LMFDB - Embedded newform 208.2.p.a.181.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(77,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("208.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$208 = 2^{4} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	208.p (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:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.959512576.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} + 7x^{4} + 81$ x^8 + 7*x^4 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2^{2}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			181.4
Root			$0.819051 - 1.52616i$ of defining polynomial
Character	$\chi$	$=$	208.181
Dual form			208.2.p.a.77.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(2.15831 - 2.15831i) q^{3} -2.00000 q^{4} +(0.707107 - 0.707107i) q^{5} +(3.05231 + 3.05231i) q^{6} +0.223888 q^{7} -2.82843i q^{8} -6.31662i q^{9} +(1.00000 + 1.00000i) q^{10} +(-1.41421 + 1.41421i) q^{11} +(-4.31662 + 4.31662i) q^{12} +(1.34521 + 3.34521i) q^{13} +0.316625i q^{14} -3.05231i q^{15} +4.00000 q^{16} +3.00000 q^{17} +8.93306 q^{18} +(-4.46653 - 4.46653i) q^{19} +(-1.41421 + 1.41421i) q^{20} +(0.483219 - 0.483219i) q^{21} +(-2.00000 - 2.00000i) q^{22} +6.31662i q^{23} +(-6.10463 - 6.10463i) q^{24} +4.00000i q^{25} +(-4.73084 + 1.90241i) q^{26} +(-7.15831 - 7.15831i) q^{27} -0.447775 q^{28} +(0.316625 - 0.316625i) q^{29} +4.31662 q^{30} +4.24264i q^{31} +5.65685i q^{32} +6.10463i q^{33} +4.24264i q^{34} +(0.158312 - 0.158312i) q^{35} +12.6332i q^{36} +(-6.58785 + 6.58785i) q^{37} +(6.31662 - 6.31662i) q^{38} +(10.1234 + 4.31662i) q^{39} +(-2.00000 - 2.00000i) q^{40} +(0.683375 + 0.683375i) q^{42} +(-5.47494 - 5.47494i) q^{43} +(2.82843 - 2.82843i) q^{44} +(-4.46653 - 4.46653i) q^{45} -8.93306 q^{46} -10.5712i q^{47} +(8.63325 - 8.63325i) q^{48} -6.94987 q^{49} -5.65685 q^{50} +(6.47494 - 6.47494i) q^{51} +(-2.69042 - 6.69042i) q^{52} +(3.63325 + 3.63325i) q^{53} +(10.1234 - 10.1234i) q^{54} +2.00000i q^{55} -0.633250i q^{56} -19.2803 q^{57} +(0.447775 + 0.447775i) q^{58} +(7.74273 - 7.74273i) q^{59} +6.10463i q^{60} +(4.00000 - 4.00000i) q^{61} -6.00000 q^{62} -1.41421i q^{63} -8.00000 q^{64} +(3.31662 + 1.41421i) q^{65} -8.63325 q^{66} +(4.69042 + 4.69042i) q^{67} -6.00000 q^{68} +(13.6332 + 13.6332i) q^{69} +(0.223888 + 0.223888i) q^{70} -0.671663 q^{71} -17.8661 q^{72} +3.79487 q^{73} +(-9.31662 - 9.31662i) q^{74} +(8.63325 + 8.63325i) q^{75} +(8.93306 + 8.93306i) q^{76} +(-0.316625 + 0.316625i) q^{77} +(-6.10463 + 14.3166i) q^{78} -10.9499 q^{79} +(2.82843 - 2.82843i) q^{80} -11.9499 q^{81} +(-11.9854 - 11.9854i) q^{83} +(-0.966438 + 0.966438i) q^{84} +(2.12132 - 2.12132i) q^{85} +(7.74273 - 7.74273i) q^{86} -1.36675i q^{87} +(4.00000 + 4.00000i) q^{88} +14.0712 q^{89} +(6.31662 - 6.31662i) q^{90} +(0.301175 + 0.748950i) q^{91} -12.6332i q^{92} +(9.15694 + 9.15694i) q^{93} +14.9499 q^{94} -6.31662 q^{95} +(12.2093 + 12.2093i) q^{96} +8.48528i q^{97} -9.82861i q^{98} +(8.93306 + 8.93306i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 4 q^{3} - 16 q^{4} + 8 q^{10} - 8 q^{12} - 8 q^{13} + 32 q^{16} + 24 q^{17} - 16 q^{22} - 44 q^{27} - 24 q^{29} + 8 q^{30} - 12 q^{35} + 24 q^{38} - 16 q^{40} + 32 q^{42} - 4 q^{43} + 16 q^{48} + 24 q^{49}+ \cdots - 24 q^{95}+O(q^{100})$ 8 * q + 4 * q^3 - 16 * q^4 + 8 * q^10 - 8 * q^12 - 8 * q^13 + 32 * q^16 + 24 * q^17 - 16 * q^22 - 44 * q^27 - 24 * q^29 + 8 * q^30 - 12 * q^35 + 24 * q^38 - 16 * q^40 + 32 * q^42 - 4 * q^43 + 16 * q^48 + 24 * q^49 + 12 * q^51 + 16 * q^52 - 24 * q^53 + 32 * q^61 - 48 * q^62 - 64 * q^64 - 16 * q^66 - 48 * q^68 + 56 * q^69 - 48 * q^74 + 16 * q^75 + 24 * q^77 - 8 * q^79 - 16 * q^81 + 32 * q^88 + 24 * q^90 + 44 * q^91 + 40 * q^94 - 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$ .

$n$	$53$	$79$	$145$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$			1.41421i			1.00000i
$2$			1.41421i			1.00000i
$3$	2.15831	−	2.15831i	1.24610	−	1.24610i	0.288675	−	0.957427i	$-0.406785\pi$
$3$	2.15831	−	2.15831i	1.24610	−	1.24610i	0.957427	−	0.288675i	$-0.0932147\pi$
$4$	−2.00000			−1.00000
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i	−0.531089	−	0.847316i	$-0.678217\pi$
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i	0.847316	+	0.531089i	$0.178217\pi$
$6$	3.05231	+	3.05231i	1.24610	+	1.24610i
$7$	0.223888			0.0846215			0.0423108	−	0.999104i	$-0.486528\pi$
$7$	0.223888			0.0846215			0.0423108	+	0.999104i	$0.486528\pi$
$8$		−	2.82843i		−	1.00000i
$9$		−	6.31662i		−	2.10554i
$10$	1.00000	+	1.00000i	0.316228	+	0.316228i
$11$	−1.41421	+	1.41421i	−0.426401	+	0.426401i	−0.887401	−	0.460999i	$-0.847491\pi$
$11$	−1.41421	+	1.41421i	−0.426401	+	0.426401i	0.460999	+	0.887401i	$0.347491\pi$
$12$	−4.31662	+	4.31662i	−1.24610	+	1.24610i
$13$	1.34521	+	3.34521i	0.373094	+	0.927794i
$13$	1.34521	+	3.34521i	0.373094	+	0.927794i
$14$			0.316625i			0.0846215i
$15$		−	3.05231i		−	0.788104i
$16$	4.00000			1.00000
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$	8.93306			2.10554
$19$	−4.46653	−	4.46653i	−1.02469	−	1.02469i	−0.999687	−	0.0250045i	$-0.992040\pi$
$19$	−4.46653	−	4.46653i	−1.02469	−	1.02469i	−0.0250045	−	0.999687i	$-0.507960\pi$
$20$	−1.41421	+	1.41421i	−0.316228	+	0.316228i
$21$	0.483219	−	0.483219i	0.105447	−	0.105447i
$22$	−2.00000	−	2.00000i	−0.426401	−	0.426401i
$23$			6.31662i			1.31711i	0.752534	+	0.658554i	$0.228831\pi$
$23$			6.31662i			1.31711i	−0.752534	+	0.658554i	$0.771169\pi$
$24$	−6.10463	−	6.10463i	−1.24610	−	1.24610i
$25$			4.00000i			0.800000i
$26$	−4.73084	+	1.90241i	−0.927794	+	0.373094i
$27$	−7.15831	−	7.15831i	−1.37762	−	1.37762i
$28$	−0.447775			−0.0846215
$29$	0.316625	−	0.316625i	0.0587957	−	0.0587957i	−0.677098	−	0.735893i	$-0.736762\pi$
$29$	0.316625	−	0.316625i	0.0587957	−	0.0587957i	0.735893	+	0.677098i	$0.236762\pi$
$30$	4.31662			0.788104
$31$			4.24264i			0.762001i	0.924575	+	0.381000i	$0.124420\pi$
$31$			4.24264i			0.762001i	−0.924575	+	0.381000i	$0.875580\pi$
$32$			5.65685i			1.00000i
$33$			6.10463i			1.06268i
$34$			4.24264i			0.727607i
$35$	0.158312	−	0.158312i	0.0267597	−	0.0267597i
$36$			12.6332i			2.10554i
$37$	−6.58785	+	6.58785i	−1.08304	+	1.08304i	−0.0868108	+	0.996225i	$0.527668\pi$
$37$	−6.58785	+	6.58785i	−1.08304	+	1.08304i	−0.996225	+	0.0868108i	$0.972332\pi$
$38$	6.31662	−	6.31662i	1.02469	−	1.02469i
$39$	10.1234	+	4.31662i	1.62104	+	0.691213i
$40$	−2.00000	−	2.00000i	−0.316228	−	0.316228i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	0.683375	+	0.683375i	0.105447	+	0.105447i
$43$	−5.47494	−	5.47494i	−0.834920	−	0.834920i	0.153265	−	0.988185i	$-0.451021\pi$
$43$	−5.47494	−	5.47494i	−0.834920	−	0.834920i	−0.988185	+	0.153265i	$0.951021\pi$
$44$	2.82843	−	2.82843i	0.426401	−	0.426401i
$45$	−4.46653	−	4.46653i	−0.665831	−	0.665831i
$46$	−8.93306			−1.31711
$47$		−	10.5712i		−	1.54196i	−0.636858	−	0.770981i	$-0.719766\pi$
$47$		−	10.5712i		−	1.54196i	0.636858	−	0.770981i	$-0.280234\pi$
$48$	8.63325	−	8.63325i	1.24610	−	1.24610i
$49$	−6.94987			−0.992839
$50$	−5.65685			−0.800000
$51$	6.47494	−	6.47494i	0.906673	−	0.906673i
$52$	−2.69042	−	6.69042i	−0.373094	−	0.927794i
$53$	3.63325	+	3.63325i	0.499065	+	0.499065i	0.911147	−	0.412082i	$-0.135198\pi$
$53$	3.63325	+	3.63325i	0.499065	+	0.499065i	−0.412082	+	0.911147i	$0.635198\pi$
$54$	10.1234	−	10.1234i	1.37762	−	1.37762i
$55$			2.00000i			0.269680i
$56$		−	0.633250i		−	0.0846215i
$57$	−19.2803			−2.55374
$58$	0.447775	+	0.447775i	0.0587957	+	0.0587957i
$59$	7.74273	−	7.74273i	1.00802	−	1.00802i	0.00805004	−	0.999968i	$-0.497438\pi$
$59$	7.74273	−	7.74273i	1.00802	−	1.00802i	0.999968	−	0.00805004i	$-0.00256244\pi$
$60$			6.10463i			0.788104i
$61$	4.00000	−	4.00000i	0.512148	−	0.512148i	−0.403036	−	0.915184i	$-0.632045\pi$
$61$	4.00000	−	4.00000i	0.512148	−	0.512148i	0.915184	+	0.403036i	$0.132045\pi$
$62$	−6.00000			−0.762001
$63$		−	1.41421i		−	0.178174i
$64$	−8.00000			−1.00000
$65$	3.31662	+	1.41421i	0.411377	+	0.175412i
$66$	−8.63325			−1.06268
$67$	4.69042	+	4.69042i	0.573025	+	0.573025i	0.932973	−	0.359947i	$-0.117205\pi$
$67$	4.69042	+	4.69042i	0.573025	+	0.573025i	−0.359947	+	0.932973i	$0.617205\pi$
$68$	−6.00000			−0.727607
$69$	13.6332	+	13.6332i	1.64125	+	1.64125i
$70$	0.223888	+	0.223888i	0.0267597	+	0.0267597i
$71$	−0.671663			−0.0797117			−0.0398558	−	0.999205i	$-0.512690\pi$
$71$	−0.671663			−0.0797117			−0.0398558	+	0.999205i	$0.512690\pi$
$72$	−17.8661			−2.10554
$73$	3.79487			0.444155			0.222078	−	0.975029i	$-0.428716\pi$
$73$	3.79487			0.444155			0.222078	+	0.975029i	$0.428716\pi$
$74$	−9.31662	−	9.31662i	−1.08304	−	1.08304i
$75$	8.63325	+	8.63325i	0.996882	+	0.996882i
$76$	8.93306	+	8.93306i	1.02469	+	1.02469i
$77$	−0.316625	+	0.316625i	−0.0360827	+	0.0360827i
$78$	−6.10463	+	14.3166i	−0.691213	+	1.62104i
$79$	−10.9499			−1.23196			−0.615979	−	0.787763i	$-0.711239\pi$
$79$	−10.9499			−1.23196			−0.615979	+	0.787763i	$0.711239\pi$
$80$	2.82843	−	2.82843i	0.316228	−	0.316228i
$81$	−11.9499			−1.32776
$82$		0			0
$83$	−11.9854	−	11.9854i	−1.31557	−	1.31557i	−0.917247	−	0.398318i	$-0.869594\pi$
$83$	−11.9854	−	11.9854i	−1.31557	−	1.31557i	−0.398318	−	0.917247i	$-0.630406\pi$
$84$	−0.966438	+	0.966438i	−0.105447	+	0.105447i
$85$	2.12132	−	2.12132i	0.230089	−	0.230089i
$86$	7.74273	−	7.74273i	0.834920	−	0.834920i
$87$		−	1.36675i		−	0.146531i
$88$	4.00000	+	4.00000i	0.426401	+	0.426401i
$89$	14.0712			1.49155			0.745775	−	0.666198i	$-0.232080\pi$
$89$	14.0712			1.49155			0.745775	+	0.666198i	$0.232080\pi$
$90$	6.31662	−	6.31662i	0.665831	−	0.665831i
$91$	0.301175	+	0.748950i	0.0315717	+	0.0785113i
$92$		−	12.6332i		−	1.31711i
$93$	9.15694	+	9.15694i	0.949531	+	0.949531i
$94$	14.9499			1.54196
$95$	−6.31662			−0.648072
$96$	12.2093	+	12.2093i	1.24610	+	1.24610i
$97$			8.48528i			0.861550i	0.902459	+	0.430775i	$0.141760\pi$
$97$			8.48528i			0.861550i	−0.902459	+	0.430775i	$0.858240\pi$
$98$		−	9.82861i		−	0.992839i
$99$	8.93306	+	8.93306i	0.897806	+	0.897806i
$100$		−	8.00000i		−	0.800000i
$101$	−6.31662	−	6.31662i	−0.628528	−	0.628528i	0.319170	−	0.947698i	$-0.396596\pi$
$101$	−6.31662	−	6.31662i	−0.628528	−	0.628528i	−0.947698	+	0.319170i	$0.896596\pi$
$102$	9.15694	+	9.15694i	0.906673	+	0.906673i
$103$			0.949874i			0.0935939i	0.998904	+	0.0467970i	$0.0149014\pi$
$103$			0.949874i			0.0935939i	−0.998904	+	0.0467970i	$0.985099\pi$
$104$	9.46168	−	3.80482i	0.927794	−	0.373094i
$105$		−	0.683375i		−	0.0666906i
$106$	−5.13819	+	5.13819i	−0.499065	+	0.499065i
$107$	9.63325	+	9.63325i	0.931281	+	0.931281i	0.997786	−	0.0665047i	$-0.0211847\pi$
$107$	9.63325	+	9.63325i	0.931281	+	0.931281i	−0.0665047	+	0.997786i	$0.521185\pi$
$108$	14.3166	+	14.3166i	1.37762	+	1.37762i
$109$	−2.34521	−	2.34521i	−0.224630	−	0.224630i	0.585815	−	0.810445i	$-0.300775\pi$
$109$	−2.34521	−	2.34521i	−0.224630	−	0.224630i	−0.810445	+	0.585815i	$0.800775\pi$
$110$	−2.82843			−0.269680
$111$			28.4373i			2.69915i
$112$	0.895550			0.0846215
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		−	27.2665i		−	2.55374i
$115$	4.46653	+	4.46653i	0.416506	+	0.416506i
$116$	−0.633250	+	0.633250i	−0.0587957	+	0.0587957i
$117$	21.1304	−	8.49717i	1.95351	−	0.785564i
$118$	10.9499	+	10.9499i	1.00802	+	1.00802i
$119$	0.671663			0.0615712
$120$	−8.63325			−0.788104
$121$			7.00000i			0.636364i
$122$	5.65685	+	5.65685i	0.512148	+	0.512148i
$123$		0			0
$124$		−	8.48528i		−	0.762001i
$125$	6.36396	+	6.36396i	0.569210	+	0.569210i
$126$	2.00000			0.178174
$127$	2.94987			0.261759			0.130880	−	0.991398i	$-0.458220\pi$
$127$	2.94987			0.261759			0.130880	+	0.991398i	$0.458220\pi$
$128$		−	11.3137i		−	1.00000i
$129$	−23.6332			−2.08079
$130$	−2.00000	+	4.69042i	−0.175412	+	0.411377i
$131$	2.84169	−	2.84169i	0.248279	−	0.248279i	−0.571985	−	0.820264i	$-0.693826\pi$
$131$	2.84169	−	2.84169i	0.248279	−	0.248279i	0.820264	+	0.571985i	$0.193826\pi$
$132$		−	12.2093i		−	1.06268i
$133$	−1.00000	−	1.00000i	−0.0867110	−	0.0867110i
$134$	−6.63325	+	6.63325i	−0.573025	+	0.573025i
$135$	−10.1234			−0.871282
$136$		−	8.48528i		−	0.727607i
$137$	14.0712			1.20219			0.601094	−	0.799178i	$-0.294732\pi$
$137$	14.0712			1.20219			0.601094	+	0.799178i	$0.294732\pi$
$138$	−19.2803	+	19.2803i	−1.64125	+	1.64125i
$139$	−2.47494	−	2.47494i	−0.209921	−	0.209921i	0.594313	−	0.804234i	$-0.297424\pi$
$139$	−2.47494	−	2.47494i	−0.209921	−	0.209921i	−0.804234	+	0.594313i	$0.797424\pi$
$140$	−0.316625	+	0.316625i	−0.0267597	+	0.0267597i
$141$	−22.8159	−	22.8159i	−1.92144	−	1.92144i
$142$		−	0.949874i		−	0.0797117i
$143$	−6.63325	−	2.82843i	−0.554700	−	0.236525i
$144$		−	25.2665i		−	2.10554i
$145$		−	0.447775i		−	0.0371857i
$146$			5.36675i			0.444155i
$147$	−15.0000	+	15.0000i	−1.23718	+	1.23718i
$148$	13.1757	−	13.1757i	1.08304	−	1.08304i
$149$	7.07107	−	7.07107i	0.579284	−	0.579284i	−0.355422	−	0.934706i	$-0.615663\pi$
$149$	7.07107	−	7.07107i	0.579284	−	0.579284i	0.934706	+	0.355422i	$0.115663\pi$
$150$	−12.2093	+	12.2093i	−0.996882	+	0.996882i
$151$	4.46653			0.363481			0.181740	−	0.983347i	$-0.441827\pi$
$151$	4.46653			0.363481			0.181740	+	0.983347i	$0.441827\pi$
$152$	−12.6332	+	12.6332i	−1.02469	+	1.02469i
$153$		−	18.9499i		−	1.53201i
$154$	−0.447775	−	0.447775i	−0.0360827	−	0.0360827i
$155$	3.00000	+	3.00000i	0.240966	+	0.240966i
$156$	−20.2468	−	8.63325i	−1.62104	−	0.691213i
$157$	7.94987	−	7.94987i	0.634469	−	0.634469i	−0.314717	−	0.949186i	$-0.601909\pi$
$157$	7.94987	−	7.94987i	0.634469	−	0.634469i	0.949186	+	0.314717i	$0.101909\pi$
$158$		−	15.4855i		−	1.23196i
$159$	15.6834			1.24377
$160$	4.00000	+	4.00000i	0.316228	+	0.316228i
$161$			1.41421i			0.111456i
$162$		−	16.8997i		−	1.32776i
$163$	−8.70917	−	8.70917i	−0.682155	−	0.682155i	0.278331	−	0.960485i	$-0.410219\pi$
$163$	−8.70917	−	8.70917i	−0.682155	−	0.682155i	−0.960485	+	0.278331i	$0.910219\pi$
$164$		0			0
$165$	4.31662	+	4.31662i	0.336049	+	0.336049i
$166$	16.9499	−	16.9499i	1.31557	−	1.31557i
$167$	−14.0712			−1.08887			−0.544433	−	0.838804i	$-0.683255\pi$
$167$	−14.0712			−1.08887			−0.544433	+	0.838804i	$0.683255\pi$
$168$	−1.36675	−	1.36675i	−0.105447	−	0.105447i
$169$	−9.38083	+	9.00000i	−0.721602	+	0.692308i
$170$	3.00000	+	3.00000i	0.230089	+	0.230089i
$171$	−28.2134	+	28.2134i	−2.15753	+	2.15753i
$172$	10.9499	+	10.9499i	0.834920	+	0.834920i
$173$	15.3166	−	15.3166i	1.16450	−	1.16450i	0.181022	−	0.983479i	$-0.442059\pi$
$173$	15.3166	−	15.3166i	1.16450	−	1.16450i	0.983479	−	0.181022i	$-0.0579407\pi$
$174$	1.93288			0.146531
$175$			0.895550i			0.0676972i
$176$	−5.65685	+	5.65685i	−0.426401	+	0.426401i
$177$		−	33.4225i		−	2.51219i
$178$			19.8997i			1.49155i
$179$	6.79156	−	6.79156i	0.507625	−	0.507625i	−0.406172	−	0.913797i	$-0.633136\pi$
$179$	6.79156	−	6.79156i	0.507625	−	0.507625i	0.913797	+	0.406172i	$0.133136\pi$
$180$	8.93306	+	8.93306i	0.665831	+	0.665831i
$181$	−17.9499	−	17.9499i	−1.33420	−	1.33420i	−0.901570	−	0.432634i	$-0.857584\pi$
$181$	−17.9499	−	17.9499i	−1.33420	−	1.33420i	−0.432634	−	0.901570i	$-0.642416\pi$
$182$	−1.05918	+	0.425926i	−0.0785113	+	0.0315717i
$183$		−	17.2665i		−	1.27638i
$184$	17.8661			1.31711
$185$			9.31662i			0.684972i
$186$	−12.9499	+	12.9499i	−0.949531	+	0.949531i
$187$	−4.24264	+	4.24264i	−0.310253	+	0.310253i
$188$			21.1423i			1.54196i
$189$	−1.60266	−	1.60266i	−0.116576	−	0.116576i
$190$		−	8.93306i		−	0.648072i
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$	−17.2665	+	17.2665i	−1.24610	+	1.24610i
$193$			12.7279i			0.916176i	0.888907	+	0.458088i	$0.151466\pi$
$193$			12.7279i			0.916176i	−0.888907	+	0.458088i	$0.848534\pi$
$194$	−12.0000			−0.861550
$195$	10.2106	−	4.10600i	0.731198	−	0.294037i
$196$	13.8997			0.992839
$197$	−2.86387	+	2.86387i	−0.204042	+	0.204042i	−0.801729	−	0.597687i	$-0.796087\pi$
$197$	−2.86387	+	2.86387i	−0.204042	+	0.204042i	0.597687	+	0.801729i	$0.296087\pi$
$198$	−12.6332	+	12.6332i	−0.897806	+	0.897806i
$199$			18.0000i			1.27599i	0.770042	+	0.637993i	$0.220235\pi$
$199$			18.0000i			1.27599i	−0.770042	+	0.637993i	$0.779765\pi$
$200$	11.3137			0.800000
$201$	20.2468			1.42810
$202$	8.93306	−	8.93306i	0.628528	−	0.628528i
$203$	0.0708883	−	0.0708883i	0.00497539	−	0.00497539i
$204$	−12.9499	+	12.9499i	−0.906673	+	0.906673i
$205$		0			0
$206$	−1.34333			−0.0935939
$207$	39.8997			2.77322
$208$	5.38083	+	13.3808i	0.373094	+	0.927794i
$209$	12.6332			0.873860
$210$	0.966438			0.0666906
$211$	6.52506	−	6.52506i	0.449204	−	0.449204i	−0.445886	−	0.895090i	$-0.647111\pi$
$211$	6.52506	−	6.52506i	0.449204	−	0.449204i	0.895090	+	0.445886i	$0.147111\pi$
$212$	−7.26650	−	7.26650i	−0.499065	−	0.499065i
$213$	−1.44966	+	1.44966i	−0.0993289	+	0.0993289i
$214$	−13.6235	+	13.6235i	−0.931281	+	0.931281i
$215$	−7.74273			−0.528050
$216$	−20.2468	+	20.2468i	−1.37762	+	1.37762i
$217$			0.949874i			0.0644817i
$218$	3.31662	−	3.31662i	0.224630	−	0.224630i
$219$	8.19051	−	8.19051i	0.553463	−	0.553463i
$220$		−	4.00000i		−	0.269680i
$221$	4.03562	+	10.0356i	0.271465	+	0.675069i
$222$	−40.2164			−2.69915
$223$		−	23.2282i		−	1.55547i	−0.628589	−	0.777737i	$-0.716367\pi$
$223$		−	23.2282i		−	1.55547i	0.628589	−	0.777737i	$-0.283633\pi$
$224$			1.26650i			0.0846215i
$225$	25.2665			1.68443
$226$		−	8.48528i		−	0.564433i
$227$	1.41421	+	1.41421i	0.0938647	+	0.0938647i	0.752480	−	0.658615i	$-0.228857\pi$
$227$	1.41421	+	1.41421i	0.0938647	+	0.0938647i	−0.658615	+	0.752480i	$0.728857\pi$
$228$	38.5607			2.55374
$229$	−1.67355	+	1.67355i	−0.110591	+	0.110591i	−0.760237	−	0.649646i	$-0.774917\pi$
$229$	−1.67355	+	1.67355i	−0.110591	+	0.110591i	0.649646	+	0.760237i	$0.274917\pi$
$230$	−6.31662	+	6.31662i	−0.416506	+	0.416506i
$231$			1.36675i			0.0899256i
$232$	−0.895550	−	0.895550i	−0.0587957	−	0.0587957i
$233$		−	22.5831i		−	1.47947i	−0.672899	−	0.739735i	$-0.734951\pi$
$233$		−	22.5831i		−	1.47947i	0.672899	−	0.739735i	$-0.265049\pi$
$234$	12.0168	+	29.8829i	0.785564	+	1.95351i
$235$	−7.47494	−	7.47494i	−0.487611	−	0.487611i
$236$	−15.4855	+	15.4855i	−1.00802	+	1.00802i
$237$	−23.6332	+	23.6332i	−1.53514	+	1.53514i
$238$			0.949874i			0.0615712i
$239$			11.9854i			0.775269i	0.921813	+	0.387635i	$0.126708\pi$
$239$			11.9854i			0.775269i	−0.921813	+	0.387635i	$0.873292\pi$
$240$		−	12.2093i		−	0.788104i
$241$		−	12.7279i		−	0.819878i	−0.912113	−	0.409939i	$-0.865550\pi$
$241$		−	12.7279i		−	0.819878i	0.912113	−	0.409939i	$-0.134450\pi$
$242$	−9.89949			−0.636364
$243$	−4.31662	+	4.31662i	−0.276912	+	0.276912i
$244$	−8.00000	+	8.00000i	−0.512148	+	0.512148i
$245$	−4.91430	+	4.91430i	−0.313963	+	0.313963i
$246$		0			0
$247$	8.93306	−	20.9499i	0.568397	−	1.33301i
$248$	12.0000			0.762001
$249$	−51.7364			−3.27866
$250$	−9.00000	+	9.00000i	−0.569210	+	0.569210i
$251$	3.63325	+	3.63325i	0.229329	+	0.229329i	0.812412	−	0.583084i	$-0.198154\pi$
$251$	3.63325	+	3.63325i	0.229329	+	0.229329i	−0.583084	+	0.812412i	$0.698154\pi$
$252$			2.82843i			0.178174i
$253$	−8.93306	−	8.93306i	−0.561616	−	0.561616i
$254$			4.17175i			0.261759i
$255$		−	9.15694i		−	0.573430i
$256$	16.0000			1.00000
$257$	15.0000			0.935674			0.467837	−	0.883815i	$-0.345033\pi$
$257$	15.0000			0.935674			0.467837	+	0.883815i	$0.345033\pi$
$258$		−	33.4225i		−	2.08079i
$259$	−1.47494	+	1.47494i	−0.0916481	+	0.0916481i
$260$	−6.63325	−	2.82843i	−0.411377	−	0.175412i
$261$	−2.00000	−	2.00000i	−0.123797	−	0.123797i
$262$	4.01875	+	4.01875i	0.248279	+	0.248279i
$263$		−	0.633250i		−	0.0390478i	−0.999809	−	0.0195239i	$-0.993785\pi$
$263$		−	0.633250i		−	0.0390478i	0.999809	−	0.0195239i	$-0.00621505\pi$
$264$	17.2665			1.06268
$265$	5.13819			0.315637
$266$	1.41421	−	1.41421i	0.0867110	−	0.0867110i
$267$	30.3701	−	30.3701i	1.85862	−	1.85862i
$268$	−9.38083	−	9.38083i	−0.573025	−	0.573025i
$269$	−12.6332	+	12.6332i	−0.770263	+	0.770263i	−0.978152	−	0.207889i	$-0.933341\pi$
$269$	−12.6332	+	12.6332i	−0.770263	+	0.770263i	0.207889	+	0.978152i	$0.433341\pi$
$270$		−	14.3166i		−	0.871282i
$271$			23.2282i			1.41101i	0.708704	+	0.705506i	$0.249280\pi$
$271$			23.2282i			1.41101i	−0.708704	+	0.705506i	$0.750720\pi$
$272$	12.0000			0.727607
$273$	2.26650	+	0.966438i	0.137175	+	0.0584915i
$274$			19.8997i			1.20219i
$275$	−5.65685	−	5.65685i	−0.341121	−	0.341121i
$276$	−27.2665	−	27.2665i	−1.64125	−	1.64125i
$277$	−14.9499	−	14.9499i	−0.898251	−	0.898251i	0.0970305	−	0.995281i	$-0.469066\pi$
$277$	−14.9499	−	14.9499i	−0.898251	−	0.898251i	−0.995281	+	0.0970305i	$0.969066\pi$
$278$	3.50009	−	3.50009i	0.209921	−	0.209921i
$279$	26.7992			1.60442
$280$	−0.447775	−	0.447775i	−0.0267597	−	0.0267597i
$281$	−12.7279			−0.759284			−0.379642	−	0.925133i	$-0.623953\pi$
$281$	−12.7279			−0.759284			−0.379642	+	0.925133i	$0.623953\pi$
$282$	32.2665	−	32.2665i	1.92144	−	1.92144i
$283$	−11.0000	−	11.0000i	−0.653882	−	0.653882i	0.300043	−	0.953926i	$-0.402999\pi$
$283$	−11.0000	−	11.0000i	−0.653882	−	0.653882i	−0.953926	+	0.300043i	$0.902999\pi$
$284$	1.34333			0.0797117
$285$	−13.6332	+	13.6332i	−0.807564	+	0.807564i
$286$	4.00000	−	9.38083i	0.236525	−	0.554700i
$287$		0			0
$288$	35.7322			2.10554
$289$	−8.00000			−0.470588
$290$	0.633250			0.0371857
$291$	18.3139	+	18.3139i	1.07358	+	1.07358i
$292$	−7.58973			−0.444155
$293$	−12.6925	+	12.6925i	−0.741502	+	0.741502i	−0.972867	−	0.231365i	$-0.925681\pi$
$293$	−12.6925	+	12.6925i	−0.741502	+	0.741502i	0.231365	+	0.972867i	$0.425681\pi$
$294$	−21.2132	−	21.2132i	−1.23718	−	1.23718i
$295$		−	10.9499i		−	0.637526i
$296$	18.6332	+	18.6332i	1.08304	+	1.08304i
$297$	20.2468			1.17484
$298$	10.0000	+	10.0000i	0.579284	+	0.579284i
$299$	−21.1304	+	8.49717i	−1.22200	+	0.491404i
$300$	−17.2665	−	17.2665i	−0.996882	−	0.996882i
$301$	−1.22577	−	1.22577i	−0.0706522	−	0.0706522i
$302$			6.31662i			0.363481i
$303$	−27.2665			−1.56642
$304$	−17.8661	−	17.8661i	−1.02469	−	1.02469i
$305$		−	5.65685i		−	0.323911i
$306$	26.7992			1.53201
$307$	12.5040	+	12.5040i	0.713643	+	0.713643i	0.967295	−	0.253652i	$-0.0816320\pi$
$307$	12.5040	+	12.5040i	0.713643	+	0.713643i	−0.253652	+	0.967295i	$0.581632\pi$
$308$	0.633250	−	0.633250i	0.0360827	−	0.0360827i
$309$	2.05013	+	2.05013i	0.116628	+	0.116628i
$310$	−4.24264	+	4.24264i	−0.240966	+	0.240966i
$311$			18.3166i			1.03864i	0.854580	+	0.519320i	$0.173815\pi$
$311$			18.3166i			1.03864i	−0.854580	+	0.519320i	$0.826185\pi$
$312$	12.2093	−	28.6332i	0.691213	−	1.62104i
$313$			9.94987i			0.562400i	0.959649	+	0.281200i	$0.0907325\pi$
$313$			9.94987i			0.562400i	−0.959649	+	0.281200i	$0.909268\pi$
$314$	11.2428	+	11.2428i	0.634469	+	0.634469i
$315$	−1.00000	−	1.00000i	−0.0563436	−	0.0563436i
$316$	21.8997			1.23196
$317$	15.4855	+	15.4855i	0.869750	+	0.869750i	0.992445	−	0.122694i	$-0.0391535\pi$
$317$	15.4855	+	15.4855i	0.869750	+	0.869750i	−0.122694	+	0.992445i	$0.539153\pi$
$318$			22.1796i			1.24377i
$319$			0.895550i			0.0501412i
$320$	−5.65685	+	5.65685i	−0.316228	+	0.316228i
$321$	41.5831			2.32094
$322$	−2.00000			−0.111456
$323$	−13.3996	−	13.3996i	−0.745573	−	0.745573i
$324$	23.8997			1.32776
$325$	−13.3808	+	5.38083i	−0.742235	+	0.298475i
$326$	12.3166	−	12.3166i	0.682155	−	0.682155i
$327$	−10.1234			−0.559824
$328$		0			0
$329$		−	2.36675i		−	0.130483i
$330$	−6.10463	+	6.10463i	−0.336049	+	0.336049i
$331$	5.36208	−	5.36208i	0.294726	−	0.294726i	−0.544218	−	0.838944i	$-0.683173\pi$
$331$	5.36208	−	5.36208i	0.294726	−	0.294726i	0.838944	+	0.544218i	$0.183173\pi$
$332$	23.9707	+	23.9707i	1.31557	+	1.31557i
$333$	41.6130	+	41.6130i	2.28038	+	2.28038i
$334$		−	19.8997i		−	1.08887i
$335$	6.63325			0.362413
$336$	1.93288	−	1.93288i	0.105447	−	0.105447i
$337$	5.94987			0.324110			0.162055	−	0.986782i	$-0.448188\pi$
$337$	5.94987			0.324110			0.162055	+	0.986782i	$0.448188\pi$
$338$	−12.7279	−	13.2665i	−0.692308	−	0.721602i
$339$	−12.9499	+	12.9499i	−0.703341	+	0.703341i
$340$	−4.24264	+	4.24264i	−0.230089	+	0.230089i
$341$	−6.00000	−	6.00000i	−0.324918	−	0.324918i
$342$	−39.8997	−	39.8997i	−2.15753	−	2.15753i
$343$	−3.12320			−0.168637
$344$	−15.4855	+	15.4855i	−0.834920	+	0.834920i
$345$	19.2803			1.03802
$346$	21.6610	+	21.6610i	1.16450	+	1.16450i
$347$	−5.84169	−	5.84169i	−0.313598	−	0.313598i	0.532704	−	0.846302i	$-0.321176\pi$
$347$	−5.84169	−	5.84169i	−0.313598	−	0.313598i	−0.846302	+	0.532704i	$0.821176\pi$
$348$			2.73350i			0.146531i
$349$	−3.01687	−	3.01687i	−0.161489	−	0.161489i	0.621737	−	0.783226i	$-0.286427\pi$
$349$	−3.01687	−	3.01687i	−0.161489	−	0.161489i	−0.783226	+	0.621737i	$0.786427\pi$
$350$	−1.26650			−0.0676972
$351$	14.3166	−	33.5755i	0.764165	−	1.79213i
$352$	−8.00000	−	8.00000i	−0.426401	−	0.426401i
$353$		−	11.2428i		−	0.598395i	−0.954191	−	0.299197i	$-0.903281\pi$
$353$		−	11.2428i		−	0.598395i	0.954191	−	0.299197i	$-0.0967189\pi$
$354$	47.2665			2.51219
$355$	−0.474937	+	0.474937i	−0.0252070	+	0.0252070i
$356$	−28.1425			−1.49155
$357$	1.44966	−	1.44966i	0.0767240	−	0.0767240i
$358$	9.60472	+	9.60472i	0.507625	+	0.507625i
$359$	−12.7279			−0.671754			−0.335877	−	0.941906i	$-0.609033\pi$
$359$	−12.7279			−0.671754			−0.335877	+	0.941906i	$0.609033\pi$
$360$	−12.6332	+	12.6332i	−0.665831	+	0.665831i
$361$			20.8997i			1.09999i
$362$	25.3850	−	25.3850i	1.33420	−	1.33420i
$363$	15.1082	+	15.1082i	0.792974	+	0.792974i
$364$	−0.602351	−	1.49790i	−0.0315717	−	0.0785113i
$365$	2.68338	−	2.68338i	0.140454	−	0.140454i
$366$	24.4185			1.27638
$367$	27.8997			1.45636			0.728178	−	0.685389i	$-0.240368\pi$
$367$	27.8997			1.45636			0.728178	+	0.685389i	$0.240368\pi$
$368$			25.2665i			1.31711i
$369$		0			0
$370$	−13.1757			−0.684972
$371$	0.813439	+	0.813439i	0.0422317	+	0.0422317i
$372$	−18.3139	−	18.3139i	−0.949531	−	0.949531i
$373$	−2.94987	−	2.94987i	−0.152739	−	0.152739i	0.626601	−	0.779340i	$-0.284445\pi$
$373$	−2.94987	−	2.94987i	−0.152739	−	0.152739i	−0.779340	+	0.626601i	$0.784445\pi$
$374$	−6.00000	−	6.00000i	−0.310253	−	0.310253i
$375$	27.4708			1.41859
$376$	−29.8997			−1.54196
$377$	1.48510	+	0.633250i	0.0764866	+	0.0326140i
$378$	2.26650	−	2.26650i	0.116576	−	0.116576i
$379$	−17.1945	+	17.1945i	−0.883220	+	0.883220i	−0.993860	−	0.110641i	$-0.964710\pi$
$379$	−17.1945	+	17.1945i	−0.883220	+	0.883220i	0.110641	+	0.993860i	$0.464710\pi$
$380$	12.6332			0.648072
$381$	6.36675	−	6.36675i	0.326179	−	0.326179i
$382$		−	25.4558i		−	1.30243i
$383$		−	2.08588i		−	0.106583i	−0.998579	−	0.0532916i	$-0.983029\pi$
$383$		−	2.08588i		−	0.106583i	0.998579	−	0.0532916i	$-0.0169713\pi$
$384$	−24.4185	−	24.4185i	−1.24610	−	1.24610i
$385$			0.447775i			0.0228207i
$386$	−18.0000			−0.916176
$387$	−34.5831	+	34.5831i	−1.75796	+	1.75796i
$388$		−	16.9706i		−	0.861550i
$389$	−3.31662	−	3.31662i	−0.168160	−	0.168160i	0.618010	−	0.786170i	$-0.287939\pi$
$389$	−3.31662	−	3.31662i	−0.168160	−	0.168160i	−0.786170	+	0.618010i	$0.787939\pi$
$390$	5.80676	+	14.4400i	0.294037	+	0.731198i
$391$			18.9499i			0.958336i
$392$			19.6572i			0.992839i
$393$		−	12.2665i		−	0.618763i
$394$	−4.05013	−	4.05013i	−0.204042	−	0.204042i
$395$	−7.74273	+	7.74273i	−0.389579	+	0.389579i
$396$	−17.8661	−	17.8661i	−0.897806	−	0.897806i
$397$	−27.6947	−	27.6947i	−1.38996	−	1.38996i	−0.825379	−	0.564579i	$-0.809038\pi$
$397$	−27.6947	−	27.6947i	−1.38996	−	1.38996i	−0.564579	−	0.825379i	$-0.690962\pi$
$398$	−25.4558			−1.27599
$399$	−4.31662			−0.216102
$400$			16.0000i			0.800000i
$401$			26.7283i			1.33475i	0.744723	+	0.667373i	$0.232581\pi$
$401$			26.7283i			1.33475i	−0.744723	+	0.667373i	$0.767419\pi$
$402$			28.6332i			1.42810i
$403$	−14.1925	+	5.70723i	−0.706980	+	0.284298i
$404$	12.6332	+	12.6332i	0.628528	+	0.628528i
$405$	−8.44984	+	8.44984i	−0.419876	+	0.419876i
$406$	0.100251	+	0.100251i	0.00497539	+	0.00497539i
$407$		−	18.6332i		−	0.923616i
$408$	−18.3139	−	18.3139i	−0.906673	−	0.906673i
$409$	30.5940			1.51278			0.756389	−	0.654122i	$-0.226962\pi$
$409$	30.5940			1.51278			0.756389	+	0.654122i	$0.226962\pi$
$410$		0			0
$411$	30.3701	−	30.3701i	1.49805	−	1.49805i
$412$		−	1.89975i		−	0.0935939i
$413$	1.73350	−	1.73350i	0.0853000	−	0.0853000i
$414$			56.4268i			2.77322i
$415$	−16.9499			−0.832037
$416$	−18.9234	+	7.60964i	−0.927794	+	0.373094i
$417$	−10.6834			−0.523167
$418$			17.8661i			0.873860i
$419$	5.84169	−	5.84169i	0.285385	−	0.285385i	−0.549867	−	0.835252i	$-0.685322\pi$
$419$	5.84169	−	5.84169i	0.285385	−	0.285385i	0.835252	+	0.549867i	$0.185322\pi$
$420$			1.36675i			0.0666906i
$421$	−15.7448	+	15.7448i	−0.767354	+	0.767354i	−0.977640	−	0.210286i	$-0.932561\pi$
$421$	−15.7448	+	15.7448i	−0.767354	+	0.767354i	0.210286	+	0.977640i	$0.432561\pi$
$422$	9.22783	+	9.22783i	0.449204	+	0.449204i
$423$	−66.7740			−3.24666
$424$	10.2764	−	10.2764i	0.499065	−	0.499065i
$425$			12.0000i			0.582086i
$426$	−2.05013	−	2.05013i	−0.0993289	−	0.0993289i
$427$	0.895550	−	0.895550i	0.0433387	−	0.0433387i
$428$	−19.2665	−	19.2665i	−0.931281	−	0.931281i
$429$	−20.4213	+	8.21200i	−0.985947	+	0.396479i
$430$		−	10.9499i		−	0.528050i
$431$		−	6.32852i		−	0.304834i	−0.988316	−	0.152417i	$-0.951294\pi$
$431$		−	6.32852i		−	0.304834i	0.988316	−	0.152417i	$-0.0487057\pi$
$432$	−28.6332	−	28.6332i	−1.37762	−	1.37762i
$433$	10.0501			0.482978			0.241489	−	0.970404i	$-0.422364\pi$
$433$	10.0501			0.482978			0.241489	+	0.970404i	$0.422364\pi$
$434$	−1.34333			−0.0644817
$435$	−0.966438	−	0.966438i	−0.0463372	−	0.0463372i
$436$	4.69042	+	4.69042i	0.224630	+	0.224630i
$437$	28.2134	−	28.2134i	1.34963	−	1.34963i
$438$	11.5831	+	11.5831i	0.553463	+	0.553463i
$439$			0.949874i			0.0453350i	0.999743	+	0.0226675i	$0.00721591\pi$
$439$			0.949874i			0.0453350i	−0.999743	+	0.0226675i	$0.992784\pi$
$440$	5.65685			0.269680
$441$			43.8997i			2.09046i
$442$	−14.1925	+	5.70723i	−0.675069	+	0.271465i
$443$	22.1082	+	22.1082i	1.05039	+	1.05039i	0.998661	+	0.0517306i	$0.0164737\pi$
$443$	22.1082	+	22.1082i	1.05039	+	1.05039i	0.0517306	+	0.998661i	$0.483526\pi$
$444$		−	56.8745i		−	2.69915i
$445$	9.94987	−	9.94987i	0.471669	−	0.471669i
$446$	32.8496			1.55547
$447$		−	30.5231i		−	1.44370i
$448$	−1.79110			−0.0846215
$449$		−	4.31353i		−	0.203568i	−0.994807	−	0.101784i	$-0.967545\pi$
$449$		−	4.31353i		−	0.203568i	0.994807	−	0.101784i	$-0.0324551\pi$
$450$			35.7322i			1.68443i
$451$		0			0
$452$	12.0000			0.564433
$453$	9.64016	−	9.64016i	0.452934	−	0.452934i
$454$	−2.00000	+	2.00000i	−0.0938647	+	0.0938647i
$455$	0.742551	+	0.316625i	0.0348113	+	0.0148436i
$456$			54.5330i			2.55374i
$457$	−14.5190			−0.679171			−0.339586	−	0.940575i	$-0.610287\pi$
$457$	−14.5190			−0.679171			−0.339586	+	0.940575i	$0.610287\pi$
$458$	−2.36675	−	2.36675i	−0.110591	−	0.110591i
$459$	−21.4749	−	21.4749i	−1.00236	−	1.00236i
$460$	−8.93306	−	8.93306i	−0.416506	−	0.416506i
$461$	−4.27808	−	4.27808i	−0.199250	−	0.199250i	0.600428	−	0.799679i	$-0.294997\pi$
$461$	−4.27808	−	4.27808i	−0.199250	−	0.199250i	−0.799679	+	0.600428i	$0.794997\pi$
$462$	−1.93288			−0.0899256
$463$			12.7279i			0.591517i	0.955263	+	0.295758i	$0.0955723\pi$
$463$			12.7279i			0.591517i	−0.955263	+	0.295758i	$0.904428\pi$
$464$	1.26650	−	1.26650i	0.0587957	−	0.0587957i
$465$	12.9499			0.600536
$466$	31.9374			1.47947
$467$	−3.63325	+	3.63325i	−0.168127	+	0.168127i	−0.786155	−	0.618029i	$-0.787932\pi$
$467$	−3.63325	+	3.63325i	−0.168127	+	0.168127i	0.618029	+	0.786155i	$0.287932\pi$
$468$	−42.2608	+	16.9943i	−1.95351	+	0.785564i
$469$	1.05013	+	1.05013i	0.0484903	+	0.0484903i
$470$	10.5712	−	10.5712i	0.487611	−	0.487611i
$471$		−	34.3166i		−	1.58123i
$472$	−21.8997	−	21.8997i	−1.00802	−	1.00802i
$473$	15.4855			0.712022
$474$	−33.4225	−	33.4225i	−1.53514	−	1.53514i
$475$	17.8661	−	17.8661i	0.819753	−	0.819753i
$476$	−1.34333			−0.0615712
$477$	22.9499	−	22.9499i	1.05080	−	1.05080i
$478$	−16.9499			−0.775269
$479$			16.2280i			0.741477i	0.928737	+	0.370738i	$0.120895\pi$
$479$			16.2280i			0.741477i	−0.928737	+	0.370738i	$0.879105\pi$
$480$	17.2665			0.788104
$481$	−30.8997	−	13.1757i	−1.40891	−	0.600760i
$482$	18.0000			0.819878
$483$	3.05231	+	3.05231i	0.138885	+	0.138885i
$484$		−	14.0000i		−	0.636364i
$485$	6.00000	+	6.00000i	0.272446	+	0.272446i
$486$	−6.10463	−	6.10463i	−0.276912	−	0.276912i
$487$	29.2507			1.32548			0.662738	−	0.748851i	$-0.269394\pi$
$487$	29.2507			1.32548			0.662738	+	0.748851i	$0.269394\pi$
$488$	−11.3137	−	11.3137i	−0.512148	−	0.512148i
$489$	−37.5942			−1.70007
$490$	−6.94987	−	6.94987i	−0.313963	−	0.313963i
$491$	21.1583	+	21.1583i	0.954861	+	0.954861i	0.999024	−	0.0441631i	$-0.0140621\pi$
$491$	21.1583	+	21.1583i	0.954861	+	0.954861i	−0.0441631	+	0.999024i	$0.514062\pi$
$492$		0			0
$493$	0.949874	−	0.949874i	0.0427802	−	0.0427802i
$494$	29.6276	+	12.6332i	1.33301	+	0.568397i
$495$	12.6332			0.567822
$496$			16.9706i			0.762001i
$497$	−0.150377			−0.00674533
$498$		−	73.1662i		−	3.27866i
$499$	17.4183	+	17.4183i	0.779752	+	0.779752i	0.979788	−	0.200037i	$-0.0641061\pi$
$499$	17.4183	+	17.4183i	0.779752	+	0.779752i	−0.200037	+	0.979788i	$0.564106\pi$
$500$	−12.7279	−	12.7279i	−0.569210	−	0.569210i
$501$	−30.3701	+	30.3701i	−1.35684	+	1.35684i
$502$	−5.13819	+	5.13819i	−0.229329	+	0.229329i
$503$			10.4169i			0.464466i	0.972660	+	0.232233i	$0.0746031\pi$
$503$			10.4169i			0.464466i	−0.972660	+	0.232233i	$0.925397\pi$
$504$	−4.00000			−0.178174
$505$	−8.93306			−0.397516
$506$	12.6332	−	12.6332i	0.561616	−	0.561616i
$507$	−0.821953	+	39.6716i	−0.0365042	+	1.76188i
$508$	−5.89975			−0.261759
$509$	5.65685	+	5.65685i	0.250736	+	0.250736i	0.821272	−	0.570537i	$-0.193265\pi$
$509$	5.65685	+	5.65685i	0.250736	+	0.250736i	−0.570537	+	0.821272i	$0.693265\pi$
$510$	12.9499			0.573430
$511$	0.849623			0.0375851
$512$			22.6274i			1.00000i
$513$			63.9456i			2.82327i
$514$			21.2132i			0.935674i
$515$	0.671663	+	0.671663i	0.0295970	+	0.0295970i
$516$	47.2665			2.08079
$517$	14.9499	+	14.9499i	0.657495	+	0.657495i
$518$	−2.08588	−	2.08588i	−0.0916481	−	0.0916481i
$519$		−	66.1161i		−	2.90218i
$520$	4.00000	−	9.38083i	0.175412	−	0.411377i
$521$			7.41688i			0.324939i	0.986714	+	0.162470i	$0.0519459\pi$
$521$			7.41688i			0.324939i	−0.986714	+	0.162470i	$0.948054\pi$
$522$	2.82843	−	2.82843i	0.123797	−	0.123797i
$523$	0.0501256	+	0.0501256i	0.00219184	+	0.00219184i	0.708202	−	0.706010i	$-0.249507\pi$
$523$	0.0501256	+	0.0501256i	0.00219184	+	0.00219184i	−0.706010	+	0.708202i	$0.749507\pi$
$524$	−5.68338	+	5.68338i	−0.248279	+	0.248279i
$525$	1.93288	+	1.93288i	0.0843577	+	0.0843577i
$526$	0.895550			0.0390478
$527$			12.7279i			0.554437i
$528$			24.4185i			1.06268i
$529$	−16.8997			−0.734772
$530$			7.26650i			0.315637i
$531$	−48.9079	−	48.9079i	−2.12242	−	2.12242i
$532$	2.00000	+	2.00000i	0.0867110	+	0.0867110i
$533$		0			0
$534$	42.9499	+	42.9499i	1.85862	+	1.85862i
$535$	13.6235			0.588994
$536$	13.2665	−	13.2665i	0.573025	−	0.573025i
$537$		−	29.3166i		−	1.26511i
$538$	−17.8661	−	17.8661i	−0.770263	−	0.770263i
$539$	9.82861	−	9.82861i	0.423348	−	0.423348i
$540$	20.2468			0.871282
$541$	14.6254	+	14.6254i	0.628793	+	0.628793i	0.947764	−	0.318971i	$-0.103337\pi$
$541$	14.6254	+	14.6254i	0.628793	+	0.628793i	−0.318971	+	0.947764i	$0.603337\pi$
$542$	−32.8496			−1.41101
$543$	−77.4829			−3.32511
$544$			16.9706i			0.727607i
$545$	−3.31662			−0.142069
$546$	−1.36675	+	3.20531i	−0.0584915	+	0.137175i
$547$	5.42481	−	5.42481i	0.231948	−	0.231948i	−0.581557	−	0.813505i	$-0.697556\pi$
$547$	5.42481	−	5.42481i	0.231948	−	0.231948i	0.813505	+	0.581557i	$0.197556\pi$
$548$	−28.1425			−1.20219
$549$	−25.2665	−	25.2665i	−1.07835	−	1.07835i
$550$	8.00000	−	8.00000i	0.341121	−	0.341121i
$551$	−2.82843			−0.120495
$552$	38.5607	−	38.5607i	1.64125	−	1.64125i
$553$	−2.45154			−0.104250
$554$	21.1423	−	21.1423i	0.898251	−	0.898251i
$555$	20.1082	+	20.1082i	0.853545	+	0.853545i
$556$	4.94987	+	4.94987i	0.209921	+	0.209921i
$557$	−8.52073	−	8.52073i	−0.361035	−	0.361035i	0.503159	−	0.864194i	$-0.332171\pi$
$557$	−8.52073	−	8.52073i	−0.361035	−	0.361035i	−0.864194	+	0.503159i	$0.832171\pi$
$558$			37.8997i			1.60442i
$559$	10.9499	−	25.6797i	0.463130	−	1.08614i
$560$	0.633250	−	0.633250i	0.0267597	−	0.0267597i
$561$			18.3139i			0.773213i
$562$		−	18.0000i		−	0.759284i
$563$	−24.1583	+	24.1583i	−1.01815	+	1.01815i	−0.0183193	+	0.999832i	$0.505832\pi$
$563$	−24.1583	+	24.1583i	−1.01815	+	1.01815i	−0.999832	+	0.0183193i	$0.994168\pi$
$564$	45.6317	+	45.6317i	1.92144	+	1.92144i
$565$	−4.24264	+	4.24264i	−0.178489	+	0.178489i
$566$	15.5563	−	15.5563i	0.653882	−	0.653882i
$567$	−2.67543			−0.112357
$568$			1.89975i			0.0797117i
$569$		−	21.6332i		−	0.906913i	−0.891278	−	0.453457i	$-0.850191\pi$
$569$		−	21.6332i		−	0.906913i	0.891278	−	0.453457i	$-0.149809\pi$
$570$	−19.2803	−	19.2803i	−0.807564	−	0.807564i
$571$	−21.4248	−	21.4248i	−0.896600	−	0.896600i	0.0985333	−	0.995134i	$-0.468585\pi$
$571$	−21.4248	−	21.4248i	−0.896600	−	0.896600i	−0.995134	+	0.0985333i	$0.968585\pi$
$572$	13.2665	+	5.65685i	0.554700	+	0.236525i
$573$	−38.8496	+	38.8496i	−1.62297	+	1.62297i
$574$		0			0
$575$	−25.2665			−1.05369
$576$			50.5330i			2.10554i
$577$		−	29.6985i		−	1.23636i	−0.786035	−	0.618182i	$-0.787869\pi$
$577$		−	29.6985i		−	1.23636i	0.786035	−	0.618182i	$-0.212131\pi$
$578$		−	11.3137i		−	0.470588i
$579$	27.4708	+	27.4708i	1.14165	+	1.14165i
$580$			0.895550i			0.0371857i
$581$	−2.68338	−	2.68338i	−0.111325	−	0.111325i
$582$	−25.8997	+	25.8997i	−1.07358	+	1.07358i
$583$	−10.2764			−0.425604
$584$		−	10.7335i		−	0.444155i
$585$	8.93306	−	20.9499i	0.369336	−	0.866171i
$586$	−17.9499	−	17.9499i	−0.741502	−	0.741502i
$587$	10.6420	−	10.6420i	0.439244	−	0.439244i	−0.452513	−	0.891758i	$-0.649473\pi$
$587$	10.6420	−	10.6420i	0.439244	−	0.439244i	0.891758	+	0.452513i	$0.149473\pi$
$588$	30.0000	−	30.0000i	1.23718	−	1.23718i
$589$	18.9499	−	18.9499i	0.780816	−	0.780816i
$590$	15.4855			0.637526
$591$			12.3623i			0.508515i
$592$	−26.3514	+	26.3514i	−1.08304	+	1.08304i
$593$		−	4.31353i		−	0.177135i	−0.996070	−	0.0885677i	$-0.971771\pi$
$593$		−	4.31353i		−	0.177135i	0.996070	−	0.0885677i	$-0.0282290\pi$
$594$			28.6332i			1.17484i
$595$	0.474937	−	0.474937i	0.0194705	−	0.0194705i
$596$	−14.1421	+	14.1421i	−0.579284	+	0.579284i
$597$	38.8496	+	38.8496i	1.59001	+	1.59001i
$598$	−12.0168	−	29.8829i	−0.491404	−	1.22200i
$599$		−	11.6834i		−	0.477370i	−0.971097	−	0.238685i	$-0.923284\pi$
$599$		−	11.6834i		−	0.477370i	0.971097	−	0.238685i	$-0.0767163\pi$
$600$	24.4185	−	24.4185i	0.996882	−	0.996882i
$601$			28.8997i			1.17885i	0.807825	+	0.589423i	$0.200645\pi$
$601$			28.8997i			1.17885i	−0.807825	+	0.589423i	$0.799355\pi$
$602$	1.73350	−	1.73350i	0.0706522	−	0.0706522i
$603$	29.6276	−	29.6276i	1.20653	−	1.20653i
$604$	−8.93306			−0.363481
$605$	4.94975	+	4.94975i	0.201236	+	0.201236i
$606$		−	38.5607i		−	1.56642i
$607$	32.9499			1.33739			0.668697	−	0.743535i	$-0.266852\pi$
$607$	32.9499			1.33739			0.668697	+	0.743535i	$0.266852\pi$
$608$	25.2665	−	25.2665i	1.02469	−	1.02469i
$609$		−	0.305998i		−	0.0123997i
$610$	8.00000			0.323911
$611$	35.3627	−	14.2204i	1.43062	−	0.575296i
$612$			37.8997i			1.53201i
$613$	27.2469	−	27.2469i	1.10049	−	1.10049i	0.106143	−	0.994351i	$-0.466150\pi$
$613$	27.2469	−	27.2469i	1.10049	−	1.10049i	0.994351	−	0.106143i	$-0.0338501\pi$
$614$	−17.6834	+	17.6834i	−0.713643	+	0.713643i
$615$		0			0
$616$	0.895550	+	0.895550i	0.0360827	+	0.0360827i
$617$	1.34333			0.0540802			0.0270401	−	0.999634i	$-0.491392\pi$
$617$	1.34333			0.0540802			0.0270401	+	0.999634i	$0.491392\pi$
$618$	−2.89932	+	2.89932i	−0.116628	+	0.116628i
$619$	−5.13819	+	5.13819i	−0.206521	+	0.206521i	−0.802787	−	0.596266i	$-0.796650\pi$
$619$	−5.13819	+	5.13819i	−0.206521	+	0.206521i	0.596266	+	0.802787i	$0.296650\pi$
$620$	−6.00000	−	6.00000i	−0.240966	−	0.240966i
$621$	45.2164	−	45.2164i	1.81447	−	1.81447i
$622$	−25.9036			−1.03864
$623$	3.15038			0.126217
$624$	40.4935	+	17.2665i	1.62104	+	0.691213i
$625$	−11.0000			−0.440000
$626$	−14.0712			−0.562400
$627$	27.2665	−	27.2665i	1.08892	−	1.08892i
$628$	−15.8997	+	15.8997i	−0.634469	+	0.634469i
$629$	−19.7635	+	19.7635i	−0.788024	+	0.788024i
$630$	1.41421	−	1.41421i	0.0563436	−	0.0563436i
$631$	5.80985			0.231287			0.115643	−	0.993291i	$-0.463107\pi$
$631$	5.80985			0.231287			0.115643	+	0.993291i	$0.463107\pi$
$632$			30.9709i			1.23196i
$633$		−	28.1662i		−	1.11951i
$634$	−21.8997	+	21.8997i	−0.869750	+	0.869750i
$635$	2.08588	−	2.08588i	0.0827755	−	0.0827755i
$636$	−31.3668			−1.24377
$637$	−9.34903	−	23.2488i	−0.370422	−	0.921150i
$638$	−1.26650			−0.0501412
$639$			4.24264i			0.167836i
$640$	−8.00000	−	8.00000i	−0.316228	−	0.316228i
$641$	12.0000			0.473972			0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000			0.473972			0.236986	+	0.971513i	$0.423841\pi$
$642$			58.8074i			2.32094i
$643$	8.93306	+	8.93306i	0.352285	+	0.352285i	0.860959	−	0.508674i	$-0.169864\pi$
$643$	8.93306	+	8.93306i	0.352285	+	0.352285i	−0.508674	+	0.860959i	$0.669864\pi$
$644$		−	2.82843i		−	0.111456i
$645$	−16.7112	+	16.7112i	−0.658004	+	0.658004i
$646$	18.9499	−	18.9499i	0.745573	−	0.745573i
$647$		−	19.5831i		−	0.769892i	−0.922939	−	0.384946i	$-0.874220\pi$
$647$		−	19.5831i		−	0.769892i	0.922939	−	0.384946i	$-0.125780\pi$
$648$			33.7993i			1.32776i
$649$			21.8997i			0.859640i
$650$	−7.60964	−	18.9234i	−0.298475	−	0.742235i
$651$	2.05013	+	2.05013i	0.0803508	+	0.0803508i
$652$	17.4183	+	17.4183i	0.682155	+	0.682155i
$653$	−13.5831	+	13.5831i	−0.531549	+	0.531549i	−0.921033	−	0.389484i	$-0.872653\pi$
$653$	−13.5831	+	13.5831i	−0.531549	+	0.531549i	0.389484	+	0.921033i	$0.372653\pi$
$654$		−	14.3166i		−	0.559824i
$655$		−	4.01875i		−	0.157026i
$656$		0			0
$657$		−	23.9707i		−	0.935188i
$658$	3.34709			0.130483
$659$	−8.68338	+	8.68338i	−0.338256	+	0.338256i	−0.855711	−	0.517454i	$-0.826880\pi$
$659$	−8.68338	+	8.68338i	−0.338256	+	0.338256i	0.517454	+	0.855711i	$0.326880\pi$
$660$	−8.63325	−	8.63325i	−0.336049	−	0.336049i
$661$	17.4183	−	17.4183i	0.677495	−	0.677495i	−0.281938	−	0.959433i	$-0.590977\pi$
$661$	17.4183	−	17.4183i	0.677495	−	0.677495i	0.959433	+	0.281938i	$0.0909772\pi$
$662$	7.58312	+	7.58312i	0.294726	+	0.294726i
$663$	30.3701	+	12.9499i	1.17948	+	0.502931i
$664$	−33.8997	+	33.8997i	−1.31557	+	1.31557i
$665$	−1.41421			−0.0548408
$666$	−58.8496	+	58.8496i	−2.28038	+	2.28038i
$667$	2.00000	+	2.00000i	0.0774403	+	0.0774403i
$668$	28.1425			1.08887
$669$	−50.1337	−	50.1337i	−1.93828	−	1.93828i
$670$			9.38083i			0.362413i
$671$			11.3137i			0.436761i
$672$	2.73350	+	2.73350i	0.105447	+	0.105447i
$673$	18.8997			0.728532			0.364266	−	0.931295i	$-0.381320\pi$
$673$	18.8997			0.728532			0.364266	+	0.931295i	$0.381320\pi$
$674$			8.41439i			0.324110i
$675$	28.6332	−	28.6332i	1.10209	−	1.10209i
$676$	18.7617	−	18.0000i	0.721602	−	0.692308i
$677$	8.68338	+	8.68338i	0.333729	+	0.333729i	0.854001	−	0.520272i	$-0.174169\pi$
$677$	8.68338	+	8.68338i	0.333729	+	0.333729i	−0.520272	+	0.854001i	$0.674169\pi$
$678$	−18.3139	−	18.3139i	−0.703341	−	0.703341i
$679$			1.89975i			0.0729057i
$680$	−6.00000	−	6.00000i	−0.230089	−	0.230089i
$681$	6.10463			0.233930
$682$	8.48528	−	8.48528i	0.324918	−	0.324918i
$683$	−10.5712	+	10.5712i	−0.404494	+	0.404494i	−0.879813	−	0.475319i	$-0.842333\pi$
$683$	−10.5712	+	10.5712i	−0.404494	+	0.404494i	0.475319	+	0.879813i	$0.342333\pi$
$684$	56.4268	−	56.4268i	2.15753	−	2.15753i
$685$	9.94987	−	9.94987i	0.380165	−	0.380165i
$686$		−	4.41688i		−	0.168637i
$687$			7.22407i			0.275615i
$688$	−21.8997	−	21.8997i	−0.834920	−	0.834920i
$689$	−7.26650	+	17.0415i	−0.276832	+	0.649228i
$690$			27.2665i			1.03802i
$691$	3.34709	+	3.34709i	0.127329	+	0.127329i	0.767900	−	0.640570i	$-0.221302\pi$
$691$	3.34709	+	3.34709i	0.127329	+	0.127329i	−0.640570	+	0.767900i	$0.721302\pi$
$692$	−30.6332	+	30.6332i	−1.16450	+	1.16450i
$693$	2.00000	+	2.00000i	0.0759737	+	0.0759737i
$694$	8.26139	−	8.26139i	0.313598	−	0.313598i
$695$	−3.50009			−0.132766
$696$	−3.86575			−0.146531
$697$		0			0
$698$	4.26650	−	4.26650i	0.161489	−	0.161489i
$699$	−48.7414	−	48.7414i	−1.84357	−	1.84357i
$700$		−	1.79110i		−	0.0676972i
$701$	11.2164	−	11.2164i	0.423637	−	0.423637i	−0.462817	−	0.886454i	$-0.653161\pi$
$701$	11.2164	−	11.2164i	0.423637	−	0.423637i	0.886454	+	0.462817i	$0.153161\pi$
$702$	47.4829	+	20.2468i	1.79213	+	0.764165i
$703$	58.8496			2.21956
$704$	11.3137	−	11.3137i	0.426401	−	0.426401i
$705$	−32.2665			−1.21523
$706$	15.8997			0.598395
$707$	−1.41421	−	1.41421i	−0.0531870	−	0.0531870i
$708$			66.8449i			2.51219i
$709$	3.34709	−	3.34709i	0.125703	−	0.125703i	−0.641457	−	0.767159i	$-0.721670\pi$
$709$	3.34709	−	3.34709i	0.125703	−	0.125703i	0.767159	+	0.641457i	$0.221670\pi$
$710$	−0.671663	−	0.671663i	−0.0252070	−	0.0252070i
$711$			69.1662i			2.59394i
$712$		−	39.7995i		−	1.49155i
$713$	−26.7992			−1.00364
$714$	2.05013	+	2.05013i	0.0767240	+	0.0767240i
$715$	−6.69042	+	2.69042i	−0.250207	+	0.100616i
$716$	−13.5831	+	13.5831i	−0.507625	+	0.507625i
$717$	25.8682	+	25.8682i	0.966065	+	0.966065i
$718$		−	18.0000i		−	0.671754i
$719$	−6.00000			−0.223762			−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000			−0.223762			−0.111881	+	0.993722i	$0.535688\pi$
$720$	−17.8661	−	17.8661i	−0.665831	−	0.665831i
$721$			0.212665i			0.00792006i
$722$	−29.5567			−1.09999
$723$	−27.4708	−	27.4708i	−1.02165	−	1.02165i
$724$	35.8997	+	35.8997i	1.33420	+	1.33420i
$725$	1.26650	+	1.26650i	0.0470366	+	0.0470366i
$726$	−21.3662	+	21.3662i	−0.792974	+	0.792974i
$727$			37.8997i			1.40562i	0.711376	+	0.702812i	$0.248072\pi$
$727$			37.8997i			1.40562i	−0.711376	+	0.702812i	$0.751928\pi$
$728$	2.11835	−	0.851852i	0.0785113	−	0.0315717i
$729$		−	17.2164i		−	0.637643i
$730$	3.79487	+	3.79487i	0.140454	+	0.140454i
$731$	−16.4248	−	16.4248i	−0.607494	−	0.607494i
$732$			34.5330i			1.27638i
$733$	6.81174	+	6.81174i	0.251597	+	0.251597i	0.821625	−	0.570028i	$-0.193068\pi$
$733$	6.81174	+	6.81174i	0.251597	+	0.251597i	−0.570028	+	0.821625i	$0.693068\pi$
$734$			39.4562i			1.45636i
$735$			21.2132i			0.782461i
$736$	−35.7322			−1.31711
$737$	−13.2665			−0.488678
$738$		0			0
$739$	18.7617	+	18.7617i	0.690159	+	0.690159i	0.962267	−	0.272108i	$-0.0877207\pi$
$739$	18.7617	+	18.7617i	0.690159	+	0.690159i	−0.272108	+	0.962267i	$0.587721\pi$
$740$		−	18.6332i		−	0.684972i
$741$	−25.9360	−	64.4967i	−0.952784	−	2.36935i
$742$	−1.15038	+	1.15038i	−0.0422317	+	0.0422317i
$743$	12.0563			0.442301			0.221151	−	0.975240i	$-0.429019\pi$
$743$	12.0563			0.442301			0.221151	+	0.975240i	$0.429019\pi$
$744$	25.8997	−	25.8997i	0.949531	−	0.949531i
$745$		−	10.0000i		−	0.366372i
$746$	4.17175	−	4.17175i	0.152739	−	0.152739i
$747$	−75.7071	+	75.7071i	−2.76998	+	2.76998i
$748$	8.48528	−	8.48528i	0.310253	−	0.310253i
$749$	2.15676	+	2.15676i	0.0788065	+	0.0788065i
$750$			38.8496i			1.41859i
$751$	15.8997			0.580190			0.290095	−	0.956998i	$-0.406313\pi$
$751$	15.8997			0.580190			0.290095	+	0.956998i	$0.406313\pi$
$752$		−	42.2846i		−	1.54196i
$753$	15.6834			0.571534
$754$	−0.895550	+	2.10025i	−0.0326140	+	0.0764866i
$755$	3.15831	−	3.15831i	0.114943	−	0.114943i
$756$	3.20531	+	3.20531i	0.116576	+	0.116576i
$757$	20.8997	+	20.8997i	0.759614	+	0.759614i	0.976252	−	0.216638i	$-0.0695091\pi$
$757$	20.8997	+	20.8997i	0.759614	+	0.759614i	−0.216638	+	0.976252i	$0.569509\pi$
$758$	−24.3166	−	24.3166i	−0.883220	−	0.883220i
$759$	−38.5607			−1.39966
$760$			17.8661i			0.648072i
$761$	12.7279			0.461387			0.230693	−	0.973026i	$-0.425901\pi$
$761$	12.7279			0.461387			0.230693	+	0.973026i	$0.425901\pi$
$762$	9.00394	+	9.00394i	0.326179	+	0.326179i
$763$	−0.525063	−	0.525063i	−0.0190086	−	0.0190086i
$764$	36.0000			1.30243
$765$	−13.3996	−	13.3996i	−0.484463	−	0.484463i
$766$	2.94987			0.106583
$767$	36.3166	+	15.4855i	1.31132	+	0.559148i
$768$	34.5330	−	34.5330i	1.24610	−	1.24610i
$769$		−	25.4558i		−	0.917961i	−0.888446	−	0.458981i	$-0.848215\pi$
$769$		−	25.4558i		−	0.917961i	0.888446	−	0.458981i	$-0.151785\pi$
$770$	−0.633250			−0.0228207
$771$	32.3747	−	32.3747i	1.16595	−	1.16595i
$772$		−	25.4558i		−	0.916176i
$773$	23.2636	−	23.2636i	0.836735	−	0.836735i	−0.151693	−	0.988428i	$-0.548472\pi$
$773$	23.2636	−	23.2636i	0.836735	−	0.836735i	0.988428	+	0.151693i	$0.0484725\pi$
$774$	−48.9079	−	48.9079i	−1.75796	−	1.75796i
$775$	−16.9706			−0.609601
$776$	24.0000			0.861550
$777$			6.36675i			0.228406i
$778$	4.69042	−	4.69042i	0.168160	−	0.168160i
$779$		0			0
$780$	−20.4213	+	8.21200i	−0.731198	+	0.294037i
$781$	0.949874	−	0.949874i	0.0339892	−	0.0339892i
$782$	−26.7992			−0.958336
$783$	−4.53300			−0.161996
$784$	−27.7995			−0.992839
$785$		−	11.2428i		−	0.401273i
$786$	17.3474			0.618763
$787$	−25.0081	−	25.0081i	−0.891441	−	0.891441i	0.103217	−	0.994659i	$-0.467086\pi$
$787$	−25.0081	−	25.0081i	−0.891441	−	0.891441i	−0.994659	+	0.103217i	$0.967086\pi$
$788$	5.72774	−	5.72774i	0.204042	−	0.204042i
$789$	−1.36675	−	1.36675i	−0.0486576	−	0.0486576i
$790$	−10.9499	−	10.9499i	−0.389579	−	0.389579i
$791$	−1.34333			−0.0477631
$792$	25.2665	−	25.2665i	0.897806	−	0.897806i
$793$	18.7617	+	8.00000i	0.666246	+	0.284088i
$794$	39.1662	−	39.1662i	1.38996	−	1.38996i
$795$	11.0898	−	11.0898i	0.393315	−	0.393315i
$796$		−	36.0000i		−	1.27599i
$797$	−34.5831	+	34.5831i	−1.22500	+	1.22500i	−0.259164	+	0.965833i	$0.583447\pi$
$797$	−34.5831	+	34.5831i	−1.22500	+	1.22500i	−0.965833	+	0.259164i	$0.916553\pi$
$798$		−	6.10463i		−	0.216102i
$799$		−	31.7135i		−	1.12194i
$800$	−22.6274			−0.800000
$801$		−	88.8828i		−	3.14052i
$802$	−37.7995			−1.33475
$803$	−5.36675	+	5.36675i	−0.189389	+	0.189389i
$804$	−40.4935			−1.42810
$805$	1.00000	+	1.00000i	0.0352454	+	0.0352454i
$806$	−8.07125	−	20.0712i	−0.284298	−	0.706980i
$807$			54.5330i			1.91965i
$808$	−17.8661	+	17.8661i	−0.628528	+	0.628528i
$809$		−	22.5831i		−	0.793980i	−0.917823	−	0.396990i	$-0.870055\pi$
$809$		−	22.5831i		−	0.793980i	0.917823	−	0.396990i	$-0.129945\pi$
$810$	−11.9499	−	11.9499i	−0.419876	−	0.419876i
$811$	−27.6947	+	27.6947i	−0.972493	+	0.972493i	−0.999632	−	0.0271385i	$-0.991360\pi$
$811$	−27.6947	+	27.6947i	−0.972493	+	0.972493i	0.0271385	+	0.999632i	$0.491360\pi$
$812$	−0.141777	+	0.141777i	−0.00497539	+	0.00497539i
$813$	50.1337	+	50.1337i	1.75827	+	1.75827i
$814$	26.3514			0.923616
$815$	−12.3166			−0.431433
$816$	25.8997	−	25.8997i	0.906673	−	0.906673i
$817$			48.9079i			1.71107i
$818$			43.2665i			1.51278i
$819$	4.73084	−	1.90241i	0.165309	−	0.0664756i
$820$		0			0
$821$	17.6777	−	17.6777i	0.616955	−	0.616955i	−0.327794	−	0.944749i	$-0.606305\pi$
$821$	17.6777	−	17.6777i	0.616955	−	0.616955i	0.944749	+	0.327794i	$0.106305\pi$
$822$	42.9499	+	42.9499i	1.49805	+	1.49805i
$823$			18.9499i			0.660551i	0.943885	+	0.330276i	$0.107142\pi$
$823$			18.9499i			0.660551i	−0.943885	+	0.330276i	$0.892858\pi$
$824$	2.68665			0.0935939
$825$	−24.4185			−0.850144
$826$	2.45154	+	2.45154i	0.0853000	+	0.0853000i
$827$	3.50009	−	3.50009i	0.121710	−	0.121710i	−0.643628	−	0.765338i	$-0.722572\pi$
$827$	3.50009	−	3.50009i	0.121710	−	0.121710i	0.765338	+	0.643628i	$0.222572\pi$
$828$	−79.7995			−2.77322
$829$	−8.00000	+	8.00000i	−0.277851	+	0.277851i	−0.832251	−	0.554399i	$-0.812948\pi$
$829$	−8.00000	+	8.00000i	−0.277851	+	0.277851i	0.554399	+	0.832251i	$0.312948\pi$
$830$		−	23.9707i		−	0.832037i
$831$	−64.5330			−2.23862
$832$	−10.7617	−	26.7617i	−0.373094	−	0.927794i
$833$	−20.8496			−0.722397
$834$		−	15.1086i		−	0.523167i
$835$	−9.94987	+	9.94987i	−0.344330	+	0.344330i
$836$	−25.2665			−0.873860
$837$	30.3701	−	30.3701i	1.04975	−	1.04975i
$838$	8.26139	+	8.26139i	0.285385	+	0.285385i
$839$	15.4146			0.532170			0.266085	−	0.963950i	$-0.414270\pi$
$839$	15.4146			0.532170			0.266085	+	0.963950i	$0.414270\pi$
$840$	−1.93288			−0.0666906
$841$			28.7995i			0.993086i
$842$	−22.2665	−	22.2665i	−0.767354	−	0.767354i
$843$	−27.4708	+	27.4708i	−0.946146	+	0.946146i
$844$	−13.0501	+	13.0501i	−0.449204	+	0.449204i
$845$	−0.269289	+	12.9972i	−0.00926381	+	0.447118i
$846$		−	94.4327i		−	3.24666i
$847$			1.56721i			0.0538501i
$848$	14.5330	+	14.5330i	0.499065	+	0.499065i
$849$	−47.4829			−1.62961
$850$	−16.9706			−0.582086
$851$	−41.6130	−	41.6130i	−1.42647	−	1.42647i
$852$	2.89932	−	2.89932i	0.0993289	−	0.0993289i
$853$	−19.9874	+	19.9874i	−0.684357	+	0.684357i	−0.960979	−	0.276622i	$-0.910785\pi$
$853$	−19.9874	+	19.9874i	−0.684357	+	0.684357i	0.276622	+	0.960979i	$0.410785\pi$
$854$	1.26650	+	1.26650i	0.0433387	+	0.0433387i
$855$			39.8997i			1.36454i
$856$	27.2469	−	27.2469i	0.931281	−	0.931281i
$857$		−	36.6332i		−	1.25137i	−0.780077	−	0.625684i	$-0.784820\pi$
$857$		−	36.6332i		−	1.25137i	0.780077	−	0.625684i	$-0.215180\pi$
$858$	−11.6135	−	28.8800i	−0.396479	−	0.985947i
$859$	25.9499	+	25.9499i	0.885398	+	0.885398i	0.994077	−	0.108679i	$-0.0346619\pi$
$859$	25.9499	+	25.9499i	0.885398	+	0.885398i	−0.108679	+	0.994077i	$0.534662\pi$
$860$	15.4855			0.528050
$861$		0			0
$862$	8.94987			0.304834
$863$			20.4707i			0.696829i	0.937341	+	0.348415i	$0.113280\pi$
$863$			20.4707i			0.696829i	−0.937341	+	0.348415i	$0.886720\pi$
$864$	40.4935	−	40.4935i	1.37762	−	1.37762i
$865$		−	21.6610i		−	0.736495i
$866$			14.2130i			0.482978i
$867$	−17.2665	+	17.2665i	−0.586401	+	0.586401i
$868$		−	1.89975i		−	0.0644817i
$869$	15.4855	−	15.4855i	0.525308	−	0.525308i
$870$	1.36675	−	1.36675i	0.0463372	−	0.0463372i
$871$	−9.38083	+	22.0000i	−0.317857	+	0.745442i
$872$	−6.63325	+	6.63325i	−0.224630	+	0.224630i
$873$	53.5983			1.81403
$874$	39.8997	+	39.8997i	1.34963	+	1.34963i
$875$	1.42481	+	1.42481i	0.0481674	+	0.0481674i
$876$	−16.3810	+	16.3810i	−0.553463	+	0.553463i
$877$	−1.67355	−	1.67355i	−0.0565116	−	0.0565116i	0.678286	−	0.734798i	$-0.262723\pi$
$877$	−1.67355	−	1.67355i	−0.0565116	−	0.0565116i	−0.734798	+	0.678286i	$0.762723\pi$
$878$	−1.34333			−0.0453350
$879$			54.7887i			1.84798i
$880$			8.00000i			0.269680i
$881$	21.0000			0.707508			0.353754	−	0.935339i	$-0.384905\pi$
$881$	21.0000			0.707508			0.353754	+	0.935339i	$0.384905\pi$
$882$	−62.0836			−2.09046
$883$	1.47494	−	1.47494i	0.0496356	−	0.0496356i	−0.681853	−	0.731489i	$-0.738826\pi$
$883$	1.47494	−	1.47494i	0.0496356	−	0.0496356i	0.731489	+	0.681853i	$0.238826\pi$
$884$	−8.07125	−	20.0712i	−0.271465	−	0.675069i
$885$	−23.6332	−	23.6332i	−0.794423	−	0.794423i
$886$	−31.2657	+	31.2657i	−1.05039	+	1.05039i
$887$			39.1662i			1.31507i	0.753422	+	0.657537i	$0.228402\pi$
$887$			39.1662i			1.31507i	−0.753422	+	0.657537i	$0.771598\pi$
$888$	80.4327			2.69915
$889$	0.660440			0.0221505
$890$	14.0712	+	14.0712i	0.471669	+	0.471669i
$891$	16.8997	−	16.8997i	0.566160	−	0.566160i
$892$			46.4564i			1.55547i
$893$	−47.2164	+	47.2164i	−1.58004	+	1.58004i
$894$	43.1662			1.44370
$895$		−	9.60472i		−	0.321050i
$896$		−	2.53300i		−	0.0846215i
$897$	−27.2665	+	63.9456i	−0.910402	+	2.13508i
$898$	6.10025			0.203568
$899$	1.34333	+	1.34333i	0.0448024	+	0.0448024i
$900$	−50.5330			−1.68443
$901$	10.8997	+	10.8997i	0.363123	+	0.363123i
$902$		0			0
$903$	−5.29119			−0.176080
$904$			16.9706i			0.564433i
$905$	−25.3850			−0.843824
$906$	13.6332	+	13.6332i	0.452934	+	0.452934i
$907$	−25.3747	−	25.3747i	−0.842553	−	0.842553i	0.146638	−	0.989190i	$-0.453155\pi$
$907$	−25.3747	−	25.3747i	−0.842553	−	0.842553i	−0.989190	+	0.146638i	$0.953155\pi$
$908$	−2.82843	−	2.82843i	−0.0938647	−	0.0938647i
$909$	−39.8997	+	39.8997i	−1.32339	+	1.32339i
$910$	−0.447775	+	1.05013i	−0.0148436	+	0.0348113i
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$	−77.1213			−2.55374
$913$	33.8997			1.12192
$914$		−	20.5330i		−	0.679171i
$915$	−12.2093	−	12.2093i	−0.403626	−	0.403626i
$916$	3.34709	−	3.34709i	0.110591	−	0.110591i
$917$	0.636218	−	0.636218i	0.0210098	−	0.0210098i
$918$	30.3701	−	30.3701i	1.00236	−	1.00236i
$919$		−	36.0000i		−	1.18753i	−0.804638	−	0.593765i	$-0.797641\pi$
$919$		−	36.0000i		−	1.18753i	0.804638	−	0.593765i	$-0.202359\pi$
$920$	12.6332	−	12.6332i	0.416506	−	0.416506i
$921$	53.9752			1.77854
$922$	6.05013	−	6.05013i	0.199250	−	0.199250i
$923$	−0.903526	−	2.24685i	−0.0297399	−	0.0739560i
$924$		−	2.73350i		−	0.0899256i
$925$	−26.3514	−	26.3514i	−0.866429	−	0.866429i
$926$	−18.0000			−0.591517
$927$	6.00000			0.197066
$928$	1.79110	+	1.79110i	0.0587957	+	0.0587957i
$929$		−	25.3141i		−	0.830528i	−0.909701	−	0.415264i	$-0.863689\pi$
$929$		−	25.3141i		−	0.830528i	0.909701	−	0.415264i	$-0.136311\pi$
$930$			18.3139i			0.600536i
$931$	31.0418	+	31.0418i	1.01735	+	1.01735i
$932$			45.1662i			1.47947i
$933$	39.5330	+	39.5330i	1.29425	+	1.29425i
$934$	−5.13819	−	5.13819i	−0.168127	−	0.168127i
$935$			6.00000i			0.196221i
$936$	−24.0336	−	59.7659i	−0.785564	−	1.95351i
$937$		−	16.1003i		−	0.525972i	−0.964800	−	0.262986i	$-0.915293\pi$
$937$		−	16.1003i		−	0.525972i	0.964800	−	0.262986i	$-0.0847074\pi$
$938$	−1.48510	+	1.48510i	−0.0484903	+	0.0484903i
$939$	21.4749	+	21.4749i	0.700808	+	0.700808i
$940$	14.9499	+	14.9499i	0.487611	+	0.487611i
$941$	−16.1217	−	16.1217i	−0.525552	−	0.525552i	0.393691	−	0.919243i	$-0.371198\pi$
$941$	−16.1217	−	16.1217i	−0.525552	−	0.525552i	−0.919243	+	0.393691i	$0.871198\pi$
$942$	48.5310			1.58123
$943$		0			0
$944$	30.9709	−	30.9709i	1.00802	−	1.00802i
$945$	−2.26650			−0.0737292
$946$			21.8997i			0.712022i
$947$	40.9413	+	40.9413i	1.33041	+	1.33041i	0.904998	+	0.425415i	$0.139872\pi$
$947$	40.9413	+	40.9413i	1.33041	+	1.33041i	0.425415	+	0.904998i	$0.360128\pi$
$948$	47.2665	−	47.2665i	1.53514	−	1.53514i
$949$	5.10488	+	12.6946i	0.165712	+	0.412085i
$950$	25.2665	+	25.2665i	0.819753	+	0.819753i
$951$	66.8449			2.16760
$952$		−	1.89975i		−	0.0615712i
$953$		−	49.4327i		−	1.60128i	−0.599143	−	0.800642i	$-0.704492\pi$
$953$		−	49.4327i		−	1.60128i	0.599143	−	0.800642i	$-0.295508\pi$
$954$	32.4560	+	32.4560i	1.05080	+	1.05080i
$955$	−12.7279	+	12.7279i	−0.411866	+	0.411866i
$956$		−	23.9707i		−	0.775269i
$957$	1.93288	+	1.93288i	0.0624810	+	0.0624810i
$958$	−22.9499			−0.741477
$959$	3.15038			0.101731
$960$			24.4185i			0.788104i
$961$	13.0000			0.419355
$962$	18.6332	−	43.6988i	0.600760	−	1.40891i
$963$	60.8496	−	60.8496i	1.96085	−	1.96085i
$964$			25.4558i			0.819878i
$965$	9.00000	+	9.00000i	0.289720	+	0.289720i
$966$	−4.31662	+	4.31662i	−0.138885	+	0.138885i
$967$	7.36584			0.236870			0.118435	−	0.992962i	$-0.462212\pi$
$967$	7.36584			0.236870			0.118435	+	0.992962i	$0.462212\pi$
$968$	19.7990			0.636364
$969$	−57.8410			−1.85812
$970$	−8.48528	+	8.48528i	−0.272446	+	0.272446i
$971$	−15.7916	−	15.7916i	−0.506775	−	0.506775i	0.406760	−	0.913535i	$-0.366659\pi$
$971$	−15.7916	−	15.7916i	−0.506775	−	0.506775i	−0.913535	+	0.406760i	$0.866659\pi$
$972$	8.63325	−	8.63325i	0.276912	−	0.276912i
$973$	−0.554108	−	0.554108i	−0.0177639	−	0.0177639i
$974$			41.3668i			1.32548i
$975$	−17.2665	+	40.4935i	−0.552971	+	1.29683i
$976$	16.0000	−	16.0000i	0.512148	−	0.512148i
$977$			9.97038i			0.318981i	0.987199	+	0.159490i	$0.0509851\pi$
$977$			9.97038i			0.318981i	−0.987199	+	0.159490i	$0.949015\pi$
$978$		−	53.1662i		−	1.70007i
$979$	−19.8997	+	19.8997i	−0.635999	+	0.635999i
$980$	9.82861	−	9.82861i	0.313963	−	0.313963i
$981$	−14.8138	+	14.8138i	−0.472968	+	0.472968i
$982$	−29.9224	+	29.9224i	−0.954861	+	0.954861i
$983$	−51.5834			−1.64525			−0.822627	−	0.568582i	$-0.807492\pi$
$983$	−51.5834			−1.64525			−0.822627	+	0.568582i	$0.807492\pi$
$984$		0			0
$985$			4.05013i			0.129048i
$986$	1.34333	+	1.34333i	0.0427802	+	0.0427802i
$987$	−5.10819	−	5.10819i	−0.162595	−	0.162595i
$988$	−17.8661	+	41.8997i	−0.568397	+	1.33301i
$989$	34.5831	−	34.5831i	1.09968	−	1.09968i
$990$			17.8661i			0.567822i
$991$	20.9499			0.665495			0.332747	−	0.943016i	$-0.392024\pi$
$991$	20.9499			0.665495			0.332747	+	0.943016i	$0.392024\pi$
$992$	−24.0000			−0.762001
$993$		−	23.1461i		−	0.734519i
$994$		−	0.212665i		−	0.00674533i
$995$	12.7279	+	12.7279i	0.403502	+	0.403502i
$996$	103.473			3.27866
$997$	40.9499	+	40.9499i	1.29690	+	1.29690i	0.930433	+	0.366463i	$0.119431\pi$
$997$	40.9499	+	40.9499i	1.29690	+	1.29690i	0.366463	+	0.930433i	$0.380569\pi$
$998$	−24.6332	+	24.6332i	−0.779752	+	0.779752i
$999$	94.3158			2.98402

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.p.a.181.4	yes	8
4.3	odd	2		832.2.p.a.753.2		8
13.12	even	2	inner	208.2.p.a.181.2	yes	8
16.3	odd	4		832.2.p.a.337.1		8
16.13	even	4	inner	208.2.p.a.77.4	yes	8
52.51	odd	2		832.2.p.a.753.1		8
208.51	odd	4		832.2.p.a.337.2		8
208.77	even	4	inner	208.2.p.a.77.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.p.a.77.2	✓	8	208.77	even	4	inner
208.2.p.a.77.4	yes	8	16.13	even	4	inner
208.2.p.a.181.2	yes	8	13.12	even	2	inner
208.2.p.a.181.4	yes	8	1.1	even	1	trivial
832.2.p.a.337.1		8	16.3	odd	4
832.2.p.a.337.2		8	208.51	odd	4
832.2.p.a.753.1		8	52.51	odd	2
832.2.p.a.753.2		8	4.3	odd	2

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	208.2.p.a.181.4

Level	$208$
Weight	$2$
Character	208.181
Analytic conductor	$1.661$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$