	−7.43093			−0.495396
$226$	3.43170	−	3.43170i	0.228273	−	0.228273i
$227$	−8.85220	−	8.85220i	−0.587541	−	0.587541i	0.349423	−	0.936965i	$-0.386377\pi$
$227$	−8.85220	−	8.85220i	−0.587541	−	0.587541i	−0.936965	+	0.349423i	$0.886377\pi$
$228$	0.896102	+	0.896102i	0.0593458	+	0.0593458i
$229$		−	22.4050i		−	1.48056i	−0.672298	−	0.740281i	$-0.734692\pi$
$229$		−	22.4050i		−	1.48056i	0.672298	−	0.740281i	$-0.265308\pi$
$230$		−	0.475697i		−	0.0313665i
$231$	0.208190	+	0.208190i	0.0136979	+	0.0136979i
$232$	2.03186	+	2.03186i	0.133398	+	0.133398i
$233$	10.8403	−	10.8403i	0.710173	−	0.710173i	−0.256398	−	0.966571i	$-0.582536\pi$
$233$	10.8403	−	10.8403i	0.710173	−	0.710173i	0.966571	+	0.256398i	$0.0825358\pi$
$234$	−1.21660			−0.0795318
$235$	12.0696	−	12.0696i	0.787332	−	0.787332i
$236$		−	8.71439i		−	0.567259i
$237$	−0.298270			−0.0193747
$238$	0.704215	−	0.520496i	0.0456475	−	0.0337388i
$239$	−4.75256			−0.307417			−0.153709	−	0.988116i	$-0.549122\pi$
$239$	−4.75256			−0.307417			−0.153709	+	0.988116i	$0.549122\pi$
$240$			4.07065i			0.262759i
$241$	−2.73135	+	2.73135i	−0.175942	+	0.175942i	−0.789584	−	0.613642i	$-0.789704\pi$
$241$	−2.73135	+	2.73135i	−0.175942	+	0.175942i	0.613642	+	0.789584i	$0.289704\pi$
$242$	2.87580			0.184864
$243$	−11.4002	+	11.4002i	−0.731324	+	0.731324i
$244$	0.449887	+	0.449887i	0.0288011	+	0.0288011i
$245$	5.76770	+	5.76770i	0.368485	+	0.368485i
$246$		−	1.25339i		−	0.0799135i
$247$			1.53288i			0.0975348i
$248$	−0.122717	−	0.122717i	−0.00779257	−	0.00779257i
$249$	7.03152	+	7.03152i	0.445604	+	0.445604i
$250$	2.01239	−	2.01239i	0.127275	−	0.127275i
$251$	8.97884			0.566739			0.283370	−	0.959011i	$-0.408548\pi$
$251$	8.97884			0.566739			0.283370	+	0.959011i	$0.408548\pi$
$252$	2.41602	−	2.41602i	0.152195	−	0.152195i
$253$		−	0.580236i		−	0.0364791i
$254$	−3.80612			−0.238817
$255$	−0.695163	+	4.63411i	−0.0435328	+	0.290199i
$256$	10.6501			0.665628
$257$			3.80109i			0.237106i	0.992948	+	0.118553i	$0.0378255\pi$
$257$			3.80109i			0.237106i	−0.992948	+	0.118553i	$0.962174\pi$
$258$	−0.166446	+	0.166446i	−0.0103625	+	0.0103625i
$259$	−7.81019			−0.485301
$260$	−3.61879	+	3.61879i	−0.224428	+	0.224428i
$261$	4.31137	+	4.31137i	0.266867	+	0.266867i
$262$	3.68363	+	3.68363i	0.227576	+	0.227576i
$263$			10.1021i			0.622924i	0.950259	+	0.311462i	$0.100819\pi$
$263$			10.1021i			0.622924i	−0.950259	+	0.311462i	$0.899181\pi$
$264$		−	0.384283i		−	0.0236510i
$265$	−6.01627	−	6.01627i	−0.369576	−	0.369576i
$266$	0.111300	+	0.111300i	0.00682426	+	0.00682426i
$267$	−2.27653	+	2.27653i	−0.139321	+	0.139321i
$268$	−14.1346			−0.863409
$269$	18.3202	−	18.3202i	1.11700	−	1.11700i	0.124823	−	0.992179i	$-0.460164\pi$
$269$	18.3202	−	18.3202i	1.11700	−	1.11700i	0.992179	−	0.124823i	$-0.0398364\pi$
$270$		−	1.57408i		−	0.0957957i
$271$	−9.56183			−0.580840			−0.290420	−	0.956899i	$-0.593795\pi$
$271$	−9.56183			−0.580840			−0.290420	+	0.956899i	$0.593795\pi$
$272$	14.6043	+	2.19080i	0.885518	+	0.132837i
$273$	−1.46578			−0.0887129
$274$			5.37634i			0.324797i
$275$	0.985754	−	0.985754i	0.0594432	−	0.0594432i
$276$	2.38815			0.143750
$277$	−7.00197	+	7.00197i	−0.420707	+	0.420707i	−0.885447	−	0.464740i	$-0.846148\pi$
$277$	−7.00197	+	7.00197i	−0.420707	+	0.420707i	0.464740	+	0.885447i	$0.346148\pi$
$278$	−1.98507	−	1.98507i	−0.119057	−	0.119057i
$279$	−0.260393	−	0.260393i	−0.0155893	−	0.0155893i
$280$			1.07024i			0.0639589i
$281$			16.2941i			0.972025i	0.873952	+	0.486012i	$0.161549\pi$
$281$			16.2941i			0.972025i	−0.873952	+	0.486012i	$0.838451\pi$
$282$	−2.21544	−	2.21544i	−0.131927	−	0.131927i
$283$	16.9907	+	16.9907i	1.00999	+	1.00999i	0.999950	+	0.0100399i	$0.00319585\pi$
$283$	16.9907	+	16.9907i	1.00999	+	1.00999i	0.0100399	+	0.999950i	$0.496804\pi$
$284$	−6.54484	+	6.54484i	−0.388365	+	0.388365i
$285$	−0.842284			−0.0498926
$286$	0.161389	−	0.161389i	0.00954313	−	0.00954313i
$287$			4.25785i			0.251333i
$288$	−6.72937			−0.396532
$289$	16.2517	+	4.98810i	0.955984	+	0.293417i
$290$	−0.937771			−0.0550678
$291$		−	14.6437i		−	0.858427i
$292$	15.1007	−	15.1007i	0.883703	−	0.883703i
$293$	−7.43751			−0.434504			−0.217252	−	0.976116i	$-0.569709\pi$
$293$	−7.43751			−0.434504			−0.217252	+	0.976116i	$0.569709\pi$
$294$	1.05869	−	1.05869i	0.0617443	−	0.0617443i
$295$	4.09551	+	4.09551i	0.238450	+	0.238450i
$296$	7.20813	+	7.20813i	0.418964	+	0.418964i
$297$		−	1.92000i		−	0.111410i
$298$		−	2.43537i		−	0.141077i
$299$	2.04260	+	2.04260i	0.118127	+	0.118127i
$300$	4.05720	+	4.05720i	0.234242	+	0.234242i
$301$	0.565427	−	0.565427i	0.0325907	−	0.0325907i
$302$	6.49379			0.373675
$303$	−2.23844	+	2.23844i	−0.128595	+	0.128595i
$304$			2.65445i			0.152243i
$305$	−0.422868			−0.0242133
$306$	−2.39838	−	0.359781i	−0.137106	−	0.0205673i
$307$	5.12036			0.292235			0.146117	−	0.989267i	$-0.453322\pi$
$307$	5.12036			0.292235			0.146117	+	0.989267i	$0.453322\pi$
$308$			0.640997i			0.0365242i
$309$	−3.08863	+	3.08863i	−0.175706	+	0.175706i
$310$	0.0566383			0.00321684
$311$	6.57519	−	6.57519i	0.372845	−	0.372845i	−0.495668	−	0.868512i	$-0.665077\pi$
$311$	6.57519	−	6.57519i	0.372845	−	0.372845i	0.868512	+	0.495668i	$0.165077\pi$
$312$	1.35279	+	1.35279i	0.0765864	+	0.0765864i
$313$	14.9655	+	14.9655i	0.845901	+	0.845901i	0.989619	−	0.143717i	$-0.0459056\pi$
$313$	14.9655	+	14.9655i	0.845901	+	0.845901i	−0.143717	+	0.989619i	$0.545906\pi$
$314$		−	4.17989i		−	0.235885i
$315$			2.27092i			0.127952i
$316$	−0.459173	−	0.459173i	−0.0258305	−	0.0258305i
$317$	9.24203	+	9.24203i	0.519084	+	0.519084i	0.917294	−	0.398210i	$-0.130368\pi$
$317$	9.24203	+	9.24203i	0.519084	+	0.519084i	−0.398210	+	0.917294i	$0.630368\pi$
$318$	−1.10432	+	1.10432i	−0.0619272	+	0.0619272i
$319$	−1.14386			−0.0640436
$320$	−5.76383	+	5.76383i	−0.322208	+	0.322208i
$321$			14.6377i			0.816997i
$322$	0.296621			0.0165300
$323$	−0.453312	+	3.02188i	−0.0252230	+	0.168142i
$324$	−4.91634			−0.273130
$325$			6.94028i			0.384978i
$326$	2.60836	−	2.60836i	0.144464	−	0.144464i
$327$	4.58546			0.253577
$328$	3.92963	−	3.92963i	0.216977	−	0.216977i
$329$	7.52597	+	7.52597i	0.414920	+	0.414920i
$330$	0.0886797	+	0.0886797i	0.00488166	+	0.00488166i
$331$			25.7077i			1.41302i	0.707703	+	0.706510i	$0.249732\pi$
$331$			25.7077i			1.41302i	−0.707703	+	0.706510i	$0.750268\pi$
$332$			21.6494i			1.18816i
$333$	15.2948	+	15.2948i	0.838152	+	0.838152i
$334$	−3.92306	−	3.92306i	−0.214660	−	0.214660i
$335$	6.64286	−	6.64286i	0.362938	−	0.362938i
$336$	−2.53825			−0.138473
$337$	−12.7408	+	12.7408i	−0.694033	+	0.694033i	−0.963117	−	0.269084i	$-0.913279\pi$
$337$	−12.7408	+	12.7408i	−0.694033	+	0.694033i	0.269084	+	0.963117i	$0.413279\pi$
$338$		−	2.31659i		−	0.126006i
$339$	−16.1936			−0.879513
$340$	−8.20416	+	6.06382i	−0.444933	+	0.328857i
$341$	0.0690850			0.00374116
$342$		−	0.435923i		−	0.0235720i
$343$	−7.55443	+	7.55443i	−0.407901	+	0.407901i
$344$	−1.04368			−0.0562715
$345$	−1.12236	+	1.12236i	−0.0604260	+	0.0604260i
$346$	−0.538738	−	0.538738i	−0.0289628	−	0.0289628i
$347$	−6.24013	−	6.24013i	−0.334988	−	0.334988i	0.519489	−	0.854477i	$-0.326122\pi$
$347$	−6.24013	−	6.24013i	−0.334988	−	0.334988i	−0.854477	+	0.519489i	$0.826122\pi$
$348$		−	4.70791i		−	0.252371i
$349$		−	1.97033i		−	0.105469i	−0.998609	−	0.0527347i	$-0.983206\pi$
$349$		−	1.97033i		−	0.105469i	0.998609	−	0.0527347i	$-0.0167938\pi$
$350$	0.503924	+	0.503924i	0.0269359	+	0.0269359i
$351$	6.75897	+	6.75897i	0.360767	+	0.360767i
$352$	0.892688	−	0.892688i	0.0475804	−	0.0475804i
$353$	19.7221			1.04970			0.524852	−	0.851194i	$-0.324121\pi$
$353$	19.7221			1.04970			0.524852	+	0.851194i	$0.324121\pi$
$354$	0.751755	−	0.751755i	0.0399553	−	0.0399553i
$355$		−	6.15178i		−	0.326502i
$356$	−7.00921			−0.371487
$357$	−2.88959	−	0.433468i	−0.152933	−	0.0229416i
$358$	−0.105872			−0.00559554
$359$		−	8.22944i		−	0.434333i	−0.976135	−	0.217167i	$-0.930319\pi$
$359$		−	8.22944i		−	0.434333i	0.976135	−	0.217167i	$-0.0696815\pi$
$360$	2.09586	−	2.09586i	0.110462	−	0.110462i
$361$	18.4508			0.971092
$362$	3.15261	−	3.15261i	0.165697	−	0.165697i
$363$	−6.78519	−	6.78519i	−0.356130	−	0.356130i
$364$	−2.25650	−	2.25650i	−0.118272	−	0.118272i
$365$			14.1938i			0.742938i
$366$			0.0776197i			0.00405725i
$367$	2.00736	+	2.00736i	0.104783	+	0.104783i	0.757555	−	0.652771i	$-0.226394\pi$
$367$	2.00736	+	2.00736i	0.104783	+	0.104783i	−0.652771	+	0.757555i	$0.726394\pi$
$368$	3.53711	+	3.53711i	0.184385	+	0.184385i
$369$	8.33823	−	8.33823i	0.434071	−	0.434071i
$370$	−3.32680			−0.172952
$371$	3.75144	−	3.75144i	0.194765	−	0.194765i
$372$			0.284342i			0.0147425i
$373$	−7.56765			−0.391838			−0.195919	−	0.980620i	$-0.562769\pi$
$373$	−7.56765			−0.391838			−0.195919	+	0.980620i	$0.562769\pi$
$374$	0.365885	−	0.270431i	0.0189195	−	0.0139837i
$375$	−9.49609			−0.490376
$376$		−	13.8916i		−	0.716407i
$377$	4.02670	−	4.02670i	0.207386	−	0.207386i
$378$	0.981519			0.0504839
$379$	−16.8684	+	16.8684i	−0.866470	+	0.866470i	−0.992080	−	0.125610i	$-0.959911\pi$
$379$	−16.8684	+	16.8684i	−0.866470	+	0.866470i	0.125610	+	0.992080i	$0.459911\pi$
$380$	−1.29666	−	1.29666i	−0.0665171	−	0.0665171i
$381$	8.98018	+	8.98018i	0.460068	+	0.460068i
$382$			4.39278i			0.224754i
$383$		−	7.34402i		−	0.375262i	−0.982240	−	0.187631i	$-0.939919\pi$
$383$		−	7.34402i		−	0.375262i	0.982240	−	0.187631i	$-0.0600809\pi$
$384$	4.86647	+	4.86647i	0.248341	+	0.248341i
$385$	−0.301250	−	0.301250i	−0.0153531	−	0.0153531i
$386$	−2.39374	+	2.39374i	−0.121838	+	0.121838i
$387$	−2.21457			−0.112573
$388$	22.5432	−	22.5432i	1.14446	−	1.14446i
$389$		−	14.4244i		−	0.731347i	−0.930743	−	0.365673i	$-0.880839\pi$
$389$		−	14.4244i		−	0.731347i	0.930743	−	0.365673i	$-0.119161\pi$
$390$	−0.624357			−0.0316155
$391$	3.42267	+	4.63077i	0.173092	+	0.234188i
$392$	6.63842			0.335291
$393$		−	17.3824i		−	0.876825i
$394$	3.84376	−	3.84376i	0.193646	−	0.193646i
$395$	0.431596			0.0217160
$396$	1.25528	−	1.25528i	0.0630800	−	0.0630800i
$397$	−7.39093	−	7.39093i	−0.370940	−	0.370940i	0.496879	−	0.867820i	$-0.334479\pi$
$397$	−7.39093	−	7.39093i	−0.370940	−	0.370940i	−0.867820	+	0.496879i	$0.834479\pi$
$398$	0.779259	+	0.779259i	0.0390607	+	0.0390607i
$399$		−	0.525205i		−	0.0262932i
$400$			12.0183i			0.600915i
$401$	2.98022	+	2.98022i	0.148825	+	0.148825i	0.777593	−	0.628768i	$-0.216440\pi$
$401$	2.98022	+	2.98022i	0.148825	+	0.148825i	−0.628768	+	0.777593i	$0.716440\pi$
$402$	−1.21934	−	1.21934i	−0.0608149	−	0.0608149i
$403$	−0.243199	+	0.243199i	−0.0121146	+	0.0121146i
$404$	−6.89195			−0.342887
$405$	2.31054	−	2.31054i	0.114812	−	0.114812i
$406$		−	0.584746i		−	0.0290205i
$407$	−4.05789			−0.201142
$408$	2.26679	+	3.06690i	0.112223	+	0.151834i
$409$	−5.89309			−0.291394			−0.145697	−	0.989329i	$-0.546543\pi$
$409$	−5.89309			−0.291394			−0.145697	+	0.989329i	$0.546543\pi$
$410$			1.81366i			0.0895701i
$411$	12.6850	−	12.6850i	0.625704	−	0.625704i
$412$	−9.50960			−0.468504
$413$	−2.55375	+	2.55375i	−0.125662	+	0.125662i
$414$	−0.580878	−	0.580878i	−0.0285486	−	0.0285486i
$415$	−10.1746	−	10.1746i	−0.499451	−	0.499451i
$416$			6.28504i			0.308149i
$417$			9.36717i			0.458712i
$418$	0.0578276	+	0.0578276i	0.00282844	+	0.00282844i
$419$	−12.7115	−	12.7115i	−0.620999	−	0.620999i	0.324788	−	0.945787i	$-0.394707\pi$
$419$	−12.7115	−	12.7115i	−0.620999	−	0.620999i	−0.945787	+	0.324788i	$0.894707\pi$
$420$	1.23989	−	1.23989i	0.0605006	−	0.0605006i
$421$	29.7741			1.45110			0.725550	−	0.688169i	$-0.241585\pi$
$421$	29.7741			1.45110			0.725550	+	0.688169i	$0.241585\pi$
$422$	−1.39549	+	1.39549i	−0.0679313	+	0.0679313i
$423$		−	29.4765i		−	1.43320i
$424$	−6.92451			−0.336284
$425$	−2.05242	+	13.6819i	−0.0995570	+	0.663669i
$426$	−1.12919			−0.0547096
$427$		−	0.263679i		−	0.0127603i
$428$	−22.5341	+	22.5341i	−1.08922	+	1.08922i
$429$	−0.761565			−0.0367687
$430$	0.240847	−	0.240847i	0.0116147	−	0.0116147i
$431$	−5.66418	−	5.66418i	−0.272834	−	0.272834i	0.557406	−	0.830240i	$-0.311797\pi$
$431$	−5.66418	−	5.66418i	−0.272834	−	0.272834i	−0.830240	+	0.557406i	$0.811797\pi$
$432$	11.7043	+	11.7043i	0.563124	+	0.563124i
$433$			31.9346i			1.53468i	0.641240	+	0.767340i	$0.278420\pi$
$433$			31.9346i			1.53468i	−0.641240	+	0.767340i	$0.721580\pi$
$434$			0.0353167i			0.00169526i
$435$	2.21258	+	2.21258i	0.106085	+	0.106085i
$436$	7.05910	+	7.05910i	0.338070	+	0.338070i
$437$	−0.731887	+	0.731887i	−0.0350109	+	0.0350109i
$438$	2.60535			0.124489
$439$	23.5859	−	23.5859i	1.12569	−	1.12569i	0.134825	−	0.990869i	$-0.456953\pi$
$439$	23.5859	−	23.5859i	1.12569	−	1.12569i	0.990869	−	0.134825i	$-0.0430471\pi$
$440$			0.556056i			0.0265089i
$441$	14.0860			0.670761
$442$	−0.336025	+	2.24002i	−0.0159831	+	0.106547i
$443$	27.3692			1.30035			0.650175	−	0.759785i	$-0.274696\pi$
$443$	27.3692			1.30035			0.650175	+	0.759785i	$0.274696\pi$
$444$		−	16.7016i		−	0.792622i
$445$	3.29413	−	3.29413i	0.156157	−	0.156157i
$446$	3.98671			0.188776
$447$	−5.74603	+	5.74603i	−0.271778	+	0.271778i
$448$	−3.59403	−	3.59403i	−0.169802	−	0.169802i
$449$	24.2719	+	24.2719i	1.14546	+	1.14546i	0.987435	+	0.158027i	$0.0505135\pi$
$449$	24.2719	+	24.2719i	1.14546	+	1.14546i	0.158027	+	0.987435i	$0.449487\pi$
$450$		−	1.97369i		−	0.0930406i
$451$			2.21222i			0.104170i
$452$	−24.9292	−	24.9292i	−1.17257	−	1.17257i
$453$	−15.3215	−	15.3215i	−0.719866	−	0.719866i
$454$	2.35118	−	2.35118i	0.110347	−	0.110347i
$455$	2.12098			0.0994329
$456$	−0.484719	+	0.484719i	−0.0226991	+	0.0226991i
$457$			26.3888i			1.23442i	0.786800	+	0.617209i	$0.211737\pi$
$457$			26.3888i			1.23442i	−0.786800	+	0.617209i	$0.788263\pi$
$458$	5.95086			0.278065
$459$	11.3256	+	15.3232i	0.528636	+	0.715228i
$460$	−3.45565			−0.161120
$461$			8.55116i			0.398267i	0.979972	+	0.199134i	$0.0638128\pi$
$461$			8.55116i			0.398267i	−0.979972	+	0.199134i	$0.936187\pi$
$462$	−0.0552962	+	0.0552962i	−0.00257261	+	0.00257261i
$463$	12.7590			0.592963			0.296482	−	0.955039i	$-0.404187\pi$
$463$	12.7590			0.592963			0.296482	+	0.955039i	$0.404187\pi$
$464$	6.97293	−	6.97293i	0.323710	−	0.323710i
$465$	−0.133633	−	0.133633i	−0.00619707	−	0.00619707i
$466$	2.87924	+	2.87924i	0.133378	+	0.133378i
$467$			6.34028i			0.293393i	0.989182	+	0.146696i	$0.0468641\pi$
$467$			6.34028i			0.293393i	−0.989182	+	0.146696i	$0.953136\pi$
$468$			8.83788i			0.408531i
$469$	4.14215	+	4.14215i	0.191267	+	0.191267i
$470$	3.20573	+	3.20573i	0.147869	+	0.147869i
$471$	−9.86206	+	9.86206i	−0.454420	+	0.454420i
$472$	4.71379			0.216970
$473$	0.293775	−	0.293775i	0.0135078	−	0.0135078i
$474$		−	0.0792219i		−	0.00363878i
$475$	−2.48679			−0.114102
$476$	−3.78109	−	5.11570i	−0.173306	−	0.234478i
$477$	−14.6930			−0.672747
$478$		−	1.26230i		−	0.0577363i
$479$	7.55004	−	7.55004i	0.344970	−	0.344970i	−0.513262	−	0.858232i	$-0.671563\pi$
$479$	7.55004	−	7.55004i	0.344970	−	0.344970i	0.858232	+	0.513262i	$0.171563\pi$
$480$	−3.45349			−0.157630
$481$	14.2849	−	14.2849i	0.651337	−	0.651337i
$482$	−0.725459	−	0.725459i	−0.0330438	−	0.0330438i
$483$	−0.699848	−	0.699848i	−0.0318442	−	0.0318442i
$484$		−	20.8910i		−	0.949589i
$485$			21.1893i			0.962159i
$486$	−3.02795	−	3.02795i	−0.137350	−	0.137350i
$487$	−12.1542	−	12.1542i	−0.550759	−	0.550759i	0.375901	−	0.926660i	$-0.377333\pi$
$487$	−12.1542	−	12.1542i	−0.550759	−	0.550759i	−0.926660	+	0.375901i	$0.877333\pi$
$488$	−0.243353	+	0.243353i	−0.0110161	+	0.0110161i
$489$	−12.3084			−0.556604
$490$	−1.53193	+	1.53193i	−0.0692054	+	0.0692054i
$491$		−	11.2742i		−	0.508799i	−0.967099	−	0.254399i	$-0.918122\pi$
$491$		−	11.2742i		−	0.508799i	0.967099	−	0.254399i	$-0.0818778\pi$
$492$	−9.10514			−0.410491
$493$	9.12893	−	6.74733i	0.411146	−	0.303884i
$494$	−0.407140			−0.0183181
$495$			1.17989i			0.0530320i
$496$	−0.421142	+	0.421142i	−0.0189098	+	0.0189098i
$497$	3.83593			0.172065
$498$	−1.86760	+	1.86760i	−0.0836893	+	0.0836893i
$499$	−10.8684	−	10.8684i	−0.486535	−	0.486535i	0.420676	−	0.907211i	$-0.361793\pi$
$499$	−10.8684	−	10.8684i	−0.486535	−	0.486535i	−0.907211	+	0.420676i	$0.861793\pi$
$500$	−14.6188	−	14.6188i	−0.653772	−	0.653772i
$501$			18.5122i			0.827063i
$502$			2.38482i			0.106440i
$503$	−30.3077	−	30.3077i	−1.35135	−	1.35135i	−0.884148	−	0.467206i	$-0.845261\pi$
$503$	−30.3077	−	30.3077i	−1.35135	−	1.35135i	−0.467206	−	0.884148i	$-0.654739\pi$
$504$	1.30687	+	1.30687i	0.0582128	+	0.0582128i
$505$	3.23902	−	3.23902i	0.144134	−	0.144134i
$506$	0.154113			0.00685117
$507$	−5.46577	+	5.46577i	−0.242743	+	0.242743i
$508$			27.6491i			1.22673i
$509$	9.78532			0.433727			0.216863	−	0.976202i	$-0.430417\pi$
$509$	9.78532			0.433727			0.216863	+	0.976202i	$0.430417\pi$
$510$	−1.23084	−	0.184638i	−0.0545025	−	0.00817592i
$511$	−8.85053			−0.391525
$512$			18.3599i			0.811403i
$513$	−2.42182	+	2.42182i	−0.106926	+	0.106926i
$514$	−1.00959			−0.0445310
$515$	4.46924	−	4.46924i	0.196938	−	0.196938i
$516$	1.20913	+	1.20913i	0.0532289	+	0.0532289i
$517$	3.91022	+	3.91022i	0.171971	+	0.171971i
$518$		−	2.07442i		−	0.0911448i
$519$			2.54221i			0.111590i
$520$	−1.95748	−	1.95748i	−0.0858411	−	0.0858411i
$521$	8.46740	+	8.46740i	0.370964	+	0.370964i	0.867828	−	0.496865i	$-0.165515\pi$
$521$	8.46740	+	8.46740i	0.370964	+	0.370964i	−0.496865	+	0.867828i	$0.665515\pi$
$522$	−1.14512	+	1.14512i	−0.0501206	+	0.0501206i
$523$	−5.35106			−0.233985			−0.116993	−	0.993133i	$-0.537325\pi$
$523$	−5.35106			−0.233985			−0.116993	+	0.993133i	$0.537325\pi$
$524$	26.7594	−	26.7594i	1.16899	−	1.16899i
$525$		−	2.37792i		−	0.103781i
$526$	−2.68317			−0.116992
$527$	−0.551357	+	0.407516i	−0.0240175	+	0.0177517i
$528$	−1.31878			−0.0573926
$529$		−	21.0495i		−	0.915195i
$530$	1.59795	−	1.59795i	0.0694104	−	0.0694104i
$531$	10.0021			0.434056
$532$	0.808529	−	0.808529i	0.0350542	−	0.0350542i
$533$	−7.78767	−	7.78767i	−0.337321	−	0.337321i
$534$	−0.604656	−	0.604656i	−0.0261660	−	0.0261660i
$535$		−	21.1807i		−	0.915722i
$536$		−	7.64570i		−	0.330244i
$537$	0.249796	+	0.249796i	0.0107795	+	0.0107795i
$538$	4.86593	+	4.86593i	0.209785	+	0.209785i
$539$	−1.86858	+	1.86858i	−0.0804855	+	0.0804855i
$540$	−11.4348			−0.492074
$541$	14.3179	−	14.3179i	0.615575	−	0.615575i	−0.328818	−	0.944393i	$-0.606650\pi$
$541$	14.3179	−	14.3179i	0.615575	−	0.615575i	0.944393	+	0.328818i	$0.106650\pi$
$542$		−	2.53966i		−	0.109088i
$543$	−14.8766			−0.638415
$544$	−1.85865	+	12.3902i	−0.0796889	+	0.531223i
$545$	−6.63515			−0.284218
$546$		−	0.389317i		−	0.0166612i
$547$	−22.2378	+	22.2378i	−0.950819	+	0.950819i	−0.998846	−	0.0480275i	$-0.984706\pi$
$547$	−22.2378	+	22.2378i	−0.950819	+	0.950819i	0.0480275	+	0.998846i	$0.484706\pi$
$548$	39.0559			1.66838
$549$	−0.516367	+	0.516367i	−0.0220380	+	0.0220380i
$550$	0.261821	+	0.261821i	0.0111641	+	0.0111641i
$551$	1.44281	+	1.44281i	0.0614660	+	0.0614660i
$552$			1.29180i			0.0549826i
$553$			0.269121i			0.0114442i
$554$	−1.85975	−	1.85975i	−0.0790134	−	0.0790134i
$555$	7.84926	+	7.84926i	0.333183	+	0.333183i
$556$	−14.4203	+	14.4203i	−0.611558	+	0.611558i
$557$	−21.0208			−0.890679			−0.445340	−	0.895362i	$-0.646917\pi$
$557$	−21.0208			−0.890679			−0.445340	+	0.895362i	$0.646917\pi$
$558$	0.0691614	−	0.0691614i	0.00292784	−	0.00292784i
$559$			2.06835i			0.0874818i
$560$	3.67284			0.155206
$561$	−1.50133	−	0.225214i	−0.0633861	−	0.00950856i
$562$	−4.32779			−0.182557
$563$		−	18.9567i		−	0.798931i	−0.916748	−	0.399465i	$-0.869196\pi$
$563$		−	18.9567i		−	0.798931i	0.916748	−	0.399465i	$-0.130804\pi$
$564$	−16.0938	+	16.0938i	−0.677672	+	0.677672i
$565$	23.4320			0.985793
$566$	−4.51279	+	4.51279i	−0.189687	+	0.189687i
$567$	1.44073	+	1.44073i	0.0605052	+	0.0605052i
$568$	−3.54024	−	3.54024i	−0.148545	−	0.148545i
$569$			30.2152i			1.26669i	0.773871	+	0.633344i	$0.218318\pi$
$569$			30.2152i			1.26669i	−0.773871	+	0.633344i	$0.781682\pi$
$570$		−	0.223714i		−	0.00937036i
$571$	8.53838	+	8.53838i	0.357320	+	0.357320i	0.862824	−	0.505504i	$-0.168693\pi$
$571$	8.53838	+	8.53838i	0.357320	+	0.357320i	−0.505504	+	0.862824i	$0.668693\pi$
$572$	−1.17239	−	1.17239i	−0.0490202	−	0.0490202i
$573$	10.3644	−	10.3644i	0.432977	−	0.432977i
$574$	−1.13090			−0.0472030
$575$	−3.31370	+	3.31370i	−0.138191	+	0.138191i
$576$			14.0765i			0.586522i
$577$	15.8161			0.658433			0.329216	−	0.944255i	$-0.393215\pi$
$577$	15.8161			0.658433			0.329216	+	0.944255i	$0.393215\pi$
$578$	−1.32486	+	4.31653i	−0.0551069	+	0.179544i
$579$	11.2956			0.469430
$580$			6.81234i			0.282867i
$581$	6.34435	−	6.34435i	0.263208	−	0.263208i
$582$	3.88942			0.161222
$583$	1.94911	−	1.94911i	0.0807239	−	0.0807239i
$584$	8.16828	+	8.16828i	0.338006	+	0.338006i
$585$	−4.15355	−	4.15355i	−0.171728	−	0.171728i
$586$		−	1.97544i		−	0.0816045i
$587$			32.4058i			1.33753i	0.743473	+	0.668766i	$0.233177\pi$
$587$			32.4058i			1.33753i	−0.743473	+	0.668766i	$0.766823\pi$
$588$	−7.69077	−	7.69077i	−0.317162	−	0.317162i
$589$	−0.0871412	−	0.0871412i	−0.00359059	−	0.00359059i
$590$	−1.08779	+	1.08779i	−0.0447835	+	0.0447835i
$591$	−18.1380			−0.746097
$592$	24.7369	−	24.7369i	1.01668	−	1.01668i
$593$		−	39.1576i		−	1.60801i	−0.594621	−	0.804006i	$-0.702698\pi$
$593$		−	39.1576i		−	1.60801i	0.594621	−	0.804006i	$-0.297302\pi$
$594$	0.509961			0.0209240
$595$	4.18123	+	0.627227i	0.171414	+	0.0257138i
$596$	−17.6915			−0.724671
$597$		−	3.67718i		−	0.150497i
$598$	−0.542523	+	0.542523i	−0.0221854	+	0.0221854i
$599$	−22.4640			−0.917856			−0.458928	−	0.888474i	$-0.651766\pi$
$599$	−22.4640			−0.917856			−0.458928	+	0.888474i	$0.651766\pi$
$600$	−2.19462	+	2.19462i	−0.0895950	+	0.0895950i
$601$	−11.2613	−	11.2613i	−0.459358	−	0.459358i	0.439087	−	0.898445i	$-0.355302\pi$
$601$	−11.2613	−	11.2613i	−0.459358	−	0.459358i	−0.898445	+	0.439087i	$0.855302\pi$
$602$	0.150180	+	0.150180i	0.00612087	+	0.00612087i
$603$		−	16.2233i		−	0.660664i
$604$		−	47.1734i		−	1.91946i
$605$	9.81815	+	9.81815i	0.399164	+	0.399164i
$606$	−0.594540	−	0.594540i	−0.0241515	−	0.0241515i
$607$	−1.75059	+	1.75059i	−0.0710543	+	0.0710543i	−0.741741	−	0.670687i	$-0.766000\pi$
$607$	−1.75059	+	1.75059i	−0.0710543	+	0.0710543i	0.670687	+	0.741741i	$0.266000\pi$
$608$	−2.25200			−0.0913309
$609$	−1.37965	+	1.37965i	−0.0559064	+	0.0559064i
$610$		−	0.112316i		−	0.00454752i
$611$	−27.5302			−1.11375
$612$	−2.61359	+	17.4227i	−0.105648	+	0.704273i
$613$	43.5150			1.75755			0.878777	−	0.477233i	$-0.158360\pi$
$613$	43.5150			1.75755			0.878777	+	0.477233i	$0.158360\pi$
$614$			1.35999i			0.0548848i
$615$	4.27915	−	4.27915i	0.172552	−	0.172552i
$616$	−0.346728			−0.0139701
$617$	−21.5095	+	21.5095i	−0.865938	+	0.865938i	−0.992020	−	0.126082i	$-0.959760\pi$
$617$	−21.5095	+	21.5095i	−0.865938	+	0.865938i	0.126082	+	0.992020i	$0.459760\pi$
$618$	−0.820354	−	0.820354i	−0.0329995	−	0.0329995i
$619$	14.7800	+	14.7800i	0.594058	+	0.594058i	0.938725	−	0.344667i	$-0.112008\pi$
$619$	14.7800	+	14.7800i	0.594058	+	0.594058i	−0.344667	+	0.938725i	$0.612008\pi$
$620$		−	0.411442i		−	0.0165239i
$621$			6.45426i			0.259000i
$622$	1.74640	+	1.74640i	0.0700242	+	0.0700242i
$623$	2.05405	+	2.05405i	0.0822938	+	0.0822938i
$624$	4.64249	−	4.64249i	0.185848	−	0.185848i
$625$	−3.03655			−0.121462
$626$	−3.97491	+	3.97491i	−0.158869	+	0.158869i
$627$		−	0.272878i		−	0.0108977i
$628$	−30.3643			−1.21167
$629$	32.3854	−	23.9365i	1.29129	−	0.954411i
$630$	−0.603167			−0.0240307
$631$			25.1748i			1.00219i	0.865391	+	0.501097i	$0.167070\pi$
$631$			25.1748i			1.00219i	−0.865391	+	0.501097i	$0.832930\pi$
$632$	0.248376	−	0.248376i	0.00987986	−	0.00987986i
$633$	6.58505			0.261732
$634$	−2.45472	+	2.45472i	−0.0974896	+	0.0974896i
$635$	−12.9943	−	12.9943i	−0.515663	−	0.515663i
$636$	8.02221	+	8.02221i	0.318101	+	0.318101i
$637$		−	13.1559i		−	0.521256i
$638$		−	0.303813i		−	0.0120281i
$639$	−7.51198	−	7.51198i	−0.297170	−	0.297170i
$640$	−7.04177	−	7.04177i	−0.278350	−	0.278350i
$641$	8.06211	−	8.06211i	0.318434	−	0.318434i	−0.529731	−	0.848165i	$-0.677707\pi$
$641$	8.06211	−	8.06211i	0.318434	−	0.318434i	0.848165	+	0.529731i	$0.177707\pi$
$642$	−3.88784			−0.153441
$643$	25.9274	−	25.9274i	1.02248	−	1.02248i	0.0227356	−	0.999742i	$-0.492762\pi$
$643$	25.9274	−	25.9274i	1.02248	−	1.02248i	0.999742	−	0.0227356i	$-0.00723759\pi$
$644$		−	2.15477i		−	0.0849097i
$645$	−1.13651			−0.0447501
$646$	−0.802624	−	0.120402i	−0.0315788	−	0.00473714i
$647$	28.7765			1.13132			0.565660	−	0.824639i	$-0.308621\pi$
$647$	28.7765			1.13132			0.565660	+	0.824639i	$0.308621\pi$
$648$		−	2.65935i		−	0.104469i
$649$	−1.32684	+	1.32684i	−0.0520829	+	0.0520829i
$650$	−1.84337			−0.0723029
$651$	0.0833265	−	0.0833265i	0.00326582	−	0.00326582i
$652$	−18.9482	−	18.9482i	−0.742068	−	0.742068i
$653$	−19.8610	−	19.8610i	−0.777219	−	0.777219i	0.202138	−	0.979357i	$-0.435211\pi$
$653$	−19.8610	−	19.8610i	−0.777219	−	0.777219i	−0.979357	+	0.202138i	$0.935211\pi$
$654$			1.21792i			0.0476244i
$655$			25.1522i			0.982780i
$656$	−13.4857	−	13.4857i	−0.526528	−	0.526528i
$657$	17.3322	+	17.3322i	0.676192	+	0.676192i
$658$	−1.99893	+	1.99893i	−0.0779265	+	0.0779265i
$659$	6.72228			0.261863			0.130931	−	0.991391i	$-0.458203\pi$
$659$	6.72228			0.261863			0.130931	+	0.991391i	$0.458203\pi$
$660$	0.644204	−	0.644204i	0.0250756	−	0.0250756i
$661$		−	10.7764i		−	0.419154i	−0.977792	−	0.209577i	$-0.932791\pi$
$661$		−	10.7764i		−	0.419154i	0.977792	−	0.209577i	$-0.0672088\pi$
$662$	−6.82807			−0.265380
$663$	6.07793	−	4.49229i	0.236047	−	0.174466i
$664$	−11.7106			−0.454459
$665$			0.759971i			0.0294704i
$666$	−4.06238	+	4.06238i	−0.157414	+	0.157414i
$667$	3.84517			0.148886
$668$	−28.4986	+	28.4986i	−1.10264	+	1.10264i
$669$	−9.40628	−	9.40628i	−0.363668	−	0.363668i
$670$	1.76437	+	1.76437i	0.0681637	+	0.0681637i
$671$		−	0.136998i		−	0.00528875i
$672$		−	2.15342i		−	0.0830700i
$673$	−4.55977	−	4.55977i	−0.175766	−	0.175766i	0.613741	−	0.789507i	$-0.289664\pi$
$673$	−4.55977	−	4.55977i	−0.175766	−	0.175766i	−0.789507	+	0.613741i	$0.789664\pi$
$674$	−3.38400	−	3.38400i	−0.130347	−	0.130347i
$675$	−10.9650	+	10.9650i	−0.422045	+	0.422045i
$676$	−16.8286			−0.647253
$677$	−3.64606	+	3.64606i	−0.140130	+	0.140130i	−0.773692	−	0.633562i	$-0.781592\pi$
$677$	−3.64606	+	3.64606i	−0.140130	+	0.140130i	0.633562	+	0.773692i	$0.281592\pi$
$678$		−	4.30108i		−	0.165182i
$679$	−13.2126			−0.507053
$680$	−3.28004	−	4.43779i	−0.125784	−	0.170182i
$681$	−11.0948			−0.425154
$682$			0.0183493i			0.000702631i
$683$	11.2185	−	11.2185i	0.429263	−	0.429263i	−0.459114	−	0.888377i	$-0.651833\pi$
$683$	11.2185	−	11.2185i	0.429263	−	0.429263i	0.888377	+	0.459114i	$0.151833\pi$
$684$	−3.16672			−0.121082
$685$	−18.3551	+	18.3551i	−0.701313	+	0.701313i
$686$	−2.00649	−	2.00649i	−0.0766082	−	0.0766082i
$687$	−14.0405	−	14.0405i	−0.535678	−	0.535678i
$688$			3.58170i			0.136551i
$689$			13.7229i			0.522800i
$690$	−0.298105	−	0.298105i	−0.0113486	−	0.0113486i
$691$	−29.0329	−	29.0329i	−1.10446	−	1.10446i	−0.993865	−	0.110598i	$-0.964723\pi$
$691$	−29.0329	−	29.0329i	−1.10446	−	1.10446i	−0.110598	−	0.993865i	$-0.535277\pi$
$692$	−3.91361	+	3.91361i	−0.148773	+	0.148773i
$693$	−0.735718			−0.0279476
$694$	1.65741	−	1.65741i	0.0629143	−	0.0629143i
$695$		−	13.5543i		−	0.514143i
$696$	2.54660			0.0965288
$697$	−13.0494	−	17.6554i	−0.494281	−	0.668746i
$698$	0.523329			0.0198083
$699$		−	13.5866i		−	0.513892i
$700$	3.66070	−	3.66070i	0.138362	−	0.138362i
$701$	−44.5963			−1.68438			−0.842190	−	0.539181i	$-0.818734\pi$
$701$	−44.5963			−1.68438			−0.842190	+	0.539181i	$0.818734\pi$
$702$	−1.79521	+	1.79521i	−0.0677559	+	0.0677559i
$703$	5.11847	+	5.11847i	0.193047	+	0.193047i
$704$	−1.86733	−	1.86733i	−0.0703776	−	0.0703776i
$705$		−	15.1273i		−	0.569725i
$706$			5.23829i			0.197146i
$707$	2.01969	+	2.01969i	0.0759581	+	0.0759581i
$708$	−5.46104	−	5.46104i	−0.205238	−	0.205238i
$709$	−9.61998	+	9.61998i	−0.361286	+	0.361286i	−0.864286	−	0.503000i	$-0.832229\pi$
$709$	−9.61998	+	9.61998i	−0.361286	+	0.361286i	0.503000	+	0.864286i	$0.332229\pi$
$710$	1.63394			0.0613206
$711$	0.527026	−	0.527026i	0.0197650	−	0.0197650i
$712$		−	3.79142i		−	0.142090i
$713$	−0.232235			−0.00869728
$714$	0.115131	−	0.767489i	0.00430867	−	0.0287225i
$715$	1.10198			0.0412118
$716$			0.769099i			0.0287426i
$717$	−2.97828	+	2.97828i	−0.111226	+	0.111226i
$718$	2.18578			0.0815724
$719$	−0.179642	+	0.179642i	−0.00669950	+	0.00669950i	−0.710449	−	0.703749i	$-0.751508\pi$
$719$	−0.179642	+	0.179642i	−0.00669950	+	0.00669950i	0.703749	+	0.710449i	$0.251508\pi$
$720$	−7.19259	−	7.19259i	−0.268052	−	0.268052i
$721$	2.78679	+	2.78679i	0.103785	+	0.103785i
$722$			4.90060i			0.182382i
$723$			3.42331i			0.127314i
$724$	−22.9018	−	22.9018i	−0.851138	−	0.851138i
$725$	6.53250	+	6.53250i	0.242611	+	0.242611i
$726$	1.80218	−	1.80218i	0.0668850	−	0.0668850i
$727$	−4.80242			−0.178112			−0.0890560	−	0.996027i	$-0.528385\pi$
$727$	−4.80242			−0.178112			−0.0890560	+	0.996027i	$0.528385\pi$
$728$	1.22058	−	1.22058i	0.0452378	−	0.0452378i
$729$			6.64417i			0.246080i
$730$	−3.76994			−0.139532
$731$	−0.611664	+	4.07748i	−0.0226232	+	0.150811i
$732$	0.563860			0.0208409
$733$		−	26.3751i		−	0.974188i	−0.873350	−	0.487094i	$-0.838057\pi$
$733$		−	26.3751i		−	0.974188i	0.873350	−	0.487094i	$-0.161943\pi$
$734$	−0.533165	+	0.533165i	−0.0196795	+	0.0196795i
$735$	7.22888			0.266641
$736$	−3.00085	+	3.00085i	−0.110613	+	0.110613i
$737$	2.15211	+	2.15211i	0.0792741	+	0.0792741i
$738$	2.21467	+	2.21467i	0.0815232	+	0.0815232i
$739$		−	20.7945i		−	0.764936i	−0.923969	−	0.382468i	$-0.875074\pi$
$739$		−	20.7945i		−	0.764936i	0.923969	−	0.382468i	$-0.124926\pi$
$740$			24.1671i			0.888402i
$741$	0.960608	+	0.960608i	0.0352888	+	0.0352888i
$742$	0.996399	+	0.996399i	0.0365789	+	0.0365789i
$743$	−21.0484	+	21.0484i	−0.772190	+	0.772190i	−0.978489	−	0.206299i	$-0.933858\pi$
$743$	−21.0484	+	21.0484i	−0.772190	+	0.772190i	0.206299	+	0.978489i	$0.433858\pi$
$744$	−0.153806			−0.00563882
$745$	8.31448	−	8.31448i	0.304619	−	0.304619i
$746$		−	2.01000i		−	0.0735914i
$747$	−24.8485			−0.909161
$748$	−1.96452	−	2.65793i	−0.0718298	−	0.0971835i
$749$	13.2072			0.482581
$750$		−	2.52220i		−	0.0920978i
$751$	−9.79500	+	9.79500i	−0.357425	+	0.357425i	−0.862863	−	0.505438i	$-0.831331\pi$
$751$	−9.79500	+	9.79500i	−0.357425	+	0.357425i	0.505438	+	0.862863i	$0.331331\pi$
$752$	−47.6734			−1.73847
$753$	5.62676	−	5.62676i	0.205050	−	0.205050i
$754$	1.06951	+	1.06951i	0.0389492	+	0.0389492i
$755$	22.1701	+	22.1701i	0.806854	+	0.806854i
$756$		−	7.13013i		−	0.259320i
$757$			31.5690i			1.14739i	0.819068	+	0.573697i	$0.194491\pi$
$757$			31.5690i			1.14739i	−0.819068	+	0.573697i	$0.805509\pi$
$758$	−4.48031	−	4.48031i	−0.162732	−	0.162732i
$759$	−0.363616	−	0.363616i	−0.0131984	−	0.0131984i
$760$	0.701388	−	0.701388i	0.0254420	−	0.0254420i
$761$	11.9242			0.432253			0.216127	−	0.976365i	$-0.430658\pi$
$761$	11.9242			0.432253			0.216127	+	0.976365i	$0.430658\pi$
$762$	−2.38518	+	2.38518i	−0.0864058	+	0.0864058i
$763$		−	4.13734i		−	0.149782i
$764$	31.9109			1.15450
$765$	−6.95988	−	9.41650i	−0.251635	−	0.340454i
$766$	1.95061			0.0704782
$767$		−	9.34171i		−	0.337309i
$768$	6.67406	−	6.67406i	0.240829	−	0.240829i
$769$	−7.60797			−0.274351			−0.137175	−	0.990547i	$-0.543802\pi$
$769$	−7.60797			−0.274351			−0.137175	+	0.990547i	$0.543802\pi$
$770$	0.0800134	−	0.0800134i	0.00288348	−	0.00288348i
$771$	2.38203	+	2.38203i	0.0857866	+	0.0857866i
$772$	17.3891	+	17.3891i	0.625846	+	0.625846i
$773$			43.3130i			1.55786i	0.627110	+	0.778930i	$0.284237\pi$
$773$			43.3130i			1.55786i	−0.627110	+	0.778930i	$0.715763\pi$
$774$		−	0.588200i		−	0.0211424i
$775$	−0.394541	−	0.394541i	−0.0141723	−	0.0141723i
$776$	12.1941	+	12.1941i	0.437742	+	0.437742i
$777$	−4.89440	+	4.89440i	−0.175586	+	0.175586i
$778$	3.83119			0.137355
$779$	2.79041	−	2.79041i	0.0999770	−	0.0999770i
$780$			4.53557i			0.162399i
$781$	1.99301			0.0713156
$782$	−1.22995	+	0.909077i	−0.0439830	+	0.0325085i
$783$	12.7237			0.454707
$784$		−	22.7817i		−	0.813633i
$785$	14.2704	−	14.2704i	0.509331	−	0.509331i
$786$	4.61684			0.164677
$787$	−14.9762	+	14.9762i	−0.533845	+	0.533845i	−0.921714	−	0.387869i	$-0.873211\pi$
$787$	−14.9762	+	14.9762i	−0.533845	+	0.533845i	0.387869	+	0.921714i	$0.373211\pi$
$788$	−27.9226	−	27.9226i	−0.994701	−	0.994701i
$789$	6.33069	+	6.33069i	0.225378	+	0.225378i
$790$			0.114634i			0.00407849i
$791$			14.6110i			0.519508i
$792$	0.679004	+	0.679004i	0.0241274	+	0.0241274i
$793$	0.482272	+	0.482272i	0.0171260	+	0.0171260i
$794$	1.96306	−	1.96306i	0.0696665	−	0.0696665i
$795$	−7.54041			−0.267431
$796$	5.66084	−	5.66084i	0.200643	−	0.200643i
$797$		−	1.47633i		−	0.0522943i	−0.999658	−	0.0261472i	$-0.991676\pi$
$797$		−	1.47633i		−	0.0522943i	0.999658	−	0.0261472i	$-0.00832385\pi$
$798$	0.139497			0.00493814
$799$	−54.2723	−	8.14140i	−1.92002	−	0.288022i
$800$	−10.1962			−0.360490
$801$		−	8.04497i		−	0.284255i
$802$	−0.791561	+	0.791561i	−0.0279510	+	0.0279510i
$803$	−4.59842			−0.162275
$804$	−8.85773	+	8.85773i	−0.312388	+	0.312388i
$805$	1.01268	+	1.01268i	0.0356922	+	0.0356922i
$806$	−0.0645948	−	0.0645948i	−0.00227526	−	0.00227526i
$807$		−	22.9614i		−	0.808279i
$808$		−	3.72799i		−	0.131150i
$809$	21.7768	+	21.7768i	0.765630	+	0.765630i	0.977334	−	0.211704i	$-0.0679012\pi$
$809$	21.7768	+	21.7768i	0.765630	+	0.765630i	−0.211704	+	0.977334i	$0.567901\pi$
$810$	0.613689	+	0.613689i	0.0215628	+	0.0215628i
$811$	18.3181	−	18.3181i	0.643236	−	0.643236i	−0.308114	−	0.951349i	$-0.599698\pi$
$811$	18.3181	−	18.3181i	0.643236	−	0.643236i	0.951349	+	0.308114i	$0.0996978\pi$
$812$	−4.24783			−0.149069
$813$	−5.99210	+	5.99210i	−0.210152	+	0.210152i
$814$		−	1.07779i		−	0.0377766i
$815$	17.8102			0.623864
$816$	10.5250	−	7.77917i	0.368448	−	0.272326i
$817$	−0.741114			−0.0259283
$818$		−	1.56523i		−	0.0547270i
$819$	2.58994	−	2.58994i	0.0904998	−	0.0904998i
$820$	13.1751			0.460095
$821$	−28.2197	+	28.2197i	−0.984874	+	0.984874i	−0.999887	−	0.0150130i	$-0.995221\pi$
$821$	−28.2197	+	28.2197i	−0.984874	+	0.984874i	0.0150130	+	0.999887i	$0.495221\pi$
$822$	3.36919	+	3.36919i	0.117514	+	0.117514i
$823$	24.1603	+	24.1603i	0.842176	+	0.842176i	0.989142	−	0.146966i	$-0.0469508\pi$
$823$	24.1603	+	24.1603i	0.842176	+	0.842176i	−0.146966	+	0.989142i	$0.546951\pi$
$824$		−	5.14393i		−	0.179197i
$825$		−	1.23548i		−	0.0430140i
$826$	−0.678288	−	0.678288i	−0.0236007	−	0.0236007i
$827$	−11.1126	−	11.1126i	−0.386422	−	0.386422i	0.486987	−	0.873409i	$-0.338096\pi$
$827$	−11.1126	−	11.1126i	−0.386422	−	0.386422i	−0.873409	+	0.486987i	$0.838096\pi$
$828$	−4.21972	+	4.21972i	−0.146645	+	0.146645i
$829$	−41.7540			−1.45018			−0.725089	−	0.688655i	$-0.758201\pi$
$829$	−41.7540			−1.45018			−0.725089	+	0.688655i	$0.758201\pi$
$830$	2.70242	−	2.70242i	0.0938022	−	0.0938022i
$831$			8.77583i			0.304430i
$832$	13.1471			0.455793
$833$	3.89054	−	25.9352i	0.134799	−	0.898601i
$834$	−2.48796			−0.0861511
$835$		−	26.7870i		−	0.927004i
$836$	0.420082	−	0.420082i	0.0145289	−	0.0145289i
$837$	−0.768468			−0.0265621
$838$	3.37624	−	3.37624i	0.116630	−	0.116630i
$839$	−28.9455	−	28.9455i	−0.999309	−	0.999309i	0.000690939	−	1.00000i	$-0.499780\pi$
$839$	−28.9455	−	28.9455i	−0.999309	−	0.999309i	−1.00000		0.000690939i	$0.999780\pi$
$840$	0.670684	+	0.670684i	0.0231408	+	0.0231408i
$841$			21.4198i			0.738613i
$842$			7.90813i			0.272532i
$843$	10.2110	+	10.2110i	0.351686	+	0.351686i
$844$	10.1374	+	10.1374i	0.348943	+	0.348943i
$845$	7.90895	−	7.90895i	0.272076	−	0.272076i
$846$	7.82909			0.269170
$847$	−6.12210	+	6.12210i	−0.210358	+	0.210358i
$848$			23.7635i			0.816043i
$849$	21.2950			0.730843
$850$	−3.63397	−	0.545132i	−0.124644	−	0.0186979i
$851$	13.6409			0.467606
$852$			8.20290i			0.281027i
$853$	32.4345	−	32.4345i	1.11054	−	1.11054i	0.117458	−	0.993078i	$-0.462526\pi$
$853$	32.4345	−	32.4345i	1.11054	−	1.11054i	0.993078	−	0.117458i	$-0.0374744\pi$
$854$	0.0700343			0.00239652
$855$	1.48827	−	1.48827i	0.0508976	−	0.0508976i
$856$	−12.1891	−	12.1891i	−0.416616	−	0.416616i
$857$	16.8001	+	16.8001i	0.573879	+	0.573879i	0.933210	−	0.359331i	$-0.116995\pi$
$857$	16.8001	+	16.8001i	0.573879	+	0.573879i	−0.359331	+	0.933210i	$0.616995\pi$
$858$		−	0.202275i		−	0.00690555i
$859$			26.4090i			0.901062i	0.892761	+	0.450531i	$0.148765\pi$
$859$			26.4090i			0.901062i	−0.892761	+	0.450531i	$0.851235\pi$
$860$	−1.74961	−	1.74961i	−0.0596611	−	0.0596611i
$861$	2.66826	+	2.66826i	0.0909341	+	0.0909341i
$862$	1.50443	−	1.50443i	0.0512411	−	0.0512411i
$863$	39.6027			1.34809			0.674046	−	0.738689i	$-0.264555\pi$
$863$	39.6027			1.34809			0.674046	+	0.738689i	$0.264555\pi$
$864$	−9.92982	+	9.92982i	−0.337819	+	0.337819i
$865$		−	3.67856i		−	0.125075i
$866$	−8.48198			−0.288229
$867$	13.3103	−	7.05857i	0.452043	−	0.239722i
$868$	0.256555			0.00870803
$869$			0.139826i			0.00474326i
$870$	−0.587672	+	0.587672i	−0.0199239	+	0.0199239i
$871$	−15.1521			−0.513410
$872$	−3.81841	+	3.81841i	−0.129308	+	0.129308i
$873$	25.8745	+	25.8745i	0.875719	+	0.875719i
$874$	−0.194393	−	0.194393i	−0.00657543	−	0.00657543i
$875$			8.56807i			0.289654i
$876$		−	18.9263i		−	0.639460i
$877$	14.5406	+	14.5406i	0.491002	+	0.491002i	0.908622	−	0.417620i	$-0.137136\pi$
$877$	14.5406	+	14.5406i	0.491002	+	0.491002i	−0.417620	+	0.908622i	$0.637136\pi$
$878$	6.26452	+	6.26452i	0.211417	+	0.211417i
$879$	−4.66085	+	4.66085i	−0.157207	+	0.157207i
$880$	1.90827			0.0643278
$881$	−0.895033	+	0.895033i	−0.0301544	+	0.0301544i	−0.722023	−	0.691869i	$-0.756788\pi$
$881$	−0.895033	+	0.895033i	−0.0301544	+	0.0301544i	0.691869	+	0.722023i	$0.256788\pi$
$882$			3.74130i			0.125976i
$883$	−44.8296			−1.50864			−0.754318	−	0.656509i	$-0.772032\pi$
$883$	−44.8296			−1.50864			−0.754318	+	0.656509i	$0.772032\pi$
$884$	16.2723	+	2.44102i	0.547298	+	0.0821003i
$885$	5.13306			0.172546
$886$			7.26938i			0.244220i
$887$	−24.3736	+	24.3736i	−0.818384	+	0.818384i	−0.985874	−	0.167490i	$-0.946434\pi$
$887$	−24.3736	+	24.3736i	−0.818384	+	0.818384i	0.167490	+	0.985874i	$0.446434\pi$
$888$	9.03422			0.303169
$889$	8.10258	−	8.10258i	0.271752	−	0.271752i
$890$	0.874935	+	0.874935i	0.0293279	+	0.0293279i
$891$	0.748553	+	0.748553i	0.0250775	+	0.0250775i
$892$		−	28.9610i		−	0.969687i
$893$		−	9.86441i		−	0.330100i
$894$	−1.52617	−	1.52617i	−0.0510428	−	0.0510428i
$895$	−0.361454	−	0.361454i	−0.0120821	−	0.0120821i
$896$	4.39089	−	4.39089i	0.146689	−	0.146689i
$897$	2.56007			0.0854781
$898$	−6.44673	+	6.44673i	−0.215130	+	0.215130i
$899$			0.457820i			0.0152691i
$900$	−14.3376			−0.477922
$901$	−4.05821	+	27.0529i	−0.135198	+	0.901262i
$902$	−0.587577			−0.0195642
$903$		−	0.708671i		−	0.0235831i
$904$	13.4847	−	13.4847i	0.448495	−	0.448495i
$905$	21.5264			0.715560
$906$	4.06945	−	4.06945i	0.135199	−	0.135199i
$907$	11.2288	+	11.2288i	0.372847	+	0.372847i	0.868513	−	0.495666i	$-0.165076\pi$
$907$	11.2288	+	11.2288i	0.372847	+	0.372847i	−0.495666	+	0.868513i	$0.665076\pi$
$908$	−17.0799	−	17.0799i	−0.566817	−	0.566817i
$909$		−	7.91038i		−	0.262371i
$910$			0.563340i			0.0186746i
$911$	1.70999	+	1.70999i	0.0566544	+	0.0566544i	0.734866	−	0.678212i	$-0.237245\pi$
$911$	1.70999	+	1.70999i	0.0566544	+	0.0566544i	−0.678212	+	0.734866i	$0.737245\pi$
$912$	1.66346	+	1.66346i	0.0550827	+	0.0550827i
$913$	3.29630	−	3.29630i	0.109091	−	0.109091i
$914$	−7.00899			−0.231837
$915$	−0.264998	+	0.264998i	−0.00876056	+	0.00876056i
$916$		−	43.2294i		−	1.42834i
$917$	−15.6837			−0.517920
$918$	−4.06992	+	3.00814i	−0.134327	+	0.0992834i
$919$	31.3165			1.03304			0.516518	−	0.856276i	$-0.327228\pi$
$919$	31.3165			1.03304			0.516518	+	0.856276i	$0.327228\pi$
$920$		−	1.86923i		−	0.0616267i
$921$	3.20877	−	3.20877i	0.105733	−	0.105733i
$922$	−2.27123			−0.0747989
$923$	−7.01598	+	7.01598i	−0.230934	+	0.230934i
$924$	0.401693	+	0.401693i	0.0132147	+	0.0132147i
$925$	23.1744	+	23.1744i	0.761970	+	0.761970i
$926$			3.38886i			0.111365i
$927$		−	10.9148i		−	0.358491i
$928$	5.91576	+	5.91576i	0.194194	+	0.194194i
$929$	18.1345	+	18.1345i	0.594974	+	0.594974i	0.938971	−	0.343997i	$-0.111781\pi$
$929$	18.1345	+	18.1345i	0.594974	+	0.594974i	−0.343997	+	0.938971i	$0.611781\pi$
$930$	0.0354934	−	0.0354934i	0.00116388	−	0.00116388i
$931$	4.71392			0.154492
$932$	20.9159	−	20.9159i	0.685123	−	0.685123i
$933$		−	8.24093i		−	0.269796i
$934$	−1.68401			−0.0551023
$935$	2.17242	+	0.325884i	0.0710456	+	0.0106576i
$936$	−4.78058			−0.156258
$937$			43.2354i			1.41244i	0.707992	+	0.706220i	$0.249601\pi$
$937$			43.2354i			1.41244i	−0.707992	+	0.706220i	$0.750399\pi$
$938$	−1.10017	+	1.10017i	−0.0359220	+	0.0359220i
$939$	18.7569			0.612107
$940$	23.2877	−	23.2877i	0.759561	−	0.759561i
$941$	−21.1526	−	21.1526i	−0.689556	−	0.689556i	0.272578	−	0.962134i	$-0.412124\pi$
$941$	−21.1526	−	21.1526i	−0.689556	−	0.689556i	−0.962134	+	0.272578i	$0.912124\pi$
$942$	−2.61941	−	2.61941i	−0.0853449	−	0.0853449i
$943$		−	7.43658i		−	0.242168i
$944$		−	16.1768i		−	0.526509i
$945$	3.35096	+	3.35096i	0.109007	+	0.109007i
$946$	0.0780280	+	0.0780280i	0.00253691	+	0.00253691i
$947$	18.2064	−	18.2064i	0.591628	−	0.591628i	−0.346443	−	0.938071i	$-0.612611\pi$
$947$	18.2064	−	18.2064i	0.591628	−	0.591628i	0.938071	+	0.346443i	$0.112611\pi$
$948$	−0.575499			−0.0186913
$949$	16.1878	−	16.1878i	0.525477	−	0.525477i
$950$		−	0.660501i		−	0.0214295i
$951$	11.5834			0.375617
$952$	2.76718	−	2.04527i	0.0896849	−	0.0662875i
$953$	−41.3291			−1.33878			−0.669391	−	0.742910i	$-0.733445\pi$
$953$	−41.3291			−1.33878			−0.669391	+	0.742910i	$0.733445\pi$
$954$		−	3.90253i		−	0.126349i
$955$	−14.9972	+	14.9972i	−0.485298	+	0.485298i
$956$	−9.16984			−0.296574
$957$	−0.716818	+	0.716818i	−0.0231714	+	0.0231714i
$958$	2.00533	+	2.00533i	0.0647891	+	0.0647891i
$959$	−11.4453	−	11.4453i	−0.369589	−	0.369589i
$960$			7.22403i			0.233155i
$961$			30.9723i			0.999108i
$962$	3.79414	+	3.79414i	0.122328	+	0.122328i
$963$	−25.8640	−	25.8640i	−0.833454	−	0.833454i
$964$	−5.27002	+	5.27002i	−0.169736	+	0.169736i
$965$	−16.3447			−0.526155
$966$	0.185883	−	0.185883i	0.00598068	−	0.00598068i
$967$			46.6687i			1.50076i	0.661005	+	0.750382i	$0.270130\pi$
$967$			46.6687i			1.50076i	−0.661005	+	0.750382i	$0.729870\pi$
$968$	11.3003			0.363207
$969$	1.60964	+	2.17779i	0.0517091	+	0.0699608i
$970$	−5.62799			−0.180704
$971$			58.8985i			1.89014i	0.326865	+	0.945071i	$0.394008\pi$
$971$			58.8985i			1.89014i	−0.326865	+	0.945071i	$0.605992\pi$
$972$	−21.9962	+	21.9962i	−0.705528	+	0.705528i
$973$	8.45175			0.270951
$974$	3.22820	−	3.22820i	0.103438	−	0.103438i
$975$	4.34926	+	4.34926i	0.139288	+	0.139288i
$976$	0.835138	+	0.835138i	0.0267321	+	0.0267321i
$977$			1.71491i			0.0548650i	0.999624	+	0.0274325i	$0.00873313\pi$
$977$			1.71491i			0.0548650i	−0.999624	+	0.0274325i	$0.991267\pi$
$978$		−	3.26916i		−	0.104536i
$979$	1.06721	+	1.06721i	0.0341082	+	0.0341082i
$980$	11.1285	+	11.1285i	0.355487	+	0.355487i
$981$	−8.10223	+	8.10223i	−0.258684	+	0.258684i
$982$	2.99448			0.0955578
$983$	38.2437	−	38.2437i	1.21979	−	1.21979i	0.252079	−	0.967707i	$-0.418886\pi$
$983$	38.2437	−	38.2437i	1.21979	−	1.21979i	0.967707	−	0.252079i	$-0.0811143\pi$
$984$		−	4.92515i		−	0.157008i
$985$	26.2456			0.836255
$986$	1.79212	+	2.42468i	0.0570727	+	0.0772177i
$987$	9.43258			0.300242
$988$			2.95762i			0.0940945i
$989$	−0.987551	+	0.987551i	−0.0314023	+	0.0314023i
$990$	−0.313383			−0.00995998
$991$	−2.21731	+	2.21731i	−0.0704350	+	0.0704350i	−0.741447	−	0.671012i	$-0.765860\pi$
$991$	−2.21731	+	2.21731i	−0.0704350	+	0.0704350i	0.671012	+	0.741447i	$0.265860\pi$
$992$	−0.357292	−	0.357292i	−0.0113440	−	0.0113440i
$993$	16.1102	+	16.1102i	0.511241	+	0.511241i
$994$			1.01884i			0.0323157i
$995$			5.32087i			0.168683i
$996$	13.5670	+	13.5670i	0.429887	+	0.429887i
$997$	−12.4953	−	12.4953i	−0.395730	−	0.395730i	0.480994	−	0.876724i	$-0.340276\pi$
$997$	−12.4953	−	12.4953i	−0.395730	−	0.395730i	−0.876724	+	0.480994i	$0.840276\pi$
$998$	2.88669	−	2.88669i	0.0913764	−	0.0913764i
$999$	45.1379			1.42810

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.c.259.16	✓	56
17.13	even	4	inner	731.2.f.c.302.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.c.259.16	✓	56	1.1	even	1	trivial
731.2.f.c.302.13	yes	56	17.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.265604i q^{2} +(0.626669 - 0.626669i) q^{3} +1.92945 q^{4} +(-0.906788 + 0.906788i) q^{5} +(0.166446 + 0.166446i) q^{6} +(-0.565427 - 0.565427i) q^{7} +1.04368i q^{8} +2.21457i q^{9} +O(q^{10})\)	\(q+0.265604i q^{2} +(0.626669 - 0.626669i) q^{3} +1.92945 q^{4} +(-0.906788 + 0.906788i) q^{5} +(0.166446 + 0.166446i) q^{6} +(-0.565427 - 0.565427i) q^{7} +1.04368i q^{8} +2.21457i q^{9} +(-0.240847 - 0.240847i) q^{10} +(-0.293775 - 0.293775i) q^{11} +(1.20913 - 1.20913i) q^{12} +2.06835 q^{13} +(0.150180 - 0.150180i) q^{14} +1.13651i q^{15} +3.58170 q^{16} +(4.07748 + 0.611664i) q^{17} -0.588200 q^{18} +0.741114i q^{19} +(-1.74961 + 1.74961i) q^{20} -0.708671 q^{21} +(0.0780280 - 0.0780280i) q^{22} +(0.987551 + 0.987551i) q^{23} +(0.654042 + 0.654042i) q^{24} +3.35547i q^{25} +0.549362i q^{26} +(3.26781 + 3.26781i) q^{27} +(-1.09097 - 1.09097i) q^{28} +(1.94682 - 1.94682i) q^{29} -0.301862 q^{30} +(-0.117581 + 0.117581i) q^{31} +3.03868i q^{32} -0.368200 q^{33} +(-0.162461 + 1.08300i) q^{34} +1.02544 q^{35} +4.27292i q^{36} +(6.90645 - 6.90645i) q^{37} -0.196843 q^{38} +(1.29617 - 1.29617i) q^{39} +(-0.946397 - 0.946397i) q^{40} +(-3.76516 - 3.76516i) q^{41} -0.188226i q^{42} +1.00000i q^{43} +(-0.566826 - 0.566826i) q^{44} +(-2.00815 - 2.00815i) q^{45} +(-0.262298 + 0.262298i) q^{46} -13.3103 q^{47} +(2.24454 - 2.24454i) q^{48} -6.36059i q^{49} -0.891228 q^{50} +(2.93854 - 2.17192i) q^{51} +3.99078 q^{52} +6.63470i q^{53} +(-0.867945 + 0.867945i) q^{54} +0.532784 q^{55} +(0.590125 - 0.590125i) q^{56} +(0.464433 + 0.464433i) q^{57} +(0.517084 + 0.517084i) q^{58} -4.51651i q^{59} +2.19285i q^{60} +(0.233168 + 0.233168i) q^{61} +(-0.0312302 - 0.0312302i) q^{62} +(1.25218 - 1.25218i) q^{63} +6.35632 q^{64} +(-1.87555 + 1.87555i) q^{65} -0.0977954i q^{66} -7.32571 q^{67} +(7.86732 + 1.18018i) q^{68} +1.23773 q^{69} +0.272363i q^{70} +(-3.39207 + 3.39207i) q^{71} -2.31131 q^{72} +(7.82642 - 7.82642i) q^{73} +(1.83438 + 1.83438i) q^{74} +(2.10277 + 2.10277i) q^{75} +1.42994i q^{76} +0.332217i q^{77} +(0.344268 + 0.344268i) q^{78} +(-0.237981 - 0.237981i) q^{79} +(-3.24784 + 3.24784i) q^{80} -2.54805 q^{81} +(1.00004 - 1.00004i) q^{82} +11.2205i q^{83} -1.36735 q^{84} +(-4.25206 + 3.14276i) q^{85} -0.265604 q^{86} -2.44002i q^{87} +(0.306607 - 0.306607i) q^{88} -3.63274 q^{89} +(0.533373 - 0.533373i) q^{90} +(-1.16950 - 1.16950i) q^{91} +(1.90543 + 1.90543i) q^{92} +0.147369i q^{93} -3.53526i q^{94} +(-0.672033 - 0.672033i) q^{95} +(1.90424 + 1.90424i) q^{96} +(11.6837 - 11.6837i) q^{97} +1.68940 q^{98} +(0.650586 - 0.650586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7	\( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) \) 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7 + 4 * q^10 - 6 * q^11 - 14 * q^12 + 16 * q^13 + 6 * q^14 + 44 * q^16 + 8 * q^17 - 16 * q^18 + 12 * q^20 + 28 * q^21 + 14 * q^22 + 6 * q^23 + 62 * q^24 - 4 * q^27 + 34 * q^28 - 12 * q^29 - 96 * q^30 + 14 * q^31 - 44 * q^33 + 6 * q^34 - 32 * q^35 + 8 * q^37 + 72 * q^38 - 32 * q^39 - 84 * q^40 + 24 * q^41 + 4 * q^44 + 48 * q^45 - 4 * q^46 - 8 * q^47 + 38 * q^48 - 64 * q^50 + 28 * q^51 - 48 * q^52 + 34 * q^54 + 56 * q^55 - 26 * q^56 - 102 * q^57 + 76 * q^58 - 40 * q^61 + 34 * q^62 + 4 * q^63 - 204 * q^64 + 18 * q^65 - 20 * q^67 + 30 * q^68 - 16 * q^69 - 26 * q^71 + 144 * q^72 + 8 * q^73 - 80 * q^74 + 142 * q^75 - 32 * q^78 - 22 * q^79 - 32 * q^80 - 32 * q^81 + 100 * q^82 - 20 * q^84 - 2 * q^85 + 12 * q^86 + 34 * q^88 + 68 * q^89 - 10 * q^90 - 28 * q^91 + 68 * q^92 - 62 * q^95 + 62 * q^96 - 2 * q^97 - 32 * q^98 + 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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